diff --git a/Kalman_Filters.ipynb b/Kalman_Filters.ipynb
index 05af25f..42a5ced 100644
--- a/Kalman_Filters.ipynb
+++ b/Kalman_Filters.ipynb
@@ -1,2179 +1,2179 @@
-{
- "metadata": {
- "name": "",
- "signature": "sha256:7bcd692a8ae1a36e1bb14d78bc58a3b8d1234f768fb0d0c6c00dee4155fa0676"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Kalman Filters"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#format the book\n",
- "%matplotlib inline\n",
- "from __future__ import division, print_function\n",
- "import matplotlib.pyplot as plt\n",
- "import book_format\n",
- "book_format.load_style()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "html": [
- "\n",
- "\n"
- ],
- "metadata": {},
- "output_type": "pyout",
- "prompt_number": 2,
- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "One Dimensional Kalman Filters"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Tracking A Dog"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
- "\n",
- "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Futhermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n",
- "\n",
- "Implementing and/or robustly modelling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from __future__ import print_function, division\n",
- "\n",
- "import numpy.random as random\n",
- "import math\n",
- "\n",
- "class DogSensor(object):\n",
- " \n",
- " def __init__(self, x0=0, velocity=1, noise=0.0):\n",
- " \"\"\" x0 - initial position\n",
- " velocity - (+=right, -=left)\n",
- " noise - scaling factor for noise, 0== no noise\n",
- " \"\"\"\n",
- " self.x = x0\n",
- " self.velocity = velocity\n",
- " self.noise = math.sqrt(noise)\n",
- "\n",
- " def sense(self):\n",
- " self.x = self.x + self.velocity\n",
- " return self.x + random.randn() * self.noise\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 3
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The constructor $\\verb,__init()__,$ initializes the DogSensor class with an initial position (x0), velocity (vel), and an noise scaling factor. The $\\verb,sense(),$ function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for $\\verb,sense(),$ you will see a call to $\\verb,numpy.random.randn(),$. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that.\n",
- "\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "for i in range(20):\n",
- " print(\"%.4f\" % random.randn(),end='\\t')"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "-0.8025\t0.4440\t1.6176\t-0.7325\t0.0304\t0.3592\t-0.1916\t1.3645\t0.2563\t-0.4732\t-0.3872\t0.2693\t0.4122\t0.1272\t0.7263\t-0.5945\t0.4633\t-1.5166\t0.5133\t1.1987\t"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n",
- "\n",
- "Okay, so lets look at the output of the $\\verb,DogSensor,$ class. We will start by setting the noise to 0 to check that the class does what we think it does"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import matplotlib.pyplot as plt\n",
- "import matplotlib.pylab as pylab\n",
- "\n",
- "dog = DogSensor (noise=0.0)\n",
- "xs = []\n",
- "for i in range(10):\n",
- " x = dog.sense()\n",
- " xs.append(x)\n",
- " print(\"%.4f\" % x, end=' '),\n",
- "plt.plot(xs)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
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4S6afkyOnPFnlyClnvHJqhY5uPa6pHDnlyao4JrwAlMZEFxgPOrwAjDsdXaAoOrwAVIqJ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\nIrq6uqKnpyd6e3s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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 5
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that *sense()* returns the dog's position *after* updating his position, so the first postion is 0.0 + 1, or 1.0.\n",
- "\n",
- "Now let's inject some noise in the signal."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "def test_sensor(noise_scale):\n",
- " dog = DogSensor(noise=noise_scale)\n",
- "\n",
- " xs = []\n",
- " for i in range(100):\n",
- " x = dog.sense()\n",
- " xs.append(x)\n",
- " p1, = plt.plot(xs, c='b')\n",
- " p2, = plt.plot([0,99],[1,100], 'r--')\n",
- " plt.xlabel('time')\n",
- " plt.ylabel('pos')\n",
- " plt.ylim([0,100])\n",
- " plt.title('noise = ' + str(noise_scale))\n",
- " plt.legend([p1, p2], ['sensor', 'actual'], loc=2)\n",
- " plt.show()\n",
- " \n",
- "test_sensor(4.0)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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KaSxeHMCdd57LtlNDQnB268aURp9y/FAw1pCzvhqu+AmfJtrh4eEEBASQlJSE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\n8O677zJy5Eg+//xzAHJzc5WLeu7QoUPExMTwzDPPkJeXR2pqKgkJCcp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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use $\\verb,numpy.random.seed(some_value),$ to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n",
- "\n",
- "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n",
- "\n",
- "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n",
- "\n",
- "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "test_sensor(100.0)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
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qxAm0Pf442hcvlt0D+7XXwvHKK+EoLr6E6GiPvx07b78dhpISFq+80oonnuiF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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 7
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "test_sensor(0.5)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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1LrZvzyIgAFJTLRw8aOXgwQAOHgxgbXIscXGFJCVlULmyz+3rIGWEdh0RERER\nr3H4sIV77omkS5cCnu6xkdDZs8idNo3CWrXMLk3KKO06IiIiIj5v374Abrstkodu/obZe3sQOSQe\nZ6dOFBpcIVrEF6jRFr/xx0sri4ByIcaUC++zZYuVMbelsSGqO8M+6oezSxfSk5PJGzaM0jqzUbkQ\nT9OMtoiIiJjqq68CGTEinJefcFG5oBPpg14rteZapCRpRltERERM8/HHQYwZE8Zrr2XTuvXF7Xst\nUhouZ0ZbK9oiIiJSqqx2O+7wcFbuasjEiWEsW5ZF06aXtzWfiDfSjLb4Dc3WiRHlQowoF+Y4e6n0\niMGDSVxyhMceC2PlSu9pspUL8TQ12iIiIlKift9gOzt35oWx2xnx3l28914mDRp4R5MtUhLUaIvf\n0NW8xIhyIUaUi1KUlUX4/ffj7NyZ9ORk5jlHM+uFK/jww0zq1i00u7pzKBfiaZrRFhERkZITEUHG\nt9+CxcLcuTaWLLGxZk0WNWp4V5MtUhLUaIvfSExM1GqEnEe5ECPKhee53TB3WiFLVl5BSAiEhbkJ\nC3MTGnrme4cDfv7ZyocfZhIT450bnikX4mlqtEVEROSyuJOS+WXYbNpnh3DLR68DkJNjITfXQk6O\nhZwccDgsdOmSQ8WK3tlki5QENdriN7QKIUaUCzGiXHiGNTmZoOkzydy4m8SrxtNzQ2/Cy/vuSIhy\nIZ6mRltEREQuWtiDDxLw+XqeDZzA/l7v8sxcF4HqKkTOoV1HxG9o/1MxolyIEeXir+XlQeEFFqf3\ndRtFQ9s+MgYOZ9Z8/2iylQvxND/4ayEiIiKeZLdb6d8/gpwcC3FxLurVc3HttS7q1z/z66FDAcSP\nu4lHH81l8OA8s8sV8VoWt9vtc2clrFu3jmbNmpldhoiIiN/54otARo4MZ968HDpEJOF8aQmrOs1j\n114bu3db2bXLSl6ehVdeyaJrV6fZ5YqUOLvdTqdOnS7puVrRFhEREQBWrgzi0UfDeP+xDbRcPJ3A\nHTtwJCQQPzgPgv43R1JQAEFBJhYq4iM0oy1+Q7N1YkS5ECPKxfkWLrSx/NG9/HjNbdz07ECcXbqQ\nnpxM3rBh53XV/tpkKxfiaVrRFhERKcPcbpg6NYQPPwzm08f3EpLfmfRBr4PNZnZpIj5PM9oiIiJl\nlNMJ48aFsWuXlWXLsqhQwedaApESdzkz2hodERERKWOsdjuuzBxGjgzn8OEA3n8/U022SAlQoy1+\nQ7N1YkR6WMNiAAAgAElEQVS5ECNlNRdWu53wfv0Ij4/nuVGHOXXKwtKlWUREmF2ZdyiruZCSoxlt\nERERP2e12wmZOZPAHTvIHZtAQo3lbN4ezsqVmYSEmF2diP/Sirb4jTZt2phdgngh5UKMlKVcWH/4\ngYj4+KJdRP6VNpqNm8NZtiyL8HCzq/MuZSkXUjq0oi0iIuLHXI0akW63Q3Awc+aE8NFHwaxZk0l0\ntGayRUqaVrTFb2i2TowoF2LEb3NRWHj+bRYLBAfz73/bePPNYFat0omPf8ZvcyGmUaMtIiLi486e\n5Bgye7bh/UuXBvPCCzbeey+LatXUZIuUFo2OiN/QbJ0YUS7EiL/k4vcnOToSEsgbNAiA3Fz4/vtA\nEhMD+frrIH79NYAPPsikZk2DFW8p4i+5EO+hRltERMTXFBQQHh9P4PbtZIxO4Kcnl5ByNJTv5pxp\nrrdtC6R+fRdt2xYwYUIu11/vJCzM7KJFyh412uI3EhMTtRoh51EuxIgv5uLkSQsffBDEDz8Ekpoa\nQJ0997Mqpwunnwqh6r8LiY0tpHlzF2PGOLjxRieRkWZX7Ht8MRfi3dRoi4iIeKnsbPjkkyBWrAjm\n22+D6NKlgFatCrj1VjcxMe1JiMmjQgUHFovZlYqIEYvb7fa5syLWrVtHs2bNzC5DRETE41wu+OKL\nQN59N5hjH22lZ+x3BCcM57bb8rVKLWICu91Op06dLum5WtEWERHxEhs2BPLEE6E0zN3EVOtTXBn5\nA/mjHia/b77ZpYnIJdD2fuI3tP+pGFEuxIi35WLv3gD69w9n0aidfGTpzpKce4gZ3omsLcnkDx1q\ndnllhrflQnyfVrRFRERMcuKEhWeeCeH994MZM8ZBQv2VBMR0JmPQ62CzmV2eiFwmzWiLiIiUkN9+\ns/DzzwE4HBYcDop+zc21kJISwKuv2rjnnnzGj3dQvrzP/XMsUiZoRltERMTL7NxppU+fCKpUKSQ0\n1E1ICISEnPm1VsE+cqvX5pNPMqlTRxeREfFXmtEWv6HZOjGiXIiRks7F999bufvuCKZMyWH9+kw+\n+iiLlSuzeOehr3kn+w5mbbmF6f9MU5PtZfR5IZ6mRltERMSDvvgikIEDI1iwIJu77y4AzlwqPbxf\nPyLi43F26UL65s24o6NNrlRESpoabfEbupqXGFEuxEhJ5WL16iBGjgxnyZIsOnd2AhD8zjv/a7CT\nk8kbNkwnOnopfV6Ip2lGW0RExAPefDOYadNCeffdLBo3dhXdnn/HHeT37KnmWqQM0oq2+A3N1okR\n5UKMeDoXCxbYePbZEFavzjynyQYgPFxNto/Q54V4mla0RURE/sLBgwH07h1BeroFtxsKC8Ht/t9X\n5+jv2XHVk1hS7sVZp6PZ5YqIl9A+2iIiIhdQWAh33hlBp05OBg7Mw2KBgACwWCDkh2TKPf8Mtr07\nyUtIIG/QIK1ei/gZ7aMtIiJSQhYutOFyWXjwQQdW65nbLKmphI8di3XnThwJCWS8/YYabBE5j2a0\nxW9otk6MKBdipLi52LcvgNmzQ1iwILuoyQZwX3EF+bfdpl1E/Iw+L8TTtKItIiJiwOmE++8PZ8IE\nB1df/YcLy4SGkj9kiDmFiYjP0Iq2+A3tfypGlAsxUpxczJ8fQvPCTdxb57NSqEi8gT4vxNPUaIuI\niPxBysqttJlxD/OP3IP11AmzyxERH6VGW/yGZuvEiHIhRv4sF1a7nbA+/ahyfzzBd3Ume2syBXff\nXcrViVn0eSGephltERERALeb0KlTWWO9k0Xt3uWNl5xgMbsoEfFl2kdbRETkv7ZssdKvXwRffZVB\n1ao+98+jiJSAy9lH2/TRkaSkJBo3bkz9+vXp168fAMuXLycuLo66deuyZs0akysUERF/Yzl16pzj\nwkJ4++1gBgyIYNq0HDXZIuIRpjbahYWFxMfH89JLL7Fr1y4WLFhAfn4+EyZMYOPGjXz++eeMHTvW\nzBLFh2i2TowoF/J7Vrud8H794NZbz1w7HUhOttK1aySvvmrjzTez6NWrwOQqxSz6vBBPM3VGOzk5\nmUqVKtGqVSsAKlSowNdff02DBg2oVKkSADVq1GDbtm00adLEzFJFRMSHWe12QmbOJHDHDhwJCWy8\n+mpqHwtgypRQ1q8P4l//yqVPn3wCTP85r4j4E1Mb7ZSUFKKjo+nWrRtHjx5lxIgRVKpUiWrVqrFw\n4ULKly9P1apVSU1NVaMtf0n7n4oR5aJsOn3awuLFwQQFQdcNT1J/89vs6jWOk2PeJLJiMPZPgxhy\nbwgDBuTz3XfpREWZXbF4A31eiKeZ2mg7HA42btzIjh07iI6OpkWLFgwbNgyAkSNHArBq1SosFp32\nLSIixXPkiIXevSOpV89FpUqFvBFyL4du+Ben9oSQ+biFjAwLcXEuPv44kzp1Cv/6BUVELpGpjXbV\nqlWpX78+1atXB6B58+bk5eWRmppa9Ji0tDSqVat23nPvv/9+atasCUB0dDSNGjUq+j/RszNWOi5b\nx2dv85Z6dOwdx//3f/+nz4cydPzOO1uZNOkG7r8/jwceyGPjxrP3VwSyzvm8qFNHnxc61ueFjs8/\nPvt9SkoKAMOHD+dSmbq9X3p6Og0aNGD79u2Eh4fTvHlz3nrrLXr06EFSUhIOh4OOHTuyb9++c56n\n7f3ESGJiYtFfFpGzlIuywWq3k/vkPDrseZl/TI6gf//8Cz5euRAjyoUYuZzt/QI9XMtFiY6OZu7c\nuXTs2JGCggIGDhxIo0aNmDFjBq1btwZg7ty5ZpYoPkQfjmJEufBvZ09ydCbvZJZjIpNfstL59gs3\n2aBciDHlQjxNF6wRERGfE7BnD6FPPkngjh183fZhBq0fxaI3C2jZ0mV2aSLiZ3z6gjUinvL72SqR\ns5QL35CWZmHatBD27SvmP0suF5ltuvBY350M/uZBVqzOv6gmW7kQI8qFeJoabRERMd1TT4XyzTeB\ndO8eSc+eEaxeHUSBwXVj3G5ITAxkxLwWXD1rHLt/DmPt2kzq1tXuISLifTQ6IiIiptqyxcrAgREk\nJaUTHAxr1gTx6qs2Dh60MrHzRm4ZHE1BTE3eecfG0qXBhITAoEF59OmTT4UKPvdPmIj4GJ89GVJE\nRMo2txsefzyUCRNyiYw8c1uvXgX0uSoJ57+ehVU7GLrqdb4OakiPHgX8+9/ZNGvmQpdXEBFfoNER\n8RuarRMjyoV3+/DDIDIyLAwceGanEKvdTni/fkTExxPSszOW/Zt58cfm7NiRzpw5OTRv7pkmW7kQ\nI8qFeJpWtEVExBR5eTBpUihz5uRgtYLlxAnChw8nb/RoshcvBpsNgHCbyYWKiFwizWiLiIgp5s+3\n8e23gbz1Vvb/biwshAD9sFVEvIdmtEVExKecPJLP889Hs3Zt5rl3qMkWET+iTzTxG5qtEyPKhXc5\nO4N9tOcj9OqVzzXXmLMtn3IhRpQL8TQ12iIiUuJ+f5LjoUZd6XNqIePHO8wuS0SkRKnRFr/Rpk0b\ns0sQL6RcmC98xAgi4uNxdulCenIyI7c9yOhxbsqXN+8UIeVCjCgX4mma0RYREY/47TcLu3ZZ+fFH\nKwAxMYXExhZyVb/7iJj/ApYQG+vWBXLgQABvvplncrUiIiVPjbb4jcTERK1GyHmUi5KRlQUffhjM\nzp1Wdu8+85WdbeHaa13Uq+fCaoXPPgvkyJEADh/uQE6OhWrVCsnMtDBvXg7BwebWr1yIEeVCPE2N\ntoiIXJSMDOjTJ5KICDdt2xZw880FNC/cROzGVTieegqjK8rk5EBqagDZ2RYaNXKZULWISOlToy1+\nQ6sQYkS58KyzTXbDhk5mzswlaEsyoTNnYt25E0dCwpl9sK3W854XFga1a5uzw4gR5UKMKBfiaWq0\nRUSkWH7fZM8e8C3h/acXNdhZb7xRdCVHERE5Q7uOiN/Q/qdiRLnwjLNNdoMGrjMr2fv2UNC1K+nJ\nyeQNG+ZzTbZyIUaUC/E0rWiLiMgF/b7JfvbZHAICIL9vX7PLEhHxelrRFr+h2ToxolxcHsfGrfTv\nHXpOk+0PlAsxolyIp/nJR6aIiHiS1W7Hdk8/AnrF067Gfr9qskVESos+NsVvaLZOjCgXF+fspdJD\nB8Uz58fuTB60g4f/Het3TbZyIUaUC/G0Yn10njp1iszMTAByc3NZu3YtX375JYWF3rNVk4iIXJ7A\nxEQi4uM53qIrTcL2kTFoOE8/W+h3TbaISGmxuN1u9189aOLEiQwfPpzatWvz3HPPkZqaitvtJi4u\njnvvvbc06jzHunXraNasWam/r4iIX3O52Le7kLv7V2T0aAejRuky6SIidrudTp06XdJzi7VOceTI\nEWrXro3T6WTbtm088cQTTJo0iaSkpEt6UxERMZnBGsvW7cHc2bsijz6aqyZbRMQDitVoh4SEcPz4\ncXbs2EHNmjWJiooiJCQEp9NZ0vWJFJtm68SIcnGuszPYtldeOef2xMRA+vSJYNasHPr3zzeputKj\nXIgR5UI8rVj7aN9yyy2MGzeOwsJCRowYAcCPP/5IbGxsiRYnIiKXLy3NwobZ22n+0XSuyviBNU0f\nwf7rEEJm2wgLc5OfDwsWhPDKK9ncfLMWUEREPKVYM9pwZnwEICYmBoCjR4/idDpNabY1oy0icmFO\nJ6xbF8SK1/IZsX4wLYO3sevOh9jWYggZeSHk5FjIyYHsbAsOh4UhQ/Jo2tRldtkiIl7ncma0i31l\nyLMN9llVqlS5pDcUEZGSc/BgAEuXBvPWWzaqVy9k8CBocdc9BPRcREObjYYAaP5aRKQ0FHvTpoMH\nD7JixQpefvllVqxYwc8//1ySdYlcNM3WiZGykosjRyyMHh1Gly6R5ORYePfdTD79NJNBgwuw9rsL\nbDazS/QqZSUXcnGUC/G0YjXa69evZ/LkyRw9epTQ0FCOHj3KlClT+Oyzz0q6PhERuYDMTJg2LYQH\nb9pD91NLSE5OZ+rUXK69Vtc5EBExW7FGR9577z0mT55MzZo1i25LSUnhmWeeoUuXLiVWnMjFaNOm\njdkliBfy11w4nbB0aTCfPL2DqcGTmRq2jYLbJ5AfZXZlvsFfcyGXR7kQTytWo52Tk0PVqlXPua1q\n1ao4HI4SKUpERIy53fDZZ4G8+8+djM2YwqjAbRSOG0v2oFc1HiIi4mWKNTrSpEkT5s6dy86dOzl8\n+DA7duxgzpw5NG7cuKTrEyk2zdaJEX/JhdMJK1cG0a5dJJMnh/F03GtcN7EDuT9sJm/YMDXZF8lf\nciGepVyIpxVrRXv48OG88847vPjii5w+fZro6GhatGhBv379Sro+EZEyLTcX3n47mPnzQ4iJKeSJ\nJ3Lp3NmJxTID/7+sjIiIbyv2PtonT55k69atpKenExUVxXXXXUfFihVLuj5D2kdbRPxdRgYsWhTC\nRy+mUbllLA8+6ODGG7XPtYhIaSvxfbQ3bNjAyy+/TFxcHNHR0aSnp7N48WKGDx9Ou3btLumNRUTE\n2GefBfL66F1MCZrMo8E7yV30LYSGml2WiIhcpGI12u+88w6TJk2idu3aRbft37+f2bNnq9EWr5GY\nmKgzxuU8vpSL06ctLBq1kw5fT2Nl2Dbc48aSq5McS4Qv5UJKj3IhnlasRtvlcp13qfXY2FgKC7VP\nq4iIJ3zySRA7Rr3GQ65nsDw2FsewRWqwRUR8XLFmtJcuXcqePXvo3LkzUVFRnD59mvXr11O3bl2a\nNGlS9LiGDRuWaLFnaUZbRPzFb79ZmDgxlE2bAvm/aYe5vn2wGmwRES9S4jPa33zzDQDLli077/az\n9wEsWLDgkooQESlr3G744IMgHnssjDvvzGfDhgzCwyPNLktERDyoWI22GmjxBZqtEyPelgur3Q6T\nn+XR/Cf5/PT1LFqUpd1ETOBtuRDvoFyIpxWr0RYRkctjtduxPTMTR9JOnnZOpMID1/JVQgbBwWZX\nJiIiJaXY+2h7E81oi4ivCEhJIXT8eAq37GR20D/5svbfmDHHxdVX62RyERFfcDkz2sW6BLuIiFy8\nggL4btcVvJNxO9ewjwpP/J1l7xeoyRYRKSPUaIvfSExMNLsE8UKlnYvjxy28/XYwf/tbOHFx0fzz\nmVh2tB3Bl9/m0bdvPhZLqZYjf0KfF2JEuRBP04y2iMhFKCyEU6csHDtmIS0tgGPHAjh61ILtBzu7\ndwXwQeqNtGvnpEuXAqZPz6FqVZ+bzhMREQ/RjLaISDG9+24QDzwQTni4m8qV3VSpUkiroO8ZsH8q\nNU9t48f7ZnJlwm06wVFExI+U+D7aIiJl3e7dAUycGMbnn2fSoIELq91OyMyZBG7fjiMhgbxBi7gm\nJMTsMkVExItoRlv8hmbrxIgncpGVBUOHRjB5ci4NGrigoICw8eNxdu5MenIyecOHg5psn6LPCzGi\nXIinaUVbROQC3G4YOzacG25wMmBA/pkbg4LI/OwzdGajiIhciBpt8Ru6mpcYudxcvLnAwd69kXz6\naea5d6jJ9mn6vBAjyoV4mhptERED1uRk8h9/lqbJBbz27XuEhppdkYiI+BrNaIvf0GydGLnYXFiT\nk4no25ewwUOYu/cODv7fCmrX1gVm/I0+L8SIciGephVtEZH/Cp0wgeA1a8gZm0B/VlK9dhDde+Wa\nXZaIiPgo7aMtIvJfAT/9hCu2OnNejOaTT4JYsyZTe2KLiJRx2kdbROQy7dkTwKpVDVi1KpiAAFi5\nUk22iIhcHs1oi9/QbJ0Y+WMurHY7YffeC9nZpKQEMHeujZtvjuTuuyPJyrKwcGE2332XQfXqPvfD\nPrkI+rwQI8qFeJpWtEWkTCi6kuOOHey7Zxz/GHAFW3aFcccdBUyfnsuNNzqxWs2uUkRE/InpK9qZ\nmZnExMQwe/ZsAJYvX05cXBx169ZlzZo1JlcnvkT7n4qRm8uXJ7xfPyLi4znavCv9W/5I++UJ3H63\nhV270nnuuRxat1aTXdbo80KMKBfiaaavaE+dOpUWLVpgsVjIz89nwoQJJCUl4XA46NChA927dze7\nRBHxYZaMDNJbdWFKreUsXRjJyJF5zH4hnfBwsysTERF/Z2qjvWfPHo4fP07z5s1xu918//33NGjQ\ngEqVKgFQo0YNtm3bRpMmTcwsU3xEYmKiViPKIJcLPvssiIICCAqCoCA3QUEQHOwmMBCWLruSNWtu\noUePfL75JoPKlTV7Lfq8EGPKhXiaqY32xIkTmTdvHq+++ioAaWlpVKtWjYULF1K+fHmqVq1Kamqq\nGm0RMXTqlIURI8I5edJCx8jvORx0JcepjNMJ+fkWnE4ID49m7dpMrrlGF50REZHSZVqj/eGHHxIX\nF0eNGjX441beI0eOBGDVqlVYLBYzyhMfpFWIsmXbNitDhoTzwI3f8kDgFIJ27iBr0SJcN9zwh0eG\nAWqy5Vz6vBAjyoV4mmmN9vfff8/KlSv54IMPOHHiBAEBAYwePZrU1NSix5xd4TZy//33U7NmTQCi\no6Np1KhR0V+Qs9vz6FjHOvbP488/r8GuxXkk1nqSiuuT2XPPPdR4YzHYbF5Rn451rGMd69h3j89+\nn5KSAsDw4cO5VF5xZcjJkycTGRnJAw88QN26dYtOhuzYsSP79u077/G6MqQYSUzUbJ2/y8uDCRPC\nSPnqVz7O7YDr4THkDRoENtufPke5ECPKhRhRLsSI31wZMigoiBkzZtC6dWsA5s6da3JFIuItDh2y\nMHRoBDExhbz2ZQVywuwQ6FUfYSIiIufwihXti6UVbRH/5nbDTz8FsGlTIJu/g6RkGykpVh56KJcH\nH8xDp26IiEhp8ZsVbREp2zZtsvLccyFs2hTITYHfMyngKVrWvppB86fRsKGLoCCzKxQRESk+068M\nKeIpvz+JQXxPRgYMGxbOoLpJHGzYjdWBvaj/UEfqvPs4TZteepOtXIgR5UKMKBfiaVrRFpESceyY\nhUqV3MUe8/jXE6G8Z+lFs3c34UhIIH3Q4gue5CgiIuLttKItfkNninuPI0cstGgRzdSpIcV6/Pr1\ngaz/IojqM4eRnpxM3rBhHmuylQsxolyIEeVCPE2Ntoh43KOPhtG/fx7vvx/M668HX/CxGRkwdmwY\nc+bkYLuljVaxRUTEb6jRFr+h2Trv8Pnngfzwg5VJk3JZtiyLGTNC+eyz/02pWe12QmbNKjr+17/C\n6NDBSadOzhKpR7kQI8qFGFEuxNPUaIuIx+TmwvjxYcycmUNoKNSuXcjixVmMHh3OgeVbCe/Xj4j4\neNzlyoHbfWZkZH0gU6bkmF26iIiIx+lkSPEbmq0z35w5ITRu7KJz5/+tTrcK3ow9dibW+3dyfMIY\nwhafOcnx7MjI3Lk5REWVXE3KhRhRLsSIciGepkZbRDxi//4AXn3VxoYNGefcHvj991QY1Jl5WW/z\nxrIoPh6RSbTNXTQy0rFjyYyMiIiImE2jI+I3NFtnHrcbHnkkjHHjHMTEnHux2byRI8kbNoyRD0Lb\ntgUMGRLOf/5TeiMjyoUYUS7EiHIhnqZGW0Qu26pVQZQ/vIN7Rzj+9DEWC0yblkt4uJuBAyNKfGRE\nRETEbBa32+3+64d5l3Xr1tGsWTOzyxARwPG1nR19nqNt5FYcX3yKOzb2go/PyYENG4K49daCUqpQ\nRETk0tntdjp16nRJz9WKtohcEqvdTni/foQMiCe1SVdyf9j8l002QFgYarJFRKRMUKMtfkOzdaXH\numYtoQPisVe+hSZh+2jz9hAIKd5VIEubciFGlAsxolyIp2nXERG5oNOnLbzzTjAHDgRw8KCVgwcD\nOJrSi3JX9KTqvmCemeegXDmfm0ATEREpcZrRFpE/tW2blaFDwmh5vYumTV1cdVUhV17p4sorCwkL\nM7s6ERGRknc5M9pa0RYRQ58+vZ3y859h8d960XhGT7PLERER8Tma0Ra/odk6z3B+a+dgw4G0e34g\n14zpSOPJt5ld0mVRLsSIciFGlAvxNK1oiwgAllOnsAwdjStpJ5vqP0K3r17ligo2s8sSERHxWWq0\nxW+0adPG7BJ8lsMB//mqIpu29aPWkz34+31nLjDjD5QLMaJciBHlQjxNjbZIGZOXB7t2Wdm61cqW\nLYFs22Zl/34rdeu6mL78bm64wWV2iSIiIn5BM9riNzRbd2GHD1sYNCic3rX28cHQ/5CcHEiTJi6e\ney6Hn346zfr1mX7ZZCsXYkS5ECPKhXiaVrRF/JzbDW+/Hcz7j+3g+YqTuKb8D+Q9+gT5fXPMLk1E\nRMSvaR9tET+Wmmrh//6+i3t2TeXGkG24xo8lb9AgsOkkRxERkeLQPtoicg63G5YvD+aJJ0L5T6V5\n1H60AzlDF6nBFhERKUWa0Ra/odm6Mw4dOjOLPX++jRUrsqi18SVcI4eV2SZbuRAjyoUYUS7E09Ro\ni/iJ33Yd5bHHQmnXLopGjVysX59Jkyb+d3KjiIiIr9DoiPiNsrr/qeNrO6cTZhF48ACuoZv55hsH\nVar43KkXJaas5kIuTLkQI8qFeJpWtEV8lOs7OyduGkBhz6F8c0U3cr7dwIxZBWqyRUREvIQabfEb\nZWG2zu2GrVutJHZ/gfzuQ/mPtRu/fJ7M3Z8PpuY1QWaX55XKQi7k4ikXYkS5EE/T6IiIl3O7YccO\nK++/H8T77wcDMPiWeMpPGcWApvorLCIi4q20j7aIl8rMhJdfDuGdd4LJz4eePQu46658Gjd2YbGY\nXZ2IiEjZoH20RfyIwwGvvWbjq1nbmRoyhW4zplCvey011yIiIj5GM9riN3x9ts7phKVLgxlx3R46\nzb2H1UG9qD+uPdd2raYm+zL4ei6kZCgXYkS5EE/TiraIydxuWLMmiCVPHmbS6XEMC9yG+59jyRn0\napm9yIyIiIg/UKMtfsMX9z89edLCffeFk5ZmYfojLq7L7oBjsC6V7km+mAspecqFGFEuxNPUaIuY\n5LvvrIwYEUGvXvksXZpLUFA18hlmdlkiIiLiIZrRFr/hK7N1ls123nrsJ4YOjeC557KZNCmXIG2B\nXWJ8JRdSupQLMaJciKdpRVuklFjtdqxPzyT7213sv/JFPv88g+rVfW53TRERESkm7aMtUsKsdjsh\nM2fisu9kSsFEHAMHMeHJQq1ii4iI+ADtoy3ipTLTsgkf/ACvRtzHLN5n9kInXbs6zS5LRERESoFm\ntMVveMtsXX4+fPxxEH/7WzgNb4hlcJMtRE34G99vc6jJNoG35EK8i3IhRpQL8TStaItcpvx82L3b\nyvakPL77IYpPPgmibl0XvXvn89xzOZQr53PTWSIiIuIBmtEWuUgnT1r49NMgtmyxsmVLIGE77UwJ\nnEzEFVa+GPMOt9xSQI0ahWaXKSIiIh6gGW2RUnL8uIXu3SOpW9dFz+pJTLNOpXz57eSPSyBv0CBq\n2/LMLlFERES8hGa0xW+U9GxderqFe+6JoEePfN4tN5yhq/sR0aczmfZk8oYN09UcvZRmLsWIciFG\nlAvxNK1oixRDVhb06RPBTTc5mTjRgWP3SHJmzlRzLSIiIn9KM9oif8HhgP79I4iNLeT553MI0M+B\nREREygzNaIuUAKvdTtDrbxB/4v+44go38+apyRYREZHiU9sgfsNTs3XW5GQi+vYlPD6epTubU5AP\nCxdmY7V65OWllGnmUowoF2JEuRBP04q2yH9Zt28n9Omnse7cyW/3JTCx2rvs3B/K8jeyCA42uzoR\nERHxNZrRljLt0CELO3cGsm9fAOFffor74CHmZQ3nVHYIN97oZNGiLKKizK5SREREzKIZbZGLlJ5u\nYfr0EN59N5imTV3Uru3imm63UKeOi7V18oiJcWCxmF2liIiI+DLNaIvfKM5sndsN62Zsp+MNVvLy\nLHz/fQYrVmQxY0Yuw4bl0a6dk9hYt5psP6KZSzGiXIgR5UI8TSvaUmYcXLGVnH/Ook32D7z9/FvE\n9W1odkkiIiLix7SiLX6jTZs2hrc7vrbz63UDqXxfPI5OnQk8sElNdhnyZ7mQsk25ECPKhXiaGm3x\na83RzT4AABT2SURBVKfW74BeQ7FXuZXcHzbT7OWhWMN0NUcREREpeWq0xW/8cbbu118D6PLwTbwy\nYTs9Ph1MhRjt0VcWaeZSjCgXYkS5EE8ztdE+fPgwbdq0oWHDhjRv3pzPP/8cgOXLlxMXF0fdunVZ\ns2aNmSWKLyksLPr2558DuP32CEaOyucf43xuB0sRERHxA6buo33s2DGOHj1Ko0aNSElJoVWrVhw4\ncIC6deuSlJSEw+GgQ4cO7N+//5znaR/tssnthq+/DqRRIxflyv0vtla7nZCZM3H9f3t3Hhx1ff9x\n/LVHTnKhMRDlkEMCUqAEZyoQqCRGPEBKFQ1XwAk1cmgDpZXqb7yKAv6KIPbnCCglaD24tKJoR1Er\nI4eSRSQtwYAoVBIuTTYk2exu9vv7w5KKfqkGNnx3s8/HDDN8srvJe+E1m3c+eX8/m5kpz+9+p7Iy\nu266KVF3312v/HyvhRUDAIBwF7bnaKelpSktLU2S1KlTJ3m9Xm3dulW9e/fWRRddJEnq2LGjdu3a\npX79+llZKkLA4sWxevrpGNXWStdd59NdA7foio3z5SwtlWfmTDVMmKBPPnHo1lsT9NBD9RozhiYb\nAABYJ2RmtP/2t79pwIABOnr0qNLT07V06VKtWbNG7du3V0VFhdXlwWIvvhitlSuj9fbbbpVsO6E/\nfDxaXWbna97HI/W/haWq/OUUPfNcucaMSdCCBXU02WjCzCXMkAuYIRcItpA4R7uyslKzZ8/Wq6++\nqpKSEklSYWGhJGn9+vWy8e4hEe2dd5y6//44vfpqjdLTDUlOOR+aLN+QobrC1UbFxdF6pH+UDONn\nevrpWuXm+q0uGQAAwPpG2+PxaMyYMVq4cKG6dOmiw4cPn7aDXVlZqfT09O89btq0aerUqZMkKTk5\nWX369Gk6//LUT6Ssw3/9yScOFRRE6/e/36qMjMv/c3tcnLJiYzRokF+BwHsaNSpKvXoNVJcugZCq\nn7X161MfC5V6WLNmHbrrUx8LlXpYW7M+9feDBw9KkqZMmaKzZenFkIZhaNy4cRo6dKimTp0qSfJ6\nverZs2fTxZDZ2dkqLy8/7XFcDBkZjm38WM9O+0TdlxToxht9VpcDAAAi0LlcDGnpjPYHH3ygdevW\nadmyZerfv78yMzN14sQJzZ8/X4MHD1ZOTo4WL15sZYmwgMPlUvRNeUqcnK/B2fYf3WR/+ydR4BRy\nATPkAmbIBYLNaeUXz8rKktf7/YvWbrnlFt1yyy0WVAQrnTqmz7G7VI/FzNHhX63WfQ8HfviBAAAA\nIcjSRhuRyeuVHn44TuvWRctmkxwOQ3a7VFT1d30dNVIrHa9oQKZDy/5Q26zP++0ZO+AUcgEz5AJm\nyAWCjUYb59Xnn9s1ZUobpaYG9PLLNYqN/eYNHQMBqbHxNwoEpGsNr7p3D8geModPAgAANB+tDM6b\nV16J0jXXJOpXP/+HXnihVpddFlDHjgF17hxQly4Bde8eUI8eAWVkBORwNP/zM1sHM+QCZsgFzJAL\nBBuNNlpcfb00a1a8/vo/pdrT7Xrd/tL1sldXWV0WAABAi6LRRosqK7OraPBezXhztNYaNyn+5qtV\nXVIiIyUl6F+L2TqYIRcwQy5ghlwg2JjRRoswDGnFihjtf3CNnnHeK/s9RaqZuEKKibG6NAAAgPOC\nHW0E3Zdf2nTTTQl64YVoFbyWK/+eHfJOKWjxJpvZOpghFzBDLmCGXCDYaLQRNIYhrV0bpWHDkjRo\nkF9vvlmjbn3j2MUGAAARidERnDOHyyXHw4/qj/Uz9MLX12vNmpPq16/xvNfBbB3MkAuYIRcwQy4Q\nbDTa+FH8fqmiwq66Osnjsam+Xord7VKPF+Yr6fNSzQ38XnVjh+rd+92KjbW6WgAAAOsxOoIfVFrq\nUHZ2ooYPT9TEiQl6aGq1EseOVe/7JurlhutVMHSPBj2XrwfmBSxtspmtgxlyATPkAmbIBYKNHW2c\nkd8vPf54rJ56KkYPPFCvceO8stkkeZyKfilX3rxnND4mRuPlt7pUAACAkGMzDMOwuojm2rRpkzIz\nM60uo1Xbu9eu6dPbKCnJ0JIlterQIexiAgAAcM5cLpdycnLO6rGMjuA0jY3Sn/4UoxtuSNSsIVv0\n17tep8kGAAA4CzTaaFJRYdPIkQn6fM0ufXb59Rq7ZqzsJ45bXdaPxmwdzJALmCEXMEMuEGzMaEPS\nN6Mic0ft0Z+THtRldZ+oIX+mqies5AxsAACAs8SMNrRtm0OT8ttoR9p1Sr3tGjVMmECDDQAAoHOb\n0WZHO8Jt2BClWbPitXRprRKzX1KD1QUBAAC0EsxoRyDbiROSpOXLYzRnTrzWrj2p7OzwP6KP2TqY\nIRcwQy5ghlwg2NjRjiAOl0uxjz4qe+URzb5qq17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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply $\\verb,randn(),$ with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. DogSensor.$\\verb,__init__(),$ takes the square root of the noise setting so that the $\\verb,noise * randn(),$ call properly computes the normal distribution."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Math with Gaussians"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import stats\n",
- "stats.norm_plot(23, 5)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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GalwoFmbEyS6FiCRz6UgGEZGnVLVcRFO3BTMSdbJLIS+1IC0Wu443w6aM40RE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\nQmCC\n",
- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 9
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n",
- "\n",
- "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpertation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n",
- "\n",
- "Let's look at 100 sensor readings in a plot:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "dog = DogSensor(23, 0, 5)\n",
- "xs = range(100)\n",
- "ys = []\n",
- "for i in xs:\n",
- " ys.append(dog.sense())\n",
- " \n",
- "plt.plot(xs,ys)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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MywvNcupQDf8mjfXMlAX0JVjEwwFfN8mHjJ4cHh4Gzy9PrO666y7cddddri2q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\nIAiC2JK4H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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 10
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n",
- "\n",
- "\n",
- "Recall the histogram code for adding a measurement to a pre-existing belief:\n",
- "\n",
- " def sense(pos, measure, p_hit, p_miss):\n",
- " q = array(pos, dtype=float)\n",
- " for i in range(len(hallway)):\n",
- " if hallway[i] == measure:\n",
- " q[i] = pos[i] * p_hit\n",
- " else:\n",
- " q[i] = pos[i] * p_miss\n",
- " normalize(q)\n",
- " return q\n",
- " \n",
- "Note that the algorithm is essentially computing:\n",
- "\n",
- " new_belief = old_belief * measurement * sensor_error\n",
- " \n",
- "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convience. \n",
- " \n",
- "If we are implementing this with gaussians, we might expect it to be implemented as:\n",
- "\n",
- " new_gaussian = measurement * old_gaussian\n",
- " \n",
- "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n",
- "$$\n",
- "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n",
- "\n",
- "In other words the result is a Gaussian with \n",
- "\n",
- "$$\\begin{aligned}\n",
- "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
- "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
- "\\end{aligned}$$"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n",
- "\n",
- "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import numpy as np\n",
- "\n",
- "def multiply(mu1, sig1, mu2, sig2):\n",
- " m = (sig1*mu2 + sig2*mu1) / (sig1+sig2)\n",
- " s = 1. / (1./sig1 + 1./ sig2)\n",
- " return (m,s)\n",
- "\n",
- "xs = np.arange(16, 30, 0.1)\n",
- "\n",
- "\n",
- "m1,s1 = 23, 5\n",
- "m, s = multiply(m1,s1,m1,s1)\n",
- "\n",
- "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
- "p1, = plt.plot (xs,ys)\n",
- "\n",
- "ys = [stats.gaussian(x,m,s) for x in xs]\n",
- "p2, = plt.plot (xs,ys)\n",
- "\n",
- "plt.legend([p1,p2],['original', 'multiply'])\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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K+TdEQCYf/ot+zF+s4fJPmBuMmspWNDd0CqjIfvDaF4v5SwsbZiKyWdXll9HZ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\nZSItykR0iF4uLERGmC+Z2+ujudtFg9VJo9VFg81Jo9VJg9VFk81JYri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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 11
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplation is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n",
- "\n",
- "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get $23m$ each time, I should conclude that the length is close to $23m$. So the mean should be $23$. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
- "\n",
- "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n",
- "\n",
- "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "xs = np.arange(16, 30, 0.1)\n",
- "\n",
- "m1,s1 = 23, 5\n",
- "m2,s2 = 25, 5\n",
- "m, s = multiply(m1,s1,m2,s2)\n",
- "\n",
- "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
- "p1, = plt.plot (xs,ys)\n",
- "\n",
- "ys = [stats.gaussian(x,m2,s2) for x in xs]\n",
- "p2, = plt.plot (xs,ys)\n",
- "\n",
- "ys = [stats.gaussian(x,m,s) for x in xs]\n",
- "p3, = plt.plot(xs,ys)\n",
- "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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XYnbWnn1tJ/nbFmmYhRCilrh6PJHsrbtoOm2c6lJqlZCJo7hy6CSX9vymuhQh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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 12
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n",
- "\n",
- "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n",
- "\n",
- "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n",
- "\n",
- "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n",
- "\n",
- "One final test of your intuition. What if the two measurements are widely separated? "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "xs = np.arange(0, 60, 0.1)\n",
- "\n",
- "m1,s1 = 10, 5\n",
- "m2,s2 = 50, 5\n",
- "m, s = multiply(m1,s1,m2,s2)\n",
- "\n",
- "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
- "p1, = plt.plot (xs,ys)\n",
- "\n",
- "ys = [stats.gaussian(x,m2,s2) for x in xs]\n",
- "p2, = plt.plot (xs,ys)\n",
- "\n",
- "ys = [stats.gaussian(x,m,s) for x in xs]\n",
- "p3, = plt.plot(xs,ys)\n",
- "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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0i7lTj2RaMuLNnzE3BwZLDsLnB5MJjSTAsadtzF9mMcZz0SOPPAIAePXVV6HT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\ncLUJCQY1YgP5P9iP17VcABAfpEaUzheHq2fmUcM8dzddug7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XNYIAnQDMASATht4+zAHg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\n",
- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 13
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n",
- "\n",
- "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Futhermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
- "\n",
- "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
- "\n",
- "$$\n",
- "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
- "$$\n",
- "\n",
- "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n",
- "\n",
- "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n",
- "\n",
- "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n",
- "$\\sigma_1^2=0$, yielding\n",
- "\n",
- "$$\n",
- "\\begin{aligned}\n",
- "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n",
- "\\text{or just}\\\\\n",
- "\\mu&=\\mu_1\n",
- "\\end{aligned}\n",
- "$$\n",
- "\n",
- "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n",
- "\n",
- "$$\n",
- "\\begin{aligned}\n",
- "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n",
- "\\text{or just}\\\\\n",
- "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n",
- "\\end{aligned}\n",
- "$$\n",
- "\n",
- "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Implementing the Sensing Step"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n",
- "\n",
- "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the sense function for a Kalman filter:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "def sense(mu, sigma, measurement, measurement_sigma):\n",
- " return multiply(mu, sigma, measurement, measurement_sigma)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 14
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "def sense_dog(dog_pos, dog_sigma, measurement, measurement_sigma):\n",
- " return multiply(dog_pos, dog_sigma, measurement, measurement_sigma)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 15
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the $\\verb,sense_dog(),$ function should make what we are doing very clear. \n",
- "\n",
- "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a $\\verb,DogSensor,$ object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at postion 2.0, not 0.0."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "dog = DogSensor(velocity=0, noise=1)\n",
- "\n",
- "pos,s = 2, 5\n",
- "for i in range(20):\n",
- " pos,s = sense(pos, s, dog.sense(), 5)\n",
- " print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "time: 0 \tposition = 0.793 \tvariance = 2.500\n",
- "time: 1 \tposition = 0.575 \tvariance = 1.667\n",
- "time: 2 \tposition = 0.277 \tvariance = 1.250\n",
- "time: 3 \tposition = 0.348 \tvariance = 1.000\n",
- "time: 4 \tposition = 0.401 \tvariance = 0.833\n",
- "time: 5 \tposition = 0.231 \tvariance = 0.714\n",
- "time: 6 \tposition = 0.386 \tvariance = 0.625\n",
- "time: 7 \tposition = 0.517 \tvariance = 0.556\n",
- "time: 8 \tposition = 0.452 \tvariance = 0.500\n",
- "time: 9 \tposition = 0.332 \tvariance = 0.455\n",
- "time: 10 \tposition = 0.298 \tvariance = 0.417\n",
- "time: 11 \tposition = 0.280 \tvariance = 0.385\n",
- "time: 12 \tposition = 0.197 \tvariance = 0.357\n",
- "time: 13 \tposition = 0.132 \tvariance = 0.333\n",
- "time: 14 \tposition = 0.116 \tvariance = 0.312\n",
- "time: 15 \tposition = 0.076 \tvariance = 0.294\n",
- "time: 16 \tposition = 0.135 \tvariance = 0.278\n",
- "time: 17 \tposition = 0.040 \tvariance = 0.263\n",
- "time: 18 \tposition = 0.003 \tvariance = 0.250\n",
- "time: 19 \tposition = 0.006 \tvariance = 0.238\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the intial value of 5.0 to 0.238.\n",
- "\n",
- "By now the fact that we converged to a position of 0.0 should not be terribly suprising. All we are doing is computing $\\verb,new_pos = old_pos * measurement,$ and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n",
- "\n",
- "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n",
- "\n",
- "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1} + \\frac{1}{{\\sigma}_2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Implementing Updates"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track nonmoving objects? The histogram used a loop of sense and update functions, and we must do the same to accomodate movement.\n",
- "\n",
- "How how do we perform the update function with gaussians? Recall the histogram method:\n",
- "\n",
- " def update(pos, move, p_correct, p_under, p_over):\n",
- " n = len(pos)\n",
- " result = array(pos, dtype=float)\n",
- " for i in range(n):\n",
- " result[i] = \\\n",
- " pos[(i-move) % n] * p_correct + \\\n",
- " pos[(i-move-1) % n] * p_over + \\\n",
- " pos[(i-move+1) % n] * p_under \n",
- " return result\n",
- " \n",
- " \n",
- "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n",
- "\n",
- "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is $\\verb,new_pos = old_pos + dist_moved,$. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n",
- "\n",
- "How is addition for gaussians performed? It turns out to be very simple:\n",
- "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n",
- "\n",
- "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n",
- "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the $\\verb,update(),$ function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n",
- "\n",
- "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n",
- "\n",
- "So, here is our implementation of the update function:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "def update(pos, sigma, movement, movement_sigma):\n",
- " return (pos + movement, sigma + movement_sigma)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 17
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "What is left? Just calling these functions. The histogram did nothing more than loop over the $\\verb,sense(),$ and $\\verb,update(),$ functions, so let's do the same. "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "# assume dog is always moving 1m to the right\n",
- "movement = 1\n",
- "movement_error = 2\n",
- "sensor_error = 10\n",
- "pos = (0, 500) # gaussian N(0,50)\n",
- "\n",
- "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(10):\n",
- " pos = update(pos[0], pos[1], movement, movement_error)\n",
- " print('UPDATE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n",
- " \n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- " \n",
- " print('SENSE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n",
- " print()\n",
- " \n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "UPDATE: 1.0000,\t502.0000\n",
- "SENSE: -0.9237,\t9.8047\n",
- "\n",
- "UPDATE: 0.0763,\t11.8047\n",
- "SENSE: 0.1727,\t5.4138\n",
- "\n",
- "UPDATE: 1.1727,\t7.4138\n",
- "SENSE: 3.2003,\t4.2574\n",
- "\n",
- "UPDATE: 4.2003,\t6.2574\n",
- "SENSE: 6.5697,\t3.8490\n",
- "\n",
- "UPDATE: 7.5697,\t5.8490\n",
- "SENSE: 7.6101,\t3.6904\n",
- "\n",
- "UPDATE: 8.6101,\t5.6904\n",
- "SENSE: 8.2152,\t3.6267\n",
- "\n",
- "UPDATE: 9.2152,\t5.6267\n",
- "SENSE: 6.5868,\t3.6007\n",
- "\n",
- "UPDATE: 7.5868,\t5.6007\n",
- "SENSE: 6.4438,\t3.5900\n",
- "\n",
- "UPDATE: 7.4438,\t5.5900\n",
- "SENSE: 7.7971,\t3.5856\n",
- "\n",
- "UPDATE: 8.7971,\t5.5856\n",
- "SENSE: 7.7203,\t3.5838\n",
- "\n"
- ]
- },
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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OD6fbvBkxb7+N/W++iaf79n3g8+5cIiztJg83b6pRrpw3wxXcUC0RJiepzymP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\nm5tRpYoXkyax4SWiKKXVwjF8OEwjRwZuQXkX1a1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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n",
- "\n",
- " movement = 1 \n",
- " movement_error = 2\n",
- " \n",
- "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the $\\verb,update(),$ step.\n",
- "\n",
- "For now let's walk through the code and output bit by bit.\n",
- "\n",
- " movement = 1\n",
- " movement_error = 2\n",
- " sensor_error = 10\n",
- " pos = (0, 500) # gaussian N(0,500)\n",
- " \n",
- " \n",
- "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Next we initialize the RFID simulator with\n",
- "\n",
- " dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
- "\n",
- "It may seem very 'convienent' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n",
- "\n",
- "The next code allocates an array to store the output of the measurements and filtered positions. \n",
- "\n",
- " zs = []\n",
- " ps = []\n",
- " \n",
- "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we just enter our $\\verb,sense() - >update(),$ loop.\n",
- "\n",
- " for i in range(10):\n",
- " pos = update(pos[0], pos[1], movement, sensor_error)\n",
- " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
- "\n",
- "Wait, why $\\verb,update(),$ before sense? It turns out the order does not matter once, but the first call to $\\verb,DogSensor.sense(),$ assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the $\\verb,sense(),$ first.\n",
- "\n",
- "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n",
- "\n",
- " UPDATE: 1.000 502.000\n",
- "\n",
- "What is this saying? After the update, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the update step.\n",
- "\n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " \n",
- "Here we sense the dog's position, and store it in our array so we can plot the results later.\n",
- "\n",
- "Finally we call the sense function of our filter, save the result in our *ps* array, and print the updated position belief:\n",
- "\n",
- " pos = sense(pos[0], pos[1], Z, movement_error)\n",
- " ps.append(pos[0])\n",
- " print 'SENSE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
- " \n",
- "Your result will be different, but I get\n",
- "\n",
- " SENSE: 1.6279 , 9.8047\n",
- " \n",
- "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n",
- "\n",
- "Now the software just loops, calling $\\verb,update(),$ and $\\verb,sense(),$ in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n",
- "\n",
- "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "%precision 2\n",
- "# assume dog is always moving 1m to the right\n",
- "movement = 1\n",
- "movement_error = 2\n",
- "sensor_error = 4.5\n",
- "pos = (0, 100) # gaussian N(0,50)\n",
- "\n",
- "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "vs = []\n",
- "\n",
- "for i in range(50):\n",
- " pos = update(pos[0], pos[1], movement, movement_error) \n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " vs.append(pos[1])\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- " \n",
- "#plt.subplot(121) \n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()\n",
- "\n",
- "plt.plot(vs)\n",
- "plt.title('Variance')\n",
- "plt.show()\n",
- "print ([float(\"%0.4f\" % v) for v in vs])"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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upO+Iv7VF8YMMC8N1xx040tPJ+8uSriWtMueF+I96jEVERMqBoPnzsS9fjmP5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\nCuNa4ti+XQ369VPEJ59Uv7Zpk0O9e8fpppv8WrW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wWMgFLOQCFnIBLwSuFOfnMikGAABAdgWuFDMpDh92wWAhF7CQC1jIBbwQuFLM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\nSjEAAABCj1IMAACA0KMUAwA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- "text": [
- ""
- ]
- },
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n"
- ]
- }
- ],
- "prompt_number": 19
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literatue, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\""
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Relationship to the g-h Filter"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n",
- "\n",
- "The equation for our estimate is:\n",
- "\n",
- "$$\n",
- "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
- "$$\n",
- "\n",
- "which I will make more friendly for our eyes as:\n",
- "\n",
- "$$\n",
- "\\mu_{x'}=\\frac{ya + xb} {a+b}\n",
- "$$\n",
- "\n",
- "We can easily put this into the g-h form with the following algebra\n",
- "\n",
- "$$\n",
- "\\begin{aligned}\n",
- "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n",
- "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n",
- "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n",
- "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n",
- "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
- "\\end{aligned}\n",
- "$$\n",
- "\n",
- "We are almost done, but recall that the variance of estimate is given by \n",
- "\n",
- "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n",
- "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n",
- "$$\n",
- "\n",
- "We can incorporate that term into our equation above by observing that\n",
- "$$ \n",
- "\\begin{aligned}\n",
- "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n",
- " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n",
- " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
- " &= \\frac{\\sigma^2_{x'}}{b}\n",
- " \\end{aligned}\n",
- "$$\n",
- "\n",
- "We can tie all of this together with\n",
- "\n",
- "$$\n",
- "\\begin{aligned}\n",
- "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
- "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
- "&= x + g_n(y-x)\\\\\n",
- "\\blacksquare\n",
- "\\end{aligned}\n",
- "$$\n",
- "\n",
- "where\n",
- "\n",
- "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
- "\n",
- "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n",
- "\n",
- "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n",
- "\n",
- "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#####Excercise:\n",
- "Modify the values of mov$\\verb,ement_error,$ and $\\verb,sensor_error,$ and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n",
- "\n",
- " movement_error = 40\n",
- " sensor_error = 2\n",
- " \n",
- "or:\n",
- "\n",
- " movement_error = 2\n",
- " sensor_error = 40 "
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Introduction to Designing a Filter"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equiped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n",
- "\n",
- "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "temp_variance = 2.13**2\n",
- "def volt():\n",
- " return random.randn()*temp_variance + 16.3"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 20
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We generate white noise with a given variance using the equation $\\verb,random.randn() * variance,$. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n",
- "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performace will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
- "\n",
- "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field \"Repeatability\", with the value \"$\\pm0.50\\%$ Reading\". Is this a Gaussian? Is there a bias? For example, perhaps the repeatibility is nearly $0.0\\%$ at low temperatures, and always nearly $+0.50$ at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
- "\n",
- "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call $\\verb,volt(),$ to get the measurement, pass the result into $\\verb,sense(),$ function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
- "\n",
- "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = temp_variance\n",
- "movement_error = 0\n",
- "movement = 0\n",
- "voltage = (25,1000) #who knows what the first value is?\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "vs = []\n",
- "N=50\n",
- "\n",
- "for i in range(N):\n",
- " Z = volt()\n",
- " zs.append(Z)\n",
- " \n",
- " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n",
- " ps.append(voltage[0])\n",
- " vs.append(voltage[1])\n",
- "\n",
- " voltage = update(voltage[0], voltage[1], movement, movement_error)\n",
- "\n",
- "plt.scatter(range(N), zs, marker='+')\n",
- "p1, = plt.plot(ps, c='g')\n",
- "plt.legend([p1], ['filter'], 3)\n",
- "plt.xlim((0,N));plt.ylim((0,30))\n",
- "plt.show()\n",
- "plt.plot(vs)\n",
- "plt.title('Variance')\n",
- "plt.show()\n",
- "print('Variance converges to',vs[-1])\n",
- "print('Last voltage is',voltage[0])"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
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FWpyzWNuu2qYFWQuUHJvs9d9hsOY9EDhHIHzERMcMFj8peR4/VjjmItif8zab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\nZEiS8vLytGfPHhUWFvpskAg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A16PvfG6SXv2wU8+u3eP2ckoKs1UwIRcwIRcwIRdwQlEXXUmqLfPpuxdO0i/e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\nUfq5uH34+8RsDTp+LGPtMVu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- "text": [
- ""
- ]
- },
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Variance converges to 0.0907297673624\n",
- "Last voltage is 15.6491261618\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the $\\verb,volt(),$ function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
- "\n",
- "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n",
- "\n",
- "##### Exercise(optional):\n",
- "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n",
- "\n",
- "> use plt.hist(data,bins=100) to plot the histogram. "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#Your code here"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 22
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "######Solution\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = temp_variance\n",
- "\n",
- "def VKF():\n",
- " voltage=(14,1000)\n",
- " for i in range(N):\n",
- " Z = volt()\n",
- " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n",
- " return voltage[0]\n",
- "\n",
- "vs = []\n",
- "for i in range (10000):\n",
- " vs.append (VKF())\n",
- "plt.hist(vs, bins=100) \n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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V5WcrtCknoBHZwtzpDmZZAADS2GhkKuYGvNNHdtIUAwuseJ1iuIe1Gm2jfraR\nKQaCwdzpDppiAAAAOI+mGL6Rq7KN+tlGphgIBnOnO2iKAQAA4DyaYvhGrso26mcbmWIgGMyd7qAp\nBgAAgPNoiuEbuSrbqJ9tZIqBYDB3uoNZFgAAx/BADyAWV4rhG7kq26ifbWSKkUijkSmdfK1v3tfI\nRDToYaUk5k530BQDAADAeTTF8I1clW3UzzYyxUAwmDvdQVMMAAAA59EUwzdyVbZRP9vIFAPBYO50\nB00xAAAAnEdTDN/IVdlG/WwjUwwEg7nTHcyyABImPDYZs6xTdGo6oNEAAOAfV4rhG7kq29aifiMT\n0Zi1T6NTM0n/uS4gUwwEg/c+d9AUAwAAwHk0xfCNXJVt1M82MsVAMJg73UFTDAAAAOfRFMM3clW2\nUT/byBQDwWDudAdNMQAAAJxHUwzfyFXZRv1sI1MMBIO50x00xQAAAHAeTTF8I1dlWyLrFx6bVPfg\neMwXD+pIHjLFQDB473MHf48DELfZh3QsdOrw9gBGAwDA6nGlGL6Rq7KN+tlGphgIBnOnO2iKAQAA\n4DyaYvhGrso26mcbmWIgGMyd7uDvcQCWFB6b1MhEdN4+bqgD0k/mOql7cDxmf352piaiU/P2FeVn\nK7QpZ62GBqwJmmL4Rq7KtpXWz+umOm6oW3tkipFso5EpvXDxWsz+U4e3x+w/fWSnM00x733uID4B\nAAAA59EUwzdyVbZRP9vIFAPBYO50B00xAAAAnEdTDN/IVdlG/WwjUwwEg7nTHTTFAAAAcN6Km+LM\nzEzV1NSopqZGJ06ckCS1t7dr165dKi8v14ULFxI2SKQGclW2UT/byBQDwWDudMeK/x6Xl5enN998\nc247Go2qublZnZ2dikQiqqurU0NDQ0IGCQAAACRTwkJqnZ2dqqioUGFhoSSptLRU3d3dqq6uTtSP\nQMDIVdm2XP28HtIh8aCOVEGmGAgG733uWPEsG4lEtG/fPuXm5uqb3/ymhoeHFQqF1NbWps2bN6u4\nuFjhcJimGDDC6yEdEg/qAAC4YcWZ4oGBAf36179Wa2urnnjiCUUiEUlSU1OTHn/8cUlSRkZGYkaJ\nlECuyjbqZxuZYiAYzJ3uWPGV4qKiIknS/v37VVJSom3btumHP/zh3L8PDQ0pFAp5fu/x48dVVlYm\nSSooKFBlZeXcnydm/+djm222137bSzzNmNexq/3+eAU9Xtd+33gFPV7Xft94xPv9Qc9Xa7Xt2u9r\nebunp0e2rc1IAAALDUlEQVSjo6OSpP7+fh07dkzxWFFT/MEHH2jDhg3Kzc3V9evXNTg4qKqqKr39\n9tu6efOmIpGIbty4oaqqKs/vf+mllxZ97YVvzmynzrZX45RK42N79fXzEk+W1evY1X5/vIIeb7J+\n38WOTdXxJuI1LNUnEa8R9Hjj/X6v+SY8NqnuwXFJ0sYdd+KT4bFJhTblpNR8yHZ6bi/c19XVpXis\n6Ay6evWqnnrqKeXk5CgzM1Mvv/yyNm3apJaWFh06dEiS1NraupKXBgAARnndm3D6yE6FNuUENCLA\nvxU1xQ8++KCuXr0as7+xsVGNjY2rHhRSU0dHh68ri0hN1M82MsVAMJg73cET7QAAAOC81Qem4Aw+\nKae2xdYZLsrPjsnzeR3LesSpjXWKkUoy12kuO3y3dJxHeO9zB7MskCYWW2fYK8/ndSzrEQPwazQy\npRcuXovZzzwCy4hPwDfWarSN+tlGphgIBnOnO2iKAQAA4DyaYvhGrso26mcbmWIgGMyd7qApBgAA\ngPNoiuEbuarUMfvUqLu/lrvrm/rZRqYYCAZzpzv4exxgUDyrR8wunTS9ZdvcEkrpuGwSAACrQVMM\n38hV2TR/6aSbklg2ySIyxUAweO9zB7MsAABYc14PEZp92BAQBJpi+Mbz34HgkCmGVUs9/e6519+d\nt8/rYUNB473PHTTFAAAgaXj6Haxg9Qn4xidlIDhkioFg8N7nDppiAAAAOI+mGL6xViMQHDLFQDB4\n73MHf48DAADmeK1eIbGCBVaOphi+kasCgkOmGJjP6yFGUuJXsOC9zx3MsgAAICUstnwbV3+xFmiK\n4RtrNQLBIVMMFyy2fFuQ6xfz3ucObrQDAACA82iK4RuflIHgkCkGgsF7nztoigEAAOA8mmL4xlqN\nQHDIFAPB4L3PHTTFAAAAcB5NMXwjVwUEh0wxEAze+9zBLAussXiewrTYsdGp6aSNDwDSDU+/gx80\nxfCNtRoTI56nMC127KnD25M2PqQmMsXAyq3m6Xe897mDphgAAKQ0ryfdLfYXs3iOBe5GUwzf+KSc\nXEzkWAqZYrjM60l3i/3FLJ5j/eC9zx3MskASeeXYFmt0Ez2RAwAA/2iK4Ru5qvh55dhodLESZIqB\nYPDe5w6aYiBOXld/uYMZAOzxiq0xn7uLphi+8Un5Dq+rv99u2MnSaUgqMsVA4nnF1hauSMF7nzuY\nZYEE8JpYJaISAABYwRPt4BvPfweCQ6YYCAbvfe7gSjEAAMAK8KS89EJTDN/IVQHBIVMMBGOp977V\nPCkPqYdZFk6J51P9Ysdy8xwApC+vFSkkKT87UxPRqXn7eD9ILwlvitvb2/X1r39dGRkZOnPmjBoa\nGhL9IxCQVFirMZ7l0BZ7cMZzr78bc6zXp/rFrgBw8xyCQKYYWBtL3TjNA5bSW0Kb4mg0qubmZnV2\ndioSiaiuro6mOI0MDQ0FPQTPRnWxP1Px4Aykk5mZmaCHAGAVWOM+9SW0Ke7s7FRFRYUKCwslSaWl\nperu7lZ1dXUifwwCkpPDiQsAwErEc1EHwUhoUzw8PKxQKKS2tjZt3rxZxcXFCofDNMUpbDTysRZG\notavy9DGDcHGzePJ8y6W/4on6+X1GmTFAAArkYz3lMXeF72yzlyBXpmkdD5NTU2SpPPnzysjIyMZ\nPwIJ8v6fb6vv1p/n7Ssv/IRnU9zf379Ww4orz5uIB2d4vQZRC6SS6Wk+pAFW+H1PifemPq97Yryy\nzqlwBdpiE58xk8Cg2uXLl9XS0qJXX31VklRXV6cXX3xRVVVVc8f89Kc/1YYNGxL1IwEAAIAYkUhE\nn//8530fn9CmOBqNavfu3XM32j300EPq7e1N1MsDAAAASZHQ+ER2drZaWlp06NAhSVJra2siXx4A\nAABIioReKQYAAAAsWhf0AAAAAICg0RQDAADAeUldjPb73/++3njjDW3atElnzpzR+Pi4vvGNb8w9\nrvTo0aM6ePBgMoeAFVpYu1kfffSRTpw4oYaGBj366KMBjhBL8arfl770JW3dulWS9OlPf1pPPvlk\ngCPEUrzq19vbq7a2Nk1NTamsrEzPPPNMwKOEl4W1+81vfqMf/OAHc/9+48YNffOb35w7F5FavM69\nc+fO6Ze//KUk6eDBg/riF78Y5BCxCK/a/dd//ZeuXLmirKwsffGLX9QDDzyw5GsktSk+cOCAamtr\ndfbsWUlSXl6e/vmf/1k5OTkaHx/XM888owMHDmjdOi5Yp5qFtZt1/vx57dixg/WnU5xX/XJycvSv\n//qvAY4Kfi2s3/T0tP7jP/5Dx48fV3l5ucbHY9c1RWpYWLs9e/Zoz549kqQPP/xQp06doiFOYQvr\nNzIyov/5n//Riy++qOnpaT3zzDP63Oc+N/fkXqSOhbV755139NZbb+n06dP605/+pH/8x39UZWXl\nkssCJ7Ub3bVrl/Lz8+e2MzMz5x4V/Kc//Unr169P5o/HKiysnSQNDg5qbGxMO3bsEPdnpjav+sGO\nhfV79913tWnTJpWXl0uSNm7cGNTQsIylzr2Ojg4dOHBgjUeEeCysX25urrKyshSNRhWNRpWVlaW8\nvLwAR4jFLKzd8PCwtm3bpnXr1mnjxo3avHmz+vpiHwp2tzV/lm8kEtFzzz2n4eFh/cM//ANXiQ35\nwQ9+oCeffFK/+MUvgh4KVuDjjz/WP/3TPyk7O1tPPPGE7r///qCHBJ/ee+895eXl6Rvf+IZGR0dV\nX1+vRx55JOhhIU6XL1/W008/HfQwEIeNGzfqb/7mb/T0009rZmZGX/3qV/WJT3wi6GHBh0996lP6\n8Y9/rGg0qrGxMQ0MDGh0dHTJ71nzpnjDhg06c+aMBgYG1NLSoqqqKp5wZ8CVK1cUCoV07733cpXY\nqP/8z/9UQUGB3nnnHf3bv/2bvvOd7/DXGiM+/vhj/f73v9eZM2eUl5en5uZm7dmzR0VFRUEPDT4N\nDg5qcnJSZWVlQQ8FcRgZGdHPfvYzvfTSS7p9+7aef/557d27V/fcc0/QQ8MyysrK9LnPfU5f//rX\ntXnzZlVUVCz7nrfmTfGsv/zLv1RhYaEGBgZ03333BTUM+NTX16fOzk5duXJFY2NjWrdunT75yU+q\ntrY26KHBp4KCAknSfffdp09+8pO6efOmSkpKAh4V/Ljnnnv0qU99Slu2bJEk7dixQwMDAzTFhnR0\ndHBjuUF9fX267777lJubK0natm2brl27ppqamoBHBj8aGhrU0NAgSXruued07733Lnn8mjbF77//\nvtavX6+NGzfqww8/1ODgIJO6EV/+8pf15S9/WdKdO3Fzc3NpiA2ZmJhQdna2srOzNTIyovfff3/Z\nyQGp47777tN7772niYkJbdiwQf39/fqLv/iLoIeFOFy+fFnNzc1BDwNxKioq0jvvvKPbt29renpa\n165dU2NjY9DDgk/j4+PauHGjfvvb3+rPf/6zduzYseTxSX2i3csvv6xf/epXGh8fV0FBgerr6/W/\n//u/kqSZmRk99thjfHJOUbO1Gxsb0z333KO/+7u/0/79+yX9X1M8++kLqcfr3Ovo6ND69eu1bt06\nfeUrX5m7Ix6px+v8u337ts6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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 23
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "######Discussion\n",
- "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Explaining the Results - Multi-Sensor Fusion"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focussed all of our attention on the position sensor. Let's change focus and see how the filter performs if the intertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30\n",
- "movement_sensor = 30\n",
- "pos = (0,500)\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "vs = []\n",
- "\n",
- "for i in range(100):\n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- " vs.append(pos[1])\n",
- "\n",
- " pos = update(pos[0], pos[1], movement+ random.randn(), movement_error)\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()\n",
- "plt.plot(vs)\n",
- "plt.title('Variance')\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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5U5x9koih4wURU8AB8uTJk1GzZk20bNnS/dzatWvRtGlTNGvWDN99950oAySEEEJCwTJ9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\nmGqBHCvuIKeeeGrHM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gQi5gQi7gJNcWwtNZTxgAAACDyLWF8OTyQm3dT5/wmYbeLpiQC5iQC5iQCzjJ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\nlOux5PNa8sVf90Rfj2/7PNG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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 24
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distintly jagged. But, it still mostly tracks the dog. What is happening here?\n",
- "\n",
- "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n",
- "\n",
- "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n",
- "\n",
- "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematicall model this sort of reasoning."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "More examples"
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example: Extreme Amounts of Noise"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intution tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30000\n",
- "movement_error = 2\n",
- "pos = (0,500)\n",
- "\n",
- "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(1000):\n",
- " pos = update(pos[0], pos[1], movement, movement_error)\n",
- " \n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- "\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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kONRo3Dj2cjSSceuthnFEMS9cGNZpxvzhhzDrNfK1Wv2WldMnTlS0yVNry0aV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ho4VqxovhkxQhCkuGyNlcDarVtjnu0UCgpgU2ceCcwgC506NU9uGBzYps+fD+/11ys5zWXh\n9nkpMcNhjmX73/+kyYIEbDx1P/CAciz3PffAq1VKXC9Va0g/Fvr1C5pcUmeyUVKltvZwDjgcSUmr\nA0h3epo71EPy0PpLShJz0YkwiLZ/8QUyAn/ETKB8rrKcE+1JTt4drqb699i2bEHWddeB27hR8+N8\n9+7wqqtMyh0sEb+DMJkbuLIyabCuQ8zIaM6K4vUmvpxwhJ+v0LUrPFGEKbTg84X92fH9+sH7058C\nbjdsX3wBoUcP8EYufgb4S0p0k9e3YLeD8fmQ9uqrUv7TUKEnH3lDTaIuxoHqd5oyMhJe8CFWgkap\n92QSnc6wG9T01Ozdq+xN8I0fD7+qWEq8HEuXgq2sBLdvH+zr15uT4s5uh2fatJQfVslWEWe/z54w\nAdlhCiBF3Z7cXJw5fRre6dMhnH9+9B+M0H724EFkxZICLgppL79s6kw48+OPyLn44tj7bZjrmtCz\nZ+Q0uHpfO3iwkhVM+jJBWalUBoMGr8tcWVlzeEa0WBb+4cMh6twAAkDmzJmGU4DqSktrvr7n5Gj3\nY53wEzE3t8W+A6a6Wklx7HrqKSn6IJB9ynD4ZASWHER77rkHLnXWilQILeYQTW7daAQ6PK8x++2b\nMAFNjz3WfByeB+z25oIXamFS/olOZ8vZDNW/R2RZcAcPIkOnOp/31luD88DKu7hjSAvXQpjMDWlL\nlijpBrXw552HjYGNZozX2zyrnyoxroiInTopIQ9ahPPOg2/SJDhfegnZU6c2F19JAt9Pfwrm+HGw\nhw9HfK/ocAA+H+z/+592CqnQk0+i4389nqhnzRMZ42hU00svJbSyYESZmXA98ojhj6nPCf7LLktO\nKjrVpraUczjguf12OAJV17iyMmyRV9MCbF9+iXQD4RTRUGKt4+z37OnT4KKo2JcwoihVcoQU1hhp\nttTx4YdJC3lzvvxy9Nmf6urinjlscb4QRWkzaKyD6EQUfNH62u7dm+tTALB98w1s27bBN3GiUggu\nXFpYTRrXMba8HPZwGdA4TgpR0vk3socPS7mrU1mIR6fgluhwSLnqVdKWLFGKgsmr+3yvXtIMd7zF\n5EJYchCdMg0Nzcm6Q39BMZbt1MIXF6NRK84tJ0dKs6Pe7W+3t9ws5vMhr2tXpdJiKKG4GA0hOWZ9\nV12FRrkTMYw0CNf597gfeABC377SZqEjR6Tk8Q5HQv794cJSvBMnwnPHHWE+rNpN3KEDmqKIuzXW\nuPAXwaZnn5VmjA3iL7gAnvvui/zGwKwrt3MnsuWsAlHK/slPIqaokqUtWxa+alqA6+GHleVgViuN\nUujJx+Ag2rZmDdgwG0mZhgZw334b1Xe1Jf5hw8AbmWFMBbkfyBdZk0IDuCNHlHSSac8/j4KQSmdM\nXV1chSq0KLNzJhWYkTkXLIj6HAAAaGhAu6IicFu3BocH6En0HoQY5Y4eDUadxSoR5AmmWAfCgSwc\nts8/Nz7La4DnzjtRv3IlPLNmQTj/fAg5OWHTwmrSGDSyhw4hTac8PAD4f/ITuMLtKZBTzSV6dTgM\nobAQnttua/G8f+TI4JV0oMUkqG/CBPBDhsB7550QunWLrciOjlY7iGaOH4+YkD3r1luRLsdDac1E\nJ+gkWbdhA6BRqls+rrwcXv/pp1Lwf0iMEbdvHxiPp7kMeCieB/v990FPsQcPNg+E9Mp+h7CtWYP0\nRx9NbMyQKOrOIAvduoXPk8owGCzHwWZnGz95RGpapB3fGRlhiyXETd48G8MNG1tZKWU2iWYDrqqP\nhSP07auUq9bKKy06nfAG0okBgP+ii6TNnlG2Pe3dd2HbsUP3df/Ikfp9PISpMdEp5ps0Cf4ELPsn\nkpibCyEnJ+Yl5oRRXSwZvx/nybGQLhdQVyedNxOcDs1/8cXS8rHqbypr8mSwoVkCkilQgMdQFcrA\n32nakiUQzjlHM5tIkGSnwIvyxos9flw3a0+0WpwvwmXYiUJNRQXAMEh/6qmIaTLjkp6u7MsS7faY\niiWJLBuc8g2IWDxMzM+HEC7Vonoza4Lk9u0rFQbTO+S332r2d6Fv35b7UELGb65nn4XYoQMyp00D\n3G5wCcws1GoH0Zn33QfH0qUtnnc+9ZRysmMrK+EMzNaKnTrBc/fdzW/UWTpIOI3jCO3bB8+6yrPl\nOgH8TEMDskNSAjr+9S845KXNKCtV2TZsaB7QJegE6h89Gg3//a/2ixFik1yPPNJcvSnB6t97D77x\n45Py3VGTT2KxhA6lpSFnwoTo0tdF+7sUBGROn44z1dXwaW3syMmBa8GC5q9t3x6uJ56IOkaYPXhQ\nWv0J106TZ/fixW3ZgpzRo8Ft3252U5LKP2oUXI8+KsVODh2qXco8FVR9htuyRcls4Hj/fSl7iNud\nlGIhviuvhBiYGLG//z643btbDlQiiGcvgePtt8HW1Bj7e1FtFvNffDE8WmGDanFmyEqkFmnM4iVv\nYnvggdi/4vvvYdu1KyXnrJyBAwG7PfLmbC0cB9s33wSnpBSE+IovyWEciZyJ1sm1LmOqqzWL1oVi\n9+yRUgxq/F5sW7eCqa+HY/nyuJoadLyEfZPF2L/8EtzevS2edz7/PJx//av0QPVDTvvb34IGJGKH\nDuELQySImJ3dcsNURoYSuwagOZm7Hq1BmPpO0+EIn/83wPnqq1JZTY5Dw7/+Fe0/IXYRBtH+ceOw\nLkm5aP2XXabk99TDVFSEjxuLV+Dfbtu+HbatW419NHDyiioXbrQ3hPKAxECcm3faNN3CLKFsO3bA\nprO5FYChmwkzY6LDsW3aBO777+OeObM635gxUsGGTp2kGy6zbn5UfYYrL8fpVauk5wMTAYzHk5Sy\n1a4nn1TO22lvvAH2zBnDN8JCUVHsOWtDwmi4LVuUjVS6jO5hSGI4h9C+vfaNepKEni9EhoGYlRXT\nzK5MGYSmoO+z1dUx/z5cDz8MprIS9jVrmp+Mc5JMmYFOUEy0bcMG6aYwXN8MqViohysvlxIWaP1e\n5Gqfrb1iYcJodBTG65V2kwPBP8iQAR23e3fYpYVE8V11VYtNlELHjkGdM2LJaq0ZPFVIBj9gAOpW\nrYJfZ2OR89lnYVdXQWIY+FMwS8sXFyubJbQwJ06gwMQZPe7wYaQFNi0lg1wxUzP+OOKHA301wkwA\nU1kpFVWI5sKZqM204Q4RLhVeqlZ/4sQePQouUP2qhSQUW0FdHRxh4hfN4PvpT+EfNQpC9+5wR1kZ\nNRnsH30klScG4Jo7F4fkQZG8mpakmegggZAvozPL9Z9/jvrVq2M7Zkge35yJE2GXbyD0RLkiKePP\nPz9psfiemTPhnj07Kd8dlaws1GpUwDVCTs+akkqgcYRYCv36SaGLBtuZM2KEfiVPm02Kq0/QIDq0\nhLrme9LSNMM5mJMnkTFjRvP7An8b8uSj889/hvNPf5JelDNnJfB31roH0TqUzh9mEA2OS/pylu3r\nr5GhcQHyzJ4Nj5ETjNcrzYSohfzRCeefD9dTT2l+3PHOO8pyWSpLA3unT28u06uB27MHw7/8MmXt\naSGBcfFaPLNn40xVVUxxZbpFSUJw+/YBQMucz1qSPIg9c/hw+MITmZlRZ2AxMyY68667kHPlldov\nJmEQzf74I5x/+UvCvq81se3YoRSRcD/6KC6QQ/IC5z/v7bfD/f/+X5IbEdtAQuzYMar86prkrCjq\n81OkQZacdYllkX3ZZbob1WW+yZNRJ084JZh73jxj6fjijL3ViomOVA4+Ivn3noJrJuPxgK2uBvvd\nd7FtZAyZaIsmBI89ckT33ybm56MhxqqMmt8XTcYbp7M5tFWFcbthV98QcRx8F18Mr5z+UhQBnw9M\nRQXYM2ek6y3NREdJb8lC7vzqctGhccCJqlgYTmNjQjYlaOVqdHzwAdKjzGbBlZcrg2gjJWqTLtkb\nWyJIf+IJ2NetS94BOA6w28GPGAHvxImGPtrw+utKdctwxPR0+IcNk4r5RJD21lvNZYWTIScn7ICj\n6bnn4FNXmrKqcOeFJAyiuR07wEWRorAt8g8eDP+oUS1fkHPrtmtnrJhJNAQhaCN3NLNoiabceKtv\nOiOdL2021C9bBn7QICmProVinsPxDxgQfgO6WeTJuBirExrFlpcj44knYNu82fiHQyZIhKKisGFO\n3K5dUgpAvZsXhwN8IquyBtoSbhKPqamBQ2O1hduyJXg1N3QClOPgWLFCmVBiq6piW/3V0aoH0bqd\nO9AxGl96Ce5Zs6TnQmZuxRTMROsu0fB8c8GVKAjFxaj76qvgrzC6IY9hIOTmxla9KVlEETWB0rqJ\n5liyJGIMoaGd73EQWdbwDZvYqVN0Mfvp6dKSdhSiSYOnxm3a1JzdJsVMjYkON1hJwiA64jK9CZjq\n6rDpClNFzM0Nij+X+4XodAIJrNAYxOdDjjoPvN2OxoULNSvhJg3HSZlyVIPoaM4h/vHj4b3tNnBH\nj5416ST5AQPiLnyWjPOFaLPBe/31UpraFLF//nnw6kO0QkM+I23ilvdkparst9MJIT9fP4sZAO91\n17UY5wAAd/BgyBMhYzeWlTKceb0xFa2KpNUOor2TJ0tlOUOfv+IK+APlL4WePeH6wx8ASEsXae+8\n0/zGVAyidbJgMFVVUjWlaDGMsqQp811/PTzqykcRiCwrpRizUHaE9GeeQWYC7xjVMufOhV3jD9IU\nMcS7CT17oiGKHcZiejoYvbi20PdmZsJlIL6VqauD88UXwVRXR/2ZViHcZtjBg+F65BH4BwxIyfHM\nYl+9WgkxSX/oIaQtXmxKO8TsbDAaN9q+SZPQ9NxzyTmowyHN0gUG776rrwZfUpLSnLm+yZPR+Prr\nwU8avF451Nc7C2t64QXNlJvxYvfsQVos2S4ChF694Asp8pEsQocOSjaYWG7Q+ZIS8MXFzU84HHA9\n9pj+B6Io+51QGRnSKmi4f1t6eotxjha+Z0947rpLeSyv2og2m7Qqm5sL/+DBcTdZZp0RU4I1vvGG\nZh5M98MPB6eyC/DMnCndCQVE2vSWECwLpqam5YxoIjZ4qZdv/P7IM9sMg8Z//jPmcqXJYNuyBelJ\nquQHSAnnw+F79DA+ox8Dvn//pMVtik5n9INoh8NYOIecnzcFG3BDmZonOsyglh8xAu5f/cpSf0fJ\nYCstlXKt1tXBsWyZadk5xJycoJnolPSLQL+XV268N90E/oILjH/NsWMJLSKivn5ZHfftt7AlqRqi\nFq1+wR47Bnsce274oUPhnT49nmZFLTTZgBFpf/0rhHbt4L/oouYnHQ7NcZAiGRukwxBzclATUusi\naiFtFLt0gU89garKCc4kOIUv0IoH0Xr4Cy4AP2xYyxdCfqie++6DP0zp5oRgGNh27ED6008HP+12\ngzl5Mr7vVg2i2cOHkVNSopu7lu/TJ/n/1hgIubnwmThY4ouL4b311qQfRywshN/IyoOR787JgS8k\nh7gum01z44Yu+eRlodWLVBC6dlU2J6dCtAVoUsnx4Yew7doF9swZaVOzSX3AX1ICf0mJKceOd7Nb\nzuWXI2fcuIQ05czp0/AZWHkEEHGAxG3Zgox7742jVfrSXngBzpdeSsp3R8XvR/bUqeYVCTKIUU+s\nGRzYcvv3G6/aabNBiFSMLJEYRrcORiRCp05hS6F7Zs6UYq1ttuZxUQL3u7Wtq184JqTX8g8bBtfc\nuS2Oy33/ffwbvNT/HpYFW1vbYrAu89x6a0pyYhvFDxiALT/5SfIOEOn3zXGWKX0bs5wc8OeeG92M\nl8OhlCKPisGUWYlkZkx045IlqElhCItQWNi8d8MqApMOylKpSYMRfuRI+K67Tnkc2i8y5s2D7X//\nS/hxa8rK4o6BZqqqpPy/qdTYCIgi3DNnQujRI+xbHe+/jzSNgmWJkLZ0KbiQEu3J1OJ8ocpUcjbw\nXnedMqgVw8QNa9KoTshUV8Pxj3/of4bjkr8SnyBiRgb8I0fqv0FOeVdUBO/kyRHrUxh1dvSgZHG5\nmvMgmpGjNitLSj0Wcly+f/+4A+C9N96IptCiMjonDM//+3/Sju0ff4yY9iilGAZmZg12z5sH95w5\nJrZAX/r8+bCvWBHVex3//KdSyS0c79VXwzNzZvSNaKMz0anG9+8P/9ChZjcjmHwRMvFGKhL20CFp\nU2YSMs5Ek+0m2dIffdTwTX67rl3Bbd0q5dCNlE7SgrH4CSP31zhv/uwrV0o3Jknm/s1vIHbpAjEz\n0/iEl8Ygmq2qCruPge/dG01mrhQYwA8eDM/tt4d9j+/aayH06AHPvfdC6NixOf1dArTaqx9TUaG5\n4UQt45FHkCUv15tV6EGr7HfPnqiJVH0qAvbYManMMhD1Xbf9ww+RvnBhXMdNKIbBBf37J+3rhUi7\nqtPTpdyUFsQeOQL2hx+ie3OUfVts315JAxQNPrBB14xBtKkx0SnmHzcuOMbPAoSOHSF07tw8CLHI\nsri6X9hXrZLilpNQsTBU9oQJYMvLDX2mrrQUtbGuqIginC+8ENNHHe+/D6FXr8iFVJK9CpfC622L\n80WCJgAyHnxQM8VssnivvdZ4m7VWVDUG1kEyM8En8dqbSEKvXvBHCItqfPNNMKdPI/NnP4PYuXPQ\nxsN4tdpBdOYvfgH7Bx+0eD7tb38DF8izyB48qGRo4Pv0gffGG1PZRAAAI4pJWVKyf/wx0pYsAaAa\nPEc4adm++SYpszaxcv/qV0mrmNXwxhuWjAOPlmPlyugLcEQ5iGYaG5FhIGxAzM1F09NPS9WwCAAp\nv2ruBReADeRdb61811wD9733Ssu+7dqlZO+AUXJF0GgL+MSKPXQItm3bDM/cCsXFEGIMo7PJRVBi\nHIj6Jk2Cd+rUsO9Jep0EC/DceWfMn2Wqq6WbtBRMImRfdBGY6mo0vfgiIBcmiZLIsrCvWwf2wIHm\nJxsbYfvuuwS30uJcLth2707417baQbR940bNpOQZjz8Oh5waTNX5na+9lvr4NEgn+oQXAwCCd6CG\nlIjVk/bee2BCKx+ayP+Tn2BdknLR+iZPjljFjz1wILgcutUEyg1HwkS7yhLDaozn3ntNGUSbmic6\nDG7bNrDHj4OR893l1LkAAB6VSURBVKy2Uv6RI8EPHAgxPR3em26yTDiHul/Ig+ikrybJIYGp/BmE\nTIxw33wT/2b0UEkcRPPdusGfwtUkrfOFyHHBGSsMYo8cCfxP8odR7MmTMafc9fziF2DOnAkaD6Wq\nBoKVMD4f5Yk2TGdmQEltpur8YoKDzaPlvfHG8KWQY6VarhELC1H38cdR5Vi0EqaiAu2TcOcYLe67\n7+B47z3Tjh9O3bp1qP/kk6jey+3ZE5QGTJdZIU1nGfaHH8Bt3ar9YhJSQzEVFbD/5z8J+75E8F19\ntbSSk5kJl86GZbMpM9FJHkQLcv7dVFYADOlfOVdcgbTQvNF6orzO+UePhl8jTWwiuO+/H55f/CIp\n3x2tum3bYk4bByClZb/jScsmnHeeFHplpJ11dchJUQ7seLFHjyJj7lzd1x3vvYeMOXOkVXYaRCeG\nmJcn/Y/6DtKEQTRXVobMBMbmBAmJeeJHjoT7N7+J/DkLDaJs27Zh+IYN5jVAECy7aY7v3z/qAgSN\nL7wAfzQ3UJGqWFmImTHRWT/7GXIuu0z7xWSU/T50CGl//3vCvq81U/cLMScHQm4uhG7dkntQjkPt\nli0Rs10kkmZ5ZAMzx1k//SnYCMv53htvRP2aNUabFhXv9Onwjx6dlO/WonW+0NrUb4g8IEvFTHRl\nJZi6OunmPZaNjCHndjFCTnFGEBKawzyp6uth27Qp/Ht8PrCVleDUIS0JcnZcMWOlMSiu3bwZTX/6\nk/SyesNJghNwR8XjAXv4cFK+2r5iBZxvvGH4c4IFdp0rTN4dnvbKK3B8+KGpbUgE7y23RFUCmdu+\nHawJhVPOOuEGK8kYRO/dG/kiQVoQOnaUNmRGGfYU17F69UrtBITWDGoUGygb3noL/pEjwZw6FX8a\n1TZOSe+Y5Jh7GVNfj8xZs8AePWr8syEF3IT8/LDXeqa6GmyExAxWwX33Hbi9e/XfIAhwrFgBsaAA\ngjyBmkCtehCtlU9R6N1bqSbmfvBBuB54QHohwQm4o5LEYza+8QZqt20z9Bm+a1d4klQ5LyaiiFOn\nT5t2eMZI4ZFWgPH7Db2f/e47ZNx/f5JaE56pMdEpHkTb1q+33ICHqagwnI0iFYJiort0QZOVsg0l\nUlpaUOni2q+/jiqXuO/aa+GbMgXc3r3BG81auaScL2w28L17A0bzNseg7n//Az98OLj9+2O7LoUm\nMIgw7rDa+SYcLtJ5yO0G43aD798ftdFmtDKg1Q6iPXfcAd/VV4d9D9+/P9wPPwxA2lUfbd7dhEni\n7LeYn294eZEfPjwpgfexcv71r8hNQqePmoVCW1JBKCgwlI+YaWxE2ttvA/X1SWyVBYUr+33BBXDN\nmyddXFuxtPfegyOQ/SfzjjukfLkkZfgBA1CvKlkt9O0bOe+zCuP1topVtnjYvv4ajn/+M+bPi3l5\nUsq5FOAHDFCuR5FS92rxjR0bNB4Qc3PhCrMXi+/ZE56bbjJ8nLao1Q6imxYtgt9AtTvvtGkQioqS\n2CINLAv2xx8Tv6s6lCCAiSLvdOPrr1uiiIDMtnMnMkwcoPF9+yZl+ceyHA7AyGx0YGbDjEwUpuaJ\nDjeIHjwY7t/9DsjKSmGDUs+2aRNsO3YAkNItWuWGsy3lD4+bib8z29dfg0thiJJWv2D37pXSusZI\n7NAB7kcfjadZsR1XzjoTJcfbbwPp6eCHDWt+Mjsb3jvu0P9QRsZZU2zF7HNPqx1EG2ZGZgKGAXvs\nGJyLFiX3OI2NyDv/fHDffpvc4ySY0L49/CNGmHZ8fvBg+KZMMe34qSba7caWCttoxUKhZ08Iubmp\nO14KN6xFy/7FF7AFcuwTYpTz2WeRFsOenUTK/NWvUlJtMJFq9u0DbzBjCltebsnQq0The/SAGGbS\nwjdxIoSCgqQdv21d/cIxYRMbf+658EyfnvzBeyBmy6z41Vj5S0qwfeRI044valV6as3sdmPFdkws\n+WxmTHTD8uWoldNkpgDfty88JhSCCsffv3/wxdwiJaKtmj/cMpqaAEGA54Yb4JcrjprA/tVXSqGz\nVNDrF4xF+m20xFgGg5GqE57lxOxs+EtKwrxBTEpqO1nbHkR7PEBDg/T/ZsxEO53gu3dPyXFFjoNt\n+/aw72GqqsBUVia9LVFjGJi5UOP92c/QZNEcuMkgFBWh8eWXo/9AG52JTjW+V6+UpgOLRv3nn6Pe\nyoWIWrumJjifesrwx9oVFcG2dq2U4ixFWSWsTDNVoAH2f/87tfnBY8Gy1m9jHPi+fcPnHHc64bvi\niqQdv01f/dJee605obiZhSZScNzGV1+F66GHwr4n7Z13kPbaa0lvS9QYBuf37Wve8dPSokob1WqE\nxs1FoGyeM2EQ3ZZiX/mSEninTTO7GcGczuBKgBaZ0Wsr/YJxu+FcvDimz9o/+gh8v34QevZMcKui\nV79sGRrefjtlx9PtF3FeezNnzza2j8QMrXxFVSwqgu/yy/VfLyhIapaeOMr1nP243bvBBXIu+i+8\nELwZA7YUFbjwTZ6MSAv13Natloq/9MyeDT5CaW5ioqwsND36aMrypJ4N2D17kHP55ahbtw5C9+5m\nNyclxKwsQ5u4SfzYY8fAyKuoMQi7qSwF/OPHm3p8me+662L/MM9Le0gsvhInOhxwfPCBlDyBrqcJ\nZ+3ffrKpOn/aP/4B9siRlDdBzM2F0L59yo+rxfHpp2ArKsxuhsI/ahTWJakYDUkMz9y5pszWWzX2\nlSsrkwY3brfZTUkZz223WSY1plX7RcJZfOBmNVr9QujY0VBKzxbk1ReL/y68118PxusFF6FCJYmN\ntX/7Sea94QZ4J02SHjCMKZsMvHfeaa0CJxbCHjqEdvSHTyyG3bcP3K5d2i8modiK1bmefjqqipgk\ncfju3eGbMCG2D1sk9MZsdatXQ+zQIfYvCFQstPrfulhUBKF797jjv62K3bsX6WFCVW0bNiBLHucl\n4/hJ++azgH/cODS++SaAwAYDE04umT/7mbUqR1noD822YQNKArloCVEzM/Y1+9prkXPJJdovtsFB\ntJW0lZhoZGWhYenS2D7LMMj8+c/BbdyY2DZZmFa/EM85p3kgHAuGwZljxyw/Ew3A3D1fScbU1sIW\npjqzyDBJrT58Fvz2UySJ1QPDHvbMGTCnTqX8uHqEjh3NbkKzVvyHT85iKS77TUiiNL70EvwTJoA5\nfRpMGwo5SpqzZeO5IJwdg/0YcAcPwrZli+7rTH19XEV1Ion5p1pfX48uXbpgoWrX49KlS9GnTx8U\nFxdjpaoMrN7zlsIwpuxgFfLywNbUpPy4Wvz9+1srC4Aooqq62uxWEB1MRQUyf/5zU45tZuyrWFCg\nHwNMg2hTtZmY6Bh5b7oJvssvB7dzJ9jApvq2oM33C0Foteck9sSJ8K8fO5bc48f6waeeegrDhw9X\nHnu9Xjz00ENYv349vvjiC8ydOzfs81ZjX7cOtnXrUn5cMS8PjEUG0fzgwRAtdGedtngx2u3da3Yz\niA7G7Ybjv/+1foqnBKtfuRK1O3dqvsb36QP3zJkQunRJcavMkz1uHDgKuzqrsLW1sLXxgaV95UrY\nV60yuxkp4ZswodWek3wXXQT/wIG6r/svvBD8eecl7fgxpbjbu3cvTp48iWGqnLKbNm1C//790SEQ\nqN+1a1fs3LkTdXV1ms8PMli6Mtm8N94IIYk/aF2CAPaHH1J/XA1Nzz9vdhOC2MrKkJWZCWvcYpAW\n5OVBE8KgzIx9FcNk0xH69YMrhiIYZzPbjh1xpVtLpDYTE00M0eoX3LZtQFZW2BzDrQG7fz+4Awfg\nmT3b7KYkBT9sGOrDVL8U+vVD3aZNSTt+TDPRv/3tb/H4448DAJjAEsGJEydQWFiIxYsXY9myZejc\nuTMqKytRVVWl+bzliKIpu1cZrxcspXHTJHTuDL+B4h8kxahiIQmw0r4OEqVWurwfrfRFi5K+1G8F\njNeb1Jjgti7s1W/RokUYMGBA0H/Dhw9Hnz590LVrV4iiCDEwCyUPpmfMmIEbb7yxxXepn2es+Mdr\n0ia2xjffRNMrr6T8uGcD39ix2E2DaOuSB88m/N20+RhHixEzMsxuAgDqFxG5XIAgwHfxxfBfdJHZ\nrUkZ3X7Risthy0Sns03lrU+1sOEcc+fObRHDPH/+fPzrX//CBx98gFOnToFlWXTp0gXdunULmmE+\nceIEunTpgvr6+hbPFxYWah5v1qxZ6NatGwAgNzcXAwYMUJZh5D+CZD0+UVmJ2sxMyPV8kn08Kz52\n/vgjSkaPhtihgyXaM+TkSTCBCktWaA89Dn6cXlWFCQDAMCk//u7du03/99Nj6XHtpk1Ye+IEUFpq\nentkVvr5WOnxtZMmoWHJEpz0+3G8vBy928jPS+t8cS2gTASY3b5kPhadTnhra1Fqgb9Psx/L/19e\nXg4AuPvuuxEvRhRjD2h84oknkJ2djXnz5sHr9aJv377YtGkT3G43xo0bh/379+s+H2r16tUYGk/1\noDhl3H8//EOGwHvnnaa1wWzpv/sdhE6dLFP8JePee+G/5BJ4b77Z7KYQLS4X2p1zDs6cPm12Swgh\nUWiXnw/P9Ongu3eHf8QI8CNGmN0k08g/iyZVhrHWiDl9GjnDh6PWInuvrGTbtm0YH2cJeluC2gKH\nw4EFCxZgzJgxAKRQkHDPW41v4kTwPXua3QxTcTt3Qhw92uxmKDx33QXRSnmrSbC0NLgefNDsVlgK\ne/AgcktKUPP999R3iTWJIjz33Wd2KyzB95OfmN2EpBOdTrA1NWCqq+mclARx7Qh67LHHMG/ePOXx\n1KlTsW/fPuzbtw9XX311xOetxLF8Obg9e8xuhqns69eD27fP7GYo+JISrG1DuUzPOiwLt0mD6NDl\ne6vg5FW2JFbIIvqs2i+IubT6BV9cDL5PHxNak2KBtLWUwCA5aFu9zKSy30Qfu28f8iw0qCckIiq2\nQshZoX75cgjnnmt2M5KPYeAfOpTOSUmSsHCOs53IsmBoEG0p9jVrUPLDD3CZ3RBiOfKGEasRaRBt\nKqv2CysR22BKSq1+IeokOGi12uDvPRVoEC0zqey31QhhCkmknElpBwmJGQ2iiYU1LlzYNmZfSTBB\noEF0ktBPVUbhHPCNGgXflClmN6OZKOK4FQvzEAAAU1ODrKlTTTm25WNfaRBtCsv3C5N5p0+Hvw1s\npgvV5vuFINA5KUloEC2z2SA6HGa3wlT8gAEQs7PNboYi7a23ULBrl9nNIHqammD/4guzW2EpQs+e\n8EyfDjE/3+ymEELCcLz1Frg2UsnPd9VVEK20ytyKxJUnOpHMzhNNrKddfj7EjAzUVFSY3RSigT1y\nBLlDhlCeaELIWSfznnvgmzgRXo0Ky6RtSESeaJqJJpbFFxXBP2iQ2c0gOkSOM7sJhBASE8e//w2u\nrMzsZpCzHA2iiWX5J0zAHhpEW5ZYVIS61atNOXabj3EkmqhfROB2AzxvditSTrdfUD53EicaRBMF\ne/QoGCstzdNGCMvjhwwxuwmEkCjldesGx9KlZjfDOihjBYkT9SCicC5YAPsnn5jdDIXIMDi3Vy+z\nm0EsiPIBEy3UL8Jj/H7YNm0yuxkpp9svaKKGxIkG0UTBffstmNpas5uh8N56K3yXXmp2MwiJGnv0\nKNrl5wP19WY3hRASAX/BBWY3gZzlaBBNFLbdu2Hbvt3sZij4IUOwlvJEEw1WjX1lDx8GADBUuMkU\nVu0XxFxa/cI3ejSEc84xoTWkNaFBNLEs9rvvkHvwoNnNICR6geVhkZaJiVVZI6ut6Rpffx3+4cPN\nbgY5y1HZb2JZjk8+QUlTE9xmN4RYjmVjX2mjkqks2y+spA2mptTqF2KnTia0hLQ2NIgmQYS8PLOb\n0EwUaeMHObvI/ZX6LbGgpiefhH/kSLObQUirQdMmROG9/HL4x40zuxnNRBFHqVoh0WDV2FeRBtGm\nsmq/sArP7Nnghw0zuxkpR/2CJAvNRBMF368fhHbtzG6GwvHee+gEgLZokbOFeM458Nx8M5CebnZT\nCCGEJBkjitbYZbB69WoMHTrU7GYQC2mXnw8xMxM1R4+a3RRCCCGEtCLbtm3D+PHj4/oOmokmlsX3\n6AGxQwezm0EIIYQQ0gLFRBPL8l1zDfb162d2M4gFUYwj0UL9gmihfkGShQbRxLpocxYhhBBCLIoG\n0cS6GAY9unc3uxXEgigfMNFC/YJooX5BkoVioolleW+4AaKNuig5ezAnTiCvXz+cqa4GqO8SQkir\nRjPRxLL4Cy7A2lOnzG4GsSCrxjiylZXS/1Aokims2i+IuahfkGShQTQhhCQKFVshhJA2gwbRxNIo\nlo1osWy/oEG0qSzbL4ipqF+QZKFBNCGEJAoNogkhpM2gQTSxNIplI1qoXxAt1C+IFuoXJFloEE0I\nIQkidOwI73XXmd0MQgghKcCIoiia3QgAWL16NYYOHWp2MwghhBBCSCu3bds2jB8/Pq7voJloQggh\nhBBCDKJBNLE0imUjWqhfEC3UL4gW6hckWWgQTQghhBBCiEEUE00IIYQQQtoUiokmhBALYSor0S4/\n3+xmEEIISQEaRBNLo1g2osWq/YI9edLsJrRpVu0XxFzUL0iy0CCaEEIIIYQQg2gQTSxt7NixZjeB\nWBD1C6KF+gXRQv2CJAsNogkhJFEYxuwWEEIISZGYBtGbNm3CwIED0a9fP9x0003K80uXLkWfPn1Q\nXFyMlStXRnyekEgolo1ooX5BtFC/IFqoX5BksRn9gCAIuOOOO/D3v/8do0ePxqlTpwAAXq8XDz30\nEDZt2gS3241LL70U11xzje7zhBDS2giFhfDS+Y0QQtoEw4PorVu3okOHDhg9ejQAoKCgAIA0O92/\nf3906NABANC1a1fs3LkTdXV1ms8PGjQoUf8G0opRLBvRYtV+IRYUoHHJErOb0WZZtV8Qc1G/IMli\neBBdXl6O3NxcXHnllaiqqsI999yDmTNn4sSJEygsLMTixYuRn5+Pzp07o7KyEg0NDZrP0yCaEEII\nIYScrcIOohctWoTXX3896LnGxkacPn0a3377LXJzczF8+HBcccUVYAIbambMmAEAWL58edDn1M8z\ntPmGRKm0tJRmEUgL1C+IFuoXRAv1C5IsYQfRc+fOxdy5c4OeW716NebPn4+ioiIAwLBhw/D999+j\nsLAQlZWVyvtOnDiBLl26oL6+vsXzhYWFmsebNWsWunXrBgDIzc3FgAEDlI4vbwygx23rscwq7aHH\n1ni8e/duS7WHHlvjscwq7aHH1nhM5wt6LCstLUV5eTkA4O6770a8GFEURSMfqK2tRf/+/bF7925k\nZmZi2LBh+Pe//40ePXqgb9++ygbCcePGYf/+/fB6vZrPh1q9ejWGDh0a9z+IEEIIIYSQcLZt24bx\n48fH9R02ox/Izc3FokWLMG7cOPh8Ptx6663o06cPAGDBggUYM2YMACkUBAAcDofm84QQ0towFRXI\nGzgQZ06fNrsphBBCkszwTHSy0Ew00VJaSrFspCWr9gtu1y7kXHIJDaJNYtV+QcxF/YJoScRMNFUs\nJIQQQgghxCAaRBNLo9kDosWq/ULo0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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 25
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter."
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example: Bad Initial Estimate"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "\n",
- "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30\n",
- "movement_error = 2\n",
- "pos = (1000,500)\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(100):\n",
- " pos = update(pos[0], pos[1], movement, movement_error)\n",
- " \n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- "\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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I84JEmBckwrwgEW9bLPTevNnff/+Nxx57DIGBgdDpdPjiiy8QHh6OWbNmoUePHgCA5OTk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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 26
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly."
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example: Large Noise and Bad Initial Estimate"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "What about the worst of both worlds, large noise and a bad initial estimate?"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30000\n",
- "movement_error = 2\n",
- "pos = (1000,500)\n",
- "\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(1000):\n",
- " pos = update (pos[0], pos[1], movement, movement_error)\n",
- " \n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense (pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- "\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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lpaWCy++9916X/W3duhUdO3b0OM6FCxdQv379wP46EhXoOyaEEEJIVdq/f7/LUMKBCKgl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\nk6bIlmXmvsKb1G6scakUtGbNbE35yuWXwzDXXy4SAW9CS7hkMid23vB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Be1XC5d4Cd9+N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437q14xyaTYXNrFxZNI7QAbT5hVkTY64N3pNuvESay1UkZeIlN9Ka4PhC4Vm2zFrEDAOxv/6V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\nR2jGDKPZlt+2LT0udk3CIxhkwe/YAWnZMmjZ2RC//x65NupHxZt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Pr7CLUYrm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tlYSAghhBBCSLagSTQhhBBCCCEa0SSaEEIIIYQQjWgSTQghhBBCiEY0iSaEEEII\nIUQjmkQTQgghhBCiEU2iCSGEEEII0Ygm0YQQQgghhGj0/3Ckugs5ZiLiAAAAAElFTkSuQmCC\n",
- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
- "\n",
- "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30000\n",
- "movement_error = 2\n",
- "pos = None\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(1000):\n",
- " Z = dog.sense()\n",
- " zs.append(Z)\n",
- " if pos == None:\n",
- " pos = (Z, 500)\n",
- " \n",
- " pos = sense (pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- "\n",
- " pos = update (pos[0], pos[1], movement, movement_error)\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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pu56ifsEwqJkxA+wFFyRfIBOhS0vB7N6d8LhAz57i/zFGDwC2n36CfcWK2BON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\nC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TfZmGb+/ndo559vv9eaBrNePRTdcQfZxHXdlpH0gd65M7IBhW/6SSdBs96znFQxvwwP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YMQtjxnhZ/NZloh4fwLnMGBYWLyT58GYqnPEzcryfSZO8RNy6h7epqAgVz59PtWeeoeb27cix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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n",
- "\n",
- "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. "
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Exercise: Interactive Plots"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the $\\verb,interact(),$ function to call a calculation and plotting function. Each parameter passed into $\\verb,interact(),$ automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from IPython.html.widgets import interact, interactive, fixed\n",
- "import IPython.html.widgets as widgets\n",
- "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n",
- " # your code goes here\n",
- " pass\n",
- "\n",
- "interact(plot_kalman_filter,\n",
- " start_pos=(-10,10), \n",
- " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n",
- " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n",
- " movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n",
- " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "pyout",
- "prompt_number": 29,
- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 29
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "######Solution\n",
- "One possible solution follows."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "\n",
- "zs = np.zeros(100)\n",
- "ps = np.zeros(100)\n",
- "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n",
- " dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n",
- " random.seed(303)\n",
- " pos = (0,100)\n",
- "\n",
- " for i in range(100):\n",
- " Z = dog.sense() + random.randn()*noise_scale\n",
- " zs[i] = Z\n",
- "\n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps[i] = pos[0]\n",
- "\n",
- " pos = update(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n",
- "\n",
- " p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- " p2, = plt.plot(ps, c='b')\n",
- " plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
- " plt.show()\n",
- "\n",
- "interact(plot_kalman_filter,\n",
- " start_pos=(-10,10), \n",
- " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n",
- " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n",
- " movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n",
- " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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XroRPnIjtl19wDR5MoF69EoxQpPQ88kgk//ynm4svDpT4vTSCLCFBvWNiRnkh\nZipKXlh+/x3nggW4hgwp1HmeXr2wHjhA9uTJuO+9lxIfagsRZZ0XBw9a+PjjEphvrJD27LHi9ZZ1\nFMH38ccOdu+2MXKkq1TupxFkERGREGRUrkz6559jVK9euPOqViV927YSikrMHD5s4ZZbYsjIsJCS\n4uX557NxOkvv/idOWPjoIwdz5oTxyy9W4uIMxozJoUsXb7n6+cjvh4wMC5mZkJ5uITPT8se2hSee\niOT117MK82FKsWgeZBERERO7dllp0CAQrMkj5Dx17JiFrl1j6N7dw+DBLv71ryh+/dXKzJmZxMeX\nXIllGLBxo53Zs52sXOkgKclHv35uOnTw8dlndp55JgKnE55+Ooe2bX0lFkewpKVZuf76GNxuiImB\n6GiDmBgj7+sVV/gYNqzwK+ZpHmQREZEgWbvWTo8e0Qwf7uaZZ3LKOhwJUcePW+jePZouXTw89FDu\nR/+zZ2cxaVI4HTvGMnNmJq1b+4N+348+cjBhQgR2O/Tv72bcuByqVv2zGE9O9tGhQwYLFzoYPjyS\nBg0CPPlkDo0bBz+WYPB6YdCgKEaMcDF8ePCXjS4K/VwsIaGse8ckNCkvxExJ58W+fRb+9a8oZs3K\nYtUqB6+9Vkqf6UqxlPb7RXo69OgRTfv2Ph577M++WKsVHn7YxeTJ2fTtG8177wWv1yIQgGeeieDZ\nZyN45ZVsNmxIZ+hQ92nF8alx9Ojh5csv00lO9tK9ezRDhkTy/fehV/o9/3w4lSsbDB0aGsUxaARZ\nREQkj9sNd90VzdChLrp08dKsmY8bb4whLs7gH/8o2XlXpfzIyICePWNo1crH2LE5pn2+N9zgZcWK\nDPr1i2b7djv3359zcuFCbDaw2QxsNnA6wVGAZ/syMmDw4CgyMix8+mkGVaoUrH0jLAwGD3bTu7eb\nt98Op3v3GC6/3M+IES7atvXl26NsGPDttzbWrrXTpo2PVq1KZvR57Vo78+aFsW5deki1M6kHWURE\n5A8PPRTBoUNW3nsvK69w2LXLyi23xPDaa1lcf30J93Lm5BDxwgvkjBkTtJXzJLiys6FXr2guuSTA\nlCnZ5/xrSk+H+++P4ssv7QQCuSvB+f3g81nytq+/3suQIW7atDEvWPfssdKnTzRXXulj4sTiPQDo\ncsG8eU6mTQsnJsZg+HAXXbt6sdtz/2zr1ztYtSr3V0SEwbXX+li1ykFSkpennsohLi54ZeORIxY6\ndIjljTe3Mvd6AAAgAElEQVSyaN++ZP5tqQdZRESkGObPd7J2rYM1a9JPK1IaNQowe3YmfftG88EH\nmUUbSUtPJ+L55/H06IG/Zct8DwubMwfr//6n4jhEZWVBv37RJCYWrDgGiI2Fd9/NOus1581z8sAD\nkUREGAwZ4qZbN0/ebA1ffGFn4MAoHnzQxaBB7mLPShEeDnfe6aF/fw8rVzp49dVwxo6NoH79AF9+\naadZMx+dOnlZvNhF/fq58w2np8OLL0bQpk0so0a5GDjQjb2YFWQgAP/6VxR9+7pLrDguDo0gS0hI\nTU3VKkhyBuWFmCmJvNi5M3eUePHizHwfZFq1ysHIkZEsXZpBgwaFWKjA4yH22mvxN2qE/YsvyBk7\nFk/v3ubHtWpF1owZZy2ixVxJv18cO2bh9tujadTIz8svZ2OzBff6gQCkpNh5441wdu2yMWCAm9hY\ngylTwpk+PYsOHUquiNy82caBA1aSknxUqpR/WfjDD1ZGj47kyBErEydm065d0WN65ZUwPv7YyfLl\nGcUuts9GI8giIiJFkJ4Od94ZzfjxZ3/K/+9/9/Lkkzn07BnNypUZ1Kx5ZiERCOSuy3HaKJ/TSebs\n2QTq18e6axfR/fph276dnHHjTms+dc6fT+Dii1Uch6A9e6z06BFNt24eHnvMVSJzC1utcP31Pq6/\nPpOdO61Mnx7O//5nY8WKDC65pGRXjrviCj9w7k9GGjYMsHBhJsuWORg6NJJWrfyMGZNDvXqFi2/L\nFhuvvRZOSkrJFsfFoRFkERGpsAwD7rwzimrVAkyaVLDp3F5+OYxJkyJwOg18Pssf/aS5vwIBC/Hx\nAa691su11/q49lovtWuf/t+s5fffCZs2Ddcjj5BXHfh8xF51FdlTp+LTpyYh5euvbfTpE82oUTnc\nfbce1DwpOxumTQtn+vQwbrnFy4MP5pj+0PhX6enQvn0sY8fm0LVryS/5V9QRZBXIIiJSYb32WhiL\nFztZsSKjUCt0/fqrBcuBAzizfsdyUSL2SlHY7bmjgHv2WPnsMzuff+5g/Xo7lSsbecVyUpKX2Ngz\nr2fbtImIcePIXLaswiwNXRq2brUxaVI4iYkBmjTx06SJn0aN/AX+u16zxs7gwVG89FI2Xbqch+s3\nB8Fvv1l4+eVw5sxx0revh5EjXWfMsOF2w6ZNdtats/Pxx07atfMW+AfS4lKBLOWaek3FjPJCzAQr\nL77+2kavXtF8+mkGiYmF/wjbsWgREZMmYd2zByM2Fn+9ehi1auHu1Qvf9dcDuS0XO3fa+OwzO2vX\nOti82U67dl66dvXSubOXypVP+S/Y6y3YfF9i6tS8MAx4660wJk8O59FHc8jOtrBjh40dO+z88ouV\niy/+s1iuVy9AvXoB6tb1Ex395/XmzXPy5JMRzJqVyVVXheYCG6Hk4EELkyeHs3ixk3vucfP3v3tJ\nTbWzbl1u3jds6KdDBy8dOvi46ipf0Hu486MeZBERkQLKyoJ//jOK55/PLlJxDODt1g1vt24QCGA5\neBDbL79g/eknjLi4vGOsVrjsMj+XXeZn2DA3J05YWLXKwbJlDh55JJIrrvDRtauH5GQfhhFGdjZk\nZ1vIybHk/b5RIz8NG5ZsD+r5JD0dRoyI4v/+z8rq1RnUrXv6987lgu+/t7Fjh41du2x8+aWdX36x\nkZZmJTraoG7dAFWrBtixw8aSJRk0aqTvfUHUqGEwaVIOw4a5mTgxnMGDo2jXzsedd7p5552s038Y\nLAc0giwiIhXOyJGR+HwwbVr2OY+1f/45GAa+9u2DGkNmJvz3vw6WLnXy5Zd2HA6DiAiIijKIjMz9\nfUSEwZdf2nnooeBM8XW+277dxt13R9Gxo5dx43IK1TYTCMChQxb27Mktltu391KjRvkq6uRMGkEW\nEZGQZhjwyy9WPv88tz933z4r06Zl5c21WlqWLHH88dFv+tkPdLmIGDcO55IlZL3+etDjiI6Gbt28\ndOt29t7Wn3+2MmhQFOvX23nllexyNxJXGgwDZsxwMmFCBBMnZp/ze2rGaoWaNQ1q1vTRpk0JBCnl\nigpkCQnqNRUzyovy7+hRC2vXOvIeWvP74dprvVx3nZfMTAu33BLDvHmZNGlS8B7P4uTFvn0WHn44\nkrlzM4mJyecgtxvnRx8R/vLL+P/2N9LXr8e44IIi3S8YLroowMqVGTzzTATt28fw9ttZf0zLdf7J\nysp9mOvwYStHj1o4cuTPr8eO5baeOBzgdBp5X51OyMy0cPx4FitXZnDxxWqJkOJTgSwiIiVi82Yb\n/fvnLo977bU+Ro7MXZnr1DaB6tUD9LjRxoe9P6L5uM4U6jPxQvL7c1fuGjLETcuW+ReY0bffDlYr\n2c8/jy8pKSRmlQgLg+eey+Gaa3z07x/N0KEuRoxwl8qCex4PrF9vJyfHgtWaO9JqsYDVamCxwMUX\nBwo9D+6pfD74/HM7CxY4WbnSwWWX+aldO0BcnEG1agEuu8wgLi5AtWoGEREGXi94vRY8nj+/+nwA\nqVx8sYZ+JTjUgywiIkG3bp2de+6J4vXXs7j++rOvtrVm5iGGPFKD2ReOoN2EjnhvvrlIRenevVZq\n1Qrku/DAlCnhrF1rZ/HizLM/QZ+ZyWnTGYSYffss3HNPNFFRBm++mUXVqgX/b3zePCcrVjjo1Cl3\nFo2/Tsd1qp9+svLee2F8+KGTiy7KfXAtEOCPXxYCgdwfOr77zsbGjelceGHB4zAM+OYbG/PnO1m4\n0EmtWgF69vTQrZuHatXUQiLBo2neREQkJCxf7uCBByKZNSuLq68+szg+OS2aceGFefu+/NLGHbeH\n8Ublh7m1xiayX3wR/2WXFeh++/dbeOyxSD77zI7VCu3b++jY0UvHjn8+ZLVli42+faNJSUnPW7jD\n8vvvGJUrB+FPXPp8PnjuuXD+8x8nM2dm0aLF2VsuAgEYPz6cRYuc3Huvi3XrHKxd6+Dyy3106eLl\npps81K5t4Hbn/v29914Yu3bZ6N3bQ//+7rO2LTzySASBALz4YsHmtXW74ZZbYjh82ELPnh569vSU\neh+6VBxFLZBL4cMZkXNLTU0t6xAkBCkvyp8PP3Ty0EORLFiQaVocA0SMGYNj+fLT9l11lZ8FS9wM\nd73Ev+s+Rdhbb+V7j5N54fPBm2+G0b59LA0b+vn++xNs2JDO9dd7WbPGQdu2sVx7bQzPPBPB4MFR\nvPhiNrVrG9i2biWqd2+ib701dyizHLLb4cknXTz3XA633x7N7NnOfI/NzoYBA6LYuNHO6tUZ3HWX\nh5kzs9i163eGDXPzzTc2OnSIpUOHGJo0qcScOWEMGOBmx44TPP10zjl7ekePdrF0qZNvvy3YxLYT\nJ4YTFxdg27Z0HnvMFbTiWO8XEkxF7kHetGkT99xzDz6fj8svv5wPP/yQ+fPn88QTT2CxWJg8eTJd\nunQJZqwiIhLC3norjFdfDWfJkgwaNDAveixHjmBfv56sadPOeK1pUz9LlmZw221/Z+tNSSSv9tK6\ntZ8LLjiziN261caDD0ZSqZLBxx//eb+ICIM+fTz06ePB58s9LiXFwYABbrpVW0/EbS9i+9//cI0c\nibtfv5DoLy6OLl28NGiQQf/+0WzbZmfChOzT2rgPHbLQt2809ev7WbQo67TXIiLghhu83HCDF58P\nNm+2Ex8f4KKLClewXnCBwaOP5vDIIxEsX5551m/p1q023n8/jPXr08v7t17Oc0VqsQgEAlx66aXM\nmDGDNm3a8OuvvxITE0OjRo3YtGkTLpeLpKQkdu/efca5arEQETm/GAZMnhzOhx86Wbgw86wLb4S9\n9hq2778n26RAPmnfPguzZoWxZYudrVvt1KwZ4IorfFxxhY+mTf3Mnu1k2TInzzyTQ8+engIVWhFP\nPIFjxQpc992Hp3dvcOY/4loeZWTAsGFRHDhgZdasTGrVMtixw0afPtHcdZebBx5wlWhB6vdDcnIM\n997r4rbbzKdYc7mgfftYHnkkh+7dtWyzlI5SnQd569atxMXF0eaPiQKrVKnC+vXrady4MXF/rCCU\nkJDA9u3badq0aVFuISIiJWTvXitOpxGURRCysuCxxyLZutXGihUZVK9+lmsaBmHvv0/2lClnvWbt\n2gaPP+4Cctsovv/exubNdtavtzN1ajjXXONj48b0Qs0H7Bo2jJynnjpvl3KOiYFZs7J4+eUwrrsu\nlsGDXbz+ejgvvJDNrbeWfDFqs8HEidkMGhTNDTecICrqzGMmTIigUSN/keYoFiltRepBTktLo1Kl\nSnTu3JkWLVrwxhtvcPjwYWrUqMH06dNZsGAB8fHxHDx4MNjxynlKvWNiRnkRXMePWxg9OoKOHWNo\n1y6W558PJyur6Nf75hsbycmxuN3w8cfnKI4B29at4PXiu+qqAt/DbocmTfwMHOhm+vRstmxJ57bb\nVhd6sQyjRo3ztjg+yWKB++5z8/rrWSxf7uSDDzJLpTg+6aqr/LRp42Xq1PAzXvvqKxsffuhk0qTs\nEhvJ1vuFBFORRpBdLhdffPEF3377LZUqVaJVq1YMHDgQgMGDBwOwcOFCLPn8Kxg6dCiJiYkAVKpU\niSZNmuRN+n4ywbVdsbZPCpV4tB0a2zt27AipeMrr9lVXtWPmzDDGj7dx9dUH2bixMm43DB+eSbNm\nVXj22dwptjZsKNj12rRpxxtvhPHiizYGDdrOE0/UK1A8W3bvJqpvXxr88X9DQeO/NjERIyyM9T/+\nyKlC5fsbattJSe1ISsogNTWV1NTSvf9NN4Xz4IMd6dPHw/79nwPQsmU7hg+P4q67tvHDDweJi9P7\nhbZLtp5ITU0lLS0NgEGDBlEURepBTklJYcyYMWzYsAGAPn36cOmll7J582aWLVsGQFJSEi+//DKX\nX375GeeqB1lEpHSkpNh54olIqlcPMH58Do0bnz4d2KZNNh5/PBKA557LPucKbYcOWRg2LIqMDAtv\nv51FnTolPz1X+Pjx2H76iax//7vE7yXF99JL4WzZYuP993M/nnjyyQj27bPy738X4+MKkSIq1R7k\nVq1akZaWxvHjx4mKimLHjh08+uijzJgxg6NHj+Jyudi3b98ZxbGIiJSs48ct/Pijld27bSxd6mD3\nbhtjx+bQubPX9KPtK6/0s3p1Bv/5j5O7746mdWsfrVv7qFzZoFIl45SvAb75xs4DD0Ryxx1uHn7Y\nle+CHMHmuv9+Ytu1w/7pp/iuu+7cJ2RkEP7yy7gefZSzrwgiJWHoUBdt2sTy6ad2YmIMFixwsn59\nelmHJVIoRXp7q1SpElOnTiU5ORmv10vfvn1p0qQJEyZMoG3btgBMnTo1qIHK+S01NTXvYxKRk5QX\nZxcIwHvvOdm2zc7u3blFsctloX59P5dc4ue663zMmpV1ztWbrVbo1cvDTTd5mD07jL17rXz3nYXf\nf7dw4sTJr1YiIw1mzDBf/KNERUaS/cILRD70EOlffEHqtm3554VhEHXffRgxMSqOy8jJZbEffzwS\nw8h9eK8wq/0Vld4vJJiK/PN/jx496NGjx2n7evXqRa9evYodlIiInJ1hwOjREWzbZqdfPze9egW4\n5BI/1asbRX4IKioKhgxxFz6QzMzcaRRKkO+66/A3b0745MmQlJTvcWHvvot1924yVq0q0Xjk7Dp1\n8vLvf4cRE2Nw882atULKHy01LSJSzhgGPP10BKmpdhYtyiA2tuxiCZs2DfvWrWfvD87KwnTer0Ky\nHDpETLdupK9dC+FnzpRg27qV6N69yVi1ikC9esW+nxSP2507iF9arTgiZkq1B1lERMx5PLB1qx2X\nC6KjDWJijD++5m4H41P/F14IJyXFzrJlmWVaHNu2biX85ZfJ+PTTM19MT4fYWPD5qHTllWSsXEkg\nIaFY9zPi48n84APz4njHDqJvu43s115TcRwiztXaIxLKVCBLSFDvmJgpD3lhGPDjj1bWrnWwdq2d\nDRsc1K/vJzbWICPDQkaGhczM3F9ZWVC9usH772fSrNnZZ4vIzyuvhLFwoZNlyzJMl2AuLZYTJ4ga\nNIjsyZMJ/DFtZx7DIKZXL3xNmuBr04ZAjRrFLo5PCtSta5oX/osuImPNGgIXXRSU+0j5Ux7eL6T8\nUIEsIlJIx45Z+PxzO+vWOVi7NnfxieRkL7ff7uH117O58ELzwjUQgI8/dvCPf0Qzb17hi+R33glj\n5swwli/PoFq1siuOMQwi770Xb6dOeLt2PfN1i4XMefOIeOwxogcOJOscK+cFRVSUimMRCRr1IIuI\nnEN2NmzcaOezzxx89pmdPXtstG3rpX17H8nJXi65JFCoB+M+/tjB/fdHFqpInjPHycSJESxfnlEq\ncw+fjX3DBiIef5yMTz455+fotq1b8TdpAk5nKUUnIvIn9SCLiATZ3r1W7rsvki1b7DRp4qN9ex8v\nvJBNixb+Yq1afOONXiC7QCPJPh/MmhXGlCnhLFlS9sUxgK9NGzJWrChQk6m/ZctSiEhEJLisZR2A\nCJy+RKTISWWZFwcOWLj11miSkrzs3Pk7H3+cySOPuLjyyuIVxyfdeKOXl17KLZK//vrMJ/fcbpg5\n00nr1rEsXuzgo48yuOSS4BTHjlWrsK9eXbyLREYGJZai0PuFmFFeSDBpBFlE5C+OHrXQrVsMAwa4\nuffeQs4LXAhmI8lZWbkjxtOmhdO4sZ833sjiqquK9kCfKa+XiIcewpKdTfbEiXhvuy141xYROU+o\nQJaQoCePxUxZ5MXvv1u47bZobr7ZU6LF8UmnFsl9+niYO9fJVVf5mDs3k6ZNg1gY/8H6f/+H75pr\ncA0bRkyPHuS43Xj69Dn7SYZBkVcfKQF6vxAzygsJJrVYiIj8ISMDevaMpl07H4895iq1+954o5dX\nX80iIwOWLs1g1qysEimOAQIXXUT2tGkE/vY3MhYvxrlgQW4/Rz5sO3YQk5yM5ciREolHRCQUqUCW\nkKDeMTFTmnmRkwN9+0bzt7/5GT8+p9QHTDt18jFpUg4NG5beQ3iBBg3IXLTI/GE7wyDs3XeJ7t4d\n17BhGNWqlVpc56L3CzGjvJBgUouFiFR4Hg/ceWc08fEBpkzJDqVugrKRnk7Uvfdi/eWX3BXwLrmk\nrCMSESlVGkGWkKDeMTFT0nlx/LiFhQtzF+5wOg2mTcsOylLQ5ZrPR+wNNxCIiyNj1aqQLI71fiFm\nlBcSTBpBFpEKIxCA7dttfPqpg08/dfD99zbatPHSpYuXfv3cQZm+LWQFAmAtwJiI3U7mvHlBWxpa\nRKQ80giyhAT1jomZYOXFDz9YeeihCC69tBJDhkTx++8WRo/O4X//+50PP8xi4EB3Qda8KLcs+/cT\n0749+Av24F+oF8d6vxAzygsJJo0gi8h5ye+H//7XwVtvhfH99zbuuMPN6tWhsRLd2TgWLcJ7001B\nXZo5/K238LVrh/pHREQKxmIYhlGaN0xJSaFFixaleUsRqUBOnLDw/vtO3nknjAsuMBg82M0tt3jK\nxwhxIEDUHXdgxMSQ/frrwZl7OD2dSs2bk7F2LYHExOJfT0SkHNm2bRsdO3Ys9HkaQRaRcsXthkmT\nwklLs5KTYyEry0JODmRnW8jOtnDkiIXrr/cxfXoWrVr5Q3tGiuxsbN99h79169xtq5Wst94i5uab\nCX/+eVyPPVbsW4S99x6+pCQVxyIihaACWUJCamqqnkCWM/w1L7KyoF+/aKKjDbp08RIRYRAZaRAZ\nyR9fDeLiDC64oFQ/GCsawyBy1CgAsk8WyACRkWR+8AExf/87gYQEPP37F/0eXi/hb75J5pw5xQw2\ntOj9QswoLySYVCCLSLlw4oSFXr2iadDAz9SpITAdm99frJ5e58yZ2LdvJ3316jNeM+LiyJw/n5gu\nXQjUqoUvOblI97AcPoyna1f8zZoVOU4RkYpIPcgiEvKOHrVw2225S0A/+2xOgWYrK0n2L74gfMoU\nMj/6qEjn27ZuJbp379xFOC6+OP/jtmzBiIsjUKdOUUMVEanQ1IMsIuelffssdO8eQ/fuHh55xFX2\nPcXZ2USOHEnOuHFFOt3y669EDRhA9ksvnbU4BvC3amW63zlzJs6lS7GcOIHlxAnw+bD4/eSMGYOn\nV68ixSUiIn9SgSwhQb1jYmb+/P/H+PHtGTzYzdCh7rIOB4CI55/H37w53s6dT9tvOXECy6FDBBo2\nPOv51p9/xnPXXblTuRWRv2VLXAkJGJUrY8TG5k4JZ7USqFy5yNcsT/R+IWaUFxJMKpBFJCR9+62N\nxx67mqeectG/v6eswwFyWx6cCxaQbrIgge2rr4gaPpzMuXPxn6WNzN+69Z+zVhSRv0mTYp0vIiJn\np5X0JCTop345yTBg1iwn3bpFM2mSP2SKYzweokaMIPu55zCqVj3jZd9115H90ktE33479g0bsOzf\nj/Wnn8og0POf3i/EjPJCgkkjyCISMtLT4b77ovjf/6wsX55Bw4YhtOqdw0H2Cy/krkiXD2/nzmRF\nRhLVvz8YBjlPP43nHH3GIiISejSCLCEh1eQja6lYvvrKRvv2sVSpEuC//80tjkMqLywWfNdcc87V\n7Xzt25P+xRec+OYbPHfcUUrBVSwhlRcSMpQXEkwaQRaRMhUIwKuvhjFtWjhTpmTTpYu3rEMqNiM+\nvqxDEBGRYlCBLCFBvWPnP8OAjAw4ftzK8eMWfvvNwvHjFubODSMry0JKSgYJCae3VCgvxIzyQswo\nLySYVCCLSFD9/ruFXbusfP+9jV27bHz/vY3du20cO2YhPBwqVw5w4YW5y0FfcIFB+/Zehg51Yw+1\ndyOfD9s335x1RgoRETk/hdp/SVJBaf7K8skw4KefrKxZ42DtWjvffGMnI8NCw4Z+Lr3UT6NGfm64\nwUuDBn7i4gyczsJdv6zywv7550SOHo2/Xj2y5sw5Z9+xlC69X4gZ5YUEkwpkESmU9HRYv97BmjUO\nUlLseL0WkpO99Orl4YUXcqhdO1Bu60lrWhoRY8Zg276dnHHj8HbpouJYRKQCshiGYZTmDVNSUmih\njyxFQlp2NqSlWdm718aePVb27LGyd6+VPXts7NtnpVUrH8nJXpKTvVx6afktiE/l+OgjIh9+GPeQ\nIbiGD4eIiLIOSUREimnbtm107Nix0OdpBFlEAPj1VwvLlztYvNjJ5s12atcOUKdOgLp1/dSpE6Bd\nOx916gS46CI/kZFlHe25WX/4gYjx47EePozlyBGsR45gycnB2749mYsWnXG8v1UrMtatI5CQUAbR\niohIKFGBLCFBvWNl4/ffLaxY4WDRIidffWWnY0cvd9/tZu7czJAYQC1OXhhVquDp0YNAtWoY1aoR\nqFYNoqJy55UzEahTpzihSinS+4WYUV5IMKlAFqmAMjLgwQcjWbXKSfv2Xvr0cTNrViZRUWUdWeHZ\n16zB36QJRlzcafuNqlXx3nzzmSfYbKUUmYiIlFcqkCUk6Kf+0rNvn4Xbb4+mdWs/3377OzExZR1R\n/s6WF9Yff8x9oG73brLefRf/XwpkOX/p/ULMKC8kmFQgi1Qg27bZ6N8/mqFDXQwd6i53D9dZjh3D\nuWQJtm+/xbFsGa6RI8maNQvCwso6NBEROY9YyzoAEcjtHZOiOXAgt484I+Psxy1Z4uD226OZNCmb\nYcPKR3F8Rl64XNh27sRfpw7pGzbgHjFCxXEFpPcLMaO8kGAqVoGckZFBzZo1mTx5MgDz58+nQYMG\nNGzYkOXLlwclQJHyyO2GL76w5/c8WLEZBmzaZGPgwCjato1l+vQwLrusMnfdFcWyZQ5crtOPfeml\ncB5/PJL//CeTzp29JRNUEFmOHsWxcuUZ+43atcmePBn3ffdhVKtWBpGJiEhFUKwWi/Hjx9OqVSss\nFgsej4fRo0ezadMmXC4XSUlJdOnSJVhxynnufOkdy8qCmTPDeP31cHw+6NHDw7PP5gRttNblgkWL\nnLz1Vhjp6RbuucfNSy9lERsLx49bWLrUwTvvhDFyZCSdO3vp3t3DwoVOvvvOxurV6dSsWarTnhdZ\n+OuvQ1YW7V54oaxDkRB0vrxfSHApLySYijyC/MMPP3D06FFatmyJYRhs3ryZxo0bExcXR0JCAgkJ\nCWzfvj2YsYqErBMnLLz4YjjNm1fiq6/sfPBBJl9+mc6aNQ5efbX4LQC//mph/PhwmjatxEcfOXn0\n0Ry++iqdIUPcxMbmHnPBBQZ33ulhyZJMvvgincsu8/P88xG43RZWrMgou+I4EMD+xRe5Q9kFYDl+\nHOd77+G6994SDkxERMRckQvkRx99lKeffjpv+9ChQ9SoUYPp06ezYMEC4uPjOXjwYDBilAqgvPaO\nHTliYezYcFq0iGXPHivLl2cwc2YWl1/u54ILDBYsyODtt8OZN89ZpOsfPmxhzJgIWreO5dix3Ov/\n5z+ZdOrkw3qWf701ahj8619uPv00g3feySq76dvS04nq25foW27BsXhxgU4Jmz4d7403YtSuXW7z\nQkqW8kLMKC8kmIrUYrFs2TIaNGhAQkICf12pevDgwQAsXLgQSz6fKw8dOpTExEQAKlWqRJMmTfI+\nGjmZ4NquWNsnhUo8Z9s2DHA42vPuu+F88glce+0B1q69gMTEAKmpqRw58ufxe/as59FHo3nyyfZU\nqRIgPHxdge5Xt+41vPpqOB98YKVDh32sX38htWoZpKamcvhwaH0/8tu2pqVhu/FG9jdrRtWlS4ka\nOJDV4eF4Y2LyPf/L1atJfvNNXCkpAOzYsSNk/jzaDp3tk0IlHm2HxrbeL7R9UmpqKmlpaQAMGjSI\norAYf61wC2DMmDF8+OGH2O12jh07htVqZdiwYXz11VcsW7YMgKSkJF5++WUuv/zy085NSUmhRYsW\nRQpWpCxlZMCCBU7efTccrxfuvtvN7bd7qFz53P+ENm2y0a9fNB9+mEnLlv58j9u928q0aeEsWeKg\nb18Pw4e7qF69fPQNnyE7G0dKCt6uXQFwvvce3k6dMOLj8z0lbPp07Fu2kPX226UVpYiInMe2bdtG\nx/umi4sAACAASURBVI4dC31ekQrkUz3zzDPExMQwYsQIGjZsmPeQXnJyMj/++OMZx6tAlvLm118t\nPP98OAsXOrnmGh8DB7q55hpfoR+8++QTB/ffH8nSpRnUr//n9Bb79llYtMjJwoVODh600revm3/9\ny03VquW0MC4OrxdLRgbGhReWdSQiInIeKGqBbA9WAA6HgwkTJtC2bVsApk6dGqxLSwWQmpqa9zFJ\nqJkyJZzffrOSmlq8WSBuuMHL0aM59OwZzZw5WXz5pZ2FCx388IONm27y8vTTObRt68MetH+V5ZDD\ncVpxHMp5IWVHeSFmlBcSTMX+r/ipp57K+32vXr3o1atXcS8pEjKys2HePCdr1gRnFoj+/T0cO2bl\nppti+PvfPYwc6SYpyYuzaM/wlb2cHBwpKThWrCBnwgSMSpXKOiIREZFiK3aLRWGpxULKkzlznKxY\n4eCDD7KCel3DoFysZGcqIwPHf/+Lc9kyHGvW4GveHM/NN+Pp2RNiYso6OhERkTxFbbHQUtMi+TAM\nePfdMO6+2x30a5dWcWzZvz/o14x86inCPvgAb1ISJ7ZuJXPxYjx331244jgjg4hRo8Ab+qv6iYhI\nxaMCWULCX6dvCgXbttn4/XcLHTv6yjqUInF++CHRffsWeIGOgsqePJnMBQvw3HEHRtWqRbtIdDS2\ntDTCX3kFx4oVOD75xPSwUMwLKXvKCzGjvJBgqsiPA4mc1b//HcaAAe6zLsgRqqw//kjEmDFkLl4c\n/OHqYFzPYiFryhRiO3TAiIwk+9VXi39NERGRIFEPsoiJ336z0LJlLFu2pFOlSjmbbi0nh5hOnXAP\nHIjnrrvKOpqzcs6YgXPRIjKXLCnHTdkiIhKq1IMsEkTvv++kc2dv+SuO/3979x0dVZ33cfwzmclM\nJg2khw1BUQGNFMnyuGJEqS6CWAFFBUE0IIg8gLtIOcuKIsLjgqAU6YKNIhrAPQiIhWJQWTl2iroI\nUoUw6dPu80ckBrkgSW4mQ/J+neORm7nlN4fPmXz5zff+riT3uHEKNm4sb9++p78QDMq2f//5n8jr\nlXv8eNmOH7d2gMUv0a8fxTEAIOxQICMshFPvWDAoLVxYPjfnlTfb/v1ybN+unKlTzyg67Z99priu\nXQsfCfhH8vIUe//9itizR0Z0dDmN9lfnKI7DKRcIH+QCZsgFrESBDPzOxo0OVatmnPOR0BUh8q23\nZP/kk3PedGckJipr0yYpPv6M1wKtW8vftq3cTz55zuvY9u9XbM+eClavrpyFC6WoqDKPHQCACwkF\nMsJCOD39aMEClx58sCD8vvV3uRTzyCOK/8tf5Jo2Tbaffzbfz24/6ynynnpKznfekWPLFtPXo55+\nWvE33CB/aqpyZ82SIiOtGHmphVMuED7IBcyQC1iJAhkoZt++CH3yiUN33OGt6KGcwdelizzbtytn\n+nTZf/xR8ampir3rLtkyM8/7HEa1asr9v/9T9NChhY8J/J1g48byfPSR8v/+d12Qy3cAAGABfgMi\nLIRL79iiRU716uVVubbdejyK/Pe/S3eszabANdcod9o0nfzySxX07Vvixzv7unSRPyVFrgULznjN\n26OHjPr1Sze2chAuuUB4IRcwQy5gJdZBBn5VUCC98opLa9eex01sZeBaulTuiRPl2bJFwYYNS3+i\n6Gj5brmlVIfmPvec5HaX/toAAFRizCAjLIRD71h6ulPJyQFddlmwXK/jfPttZS9ceO7i2DBk37Gj\n/AYRFyc5wv/fx+GQC4QfcgEz5AJWokAGfjV/fuHNeeXJtn+/Ivbskf/GG8+5n2v+/MI+YZ+vXMcD\nAADORIGMsFDRvWMffODQkSM23XRT+RakzvR0+W6++ZyrQzi2blXUlCnKWbKkwleRqGgVnQuEJ3IB\nM+QCVgr/71iBcub3S6NHR+uf/8wr964D27Fj8t55p+lrkevWyblihRxbtihn5kwFL7mkfAcDAABM\n2QzjHE8dKAcbN25Uq1atQnlJ4Jzmz3cpPT1Sb72VXbFrH+fkKHrUKAWuukoFaWkVOBAAACqHHTt2\nqEOHDiU+jhlkVGknTtg0eXKU3nyzgotjSYqJUe6MGRU8CAAAQA8ywkJF9Y49+2yUunXzKTk5vB4r\njUL0FMIMuYAZcgErMYOMKuvbbyO0cqVT27Z5KnooAAAgjNCDjCrJMKQePWLVoYNPgwaV79JuAACg\nYpS2B5kWC1RJ69c79NNPERowIDTFcdQzz8h27FhIrgUAAMqGAhlhIZS9Y16vNHZstJ56Kjckywzb\n9u+Xa948GdWqlf/FKhl6CmGGXMAMuYCVKJBR5cyd69LFFwfVqZM/JNc7n4eDAACA8MFNeggLqamp\nIbnO0aM2TZsWpbVrs0JyPUlyvvWW8v72t5BdrzIJVS5wYSEXMEMuYCUKZFQJhw7ZtG2bQ0uWuNSj\nh1eNGwdDcl3b/v2K2LtX/htuCMn1AABA2dFigbBgZe+YYUjffx+hV15xasiQaP35z/Fq0yZey5c7\n1a6dT6NH51l2LQWDsu/cedaXnenp8nXpQntFKdFTCDPkAmbIBazEDDIqjb17I7RihVMrVzqVk2PT\ntdf6de21fj3ySL6aNg0qIuhXTFqabPcfV6BlS/lbtpT/+utl1KhR6mtG7N+v2N695evYUXnjx8u4\n6KLTXi+4/37ZsrPL+tYAAEAIMYOMsFDa3rHDh22aPduljh3j1LVrnE6csGnWrBx9+eVJzZuXowcf\nLNCVVwYVESFFTZ4s2/Hjyn/kERlut5xvvCH7N9+UadzBpCSd3LZNRlSU4tu0kfONNwqnsE+Ji5OR\nkFCma1Rl9BTCDLmAGXIBKzGDjAtSRoZdkye79dlndnXp4tMTT+Tphhv8cpwt0YYh24kTypk9W0bd\nuvJ36nTO87vHjVOgUSP527dXsGFDKSdHjv/8R36zD+D4eOU9+6y8vXopevhwOV97TTnz58uoWbPs\nbxQAAIQcM8gIC+fbO7Z/v00PPRSj/v1jdccdXn399UnNmpWrDh3OURxLks2mvClTZNSte17X8bds\nKcf27Yrr3FnxrVur2jXXFM4On0OgVStlbdggb8+erHlsEXoKYYZcwAy5gJWYQcYFITdXeuGFKM2Z\n41L//gWaOjVHsbHldz3fnXfKd+edhTfhffmlFAwq0LLlHx/ocMjbu3f5DQwAAJQ7CmRUqEBAGjbI\nrq2f/FVXJBu64oqAmjYN6IorArr88qAcDmnVqkiNH+9WSkpAmzZlKSkpNEu0SZIiIhRo3jx018Np\n6CmEGXIBM+QCVqJARoUJBqXHHovWz5u+0SrX37Wz3Rx9dbSu0tOdmjzZrp9+ilCNGoZq1gxq9uxc\ntWkTmiffAQCAqo0eZFQIw5CeeMKtPXvsev2JDEV2rq97n79eo+/6UosX5ygjw6O9ezO1YkWW3nsv\n67fi2DAUNXGi7F99deZJvd6iP9oyMxVz331SnoVrHiPk6CmEGXIBM+QCVqJARsgZhvTkk25t3+7Q\nsmVZcvbvqb133KH8v/1Ncd27K+LrryVJbrfUtGlQdvuvBwYCin7sMUVu2qRg/fpnnDe2Z09FDxyo\niF27FD10qIKJiYUnAQAAKAGbYRRftLX8bdy4Ua1atQrlJRFmpkyJ0qpVTq1enaWaNU+PX+TKlbJl\nZ8vbt+/pBxUUKObhh2XzeJS9ZIlM79DzeBQ1d65cs2cr+Kc/KWvdOsnlKsd3AgAAwtmOHTvUoUOH\nEh9HDzJC6sUXXVq2zKk1a84sjqXC1SPOkJ2t2D59ZMTFKfv1189e9MbHK3/ECOUPHFh49x/FMQAA\nKIVStVgcOHBAqampuuqqq5SSkqINGzZIkpYtW6bGjRurSZMmWrNmjaUDxYVv0SKn5s51adWqLNWt\ne3pxfK7eMcfWrQo2aKCc+fPPr+iNiZHi48s6XIQBegphhlzADLmAlUo1gxwZGalZs2apWbNm2rdv\nn9q0aaMffvhBo0aNUkZGhvLz89WuXTt169bN6vEijHm90ujRbv34o115eVJenk25ubaiPzud0urV\nWUpMNBTx448KJiScV8Hr79xZ/s6dQ/AOAAAASlkg16lTR3Xq1JEkJSUlyev1atu2bUpOTlbt2rUl\nSQ0aNNDOnTvVokUL60aLsPbUU4XF8cCB+YqOltxuQ263oehoKSrKUPXqhpxOSYahmH79lDd6dNEj\nn1m/EmbIBcyQC5ghF7BSmXuQ161bp5SUFB05ckQJCQmaM2eOatSooXr16ungwYMUyFXEu+86tGqV\nUx984FGNGue+79Oxdatsubnyl6JpHgAAoLyVaZm3Q4cOaeTIkZo5c2bRz9LS0tSjRw9Jks1mK9vo\ncEE4cMCmoUNjNHdutmoax/5wf9fMmcofNEiK+C1+9I7BDLmAGXIBM+QCVir1DHJ+fr569Oih5557\nTpdccol+/vlnHTx4sOj1Q4cOKSEhwfTYRx55RElJSZKkatWqqVmzZkVfjZwKONthuv3RR7pywQLV\nnDRJRt26+uCDLRoz5lqlpRXoL38JyJHcVkdbtVL1uXOlqKgzjv/PG2/ouq1b5Z0797Tzn1Lh74/t\nsNr+4osvwmo8bIfH9inhMh62w2Obzwu2T9m8ebP27dsnSRowYIBKo1TrIBuGod69e6tt27YaNGiQ\nJMnr9app06ZFN+m1b99eu3fvPuNY1kG+sLlmzJBzxQplrVkjxcXp6aej9NlnDq1Yka2ICMl28qSi\nH3tMEd9/r5z58xW8/PLTjnc//riM6tWVP2ZMBb0DAABQVYR0HeQtW7Zo5cqV+vbbb/XSSy/JZrNp\n7dq1mjRpkq677jpJ0rRp00pzaoSxyHXrFDV7tjzr1klxcdq0yaFXX3Vp0yZPUbeEUa2achYulHPx\nYsV16aK8J5+U9557pF/bbXydOyvQvHkFvgsAAIBz40l6kDweKS6uqIg1E/H114q79VZlv/qqAq1b\n6/Bhm9q1i9fs2Tlq29Z/1mNiBg9W9pIlMhITzzmEzZs3F31NApxCLmCGXMAMuYCZ0s4gl+kmPVQO\n7gkTFNOvn5Sdbb5Dbq5i771XeU8/rUDr1goEpLS0GN1/f8FZi2NJCl55pbLee+8Pi2MAAIBwQoFc\nyX31lV3XXBOvXr1itXev+V933oQJMuLiFN+5syK+//7MHaKjlbN4sbw9eyoz06YRI6IVDEp/+1v+\nHw/gPFcy4V/9MEMuYIZcwAy5gJUokCuxt9+O1G23xWr48Hylpvp0001xeuqpKOXk/G7HqCjlTp+u\n/AEDFNelixzr159xrqzLmuv5511q3brwEc4LF+bIbg/BmwAAAAgxCuQ/4PNJ69ZF6sEHY7RiRWRF\nD+e8BIPS009Hadw4t1asyFavXl49+miBPvzQo30/2nRdY5/SF3h0Wve5zSZv//7KXrxYMY89Jse2\nbZIK3/+iRU61bl1Nn3/u0DvvZGnatFzVrGlt6/rvl28CJHIBc+QCZsgFrFSqVSyqgq++suu115xa\nscKphg2Duvlmr554Ilr/8z9ZSkoKVvTwzsrjkQYOjNHJkzZt3Jil2rV/K2Tr1ze0uPmz2rb3uB6d\n/5wWrjY0YUKeEhODCgYLC+tgo2tlLN+sQPUa+vjNSD3zjFuJiUEtWZKtVq0CFfjOAAAAQoMCuZj8\nfGnxYpdee82pX36J0N13F2jNmixddllhQWyzSY8+Gq1Vq7KLPwQubOzZE6H77otVaqpPixblyek8\n/fWIPXsUNX26/rxxo96vn6X5813q0SNWeXmFD7X77b94RURISUlBTZmSqxtvPPuNeFahdwxmyAXM\nkAuYIRewEsu8FTN6tFtffmnXiBH5uv56/xlFcCAg3XxznO6806uHHy4I+fiOHbNp7lyXcnNtCgQK\nZ3z9fikQsMnvl959N1KjR+epb1/vmQcHg4rt1k2+7t1VMHBgyMcOAAAQaizzVkbbt9u1apVTixbl\n6IYbziyOJclul158MUdTpkSddUWI8rJ1q0M33BCvo0cjVLt2UImJQV1ySVBNmwbVooVfrVv7tXx5\ntnlxLMm1YIFsgYAKHnoopOM+X/SOwQy5gBlyATPkAlaixUJSQYE0dGiMnnkmVzVqnHtC/bLLgho5\nMl+DB8do7dqscl/JIRiUpk6N0ty5Ls2YkaNOnUrX7hC49FLlzJghlp4AAAA4N1osVLjiw3ff2bV4\ncc55LdsbDEq33Rarjh19Gjq0/Fotjh61KS0tRgUF0ty5OapfP6R/VQAAABe00rZYVPkZ5C++sGvx\nYpc+/NBzvs+0UESENGNGrjp2jFPnzj41bWr9qhabNzuUlhaje+4p0KhR+XKY/E053ntPzpUrFWjV\nSv5WrSS7XY7331cgOVn+UoQBAAAAVbwH2ecrXJVi/Pg81atXstnZhg2DGjMmT4MHx8jns3Zc06e7\n9NBDMZoxI0djx/5aHOef+dS6QOPG8rduLfvOnYp+9FHFPPSQIg4ckFGjhrUDCgF6x2CGXMAMuYAZ\ncgErVekZ5BdeiFKtWobuucf8xrY/0revV2vWODVtWpQef/w8Hrt8HubNc2npUpfee8+jhITCot2e\nkaGY//1feT78UMWnko3ERHkfeEDeBx6w5NoAAACopDPI773nUEpKvDp2jNOqVZHym9zXtmtXhGbO\ndGnq1Nzzbq34PZtNev75HM2d69LixU6VtZv7nXciNXVqlJYvzy4qjm0HDyq2f3/ljh8v0z6LSoL1\nK2GGXMAMuYAZcgErVaoC+ZdfbBo4MFrDh0dr0qRcDR+er3nzXEpJidfMmS55PIX7BQKFq1b8/e/5\natCgbP3Df/qTofT0wodu9O0bo+PHS1dtf/KJXcOGRWvp0mw1bPjrmLxexfbrp4IHHpC/c+cyjRMA\nAADnp1IUyIYhvfGGU9ddF69atQxt2eJRp05+3XyzT2vXZmvhwhzt2OHQ1VdX09ixbj37bJTsdkP9\n+1uzAkXTpkGtX5+lhg2Duv76eL3/fslmevfujVCfPrF68cUcXX31b49zdo8erWDNmsofMcKScYYz\nesdghlzADLmAGXIBK13w39n/978RGj48WseO2fTaa9mnFZintGoV0Lx5Ofrppwi99JJLy5Y5tWKF\ntY+LdrmkCRPy1L69T4MHx+jOO70aMyZPLte5jzt61KaePWM1alTeaWscR3zzjSK3bJFn3TqF5XOt\nAQAAKqkLeh3kpUudGj/eraFD8zVoUIEiIy05bZn98otNjz0WrZ9+itCLL+YqOTlg2ueckyPdemuc\n2rf3afRok5v8Cgr0hxU2AAAATFWpdZD9fmncOLc2bIjUO+9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- "text": [
- ""
- ]
- },
- {
- "metadata": {},
- "output_type": "pyout",
- "prompt_number": 30,
- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 30
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Exercise - Nonlinear Systems"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Our equations are linear: \n",
- "$$\\begin{aligned}new\\_pos&=old\\_pos+dist\\_moved\\\\\n",
- "new\\_position&=old\\_position*measurement\\end{aligned}$$\n",
- "\n",
- "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
- "\n",
- "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n",
- "\n",
- " Z = math.sin(i/3.) * 2\n",
- " \n",
- "Adust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#enter your code here."
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 31
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "###### Solution:"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30\n",
- "movement_error = 2\n",
- "pos = (100,500)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "\n",
- "for i in range(100):\n",
- " pos = update(pos[0], pos[1], movement, movement_error)\n",
- "\n",
- " Z = math.sin(i/3.)*2\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- "\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['input', 'filter'], 2)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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AFv86opwPPAD3HXfAzNlDyEuhVSNss8G0bBnsPXsqMlp07VojXnklClu2ZBUO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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 32
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "######Discussion\n",
- "\n",
- "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n",
- "\n",
- "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the predition and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n",
- "\n",
- "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption."
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Exercise - Noisy Nonlinear Systems"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Implement the same system, but add noise to the measurement."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "#enter your code here"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 33
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "######Solution"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "sensor_error = 30\n",
- "movement_error = 2\n",
- "pos = (100,500)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "\n",
- "for i in range(100):\n",
- " pos = update(pos[0], pos[1], movement, movement_error)\n",
- "\n",
- " Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
- " zs.append(Z)\n",
- " \n",
- " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
- " ps.append(pos[0])\n",
- "\n",
- "\n",
- "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
- "p2, = plt.plot(ps, c='b')\n",
- "plt.legend([p1,p2], ['measurement', 'filter'], 3)\n",
- "plt.show()"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "metadata": {},
- "output_type": "display_data",
- "png": 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qBfMTT3js/e/fZ7BpkwYvvWTA779n4eRJHi+8EAhThQhaGS7FuIsXZdMkiG9o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\n7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- "text": [
- ""
- ]
- }
- ],
- "prompt_number": 34
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "###### Discussion\n",
- "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
- "\n",
- "Very shortly after practioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions."
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Summary"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This information in this chapter takes some time to assimulate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n",
- "\n",
- "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": [],
- "prompt_number": 34
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "author notes:\n",
- " clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end.\n",
- " \n",
- " "
- ]
- }
- ],
- "metadata": {}
- }
- ]
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+ "metadata": {
+ "name": "",
+ "signature": "sha256:7bcd692a8ae1a36e1bb14d78bc58a3b8d1234f768fb0d0c6c00dee4155fa0676"
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+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Kalman Filters"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#format the book\n",
+ "%matplotlib inline\n",
+ "from __future__ import division, print_function\n",
+ "import matplotlib.pyplot as plt\n",
+ "import book_format\n",
+ "book_format.load_style()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "html": [
+ "\n",
+ "\n"
+ ],
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 2,
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "One Dimensional Kalman Filters"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Tracking A Dog"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
+ "\n",
+ "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Futhermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n",
+ "\n",
+ "Implementing and/or robustly modelling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import print_function, division\n",
+ "\n",
+ "import numpy.random as random\n",
+ "import math\n",
+ "\n",
+ "class DogSensor(object):\n",
+ " \n",
+ " def __init__(self, x0=0, velocity=1, noise=0.0):\n",
+ " \"\"\" x0 - initial position\n",
+ " velocity - (+=right, -=left)\n",
+ " noise - scaling factor for noise, 0== no noise\n",
+ " \"\"\"\n",
+ " self.x = x0\n",
+ " self.velocity = velocity\n",
+ " self.noise = math.sqrt(noise)\n",
+ "\n",
+ " def sense(self):\n",
+ " self.x = self.x + self.velocity\n",
+ " return self.x + random.randn() * self.noise\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The constructor $\\verb,__init()__,$ initializes the DogSensor class with an initial position (x0), velocity (vel), and an noise scaling factor. The $\\verb,sense(),$ function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for $\\verb,sense(),$ you will see a call to $\\verb,numpy.random.randn(),$. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that.\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "for i in range(20):\n",
+ " print(\"%.4f\" % random.randn(),end='\\t')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "-0.8025\t0.4440\t1.6176\t-0.7325\t0.0304\t0.3592\t-0.1916\t1.3645\t0.2563\t-0.4732\t-0.3872\t0.2693\t0.4122\t0.1272\t0.7263\t-0.5945\t0.4633\t-1.5166\t0.5133\t1.1987\t"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n",
+ "\n",
+ "Okay, so lets look at the output of the $\\verb,DogSensor,$ class. We will start by setting the noise to 0 to check that the class does what we think it does"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import matplotlib.pyplot as plt\n",
+ "import matplotlib.pylab as pylab\n",
+ "\n",
+ "dog = DogSensor (noise=0.0)\n",
+ "xs = []\n",
+ "for i in range(10):\n",
+ " x = dog.sense()\n",
+ " xs.append(x)\n",
+ " print(\"%.4f\" % x, end=' '),\n",
+ "plt.plot(xs)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that *sense()* returns the dog's position *after* updating his position, so the first postion is 0.0 + 1, or 1.0.\n",
+ "\n",
+ "Now let's inject some noise in the signal."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def test_sensor(noise_scale):\n",
+ " dog = DogSensor(noise=noise_scale)\n",
+ "\n",
+ " xs = []\n",
+ " for i in range(100):\n",
+ " x = dog.sense()\n",
+ " xs.append(x)\n",
+ " p1, = plt.plot(xs, c='b')\n",
+ " p2, = plt.plot([0,99],[1,100], 'r--')\n",
+ " plt.xlabel('time')\n",
+ " plt.ylabel('pos')\n",
+ " plt.ylim([0,100])\n",
+ " plt.title('noise = ' + str(noise_scale))\n",
+ " plt.legend([p1, p2], ['sensor', 'actual'], loc=2)\n",
+ " plt.show()\n",
+ " \n",
+ "test_sensor(4.0)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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KaSxeHMCdd57LtlNDQnB268aURp9y/FAw1pCzvhqu+AmfJtrh4eEEBASQlJSE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\n8O677zJy5Eg+//xzAHJzc5WLeu7QoUPExMTwzDPPkJeXR2pqKgkJCcp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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use $\\verb,numpy.random.seed(some_value),$ to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n",
+ "\n",
+ "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n",
+ "\n",
+ "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n",
+ "\n",
+ "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "test_sensor(100.0)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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qxAm0Pf442hcvlt0D+7XXwvHKK+EoLr6E6GiPvx07b78dhpISFq+80oonnuiF\nYcPMWLbM81iMM42NwMiRMdDrGxEf7/jzMpmA3NxobNjQgvHjlT8IqdfrMW3aNK+eSzvahBBCCAkJ\nQnSkc0f74sWeUeZ8/bUKn32mwV//ehkMIxzyy8014eBBz+MjYg9t9tw5aJculT0qvauZM42YN6+j\n20U2YD+G/fx5tts9tLuKjgamTzfh3/+W3tXevl2N1FSLT4rs7uoZK5AQBVDmkkihdUGk0LoITdXV\njE1G2/OhNb5YFwYDg1WrIrFhQ4vdwczcXBMOH/a80DYYhOiIpV8/NBw54nGBLRoxwoz16y97/Dwp\nthntCxeUzWiLFixol4yP8DzwxhvhWLVKuR10JVGhTQghhJCQYDDYH4YMdEbbYgEeeigSS5a0Y+JE\n+wjLuHFm+QciTZ3Ptcto95Dxh8IYdgY877tCe8oUE0pLWRQX25eue/eq0NrKKJI19wUqtEnIoL64\nRAqtCyKF1kVoqqpira3d4uI6h6jIpfS6ePPNMLS1MXjqKcdOGKNHm3D6NIc2F00yxEOOEc8/DwAw\nm4HaWgZJST3reF1ysgXV1SyqqhhotTwiI5V/D5UKuOMOx0ORr78ejkcfbet25xRf6aGXRQghhBAi\nH88Lw1KSkoTdVKHrSODKnPx8Dm++GY6//71FcuM5MhIYPNiM/HzHqYe2XURMM2ag9Te/ASB8f7Gx\nPDTy5rf4TXi40Lc8P1+leMcRWwsXdmDbNo11ENGJExxOn+Zw550dPnvP7gq5QrtrWzziPZ7nEUxN\naShzSaTQuiBSaF2Envp6YSKhGFcOdEZ73bpwPPlkm8sYRW6uyT4+YrEg8p57rAV210OOrnpoB1pK\nCo+DBzmfxEZEw4ebERkJ/PST8DN7440wLF/e5k1E3W9CqtDW6XQoLy+nYlsh9fX1iImJCfRlEEII\nIW5VVXX20Aa8G1jjzJ/+FI7ycvmvVVPD4LvvVFi40PUBvdzcLjltlkX7gw867SIidBzpmRtgKSkW\nHDzo2x1tYSS7cCjywgUW33yjxr339sxDkKKekaJXiEajQXJyMgwGQ6AvJSSEhYVBq9UG+jJko8wl\nkULrgkihdRF6hHx2Z5HnzcAaZ+viH/8IQ2Mjg9/+tlXW62zerMHs2Ua3rfNyc0144YUI8LxQRAKA\nadIkp483GBiHYTU9RUqKBZ98osHtt/s2xnHnnR249tposCxwzz3KtCf0pZAqtAGh2KYBK4QQQsiV\nxXb8OqDEg9thAAAgAElEQVTcjnZ7O1BXx+CDDzR4+ulWREW5fjzPA++/H4Y332xx+hhOr4f6u+/Q\n97+fgMkElJczsgbXVFT05OiIBa2tjE+jIwCQlsZj9GgzNm/W4MiRBp++lxJCKjpCrmyUuSRSaF0Q\nKbQuQk/X6EhMDI+WFsa2M55bUutCbKc3ebIJmza5DwPv36+CWg3J4SnWQ4733AM+JgYMeIwbZ5Ld\n5k/sod0TiZEWX0ZHRA891IZHH21DamrPjNHYokKbEEIIIUHPtoc2ALAsEB3teYu/rsrLWfTubcHD\nD7dhw4YwmN0MH3zvPQ2WLm23RkEAgDtyxFpgm6ZPFzLYy5YBDON4INKFnl1oC9fl6x1tAJgxw4Rf\n/cpFX8QehAptEjIoc0mk0LogUmhdhJ6u0RHA85y21LoQCm0e48aZkZTE44sv1E6fX1/P4Kuv1Jg/\n3z6nrPrpJ/sCOzzcep/DgUgXKiuZHn0YMjHRgl69An0lPUvIZbQJIYQQcuURxq/bF6Gxsd3PaZeV\nCTvaAPDww214661w3HKL9BTCLVs0uPFGo92odQBof+ghp69vO7jGpv6W1JN3tIcPN2PtWmVGuocS\n2tEmIYMyl0QKrQsihdZF6HG2o33xovxSR2pdlJez6NNHeN3Zs42oqGCQl+c4ZIbngR//Xogl93jW\nbs7V4BpbbW1AUxODhISeuaMdEQHccUfPHIMeSFRoE0IIISToSRfang+t6aq8nLHuaKtUwPLl7fjb\n3+y3nrm8PJhuXIi/l9+Cif0uePwecnLaVVUskpL4HjtqnEijPy4SMihzSaTQuiBSaF2EluZmwGKB\nQ+u92FilMtqdBfzixe347jsVysoYcHl50C5YAO3SpdhhmY13nz0G9Pa8xfC4ce5z2pWVPbeHNnGO\nCm1CCCGEBDVht9di1+kDEKIj3e06YpvRBoDoaGDhwg4cWPMltEuXwjhzJs5/q8fjRY9g/j3evVdu\nrgmHD7sutA8fVvmlowdRFhXaJGRQ5pJIoXVBpNC6CC3V1azDQUhAGFpTX+99Rru5GejoYBAfb//a\ny5e347kfbkXZf4RR6du2R2HaNJPX+el+/SwwGoGyMulC/cwZFuvWheOZZ+RNpiQ9BxXahBBCCAlq\nBgPjkM8GgLi47mW0xdgIA/sCOiPDgqsnc/jgo2jwPLBxo9A721sM4zyn3d4OPPhgJH7961YMGUI7\n2sGGCm0SMihzSaTQuiBSPF0X1dUMnn02wkdXQ5yprWXwn/+470RcVSU9mtzTMexd10XLf47gvfpb\nof74Y4fHPvSQMMDm4EEOra0Mrr3WgxGUEpwV2i+9FIF+/SxYsqRD4lmkp6NCmxBCCHGhvR1YskSL\nt98OR7v3m5bEC99/r8Jzz7n/C47QccQxtuHpwBqROCp9/CuLcWbADTDefLPDY8aPN0On4/Hww5FY\nsqS9291ApAbXfPONCp9+qsFf/3rZIX9OgkPAC+0XX3wR2dnZyM7OxksvvQQA2Lp1K4YMGYLMzEzs\n2LEjwFdIggVlLokUWhdEitx1wfPAU0/1QlKSBcnJFtTWUrXjTzU1LM6c4dDS4vpxVVUMkpK6v6N9\n8IsvhFHpS5bANGMG1t53AqenPACEhUk+/uGH23DhAou77ur+brPt4BoAqKlhsGpVJP72txaHATgk\neAS00C4pKcH777+P48eP4+jRo9i4cSMKCwuxZs0a7N+/H9988w1Wr14dyEskhBByBXvnnTDk5amw\nfn0LdDoL6uoCvj91RamtZWCxMDh+3PUwF4PBsYc2IGa05f+ZdURGwnjbbcKo9PvvR2lVhF3Hka5u\nucWIr75qQlJS9wvhyEhg0CBhcA3PA488Eom77mrHpEndi6SQwAroCPbo6Gio1Wq0trbCbDZDo9HA\nYDAgOzsbiYmJAID09HTk5+dj1KhRgbxUEgQoi0uk0LogUuSsi717VXjttXDs2tWEqChAp+NpR9vP\nqqtZREbyyMtT4eqrzS4exyAlxbHYjYoSoj/t7U43pe1cO3kybPemu/bQ7orjgNGjnV+Xp8Scdn6+\nCnV1DNasaVPstUlgBLTQTkhIwGOPPYb09HRYLBa8+uqrqK6uRmpqKjZs2ID4+HikpKSgsrKSCm1C\nCCF+c/48iwceiMSGDS3o108otBISeNrR9rPaWgZTphhx5IgKgPOAvNRUSEDo5iHGR2wLcU6vB2sw\nwHjTTS7f33b8uj/k5prx1lthKC9n8eWXTVCr/fbWxEcC+olx7tw5vP322zh//jzOnj2LV199FW2/\nhJOWL1+OefPmAQAYOgFAZKAsLpFC64JIcbUumpuBRYsi8fjjbZg8ufOf7XU6ymj7W3U1i5kzjThy\nxHl0pKMDaGxknPawts1pi4cctUuWgGlqcnis7brgefc72krLzTXh2DEVXnqpFQMGUCu/UBDQHe0D\nBw4gNzcXUb/MTB0zZgxKSkpQWVlpfYzBYEBqaqrDcx9++GFkZGQAAGJiYjBixAjrPwWK/49CX19Z\nX4t6yvXQ1z3j6+PHj/eo66Gve8bXoq7379mzD6+8Mg5jxvTCgw+2292v0/E4erQc+/adCfj1Xylf\nl5V1QKM5gJqaKbh4kcHJk3sdHl9TEw6dbhpYVvr1OO4aWA4cQ+SLf4BZr8eZO+9E+saNQFiYy8+L\nixcZsKwRR4/u8+P3uwdr18Zj4cKsHvHzv1K/Fv93aWkpAGDZsmXwFsPzfMCOsh4+fBjLli3DwYMH\nYTabMXr0aGzbtg1z5szBgQMH0NbWhqlTp6KoqMjued9++y1ycnICdNWEEEJC1Z//HI4vv1Rj+/Ym\nh0zvP/+pwZEjKvz1r5cDc3FXGJ4H+vSJRUHBJdx1lxarV7dh2jSTw+Py8jg89VQv7N7tuEMNCP86\n8Vb93Ui682q0L14sL6wN4NgxDitX9sLevdKvS64cer0e06ZN8+q5KoWvxSPjxo3D7bffjjFjxgAA\nHnjgAYwcORIvv/wyrrnmGgDAunXrAnmJhBBCrhBtbcD69WHYvduxyAbEjDZFR/yluVnIWGu1QE6O\nGUeOqCQLbWH8uvOYRWwsj+03bsQ993jWgs/fsRESmgJ+quP555/HyZMncfLkSTz55JMAgPnz56Ow\nsBCFhYWYPXt2gK+QBIuu/yRMCEDrgkiTWhdffqnGiBFm9O0rXVwJXUcC/mvzilFbyyIxUfizGDPG\n5DSnXVXFWIfVMFVVDvfHx8vvpW27LoRCm/pXk+6hTwxCCCEEwJYtGixY4HzXU+ijTTva/lJdzUCn\nEwrdnBwz9HoVpMKuBgOLsZaDiFy4EFG33gqY7dvtCYchPS93aEebKIEKbRIyxMMMhNiidUGkdF0X\nNTUMfvhBhZtvdlVoUx9tf6qtZa3THtPTLTCZgIoK+58/p9fjrg/uwH2f3QXTjBlo3LNHaG5tIz7e\nIntH23ZdlJX5t7UfCU1UaBNCCLniffyxBjfeaMQvTbAkxcTwaGlh0NH9adtEhpqazh1thunMaYvC\n//IXaJcswb7oG/HZX/LRfv/9kgcdY2N51Nd7/hek8nKGdrRJt1GhTUIGZXGJFFoXRErXdeEuNgIA\nLCvkfSk+4h/V1Z072oBjTrt90SI05OXh3fCHkdjH+WSX7mW0qdAm3UOFNiGEkKD12mvhsosoZ06f\nZlFVxeK66xw7WnRF0yG99+ijvfDDD/KbndXWMkhM7Axl5+SYoNd3Pp9PSgLCwmAwsEhJcV4Q2w6s\nkctsFqZNpqZSoU26hz4tSMigLC6RQusidPE88MYbYTh71vNfZbbrYuvWMMyb19E12iuJpkN6p6UF\n+OgjDU6dkvFD/kV1NYuhTYcQeffdYM+dw5gxZhw5wsFiU/taLEJBnpTkvDtIXJxF9mFIcV1UVTGI\ni+PlttwmxCkqtAkhhASl6moGjY0smpu9L3zNZmDrVg3mz2+X9XidjqIj3vj+ezXa2hiHw4zOcHo9\nnt57O2ZuWATTtGmwpKYiMZFHdDSPn3/uLF3q6xlotTw0Guev5Ul0RESxEaIUKrRJyKAsLpFC6yJ0\nFRcLu6NNTZ4XvuK62LtXhaQkC7Ky5BVVwo42/er01BdfqDFqlAmVla5/duzZs4hcuBDaJUvwtWoW\n8v+f3u6QY9cDkVVVrMvdbACIiBD+9eOyjIGe4rooL2eRlkaFNuk++rQghBASlIqKhF9h3hTaoi1b\nNFi4UH4bkYQEavHnKbMZ+OorNf7rv9pRUeGm7NBoYJoxAw15eVjX8TAS+9hvVefkmJCX1xk/MRgY\nl1MhAaFjiae72tTajyiFCm0SMiiLS6TQughdxcUcGIb3qtC+9tpr0dwM7Nypxty58gttf+xom0xA\nWVnoFPOHDnFITrbg6qtNbgttS3o62u+/Hx1MGFpaGMTG2u9WCzntzh3t6mrXByFFsbHyhtaInxcU\nHSFKoUKbEEJIUCouZjFkiMXrjPaOHRpMnGiy62zhjtB1xLdF8LffqnHvvVqfvoc/7dqlwaxZRqSm\nWlBRwYLnhQw2W1Dg9DliD222S5UyapQJJ09yMBqFr23Hr7viydAagAptohwqtEnIoCwukULrInQV\nF3PIyTF5ndGW0zu7q8RE30dHTp3iUFDASY4bD0Y7d6oxa5YRWi1wFXsQYXcuhPaee8CWljp9Tm0t\ni8REx0I3Ohro08eCM2eE+IjBwLqNjgBCiz85Q2vEz4uKCiq0iTKo0CaEEBJ0OjqEXcfhw81eFdo1\nNeE4dozDDTcYPXpeQoLF5320CwpYtLQwKC8P/vhIUZHQFWas5RAiFy7E5vY7YBg9Ew15eTDNmOH0\nedXVnVMhu7LNaQuHIeUV2pTRJoFAhTYJGZTFJVJoXYSmkhJhxzEhgUdTk+fPP3/+Gtx2mxHh4Z49\nT6fz/Y72mTMcYmM7d22D2c6datw27SK0Kx+Gafp03HftaeRd/SDc/eBrapwX0LY57aoqBikp7rf+\nhUJbXka7vR24dMl1b25C5KJCmxBCSNApLuYweLAZUVG8xxltngc+/DAMCxbI651tKy6OR2MjY80I\nK81sBoqKOMyaZURhYfAX2rt2qTHlFg0af/wR7cuWITFdg/Jy96VHba3zHW3bUezV1fKiI55ktCsr\nhdeUM8CIEHeo0CYhg7K4RAqti9BUXMxi0CALtFrPu44cPcqhsbEN48ebPX5flpWf9/XGhQss4uN5\njBtnQkFBEFZ6Ns2qa2sZnDrFCaPtGeHnlZZmcd/iD0IBLZXRBoDhw804e5bD5ctCdETpjHZ5OcVG\niHKo0CaEEBJ0ioo4DBok7Gh7Wmjv369Cbm6VWPt5zJedR86c4TB0qBlDhliCqtDm8vKgXbAAkStW\nWG/76is1Jk822Y0xl1touxqrHh4OZGaa8eOPQnwkKsr99XmS0S4ro4OQRDlUaJOQQVlcIoXWRWgS\noiMWrwrthgYG2dmpXr93YqLvemkXFLDIzDQjM9OMwkK2x3ceEQts7dKlMM6ciZb//V/rfTt3qnHT\nTfYZG7HFnzvV1Sx0OufF7pgxZuzapZZ1EBKQP7Dm2muv/aW1Xw//wZOgQYU2IYSQoCNER7zLaDc1\nMYiO9r6Q8uV0SHFHW6fjwXFC942eqteqVdYCuyEvz25UemsrsGePGjNm2BfaSuxoA0JOe+dOjazY\nCADExlpQXy+v5KEe2kRJVGiTkEFZXCKF1kXoqatjYDIJPa29yWg3NjKoqnI+LMUdnc53Lf4KCjhk\nZgrZ8SFDzD06PtK+fLlDgS3as0eNkSNNiI+3L5Z79+ZlFdo1Na53tHNyhCmTcobVAMKO9qVLcjPa\nDGW0iWKo0CaEEBJUioqEg5AMA0REAEaj0FdbrsZGBr16mbx+/4QEHjU1yu80WyxAYWFnoZ2ZaenR\nnUfM2dkOBbZo5041brzRsTVLdDQPngcaG52/rsUi/GXK1cTOzEwLIiN52TvaYkZbThSHMtpESVRo\nk5BBWVwihdZF6BFb+wFCMwtP4yONjQyuumqo1++v0/E+2dG+cIFFbCyP6Gjh68xMMwoKAvtrmtPr\n0Wv1asAk/y8mFgvw5ZeO+WxA+PNyFx+5eJFBVBQPtdrFdXHAyJEmpKTIK4jDwgCNBmhudv24zow2\nFdpEGVRoE0IICSrFxRwGDeoshLwptGNivM9o63QWn2S0xXy2KJDREU6vR+TChdAuWQLziBHw5FSm\nXs8hNpZH//7Sxaq7QtvVVEhb99/fLrQOlCk21v3QmqYmwGhkEBdHhyGJMqjQJiGDsrhECq2L0CMe\nhBRptfAop93QwKCw8JDX7y/saCtfaIsdR0RC5xHfFtq7d6uwY0fn1jF3/Li1wDbNmNGZwXa1vdyF\n0G3EeZbHXaFdWytvrPrcuUbk5MjvhS5naM1nnx1F794Wr1s/EtIVFdqEEEKCSlFRZ3QEwC8t/uQ/\nv7GRQWRkdzLavmnvV1Bgv6OdmsqjtZXx2XAcANi7V41//1tj/ZotL7cvsJ1ksF3ZuVMjmc8WKbWj\n7Sk5Q2tqayOQlkaxEaIcKrRJyKAsLpFC6yK0mExAaSlrF0vwpJc2zwu73zNmjPf6Gny1o33mDGe3\no80wQnyksNB3v6rr6hi7HLjxxhu9LrABoKSERX09g7Fjne80uyu0a2rk7Wh7Ss7QmtjYEZTPJoqi\nQpsQQkjQOH9eGLkdEdF5myeF9uXLQgrCgySEA7FVnNnzCe5OiR1HbHe0AfFApPLxEU6vBy5fRn09\ng+JizpOzji59/rkaN9xgBOuiukhLc93ir7bWNzvawtAa12UPjV8nSqNCm4QMyuISKbQuQkvXg5AA\nPOql3dgoDKvpzrrgOCAmxn0MwRNlZSyiozs7joiULrRtDzlyZ8+iro5FRweDkhJlyoFPP9Xgtttc\n91oUdrSd/+yqq1kkJvpiR9t9Rluvr6EdbaIoKrQJIYQEjaIi1i6fDXi2oy0W2t2l0yk7HbKggHXY\nzQaUOxBpW2CLGWzziBGor2fQv78yxfyFCyxKSlhMmuR6e9z9YUjXUyG9JTejTYU2URIV2iRkUBaX\nSKF1EVpse2iLvCm0u7sulJ4Oefq0fT5blJlp6XYRzB075thF5JcMdl0dgwkTTIoU2p9+KvTOdhfL\niY8XDnlevix9f3W166mQ3pKT0W5piafoCFEUFdqEEEKChtDaz74Q8qSPdkODMjvaCQlK72hLF9rp\n6ULcwZOuKl2ZR4xAg17vcMjRbBZ+HldfbVJkMI6c2AjQObSmslL6PX21oy1ktJ3/mfE8aFgNURwV\n2iRkUBaXSKF1EVqEjLZ9QervjDYgRkeU+xXatbWfiGWBQYPMKCqSueNskSgSGUYYi9jFpUvCzyI7\nu/vRkbIyIectd4CMs/gIzwtdR3yxox0ba0F9vfM/s/p6BhxnRGSk4m9NrmBUaBNCCAkKjY3A5csM\nUlPtdzsDkdEWemkrs6PN82LHEeniUs6BSDGDHf7aa7Lft66OQUICj8GDzSgu5rrVReXTTzWyYiMi\nZ4V2c7Pw9wKt1vtrcUbsFuNMeTkLna5V+TcmVzQqtEnIoCwukULrInQUFXEYONDsMLUvMBlt5Xpp\nl5WxiIrinY6Fd5XT7nrIsW3VKtnvW1/PID6eh1YrZM7Pn/e+JPjkE3mxEZGzFn+1tb7pOAK4PwxZ\nXs4iMzPC6f2EeIMKbUIIIUFBqrUf4FlGu6lJqa4jyk2HPHOGxZAhzreTJYfWGI2IvOsup4cc5air\n64xodOfQpaexEcB5iz9fTYUEhEK7oYGRTNcAlM8mvkGFNgkZlMUlUmhdhI6iItYhnw0AUVEISEZb\nqR1tZ/lskWR0RK1G+333dWtUem2tsKPd+R7elQSffqrBrFnyYyOA8+hIba1vpkICgEoFREbyaGx0\n/HPjeWDnTjXCwgp98t7kykWFNiGEkKBQVOR4EBIQoyPyXkO5PtpK7mhLdxwR9e8vdOho7RIfNs2c\naS2wLRbg7rsjPcqN19ezSEgQfhZDh3p/IFJutxFbzgrtmhrf7WgDzlv8ffihBnV1DGbMKPXZe5Mr\nExXaJGRQFpdIoXUROoQe2tLREU92tGNiup/RVrK9n6sdbU6vR+S7/4t+/Sw4e9Z5Ifzll2rs2qXx\naMJjXR2D+HgxOuJdoV1WxuDsWRaTJ3s2wz01VbrQrq723Y42IByI7JrTrqxk8PzzEXjjjcu4/vpr\nfPbe5MpEhTYhhJAez2wGSkpYDBzoWJBqtUJGm5exEapUH22xJ7OzvK9cPC8W2vYvZHvIkVer3UY7\n3ngjDFotj+pq+b/W6+sZ6462kAPnPP5+PO02IkpMFDqAtLfb315byyAx0Xc72rGx9jvaPA88+WQv\n3HtvO0aM6EbbFUKcoEKbhAzK4hIptC5CQ1kZi/h4XrLHsVot/Nc1WiFFqYy2Wg1ER7ufNOhOeTkD\nrZZHbKxQXEqNSu+4914MGWLGmTPSO86HDnGoqGBx660dqKmRfz11dZ3RkehooQi9cMGzssCb2AgA\ncByQnGyBwWD/fr6aCikS/oLU+Z4ff6xGSQmHJ55oA0CfF0R5VGgTQgjp8YqKWIfR67bkxkeUymgD\n4tCa7hXaXfPZ6l27JLuIZGYKO85S1q8Px0MPtSM11YKqKu+iI+J7eHIg0tvYiEiqxZ+vpkKK4uIs\n1r8c1dQw+NWveuGNN1q8OUtKiCxUaJOQQVlcIoXWRWiQmghpy9NCW4l1kZBgQV1d936Ndh293vbs\ns5JdRJwdViwpYbFvnwqLFrUjOdn76AggFNrOds2lbN/uebcRW1It/nw1FVJk20v7mWd6YcGCDowd\n2/nzp88LojQqtAkhhPR4xcWs5EFIkZxe2jwvtAGMigr8jjZ79iwAYUfbVWs/0cCBwkAZo9H+9rff\nDsPSpe3QaoHERIvX0RHA884j3sZGRGlpFpSX25chNTW+3tEW4j6ffabGiRMc1qyhSZDEt6jQJiGD\nsnVECq2L0OBuR1urdb+j3dIibBSr1cqsC286j4gZ7Kg5c8A0NLjtoS0KCwP69LHg5587f23X1zPY\ntk2DBx4QThQmJ8uPjnR0CJl22xiNJ51HysoYFBd7HxsBHFv8dXQAzc2MNa/uC/HxPM6e5fDMM73w\n+ustiOgyCJI+L4jSqNAmhBDS4xUVSbf2E8mJjiiZzwY866XtcMjx8GFYomNQUMBhyBB5UYmuhfC7\n74bhppuMSEkRvqfERF72jrY4ft12nH1mpgWFhZys7i1ibESjkfV2kroW2mIPbdaHlUlcnAW7d6tx\n660duPpq6jJCfI8KbRIyKFtHpNC6CH7NzUJbPlfjsT0ttJVYF3KnQ2o+/FByVHpFBYOICN46ndEd\nsQUfALS1Ae+8E4aVK9us9yclWWRntMVC21ZsLA+tlkd5ufvvqbuxEcCx0K6tZZGY6NsR6H37WpCd\nbcJzz0lHRujzgiiNCm1CCCE92tmzHPr3N7vc6ZST0Vaqh7ZI7o52xy23SI5KlxsbEWVmWqw72lu3\najBihBnDhnUWplqt8H+bm92/lpDPdixq5RyIvHCB7XZsBBAK7crKzp9fdbVvp0ICwJAhFuzZ02T9\nWRHia1Rok5BB2ToihdZF8CsuZjFokOudTq0Wbsew2+5oK5XRlrOjjchIhy4igPvR612J7fcsFqGl\n3yOPtNndzzDCgUg5u9pCaz/HolZOTnvLFg1uv72jW7ERAEhOFjLu4gHP2lrfToUUMS7+yOjzgiiN\nCm1CCCE9WmGh64OQQKAy2p2HIcUMtmr3btnP93RHe/BgM86e5bBrlxoRETwmTXLcUU5K4lFd7b74\n79raT+Su8wjPA5s3a3DXXd2LjQDCoVSdjkdVVWdfa1/vaBPib1Rok5BB2ToihdZF8Dt1ikNWVvcL\n7aYmZTPaCQkWpFcehnbBAmsG23TNNbKfL+xoy9/BjYwU4iq//nUEHn20TXJnVm5O23l0xOIyOnLg\nAAe1GsjJUeYgYWpqZ067utr3GW136POCKI0KbUIIIT3aiRMcRoxwX2i7y2gruaPNVFZi4Kr5+N+L\n89A+Y6ZkBtudwkLWo+gIIBTCRiNw661GyfuFHe3uR0ecdR754IMw3H13u8v4hSdsD0T6eiokIYFA\nhTYJGZStI1JoXQS3xkYhu9u/v7uMtmfRke6uCz42Fqabb8LY6EJU37HMowJbuBbAbJYudl2ZOdOI\nZ59tczqNUdjR9j46Eh/PIzycR2Wl42u0tACffabGvHndj42IbAvt6mrfToWUgz4viNKo0CaEENJj\nnTypwrBhZnBu5qjIzWjHxCi0YxoRgY6lSxGdqPFqOmRZGYs+fSwe7wwvW9aOhQudF7qeREfi46WL\nWmcHIj//XIPcXDNSU5XbdbbtPEI72iQUUaFNQgZl64gUWhfB7fhxDsOHu49X+KqPNqfXQ7Vnj9P7\nZXce6UIstJXW3cOQgPMDkZs3a7BwYXu3r9FW796dO9o1NYHf0abPC6I0KrQJIYT0WEI+232/ZqX7\naNtOcmRqa50+TqezoKbG81+lviq0PWnv56zQljoQWVbG4NgxDjfdJJ0N91ZaGo+KCqFlYV0dg8RE\n2tEmoYUKbRIyKFtHpNC6CG4nT3LIzna/o61URtthVHpeHoxz5zp9ze7saLuadOmt5GS5O9qeRUe2\nbAnDnDlGhIcrcplWQkabwcWLDKKieKfZc3+hzwuiNCq0CSGE9Egmk9ACz11rP0ChPto8j4jf/95h\nVLoriYnypkN25csd7Zoa1mnXEAC4fBkwm4V2gVLEwTjia3T2zlY2NgIAKSkWGAwsqqqohzYJTapA\nXwAhSqFsHZFC66J7TCZAFaDfFMXFLNLSLLLGZUdGAq2tQgHp7OCk24w2w6D5o488usaEBB7nz/ec\nQrtXL2EQjKuDn/X1QrcTZwcxdToeLCuMRE9O5nHgAAeOA8aOVaZ3tq2wMCAmhsfp05xfpkK6Q58X\nRGkB39E+cOAARo4ciaysLCxcuBAAsHXrVgwZMgSZmZnYsWNHgK+QEEKuTEYjkJUVg9bWwLz/iRPy\nYi+pYS0AACAASURBVCMAwLJCsd3S4vwxtoU2U1+vxCVCp+NRV9dzCm0ASE523eKvvl56WI2IYezj\nI5s3K9s7u6u0NAuOHlXRjjYJSQEttC0WC5YsWYK3334bp06dwvr169HR0YE1a9Zg//79+Oabb7B6\n9epAXiIJIpStI1JoXXivuppBbS2L4mI3vfV85MQJldtBNba0Wh6NjdLVIM8Dzc0M4orzELlwIXDj\njXCZr5ApIcHicXs/kwmoqmKRmuqbQtvdgUhXByFFQ4cKByIvX1a+d3ZXaWkWHDvWM3a06fOCKC2g\nhXZeXh4SExMxceJEAEBCQgIOHDiA7OxsJCYmIj09Henp6cjPzw/kZRJCyBWpqkr4FVFQEJhfFXJb\n+4lc5bQ79uuxA7cg5j7hkOP+V16BElu0Oh3vcaFtMAh5ZI2m228vKSmJR1WVqx1t94W2uKP9xRdq\n5OSYkZbmu93mtDQL8vM52tEmISmgGe3S0lLExMRg1qxZqKqqwgMPPIDExESkpqZiw4YNiI+PR0pK\nCiorKzFq1KhAXioJApStI1JoXXivs9DmACjb1k0OoeOI+9Z+ImeFdvjvfofITR/i+8hncVXeO0BY\nGCYqdI06ncXj6IivOo6IkpJctxysrXUdHQGEQnv7djVKSsKwaJHyhyBtpaXxaGxkkZgY+B1t+rwg\nSgtood3W1ob9+/fjxIkTiImJwbhx43D//fcDAJYvXw4A+Pjjj8H4KhhGCCHEqaoqBrGxjj2V/fXe\nRiPQu7f8XU5nvbTb770Xp25+Bv9+KAFPhzUqeZnW9n48L3+DvLzcd/lswP3Qmro696PfMzPNyM9X\nQa3msWmTb/+SlZYm/CxoKiQJRQEttFNSUpCVlYU+ffoAAMaOHYv29nZUVlZaH2MwGJCamurw3Icf\nfhgZGRkAgJiYGIwYMcL6N1ExY0VfX1lfi7f1lOuhr3vG13/729/o88HLrw0GFsOGVeHo0SiI/PX+\n7e3XY/hwM/bvl/98rZbHoUMF0GgqHe5XqfoiOppX/PPi0KF9UKtvtHb5kPP8ffsGok+fAT77+TU2\nZuDixaFO7z95cgSmTEly+XrXXHMtVCoeV19diry84z79866rSwAwETqdJeDrnz4v6GvRvn37UFpa\nCgBYtmwZvMXwvAKnQbzU0NCA7OxsHD9+HJGRkRg7diw++OAD3HbbbThw4ADa2towdepUFBUV2T3v\n22+/RU5OToCumvRU+/bts/4/CyEiWhfee/zxXsjMNOPFFyNw7twldy2lFfX662GoqmLx+9/La3nC\n6fU4c++byH/oL7jzoRiH+7/+WoW//z0c27Y1A1B2XYwdG42tW5sxcKC8XeqnnorA4MEWPPigbyIZ\nu3ap8e67YdiypVny/vvui8Qtt3Rg7lzXO9UrV/bC8uXtGDlS+bZ+toqLWYwfHwO9vgH9+gU2PkKf\nF0SKXq/HtGnTvHquSuFr8UhMTAzWrVuHqVOnwmg0YtGiRRgxYgRefvllXHPNNQCAdevWBfISSRCh\nD0cihdaF96qqGEyfbkFGhgVnz7LIyvJfEXT8uApTp7qPLHB6PcL/+EeoTpxAcf+nUW9yLLIBx2E1\nSq6LhAThQOTAgfIeX1bGYsoUk2Lv31VSkrv2fu4PQwLA+vWXlbwsp8TuKzodZbRJ6AlooQ0Ad955\nJ+6880672+bPn4/58+cH6IoIIYQAwmHI5GQLhg414/Rpzq+F9okTHB57rM3p/WxBASKefx6qEyfQ\n9vjjaNm4EfpXY6BpAwDH57mdCtkNOp04HVLezq8ve2gDYqHdvfZ+/hQZCXzxRaOswUSEBJuAD6wh\nRCm22SpCRLQuBIcOcfjwQ8/6yRkMLFJSLHbDS/yhtRUoLWUxZIiLwtVsdhiV7qq9X9dCW8l14WmL\nP18X2omJwvVYnLxFfT2L+PjA7x7buvpq38ZT5KLPC6I0KrQJIeQKsHu3Gtu3q2U/3mIBamsZJCby\nfi+0z5zhMGCA2WWfaUtWlrXAFrkrtJ2NJO8uT1r8NTYCRiODuDjf7SiHhQGRkTwuXXL8WfC8vK4j\nhBBlUKFNQgZl64gUWheC0lIW5eXyP/Lr6hhotTzCwoQpgf4stE+c4KwTITm9HuyFC7Ke56rQbmjw\nfUZbjvJyoYe2r7vWJiZKD61pahIK8fBw375/sKLPC6I0KrQJIeQKcO4ci4oK+R/51dUskpOFwnTQ\nIDPOn2fR4bsp3HZOnOAwPeYgIhcuhHbJErAlJbKeFxUFNEs32vBpRjsxkXc5IMaWr2MjouRk6aE1\nPTE2Qkgoo0KbhAzK1hEptC4E585xqKtj0SqvWx4MBgbJyUJBFhYGpKcLnUd8jdPrsXTbHbj7/91l\nzWCbrrtO1nO12sBktAcNMqOwUN7PxtfDakSJidJDa3raQciehj4viNKo0CaEkBDX1ia0dEtPN8ve\n1a6qEg5CivyR02ZqaxG5bBk+ar0JFXvyHDLY7nhyGFJJQ4eaUVzMwShjgKK/drSTkiyoqpLa0aZ8\nNiH+RIU2CRmUrSNSaF0AFy6wSEsT+mHLzWkLrf06CzJ/FNq8TofjH+mxJeEhxKd61iEF8KzQVnJd\n9OoF9O5tQVGR+59toKMjdXUsEhIoOuIMfV4QpVGhTQghIe78eRZ9+1qQluZJod0ZHQGEXdszZxQs\ntNulpyKeOKXG8OHeDXOJiuLR3Oz/HW0AyMoy49Qp9z8ffxXarqIjtKNNiP9QoU1CBmXriBRaF8D5\n8xz69bOgd2/5hbbBwNoV2pmZynQe4fR6RC5ciF7//d+S9x8/zmH4cO96KrvLaNu291N6XQwfbsbJ\nk+5nwPkzOiI1tEbuVMgrFX1eEKVRoU0IISHu3DkWffua0bs371F0JCWlsyAbNMiMkhJWVg5Zilhg\na5csgWnGDFz+858lH3fypPeFdliY0Ce662a5xQK0tAjtCn0lO9uMkydd/0XEbBb+ApOW5o9C29mO\nNkVHCPEnKrRJyKBsHZFC66IzOtK7t8WDw5D20ZGICCAtzYKSEs9/bUQ+8AC0S5agdcoMPDv/JC7c\nsszpIcfu7GgzjHROu7lZuH7Opg5Wel3IKbSrqoRBNR6c7/Saqx1tio44R58XRGlUaBNCSIg7f561\niY64n5TC8+JhSPudT29z2m0rVqD2pzzcvXcVPv48CnPnalFf73gdDQ0M6utZ9O/v/Y6rVE7b1/ls\nQGh/2NzMoK7O+c+3rEwYVuMPOh2P+noG5i5/Z6H2foT4FxXaJGRQto5IudLXBc8LPbTFHW050ZGm\nJmH3V6u1v93bziMdo8fi4cfjYTQy2Lu3ETNmmHDHHVo0NNgXpSdPchg61Gy38+wpqZy2VKGt9Lpg\nGCA72+TyQKS/8tkAoFYDMTG8Q+FfV0cDa1y50j8viPKo0CaEkBB26RIDhuERG8sjLo5HRwfjdHqi\nqOtBSJGrA5GcXo+IX/9aqOxt8Dzw3//dC9XVDP75z2ZoNMBvftOKq64yYd48LZqaOh974oT3sRGR\nVHTEHzvagPv4iD8LbUDIaXdt8UeHIQnxLyq0ScigbB2RcqWvi3PnhNgIwwi7rnJa/EnFRgAhOlJQ\nYP9cLi8P2gULoF2yBJZ+/YSTh7/geeC55yJw6hSHf/2rGRERwu0MA/zhD63IyjLjrru0uHxZuP3E\nCQ4jRnjX2k8UFQVZhbYv1kV2thknTjgvtP01FVIkDK3p/FlYLMDFi0JOnEi70j8viPKo0CaEkBB2\n7hyLjIzO4k5OfEQ4COlYjA0ebMbZsxxMJoA7elQosJcuhXHmTDTk/TLJ0Sb38fLL4di7V4Vt25oR\nFWX/WgwD/PnPl5GebsHixVq0tQmFdnZ293e0u+7Y+3NHu6dERwCh0Lbd0W5oEDqvqNV+uwRCrnhU\naJOQQdk6IuVKXxelpcKOtkhOoW0wsEhKciwIe/USJg6eO8eCKyiwL7C7tNJ4/fUwfPKJBh991IzY\nWOkil2WBN964jJgYHvfdF4nCQg5ZWd0rtJ1ltG17aAO+WRfDhgkZdpOTTXl/F9qJibzdjjYdhHTv\nSv+8IMqjQpsQQkKYeBBSJDc6kpIiXRCKByI7FiyQLLAB4IMPNHj33TB8/HETEhNdF3YqFfD3v7eA\nZYVr63oA01NRUTwaGwOT0dZqgZQUC37+WfrnG4gdbdsWf1RoE+J/VGiTkEHZOtLVqVMsKiunBvoy\nAkocViOS00u7urozOsIdPQrbLdqhQ11PiGxtBV56KQLvv9+C3r3lFXVqNfCPf7Tgww/dnNKUQeow\nZEMD65eMNuA8p93cDLS2+rfQTU7mUVPT+bOor6dhNe7Q7xGiNCq0CSEha8cODTZv1vj1PdvbgcpK\nBqdOsdi3T4Xt29XYskXj0M/YX7yJjlRVsRjadEiY5Lh4Mdhz56z3ZWaaceaM8+dv2hSGsWNNHncP\nCQsDBgzofhEYqD7aImc5bfEgJOO+jbliEhPtd7Rra2lYDSH/v707j4+qvvcG/jkzk5B9gUkC2RAi\nCTuSgAubIuBScUELUluwFSpVbKvW57m2vbba26rX1kpvq1ZtfSrt7VUQ7b1qe627IBggQQIia4CQ\nkG0SkpB1lnOeP44nmeXMzJmZM5mZzOf9et3XbZLJ5Mzwc/Kdbz6/72+4sdCmEYPZOnJ34IARx44N\n+L+hDjZtGoWioiwUF2dh8eIMrFuXhsceS8LWrYl46KFk1NSEMBzajcUiuE/RU2W3ywVeUZH2QttY\nXY2Hq27CvCe/AfuyZeisqoJ44YWDX/c1S9tmk7PZ997br/3B6CxSc7QV3kb8nTkzfIfVKPLyJJdC\nm6P9/OPvEdKbScuN2tvbkZCQgPT0dPT19eGDDz5ASkoKFi1aBIOBtToRRacDB4xobU2GJNnC3kl8\n990E/PGP3Vi2zO7xs779bXmj3+zZ+rS1r78+HY891osrrvA9Cu/sWQPMZtcjvwsKJJw9a4AkweM6\nTTt2IPU738Gbjh+h+IMXMXqc518DSksdOH7cCIcDHgfLvPpqIiZOFDF3boTa94jsHG3Ae6E93Pls\nQOloO2+GNMBsZnSEaDhpqpJ/+ctfoqWlBQDw7LPP4oMPPsCbb76JP/zhD2G9OKJAMFtHzjo65OO8\nk5IEnDsXWJV9//0pGAigES6KwIEDJsyZ41At6EtLHTh6VJ+mRFubgCNHjNi923+fRD563bXoVQpO\n9w2DAGC/7DI07ajC78S7kT1WPXKTlgaYzSLq6lwfj8MBbNqUhPvui1w3G9BeaIfr9WL8eBEdHQZ0\ndLhew3DP0AaAMWMkdHYKsNnkj9vaGB3xh79HSG+aXvnPnj2LkpIS2O127N+/Hw899BAefvhhVFZW\nhvv6iIiCcuCAPJO5qEhEfb32IrerC/jTn0b5POHP3alTBmRmil6LmGCPLleze7cJyckS9uzxX2jL\nGyFdi7vBQ2vqVb7BaERLZzJyc31nicvKRBw+7Pp43norAenpEhYtCu3AmVB5y2hnZg5PkWswyGP+\n3HPakehoG41ysW2xyM8HoyNEw0/Tb5+kpCS0trbi4MGDKC4uRkZGBpKSkmD3NiyUKAKYrSNnNTVG\nzJxpR0qKxe/mP2dnzsgF0r59mpJ1Tj/Le1xCz0K7stKE1autqKoyOh/CqKquzrPQNlZX409tNyD5\nRfW/SDY1qR9W40x+PEPPqSQBTz2VhPvv7x/WzX5qIp3RBtTjI5EotAHXDZFtbQaMHs3oiC/8PUJ6\n0/Tb5+qrr8b999+PX/7yl1iyZAkA4PDhwygoKAjrxRERBevAASNmzHDAbO4PqKOtRCKqq7UXxjU1\n8s/yZuJEeQNivw6pispKE66/3oqMDAknTvh+XKdOGQcnjhirq+UpImvX4sjEq7Fjyh2q3+NrhrbC\n/Y3D+++bMDAg4JprbAE+Gv1lZKiN9xu+jDYQXYV2bq40mNNmR5to+Glq2dx888249NJLAQD5+fkA\ngJycHGzcuDF8V0YUIGbryFlNjQl33z0AiyU34EJ7zhw7PvsskI62CevXew91JyQAxcXyQSZTpwZf\nbA0MyMeUV1TYMWeOA3v2mDBpktXr7U+dMmBCTidSV38LpoMH0X/ffeh56SUc3pQJezMAeFb+zc0G\n5OX5vsbJkx148cWhHZZPPSVns6Nhb3x6OlwKbYcD6O2Fx0E44Xy9mDbN7jJW0uEAGhsNyM+PRKHt\n3NFmoe0Pf4+Q3jS/LObn5w8W2QCQl5fHjjYRRaW+Pnkj4OTJDhQUSAFFR+rqDLjmGhtOnzagp8f/\n7SVJ6Wj7jtLJ86dDi4/s329ESYkD6enAnDl27N3r+81AXZ0BRZOTYV292uWodF+H1jQ3+4+OyJs7\n5ejKp58a0dBgwIoV3gv+4ZSWJqGnB4PjD7u7BaSmYljfBEydKnf8ldnpLS3yEfDJycN3DYrcXPnQ\nGptNfi7cj6InovDS/NJz6tQpbN26FS+88AK2bt2K2tracF4XUcCYrSPFoUNGXHihA4mJQHv7ZwF1\ntM+cMaCkxIHJkx2oqfHf1W5slLun+flacs2hFdqVlSZccolc0M+da8eePd7vr7tbLqzyxgK2m25y\nOSrd1yztpib/He2MDCArS8KZMwY89VQyvv/9fpi0/wEgrIxGICkJg2+SvI32C+frRUYGMGaMiFOn\n5Oc4UrERQM5oNzcbcO6cgOxsKSr+6hDN+HuE9KbpP7n3338fjzzyCJqbm5GcnIzm5mb827/9G955\n551wXx8RUcCUfDYA5OT0BVxoFxWJmD3bjn37/BfGNTUmzJihPtbPWVmZ3AUOxe7dJlx8sVxoz5jh\nwMmTRpw/L3/NWF2NxJdfHrxtXZ38ONSuKz/fe6EtR0f8dz0nT3bg1VcTcfCgEatXR0c3W+E84m84\nZ2g7mz59KKddXz/8h9Uo8vLk6AhH+xFFhqbfPq+//joeeeQR3HPPPfjGN76Be+65B4888gj+9re/\nhfv6iDRjto4UNTWmwSkg119fgdZWAVqHJNXVGVBcLGL2bIemySM1NUbMmuX/zsvKxJA62pLk2tFO\nTJSLuVNb9w9ucnR+kKdPGz1maCuU6Ija6ZJydMR/UVhW5sCvfpWEu+7qR1JScI8pXLQU2uF+vZg6\n1YGDB4cK7Uh1tJXoSHu7AWPGcOKIP/w9QnrTVGj39vZi7NixLp8bO3Ys+vXYQk9EpDPnKSAJCYDZ\nLKGpyf/cua4uYGBA3jCmtaPt3D33paTEgVOnDIOHhwTq5EkDEhOBwkK5aDRWV+MPzTdg1iNDR6Vb\nv/GNwdurzdBWpKUBiYkS2ts9nxMtmyEBudBOTpbwzW8OzxH3gXCepT2cM7SdTZs2NEs7EofVKJTo\nCDdCEkWGpkJ71qxZ2LRpEz7//HM0NDTg4MGDeOqppzBz5sxwXx+RZszWESA3dQ8fNmLaNLm7u2PH\nDhQWaju0pr5+KG5RWir/yd39hD93+/cbMWuW/0I7OVmObJw8GVxI1rmbDQCJL7+M7oXLsOayLwY3\nOTo7fdp7oQ2o57TtduDcOQE5Of4LsptusuKvf+32mOYRDZxnaUciow24jviLZEc7L0/paDM6ogV/\nj5DeNG1fWb9+PV5++WU888wz6OjoQGZmJubMmYPVq1eH+/qIiAJy7Jg8BzojY+hzQ0Wl74L4zBkj\niou/nDttBGbMsOOzz4y44gr1aEh7u4DOTsPgrGp/lGkdpaWBF13uhXbfE08gvUHArsWpkKROjyz2\n6dMGn6c0FhRIOHvW4HLQTmurXIxp2diYkQFceqn/NxiR4BwdGe4Z2ooJE0RYLAZ0dUW20M7KktDT\nI+DsWUZHiCJBU2slJSUFN954I26++WbccsstuPnmm3HDDTcgJSUl3NdHpBmzdQQABw+aXKIcCxYs\n0NzRljcQDn2vv5y2MtZP6ySHYHLahjNnAHgW2oBcLCckYHC6hbNTp4wBd7S1xkaiXTRktI1GOV5z\n6JAxooW2wSBHp44cMbKjrQF/j5DeNP16+Pjjj3Hvvfdi586dqK+vx65du3Dffffho48+Cvf1EREF\nRO04dF/j7JwpGyEV/nLa/k6EdOd+dLkvgyc5Xn89Ohr70dBgwLRpnj9LbZ62JCmPxfu1yc+Jaxtc\n68SRaOee0Y5ERxuQ4yN79pjQ0yPAbI7c85qXJ+LwYSMz2kQRoOkV/+WXX8bDDz+Mhx56CN/73vfw\n0EMP4ac//SledholRRRpzNYRoGxOHOr8BpLRVkbiKfx3tE2a8tmK0lL/s7Sdj0q3L1uGrspK7DmY\nhvJyu2qkY+5cO/budb3PlhYBqakS0tO9/xy1EX9NTdomjkS7aMhoA/JUmHfeSUBBgRjR+dU5ORJO\nnGB0RAv+HiG9afpP3+FweJwCWVBQAFHkf7REFD2UUxrdO9qBbIZ07mhPmCCiu1suXNUcOGDEzJka\n5wYCmDTJgRMnhk4MdDfqhRcGC2znkxwrK4fmZ7ubM8eOPXtcK/BTp1wfhxpv0ZGxY2P/dd35GPZI\nd7R37TJFLDaiyM0VIYrcDEkUCZo2Qy5atAiPPvooli5dioyMDHR0dOD999/HokWLcPDgwcHbTZ8+\nPWwXSuQPs3VUX29AUpI8O1ixYMECWCzaoyPOHW1BAC66SO5qX32161y+7m55bNukSdqLqPR0YPRo\nEWfOqG+gtK5ciYG1az0miFRWmnDvverjVGfNkjdY9vYCyraZujqj3w2a3grtKVOic4NjINLTpcFY\nTKQy2oA8S9vhECJ2WI0iN1f++YyO+MffI6Q3TYX2zp07AQCvvPKKx+eVrwHA008/reOlEdFIJElK\nJ1j/gs5bZnrMGAl9fQJ6eoDUVPXv7e4Gens9R9uVl9tRXW30KLQPHjRi8mQHEhICu8bSUnlDpFoh\nLGVleXzOZgP27zdh7lz1jnZyMr48Lt44OAVEnqHt+/nNzxfR2GiAKGIw1tDcLOCKK0ZCRzs6MtpZ\nWRIKCsQo6GjLj3/06Nj/tyWKNZoKbRbQFAt27NjBbkQMOHTIiFtuScOxY52637cyBcSZsi6UDq63\n0XpnzsiTIdzH5M2e7cCf/zzK4/YHDpgC2gipuCq7EuU/+QWMuf8Hjtmz/d6+psaI8eMdLuMK3c2Z\nY8fu3SaXQtt9Qom75GS5ILVYhMFCrKlpZEwd0ZrRHo7Xi5kz7X5jPOGWmysiIcF3Zp9k/D1Ceovg\n9gwiikdnzhjQ1mZAZ6f/kxoD5euURn85bfd8tkKZPOJ+XLl8UI32fLayyfHu91ZjR+a1cEydqun7\n1Mb6uZM3RA71TerqtM32do+PyBnt2I8XRMMcbcVTT/XillusEfv5gNzRHjNG8ngTSUThx0KbRgx2\nIWKDUuzW1ur/8lNTY/KIpCjroqDAd6FdV2d0yWcr8vMlGAzw+F6tR68b6upcpojsfGkfnhbv9shh\ne7N7twkXX+z758yZ48DevabBNwP+ZmgrnAttSZI3fSp53ljmXGifPx+5jDYgF7lJScPyo7wqLXXg\nhhsiW+zHCv4eIb2x0CaiYRWuQrutTcD584LXAtPfLG1vc6cFwXOe9sAAcPy4EVOn+i+0pfR0lyki\npTMScPSoZ4dc9XsludD219EuLhbhcAANDQIGBuQTHrVswHMe8dfeLiAlJfJFoR6UjLbDAfT2IiqP\niR9OOTkSHn+8L9KXQRSXWGjTiMH5p7FBPiVPHnOnJ2+nNCrrwl90xH3iiDP3edqHD8ubGZOT/V+X\nlJ09OKYPkDfIpaZKHofFeLsmAH4zvoIgx0f27DGhvt6A/HxR0zHqzm8+mpuFEXFYDTCU0T5/XkBa\nmqQ6w5qvF6SG64L0xkKbiIZVfb0BixbZcfKkvi8//qIc/jraZ854nz3t3tGuqfHMZxurq2GsqtJ0\nrWVl8kg+f5T52Vqytco8bXniiLb4R0GBNPicNDWNjBnawFB0JJITR4iIABbaNIIwWxcb6usNuPxy\nexg62p75bGBoXRQWhlJoO/DZZ0YoZ3Q5jxEcPMlxzRoYzp7VdK1aTogEtG2EVMydK+e0T58OpNB2\n7miPjIkjgDxPfGBAjsNkZqoX2ny9IDVcF6Q3FtpENGxsNjk/PG+eTfeMtr/Z3EpRqZaN7u2VN825\nz9BWmM0SMjOlwWuuqTFhUfLuwQLbvnQpOquqYLv+ek3XWlYmaiq0d+82ai60L7rIjkOHjDh61IgL\nLtA2dnCkRkcEQe5qnz1rYEebiCKKhTaNGMzWRb+mJgNyciTk50uwWgV0dOgzb6ynR+6Ul5Z6FpjK\nukhNBZKTJbS1ef5MZYa2WpZXoZwQ6XAARz8XMfelHwwW2APr1yOQXYRydMT3y29XF3D6tLbJJoD8\n+EpKHHjrrUTNc5vHjRPR0iJvGhxJHW1A3gDZ0OC90ObrBanhuiC9sdAmomEjb4SUD4WZONGhW1f7\n88+NKCvzf0qjtw2RvjZCKpQTIo8fN2B0nhG9778TcIGtKCtz4PBh35NH9uwxYdYse0AnT86da0dD\ng7YZ2gCQmAiMHi2huVn4cob2yCm009Ml1Nezo01EkcVCm0YMZuuin1JoA8CECaJuhfaBAyZMn67e\n+XVeF95maXs7rAaA3FqGktM2DWXBQzj9w2yWDw9pbfV+H6+/noiFC7UfiAPI87QBaM5oA0PxkZEU\nHQH8R0f4ekFquC5Ibyy0iWjYOBfaJSUO1NbqsyGypsZ3PlvhbUOk2mE1xqoqpN16K9LWrAEAzJrl\nwMGDRuzbp+1n+SIIclfbW0571y4TPvggAd/5Tn9A93vxxXZkZYkYPVp7wazM0h5p0ZH0dHmEIjva\nRBRJLLRpxGC2Lvo5F9oTJ+rZ0ZZnaKtxXhe+oiPKYTWDBfbtt8N21VXo3rIFAJCZKWHcOBGvv56I\nmTMD6zSrKSsTVUf8Wa3A/fen4LHHepGREdh9Tpwo4tNPuwJqto/UQjstTWJGmwLGdUF6Y6FNRMPG\ntdDW59Aamw04csSIadP8d5m9RUeUjHbygw8OFtjKSY7OR6XPnm1Hc7Mh5I42oIz487yW3/0uA/xh\nvwAAIABJREFUCePHO3D99bag7jc3N7AObkGBOHhSZXp6UD8yKqWnS2hsZEabiCKLhTaNGMzWRT/3\njrYeh9Y0NwvIypK8HrPtntFWi44oGe2Bb39btcBWXHSRA+PGiV7HAAZCLTpy8qQBzzwzCk880RdK\nBDwgBQUiqquNyMsTh+1nDof0dAl2u/foCF8vSA3XBelNwyG9RET6cC60c3KGRvxlZQVfuDY2GjBu\nnLbIg1pGu68P6OiQNwKKhhKf379smQ09PfpUo+6FtiQBDzyQgu99r1/zeD49FBSI+OILIy6+OPQ4\nTDRJT5fXFDvaRBRJ7GjTiMFsXXTr6pKLSeWkPmXE34kTob0M+Ts63HldjB0rYXzLXiSvv1Mevg25\n+C8o8D1DW3HhhSIeeCCwDYre5OdL6O0VcO6cXLi/9loCWloE3HXXgC73r1VBgQhRHFkTRwA5ow14\nL7T5ekFquC5Ibyy0iWhYKAWtczxBj/iI1o62sboamd9YjW24BZaySwGT/Ac9LTO0w0EQhnLaHR0C\nHnooBb/+dW9Ac7P1MHasBINBGlEbIQF2tIkoOkS80D5//jzy8/Px5JNPAgC2bNmC0tJSlJWV4c03\n34zw1VEsYbYuujnHRhQlJaFviGxqEjB2rPdiatHo0fJR6WvXwr5sGVbNPoz98+8czGCfOeNjhnaY\nKfGRn/0sGV/5ihVz54a+yTJQJhOQlyeNuI62v0KbrxekhuuC9BbxjPYvfvELzJkzB4IgwGq14sEH\nH0RlZSX6+/uxePFiLF++PNKXSEQ6UCu0J0wQ8dFHob0MNTUZMH++93yx0NUF+7Jl6HnpJWDUKOTt\nSkBDw9BEj0gX2i+/PAqnTxuwa1dXRK4BkOMjI62jrRTY7GgTUSRFtKN95MgRtLa2oqKiApIkYffu\n3Zg2bRpycnJQVFSEoqIi7N+/P5KXSDGE2broplZoy8ewh9bR9hcd+chud5ki4j5LW+2wmuFSViai\nstKEn/+8dzC7Hgnf+tYALrtsZG2GTEsDDAbv02j4ekFquC5IbxEttH/4wx/i4YcfHvy4qakJ48aN\nw3PPPYetW7di7NixaGxsjNwFUtxqahJw//0pkb6MEUU9OhL6oTWNjfJmSGN1NQSLxe/t5RF/Q0Fx\n58Nqhtsll9jxox/1YcWK4GZm6+VrX7NiwoSR1dFOT5eQni6NqJGFRBR7IlZov/HGGygtLUVRUREk\nybWTs2HDBqxcuRIAIPBVkjTSM1t3/LgRf/qT/Cd90odaoW02S7DZhiZvBCO/YS8uemgV0tauheHE\nCY+vu68L9472mTOR2QwJAFlZEh54oJ/FYBjk5oqYMsX7GyhmcUkN1wXpLWIZ7d27d2Pbtm347//+\nb1gsFhgMBmzcuNGlg610uNXcfffdKC4uBgBkZmZixowZg/+BKH/64cf8ONiPd+wYB2AO/va3BFRU\nvBfx6xkJH9fXfwWFhaLL1wUByMvrxOuvH8Add0wP6P4uT0lBwmNPYHPPIZwoXY6iv8oZbH/f39JS\nhSNHZgMABgaAtjYJx49vR0FBdD1f/Dj0j//+9+6ouh5+zI/5cWx8rPzvuro6AMD69esRLEFybydH\nwCOPPIL09HR897vfRVlZ2eBmyCuvvBLHjh3zuP17772H8vLyCFwpRbMdO3YM/scSqhdfTMTzzydh\n1CgJH310Xpf7jGcOB5Cfn4UzZzqQmOj6tXXrUnHNNTasXGnVfH+G06eRvnw5znz9Plz1yl34dJ/3\n2dPu66K9XUBFRQZOnuzEiRMGrFyZhurqyG1EpMjQ8/WCRg6uC1JTXV2NJUuWBPW9Jp2vJSQJCQl4\n/PHHMX/+fADApk2bInxFFK8sFgOuu86Kl18ehaNHDSgtHVn51eHW1CTAbJY8imwguENrxPHj0blv\nHw5UJmH0xwkAtB/ykp0tx1W6upR8Nv9tiYgoPKKi0P7pT386+L9XrVqFVatWRfBqKFbp2YVobxdw\nwQUibrzRitdfT8S//Is+pwHGK+WwGjUTJ4r48EMfL0V2++DhMi5MJr8ztAHPdSEIyoZIQ8QOq6HI\nY9eS1HBdkN6404tIhcVigNks4uabrXjttUREPmClj6efHuW7qA0TtY2QCrmj7Tniz1hdjdTVq5H8\nk594vd+zZ7WdCulOKbTr69nRJiKi8GGhTSOG8yaGULW1CRg9WkJFhQMDA8Dnn4c26zka2GzAU08l\n4fe/HzXsP7uhwVeh7TriTymwlZMc+5z+4uWuqUke7eeL2rooKJAnjzA6Er/0fL2gkYPrgvTGQptI\nRVubnCkWBHzZ1U6I9CWF7MMPTcjPF7FrVwLa24d3npyvjrbZLMHhEHCuHUhdu3awwO6sqnI5aEZN\nU1NwHe3CQiU6ErnDaoiIaORjoU0jhp7ZurY2A0aPlguwFStsIyI+sm1bItassWLJEhv+53/0eeMg\nSdD0vPgqtAUBKClx4EStEQN33qmpwFY0NQkYNy6wjDbgXGhH7rAaiixmcUkN1wXpjYU2kRtJkjva\nY8bIBdz06Q6MGgVUVcVufKS3F/jf/03AjTdaccstVmzbpjL+Iwg/+1kynnvOf0Hsq9AGgAkTRNTW\nGmFfsEBTga1QToUMVEGB/PPa2vxvpiQiIgoWC20aMfTK1p0/DyQkAMnJ8seCAKxYIW+KjFVvv52A\nigoHcnMlLF1qw6FDRpdjyIPR0SHghRdG4a23/HfHnQttY3U1kn71K5evT5zoCPgodkmSoyN5eYFn\ntAsLRezfb8S4caLqQBMa+ZjFJTVcF6Q3FtpEbtrbDRgzxrV4W7HCiv/+70Q4YjRlsG1bIr76VflA\nmFGjgK98xYbXXw/tjcPmzYlYvNiGzz4zobfX++3OnwesVgHmk1WDmxyl7GyXzElJiRhwod3ZKSAh\nAUhLC/za8/NFDAwIzGcTEVFYsdCmEUOvbJ3FMhQbUZSViRgzRsSnn8Ze+7OjQ8D27Qm47rqhkxdv\nuSW0Dr3dDrzwQhJ+8IN+TJ/uQGWl9+el4939eBPLkX672yZHYaijPmGCA7W1gUVzzp4VNG2EVFsX\nKSnAmDEiC+04xiwuqeG6IL2x0CZy097uWWgDGJypHQyHA6ipiUzG+403EnDFFTZkZAx9buFCOxob\nDTh+PLiXgDffTEBRkQMXXeTAokU2fPyx9/iIY/tu7C+8xucmx2A62sFOHFEUFooc7UdERGHFQptG\nDL2ydcphNe5WrLDhjTcSYLcHdn+SBNx3XwquuSYdNpsulxgQ59iIwmgEbrwx+E2Rv/99Eu66Sz72\nfNEiO7Zv997R/nDmRlRfcqfPTY5jxkgQRQQ0dlDLDG3A+7ooLhYxYQIL7XjFLC6p4bogvbHQJnKj\nHFbjbvx4EePHi/j4Y+3xEUkC/vVfk3H4sBF5eSKOHRve/+QaGwXU1BixbJlnhf/VrwZ36mVVlRFN\nTQK+8hX5PufMsePoUSN6Kw+pzvrzdViNQhA8D67xJ9SO9qZNvbjpJqv/GxIREQWJhTaNGHpl69ra\n1DvaQODxkV/9KgkffWTCli3dmDPHgf37hzfj/be/JeLaa21ISvL8WkWFAzZb4JGW554bhW9/ewDG\nL78t5fNq/DNxObJvWwXh7FmP2/sb7aeQC23t19LYqG00n7d1kZ0tITF2B8lQiJjFJTVcF6Q3FtpE\nbrx1tAE5bvH3vydgYMD//Tz33Ci88koitm3rRlaWhJkz7di/f3hz2mqxEYUgIOCZ2mfPCnj33QSs\nWTMwdFT6mjVov2Qp/s+KzyEVFHh8j/ZC24ETJwLraAczQ5uIiGi4sNCmEUOvbJ1y/Lqa/HwJ06Y5\n8OqrviMXf/1rIn73uyS8/no38vLkG86a5RjWDZEnThhQX2/AwoXeQ+VKh17UWK+++OIorFplxZgd\nf0famjWwL12KzqoqJP1gHd7fma76PYF0tE+e1P6SpPWwGmYuSQ3XBanhuiC9sdAmcmOxDB2/rua+\n+/rx1FNJmDUrAw8+mIzt200uGyTfeCMB//Zvydi27bzL+LiZMx04eNCkuagN1bZtibjpJqvPA1mm\nTBGRna1tbGFvL7B5sxwbsS1ZIk8RWb8eSErCrFkONDYKaG523czocMgFcX6+to52YNERbfdLREQU\nKSy0acTQK1vX3u69ow0AV15px549XXjllW6YzRJ+8pNkTJ6ciY0bU/DMM6Pwgx+k4OWXu1Fa6loE\nZmVJGDNGDCgeESxJkgvtW27xv9nvllusePVVH/GRL1v3W7cmYs4cO0pKRHmCiFPw22gE5s+3Y8cO\n14K9pUVAdrak6VT1khL5udGyOdPhAFpbBeTmBp/RpvjGdUFquC5Ibyy0idyoHVjjThDkbvADD/Tj\ngw/O44MPzmPmTAc++cSEzZu7MWuW+hGSM2cOT3zkwAEjrFZgzhz/R1nefLM8ttDqVpMrGeyEbdsg\nSfJIv+98x3s4feFCOz76yHWedn29AQUF2rrOo0dLkCTg3Dn/I/4sFgFZWdzMSERE0Y2FNo0YemTr\nbDagt1dAZmZgM++KikRs2DCA//zPHlx6qffiVs5ph3/yyKuvyt1sQcNY6uJiESUlIj78UL6uwU2O\na+WTHG3XX48PPzTBaJR85r0XLbJ5zNPWms8G5DcvSlfbn0BG+zFzSWq4LkgN1wXpjYU2kZO2Njnq\nYAjTfxkzZ9rD3tEWReC117TFRhS33GLF238971JgO5/k+OyzcjfbV+E+ebKIvj4Bp08PPXmBFNqA\n9hF/8kbIAAeAExERDbPhHepLFEZ6ZOu8Hb+ul5kzHdi/3whJgqZuczB27DAhK0vElCnaC9wbb7Ti\nFz/LxYxJt+LjWa/C+sEoiO/JRbvDIR96s3mz78JdEOT4yMcfm7BmjXzbhgYDLrhA+3VMmKBtxF9T\nk6B5tB8zl6SG64LUcF2Q3lhoEznxdvy6XnJzJSQnA2fOGFBcrP/PkSTg0UeTcffdGgZ9u13XK6/2\norFxFVYYAYPBCoMBX/6fhJISUfXQG3cLF8rxEaXQrq83YMEC7WfWT53qwNat/oPXjY2hnQpJREQ0\nHBgdoRFDj2ydr8Nq9DJrVvgOrnnrrQR0dwO33uq9+2ysrkbCm296fP6SSxy46SYbrr/ehuuus+Ha\na224+mobli2zY+JEbUXtokV2bN+eMDg5JNDoSHm5A9XVJr+TR7TO0AaYuSR1XBekhuuC9MZCm8iJ\nr+PX9RKuySM2G/CznyXj4Yf7Bo9Hd+a8yVHo6dH95wPABReIGDVKwpEj8ktLoIV2UZEIh0M+gdIX\neTMkM9pERBTdWGjTiHHZZaFn64ano+3A/v36p7b+8pdEFBSIWLLENarhPkWks6oK1ltv1f3nK+Sc\ndgJ6eoC+vsAy74IAzJ7twL59vp8fZrQpVFwXpIbrgvTGQptGhEceScaaNakh34+v49f1MnOmfXBD\npF66u4EnnkjGT3/a57HJMunZZz2miITT5ZfLOe2GBnmGdqCbPmfPtmPfPt8d/0DG+xEREUUKC22K\neU8/PQp/+UsivviiP+T7slgMGDMmvAVcfr4EUZS7snp5+ukkLFxow0UXec7w7nnhhWEpsBULFsgn\nRJ4+rf2wGmcVFXZUV3vvaA8MAJ2d2t8QMXNJarguSA3XBemNhTbFtC1bEvH73ydhy5ZudHSEXkiG\ne7wfIMcj5Jy2PvGR5mYBzz8/Cj+985Qu9xeqsWMljB0r4R//SAwon62QoyNGiF6+taXFgJyc8M06\nJyIi0gt/VVHMeucdEx56KBlbtpzHjBkO9PQkwuH/xHGftBy/rgc9J49s/b8H8VHGckzZeD1g1z5K\nL5wWLbLhtdcSgiq0zWYJmZkSamvVX54aG4WAYiPMXJIargtSw3VBemOhTTFp714j7r47FZs3d2PK\nFBEmE5CVJaGtLbQ4Rnt7+KMjgD6TR4zV1RCu/xrueOtrGPutK9H18ceAKTpG4y9aZEdXV2ATR5yV\nl3vfEMl8NhERxQoW2hRzjh414BvfSMPvfteLSy4ZamGnpHTDYgm+0JYkeTPk8HS0Q5s8MmrTJqSt\nXYv/6vwKXvxhDUzfG74Mthbz59thMEhBF9qzZ9tRVaX+RiSQGdoAM5ekjuuC1HBdkN5YaFNMaWgQ\nsHJlGn7ykz5cfbXN5WuZmVa0tga/pM+fl2vV4ahXL7hAxPnzCPqNgfXrX8c7z36GX5y7B+vu1vni\ndJCVJWH9+gFMnRpclsdfR3vsWM7QJiKi6MdCm2KGJAFf+1oa1q0bwG23eZ58OGlSBlpbg+9oh/v4\ndWdDGyKDi49IOTl4+LEs/PCHfUhO1vnidPL4433IyQmuIJ41y47PPzfCZvP8WlMTM9oUOq4LUsN1\nQXpjoU0x4/BhA86fF/Dd7w6oft1sFkPqaA/HYTXO/BXaxupqpN52Gwy1tR5f6+oCDhww+TxqPZal\np8unRH7xhefzE2h0hIiIKFJYaFPM2LEjAQsX2r0egNLbezKkjvZwHL/uzFtO2+UkxyVLIBYUeNxG\njk+IqketjxTl5XZUV4deaDNzSWq4LkgN1wXpjYU2xYzt201YuND7+LqsrNAy2sO1EVIxc6bdpaNt\nqK31OCrd20Ezzc0jv6vr7Sj2piYD8vOZ0SYioujHQptigigCn3xiwoIFKqHdL82bVxJiR3t4C+0L\nLxTR0mJAZ6d8zVJiouaj0uNhQ6BaR7u7Wx4VnpGh/bEzc0lquC5IDdcF6Y2FNsWEgweNMJsljBvn\nvcAym0VYLMEv6eE4ft2Z0QhMm+bAgQNyMSkVFmo+Kr2xURjxHe1p0xw4edKI3t6hzymRGW/xISIi\nomjCQptiwvbtJixY4PvUw1OndsdER9tYXQ3DF18ACP6EyKYmA/LyRnahPWoUUFbmumE0mMNqmLkk\nNVwXpIbrgvTGQptiwo4dJixc6D02AgxltKUga+VwF9rOmxwN9fUAgh/xFy+nI8rxkaGcdlOTMOIj\nM0RENHKw0KaoZ7cDu3b572gvXXoZjEY5xxuMtrbwREdcpoh8mcG2L1sGIPgTIpub46PgdN8QefZs\n4JtAmbkkNVwXpIbrgvTGQpui3v79RhQWijCb/ReWOTnBz9IOS0e7pwep99zjdZNjWZkD9fUG9PQE\ndrdKVnmkmz3bjn37XKMj8fC4iYhoZGChTVFPSz4bkLN1ZrMUdE5bnqOtc6GdmoquTz7xuskxIUEu\ntj//XHt8RJLiI6MNAKWl8mSWc+fkf1NmtEkvXBekhuuC9MZCOw7V1BghxlCNtn17gs/52c5yc4Pr\naA8MAP39gY2N8+A8HsOZnxEZck5be3ykq0uA0QikpQVycbHJaJQ3jCpdbfn49ZEfmSEiopGBhXYc\n+trX0nDoUGwcKWi1Anv2mDB/vv9Ce8GCBTCbJVgsgXe029vl49eDGRunZLBT77wz8G8GMH360Ig/\nLeRiM4beKYXIOacdzPHrzFySGq4LUsN1QXpjoR1nenrkYkX5U3y0q642oqTEgawsbV3MYDPawWyE\ndN/k2PPHPwb8cwFg/HgH6uq0X3O85ZSVnLYSmYmnx05ERLGNhXacOXVK7pzGSqEdSGxkx44dyMkJ\nLqMd6EbIlO9/X9NR6VoUFYmor2eh7U1FhQPV1SZ0dAhISpKQkhLY9zNzSWq4LkgN1wXpjYV2nDlx\nQv4n7+iIlULb//xsZ2ZzcB1tiyWwQrt/w4aQC2xFYaGIhgaD5tx8U5OAvLz4ySkXFYmw2eS/bsTD\nSEMiIho5WGjHmdra2Cm0+/qAfftMuPRSbR3tBQsWIDc32I52YNERcerUkAtsRWoqkJqq/bqDySnH\nMkGQc9p//3tiUI+bmUtSw3VBarguSG8stONMba0RRUUOnDsX/f/0e/aYMGWKA+np2r8n2I62WnTE\nWF2NlHvvlU/MCbOiIhFnzmi77ubm+Cq0AfmEyH/8IwH5+fH1uImIKLZFf7VFuqqtNaC83BETHe1A\nYyM7duwIoaM9VGgbq6qQduutSFu7Fo4ZMxD0me4BKCzUXmjLs6TjK0JRXm4POpvOzCWp4bogNVwX\npDcW2nHm5EkjysvtMbEZcscO7RshFVlZErq7BVitgf2stjYDJvV8JhfYt98O21VXDWWwExICu7Mg\nFBcHUmgLcdfRnj3bAQDMaBMRUUxhoR1HenrkaSPTpjnQ2RndhXZ3N3DwoBEXX6y90F6wYAEMBmDM\nmMBnabe1CRhrr3ctsHXKYGuhdfJIPJ0K6SwnR0JRkSOo+eHMXJIargtSw3VBetN+HB3FvJMnjRg/\nXsTo0VLUd7QrK02YNcse8Cg3QJ6lbbEYkJ/v0Pw9bW0GOK69BgPTtH+PnoqKRHzwgf//HDs6BIwa\nFfiIu5HgJz/pwyWXhD8vT0REpBd2tONIba0BJSUOZGdHf6G9fXsCFiwIrKhSsnVms++ctrG6Wm7v\nO5Ez2pHrEsubIf2fDinHRuIzPnHLLTbk5AT+2Jm5JDVcF6SG64L0xkI7jtTWGjBxoojsbBEdHdH9\nT79jhyngfLYiN1d98ojzSY7GEycGPy9JQ0ewR4oydcTfvkt5I2R8xUaIiIhiVXRXW6Sr2lojJk50\nIC0N6O0FbNoHegyrri7g6FEj5swJrNBWsnXuHW33o9I7q6rgmDlz8OudnQJSUiQkJupz/cHIzJQG\nr8WXeDsVUg/MXJIargtSw3VBemOhHUeUjrbBIBd20bohcufOBFRU2IPei+jc0TYeOOD3qPRAj18P\nB0HQNktb3ggZn9ERIiKiWMNCO44oHW1AHoMXrbO05fnZgcdGnDPaytQRx/Tp6Kyu9jlFJNDj18Ol\nqMjht9Bubo6/0X6hYuaS1HBdkBquC9JbRAvthoYGLFiwANOnT0dFRQXeffddAMCWLVtQWlqKsrIy\nvPnmm5G8xBGjp0eeWJGfLxeUWVnRuyHyk09MmD8/iFyLKBegOTkiWlq+XNqCAH+ZkECPXw8XLR3t\neDt+nYiIKJZFdLxfQkICnn32WcyYMQN1dXWYN28eTp48iQcffBCVlZXo7+/H4sWLsXz58khe5oig\njPYzfFnHZWdHZ0e7o0NAba0R5eXax+wZq6uR9MQTWFpejv5Fi5CTE9gc7WiIjgDaoyMstAPDzCWp\n4bogNVwXpLeIdrRzc3MxY8YMAEBxcTGsVit27dqFadOmIScnB0VFRSgqKsL+/fsjeZkjgjLaTyFH\nR6IvObRrlwlz59o1Hcbovsmx//vfBwCYzepTR7yJrUI7fsf7ERERxZqoqbTefvttVFRUoKWlBePG\njcNzzz2HrVu3YuzYsWhsbAzbz+3pAe6/P8V9rPKIo2yEVGRni1EZHdmxw+R/frbNhtSvfc1jk+OO\nPXsAYLCj7W9UniJWoiOSBDQ3x9+pkKFi5pLUcF2QGq4L0ltUFNpNTU144IEH8Mwzzwx+bsOGDVi5\nciUAQBDCVxCePm3An/40Chs3pmouzGLRiRNDGyEBeepIINGRgQF5JGC4acpnJyRg4I47vE4RGTUK\nSE7WPlUlVjra587JYwiTk4fxooiIiChoET+Cvb+/HytXrsSTTz6JCRMm4OzZsy4d7KamJowbN87j\n++6++24UFxcDADIzMzFjxozBbJXyjlTLx62tBkye3I4jR4Bf/jIZ//f/9gf0/bHy8WefzcPKlYmD\nH3d0TITJVKL5+//2t4kASvCrX/WF7XqnT1+I2lojens/xo4dku/bJydjwZcFttrX09MXo6VFQFaW\n5PfnHz/egUmTTgEoHbZ/D7WP581bgJ4eAe++uwtJSQ6Pr48evQhjx/p/PPzY9WPlc9FyPfyYH/Pj\n6P1Y+Vy0XA8/jszHyv+uq6sDAKxfvx7BEiQpcn1cSZJw2223YdGiRbjrrrsAAFarFZMnTx7cDHnl\nlVfi2LFjLt/33nvvoby8XJdrePXVBPzjH4l49NFeLF2agV/8ohc33BClJ7mEYOrUTPzzn10oLJT/\nuf/rvxLx8ccmPPustjb1j3+cjO3bTfj44/Nhu8Z//CMBL7wwCq+91g1AzmCb9uzBwIYNAd/XV76S\nhn/9137Mm2f3e9ulS9Px+OO9mDNH+wbMcJk7NwN/+Us3yso84yHvvWfC008nDT4/REREFH7V1dVY\nsmRJUN8b0ejIJ598gm3btuH555/H7NmzUV5ejra2Njz++OOYP38+lixZgk2bNoX1GlpbDcjJEZGX\nJ+HPf+7GD36QggMHjGH9mcPNfbQfEPgcbYtFwKFDxrBm2ZV8tvMmRymAU2uc34mazRJaWmIrOgIA\nhYXe4yOcOBIc53VBpOC6IDVcF6Q3UyR/+IIFC2C1Wj0+v2rVKqxatWpYrqG1VUBOjlxkXXSRA//+\n7734xjdS8e675wc/H+vcR/sBymZI7e+zlCkeNTUmXHaZ/y5xMDre2YeHRz+CtBcPoP+++9Dz0kte\nD5nxJzdXhMWi7fFFy2ZIQM5p19erX3dzMwttIiKiWBIVmyEjqbXVALN5qHi5+WYbVq2y4vbbU6Hy\nHiAmuY/2AwLfDGmxCJg714GqqvB0+zs6BEw//b9IWrHU6yZHf5wzdmazhNZW/4+vvx+wWoH09IAv\nOSx8bYjkaL/gOK8LIgXXBanhuiC9xX2hbbEIyM11LV5++MN+mM0SHnggZURMInEf7QcEfmCNxWLA\n1VdbUVUVnj+C7Nplwjvz/xWODYEX2Gpyc7XN0lZiI2EcbBOQ4mJGR4iIiEaKuC+03TvaAGAwAM88\n04PqaiM2b/Z9fHcscB/tBwwdwa7ljYQoym9IrrrKhurq0DvahuPHPT6naX62H+4ZbS2nQ7a1GTB6\ndPQUr3JHW/05bmzkDO1gMHNJarguSA3XBemNhXarZ0cbANLSgEcf7cOf/xx6dzXSTp707GgnJQEm\nk7bZ2B0dAtLSJEyeLKKrS9C8ydCdsskx/aabIHR0uHxN0/zsAOTkSGhp0dbRNpuj588WvqMjBowb\nFz3XSkRERL7FdaEtSeodbcWll9px7JgR7e1RkisIUm2tZ0cbGOpq+6NsGDUYgPJyB6rYUqMDAAAa\nl0lEQVSrA4uPuB+V3llVBSkra/DrHR0CamuNmD07tPF6ztm6nBxRY0dbwOjR0VO8jhsnorVV8Ngf\nIIryvwM72oFj5pLUcF2QGq4L0ltcF9rd3YDRCKSmqn89MRGYN8+GDz+M6HCWkPT0AJ2drqP9FNnZ\nIjo6/C8Bi2XozUh5uT2gDZGJr7zicVS6ewZ71y4T5syxI1HHlI72jrb3N1qRYDIBeXkizp51vfb2\ndvmvCjrE14mIiGiYxHWh7aubrVi82I4PPkgYpivSn9poP4XWWdotLUPxijlzHAFtiLQuX+53ioge\n+Wz5foaydRkZEqxWoK/P9/dYLNHV0QbU4yPcCBk8Zi5JDdcFqeG6IL3FeaEt+J2VfeWVNrz/fkLM\nTh85ccKgGhsB5MkjWqIjFot8qA8gd7T37TNC1Frzpab6nSKidz4bAARB3hDZ1ub78bW3G6Iqow2o\nF9qNjQLy8qLrOomIiMi3OC+0hwpIb0pKRCQkSDh8ODafKrWNkAqts7Sd35Dk5EjIzJRw4sTQ86Fk\nsE3vvhvw9emVzwY8s3W5uaLf+IjFIkTNYTUKtUKbh9UEj5lLUsN1QWq4LkhvsVk96sRi8T9xQhCA\nK6+04/33YzM+ojbaTxFMRxsY2hDpvsnRvnBhwNcXjny2QsuIv/b26Dl+XaF2DLs8cYSFNhERUSyJ\n60K7pcWA3Fz/xYsSH4lFvjraWg+taW11fUNyeekZzHt0pd9Njlrolc+W78s1W5eTo6WjHT3HryuK\niz2PYeepkMFj5pLUcF2QGq4L0ltcF9paOtoAsGiRDXv2mPxurItG3kb7AUBWlrapI3LEZuh5mjIv\nHf8j3BBSga0IRz5bkZPju6Pd3Q00NBhQVBRdhTY3QxIREY0McV1ot7T4z2gDQEYGMH26HTt3xtaY\nv+5u76P9AO1ztC0WweV5mj4nAY9ZNqBfCm3WXGenfvlswDNbZzb77mh//HECKirsSE/X5cfrprBQ\nHu/nvOG0qYmnQgaLmUtSw3VBarguSG9xXWjLBaS2P8fHYk771Cnvo/0A/+P9jNXVMH30kUdHOyUF\nKClx4OBB//O0fZ08Gc58NgDk5vruaL/9dgKWLQtPNz0USUnyRtWmpqFrZ0abiIgo9sR1oa1l6ogi\nFnPavkb7Ad4z2i6bHBst6O+X51I7Ky/3P0/74EEjJkzIwoYNKTh+3HOp6ZnPlu/PNVtnNotobVVf\n4pIEvPNOAq6+OvoKbcB1Q6RyKmRuLjPawWDmktRwXZAargvSW5wX2to72rNmOdDaKqC+PnaOY/e1\nERLwnDqidlR6/YKvwmyWILg97IoKO6qrfXe0n3giCfff349Jk0Rce206Nm5MwalTQ0sunPlsQO5o\nt7aq/3vV1BiRmiqhpCQ6u8RFRUMbIi0WAZmZUtg6/0RERBQecVtoW61Ad7eA7GxthbbRCFx+eWyd\nEulrtB/gFh2RJCQ/9pjHFJHWVvXJLPJR7N472p9/bsSePSZ897v9eOCBfuzd24XCQhFLlqTj3ntT\n8PnnRpw4oV8+G1DPaFss6kv8n/9MwFVXRWc3G3DdEMl8dmiYuSQ1XBekhuuC9Ba3hbZ8UInkNb+s\nJtbiI7W1vjvaGRkSenoE2O0ABAHdW7d6TBHxNpmlrEzeaOhtM+UTTyRh48Z+pKTIH2dmSvjhD/ux\nZ08XxoyRO9wVFeHLZwPAmDES2tsFOFRq+bffjoVCW/6LQXMzR/sRERHFojgutLXnsxWLF9vw8ccm\n1cItGp08qd7RFtraAAAGg1xsd3Z6j8N4y7EbjcBFF9lRVeUZHzl0yIDKShO+9a0Bj6+NHi3hoYf6\nUV3did/+tieQh+OXe7YuIUF+fO5vBlpaBBw/bsBll+mXD9ebc0e7sZGj/ULBzCWp4bogNVwXpLe4\nLbRbWrTN0HaWny9h7FgJ+/b5n7YRaWqj/QYz2F/9qrwbEP4nj7gfVuOsokI+IdLdE08kY+PGfqSm\ner8+s1lCYWH4u7Rms4SWFtfH9+67Cbj88vB200NVXOxwiY6w0CYiIoo9cVtoWyzaToV0F03xEUmC\n1+iG82g/902O5//3f6HsbvR3DHtrqwFms/rzVF7uuSHy0CEDPv3UhDvu8Oxmh5tati431zOn/fbb\n0TttRFFYKG+GlCSO9gsVM5ekhuuC1HBdkN7ittAOpqMNhFZoHzpkwB/+ENohL84qK40oKcnC3LkZ\n+P73U7BlS+LgVBRltF/SL37h86j0zEzfHW2LxftYuYoKeUOk5PTlX/7Sfzd7OJnNrpNHrFbgo49M\nWLo0ugvtjAzAZJLfBDU1CcjLY0abiIgo1sRtoR1MRhsALrvMjkOHjD5zzd68/XYitmzRL69w6pQR\nt9xixUsvdWPaNAfeeisBixdnoLw8A7/+dRImThQxcPvtPo9K9zZLW+Gro52fL4+cq6uTl9GhQwbs\n2hWZbjagnq3LzXWdpb1rlwkXXijGxEzqoiIRdXUGNDczOhIKZi5JDdcFqeG6IL3F1pniOmptFTB5\ncuDFVlIScMkldnz0kQk33BBYV7SmxjhYlOqhocGAwkIRU6eKmDp1AHfeOQBJAg4flgveyy6zQyos\n9Hkf2dkizp3zfk3+Zo1XVNixd68cU/nVr5Jx993R080G5I628+mQ//xn9MdGFMqGSGa0iYiIYlPc\ndrQDORXSXbDxkZoaI1paDD6PJQ+EUmgbq6uRunYthNZWCAIwZYqIO+6wYsoU/4/P32ZIi8V7RxtQ\nctomHDpkwM6dJqxbF5luNqCerTOb5TGEimifn+2sqEjEqVMGn/Ed8o+ZS1LDdUFquC5Ib3FbaFss\n2k+FdCcX2q7ZZH+6uoCWFjk3rVdXO/VQNb7215vlDPbll0PKyAj4PrKyvG+GFEX/z1NFhXwUezR2\nswH5dEilo338uAG9vQJmzoyN+YyFhSL27TMhK0tCQnTsvyUiIqIAxG2h7St77E9pqQhRFHDsmPan\n78ABE6ZOdWDCBDHkQttw5AhSV6/Gj6tXofdy9U2OWvnqaHd2CkhN9X3096xZdtTUGPHJJ5HtZgPq\n2TrnjvY//5mApUttHsfJR6uiIhF79xoZGwkRM5ekhuuC1HBdkN7istCWpNA62oIAXH65DTt3ao+4\n799vxKxZdhQXizh9OsQ53A4H7MuWYWbyURjuCa7AVvjaDOkvnw3I0zEuuECMqkkjzpw72rGUzwbk\nQru+3shTIYmIiGJUXBbaHR0CkpOlUOpTXHyxHZWV2gvtAweMmDHDgfHjHTh9OrSnXZw6FZZV69Bj\nT0J2dmhFmDxHW/16tHb9X365G3fdFdluNuA9o22xGNDVBVRXm7BoUWwV2gDY0Q4RM5ekhuuC1HBd\nkN7istBubQ19c9nFF9uxe3cgHW0TZs1yoLhYe3TEWF0NQ12d6tcaGgwoKBBDjkFkZoohdbQBoLhY\njNoMcVqa/P/feisRF19sH/w4FpjNEpKTJRbaREREMSpOC+3g89mKsjIR7e2Cx/Heanp7gdOnDZg8\n2YHx40W/HW3nkxwNJ0+q3kYptEPlKzoS7KzxSPGWrTObRfznfybGzLQRhSDIGyJZaIeGmUtSw3VB\narguSG9xWmgHn89WGAzA3LkOTV3tQ4eMmDTJgcRE+Cy03Y9K76yqgv3yy1Vvq1ehrUwdUZug0toa\n3OmZ0cZslrBzZ+yM9XNWViZvoCUiIqLYE6eFtj6d2ksu0ZbTVvLZgNxBFkXBo4sstLUh9dvf9npU\nuju9Cu3kZPlNQ1+f59fk5yl2Cm1v2brcXBGlpQ5ccEHsFax/+lMPLr/cHunLiGnMXJIargtSw3VB\neovLkyH16GgDck775z9P9ns7JZ8NyHEAZUNkVtbQPGdpzBh07dkjV70aNDQYcPHF+hRg8oZIASkp\nrs+JPJkl9opTdzk5Ei68MPa62YDm5UBERERRKC5/jevV0S4vt+Pzz43o7/d9O7mjPVQUlxT2qcdH\nAqiq9OpoA0BmpoSODs+fHWsdbW/Zun/5lz7cf7+ffyQasZi5JDVcF6SG64L0FpeFdigztJ2lpgKl\npQ589pn3udg2G3D4sBHTpzsGM9g/PHlXyCP+9Cy0s7PVJ49YLELIm0ajQX6+hKys2HnDQERERCND\nXBbaLS36TdPwN+bv6FEjrjVXInfd0CbH7Wt+G9LpkJKkd6Gtfgy7/DzFToHKbB2p4bogNVwXpIbr\ngvQWl4W23KnVp4D0V2jn3vdtPGf5qssmx8KShJBOhzx3TkBiooT09KDvwoUcHXEttPv75f/LzIyd\nQpuIiIgomsRlod3aakBurr4dbbXxeACwrfAePPfAAZcpIsXFoZ0OqWc3G1DvaCtvRkI9EGc4MVtH\narguSA3XBanhuiC9xV2h3dcn56b16gYXFspHudfWqj+V/9N0KaZXuHa8i4tFnDlj8Fqc+yMX2vp1\nmrOyPDvasXZYDREREVG0ibtC22Ix6N6pvW3SpzD9y0Nwr5xFETh40DQ4Q1uRlgakpUlobg7uIsLR\n0XafOhKLh9UwW0dquC5IDdcFqeG6IL3FXaHd0qLfbGhlisi/7luF/d0XypW1k9paA0aPFpGd7Vmw\nFheLQW+IbGgQdC20s7JEj+iIXiMQiYiIiOJV3BXaciQitE6tcf9+l6PSq1/Zh8e7NgJG1w2ONTVG\nzJzpUL2P8eODL7Tr6/XtaKtHR/QZgTicmK0jNVwXpIbrgtRwXZDe4u5kyJaW0GdDG48cgX3ZMvS8\n9BIwahSm2uTit6NDcJnXXFNj8lFoO76cPBL4iYUNDQYUFuodHWFHm4iIiEhPcdnRzs0NrVNrXbXK\nZYpIQgIwe7Yde/aodbTVj0kvLhaDnjyid0Y7K0t96kisdbSZrSM1XBekhuuC1HBdkN7irtAOpKNt\n3L8fsKsXyu7c52lLku/oSLAZbVEEmpoMyM8Pb0e7pcUwIk6FJCIiIoqUuCu0tXS0lU2OabfdBsPJ\nk5ru173QbmgQYDIBY8eq/6zx44PraLe0CMjMlJRmui4yMiR0dwtwOL0nsFiEkDv/w43ZOlLDdUFq\nuC5IDdcF6S3uCm15bJ16p3awwF6zBvalS9FZVQVx0iRN9zt3rgP79pkGG+C+8tkAUFgoorHRoLVh\nPkjv2Agg7+FMS5PQ2TnU1ZbHILKjTURERBSsOCy01Tvapk8+cSmwB9avB5KSNN9vVpaEggIRBw/K\nOW1f+WxAjnebzRLOng3snyAchTbgGh+RJH2PqR8uzNaRGq4LUsN1QWq4LkhvcVhoq3e07ZddFlSB\n7eySS4biI77y2Qp58khg/wR6j/ZTOB/D3tEhIDlZ33gKERERUbyJq0Lb4QDOnRMwZrRKoWowBF1g\nKy6+2I7KSrnQ3r/fd3QECC6nHa6OdmbmUEe7tTX2Jo4AzNaROq4LUsN1QWq4LkhvcVVo935YjX8Y\nrkPqi8+H5f6VjnZrq4CeHrmQ9iWYEX/DER2RD/VhPpuIiIgoFHFRaBurqpB2663I23g7dmZ/BQPf\n/GZYfs7EiSL6+4F//CMBM2c6IAi+bx/M6ZDhKrTlWdrytcjxmtjraDNbR2q4LkgN1wWp4bogvY3s\nQrunB2m33oq022+H7aqr8PbvPsN7ZRsQrvCxIMjxkT/+cZTf2AigREeMfm/n7OzZcHW0RbeOduwV\n2kRERETRJGYL7aNHDbBa/dwoNRUDt90mb3Jctw7NHUlh79RecokdBw74z2cDQHGxI6COts0mTwPx\nNps7FM6nQ+pxTH0kMFtHarguSA3XBanhuiC9mfzfJDrddlsaGhrkExJLSkSUlDhw4YUirrvO6lKI\n2m68cfB/t7aGP3t88cXySD9fo/0U48bJxW1fH5Cc7P++m5rkTrMpDP9qWVkSvvhiqKM9dar/NwpE\nRERE5F3MFtp793bBagVOnzbg3D8/Q3/1ETx/5pt45x0TXn65R/V7hmOaxkUXOXD55TZMmuS/oDca\ngYICEWfOGFBa6v/29fUGFBaG542C82ZIX4f6RDNm60gN1wWp4bogNVwXpLeYjY4AQPLBalz00Cos\ne/Y2LL2iHy+80IN9+0w4ckT9YQ1HRzspCXj99W4YNUavA5k80tAghCWfDbhGRyyW2BzvR0RERBRN\norbQ3rJlC0pLS1FWVoY333zT4+upq1cjbe1a2JctQ2dVFaxr1iA5GbjjjgE884z6POxonA8tTx7R\nVpWHa+IIoGyGVKaOxObx68zWkRquC1LDdUFquC5Ib1EZHbFarXjwwQdRWVmJ/v5+LF68GMuXL3e5\njX3ZMvS89JLHBJF16wYwd24GfvxjweOo9WicDx3I6ZANDQaUlISvo+0cHVE7pj7aNTU1RfoSKApx\nXZAargtSw3VBeovKjnZlZSWmTZuGnJwcFBUVoaioCPv373e5zcC6dapj+sxmCStW2PDHP3p+raUl\n+jragUVHwtfRVqIjAwNAX5+AzMzoep60GMUz40kF1wWp4bogNVwXpLeoLLSbm5sxbtw4PPfcc9i6\ndSvGjh2LxsZGzd9/1139+H//bxR6e4c+J0lyRzvaIhGBHFoTzkJbmXpSX2+A2Sz5PWyHiIiIiHyL\nykJbsWHDBqxcuRIAIARQ+U2aJGLuXDteeSVx8HPd3fKUj9RU3S8zJPKhNZEvtAVBnjxy7Jgx6t6M\naFVXVxfpS6AoxHVBarguSA3XBelNkCQp6jICn3zyCR5//HG88cYbAIDFixfjN7/5DWbOnAkAeOut\nt5CUpL7hkYiIiIhIL/39/bjuuuuC+t6oLLStVismT548uBnyyiuvxLFjxyJ9WUREREREmkXl1JHE\nxEQ8/vjjmD9/PgBg06ZNEb4iIiIiIqLARGVHm4iIiIgo1kX1ZkgiIiIioljFQpuIiIiIKAyiMqPt\ny86dO/HKK68AANauXYuKiooIXxFFQnt7O5566in09vbCZDLh61//OmbOnMn1QQCAvr4+3HvvvVi+\nfDmuv/56rgvCsWPH8Nxzz8HhcGD8+PG49957uS4IW7duxa5duwAA8+bNw1e/+lWuizi0efNmbN++\nHRkZGXjyyScBeK83A14fUgyx2WzSxo0bpc7OTqm1tVW65557In1JFCEdHR3S6dOnJUmSpNbWVmnD\nhg1cHzToL3/5i/T4449Lb7zxBtcFSQ6HQ/re974nHT58WJIkSerq6uK6IKm5uVm65557JIfDIdls\nNumee+6RGhoauC7i0JEjR6QTJ05I999/vyRJ3uvNYF43Yio6cuzYMRQWFiIjIwNmsxlmsxmnTp2K\n9GVRBGRmZqK4uBgAYDabYbfbcfToUa4PwtmzZ9HV1YWJEydCkiQcP36c6yLO1dbWIiMjA2VlZQCA\n9PR0/j4hJCcnw2QywWq1wmq1wmQyoaOjg+siDpWWliItLW3wY2+vD8G8bsRUdKSzsxPZ2dl45513\nkJaWhszMTHR0dET6sijCPvvsM0ycOBFdXV1cH4S//vWv+OY3v4kPPvgAANDR0cF1EecsFgtSUlLw\n6KOPorOzE0uWLEFGRgbXRZxLT0/Htddei7vuuguSJGHNmjX8PUIAvP/e6O/vD3h9xFRHW7Fs2TJc\ndtllkb4MigIdHR3485//jPXr1w9+jusjfu3duxfjxo2D2WyG5Da5lOsiftlsNhw5cgQbNmzAww8/\njLfeegvNzc0AuC7iWUtLC9555x0888wz+O1vf4s33ngDVqsVANcFybytg0DWR0x1tLOysnDu3LnB\nj5UON8Unq9WKX//611i7di1yc3PR3t7O9RHnjh8/jsrKSuzduxddXV0wGAy4+uqruS7iXFZWFgoL\nCzFmzBgAwMSJE2Gz2bgu4tzx48dRUlKC5ORkAMAFF1yAlpYWrgtCdna26jro6+sLeH3EVKF94YUX\nor6+Hl1dXbBarWhra8P48eMjfVkUAZIk4ZlnnsGCBQswa9YsAFwfBKxevRqrV68GIE8TSE5OxjXX\nXIN7772X6yKOlZSUwGKxoLu7G0lJSairq8OKFSvw4Ycfcl3Esby8PJw4cQJ2ux2iKOLkyZNcFwTA\nez1ht9sDrjNi7mRI57Eqt99+O8rLyyN8RRQJhw8fxiOPPIKioiIAgCAIePDBB/HFF19wfRCAoUJ7\n+fLlfN0gfPrpp3jttdfgcDiwYMECrFixguuCXMb7XXHFFbjhhhu4LuLQH/7wB+zZswddXV3IysrC\nunXrYLVaVddBoOsj5gptIiIiIqJYEJObIYmIiIiIoh0LbSIiIiKiMGChTUREREQUBiy0iYiIiIjC\ngIU2EREREVEYsNAmIiIiIgoDFtpERCPQCy+8gG3btkX6MoiI4hrnaBMRxagtW7agubkZ3/3udyN9\nKUREpIIdbSIiIiKiMGBHm4goxnzxxRd47LHHYLfbIUkSEhISIAgCfvvb3+LYsWP4zW9+A5vNhhtv\nvBGrV68e/L6NGzeisLAQJ0+exJVXXon3338fc+bMwZ133gkAqKurw4svvojTp08jNzcX69atQ2lp\naaQeJhFRzGNHm4goxkyZMgWbN2/GihUrMH/+fGzevBkvvfQSMjIyUFFRgc2bN2PhwoUQBMHje6+7\n7jpcccUVOHDgADZt2oTt27fDbrejr68PP//5z7Fw4UK8+OKLWL16NZ588klYrdYIPEIiopGBhTYR\nUYySJAm+/iip9rW8vDyMHTsW48aNQ0pKCtLS0tDV1YWqqipkZ2djyZIlEAQBs2fPRkZGBg4fPhzO\nh0BENKKZIn0BREQ0fAwGw+D/KR+Looi2tjacOXMG3/rWtwZva7fb0dHREalLJSKKeSy0iYhilFIs\ne6MWHfHGbDZj2rRp+PGPfxzqZRER0ZcYHSEiilFZWVk4e/YsRFH0+Jq/WIm78vJynDlzBp9++ikc\nDgf6+/tRWVmJnp4ePS+ZiCiusKNNRBSj5s2bh507d2LDhg0wmUz493//d/zHf/wHjh49CpvNBkEQ\n8Pe//x2XXnop7r77bgDeu9zJycn40Y9+hJdeegnPP/88DAYDpkyZghkzZgznQyIiGlE43o+IiIiI\nKAwYHSEiIiIiCgMW2kREREREYcBCm4iIiIgoDFhoExERERGFAQttIiIiIqIwYKFNRERERBQGLLSJ\niIiIiMKAhTYRERERURiw0CYiIiIiCoP/D5FVzLQgPmVUAAAAAElFTkSuQmCC\n",
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "test_sensor(0.5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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1LrZvzyIgAFJTLRw8aOXgwQAOHgxgbXIscXGFJCVlULmyz+3rIGWEdh0RERER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\noNEGAAAAWgCNNgAAANAC/h/iAvHO/LCNcgAAAABJRU5ErkJggg==\n",
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply $\\verb,randn(),$ with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. DogSensor.$\\verb,__init__(),$ takes the square root of the noise setting so that the $\\verb,noise * randn(),$ call properly computes the normal distribution."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Math with Gaussians"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import stats\n",
+ "stats.norm_plot(23, 5)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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GalwoFmbEyS6FiCRz6UgGEZGnVLVcRFO3BTMSdbJLIS+1IC0Wu443w6aM40RE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\nOp2289zpmTlz9kWh9OF0OOViz7T9fpIJ0/8cDr9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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n",
+ "\n",
+ "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpertation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n",
+ "\n",
+ "Let's look at 100 sensor readings in a plot:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "dog = DogSensor(23, 0, 5)\n",
+ "xs = range(100)\n",
+ "ys = []\n",
+ "for i in xs:\n",
+ " ys.append(dog.sense())\n",
+ " \n",
+ "plt.plot(xs,ys)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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MywvNcupQDf8mjfXMlAX0JVjEwwFfN8mHjJ4cHh4Gzy9PrO666y7cddddri2q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\nIAiC2JK4H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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n",
+ "\n",
+ "\n",
+ "Recall the histogram code for adding a measurement to a pre-existing belief:\n",
+ "\n",
+ " def sense(pos, measure, p_hit, p_miss):\n",
+ " q = array(pos, dtype=float)\n",
+ " for i in range(len(hallway)):\n",
+ " if hallway[i] == measure:\n",
+ " q[i] = pos[i] * p_hit\n",
+ " else:\n",
+ " q[i] = pos[i] * p_miss\n",
+ " normalize(q)\n",
+ " return q\n",
+ " \n",
+ "Note that the algorithm is essentially computing:\n",
+ "\n",
+ " new_belief = old_belief * measurement * sensor_error\n",
+ " \n",
+ "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convience. \n",
+ " \n",
+ "If we are implementing this with gaussians, we might expect it to be implemented as:\n",
+ "\n",
+ " new_gaussian = measurement * old_gaussian\n",
+ " \n",
+ "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n",
+ "$$\n",
+ "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n",
+ "\n",
+ "In other words the result is a Gaussian with \n",
+ "\n",
+ "$$\\begin{aligned}\n",
+ "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
+ "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
+ "\\end{aligned}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n",
+ "\n",
+ "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import numpy as np\n",
+ "\n",
+ "def multiply(mu1, sig1, mu2, sig2):\n",
+ " m = (sig1*mu2 + sig2*mu1) / (sig1+sig2)\n",
+ " s = 1. / (1./sig1 + 1./ sig2)\n",
+ " return (m,s)\n",
+ "\n",
+ "xs = np.arange(16, 30, 0.1)\n",
+ "\n",
+ "\n",
+ "m1,s1 = 23, 5\n",
+ "m, s = multiply(m1,s1,m1,s1)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
+ "p1, = plt.plot (xs,ys)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m,s) for x in xs]\n",
+ "p2, = plt.plot (xs,ys)\n",
+ "\n",
+ "plt.legend([p1,p2],['original', 'multiply'])\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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K+TdEQCYf/ot+zF+s4fJPmBuMmspWNDd0CqjIfvDaF4v5SwsbZiKyWdXll9HZ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\ngtMC7VJ7AAAAAElFTkSuQmCC\n",
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplation is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n",
+ "\n",
+ "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get $23m$ each time, I should conclude that the length is close to $23m$. So the mean should be $23$. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
+ "\n",
+ "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n",
+ "\n",
+ "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "xs = np.arange(16, 30, 0.1)\n",
+ "\n",
+ "m1,s1 = 23, 5\n",
+ "m2,s2 = 25, 5\n",
+ "m, s = multiply(m1,s1,m2,s2)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
+ "p1, = plt.plot (xs,ys)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m2,s2) for x in xs]\n",
+ "p2, = plt.plot (xs,ys)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m,s) for x in xs]\n",
+ "p3, = plt.plot(xs,ys)\n",
+ "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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XYnbWnn1tJ/nbFmmYhRCilrh6PJHsrbtoOm2c6lJqlZCJo7hy6CSX9vymuhQh\nhCIywyyEELXE/jF/wqvHPQRPGKa6lFonNW4j5z//hk7rFqPRaFSXI4SoJplhFkKIOujSroPkn04m\n8PGHVZdSK/kP7UPJ1Wtkb5GP0YWoi6RhFoDMUqkk2atVG/I3mUwkvPE+YX9+Cq2DvepyKsVW8tfo\ndITPeoZTby7GZDCoLscsbCX72kryty3SMAshhI3L2vgzxiI9foPvV11KreZ9fxfsG7qRGrdRdSlC\niBomM8xCCGHDjCUl7OzxGC3mPI93r86qy6n1cn89wqFJr3Lvzi/ROTmqLkcIUUUywyyEEHVI6lff\n4eDlgVfPe1SXUic0jInELTKclKWrVJcihKhB0jALQGapVJLs1bLl/A3Xi0j8x8c0f+UZmz1zgy3m\nHz5zEufeW0ZxXr7qUqrFFrOvTSR/2yINsxBC2Kjkj1fSILoVDdq3Vl1KneLSvAne93fl3KJlqksR\nQtQQmWEWQggbVHL1Gts7DaPTN+/jEh6iupw653pqJrt6PU7sjhU4enuoLkcIUUkywyyEEHVA0r/j\n8OrRUZplReo19sFvcB/OLfpCdSlCiBogDbMAZJZKJcleLVvMv/jKVZI/WkmzF59UXUq12WL+N4U+\n/zipX26gKCtHdSlVYsvZ1waSv20pt2GOi4sjPDyc5s2bs2HDhrs+LjU1ldjYWFq3bk379u3ZunVr\npdcQQghRvuR/x+HdqzP1mwapLqVOc/Lzxm/oA5yVWWYhar0yZ5j1ej0tWrQgPj6ewsJCevToQWJi\n4h0fm5WVRWZmJpGRkaSkpNClSxcuXLhQ4TVkhlkIIcpXfOUqP3cezj3f/pv6TQJUl1PnFWZks/O+\nR+m6/QucfLxUlyOEqCCzzjDHx8cTERGBt7c3gYGBBAYGcujQoTs+tlGjRkRGRgIQFBSEXq+nuLi4\nUmsIIYQoW9KSr2h0f1dplq2Ek683/sP7ce49OcosRG1WZsOcmZmJn58fS5YsYeXKlfj6+pKenl7u\nops3b6Z9+/bY29uTkZFRpTVEzZJZKnUke7VsKf/iy3mkfLqKptPGqS7FbGwp/7sJffZR0r7eRGFG\ntupSKqU2ZG/LJH/bUqEv/U2cOJFhw4YBlHty/IyMDKZPn877779/y+Mrs4YQQojbJS35Ep8Hu+Ec\nIkeXrYljI08aD+/H2X99rroUIYSF2JV1p5+f3y1Hg28eLb6bwsJChg0bxvz582nSpEml15g8eTJB\nQTe+xOI86HR1AAAgAElEQVTu7k5kZCSxsbHA/34Tk23LbN+8zVrqqUvbsbGxVlVPXdu2lfxNVwvQ\n/2cNnTd9YhX1mGvbVvIvb9sYE0bxSwsJffYx9p1JUF6PbMu2bN+6ffO/U1JSAJgwYQKVUakv/fXs\n2ZPTp08DMHPmTDQaDXPnzgXAZDIxevRounXrxjPPPFOhNX5PvvQnhBB3d2reEvQXc2n9jxmqSxF3\ncfK19zAWFtHq739SXYoQohxm/dKfg4MD8+bNo2vXrvTq1YsFCxaU3peRkUFGRkbp9s6dO1m1ahUf\nfvgh0dHRREdHk5GRUeYawnr8/jcwUbMke7VsIf/iK1c5/9k3hD73uOpSzM4W8q+oJpNHk75mi82c\nl7k2ZW+LJH/bYlfeA4YPH87w4cNvu33p0qW3bMfGxqLX6yu1hhBCiPKlfPI13r264Bzsr7oUUQZH\nbw/8hj7AuQ9W0OKvz6ouRwhhRmWOZNQkGckQQojblVwr4OeOj9Dxm/dxCQtRXY4ox/XUTHb1epx7\nd8Xh4OGuuhwhxF2YdSRDCCGEWuc/X4tHl3bSLNuIeo198Ol3H8kfrVRdihDCjKRhFoDMUqkk2atl\nzfkbCotIWryC0Bdq3+zyTdacf1U1ee4xUj5dTcnVa6pLKVNtzN6WSP62RRpmIYSwUqlffotb63Dc\nWoerLkVUQv0mAXjd15GUT1epLkUIYSYywyyEEFbIWFzCz52HE7X4NRp2iFRdjqikqyfO8OvwF+ge\n/zU6ZyfV5Qgh/kBmmIUQohZIX70F55DG0izbKNeWTWnQoTXnl69TXYoQwgykYRaAzFKpJNmrZY35\nmwwGzv7rM5pOHau6FIuzxvzNpekLY0l6fznGojufclW12py9LZD8bYs0zEIIYWUyv92OnbsrHl3b\nqy5FVIN725bUDw8h9etNqksRQlSTzDALIYQVMZlM7On3FKHPPYZPv+6qyxHVlPPLfo7PeIfYn5ej\n0coxKiGshcwwCyGEDbu89zDFuVdo9ECs6lKEGXh0bYeuvjNZW+TjdyFsmTTMApBZKpUke7WsLf9z\ni1cQ/PRINDqd6lJqhLXlb24ajYYmk8dwbtEXqku5TW3P3tpJ/rZFGmYhhLAS186eJzf+MI1H9FNd\nijAjn/7dKcrKIffXI6pLEUJUkcwwCyGElTg+4x/YNXAlfMZE1aUIM0v+ZBU5O36l3dJ5qksRQiAz\nzEIIYZP0l66Q/s33BD/5iOpShAUEjOzP5b2HyU9MVl2KEKIKpGEWgMxSqSTZq2Ut+Z//bA2NHuyG\nYyNP1aXUKGvJ39J0zk4EjhtC0uIVqkspVVeyt1aSv22RhlkIIRQzFulJWbqakIkjVZciLCj4iaFk\nrP+Roqwc1aUIISpJGmYBQGysnMJKFcleLWvIP231FlxbNcW1ZVPVpdQ4a8i/pjh4NcR/8P0kf7xS\ndSlA3creGkn+tkUaZiGEUMhkMpG0eAUhk0apLkXUgJBJIzn/+VpK8q+pLkUIUQnSMAtAZqlUkuzV\nUp3/xR/j0eh0eHaLUVqHKqrzr2nOIQF4dm3PheUbVJdS57K3NpK/bbFTXYAQQtRlSYtXEDJxJBqN\n5pbbrxaVkHlVT0a+nsyrerLy9eQVlVBYbKTIYKSw2EhhiRF7nQZHOy1Odloc7bQ42+vwdnHAx8Ue\nHxdHfF0d8HS2R6fV3KUC8UdGo4lrV4u4knudvNzr5F2+8Y++qIRivYHiYiPF+hKMBhN29lrsHXTY\n2euwd9DhVM8etwb1cG9YD7eGN/7tVM/+lj/fJpNHc3DCbIKeGIrWXv4aFsIWyHmYhRBCkbxjp9k/\n5k9E//wViXnFJGQXcCq7gISL17hebMTXxQEfVwd8XBzxcbHHvZ4dTnY6HO00ONnpcLLTUmI0UVhi\noLDkRhNdUGwkO/9/jXZmvp58vYGmHvUI93Ym3MuZ5t7ONHZ3RKuRJtpkMnH5UgEZF6789588stLz\ncHC0w62BU2nj6+ZeD0cnO+wcdNj/tznW6bSUFBsoLjb8t5E2cP1a8Y0GO/c6Vy5f58ql69jZafEN\ncP/fP43dOfLYNAIfHYT/0AdURyBEnVTZ8zDLr7ZCCFHDDEYTJ7OvkfDmJyR16s7CNado5ulMuLcz\nPZs1ZFLnxvi6ONx21LmqrukNJF4sIOFiAXtSrvCf/ekUlRjpEOBKTKA77Ru74uZUd/46KCosJul0\nDudOZXPu1EW0Wg2+jd3xDXCjS6+m+DR2x6mevVn2ZTKZuHql8EYznnqFfb8kkZl6Bc/Atlye9wkl\nbTvQOKQhOp1MSAphzerOO6Qo0y+//CLf2FVEslerpvI3GE3sT81jW2Iu+y7kEVicT5+9++n17ac8\nH+aHnQVHJuo76IjydyXK37X0toyrRfx6Po8fEi+x8JcUQhrWo1toA3qENqShs3maxYqoqfyvF+g5\neSidhKMZZKbm0TikIaHhXnTqHkpDr/oW269Go8GtQT3cGtQjvLUvcGPkI/18LseGbGHXonVkNwgk\nuJkXLdv6ERrujc6uZppnee9RS/K3LdIwCyGEhZhMJs5eus73py/x45lcfF0d6NXMgwkd/bm04GMM\nIx6kVXN/JbX5ujoysJU3A1t5oy8xcig9nx/P5vL5gQxa+9Snd5gHnYPccaih5s0SDCVGziZkc+xg\nKilnLhHa3JuY2CYENfXE3kGnrC6tVkPjYA94+QnSVm1m4GujOXMyi/2/JLFl9VGat/EjItof3wB3\ns33KIISoHplhFkIIM9MbjPx0Jpc1x7LJLzLQO8yDXs0aEuDuBEDJtQK2xwyl88aPcA5urLjaW10v\nNrAz6Qrfn75EYk4BfcI8eDiiET6uDqpLq7D8vEIO7k7h8K/n8fRxISK6MeGtfXB0qrkj5xVh1Bez\nvdMjtP/sbdwimwNw+VIBJ35L49jBNHQ6Le27BtOyrT/29uoafCFqo8rOMEvDLIQQZnKlsIRvT1xk\n3YlsQhrWY0hrbzoEuN325brkj1ZyafdBoj+eq6jSism8qmft8Ww2n8qhnb8rQyIb0bKR5cYXqisz\nLY/9O5M4ezKblm39aNclmIae1lsvwLn3l5N3JIGoD1675XaTycT5s5fYtzOJjPNXaNMxkOh7gqjv\n6qioUiFql8o2zLb7WZswKzkfpDqSvVrmyD+noJhFuy7wRNxx0q8W8fcHmzGvbzM6Brrf1iybDAaS\nPvyKkGes/0IlPq4OPN2pMZ+PiKCVT33m/pDE1HWnOJCah7mOtZgj/wtJucR9tJdvPj+Al48LE6Z3\no9fAVlbfLAMEPvYQF3+KpyAl/ZbbNRoNQU09GfJ4e0Y+3ZHrBXo++b8dbFlzlLzL182yb3nvUUvy\nty0ywyyEEFWUV1jCV4cy2XQqh95hHnz0SEs8yvnCXOZ323Fs5EHDDpE1VGX1OTvoGNy6EYNaebP9\nbC7/2nkBr/r2jOvgR4SPi7K6MlKv8Mv3p7mUlU/nns1oFe1vc2ebsHOtT8CogSR/+CUt35h2x8d4\neLtw/0MRxN4fxq87zvHZv3bRqq0/ne4LlSPOQtQQGckQQohKKtAb+PpIFmuPZ9OtSQNGR/viXb9i\nM767+z9Fk2dG4zugh4WrtByD0cSW05f44mA6IQ3r8UQHP5p6OtfY/i9m5rNz62nSz1+mU/dQImMC\nsbPhLycWpmezs8ej3Lt7JQ4N3cp9/LWrRcRvP8vxg2m0iQmgY/dQs50GT4i6Qs7DLIQQFmIymfjh\nTC4f7U2jjZ8L/3qoOf5uFT/Cl/vrEfQXc/Hp282CVVqeTquhb3NPejVryHcnc5i16Qxdgt15ooO/\nRc/nXFRYzK5tiRw/mEZMt1D6DWuj9GwX5uLk5433/bFcWPYNoc89Xu7j67s60nNASzrEhrD7hzN8\n8s8dxPYJI7J9ABq5oqMQFmG7v5ILs5JZKnUke7Uqmv+ZnAL+tOE0q45k8UqvEGb2CKlUswz/vQz2\nUyPQ6Gy/yQNw0Gl5OMKbjx5piZ1Ww/ivT7DueDYGY8U/uKxI/iajiSP7L/DJ//2CvsjAuKmxdOzW\npFY0yzeFTBpJ8sdfY9QXV/g5bg3q8cCQ1gwZ156j+1NZ9sFu0s9frvDz5b1HLcnftsgRZiGEKMM1\nvYFPfk1jx7nLPN7ej77NPdFV4SheQdIFLu0+SOS7r1igSrVcHe2Y0iWQvs29WLT7At+dzOH5roG0\n8qn+l+4y0/LYuvYYJhM8/Fg7/ALczVCx9XGLCMMlLIT0tVtpPKxvpZ7r29idUU934vhvaXyz7CAh\nYV5079sc5wqOCQkhyiczzEIIcRfxKVdYuPM8HQPdeLKa4wbHZ/0TOxdnwmdNMmOF1sdkMvHT2VyW\n7EnlvqYNGdfBH6cqzBeXlBjZ80Mih369QLcHwmndrnGtHzfI3rqLU/OW0OX7T6t8wZKiwhJ2bTvN\nycMZ9BzQkuaRvmauUojaQU4rJ4QQ1ZRXWMLbPyWxaPcFXuoezNTYoGo1y/rcPNJXbyboyaFmrNI6\naTQaejT1YMnQluReL2HS6hMcTr9aqTXSz1/m8/d2cTEzn7HPdSGyQ92YzfXqeQ/GomIu7dxf5TUc\nnezo0b8lD41py86tp1n7xUGuXS0yY5VC1E3SMAtAZqlUkuzV+mP+u5IvM3H1SVwc7VgypAXR/q7V\n3sf5z7/Bu8+9OPl6V3stW+HuZMfMHiFM7BTAvB+TeW/Xea4XG2573O/zLyk2sH1jAms+P0Dnnk15\n6NFoXNycarBqtTRaLSETR5C0+Mtqr+Uf1JDHn+1CQy9n/vPuTk78lnbbubPlvUctyd+2SMMshBDc\nuCT0/+1IYcmeVGb3DGFy5wDqmeFyxEZ9MSmffE2TSSPNUKXt6RzszpKhLSgoNjLlmwROXyy44+Mu\nZuaz7IPdXL5UwLjnY2nRxq/KYwm2zH/og1z57QT5p5KqvZadvY5uDzRnyNj27P7xDN/FHaaosKT6\nRQpRB8kMsxCizjuTU8DcH5II93bm2S6B1Dfj2RdSv/qOtNWbiflqodnWtFU/nsnl/d0XGBHlw5DW\n3mg1GkwmE4f2nmfn96fp9mBzWrdvXCcb5d87/c5HFGXl0PqdP5ttzWK9gZ++O0lS4kX6D4/CP6iB\n2dYWwhbJeZiFEKKCTCYT3xzLZvlvmUzs1JjeYR5mX//c4hU0f3WKWde1VT2aNqRFI2fe+jGZA6l5\nPNvBn183JXAlt4CRT3fCs5G6qwZak6BxQ9gRO4rwPz+Ng1dDs6xp76Dj/ocjOHU0g28+P0C7rsF0\n7BaKtg7MhgthDjKSIQCZpVJJslcjv6iEv35/lrW/pbBwULjZm2WAnO17wWTC675OZl/bVvm5OjJ/\nQBhNtCaW/msnqVdyGf1MZ2mWf8fR2wPfAfeR8p81Zl87vLUvjz3bhaTTF/no/7ZyLV++EKiKvPfb\nFmmYhRB1ztmc6zy7NgFfV0eeCC6s9AVIKurc4hWETBxZ50cMfs9kMnFk73n0v56nw/1hfO/szurj\n2bd9Ia2uC3l6JCmfrsZQaP6G1tXdieHjO+LSQMuyRZW72IkQdZXMMAsh6pStpy+xJD6VZ+5pTM9m\n5j+qfNPVE2fYN3Ia3fd+jdZRLiABUFxsYOvaY2Sm5vHQmGgaetUnK1/P37adw7u+A9O7BeFci67e\nV137Rv8J3wH3ETB6oMX2kXg8k81rjhHbuxltOgbKL3eizpDzMAshxB0UG4ws2nWeZQczeLtfM4s2\ny3DjMthBTwyRZvm/Ll8qYMXiPRgNJkY/cw8NvW5cBbCRiwPz+4fh5qTjubUJpOQWKq7UejR5ZhRJ\ni7+06NH3Zq18GDWxEwd2p7Bp1VGK73DqPyGENMziv2SWSh3J3vKuFJYwY+MZMq7qee+hcJp41Cu9\nzxL5F2ZeJHPTDgIfH2z2tW1Rytkcli/eQ+v2jek3vA0ODv/7vvkvv/yCg52WqbFBDGvjw5++Pc3e\n81cUVms9PGLbo7HTcfHHeIusf/O17+FVnzGT78FQYuCrf+8lP09+aakJ8t5vW6RhFkLUasm513l+\nbQKtGjnzWp9QXBwtf3KglE++xn9IHxw83C2+L2t3ZN8FNqw4RP/hUbTrElLmR/4PNvfktftD+eeO\nFFYfzarzc80ajYaQSaNIWrzC4vtycLCj/4gomrVsxBcf7CEzLc/i+xTClsgMsxCi1tp3IY+3fkrm\nqY7+9An3rJF9lly7zvaYodzz7YfUbxJQI/u0RkajiZ83JXDmRBaDH2+Hh3fFz4KReVXPX7acoWWj\n+jzXNRC7OnzqM6O+mO0dh9Jh+T9xbdWsRvaZcCSDrWuPcf/DEYS39q2RfQpR02SGWQhR5908v/I7\n25N5tXeTGmuW4caFSjzuiarTzbK+qIRvlh0gMy2P0c/cU6lmGcDH1YEFA8O5VFDMzI2J5NXhq9Np\nHewJevIRzpnhctkV1TzSl6HjOvDDhhPE/3Smzh/pFwKkYRb/JbNU6kj25mU0mVi8J5UNJy6yYGA4\nkb5lN2vmzN9kMJD84ZeETBpltjVtTX5eIV9+GI+LqyOPPNGBes5lf+nxbvk7O+iYc38ozTzrMXX9\nKdKv1t3zBQc+9jBZm3dQmHnRrOuW9dr3DXBnzDOdOXU0k82rj2IwGM26byHv/bam3IY5Li6O8PBw\nmjdvzoYNG8p87PTp0/H19SUyMvKW23U6HdHR0URHRzN16tTqVSyEEHehLzEy94ckEnOu838Dw/Cz\n0PmV7yZz0w7sPRrQICay/AfXQjlZ+SxfEk94pC/3PxyBTle9YzI6rYaJ9wQwqJU3L64/TeLFAjNV\nalscGrrhP6QPKZ98XaP7dXV3YsRTHcm/WsQ3yw6i19fdI/1ClDnDrNfradGiBfHx8RQWFtKjRw8S\nExPvutju3btxcHBg3LhxHDlypPR2V1dXrl69WmYhMsMshKiOq0UlzPn+HA3q2fHn7sE42NX8B2h7\nBk4k5KkR+A7qWeP7Vi01OZe1Xxyk2wPhtG5v/nGUHecu8+7O88y4L5j2AW5mX9/aXTt7nj0DJtL9\n11XY1a9X/hPMyGAwsmXNMXKy8hn8eDvqu9TsL6JCWIJZZ5jj4+OJiIjA29ubwMBAAgMDOXTo0F0f\n37lzZzw9a25WUAghALLy9by44TTNPOsxu2eIkmb58v6jFGVcpFG/bjW+b9VOH8vkm2UH6ftIpEWa\nZYB7mzTg1d5NeOunZLaevmSRfViz+qGBNOwYSdrKjTW+b51Oy4NDWxMS5sWKxfHk5lyr8RqEUK3M\nv1UyMzPx8/NjyZIlrFy5El9fX9LT0yu9k8LCQtq3b09sbCw7duyocrHCcmSWSh3JvnpScguZtv4U\nD4R5MOmexmgreaUyc+V/7oMVBD89HK2d5U9bZ00O7T3PtvXHGTquPU3CvSv9/MrkH+nrwjv9m/Hp\n/jTiDmdWel+2LmTSKJI+/AqT0TzzxJXJXqPREHt/GDH3hvDlh3vJTJVzZVeXvPfblgq9s0+cOBGA\n1atXV+mymampqTRq1Ih9+/YxePBgEhMTcXS8/SOdyZMnExQUBIC7uzuRkZHExsYC/3thybZltm+O\n0FhLPbIt2xXZbtSiHa9uPsO9Da7hm3cZjcZHST0/r1pHwfZ4IhfMsqp8LL3tYPTnUPx5mkXrSDx3\nBN/Glt9/cMN6jPa5wrLfirhWZGBcBz927txpFXlYertr167YudZn+8J/YxcTUe31bqrM86M6BZF8\n/iwr/r2HR8bGENDEw2rysbXtm6ylntq+ffO/U1JSAJgwYQKVUeYM886dO5k3bx7r168HoEePHixc\nuJA2bdrcdcGkpCQGDhx4ywzz73Xq1InPPvuM5s2b33K7zDALISrjcHo+f9t2jqmxgXQNaaC0lhOv\n/B9aRwea/2WK0jpqislkYseWUyQez2LYkzG4ujvVeA2Xrxcza9ONczVP6RJQ6U8WbFX6N9+T8uka\nOn3zvtI6kk5f5NuvDtFveJsqfbIghGpmnWGOiYnh2LFjZGdnc/78eS5cuFDaLM+cOZNZs2aVu4Pc\n3FyuX78O3GimU1NTS48iCyFEVew9f4W/bTvHrB4hypvl4st5pH29ieAJw5XWUVNMRhNb1x4nOTGH\nkU93UtIsAzSoZ887/cM4l3udd7YnU2KsG+cK9unfg+vn07ny2wmldYSEeTH48XZsXHmEhCMZSmsR\noiaU2TA7ODgwb948unbtSq9evViwYEHpfRkZGWRk3Po/yZQpU+jSpQsJCQkEBgayYcMGTp48SXR0\nNFFRUQwZMoSPP/6YevVq9hu+onx//IhI1BzJvnJ+OpPLP7an8HqfUKIbu1Z7vermf/7ztXj37oqT\nX+0/ymYwGPlu5WFysvMZPr4jzvXLPsdyRVQn//oOOuY+2Iy8QgN/23oOfUntP1ew1t6O4AnDSFpS\n/QuZVPe17x/UkEeevHGBkyP7LlS7nrpG3vtti115Dxg+fDjDh99+5GTp0qW33bZo0SIWLVp02+0n\nT56sYnlCCPE/35/O4eNf05jXtxmhnup/8Tbqi0n+5GvaL/uH6lIszlBiZMNXhygpNjB0XAfs7XWq\nSwLAyU7LnPtvnD3jr9+fZc79oTgqOEtKTQoYM4ifFw7lemom9Rr7KK2lkZ8bI5/qSNwnv1JSbCC6\nc7DSeoSwlDJnmGuSzDALIcqyMSGHz/enM69vM4IaqhkD+KPUlRtJi9tIzMp3VZdiUSUlRtYvPwga\nDQNHtcXOChtSg9HE29uTyb1ezGv3h1LPShp6Sznx14VotDpa/PVZ1aUAcPlSASs//pV2XYJp3zVE\ndTlClMusM8xCCGENNpy4yLID6bzd33qaZZPJRNLi2n8Z7JJiA2uXHUCr0zLISptluHFVwJe7B+Nd\n34FXNp+lQG9QXZJFBY8fTuqXGyjJt45zIjfwcGbEUx05uDuFvT+fU12OEGZnne98osbJLJU6kn3Z\n1hzN4qtDmbzTP4wAC3zBrKr55+zYh6m4BK+e95i5IutRrDew5vMDODrZMXBkFDoLNMvmfP3rtBr+\n1C2IAHdHZm06w7Va3DQ7B/nheW8MF5ZvqPIa5n7vcWtQjxFPdeTIvvPs+fGMWdeujeS937ZIwyyE\nsFqrjmSx5lg27/Rvhr+bdV2ON+mDFYRMGlmlc9PbgmK9gdWf7ae+qyP9hrVBq7ONvy60Gg0vxAbS\n1LMeMzYm1uqmOWTSSJL/HYexpER1KaVc3Z0Y+VQnThxKZ9e2RNXlCGE2tvEOKCzu5gm+Rc2T7O9s\nzdEs1h7P5h/9w/B1tVyzXJX8r548S97RU/gN6WOBitQrLr5xZNnV3YkHh0ZatFm2xOtfq9HwbJcA\nwr2cmb3pDNeLa2fT3KBdBI5+3mR993OVnm+p9576ro4MnxDDycPpxG8/a5F91Aby3m9bpGEWQlid\ndcezWX00m3f6hdHIpfqnLjO3pCVfEvTEUHRO1nXU2xxuzizXd3W40SxrbfMIukajYUqXAIIbOvHq\nlrMU1tJTzoVMHMm5JStUl3Gb+i6ODB8fw5F9F9j3S5LqcoSoNmmYBSCzVCpJ9rfacOIicYczebt/\nM3xcLd8sVzb/oqwcMr/bTtDYwRaqSJ2SEiPffHEQp3r29K2hZtmSr3+tRsPzXQPxrm/PnO/P1srz\nNPs8eC/6i7nk/nrnq+uWxdLvPS5uTgwfH8PB3ckc3JNi0X3ZInnvty3SMAshrMbGkxdZ8VsGb/cL\nw8+CYxjVkbJ0FX4P98bBU+0VBs2tpMTIui8O4uBgZ1Mzy+W58UXAYFwddPxt2zmKDbWradbodIQ8\nNYKkxdZ3lBlufBFw2PgY9m4/Kxc3ETZNzsMshLAK35/OYem+dN7p14zGii63XB5DQSHbY4bQaf0S\n6ocGqi7HbAwGI+tX/IZGo2HAyCh0taRZ/r0So4k3tp1DA8zu1QQ7Gx01uZOSawVsjxlK540f4Rzc\nWHU5d5R78RpffbSXex8IJyLaOmsUdYuch1kIYXN+OXeZj/emMe9B622WAVLjvqNBTGStapZNRhOb\nVx3FUGJkwIja2SwD2Gk1zOoZQrHRxFs/JWEwWsWxIrOwq+9MwOiBJP87TnUpd9XQqz7Dnozh502n\nOHk4XXU5QlRa7XxnFJUms1Tq1PXs913I492d53njgaZKLkpS0fxNRiNJH35Vqy5UYjKZ2Lr+OHlX\nrjNoTLRFzrNcnpp8/TvotLzaqwl5hQbm70jBaB0fsJpF8JOPkPb1Joov51X4OTX93uPZyIVHxnXg\nhw0nOH08s0b3bY3q+nu/rZGGWQihzNGMfN76KZm/9m5CMy9n1eWUKWvLL9i7udCwU5TqUszCZDLx\n8+ZTZKbmMfix9tjX8ktJ3+Rgp+W1PqFkXdWz8JfztaZpdvJvhHfvLpxftk51KWXy9nNl6Nj2fL/m\nGGcTslWXI0SFyQyzEEKJUxcLmL3pDDPuC6Z9gJvqcsoV/9AzBD0xFL+He6suxSz2/HSGk4fSGfFU\nR+o5W9+p+yzterGBmRvP0MyrHlM6B9SKC9DkHUlg/+Mv0z3+a7QO9qrLKVP6+cus/uwA/Ye3ISTM\nS3U5og6SGWYhhNVLzr3OXzaf4YXYQJtoli8fOM711Ex8BtynuhSzOLArmaP7UnnkiQ51slkGqGev\n480Hm5KQXcBHe9NUl2MWbpHNqR8aSMb6H1SXUi6/wAY8NCaab786xIWkXNXlCFEuaZgFILNUKtW1\n7NPzipi56QxPdWxMbIj6U7NVJP+kxSsIeWo4Wju7GqjIso4eSOXXHecYNr4DLm7qv2Cp8vVf30HH\nmw80Ze+FPOIO1Y6Z2pCJo0havIKKfHis+r0nIKQh/UdEse6Lg2SlV3z2urZQnb+oHGmYhRA15uI1\nPX/emMjIKB96h3moLqdCClLSydnxKwGjB6oupdpOHc1gx+ZTDHuyA+4NrXtmvKa4Odnx9websv7E\nRTaevKi6nGrz7t0Zw/VCLu06qLqUCgkJ86LXoFas/s9+cnOuqS5HiLuShlkAck17lepK9pevFzNj\n4xBd5rkAACAASURBVBn6t/BiUCtv1eWUKi//pCUrCBgzCDvX+jVUkWWcO5XN1rXHGTq2PR7eLqrL\nKWUNr3+v+g7M69uU/xxIZ8e5y6rLqRaNVkvw0yMrdCETa8geoHmkL517NuPrT/aRn1eoupwaYy35\ni4qRhlkIYXHX9AZmbTpD12B3RkT5qC6nwvQ5l0lftZngCcNUl1ItF85d4ruVR3j4sWga+Vv/zLgK\njd2deKNPU97deZ6DqVdVl1MtjYf15cqBY+QnJqsupcKiOgbSJiaAr5fuo/B6sepyhLiNNMwCkFkq\nlWp79kUlRv6y+QwRPvUZ18FPdTm3KSv/lE9X49PvPpx8reeIeGVlpuWxdvlvDBjRBv+ghqrLuY01\nvf6beTnzl15NmPtjEgnZtjseoKvnSODjg0n+sOwLmVhT9gAdu4cSHObF6v/sR68vUV2OxVlb/qJs\n0jALISzGYDTx9x+T8HZx4BkbO3WXoaCQlKWrCHnGdi9UcvlSAWs+28/9D7UiuJmcuqsi2vi58OK9\nQby65SwpubY7HhD05FDS125Fn2M7IyYajYb7HmxOQy9n1i3/DUOJUXVJQpSShlkAMkulUm3N3mQy\nsWjXBa4XG5jeLQitlTbLd8s/9atvadChNS5hITVbkJkU5OtZtXQfne5rSnhrX9Xl3JU1vv47B7sz\noaM/MzclkpWvV11OlTh6e+DTrzvnP1tz18dYY/YarYYHBrdGp9Oy8evDmGrRJcz/yBrzF3cnDbMQ\nwiKW/5bJiexrvNo7FHudbb3VmAwGzi1eQZPJY1SXUiV6fQmrP9tPeKQv0fcEqS7HJt0f5snQyEbM\n2JjIZRudqQ2ZOJKUpasxFBapLqVStDotA0ZGkX+1iG3rT1ToFHlCWJpt/S0mLEZmqdSpjdlvSshh\nU0IObzzQlPoO1n3J5Tvln/ntdhwbedKwYxsFFVWP0WBkw4pDeDZyIfb+MNXllMuaX/9DWjfi3iYN\nmL35DNf0BtXlVJpri1BcI5qRvub7O95vzdnb2+sY/Fg70s5fZte2RNXlWIQ15y9uJw2zEMKs4lOu\nsHRfGnMfbIqns3VfnvdOTCYTZ99bRpMptnd02WQyseWbY5hMJvoMjrCpmXFrNa69H+Fezsz5/ix6\nG5ypDZk0iqQlX9rkUVpHJ3uGjmvPyUPpHNiVpLocUcdJwywAmaVSqTZlfzLrGv/4OYU594cS2ED9\nVeQq4o/5X9p5AENBAY362N6fy86tiWRnXGXgqLbobGQMxtpf/xqNhme7BOLmZMfb25Mx2ljj6dkt\nBjQacrbvve0+a88eoL6LI4882YG9P5/j5OF01eWYlS3kL/7HNt5RhRBW78KVQuZ8///s3Xd4VFX6\nwPHvTHrvvfeEEiAJIF3pICJVLBTFgj/rrm1trF1RV8WyFtZV7AIigiBdkd4hhUB6771PJpO5vz8Q\nd1kxJGFm7szkfJ7HRwZmzn3zPjd33jnz3nNyeWhMMHHeprvJR94/vyLsnltQKE3r8ph8pJBzKWXM\nWZKItY3pb+FtTCyUCv42LoT6Ng0fHi4xqdlahUJB6LIbyevGRibGysXNnjlLEtn941kKc2rkDkfo\no0zrHUHQG9FLJR9zyH1tawdPbsthSaIfI0Jc5A6nR/47/03p2TSlZ+M/d4qMEfVcVnoFB3/OYd6t\nSTg42sgdTo+Yyvlvbank2UlhnC5tYl1qpdzh9Ij/7Ek0n8ulMS3zor83ldwDePs5c92Ng/jx22Sq\nyk17Y5kLTCn/giiYBUG4Qq3qTp7ensOkKHemxZr2Wr95739FyB3zUdpYyx1Kt5UU1LFjwxlmL0rA\n1cNe7nDMmqONJS9NjWDjmSp2ZdXKHU63KW2sCb1zAXn//EruUK5IcIQHE2bE8f1nJ2isb5M7HKGP\nEQWzAIheKjmZcu47OrW8sDuPKE97Fg4x3rV+u3Ih/21FZVTtPkTQ4lkyR9R9NZXNbPzyFNPnD8Q3\n0LRm9i8wtfPfy8Gal6ZGsOpICSeKG+UOp9uCFs+i+tejtBaU/P53ppZ7gNhBfiSOCuG7T4/T1mqa\na2RfYIr578tEwSwIQq9IksRb+wqxtlDywKggk1+RIf9fawm4cQZWLk5yh9ItzY0q1q8+zrhpMYRF\nm+7W3aYo1M2O5RPDWLGngOzqVrnD6RZLJwcCb5lJ/gem28t8QdLoMMJivPjhi5N0dJjecn+CaRIF\nswCIXio5mWruPzlWSmmjmifGh2KhNN1ief/+/ajrGild+xOhd94gdzjd0q7qYP3qEwwaHkz/hAC5\nw7kipnr+D/R15IFRQSzfkUtZk2lsDBJ65w2U/bCT9qrz7SSmmnuAq6fG4ORiy09rUtCa6G6Appz/\nvkgUzIIg9NgPZ6o4UNDA85PDsbU0/ctI0Wff4zV5DLb+3nKHclkajZYfvjhFYKgbw8aGyR1OnzYm\nzJUbB/nw1LYcGlQaucO5LBtvD3xnTqDwk+/kDuWKKZQKps6LR6Xq4GexG6BgAArJSM6y3bt3k5CQ\nIHcYgiBcxt7cOj48XMKb10Xh62RaKzJcSqeqnV+HzmXo2rdxiouQO5wuSVqJzWuSkSSJGTcORmnC\nM/vm5N/HSkkubeLV6ZHYWRn3zpYtecUcvvZOxh39DktH013+8YJ2VQffrjpKTLwvV11t3L+/gnE5\nefIkEyZM6PbzTX9qSBAEg0kpa+Ldg8W8MCXcLIplgNJ1W3EZFGv8xbIksWfrOVqa2pk+P14Uy0Zk\naZIfga62vPxzPp1G3h7gEBaIx+gkir7cJHcoOnFhN8CUY8WknSiWOxzBjImCWQBEL5WcTCX3ebVt\nvLg7nyfHhxJhJsuXSZ2dpL/5iUlsg318fz75WTXMWpSApZHPYvaEqZz/XVEoFDw0JphOSeKdA0VG\n3x4Qdt9CClatYd8ve+QORSccnW2ZuySRvdszycuskjucbjOHc78vEQWzIAiXVdms5untOfzfiECG\n+JvGKhLdUbFtHwpHe9yuGix3KF1KP13KyYMFzLstCVs7K7nDES7BUqng6fFhZNe08sXJcrnD6ZJL\nfAwOUSFo9p2SOxSd8fB25PpbhvDT2hTKihvkDkcwQ6JgFgCxHqScjD33jSoNT23LYfYAb66JcJM7\nHJ2RJIm8d78g/vG7jXpJvILsavZsOcfcWxNxcrGVOxydM/bzvyfsrS14cXIEu7Nr2XKuWu5wuhR+\n/yIsdxxB6jSfZdkCQtyYMmcAP3xxkrqaFrnDuSxzOvf7AlEwC4Lwp9o1Wp7dmUtSoBPzBhr/ChI9\nUfPrUTQtbfhMGyt3KH+qorSRzWtSmHnzYDx9zGdm35y52Vvx8tQIvjhRxqEC453pdB+ViKWzExVb\nfpU7FJ2K7OfDyPERrP/0BC3NprHcn2AaRMEsAKKXSk7GmvtOrcSKX/LxcrTmzuGmvdbvpeSs/Izw\nBxZx4OBBuUO5pPraVjZ8foJJ1/cjMMxd7nD0xljP/ysR4GLLs5PCeXNfIWcrjXOmU6FQ0D55KDlv\nf2b0Pdc9NWh4MLGD/Pj+sxOo2413uT9zPPfNmSiYBUH4A0mSeP9QMS0dnTw8NhilEbcs9EbdkWRU\npZX4zZ4kdyiX1NqiZv3q4wwfF070ANPccryvi/V24NFxwTy7M5eiepXc4VySRWIcSBJVu4zzQ+OV\nGDUxEi9fJzZ9c5rOTq3c4QhmQBTMAiB6qeRkjLn/NrmCMxUtPDMxHGsL87tM5Lz9OWH3LURpaWl0\n+VerNWz4/ATR/X0ZMiJE7nD0ztjyr0vDglxYOtSfJ7flUNPaIXc4fzBmzBjCH1hMrhnOMisUCibP\n6o9CoWDHhjNG+fOZ87lvjszvnVAQhCuyI7OGn87V8NLUCByszWf5sgsaUjJoOptN4ILpcofyB9pO\nLZu/Tcbdy4HRk6PkDkfQgSnRHkyN8eDp7Tm0qI3vBjvf665BXddI7UHzWTHjAqWFkutuGkRNZTMH\ndmbJHY5g4kTBLACil0pOxpT7o0UN/PtYKS9PjcDD3jyXL8t9+zPC7r4JpY01YDz5lySJnRvT0Wol\nJs8eYNQrd+iSseRfn24e7EOslz3P78qjw4jaA/bv34/CwoLw+xaS+/ZncoejF9bWlsxZnMi51HJO\nHy6UO5yL9IVz35yIglkQBAAyqlp4/ddCnpkYTpCr+S1fBtCcmU/dkWQCF14vdyh/cHB3NpVljcy8\naTAWZtgG05cpFAruGxmErZWSN/YWojWy9gD/eVNpySmk/mS63KHohb2jNfNuTeLQLzlkpVfIHY5g\nosRVWQBEL5WcjCH3JQ3tPLMjl4fGBNPPx0HucPQm953PCbljPpYOdr//nTHkP/lIIWdPlzFnSSLW\nNpZyh2NQxpB/Q7BQKnjimlDKm9R8cqxU7nCA/+ReaWVJ2D23kPv2ankD0iNXD3tmL0pgx/dplBTU\nyR0O0HfOfXMhCmZB6OPqWjt4ans2ixP9GBHiInc4etNaUELVz4cIvm2u3KFcJDu9goM/5zDvtiQc\nHG3kDkfQI1tLJc9PDudgQQMb0irlDucigTdfR8OpszSdzZE7FL3xDXRh+g3xbPzyFDWVzXKHI5iY\nyxbMa9euJTo6mpiYGDZv3tzlcx955BF8fX0ZOHBgr8cQ5CF6qeQjZ+7bOjp5ekcO4yPcmR7rKVsc\nhpD77hcELZ6FlcvFG4DImf+Sgjq2f5/G7EUJuHrYyxaHnPratcfZ1pKXp0awLqWSvbnyznT+d+4t\n7GwIXXYjOW+tli8gAwiL9mLstBjWrz5Oc6O8y/31tXPf1HVZMKvVah5//HEOHDjArl27+Mtf/tLl\nYHPnzmXLli1XNIYgCIah0Uq8sDuPSA97FiWY91q/bUVlVGzZQ+hdN8odyu9qKpvZ+NUppt8Qj2+g\n+c7sC3/k62TDC1PCefdgMSllTXKH87ugW+dQe/AkTedy5Q5FrwYkBBA/LIj1q0/QrjK+5f4E49Rl\nwXzkyBH69++Pl5cXQUFBBAUFkZyc/KfPHzFiBB4eHlc0hiAP0UslHzlyL0kSb+4rxFKp4IFRQWa/\nIkPOO58TtHgW1u5/LEzlyH9zo4r1q48zdmoMYdFeBj++Memr154ID3uevCaUF3fnk1fbJksM/5t7\nSwc7Qu++iZy3PpUlHkMaPi6cgBA3fvjyFBqNPCuX9NVz31R1WTBXVFTg5+fHRx99xLp16/D19aWs\nrKxHB9DFGIIg6NYnx8soaVDx5PgwLJTmXSy3FZVRsfkXQpfdJHcoALSrOli/+gSDhgUxIMH8thwX\num9IgBN3XxXA09tzqGxWyx0OAMG3zaH2wEmaM/LkDkWvFAoF46+Lw9bWim3fpSJpjWvlEsH4dOum\nv2XLljF//nyAXs9E6WIMQX9EL5V8DJ37jWeqOJBfz/OTI7C1NP/7fnPf/YLAhddfcnYZDJt/jUbL\nD1+eIiDUjWHjwg12XGPW16894yPdmdXfi6e259DcrjHosS+Ve0sHe0KXLSC7D8wyK5UKpi+Ip6mh\njV+3ZRj8+H393Dc1Xa5f5Ofnd9FscHl5OX5+fj06QE/GuOeeewgODgbAxcWFgQMH/v6VxYUTSzzW\nz+PU1FSjikc81s9jbUB/1iRXcLNvA6nHD8sej74fJ4ZGUv7jz1i/8Veq9u+XNR5JkqgvdsLWzgob\ntxoOHDgge37EY+N47NuQhS/WPLMzj1emRnD08EGDHP+C//33klh/Wt/9gubMfByjQ2XPjz4fW1lZ\n4BfVwZnDBTg625I02nA/7wXGlA9zfnzhz4WF5zewueOOO+gJhdTFButqtZrY2FiOHDmCSqVi/Pjx\nZGWd317yiSeeQKFQ8PLLL1/0mvz8fK677rrfC7Cuxvhvu3fvJiEhoUfBC4LQfSllzbywO48V0yKI\n6CMrMpx57HUsnR2IefoeuUPhly1nqShpZN5tSVhamd+W48KV0UoSr/ycjxZ4anwoSpm/ic1553Oa\nz+Yw6IPnZI3DUBrr2/jmoyOMmxZDbHzPJgYF03Ty5EkmTJjQ7ed3+X2stbU1K1asYNSoUUyYMIGV\nK1f+/m/l5eWUl5df9Px7772XkSNHkpGRQVBQEJs3b+5yDEEQDCOvto0Xd+fx5DWhfaZYbiupoPzH\n3YTdLX/v8rF9eeRn1TBrUYIoloVLUioUPDouhIY2DR8eLqGLuSyDCFk6l5q9x2jOypc1DkNxdrVj\nzuJEdv94lsKcGrnDEYxQlzPMhiRmmOW1/7++rhYMS9+5r2xW89cfM7ljmD/XRLjr7TjGJv3xf2Dh\nYEfM8nu7fJ6+83/2dCl7t2dy07LhOLvaXf4FfYy49lysuV3DQ5uzmBjlzg3xPno91uVyn/P2ZzRn\n5jHon8/qNQ5jUphTw4/fJnPD0qF4+Tld/gVXQJz78tLpDLMgCKatqV3DU9tzmN3fq08Vy20lFZRt\n3EXY/90saxwF2TX8suUcc5YkimJZ6BZHG0temhrBpvQqdmXVyhpLyNJ51Ow52mdmmQGCIzyYMCOO\n7z8/QWO9PMv9CcZJzDALgplq12h5Yms20V723H1VoNzhGFTao69i5eIka+9yRUkD360+wcybBxMU\n1nc+rAi6kV/XxmNbsvnb1SEkBjrLFkfOO5/TdCaLwR+9IFsMcji+P5+UY0XctGw4dvbWcocj6IGY\nYRYEgU6txMs/5+PtaM1dw/vWWr+t+cVUbNlD2L0LZYuhrqaF7z8/yeRZ/UWxLPRKqJsdyyeGsWJP\nAdnVrbLFEXL7fOoOnaYxLVO2GOSQNDqUsBgvfvjiJB0dnXKHIxgBUTALwB+XuREMR9e5lySJlfsL\n6dBqeXhssOx32xta9j/+Tcjt87F2696snK7z39LUznefHmfkhEii+uu3B9UciGvPnxvo68gDo4JY\nviOXsqZ2nY/fndxbOtgRdv9Csl79l86Pb+yunhqDk4stP61JQauHjU3EuW9aRMEsCGZm9fEy8utU\nLJ8QhpVF3/oVbzqXS/Weo4TetUCW47erOvhu9XEGJAQwaFiQLDEI5mVMmCs3DvLhqW05NKg0ssQQ\ntGgWTenZ1J9Ik+X4clEoFUydF49K1cHPP56VfeUSQV6ih1kQzMiGtEp+PFvNW9dF42JrKXc4Bnfq\n9idxTRxA2D2Gv9lP09HJ+tUn8PBxZMJ1cWJHU0Gn/n2slJSyJl6dHiXLDp1FX26k7IddDPvuXYMf\nW27tqg6+XXWU2Hhfhl8dIXc4go6IHmZB6KN+yallXWolr0yN7JPFckPyOepPpBF821yDH1urldiy\nNgV7R2vGzxDFsqB7S5P8CHC24aXdeWj00B5wOQELrkVVXE7N/uMGP7bcbGytmHtrIslHi0g9USx3\nOIJMRMEsAKKXSk66yP3x4kY+OFTCS1Mi8HHqm3d0Z61YRcSDS7Cws+nR6640/5IksXtTOu0qDdPm\nx6NUimK5J8S1p3sUCgUPjQ0B4M29BWh18OVwT3KvtLIk8tE7yHzloz7ZmuDobMu825LYvyOLrPQK\nnYwpzn3TIgpmQTBxGVUtvLqngL9PDCPMvW+u9Vt3JJmW7AICb5lp8GMf3J1NeXEDsxYOwVKGr8qF\nvsNSqeCpCWGUNan5SIbdAP1mTaSzpY2qnQcNelxj4e7lyOzFCezYcIbCXLEbYF8jepgFwYQV1at4\ndEsWD44OZkSIi9zhyEKSJI7OvpeAG68l8MZrDXrs04cLOX4gn5uWDcfBsWcz24LQW83tGh7ZksXY\nMDduHuJr0GNXbP2V7H98wsidn6JQ9s0PiBd2A5x7ayK+AX3zumsORA+zIPQRNS0dPLkth1uT/Pts\nsQxQtesg6po6/OdNMehxM1LLObwnh3m3JYliWTCo87sBRrI9s4bNZ6sNemzvqWNRWltRtmGnQY9r\nTIIjPJg8uz8bPj9JbVWz3OEIBiIKZgEQvVRy6k3uG1UantyWzbVxHkyN8dBDVKZB6uwk88X3iXn6\nHpSWvbvRsTf5L8iuYfemdOYsScTV3b5XxxXOE9ee3vGwt2LFtEi+OlXOnpy6Xo3Rm9wrFApilt9L\n1opVaNvVvTquOYjq58PoyVF89+lxmhpUvRpDnPumRRTMgmBi2jo6eXp7DgkBTiyI79sbY5Ss2YqV\nmzNek0cb7JilhfVsXpPMdTcPxttPvi2LBcHP2YaXpkTw/qFijhc3Guy47iOH4BgbTsGn6w12TGM0\nMDGQISNCWPfJMdpa++6Hh75C9DALgglRa7Q8vSMHPycb/jI6qE8vX9bZqmLvqAUM+fglXBMHGOSY\nVWVNrPvkGFPnDSQ8xssgxxSEyzlT3syzu/J4fnI4cd4OBjlm07lcjs29jzEHvsXKtW9/cNy7LYPC\n3FpuuH0o1jZ9b0lPUyV6mAXBTGm0Ei/9ko+LrSUPjOrbxTJA/sdrcU0cYLBiua66hfWfHWf8dXGi\nWBaMSn9fRx4dF8wzO3LJr2szyDGdYsPxnjqG3He/MMjxjNmYKdF4+Tqx8atTaDRaucMR9EQUzAIg\neqnk1J3cayWJN/YW0KmVeGxcCBZ9fK1fdU09+R9+Q/STd1/xWN3Jf2N9G+s+OcbICZHExvtd8TGF\n/xDXHt0YFuTC3VcF8OS2HMqb2rv1mivNfeSjd1D89Y+0FZdf0TimTqFQMGlWf6xtLPlpbQrabm4s\nI8590yIKZkEwcpIk8d7BYiqbO3h6QhhWFuLXNmflavyun4hDeJDej9XS3M66T46RMDKE+KH6P54g\n9Nb4SHduiPfh8a051LZ26P14tr5eBC2ZTdZrH+v9WMZOqVRw7YJBqNo62LXxTJ/c3MXciR5mQTBy\nnxwr5URJI69Nj8LB2kLucGTXWlDCoWl3MPrXr7DxctfrsVRtHaz9+Cjhsd6MnhSl12MJgq58eaqc\nvbl1vH5tFC62+u2p1TS1sHfEDSStWYlzf/E7om7XsO6TY/gHu3L19Ng+3zpnzEQPsyCYkTXJFRwq\naODlqZGiWP5N5ssfEnrnDXovltVqDd9/doLAUHdGTYzU67EEQZduGezD8GAXntiaTXO7Rq/HsnRy\nIOIvt5L54vt6PY6psLaxZO6tSRTl1XFgZ5bc4Qg6JApmARC9VHL6s9z/mF7FT+eqWTEtUu+zRKai\n7kgy9cfTCLnrRp2Nean8azRaNn55CjdPB665VswS6ZO49uieQqFgaZIfA3wdeWp7Dq3qzks+T1e5\nD1o8i9bCMqp29c0ts/+XrZ0V825LIiu9ksO/5Pzp88S5b1pEwSwIRmh3di3fnK5gxbRIPBys5A7H\nKEhaLWeXv030U/+HpYOd3o6j7dSyZU0y1jaWTJndH0Ufv8FSME0KhYL/uyqAUDc7ntmZi0qPqzco\nra2IffZ+zj37Dlq1/nunTYG9gzXzlyaRdrKE4/vz5Q5H0AFRMAsAjB5tuI0fhIv9b+4PFtSz6kgJ\nL0+LwM9ZbLl8Qcman1DaWOE3e5JOx/3v/Etaie0b0uhQa7h2wSCU4gZLvRPXHv1RKBQ8MCoITwcr\nnt+Vi7rz4qJZl7n3mjgSuyB/Cvv4Zib/zdHZlhtuH8rJQwWcPlL4h38X575pEe8GgmBEDhc28Na+\nIl6YHEGom/5mUU2NpqmFrBWriHv+Qb21R0haiR0/nKGhto2ZtwzB0lJcHgXTZ6FU8MjYEGwtLXjp\n53w03VzyrKcUCgWxzz1Aztufo67u3Vbd5sjZ1Y4blg7lyJ5c0k6WyB2OcAXEO4IAiF4qOV3I/dGi\nBt7YW8gLk8OJ9rKXOSrjkvP2Z3iMG4bLkH46H3v//v1IksSuTenUVjUzZ0ki1taiZ9xQxLVH/yyU\nCp64JgStVuLVPfl0/lY06zr3jtGh+M+ZJJaZ+x+uHvbMuy2JfdszOZdS9vvfi3PftIiCWRCMwPHi\nRl7/tZDnJoUTa6CtbU1Fa34xxV//SPRTV75JyaVIksTuH89SWdbInCVJYmtbwSxZWShZPiGMRlUn\nb+0rRKunFWUjH7mdip/20JSerZfxTZWHtyPzbk3i581nyT5bKXc4Qi+IglkARC+VnBzCBvHqngKe\nmRhGPx9RLP+vc8+9R+jdN2Hr46nzsSVJoqPek/LiBubdloSNWI3E4MS1x3CsLZU8OymM0sZ23jtY\nzKhRo3R+DCtXZyIfXsrZ5SvF5h3/w8vPiTmLE9n+fRr5WdXi3DcxomAWBBkllzbx8i/5LJ8QxgBf\nR7nDMTo1+47TdCab0LsW6HxsSZLY89M5SgrrfiuWxWokgvmzs7LghSkRZFW3supIiV6K2sBF16Ou\nqafip191Prap8w10YdbCIWxZk0xhTo3c4Qg9IApmARC9VHJIKWvmxZ/zud6riXg/USz/L626g/Qn\n3yT2ufuxsNXtaiGSJLF3WyZFeXUExXViayeKZbmIa4/hOVhb8NKUCA5ml/OhHopmpaUlcS/+lXPP\nvIOmpU2nY5uDgBA3rrt5MN9/cYyCbFE0mwpRMAuCDM6UN/PC7jyevCaUUAf9rY9qyvI/+gb7EH+8\np47V6biSJLF/Rxb52dXMX5qEpbVYZ1noe5xtLVkYpCK9ooX3D+m+aPYYnYjbsHhyVq7W6bjmIjjc\ng+ghdmz+9jT5WdVyhyN0g0Iykiaj3bt3k5CQIHcYgqB36RUtPLMzl79dHUJSoLPc4Ril1sIyDk1d\nyoitH2MfEqDTsQ/syiIrvYIbbh+GvYO1TscWBFPTou7kia3ZRHnac+/IQJQ6XLaxvbKG/VcvYviG\nf+IYE6azcc1JcX4dG786xfT5AwmL9pI7nD7l5MmTTJgwodvPFzPMgmBA5yrPF8uPjgsWxXIXzi1/\ni9C7Fui8WD64O5vMtArmLx0qimVB4Hx7xivTIsmpaePdA0U6XT3DxtuDyIeXcubxf4gbAP9EYKgb\nsxYO4ad1qeRmVMkdjtAFUTALgOgjNISzlS0s35HLQ2OCGRbk8vvfi9xfrHL7PlpyCgn7v5t1NqYk\nSRzcnc25lDJuuH0oDo7/6YkW+ZeXyL98LuTewdqCl6dGUFCn4u39ui2ag2+dTWdLK6XfbdPZvoDX\nmQAAIABJREFUmObiQv4DQtyYvSiBrd+lkiOWnDNaomAWBANIKWvi7zvOzyyPCHG5/Av6KE1LG+lP\nvUW/Vx5BaaObGWBJkti7PZPMtHIW3DEMByex3bgg/C97awtemhpBcUM7b+4t/H1zkyulsLCg/6uP\nkvnC+3TUN+pkTHPkH+zKnCXnl5zLTq+QOxzhEkQPsyDo2bGiRl77tYAnx4cyxN9J7nCMWsZLH6Aq\nLmfQB8/pZDxJK7F781nKiuqZd1sSdvaiDUMQutLW0cnfd+Ti5WDFw2NDsFDqpqf5zN9eB6D/q4/q\nZDxzVV7SwPerTzDx+n5ED/CVOxyzJnqYBcGI7M+v57VfC3h2Upgoli+jOSOP4q9+JObZ+3UynlYr\nsX1DGlVljdxw+1BRLAtCN1xYp7mmtYPXfy3Q2Uxz9BPLqNy6l/qT6ToZz1z5Brgw97Ykdm1KJyO1\nXO5whP8iCmYBEH2E+vBzdi3vHijipakR9Pf583WWRe5B6uwk9aGXiXr0dp3s6NfZqWXLmmQa61XM\nvcymJCL/8hL5l8+f5d7WUsnzkyOoV2l4dU++TopmK1dnYp69n7SHX0Gr7rji8czBn+Xfx9+Zebed\n30b7XEqZgaMS/owomAVBD7Zm1PCvo6WsmBZJtKe93OEYvYJ/f4fSyoqgJbOveCxNRyebvj5Nh7qT\nOYsTsLYW210LQk/ZWCp5flI4LWotL+zOQ9155evF+82ehF2gL7nvfK6DCM2bt9/5ovmXLedIPVEs\ndzgCoodZEHRuQ1ol36VW8ur0SAJdbOUOx+i1FpRwaNodXLV5FQ7hQVc0Voe6kx++PImNrSXX3jAI\nC0sxJyAIV6KjU8uKPQU0t3fy7KQw7Kwsrmg8VVkVByYsYdj6d3GKi9BRlOartrqFdZ8cI2lUKImj\nQuUOx6yIHmZBkNG3yeX8cKaKN2ZEiWK5GyRJIu3hFYTfu/CKi+V2lYb1q4/j4GTDjAWiWBYEXbCy\nUPLkNaF4O1rxxNYcmts1VzSerZ8X0U8uI+2vL6PVXNlYfYG7pwM33TWc04cLObg7W6xnLSPxjiIA\noo/wSkmSxKfHS9mZWcsbM6Lw7cHSZX0598VfbULT1ELIsgVXNE5bq5p1nxzDw9uRaXMHorTo/qWt\nL+ffGIj8y6e7ubdQKvjrmGBivO15ZEs2dW1X1oMceMtMLBztKVi19orGMXXdzb+zqx033jWcrDMV\n7NmaIYpmmYiCWRCukFaS+PBwCUcKG/nHjCg8xQ5y3aIqrSTz5Y8YuPIplJa97zNublSx9uNjBIS6\nMfH6fih0tAyWIAj/oVQouHt4ACNDXHh4cxYVTepej6VQKBjwxuPkvvcFLblFOozSfDk42bDgzmGU\nFtSx/fs0tDroKRd6RvQwC8IV6OjU8o+9hVQ2q3l+cjhONuIGs+6QJImTix/DZVAskY/c3utx6mpa\n+O7T4wxICOCqayJQKESxLAj6tiGtknWplbw0JYIwd7tej5O/ag0VP/3KsO/fQ6EU83fdoW7XsOnr\nU1haWnDtjYOwusKe8r5M9DALgoG0dXTyzM5cVB1aVkyLFMVyD5Ss+Ym24nLCH1jc6zHKSxr4dtVR\nho8LZ8T4SFEsC4KBzB7gzZ3D/PnbT9mklTf3epyQ2+chdXZS8O91OozOvFnbWDJ7USKWVhZ898lx\nVFfYHiN0nyiYBUD0EfZUfVsHj/2UjYe9FX+fGIbNFdxg1tdy31pQQsbz/2TQ+8+itP7z9ZG7UpBd\nzfrVJ5g4sx/xQ6/sZsG+ln9jI/IvnyvJ/TUR7jx2dQjP7crjUEFDr8ZQWFgQ/+5yct76jKazOb2O\nxVT1Nv8WlkquvSEenwBnvl11hOZGlY4jEy5FFMyC0EMVTWoe2pxFgr8TD40J1tnWsX2B1NlJyv0v\nEP7Aol4vKXUupYzNa1KYefNgovr76DhCQRC6KynQmRenhPP2/kK2ZtT0agz70EBinv4/Uu57Hm17\n7/ui+xqFUsE118YSN9ifrz86Qm1V72f6he4RPcyC0AOZ1a08syOXG+K9mT3AW+5wTE7O259Rs+84\nQ9e+3eOeRUmSOL4/n5MHC5izOBEvP7HVuCAYg+IGFU9ty2FCpDuLEnx73B4lSRKnlj6BQ3gQMcvv\n1VOU5ivtRDF7t2cy8+YhBIa6yR2OyRA9zIKgJ0cKG3hqWw73jgwUxXIvNJw+S8GqNcS/s7zHxbJW\nK/Hzj2c5c6qEm5YNF8WyIBiRQBdbVl4XzbHiRl7fW0hHD1dwUCgUDHj9b5Su307twVN6itJ8DUgM\nZPr8eDZ+dUpspa1Hl33XWrt2LdHR0cTExLB58+ZePdfCwoIhQ4YwZMgQ/vKXv1x51ILOiT7Crm0+\nW81b+wp5fnI4o0NddTp2X8h9Z6uKlPueI+6lv2Lr37MPG2q1ho1fnaKmqoWb7hqOs2vv78q/lL6Q\nf2Mm8i8fXebezd6K16ZH0tLeyVPbc2hRd/bo9daebgz4x+OkPPACHY19o71Al/kPjfJk/tIkft2a\nwdG9eWKtZj3osmBWq9U8/vjjHDhwgF27dnVZ7Hb1XHt7e06dOsWpU6dYuXKl7qIXBD3TShL/PlrC\n+tRK3pgRTZy3g9whmaSM59/DeVAsfrMm9eh1LU3trP34GLZ2lsxdkoiNbe9uEhQEQf/srCz4+8Qw\ngl1t+euPmVQ296wn2WviSLwnjiT9iX/oKULz5u3nzE3LhpN+uoRdm9LFWs061mXBfOTIEfr374+X\nlxdBQUEEBQWRnJzc7eempKToJWhB90aPHi13CEZHpdHy0s/5pJa3sHJmNAEu3d+9ryfMPfflm3+h\navch+r38cI9eV1XexFcfHiYs2pOpcwfqbatrc8+/sRP5l48+cm+hVHDviEAmR7nz4KZMzlW29Oj1\nMX+/j6bULIq/6fobbXOgj/w7u9px013Dqa9pZcMXJ2lXiWXndKXLd6CKigr8/Pz46KOPWLduHb6+\nvpSVXbo/pqvnqlQqEhMTGT16NPv27dP9TyEIOlbdoubhzZlYWyh4bXokLrZijeXeaM0vJv1vrzN4\n1QtYuXS/7zjnXCVrPz7KmElRjJoYJdZYFgQTolAomBfvw/2jAlm+I5c9OXXdfq2FvS2D//UiGS+8\n3yeXmtMFG1sr5ixJxNnNjq8/PEJ9bavcIZmFbk3ZLFu2jPnz5wNc9o3rv597QUlJCSdOnGDlypXc\nfPPNtLe39zJcQV9EH+F/ZFa38sCmTEaHuvLYuBCs9TSzeYG55r5T1c7pO58m4qGluAzp163XnF8J\nI48dG84we3ECcYP99Ryl+ebfVIj8y0ffuR8Z4sqKaRF8fKyEL06Wdbuv1jEmjNjn7uf0nU+hae7Z\nDLUp0Wf+LSyUTJzZj0HDg/jmoyMU53f/Q4twaV1Om/n5+V00o1xeXo6fn1+Pn+vtff4mn6SkJPz9\n/cnPzycmJuYPY9xzzz0EBwcD4OLiwsCBA3//yuLCiSUe6+dxamqqUcUj12MpYADvHChiskczQc31\nKBS+RhWfKT1W/WsDnqGBBC+d263na7USbdVulBc3EJ1kQW7hGfyDjefnEY/FY3N7fIE+jxfhYc9C\n3wbWpKsorFfxyNgQjh0+ePnX+znhNmwQZx59jcabJ6JQKGTPlynmP2FECKXleXy3+igTZw5gQEKA\n0fz8cuR7//79FBYWAnDHHXfQE12uw6xWq4mNjeXIkSOoVCrGjx9PVlYWAE888QQKhYKXX365y+fW\n1dVha2uLnZ0d+fn5jB49mqysLOzsLr7TXazDLMhJK0l8cbKcHZk1PDspnChPe7lDMmmlG3aQ/drH\njNj+CVbOjpd9fktTO5u+Po2tvRXX3hCPtdhmXBDMSrtGy5v7CiluUPHMxHC8Ha0v+5rOtnYOX3sn\nQbfOIXjxLANEab5qKpvZ8PlJIuK8GDc1BqWFWFW4p+swd/muZG1tzYoVKxg1ahTARStclJeXX9Se\n8WfPPXv2LEuXLsXGxgYLCwv+/e9//6FYFgQ5tag7WfFLPi0dnbx3fQxu9mIlhivRnF3A2adWMnTt\nym4Vy2VF9Wz6+jQDEgMYOT4Shdg5URDMjo2lksevDuG71Eoe2JjBk+NDib/MeuoWdjYM/teLHL7u\nblwGx+ES/8dvpoXu8fB25JZ7rmLLmhS++/Q4M24ajL3D5T+0CP8hdvoTgPNfU1z4+qIvKaxX8ezO\nXBICnFg2PAArGT51m1PuNU0tHJ5xFyF3zCdo0eVnhFJPFLN3awaT5wwgqp8821ybU/5Nkci/fOTK\n/YniRl7dU8AtQ3yZ2c/zsvdGlf2wi8yXP2TE1o+x9tDtOvhykiP/Wq3E/p2ZnEspZ9YtQ/D2dzbo\n8Y2J2OlPELrpUEEDD2/OYsEgH+4bGSRLsWxOJK2W5Hufw234IAIXXt/lczs1WnZvSufor7nceNdw\n2YplQRAMLzHQmbdnRvPTuWre2FtIu6br9YL9Zk3E97prOH3n02g7NAaK0jwplQrGTolh7JRo1n16\nnLOnS+UOyWSIGWahz+nUSqw+XsrPOXU8PSFMbEaiI5mvfEjdkRSGrn0bpfWft7U01rex+dtk7Oyt\nmH5DvNiMRBD6qLaOTt7aV0hRQzvLJ4Th7/zna91LnZ2cXPwYdkF+9FvxiAGjNF9VZU1s/OoUYdGe\njJsei6WeV4QyNmKGWRC6UNPawWM/ZZNd08b7s2NFsawjpRt2UPb9ToZ8/FKXxXJ+VjVffXCYiDhv\nZi1MEMWyIPRhdlYWPHFNKNNiPHhwUyYH8uv/9LkKCwviP3iOmgMnKPxsg+GCNGNefk4sum8EzY3t\nfLvqCA11bXKHZNREwSwAf1zmxhwllzZx3w8ZDPF35MUpEUazGYmp574h+Rxnn1pJwmevYu3pdsnn\naLUSB3ZlsW19KjMWDGL4uHCjubnP1PNv6kT+5WMMuVcoFMzs58ULk8P58HAJq46UoNFe+otvK2dH\nEj57jezXP6b24CkDR6p7xpB/G1srZt4ymJiBvnz1wSFyM6rkDsloiYJZMHudWolvTpfzyi/5PDI2\nmIUJflgYSbFm6torazi19An6v/4YTv0iL/mclqZ21q8+TlFeLQvvGUFQuLuBoxQEwdjFejvwz1kx\nFNSpeGxLFpXN6ks+zyE8iPh/PsPpZctpLRD9t7qgUCgYOiaMmTcPYecPZ9i3PZPOzq77yvsi0cMs\nmLXqFjWv7ilAK8Hj14TgJZbR0RlNcwtH59yH99SxRD502yWfk5dZxbb1aQxMDGDkhEix9qcgCF3S\nShJrUyr4PrWKB0YHMTr00qtiFHy8jsLPvmf4xg+xdncxcJTmq6W5na3fpdLe1sG1Cwbh6m6+exKI\nHmZB+M3hwgbu/SGDQf5OvDY9UhTLOqRVd3Dqjqdwjo8h4q+3/uHfOzVa9mw9x44NZ7h2QTyjJ0eL\nYlkQhMtSKhTcOMiX5yaHs+pICe8cKLrkKhohd8zHa8JITi55jM62dhkiNU8OjjbMXZz4W4vGYc6l\nlF3+RX2EeAcTAOPopdIVtUbL+4eKee9gEcsnhLFwiK9Rt2CYWu4lSSLtoVdQWlvTb8Ujf1hDta6m\nha8/OkxdVQuL7htJcLiHTJF2j6nl39yI/MvHmHMf5+3AB7NjaWrXcP/GDPJq/3hDWszf78UuyI/k\n//s7Wo3pLTdnrPlXKBUkjQ5j7pJE9u/MYvv3aajVppdfXRMFs2BWcmpauW9jBtUtHXwwO5YBvpff\naU7omcyXPqA1v5jBHz6P0vI/N05KkkTy0SK+/uAw/YcEMGtRgthJShCEXnOwtuDJa0KZM8Cbx37K\nZn1qJdr/6iJVKJUMXPkUna0qzj75JkbSYWo2fANdWHzfSDo7tXzx7kFKC/98FZO+QPQwC2ahU/tb\n31taFXcN92dipPtld48Seq7g43UUrl7P8E0fXdQ32NyoYvuGM7Q2tTNtfjyePuKDiiAIulPa2M5r\newqwslDw6LgQvB3/82Fc09TCkdn34Hvt1UT89dL3UwhXJiO1nN0/phM/NIgR4yOwMIMWO9HDLPQ5\npY3tPLw5i5MlTfxzVgyTojxEsawHpeu3k/vPL0n8+q2LiuXMtHI+f+8gPv7O3Hz3VaJYFgRB5/yd\nbXhjRhSJgU7c+0MGO7Nqfp9RtnRyIOnrNyn+ZguFq7+XOVLzFDPQl8X3jaSitJGvPzhMdUWz3CEZ\nnCiYBcB4e6m6opUkNqVX8eCmTMaGu/Lq9MiLZh1MhSnkvuyHXWQ89x5J37yFfbAfAK0tarasSWbf\n9kxmLUxg9KQoLExwpyhTyL85E/mXj6nl3kJ5/obAFdMiWJdSyXO78qhp7QDAxtuDoWtXkvvuFxR9\ntUnmSLvH1PLv6GzLnMUJxA8LYs2/jnB0bx7aPrT8nHHs3CAIPVTcoOLNfYVotfDGjCiCXW3lDsls\nlW/Zw9nlKxm6ZiVOseFIkkRGajm/bDlHbLwvi+4fibW1uJQIgmAYER72vDcrhq9PlXP39+e4c5g/\nk6LcsQ8NZOi6dzg69z6UlpYELJgud6hmR6FQMGhYECGRHuz4Po2M1DKmzh2Il6+T3KHpnehhFkxK\np1ZifWola1MquGWILzP7eRn1ChimrnL7PtIeeZWkr9/AeWAMzY0qdm1Kp7aqhalzB+IffOk1UgVB\nEAwhu7qVN/YV4mZnyYOjgvFxsqY5K59j8x8gZvm9+M+dIneIZkuSJFKPF7NveyaDrwrmqqsjTOpb\nxp72MIuCWTAZWdWtvL2/CHtrJX8dHYyfs43cIZm1ql0HSf3LSyR+db5YTj1RzL4dWQwaGshV4yOx\nNKELoyAI5kujlViXUsH61MrfJ1LasvI5dsODxD73AH6zJsodollralCx84czNNa3MWlWfwJC3OQO\nqVvETX9CrxhzL1WLupMPDhXz1LYcZsR58uq0SLMqlo0x9xVbfyX1wRdJ+Pw11D4BfLPqCKnHi5l/\nWxKjJ0ebVbFsjPnvS0T+5WMuubdUKrhpsC9vzojmQH4D92/MoNTdh6Rv3+Lc39+mZN1WuUO8JHPJ\nv5OLLbMXJ3DV1RFs+vo0Ozak0dZ66a3NTZloPBSMliRJ7Muv58NDJSQGOvGveXG42IpTVt+Kv9lM\n1isfMejz10musCRt6zFGT4wkfmgQCtH+IgiCkQp2s+X1ayPZlV3L8h05jA1zZf7Xb5G+5FE6GpoI\nveMGuUM0WwqFgthBfoRGe7J/Zxar3z7A2KnR9BvsbzarVomWDMEoFdWr+OBwMVXNHTwwOoiBYgMS\ng8j78BsKPl6Hx/NPcSiticBQd8ZNi8HByXxm9AVBMH+NKg3/PlbK0aJGbguywPZvz+I3axKRj95u\nNgWcMSsrbmDXD2ewtrFk/Iw4vPyM76ZA0cMsmLQWdSdfnixjV3YdCwb5cH0/T6zMYIF0YydJElmv\nfETpj79QOXcpbdaOXDMj1ui3tRYEQejK2coW3j9UjG1TI9M+fgffkUOIe/EvKJTifUXftFqJlKNF\nHNydTfQAX0ZNisTO3niWfhU9zEKvyN1LpZUktmbUcPu6dFrUWlbNiWXeQO8+USzLnvsODSkPrSB3\n46+cm7CQ6NFxLLp3RJ8pluXOf18n8i+fvpD7OG8H3p4ZzaRh4Xy66H7OHkrj2LJn0LbL32Nr7vlX\nKhUMviqY2/46GoUCPnlrPycPFZjs2s2iIVSQ3YniRj4+VoqNhZLnp0QQ7Wkvd0h9RltVPQdufoyG\nxnZcHn6UJTMGGNUMgCAIwpVSKhRMjvZgVKgr30Q/TcULb1IxdRljv34dFz9PucMze3b21kyY2Y/4\nYUH8svkspw8XMnZqDBGxXibVHiNaMgTZ5NS08q+jpZQ3qbl9qD+jQ11M6pfHlGm1EilbTlD02PMo\nBg7kqrcfw9PP5fIvFARBMHGl9W1sf/I9HPfsxf4fzzB1aqJYz99AJEkiN6OKvdsysbO3Yty0GPyC\n5FnPv6ctGWKGWTC4sqZ2vjhRxomSJm4Z4sv0WE8sxcXKICRJIi+zmsOrfsL1h68IfeA2Bj54k9xh\nCYIgGIy/qx23vf8oJz+Lo/jBp3jmpiVMXTqdUSFi0kbfFAoFEbHehEV7ceZkCRu/OoV/sCujJ0Xh\n7mXcN/ebf4Oo0C2G6KWqbFazcn8h9/2QgY+TDZ/M78fMfl59vlg2VB9bYU4N33x4mKMvforXT2sY\n/vkroljG/PsIjZ3Iv3z6eu4TlsxgzLdvMGbDNxx55d/ct+EsR4saMNQX7305/0qlgoFJgdz+0Fh8\n/J355qMjbP0uhfraVrlD+1NihlnQu5rWDr49XcHPObVMj/Hgk/n9xHrKBlScX8eBnVk0V9UTdXoH\nFtWVDP5pFQ5hgXKHJgiCICu3xAGM3fYxzsuWM/DLQj5rXMhX7s4sSfRjiL+TmHHWMytrC4ZfHcHg\nq4I5vj+fL/95iOgBPlx1TQTOrnZyh3cR0cMs6E1ls5p1KZX8nFPLpCh3FsT74GZvJXdYfYIkSRTl\n1nL4lxzq69pIDFHS8ua7eIxNIvb5B7GwFesqC4IgXKDt0JD50geU//gznX9/hK/UbrjYWnLTYB+G\nBjqLwtlA2lrVHN+XT/LRIqIH+DB0bBhuHg56OZZYh1mQXVG9irUpFRwsaGBqtAdzB3rjLgplg5Ak\nidxzVRzek0N7m4ahY0NxSj1GzusfE/fSX/CfPVnuEAVBEIxW5fZ9pD28gpB7bqFg8lTWJFegVCq4\naZAPo0Jdxc2BBtLaoubkwQKSjxQSGuXJsHHhePnqdvMTUTALvbJ//35Gjx59RWOcrWxhfWolyWXN\nXN/Pk5n9vHAWrReXpYvcd2q0nEsp49j+PJRKJcPHhRPsbcW5J/5Ba34Jg1a9gGNkiI4iNi+6yL/Q\neyL/8hG5v7TWwjKSly3HytWJfv94nGSNLd+cLqdZ3cm8gd5MiHTHxvLKbwET+b+8dpWG00cKOXEg\nH78gV5JGhxIY6qaTGX+xSoZgUJ1aiYMFDaxPraSmtYPZA7x4eGwwdlYWcofWJ7S1qkk+WsTpw4V4\neDsybmoMoVGelG/6mUM3v0XAjdcy6IPnUNqItZUFQRC6wz7Yj+GbPiT33S84NOk2Yv5+LytvmEZK\n+flJodXHy5gR58l1cZ6izVDPbGwtGT4unISRIZw5UcKODWlY21iSNCqU6IG+WBhwczMxwyz0SlO7\nhh2ZtWxMr8Ldzoq5A70ZGeIivq4ykKryJk4fLiQjtZzIft4kjgrFy9cJdU096U+8QVN6FgPfWY5r\nQn+5QxUEQTBZjWmZpD74ErZ+XvT/x9+w9fWisF7FD2lV7MmtY1SoC9f38yJSbLhlEJL2/DrOx/fn\nU1/byuCrghmYGIi9Y88nhURLhqBXWdWt/Jhezf78eoYGOTOrvxdx3vppyBcu1qnRkpVewenDhdTV\ntBI/NJDBw4NxcLJBkiTK1m8n44X38ZszmajH7sTCTtzYJwiCcKW06g5yVn5G0WffE/XEMgJvvg6F\nUkmDSsNP56rZfLYaTwcrrovzYmyYK9Y6aNcQLq+ipIFThwvJOlNBRJw3g4cH4xfU/bW0RcEs9EpX\nvVRtHZ3szatny9lqats6uDbWk6kxHrjZia+idOFyfWz1ta2kHS8m9UQJ7p4ODL4qmMh+3r9/FdWU\nnk36k2/Q2aqi34pHxKxyD4k+QnmJ/MtH5L5nGtMySX/iDaQODf1eeRiXIf2A862JR4sa2ZReRXZN\nG5Oj3JkS40Gwq22X44n860Zbq5q0EyUkHynC2taSQUMDiR3kh41t1zWK6GEWdEKSJNIrWtiWWcOB\n/AYG+jpy02BfhgU5i7YLA+hQd5J1poLU48VUVzQRN9if+UuH4unzn52QOhqayH79Y8o27CTysTsJ\nWjgThYXoHRcEQdAH5wHRDN/4AaXrtnFyyd/wmjyK6CfuxtrDlREhLowIcaGkQcVP52p4dEsW/s42\nTIn2YGyYK/bW4tqsL3b21gwdE0bSqFDys6tJPV7M3u2ZRMR6MyApgKBQdxQ6qFvEDLNwkbKmdn7J\nrmNXdi0AU6M9mBjlLpaFMwBJK1GcX8fZ5FIy0yrwC3JhQGIgEXHeWP7XV3xadQdFX2wk9+3PLrpg\nC4IgCIbx3xMWYfcuJPi2uRe1wWm0EseKGtmWWUNqWTMjQlwYH+HGYH8nMelkAK3Nas4ml5J6vJiO\njk5mL0rA0+fiZelES4bQYw0qDXtz69idXUdJYztjw1wZH+lGP28HsVi7AVSVNZGeXMq55DJs7ayI\nG+xH3CB/nFwu/jpP6uykbMNOsl77GIfIEKKfXIbzgGiZohYEQRCaM/PJenUVDafSiXh4KQELpqO0\nvPjL+9rWDvbk1rE7u5aa1g6uDndjfKQ7UR524j1WzyRJorykEU8fR6z+Z/UuUTAL3VLf1sHBggb2\n5dVztrKFMFs1C0ZEkxTojKX49KtXkiRRXd5MRlo5mWnlNDe1MnhYKHGD/S+5MLuk1VK5Yz9Zr/4L\nSwc7op/8P9xHDpEhcvMk+gjlJfIvH5F73ak/eYbMlz5AVV5N1KN34HvdNZdskSusV/FLTh0/Z9fS\nrlIxqZ8fY8JcRfEsA9HDLPypymY1hwsb2J9fT1Z1G0mBTkyL9eDvE8M4ceQQVwW7yB2i2ZK0EuUl\nDWSnV5KZVk6nViJ6gA/T5g0kOz+VMWNi/vAabYeGsg07yXvvS5S21kT97U68p4wRF1VBEAQj45rQ\nn6HfvUvN3mNkv/4xWa+uIuyem/GfPw0L2/+0agS72rIk0Y/FCb58t/sQTcDLP+fTqZUYE+bKyBAX\n4rwdRNuGERIzzGZMK0lkVbdyuLCRw4UNVDWrGRbkzMhQV4YGOutkpyLhz6nVGgqza8g+W0luRhV2\n9tZExHkR3d8XnwDnPy18NS1tFH/zI/kffIN9WCDh9y/CY+xQUSgLgiCYAEmSqDuSTN67X9CYlkXI\nnTcQtHgWVs6Of/r8vFoV+/LrOVTQQE1rB0ODnLkq2JmkAGdxw6CeiJaMPq6urYMTxU1zRgh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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n",
+ "\n",
+ "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n",
+ "\n",
+ "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n",
+ "\n",
+ "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n",
+ "\n",
+ "One final test of your intuition. What if the two measurements are widely separated? "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "xs = np.arange(0, 60, 0.1)\n",
+ "\n",
+ "m1,s1 = 10, 5\n",
+ "m2,s2 = 50, 5\n",
+ "m, s = multiply(m1,s1,m2,s2)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
+ "p1, = plt.plot (xs,ys)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m2,s2) for x in xs]\n",
+ "p2, = plt.plot (xs,ys)\n",
+ "\n",
+ "ys = [stats.gaussian(x,m,s) for x in xs]\n",
+ "p3, = plt.plot(xs,ys)\n",
+ "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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0i7lTj2RaMuLNnzE3BwZLDsLnB5MJjSTAsadtzF9mMcZz0SOPPAIAePXVV6HT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\ncLUJCQY1YgP5P9iP17VcABAfpEaUzheHq2fmUcM8dzddug7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XNYIAnQDMASATht4+zAHg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\n",
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n",
+ "\n",
+ "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Futhermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
+ "\n",
+ "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
+ "\n",
+ "$$\n",
+ "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
+ "$$\n",
+ "\n",
+ "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n",
+ "\n",
+ "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n",
+ "\n",
+ "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n",
+ "$\\sigma_1^2=0$, yielding\n",
+ "\n",
+ "$$\n",
+ "\\begin{aligned}\n",
+ "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n",
+ "\\text{or just}\\\\\n",
+ "\\mu&=\\mu_1\n",
+ "\\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n",
+ "\n",
+ "$$\n",
+ "\\begin{aligned}\n",
+ "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n",
+ "\\text{or just}\\\\\n",
+ "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n",
+ "\\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Implementing the Sensing Step"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n",
+ "\n",
+ "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the sense function for a Kalman filter:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def sense(mu, sigma, measurement, measurement_sigma):\n",
+ " return multiply(mu, sigma, measurement, measurement_sigma)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def sense_dog(dog_pos, dog_sigma, measurement, measurement_sigma):\n",
+ " return multiply(dog_pos, dog_sigma, measurement, measurement_sigma)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the $\\verb,sense_dog(),$ function should make what we are doing very clear. \n",
+ "\n",
+ "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a $\\verb,DogSensor,$ object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at postion 2.0, not 0.0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "dog = DogSensor(velocity=0, noise=1)\n",
+ "\n",
+ "pos,s = 2, 5\n",
+ "for i in range(20):\n",
+ " pos,s = sense(pos, s, dog.sense(), 5)\n",
+ " print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "time: 0 \tposition = 0.793 \tvariance = 2.500\n",
+ "time: 1 \tposition = 0.575 \tvariance = 1.667\n",
+ "time: 2 \tposition = 0.277 \tvariance = 1.250\n",
+ "time: 3 \tposition = 0.348 \tvariance = 1.000\n",
+ "time: 4 \tposition = 0.401 \tvariance = 0.833\n",
+ "time: 5 \tposition = 0.231 \tvariance = 0.714\n",
+ "time: 6 \tposition = 0.386 \tvariance = 0.625\n",
+ "time: 7 \tposition = 0.517 \tvariance = 0.556\n",
+ "time: 8 \tposition = 0.452 \tvariance = 0.500\n",
+ "time: 9 \tposition = 0.332 \tvariance = 0.455\n",
+ "time: 10 \tposition = 0.298 \tvariance = 0.417\n",
+ "time: 11 \tposition = 0.280 \tvariance = 0.385\n",
+ "time: 12 \tposition = 0.197 \tvariance = 0.357\n",
+ "time: 13 \tposition = 0.132 \tvariance = 0.333\n",
+ "time: 14 \tposition = 0.116 \tvariance = 0.312\n",
+ "time: 15 \tposition = 0.076 \tvariance = 0.294\n",
+ "time: 16 \tposition = 0.135 \tvariance = 0.278\n",
+ "time: 17 \tposition = 0.040 \tvariance = 0.263\n",
+ "time: 18 \tposition = 0.003 \tvariance = 0.250\n",
+ "time: 19 \tposition = 0.006 \tvariance = 0.238\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the intial value of 5.0 to 0.238.\n",
+ "\n",
+ "By now the fact that we converged to a position of 0.0 should not be terribly suprising. All we are doing is computing $\\verb,new_pos = old_pos * measurement,$ and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n",
+ "\n",
+ "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n",
+ "\n",
+ "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Implementing Updates"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track nonmoving objects? The histogram used a loop of sense and update functions, and we must do the same to accomodate movement.\n",
+ "\n",
+ "How how do we perform the update function with gaussians? Recall the histogram method:\n",
+ "\n",
+ " def update(pos, move, p_correct, p_under, p_over):\n",
+ " n = len(pos)\n",
+ " result = array(pos, dtype=float)\n",
+ " for i in range(n):\n",
+ " result[i] = \\\n",
+ " pos[(i-move) % n] * p_correct + \\\n",
+ " pos[(i-move-1) % n] * p_over + \\\n",
+ " pos[(i-move+1) % n] * p_under \n",
+ " return result\n",
+ " \n",
+ " \n",
+ "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n",
+ "\n",
+ "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is $\\verb,new_pos = old_pos + dist_moved,$. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n",
+ "\n",
+ "How is addition for gaussians performed? It turns out to be very simple:\n",
+ "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n",
+ "\n",
+ "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n",
+ "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the $\\verb,update(),$ function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n",
+ "\n",
+ "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n",
+ "\n",
+ "So, here is our implementation of the update function:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def update(pos, sigma, movement, movement_sigma):\n",
+ " return (pos + movement, sigma + movement_sigma)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What is left? Just calling these functions. The histogram did nothing more than loop over the $\\verb,sense(),$ and $\\verb,update(),$ functions, so let's do the same. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# assume dog is always moving 1m to the right\n",
+ "movement = 1\n",
+ "movement_error = 2\n",
+ "sensor_error = 10\n",
+ "pos = (0, 500) # gaussian N(0,50)\n",
+ "\n",
+ "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(10):\n",
+ " pos = update(pos[0], pos[1], movement, movement_error)\n",
+ " print('UPDATE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n",
+ " \n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ " \n",
+ " print('SENSE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n",
+ " print()\n",
+ " \n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "UPDATE: 1.0000,\t502.0000\n",
+ "SENSE: -0.9237,\t9.8047\n",
+ "\n",
+ "UPDATE: 0.0763,\t11.8047\n",
+ "SENSE: 0.1727,\t5.4138\n",
+ "\n",
+ "UPDATE: 1.1727,\t7.4138\n",
+ "SENSE: 3.2003,\t4.2574\n",
+ "\n",
+ "UPDATE: 4.2003,\t6.2574\n",
+ "SENSE: 6.5697,\t3.8490\n",
+ "\n",
+ "UPDATE: 7.5697,\t5.8490\n",
+ "SENSE: 7.6101,\t3.6904\n",
+ "\n",
+ "UPDATE: 8.6101,\t5.6904\n",
+ "SENSE: 8.2152,\t3.6267\n",
+ "\n",
+ "UPDATE: 9.2152,\t5.6267\n",
+ "SENSE: 6.5868,\t3.6007\n",
+ "\n",
+ "UPDATE: 7.5868,\t5.6007\n",
+ "SENSE: 6.4438,\t3.5900\n",
+ "\n",
+ "UPDATE: 7.4438,\t5.5900\n",
+ "SENSE: 7.7971,\t3.5856\n",
+ "\n",
+ "UPDATE: 8.7971,\t5.5856\n",
+ "SENSE: 7.7203,\t3.5838\n",
+ "\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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OD6fbvBkxb7+N/W++iaf79n3g8+5cIiztJg83b6pRrpw3wxXcUC0RJiepzymP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\nm5tRpYoXkyax4SWiKKXVwjF8OEwjRwZuQXkX1a1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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n",
+ "\n",
+ " movement = 1 \n",
+ " movement_error = 2\n",
+ " \n",
+ "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the $\\verb,update(),$ step.\n",
+ "\n",
+ "For now let's walk through the code and output bit by bit.\n",
+ "\n",
+ " movement = 1\n",
+ " movement_error = 2\n",
+ " sensor_error = 10\n",
+ " pos = (0, 500) # gaussian N(0,500)\n",
+ " \n",
+ " \n",
+ "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next we initialize the RFID simulator with\n",
+ "\n",
+ " dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "It may seem very 'convienent' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n",
+ "\n",
+ "The next code allocates an array to store the output of the measurements and filtered positions. \n",
+ "\n",
+ " zs = []\n",
+ " ps = []\n",
+ " \n",
+ "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we just enter our $\\verb,sense() - >update(),$ loop.\n",
+ "\n",
+ " for i in range(10):\n",
+ " pos = update(pos[0], pos[1], movement, sensor_error)\n",
+ " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
+ "\n",
+ "Wait, why $\\verb,update(),$ before sense? It turns out the order does not matter once, but the first call to $\\verb,DogSensor.sense(),$ assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the $\\verb,sense(),$ first.\n",
+ "\n",
+ "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n",
+ "\n",
+ " UPDATE: 1.000 502.000\n",
+ "\n",
+ "What is this saying? After the update, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the update step.\n",
+ "\n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " \n",
+ "Here we sense the dog's position, and store it in our array so we can plot the results later.\n",
+ "\n",
+ "Finally we call the sense function of our filter, save the result in our *ps* array, and print the updated position belief:\n",
+ "\n",
+ " pos = sense(pos[0], pos[1], Z, movement_error)\n",
+ " ps.append(pos[0])\n",
+ " print 'SENSE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
+ " \n",
+ "Your result will be different, but I get\n",
+ "\n",
+ " SENSE: 1.6279 , 9.8047\n",
+ " \n",
+ "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n",
+ "\n",
+ "Now the software just loops, calling $\\verb,update(),$ and $\\verb,sense(),$ in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n",
+ "\n",
+ "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%precision 2\n",
+ "# assume dog is always moving 1m to the right\n",
+ "movement = 1\n",
+ "movement_error = 2\n",
+ "sensor_error = 4.5\n",
+ "pos = (0, 100) # gaussian N(0,50)\n",
+ "\n",
+ "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "vs = []\n",
+ "\n",
+ "for i in range(50):\n",
+ " pos = update(pos[0], pos[1], movement, movement_error) \n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " vs.append(pos[1])\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ " \n",
+ "#plt.subplot(121) \n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()\n",
+ "\n",
+ "plt.plot(vs)\n",
+ "plt.title('Variance')\n",
+ "plt.show()\n",
+ "print ([float(\"%0.4f\" % v) for v in vs])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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upO+Iv7VF8YMMC8N1xx040tPJ+8uSriWtMueF+I96jEVERMqBoPnzsS9fjmP5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\nCuNa4ti+XQ369VPEJ59Uv7Zpk0O9e8fpppv8WrW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+ "text": [
+ ""
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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wWMgFLOQCFnIBLwSuFOfnMikGAABAdgWuFDMpDh92wWAhF7CQC1jIBbwQuFLM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\nRK5CYII=\n",
+ "text": [
+ ""
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literatue, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\""
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Relationship to the g-h Filter"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n",
+ "\n",
+ "The equation for our estimate is:\n",
+ "\n",
+ "$$\n",
+ "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
+ "$$\n",
+ "\n",
+ "which I will make more friendly for our eyes as:\n",
+ "\n",
+ "$$\n",
+ "\\mu_{x'}=\\frac{ya + xb} {a+b}\n",
+ "$$\n",
+ "\n",
+ "We can easily put this into the g-h form with the following algebra\n",
+ "\n",
+ "$$\n",
+ "\\begin{aligned}\n",
+ "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n",
+ "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n",
+ "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n",
+ "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n",
+ "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
+ "\\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "We are almost done, but recall that the variance of estimate is given by \n",
+ "\n",
+ "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n",
+ "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n",
+ "$$\n",
+ "\n",
+ "We can incorporate that term into our equation above by observing that\n",
+ "$$ \n",
+ "\\begin{aligned}\n",
+ "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n",
+ " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n",
+ " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
+ " &= \\frac{\\sigma^2_{x'}}{b}\n",
+ " \\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "We can tie all of this together with\n",
+ "\n",
+ "$$\n",
+ "\\begin{aligned}\n",
+ "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
+ "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
+ "&= x + g_n(y-x)\\\\\n",
+ "\\blacksquare\n",
+ "\\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "where\n",
+ "\n",
+ "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
+ "\n",
+ "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n",
+ "\n",
+ "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n",
+ "\n",
+ "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#####Excercise:\n",
+ "Modify the values of mov$\\verb,ement_error,$ and $\\verb,sensor_error,$ and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n",
+ "\n",
+ " movement_error = 40\n",
+ " sensor_error = 2\n",
+ " \n",
+ "or:\n",
+ "\n",
+ " movement_error = 2\n",
+ " sensor_error = 40 "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Introduction to Designing a Filter"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equiped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n",
+ "\n",
+ "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "temp_variance = 2.13**2\n",
+ "def volt():\n",
+ " return random.randn()*temp_variance + 16.3"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We generate white noise with a given variance using the equation $\\verb,random.randn() * variance,$. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n",
+ "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performace will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
+ "\n",
+ "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field \"Repeatability\", with the value \"$\\pm0.50\\%$ Reading\". Is this a Gaussian? Is there a bias? For example, perhaps the repeatibility is nearly $0.0\\%$ at low temperatures, and always nearly $+0.50$ at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
+ "\n",
+ "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call $\\verb,volt(),$ to get the measurement, pass the result into $\\verb,sense(),$ function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
+ "\n",
+ "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = temp_variance\n",
+ "movement_error = 0\n",
+ "movement = 0\n",
+ "voltage = (25,1000) #who knows what the first value is?\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "vs = []\n",
+ "N=50\n",
+ "\n",
+ "for i in range(N):\n",
+ " Z = volt()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n",
+ " ps.append(voltage[0])\n",
+ " vs.append(voltage[1])\n",
+ "\n",
+ " voltage = update(voltage[0], voltage[1], movement, movement_error)\n",
+ "\n",
+ "plt.scatter(range(N), zs, marker='+')\n",
+ "p1, = plt.plot(ps, c='g')\n",
+ "plt.legend([p1], ['filter'], 3)\n",
+ "plt.xlim((0,N));plt.ylim((0,30))\n",
+ "plt.show()\n",
+ "plt.plot(vs)\n",
+ "plt.title('Variance')\n",
+ "plt.show()\n",
+ "print('Variance converges to',vs[-1])\n",
+ "print('Last voltage is',voltage[0])"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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+ "text": [
+ ""
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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A16PvfG6SXv2wU8+u3eP2ckoKs1UwIRcwIRcwIRdwQlEXXUmqLfPpuxdO0i/e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\nUfq5uH34+8RsDTp+LGPtMVu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+ "text": [
+ ""
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Variance converges to 0.0907297673624\n",
+ "Last voltage is 15.6491261618\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the $\\verb,volt(),$ function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
+ "\n",
+ "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n",
+ "\n",
+ "##### Exercise(optional):\n",
+ "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n",
+ "\n",
+ "> use plt.hist(data,bins=100) to plot the histogram. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Your code here"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "######Solution\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = temp_variance\n",
+ "\n",
+ "def VKF():\n",
+ " voltage=(14,1000)\n",
+ " for i in range(N):\n",
+ " Z = volt()\n",
+ " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n",
+ " return voltage[0]\n",
+ "\n",
+ "vs = []\n",
+ "for i in range (10000):\n",
+ " vs.append (VKF())\n",
+ "plt.hist(vs, bins=100) \n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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V5WcrtCknoBHZwtzpDmZZAADS2GhkKuYGvNNHdtIUAwuseJ1iuIe1Gm2jfraR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\nfeUrX5m7Ix6px+v8u337ts6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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "######Discussion\n",
+ "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Explaining the Results - Multi-Sensor Fusion"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focussed all of our attention on the position sensor. Let's change focus and see how the filter performs if the intertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30\n",
+ "movement_sensor = 30\n",
+ "pos = (0,500)\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "vs = []\n",
+ "\n",
+ "for i in range(100):\n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ " vs.append(pos[1])\n",
+ "\n",
+ " pos = update(pos[0], pos[1], movement+ random.randn(), movement_error)\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()\n",
+ "plt.plot(vs)\n",
+ "plt.title('Variance')\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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5U5x9koih4wURU8AB8uTJk1GzZk20bNnS/dzatWvRtGlTNGvWDN99950oAySEEEJCwTJ9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\nmGqBHCvuIKeeeGrHM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+ "text": [
+ ""
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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lYblulk9DDL1dMCEXMCEXMCEXcFJalk9jRhgAAABuw8NySCt6u2BCLmBCLmBCLuAk1hEG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\nlOux5PNa8sVf90Rfj2/7PNG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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distintly jagged. But, it still mostly tracks the dog. What is happening here?\n",
+ "\n",
+ "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n",
+ "\n",
+ "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n",
+ "\n",
+ "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematicall model this sort of reasoning."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "More examples"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example: Extreme Amounts of Noise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intution tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30000\n",
+ "movement_error = 2\n",
+ "pos = (0,500)\n",
+ "\n",
+ "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(1000):\n",
+ " pos = update(pos[0], pos[1], movement, movement_error)\n",
+ " \n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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kONRo3Dj2cjSSceuthnFEMS9cGNZpxvzhhzDrNfK1Wv2WldMnTlS0yVNry0aV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ho4VqxovhkxQhCkuGyNlcDarVtjnu0UCgpgU2ceCcwgC506NU9uGBzYps+fD+/11ys5zWXh\n9nkpMcNhjmX73/+kyYIEbDx1P/CAciz3PffAq1VKXC9Va0g/Fvr1C5pcUmeyUVKltvZwDjgcSUmr\nA0h3epo71EPy0PpLShJz0YkwiLZ/8QUyAn/ETKB8rrKcE+1JTt4drqb699i2bEHWddeB27hR8+N8\n9+7wqqtMyh0sEb+DMJkbuLIyabCuQ8zIaM6K4vUmvpxwhJ+v0LUrPFGEKbTg84X92fH9+sH7058C\nbjdsX3wBoUcP8EYufgb4S0p0k9e3YLeD8fmQ9uqrUv7TUKEnH3lDTaIuxoHqd5oyMhJe8CFWgkap\n92QSnc6wG9T01Ozdq+xN8I0fD7+qWEq8HEuXgq2sBLdvH+zr15uT4s5uh2fatJQfVslWEWe/z54w\nAdlhCiBF3Z7cXJw5fRre6dMhnH9+9B+M0H724EFkxZICLgppL79s6kw48+OPyLn44tj7bZjrmtCz\nZ+Q0uHpfO3iwkhVM+jJBWalUBoMGr8tcWVlzeEa0WBb+4cMh6twAAkDmzJmGU4DqSktrvr7n5Gj3\nY53wEzE3t8W+A6a6Wklx7HrqKSn6IJB9ynD4ZASWHER77rkHLnXWilQILeYQTW7daAQ6PK8x++2b\nMAFNjz3WfByeB+z25oIXamFS/olOZ8vZDNW/R2RZcAcPIkOnOp/31luD88DKu7hjSAvXQpjMDWlL\nlijpBrXw552HjYGNZozX2zyrnyoxroiInTopIQ9ahPPOg2/SJDhfegnZU6c2F19JAt9Pfwrm+HGw\nhw9HfK/ocAA+H+z/+592CqnQk0+i4389nqhnzRMZ42hU00svJbSyYESZmXA98ojhj6nPCf7LLktO\nKjrVpraUczjguf12OAJV17iyMmyRV9MCbF9+iXQD4RTRUGKt4+z37OnT4KKo2JcwoihVcoQU1hhp\nttTx4YdJC3lzvvxy9Nmf6urinjlscb4QRWkzaKyD6EQUfNH62u7dm+tTALB98w1s27bBN3GiUggu\nXFpYTRrXMba8HPZwGdA4TgpR0vk3socPS7mrU1mIR6fgluhwSLnqVdKWLFGKgsmr+3yvXtIMd7zF\n5EJYchCdMg0Nzcm6Q39BMZbt1MIXF6NRK84tJ0dKs6Pe7W+3t9ws5vMhr2tXpdJiKKG4GA0hOWZ9\nV12FRrkTMYw0CNf597gfeABC377SZqEjR6Tk8Q5HQv794cJSvBMnwnPHHWE+rNpN3KEDmqKIuzXW\nuPAXwaZnn5VmjA3iL7gAnvvui/zGwKwrt3MnsuWsAlHK/slPIqaokqUtWxa+alqA6+GHleVgViuN\nUujJx+Ag2rZmDdgwG0mZhgZw334b1Xe1Jf5hw8AbmWFMBbkfyBdZk0IDuCNHlHSSac8/j4KQSmdM\nXV1chSq0KLNzJhWYkTkXLIj6HAAAaGhAu6IicFu3BocH6En0HoQY5Y4eDUadxSoR5AmmWAfCgSwc\nts8/Nz7La4DnzjtRv3IlPLNmQTj/fAg5OWHTwmrSGDSyhw4hTac8PAD4f/ITuMLtKZBTzSV6dTgM\nobAQnttua/G8f+TI4JV0oMUkqG/CBPBDhsB7550QunWLrciOjlY7iGaOH4+YkD3r1luRLsdDac1E\nJ+gkWbdhA6BRqls+rrwcXv/pp1Lwf0iMEbdvHxiPp7kMeCieB/v990FPsQcPNg+E9Mp+h7CtWYP0\nRx9NbMyQKOrOIAvduoXPk8owGCzHwWZnGz95RGpapB3fGRlhiyXETd48G8MNG1tZKWU2iWYDrqqP\nhSP07auUq9bKKy06nfAG0okBgP+ii6TNnlG2Pe3dd2HbsUP3df/Ikfp9PISpMdEp5ps0Cf4ELPsn\nkpibCyEnJ+Yl5oRRXSwZvx/nybGQLhdQVyedNxOcDs1/8cXS8rHqbypr8mSwoVkCkilQgMdQFcrA\n32nakiUQzjlHM5tIkGSnwIvyxos9flw3a0+0WpwvwmXYiUJNRQXAMEh/6qmIaTLjkp6u7MsS7faY\niiWJLBuc8g2IWDxMzM+HEC7Vonoza4Lk9u0rFQbTO+S332r2d6Fv35b7UELGb65nn4XYoQMyp00D\n3G5wCcws1GoH0Zn33QfH0qUtnnc+9ZRysmMrK+EMzNaKnTrBc/fdzW/UWTpIOI3jCO3bB8+6yrPl\nOgH8TEMDskNSAjr+9S845KXNKCtV2TZsaB7QJegE6h89Gg3//a/2ixFik1yPPNJcvSnB6t97D77x\n45Py3VGTT2KxhA6lpSFnwoTo0tdF+7sUBGROn44z1dXwaW3syMmBa8GC5q9t3x6uJ56IOkaYPXhQ\nWv0J106TZ/fixW3ZgpzRo8Ft3252U5LKP2oUXI8+KsVODh2qXco8FVR9htuyRcls4Hj/fSl7iNud\nlGIhviuvhBiYGLG//z643btbDlQiiGcvgePtt8HW1Bj7e1FtFvNffDE8WmGDanFmyEqkFmnM4iVv\nYnvggdi/4vvvYdu1KyXnrJyBAwG7PfLmbC0cB9s33wSnpBSE+IovyWEciZyJ1sm1LmOqqzWL1oVi\n9+yRUgxq/F5sW7eCqa+HY/nyuJoadLyEfZPF2L/8EtzevS2edz7/PJx//av0QPVDTvvb34IGJGKH\nDuELQySImJ3dcsNURoYSuwagOZm7Hq1BmPpO0+EIn/83wPnqq1JZTY5Dw7/+Fe0/IXYRBtH+ceOw\nLkm5aP2XXabk99TDVFSEjxuLV+Dfbtu+HbatW419NHDyiioXbrQ3hPKAxECcm3faNN3CLKFsO3bA\nprO5FYChmwkzY6LDsW3aBO777+OeObM635gxUsGGTp2kGy6zbn5UfYYrL8fpVauk5wMTAYzHk5Sy\n1a4nn1TO22lvvAH2zBnDN8JCUVHsOWtDwmi4LVuUjVS6jO5hSGI4h9C+vfaNepKEni9EhoGYlRXT\nzK5MGYSmoO+z1dUx/z5cDz8MprIS9jVrmp+Mc5JMmYFOUEy0bcMG6aYwXN8MqViohysvlxIWaP1e\n5Gqfrb1iYcJodBTG65V2kwPBP8iQAR23e3fYpYVE8V11VYtNlELHjkGdM2LJaq0ZPFVIBj9gAOpW\nrYJfZ2OR89lnYVdXQWIY+FMwS8sXFyubJbQwJ06gwMQZPe7wYaQFNi0lg1wxUzP+OOKHA301wkwA\nU1kpFVWI5sKZqM204Q4RLhVeqlZ/4sQePQouUP2qhSQUW0FdHRxh4hfN4PvpT+EfNQpC9+5wR1kZ\nNRnsH30klScG4Jo7F4fkQZG8mpakmegggZAvozPL9Z9/jvrVq2M7Zkge35yJE2GXbyD0RLkiKePP\nPz9psfiemTPhnj07Kd8dlaws1GpUwDVCTs+akkqgcYRYCv36SaGLBtuZM2KEfiVPm02Kq0/QIDq0\nhLrme9LSNMM5mJMnkTFjRvP7An8b8uSj889/hvNPf5JelDNnJfB31roH0TqUzh9mEA2OS/pylu3r\nr5GhcQHyzJ4Nj5ETjNcrzYSohfzRCeefD9dTT2l+3PHOO8pyWSpLA3unT28u06uB27MHw7/8MmXt\naSGBcfFaPLNn40xVVUxxZbpFSUJw+/YBQMucz1qSPIg9c/hw+MITmZlRZ2AxMyY68667kHPlldov\nJmEQzf74I5x/+UvCvq81se3YoRSRcD/6KC6QQ/IC5z/v7bfD/f/+X5IbEdtAQuzYMar86prkrCjq\n81OkQZacdYllkX3ZZbob1WW+yZNRJ084JZh73jxj6fjijL3ViomOVA4+Ivn3noJrJuPxgK2uBvvd\nd7FtZAyZaIsmBI89ckT33ybm56MhxqqMmt8XTcYbp7M5tFWFcbthV98QcRx8F18Mr5z+UhQBnw9M\nRQXYM2ek6y3NREdJb8lC7vzqctGhccCJqlgYTmNjQjYlaOVqdHzwAdKjzGbBlZcrg2gjJWqTLtkb\nWyJIf+IJ2NetS94BOA6w28GPGAHvxImGPtrw+utKdctwxPR0+IcNk4r5RJD21lvNZYWTIScn7ICj\n6bnn4FNXmrKqcOeFJAyiuR07wEWRorAt8g8eDP+oUS1fkHPrtmtnrJhJNAQhaCN3NLNoiabceKtv\nOiOdL2021C9bBn7QICmProVinsPxDxgQfgO6WeTJuBirExrFlpcj44knYNu82fiHQyZIhKKisGFO\n3K5dUgpAvZsXhwN8IquyBtoSbhKPqamBQ2O1hduyJXg1N3QClOPgWLFCmVBiq6piW/3V0aoH0bqd\nO9AxGl96Ce5Zs6TnQmZuxRTMROsu0fB8c8GVKAjFxaj76qvgrzC6IY9hIOTmxla9KVlEETWB0rqJ\n5liyJGIMoaGd73EQWdbwDZvYqVN0Mfvp6dKSdhSiSYOnxm3a1JzdJsVMjYkON1hJwiA64jK9CZjq\n6rDpClNFzM0Nij+X+4XodAIJrNAYxOdDjjoPvN2OxoULNSvhJg3HSZlyVIPoaM4h/vHj4b3tNnBH\nj5416ST5AQPiLnyWjPOFaLPBe/31UpraFLF//nnw6kO0QkM+I23ilvdkparst9MJIT9fP4sZAO91\n17UY5wAAd/BgyBMhYzeWlTKceb0xFa2KpNUOor2TJ0tlOUOfv+IK+APlL4WePeH6wx8ASEsXae+8\n0/zGVAyidbJgMFVVUjWlaDGMsqQp811/PTzqykcRiCwrpRizUHaE9GeeQWYC7xjVMufOhV3jD9IU\nMcS7CT17oiGKHcZiejoYvbi20PdmZsJlIL6VqauD88UXwVRXR/2ZViHcZtjBg+F65BH4BwxIyfHM\nYl+9WgkxSX/oIaQtXmxKO8TsbDAaN9q+SZPQ9NxzyTmowyHN0gUG776rrwZfUpLSnLm+yZPR+Prr\nwU8avF451Nc7C2t64QXNlJvxYvfsQVos2S4ChF694Asp8pEsQocOSjaYWG7Q+ZIS8MXFzU84HHA9\n9pj+B6Io+51QGRnSKmi4f1t6eotxjha+Z0947rpLeSyv2og2m7Qqm5sL/+DBcTdZZp0RU4I1vvGG\nZh5M98MPB6eyC/DMnCndCQVE2vSWECwLpqam5YxoIjZ4qZdv/P7IM9sMg8Z//jPmcqXJYNuyBelJ\nquQHSAnnw+F79DA+ox8Dvn//pMVtik5n9INoh8NYOIecnzcFG3BDmZonOsyglh8xAu5f/cpSf0fJ\nYCstlXKt1tXBsWyZadk5xJycoJnolPSLQL+XV268N90E/oILjH/NsWMJLSKivn5ZHfftt7AlqRqi\nFq1+wR47Bnsce274oUPhnT49nmZFLTTZgBFpf/0rhHbt4L/oouYnHQ7NcZAiGRukwxBzclATUusi\naiFtFLt0gU89garKCc4kOIUv0IoH0Xr4Cy4AP2xYyxdCfqie++6DP0zp5oRgGNh27ED6008HP+12\ngzl5Mr7vVg2i2cOHkVNSopu7lu/TJ/n/1hgIubnwmThY4ouL4b311qQfRywshN/IyoOR787JgS8k\nh7gum01z44Yu+eRlodWLVBC6dlU2J6dCtAVoUsnx4Yew7doF9swZaVOzSX3AX1ICf0mJKceOd7Nb\nzuWXI2fcuIQ05czp0/AZWHkEEHGAxG3Zgox7742jVfrSXngBzpdeSsp3R8XvR/bUqeYVCTKIUU+s\nGRzYcvv3G6/aabNBiFSMLJEYRrcORiRCp05hS6F7Zs6UYq1ttuZxUQL3u7Wtq184JqTX8g8bBtfc\nuS2Oy33/ffwbvNT/HpYFW1vbYrAu89x6a0pyYhvFDxiALT/5SfIOEOn3zXGWKX0bs5wc8OeeG92M\nl8OhlCKPisGUWYlkZkx045IlqElhCItQWNi8d8MqApMOylKpSYMRfuRI+K67Tnkc2i8y5s2D7X//\nS/hxa8rK4o6BZqqqpPy/qdTYCIgi3DNnQujRI+xbHe+/jzSNgmWJkLZ0KbiQEu3J1OJ8ocpUcjbw\nXnedMqgVw8QNa9KoTshUV8Pxj3/of4bjkr8SnyBiRgb8I0fqv0FOeVdUBO/kyRHrUxh1dvSgZHG5\nmvMgmpGjNitLSj0Wcly+f/+4A+C9N96IptCiMjonDM//+3/Sju0ff4yY9iilGAZmZg12z5sH95w5\nJrZAX/r8+bCvWBHVex3//KdSyS0c79VXwzNzZvSNaKMz0anG9+8P/9ChZjcjmHwRMvFGKhL20CFp\nU2YSMs5Ek+0m2dIffdTwTX67rl3Bbd0q5dCNlE7SgrH4CSP31zhv/uwrV0o3Jknm/s1vIHbpAjEz\n0/iEl8Ygmq2qCruPge/dG01mrhQYwA8eDM/tt4d9j+/aayH06AHPvfdC6NixOf1dArTaqx9TUaG5\n4UQt45FHkCUv15tV6EGr7HfPnqiJVH0qAvbYManMMhD1Xbf9ww+RvnBhXMdNKIbBBf37J+3rhUi7\nqtPTpdyUFsQeOQL2hx+ie3OUfVts315JAxQNPrBB14xBtKkx0SnmHzcuOMbPAoSOHSF07tw8CLHI\nsri6X9hXrZLilpNQsTBU9oQJYMvLDX2mrrQUtbGuqIginC+8ENNHHe+/D6FXr8iFVJK9CpfC622L\n80WCJgAyHnxQM8VssnivvdZ4m7VWVDUG1kEyM8En8dqbSEKvXvBHCItqfPNNMKdPI/NnP4PYuXPQ\nxsN4tdpBdOYvfgH7Bx+0eD7tb38DF8izyB48qGRo4Pv0gffGG1PZRAAAI4pJWVKyf/wx0pYsAaAa\nPEc4adm++SYpszaxcv/qV0mrmNXwxhuWjAOPlmPlyugLcEQ5iGYaG5FhIGxAzM1F09NPS9WwCAAp\nv2ruBReADeRdb61811wD9733Ssu+7dqlZO+AUXJF0GgL+MSKPXQItm3bDM/cCsXFEGIMo7PJRVBi\nHIj6Jk2Cd+rUsO9Jep0EC/DceWfMn2Wqq6WbtBRMImRfdBGY6mo0vfgiIBcmiZLIsrCvWwf2wIHm\nJxsbYfvuuwS30uJcLth2707417baQbR940bNpOQZjz8Oh5waTNX5na+9lvr4NEgn+oQXAwCCd6CG\nlIjVk/bee2BCKx+ayP+Tn2BdknLR+iZPjljFjz1wILgcutUEyg1HwkS7yhLDaozn3ntNGUSbmic6\nDG7bNrDHj4OR893l1LkAAB6VSURBVKy2Uv6RI8EPHAgxPR3em26yTDiHul/Ig+ikrybJIYGp/BmE\nTIxw33wT/2b0UEkcRPPdusGfwtUkrfOFyHHBGSsMYo8cCfxP8odR7MmTMafc9fziF2DOnAkaD6Wq\nBoKVMD4f5Yk2TGdmQEltpur8YoKDzaPlvfHG8KWQY6VarhELC1H38cdR5Vi0EqaiAu2TcOcYLe67\n7+B47z3Tjh9O3bp1qP/kk6jey+3ZE5QGTJdZIU1nGfaHH8Bt3ar9YhJSQzEVFbD/5z8J+75E8F19\ntbSSk5kJl86GZbMpM9FJHkQLcv7dVFYADOlfOVdcgbTQvNF6orzO+UePhl8jTWwiuO+/H55f/CIp\n3x2tum3bYk4bByClZb/jScsmnHeeFHplpJ11dchJUQ7seLFHjyJj7lzd1x3vvYeMOXOkVXYaRCeG\nmJcn/Y/6DtKEQTRXVobMBMbmBAmJeeJHjoT7N7+J/DkLDaJs27Zh+IYN5jVAECy7aY7v3z/qAgSN\nL7wAfzQ3UJGqWFmImTHRWT/7GXIuu0z7xWSU/T50CGl//3vCvq81U/cLMScHQm4uhG7dkntQjkPt\nli0Rs10kkmZ5ZAMzx1k//SnYCMv53htvRP2aNUabFhXv9Onwjx6dlO/WonW+0NrUb4g8IEvFTHRl\nJZi6OunmPZaNjCHndjFCTnFGEBKawzyp6uth27Qp/Ht8PrCVleDUIS0JcnZcMWOlMSiu3bwZTX/6\nk/SyesNJghNwR8XjAXv4cFK+2r5iBZxvvGH4c4IFdp0rTN4dnvbKK3B8+KGpbUgE7y23RFUCmdu+\nHawJhVPOOuEGK8kYRO/dG/kiQVoQOnaUNmRGGfYU17F69UrtBITWDGoUGygb3noL/pEjwZw6FX8a\n1TZOSe+Y5Jh7GVNfj8xZs8AePWr8syEF3IT8/LDXeqa6GmyExAxWwX33Hbi9e/XfIAhwrFgBsaAA\ngjyBmkCtehCtlU9R6N1bqSbmfvBBuB54QHohwQm4o5LEYza+8QZqt20z9Bm+a1d4klQ5LyaiiFOn\nT5t2eMZI4ZFWgPH7Db2f/e47ZNx/f5JaE56pMdEpHkTb1q+33ICHqagwnI0iFYJiort0QZOVsg0l\nUlpaUOni2q+/jiqXuO/aa+GbMgXc3r3BG81auaScL2w28L17A0bzNseg7n//Az98OLj9+2O7LoUm\nMIgw7rDa+SYcLtJ5yO0G43aD798ftdFmtDKg1Q6iPXfcAd/VV4d9D9+/P9wPPwxA2lUfbd7dhEni\n7LeYn294eZEfPjwpgfexcv71r8hNQqePmoVCW1JBKCgwlI+YaWxE2ttvA/X1SWyVBYUr+33BBXDN\nmyddXFuxtPfegyOQ/SfzjjukfLkkZfgBA1CvKlkt9O0bOe+zCuP1topVtnjYvv4ajn/+M+bPi3l5\nUsq5FOAHDFCuR5FS92rxjR0bNB4Qc3PhCrMXi+/ZE56bbjJ8nLao1Q6imxYtgt9AtTvvtGkQioqS\n2CINLAv2xx8Tv6s6lCCAiSLvdOPrr1uiiIDMtnMnMkwcoPF9+yZl+ceyHA7AyGx0YGbDjEwUpuaJ\nDjeIHjwY7t/9DsjKSmGDUs+2aRNsO3YAkNItWuWGsy3lD4+bib8z29dfg0thiJJWv2D37pXSusZI\n7NAB7kcfjadZsR1XzjoTJcfbbwPp6eCHDWt+Mjsb3jvu0P9QRsZZU2zF7HNPqx1EG2ZGZgKGAXvs\nGJyLFiX3OI2NyDv/fHDffpvc4ySY0L49/CNGmHZ8fvBg+KZMMe34qSba7caWCttoxUKhZ08Iubmp\nO14KN6xFy/7FF7AFcuwTYpTz2WeRFsOenUTK/NWvUlJtMJFq9u0DbzBjCltebsnQq0The/SAGGbS\nwjdxIoSCgqQdv21d/cIxYRMbf+658EyfnvzBeyBmy6z41Vj5S0qwfeRI044valV6as3sdmPFdkws\n+WxmTHTD8uWoldNkpgDfty88JhSCCsffv3/wxdwiJaKtmj/cMpqaAEGA54Yb4JcrjprA/tVXSqGz\nVNDrF4xF+m20xFgGg5GqE57lxOxs+EtKwrxBTEpqO1nbHkR7PEBDg/T/ZsxEO53gu3dPyXFFjoNt\n+/aw72GqqsBUVia9LVFjGJi5UOP92c/QZNEcuMkgFBWh8eWXo/9AG52JTjW+V6+UpgOLRv3nn6Pe\nyoWIWrumJjifesrwx9oVFcG2dq2U4ixFWSWsTDNVoAH2f/87tfnBY8Gy1m9jHPi+fcPnHHc64bvi\niqQdv01f/dJee605obiZhSZScNzGV1+F66GHwr4n7Z13kPbaa0lvS9QYBuf37Wve8dPSokob1WqE\nxs1FoGyeM2EQ3ZZiX/mSEninTTO7GcGczuBKgBaZ0Wsr/YJxu+FcvDimz9o/+gh8v34QevZMcKui\nV79sGRrefjtlx9PtF3FeezNnzza2j8QMrXxFVSwqgu/yy/VfLyhIapaeOMr1nP243bvBBXIu+i+8\nELwZA7YUFbjwTZ6MSAv13Natloq/9MyeDT5CaW5ioqwsND36aMrypJ4N2D17kHP55ahbtw5C9+5m\nNyclxKwsQ5u4SfzYY8fAyKuoMQi7qSwF/OPHm3p8me+662L/MM9Le0gsvhInOhxwfPCBlDyBrqcJ\nZ+3ffrKpOn/aP/4B9siRlDdBzM2F0L59yo+rxfHpp2ArKsxuhsI/ahTWJakYDUkMz9y5pszWWzX2\nlSsrkwY3brfZTUkZz223WSY1plX7RcJZfOBmNVr9QujY0VBKzxbk1ReL/y68118PxusFF6FCJYmN\ntX/7Sea94QZ4J02SHjCMKZsMvHfeaa0CJxbCHjqEdvSHTyyG3bcP3K5d2i8modiK1bmefjqqipgk\ncfju3eGbMCG2D1sk9MZsdatXQ+zQIfYvCFQstPrfulhUBKF797jjv62K3bsX6WFCVW0bNiBLHucl\n4/hJ++azgH/cODS++SaAwAYDE04umT/7mbUqR1noD822YQNKArloCVEzM/Y1+9prkXPJJdovtsFB\ntJW0lZhoZGWhYenS2D7LMMj8+c/BbdyY2DZZmFa/EM85p3kgHAuGwZljxyw/Ew3A3D1fScbU1sIW\npjqzyDBJrT58Fvz2UySJ1QPDHvbMGTCnTqX8uHqEjh3NbkKzVvyHT85iKS77TUiiNL70EvwTJoA5\nfRpMGwo5SpqzZeO5IJwdg/0YcAcPwrZli+7rTH19XEV1Ion5p1pfX48uXbpgoWrX49KlS9GnTx8U\nFxdjpaoMrN7zlsIwpuxgFfLywNbUpPy4Wvz9+1srC4Aooqq62uxWEB1MRQUyf/5zU45tZuyrWFCg\nHwNMg2hTtZmY6Bh5b7oJvssvB7dzJ9jApvq2oM33C0Foteck9sSJ8K8fO5bc48f6waeeegrDhw9X\nHnu9Xjz00ENYv349vvjiC8ydOzfs81ZjX7cOtnXrUn5cMS8PjEUG0fzgwRAtdGedtngx2u3da3Yz\niA7G7Ybjv/+1foqnBKtfuRK1O3dqvsb36QP3zJkQunRJcavMkz1uHDgKuzqrsLW1sLXxgaV95UrY\nV60yuxkp4ZswodWek3wXXQT/wIG6r/svvBD8eecl7fgxpbjbu3cvTp48iWGqnLKbNm1C//790SEQ\nqN+1a1fs3LkTdXV1ms8PMli6Mtm8N94IIYk/aF2CAPaHH1J/XA1Nzz9vdhOC2MrKkJWZCWvcYpAW\n5OVBE8KgzIx9FcNk0xH69YMrhiIYZzPbjh1xpVtLpDYTE00M0eoX3LZtQFZW2BzDrQG7fz+4Awfg\nmT3b7KYkBT9sGOrDVL8U+vVD3aZNSTt+TDPRv/3tb/H4448DAJjAEsGJEydQWFiIxYsXY9myZejc\nuTMqKytRVVWl+bzliKIpu1cZrxcspXHTJHTuDL+B4h8kxahiIQmw0r4OEqVWurwfrfRFi5K+1G8F\njNeb1Jjgti7s1W/RokUYMGBA0H/Dhw9Hnz590LVrV4iiCDEwCyUPpmfMmIEbb7yxxXepn2es+Mdr\n0ia2xjffRNMrr6T8uGcD39ix2E2DaOuSB88m/N20+RhHixEzMsxuAgDqFxG5XIAgwHfxxfBfdJHZ\nrUkZ3X7Risthy0Sns03lrU+1sOEcc+fObRHDPH/+fPzrX//CBx98gFOnToFlWXTp0gXdunULmmE+\nceIEunTpgvr6+hbPFxYWah5v1qxZ6NatGwAgNzcXAwYMUJZh5D+CZD0+UVmJ2sxMyPV8kn08Kz52\n/vgjSkaPhtihgyXaM+TkSTCBCktWaA89Dn6cXlWFCQDAMCk//u7du03/99Nj6XHtpk1Ye+IEUFpq\nentkVvr5WOnxtZMmoWHJEpz0+3G8vBy928jPS+t8cS2gTASY3b5kPhadTnhra1Fqgb9Psx/L/19e\nXg4AuPvuuxEvRhRjD2h84oknkJ2djXnz5sHr9aJv377YtGkT3G43xo0bh/379+s+H2r16tUYGk/1\noDhl3H8//EOGwHvnnaa1wWzpv/sdhE6dLFP8JePee+G/5BJ4b77Z7KYQLS4X2p1zDs6cPm12Swgh\nUWiXnw/P9Ongu3eHf8QI8CNGmN0k08g/iyZVhrHWiDl9GjnDh6PWInuvrGTbtm0YH2cJeluC2gKH\nw4EFCxZgzJgxAKRQkHDPW41v4kTwPXua3QxTcTt3Qhw92uxmKDx33QXRSnmrSbC0NLgefNDsVlgK\ne/AgcktKUPP999R3iTWJIjz33Wd2KyzB95OfmN2EpBOdTrA1NWCqq+mclARx7Qh67LHHMG/ePOXx\n1KlTsW/fPuzbtw9XX311xOetxLF8Obg9e8xuhqns69eD27fP7GYo+JISrG1DuUzPOiwLt0mD6NDl\ne6vg5FW2JFbIIvqs2i+IubT6BV9cDL5PHxNak2KBtLWUwCA5aFu9zKSy30Qfu28f8iw0qCckIiq2\nQshZoX75cgjnnmt2M5KPYeAfOpTOSUmSsHCOs53IsmBoEG0p9jVrUPLDD3CZ3RBiOfKGEasRaRBt\nKqv2CysR22BKSq1+IeokOGi12uDvPRVoEC0zqey31QhhCkmknElpBwmJGQ2iiYU1LlzYNmZfSTBB\noEF0ktBPVUbhHPCNGgXflClmN6OZKOK4FQvzEAAAU1ODrKlTTTm25WNfaRBtCsv3C5N5p0+Hvw1s\npgvV5vuFINA5KUloEC2z2SA6HGa3wlT8gAEQs7PNboYi7a23ULBrl9nNIHqammD/4guzW2EpQs+e\n8EyfDjE/3+ymEELCcLz1Frg2UsnPd9VVEK20ytyKxJUnOpHMzhNNrKddfj7EjAzUVFSY3RSigT1y\nBLlDhlCeaELIWSfznnvgmzgRXo0Ky6RtSESeaJqJJpbFFxXBP2iQ2c0gOkSOM7sJhBASE8e//w2u\nrMzsZpCzHA2iiWX5J0zAHhpEW5ZYVIS61atNOXabj3EkmqhfROB2AzxvditSTrdfUD53EicaRBMF\ne/QoGCstzdNGCMvjhwwxuwmEkCjldesGx9KlZjfDOihjBYkT9SCicC5YAPsnn5jdDIXIMDi3Vy+z\nm0EsiPIBEy3UL8Jj/H7YNm0yuxkpp9svaKKGxIkG0UTBffstmNpas5uh8N56K3yXXmp2MwiJGnv0\nKNrl5wP19WY3hRASAX/BBWY3gZzlaBBNFLbdu2Hbvt3sZij4IUOwlvJEEw1WjX1lDx8GADBUuMkU\nVu0XxFxa/cI3ejSEc84xoTWkNaFBNLEs9rvvkHvwoNnNICR6geVhkZaJiVVZI6ut6Rpffx3+4cPN\nbgY5y1HZb2JZjk8+QUlTE9xmN4RYjmVjX2mjkqks2y+spA2mptTqF2KnTia0hLQ2NIgmQYS8PLOb\n0EwUaeMHObvI/ZX6LbGgpiefhH/kSLObQUirQdMmROG9/HL4x40zuxnNRBFHqVoh0WDV2FeRBtGm\nsmq/sArP7Nnghw0zuxkpR/2CJAvNRBMF368fhHbtzG6GwvHee+gEgLZokbOFeM458Nx8M5CebnZT\nCCGEJBkjitbYZbB69WoMHTrU7GYQC2mXnw8xMxM1R4+a3RRCCCGEtCLbtm3D+PHj4/oOmokmlsX3\n6AGxQwezm0EIIYQQ0gLFRBPL8l1zDfb162d2M4gFUYwj0UL9gmihfkGShQbRxLpocxYhhBBCLIoG\n0cS6GAY9unc3uxXEgigfMNFC/YJooX5BkoVioolleW+4AaKNuig5ezAnTiCvXz+cqa4GqO8SQkir\nRjPRxLL4Cy7A2lOnzG4GsSCrxjiylZXS/1Aokims2i+IuahfkGShQTQhhCQKFVshhJA2gwbRxNIo\nlo1osWy/oEG0qSzbL4ipqF+QZKFBNCGEJAoNogkhpM2gQTSxNIplI1qoXxAt1C+IFuoXJFloEE0I\nIQkidOwI73XXmd0MQgghKcCIoiia3QgAWL16NYYOHWp2MwghhBBCSCu3bds2jB8/Pq7voJloQggh\nhBBCDKJBNLE0imUjWqhfEC3UL4gW6hckWWgQTQghhBBCiEEUE00IIYQQQtoUiokmhBALYSor0S4/\n3+xmEEIISQEaRBNLo1g2osWq/YI9edLsJrRpVu0XxFzUL0iy0CCaEEIIIYQQg2gQTSxt7NixZjeB\nWBD1C6KF+gXRQv2CJAsNogkhJFEYxuwWEEIISZGYBtGbNm3CwIED0a9fP9x0003K80uXLkWfPn1Q\nXFyMlStXRnyekEgolo1ooX5BtFC/IFqoX5BksRn9gCAIuOOOO/D3v/8do0ePxqlTpwAAXq8XDz30\nEDZt2gS3241LL70U11xzje7zhBDS2giFhfDS+Y0QQtoEw4PorVu3okOHDhg9ejQAoKCgAIA0O92/\nf3906NABANC1a1fs3LkTdXV1ms8PGjQoUf8G0opRLBvRYtV+IRYUoHHJErOb0WZZtV8Qc1G/IMli\neBBdXl6O3NxcXHnllaiqqsI999yDmTNn4sSJEygsLMTixYuRn5+Pzp07o7KyEg0NDZrP0yCaEEII\nIYScrcIOohctWoTXX3896LnGxkacPn0a3377LXJzczF8+HBcccUVYAIbambMmAEAWL58edDn1M8z\ntPmGRKm0tJRmEUgL1C+IFuoXRAv1C5IsYQfRc+fOxdy5c4OeW716NebPn4+ioiIAwLBhw/D999+j\nsLAQlZWVyvtOnDiBLl26oL6+vsXzhYWFmsebNWsWunXrBgDIzc3FgAEDlI4vbwygx23rscwq7aHH\n1ni8e/duS7WHHlvjscwq7aHH1nhM5wt6LCstLUV5eTkA4O6770a8GFEURSMfqK2tRf/+/bF7925k\nZmZi2LBh+Pe//40ePXqgb9++ygbCcePGYf/+/fB6vZrPh1q9ejWGDh0a9z+IEEIIIYSQcLZt24bx\n48fH9R02ox/Izc3FokWLMG7cOPh8Ptx6663o06cPAGDBggUYM2YMACkUBAAcDofm84QQ0towFRXI\nGzgQZ06fNrsphBBCkszwTHSy0Ew00VJaSrFspCWr9gtu1y7kXHIJDaJNYtV+QcxF/YJoScRMNFUs\nJIQQQgghxCAaRBNLo9kDosWq/ULo0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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example: Bad Initial Estimate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30\n",
+ "movement_error = 2\n",
+ "pos = (1000,500)\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(100):\n",
+ " pos = update(pos[0], pos[1], movement, movement_error)\n",
+ " \n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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I84JEmBckwrwgEW9bLPTevNnff/+Nxx57DIGBgdDpdPjiiy8QHh6OWbNmoUePHgCA5OTk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\n6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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example: Large Noise and Bad Initial Estimate"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What about the worst of both worlds, large noise and a bad initial estimate?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30000\n",
+ "movement_error = 2\n",
+ "pos = (1000,500)\n",
+ "\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(1000):\n",
+ " pos = update (pos[0], pos[1], movement, movement_error)\n",
+ " \n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense (pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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lpaWCy++9916X/W3duhUdO3b0OM6FCxdQv379wP46EhXoOyaEEEJIVdq/f7/LUMKBCKgl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\nk6bIlmXmvsKb1G6scakUtGbNbE35yuWXwzDXXy4SAW9CS7hkMid23vB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Be1XC5d4Cd9+N\nYoahAiAQQGdl0D9pEgq7d4c8dCiU888nSZZqzm842BiSY8ZA7diR4FCrU+VLJm1wQrl37wyscWDI\nEMI7TCtlOZraAMA7cyb5D9PhsLCw5n34ZswAv317huprasQIpHIoPdp6MCQJ3nfegX/cOBjBoNUz\noxcXE/iWMzllGORc5vw1gkHLUT2+bVveGPjAbbcR/nBVhXfmTFJJcDpfbALC4XRlw/Bz8bh978nl\nrLnNSWavdzpfLMyK7jHxxx9Ps4sA2aGmjFHIj7B5c1Yn2srQs/s6gMJOncAdPYpw794QV68mx2Mq\n8LnoYt0UC1MjR9rWgvj48WQtpOc8AQwxp2mQL7sMiXy4ov/HTrT03XcoGDUKvn/9C74337QHQX/S\n/lJOtPTVVwiMGpXJDWpmiqj0tnLZZRlE50Y4TJoxmAFiFBai6ttvIc2fDy/Drxnu1o0M0iyDnT9y\nhJS1zEYMvUkTJO+4AwAZZDJDdWX7HYsfcy7YNFtAJybN/OTieBVFqB072rBVhs+H1B132OnJGF5h\ntUMHgv11y4DG45kRmGOS2v50/Dgh53dmot9+21bCs8zMzBnFxaRkzx4rHif3WlWF2MsvIzliRPpv\nR48ChoGWLXUMHSrjqacSmD07hk2bjmPkyAKMH+/HgMkXYQZGQJXJtSrdullZJus49Jk7nqfWuTMq\n9+zJyYWcy8RlyyBs2QJ+xw4UjBoFni1xOceQmR3nZDmtWGi7GC2zDMlkyiEI4CorbeVpackSeCmN\nEh1H5mKefPBBwhfraNA0BAF8WRnCeTSF0aBVWr48A7fLlZURzHAsBn7PHgRuuw3hXr1yN4QKQloY\nKds5RRHKeechee+9FkyEU1X4HM1KbDCttW5tZV38ophWLKQZS1WFsG4dPG+9lYZztG2LqhUrrA0n\nw0yn1RCEE5K5NRo0QHzKFEsEw3VTYDdhpolTXL4cng8/JFR4P/xgjRm9YUPo9erBN3kyilq2tK8h\nziYm+nx0wkPv5OOmECxbadV02pL33ZemTjNNPeeczKzjCYjRCOvXk8qMY63QGzdGYsIE8o9qNs7Q\nNddYPOwAybDpDsW4rGp8plHsq9q9O+nEB5AYPx7xiRPTVQrGuMOHUXDHHfC8/z70xo1JUx7IXgSO\nI41qR49mCKJkmKMioAwYkCEmRK+dS6XAVVSQtThXlYQGjNSR1XUYHk/6uLRR0LGGG3XrZl3r+AMH\nbPhZz9y54CsqyFjz+dK0r6EQUbdzCdoMnidjd+XKtBN9gs1keoMGSN5+O+LPPkvgLG4ZVAqnKymB\n4qxwmEG0uGSJTeY8OXasK4TMFROt65mVDuZZO3tG9MLCNCey+bsU1W6gRtfnVCozIWGaEQikne1s\nom/mXBF277Y/WyY7bq2xHIeqhQuJimIuCBF1oh3rXMGoUfB88AGk+fNh1KtHmo/ZhFy+lk/jns8H\nPRw+5YInOc18l/zRo1ZTbjYu9ZOxv5QTbRQWQlq2jGwADD5P2LwZod69rWY64Y8/MjNrHIfKAwfs\nTkskQgbzoUO2yIPfsYPwjxqG6+TnjxyBUadOOhPj8RB+TsMgUV+Whi8nB7PNaPac56FeeCFh8RBF\nG6+lZebm6/o3QYDcuzeBlrB4V02z6AEtiWqHeebPh/+hhxw3myMTbQ5015Ke2yQwAwP1nHPIhsVg\nqbl4HNKXX6Jg3Dgo/fohwSx82UpgHg8wZIiMpUurcFbjY3gfN6LxaTXQuXMY5/w8EzdNbI9165hJ\nyzqjp8D4X38lsJpPPyUwi2QSwk8/2WkCs2UyAILT7dDBJrrCVVbaGtmUiy5CkmLizEWIq6yEtHx5\nmqeVln8LCqCfdhoSzz5Lynnse3GW4yl0qDo8O2CV95Xzz89QOuTMCoK4eTMK7rwzzVKTQ9QBmlb9\nIsXzkAcPzsSyMvPXSS+mXHklFBPvyOKO41OmQLnqKsILv28fpO+/h96kCWIvvACjqIg4ry7X43vq\nKXhff5080+eeq7aBLnz22ZnjlG7+Lk4Ay6Wrtm9vMWMI27dD2LSJ4Jx37SLqhyClb7VHD3BHj5JN\nmpn7Nhott+flHPMMRaNlokioz9yc2SwQOc6ELlVnNulk5zXS81XT0Cv88YdFYQiQ5lvFdIQtM+cC\n/+uvCPXqlfVYLM+u1r49lAEDXJvLpUWL4J0zB9zx49BbtbIEtYJ/+xu4I0esgNmNMs5mDrrI4HXX\nZeJ46b8TCXhmzSLvNFfWUtOIY0QpEI8ehXreeVZlkkskyP7ErOHeadMsVU9Xc9CfWlznLhUHpXt3\nxJ9/3v6hYUDt1g38zp1k3FLIgbMPpRozatSAPGAA4YquVcsVjqma8CetXTukmKQLuTjSG8QfO2ZT\nRZWHDCFwmjycesPvz3DOaSZXLymB1qqVLatdtWpVWpgsm7NoBjTiqlVZG5bVyy5D7M03QdlL3Hqi\nOLNpmVwocy/mmqLXrm3BEsXvvoNeVESaDnNoGXDJJIFnOZ6NtHw5xHXrCL9zJGLfj0+1Ew0yr0+I\nh/pkjWVNMce9tS+dQgaRv5YTHQ6DSyQgDxwIhc32mqUNayLlWQoI/P3vkL76ClxlpW1xpg6HkSUL\ny5WVWRPbysSwzmY06u6oMZNBN2l3+O3b4Zk9O70piiKUSy+F9M03MAQBkVWrrO9a90avyQXbFvzb\n3+CdMweeefNgSBKkefPgmzAB4saN8M6aBcPjQWTTJncVQpYCDQB34AAps2bLwJn348rgwfyGKy2F\n/4EHoLVrh9irryI4cCBCAwbYAhcjHCYRuNvgzYEjW7VqFSQJeGrQBnyHi/H7liOYPTuK1zq/jota\n7MMttwQxdqwfR49yuZ1oTSMURdU0fbAWHD6cwFZMh83gOHCahuS99yJ5221Q27UjwQITjBnFxag4\ndow4bjQTzQZ25kImLlkC79SpiM6bZy3kFAOqduwI5aKL7IIvAKo++YRk30UR0uLF4BSFUDH99BO0\njh0RZfDDke+/J2O4Ogo6wMY1nkF9lkhA2L0boauugrR2rfVswz16QNyyhQRzTsuDttAIhWzf4Xft\nMk/IZH4Y3LTTlHicYO90nbDDhEIWTzk0jcAphg0Dd/AgpDVrwEWjGXRdXCQCo1at7MqSDuMPHswc\nW7TU7vacmUxXYtKkdBMmfT7ms7b9lsJ/HBUqrXVrwlLhOI/Wpg3BnTvPbxjQw+G04mMqBXHdOgSH\nDHHlS3ZzotXu3cGpal7iCUrv3unqIOMQeWbNItWpPPmmM1hJKivTY4Mx/tgx16y0hX2tBiqRPqG5\nHjnu3QgGkbrjjjSbRTXOhA2/bRgESuP8DU1KJJOAqkKvU8cekJsW7tiRwEc0DbE334TepAmEtWsR\nuPtuW6YeqRRpjKtVy1Kh43fvzlQXNY3/7TeSiXN5Lp5PPyVN9GzjKpWwZk2SoFx9NZHoNu83Nm2a\n63z3zJkDcc0a12ux4Y2pQE3Ggwij4tixdEOvLKfZMsy91MgmxuNwQN0w0UatWkg8/bTtMy4WQ/Lu\nuyHfcgsS48dnwJ6swzufC0hVQ9ywARBFFDzwQNb3YH1f08i+WFiYwUKUGjKEJPOCQXvwR7PjDHzP\nM3cuxA0bSFUghxOtdulCKtXOvdbMigu7doE/ehTSN9+kWVbycKJ9zz+PoiZNSCDk/H4iQSqD7EfP\nPHPKuZrdrLhWLfA7d0Jv0YJoHTDXl9e+mKf9pZxoj4l/5I4dQ7hjR6uz1gLZm5ZVYchpZtQm/Pwz\nJFru1HWSgaZOjtsElGWSAWB4NfV69Sy1qFD//hDcGrE0DfIVV6Di4EGkTKyjsGMHpAUL4Pn00/Rm\nIEkk4hVFMpjMFyts2oTiOnVscI6C++6Dd+pUhGg5ShBI6TkWI8eJRonc5hlnQGvXDtEvv4SwZYuN\n2gogm5F3+nR4P/kEheakFP/zHwDIXnrXNOgNGsAoLCQNBuwmyJLQRyKQVq8GzEwpxbaxpeTI99+T\nLKfb4HUJZvht2+yUXubfAz4NLVro6NDwMEZ2Xo9VqyLQdQ5duoQxevvduK7dFsz4oklmnCUIEDdu\nRMCluTKrmdfFHzpEZHhNZ19r0wbyDTdYG4fngw9QQCXd6U/dmqIAS42MP3KEiPawZm4MoauuIkIZ\njmeinXWWXeXMMCBs2kTkcj0eSAsWpIUYatWqXm2OQh5OOw0IBt1ZG5yLsrPBx0UW1vD5IA8ZgoK7\n73blNBWXLAG8XsiDB1ufWVzajBMdnTULGoMrDfbvD9HEwa8dPx5q9+5pFhpJgvjDD/A//bTtuYmb\nNpHeA2RWVLhYLEPFMJuJK1eSzdps+rWaemUZcp8+af5l1hjMJb97twWl4ioriagFfdYOJ1rcuJE4\nnOzngoCqefPcOX3dBC10HXrz5tZ12e7dZVxalGOMJceOhdqmTV7Ob2LChHQmnxkj4sqV4PfsgVFS\nkp98uAP+JC5fDj/LbW+a9623SJZYUWwUa5blKWhF71nYto00/VHTdWjNm0Nv1Ahynz5Qq6PaNDPR\nnnfegXfqVBIMOB0KRYERCICLxwkX/JAhEH/5JYN+ki8vh7BtG6S1a62gQnAJGKxKqShae1OuCpH4\nww/wzJ1rx/2CsOXw+/fDN3myq0S30/jdu8naRRmCBgwAPB4I//mPrZlSXLUK0hdfuDfwM1AJw+uF\nsHcv4XrPdd6dOxEymVIMM1PsbBzm9+yBNHeuNXdSI0dWez/c/v3W95OjRiFx//0AAP/kyWm6Xfrd\nI0fAlZdD7t8/g4GKi8WgNW0KrUOHrBUGYcMGq78Fug6le3eo7duTdYsxo359V5EiLpEAv2MH5IED\n0wk+c9+QBw/O6vQDZl/ZBRdkVGQMBsctrl4N/8SJUDt1gtqhg/u65ryn7dvBVVVB7dwCir0MAAAg\nAElEQVSZwPPY662shJ+tOv+vzexvk2+4AdLq1fBQyfNTyA7yl3KiaelZ2LsXwu7daVokhgYHQP6g\ndEd5gd+9G9Jnn5FFhuMQf+4510gr/vLLEDdtQmrYMHg+/pic8qqrkKKDP1uzmK6T62RLY5oG6euv\nIa1caZWuDUmC4fcjNWyY7ecWvlIQYBQUQL7mGlJOMgwIZiMfhWrotWsTuiKeh1FcTNSjzE1KXLEC\nHkdJj6usJCTqAMHAmdcrX3mlTcHK9hsq/6mqhLaH0qg1bAiFoR/kNA3C1q3wvvYauUZ6/5TCyDS3\nhlBxyRKywTuep/j99xC2bbOwbErv3qhasMBy0OMvvAD55ptRVGTghRfi+OKLKvgv7ICeQ2tg0Td+\ntG9fiMmTfZnV7+PHc2ejYzEUtm4NYe1acs+GAWHLFnhnzkRg9GiLG1Rr3x5Vy5aR3zhoBwFAvv56\nxM3nYbNkktyDi6qk4fGQBZg2lznLeezN0Ow9k3ETV6+GsGsXhB9/hG/SJISuuQZQVRSefnpmIyiA\nwrZtwZWWIvnoo0S5rE6djA3YSU3Gvr+stGHhMBJPPgnP++8TsQyH8RUVmdzKNEhmG3Jr1kTSFCIB\nYHNKzxo6FMq111rjMDV4MLQzz4Swc2cmlpj+2+HEcdEocaJlGYGhQzPvgzX6HFQVXCoFz3vvkX87\n1yYAwX79IC5eTBQWf/kF3ilT4B8/HqI5XqRFi4gzQ9cxNjAxnWjr2hnTzzjDlS2DCvTYv+zgADeP\nZUiSu5OVrSHK4wESiep5aM0KgHzllZBWr05nNKnwj8eTHz+7s4fAyTxBy+v0e4kE/JMnE3gT0thX\nrXlzpO68k2CPc/HcUzaKeNzeWKnrpFHZLbvmYup55yE6eza4WIxkyN2a3lQVsSlToDVqRBp2KyoQ\nuuqqDDw7FMVyZq2KovkM2PkgX3NNptOUqwqkaWTOMqJctjlM4WTVCCAZwSAJjtnnoqoI3HxzmrbS\nvGYuFnNl/tEbNrScQKVvXwTuuAO+qVPB//571vfFMfu5esklacYrZnzwu3bB+957AM8jPmGCtRfn\n0hsIX3wx6csByPfNMeaklwMA3yuvwPP++4Dfj8iKFaQRlgaoTHadnY/hc86BzxTW4Y4ds/Z5tUMH\nKL162ZozqzNOURC45RYi1BMIEAo6s7KeuvVWmyy8q0kSocs1zTtlilUZAYCCe+4BQKgaq5YuRSQf\nikvKClajBmGGYpobuWQy776KU21a06bpfYXtV7joorwYuvK1v5QT7WwUs2AHsgzxxx/hmzwZaseO\n7owbyaStsx8AaeJiOvb9jz+O4K23WgucPGyYfQM0ozyushLeGTMAn89qerNZtkXVrVNe06yMrNXF\nK0kwwmFLqcz66plnQmvUCMrVVyP+yitIPvwwuEQCni+/TG8aZgBghMNQ+vSxNhnD6wUnyyi44w4S\njLjhrJ3m3GidJggks+xw5vQWLQhfJXvfQHpxZpzo4rp1CXUZ4LpRe99+G7EXX7TkcC1zTjyvl8BK\nBIFk9BwbcqtWOp54JYTrR3jw8cdRfPJJFRYvlnDzzQHMuPQLjL5Zw0hMx0W/v4nLuwt45x2Pew+G\nKII7ehQ8q0xJG3yycCkLv/xCFm6nuTxbChFyK0MaDRsiNmOGvQkVIM6tCeOwHdswwO/cmWZyMB1r\nvrSUZAB37gSn6+CPHXNV+nNSOMVffBGqE2fqcAb0unWhtmkDvV49JB5+OGvGhTt4EJxhWJuHzZjN\nUPr6a4jffAPD70f8n/+00cghHCZz1Dp59vGqde6cDgbZa9I06DVrQu7d2ypReubMsYI3IxAAVBVS\nNZAOGjxwqmpVuMQlS6CdfXZGMMxVVEDcsgWezz9Hctw4Mm7YxkVKTdW2LZK33Wafm8z95d3o6MKb\nr59+OnEi2OdQuzb0pk0Juw7r7ABAIEAqEk7zeCDs2YNwNRy0AKxg0jtjhlXl4hIJiN9+S4K0PGju\nMvYAx73Fpk1DhFkP6RwSGUEU8ZtvwJeVQW3fHt5XXiFreTZzNPVapmkI3nADSTi4zePjxyFs3kwa\ncSnmMhAgct0mdZsTmxz5+msoffuSnho2uHPBkBteL1KDB6ex5nTtZWB6yYceyuhhgKZBWrIEPvbd\nM/eqdutGpMIBqxE88cQTUNu2BVQVBePGoahdO/C7dtka9lgzQiFwx4/bKm383r0kW86uaYYp++2y\nRsTeew+6ScXJ4p0LHn44LQPuNLdeCydsh55PFK1qcLXmJDKg5lIhtRJBPA8jGIR/wgT4KW7c0UhM\nTdixIy3+ZDJYAWTNUnv1ys0p7hh7x9esse2NRa1aQdy06aQxxr5//5vAZCjUiL6rE2m8o2ujpsEz\nd66dtSmRgLBnD6HrBellkObOPalrPWFjgiC1c2ekhgwhVK+yfNIkA66nOWVHOhVGu06dA1HXgWQS\nws8/Q69bF+K6dXbqK5AsM8vBCZBNqODRRyFffz30mjWhXHIJtMaNbZEYa96ZM1F4zjnpScXzgMcD\nceVKFNx5JwAgOHAg+L17XTc4rVOnzMnAZlEoLZBb2dz8u/O4wtatENevt37Ll5XBM2dOuhGDOlwm\nrkxauZJky7I1GgFImc0z1TnReqNGBI9GnUjz/6OzZhElKuvGGQcDSG/QhgGtVat0c5vfD6OgAAV3\n3QWvKXvKaRrBejqCD7VrV2hNm7pi2fwPPujODsLYmWfqmDu3Ct26qfhxexEuXjAOXbAOD/GT8LDn\nOSxeLOGyy8KorHTcP21IMu9JWrAAWtu2MEIh6HXqIOFCjM/nwTkZuvRSkqmXJFKGzAYlAtLZFXMs\nK336oHLvXrLpsZyuuo6CJ5+ESEuwNDut62QxlCRU0lKxLMM7dWo6oAHsiz4IBZpT+ETt3t3ChRo8\nj+iHHyI6bx4pSycSWbFlYbMJOBtWGDwP/2OPEZqnJUsg7NwJ9ZJL0kwOLib8/rslX+7K+6rrUNu1\nQ+q22wAAnnfeAV9aCs/ixVAvusjKRPumTIHvlVfSTjQVzsnVbELvg44Nnkfo+uuhn3aafS4AhI+c\nEVuh7B/0GErv3tCaNiUsNl26pFUlf/8d3JEjSN14IxKPPpq3aljs7bczGqSMoiJoLMcrDVzMjU5a\ntMj2fc/HH2cINAGZzZ2sCVu22LjblUsvJSqxDRta2Uyuqgrejz5C4rnnbFRcbqZ062ZrJBTWryd8\nwsw8MerXJ/dF1y0aTJtr06pVqxAaNAjhiy6C76WXrLEmzZ3rKhyj166NxAMPIHXzzUSK2iyhJ556\nCpxhQLngAiTN8r7t3n/9Ff6HHkL4ggtsGHPDdKIBwlPMmtGwoeWcGIWF1vu1rdXUuXbKZZv3J65c\nmR1nDJKp5FIpV+5/Tteh169Pql0AwPNI3XgjmQNmE7uwbRuB9hw7ljFGrPsIhUgDOQu3c4MmAe7C\naCBNkr5nn0VgyJB0hYjjwJWX2wNpAEgmCS2fC5e52rUrEk88QX5eXg7f88+7YqQrbr4ZQSf3Or2f\nbLhqRyaaO3rUlgjyvvUWvO++m74/dj/lOOjm3EgNH56enzRYYxIyRigEfudOkuFmTC8sRMwpD276\nJtKnn4I7dgx6rVrkeZ0k2wSnaYi/9FJm4+aJKPuxgahjHaWJC+7AAQAk2JUWLz6paz1hY3utvF4Y\nhYUEDncKmTmAv5oTbWaNaDmFdSJiM2dC+uILxKdMgd6gQcaCyGkahL17bWwEFO+o169P/tegAfQW\nLUh21cV0Gp0oiuXkGj4f+MOHCYYRdgfRaUYolImVZp1iSQKqqiB9951djZH5e0Y2iDo5VHa8ogLC\n3r1ImtheimW0ypw8Txxsp5NuGNBOPx0V+/cjbi46GWTy2czJDODz2QeiIxOtdegA3Wz20mvVsp6d\n0rs34tOmEZUm2qxEgxXGvK+8Ar60NO3sO4yLRKqlUANIwufOO1P4oNYY3Io3MRIz0EeZj6v5L/HB\nBzH07KmgffswRo4M4PPPzUWDsqKYz88zezbULl2gnXEG2Tg6dQJXXk7+V1lJ4BlsIBKPo+CeeyxK\nLOGXXxC64AKIGzdCWrwYWps2BOZBHZrZszP4lg1BIA4JlVI1LXTddQRTN2oU1B49SFMK++xo5sQw\niCNHaeAAQFHg+ewzOz2fw4n2PfOMe8nd/E5sxgzop51GFv1duwjUI1uDBh0fbtlUugm9+iqMcBg8\n5eCtRtWOP3LEglexFrjpJghr15JmukaNoPboAf7331Fw331Wc6shilbgKWzdCnHtWlQtWACtc2ei\nBJhIWNhpV1NVqJ06kfI5bWrKEghxtEmTzi/DgLhhgxVga2edZVH1Kf37Iz51KqDr8D/1FMS1a8k5\nOI5QUlbHZyrLJPCpRtSHYvSNwkJSBnauD25iKyBrqNqxoyXgwxpLh8gdOQJhxw4i092gQVqq+ATE\nhqILF9ocbd/06QTj7zLGtEaNkPjHP9L34ZIxtIReeB7imjWEl9hhSv/+SJocyfzBg1ajrNasGbiq\nKugNGkBr2zbzYs3npTVqZMeN+nyAICD+1FM56cZSo0cjZYqC2O6PCvgwMJZg//5pwZV164iEcRZL\njBtHVD3dII/OSmlBAWnyotlc+gzNtUnYsgUBJ2NNKgXht9+gN2yI5COPWB9zbg22JrzRlX0iFoNn\n9mzCm03HiGFA3LyZcOGDVKlCPXqAP3IE/kcecd0rjOJiAnMC2RulFStcx0ud9eshOYIP7tgx0p/h\nwM9zx46R8bxli411pLBjRxIg0Tmv6yTIZFkgzHtRzzkHVWYQYrDZckUBX16OQjbADQYhbt4M7zvv\n2O+tsJBw/bP3Y5IN+J9/nsiix2JEGdZFTCsvMwwoF10EtXt3CwsO4MRYOVg4kDPwMJ8f9QGQSED6\n9lv4x40ja/Z/0aq++MLu62kaEI/n5TuciP2lnGiuqgrJv/+d0L8B9iyuSUnHl5a6KxEyA5ta7O23\niSPh95MsS3Ud26bDwaVS6e8VFIA7dsxqIuBkGXrNmu7lE3PR5o4cAb97NwDSVa/QTJUogquqgrR0\nKRST/iY4YIDVBGjUqYOoI8NuLTDmoI7/619QunUjVD4gnNnxp55CaswYQpWm6/C9/LJ7RpzjiAqk\n2RGu16tn0QhlM/Hbb0njGj2Gi+ktWkDp0QOezz6Db+JExP/9bxzftYs0NtWsCf7IETvekN1YHdRQ\nAOEyFTdsQGrMGHd+z6oq1672rEZhEX4/UjfeaL3bp55KYO3aCLp3VzBhgh/33FOAjRsF7BebQIun\nkBo4kDBEmHRxFIPsHz8eoT59ELj9dkjLl9scWWnFCnhnzrQ31NFSLIPDUs87D8lx4xC4664MDmM+\nEiG4+OLi9IeyDHH9eiJBL8uEA9fnA0IhaM2aQVq4kHBJm5ksccMGCKWlaUYAiu10bnKsmIBbuRRA\n4tFHcXz1aoK7B2Gp0OvXR/L225EcM8b9mdN3ypzPN2ECwQXrOrholPC0BoNpDKRj4eZ37cqkRTOf\nJTsuuKNHSZWEyQRJ335LxBFq1yaPb8AAxNnyNO1f0HXCe+241gzTNAIjo1UCQbCyQlxZmZ3ii2JP\ndd0S8BB27EizSbix0USj8CxcmM5c8zwK7r8fRSbPt/jtt664bXHFCgSzBJu+p56ypMaNQADyDTeg\naulSEqjnoVgoffYZIIqIvfQSoGmE6o6pVOgNG0Jt145cx8aN8E2aRD5nnGgaCPvdpJ9NE9audZd+\n1zQYxcWuMBOjRg3CkEDvgxkXqUGDCLSH5VTPwQAEkCwtK7ZCHRrvRx+BKy3NZAKhGUXHcQ2T91fp\n1ataDLjFic7uST4fjm/dahNQEdevh9a5MyJLlhDokDOBE48jbDIo6c2bk2SQyz6ntWoF1SlRH4mA\nO3wY8s03EwYDIH1PqmoXMALAlZXBO2MGkgw/sm/8+HTTPHNeefBgcj6XeWXwPDhVtTnY9L8lc8xy\n5eUQf/6ZBBE+H3Fgc/VDufgA1jW64HL5XbvgnzQpoyroefdd+F55hWD72XFJKwS6Dq60FMKuXWnB\nJ5BkXeKBB4BEArF33kk38DF+B6eqJLnH9GfQIIwG1gBR39VbtkRw8GBbPwLNmlvNgMkkUiNH2n6b\nzaRPP83sRWGgdUmW/vYEgt/EI48g9tprpLriECzS69QhiScTc87FYuDLy+GbPp1Uiv6LZtSqBYgi\n6U1Zv54kGJPJ/7+daEMUIQ8YAL1ZM+glJXbVJVoGk6Q05zJr9N/Oz3ke+mmnIf7KK9AbNIBy6aVZ\nz6/XrInEgw8SeIEZmRs+H2lOiUSI5nwqhei8efZSKb1+ngdXVYWiVq3gmzqVHLN1a6uUo9eunQmh\nSKVyso3EZsyA2rkzqiimlRVZAYBwGPyhQ/BOnQpx6VJCwwVkdJMbJSUZJRuta1eo556bU42Li0bJ\nYgFkbRAwiouhnn8+uEOH0hGnaXqtWuD/+MMq7wOwO0tmVs/2m9q1c18TVfRzWZwLxozJqAZwmkYc\nwZ9/Rvxf/7ItmHXrGhg2TMbSpRH4fAbuHePBOcmVOHP8LWjx5St4fOdwvPTrZfi4zigYigqdE8Dv\n2gXhjz+shSx5333QKB6XOlP0HBwHzjAgX3UVUYKiz6xmzfTC51j0K3/+ORPrSI9HM0bmGNJOOw3x\nF18EF49Db9CAvE/meLRMKfz2GxkbLk40d/gwCXJcGiQBQG/ShOAX6eJjQkWM+vUzVR1BNj++rIw4\n2My75ktLwR85QnChlBLQdKL1evUyuN+DDprE+HPPEelsTUOoZ0/wlG/ZzDaqXbumObfNZ6B27ZrG\n2bINv/QZsWMxh5Ol9OljVQaMcJjgwc2sUGD4cIgmKwr7fFg4B0AabwBSscrA5FEu4GQSaqdO0Nq2\ntQVinCzDs3AhYUBgzSUIpcaXllpQI6NGDSSpI+vxZDpZDGUWtQKK5y4ogHb66Qj8/e922i5FsQK9\nwPDh8CxeDH7XLhhFRZYTTQOvXMmLcJ8+7rhlTYPapQsSzzyDgCNQSN11F+RbbiE84E4BCUEgY9nF\niRZppjKVsgmoqB06IPbWW+njmPhtfu9eeD/6CB5HltAKOhyBqXLJJYhPmkTGWjXcydLCheQ2WUEZ\njoNRVEQ4q831wvB6odetS+ZaFtiRjQaQ4ci2XXKPHlD697d9JmzbBv/kyUiNGIEkldGmTC0mhaT1\n3Y0bUfDAA2SuMiJO0tKlVrMc66CoF14I5eKLMyEJ5jmQSllBBwDIffqQY1DsPLOn68XFZFyZwQy/\nb1+mg69p0EtKIJssK95p09I9GW5QLU0jsIuGDa31NHT55YQO1zCgNWpkJavoMfTatWGUlJAxMW+e\nzYlGOAzvhx9CdEDNEo89ZrGEKJdfjvjEiTZebK1NGyTuvz9dCQdZr1N/+xuBarDX7vNBa9oU4pYt\nJPD0+9PsXj/84ApZsn46bRr4/ftJYz09poN8QWvWDHqdOhAXLyaQ2TwaHvUzz4Q8aBD8TzxBGu/Z\n5vDmzZEcNSoN66im2niqjP/1V2t8SEuXwvPll0g8/TTkQYP+/3ai1fPOg1GvHtT27QldEivfSTd3\nWkZ1OlDZolAma623bJlm2ADgeestSyoaALQuXZB88EEYBQVI3n03AiNGIPmPf0CvWxfSypXwTZlC\nKMqyNciwmxkzkJSePVH14YcQdu2yVJL4ffsIwJ7NjpuRJWQZSCQgLl1qZXAtaitz8RbWr4fHlIXl\nDxyAuG6dXfr1pptsl2bUqmVhRVnzP/lkhkqd854MrxcVx45ZzX/S119nbCrJe+8lz87xbLQzzrCw\n5ZYxQYRyxRW2ZhmAROY0O0mxr9LcuSguKSGltkgEwubNCDJKjgDgHzcO0nffZaoy6jpS119PaLZE\nkWQIHItqOAw880wCa3s/gl1jnsGs6Ucw9alDMHRge+o0PLb9ZtTfvgItR/bBo7tvw3u4EUu/5hCJ\n8jYqObo4+l56Cf5HHyVc5IaB1J13Qs0mvU0tEoGwZQuMBg0y/8YGiWwGmZbQFAXKhRdCP+MMqGaA\nF5s6FUYwiOSoUVaAxY6R4zt3wiguhnfmTHjffBOcLOeUjWWfJ3/kiCu9HQDL8U1dfz3kvn3TfzAd\nC6OkJJ2VN9kfAGRCFzSNVFVMZ8egFQFNA//TT5CWLSMNK5oGaeVKSN9+mw5MmE3CcHMqHE602qVL\nxtrBb92a3pT8/jRGORiE/Le/pbGUplgNtaply4gjfOaZ0Nq1Q+K++6A1aUKCBxDnwgnVsda6eBzK\n1VdD7dkT8g03QKY4Ttp34GhuzUalSP5ob4wSlywh48uFKcNi4mHNHFt6kyaIvf8+SSqwQQdDAUrn\ndOC22+B9/XWCQQfSa2I1GEvXRAINEESRsLzIMtnUGbo+o0YNRGfPtsb8qlWrkBw9GtpZZ8E3ZQpx\nsgsLrWcRHDKENDtt2oQgm9n3+4lyHq1aMWwxVNHTdr20amPuL9KCBUTCPRQiqm+mtLPThLVrLcdO\nO+ssVH3+OVRK78iY1qYNqdZUVpKKUzIJaf58AjkyDCCZhOfdd9PP2FG1zZvByoUGU+3a1aq6scfl\nYjGiK+AcJyakQe7d2wqEpc8+IxXWQACaM/sN4gRzVVWAJEHYvBmxqVMtikTOuZfrOoziYhJUmvPA\nM3s24SC3XbgKvVEj4rBGIvA/84zltKXcnDdzfEXnzrWUMbmyMuKYUlicI8hODR9OGhbptVEBE9Oc\nEuwAyN/N8WQUFpLqZioFcdUqy+HmDx+2M0YoCvmNs7lREBD98ENyrYqSDlIBSKtWkf4SB72tZakU\n4PMhfP751jtPjh1rS5zE3noLSKUQuP12BIcNQyFNfiWTCNxwg/tx6fm/+QZGQUFmso0dn8z+opm8\n+VxZWaaKbzaLx6sVbQIIYQGtaEBP8/Vz0SihG3Y2Vv8J+0s50Zaj6NIta+HSqBqf04mmL84xgLXT\nTsvaMCStWOH+MH0+wpyRSsGoUYM4zibVnG3jcFoWJ5rel+/FF63Ij9+xA97337eVksTVqxEcNAie\nOXNQMHYsfK+/Dq6iIk34D1g8oMIff1gSlpZTZZbHM66FtWjULrZgYph8EyfamoQAAPE4yV46nYvS\n0kzBBo7LzGQaBuQbbiDYP/ZzZmFKjRqFwPDhVuNBcOBACDt2QNiyxZYpopFs0emnQ9i3D3q9ehm8\nv+KGDaS87lgwY9Onp6mgOA6RNWuylqv4igpoTZrg7MtqoMfwhpjQ8FX8e8wWrFkTwdJlUcz7NArD\nAGbiZozH47jkn72xR6mP/ROmkQPQiDuVAgQB/3iuOe4+9Ag2Bc9HsqaLc2w+J4A0XbhxqnKlpSig\npTaGHQIA9DPOIFl5phyvN24M5bzzyGItSUhMmJCWjnfOG44jmStzYXJmBLnycpsAA3foEMRVq8BF\no1a1JcMonVo4jMRzz6Vv0+dLO2/mmNLatIE8ZAi4Q4cQ7tnT5khzmgZp/nwLI2mVmc3Ms4W/MwxS\nHWC7+plmF76iAgUPPGD9KTVkSLpSY44D5fLLM8a5+NNP8DqEAlhTe/aEtGgRpOXLbU6gUVQE/cwz\noVxxBXwvv0wiNAd0BiDBqHfaNNtnNIjhqBSzs8Lm3KAdmSRqws8/wztnjm0d8ixYAGHDBugtW5Lg\n1nYzaiZvuSPLzVVV2SqA6sUXI/rGG/brj0QgrVxJ6McAa0wKmzfnpE4zKF0Xq7BJ743jLAaDwK23\noshByaleeKGtIqKfeaZVGUqOHQv5ppvSe4Y5hjzz5lmMCemLZ7K8gQC0Jk3Sz4AGyQcOEMfa44Gw\ndSuSY8aQtUWWbU6zEQrZK6mKgnDnzoSthJ43V3MxCNyDq6iA4feTJl4KWzKVSP20CdcBKVG7dMkM\n0kzjf/8d/kcfTX8gSRA3b7b45WMvvIDEk09Cr1GD9N048bipVGa1ShCgnn02YoxTG7zlFgKVyGLB\n668n+g+SRDLZBw7AqFMHsX//2wZ9AMyApbgYXCSSdlDdqPyYz7hIhMylHBAttwCUi8VIptKkGDWc\n0EM6hynj1p13IsGKEbnAhrjjx+2Bihl0iMuXW1A+7vBhW3WKk2VSdXc40YXNmqX7tUIhJMaPt5oU\nDVGE+P33CF9xhavPw9HMP4NbTt5/v21d0s44A9EPPkivZ/Q4HAfJ5Oh3NcMAf+gQUrfeijhd08z3\np/TqhbhZjVB79IARDCL2r39Z2Xlx9Wr4mX0ilxW1bJmhyeBm3PHjacinrhPBsMsvR+qmm2DUqpVR\nxfgz9pdyoi12Dmfkb5LU6/Xrw5AkqF26QDZJ16lpZ51FeAEdA7hq1Sp4Z8+GZ84c+O+/H+LixQia\nTX1GQUHO8gIls5evv55gnUBEQ7JlVWzdzG60eGwWkU54lgKIbhqUW1UUYdSti5TJDAKQoEC59lq7\nw0rLxroO5cILbc/SZskkxB9/JBkT6ybJ79zkocVNm1Bw//0Z0JmC++935f60omdquo6ihg3TtD6K\nAu74ccRefhkyU1bkKyqs98bv2kXKVf/5Dzzz56exr8zzTDz8MPQGDTJx34ZB3qmjjKp27+7Kr+tm\nXEWFjRWBKy9H4NZbIR09jCaFFejyz+swsfGr+Aa9sAbdcFX73bjkytpoc0dvDB0awBvftcZruB2/\nHq2Liet7Y9n6ImgGj2HDArj44jC+/SyOOa9FMXBgEDfdFMBDeBqTK0Zi0yYBWkrFlmRzvPmmFyNG\nBPDEE36kUkRNzEvVCJnxARC+bK1du0xYjFnhCHftSrI+0Sjkvn3d8aV0cwQyonzPBx/A98orhEJy\n506EL74YgbFj079zM1WF2rlzptoZU+I2CguhFxZCb9IEqZEjEf3sM/BlZQgwlSIrA2WOTb15c6id\nOpFMNN0MTKcaXi84RQH/++/wvfACKb3WrAm9SRNUzZljw+QnR40imE6mEciJ5QNIadMphMFa7I03\n0kG4m5AI44RSyAlAsmjiihXg9u8nXORmMBibMgVau3bwP/kkQn36kKYf2oDMVizYxS8AACAASURB\nVKtsF6nB8+WXGapgFu0he0/mWqNccYW9TA0gec89mV3z5lrlef99CD//DC4ahcgq5kmS1V9BjfKo\npz8QkHjoIUjff5/ptJpW9cUXSA0ZguDQofB8/rn1uXruuVaVygiFwFVVgS8ry5jfrNH1InXrrRY7\nAgDIV18N9YILSHZX09Kc+fv2wTdxInwvvgi9Th3I115LmGzefpvQ1H3zDWGtMZ974VlnAZpGMsXx\nONQLL4RRUpLpkAUCdoypLIM/eJCM52PHCAVkIpG7R8ccPzSrzek6tBYtCCsGi2E38cVBEw6BUMhd\nlAckE0erK9yRI+l3bu5p8rBh8E2cCL60lDClsONHVUlwx/PgDhxICzu5NA+mbrzRXoVyWiCA5O23\nI/bOO2RdoOuOcz8ESDJm0CBSKWCDSUEA/9tvlniJ3qiRxaPNOY6hT5mSCStxCUC5aJQ40TQTzTjR\nRnFx+t/mc5EHDrQfk1mTaKIpOHCgxSpETsKR5FwikU6GtGoFjVVoVRSIP/5I9lm2UY8JrI0aNVBw\n773pZJo5VoA0G4bNzEy00zH3P/ggfJMnE6iT10toFR29BtX1k3GRSJrmEQA0DcVmPwr8fgv2pfbo\nAbVrVyLiRmXL16yxhPaqMy4et3ORZzH++PF0w69ZQePKymDUrk3WlBzQvRO1v5QTTTFBRmGhTbPe\n+8Yb8D/5JOSrrgKCQeitWqXLhYxFNm60yV3TCJDfswfcoUOQvv8eXDRqcQBX50TTQWcUFlrYJP30\n07NnMY8cSbMhOJ1oyudcVAT52mvhe+UV4iSz9DqqSgYIdbRdBq7etCnka64hmRTakEZpkRIJMkG9\nXtdrlJYvR6h/f4hsFvn/MXfeUVJU6d//VFXn6Zkh54wwBIkqQZEgiEQVMCAoZkQxoIhiBANGBERF\nQUQUBQNgABREMJBzDpLzkIaJnbuq3j9uVXV1T6O7++75nX3O2bO7w0z3rapb9z73eb7BrL6kq65f\nbOO+yM/MygKItqV05kyiiuNy4Vi3jozBg4l36SL0kI2wt8CkQEC8ZFWq4P7wQ9uFJya92rSpWAxS\nExdNE/Pm38VdlZSIKhggFRRYJ1h53z5ivXsj5+YKzJ+qomzYkIRXHjtwO/v3F7J3bwEdO8bZdroq\nf5bpy42bXmJvfhW+WxDmtcM92bixiEceCfPmGFg4NY/bbovQu3cMR1k/hzvfwUMPZVDz9t503/Eu\nO3YoXFVxL4fn7uC66zJZfqAO+7mEEjKIX3MNgRkzcC5fbo0ZKO1UZla5TFm84mKiAweWTmzBUpII\njh1bmgxlzEXlwAEyhgxJGAJB0kFN2bQp4TCaDqer68JgxJZER03IkdMpVHkgeb6rKnqZMlYSHb/q\nKqJ33mnptJobVsn8+cRbtLCY786lS1EbNiQ0blyCGGo7+GpNmqA2bky20d1Sc3KIPPIIoRRnPM1M\noo13OWPQoFKmI9b9Stc+tx124m3bWgc5x7p1QsM7Hsexdi1+Q6UhescdxLp1E4u9w4FWr56F70xi\nwNvDxFJfTNIypc0v5+am78ylIWtLxuaT8eijFlH6Yhvp3+IMzSruRSAG8fbtIStLuILaPj/y2GOo\nLVtany8VF1tjlwoKyL4Imco5f74gcdu+T23XLnGAVFWri+X67DPc06cj5eWh16hB5JFHrPGqjRsj\nnzyJcuKE5VYpaZo4kBlusRbXw5aQyUeOWKYViQEYii6GY6F3zBgBwfunSqksE5w8GbV2baSiIuIt\nWhDv0iW5S2DMMce6dfiGD0dOo0JihW1PkQ8dEtJxkNi3ALxepGAQtX59AeMxwjVnDpKuE2/VCsf6\n9QliWDr4iMkLSBNlatdGKiwkMnSoOITYoC9anTrWM4/27y9sr2vVInrbbWLdN2FNBpxGikQsSKZe\nubIFmUqFd8auu45Y3764TTIngq8T79IlecyRiEjwKlYU32e7L4W7dyd5IIgPTrluo1imbNiQcGFN\nwzco3LdP3HPjGYZefJHMm25KvJuxWMIAxqZeYo5Tq1IFrWZNdKcT9zffiL3W4UCrUwetalUcacyR\n0lWiQRibOZcuxTNxojh8G4cy+3XKf/2VIG+nCSkvL7GGm/fBPmZbxLp1S1Lh+Tur8rRh3DNl3Tq8\n9oOqfTyFhWTcf79Yr00SuXn4SCMl/P8T/13BvP/PMG9sksECWBt5qs/9P4V/wABB8giFhBh/cbGA\nO5gP2OtNzwo3QopEEouLfeKVlIiXKXWRMDGERgWMoiIcO3cKIpzPJ5KC8uWJ3nwz3okTifbqRWDq\n1IRNdjAoCDnmCTjN4uR56y3IzEQ+fhzlyBGUtWvJGD4cKRLBuXSp0BROZeAaoack1vKRIwLXqmnJ\ni6jteuKtWxNMZ5iRQjhx/vqrYOIb98j7xhuigm5UTrUqVdKrqpj31kyig0HB+r/8clwLF7Lyjz/o\n0KlT0suoNm0qFtB0yg3/dDBKE/6778a5bJnAfUejYl4AGY89ZlWz7PjH4OuviwOa2y1UVjQNn1fi\nvvsicF8NoIawIpYkwvUE0U05eoRBVzu469x85Lw8Is0G45k6leDBd4xRFBH4ajGZP36LNukTHMv2\n8fC+D5k1+AduG34rbnpRqJSjWVeNq6+Oc/TrgYzopnNplyjK+g1C7zUWx3zCgU8+EXPOVJAoKRFz\nPxwW98lmWWthhl2uUpVoSdOErrKtiqNVqYKenY3766/Rqlcn/PzzeF9/Hefy5aLCmU7lIxJBzs0V\n6igAPl8Sft5Mzu1JhVa7Nlq5cqW7JKpKzFCwkDRNYN19PtGxMg4PJs5UPngQZds25JMnyWrfXkB5\nMNq2RlJbdBHdXb1cOUEMzcsTKjN5eaXXi1hMVJjTOdTZqs+BTz5J/INZRQwGxXtnT6TMQ21Kqz/W\nty+xDh1wLlmClpNjmXDEevcWhi3mQdp8jrqO2qCBMGRCVB1dixYh5+YKHGQqryMNRC7ar19ijUuX\neBcVkd2uHYW7d6PVrInatGmplq/744+J9egh2qd/Z/t9MY3uYBDl0CFhYGKbB1JenkWitseqP/6g\n9wMPUHDkSKmEP6k6aT5Hc4O1r0sGLC4waRKejz4SGtq1alnjl1QVzeEQnUoTPmce7BAbuGK6Tprf\nHYuJd8J4x6R4nMjAgaWkA50//4zz++8JTp1q7Xtq69Y4li7F+8or4pZMm5aMYZckCjduJKttWyGl\neJGDjrJ5s7BoNmES0ajoup0+jWfaNKI9ewpeks8noBAeT3JF27h/oWefJbt9e2KGqk14xIjS8KBY\nDNfs2ahNmlhJsRm6zyfed3M/crutexu/8kpLf1qvWFHo45sRjVqytabcXVq3TttYzee6cuVKOlap\ngu/ll4kYyiJa48aE7fffIOqZXRrJXKvShGX4Ztuf5QMHcC1cSHTwYLLMroD5O2kOFJKqopm5iCQJ\nMn04DF4vwQkTyBgxgvjll6O2aWNdi244g9q5Bq558wg/9JBViY4MHpy2gxYZNEjM11SctbH/Ov/4\nA/n4cVHxx+AF2IpbAN4XXiAyeDCaTVPeO3o07tmzkzXlJQldUXCsWYOuKEm4+HTcrH81Ah98YCXr\nzj/+wDN1qpBpTAnLcC4aRW3ZEq1yZWGoZb6nf3N4/Xfjf6oS7XnjDUuSyTNhQqISmQZP+C+FccPk\n06dxzZuHcuIErsWLrQ3exJqZIeXmJmN9o1GreqRVrGhpMfrvuUfIPaX5vsjtt1O4cyfhkSPJ6toV\n17x5OP74A/eHH1p4xyTcckZG6Y3KBufw338/7smTE+x0Y3MtXrSIwk2bkCIRS24s1rMngU8+QTp1\nqpRQvnTqlMBg28Lx55/IBQUiWbhIEq2XK4dWtSr+vn2TFDMk26YnnzmDsmULeoUKlqSYhZFWFLSG\nDSn58UfRMk83ee04slBIVEIMqIZsa+kBRAYOFJVit7t0FUDTCI0cSfTmm0t/x9+EXQFCq13bagPp\nNkKkc+VKq+WvV6tGZNgwaxPzjRpVGjubUo11f/qpVYnVXS7RlkrZaMs4A3h9CUlDWVcZMCBG7tOv\nc46KnF65mWeeCREMwhXubQwZVZc6DSpSrV9X2netQq1G1Rjer4jTpyXOxsuxba+PrwJ9mb2gLB+o\nDzJhcQv2dnsGuVNv657u2qXw4m/dmXR0AFM3XMGvRxomjelih57w0KGo9epZxg+RwYMt7XOtcmVi\n116Lz7ZYSsXFaOXLo1erJkipqkrYhs208NW2DbH4l1/Q6tSxkqfMLl1Qtm9Hz8pizauvCniHYRyh\nOxw4f/lFYJBtc8y5eDHuWbPQs7ISlR3EYc3e7TJD2bYtwQ0wmPvyyZO4PvtMSAzG40inTgnICCIR\nCY4fn4BdpN47E85x8iTyX38JTeudO0UCGI+LeayqSCdO4PzhB5AkoWm8b5+YlyZ0weUiOHkynhkz\n8L7wQvL3GC1w5+LFZJpyfbou5rLBBZCPHEkknWkw1OmqM8FJk6zDlnzkSGlugyRZRMfipUuTFBvM\ncC5dKgw0srL+XvIt5T03Qzl4kMxrr0U5ckSoWBj/7pk4UYxrzx7LDQ1AiUTEmFO0f5O+w6hgWuuR\nw4Fz2TJ8Jo7bKGLoNWqg1q9PrFcvIo89loznN9Zs3eXC9c03uL7/XqhGnT5NZo8epZMmI5GySJ3x\nuNBzDgSSWv3S+fPgdCIfPiw6pmbVbf9+Yp07C7dG81psz1GrV0/IwBUVpS2IuL7+Gs877+Bcvjxx\nH6JRAZF0uXDPnCl01Q0513SFCK1mTWJduwoCciCQsODu3Bm9alXkffss/oQUj+NcvRpl2zYy7Nhw\nsORiLfimy4Wcl1daASUlnMuWETfgilrt2kJVI1VkoKhIVNdVFbVOHYEZTo2UOSadOycSaL+fAhvB\nzT11aintZqmgAOnUKaJ33EH80kuTEngpP59469biuZKAuzl277YcJF0zZljV/9S8xn7ftUaNcKxf\nj2w/RBh5gXLoUAIOaRNciLdoQbxTJ8LPPpskoGBG+MUXwe8XfAF7QU2SrHXX+fvvIMvEunYl1qtX\nkrQvIPgwKeRmZft2pJISQnasPYDTifOnn4R2938porfdlnDV/Rt4SfyKKyw1tFjPnsR69kQ+d07I\ndl6smPcfxv9UEu1cuBDZ1IwNBhNl/nTt4X8l0mCe3DNnWhMv1qtXkuSdc8UK3EaLyvP22xQvWYLr\niy9wff458a5dRQUHMGXLSoWmiaTLrPIYqgmOTZtwLVmS0GQ2Wp+pLmPWWBUF3eMhfvXVYtENBBIk\nO6M6rVepIoTEZRmtWrUkPU7l0KFShCU5N1fo0KaMN3LHHaitWqVdeM1qh5yXJzQzjSREy8pK1gdW\nVVxLluAzbc1t127HhqVzr3LOnSuSJE0Tv28S3YwDx5XGKTx6660ULV5McOJEwbgvV47CFPxl8J13\nRCUllSCZEvK+fUkbbHjYMCK33CI+44MP8L7wAp5x43CuWWPdF+/zz5N13XVWch/r0YOAiVM2q0y2\nCD/3XGK+INQ6lIMHE7i0NFAdPSvLYizbOx8KGhLgkDW6dYvz1lshRpf9iG3f72DLylOc99Xi448D\nrL/lNarET9C6ZSZtLnUyrF+Aeac78sc7u9lVpTPHI5W4Z89oah74g+7dM3mpwiz63ehHanQJB+p3\nY9v5GgxddS+TJ7spLEzG/iWN0+EgevfdBN5/P3Eo8nqtapLWoAGR++7DtXChUKCJRhNYQwTsycLs\nmp9pVphSvi92ww0JbVvTbMHhoPmQIcQ7drQgIeoVVwjozaFDpSAhFrbavvjbCMLShQsWrtJMNOUD\nB3DNmiVUOOx/G4+L98G0dI5GhcLA+vUQi1G2XDmhInPmjNAn3bsXzyuv4Jk+Hf/AgbgWLcKxfbtQ\nDlBV0cqOx1H27hXuZ5KEcvQoUjiMf8iQJPiIVqcOsS5drAqgFcZ7pTudltubCcVI/HFK5Sk1zApX\nmgiOGYP3nXdKK07Y8avGRhwdMIDAhAm4Pv1U/Nzsqjmdf1+JtpHI7KErClIkgpqTIw7pZgHCSAKU\nv/7C9+STOIwKePsWLQQDf/58gm++KdZN27PTKldGL18e3e+naP16q2siFRZac1LSNGEqsnNnskJD\nmiQapxN5//5Ex840u0pHenM40MuXF1A2VcW5fDnZHTokGQhJ+fnoZctalUT7e6E2bmxJq+qZmQmo\nD0AgkKjWp+F/OH/+WbgR2uQNpVgs+f8bFXpl7970HVrDbMo6QNjnUTCI99VXRbUPCHz0kZDo0/VS\nOvgoiuhmmZ9ToQKu777DN3o08t69pb/XDNt+HrnvPiHXl2IrLhUV4Zk0Cb1SJbH+Gklghw4d0kKc\nQMiiOv/8U8wpOywpjZygc+FCvOPGiWv88kvBwzI7JOZcCYVEgcWWqJrQIvn0aasYFevUSagCmeH1\n/j0UUdPQs7Px33YboaeeEvrlBw+Kr1YU1DZtSucU5rgXLMCxbBkAxb/9Jop34bA4jJocLRDdDlmm\n5NtvCcyYQZEpqRmNiudtdshtYR6+1caNxb5q5m0Oh1j308xH7+jRlopWkirJvxN/4zAbfPddQdQ0\nn7WtaxMdODCxz/4X4n8qiXbs3p14MW0TWNI0pLNn8Q0bdtG/lQoKSjMuNQ355MnSWDzjhqotWyZr\n05oEPcD90UcikfN6S2kW6ymYoqS/t+NE9++HcNjCroYMHU7d70eX5VKkBPMFiN5xh9A0vOMO1Jwc\nUeU0E/NUO1gzMTVOV95nnxVuchfDSKaGMd7I3XdTPHdu8nWmyD5Z8k+VK1sVQPvPk77TaJlIkYiw\nYzfHmjIO75tvUvLFF5YdZ+G+fQCCGW//TK9XtLVSJLXsoV5+efIiaETG4MFJm0LmDTckVSUtxRcz\nIpEEQcrcLBUl2UAl6YtVMh5/vPTJOGWMUkGBhUtL14aMX3tt0kHNvFda9eqoDRok20DLMrKkU/ns\nLjKC57n0UpV6ZS/warelHHn+PfLK1GN7h6HM127kq3A/phQN4e23Q2zr+zSHetzP3XdHcOpRfv+t\ngOeeC/PWWyEm/lCZLxfIbN3qoEWLLG64wc+yvFYs5jr2cwnHEC3MuCmrZDsU6W53UvVKPnsW4nFB\nTC0pEQY59ta3WaE9fRrP+PHEr7iCWLduQqPdfk/at7fawZLt/UwNrWZNQSB1uZLfd00j3r69sAY2\nMI/u6dMFucrcDEIhC4ZgVqeV/ftx/vQTkWHDBHTCjoE0DvXK2rXEevUi3qYNmddfLxIyU1/49Gmc\nixYReeABUR1UlFKEuOiAAcI8QxMGOum4DKlYY618+VJdI93Uzbe9X/FWrZLsqiVVFWRPh0Mk+Clu\nYVI8Tjyl7W6Nc/BgkaCbUnFGeCZNSr4mw9UxOmAAPlNzWNNwLl+O2qTJxclup05ZCaw1R8ww5onZ\n9Ql89hnF8+db45BiMUGWM0iL5hx0rFxJrG9fvGPH4lqwwBqf+Z6HXn1VzDUzITZ1pUGsW9EovmHD\nkg8jNoiAdPYsaq1aws321CnxuTZ5L93hEJVVI8HSq1ShaPFicLmIX3VV8rtvWxPl/HxRBJBlYdJl\n3o8UuTW9UiXCNsUZxUimpGAQ6fx5/EZRwAzXjz+iHD6MVr16QrnDOAAW7tkj5p6mCWjb6tWi+5La\nXTPcFK2Cge2g4Jo3TxRpTLx1bq7Yj9PJ0coyxfPnW/BNtWlTUYWNRvH+DWQzrRlUajHCkOXTy5cv\nRZ61xpG6TqcbI5SGPZi/a+6DkoRr7lwyTOMZY/+XAgExj+1/a94rGz463rVrkt9E2g6AfV9yuSg8\ncEAkp/E4zl9+ETBV87r/Jvx33onTSKKtywuFcE+eLIqCqXt3asRiouBoGs7YwzjAS6qK89dfLZdL\nXVGEz8TOnWQYxQ7XjBmCzDttmtXNi3XrlnyY+C+FLstWsVMvX55Yu3agKMR6904Y4fwX4n8qiQaS\nTgzWZDVOQE7jRCvv3l2q9eP47TcBMrdNXElV8Q8ebFUZA1OnopUrR4mhr1wq7AuVgSXVypbF9/LL\nOH79FXnfPqGVmO7lAqI33yyqnHaIiLFQiUHaFh+PJ0nv1LxmPeX0KxUWIuflWZuzsnWrddo3741F\n5FJV0XIuLi69UNjGG3z1VTLuvVdokJrX6/cTv+aapD+Jd+5MaPz4UqSmot9+E45gZpjM9JQXUc/K\nomDfvkQFyu1Gz8zEN3w4bhNjq6oCAuJwYBoNAASnTkUrX551KcL1/0k4f/89+dBjO3mDaP0kVXVc\nrgT+MS+PeJMmYlFUFEoMW+CkMJO2f9JmlSQBC6patVQFpVTYDmrRW26haN060VozkxZjDtrVLMy5\nkOmKIGmiTV38/ffW2FxffikIF1fkcNttUd7mKaoZqntSfj6umTNp2VJlxowAGzcWMWhQlEeWDuC5\nClNpzB7asZYhvU7ytP99Pv/cxU0vtObqvZ8werSXA8VVKK5Q2xqLf+DAhP11LCaSaDMh1DTko0eF\nNnVREd7XXsM3dixq3bpJMlmlbsnx4xYTfWW6eaFpaDVqWG1F54IFQqZuzhwwpKukkhJcM2fiGzs2\ngeEz54ZJQurQQbybZhWQRIVUUlULJuZ78UXhXlqmjLg2j4eosdZYigXm+2yYS4SHDiX0wgtolSqh\n1aqF1rChSGDCYVyLF+OeOpVonz4E335bbNI2tQr7c7dH+LnnhNqILaHQK1VKNsIxMdMOB8qOHXjf\neSfpM3wjRlwcq2gkDuEXXkgybErVFA8/8YR4j+yJjabhmTqVWI8exEzN65Qoc+mluD//nHjz5mi1\nalmOtc4ff0yCYIDAqcc7d04k8+baYtyTLcYe4Z49W9w7I7FxLF2Kc+lSC8sa69EDfD60WrUIP/YY\n4VGjkIqLcc2ZI5xNhwwBl4tojx6WFJderZpohWsarp9+svDMyl9/JfDaZrHD4cDz/vsJ8ymHI4nU\nq1WunIA1pEACtLJlS0ulma38i9l+G6Ru3dAkTmdxDuKQEjccdLWaNYldc404HBnzWvnrL9HZbNMG\n54oVyX/scIh5blxjEtY5hYTumjsXx+7dIuFLk4hKsRj+668X0CRTvcn4jnShbNuGc8mSUhV+rXJl\nofBh/I579uy0bf7CQYPINCFX6YpqF4MZ2iCWUl5e0u96X38d1+LFiSKS0XUxZfJMzfrAu+8KaAE2\nbHxxcenvdLsT2sZArH37Un4PINYW5w8/oBw8SHj4cEGY/bsk2ixGpuGWoCiEXn2V0JgxCf6PPYmO\nxQSpMBIR4gA7duCaN6/057vdiUOqruOcP5/gO++Ia3U4kI1DsvvLL62uuglVUVu0oCSd2VJxcSnj\ntHTXddGwv0OKIg6n/wmi4R/ify+Jtsn2WDjYESMIjR5tuWApx46VwvyiqrgWL05qB5mbtlanDlr5\n8kL+zeFIb2YBSZVoU1XCxMdKqiqUPc6eTdvmAbHIOtasERPO/u823JJk4CtDzz+f9sSnNm6cvHia\n4zEWrugNN1gbtXWfjJOg5aBlwCiSB6cTb9OG/GPHiN5yC67vvkPZvbsU2TBtmDCRfftENdbnSx67\npiXLFCESU71CBaENbGx0atOmlPzwA4716/GZ2prp9D6NCD/8MOrFjG3+nUiBA+kpC7vWoIG1sQAC\nTmKM2bV4MaEXX7Rkj+Lt2gm926Ii8Z9AIHGKj8WQzp7FPXmyBWGRDx0iy0xmZJnIY48Ru+kmC9uu\nbNlCps3J0Iz4FVcQSDns+Z59FtfXX+MfMIBYr17JbTCzC2IyqM05YWxOUjSK87ffiLduLVRubPqf\nANKZM3hsaigVKujcemuUzZuLWHXTGxSRxbSXDtK8SxlKClTWLQlwQ6fzvF5lIh4P9HiqHTV/nsmQ\nIRmsX6+wNdKY9VzB3PiNnD+joZUta5HczA6Rc+HCpKrGPxFCpZKSBJ7QFpmdOiX0e7OzBaxj9248\nb79tOfxJsZil8KAYHasSA5Jhujn6nngCtVEjwk89JTZCO2Y6HicyZIioDhpJtCnFKZ86lZBiM7sF\nphqPUQ1xrF5NvEsX8RlXXy3wnIDavDklixYlMIdbt4r3xoCM2Vv9AFqtWskdiWBQHNpl+eLJAIif\nS5JQQEqHF7ZLpqWGLKfnMpifYUCxlJ07hZRVunH8E5HH6aT4999RNm+2JNgy7J3HNBXI4NixyRAL\nQHW7rTXNMuWSZRzbtiGfOkVxyr4RGTaM6JAhQgUmP1+0t30+Yh06iGdRo4ZlxAFQtGyZqGLF42i1\naxNr1w7H5s0JXLbRJQiNGZN0GE+N4OTJonOGMe/NQ7sB57BXPN3TpgkJMFnGsXZtUhHFilgMtWVL\nihcsQCtT5uJ4UbsmcOvWRO+806psWl0lYx2RLlzA37ev9fvhZ58VhaL9+9H9/qRDlzl/zXlikR5T\nDFsAAu+/j1q7Ns6VK1F2705S8pAKCqxDgvvjj/E9+ijKzp0oW7YIzkDqXuHxWMm8fPAgjhUr0s61\nyhs2WImcOUb52DHB6ZBlQdQ3DuhSYaHgR23fnriPsRjZjRsndxA1TaitmMUwg+yMrqO2akWxSbK1\nd48NbHxW584JxRsjSmbMSKrEa3XqCCWo1GfpcOAx9hjd5xOqS8aa4FizJlkHHKx3pJQJmZFEx9u3\nJ9azJ2FTf9kOQzlzhswBA4h16ULQ1HJOHY+516iqxRtyf/65kPGLGzbn5kEjHC6lcITXm1Y1yvPu\nu2SlQtdsEb/mmovLrAKBzz8nbrxj9uv9b8f/XhKdphINyVABq31pC6tSZPub4l9+EbAAh0O8aP+g\ndWhPos0N0tQ31D2eRDsrI+PiG46iIJ09i2wYF8QM61PzmuQTJ3B/+SWRYcPA58P7wgtJVfXilStL\nkXcAa3GODRiQRBpQmzUjMGMG8WuvJfDpp0j5+SJBTWWmmy+4328lUK4ffkhLBrKHvHcvGYZOtf+e\ne0oR6JS1a1GOHCFy++24fvnF+uzwk08KqIzHI7B69hfY/pLaFAxSI/LYISQZ2QAAIABJREFUY7RP\n4+b1b0cqMfUf5oFu4DfDDz0ktDvNDU3TwOEg45FH8N95J97XXhM4VnPuxWL4Hn8c39ixydAi455o\ntROVWq1qVQIffURW167J5BEz3O4kbLd84IAghhoJS6xrV8vEQ61TB8+4cbg/+8wap1xQICpx5iIW\njaIbJE+tQQMh7m+7J5K5EKaJ8PDhxH//mavurce990aYePPvfFbUn0HDvVzZ6DxvH7qZveuPs2/z\nCdq2jfPooxnceupdBvMln4du4aoBDZi2uhVfFfdh2W1zIK5ypjiD5Web8czEWgznfYYylQ5LX+Hq\nqzMZOtTHhAke3hgV4K67Mhg1ysv+/cmSSR1stvZWtU/TOBKoyL59Mq4FC3Ds3Cl4AwCxGEVr1ohn\nYM4/4z3LNGFVRlck3qGDSKJtlWhUVSSgppuZoljdKjMJd33zjXXo3n04g98DV/DMgk7MPXQZyuo1\naJUrC1Z7GkMGM4kqxi/+yRyjAQ9wT5+O5+WXCT/3nDCGMafJF1/gNchTqeuie/JkKwnXqlUjetNN\nFG3ZIqzW7fhwXRfra4pRkuvrr8X/NKtLP/+c3CULhwm+/LIYaySScAC0yXZGjETYNX8+/1JoGp4p\nU3DNmSPmbNmyQs4rBTepVaggtOJTktTWN92UkCo0yJK6oqS/5/YwCIbm75htcvd77wmooEk4MzpS\n1uHf3K9sh1Ld5UJt0iSpgJAuzMTbPWeOJYcWmDaNWM+eSeOVjx9Hbdw44Y2QpoCT1asXRCKi++Dx\npO2K6X5/wrTMHrJM6KmnEvPKdmgyYSJmKJs34339dUpmzUpcx6xZCaK9ua7KMmqjRsRNDXsjpLNn\nxTwxClxWgmXCoA4fxvP22+J/G2T4zG7dxLNxuQQn5SIHMotjkObf3cbnF/z1l1VcUzZswP3JJ6Ao\nODZuxGPwiJzff5+oMpvdArObZOwd8uHDQsmiUiVrb1Nzcog8/DBaxYpJBZBUGVuczvQHTU2zDuP+\nfv2IX301njffLC1iYIxBCofB7SY8apS1V0h5eQKKaOtym5Ar188/J39OSlIZGTFCFA7s+4Ipner3\no1epgtqwIVrlyrhmzrS0qIOTJhGYNk3MLbPAaKwnsa5dUZs0SSKzuhYtMj78XyjgpUSZChWsNS3e\nti0Fdrv7lDAFE5S1a4Urs6L8bdL9n8b/lMRdtHdvy741nMIuTcWDEgySdfnlFBmC7xfVNFYUdL+f\nkm+/hWAwuW2fElrVquKBg5io4bD1vVIwiLJ/P7rLRTBdS98cWn4+2e3aEe3TB93rJXrPPaI9+dFH\nxoWkWInGYn9rHlD0xx+UrV2boOlOlRpeL/L+/TiWLxeXawiRp7ZOterVid52m3UtIITP1RYtSrkl\n2UMKh5FPnkTLzka94ookAwMAx65dyPv2ERo3Tmhupr4YxqT1PfQQgTlzjA9NcYH6Nya2e+pU0VI2\n4RAm2cH8uj//xLloESG7W5ZNfgpIkg9zffEF8fbtLeUVZefOBDnI2Mj0zEziXbqIyqmiIOXn49i2\nTXQNVJXAZ5/haNw4mUBnzkdjUVFr1RISgGaYGO9/MUxCo2QQ5azrUVVKvv8ez3vvCS3U7t1FNQaj\nOmRspo6tWwWZQlWRd+8mu0OHRLWouFh0cC7yHPTq1VHt3RvzfmZloezbh7J/P2pODh6Xi+GjRvHI\ndbvIbtOG8NChOH/7jeWj5vPx0gaop8qzf2t3ntt/L2eORslRd9O9u0YZDuFoVJfrXi1P2bJBDnyy\nll1HmuH44muun/4AO3Y46NMnk9r1ztIkuJWb5uYR+3g2rwSeJKdyPp1LBjH/odpI3MvGbR7c6xSa\nuu8mSF/qFJelpOIF9j7anLyIn7Zt40zQL6EG+7hwQWL6dDc7WEAlzlJucwVa/eQkI0MnY09F8kuq\ncXKmiwoVdDoOeYQL+RLVouCuXZvjd4xk9/RNOLZnc3jWPqTz/ZHeykO7tg+ncTDl4UY0Cj5K/bCb\nV/feyD3cR4PvCpBWZlLecxk1zr3D3ZsV1qxxEApJ1Il2Qbt0Ai8fGEK5ZZC/wE1Mup3MA2Ee+tTF\nXYURiiZ9R3bLK+D6nqWfBaKCFrbpE8unT6OZLpY5OUQMGTK9QoVkYqcJx7K/l6qKb/hwC56h5uTg\nHzyYfDuXIBoV6h+SRBnDfER8sTE3NS2RmP1d8QISLWczedu2DTIy0KtWpXD3bhyrVuF+7z2h4wyW\nkYmycSOxq69Ojz81D7+ShC7LyJqGsn69eG8zM5FOnhS+ApJEtG9f1AYNrOp3ZNAgXHPmoOzdKyzC\nb70VrW5dikzDGHPdMq7Vjr8tWrNGJIU26bZ04bDh0i1sq1Es0WrUsFSGdI8HvVYt1EsvFQnVxdrY\nNihiOk3u4Msvp/VXAAiPFlKc7q++SiR4qfyb4mIyb7qJWNeuSZ07x5Ytoqvp9ycOOw4Hsc6d0Ro0\noMRc90FwQmxrtu7xWNVKrVw5UXSxJ5xgHXCiN9yAc/Fi4Zx55gx62bIJNSjz9zMyCBtFH+eCBTgX\nL0446EGSxr9ZwNHLlUMKhXD++CP+fv2E8oVh3BU2yfLGmmse6twff4xz9WrinTpZ/Bq9fHmcP/+M\ndO4cUZulfOyGG1BbtsT1xRfCydPtFsl7Sq4inz1reWU4Nm2i5LPP0h4+tYoVcWzbRrxChaRCiHzw\nIK7vvsO5dCm+0aMJmjreKbAr+cABwU9Io3oW69wZZBnXrFlC3SczE+XYsURS3LkzOJ14pk0j3qaN\ngDi1aJH4ANO8zRAliN52m1ChMt/PSCQBY/oHhQwtTXVa0jScixeLd8NQN3P8+iuZt9wiJGoxDhJ7\n9wqODOD6/nu0OnWSNM//m/E/VYmO3nKLVfnF70+QKhBJtHmTUBTk8+dR7FqINtJHUtg1AX0+Qgaz\nFkD+6y/cU6ZY/z/erRsRw80vOnAg2YZmpZqTg7Jpk5Cp+VfbAdGolZTEL7uM4q+/xrF0qeVspWza\nJNy/7FXRWEz8XSQC4TDK1q0oBunjYkkugHL4sBCcty2u4RT7aK1WrYS5hflSxeN4xo8XJgcXC1lG\nq1SJQsNJUIpGUXbtwmNoliqbN+P+9lv0ChWSKmSlIlVSx7xNAwemlRozw8S+umbMoGy5cgn7a4R7\nmN1K2Pfgg0L7OqV6kmr+oV5yifVsXAsWkHnjjbiMykpmr14Ex48n8OGHQtNYVdErVyY4cSJF69eL\npMGU2froowRu3+hcSIEAWpkyZDz6qOgwGEl06PXXk8XooRQWVz50COkiGt9JpBj74mdeWzgsSHgt\nWhDr3h21fn3Cjz2GetlllHz5pYBwmO9CRgZqrVoUGIRXx/btAlutaRf/fnvYvt9yjTQreWC5wcW6\ndyfapw9XtNOZOjXIzGd3sKbJ3Ux8L8r++19hHe0Y+XARI5nAg/V+5ppr4rRqpTJ09nVMWN2B8dIo\nbmq+h9eqTOLPP4sYecNuGvhO8NzbVRi7dQBPd1nJJbkrWRa9mkGdj3Cr70cW/hxk48ZCOtU8wBhe\nomW109xSfSUfP7CSlSuLaNxYpW3gdypwnpYtszlyRKaL8if1LgGvHOHTT91MmODhxS038Wlub7b+\nks/MSSEatq5Or5urUrt2GS7v25DLxtzM+BO38fysZvzR/EHWdn+WNeca8kdBK04Mfpwlc47x6zUv\n8+6YE/y5IcYpRy3GT3fy7rtBHnjCQbVB7Rk+PIPt2xVCIVhyuDF/NHuIFyZ6uGekhx9/Vfnz+6PM\nqPI0ixe7qPrGaFqzmXJ3DeLNkbYqsq2a5PruO8FzMCOlm6ds24bj99/RTM1rM9JBOezvjNdL8ZIl\nAiZhzGfpxAnL0RVIwo4CIvlI5SH8K6EKIwll794kkqFUXCxgHkVFCV4Agkwceu45i8+xcuVKotdf\nT7xVK9EaVxRxqDUOxL4nnrDgPNlt2iT4K1lZSWx+LSdHVLQNHLkUjye0gbFV6GThC+D48088xsHd\nVE3S3e60BZKMO+9EKiggcvvtBF99lVi7dkRTix61agkMq66LyrKdC6HrSLm5OE3CpHkvDIy2nqbT\nFm/ZMjnZ+btH0LSpKB6k6mcbkWqVrRuV1dATTxDr1w8A3/PPi31FUYh36iTUjhYuFNfhdluqEng8\nqEaiHZw4UehNm2ud8d9a1aoJLXsjwfeOH18aGx6Pi8R39GjkgweFiY6xPkXTHWZMTPAbb6BnZSEX\nFor7Zr439oKXsebFO3Yk9NZb1n0xiy5WpOt4OJ24p08n49FH0atWRS9XDl1RBNnTPDxhqBYVFSVs\nwl2uJCMyNA2KiggZe69av34SWVfZvx+XqRpkr/6Hw6i1a1v5U2avXkIsITOzVLEy8MUXoChkPPYY\n3ldeIcsgkUsFBcLI59w5MbaSkiTOiP1ada83ucptgyZJkUjivTZhJidOpNW1jvXpQ+D990v9PLWa\n7LC7QQLKnj3Cp8GMlP3f+cMPltvmfyP+pyrRSfiVv4s0Kg92i0d7aDVrXrTCJp85g3PxYitxtkf0\nlltEYmVWPL3ei6oDSOfOIR88mMS0RVEsUoBeuTJa3br4Bw4UzGhFwbF6tcBX2whm7s8/R9m9G7V2\nbeRz58RklCQiBtv1omHDw2qVKpVSE0kNizBiIz65p0/H99RTFK1YYREipIICpLy8RHvM5RJqI4WF\niSrK350mNQ2iUQJTplgSVOKDE/cwNGYM/v79Cb30EtL587hnziyFBYYUEpPJ2Dc0V82t2rFunRDq\nT8HWFs+dm/SdljQdhqpEYWHiJYvFBFHMqKhY7WBIHPDsLW3j3gSnTEErX14Q6LKz4exZ8ZnG/Y2l\nwT2nqp64P/xQVAxTnrd85Ahe0/BGVcWYjOtRmze3lDHME77WsCGxrl0FeSk7m3jHjsQ7dsT32GM4\nNm/GsXVrgvQGlnGNsmcP/iFDKLaRW0x3NlNvWCosFFbBpqrLfffhWLVKJBk2dQPxQByEbZrGutuN\nOx6gffs4XDGK/NHDweUScCejO2BCW8xnIp85g3PBAio/8AB92uTi2vUVjz5/CdxxB3LrF+l/4kcc\nub8TaDsb39evUNRI4K5HtvkN74qldLiyK74fnyGW1ZGSR77nuefCvOKdgD5jNqHtG5FlyF4ynfDd\nT6JsXUxwajeRaFaujNa4Me53pyBfuEDRzy/hdIp1/9AhmXLldGp99i2OdesIjJ0EbjdZ7R8gpn1D\ncPJHIJUj1r077i+/RH3vPcroebRtqyKdPglVFHr0qMrYspPQatVKYMVTQo5pXOLeyNdfl6C9MZmy\nb73EWSpx5S+H2XG7QosWKpW2tWbdgUrUK+vh7vM+HFo5sgHHqlV4PvyQoMk9ABwbNiDv3Uu8Uyei\nvXolkmdNSGcpa9cm1rDUKpWqCuJUcTHOFSvw3347+SdOJNZW+yHP6ST0+utkdutGwOjASYWFKBs2\noJoynymhVagg7LDz8tBq1xbFA1v3UStTBvnCBTJvvRX58GEKbdyX1I6OXqMGsU6d8E6aROj558Xn\n7d1rbexScTG+hx6yEjPrbb6ICYWdgCrl5aGXL49WvTqur74i2r8/7pISkaylJK7R/v0t4wplwwY8\nH35IYMYMHBs3ina7sfZrOTnCcTPpInR8Y8cSeeQRdLcb2VzTjfVEOXgQ99SpwuwJ0MqVS2gie70U\n2d5hgGJTmSEaJeO++wh8/nna5xCYOpV4mzYomzcTvf32ZKt2G7cnKRSFyH33ldImVm1YcvnYMQEj\nM1RoTD1z3eMBr5dAtfoEy1zCqWAjyk1+g2o6oGmEnnySDVc/ysZvT+I7GMIRq0m3fPDF4/x1pixv\nPuAjL0/m9tsj3KKqaIpTnOePH8e5YkWpw0nyABNdHCuJMx39oHSxwv4+6DrR/v0JvvZacjU8VbnL\nJCSmhqLg+uEHtNq1UZs1AwTUxbF9u9hbTUEC25yUCgvJat2agAGpjA4aJOznz55Fr1QpsU/ZdJ9B\nVHSLTQiFbYx6drYwREsNm363FeEwjo0bURs0sIpFpZR0MGy9O3Ui85prrHmiNmlCiUFGDI8YgXz6\ntDCIcjrx9+0rzJhOnUoqcILomJVSWIFS80+rWjVprpVyiDSeXXbjxhTu2iW4QS1bWpyE/9/4P6tE\nf/PNNzRs2JCcnBwWpuoVW6MpPRz3u++KaqNtUqj16wvpKVtrJnbDDcSuvLJUq6tk3jxcX32Fc+5c\nMoYMwbFsGV5TRuwibS/xhyWCQAcUz5+PWqcO8TZtCJgtEuN35KNHUbZtwzt+PG6DYap7veD1ErJD\nMMwWmfkyGpW7JLyU2VY174XDIaqYxsnzomFK62ga8csuS2pZJUUkgnTuHL7Rowk9/ngiidY0cb2Q\n9MK75s4VMjRmtdXtRopGyezTB9mohDhSpLLsIe/fT1anTuLkamwY0oULBKZMEZheI6SiIgsKkfr8\nLOyr/ed2sqW9wmC04FKrP6mqIwDeZ54RBBmPRxDWPvtMfIddTQWIXXMNZZo3t77ff/31yThHI3mI\nd+gg3BJLStCzs8XvGIoj9rHLR44kdEVTJJeSKnu2cH35ZUKeyHSRMt6VwBdfiEXcMKmxwqhG+YYO\nxWksoNGbbkKtW1c8M3uy4HSilSlDdPDg0g6ZkycLbGw0irJhA1lXXoln6lTr+8OPP07J3Lni382N\nKB4nMmiQZYxghu7xJJ6NwyEw3R4PJbNmEXznHaS8PDJNh71AQFTzbEQerVo1cUhSVXzZ2VaSY2Ih\nicchHMY3YoQg0rZtS7xVK0LPPpuEBY3cdhvaS88klhuzvWw8J+fChZYSED4fBIPWlHC5oFEjjUqV\ndMKjRiEbms663y8UTgzDFDFgW8Xe2LA9n3xCdps2yAcOWFhqbPhkx9KleI0ukl6+vJDAA3xSCBmd\nKpzhj8930bNnjGgUtuVW5srDc9g1ew9dVr5Bq9H9ePppLz/97ORtnuT3g7UteKTucKDHVFavcTKv\n36f8+rtHPG6fj8DUqXjt1ZtUCJQxXzJGjEisxT5fQo3ChA3Z8JtSfj6mVJt86pTo3KSGrlP81VdE\nBw/G+8wzKAcPErnrLuRz50T3xPy1cuXE5xUXi+LDRcJcL8Ivvij4DMa44p07E7v2WkEuKykRSg8u\nF8quXbg++wzvM88I7eVBg5Dy8oQzrCzjmjtXqLsgDuk+g3wVvfVWlH370OrVQ23WTCSDKftXdMgQ\nS8VICgSs4obucgncqqGIER42zDLosN9/C/Zgg1XkNWpLrGOnpM7P4cMyS+NdWDl0LvNfOUinLtk0\n7N+esWO9rF+viFtgdhFkWcALdR15zx6LxGmN+eabkY8cwT1zpljT7Lwkszghy8gHD1o48Xw1i0gE\n/vpLtuZavGlTwsMe5Pvvnbz9tocZ+zryV14FwkVRoi4/xVoGu254ku8bjmToUB+XX55Nq1bZPPBm\nU3od+ICWLbO4e9ldXDVnJAOHVWdHcR2Wu3rwU+xaWnarS69VY7jurT40bRTj/hNjeeMNL9d9fg9N\nlrxPnTpleODdVlzHYu7e8jh798rE33uvdFUztVpqPJuYpqCrmgUFymrZEte8eclQRmN9SUqgIaly\nrOzcCdEo2Y0bW6Y21u9lZWFqlFs/MwoVlJQkiMIpCiF2ZSmtShXcM2fiNuGl5mfZITEgiiAG1lo8\nyOTDoufll/GNGCEgVLZ7YXc1lcJhURR58knCjzyCnJ+PfPw4F4voLbfgffll5AMHkoowkQcfRM/M\nRPf7UTZtwrlqFcq+fUmk9ouGeR9S80RVTZbIs8tVgiVTKZ0/n3jm/wAl+Xfi/6QSHY1GGT16NOvW\nrSMcDtOlSxf6pBEF19O0B9wzZuDYtIl4mzZEjAVMr1aNaP/+KJs3IxUUiHadolCSkpxLFy6glykj\nsMx+P8rWrUj9+lmtTN1R2lbb+ttg0BqPXqMGbNmC7vUmKXs4Nm7E8+67RO67D93jQT56VMiXmXJS\n9jCSaK12baIDB+L++GN0r1fgdmxJtHL4sHgxzST6b/DSVpjJWDAo8H/2ZMo+hC1bLDvSeLduIEkC\n+qDriZZRiu6r3RJXq1kzCYLgWLXKao2m+y4pLy/x0rtcSLm5ZPXoQeHOnQKjboYk4R88mPDIkUnC\n7K4vvyTWqRN6xYppCTpmUm+FpkFGxr9k+63s3i0SGCNpdWzYkEgcjBdQPnSIyNChuGfNshIjx8aN\nxNu2RTH0rFPvtVa+vNAGDgZBUdBq1qTIxkb2Pvss0TvuEJVpTUOrUIHiRYsEMzwatcaj7NqF94UX\nKJk/37rnusNB5P77idx1F96XXyZSqZLVzpPC4eSxmIeWeDxhqXv11binTEHZs8eSXBI32iVcL4cO\nxW+TMLPuqSwj5+aSaTtAJJ38Efhr9+efC5e7NCxoefdugftM11b1+cTh5/z55AOF15sEx1KbNUNt\n1kzIHtk2mMJNm0TSHY1ahLjABx+gtm6NesUVOFesSDqc6FWrIpWU4Hv8cYITJ6JdcgnRm29GHzYM\n56JFOJcuJWrApywLZMDz2mvi/R08OHHdpnSfxyPIuynkPBRFdCI6dcI1ezbOX34RCVVeniAHnTsn\nrLN37RKfFwgIpzqMJNrsktnas9laAYMHi3nvLrsET+4c7u9ahGPbNg49/hafbGvHpHktqEYJ3y5r\nw/4fs+nVK0belhvYf/RWfFu81Kihcf5YmDF6Fk8/HULZW4MKea1obToU21qgJSUQOK9TFgSmsWxZ\nIQNou07J9tzs98Y0YdH9/vQ665JEvHt35L17cX/7LaGnniLavz++kSOT8N162bIiibbN2+ycHAo3\nb05qK8u7dyOpqqju2dZ3tVkzlHXrkHNzE7KjioLntddERS0jA71sWQsK4PrmG0KjRyMZSjLmWF1L\nlhDevBm1dWvk3FwyHniAwp078YwbZ90vx7JlKLt2EXn00cR12iEzLheZ/fsT7ddPOMKmWmabz1tR\nUFXY2aQ/ZVoGWfKFixdf7MoNN8QYc/USCoL1eG2oj+XLnTQJPYljtYb3t7OM/jJMTo7KRx+5efjh\nDOrXV3n++TB166osWeLlvPQUl6/XaLdzNcru3cTaX0k8DmfPSmzc6KBg0yX4TnRn3cuVOdn8CA/8\n7qBTpzh+Q+pPzcnBsXARSzdW5O38Nmzf8BJh1UmlGRIFBRKXXqrS+uSznH2lCTuPe+ndO8q6bX7G\n7OpCkZSNHvuTTIrxb86m+jkYMCDKo49GuPRSFfn4cVzTPmbr4FdZ81Mtbm8co1mHQjIz3YCb7Kad\nOPTVMrY8vpDL7zlAmVu7UGbcG1x97El++81JzZoqVasW8uMbF6j6x+cc8nWlf/8uxOMDKZ8Zodrk\ns7QbUIkGDVQa6i1YH27BD/38tMm7nxrU5diBjsx4pi/NynTl+iptaPeXk6uOHUPZt4+irVspKRFT\n2qtp6JLML784yMuT6dIlRpUqIsmVTp5EOnWKzB49KNy6FZxOYr17J0lOlixYIFyIzeRdh/O9BhK4\ncS2O/CCyM4sVKxzsP3kTA0o8ZIOV1EuqSvS669ByctAXL8b7zjuER49Gkx3EchoTvnUgzk1/A1dI\nqZY7Nm7EYagYhZ56imjFagTwsSvYiMNUplztDCq+/C3xPT6857z4C8VaIJ84UcrS3YzIsGG4vv46\nAfezRbxFC6RwWLhnQpKq199Gipylc9485DNn0CpXTtqPJEMy0ffQQwLfbiIIjBxMv5ja0H8Y/ydJ\n9Lp162jatCkVjQppzZo12bZtGy1SW1hp2gNSSYlIZlNOH3rZsgQ/+ICy5coReu45AdhPiaz27Sky\nJG8ca9cmoBPmBm+w69NFqXaFfeIFAsKp6sgRnH/8IbCzhlg9iKqJWq+eaH3+/rvQBq5RA0lV0erW\nJVq3LhkPPYSekUHJN98kKp/xOM5ly1Dr10f3+dAdDuR/0B6Wjx3D9/zzxK68Es+0aYQffDAJQC+d\nOIEUiwmcng3SoNati3bLLfjvuAP69Em0jOwJqDFeqxKu6xZY3yLctWqFY8sWXDNnEjWqZiCgCXrV\nqqKy7nSKU3xqq8t2b+WzZ4UcmS0RdH/xBVsDAdrNnCnasamRUomWNE3gq/+FJNqEDyS5KRlamGZ4\nX3xRkCVT/i7w8cdkXXUVsR49RAvTfEkliWIDp+eaPz+JrCXl5gojBINwQTSKf9AgCvftQ9mxA99T\nT6HVrZtI9lQ10RUwno0lMeR04li5UiwQdeqgrF1LYMqUJDWP0MiRIMsojz+etGA4jIRes2HsdYdD\ndGQMTeek0HVhCfzss9aP1EsuITRuHFJeHt4xYwi+/76Q1YKEGUlKy825fDny0aNpoTqJwSVrZ6sN\nGqSVyEJVKQ4EcJrt9ooVBUHXPPTF48LNDFB27EDetw+tVi0848ahZ2QQGTFCtPGNdaDYxlpX9uxB\nUlVrvuk+nyVhJRUXl0oErSRakggPG4brq68S/1ZSIqpPkkTJd9/hffZZAY+xX6th+534o/TymeEn\nnkA+cwb3rFk4f/7Z2pAjDz2E7vHg2LkTKRCgcm0Xo3uGebHu97hmzyYwbRon4kX8NLOQ6qumkRP8\nlXp/LEXSNcpUqMCHr53iq6/KEz1bm/yjD3K8aTZ9+sRo2kAip+0Y3rrez+bNDpxOHa+US4U/g9xb\nLZ/6xR1oGwO1zXV4F3yCLsvEO3RAz8oyoJsSZc+fx3/77RRP+5gDqy+QufMbKpW6MuOy7ZwWp1Mc\nKvx+UVjYsAGtbl1RMDEdGU+fFvjMlLmRO2UKtatVE9Vhg6dQ6jsMR0Hd5RKHtbJlkz/HxL926CCs\n7M29x1w/0+0ZtkOHfPKkRfC2vtvEUJNok0dvvjn5MAtkN2hA4ZYtLFnuY502ns9zssnKyiL3hE6H\nRmd5+22dZcucNH+4J37tKu7vqTF+fCFlCrxkDB6MY9cu8nuKivdbb4WIRkM8/7yX22/P4OQJidZN\nglyp1OC2O8pwS6NOnM29mjUtszhzSsfp0GnXAao6yqEWtKZWJWizDxdtAAAgAElEQVTR0sXTT3tw\nOKD5+WcI8yjHlvVm/9Yw1bKKGT0pQt9XtqI4JfSmTYhEYNUqB0eHHcZ3dgNvTKhIhSvrU3bi3RAX\nBPf86o05uf4MNVcsEN0o+22sWZPwKy/TCI1GjZK5MlJBAVrZslSooHNDhZVEyzcgZlR+fR6N3r0T\na9ewa/8i47OviNc+w4Nf9eP77zdR67SDyAvvsOTwVObvqMDOnR1p2FDl3nsjbHk/i12Z7ajijvPd\noggrVlRn5eqhjOnlQ6GAe7ZuJ2uSmwkTxP7Us+7jHPytKkG3j4YNVV591ctnz2ymxfQfKFfdzYlQ\nBbZoHWkZFh1JrX59i7wO4hXX4yrfbGjA4sU+Vq50UlQkoUQ/JL7Iiex4iEavQMXqt/PC404qvqZx\nSS0XncNPsvbtDhQfvZRn1ipknK5FINKFz4b7+XlRTxzRToTeyCBbLqbmdZn07h3lkUciSBIUFkpM\nm+ZmxfnveHqdl8t6CmjaN4cfoW1kEV9/3p/6xU5+3J7FSc6TuTXC5aymJK8yucsq4eJO8m8rT6G7\nIhpBnlmwm2HXQZkH7iHw6jhO6tV48kkfmZk6XbvGKT5/J1Vf3su6ei2QMnyMHBkiKwtOtejO+fMS\njvwfqcb5i64JpcLtpmT2bKtr7tiyBc+UKQmunBnGPiAVFSFFIkI4oFYtsc7acPX/rfg/SaLPnDlD\n1apVmTp1KuXKlaNKlSrk5uaWSqJ9jz5KeNgwtCZNhLPN6dPI+flpWaRmxJs2FWSEdGFWFmMxXEuW\noNavj/vTTy2npFQ4h3zsGIRCaDk5VovWDK18eeu0kzFihGi/2cHyHo/Vmos88AC4XPhvvBE5N1ck\nOyYhzIjCVavE2OykOvPfTdFyh0PI7kSjQuLIlqQmXSPCU14qKhK4onAY17x5RAcPxjV/PvK5c0Tu\nvjuJ6SvFYjh/+klU6StXBpPoYd8gVFUwritWJOOee1C2bydoVj51XUgmNW8u2NmpSa6pV60oRG+/\nXfzN6dPpJ6+NVW5Pak2oi/2zY3aHJ58vuW2l62g1a1Iydy6Z3bsTmDRJSIqlCwPu4Pnkk8TPNC3Z\ntU0WhjEAzsWLhUGDIWEVeuYZKyHN7NaN4Pjxye6XkUjSgcD1008JTVQjuXYYpEnLTjkaTVj22ggq\nputSksuS7UCS8cQTlEyfLhLAoiJiN96YcG5MJRkZ9zo4YQKmJbPu96PWry+S6NSqgKaVxvTZkhGz\nmhB+8UU806dDOIyWk4MaDuMdPZqQDctNRgZq06Z4XnsNtVkzC89phlkhCI0ejWf8eKEbvG2bNf6s\n5s0p/ukn1CZN2DpiBJfVqEG8fXvxx04ncm4u7k8/FcmScW2uWbME72H4cAEZshvjpONKRCLErrrK\nwoLqGRlIwSDeMWNwzZ0rWpm7d+NYt07M62jUes4Ro5JthvPXXy2jDun8eeTDh8Xv5ucjnzghDnEu\nlzjkL18ulA0kCceffwoGvf15ezyEnnpKdEXM96W4WEBojE0hftllZAwfLmx9DbksvXJlqqMzvP5P\nZBwVxLd8CZBk9KpVGdQ3j9uGeVDWbsQ3ZgxbPljKbzNO8eeLh5nTYgT33x9h3rwSQhv2UHKqhP2T\nljHvwDBmHn2AHVXL4Nd/pcezKl3eL+TouLmsGnM1O45nE41KlOEETfbsZmufK/C5YkQLrySnn59x\n44I0aVL6YCRuuNF1MTku4TBZvXoRvf56SubMwWdo4HoNrLdr3jzRcTCkOh3hcIKonKqHbX6H14vu\ndAqJPKNj5PrhB9SJE0X124C56VWqWIo2BXv3kjFsmDBuSknclbVr8UyeTNg4aGaMGEGwaSt27VKo\nWVMVeaKhD5yfL7Et1haVynz3ex9WrXQQKY5RqZ6XHj1iVLnQl4WPVWTrJrhRjfLbb8XUrKkhvTgO\nVxkfkQGPM2BAjCm9luD7YibBxwXURMuqlXY+V2xUj4nvv4/e3YX68LM4HxqJ9+VxDJ11DVPG6LSr\nfIjH32lEy4410CIqkW9Pouw8iG/YKIqfFuvT4MFR1q9XyB2+GkenppQZHKR9v0vwXXct0Rs/AASH\nRj5xAl80Steu9cjyfwxFEIxOxD3wOWs88smTZOXkUJ4d5Kfwi9zvv291m9OFe8oUYtdfj161KlpO\njijMSFKSHjgIaUetVi3i11xDyaefoihQuXKI9lkhMllIp6F/obZMrM1SQQE3r5yD3jFLPH+vSvPm\nKm79fdSaZzh3JMRzRc+wa42TVcvP4SvIZcZvDbmldZwrryzC64VffnEw8L5mBOQTuM+paJ/KVI7d\nRpW7K1K75CO0nI24enak1vafWaF3YO3e8jRwTkYqV4Z7n4jz9NNh6tbV8D0zmqKqDQjdfa91vigp\ngbzDARZMPsVprRK3tj1AbqUogwY1pYanD2VoQO9WGq8M24f02wrcQ2/l/HmZkydDvPSSly+/dBOP\nw5kzMt27x+hXYy3PvzOU/Y948Hh0bnK7mR6/iytZRfSIm0mTqtJlaEv0++4gY9IEoj16CAfWFStA\ng7zDZzk76Dnu2vwqn7XP4srTg/lhaQ5Ot8SgQVHKl9dYssRJlVhNVv+u0Lh+CcfzM7j88mzKlNE5\nd06iYkWdzNyxHKMKAzdvoBUZ3JiS5km5ucinT6Oa7siSJPZgMy4CydAqVSJ++eWCe6BpliKbpKri\nZ/8kd/lvxv8psfABQy5m/vz5SGkIeu4vviBy552AqIia4ujOlSsvCgLXK1QoDQMxE4HUtrIs41yz\nhuj11wMCYxky8dGAc9Ei5GPHCL3+OtKFC0Iw3wi1XTuLdGPZfptPPBLBPWcO0d690erVS1QzjVam\nY+NGnMuWJbkPaQaTOinMz5NlcLstuT35/Hm0FJkaKxQFtUYN1JYtE1rZkQje554jOngw8unTeD76\niFjHjrjstt6xGJKmERoxgniHDjgMDKj9UGFWTZWDB3GZznfG/Qy+9Zawu5Ukgq+8kmh52q/F0FKV\n9+0TCUKaE6B7+vSE4UssBiZ5D8DhoJnhcR+76ipCr74qkj0jSn78MemzAh9/LOA0Hg/Krl0oR4+m\nTaLlY8cEPjweJ96ihZBO+uUXyMykZNEiPOPHCzOaPXuIDhhAwcGDZLdsKVRSjMpH9K67sNLNWCyZ\nyACl5HR8o0ZZah+mvqwUj4Ou45kwAWX/fmLXXmspeJRiZdv/G5JwbXpWFlJREcqePdYzAcETcP76\nq0j4DHlDUxLJ+8orKNu3U3joEHqNGgRmz0bKzbUIldbXpJMgNMeR8jzNw0D8qqvQKlTAP2QIsZUr\nhdKArRInnzyZpJlthVGdDY8aRdiQMtOqVydstMUtMqTfT8uBA1HBUhzQs7KIX3YZ8qFDCXUCwzVQ\nMshhkqYlK+EYz0w+fhz3e+8ReustpEgEtUkT3N9+i7x3L1r9+kR79hTtTgN/rRw5gvPXX4ndeKNV\nhQZEB8Q8BOk6asOGSKEQ3lGjUJs2FQd5IzH233030X79xO+rKq5584hfeaVQCSgqwrF5M9EUa1q9\nenWiffta+ELlyBF8jzwiTC/iccKjR+M3iVSpUpppDq+mrrRue5aXXKKR0/8EI5eNoOjXBKmsYr/O\nlMybR45vOZ3mj0bXQVUL8LZuyxMZq1j0UwbNNZXHbj5Ck5scVPp5NmdGvs+fdGTSFA81s4pwvPI6\nH/T+hZtvzuTxx8Ncc02MevVshYOUccbjMOvLTC7wCqE9l5L7XU8aBPLJZi/3x0/jQmjdX9h2BPc1\nJ9H79qRG+fLIW7YgvfmmSIicTvRAkN/WZVHlSAYZl99J7foN8DoclCxcSMaQIfwVrk0FqjDt1zYc\nO+mld9MsasUuZelHbqrtas6B/ApcCNZG+/0WSriHR49mcIlxlo/iQj5zhljXrmzt+gjvDfdxlJXs\n3dOE8vdkkJsr07ChyhVlLuPgjmasbZFN45rvILOXTmUcjO2/ntofjGF3w9Es3tWJHfq1NGuh8e49\nG6jedxT5NQW8yiPH0JTE81Tq1iDeI6GGJOXmikNaSsgFBSiGekHm2QMEZBk9I4Nq/iLe7Pkr8vHj\nhHJ64IkZKhanTiEfO5YEk5NlaNdOJbPMDwQfuAr1Mo2ynCeix6w1ULpwAfe33yKdP09o3DiK1q7F\nf/PNIEk4V68mMmgQjtWrBdEyBYdshu/FFwXE5WJmaGbnBgjZCLNWV8d4n71vvUXxzz8LPoGRG3To\n0AFpyZLkuWaE5623kAoKxKHYDomTZZyySvmx9/FheQ29YgnyngP4H76bUTYukFRQQPcOLja/s5as\nbz4nVKkWGS3q4nntNWZfvwrt/3H3nWFSVGnbd4WOk8kZJIPkjIyigC6YFQQRFwVdCS7qqougJNOK\nSxIEE6Ioa0JdFFwFRAFpBAlKzmGQIEmGmencFb4fzzmnqrqrWXe/93svr+/5AzPTVV116tQ5T7if\n+976LaRgHZS2uQKnV0cx8q6DeP0jFSXzd6LNzbXgb23tacZllyGnKA8eW4I+NxcoMA/jqdAgmLVz\nYeyuhfijj2LkpI3wffQR/HPmoHTkBQC1gPaD2DEGGjQwsHx5BbZtU5CTY6JxY4MN+VAMQxzxoyXw\nrvoa+V8tgXp6LSSYwE9AaY8LSO4mOMjFvzxMY/rEE4TB/vhjyB4FjfLO4psnv8Dy/DtwaPh+TPj8\nAKq1qyH6UpCbi9ybXoLn7HqUjdgEo3Eejh0jzHwL72EEPv4QvkWLcOq0gtlF7+JN3I+p3fLRqpWO\n+vUN1Kun43blJzR45G6UnjzpfC5isNwdYb1rV+hdu0K95x7Xz6T69XOFDv+39r/SWFizZk38YqPO\nOn36NGrybHCaLVy0CFOnTsX6DRtwnmdHUykcOnrUIfUbCoWw97XXhKO2eelSbGZOlX/ePBTVqAE9\nlYJ0+rSAKER46d80EQqFsG73bkHJEwqFcPTwYbEhht9+G/ttFEKhUMj6fknCgX37cJAtWrwDu6Kk\nRGxcm5Ytg2ftWnJWGRn7Ssb7mXE+9vM37dtDr1sXiQcfxKru3bFGVWFUrgzvkiU4evhwxudDoZBw\ntrZu345oOAz/jBlU/kwmEQqFBEZxz65dSHGnKycHm7dtwzHb9a5u3x5rZ89GinVNb1yxAuc2bKBS\neRoHq5mTg+9UFQeOHaOmQMPAydOnHdd35tw5nD5xAmYggOC4cdi/cCE2ctwxv/7vvkNw7FhE3nsP\n4Zo1sbFLF8TGjhV/v8CI9ZM33IAtf/gD1lZUCMiP2/it0XXhxJy9/HLs3rcPiESQc/fdjs8HH34Y\n2LIF+3btonvz+1FeXm6dT9ct2VxWBTESCeDiRdGUYD+fpGmIjh2LnTbRnND69Qjx5jSWXTt95oxo\nCAp9/71QBuOl36/79hVl+p9++glRVrbSGzTAuTZtsIlDAQBUhMPYvm0blM2bYebkYO+GDThSUkLn\n270bJ77+GqFQiKgg2bsTCoVg1K0LMy8PpRUV0GwOSygUwrrDh1GxcqVjfI1q1RwwETMQQOraaxEK\nhfDDli2Qz52DdO4cQqEQEpIkMPW71qxB4uJF+BYsgLJlC34+cgQ/M3J+6DoO2OZzYOJEfP/NN1j/\nww9CDCW0dSvN7ypVkOrfn6jLOHe32/PfvBn727YVFZwN331Hf9d1JO65B9/XqYNjJ08Cug7/zJm4\n8O23OM7GUyovR5KNF68G/DBxIkK//EJO9LBhOHPqFN0fUwP9tbQUOz77TGTOQqEQvj96VDAkhNav\nx9dMZli+eBGHWNOlnfv0+169kOrZE5Km4fyJE9hfUiLWn/0HD7q+7zxbHQqFsHnfPsIdKwrOnj6N\nTVu3ikD6+0AAG7t2Fccf2r8fZQ0aiEpLKBRCnKvUJZPY/cMPKOGBjceDsKY5vt8AsG3fPlEpWr8+\nBG+3Tsg5eQjTHj+GBx5Ygb/mTMW1V5ShRg0TwRcmo2HRaYzE66hbI4UtJ47jZP1auP/+BF54IYpV\nq87hmmsCGDQoF3fd4cWQRwowCB9iytbbMHFiADfdFEPnzgo+/TwAExLU1DkUFe3D6T/cha/a/BWX\nLZ2HXITRdfNraLhoKno93AGzZh3A0TM5+PZkC3zx1hn8dfXlWDZyNQbcqOKRR4C7XmiLW3a+iLb9\n26Ndcg2aN/eh/Zq5uPa7Z9AQR7D8UH00aGBgwtwGGHxiGr7++le89uMVuBDPQSRyBG2wAy2xB9c9\n3g2XN1FQiFLknjqIHk9ciz4bn0Pfm/PRrJmOFzAe31fug7eHT8Oet1fhueeiSNTQ0fbWKA4duogV\nX5VhXaAXiotXoVeHC2hXuhZX734Wd978Bf4R/BMeeiiBA8d2ocJGqXfi+HGU2PpP1paW4ltbkHXi\npZcg22Sd9Z49sYlXRWRZyLybsozorFlYX1JC+53NkTUUBXn9+sH/wgvQf/kFh3kVic2XSGmpcGIB\n4PyZM+L/8cGDEf78c7G+b1q5Eub27QLmdhRAjAWupqJg05NPIsSoMPn5AZAyI9zX95PHjolA3PF3\nVcWGdeusn2UZ60+dwmobVCQUCmEPp5Njc1t8XlFwOBjEWhs9ZCgUwpGjR6mi07w51u3fT59ncDH7\n8YFx41AyYwbOHPsROd4UKhvncOSXnyGZSfS/5izuw1u4XX0PTZt+i7/VewU39DiPAwfWIdlTEg40\nP19ixAgkBw7MuP8ft29H2O9H+ebNgKpi97ZtKH3uOVExcxuvUChEAdChD1B5+n3YsMH590Orv0TB\nhwsJZ50GIUs/35mff8aBoiIaf0nCuQsXsH/vXvTurWFszlz8fOwHhEIhqJs3I++OOxAKhXCR7V/y\nuXOQunTBL3u/RPuVM6GePwPj3Xchnz6NornjMeG1Inxd7TaMGrUe11+fRF6eiY8/Lse1z/XCGMzB\n8mXAunWZ93fK5lMaxcX4nmOs2d/PX7ggfJdQKIR4URF+OnYMz61fjxFvvonRLqxs/439r2SiO3fu\njN27d+PcuXOIx+M4ceIE2mRRyrv3vvugt24N32uvWRyKkoRGzZqhLmtmkU6fRp8ffoB/2jQq48ky\nrty9m7IxN9wgXmTVNJHzpz8h8cAD8Hz3HTB/Pswbb0Rs3DgUp2WCe2/bBvXsWcLOACiqXh05TZuC\n52WLi4uhrloFz9ixgCyjaZMmotSvXXcdtM6d4R8+HMqmTZCPH0d3hnXjIHd+DtjOZzfxM3PSxM8s\nam5YqxZquR1/6hRgGOjQqROCPh/0nTth1K4NxTRRXFwMk8ncXt68OTy5uUBZGVLXXYfuqRTkunVF\n1l4oA54/D2XLFvSoWhXBX39FxahRQrwDoOzVxX370D0YRP5TT1E53TBQu25dVLJdX/UaNaB16YLw\nH/+InLvuQqvGjZEqLoZZWIjgyJHo3aYNEsOHE2NAURGM999Hm8aNRcRZXFyMnKpVsW37djRZtAjN\n0+ZJ1vFjVlS3LnLq1YOWTEJdvx7F9sywokBVVTTt2RNYtgx648bwjRtnncOGi/bNnw+tZ0/Iug54\nvaj48EOYeXnO79M0VD17Fjm1aoHnONL/DgA1qlSBIUl0fNu2lvIUW2zsx7Tv2BHBQADlAJLDhkEd\nNgwdYjGq7eXmIi8/H21bt0beLbcgdc01uLxuXcjBIHD0KGCaqF+/PqoXFyP69NNQjhxBcXExPCtW\nQN24Eal+/VCYSkG1dVdfVakS5BMnMq4/XlwMqCoCzz8P0+tFxfLl0Fu3RjGIkgkAcu69F8X/+hfU\ntm2RNE2YALp+9BHUc+eQ8HohaRrq1aoFeL2IgzLKTVu0QAP2Hf5589A7mUTsxRdRztgC3J6v7+JF\n6KtXC9qj9PfJ99NPwJkziM6eje5XXQVlxw54VqxAbPx4dBwwAL6TJ0ko57PPUGfXLsQefxxxgOjE\ncnJQfMUVkD75BKbPh6YjRsDeOlm9alWoeXlQpk5Fsm9fVK5aFUWHDwtsOb8W+3oBAOYnnwCmicYM\nCpbs3x+pa69FYOpUtB0yBEY8DtPvR9WCAhS0aYPU1Vcj1aMHmjZvjss6dYJvzhwkHnrIutcvvqD1\n4YorEHz4YUgVFUgOGoTcQYPQ+dw5sfZ1YskBbo0bNoQvGBROU3FxMfy5uQhrGuSSEnRZtMgSElFV\n5AQCTlVIjwetBg9G+P77gVgMvUpK4OcYdF2nTN8nn0BnfS/enBx6j0pLAUlC+0GDAFZWvfnmFG6+\nOR9nz0ax+ZsYfA8+hHN12gDtq+JgbktUj5Xg3nvroFYtE507VqBqjQlIdB+M6HMDAKSg637sGDAT\nbde+gr01+6FR3Tg+027C+6vvwlub66Ne7kV4fz2Nhr9UxvxTN+OOu09hwLXnULiYGHg2jXoN4XAB\nqldPoXTq52h7a20Ev1kOOeiHnnMZxqy4CZ7Vq4mp4sgRQA7CaFATeds3Qjl4ECMXXYGSdzai+tld\nCG5Yi59qDcW5ZAEuX9wEtWqZKJqyDrq/LupduABsXoVu4zqhWzcbx3R5EmjXjsaXra3V4nFc0aGD\nwEvz9Zy7xXVq1oRRowa0bdsgnT+P4j59HM+3Yd26MG3Vy0q//oquHC5pryQpCrQePdAdgOrxQLM5\n3pLfD/n4cWgdOkB77DG0ungRvLuEr8cRmxNdqUsX8DbSyowBwmBrXQ8A3ooKJBjDTv369eEDoLOG\nzpbNmqHLzTej/MsvoXfrZs01FiSnv/9XNmuGgq+/RowFgfa/VyxZgu7t2sGzciXMVatgKgq6d+li\nUZICaDt7NuoxhiNJ05znVxQ0qFcPNdPXk927aT0FUNy9OyWMysuBVMp5vCyjaaNG5A9s2wYpHkeT\n1q0htW0Lo04dlH/3HfIeeADXLltGvRiqiuJWrRwBySX3M11Hjw8/hMz2A9PjQbsTJ6Akk0hefz2U\nnTszx6tJExS2aIHInDmQwmHUrVwZVdLuT2F0frHx45EcOBD+adMEw5I4X3k55NJS1KhUCVUZvV3w\nkUfgGT0auQ0awAAAw0Dnbt1gVq8Oc+NGwDTRe+9eaNOmwbz1VpiqivxIBFc0awbfU09B79AB/rw8\nGJJEa3kyCSz/CsMaNACtoCn85S9+fPjoTsTfOYpnplVCjbp90b27huXLJRQUmOjduydq1PgXDFDS\noejkSfTo0EHQVRYXFyPn7beRZE50cXExPDVqoF3nzmjNKHwB4EdbIPff2v9KJtrr9WLq1Kno0aMH\nevfujZdeeinrZ+0Ub2ZuLpK33Ybo3/6GJIN5AFQ+8b35JqRkEom77oLeoAERsM+aRcp9NglWeL0w\nGjeG6fEQp26lSo6Xi1tw0iR4v/jCKoEqSkaTlRQOE70SK6WnevUSmRkzPx9GpUrEGHL+vIXVTaWQ\nGDQI5V9+Sbe1Zw88n3+edtNWFGg0buykZ+HZwmxiBXZ1KQ4pSKWskhU/VywGrU0bXDx6FEaNGpAP\nHoRn1SpHsyEA+F9+GfnXXQfoOuE2AUeJVSkpoRKZJMG47DKkrr9eCMjYTW/TRmTohVhAfj7Kf/wR\n6o4dCE6YQFlydpzetm0GeXvy9tsRsVPz/Adm5uRQQ1ga0TrAsNYVFTCaNoXEsKMpO50WbwCSZXg2\nbqQmP94t37kzjUsiQQ2m5eWEbQ0EIJeVCREEddUqABTwFTCaK5gmonPnWqIHkgTpwgUoBw5AT1Nn\nMho1QkWamIJvwQIEXngBeVdeSU1JjRtTY11hIWUkOdbLXspXFDFHla1bSaWyeXOaK7Y5pW7ZAm/a\n9wljn+MOtHT+PMEmqlVDZN48MdfDH39sCVLwecXIlfU2bSwuXD1T6t0hC5/FJMOAn2XUhCWTKOCL\nIrvv5B13EHXZxx9DPnPGWT7WNCF5zQWJ5EOHoO7Zg9xBg5C45x53VTdNQ+LBB5EYPJga2mSZ4CL/\nTolPkoBkEuqGDdBbtECqZ0+CZPB+C78fZfv3Qyoro9/l5loUlckkAtOnO05n1KpFcI5oFN4PPyT+\n4HjcYpXJ1ijN1gi74E/yppuorMklrJmZspx5XzaWFCkWQ2DSJPqM12tRbtWrZ5VdWeOeONbFqlUz\ncVOPs7gDn+C+K/di8DeDMLXaDDx6+Zfo3z+F7t01qN60pj46NYor7Yb/pUnoWqMElfNTGN5kLZYu\nDWP53RPwzf0LsQbXYPaY3fi61RgMve44cn/eDwCIzpuHVq10dOum47LLDHR4/Y9Q+vWCVLmIxvvZ\nZ4mfllUNjYYNBQOOmZuLyJtvAsXd0DLvZxQM6oXAgGtxzbaXccfBF1GrFq3jWpcuSN55p3ujLgiC\nGOZZYu7g8jI4hwPZaLiUH36A/5VXAFmGunVrpnwzOz55552IvP46fYe93ycN0igOueYapFi1BLDx\nAjMGCFNRkM+SJABIcCc3F/LRo9DatHGo4krl5cSgwvcK/p2MFSExeDDKly9H9PnnERs/XvQyyOn9\nFppGoiygChWnTJTOnRNVl3TTO3UCVBXq5s1EK+ciNlPDLijG/ibv2QNlxw4Ba/JwJqTyckgnTlA/\nBu9LOX0a+cXFTkpa+5ja1l2jbl16xkuXkuaAqkLZtw/++fNp31BV5N53n8VOcSmLxyFduADPhg0O\n/n3/ggUkZc0Ym7h5330X3oULaY0CIB89SpX4bHAIRYHeqROSgwY5WIe4edavR2D8eMSmTEGS45Fj\nMaQYOwg9ABsdJmuM9k+fDqNePepP8PtpbOJxopXcv5+qrxwy5PU6RGP4aYb22I9HMQtrF+7EHXck\nkboQRpXKBsrKJDz4YA6qvDsPNfELHv5jAiMjM/GDk60R0RkzHBz8hmZg1eZKeOqpAFatUrMKf/6n\n9r/GEz1w4EAcOHAABw4cwA2XIkC3PwwmdJFBR8JEGADivjXr1LEolpjABwCUr15Nm4RhQOOlzSwb\nTeKuuwivaNv8M14WVto3g0FyDvx+lLGX0ywoEAIR0q+/CjhA8rbboHfuLPDUyt69Gc5KQePGQus+\nvHixyIaL7wQynFRuZuXKqPjqK5KkXbsWyp49yHn4YdFcxZrPCewAACAASURBVJ0a6eJFuvaCAnIK\nIxGomzcLlStuGqsQ+BYsgHz+PKSLF5HHmA6MwkL47HyOhgH/zJnQ2rdHcuBA53j+6U8WP3M8bokF\nAFbQkExeUgEyNWAA2rmRrf8GM3NzKcPr1pRq75J3E9Bhm0ls0iSqIvDPs2vNHTgQwXHj4Fu0CIHn\nnhNiPOratcj585+h/PSTaDoEYPEcN2zo+JrozJnIZ/CZCo7X4+bxOPi+1W++QeDvf6dnl0widdVV\n5EzpOvR27ZDz2GNENWbnIgecxPOKQjzihYVE75eOmWWfk375RcxHgN6N8hUryPkG4PnmG+LRBWPQ\n4EwidnpEuxOdSiF1003QrruORBZcnnt6ORHJpCvGk88dkSlh3OPib+x7vR99RNUnQOCvEyNHEpbS\nHigDyB0+XJxLb98+Y0EHyAk1iopgNGhAVHyKkkGR6fnsM2KYcRwoQaqogO+DD6C1akV0meksNZIE\nZd8+q0GaB0E2zHlg3Dh4338fiYceQvKOO4j5g8FsOD99OruJ9913SZFV16E3b474n/+MiE2COT5x\nIsxatRx4dT4uUkUFPPaeg2RScJWbqirmWfmaNbSZulB6RubPR/jtt61g2s3SsdD2DdlmdkgRQOwy\nRo0aJN4RCIh1sva0aYIz1uSOaDrfrptx7L8NuqZs3kzUdakUlE2bKMjh/My8t4Ffq+3ceuPGMOrU\ncTqyWUwEkx4PSZxv3Uo/2xuLy8thVKuG1LXXUv+Iy30En3kGUjhsNaPamirte4fb3AaAxL33Ijlg\ngPXd7DnIhw87xsS7dCl8r7+O6LRpxEAFQF23DuquXTCKijKSN3rDhjReigKzdm14VqyAb/FiwbLi\nYEcCUWUGWT+EXFIimHHE2hQOZ6d95cGgS++Nyub3xcOHiWse1OztWbpU3G/OqFE0z9esQc6jj5IE\nus8H6cQJa21h4yofOCAqcfx4rVMnJIYNQ+zxx50c+bZ3SwqHBaQlG0OEvG8fgkwEJfjww6RhAFjP\n3SZwZAYCjt4t+cQJyL/8AtPrhVGzJvlDqZQlGGQf67TkV/xPf8rECjNqRrNqVZjVqiExeDDUzZsd\nDdTh996zhJF4rw47LnHvvdQ3wvYt0+cjGXDASU/rYrwnyG/EMHhwEtNer4ann83Bi50+wIYN5di9\npxwfLDPR/cfX0Ejbj7vH1MGTTwYYVaOC2e9Wx8ETOdBWrMXfx8fQ+fgSTHqlAXJzTUyeHMTcuZma\nDP+N/a850b/FtA4drA1vyBByYmrVynywtgevbtuGnCFDHIswfziCp1jXqQnN50PizjszorLApElE\nnF+njmj8gWk6NkiptJQiP1lGbNo0choliTZFQMiGqj/+iLyBAxF46imkevdG7O9/FwqAAJu46ZtE\nMJgZkTO7ePw4zNxc9+wYAKgqlG3b4Fm6FP7p0wW+NjFsGGAYSNx/P/TGjWFWrYrkrbfSNcRiMPPy\nYNSqBb1ZM1okmKX690fqqqssKU02rlrr1og/+aQzi6/rUDdvhhkMwkjjDbabd/lyeHhjIh9bwHKm\nIhGxaFzKpLIyeO2wDMNwXYjyevZE/JFHqLHEbVPmP3u9iM6cCXXXLvo5HCYBFr7gcAo1rxepnj2t\neadptLCxRrPyHTugcwqunBxnFYPhaI2CAsRtTawAiKzf60Xp8eMWY0wWk3/9lRZgzjxhE/FIDB0K\nU1WRuuoqJAcMEOTygJNai2e3jLp1SZrbnt0rKSHnEEDh5ZfDzwn8AZjVq5PSHN/w7GPKHIqc0aPB\nZXiVLVsglZUh2a8f0YjZ3iNl507EpkzJpA60zQn/s89CPnUKuWmQhPKvvoJZqRLU9esReOopSGfO\nkGPHnkvq9ttFYzJME6bPh8SgQSQawa/V7vik2yWcrOjMmUhdfz3x+tarh8Rdd2WwP3jWrHF1oh08\n6wBlXuyBsqbRM2RzINWzJ1FS2pxiKRyG7623hMNsp+DkDq138WJUsIoXQA3JwQkT4J82DVqPHkj1\n7+9+c2kKX0bDhgj/4x8IMCYMgIQdch5+WFyLVFFBFZi8PMhHjiA/TTWQz7XULbdYIhLZvhu2hub0\nZnAApRcuIPbMM/C99JKYY7G//Q3addchce+95Bim9W3wf8W7wPsPdu6ExLJ00q+/Erc+iCowMWKE\n1cwLWvPVHTsgRaPI79uXVGQ58wd3ptl3xWwUkLHJk4kaj0tcXsK4WIfJ1enY3mQWFgqhHSgK9BYt\nSLjFpSFfmH0MWDY2PmYMNJbACc+fL1hM0i06cyZiTLZcOHj8XbGtscHx44kxoXNnQU8nM6y20bSp\naPw2FYUqtTVrIvz222LfkGIxcQ9GtWoZSRwzN9dKmtkrJKoKvX59YpTau5eaJW0iReLzqor4yJEw\ng0Eo27cjlzMAcdaXoiJ6lzifvSzDLCqi702lqNLF7tn0+6G1b4/gxInERiXLMP1+GA0awD9jBjG1\nsOcD04RZsybUjRszhEOMhg2RZNcRefVVYvlKC3jtJpWXk34DQLzTZWUwioqgXXkl/Y4HEbzRmh9X\nVgbf/PlQ9u1DzogRiI8Y4XBouclHj1JG3IV4IcXWZd+rr9I6fvEiVdbPnSO+6759oZSUQF27Vhym\nd+lirR9clp49u/iTT1rBZyIB+HyIPfssKpYs+bfvhsH3RBtlbWz8ePiYYmNhEdC+hw8PqG9hbOBl\n/HPmbkSjEjp3zMOjo2Xs3avghhvyUGfIDdi1KYVJ79XB6u8TGD8+jnXrynH//S6aBf+F/a6c6Pjj\nj1sObjAI5OUhNmWKo2wEwFl6VFWacDwCtmUW5RMnMuhM4hMmWIt6IoHA2LGQDx2CXFKC5M03I8kY\nNPQWLRyKiMqPPyIwa1bWRSz6/PMO9g0pPfozTSoXucEL8vII65pI0KYcj1Mm7uefSYK4Zk1XJTtx\nbXv2kAKW7T6jM2ZYC/ykSc5NlDnRMAz4X301o6xkVK9ukaTLMoyCAlSsXQutVSuCYJSXI/jAA2Jh\nyu/XDxJvGnOxizt2ILJokWMs6MIVJO65h4jX02RquYVCIUgnTiA4ejQKL7sMOTYBg8CTT1pqTQBy\n7r6baL9KSoj/2p6Jst8fz4ypKqTTp5EzYgSV73btQs6YMUgOGYLyNWuQuvFGWtADAYQ//ZSaOmBl\nlkUWGqDKRSRCODdFQeDFFyGdOUPzxe9HdM6czJvjGzELEpUffsgq/iOcKXummY9jIgH4/TCaN4fW\nvTvhbv9AnfuJQYOQHDZMjLek60gxdpoy3nMAwPfGG/B+8YWlQnWpBc6e6ealU9uG51m+HMrhw9Cu\nvBJa584ORhXIMkESOIUZN3YvUiwG/5tvIu8Pf4Dy889AeTn8XPnT46EFurQUpT/9REpX06eLa/HP\nmmXx7pomCfy43UeaE21UqYJk//7um5quw/fyy3S9gQCMoiKYRUVUZUmrVpk5ORniAqm+fRGdPh1G\nlSqIM6fUrFIFFaxXgY9h/KmnxNqSvPdeEjGwV80MA/KpUwiyxlspEiHO63vvhVFQAKRSCEyc6GT9\n4bLuNgiHq6XBOXyvvw7fa685xim8dCllGgH4ORyPH5d2PEDzzi7bfcnvtv/r8r5yU/bvp3K97R1J\nDh6M1A03CHXDUCgkZJR9H3xAardcTdAw4P/734XKavCRR8TaZxYV0f2lK6OyaigAxP/8Z5HMEMEp\nr3wsWSI4ws2qVcnBzKJD4Js3Dx72/HmjaeKBBxyfMYuKLLEWm2Ih/ZGpDdp6VQA4Mv48Cx57+mno\nXbvCqFIlQ0E0mxn161vPwS1jmi6YxPa55G23IfHIIwCAvIEDxRqid+uGvBtvBMrLEfjb3+BZsQLy\nwYMo27vXoaQXe+wxgmbywMqWKRVZfXY9wUcegZJeqWLraeKRR6Ds2wfvZ58J6JZmT4idO0cqlMyJ\nTIweTfshWHaU+wyyDCmRgPfzz+FZtoyedX4+KlaudCQqjKIiV2pSYTyIA8GxwESkfAsWUNXPZtLF\ni1D27HFAoaSyMhhNmpBOQHm5SArozZo5nrlUXg65rIyy+5qGxKhRiE2YYO0zzHLvvBNySQmMevWc\nstrBoJCDDz71FHxvvomchx+GZ+NGeN9/H/7p06HyyruLpgcAyrIHg473hu/DUiJBDFdVqkC78koa\na9OEfPiwI5HHTbvySoTnzxf3aKoqVZnS3ikpHodZWIi29S7gpZeiOP3YM9h8/VN49dUoDhwow9E+\n9+L9h9fimms0qCqgrlkD77erXBEu/439rpxoBwfgJcxegjArVaJJxqm5DAOxKVNQsWQJjMsuo0mb\nzQE1TfjefRdmjRpEp2dbQOOPPQaNldoBWBuSSxZL2bqVshq2hjSjVi3BdMEt9/77XTOjpixDMk0E\nJk8m3OuLL8I/bx6UXbvgmz8fiSFDMp0Ou9mcKr1OHWssmKVuvNFRDlW3baPr4HzUpgn/iy8ir08f\n+BYsoMCFNa5IpaVWZoDxCEu6TnhqvsBxnuN0Y2p5Zp06rjh0+HyIPfMMcoYPh3zhAgJjx8JrKzcD\nFIz4Fi+m0lq6pWEOPevWUUbA6yUFQkWBWakSIjZHG2AwDZ9POLh0MC3SptdL9IJt2lg0bGwRFPdg\nx/2x/8cffJAoyrxeh/wq55VO50QW42ObC3kDBrgKxciHDpFTw4/hz9swoHXpQpUF24qgt24Ng0Ev\nzNq1RQbUVBQgGkVwxAjBDMItvGgRIrNmIY9nO3Qd/qlToa5c6RQYSSSog55dt+nzkbNkW6gllsUx\n/X6kBgyAZpN4d9uU9fr1RYOefOiQ47qkRAI+trCLDYpXc2TZIZriWbbMEgsyDHrGLkFJbPx4x89m\nYSFSPXq4UybJMoKTJ1uwKi4/zcfTNu/VH3/MlLYOBKjhiD/n8nLI+wmfG3jiCSGd7GoskwrTzNw4\nIhEKvvh6YssqqV9/jYLGjeHlZeB/pwgmSTCqVaN+EoAcD662yI0HcaWlImtctm0bPfv0z4IqY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437q14xyaTYXNrFxZNI7QAbT5hVkTY64N3pNuvESay1UkZeIlN9Ka4PhC4Vm2zFrEDAOxv/6V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\nR2jGDKPZlt+2LT0udk3CIxhkwe/YAWnZMmjZ2RC//x65NupHxZt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Pr7CLUYrm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tlYSAghhBBCSLagSTQhhBBCCCEa0SSaEEIIIYQQjWgSTQghhBBCiEY0iSaEEEII\nIUQjmkQTQgghhBCiEU2iCSGEEEII0Ygm0YQQQgghhGj0/3Ckugs5ZiLiAAAAAElFTkSuQmCC\n",
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
+ "\n",
+ "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30000\n",
+ "movement_error = 2\n",
+ "pos = None\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(1000):\n",
+ " Z = dog.sense()\n",
+ " zs.append(Z)\n",
+ " if pos == None:\n",
+ " pos = (Z, 500)\n",
+ " \n",
+ " pos = sense (pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ " pos = update (pos[0], pos[1], movement, movement_error)\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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pu56ifsEwqJkxA+wFFyRfIBOhS0vB7N6d8LhAz57i/zFGDwC2n36CfcWK2BON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\nC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TfZmGb+/ndo559vv9eaBrNePRTdcQfZxHXdlpH0gd65M7IBhW/6SSdBs96znFQxvwwP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YMQtjxnhZ/NZloh4fwLnMGBYWLyT58GYqnPEzcryfSZO8RNy6h7epqAgVz59PtWeeoeb27cix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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n",
+ "\n",
+ "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Exercise: Interactive Plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the $\\verb,interact(),$ function to call a calculation and plotting function. Each parameter passed into $\\verb,interact(),$ automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from IPython.html.widgets import interact, interactive, fixed\n",
+ "import IPython.html.widgets as widgets\n",
+ "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n",
+ " # your code goes here\n",
+ " pass\n",
+ "\n",
+ "interact(plot_kalman_filter,\n",
+ " start_pos=(-10,10), \n",
+ " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n",
+ " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n",
+ " movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n",
+ " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 29,
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "######Solution\n",
+ "One possible solution follows."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "zs = np.zeros(100)\n",
+ "ps = np.zeros(100)\n",
+ "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n",
+ " dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n",
+ " random.seed(303)\n",
+ " pos = (0,100)\n",
+ "\n",
+ " for i in range(100):\n",
+ " Z = dog.sense() + random.randn()*noise_scale\n",
+ " zs[i] = Z\n",
+ "\n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps[i] = pos[0]\n",
+ "\n",
+ " pos = update(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n",
+ "\n",
+ " p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ " p2, = plt.plot(ps, c='b')\n",
+ " plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
+ " plt.show()\n",
+ "\n",
+ "interact(plot_kalman_filter,\n",
+ " start_pos=(-10,10), \n",
+ " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n",
+ " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n",
+ " movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n",
+ " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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XroRPnIjtl19wDR5MoF69EoxQpPQ88kgk//ynm4svDpT4vTSCLCFBvWNiRnkh\nZipKXlh+/x3nggW4hgwp1HmeXr2wHjhA9uTJuO+9lxIfagsRZZ0XBw9a+PjjEphvrJD27LHi9ZZ1\nFMH38ccOdu+2MXKkq1TupxFkERGREGRUrkz6559jVK9euPOqViV927YSikrMHD5s4ZZbYsjIsJCS\n4uX557NxOkvv/idOWPjoIwdz5oTxyy9W4uIMxozJoUsXb7n6+cjvh4wMC5mZkJ5uITPT8se2hSee\niOT117MK82FKsWgeZBERERO7dllp0CAQrMkj5Dx17JiFrl1j6N7dw+DBLv71ryh+/dXKzJmZxMeX\nXIllGLBxo53Zs52sXOkgKclHv35uOnTw8dlndp55JgKnE55+Ooe2bX0lFkewpKVZuf76GNxuiImB\n6GiDmBgj7+sVV/gYNqzwK+ZpHmQREZEgWbvWTo8e0Qwf7uaZZ3LKOhwJUcePW+jePZouXTw89FDu\nR/+zZ2cxaVI4HTvGMnNmJq1b+4N+348+cjBhQgR2O/Tv72bcuByqVv2zGE9O9tGhQwYLFzoYPjyS\nBg0CPPlkDo0bBz+WYPB6YdCgKEaMcDF8ePCXjS4K/VwsIaGse8ckNCkvxExJ58W+fRb+9a8oZs3K\nYtUqB6+9Vkqf6UqxlPb7RXo69OgRTfv2Ph577M++WKsVHn7YxeTJ2fTtG8177wWv1yIQgGeeieDZ\nZyN45ZVsNmxIZ+hQ92nF8alx9Ojh5csv00lO9tK9ezRDhkTy/fehV/o9/3w4lSsbDB0aGsUxaARZ\nREQkj9sNd90VzdChLrp08dKsmY8bb4whLs7gH/8o2XlXpfzIyICePWNo1crH2LE5pn2+N9zgZcWK\nDPr1i2b7djv3359zcuFCbDaw2QxsNnA6wVGAZ/syMmDw4CgyMix8+mkGVaoUrH0jLAwGD3bTu7eb\nt98Op3v3GC6/3M+IES7atvXl26NsGPDttzbWrrXTpo2PVq1KZvR57Vo78+aFsW5deki1M6kHWURE\n5A8PPRTBoUNW3nsvK69w2LXLyi23xPDaa1lcf30J93Lm5BDxwgvkjBkTtJXzJLiys6FXr2guuSTA\nlCnZ5/xrSk+H+++P4ssv7QQCuSvB+f3g81nytq+/3suQIW7atDEvWPfssdKnTzRXXulj4sTiPQDo\ncsG8eU6mTQsnJsZg+HAXXbt6sdtz/2zr1ztYtSr3V0SEwbXX+li1ykFSkpennsohLi54ZeORIxY6\ndIjljTe3Mvd6AAAgAElEQVSyaN++ZP5tqQdZRESkGObPd7J2rYM1a9JPK1IaNQowe3YmfftG88EH\nmUUbSUtPJ+L55/H06IG/Zct8DwubMwfr//6n4jhEZWVBv37RJCYWrDgGiI2Fd9/NOus1581z8sAD\nkUREGAwZ4qZbN0/ebA1ffGFn4MAoHnzQxaBB7mLPShEeDnfe6aF/fw8rVzp49dVwxo6NoH79AF9+\naadZMx+dOnlZvNhF/fq58w2np8OLL0bQpk0so0a5GDjQjb2YFWQgAP/6VxR9+7pLrDguDo0gS0hI\nTU3VKkhyBuWFmCmJvNi5M3eUePHizHwfZFq1ysHIkZEsXZpBgwaFWKjA4yH22mvxN2qE/YsvyBk7\nFk/v3ubHtWpF1owZZy2ixVxJv18cO2bh9tujadTIz8svZ2OzBff6gQCkpNh5441wdu2yMWCAm9hY\ngylTwpk+PYsOHUquiNy82caBA1aSknxUqpR/WfjDD1ZGj47kyBErEydm065d0WN65ZUwPv7YyfLl\nGcUuts9GI8giIiJFkJ4Od94ZzfjxZ3/K/+9/9/Lkkzn07BnNypUZ1Kx5ZiERCOSuy3HaKJ/TSebs\n2QTq18e6axfR/fph276dnHHjTms+dc6fT+Dii1Uch6A9e6z06BFNt24eHnvMVSJzC1utcP31Pq6/\nPpOdO61Mnx7O//5nY8WKDC65pGRXjrviCj9w7k9GGjYMsHBhJsuWORg6NJJWrfyMGZNDvXqFi2/L\nFhuvvRZOSkrJFsfFoRFkERGpsAwD7rwzimrVAkyaVLDp3F5+OYxJkyJwOg18Pssf/aS5vwIBC/Hx\nAa691su11/q49lovtWuf/t+s5fffCZs2Ddcjj5BXHfh8xF51FdlTp+LTpyYh5euvbfTpE82oUTnc\nfbce1DwpOxumTQtn+vQwbrnFy4MP5pj+0PhX6enQvn0sY8fm0LVryS/5V9QRZBXIIiJSYb32WhiL\nFztZsSKjUCt0/fqrBcuBAzizfsdyUSL2SlHY7bmjgHv2WPnsMzuff+5g/Xo7lSsbecVyUpKX2Ngz\nr2fbtImIcePIXLaswiwNXRq2brUxaVI4iYkBmjTx06SJn0aN/AX+u16zxs7gwVG89FI2Xbqch+s3\nB8Fvv1l4+eVw5sxx0revh5EjXWfMsOF2w6ZNdtats/Pxx07atfMW+AfS4lKBLOWaek3FjPJCzAQr\nL77+2kavXtF8+mkGiYmF/wjbsWgREZMmYd2zByM2Fn+9ehi1auHu1Qvf9dcDuS0XO3fa+OwzO2vX\nOti82U67dl66dvXSubOXypVP+S/Y6y3YfF9i6tS8MAx4660wJk8O59FHc8jOtrBjh40dO+z88ouV\niy/+s1iuVy9AvXoB6tb1Ex395/XmzXPy5JMRzJqVyVVXheYCG6Hk4EELkyeHs3ixk3vucfP3v3tJ\nTbWzbl1u3jds6KdDBy8dOvi46ipf0Hu486MeZBERkQLKyoJ//jOK55/PLlJxDODt1g1vt24QCGA5\neBDbL79g/eknjLi4vGOsVrjsMj+XXeZn2DA3J05YWLXKwbJlDh55JJIrrvDRtauH5GQfhhFGdjZk\nZ1vIybHk/b5RIz8NG5ZsD+r5JD0dRoyI4v/+z8rq1RnUrXv6987lgu+/t7Fjh41du2x8+aWdX36x\nkZZmJTraoG7dAFWrBtixw8aSJRk0aqTvfUHUqGEwaVIOw4a5mTgxnMGDo2jXzsedd7p5552s038Y\nLAc0giwiIhXOyJGR+HwwbVr2OY+1f/45GAa+9u2DGkNmJvz3vw6WLnXy5Zd2HA6DiAiIijKIjMz9\nfUSEwZdf2nnooeBM8XW+277dxt13R9Gxo5dx43IK1TYTCMChQxb27Mktltu391KjRvkq6uRMGkEW\nEZGQZhjwyy9WPv88tz933z4r06Zl5c21WlqWLHH88dFv+tkPdLmIGDcO55IlZL3+etDjiI6Gbt28\ndOt29t7Wn3+2MmhQFOvX23nllexyNxJXGgwDZsxwMmFCBBMnZp/ze2rGaoWaNQ1q1vTRpk0JBCnl\nigpkCQnqNRUzyovy7+hRC2vXOvIeWvP74dprvVx3nZfMTAu33BLDvHmZNGlS8B7P4uTFvn0WHn44\nkrlzM4mJyecgtxvnRx8R/vLL+P/2N9LXr8e44IIi3S8YLroowMqVGTzzTATt28fw9ttZf0zLdf7J\nysp9mOvwYStHj1o4cuTPr8eO5baeOBzgdBp5X51OyMy0cPx4FitXZnDxxWqJkOJTgSwiIiVi82Yb\n/fvnLo977bU+Ro7MXZnr1DaB6tUD9LjRxoe9P6L5uM4U6jPxQvL7c1fuGjLETcuW+ReY0bffDlYr\n2c8/jy8pKSRmlQgLg+eey+Gaa3z07x/N0KEuRoxwl8qCex4PrF9vJyfHgtWaO9JqsYDVamCxwMUX\nBwo9D+6pfD74/HM7CxY4WbnSwWWX+aldO0BcnEG1agEuu8wgLi5AtWoGEREGXi94vRY8nj+/+nwA\nqVx8sYZ+JTjUgywiIkG3bp2de+6J4vXXs7j++rOvtrVm5iGGPFKD2ReOoN2EjnhvvrlIRenevVZq\n1Qrku/DAlCnhrF1rZ/HizLM/QZ+ZyWnTGYSYffss3HNPNFFRBm++mUXVqgX/b3zePCcrVjjo1Cl3\nFo2/Tsd1qp9+svLee2F8+KGTiy7KfXAtEOCPXxYCgdwfOr77zsbGjelceGHB4zAM+OYbG/PnO1m4\n0EmtWgF69vTQrZuHatXUQiLBo2neREQkJCxf7uCBByKZNSuLq68+szg+OS2aceGFefu+/NLGHbeH\n8Ublh7m1xiayX3wR/2WXFeh++/dbeOyxSD77zI7VCu3b++jY0UvHjn8+ZLVli42+faNJSUnPW7jD\n8vvvGJUrB+FPXPp8PnjuuXD+8x8nM2dm0aLF2VsuAgEYPz6cRYuc3Huvi3XrHKxd6+Dyy3106eLl\npps81K5t4Hbn/v29914Yu3bZ6N3bQ//+7rO2LTzySASBALz4YsHmtXW74ZZbYjh82ELPnh569vSU\neh+6VBxFLZBL4cMZkXNLTU0t6xAkBCkvyp8PP3Ty0EORLFiQaVocA0SMGYNj+fLT9l11lZ8FS9wM\nd73Ev+s+Rdhbb+V7j5N54fPBm2+G0b59LA0b+vn++xNs2JDO9dd7WbPGQdu2sVx7bQzPPBPB4MFR\nvPhiNrVrG9i2biWqd2+ib701dyizHLLb4cknXTz3XA633x7N7NnOfI/NzoYBA6LYuNHO6tUZ3HWX\nh5kzs9i163eGDXPzzTc2OnSIpUOHGJo0qcScOWEMGOBmx44TPP10zjl7ekePdrF0qZNvvy3YxLYT\nJ4YTFxdg27Z0HnvMFbTiWO8XEkxF7kHetGkT99xzDz6fj8svv5wPP/yQ+fPn88QTT2CxWJg8eTJd\nunQJZqwiIhLC3norjFdfDWfJkgwaNDAveixHjmBfv56sadPOeK1pUz9LlmZw221/Z+tNSSSv9tK6\ntZ8LLjiziN261caDD0ZSqZLBxx//eb+ICIM+fTz06ePB58s9LiXFwYABbrpVW0/EbS9i+9//cI0c\nibtfv5DoLy6OLl28NGiQQf/+0WzbZmfChOzT2rgPHbLQt2809ev7WbQo67TXIiLghhu83HCDF58P\nNm+2Ex8f4KKLClewXnCBwaOP5vDIIxEsX5551m/p1q023n8/jPXr08v7t17Oc0VqsQgEAlx66aXM\nmDGDNm3a8OuvvxITE0OjRo3YtGkTLpeLpKQkdu/efca5arEQETm/GAZMnhzOhx86Wbgw86wLb4S9\n9hq2778n26RAPmnfPguzZoWxZYudrVvt1KwZ4IorfFxxhY+mTf3Mnu1k2TInzzyTQ8+engIVWhFP\nPIFjxQpc992Hp3dvcOY/4loeZWTAsGFRHDhgZdasTGrVMtixw0afPtHcdZebBx5wlWhB6vdDcnIM\n997r4rbbzKdYc7mgfftYHnkkh+7dtWyzlI5SnQd569atxMXF0eaPiQKrVKnC+vXrady4MXF/rCCU\nkJDA9u3badq0aVFuISIiJWTvXitOpxGURRCysuCxxyLZutXGihUZVK9+lmsaBmHvv0/2lClnvWbt\n2gaPP+4Cctsovv/exubNdtavtzN1ajjXXONj48b0Qs0H7Bo2jJynnjpvl3KOiYFZs7J4+eUwrrsu\nlsGDXbz+ejgvvJDNrbeWfDFqs8HEidkMGhTNDTecICrqzGMmTIigUSN/keYoFiltRepBTktLo1Kl\nSnTu3JkWLVrwxhtvcPjwYWrUqMH06dNZsGAB8fHxHDx4MNjxynlKvWNiRnkRXMePWxg9OoKOHWNo\n1y6W558PJyur6Nf75hsbycmxuN3w8cfnKI4B29at4PXiu+qqAt/DbocmTfwMHOhm+vRstmxJ57bb\nVhd6sQyjRo3ztjg+yWKB++5z8/rrWSxf7uSDDzJLpTg+6aqr/LRp42Xq1PAzXvvqKxsffuhk0qTs\nEhvJ1vuFBFORRpBdLhdffPEF3377LZUqVaJVq1YMHDgQgMGDBwOwcOFCLPn8Kxg6dCiJiYkAVKpU\niSZNmuRN+n4ywbVdsbZPCpV4tB0a2zt27AipeMrr9lVXtWPmzDDGj7dx9dUH2bixMm43DB+eSbNm\nVXj22dwptjZsKNj12rRpxxtvhPHiizYGDdrOE0/UK1A8W3bvJqpvXxr88X9DQeO/NjERIyyM9T/+\nyKlC5fsbattJSe1ISsogNTWV1NTSvf9NN4Xz4IMd6dPHw/79nwPQsmU7hg+P4q67tvHDDweJi9P7\nhbZLtp5ITU0lLS0NgEGDBlEURepBTklJYcyYMWzYsAGAPn36cOmll7J582aWLVsGQFJSEi+//DKX\nX375GeeqB1lEpHSkpNh54olIqlcPMH58Do0bnz4d2KZNNh5/PBKA557LPucKbYcOWRg2LIqMDAtv\nv51FnTolPz1X+Pjx2H76iax//7vE7yXF99JL4WzZYuP993M/nnjyyQj27bPy738X4+MKkSIq1R7k\nVq1akZaWxvHjx4mKimLHjh08+uijzJgxg6NHj+Jyudi3b98ZxbGIiJSs48ct/Pijld27bSxd6mD3\nbhtjx+bQubPX9KPtK6/0s3p1Bv/5j5O7746mdWsfrVv7qFzZoFIl45SvAb75xs4DD0Ryxx1uHn7Y\nle+CHMHmuv9+Ytu1w/7pp/iuu+7cJ2RkEP7yy7gefZSzrwgiJWHoUBdt2sTy6ad2YmIMFixwsn59\nelmHJVIoRXp7q1SpElOnTiU5ORmv10vfvn1p0qQJEyZMoG3btgBMnTo1qIHK+S01NTXvYxKRk5QX\nZxcIwHvvOdm2zc7u3blFsctloX59P5dc4ue663zMmpV1ztWbrVbo1cvDTTd5mD07jL17rXz3nYXf\nf7dw4sTJr1YiIw1mzDBf/KNERUaS/cILRD70EOlffEHqtm3554VhEHXffRgxMSqOy8jJZbEffzwS\nw8h9eK8wq/0Vld4vJJiK/PN/jx496NGjx2n7evXqRa9evYodlIiInJ1hwOjREWzbZqdfPze9egW4\n5BI/1asbRX4IKioKhgxxFz6QzMzcaRRKkO+66/A3b0745MmQlJTvcWHvvot1924yVq0q0Xjk7Dp1\n8vLvf4cRE2Nw882atULKHy01LSJSzhgGPP10BKmpdhYtyiA2tuxiCZs2DfvWrWfvD87KwnTer0Ky\nHDpETLdupK9dC+FnzpRg27qV6N69yVi1ikC9esW+nxSP2507iF9arTgiZkq1B1lERMx5PLB1qx2X\nC6KjDWJijD++5m4H41P/F14IJyXFzrJlmWVaHNu2biX85ZfJ+PTTM19MT4fYWPD5qHTllWSsXEkg\nIaFY9zPi48n84APz4njHDqJvu43s115TcRwiztXaIxLKVCBLSFDvmJgpD3lhGPDjj1bWrnWwdq2d\nDRsc1K/vJzbWICPDQkaGhczM3F9ZWVC9usH772fSrNnZZ4vIzyuvhLFwoZNlyzJMl2AuLZYTJ4ga\nNIjsyZMJ/DFtZx7DIKZXL3xNmuBr04ZAjRrFLo5PCtSta5oX/osuImPNGgIXXRSU+0j5Ux7eL6T8\nUIEsIlJIx45Z+PxzO+vWOVi7NnfxieRkL7ff7uH117O58ELzwjUQgI8/dvCPf0Qzb17hi+R33glj\n5swwli/PoFq1siuOMQwi770Xb6dOeLt2PfN1i4XMefOIeOwxogcOJOscK+cFRVSUimMRCRr1IIuI\nnEN2NmzcaOezzxx89pmdPXtstG3rpX17H8nJXi65JFCoB+M+/tjB/fdHFqpInjPHycSJESxfnlEq\ncw+fjX3DBiIef5yMTz455+fotq1b8TdpAk5nKUUnIvIn9SCLiATZ3r1W7rsvki1b7DRp4qN9ex8v\nvJBNixb+Yq1afOONXiC7QCPJPh/MmhXGlCnhLFlS9sUxgK9NGzJWrChQk6m/ZctSiEhEJLisZR2A\nCJy+RKTISWWZFwcOWLj11miSkrzs3Pk7H3+cySOPuLjyyuIVxyfdeKOXl17KLZK//vrMJ/fcbpg5\n00nr1rEsXuzgo48yuOSS4BTHjlWrsK9eXbyLREYGJZai0PuFmFFeSDBpBFlE5C+OHrXQrVsMAwa4\nuffeQs4LXAhmI8lZWbkjxtOmhdO4sZ833sjiqquK9kCfKa+XiIcewpKdTfbEiXhvuy141xYROU+o\nQJaQoCePxUxZ5MXvv1u47bZobr7ZU6LF8UmnFsl9+niYO9fJVVf5mDs3k6ZNg1gY/8H6f/+H75pr\ncA0bRkyPHuS43Xj69Dn7SYZBkVcfKQF6vxAzygsJJrVYiIj8ISMDevaMpl07H4895iq1+954o5dX\nX80iIwOWLs1g1qysEimOAQIXXUT2tGkE/vY3MhYvxrlgQW4/Rz5sO3YQk5yM5ciREolHRCQUqUCW\nkKDeMTFTmnmRkwN9+0bzt7/5GT8+p9QHTDt18jFpUg4NG5beQ3iBBg3IXLTI/GE7wyDs3XeJ7t4d\n17BhGNWqlVpc56L3CzGjvJBgUouFiFR4Hg/ceWc08fEBpkzJDqVugrKRnk7Uvfdi/eWX3BXwLrmk\nrCMSESlVGkGWkKDeMTFT0nlx/LiFhQtzF+5wOg2mTcsOylLQ5ZrPR+wNNxCIiyNj1aqQLI71fiFm\nlBcSTBpBFpEKIxCA7dttfPqpg08/dfD99zbatPHSpYuXfv3cQZm+LWQFAmAtwJiI3U7mvHlBWxpa\nRKQ80giyhAT1jomZYOXFDz9YeeihCC69tBJDhkTx++8WRo/O4X//+50PP8xi4EB3Qda8KLcs+/cT\n0749+Av24F+oF8d6vxAzygsJJo0gi8h5ye+H//7XwVtvhfH99zbuuMPN6tWhsRLd2TgWLcJ7001B\nXZo5/K238LVrh/pHREQKxmIYhlGaN0xJSaFFixaleUsRqUBOnLDw/vtO3nknjAsuMBg82M0tt3jK\nxwhxIEDUHXdgxMSQ/frrwZl7OD2dSs2bk7F2LYHExOJfT0SkHNm2bRsdO3Ys9HkaQRaRcsXthkmT\nwklLs5KTYyEry0JODmRnW8jOtnDkiIXrr/cxfXoWrVr5Q3tGiuxsbN99h79169xtq5Wst94i5uab\nCX/+eVyPPVbsW4S99x6+pCQVxyIihaACWUJCamqqnkCWM/w1L7KyoF+/aKKjDbp08RIRYRAZaRAZ\nyR9fDeLiDC64oFQ/GCsawyBy1CgAsk8WyACRkWR+8AExf/87gYQEPP37F/0eXi/hb75J5pw5xQw2\ntOj9QswoLySYVCCLSLlw4oSFXr2iadDAz9SpITAdm99frJ5e58yZ2LdvJ3316jNeM+LiyJw/n5gu\nXQjUqoUvOblI97AcPoyna1f8zZoVOU4RkYpIPcgiEvKOHrVw2225S0A/+2xOgWYrK0n2L74gfMoU\nMj/6qEjn27ZuJbp379xFOC6+OP/jtmzBiIsjUKdOUUMVEanQ1IMsIuelffssdO8eQ/fuHh55xFX2\nPcXZ2USOHEnOuHFFOt3y669EDRhA9ksvnbU4BvC3amW63zlzJs6lS7GcOIHlxAnw+bD4/eSMGYOn\nV68ixSUiIn9SgSwhQb1jYmb+/P/H+PHtGTzYzdCh7rIOB4CI55/H37w53s6dT9tvOXECy6FDBBo2\nPOv51p9/xnPXXblTuRWRv2VLXAkJGJUrY8TG5k4JZ7USqFy5yNcsT/R+IWaUFxJMKpBFJCR9+62N\nxx67mqeectG/v6eswwFyWx6cCxaQbrIgge2rr4gaPpzMuXPxn6WNzN+69Z+zVhSRv0mTYp0vIiJn\np5X0JCTop345yTBg1iwn3bpFM2mSP2SKYzweokaMIPu55zCqVj3jZd9115H90ktE33479g0bsOzf\nj/Wnn8og0POf3i/EjPJCgkkjyCISMtLT4b77ovjf/6wsX55Bw4YhtOqdw0H2Cy/krkiXD2/nzmRF\nRhLVvz8YBjlPP43nHH3GIiISejSCLCEh1eQja6lYvvrKRvv2sVSpEuC//80tjkMqLywWfNdcc87V\n7Xzt25P+xRec+OYbPHfcUUrBVSwhlRcSMpQXEkwaQRaRMhUIwKuvhjFtWjhTpmTTpYu3rEMqNiM+\nvqxDEBGRYlCBLCFBvWPnP8OAjAw4ftzK8eMWfvvNwvHjFubODSMry0JKSgYJCae3VCgvxIzyQswo\nLySYVCCLSFD9/ruFXbusfP+9jV27bHz/vY3du20cO2YhPBwqVw5w4YW5y0FfcIFB+/Zehg51Yw+1\ndyOfD9s335x1RgoRETk/hdp/SVJBaf7K8skw4KefrKxZ42DtWjvffGMnI8NCw4Z+Lr3UT6NGfm64\nwUuDBn7i4gyczsJdv6zywv7550SOHo2/Xj2y5sw5Z9+xlC69X4gZ5YUEkwpkESmU9HRYv97BmjUO\nUlLseL0WkpO99Orl4YUXcqhdO1Bu60lrWhoRY8Zg276dnHHj8HbpouJYRKQCshiGYZTmDVNSUmih\njyxFQlp2NqSlWdm718aePVb27LGyd6+VPXts7NtnpVUrH8nJXpKTvVx6afktiE/l+OgjIh9+GPeQ\nIbiGD4eIiLIOSUREimnbtm107Nix0OdpBFlEAPj1VwvLlztYvNjJ5s12atcOUKdOgLp1/dSpE6Bd\nOx916gS46CI/kZFlHe25WX/4gYjx47EePozlyBGsR45gycnB2749mYsWnXG8v1UrMtatI5CQUAbR\niohIKFGBLCFBvWNl4/ffLaxY4WDRIidffWWnY0cvd9/tZu7czJAYQC1OXhhVquDp0YNAtWoY1aoR\nqFYNoqJy55UzEahTpzihSinS+4WYUV5IMKlAFqmAMjLgwQcjWbXKSfv2Xvr0cTNrViZRUWUdWeHZ\n16zB36QJRlzcafuNqlXx3nzzmSfYbKUUmYiIlFcqkCUk6Kf+0rNvn4Xbb4+mdWs/3377OzExZR1R\n/s6WF9Yff8x9oG73brLefRf/XwpkOX/p/ULMKC8kmFQgi1Qg27bZ6N8/mqFDXQwd6i53D9dZjh3D\nuWQJtm+/xbFsGa6RI8maNQvCwso6NBEROY9YyzoAEcjtHZOiOXAgt484I+Psxy1Z4uD226OZNCmb\nYcPKR3F8Rl64XNh27sRfpw7pGzbgHjFCxXEFpPcLMaO8kGAqVoGckZFBzZo1mTx5MgDz58+nQYMG\nNGzYkOXLlwclQJHyyO2GL76w5/c8WLEZBmzaZGPgwCjato1l+vQwLrusMnfdFcWyZQ5crtOPfeml\ncB5/PJL//CeTzp29JRNUEFmOHsWxcuUZ+43atcmePBn3ffdhVKtWBpGJiEhFUKwWi/Hjx9OqVSss\nFgsej4fRo0ezadMmXC4XSUlJdOnSJVhxynnufOkdy8qCmTPDeP31cHw+6NHDw7PP5gRttNblgkWL\nnLz1Vhjp6RbuucfNSy9lERsLx49bWLrUwTvvhDFyZCSdO3vp3t3DwoVOvvvOxurV6dSsWarTnhdZ\n+OuvQ1YW7V54oaxDkRB0vrxfSHApLySYijyC/MMPP3D06FFatmyJYRhs3ryZxo0bExcXR0JCAgkJ\nCWzfvj2YsYqErBMnLLz4YjjNm1fiq6/sfPBBJl9+mc6aNQ5efbX4LQC//mph/PhwmjatxEcfOXn0\n0Ry++iqdIUPcxMbmHnPBBQZ33ulhyZJMvvgincsu8/P88xG43RZWrMgou+I4EMD+xRe5Q9kFYDl+\nHOd77+G6994SDkxERMRckQvkRx99lKeffjpv+9ChQ9SoUYPp06ezYMEC4uPjOXjwYDBilAqgvPaO\nHTliYezYcFq0iGXPHivLl2cwc2YWl1/u54ILDBYsyODtt8OZN89ZpOsfPmxhzJgIWreO5dix3Ov/\n5z+ZdOrkw3qWf701ahj8619uPv00g3feySq76dvS04nq25foW27BsXhxgU4Jmz4d7403YtSuXW7z\nQkqW8kLMKC8kmIrUYrFs2TIaNGhAQkICf12pevDgwQAsXLgQSz6fKw8dOpTExEQAKlWqRJMmTfI+\nGjmZ4NquWNsnhUo8Z9s2DHA42vPuu+F88glce+0B1q69gMTEAKmpqRw58ufxe/as59FHo3nyyfZU\nqRIgPHxdge5Xt+41vPpqOB98YKVDh32sX38htWoZpKamcvhwaH0/8tu2pqVhu/FG9jdrRtWlS4ka\nOJDV4eF4Y2LyPf/L1atJfvNNXCkpAOzYsSNk/jzaDp3tk0IlHm2HxrbeL7R9UmpqKmlpaQAMGjSI\norAYf61wC2DMmDF8+OGH2O12jh07htVqZdiwYXz11VcsW7YMgKSkJF5++WUuv/zy085NSUmhRYsW\nRQpWpCxlZMCCBU7efTccrxfuvtvN7bd7qFz53P+ENm2y0a9fNB9+mEnLlv58j9u928q0aeEsWeKg\nb18Pw4e7qF69fPQNnyE7G0dKCt6uXQFwvvce3k6dMOLj8z0lbPp07Fu2kPX226UVpYiInMe2bdtG\nx/umi4sAACAASURBVI4dC31ekQrkUz3zzDPExMQwYsQIGjZsmPeQXnJyMj/++OMZx6tAlvLm118t\nPP98OAsXOrnmGh8DB7q55hpfoR+8++QTB/ffH8nSpRnUr//n9Bb79llYtMjJwoVODh600revm3/9\ny03VquW0MC4OrxdLRgbGhReWdSQiInIeKGqBbA9WAA6HgwkTJtC2bVsApk6dGqxLSwWQmpqa9zFJ\nqJkyJZzffrOSmlq8WSBuuMHL0aM59OwZzZw5WXz5pZ2FCx388IONm27y8vTTObRt68MetH+V5ZDD\ncVpxHMp5IWVHeSFmlBcSTMX+r/ipp57K+32vXr3o1atXcS8pEjKys2HePCdr1gRnFoj+/T0cO2bl\nppti+PvfPYwc6SYpyYuzaM/wlb2cHBwpKThWrCBnwgSMSpXKOiIREZFiK3aLRWGpxULKkzlznKxY\n4eCDD7KCel3DoFysZGcqIwPHf/+Lc9kyHGvW4GveHM/NN+Pp2RNiYso6OhERkTxFbbHQUtMi+TAM\nePfdMO6+2x30a5dWcWzZvz/o14x86inCPvgAb1ISJ7ZuJXPxYjx331244jgjg4hRo8Ab+qv6iYhI\nxaMCWULCX6dvCgXbttn4/XcLHTv6yjqUInF++CHRffsWeIGOgsqePJnMBQvw3HEHRtWqRbtIdDS2\ntDTCX3kFx4oVOD75xPSwUMwLKXvKCzGjvJBgqsiPA4mc1b//HcaAAe6zLsgRqqw//kjEmDFkLl4c\n/OHqYFzPYiFryhRiO3TAiIwk+9VXi39NERGRIFEPsoiJ336z0LJlLFu2pFOlSjmbbi0nh5hOnXAP\nHIjnrrvKOpqzcs6YgXPRIjKXLCnHTdkiIhKq1IMsEkTvv++kc2dv+SuO/3979x0dVZ33cfwzmclM\nJg2khw1BUQGNFMnyuGJEqS6CWAFFBUE0IIg8gLtIOcuKIsLjgqAU6YKNIhrAPQiIhWJQWTl2iroI\nUoUw6dPu80ckBrkgSW4mQ/J+neORm7nlN4fPmXz5zff+riT3uHEKNm4sb9++p78QDMq2f//5n8jr\nlXv8eNmOH7d2gMUv0a8fxTEAIOxQICMshFPvWDAoLVxYPjfnlTfb/v1ybN+unKlTzyg67Z99priu\nXQsfCfhH8vIUe//9itizR0Z0dDmN9lfnKI7DKRcIH+QCZsgFrESBDPzOxo0OVatmnPOR0BUh8q23\nZP/kk3PedGckJipr0yYpPv6M1wKtW8vftq3cTz55zuvY9u9XbM+eClavrpyFC6WoqDKPHQCACwkF\nMsJCOD39aMEClx58sCD8vvV3uRTzyCOK/8tf5Jo2Tbaffzbfz24/6ynynnpKznfekWPLFtPXo55+\nWvE33CB/aqpyZ82SIiOtGHmphVMuED7IBcyQC1iJAhkoZt++CH3yiUN33OGt6KGcwdelizzbtytn\n+nTZf/xR8ampir3rLtkyM8/7HEa1asr9v/9T9NChhY8J/J1g48byfPSR8v/+d12Qy3cAAGABfgMi\nLIRL79iiRU716uVVubbdejyK/Pe/S3eszabANdcod9o0nfzySxX07Vvixzv7unSRPyVFrgULznjN\n26OHjPr1Sze2chAuuUB4IRcwQy5gJdZBBn5VUCC98opLa9eex01sZeBaulTuiRPl2bJFwYYNS3+i\n6Gj5brmlVIfmPvec5HaX/toAAFRizCAjLIRD71h6ulPJyQFddlmwXK/jfPttZS9ceO7i2DBk37Gj\n/AYRFyc5wv/fx+GQC4QfcgEz5AJWokAGfjV/fuHNeeXJtn+/Ivbskf/GG8+5n2v+/MI+YZ+vXMcD\nAADORIGMsFDRvWMffODQkSM23XRT+RakzvR0+W6++ZyrQzi2blXUlCnKWbKkwleRqGgVnQuEJ3IB\nM+QCVgr/71iBcub3S6NHR+uf/8wr964D27Fj8t55p+lrkevWyblihRxbtihn5kwFL7mkfAcDAABM\n2QzjHE8dKAcbN25Uq1atQnlJ4Jzmz3cpPT1Sb72VXbFrH+fkKHrUKAWuukoFaWkVOBAAACqHHTt2\nqEOHDiU+jhlkVGknTtg0eXKU3nyzgotjSYqJUe6MGRU8CAAAQA8ywkJF9Y49+2yUunXzKTk5vB4r\njUL0FMIMuYAZcgErMYOMKuvbbyO0cqVT27Z5KnooAAAgjNCDjCrJMKQePWLVoYNPgwaV79JuAACg\nYpS2B5kWC1RJ69c79NNPERowIDTFcdQzz8h27FhIrgUAAMqGAhlhIZS9Y16vNHZstJ56Kjckywzb\n9u+Xa948GdWqlf/FKhl6CmGGXMAMuYCVKJBR5cyd69LFFwfVqZM/JNc7n4eDAACA8MFNeggLqamp\nIbnO0aM2TZsWpbVrs0JyPUlyvvWW8v72t5BdrzIJVS5wYSEXMEMuYCUKZFQJhw7ZtG2bQ0uWuNSj\nh1eNGwdDcl3b/v2K2LtX/htuCMn1AABA2dFigbBgZe+YYUjffx+hV15xasiQaP35z/Fq0yZey5c7\n1a6dT6NH51l2LQWDsu/cedaXnenp8nXpQntFKdFTCDPkAmbIBazEDDIqjb17I7RihVMrVzqVk2PT\ntdf6de21fj3ySL6aNg0qIuhXTFqabPcfV6BlS/lbtpT/+utl1KhR6mtG7N+v2N695evYUXnjx8u4\n6KLTXi+4/37ZsrPL+tYAAEAIMYOMsFDa3rHDh22aPduljh3j1LVrnE6csGnWrBx9+eVJzZuXowcf\nLNCVVwYVESFFTZ4s2/Hjyn/kERlut5xvvCH7N9+UadzBpCSd3LZNRlSU4tu0kfONNwqnsE+Ji5OR\nkFCma1Rl9BTCDLmAGXIBKzGDjAtSRoZdkye79dlndnXp4tMTT+Tphhv8cpwt0YYh24kTypk9W0bd\nuvJ36nTO87vHjVOgUSP527dXsGFDKSdHjv/8R36zD+D4eOU9+6y8vXopevhwOV97TTnz58uoWbPs\nbxQAAIQcM8gIC+fbO7Z/v00PPRSj/v1jdccdXn399UnNmpWrDh3OURxLks2mvClTZNSte17X8bds\nKcf27Yrr3FnxrVur2jXXFM4On0OgVStlbdggb8+erHlsEXoKYYZcwAy5gJWYQcYFITdXeuGFKM2Z\n41L//gWaOjVHsbHldz3fnXfKd+edhTfhffmlFAwq0LLlHx/ocMjbu3f5DQwAAJQ7CmRUqEBAGjbI\nrq2f/FVXJBu64oqAmjYN6IorArr88qAcDmnVqkiNH+9WSkpAmzZlKSkpNEu0SZIiIhRo3jx018Np\n6CmEGXIBM+QCVqJARoUJBqXHHovWz5u+0SrX37Wz3Rx9dbSu0tOdmjzZrp9+ilCNGoZq1gxq9uxc\ntWkTmiffAQCAqo0eZFQIw5CeeMKtPXvsev2JDEV2rq97n79eo+/6UosX5ygjw6O9ezO1YkWW3nsv\n67fi2DAUNXGi7F99deZJvd6iP9oyMxVz331SnoVrHiPk6CmEGXIBM+QCVqJARsgZhvTkk25t3+7Q\nsmVZcvbvqb133KH8v/1Ncd27K+LrryVJbrfUtGlQdvuvBwYCin7sMUVu2qRg/fpnnDe2Z09FDxyo\niF27FD10qIKJiYUnAQAAKAGbYRRftLX8bdy4Ua1atQrlJRFmpkyJ0qpVTq1enaWaNU+PX+TKlbJl\nZ8vbt+/pBxUUKObhh2XzeJS9ZIlM79DzeBQ1d65cs2cr+Kc/KWvdOsnlKsd3AgAAwtmOHTvUoUOH\nEh9HDzJC6sUXXVq2zKk1a84sjqXC1SPOkJ2t2D59ZMTFKfv1189e9MbHK3/ECOUPHFh49x/FMQAA\nKIVStVgcOHBAqampuuqqq5SSkqINGzZIkpYtW6bGjRurSZMmWrNmjaUDxYVv0SKn5s51adWqLNWt\ne3pxfK7eMcfWrQo2aKCc+fPPr+iNiZHi48s6XIQBegphhlzADLmAlUo1gxwZGalZs2apWbNm2rdv\nn9q0aaMffvhBo0aNUkZGhvLz89WuXTt169bN6vEijHm90ujRbv34o115eVJenk25ubaiPzud0urV\nWUpMNBTx448KJiScV8Hr79xZ/s6dQ/AOAAAASlkg16lTR3Xq1JEkJSUlyev1atu2bUpOTlbt2rUl\nSQ0aNNDOnTvVokUL60aLsPbUU4XF8cCB+YqOltxuQ263oehoKSrKUPXqhpxOSYahmH79lDd6dNEj\nn1m/EmbIBcyQC5ghF7BSmXuQ161bp5SUFB05ckQJCQmaM2eOatSooXr16ungwYMUyFXEu+86tGqV\nUx984FGNGue+79Oxdatsubnyl6JpHgAAoLyVaZm3Q4cOaeTIkZo5c2bRz9LS0tSjRw9Jks1mK9vo\ncEE4cMCmoUNjNHdutmoax/5wf9fMmcofNEiK+C1+9I7BDLmAGXIBM+QCVir1DHJ+fr569Oih5557\nTpdccol+/vlnHTx4sOj1Q4cOKSEhwfTYRx55RElJSZKkatWqqVmzZkVfjZwKONthuv3RR7pywQLV\nnDRJRt26+uCDLRoz5lqlpRXoL38JyJHcVkdbtVL1uXOlqKgzjv/PG2/ouq1b5Z0797Tzn1Lh74/t\nsNr+4osvwmo8bIfH9inhMh62w2Obzwu2T9m8ebP27dsnSRowYIBKo1TrIBuGod69e6tt27YaNGiQ\nJMnr9app06ZFN+m1b99eu3fvPuNY1kG+sLlmzJBzxQplrVkjxcXp6aej9NlnDq1Yka2ICMl28qSi\nH3tMEd9/r5z58xW8/PLTjnc//riM6tWVP2ZMBb0DAABQVYR0HeQtW7Zo5cqV+vbbb/XSSy/JZrNp\n7dq1mjRpkq677jpJ0rRp00pzaoSxyHXrFDV7tjzr1klxcdq0yaFXX3Vp0yZPUbeEUa2achYulHPx\nYsV16aK8J5+U9557pF/bbXydOyvQvHkFvgsAAIBz40l6kDweKS6uqIg1E/H114q79VZlv/qqAq1b\n6/Bhm9q1i9fs2Tlq29Z/1mNiBg9W9pIlMhITzzmEzZs3F31NApxCLmCGXMAMuYCZ0s4gl+kmPVQO\n7gkTFNOvn5Sdbb5Dbq5i771XeU8/rUDr1goEpLS0GN1/f8FZi2NJCl55pbLee+8Pi2MAAIBwQoFc\nyX31lV3XXBOvXr1itXev+V933oQJMuLiFN+5syK+//7MHaKjlbN4sbw9eyoz06YRI6IVDEp/+1v+\nHw/gPFcy4V/9MEMuYIZcwAy5gJUokCuxt9+O1G23xWr48Hylpvp0001xeuqpKOXk/G7HqCjlTp+u\n/AEDFNelixzr159xrqzLmuv5511q3brwEc4LF+bIbg/BmwAAAAgxCuQ/4PNJ69ZF6sEHY7RiRWRF\nD+e8BIPS009Hadw4t1asyFavXl49+miBPvzQo30/2nRdY5/SF3h0Wve5zSZv//7KXrxYMY89Jse2\nbZIK3/+iRU61bl1Nn3/u0DvvZGnatFzVrGlt6/rvl28CJHIBc+QCZsgFrFSqVSyqgq++suu115xa\nscKphg2Duvlmr554Ilr/8z9ZSkoKVvTwzsrjkQYOjNHJkzZt3Jil2rV/K2Tr1ze0uPmz2rb3uB6d\n/5wWrjY0YUKeEhODCgYLC+tgo2tlLN+sQPUa+vjNSD3zjFuJiUEtWZKtVq0CFfjOAAAAQoMCuZj8\nfGnxYpdee82pX36J0N13F2jNmixddllhQWyzSY8+Gq1Vq7KLPwQubOzZE6H77otVaqpPixblyek8\n/fWIPXsUNX26/rxxo96vn6X5813q0SNWeXmFD7X77b94RURISUlBTZmSqxtvPPuNeFahdwxmyAXM\nkAuYIRewEsu8FTN6tFtffmnXiBH5uv56/xlFcCAg3XxznO6806uHHy4I+fiOHbNp7lyXcnNtCgQK\nZ3z9fikQsMnvl959N1KjR+epb1/vmQcHg4rt1k2+7t1VMHBgyMcOAAAQaizzVkbbt9u1apVTixbl\n6IYbziyOJclul158MUdTpkSddUWI8rJ1q0M33BCvo0cjVLt2UImJQV1ySVBNmwbVooVfrVv7tXx5\ntnlxLMm1YIFsgYAKHnoopOM+X/SOwQy5gBlyATPkAlaixUJSQYE0dGiMnnkmVzVqnHtC/bLLgho5\nMl+DB8do7dqscl/JIRiUpk6N0ty5Ls2YkaNOnUrX7hC49FLlzJghlp4AAAA4N1osVLjiw3ff2bV4\ncc55LdsbDEq33Rarjh19Gjq0/Fotjh61KS0tRgUF0ty5OapfP6R/VQAAABe00rZYVPkZ5C++sGvx\nYpc+/NBzvs+0UESENGNGrjp2jFPnzj41bWr9qhabNzuUlhaje+4p0KhR+XKY/E053ntPzpUrFWjV\nSv5WrSS7XY7331cgOVn+UoQBAAAAVbwH2ecrXJVi/Pg81atXstnZhg2DGjMmT4MHx8jns3Zc06e7\n9NBDMZoxI0djx/5aHOef+dS6QOPG8rduLfvOnYp+9FHFPPSQIg4ckFGjhrUDCgF6x2CGXMAMuYAZ\ncgErVekZ5BdeiFKtWobuucf8xrY/0revV2vWODVtWpQef/w8Hrt8HubNc2npUpfee8+jhITCot2e\nkaGY//1feT78UMWnko3ERHkfeEDeBx6w5NoAAACopDPI773nUEpKvDp2jNOqVZHym9zXtmtXhGbO\ndGnq1Nzzbq34PZtNev75HM2d69LixU6VtZv7nXciNXVqlJYvzy4qjm0HDyq2f3/ljh8v0z6LSoL1\nK2GGXMAMuYAZcgErVaoC+ZdfbBo4MFrDh0dr0qRcDR+er3nzXEpJidfMmS55PIX7BQKFq1b8/e/5\natCgbP3Df/qTofT0wodu9O0bo+PHS1dtf/KJXcOGRWvp0mw1bPjrmLxexfbrp4IHHpC/c+cyjRMA\nAADnp1IUyIYhvfGGU9ddF69atQxt2eJRp05+3XyzT2vXZmvhwhzt2OHQ1VdX09ixbj37bJTsdkP9\n+1uzAkXTpkGtX5+lhg2Duv76eL3/fslmevfujVCfPrF68cUcXX31b49zdo8erWDNmsofMcKScYYz\nesdghlzADLmAGXIBK13w39n/978RGj48WseO2fTaa9mnFZintGoV0Lx5Ofrppwi99JJLy5Y5tWKF\ntY+LdrmkCRPy1L69T4MHx+jOO70aMyZPLte5jzt61KaePWM1alTeaWscR3zzjSK3bJFn3TqF5XOt\nAQAAKqkLeh3kpUudGj/eraFD8zVoUIEiIy05bZn98otNjz0WrZ9+itCLL+YqOTlg2ueckyPdemuc\n2rf3afRok5v8Cgr0hxU2AAAATFWpdZD9fmncOLc2bIjUO+9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+ "text": [
+ ""
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 30,
+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Exercise - Nonlinear Systems"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Our equations are linear: \n",
+ "$$\\begin{aligned}new\\_pos&=old\\_pos+dist\\_moved\\\\\n",
+ "new\\_position&=old\\_position*measurement\\end{aligned}$$\n",
+ "\n",
+ "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
+ "\n",
+ "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n",
+ "\n",
+ " Z = math.sin(i/3.) * 2\n",
+ " \n",
+ "Adust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#enter your code here."
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "###### Solution:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30\n",
+ "movement_error = 2\n",
+ "pos = (100,500)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "\n",
+ "for i in range(100):\n",
+ " pos = update(pos[0], pos[1], movement, movement_error)\n",
+ "\n",
+ " Z = math.sin(i/3.)*2\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['input', 'filter'], 2)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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AFv86opwPPAD3HXfAzNlDyEuhVSNss8G0bBnsPXsqMlp07VojXnklClu2ZBUO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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "######Discussion\n",
+ "\n",
+ "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n",
+ "\n",
+ "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the predition and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n",
+ "\n",
+ "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Exercise - Noisy Nonlinear Systems"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Implement the same system, but add noise to the measurement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#enter your code here"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "######Solution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "sensor_error = 30\n",
+ "movement_error = 2\n",
+ "pos = (100,500)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "\n",
+ "for i in range(100):\n",
+ " pos = update(pos[0], pos[1], movement, movement_error)\n",
+ "\n",
+ " Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = sense(pos[0], pos[1], Z, sensor_error)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "\n",
+ "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
+ "p2, = plt.plot(ps, c='b')\n",
+ "plt.legend([p1,p2], ['measurement', 'filter'], 3)\n",
+ "plt.show()"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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qBfMTT3js/e/fZ7BpkwYvvWTA779n4eRJHi+8EAhThQhaGS7FuIsXZdMkiG9o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\n7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+ "text": [
+ ""
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "###### Discussion\n",
+ "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
+ "\n",
+ "Very shortly after practioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions."
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Summary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This information in this chapter takes some time to assimulate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n",
+ "\n",
+ "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "author notes:\n",
+ " clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end.\n",
+ " \n",
+ " "
+ ]
+ }
+ ],
+ "metadata": {}
+ }
+ ]
}
\ No newline at end of file