diff --git a/05_Kalman_Filters.ipynb b/05_Kalman_Filters.ipynb
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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# One Dimensional Kalman Filters"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- "\n",
- "\n"
- ],
- "text/plain": [
- ""
- ]
- },
- "execution_count": 1,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "#format the book\n",
- "%matplotlib inline\n",
- "%load_ext autoreload\n",
- "%autoreload 2\n",
- "from __future__ import division, print_function\n",
- "from book_format import load_style, figsize\n",
- "load_style()"
- ]
- },
- {
- "cell_type": "markdown",
- "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."
- ]
- },
- {
- "cell_type": "markdown",
- "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 reasonably 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. Furthermore, 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 modeling 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. We will talk about this in great detail later, but we need to model two kinds of noise. The *process noise* is the noise in the physical process. Something moving at a notionally 'constant' velocity will never maintain a perfectly constant velocity. Undulations on the ground, wind, and a host of other factors mean that there will always be slight variations in the velocity. The second noise we want to model is the noise in the measurement as no measurement is perfect."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "from __future__ import print_function, division\n",
- "import matplotlib.pyplot as plt\n",
- "import numpy.random as random\n",
- "import math\n",
- "\n",
- "class DogSensor(object):\n",
- " \n",
- " def __init__(self, x0=0, velocity=1, \n",
- " measurement_variance=0.0, process_variance=0.0):\n",
- " \"\"\" x0 - initial position\n",
- " velocity - (+=right, -=left)\n",
- " measurement_variance - variance in measurement\n",
- " process_variance - variance in process (m/s)^2\n",
- " \"\"\"\n",
- " self.x = x0\n",
- " self.velocity = velocity\n",
- " self.noise = math.sqrt(measurement_variance)\n",
- " self.pnoise = math.sqrt(process_variance)\n",
- " self.constant_vel = velocity\n",
- "\n",
- " def sense_position(self):\n",
- " pnoise = abs(random.rand() * self.pnoise)\n",
- " if self.velocity > self.constant_vel:\n",
- " pnoise = -pnoise\n",
- " self.velocity += pnoise\n",
- " self.x = self.x + self.velocity\n",
- " return self.x + random.randn() * self.noise"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The constructor `__init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `sense_position()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense_position()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. and a standard deviation of 1.0. *Variance* is defined as the standard deviation squared, so in `__init()__` we take the square root of the variances to get the standard deviation. Therefore the expression `self.x + random.randn() * self.noise` computes a simulated measurement with the variance that we desire. \n",
- "\n",
- "Let's look at some example output for that."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " 1.1006\t-0.2120\t-0.4838\t 0.3862\t 0.8021\t\n",
- "-0.2236\t 1.1977\t-1.5618\t 1.5419\t 2.1203\t\n",
- "-0.2861\t-1.1764\t-0.0429\t 0.5016\t 0.2213\t\n",
- " 1.0790\t 0.7600\t 1.5109\t-1.0479\t 1.0137\t\n"
- ]
- }
- ],
- "source": [
- "for i in range(20):\n",
- " print('{: 5.4f}'.format(random.randn()), end='\\t')\n",
- " if (i+1) % 5 == 0:\n",
- " print ('')"
- ]
- },
- {
- "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 `DogSensor` class. We will start by setting the variance to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal, so the results should be a straight line."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
- ]
- },
- {
- "data": {
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DunXrpksvvVQbNmzQc889pxtuuCFU+QAAQAOyb98+ZWVlyVqrjz/+2Flv0aKFUlNTZYzR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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "import matplotlib.pyplot as plt\n",
- "import book_plots as bp\n",
- "\n",
- "dog = DogSensor(measurement_variance=0.0)\n",
- "xs = []\n",
- "for i in range(10):\n",
- " x = dog.sense_position()\n",
- " xs.append(x)\n",
- " print(\"%.4f\" % x, end=' '),\n",
- "bp.plot_track(xs, label='dog position')\n",
- "bp.show_legend()\n",
- "plt.show()"
- ]
- },
- {
- "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 position is 0.0 + 1, or 1.0.\n",
- "\n",
- "Now let's inject some noise in the signal."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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bt29Hfn4+AECn06F///6QZRkjR46Eq6vrgzdWVAR8+inwwgvAzZtqFcYJEwB3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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "def test_sensor(measurement_var, process_var=0.0):\n",
- " dog = DogSensor(measurement_variance=measurement_var, \n",
- " process_variance=process_var)\n",
- "\n",
- " xs = []\n",
- " for i in range(50):\n",
- " x = dog.sense_position()\n",
- " xs.append(x)\n",
- "\n",
- " bp.plot_track([0, 49], [1, 50])\n",
- " bp.plot_measurements(xs, label='Sensor')\n",
- " plt.xlabel('time')\n",
- " plt.ylabel('pos')\n",
- " plt.ylim([0, 50])\n",
- " plt.title('variance = {}, process variance = {}'.format(\n",
- " measurement_var, process_var))\n",
- " bp.show_legend()\n",
- " plt.show()\n",
- "\n",
- "test_sensor(measurement_var=4.0)"
- ]
- },
- {
- "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 `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 dotted red line drawn over a straight black line. The black line shows the actual position of the dog, and the dotted red line is the noisy 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 sensor output.\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 several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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e3t7Yu3cvVy1jjLHqbvRowNsbcHU1dCSMGb9vvxXL117jxMwI5efnIyoqCoqi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\nP6tFsstXfeGFAAAAAElFTkSuQmCC\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "test_sensor(measurement_var=100.0)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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//BFo1gwpa9dizZo1UBQFu3fvVhe1t7dHWHAwZFnGgAEDoNVqS3cfdevqL2kk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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "test_sensor(measurement_var=0.5)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n",
- "\n",
- "So let's first look at the plot with some process noise but no measurement noise to obscure the results."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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29YWHh2PbNrZtU7NmzWtRudxA3D4JtYiIiIiI26Snw8SJ8PLLcPw4hIfDAw+A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\npw9hYWHY7XZmzpxZYsz48eMJDQ2lSpUqdOvWjd27d7uhUvEUkyZNom3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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "import numpy as np\n",
- "np.random.seed(1234)\n",
- "test_sensor(measurement_var=0, process_var=0.5)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will stay there until the random changes in velocity happen to result in the track going back to the original track. \n",
- "\n",
- "Finally, let's look at the combination of measurement noise and process noise."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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L+rN3CCGEEEKI+mvrVpg5E/77X/D1tXY1N3X48GFUVUVVVVJTU/V2Dw8PwsLC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\nOH4csrPhu+9g2bI/+tLSwN8///hbbvm9K41ly5ZhmiYJCQnk5eUB4OX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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "test_sensor(measurement_var=1, process_var=0.5)"
- ]
- },
- {
- "cell_type": "markdown",
- "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",
- "execution_count": 10,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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F8eS0U/hxx5dQlRRXcCQR1RcswImoVhxJ2oXf9/0A7d9uGJNAgnGDp2BAz1dE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\nCCGEED+iApwQQgghhBA/+n9wJsSfsI5CQQAAAABJRU5ErkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "import stats\n",
- "with figsize(y=3):\n",
- " stats.plot_gaussian(mean=23, variance=5)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Notice how this relates to the bar charts from the Discrete Bayes chapter. In that chapter we drew bars of various heights to depict the probability that the dog was at any given position. In many cases those bars took on a shape very similar to this chart. The differences are that the bars depict the probability of a discrete position, whereas this chart depicts the probability distribution of a continuous range of positions. \n",
- "\n",
- "This graph corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly speaking positions 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 interpretation 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",
- "execution_count": 11,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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jj909NKdgaDkBGstSqVQqVFRUQKPRyNqXFMsJR2nrSX5+vih4AM+LfPPuj4Br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\nBEEQBBEi/g8/FuTont3LTQAAAABJRU5ErkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "dog = DogSensor(x0=23, velocity=0, \n",
- " measurement_variance=5, process_variance=0.0)\n",
- "xs = range(100)\n",
- "ys = []\n",
- "for _ in xs:\n",
- " ys.append(dog.sense_position())\n",
- " \n",
- "bp.plot_track(xs, ys, label='Dog position')\n",
- "plt.legend(loc='best')\n",
- "plt.show()"
- ]
- },
- {
- "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 preexisting belief:\n",
- "\n",
- " def update(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 convenience. \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 of multiplying two Gaussians is a Gaussian with \n",
- "\n",
- "$$\\begin{aligned}\n",
- "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
- "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
- "\\end{aligned}$$"
- ]
- },
- {
- "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",
- "execution_count": 12,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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cobhKlSrFhg0bUo5tNhuzZs3iypUrKaN2S5cuxcvLK6XNgAEDqF69OuPGjWPK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\nc8XR3hVne1cc7VxxsnfB0dbZpM9XhGgKNxScLVy4kLlz55KTk0Pbtm3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ADvRNYOrUqaxY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\nrkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "from __future__ import division\n",
- "import numpy as np\n",
- "\n",
- "def multiply(mu1, var1, mu2, var2):\n",
- " if var1 == 0.0:\n",
- " var1=1.e-80\n",
- " \n",
- " if var2 == 0:\n",
- " var2 = 1e-80\n",
- " \n",
- " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
- " variance = 1 / (1/var1 + 1/var2)\n",
- " return (mean, variance)\n",
- "\n",
- "xs = np.arange(16, 30, 0.1)\n",
- "\n",
- "mean1, var1 = 23, 5\n",
- "mean, var = multiply(mean1, var1, mean1, var1)\n",
- "\n",
- "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
- "plt.plot(xs, ys, label='original')\n",
- "\n",
- "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
- "plt.plot(xs, ys, label='multiply', ls='--')\n",
- "\n",
- "bp.show_legend()\n",
- "plt.show()"
- ]
- },
- {
- "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 multiplication 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 23 meters each time, I should conclude that the length is close to 23 meters. 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",
- "execution_count": 13,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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2zNhhCJFpLw7RmjVrFjt37sxU3Vc9T0EeDiYJuhBCFFBarZZx48Zx+/ZtvfJZ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TYzPrfbzVdffcXChQuDyidPnsyOHTvCHrNz507Gjh1LREREUPySJUs4ceIEGRkZ7Ny5k8mTJ4ec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\nSUVORK5CYII=\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "xs = np.arange(16, 30, 0.1)\n",
- "\n",
- "mean1, var1 = 23, 5\n",
- "mean2, var2 = 25, 5\n",
- "mean, var = multiply(mean1, var1, mean2, var2)\n",
- "\n",
- "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
- "plt.plot(xs, ys, label='measure 1')\n",
- "\n",
- "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
- "plt.plot(xs, ys, label='measure 2')\n",
- "\n",
- "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
- "plt.plot(xs, ys, label='multiply', ls='--')\n",
- "plt.legend()\n",
- "plt.show()"
- ]
- },
- {
- "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",
- "execution_count": 14,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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EfdeuXZg9ezYWLVqE2NhYBAUFYfDgwUhNTa3w+NOnT6Nz587Ys2cPrl+/junT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\nIYQQokKoQCeEEEIIIUSF/D8YwdxN2xDhkAAAAABJRU5ErkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "xs = np.arange(0, 60, 0.1)\n",
- "\n",
- "mean1, var1 = 10, 5\n",
- "mean2, var2 = 50, 5\n",
- "mean, var = multiply(mean1, var1, mean2, var2)\n",
- "\n",
- "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
- "plt.plot(xs, ys, label='measure 1')\n",
- "\n",
- "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
- "plt.plot(xs, ys, label='measure 2')\n",
- "\n",
- "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
- "plt.plot(xs, ys, label='multiply', ls='--')\n",
- "plt.legend()\n",
- "plt.show()"
- ]
- },
- {
- "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. Furthermore 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",
- "Of course, this example is quite exaggerated. The width of the Gaussians is fairly narrow, so this combination of measurements is quite unlikely. It is hard to eyeball this, but the measurements are well over $3\\sigma$ apart, so the probability of this happening is less than 1%. Still, it can happen, and the math is correct. \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": "markdown",
- "metadata": {},
- "source": [
- "## Implementing the Update 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 update function for a Kalman filter:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "def update(mean, variance, measurement, measurement_variance):\n",
- " return multiply(mean, variance, measurement, measurement_variance)"
- ]
- },
- {
- "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 is with the new measurement. Perhaps this would be clearer if we used more specific names:\n",
- "\n",
- " def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n",
- " return multiply(dog_pos, dog_variance, measurement, measurement_variance)"
- ]
- },
- {
- "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 `update_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 `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 position 2.0, not 0.0."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 16,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "time: 0 \tposition = 1.074 \tvariance = 2.500\n",
- "time: 1 \tposition = 1.349 \tvariance = 1.667\n",
- "time: 2 \tposition = 0.307 \tvariance = 1.250\n",
- "time: 3 \tposition = -0.297 \tvariance = 1.000\n",
- "time: 4 \tposition = 0.058 \tvariance = 0.833\n",
- "time: 5 \tposition = 0.634 \tvariance = 0.714\n",
- "time: 6 \tposition = 0.548 \tvariance = 0.625\n",
- "time: 7 \tposition = 0.504 \tvariance = 0.556\n",
- "time: 8 \tposition = 0.402 \tvariance = 0.500\n",
- "time: 9 \tposition = 0.160 \tvariance = 0.455\n",
- "time: 10 \tposition = 0.126 \tvariance = 0.417\n",
- "time: 11 \tposition = 0.393 \tvariance = 0.385\n",
- "time: 12 \tposition = 0.361 \tvariance = 0.357\n",
- "time: 13 \tposition = 0.287 \tvariance = 0.333\n",
- "time: 14 \tposition = 0.103 \tvariance = 0.312\n",
- "time: 15 \tposition = 0.268 \tvariance = 0.294\n",
- "time: 16 \tposition = 0.282 \tvariance = 0.278\n",
- "time: 17 \tposition = 0.253 \tvariance = 0.263\n",
- "time: 18 \tposition = 0.333 \tvariance = 0.250\n",
- "time: 19 \tposition = 0.350 \tvariance = 0.238\n"
- ]
- }
- ],
- "source": [
- "dog = DogSensor(velocity=0., measurement_variance=5, process_variance=0.0)\n",
- "\n",
- "pos, s = 2, 5\n",
- "for i in range(20):\n",
- " pos, s = update(pos, s, dog.sense_position(), 5)\n",
- " print('time:', i, \n",
- " '\\tposition =', \"%.3f\" % pos, \n",
- " '\\tvariance =', \"%.3f\" % s)"
- ]
- },
- {
- "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 initial 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 surprising. All we are doing is computing `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": "markdown",
- "metadata": {},
- "source": [
- "## Implementing Predictions"
- ]
- },
- {
- "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 non-moving objects? The histogram used a loop of predict and update functions, and we must do the same to accommodate movement.\n",
- "\n",
- "How do we perform the predict function with Gaussians? Recall the histogram method:\n",
- "\n",
- " def predict(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 `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 `predict()` 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 predict function:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 17,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "def predict(pos, variance, movement, movement_variance):\n",
- " return (pos + movement, variance + movement_variance)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "What is left? Just calling these functions. The histogram did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 18,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "PREDICT: 1.0000 502.0000\tUPDATE: 5.9374 9.8047\n",
- "PREDICT: 6.9374 11.8047\tUPDATE: 6.0781 5.4138\n",
- "PREDICT: 7.0781 7.4138\tUPDATE: 4.6672 4.2574\n",
- "PREDICT: 5.6672 6.2574\tUPDATE: 5.6747 3.8490\n",
- "PREDICT: 6.6747 5.8490\tUPDATE: 6.1235 3.6904\n",
- "PREDICT: 7.1235 5.6904\tUPDATE: 7.2806 3.6267\n",
- "PREDICT: 8.2806 5.6267\tUPDATE: 8.4183 3.6007\n",
- "PREDICT: 9.4183 5.6007\tUPDATE: 10.2644 3.5900\n",
- "PREDICT: 11.2644 5.5900\tUPDATE: 13.1794 3.5856\n",
- "PREDICT: 14.1794 5.5856\tUPDATE: 12.7885 3.5838\n"
- ]
- },
- {
- "data": {
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xpX/HYVzfaThuru5OqLByuBhd8PH0x8fTHwKBf9wNq3+n/asf0n7EvdC+vV17q9V6US+n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\n0K4dbN0KKSmQlXXtcXPmmMVj587mNh0qHkVEREREak0FpHi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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# assume dog is always moving 1m to the right\n",
- "movement = 1\n",
- "movement_variance = 2\n",
- "sensor_variance = 10\n",
- "pos = (0, 500) # gaussian N(0,500)\n",
- "\n",
- "dog = DogSensor(pos[0], velocity=movement, \n",
- " measurement_variance=sensor_variance, \n",
- " process_variance=sensor_variance)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(10):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n",
- " \n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- " \n",
- " print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n",
- "\n",
- " \n",
- "bp.plot_filter(ps)\n",
- "bp.plot_measurements(zs)\n",
- "bp.show_legend()\n",
- "plt.show()"
- ]
- },
- {
- "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_variance = 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 `predict()` step.\n",
- "\n",
- "For now let's walk through the code and output bit by bit.\n",
- "\n",
- " movement = 1\n",
- " movement_variance = 2\n",
- " sensor_variance = 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, \n",
- " measurement_variance=sensor_variance, \n",
- " process_variance=sensor_variance)\n",
- "\n",
- "It may seem very 'convenient' 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 `update() ... predict()` loop.\n",
- "\n",
- " for i in range(10):\n",
- " pos = predict(pos[0], pos[1], movement, sensor_variance)\n",
- " print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
- "\n",
- "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `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 `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",
- " PREDICT: 1.000 502.000\n",
- "\n",
- "What is this saying? After the prediction, 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 prediction step.\n",
- "\n",
- " Z = dog.sense_position()\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 update function of our filter, save the result in our *ps* array, and print the updated position belief:\n",
- "\n",
- " pos = update(pos[0], pos[1], Z, movement_variance)\n",
- " ps.append(pos[0])\n",
- " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
- " \n",
- "Your result will be different, but I get\n",
- "\n",
- " UPDATE: 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 `predict()` and `update()` 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. The variance is plotted as a lightly shaded yellow area between dotted lines."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 19,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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uXYIBBW7vDHvC4ft34G8W3Sk1mTgWc4Jdxw5yNvH8Vds2bOBBaJsQ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mD/0KFDVVBQ4K0Y8FMHDx5UYmKiOnXqpFtvvVWHDh2yOhL80KFDh1RUVNSgHwoPD1f//v3ph3BB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\ngg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Variance:\n",
- "\t2.5200 4.0428 3.6649 6.0266 5.8804\n",
- "\t5.2240 6.3572 6.5137 7.9885 8.0157\n",
- "\t9.6223 12.5884 13.0473 12.9739 12.8976\n",
- "\t13.6351 16.7189 18.5777 18.9743 19.9421\n",
- "\t20.6522 22.9380 24.0564 27.1851 25.4667\n"
- ]
- }
- ],
- "source": [
- "%precision 2\n",
- "# assume dog is always moving 1m to the right\n",
- "movement = 1\n",
- "movement_variance = 2\n",
- "sensor_variance = 4.5\n",
- "pos = (0, 100) # gaussian N(0, 100)\n",
- "\n",
- "dog = DogSensor(pos[0], velocity=movement, \n",
- " measurement_variance=sensor_variance, \n",
- " process_variance=0.5)\n",
- "\n",
- "zs, positions, variance = [], [], []\n",
- "for i in range(25):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance) \n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " variance.append(pos[1])\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " positions.append(pos[0])\n",
- " \n",
- "bp.plot_measurements(zs)\n",
- "bp.plot_filter(positions, vars=variance)\n",
- "bp.show_legend()\n",
- "plt.show()\n",
- "\n",
- "print('Variance:')\n",
- "for i in range(0, len(positions), 5):\n",
- " print('\\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(\n",
- " *[v for v in positions[i:i+5]]))"
- ]
- },
- {
- "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 literature, 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": "markdown",
- "metadata": {},
- "source": [
- "### Animating the Tracking"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n",
- ""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
- "\n",
- "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Implementation in a Class"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n",
- "\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance) \n",
- " \n",
- "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n",
- "\n",
- "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n",
- "\n",
- " class KalmanFilter1D:\n",
- " def __init__(self, initial_state, measurement_variance, movement_variance):\n",
- " self.state = initial_state\n",
- " self.measurement_variance = measurement_variance\n",
- " self.movement_variance = movement_variance\n",
- "\n",
- "That works, but I am going to use different naming. The Kalman filter literature has settled on one letter notations for each of these concepts, and so you might as well start getting exposed to it now. At first it seems impossibly terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondence with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them. If you do not make this effort you will never be able to read the Kalman filter literature.\n",
- "\n",
- "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the movement error. This gives us:\n",
- "\n",
- " class KalmanFilter1D:\n",
- " def __init__(self, x0, P, R, Q):\n",
- " self.x = x0\n",
- " self.P = P\n",
- " self.R = R\n",
- " self.Q = Q\n",
- " \n",
- "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n",
- "\n",
- " def update(z):\n",
- " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
- " self.P = 1 / (1/self.P + 1/self.R)\n",
- "\n",
- "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n",
- "\n",
- " def predict(self, u):\n",
- " self.x += u\n",
- " self.P += self.Q\n",
- " \n",
- "That give us the following code. Production code would require significant comments. However, in the next chapter we will develop Kalman filter code that works for any dimension, including 1, so this class will never be more than a stepping stone for us, since we can, and will use the class developed in the next chapter in the rest of the book."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 20,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "class KalmanFilter1D:\n",
- " def __init__(self, x0, P, R, Q):\n",
- " self.x = x0\n",
- " self.P = P\n",
- " self.R = R\n",
- " self.Q = Q\n",
- "\n",
- "\n",
- " def update(self, z):\n",
- " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
- " self.P = 1. / (1./self.P + 1./self.R)\n",
- "\n",
- "\n",
- " def predict(self, u=0.0):\n",
- " self.x += u\n",
- " self.P += self.Q"
- ]
- },
- {
- "cell_type": "markdown",
- "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* and *h* 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",
- "$$ \n",
- "\\begin{aligned}\n",
- "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a} \\\\\n",
- " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}} \\\\\n",
- " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
- " &= \\frac{\\sigma^2_{x'}}{b}\n",
- " \\end{aligned}\n",
- "$$\n",
- "\n",
- "We can tie all of this together with\n",
- "\n",
- "$$\n",
- "\\begin{aligned}\n",
- "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x) \\\\\n",
- "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
- "&= x + g_n(y-x)\n",
- "\\end{aligned}\n",
- "$$\n",
- "\n",
- "where\n",
- "\n",
- "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
- "\n",
- "The end result is multiplying 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 predictions 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": [
- "### Exercise: Modify Variance Values"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Modify the values of `movement_variance` and `sensor_variance` 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_variance = 40\n",
- " sensor_variance = 2\n",
- " \n",
- "or:\n",
- "\n",
- " movement_variance = 2\n",
- " sensor_variance = 40"
- ]
- },
- {
- "cell_type": "markdown",
- "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-equipped 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. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "def volt(voltage, temp_variance):\n",
- " return (random.randn() * temp_variance) + voltage"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We generate white noise with a given variance using the equation `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",
- "\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 performance 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 $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability 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 a Kalman filter that performs well. "
- ]
- },
- {
- "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 predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict 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 known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change over time. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `movement_variance = .2`. This is just the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n",
- "\n",
- "Let's see what happens. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 22,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
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HkydVvYBnnrF1JLnTzJnw/fdJ04StPRPj6tWkpQvlyln3XLbyxx/QpImqeptT36+FyAMk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sbTQG7f6yIHkU8SHBxMlSpVWLNmDb0zXQAyB5FXC+BJVNy4LFqEZUAAD4YNI7ZOhuHy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\n+6942qahoWE4oqOFqXl+/CKLis7vTmein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- "text/plain": [
- ""
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- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
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AAACuCr8K3zVnz6jidLmvywAAAACuCr8K3xLrvgEAABC8/DB8s+4bAAAAwcmr8P3CCy/I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\nFnl++/zn/HZoSJjXdQEAAAQ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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Variance converges to 0.858\n"
- ]
- }
- ],
- "source": [
- "movement = 0\n",
- "variance = 2.13**2\n",
- "movement_variance = .2\n",
- "actual_voltage = 16.3\n",
- "\n",
- "N = 50\n",
- "zs = [volt(actual_voltage, variance) for i in range(N)]\n",
- "ps = []\n",
- "estimates = []\n",
- "\n",
- "kf = KalmanFilter1D(x0=25, # initial state\n",
- " P=1000, # initial variance \n",
- " # large says 'who knows?'\n",
- " R=variance, # sensor noise\n",
- " Q=movement_variance) # movement noise\n",
- "\n",
- "for i in range(N):\n",
- " kf.predict(movement)\n",
- " kf.update(zs[i])\n",
- "\n",
- " # save for latter plotting\n",
- " estimates.append(kf.x)\n",
- " ps.append(kf.P)\n",
- "\n",
- "# plot the filter output and the variance\n",
- "bp.plot_measurements(zs)\n",
- "bp.plot_filter(estimates, vars=ps)\n",
- "bp.show_legend()\n",
- "plt.show()\n",
- "plt.plot(ps)\n",
- "plt.title('Variance')\n",
- "plt.show()\n",
- "print('Variance converges to {:.3f}'.format(ps[-1]))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The first plot shows the individual sensor measurements 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 `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 section **Explaining the Results - Multi-Sensor Fusion** explains why this happens."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Animation"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
- "\n",
- "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- ""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. \n",
- "\n",
- "> If this is not clear, I urge you to go back and review the g-h chapter. This is the crux of the algorithms in this book. "
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Exercise(optional):"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "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",
- "execution_count": 23,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "#Your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Solution"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 24,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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ww5Ikn8+n5ORkWa3WoOdwu93aunWrtm3bptmzZ/vPk52drZ07d2rOnDnhvg4AAABgRBr0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\nAACAgQjkAAAAgIEI5AAAAICB/h/dEpsQ5+ltYwAAAABJRU5ErkJggg==\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "variance = 2.13**2\n",
- "actual_voltage = 16.3\n",
- "\n",
- "def VKF():\n",
- " voltage = (14, 1000)\n",
- " for i in range(N):\n",
- " Z = volt(actual_voltage, variance)\n",
- " voltage = update(voltage[0], voltage[1], Z, variance)\n",
- " return voltage[0]\n",
- "\n",
- "vs = []\n",
- "for i in range(10000):\n",
- " vs.append(VKF())\n",
- "plt.hist(vs, bins=100, color='#e24a33')\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Discussion"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "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": "markdown",
- "metadata": {},
- "source": [
- "## Explaining the Results - Multi-Sensor Fusion"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "**author's note:** I am not overly keen about this explanation. It is true that multiple sensors improve results, but we get good results merely by having an accurate model of the process. I explain this much better in the next chapter. I'll leave this section here while I mull how best to explain this at this stage of learning. For now don't worry if this section is not entirely convincing; it does need work.\n",
- "\n",
- "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 focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 25,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
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NAS27dv3DhQuHmT79Oaytsxg3blBeW1VVWbljM9XCbzN66TGu+rpzJqAOodfD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\n0s2ydRlYwL5xY2KOH6d632HIsi3p6YlYW9tgbV2DZ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- "output_type": "display_data"
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AABBsLuo+3/5UVlGiZt5oBQAAAGgXLAvfHtOjiirueAIAAIDgYVn4lqSyimIrDw8AAAAE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\nfNr+vGGRKqrKLao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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30\n",
- "movement_sensor = 30\n",
- "pos = (0, 500)\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, \n",
- " measurement_variance=sensor_variance,\n",
- " process_variance=0.5)\n",
- "\n",
- "zs, ps, vs = [], [], []\n",
- "for i in range(100):\n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- " vs.append(pos[1])\n",
- "\n",
- " pos = predict(pos[0], pos[1], movement + random.randn(), movement_variance)\n",
- "\n",
- "bp.plot_filter(ps, vars=vs)\n",
- "bp.plot_measurements(zs)\n",
- "plt.legend()\n",
- "plt.show()\n",
- "plt.plot(vs)\n",
- "plt.title('Variance')\n",
- "plt.show()"
- ]
- },
- {
- "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 distinctly 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 disagrees 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 mathematical model this sort of reasoning."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## More examples"
- ]
- },
- {
- "cell_type": "markdown",
- "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 intuition 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",
- "execution_count": 26,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
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pZyXNEAq43i7WWZhw7irTpJISsn9jArkrNedqGsz33qMU5QAJ7yNG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\n4ZoA1NlTUcHzyeVilZu4ON4jNZUGxvLl1nlByckEYCJRUQQ7ixZxPmS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DDbH8t28PPwAv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fpNdjaZty+/VBuwtJSKfMAA5UIcNIgudB0AB4NqLD/5hEzhLbfQSNIbCzVsaH1gybuY\n2btAgPcxl5kS0Q/WNm1UwppUhNBFD1UJhdT8DBxIdik9PTxW1+5ZRRwOlRh5/fW0wKuryZQ7ncaw\nDDuRObzjDhpFq1aRubr/fgWydYUo7+H1qjq769fzGaqr+aeiwpo519kaO6/A8OHcV+YYPoBehpdf\n5r5Ys4bvLN3i4uLocQBoIJ17rorrmzpVMc7R0fz5I4+oZ1mwgOt+82a1twVsaQ3KogsLEbdnD92T\nM2cyLEBvlS3fkTU3dSoP6BYtjAYBYAwXk/Xy6qvcq7rOadqUYC0xUc2HOYFSlyNHGAYhjXIA3ldY\nzeHDVSiWmZl88UXF1JvBuQCcadPU/On7QZjEV15R76aDczMIlevLIWglc+aosprdupFEyM/n4da4\nMddoYiKvq1dXMYvsgzlz6KU76ywaThddxMOyDu7jP6WqirpR8l/093E4EAqFUHDxMBQW7EZll3R0\nqi5DYpwWU2o2JsxgffduvlvbtuH6plkzGuwNGoTvnUaNaOCYwy9FoqO5ZmfPVsx5ejp15dq1BB1i\nEIuOKikhmKyu5p6xq8A0ZgwNTL3Lql1i6ddfc0/cfDPPQL2qhcul1qXswagoGrjnn28E53rCtj6W\nVjpF1u6sWTwTbr7ZHph27UqvrS5CLvXuHe5Bljl6+GHqUAmP6NKF62zUqHBmeOJEIC8PwZgYdpI1\ne45kL8m9xBAVnSqgUES+u2kTkJuLgNsFlzmxHDCOTdeuCLVsiX1Ht+GPI78jGAwgrX5jdG97DuLn\nLkTN0sXYff0wxBzeAmeaG+vuHoi8Y1lomVOIlFAMyoIe5FSuwLF3FiIUCgI3N0fs6pdxVuHZuPTs\nG+B2RSGnYRAnSrbCtWk+4mMS0DKjLRq9+iqJTNERkZhzvVhGYqJ1zlggQH1glccG0ODU7yEFE3Q9\nDfD/Ms/Nmyu91Lw5yY3SUho+fftyHubNU82GBBuNGcNz5NdfqV/0ylvimTcnSFvJ6NEkyuxqx2vy\n1wHnAEFcvXoc4Px8KhyZcAHngJGlAzhJ4p4RYHHnnYyr1t1bEtceG8tNLm4XXXJyOFkDB6rygfqi\nW7yY1ywpUUrOrHT0w27KFMaSjRzJxaEv9pwcBVpETp7k8wqDkZHBMYmOppKRMv3Xe5EAACAASURB\nVH8ierymWIYOBxevniR06hRZBmHmAOMGAPjvZ5+1ZnP1ECK5XocOBAzDhqkksokTjc8YCqkOmcII\nAeEbsGfP8BbiuhQXk8GZOZP/37uXrrsXXyQILC8nkBaG6eWXuTHHj6dLVti/++6j+10MKXknqyTP\ntDTFjpsZGzv58UeyMHoFguPHOc8CgIcPZ+iS1drRRQ60K6/ku8bGciwl8fj22+k+9fsJiGNj1fhK\nCI0eyywHyiOPECDrSVNmcG7FcokhZ/XMqam8p8+nmj4tW8b3bttWlQaLiyPjOn68YvGkZFt0NBm3\nBg3Us7RsSdA2bRoNOElE1MHe6edxSsWDv/0tvFqKsEDR0TSozclg4g0COIdmkfHRwfl559F4aNaM\nRnLHjuq5P/44vPJRVRVJh5gY5TrV90Tz5qoUq5mZlHhbwOglSkwMr7VsBpkCKHT3rJk510Ho6NEE\nGPL7t96ioaOXjHv7bRpCzZrR6Ni7l16RnBzu07FjVcUcp5OJeFdfrfaZyGnAmjfuPqwbez22byxH\nWWUJogfHIKbvUET5goit9qLxkrcxpNdVSE/JpI4sLDQyhgDZ3ttuA44exbGTR7Hj4AaUVRajaGAq\n8ja/g9LfNNf+Fe0R9/Hd6H/WMGQ2bI7WGe2RcvRoODi3GseWLZVn9+efCfRuv13lCphBYloaiYHC\nQmN9cxExUPQQSLebVSV+/plgUge8EtKSnGwsQWfXIVQH4jfcwFh5q2TXt9+mIZGRwb0bG8t1vXix\n8grINWV9VlWRbU1MNILzQYOMCY9OJ8Oh7rrLSJA0bEidLlXEzCUIly9X6zYlJbwog89H0K2XuDS/\n+6RJnC99vdgZSqcNkVMXXIBTF1yAhqtXRwbnImJEnv65z+/Dgfxd2O/ZjbzRfVDV0Y3Cqj9Q9fLF\n6L78HfRt0gcJAScKYvwIjr8TaaFSVB/ahEAwgKiL+mLF1oXYNdfYnfqr5afjtl+7FCj6GZj/s/pl\nowQca9RCez9jLX9P0IuNf6zExj9Oe/Rv6Q3gELB6lvrQ5MtQ37kOgw5l4yxnb6QFgwzruuUWni92\ncvIkSSDJeyoqIhYIBKj7I1UG0/OO9EIXOlkioDk1VTVei47mmD/6KHHjxo38nrD04oWVa1dVqbyM\nJUuM4DwuToXp1QbOa6skpX+0Tp/6bxcZDAGFDzxAZsvrJWMLcHDNkygKS68vK8k2I0eSMZCDYPx4\numg9Hk5GcjIX3G23hceQBwKsmiBtiINBlWQKqHgnUarXX6/qOwsIkgk0x/jqEz93rlFhVFURNA0b\nppKKhA0DjF0yRfQQhWnTCELHjWOGud4ERw5JfcHeeqsxkSgUohKzAuc6KAHI1pw6xec57zwV5ztt\nmjEJTECRAAg99m7ECGMzoUgSCBjLYxYW0u0tiWlHjvAQefVVhl6sW0fgsH278Toffhie5CVjYq6i\nAHBtScxqXURK/+kiQEgOXalIUhfmPBjkWujVy1giLiqKRpvbTaNt0iSybHZMh8QFnjxJhsrciEVc\newDXj7niDhBe+xqgR0EvtSWhUwDH+pJLeHiaFZ5uCDmdBK0ffEADrbLSGAv5ySe897x5jMs0Gw4X\nXQR/QgKc5oNdF2FkLrmE1xbgJWE47dsrxkt6ANx4o2oAJnv9gQcINAMBAtKaGo5VTg7Ba9Om3EN6\nXLxIVRVZXT1BcNAgPvMLLxDkSPx5KMQ1J4ZOMEjD+fhx5XVISeF9tm41HhjmdSWA4tQpes900AzQ\ncDY3WZKSewDfefhwY9Ko6FF5tsxMPm9Ojkp8F9YcYFjQ7bcD55+P0msuw4Y/ViAnbydKjh/Gsesa\nA2gM1OQApx2cvmgHKlNVvPrhXcvw265luLDPNbgwPxruTz/HyY/fx/6cTXBWVMKbWh8n8nJwcGQb\n7J+iHbwAkBULeMMT26prKrFskzLS44fGIf3IPKS+sASFrRqj9O9N0XjrxxiQUIUOzXsgxudDmTuI\nA4U74cty4ayVyxF3wWACaBm/jAz7ZO/u3QlizHHDs2fz75wc6mPREzJvejk4Od8EeMo+smPOzSES\nn3/O++m5BxIrrxuuANfKhReSYBo+nD9fu5b3+/VXJtWmpZFF1ZnzhASCe82A9nbtDLcDqD55HPGh\nEBwOB3X0smVkV3ft4v2dThi6fw8eTCJj506OsX6myfOb93wgwPUrBq3odX0c7LwH+r4AaERr50XA\n70WhtwSJA/qiXp/PgRkz4L3iMuz2HMWyKTfheM0pOKbdiCqPtt46NwZQDtSLBRDCxr2rsHHvKvX7\nVAA4DiyoQw+C/7CcqinFvFUfYd6qj4D7zkKPopVwneVC213L0bX12YiNjuMY1atnDBGRng133klm\necIE4gKrfjG66OOte0V14k48GEIiJCXx2lIZDeBZ43AwVEn2oo51qqtVx+WoKNUdtkMHlXuzcKE1\nOC8s5D337VOdpWtrMof/YnD+3nvv4fXXX0dBQQE6deqEyZMnY4BdAxUpIyZy992cnKoqZQlVVSmA\nI224rYCN08kN/PnnxkGeOvVPcO6NcuKP/esQl7cTTStKEWP+vrnaSf36PFiWLKESadhQJWu53bQM\nhVndtIkHuiTnmMG508nDXxaQzgCWldF1qicw6qIrQJ+Pylykpiac3QY4FjfcQCNEAInLxYW9e7cK\nDdCvr7uhf/+dClg22dKl9Go88QTZtEsuMSpInf3eupVsYE0NN1G9ekZwLh3xXnmFz2XX9RUID4F5\n5hmC9XbtCKDFzSbs3aZNBAtmt7gVIyxj4nTSqNu2TTHmu3bVXhvd6loiV1zB+UxKMo6TdFWsCzjP\nzub6LytTwPL998lEAqrxjIDB9u2NjTj036WmWh/kpaUKNFx6qfXzWIHzIUPsYwqlrfqcOeG13WUv\ny78TEhjfJzGIZqmuJliuqAgvrde4MTytWpE5dzgIHCQsTuSaa/ict9yi7imG486dBNZjxpCBueMO\nkgI//UR3u9Qkd7sJZHNzOQ/CosyerUJOunblnyef5LrXw0IeeEB5swRgNWlCZlTCBuLiuFdXrOBc\nSfdVYUc7daLR2a+f8hJ16AAsXIhAwI/tB9ajtE8mOp46hjRZw8uXq87Azz1HcB4Xp8oR9uunuiDa\niW7QLlzIMdHB+ebN8C1ZDM+mtdiaWIpjrYMIrf8EjgWvI3Xej+jRtytce7bhm+qN2PbRQgRDEdZ9\nBFm8/mssBoCBgGPmXQjBBISbJll8q25SlRCNQwnAIVQDRQeAOBfKSw9i7w+vwe2KQnKLAE76jwE/\nqLKTjR8fhIEntqNXw/ORe353HJr0OJITUtGmqhT14pOpSzp3BhwOVMVF4V9rP8TRygJkNWyOS/tf\nj/SULAVOnn+efwcCNBQ//5z6S8ClVCQSg1K8EJKgacecm71ncr8JE3jNdu1osEt5Ot0IE32p70uv\nl+/UuTPX7wcfcM+It1eLby4uK8LcX2Zg2/51wKTLgJ3vIy13Afp2vAAdDpWiiZRiFM+Z2w089BAC\nAT8Cj45FdFISdfDixShvkIT1xzeg5OXv0GrEjejUtj+irfoVBIM0WvU8ALNetonrDqSnIT8xhAOF\nJHViUjvhWMVh5P3wPXKP7ETxHe0QWKOq8cT/LQk1gZ8R+GE5fxDtADxncF78l8vm49uATg2wYclb\n+GzJW8hq0AxdWvRG36RopIiRpcu0acRJTzwBbN+O0LPPovyH+QjO/AgJX8xBlNsUnnr22X8SQaFQ\nCEVfzcQvf2uL/fu+AK5uhgbzX0RUfgFc56QiqTgGrfK3I7BpEU6UFiCtfhBtfR64XVFwhULwIYhD\nh7ai8OxmKBp/HWqqyuFuWoMmv81HK7cfFemxKH31ERR6SvDH108hetceNB95OxomZyD08j/h81Qh\nIz0WScu+R8zIK5DQ8jRLf/XVxI6PPUag7vdzjdfSLfS/Epx/9dVXePDBBzF16lQMGDAA7777Li6+\n+GLs2rULTcxhHABm/etZHPIXo3VWJ5zVoje2DWiAyj070DhYg3McHqS98ALZt6Ii5VJ6+WXreMRR\noxj3PGgQQq1aIbfoAE51aoRgchKySgvgHdQHH6x8HScrTrN7f89C0y8ewfBzbkQ7uUYoRNe2sLpP\nP01GNBDgodS9u4E592U1xraPX8PJ9V8jOq8AyV0z0TxQhRTAGpynp1ORZmXRvRIMEnyJInznHTL3\nksg4cSLBvl4PvaiIoE8Abnm5AjvV1fx9WppKtLnlFt67cWMmSdx5p5F1f+opVU5IElxychiics89\nqsyTw8GF+vTTxvbOUVEcM72V+wMP8JrPP08w3b69qk6isxN16Vapg/O77+a7uVyMd33rLSqE558n\nyPjjD2VlHzmiqrn88Yc1GL76agKetDTGdQeDfM7o6HB38YEDXBd2MbTmQ0BK4QlDJOD83nsZ22dV\nO3/WLN63Rw8eflIvV1zR48aFezwAGkZz56ouonpcvM7iSrKNx6My6Tt0iJzgCqgKHxK7CfA7undH\nl4ICGqLi1nzhBQK6xEQCXDH4dBZdDtTNm6ngf/qJP9cTs8zAG0DI5YJTSrEOGRLuHdHDXAIBvrtU\n2JBwDTFUHQ7FjFRWksk76yw+y223cbzeeUeBc2Fkjh9nVac33lBjrINzqcwAcE/edReNAZkbl4ug\n/7nn+Ay6l0w+88knND6czj/DA7whP9aNH43v+zUiYzesBeYteh6Djo/AJf3+jqgBA1D29Wconf8v\nBNNi0DQUgiM21tguvjY5rbdDoRD8z41H6Hg+qlGDmFdewsp+jfH7t+ORf/Iwgi9eDOAYUA8A3MDB\n1UC3evj29/eBrgB8FkmL/6aEAfP/oPgDPpy0SNU41jgJX+Qtwxd5y4ArmgK/fAQAcDpd6N66P5q8\nNhXbx1yL3GN7UXNfNyCPMbBFp/Kx5+jvGNR9BBomZ+Bk2XEEQyF0aNYdzTPaIpichEpfJbwn85C/\naAMaXnQFknt2xaE7r0V2YjSSnE6SHU4nDfWUlPB64QDXeEkJvVliUBYX0xCfOZP6U2eQCwoQdDpQ\nlJGEI/06oV2gGklduqDwvTdQcGA7qrf8iIysFBTvW4Mjx/fiVO4B+C7KRk1aHtJzfkSzijbwB3zI\nLTqIQwV7kFt4IOyRikqP4bu1n+E7ABgItPnmGTRAARrceB4SzuuB0rWfY+2OJajIPokGD/RDfNUq\nOLoFcSjpFOA9BcQDvyydAtfyd9E4Pg1JFzaGd85TaN+0G87pchESouKBQAAhlwuFp/JR0boh6p8q\nQH5FAXYf3oLtB9Yj6Pcj8f5+SPrsUaRntoaj2oNDpUdxpPw04XXaab56n6k8qNOo96tc/9k1mBHX\nABlrt2Fb1ywETUdOlD8En1v9sFmjNsho0BRx0fFo3LAZulTGI7r/uXDNno1fO6VgxdbvUHQqH45g\nCKmVAWQE49AgFIM/WiSjsCQPdZG8k4eRd/Iwfhw3ECkf3YEWme1RUn4CJ0uPw+F0IrVeGjr46qG0\nT30cTTqFUzNuQ1lVCTDACbw7EvVik5EYnYCm2R24zntnYn/eBmyeMgm4txOAQ0CjlkBZHuAA8g5v\n5I3bJQNIxtJvXwx7JrcrCikdAqisWIyq1T5gWDMAVUADF4BEYN0s4I6zgF8mATHgn7ITQHYsdqz5\nlBfpFg0gGuh3molf+DiaNmqDQZl90OLoPiSfKlG5Ajt2kNCxatioiSMUqmNF9P9D6du3L7p164Zp\n2qHdtm1bXH311fjn6YL+pZpb/ZlZNgkDp6VefH1cNuBmNJr2CaoWfYfkZ19C5t8jZMu2bImCeZ/h\n4x1fIe/EoTo/d5u9Regy4HL0ue1JxIx7GsGnnoTbpQyASk85Dg3sgRN9u8DRug3Sh4/ET+vnIOfY\nrrBrOeBAWv3GSNy8A0nZLTFg1Fh4b7sJhy7sj6oNa5D8wKNI/PgLtGzaGf64GIS+mYOsz76Fq0VL\n+F0OOEKAq6KSh3tGBlnoYJAg95prCNDy88nwpaby/xMn0rrr2ZPgYPVqgqCzzyZgmDOHVUjmzOE1\nhD0QNsXvp9LOyyMTKAD03Xep5O+9l58TcN61Ky3IQ4cIgs2GV79+ZOeeeYYhRoEA/1x5JZ917Fh+\nTo8/NsnGjRvR4Pvv0eLQIRXeAJC9mz5dJW8ePcrwjzfeYGWS1auZNzBlCoHa5MlMXF2+3Bh/bZaU\nFF5j9GgagHPnMqxF8hNknEaOJBAzx6K/+SafZdIkei2SkzmOX33F53/lFWV02cm4cTx4n3wy8udE\n6tcn8y3v1Lw5D2SpL967N8FtMMjYuiefJBNWUEDgbC5ZZifduxOcSwUYwN5I0SsYXHkla9E/8QTD\njhITyfadcw4ZLp+PIU4xMQTg5eUEr2PH0o0OEPh26QIcP45AwI9fdyzGHz9+gfp5RWh89hAkrd4O\nd+uzkHR0H0p//hE1UyYhuOZXdHroRcTH0qg5UVqAkvITSC4ohuvCi5D09beIumCI8bk3bOD8d+7M\nNZ6ZyX128830UIRCTIK74AIawG+8oRoH7d1LI2DfPhoe27dbN/AAaHyMHk1D7J57eP0pU/j55cs5\nLwsXqhjL8eOBO+5AKDsbJSsXI+/tl3F83APIyduJXYc2Wd8D1J0JsfVQUHz0z5+1aNweV553G5pl\ntMXRwgPYl7sNblc0urXuj6QEU8jF1VejatTV2NgiDnuP7UZO3k5UecrhCIYQctrM/b8piYjC3y64\nHR1rElD9x054gz7U9OyKHSf2YPX2RQgE6hbrKZKS2BAxOQdR2aIJ0muc6PPZMjQ7UoLYrDaIWrkM\nuw9vQf6JQ9iasxbFZYW1X/D/SKLdMacrbVi/r8vlRovG7ZHZoCkKTxxF/N4D8EW74WjfHnHRCchO\nb4k+HS5AXGkF8NBDCFVUAL17wTH2EZ4VcXGo3vk7PBcNQf3s1sgddja2922F/A8mozA9EQUZ9Szv\n+/+DOB1OtMmtgKOsHPs7N4HPX0tfi/+gJCekonX2WUhLbow0ZzzqXz8ah6a+gl2nDuBA7s6w/eMM\nAUmVfgTT05CemoVzu1yCLiUuuPr2w4kH7sThFDfit+9GQlwSMu56GNEPP4rQb7/BsW0bwxXNJf92\n7KAe++abP0N/g04HQg4HXP+468/QqcA7b2PT1sXYMu0FlPXqgqPV/z174b9JovxB9Mj3w9+0CWry\nj+LaJ7/483fJFt2E/+uYc6/Xi82bN+Oxxx4z/HzYsGFYEympIIKUV53Cpz9NAVoAuLs/UPg9kj/8\nDQ9d8zJSk8i+1fg8+PrnaVi/+2fggS7AilfP+D772qZhX+Gv+OaVvwHYAvfU69C7/UB0atELC3/9\nBMdLcoG/dwIQAIJ/AAsm2F4rhBAKT+WjsGUqgFPYOvcZ4NJmAPKA/s2ADf8COroAnAb2I1sBCx4C\nJjNRzOUPoPX3L6F9i55o0TQZmYXHEDtnHsHRvHkEWcEgY70kREZcgz6fqvYioRRDhhD83HOPSsjR\nE3zEra6XMBJ3YFkZk2Pvvlt9Xn4v9VT1GCxh2MVrsGsXFcS33wJFRajxVGLdHytw/OfpiI6KRnr0\nSTj8AfgWTEWbcy9FekoWnA7FrDskVl3vtAoYayg3aWIsvykgOiaGQOjVV62ZJbN4vaoxw7hx/HvB\nAgKnzz5T77Z7t5GdfecdsuP9+6vnk2Q5AehxcbUDcxk/q9jxOXMYs6p3jbSSjz7ieEtsXm6usdOZ\nhLWY4ytrk19/VYC7SxdW75FErJwcGkvt2hF06uWoHA66zyWhVP7+9VeCbsntADh3S5cSGNerR4/P\nXXcBmzejpmEKNm5fjF9+/x7HTh4B4gC0jgOKfgXdXmuA5gBu7QVs/QyIBzDtBut3GT8McXs+wiWp\nHvTpMAjHS/IQGx2HmobR8AeLkeIrRwoAR34+P3/33ZxzQJWFrKykoSrgXF+b+j6yEokL9/lUV9F/\n/ONPb1Zhaiw27FmEQNE6tGvaFY0eewBb963BTz8+jYrqUuC8FODX2REmi1JedQrlVcY43YPH/sAb\nXz0W9tkFq2ehTXZnRLmiUOWpQEJcElwtqrEp70vARKz9T4F5WnJjtPDFIX7vAURfcTXa3vIQWkye\nhajOFwL9+yNl4kTuJQDtcC7O73YpFq//Gut2GUMgsxIaIWHfIZTXi0GDRs3hzz2C4mAV+g65EUPO\nuwGOmBgae59/DqxjMnmNowAx8fXRpwO9fJcNuAWnPpqKwq1rcLxtNpz5+ag3+h5EuaOw69Am7Di4\n8f8UvHv9keNZAwE/cnJ3ICf3tBdS8v73szjAut3L8c3KGYit8cPbNxrBkAMJwa1o89MkdOqVje1n\nZWDXnIfgv03ynTYC6zYCXRr/Z17o/1CCoSD2ZMUDWfHA/yEwd8CB+Lh6aJ7RFr1f/wRNd+eiQVGF\nMezDMwZtOlyEoacLX1QkRCO+yovQm2/g5KE9aFDjgOuXVcCk+0mopKT8mfzd0ONAw6pEoNcwkhzr\n1wPBIBw5OQwrCgbDwblEFmiljp1dujIE9L33qK83bIArLR19cnLQp+uNwJwFKN65CT/OfBYebxUa\nJaSh6oOp2HReO1TX/O95vf5/FJ/biXVNowEcBzKjcW0tn/+vA+cnTpxAIBBAIxNjlJ6ejgK9Y9j/\nUEorTuK5mXeiY2ZftPWmYEPFNuR58v/Xrg/Qlbl25xKs3bmk9g//L0vA7cKevB3Yk7cDuL4D8PPz\nQAOg+WdPokluGbzd4hFs0xLRCWVw+CqRvGIhOuXmomG9RPj9fpQGq7Hzhy+RXu1Ct0OHsDEnBwkl\nJWi6ciWK6tdHc5CVBgCnx4Oubje2bNyItDvuwMnduxE8fBg9HA44ARwpLERaZSV2rVuHngDyjxxB\n/saN6ODxIAFAWc+e2Ffw/9h77/Cqyqx9+D41J50khFRIIJRQpXcR6QpiQQTUUcRRVBRHHdsM9sLY\nULGCYgMcseGMiIBKESnSS+iEDgmEhIT0nJxzvj/uLJ5n77NPwHnfmWt+vt+6rlxJTtn72U9Z6149\nH4HiYsT8+iuSP/kEe996C21LSpC7bx/a5eXB99ln2JOdhEWfTsGh06aKBWKoOZQPHFqMqLAGaJHc\nCS2SOsHjioCtthanzpxB2dNPI27QIOS+9BKQkoKktDQ4b74Zx02W34YHDiBz1izkV1ai7Jpr0HzN\nmnPA3BcejgPPP4+Sumc3U+e6hCh7nQJSnZyMw0lJyJw5E9vWrUMHtxOfL3gXzh7xiN6wCIkV5bDb\n7Mh+911E7diBbTffDHvTpqjasAEdAwFs37gRvpgYxB08iLiiIuSuX4/I1b9gb/MEHDmbC5+/Fu6T\npxDdrAMaxWYgNqIhmp44gdqKCuRv2IDIHTvgyc1F4ciRaLh5MyL37sWBdb/C66tGxYalaLh0Oao7\nJKI8sRXC165EmDMcJU4vzlzRA9U7fkB8vwy4f1mM2EYM0fL5a1HRoz3cTg9avvUeKmJjUVA3F4Vl\n+dh69GcUleWhYXQaEqPTkB7XErERCYY5cp84gQ45OdizciVK6xSU6A0bkPX226hJTcWerCxEHzgA\nSSktKi6Ge8QIwGaD1IioSUxE4YgRaLB0KXZoa9G6ZUvk7dyJrO3bcejSXigp3I/i7+cgbPG3+H58\nVxRLxYL/BaqsqcBXK97HVyveN77RJwLA7nOKcsqJs4jcOBtJ7TyIW74AEYePIjI9HAfG3AJv/mHk\nfToFOHYIUa5otM8Ix8F/zkD0mL4IbFiM6KPNEOmOOSekz1YWYXfeepw5fQDuy5OQuvkf6BJRi5Jp\nzyC5cQNUt2yMH+Y9gz3jmgEHlwEHgR83fo3/BHlra4Kt8Om/oZRhHUV74pDpTkXagsXYO2oYjhbt\ng9dHwGkLANlpPdAlYwDif16JhPWbkDsmG3Ft+2Kn3QHvhg1oVVWF4zk5KDPFdLaK64WGFzXF4e2L\nkXi8EAkjb0P8sQJkff4wvImJyLt5KEqvuAkdBwzA9v4PY+PGjehst2PL+vWIO3IEknp+4o9/RKHp\n/McVnEVMuRvhR3zwHK7CkWInvAggM6ozMtp1wpmKUzhbWYiosAZIqg1HxWdvYVuGB0cdJSiLsoh3\n+S+gqjAnUBfbX273YcuhddhybZ0yHcIq/+8gjysSLZM7o22xB80ffwLznp6AvaV7/+XruWt8sIdH\nosp3AeGQ/wI5bA4kOeLQYN8hFF7UBuHuKDSKaYKUQwVo9vV3yM/OxKGkMCScqUJUmx6obdcJ4e6o\nc2e8w7aX4DxbgQ11HcpT3n8fp667Do5330Xyvffi5A03oD2AqPI65eG+B4BRo3Da4UBMRQUCd92F\ng888g8oWLeDZvx/tABTk58NXVgZvVRVObtgA98mTSOjWDYHXXkPy7NkoGjIEpVOnIuzYMeTXhauF\nHTuGlqmp2O50MnwOQGqXLmh08CC2bNiA+Px8xO3fj2ivF9u3boWvRw90uecexAcCaBVPxRh+P1w3\nPIXMRonIGDEQvwztgE09s1DqNdVNPw+5a/zwuh0XFIrm8QbQJL0LUuOyULV1FRxHDyOvV2c49uxA\ncZQTNbExqPXXoLzaegxJMRlI33cChdEOHIqogt0PuMMiEe6OQoQ7CuGuKISVliNh1RrkDuyJ8spi\n2POOozLMjtroaDira1Dp/J8HpPzXgfP/DUqs9eCMrRK1jvNbZ3ae+BXBQSVGctvDUONX1gi3w4PW\ngSRc9+4P+PnZP2NF3k+o+l+IhUwsC8Dt9eN4XD2leP6HdOj0ThzyAGgZCSAS2Pftufe+awFgipZ0\nu+8zeGxu7BzbEeGndyMqUITydA9KnSU41TUde1fORlhcEtLTOsIb5kJ+8SEc7JeNGP9ZxAfCAYcD\nfl8tDkX7UJAZjZLyU8hLikalrRaBQAAVqSmI3LULG/48EfvyV6Gk4jQqffmIGBQPz/7vcLhjJI7t\nn49tYztibc+6TmxmYG5BZdXF2Hx4GTYfXoaEyBR09vhgS7fhZJNaxCee7dXJvAAAIABJREFUxcmD\nPyA+MhlVYRWIcdWgpKIQNhsQ5YmDDTaUdu+OM5dcAr/Hgwq9ZjXYhKQkVGJyIAC7zweflsuwcsok\nbPUcgvuGtkDuQsx7egiqDywGLkoAilfCsXYNGse3hD09HNkHXKhJT0dp1Rnk7P8OqyZ0gv3oDzjt\nLUJZ2GlEDYxE1frXUYkyQMvlhQPAYc0i2AVo4K3A2dVT4fIDaQEvfLu9iI/Iw6kuNhxfo1XT6d8A\nQF0owq+vBD/T4Cxg31y4DrjhcnhQU1uJWj+TiqN6Ai19p9CksgjHzuzDpkNL4Q9QKTlSuBtHCndj\n06GlyE7phuzUbigqy0dpVTGanqpBaZQbgaICNFixAt6EBNh8PgRcLrgKCtB29Gjse/QhVEaFw15T\ng7MRDlSmRCK2oASVDSPhddkR6ffDbwMqPU5U1pQhec0GlBzYivemXIPTBZtQ9fww1IQJezsGjOsE\nwCKZ9z9AeakxgPcY9neIA7bWAfkrMgAUAfHRQEEO4xhRhu2XZwAHvwcaAzj6HXAUcDs9iPbEw+ev\nRXGFZoFNjsDRiu349dqmADYCD9Q1vcoPHaYSimz+ABo1yECXzEFwOz3YeWIt9p/cem49/90UG94Q\nvZoPR6MYhrZFbd6MtNxaNGp5FRynT6PYXoUKhx8NIhoizEWPV8BmYxdGAIe1ZPCAw3Hu9ZZ33okD\nU6eiti5ZOSEqGQm9VBikL7IC1enpsFdWGusl1wGlQF2Cf6DOoxFwOOCNj0eHyy7DtoULz33uzKBB\nODNoEPMWTKXSbDYb4iOTEB9Jg5P95El0+3Y1Gj7zDOD340T75kiY8iCKhg2Fq2MfIDoW+wq2Iq9w\nHxx7dsCV3RndZn0Fe9eLkbJuK8IzsnEmPRmb+7fFieIDqN27DScS6k8u+2+hCEcEKnys0hFh9yDZ\nHwV/w0ZIjE5HeXUJTpw5gGpvBZLjmqJJfCs0imkMjysS4QcPIvxkLmJ8LvRr2BfNMnvh+LEtsFeU\no3L7GuS1bwE/AnAGbIguqUBs867o9vzrKGnaBLuG9YGn0otGbS9GQlQquoy4Ejs//hjFMW4Uleej\nYPdq5FYfRVWYtdx1OcLgqKpChM2DhmltkXjyLKK2bEb+4AFI+OpLnLzmKkQv/Bb+sX9E7ydfRdlf\nnoejqgpNFz4F76/lyH3pJfg9HkSd2IiGJTUIL3WizZa9iF27FoVDSxD75yewZdkyZN96K/a//LLh\n3o7iYqTNmIHTI0eiJjkZccuXo/Dyy1GdmoqiIUOQ8tFHAAikS/r0gW3tWth8PvjrFFNfdDSqU1NR\nnZbGJmt1e7wmJQV5EyYgZdYsBOx2OEtKkPWXv+DU6NHn7u1t2BCHHnvMMJ78m246B95L+vZF49df\nh72qit5pAAG3G9V1uUAZzzyDY5Mnw5uUBDuApFNluHzlCWTc8xpS7r0Ty8ddgtOxbsSsWAZPowwc\ni/bjaKQq6Zp0shTtelyPJkV+tHzpVeR89AGi33sLBXFubO6YivKc1aiMjkBMems02bIX7gZJaOZM\nRpOlq3Fg6uUAgPiqXMTuP4iDN1+J9IUHURsXh5NjxiD84EG4j+5E/Duv4+93DERuSjiSG2Sia+Yg\nxITHI235G/BFR8Pm9cLm8+GEFOioC8cMO34cace3ILPNOGSPH4+ouhKnG9avR6PPPkNx4WH8OKgl\nTp3cjQrHv8ZD/+tizmtqahAZGYnPPvsMo0aNOvf6pEmTsHPnTixbxtqcesy5Pb0Riru2x6koO9Kv\nuxVJny8AKipweO67WPHzXBQd3YfjEX5U11QG3e981LXVJbhxyGTYH38C5R4nvH+6B7GR8bCtWMGw\nhYoKVG/4FbsPb8b63Suw+8gW1Hjr18hbNu6As+VnkF90FDbYcFFtHK4tjEdMQQnDTG67DVU1lThe\ncBCvf2mMG26T2QVx875BqceBbRelhrjDf5bsNjscNV54XYq5JcQmoeH6HShICEdRQmTwdwIISlD5\nb6CY8Fh0btUPPdYcQlRpJfKvHor9j09GeaQbZ2M88LdojojO3dG5ZV+0yVSVZY6c3I+TRcdQum09\njn3/Bc5GuLC31XkSJC0oPjoRZ8oK2fzh/wi1tCege2J7lMybjUqHHweaxuNA+r8/btURACLKqlEe\n4YLNZodPi9CJrvLDaw+gym0U2Ak1dlTY/aj8HZg12uzIR5Mu/dFxwBiktOwMm0kUlJQXYde25fDO\nnY2sviOQdMNt2L3mO3yxY/65MA27zY4oexjKvBXwnydUpV2z7hjW/Tqkfvwl/EOGwPWXKfD+uBjY\nuBHu9h2NH96zh6XyHn2U8fMTJ6ouw0KLFzOv4403GBsrNGQIcxGGDGHi8+7dxgRoK+rXjyFGl1zC\nkKi//pVhZPPmMR+jXTvg0UdRvX8/jjz4IFrcf7+xtCvABnGASnjOyWECfYLRc4S8PIYG6p7gtm0Z\n/peZyXK4zz/P+w4fzkpFiYnMvVm0iOE6GRnMwwE45p9/hs9uQ+G8j1D+1GMI++ZbJLfpCluNF35P\nGI7nbkH12OuQtmQ1ftm+CNtyf2UYVk0lMnMLkBLXGOFduuPI4RysLd6F8soLt2y6nG60zuiEFvFZ\niNm8E42eexXuHbtQUnEGG3avgMcdjsaNmqN9Vne4nWGoqC5DSWYqkqdOh+2nn5hL8/XXTHBv3Jhz\nYC55+NVXDC0qKADmzDFWePJ4+HmPh3kbI0bw9/PPMxnb3NVx5kwWKJBu4osWAffdh5ITB7H71cdx\n9tsvcfZPd8HjDkebzK5omtKKjf6GD2eloiVLmPP0+ecqJDQujomykZHAwoXIyctDm5tugj0lRVXJ\nKSpi8vgNNzC3COBab9/OHB+bjeGjGzfy/0CAiYPt2nHPJCdzP338McvfTp7MkMsZM7hfx49n9bOq\nKhYmyMgwPndJCcF5tMZbn36aOWF9+3INJk9mCKZO337L96RHiE6lpSwGII11WrRgff0WLTjezZtV\nFR5Jnt+xg2fzgQeYV9akCfPRHA6ewRtuYC5NZCRDWQcP5lkLC+P4srJYLMJm42d27CAfuOgixsYf\nO8Y5+/BDjmHtWuZqPfoow0S3bOF5P3WKzzVmDAJ//7sxhEgqcb33HkNVpfdK69Y8j5LLAzCHasIE\n5qQdPsz7HTjAPTN9Ospyd2PJqK44WXQMTZKy0GjzXjhzD6LZ42+cu8T/EzHnbrcbXbp0wZIlSwzg\n/IcffsBoTavTKXr7HkRfdRUaH68A3A1YIi85GRnJLXBTo/7APe8gMGcOAlWV+DznK6yOKLG8jlDX\nxHbo2OMKpCc2Q3xMHcByOBBZXg1s2M5EQamPvX07whxuXNS8Fy5q3gveWi9w8CB8fXtjxZTxWBle\niLPlZ2D3B9B5+0mMemsJIsNjgC1bUJbSEIiJQdSEicBndYlhda2IPTY7stLa4PWYK3Fq8Xz4N21C\n8p6j3EBtxwEtWiAwYwZKZ89CZGZzFG9bj60fvoRjBQfQMCoRzr+9iJ3XD0Xhod0oifj3WeIBxun5\nXcZ7FJacRGHL0ALxfwOYN/J74PIBee4aNPDEwpZ/EoWx/zML0tnKEizf8i2Wh4Mxyav2A0O1g4hy\nYNcyrNu1DB2yemJYj+uw/ev38H3VLvWRTv+60lRUWvAvf/f/VdrrL8Tek8uB/sGVmP4dFBMZh5uH\nPYAWr34ITJsGvw04Ne56HLjnLnTt0hXuN98GfvoeOH4c5RvXYuehTTg+63U073Ax2q7dB1vBaRyx\nl2P25U2ZR6KRA3ZEVflR4glx8/8CGpY9DIMG3AK32wP0uRNo0Ul10AMoVJ59FrHNmqFnUkfguweA\nF+YA9jvQNrU9WnQagB2/fgfnE0+h+cLVCP9hGXzvvoMTH0xHYclJnP3kfYT/uhFlvbqg7PB+xI+7\nBekX9UFGcl3VnYdUgyv3l/MBMzAHKPykRJ/NZl3CdOhQgoOnnmI+hZDeFKm2lvXdx41TVYis6NZb\nVXUtvU72mDEUyF99BaxYgcqLL1Y1r821rz/5hGOVqjoPP8xcA3NpUav+BFL5R29CFBvLxPSiIv4v\nDcRGjjTmgNQ9q8MfQCN7FLDzGJDRBrCxupbjiivQpNwB/LwNyM/HkGaXYshFIwk69GZC//wnOs1Z\ng5H/+AcqRl+Ns6uWovKLv6PR3mNYUrQZ66PL4ff7EH3sFNrHNMMlk6bC569FdHgDuF11oTknvgTy\nzgJvzkJidjaaj75LXb+u90bE+PGIyC9lfpOs09dfcz3T0qzzWKQi088/B78nVY+2bCFQlTWZOJEg\n2ky3307QdeWVTLyu2y+xZ6vRw54KbCgA+t1qrPCkV02TsehVaiQMt6KCysawYbB7vcYGOrGxBISX\nX06An5PDeG69bG1REedA6m/L/fUSwikpBKNXXME8lhkzuGeaN6dS0qiRsZKafn8zyR6WqmBWZWgd\nDqMiqVN0tLF/ioBaIDj36ZtvVGEEyUdbt041jpJrSJngvn1ViWKZ+2eeMY6xvJzKTHY28+G6d6cS\ndegQAXx1tWoYJE2v9G6edWMOKuko45b8MSGPJ1jZq63lej39NA0Fgwerru2tWiEqLg7X9PuD+nzs\nTqDdadSPQv8LwTkA3H///fjDH/6A7t27o3fv3nj33XeRn5+PO8S1YKbMTFoetm3jpHbrplow+3zA\nqVOwPfEEbLGxGDt9Osa89ioqP3wPaxe8j8V7FqOypgJ22DC0xxgMmbkYjr7NgCyt+6c0SfH7WRXh\n8GF1QMPDmdjn9QKffQbXLbcAJ/LgiorF0MmvYIjfj6rxNyLsx+WwnzgBfFDHVCdNQtSQIYzlks0W\nG8vD+MADFAh33w1bhw5IqqwEflrDjTlixLkDa8vJQUxRGfCXG5Ewey4M6RzzrsGQ8HCgZ08UvfQM\nVpzdCe+XnyPQvz9KE6JxtqIYlTXlCHdH4nDeHgT+C63YVhQZHoOBzfojrXlHtPriR9hPFVBjPXAA\nGDgQeRtWYM2OH7HjwHoUlOT9W8eyLXcttuWu/bfeoz6y2Wzo0XoAEj76DEeHX4JtBecL0DJSrCMC\nteWlKPdYK2/RFbUojQhmEU6HC7U+r8U3gDCXBz0OVSM2+yKs8B/G2XKLUo//YXLU+pEW3xjpTdog\nu0kndGjekwnDjz8OfPQR7FFRiNi7F3E7dsONOmCXkQFMmoRITzS6ZV+CbgemAz0aA+4jQK9eaNKv\nHx51OnAqUAHf7bchpcvFCMycCYefQrJg/c84nL8XJbu3ojo6AvtzN+Fg9alzFTRSPQ3RICwGjUq8\naNj/Muz97B0cT2+AKpsPSXuOIrprb5yyVaKotCDI4xcTEYfsjI5wOcOQu2kpTjqrGeJRVwElzBtA\nRtMOuKTdZWjboT927V6Ns8uXoOWxMiQ8PhU49hYgYEqEkt6vYPt21TBNypxGRtL6bLfD7QpDp+QO\nwOFyIIz1qx21PjRulIXGjbKAM58CR6qBFuHA9AWha8/PmsXrr1hB66/l4jlUXW4rsqo33aYNk942\nbKC18OBBVsypj0K1CAcMIOP0FVegKjMzuBswQEChJ/HqnZ4BWv0mTiSQs2pVLuUwzdd1OAjGW7fm\n3+bEPblWkyZ83shI3rtnT65jZSUth7NmEdQ1bcqfDz6g8vHrr7SWxsYCxcWw2WyIrKpFZH4pcKwU\nuGE8rgmbiHOt+m66CRjUF4gyeQQABQCPHg2uNFRUxGTthQuD50d6ZIRKMreabyGnk16Hfft4bVFc\nQnXxBAi6Cgtpaf3uO5X82KULewRICVdRWnVw3rQpQWCPHgSGXbqoZG8AiIxEQIC7DojlLA0cyLW5\n/nrOf79+6jOBAL0q48apeZFnlHlo0IDAXJ4RMM6NufyyTj4fLcwff0zr/FNPUSnKq5OVVvMVHV1/\nrw4pU/zCC5TDelMgHfRKV2NAFWO4+mpVkld6sIhyarV++nw+/DDv6XCwLOELL6izGhZG3lBby/Pf\npw+9T+npnFNdGfD5WIyhWTNjU8PvvqM3bPx47q0uXThuMzj3elWToeeeo5Kenc33hg4Nni8pvWtu\n5Gei/0pwft1116GwsBDPPvss8vLy0L59eyxcuNCyxvk5mjuX9cmliYporLJpKyroXmzRAraMTERU\n1mJA80vR9+KxOPrIJDTMbI3YnmOB934IZgLvvKPqckszFGGisljFxbSS9OhB92tdfWKbzYbwqlpq\ns7qAEC3O61Wb+YW6CjFbt6pDt2sXN0ejRixfmJfHhkaJiWTWZWXAZZcFz4dsfp8P8eFxuPqiW4Cj\nYcDt9xrrHy9YAP/CzTh87WAUX9oH8dGJ8Af8cDpciOl7Kba9/zds+MdMHGoSCwSAMNgRVVGL5HY9\nELltJ3KialBu46FyOd1IT2yGIyf3hyzj5bI54DXFsdrtDjRPa4sebQYg9kQRyt54BaVPPIqD/5yD\nExWnkBDVEJnbDiNq0GXo1Lw3IgYOrVOMVqsNHhkJ9OyJlIQmuKbfBFzTbwLyCo/gyx8+xJnyU0hK\nTEFyQQXyNv+CXVlxiPAGUB72GyqN/A+pVWRjRKZloqK6DF1b9UO37P7w1tZgw56fsfvwZuw7th3l\npuYTGY2aI37xClTERsDVsjVaR2eg0fJ1qD6UC29JEVp9/yuiGqUBJ+OAIcNQeaYAPzw5AftGXozE\n2BS0WbsXZ3M2wZ3VEmWnjqGof09Epmag4w9b0PjlGbCvWQvcdRcCGzZgzY4fkbPmW4TlHsLFk19E\nsy+XAG/8DThxAjkH1iN33gzE2yPQ8raHkBiXirzTh/HdJ08iz1aBsoAXTlcYWrXojit634iE2ycD\nXVqjx4g/YfG6z7F792rUnMpDRbQHXocNLj8T+2p+g0Mn3G9Hpd2PcLhQjVr4QyQGxUTGYWCHEegQ\nkQFPVktEFp6Fr0d3OJa+ZHRFAmT0HTsCLhdiFi+mu7tZMwrHxESjMDF3nvviC9hjY5F8zTVASS3g\ncgP+ujE1aIDEBilIbJACZNeBzmf6w//EEyid/jJivlkI25IlyoAAoN9f3wb6jKFwmNQO2DQdKCiA\nf9sPOPPXP6N4wVew/fgj4qbPQExkPBz2uslbdAD+7dthW7QItnvvhX/YUGDaq7AveYY8pNaHtk27\nAv2uVk2nQnVBFZJGaoACFADBnYB4ve69GYQCPI8itMxUXExL9x//SHDTv3/o0qQOB8H7sGHW74sA\n//BD9kjIzGTVpfh4VUYzJiZYoIaixYsZaqBXctJARrEAYyuwKNZA/X89/nztWrrsU1OD5+uKK1g+\ntWXL4Ot6PCxfau4YK1RbyxKeU6cScEkzsFmzaKldv/5c1Y5z3ULlWtXVqumPlFSVa37/PSsd9ehh\nBC31VWkaPJjvt22rmv3p8yHdr0URWbWKADU2VpVrtQKI5wPnjz7KcAa9Q2N94BwgmHrtNYaGPP20\nOh8A502e8bnnWPr2oov4f1YWG5p9/TUVIl2xvesuerXljOn7X7fE+/3kMd9+y9LDQoGA6vgKWFvO\n9XkwdzsH6FnR+yPotH49w0DsdoYIAVQENm/mM5vna/lyjkEqZPXqxeII+vW3buX7jzzCcBtRykJV\nDQPoiQKUEUA/K3rPCvN4qqpoCV+0iAqnPIs+F3a7CnkpL1fPWlBAZWDpUu6ZHj0YXrNyJavPjBtn\n3OeHDtGrsXMnrfC//squ8OvWGXtlCI+Usda3534D/VeCcwC48847caeU3rtQio8nU/V4qPkePaoW\nurxcCSV5ze+H2xWGrKzOKj5Lb3UsJG2Jq6qUu+iiixj7NmCAaskK8LA5HNxA0kGvqorMVWdWYmVx\nOoPvJ8IuECATuP56xTjsdl6vRQsCd7NGW1pKBi0xeenpPEixsbTaTJpk/Pyrr8J+8CCa4lqgaXfV\nHCkmBnBE4OJmF+Pixy9HxdyP4d6aA+fIKxmj9pe/AisfRLU7HrnXDUWtz4us1NaInP0Zyi++Fnsj\na+CtrUaDqAQkxzdB9Cd/h+2uu4AFC1A58BJUpTSC/fARlFafRUpChgIbrQLAANpoLnnve+DteRSY\nB+cBjsZAeZ1lymajBWLqVM5VUhLbomuUktAEvZqzeUzXrl3JYL9Yee79wO234XR2JmLmfwfH6jUo\nj3Tjs3uHYV+yBwG/H7W+GrjhREpKFhs0xDfGmW/mYZWnEOVua1dDA0cEOnYYhAZRCUiISULD2GQk\nxacZ6t0LuV1h6N1uMHq3I0g7lL8Xx+bPRnRkHFpfPwnuyhrg+hju6Rm31THJzUDznnTLhtcx/htZ\n7i+8shIjVx4H5taVSlzxKOBpAVx2KxnnxCtpsZk7HgiA+3HNGthsNvQucKJ34gBgwYdAajbweM9z\ngrpds25oVzqfLvD4dGDpUqTNnInbL7qIn/nkEzKtzEy1R30+xEQ2wOhLbwfsrYC7+jNGduNGjrd5\ncxxolYJlbz+CXTG1CERGnKspnHG6Bl2uuRM9dxVjd+skJKRlIT2xGWp93nMd4k6/8yq2Ht0I+7XX\nIeuOh1F5SR/E2MOR8oKK4+P+j4GjY6fQliSv99yZtldVcY6ljKvfT8HTqZMCaHqLcp9PWW71hmbP\nPRd8n9pa2J1OxFZpgueOO3i++/ShAt6qleJNy5cDhw/D/vrrSHjxJST4ooDaSCA6Mfi6djsF/aBB\nsK9abbSySU1+3Q2vCw8roK6DTB2cX365+owOFM0g9M03aSxZty742gBd5C+9RHBu5Wo3jwVQpVXd\nbqM1TjqvTpjA+FTZg7W1CmDHxhrB+cmTBKSmZG8AtKiuWKGuAxgSRBvOnw+HCHxpRuXxsEmPxA3r\nY9dBeE0Nxx8VxdAHgNb9uDiGX7z6qjGsRSgsjFbCggJj900h2YM2m2oQBBC8dOtGy6cOXMwdQmXP\n1VnOATDGtm1bY5v6/Hzy26ys+tuqe70ENevW0cJ89iwVHlnL2lqO1emkvDp1il4ZAeehLOcLFhCA\np6cb3/v0U5YHlvAKGa+sT2VlMFh1u3nfBQsIynRgLt+V8c6eTaOcHucu70dFKX6hvV6TnIyj992H\nxjporqlRZ0n21DFjWFzQ2svnBXe8+iqNjKWlNNS1b0+j3unT6juyt6xI5ra8nJ4TgNbdhx/m3+ae\nFTfeyOsJON+0KXh9PB6lYAwZoroYC8/MzuY+10OodJo4kYbV4mJ6cA4d4t6xAuduNxsGyj7RFUVz\nB1sB57IfunVjTP/KlXwtIoI8rVEj7h/zc8n9KyqMynqBKfQ0Kopn9P8KOP+X6L33+HvhQrrPFi2i\nxgNwgvXW54BiSndpcXHS6lin7duZoHD//eqQREQwIeTIEWUBB5TgfuIJ4P331WvR0UaG73Qqd86I\nEdTKAMXMa2vVYdY3TfPmZDSdOzO+SWqOA7TMP/wwN7k019HbnuubWP6uqeEz+f2cq02bqD1++qnB\nVRdhcwF2h/HADBiAMI8HbTI7q3ssWIDIpCR00q2O+pz7fAh3hCG8tAYo9yI2uhGvq8+/0NSptPgI\nI/d6jbXBW7dm4ldVlWII9dFeY/ktW5gHifZIwOYEfAHEnq3GxG0Aul4PlJTAv2c3bGFhsN2rNTfq\nMAwDkxKw5afPsP3AOuw5vAVeXw3SY9IwZulxZIy6Duh31fnHYkGZyS2Rub8CSIkFnGGAr+5Zq6pU\nXKXTSQvv3LnBzMTrNXYMFS9S//7q+4BS6MQSfN99tCB9+WWwFUJI3zOBgLIsHT2qwkCEbr/d2FCq\ndWtaKy69lD/NmwOXXopmAJq1G6u6x5ppXDY6fv01kJAJ2GyG1s0NnVEYWBAOdB4JnP4TMPp2o/DU\nSa+ZbiavF7jpJpQUFcFVVGRsqVxdTUuRdA6Vrpp+P0PopCmW02l83rNnuW9ffpkKPKA+99RTFKQ+\nH3mHWCoFHJw8SWG/ejXvIWQWEEK33sq45Joagrxnn6XlDOC5efddBc4nT6YXUK+j36tX8DX10ArZ\ncwDnYe5c3lMXihkZ9OrpdMMN/LGiqioFliShLhTJWKUzrPBZIT2s5YDWTVJ6NdxxR7AresECWmwF\nnGzdSlezy6XCK3TSBL6zuBiOigrW5bfZOP7KSs7rm2/y2VJSeKbM4FwUHZeLlvKffuKa3HMPxwkQ\nWIfyIlx5JfdUXf32c7RxI8fXvTvHJMBZ7qfLNPnbCpw3aKDAucTJ6/NbWkrZqvcVkKRYnRfJ599/\nn6Bl1y4+q8NB70Hv3gRrLhfBkXTu9nr57FbeFlGk9LChn36i5XTyZK6py8W5F5mfmEj+N348w1fG\naJWlP/iAwHjBAmsFdcYMJWvMyieg5KDHo4Ct/jqAwiFD0Lh1a/WebjkfMoRy1ulUic5/+xvPvU6R\nkcQd8r26ZkBYtoy8ZPlyes5XrSIvtoouKCqiYtWmjVqb4mJiJHnf5eLZTktT3wsECLrj45XM0PmB\nTrKHamoYS9+uHUNnoqN5b33+Nm6k8ieerdJSrpPPRyPSiy/SANi6tXEvPPYY+WREBJWFmBijp0VX\nQGXuyssVrxHDa2QkjathYbyH5JSY485lLSsrFe89eZLnpKaG+/qii5RXKhQ4LynhOA8d4r2s8gEs\n6D/n1/9P0oABdFfX1nLyrr3WCM4vvpi/rdxkdjs3q84gT5zgIdYt5wAByt1385AJQxe3mu7qjYsL\nZji65TwjQ7VKnzWL2rHPFxw7VlpKxpOVpazy+obKzSUYsEqe0u8rB2XbNtUi3OejJp6ebvz+unVk\nDrqmKpvvsssItnQK1TylSRMymD176A5cuJAa808/BX+2oIDPtWULY1EbNuR6Nm5Mj0RdxR4AFIJT\npihFqD7SgdcTT3AuunRRcWEeDw/u7t3A9u2w1/pgcwUnmIbXAr3aDsLtV/wFL975KV54ezseuuQB\nZOw8Wn/san20di2FjD6/DgfdcE8+SaapM0YrC9MPPygLh3xf9ri+7i1bGq27b9RZm81WCJ30+0kT\notGjKcRTU437UAC4UKNGap+Y3bJXXVW/VXvuXFpYzaRfx26nAEma2o8SAAAgAElEQVROtr5OfeT1\nAllZqGrSRFnO16zh67W1ynJ1000UbtdcQ34i92/Zkgrwn/6kAM2MGfx/7lxg+nQCqjNnuAbdu3Od\nBg82rolQUhItYR6PMfysY0cVZwqQP3m9tG5KDLQ0AdM/N3GiGqvbzf0uz/Ttt4YGI4a5FR6QnU2e\nBJCHPvgg/05J4RkCyI90A8f5aNkyAgkRlFZJfkK7dlEwXnVVsOWttpbflxhO83vh4ZyfyEgjONcs\n4QAYMiPWMJeLVn1Zl3vvpbJTWAgMHQpXYSHLK6akqEZua9bw3DVvTj5fVVetq00bY6UW3QsBcB/s\n3Knm2u2mEUiaoVVVkV8K6euik1jNH3qI6yOgSwfnXi+VQXNYi91O8OD1EkgNHWqUfTo/MvOc11/n\nvpQYcn2c+vd1D4tQx45cmwkT+PqwYTwbqanGZxZq2ZJy8uRJNb+HDytg5PPxWRs1ojcKIHjt0IEy\n7Jdf1LVefJEYQQxb+poIPfWUCvexCtvSPQo6NWlyLqyjtmFDo9EiOlolJ44dy7AK/d6TJ3P9dYqI\nUPtBJ4eDxqbJk7n/Vq6kx8dqf6xdSyPWffepcBL9vkVF3CPmhGk5I6mpVIJ0pc5Mct8zZ1T+yBVX\ncE8Ln/P7CZZFCROSeXY4aJCbOZP3OHTIWIVp2zbGj0uHaIDec1Eo/H7eR6rj3Hor94rkDTgclEML\nF9IgJIoOEMwTXnuNuOfMGSqjAvAbNeIz1fGDc3THHcog6nTy+yKf3n6bPH3UqPPnvmj0+wTnV1+t\nYt/S0ijcR45UMZ59+1JoWlltrrySISjCAIQCAR4u3Woh2dhhYUbL+cGDPFCiNf/978HWjvbtuckc\nDo5HyhSJUBDwrgOXqChu2ksvVVY1ySY+e1YdkO+/p+IgNGcOLT1yXRlrx47KiuXzcVM3bUolQCoE\nnD5NsCqHsn37YLB04gTnE1Dg3MuqNedoxAgK2oceoiVzyJBgy5KQxKGNGsVyWJ06MZ5/+HAejP79\njZ/Xw4rqI2FII0aQ6cnc33MPhfDw4QRUeodQv98QGwzAwJwcDifC/3ALtWlJTALIWDaa6k3rjAOg\nsBQgddddBMm6MIyOpiLz2GOc13vuUQLh4YeDhUN4OD/3+utkQK1bq9yLTz9VmfK33qoSjgDlfhw6\nlJZWQClE+mfkuWWNU1LoKrRKeglFb72lKhEAXJN586w/W1TEGElhmhMmULjMn8+51cG5WZkYPpzW\npPPRr7/SC+VwKHA+ciSZsihDkyZxDLr1TpLXPB7GqQNk3NHRKgQD4PmaNo2AQ1zGOTnKtarv2+3b\nVd6JzlMAhiPpVT8KCoxCScB5u3bWyox8ZsUKBXLbt7dWjN5/X3VujY6mgWPtWobXyTzHxxstkb+F\n3nmHa+vzcSxiLLEil4v3tPKObdhAI8WDD3KOZU9LXHNEBOfwlluoXAmZY2E9HlotT53imrz3nlqX\nf/6TBpiaGmDJEoQdP66+a7Px3PfuzdC7664jP5bz+/jj5HNCZnCuJ74BwfvhwAEF5r76Ss3ZwoUX\n1q3Y6yWomjuX89y7NxXY+HjeS+TJt99SUXA46A02hw1VVNDKLHuouJjX/uIL8jCzpVDmp18/Iziv\nq49tMFTJ+8OGGeN4rcjvp0wQQK4nHPr93LMPPKA+/957nGMJQxKaPZtyTQBXqBwMPQzMLF/Eo7B7\nN+dCAOBjjxlzVXSKjCR//ekntX4ul7p2eDgxyb59Ro+3mbZu5b7Py+MznjnD5y8psS4ZKuM/fVrd\nywzO9+wJDhfSx92woVJIzBZmwMh/zTJd7j92LGWG2fou8l6/lsMRvMfj4ojt8vOVJf/BB8nH9u8n\nP+jZU/HeRx/lWZHSkPWFm5h5gvz92Wc0jpm9lmaZs3w5ZUmvXpQHDz9MnrFlC8+gzxecIHse+v2A\n8z17jPHXOqMbOpQulgkTyKg+/JCC0lx/FqA12O02LpTO1KZqDVx0ZpuczHu6XBRo27ad66plSVOn\n8oB98gkXPj1dJZbecw83XXU1D72UORKSzd64MQXLypUUErowb9lSxYHNnatCOi6/nMBl4UI+Y2Ul\nLX2TJ5PRNm1KcC+uQTlIwpibNw8uDZaXx/kFFHDLy1NZ6KWlFH66a0yeY9QoY6gKoEJtzF6DRYus\n5zKUNl9HTV58kc8olvNXXjFaPqKjCTTEcqCDc6eTB08n872mTOHeePttAj2AjOXNN42fc7kUML39\ndgKenLoW2lYZ6rrCVVzMtZGmEE8+GWzxsdlo1d2+nWs/bpxymaamKmHUvLlKfAkE+ONw8P3Eupjm\niy4iuNi0idft2lXlK8gaX3stz50Ayguh7GzGtgYC6lmthFltLZ/5hx/UfJeV8TuLFhHgbdjAkmSv\nvBJsNc/LC22RF3rtNZ7tTz5BRfPmONut2zmgjjNnaA0pLua6fvqp+t5HH9EtrisvAC3Mq1dTeRQB\n8fDDHMsll6gY7GXLCJL37VPhbADXTASSGZybSayoZ88SFI4eTWEUyms2btwFu1PRvr2xFjLAM5mX\nFzrkwop8Pp4L83fk/D/wQP1ePiG/n/NptpzrluT77lPhHAcO0Po9fjz5XdOmxpBCs5AMD6diLN4N\nQL0vBoS61xv88gsidMuuGHhatQr6bBDNnq1qPss4AGtwvmcPlVa51rPP0gji95PfrzVVifrzn4P5\nzbp1NBJIQqnTSWvgH/9IvjtrFsFO9+7WYy4upldk6VKj93ToUBVKo8d4Azyja9dyLuLiVIlIgKDc\n7aZ80efgQmN0fT5+X+ZLt3aGhxMUDR+uPi85IhUVxnsIsHrpJf4/eDDH/fTTVE6uv577RdbZbDk/\nfpzyfdUqGkCefloZjLZsMYYWWtHKlcpbpBvLhFatorwKRUeP8hqA8o5K+cFQnhUBh2Fh5O1iOBw4\nkPdbvtxahgYCCpiGCmkB1F7u3Nm6ipHPR6NKaakyetXW8t7mZG1dBuq8Q85aTAz3Zp8+ykv03ntK\nsdQ95JKPlpPDPR+KBg0yhkU6HNznt93G++oWfHlfn2sJB1u9mt4aCdP66itGXUgOYT04xUy/H3D+\nxz8y41jIStsFaM0VK3IoMmejjx5NrfPpp42fkwQfgIf51VdpSfzkkwuz5DqdRoE5bRrLJcoBCAvj\nhnn1VdVwQr53yy08pMuW8aBK3U7Z1JJcI58/epQgSuoBh7ODJ665hlpxeTkZlIAcPXlH4uLuuy/Y\naq1/RsYslkWZm/JyAiGZE9nUerKXTgLWdXB1/DhDBaxImJMe7qKRraZGxVenpfG6drtx7nv1UteX\n9a+tVSWZSkuVshVKmOj7weEgiDtyhP9LtQm55/79nJf63KXdu6v4TpuN66Rnkwu9/74KUQoLC80E\n7r+fDFInEXDmROg+fQgk9MYvAu4lrKW+qg3no7VrjW7UH34g4H3rLf6/aZN6z2bj+cvPVyFjABnu\nCy/Q+2AOG9u8meOdMkWVQjVTRQXvk5ODwpEjcejJJ+kSDwT43uefq8/qipDXq8JbzNSwodFyLvTU\nU8oyVVXFdcrJMSZv6UIpLExZe60AsQhlOTsSwxwK7E6fHgy4fwvZ7WqPhaKcHCosYmWtqOCZMJ/v\nrCxa+E+evLB7V1fzOmbLeSjP28sv87MdOwZX6AGCXdhyJvUyhXoohqmmtUc8gqtXKwCXkKDAdSj+\n0LevMTFRV8jnzOH+l/d376YRSa61ZYsCOTZb8J545RWeIZ0OH6blb+HC0OPyeAi+rEI7JkygchkX\npwCVeGjk7JsbMf34I3mpeEN0HmE1hksvVWFT5yO/n+PUwblce9o0ZZkXstt5jioqgq2iPh/fi4qi\ntfWOOxim9fPPVEL1vXX//Tw/ArpPnDAaexYuVM91333ncIhDDzHUSc8B6Ns3GFc8+GBoQxTAedQB\naFmZmhvJC9BJ9o3Px1CrLVs43oYNeVZiY+tPIhVyu4OVQoB8cN06yrunngouUiHnQsZcW8tQnI8/\npjwz56sIHzRbp6UqzuzZ/N7q1TT6AaGr+Qg2aduWXiwJPQE4T48+yr8nTzYaW5xOYq/sbCr4Es4n\nFKpqjpBU9dIVyvMYEc30+wHndjuFt4SjREZau2msqrFs2GCMBTJr8zU1ZJpml+NHHxmZ2t13E8w4\nncA//hHsrjkf6XHoAK2Y06ZRK1uwwPg5qUsqCaPyXcnUt9loQT14kM+Tn6+S0yR73W6nBTYpie+3\nbGlMnigr4zVF483IoMXPyhIm8zV6NK2Rema6bGS9MQhgLA8ldPo0D4nNZgTn9bmE/H4KicsvpyVA\nLLmpqXAWF8MmB3TAAAqwjAwKndatz1U6CbrekiV0H159NV87cEAx5xBKgOGZzcnHixcbX5dyTz4f\n10gEwT33qKoY5rhqudayZcYaqd9/TxAv4FxnAosWKRfpiRNGcJWfr5p+mJWuBx+k0LLbeZak6yFA\nxrh2bf2lynJzjfHvOs2ZQ4uJHlO9cSPn/Pnn+T19T9hstJSLEir3fPnl+q1uUpFh9WprK7SsgZmp\nnzqllAT9WkLm8ASd3n2XypL+bICK1wRU7soddyivweefM4TH4eD1+/alNefpp63BuZ7/4fMpoWkO\nn/vfIj3uOBSVlXE+GzdmOMjhw9aJ2h07Ugm6EKu5UGWl4m36mKzGYxXLr1NSkjEnQgfnr7yi9gUQ\nlGdTnZSE0xJqopfAy8hQrv8LsQSPGqVyolq04F4YMkTts6VLaVDRr1VYSG+AlQwDgl+TcCs9cdmK\nrPbz008zdEp4p3hqX3yRXtjCQjUOfYwyb8uWUcHv1EntSasxRERceK7I55/TO+Lz0WC1eDHvd9dd\n9BCYyWaj0i6x9UIOB0P73G56sE+fpncZIH+UsniyP8eOJW+SM20GZps2GZNH677XccAA6/2pK1eJ\niSrf7ELo0UcpL+QslJeTZ+oK5COPGL8jhkp9b0ZEUPnv2JH8PBDg3q8PpDscqpyk+Xmio5lvZZV8\nv2YN5YzsMd1Il5JCD9rSpYrnZmUxN8bMm8Vy3rev4iuyRlZ8XN6XZ96+3VimsrCQskG8/uZnFcUy\nlHFErOGnT1tX2ZHQRx2c/58Ma7HbeYgkzrRDB2PXOCGrRZw6VWVJi5tfn8T+/QnSdIbv9aoYKDPp\n2e0XQkuW0K0qZRV1ICDCQR9PXh6B4uefU+sVwJKWRvdndDSZxfDhBFh5eWQseoUWsR7L5s7KIhgd\nNkx1WevbV3kjvF5VNUXmISdHuWyEMVx6KRmyzvDN4FzuKS5enbnrbuVduxTQDmUN/ugjMkexqCxd\nSsWobp7cx4/DJslCAsh1MoMogJaAK6+kpq67usLCOCd61zeddG+BPJNZGOkKiYDzZs3IOABaFCXj\nXhcC+r697z5jPL9eQiw+3sgENmwg6JNn1YWww0Fh9NprFHRWYSBiHdOfw+msH4jMnUvwM3Ei/1+2\njKEhQsuX06NQU0NhsGuXmrsTJ2gFttvVWB0O47zqCo7sieeeUwIWoMU8M5Off+01YwdM/dkAYOZM\nJJiFisNBwS7x9HL/w4e5x8xgprCQzyR8oXv34HAdn4+CaPNmznVqqooR/e47WrSEmQ8fzns/9pj1\nvhdg+uKLPOviYZGcAaGHHlIu11mzflvipk4yBllT87N/8AHBuVi3Nm0iD7YC57rguhAqLKTFz5w8\nHipBUnjUqVPGmG+hq682WsLEZa270kOEtXgTE1EbE0NQc+gQ+WvTpuQtEybQkjdhwvmf6Z//pLHg\n7be5T3w+8tPSUlp69RwhoUcfJeA1yzDhoxs30pIvPE0/m/VZ9M3nG2CelCTvCbhr0IBhn4WFVAZl\nT+jf1b2RDz7I8MgpU/h/ZCRlTGkpnyM/3xguBnAerJT6o0dVYp7PR37Zpg1zkX75RRkrdu5U+Vv5\n+TQmrVtnlNN2O8/a4sXBIawCzm+5xagMWnUI1UnGrIFzWyBgndxqt/O8642LAMqdrVuDP6/TwoVU\nmtq1M3av3LVLyQ0zH2/QgJZj3egYFaUSTWU//fnPoTuB1kdiJZZnE+/umDF8PTWVe0T2yZAhPCP6\n2T1yhOsxeDA9L1IRSg95lfws3VAqv0OBaB2buFy8XnU199L69VSwZ84M/p4OzkMZAEpLuWaZmfWD\n8/h4rkHnzucPtdTo9wPORRs1ayarVxtj8ex2Mnk9jtgc4xQXZ7xO9+5kpDo4dzg46dOmKYu0kGwG\n+X3oUP0WpyNHlKvp3nthaB8tAE5nILm5/K03bXA46MK9445gK50cHnkmCb8IpbHrbqUBA4xWBD1G\nbutWMnGrWDQzOC8s5OFzuSjY7rtPtVbWn83p5NgklmzRIioie/ca2xwLLVzIa910kxqjdgAc5eXK\nci60cSOZgN1Oa6zE70kpwrZtaSEwC36rMms6deqk4hhDlVXSwfnOnUbXvjlsp7yc1/zDHwiwzLWK\nzeOaOJF7R1dkdIasKw+AUgbvvjv0M0lcqZVgX7Ys2MIMKCuuAM/cXGNybFUVgW9NDRXM/fuNbk+n\nU42/dWtazfW9pCtw8rmjR1UyLsDwML0xhJXFQt4rL4fbHGIRFcX1F0/Sxx9zD27cSIVUxvrzzxSS\n8+fTpev10ns0dy5DCjp04PolJnItVq3ivK1ebTw3ogTJ/tLB/x13BIfiiWIiyrPsjU2bjNVPPv1U\nGQl8PlW+7ELphx/o7pe5ksTv3FwqBgDP9t/+RoAiceHV1aoai5m6dOEZu5D49X79aGV+553g91wu\nAhXhh0ICzquqrHmGmWbMIMCVZ3zgAbVfXniBQComBkhPR62UOiwo4Pl0uZQCkJdHXi8xurm5wXWs\nhRwO8iDdqnznneQJPXuqXBTdECB82RzWIsDoxAnyC6lcpZ9ZhyN0qVHpDQJwfxw5oqrdCHDXeWH3\n7jTiiMVaT+QcPFgZA6yeuWlTXnvnTgIjAYjr1yvA2rNn8HePHWNccVqaAtQZGZQlunzau1cZZ+66\ni/fo3NlYMlT4bGFhMDgXI8cjjxgt+ucD53L/3FyjIcBqj9tsPLd6GC7A+GRzu3gz6XH+zZur0Lq+\nfVWYoDm3pH177vGZM60bFur7KdSZ7NEjdDiwDs6dThWSOH++9fVqazlGfU85HATOP/7ImH8hnS83\nbsyx6t/95ReeRas1+eUXerwlF8Xp5B6bPJl87b33Qsfpjx9PJa9hQ+uKVpGRVD6//prP//zzxnyH\niRN5rnw+XuvZZxlSIzldF0C/H3AuB8xsZTp4kKDwlVfIeGw2WhPHjVOhLDo4X7zYutGDw0GGIhtU\nNsOZM8bKKIAq0bR7N6/dtm1w0sP+/cotumABLU+yUWpq6H7ZtUtZh/TnkhJmOTl079nt1Mxkc545\now6o18uEsTZtjJZzKRknwlQ/ROHhVDxEAWnTRm3gqiqljMihbNaMiRM6OZ1Kg5b7PvMMNeL+/XmA\nxcKrAyfJBn/1VQqu5cvJcL/80lrBcTgoIKVW++jRDAvRLM7nLOcy/rffJtiVUKh587gfNm5UseFm\n17jHExqcT5+uPBMS4ypWDF1AulxKQIrC0rQp53fdOlUeU+jYMY5hzhwedAFGNhvnUr+u18sxXH89\nLSADB3KPbdnCe91/v6oFrM+1/ozz5vG7AC3EEmbx5JPW9XMBAk2rhNnsbLXndUXtoYcYhiPg3O/n\n/qysDAbnERFKULtcZHJDhqg1kvhXwFj20DwW/bf5vbr1DOh78JZbuC5+vwJaUopOxigMu6SEoMzl\n4pyVlRkbh7jdDFVq3pygye+n0Jo50wjOHQ6CCKnooo933jxjF0KA4zp7Vu1z+f3TT0b+pQsfqR5w\nPnrgAeWBzM8n4GjXjv/LPOXlqfvIPhJwvmqVeg4rcD5qFKuQtGplTLC3InNFE51at+Z9pF65kFh6\nZX5zcgh866OHHlINkV56Sc3/8OGs9uB2A0ePoiYpCTYJG6uooBI/YAB5x7JlFNJCb74ZOt/BHJIj\n3lG7nYBAvB16mEFkpEpUGzRIva6fYem+CfB3kybkBYEADR0FBZRXVVUq7HLZMhVv+8YbNFZIJSJp\nSKfXv/71VypN11xjLBUo9+zalXxkyRLje19/zddPn+az6nlhGzdyP4WKyxV5+8knvPesWUZrtd/P\n8/nYY4onjB9v3eRKB3968xhAeRclVBLg3On5RFZAUHJecnNZnUPICoxdcgkBo5XBoLiYa2FOQNTn\noUcP7ucHH1RlIwMBjjuUBxRgXoRVrwS7PfQ+FSotDZ1vIp5bwOi1NXu7X3lF8XmHg3tQEuJ1o5+c\n+SZNjDzdZiNms9mMe/7QIWKQJ54wWtoXLSKPEIVHriVGG1lTK94iuOTaa1kYwYpkvG43+dmkSfRu\n5edzHyYkKEPEv0C/H3DeqlVwwx6Am+XECTKFf/yDQGDMGE6gxG3r4Pynn6yTHhISeOhkEwtoFoC6\nYwc1ozNnqK1FRvIQyqY2H5jp08nUH3xQWfyiogiMZ8xg/Nb+/YxHvPpq43NJXP3Ro/zdoweBgQhw\nl8sYjjJ6NA+73U4gtWmTMebyySdp9RMaP55CRpieOfFKmK48e2amsTQfQKElNVWlfjhAICrzYbcH\nu/FE0LtcivnabNaVdQA1NhFsn35KS3rd2tr8fuQ+/7wqSSad0fQ19/lo5ZTGMnJdYQAZGXzWUOD8\nkUf4+r33qv3RsycVJrlHTAyFoiRtTZ9Oa07nzqrKj5n06hQNG1KISsycXmpLb+Dx1Ve01qalcT/O\nn88xSGlMs+VcZ3JnzypQsHw5wUXHjhRmTz5pjNcDKCAjIoI7YjocBK9iNdRBaG4uxxITo5LMqqqU\nh0e+73JxrwjwcrnUGgwYQKttu3YMo5oyhQqcVUytVV6DkCiUffrAWVKCpLlzyeilfvbMmbR4FBby\nPlIJYPBggiOxfst4f/qJFl49IWvaNJ7h+fP5Hb+fuTBRUTyTIoTtdr4+bJhqfw3w86WloTtp+nw4\n14gICI4fljX+8MMLS1IHOJeyX+R6ujdDxqWHNejgvHdvnlfdA2ZFDz98ftAsPCiU59EqXCMqihbv\nhQtpnKmuJggQi6UV/elPoTsYaiCjuH9/lLdrp8C5x0Nlc9u24PMkAGD16uCSrHpIjl53XECrXl0J\nYKii8JM+fYzWap+P+zMy0jgfnToRGNTUAH/9K1975x0C8A8/pEz88Ucj75aE/tpaAssdO8inRo2q\nfy3NdPBgcFhnWRn3aY8eygMmc6CHAYQC5/JZ2Qs6WC4poZU1J0fxgfMlrI8fT74qXj2PhwBr+nTu\nEzEMiMIj89qoEedmzBglCyWE9tixc8azDevWWYPzvn1poLIam+wTq1woedbMTGPCrT4n+/dbFw0Q\nkpLQp05RIV20yNgpN1RMdH15HIID3n+fa15ayvNnjrG++WZlNPR4KGukYZrk2ujPYg6btNmUNyMm\nRvXncDi4lubuwdKESL4rVYKEn0kSrd/P9/QcEoC8f8UKyiwp7KCTzIfbzXU+cYIeRD3/4cYbf1up\nYY1+P+D8rbfobrMC5wIMnU5ubAGmVpsgVGJB//4UJFLxQISGMLMNGxjb+s03BNySDS7uXTNwcLmU\n5euRR3igb7mFoEM+Gx5Oze+vf1VZyQCv+cgjZKp9+lh3+ZNrCGNJTydonTSJG02e8913Q8du6slQ\n777LnxtuUIkZusZcH3k8qv6sz6cS4mw26xJFfj/nWcC53c41M7cW1j8P8BD4fIwn69YNAFRIi6yv\nuFwrKoyCASCw18N35O/evQlCs7KsS1yJAmOOe9u6VYGq+fMZPiICTjq9ut3UzK0s03qdV6eTAs8q\ndnrMGO4Bs0VHD61xOpnkpe8VXQHRnwOggnr0KMM5Nm/m/jYrJsJQzeDIbqdyIMqjOcQJ4FweParG\ne9VVBADdunGsrVsbu+U1bGgUdHffTSXk/vtpLcrPt1ZwJDnKShBGRXH+O3eG58gRNH7tNYaEBAI8\nuzfeSEEn5QDtdiWIli/n3EhMo9z7lVeM8fUXX0xQdffd3HM6qB071iic/H5eX+I+n3iC95B+CFYk\nnYRXr6ZQN4NzUV7/+McLB+c6P5Dr2e3GHB4rcD5xogpz8nj43fo698bFhVY6hM6cUZZcK7LKexg7\nlsqBeDl1HqF3XbWiX39VRhshDWSc7dkTFdnZfPZRo2iVE6uf2YjhctGN3qcP31+xQr2nfzYQIO/f\ntEklgaamGvMDpkwxJkPrVFtLRWTMGKO1cs4cKtA33WQMidOVgdpaY+k/2d+1tTTQSDjRiBHGWvHn\nI2nkpZPDoZpnCdjdsYNnWMB5qNKK+hqKMUvPC7jpJlU0QTe6hDo3AHn62LEE9B9+SKvrwIGcex3Y\n22zGiiJJSSr3YvBgWkdFDko1MH18VhQqOTAQIGh+6CHr75l5vF7nHSCfFJ5iRadOUa46HJSTFRU0\nwMg5DTVml4tGR6trv/oqjQq33cb8icJCGnLqKx344osM19M9h2bLeaj1mzmTRrC776YRUO5hDmvW\nwTlA2ZuZqcD58OHksT4fQ2zNIXBr13KvvfOOsXKXkIxX1jtUKOu/SL8fcA5QeOvxVrt2KSsYoDaC\n2RXcvbuyVoVKLACoEQo4T06mFVRnZkuX0gXqcFBLDA/n5ggLC970Tqd6b8gQWiaFZHHFBdWggbG2\neFUVwZwUt9epqopCSa6RmsrNmJxMYK1rwF4v468k3ksSgIRZx8Rw3MuWqYou3burOdZjzYTWrWMc\nuplknLW11p4EIYmxb9BAHSyxsliBCx1ILFzI64aH85kHDw7+jrRa3rOHmu6DDyowo7u4evWiN2bN\nGoL2pCSCpF69VHJNIMDwEmHkZsWuSRO1DgMGcG3EMg0ot9qoUcoz8PTTKqRAH7vTqRJ5zU1bBgxQ\nTEq/v92uOqBKEqdujXO51ByvXMl1EUb37rsqXOWzz5iApTParCwy+VDgvFUr43PoceI33aRcfTLe\nnj35XFOm8Iz5fEZF6NprjbkYP/1Ea4lc01xvWSgpideur8Y3d4gAACAASURBVFKFwwGfWE3DwhhK\ncP31fD5J6BJhKnte9p08m+yhfv2sE4bFohnKbX/VVapJFMAzPHMm61OHqnoj17XbqeTecQcVFXPy\nrngoLrRSgA4cdXCuJ9XpzyFKniSMA/y7SZP6Sy9eCAkvlvKsZrKqACKeNz28Q/ZZo0a0kOkJ1Tr9\n7W/BnlOrXCYJGWnRgvc/ciS4NGpYWPA8Cs2Zo7oR5+QoD1HDhpzPyy9XIQsAwdqYMdbdImVv6esh\nlJLCa+pVn8QTIXkLOs8Qg9LUqeR3+txGRIR28ZspL49gaNUqZRDRQ9D0vVJYSNl96lT9YS2bN3Ns\nIp+kqtUrr/DMmXO9xKNqZdDo35/rWlTE5xJeIqQDQ6czWKbpPO2uu357d2KrPSWv10dPPskQjpoa\nKppXXUXFQtbwuuuMHYLNpCsc33yjZLl8PxSwdzoJVKVfik4ul7I6jxhBHiny0WYj37DKQ9BDEXv2\nVAa8nBz+hALnJ04oxVtXoszKgN5JFOC83XqrAuexscQzt95qzR/PnlUeXiv5IfxIjEb/Pzivh+bP\nN3YfvPhiHngzOJcDIJVMnnlGxYmHspwDBOcSW+ZyMb5oxw6j4KiuVpZmqbFq1fxDB+c6SVUUwDo+\nDGCYRXIyGbYuDHbu5H1HjqTFb+VKbmJJiJD7CuiT7qAOB61iEyYQXEtiw6JFtBqLQqJb0gHrGqV7\n9liXU9K9FFLn+fRp64YNUgJr7FiCQGHkVsJ53DgeMJ3Cw6lsPPkkKsytvfXDK/GGsi8k0eTjjylY\njhxR7n2d9u7l5yoqKKx04Vgfc42IMOYe6HGMQhs2cF4A49pKqUy3mwDCSrmRere6laxbN9Wy3ayo\n2Gw8Hy+8wD1TUmKcH90yJdYuoeJilR9hZkajR5NJi1X0iiuUm9ZuZ1KSxGyLUNSFw+zZfNb77lNl\n4Mykgwq7nXHCEotupjVrrGt8y3XvvhunpbKKvh5btqjKG8L4k5JoXRMAK4xbQsokjv2774wJvgIi\n33hDlbjTaehQ1cAKoBU1P58/9VU1ee45hvc0aUJ+t2aNEQQ++aQCDtdfH1yO0Ip0K6UOKgMBZRnX\nhWJUlHV4ijTA+Z+Q7OXZs62tiVZhLZLE2KYN51T4Vu/e5Ct//3twwx4hKyOAlQVw9WoVb+1ycR2+\n/55x01JLWTfKmMH5iBE07kyZonJ4AgGuYXQ0PUfmsnWTJxsb+AhJ+d1OnVQInk46XxL5dj5wfvPN\nxnjs557jPjKXka2pCc3zZs2isUFyaQ4epHxp0IDKdVwcZYjdzjNx4ADHZxVepIPfM2do7d26lffo\n3Zu8Rp5bejN07EjPWcOGwXXDX3xRJUdana+//73+yiU6YJswIXR3zVA0YkSwEj9lirUXXKfLLiMY\nPHlSKSd9+nC/hOobUFWlQnfMAFLkiN/PtQ0VEuN08jqhjBy6wTMnh/Pz5ZdKOdJjwWfNIr/QqwSl\npVHRePllgu8vvuB+tpJzIt/lfvIsZoCdkGCU36IsRETQgt6tG/fVPfdYn3ExxlpVMwJ4Vps0UR6x\nUOC8vJy5HuvWXbj3EkCImf6dUGoqD0Dv3ozFlQkeNEiFiVhNeqgOX7rlHKAL8rnnKAA++4yv6WBF\nAJUe0yUkMU/mzXfPPSoOW7dy6vTII2pz6oxl7Vq6X+Q1vcmLfl/ZIJs3K/eijNucqDRnDp9bjz2X\n58vKMta/BlSDGjO1bMnxVFYS3D78MN2maWnGlssAAcxTTzHhaNgwMt6mTYM7iQL0OtxwA61KovVv\n2cLD0Ls3vOYurXIAr7qKc9GvH+fjxRd5aGNiOC+ZmaGTDEVRkAQtASrffEMLwa23Bn8HCAbnvXsr\nBp2XRxe5zmwaNGAce1ER952AeSvr0ujRKuxAmJC+lqE8DydO8GxYJR6bLaP6e04n1/OBB1QZSKFu\n3egNeOMNnkG9fKUZDNxwAxm1WSEW4ffaa7TKTJtmfN8MztPSzh8iYSZZ36wsVErFD7ebwLhFC6MA\nnjiRe7BxYyrzEtJyxRWM901LY5iNw0FBKJ6u6GiekfJyXqu+VvU66XxBD2nTyeulgWHnTmPIg66s\njh6t1tXtDlZkrUj3Rl13ndH6fffdtBRmZyvlIzLSmLNyoSQWfTOY1Ombbzi/d9/NM62T30/gZa5C\nIusaE0PQJ+egRw+uRyirJcDXX3xRGR2efZZWVr8faNkS9vffhz8iwpgXIHtEShrKOWvalGufkWGt\niC9YQF5jTqoUWVJSwrOvJ9ZbAUlZ97vusi6VabNx/+XnB4e12O00Bsj/nTsrhUrn9enpfD69+MHH\nH1O53r8/WA4I6TxFjCt2u0ow/stfKLcyMxkW0bWrdR+J5GSOpbiY+VUNGvC+ktci8cNZWQq0vv66\nqmayZYtS3mfOJN+vC3205IsSzxyK6uuWeSFkttQDNPbVVw1MJ4eDfFESkFesoDJiFd+cl8d56NpV\nGRtkXWVP+v2UR6H6NyxcGDqvBzDGvl93HddLOnLqsqe8XMlxs3wNC6M8KS7m+KQ3iJl0cD5ypDI4\nmM91mzb0KIq3OhBQuReAMW/DDOy//16Vts3Nta5sd/vtxEYuFw1c0snd6aQs7taNZ3vhQib1L1nC\n/WpumBeCfl+WczOlpBAQSRt5sUwNHGhMNNOpWzdVDs9MnToZy+p4vWTSiYn82+OhIDtxgi7mtm25\nSfUW3UJNm9JCYAbnNTXKcqBbvM0km106XJWVqUxzs+vpxx+N7X4lFOXSS9VBEHBut1M5kbi+w4dV\nxz+7nd+R5EqhTZtUTJbEeRUVGYXp+PHMYN64kVaM9u2DYzSFSkoYg/nUU7RwNWvGEJV777Wei/Jy\nBdR69LB2vQnFxnJdJI73ssvIzHv3JuBYs8YYj2nFjHQrtMtF4GazcdxibTl92hhjWllJZir1qAGO\n4957ad1MTVU144VxZmcTnH7yCa89Zw73i9OpwnOEBJiPGkXwuGoV95hY36ZMsa6/XFmp4v9vvlmB\nrIwMxZDmzQsG5y4X1/qyy6yVwDVrrC1qzzwTLEDmzg1WRKXaxooVimleeik9C2vW0DKtg/MLrZmt\nk3i2APjES+V2EyTs2cP7Fxdz34aHG/MCZO/GxqpKFqmpvKYOwiorVVWTUEleQkuXqhrNOl8Ile0f\nHU1+I/vV4eBrAwcaPyfvJySEFng6PfOMqgaSlsbzd+QIE9wBrmvjxsZQu3+FvvnGWDkjFMl5M/Pq\nU6cY0jBmjPF1sXS53fw7I4NnaNo07unztdHWFfqlS6k8Op3Avn1wWPWuGDGC4LV3b/4t53fsWALY\nuXPJU80Vd+pruQ7Qunz//ep/2XNLlwZ3gQxFy5axEEJBAcPJJHfD7eb5laR8ATDjxqnwJZ3/3XQT\ngb8+b5KEHMqN37GjEZxfeil/694beT8sLHSctZDfzxjhrVsZdqMDKr+fslZPTp892+gxEJo/3xjW\nZAXO9TKtViRzs3+/MZH+QmjVKuv1i4i4MAPDd9+pwgNffmlUrqxIjCsnT6r50A2IAMcfCpgDHJce\nimQm3TMOGJUMsbrfcQe9uLt28bWwMGOkg36t+kJDdHA+dSp51JEjqrqdUIsWlLkCmusjM0+Qv1et\nCg4VFNKNXx98QMt4TAz57HvvcTy//EIM5fP9ttBC/J7A+f79wRbv1FRqjVLHc8gQCsrp01Wr3+xs\n43f69VP1mXUqL2dSlR4mobsqu3ZVVt42bchAv//eWIJKp/Hj6e6ZNEm9Vl3N7z3zjKq3fuhQcKMG\nQDWFcDhouezenRY02UQ9eqjkp2XLVO3jrl2VsgKQSd93HxUSh4P/792r4nuFCcnh79Il2Pq3bZti\nNtHR1CY/+EBZ/Hw+Apz8fDJFYYbFxcEgE+BBTk83uv1Onw7dmVNnTOvWqZKDdfdpc/31nBuAgumx\nx4yxqg4HQbIkp54PnOshNh6PKgf33HNqX+3ZoxQngArMggXKAvzoozz0ZquzDs4lplv+joujkuJ2\nq3KaQrImN9xAa5w0YBFLWkKCNePXk3MjIxWAuOoqgkmpt/zss8Z29U4ngU5cXLDnAwidV5CVpeLr\nfT7u8yuuCBYMNTVkwN9+q9ZWFMaNG6m07d5N5vnEE6EbQ9VH8+bx3Lz0EgIyVrHQ+f1cy23b+Ozm\n8qrNmwcrJd9/T36iP/crryiBpVfYsaLdu7l/AXWNqChrTxSglJJJkziWUMquzRbc2rw+atkymAdK\nqbr6QrfMrz/1VGhDB8AQPKnoFIqkDKqVazmUUiYxxN27syJJRISyksqzhBKSZlAge0HubQWABgwg\nX5T5t+IZ6enBnQjF2hvKQPHaa8ZryVjWrVOK/9Sp9cf179nDa/ztb/x9662ck0mTuK+lzroVMKus\nNIZgmT1rEmtr9bzNmhGo6N8JD+c86aUGzUDs66+tw0mkOaDHQz7Ws6fRUhoRwT2rK2o6wNY9luJ1\nk/PbvDmNSa+/TmXohReoSIRSZEtKODdvvkkA+NBDxAYXSuvXB5eZ/C20fbuSGyKbzwfOBRy6XMQN\n4h3JzqZMXrLk/MCxPm+B38/rDhjA/6WkMMD1On2ahgenk3MXCPBMWHUkPV+VHY+HvPL225VR6osv\n6BExP4Ocx+XLgyvK6TR8uDF0SgyVwgetap3r/EfKcpeU8DrCs959l8ZZkXX1PZf58hf8yf92+vOf\ng+stp6SoSRM6dszYmctsCQm1MXbtCrZ86eC8Xz9a3G68ka6mC4ktcruNVraPPqKWpWuTBw4QwJrB\n2GuvEdx+8QUPqoTQyOGprjZWHtm1i/Gi0kEUIAAYN04lYQrg+utfVWMNOZD33EPryW23BWc164dW\nkjAqKowx8zInegOBULH9lZXBwG73boJqKxLGJMqI3a7CVgDYKyrU9Tp2pFARy5rQddcpN9yFgHO9\njJJ4InTXdSBgbPgijEEs2YcPUyA4HMaQAD0sauRI5fGQuEyz9Q2g0iJW7rCw0EygZ89gwSd5B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Txwez8jzEzz9jcuPgwehF6t9fiZ0FwKNKUYyqEddfryRmUnWrt94S75a6d8dFwExm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\nkdUO8+dHr9RlhHBuhrWUlQHk5TlSPw4ODg4ODtGGJAEkJQEkJ4e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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30000\n",
- "movement_variance = 2\n",
- "pos = (0,500)\n",
- "\n",
- "dog = DogSensor(pos[0], velocity=movement, measurement_variance=sensor_variance)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(1000):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- " \n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- "\n",
- "bp.plot_measurements(zs, lw=1)\n",
- "bp.plot_filter(ps)\n",
- "plt.legend(loc='best')\n",
- "plt.show()"
- ]
- },
- {
- "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": "markdown",
- "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",
- "execution_count": 27,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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vvfcejhw5gn379sHc3ByDBg1CSkqKZp/Q0FDMnTsXCxYsQHR0NFxcXBAUFITM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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30\n",
- "movement_variance = 2\n",
- "pos = (1000, 500)\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(100):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- " \n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- "\n",
- "bp.plot_filter(ps)\n",
- "bp.plot_measurements(zs)\n",
- "plt.legend(loc='best')\n",
- "plt.gca().set_xlim(0,100)\n",
- "plt.show()"
- ]
- },
- {
- "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": "markdown",
- "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",
- "execution_count": 28,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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B2CRyOfDsmbWlIAiilELKuYFwHIe3u01EBfdKovJ9ZzYgJ/+llaQiCIIgbI4t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\nMua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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30000\n",
- "movement_variance = 2\n",
- "pos = (1000, 500)\n",
- "\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance) \n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(1000):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- " \n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- "\n",
- "bp.plot_measurements(zs, lw=1)\n",
- "bp.plot_filter(ps)\n",
- "plt.legend(loc='best')\n",
- "plt.show()"
- ]
- },
- {
- "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",
- "execution_count": 29,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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dAz+/H1QJ4by4tAAzvp2AvCI/BPT77lM6/MfEmO/ob7mF/KgYs2dTcIIaNpm2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XL5MgFkGdDInS5eeEGc2bg4EZnjdbpeapbbTRGBPXvEz+QOCcx8mUxUS8C5k1pwXlMjZhiw3H+/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\nRUWRoqIiQ5sXXniBREVFkd27d5Pff/+d9O3bl3Ts2JH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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30000\n",
- "movement_variance = 2\n",
- "pos = None\n",
- "\n",
- "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n",
- "\n",
- "zs = []\n",
- "ps = []\n",
- "\n",
- "for i in range(1000):\n",
- " Z = dog.sense_position()\n",
- " zs.append(Z)\n",
- " if pos == None:\n",
- " pos = (Z, 500)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- "\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- "\n",
- "bp.plot_measurements(zs, lw=1)\n",
- "bp.plot_filter(ps)\n",
- "plt.legend(loc='best')\n",
- "plt.show()"
- ]
- },
- {
- "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 range finders, 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": "markdown",
- "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 `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 30,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "text/plain": [
- ""
- ]
- },
- "execution_count": 30,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "from IPython.html.widgets import interact, interactive, fixed\n",
- "import IPython.html.widgets as widgets\n",
- "\n",
- "\n",
- "def plot_kalman_filter(start_pos, \n",
- " sensor_noise, \n",
- " movement, \n",
- " movement_noise):\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.))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Solution"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 31,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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wdlKabXujYFtERESkLvbuNQPto0fN51deCevXQ9++db5ESamNbQeTWbM9gU2/\nH6OwuLTavqH+nvxhTH/GDIrA0UHpiu2Vgm0RERGR2mzcaO4KmZl5pi0zExYsgA8+qPFUwzA4cOQ4\na7YnsG5nIidOVV0fu0xEsA9/GN2fi8/tgdWqCm3tnYJtERERkZqcPFk50AaYMgXefrva05KPn2TN\n9gTWbE8g6Xhurbfp08OfqaP6MaxPmILsDkTBtoiIiEhNvLzMGtrXXQe202X47rrLrKN9VqniE3mF\nrN+VyOrt8exLPF7rpQN93Rk7OJLRA8PpHqjdHjsiBdsiIiIitbn2WnjrLXOXyHnzzMfpTfiKikv5\ndd8xVm+LZ+uB5GpL9pXxdHPm4nO6M2ZQBH3DAzSL3cEp2BYRERGpizvugMGDYcgQbDaD3YdSWb0t\nng17jnKqsOb9QZwcrQzrHcqYQREM7R2Kk6OqinQWCrZFREREyhQXw2+/wQUXVHk4ISyKNSu3s3bH\nYTJyTtV6uf4RAYwdFMGIc3toA5pOSsG2iIhIZ2EY5akPUoVTp2DaNPjhB/j+exg3DoCMnFOs23GY\nNdsTiE/JrvUy3QK8GDvIzMMO8vNs7lFLG6dgW0REpKPbtw9uuMH8euedsHAhaLdme5mZcNVVsGED\nAKcmX8eGtz5hTZ4TOw+lUs2mjuW6eLoyemA4YwZF0DO0CxZ9qJHTFGyLiIh0ZGlpMGGCueMhwL//\nDU89pWC7oqNH4fLLKfl9H9u8QlntG8km7zCK3vgaRoyo9q8BLk4OXNTfXOg4MCoIB208I1VQsC0i\nItJRFRTA5MlnAm0/P1ixwvwqABglJRy4Yiqrs935uc+1nHA4/SHE2xuGDq0UaFstFgZHBzNmUAQX\n9A3DzcWpFUYt7YmCbRERkY7IMGDmzPK0CABcXWHLFoiObr1xtQGlpTYOHD3O1gPJ/LzzMEkXTIdf\nfz1TQ9vfH4YNA6czgXR0mB9jBkUwckAPuni5tdLIpT1SsC0iItIRrV1beRvxvn1h6tTKfTvBwsnU\nzFx+O5jMtoMp7IhLtS/VFxAAgwbBtt8gKBjOOw8cHLThjDQJBdsiIiId0Zgx8P775oLI4mKIiYHP\nPrObrQXMQPvOOyE01Mzl7iBBd35hMTvjUtkWm8K2g8m1b5ceFgYuzniGhTByYARjBkXQp0dXbTgj\njaZgW0REpKO69VaIijI3Y/nmG+jSpXKfF180tyIHiI2F994z003aGZvNIC4pk20HU9gWm8zvhzMq\n7+SYmwt4lRtnAAAgAElEQVRJSeYHjwqcHK2c3yeMMYNGMiQmRBvOSJNSsC0iItKRXXwx7NkDDlUE\nkJ9/Do8+eub5xx+biymXLzdTK9q44zmnymeut8emcuJUYfWdjxyBXbugtBTc3fGOiWJwdDCDewVz\nQb9u2nBGmo2CbRERkY6uqkAbICQEunaFjIwzbRs2mLsn/vCDOSvehhQVl7I7Po1tB5PZFpvC4dSc\n2k8qKYFdu3A8kkjfUxkMzk3mvBXriHzsP1j79mn+QUunp2BbRESkvbPZ4L774LbbYMiQup930UWw\naRNceaW54U0ZLy8IDGz6cdaTYRgcTs0xg+uDKexOSKO4xFbn88OcDc77/mMGx+3gnLw03GwlZw5+\n/BE8/XQzjFrEnoJtERGR9m7ePPj738186w8+gOuuq/u5PXvCxo1mlZIff4TgYPj2WzPgbgU5uQVs\nj005nR6SQubJ/Dqf6+HqxKBewQzqZaaHBDkDnzwNJ5POdHJzg//7P/jTn5p+8CJVULAtIiLSnn34\nITzzjPl9fr4ZNL/9trkosq58feH77+HBB2HGDOjevVmGWpWSUhu/H07ntwNmakhcUladz7VaLMR0\n9+O86BAGR4cQHeZXeRfHpUvh/POhsBD694dPPzW/irQQBdsiIiLt1caNcPvt9m0BAXDppfW/lpMT\nvP569ccLCswygW6N29DFMAzScgrYfyyH7/euZeehNAqKSmo/8bRAX/fy4HpgVBAetS1sHDAAXnkF\nfvvN/Oru3qjxi9RXrcH2unXrWLhwIb/99htJSUn885//5NZbby0/PmPGDP71r3/ZnTN8+HA2VNyx\nSkRERJpWbi5MmWLO2JZxdoYvv4SIiKa9l81mznjHx8PXX0NQUJ1OMwyDjJxTHDyaSewx83HwWCZH\nk9MA8PX1rfUars6ODOgZyODoEAb3Cia0qxeWs2uB22zwzjvwxz+Ch0fli9x9d53GK9Icag228/Ly\nGDBgALfeeiu33HJLpTe4xWJh/PjxfFBhlypnZ5XPERERaVaenmbu8S23mOkjYNbLHjGi6e81d66Z\nfgFmpZIVKyqlYhiGQeaJ/PKAOi4pk4NHM8nJq6EcXzWiQrucnr0Opk+PrjXXvU5PN+uJf/+9udiz\nrGa4SBtRa7A9ceJEJk6cCJiz2GczDANnZ2cC28CqZRERkU5l6lRzFvuaa8yZ55tuavp7fP45PPvs\nmeeHD8NFF5G95BMORg84M2N9NJOs3IIG3cLPy6285vWgXsH4eNZxU501a8zZ7KTTCyDfew8uuQSm\nT2/QOESaQ6Nzti0WC+vXrycoKAhfX19Gjx7Ns88+S0A7KIYvIiLS7g0dCtu3g79/81z/0ks5MX4i\nBzduJ87Nj4NufsS6+ZHxxBJzlrsBv+9dnRzoEeDBpNGDGBwdQniQT+XUkJoYhrm1/F/+YqaQVPT4\n4+aHEP2VXdqIRgfbEyZM4LrrriMyMpL4+HiefPJJxo0bx9atW6tNJ9myZUtjbyvSIvRelfZE79dO\n7vDhJrnMqcISjmTkcfT4KY5k5HEkI4/MqEm40ReX5OTyfiVenuQ5OGBkZ9d4PWdHK9383ene1aP8\n0dXLBavVAuSRcTSWjKP1H2fE5s10PSvQPjlwIIeeeYbinTvrf0GRakRHRzfq/EYH29dff3359/37\n92fIkCGEh4ezYsUKJk+e3NjLi4iICOC5dSs4OJA7aFCTXbOgqJSjx/M4knE6sD6eR8aJKnKsLRby\ne/XC5uaGW/whbC6unOrbD8NqX2bPycFKmL873f3d6dbVgx5dPQj0cT0dWDetxD//Gc/du3FNTMSw\nWEi+7TaS7rwTHFVoTdqWJn9HhoSE0K1bN2JjY6vtM3To0Ka+rUiTKpsh1HtV2gO9XzuB2FgzPSI3\n16yhfcst9b5EYVGJXUWQ2GOZHMs4ad/J6oavbw2l/Xx9wd8fq4cH/l18iAz2pVeYH73C/Iju5k+3\nAG8cz65zXYUme89+9RVcey2Wd94h9NJLCW3c1USqlJOT06jzmzzYTk9P59ixY4SEhDT1pUVERDqf\nrCyYNAkyM83nt95qbq2+YEGtp9psBrsOpfLTtng27Dlar3rWFTlYLUSUB9bDiA7zIzzYt3JgffIk\nJCY27aYx8fFmecM+fSofGzQIDh40a4SLtFF1Kv138OBBAGw2G4cPH2b79u34+/vj5+fHvHnzmDp1\nKsHBwSQkJPDYY48RFBSkFBIRkc5k3TpYvRoefRRcXFp7NB1HcTFMmwb799u317Ixy9H0E/z0Wzyr\ntyeQkXOqXrd0sFroEehTYcbaj/AgX5ydaii/B1BSAjfeCGvXmmUCr7iiXvet0rJl5k6YYWGweXPV\nr1uBtrRxtQbbmzdvZty4cYBZeWTevHnMmzePGTNm8MYbb7B7924++OADsrOzCQkJYdy4cSxbtgyP\nqorKi4hIx1NYCDNnmgHhxx/Dm2/CmDGtPaqOYc4c+M9/7Nv++Ed44olKXU+eKmTdjsP8tC2eA0cz\n63R5iwW6B3iXp4H0CvMjMtgXF+cG/OH7oYfM+tsAV10Fr70Gs2bV/zpg7lY5Zw4sWmQ+z8mB++83\nU2hE2pla/28aM2YMtrPL6lSwcuXKJh2QiIi0My+8cGbmdf9+GDfO/FpxBf+yZeYW4nXYMVAquOIK\nWLzYTM8AuPBCc6fE02XySkptbN53jJ+2xbNlfzIlpdX/vgbw93bj3J6B9Ao1Z617hnbBzaUJZobX\nrjWD6zI2G8yeDQcOwMsvg0Mts+IV7dsH118PZ1cUeecds3722LGNH69IC9KSXRERabgDB+w3PAHz\nz/4VA+2ffzaDp27dYMkSGDmyZcfYnk2cCBs3mjnbNht8+SWGiwsHjxznp23xrNtxmJP5RTVewsXJ\ngRHndGfs4EgG9AxqlsogjB4Nr74KDz5oX/f6tdegVy/4f/+v7tfauLFyoO3kBH/9q/5iIu2Sgm0R\nEWkYw4C774aiCsFeYCA8//yZ59nZ5q6GNpu5cG7MGLOqxty5yrWtq/794ddfyUg4xurfM/jpo80c\nTT9Z4ykWCwzoGcTYQRFcdE73ppm9rs1990HPnnDDDZCXZ7aNHQt33VW/68yYYabOfPSR+TwqCj75\nxNy8R6QdUrAtIiINk5tbecHa3/4Gfn5nnr/4ohlkl7HZ4Jln4IcfzEV04eEtM9Z2Kr+wmI17jvLT\ntnh2HkrFMGruH9bVi3GDIxk7OIIA31ZYOzVpEqxfb3719DS3eq/vTo4Wi5n3/+uvZoD91lvg7d08\n4xVpAQq2RUSkYby84JtvzIDqvvvg3HPNahQVzZtnzny/9JJ9+6FDqlpytqIi2LIF2/AL61Wuz9PN\nmdEDwxk7KIKY7v712/a8OQwaZAbKBQXQpUv1/QzDzO3v3bvyMS8vM53E3788P12kvVKwLSIiDWex\nwNSpMH68mTpwdmDk4gILF8Lll5v1ocu2+37vPQgObvnxtlWGwdE7ZvHTf7ay+rJpZITWPOPvYLUw\nrE8o4wZHMrR3KE6O9ViA2BJCa9heJiuLoA8/xGPnTvjlF9iyBfr2rdyva9fmG59IC1KwLSIijefj\nYz6qM368uejt9tuhe3czzUDOlOt7+zMObMsD/z6wdSccPwHn9AeL/aYx0WF+jDsvklEDwvH2aId/\nGSgqgpEj6b5nz5m2adPMmXC3GnauFGnHFGyLiEjL6NoVli83Nz+pSmmpOeM9Y0aHXjxZUmpjy/4k\nfvztkFmu71gSbNlj3yk93fw5OTnj7+3G2EERjB0cSY+gGj7QtHVlC2r3nPVad+82N0N69dXWGZdI\nM1OwLSIidffhhzB8uFkhoiEsluoD6RdeMDdrefdd8z4NvUcbZBgGsccy+fG3eH7emciJU4XmgZwc\n2PYbVFz46OSEy0XDGXF+TPOW62tphw6Z9dbPNniwWZNbpINSsC0iInXz++9w223mBiXz5pk7BjbV\nDPSvv5rXBNi0yVxk9/e/w803t9sFcqWlNuJTsvntQDKrt8dXXa6vpASsDkApFmDAqTTGPno3F91y\nTcuU62tJUVHw3/+au0sePmy2/b//Z9bP1mJZ6cAUbIuISO1sNrNecnGx+XjsMfjpJ1i1qmmu/z//\nY59ekptrLqj87jtzptujFcrY1VNRcSkHjh5nT3waexLS2ZeYQX4tlUTw96fbVZcxdvk/Gbt3AwGv\nLoQ7p7bMgFvDuefCgQMcXLSI/PBwBlx7bWuPSKTZKdgWEZHavf++uRNkRbff3nTX/+IL83pff23f\nnpICrq5Nd58mlJdfxN7D6exNSGdPQjoHj2XWul16GS83Z0YNDGfc4Eiiu/lheeAKs+54fTeAaY+c\nnckZMaK1RyHSYhRsi4hIzdLSzJnniiZONKtINJWyxZNvvQVz5kB+vlmj+YMPzLSVNiDzRD57EsxZ\n670J6SSkZte6yUxFNZbr8/XtHIG2SCekYFtERGq2aROcOnXmuZubmU/d1LnUFotZrWL0aJg+3Vws\n2b17096jjgzDICnjJHsPm7PWexLSSMnMq/d1fDxc6B8RwMCoYC4+twfeJ7NUX1ykk1GwLSIiNbvq\nKrM82913w48/wvz5EBnZfPfr2xc2bwbHan5FJSeb+eLTpzdZwG+zGcQnZ5mz1qdTQ7JyC+p9nWA/\nD/qFB9A/IpD+EQGEdvU6s6Pjr7/C2LEwdy488ki7XfgpIvWjYFtERGrXqxf88IOZ6tESG9JUF2jb\nbObCyR9+gG+/hUWLzBSMeipbzLj39Kz1vsTjnCosrvd1IoJ96B8RSL/wAPpFBNDVx73qjkeOwDXX\nmH8hePRRs7LLW2+pCodIJ6BgW0RE6sZigcmTW3cMr7xiBtoAn3wCGzbAkiUwcmSNp+XlF7EvMaM8\nJeTgsUyKS+q2mLGMg9VCdDe/8pnrvuFd8XKvQ7CcmwtXX20u9iyzeDFcd535VwMR6dAUbIuISPuQ\nkwNPP23flpgIY8aYqRlldbqB7NwCdsenlc9cx6fUbzEjgKuzI316+JfPXPfu7o+Lcz1/bdpsZq3w\n7dvt2x95RIG2SCehYFtEROzZbLB6NYwb17byin18zJns6dNhx44z7TYbecU2du89yo64VHYeSuVw\nak69L+/t7kK/iK7l+daRIV1wdLBWf4LNBhkZZg55UpL5deJECAk50ycxETZutD/v6qthwYJ6j09E\n2icF2yIiYu+99+DOO82Z19dfhx49WntEZ/TrB5s2UfTnx9j77sfs9AhiR/RgYm29sS35ufbzKwj0\ndTdnrSMC6B8RQLcAb3MxY1kQvXuXWQ3Fz6/yyTfcAJ9/br8RD5h55FdeeeZ5RIS52POqq8wPCAMH\nmlvRt5FyhiLS/BRsi4jIGamp8PDD5vfffGNW/fjwQ3NxXysqLbVx8FgmO2JT2Hkold+9L6D4hgiz\nSsqQC4DaZ+B7BHjTv4c//aKC6R8RQIBvhV0pFywwF38mJ5u51WVB9KefVl1P3MmpcqAN5gz32bp3\nh/Xr4cEH4X//Fzw96/SaRaRjULAtIiJnPPQQZGefeW4Y5mxsC7PZDBLTctgRm8KOuFT2JKRXrhYS\nEGDma1eR6mKxQK+sZM7Zs4n+hVn0O3YQr+Qj8M47MGh45RsePmzOQJ8tObnqAYaGVt1eXX9PT3j7\n7aqPiUiHpmBbRERMP/xgzmJX9PTTZipEMzMMg5TMXDPn+nTedU5eYe0nVgi0ewR6M6BnEAN7BXOO\nlxXP84fYVwCBqmeeofrgubr+ZXnZPj7m96Gh5tf+/Wsfs4h0Kgq2RUTE9PLL9s8HDoT772+222We\nyGdHXAo741LZEZdKes6p2k+qINDXnYFRwQyMCuLcnkH4ebuZBwyjcqm9MtXNPFdc1AhmEB0aam4Z\nX5U774SZM8G9mrraIiKnKdgWERHTl1+aucvPP2/mI//jH9VvLtMAJ08Vsjs+jR1xqeyIS+Fo+sl6\nne/j4WLOXEeZs9dBXTzO7M5Y0YYN5kLFqlRMkalo0iT4+Wcz6A4JqT2I9vCo+biIyGkKtkVExOTq\naqaN3HijuTDy/PMbdbmCohL2JqSbs9eHUolLyqpXrWt3FyfOiQxgYFQwA6KCCA/yqTq4PtuIEbB1\nq5mD7ednzlCHhkJwMLi5VX1OWR8RkSamYFtEROz17Ws+6slmM9h/JIPtpxc17j9ynJLSuu/S6ORo\npV94QPnsda8wPxxqqnNdk/POMx8iIq1MwbaIiDRKXn4RP22L57tNB+uVGlK2/fnAqGAG9AyiT4+u\nODup/rSIdCwKtkVEOqvMTHB2bnDd58TUHFb8coCftiVQUFRFzekqRAT7lC9q7B8RiLurU4PuLSLS\nXijYFhHprGbPhv/+F954w37XwxqUltrY9Psxvt14gF3xabX2D/HzZEBUUHnFEF9P18aOWkSkXVGw\nLSLSGa1cCR9/bH4/aRJMnWpu+OLjU2X37NwC/v1rLCs3x5FRQ4k+B6uF4f26MSQmhIFRwQR2UdUO\nEencFGyLiHQ2p07Bvffat8XFVSpnZxgG+48cZ8UvB1i/60iNix39vNyYeEEvLhsadabetYiIKNgW\nEel0/vIXiI8/89xqtaupXVRcyrqdh/l24wHikrJqvNQ5kQFcOTyG4f264djQyiEiIh2Ygm0Rkc4k\nMREWLrRvmz0bhg4lNTOX7zYd5IcthziZX1TtJVycHBg7KIIrL4whIti3mQcsItK+KdgWEelMevSA\nr78200gSErCFhbHjtvv49l9r2bw/qcZNZ0L9PbnigmguHdITDzfnlhuziEg7pmBbRKSzmTiRvK3b\n+PGxF1nhHErS0l+r7WqxwLDeoVxxQTSDo0OwWuuwg6OIiJRTsC0i0okkpGTz3S8H+WlbPIX+51bb\nz9PNmcuG9mTiBdEE+zWsDreIiCjYFhHp8EpKbWzae5QVvxystTZ2zxBfJl0Yw6gB4bg461eEiEhj\n1bp0fN26dVx99dV069YNq9XK4sWLK/WZP38+YWFhuLu7M3bsWPbu3dssgxURkbrLOpnPJz/t5o4X\nlvP8x/+tNtB2dLAyemA4L951Ka/MnsD4oVEKtEVEmkit/5rm5eUxYMAAbr31Vm655RYsFvt8vRde\neIGXX36ZxYsXExMTw9NPP8348ePZv38/ng3cAlhERBrGMAz2JWaw4peD/Hf3EUoKi2DdOggNheho\ncHAo7+vv7caE83tx+bAounipNraISHOoNdieOHEiEydOBGDGjBl2xwzD4JVXXuGxxx5j8uTJACxe\nvJjAwEA++ugjZs6c2fQjFhGRSopKSvlhSxwrfjloXxv74EHIyzO/JiXBuedy7vn9uXJ4NBeoNraI\nSLNr1N8J4+PjSU1N5bLLLitvc3V1ZdSoUWzYsEHBtohIM7HZDI6mn2D/kQxW/hzP7sRsnN3O+mvi\niRxzZ0jAxShl3JEdXDnEi/A772uFEYuIdE6NCrZTUlIACAoKsmsPDAwkKSmp2vO2bNnSmNuKtBi9\nV6WtKCguJTE9j4S0XA6n5ZKQnsepwhK7PqcKs888MQw8d+6gR+EJrjx+kEuyDuEY4Mee668lXe9r\naSP0b6y0B9HR0Y06v9lWwJyd2y0iInVjGAbHTxaSkJZLQpoZYCdn5WOraceZCiwWGHYyiZt2fs3A\n3FSsmOcdfPhhbO7uzTl0ERE5S6OC7eDgYABSU1Pp1q1beXtqamr5saoMHTq0MbcVaXZlsy16r0pL\nKCouJfZYJr8fTmffkQz2JR4nO7egQg9nvH2q37ExO9uc0e4eEshlw6KYeH4vgk5lQ95e+PJLs9Pk\nyUQ/9FAzvgqRutO/sdKe5OTkNOr8RgXbkZGRBAcHs2rVKoYMGQJAQUEB69evZ+HChY0amIhIR5WR\nc4p9iRnsS8zg98PpHErOpqTUVu/reLo507u7P84lHoQHePCHK8bg7HS62oifJ3zxBXz1FTz2GLz2\nWhO/ChERqYs6lf47ePAgADabjcOHD7N9+3b8/f3p3r07DzzwAAsWLKBPnz5ER0fzzDPP4OXlxfTp\n05t98CIibV1JqY345Cx+P5xRHmCn55xq0LW6BXjRt0cAfXp0pU+PrnQL8MZqtZTPEpYH2hVdcw1c\ndRVYVXVERKQ11Bpsb968mXHjxgFmHva8efOYN28eM2bM4L333uORRx4hPz+fWbNmkZWVxfDhw1m1\nahUeHh7NPngRkbYmJ7fgzKx1YgaxxzIpLC6t93VcnR2J6eZH33AzuO7d3R8vd5eGDUqBtohIq6k1\n2B4zZgw2W81/3iwLwEVEOhObzSAxLac8HWRfYgZJx3MbdK1gPw9zxrp7V/qGBxAe5IODamCLiLR7\n2o9XRKQODMMgLSuPg8cyOXj0OAePZhJ7LJP8opLaTz6Lk6OVXqF+9A3vWp4S0tgdHN3274fHH4fX\nX4eYmEZdS0REmo6CbRGRKmSeyDeD6tPBdeyxLE6cKmzQtfy83MoD6749utIztAtOjlXkVzdUaSkR\nzz4Lv/8OAwbAE0/AI4+ASwPTTkREpMko2BaRTi83v4jYY5kcOHKcg8fMWevjJ/IbdC0Hq4XIEF+7\nhYwBvu7NuvdA4Gef4fH77+aTwkKYOxcuuAAq7O4rIiKtQ8G2iHQqBUUlxB3LtEsHSc5sWJ41gLe7\nC316+Juz1uEB9Arzw9W5Bf9pfesterz0kn3b1KkKtEVE2ggF2yLSYRWXlJKQks3Bo5nlKSFH0k7U\neSfGs7k5O9IrzI/obn6nv/oT1MWjdXfM7d7d/rm3N7z6auuMRUREKlGwLSIdgs1mcCQtx27GOiE1\nm+KS+m8WA+YixshgX6K7+RN9OrAuq2vdotLS4OuvIT4enn228vFLLqHUwwOHvDzz+XPPQWhoy45R\nRESqpWBbRNodwzBIycy1m7GOS8qioAGVQcDMs+4R6EN0NzOo7hXmR0SwL46tVXovMdHcZv2LL2D9\nerDZwMEB5swBf3/7vi4uZF98Md6//ILTAw/APfe0zphFRKRKCrZFpE0rKCohMTWHhJTs8kd8Sja5\n+UUNvmaov2f5jHVMd396hnTBpSXzrGtis8HQoZCebt9eWgrffAMzZlQ6JfF//odST0+GDh/eMmMU\nEZE6ayO/XUSks7PZDJKPn+TwWYF1SlYuDUyxBiDAx90uxzo6zA8PN+emG3hDGQaUlICTk3271Wpu\nsf7OO5XP+fLLKoPtUl/f5hmjiIg0moJtEWlxObkFdgH14dQcEtNyGrSteUXe7i7EdPcjOsy/PMBu\n7GYxTaq0FDZuNNNDvvjCrIV9772V+02ZYh9sDxpktk2Z0nJjFRGRJqFgW0SaTVFxKUfSKsxUp2Zz\nOCWHrNyCRl/b3cWJXmFd7GasA1u7Mkh19u6F116D5cshNfVM+xdfVB1sjxsH48fDhAkweTJERrbc\nWEVEpEkp2BaRRrPZDNKy8zh8Op/6cKoZXCdl5Da4zF4ZiwVC/DyJCPYlPMiXiGDzEezn2fKVQRoq\nPR3eeqty+5o1cPx4lYseWbWqRYYmIiLNS8G2iNTLyVOFdnnVh0/PVuc3sBJIRd7uLkSG+BIe5FMe\nVHcP9GnZTWIaKjsbNmyAK66ofOziiyEgoPKiRycn2LYNLr20ZcYoIiItrh38BhOR1pKbX8SBI8c5\ncPQ4B44c51ByVoO3Ma/IydFKj0Afu6A6ItgXX0/XtpkGUp3UVPjqKzMd5McfzQWPx45VrnPt4HBm\n0aO3N0yaZOZfT5gAHh6tM3YREWkRCrZFBICSUhvxyVnlwfX+I8c5lnGy0dcN9vOwS/8ID/Ih1N8L\nh9aqYd1UbrgBPvvMLNVX0fLlVedhz55tBtjjxplpIiIi0iko2BbphAzDIDUrjwNHjrP/SAYHjh4n\nLimrwbstAni6ORMR7GMXWPcI9MHd1an2k9ujLl0qB9pQ/aLHgQPNh4iIdCoKtkU6gYrpIPuPZHDg\nSCYnThU26FqODla6BXiZAXWQL+GnA2t/b7f2lQJSm8JCWLkS3N3NyiBnu/FGePNN+7aYGLjoIrOG\ndkf6WYiISIMp2BbpYMrSQfYfOV4+c510PLdB17JaLIQH+RDT3Z+Ybv7EdPenW4B3621j3txKSmD1\navj4Y3OGOicHRo6sOti++GIIC4OuXWHqVDNFpG9fBdkiImJHwbZIO2YYBimZuWcWMTYyHaSrjzsx\n3fyI6eZP7x5diQrtgptLB00DOVtcnDkrnZZm3/7zz3DkCHTvbt9utcLOneDn13JjFBGRdkfBtkg7\ncvJUIQePZjZJOoibsyO9wvzo3d2cse7dvSt+3m1ot8WWFhEBjtX8k7h0KTz0UOV2BdoiIlILBdsi\nbZTNZpCYlsPu+LQmTQfpfTolpHugT/vZFKap7NsHn3wCd95ppoBU5OAA06bBK6+caQsIMNvGjm3Z\ncYqISIehYFukjTAMgyNpJ9h1KJVd8WnsOpTW4Fnrrj7u5UF1THf/zpUOcrbDh80A+5NPYPt2s83b\nG+bMqdz3xhvhn/80869vvNEMsqub7RYREakD/RYRaSWGYZCUcZJd8WnsjEtld3waWbkF9b6Om7Mj\n0afzrJUOcpa//a3qoPqTT6puHzbM3KhGdbBFRKSJKNgWaSFlta13HUpl56FUdh1Kq/dujEoHqacL\nL6y6ffNmiI2FXr3s2y0WBdoiItKkFGyLNKP07Dx2xqWWz16n55yq+8mGgUf2cfpnJNLfdoKY8/rS\n6+HZuDqf9b/thg1n8owN48xjxIiqZ2/XrYO//rVy/1Gj4NFHK/dfvRqefdb83sHB3F7cwwPOOw8e\nfLCKF50OW7eafTw9z3z19ja/NqW8PPjmG/jtN3jxxcrHL7gAIiMhPt58brWaqSE33ACBgU07FhER\nkSoo2BZpQpkn8k/PWpuz1ymZefU6383Zkf4RXTk3LYFzl75H1Nb/YsUwDzpOA+cHKp+UmGhuG362\n6nKNk5Lg228rt3t5Vd0/NRV+/LFye3Z21cH2pk1w1VWV2ydOhO++q9y+cSM8/rh9cO7hAYMHw223\nVX0D0AgAABwBSURBVO6fmQmrVsFXX8HXX8Op0x9g7r4beva072uxmLnXP/1kfp02DYKDq36dIiIi\nzUDBtkgjZOcWmAsaD6Wx81AqxzJO1ut8FycH+oUHcG7PQAb0DCIqzA/HWffCW2/V/SLVbaJiGM3b\n38Oj6va8aj5gVNf/2DFYs6Zy+5QpVQfba9eagfPZPv0UHnuscvtf/nJmZl5ERKSFKdju7AwDFi+G\n3bvh5pth4MDWHlGbdvJUYXlgvetQKolpJ+p1vpOjlb49unJuzyAG9Awiprt/5d0Y//jHqoPt6oLh\n+qrvDofV9a8uJSS3mvKE9e1fXXBeXf+PP6462LZ20N0uRUSkXVCw3dk99xw88YT5/auvwvvvm8Ge\nAJCXX8Tu+LTynOv4lOx6ne/oYKV3d38G9Azi3J6B9O7eFWcnB/OgYVQdyI4cCaNHmzO4ANdea6Zg\n9OlT9U0uvNCsrlF2LYvFfHTrVnX/ESPMFIyz+4eEVN1/9Gj44Qfz++Jic+Y6Lw+ioqruHxwMl11m\nBsW5uWbf3Fzw96+6f31nws/u360bXH+9Odtd3c9URESklSjY7uz+8AczqFu1CkpK4KabzBzdqhbW\ndXClpTaOpp/gUHIW/9mUSHxqLnlfxmKrx4yyg9VCdDe/08F1EH17dMXl7AWNBQXw3nvmh5s1a6oO\ncufOhXfeMT8I9e9f80179DAfdRUWVnlDl5oEBZmPurrySvNRV5Mnmx8kyoL4sgD9nHOq7u/nZ35g\nGDjQXOg4YoRmr0VEpM1SsN3Z9eoF8+eDkxOsWGG2PfSQuYjuxRc7bBBTXFLK4dQc4o5lEpeUxaHk\nLOKTsykqKQUgO9ucwfb1rXkjGKvFQq+wLpzbM4hzIwPpFxFQ/eYxp07BP/5hVgJJSjLb/vpXePnl\nyn3HjTMfnUFoqPmoq2nTzIeIiEg7oGC7s7NYzB32Vq2yb3/pJXPGcPLk1hlXE8ovLCYhJZu4pKzy\n4DoxLYdSW/1zoC0W6BnShXMjAxkQFUS/8AA83JxrP3HFCnOxX3q6ffubb5rl9lSGTkREpENSsC3m\nn+IDAszA+uTpahp3323mCrczuflFHErKIi7JDKrjkjI5lnGyUWsLw4N8ynOuz4kMxMu9AZue9OwJ\nGRmV2202s/TdNdc0fIAiIiLSZinYFtMll5i52xMnmjPar7/e5heaZZ7I51CyOVt9KDmLuKQsUrPq\nV9f6bF08XYkK64KlwI0wf3emThiFj6dr4wfbty9MnXqmHrabm/mB5uGHq1+YKCIiIu2egu3OZudO\neOopM084PNz+2ODB5oYkQUHmToFthGEYpGXlledWxyVlEncsi6zcgkZdN9DXnahQP6JCuxAV5kfP\nkC74ebsBsGXLFoD6BdppaWb6za23Qr9+lY8/+SSsXAn33msuQFXqiIiISIenYLszsdngnnvM7b2/\n/x7+93/NxZDOFXKOzw7AK/r/7d17VJR1/gfw9wzDZUZgQAWZAWRGRHTxQoEorCWVF8qktW2zdrPW\nWt3dtFovxy23DVKP6e5mWXax2x7azqqnbbMsV+u3psVS4W7iBUlDUBEYLnJzuMhlnt8fXxgYUUHm\n8szI+3UOx5kvM8/zVec8582X7/P5FBUBDQ1AfLwTpyih7PyFS7aC1MLc3DrgYyoUQPjwAETrRaCO\n1gdjlD54YNtBLqesTNzouHUr0NwsmrS8917v102cCJSXX7mkHREREV137A7bmZmZWLNmjc1YWFgY\nyrqqLZD7yMoSQRsQoXD1arGanZbW93srKkTt5MpKYOfOa6qUIUkSWlrbUWduQZ25BbUXWqyP68wt\nqDU3Wx/XNLRYK4IMhJdSgZGhWutqdbQ+GIawoCtXCLFHZSWwZo0o0XfxYvf4tm1ARgYQE9P7PQza\nREREg4pDVrbHjh2L/T3aLXu50RYE6nT+vNgf3NPcuf0L2hcuAHfcAZw6JZ7ffjukd99Fy0/uvnx4\nvtCMusYWm3B9sW3gAfpKvFVKGMOCxIq1XqxYR40I6m4a42wdHb2DNiB+g/DSS8DLL7tmHkREROS2\nHBK2vby8EMr9p+5t9WoRuLuo1aKpSg89V6BtAvSu3ag1eaFu5E2oU/mh1luNurX/xMWdpwCj0SXT\n1/h6w6gLEivWnfusI0IC4XVpq3NX0umARYvEzaRd9Hpg1SoxTkRERIOeQ8J2UVERwsPD4evriylT\npmD9+vUwuiiEUT9Ikmih7eMDtHbufX76aViiDDj8Qzk+/28Rfig9f5UV6FBgWjpw/Ljt8LFjgFYr\nOvo5UKDGtzNUB3euWA9F2FB/KJUyVUfJzxf/hpfraLhqldirrdOJetkLFwJ+DqheQkRERNcFu8P2\n1KlTkZWVhbFjx6KiogLr1q1DSkoK8vPzMdTBIYwGSKEQFUh+8QtgyRLUnTPh/5LmYO+mXTDV9LNU\nXnQ04OsLHM4DuprBjB7d76DtrVIiaIgfggP8EOQvvoID1NbHQf5+CO78U+PnDYUblB1UnzgBbNgA\nfPABMHNm78Y/ABAZCezbByQl2d5oSkRERARAIUn2tPvorampCUajEU8++SSWLVtmHa+vr7c+/uGH\nHxx5SuoHi0VCoekCvv6+EscKK9GuGtgNg961tdAUFKBt+HC0jotFgNpbfPl5I0Ct6n6u9oa/2huB\najHu5+3lFgG6PzQFBdC/+SaCvvrKZrzgnXfQOGGCTLMiIiIiOcT0KHig1Wqv+f0OL/2n0WgQFxeH\nwsJCRx+aBsDc3Ibcwmp8c6IaVQ2ddamvErRVXoo+A3RIxUj4xhjgq/b1mADdX8qWFoxZsgSqrk6a\nPejefhuFL74ow6yIiIjIUzk8bLe0tKCgoAC3XqU0XGJioqNP239VVUBxsagVfZ3+2l+SJBwtqsSe\n3EJ8ffwc2jssgNIPQUG99xJ7q5T48fhIzJ48GsawIPu3cBQUiPJ2I0fa8TeQ2cqVonRfTzfcgKAV\nK+T97BJdQVcTJn4+yVPwM0uepOfujIGwO2yvXLkS6enpiIyMRGVlJdauXYvm5mY89NBD9h7a8dav\nB555RpRs+9GPRDe/yEi5Z+UwDY0X8e/virD34CmUnjwDtLWJbpCXERESgLTJo3HrjUbHNXcpKRG1\nuC0W8W/r7lsumpoAjab3+OOPo/0vfxGr21OmiOY/d9zh9u3riYiIyP3YHbZLS0tx//33o7q6GiEh\nIUhOTsY333yDSHcMsXFxImgDorLGnXcC2dlAQIC887KDJEnIP12FPbmFyMkvQVu7RYTdI4eBC2ZR\nhSQuDtBo4K1SIiUuEmlJoxFnCHHsFpCaGmD2bODcOfH8ppuAXbvEn+7m0CEgM1N0ejx4sHeIDgpC\nyYoVaBs6FGOWLmXIJiIiogGzO2xv27bNEfNwLLMZ8PfvNVw7/Tb8Z9w0lNY1Y3hbE6KLKjFq/s8R\n+PGHgMqzOtdfaLqIfd8VY+/BUyiparD9ZlGRCNoAYDJBX3YaaRtW4dZb4qH1d1JZui1bxBaSLvX1\nooLH9u3AT37inHNeq7w8EbI/+qh77JNPRHOfS5yfM0c8YNAmIiIiO3hWwrwaSQK+/lp07tuzR+zL\nDg5G88U25BwrwYHDZ3D4lAkWr0hgWI/3lQAh92Vi1F2zRF1nnWjzPSxQ7XY3/0mShO/PVmNPbiG+\nOnpWrGJfqqkJOHkSKsmC5IZzSKspxIT75kIxd6pzJ/eHP4j25a+80j128SLw05+KED5mjHPP35el\nS23n1iUzU/yGw83+r4mIiOj64Plhu6UF2LFDtMb+3/8AAO0KJb57/k3sj/sxcr8vtW3UkpYmQnnX\nZne1GlVhEagqKMW3BaXWl13aWGWULhi6YQGyNFYxN7dif95p7MktxJmKq2/SDys4jLTS/+G2umIE\ntbcAw4YBGzc4f5JeXuL/QK8XwbvL2rXyB21AbKW5HJUKqK4GQkJcOx8iIiIaFDw/bD/2GPDWW7BA\nge81IdgfZEC2diQufH4S6IjovWLp7S0akGRni2okSUmX7fjX0HQRhwpNOFRoso6pfVSdLcOHWkN4\nZKgWKie0DJckCSdKzmNPbiGyj569QmdHwUupwNQfRSAtZhgmblsNZfXp7m9u3CgCtysoFKItfFgY\nsHgx8NvfAk895Zpz9+Xhh4HnnhM3cQLi/z0zU/zwxVVtIiIichKPD9tn774f+3cdxIGgKFR6D+n+\nhlIJNDf3qjYxSheEpLHhOD8mBKeaJJytbRKl8fqhubUdx89U4/iZauuYt0qJqBFaROuHii0o+mAY\nwoLg6zOwf9rGzlXsvQdPodhUd9XXjggegtmTozEjYRSCA9RiMD9fVF3505+AxETRPtzVHn5YtDZP\nSHBtkD18GHj9dbGVyPuSWuK+vuIHgXfeEd00GbKJiIjIBTwjbF+8COTkALfcAgA4X9+EL4+cwf68\n0ygqqwViUoC6OkABIHQEYDQCw4dbw1RokAap8QZMn2TAyBGdnX9mTgQAtLV34GxFPYrKa3GqrBan\nympQXF531ZXkntraLSgsrUVhaa11TKlQICIkQATwrn3g+mAMUV++rrckSfjhXA325BbiyyNn+lzF\nThobjrSk0YgfHdZ7W4tGA6xbByxYIKqSKB2/6t4vSUlX/t7Ro0BEBBAc7JhzHTkiAvQ//ymeJyYC\njzzS+3WLFgG//jVDNhEREbmMe4ftsjKxUrl1Kxpr6pGzcx/2lzfjaHElrE3mFQpgdDRQUwsYDKKh\nCoAAtQ+mTRiJ1HgDxo4cfsW91t4qL0SHD0V0+FDM7ByzbN+O0inTUVTf2iOE18Lc3NqvaVskCWcr\nG3C2sgFf5J22jocNHdIZvEUIjwgJxKEfyrEntxBF5VdfxQ7RajB7cjRmJkZjaKC670nExvZrri5X\nWAjcdpuo/71nDxAePvBjHT8u6qZ/8IHt+Lp1wIMP9l7d9vIa+LmIiIiIBsA9w3ZuLvDii2j7xwf4\nrzoU+4PG4GBsONre/JdoRnMpnR7Q6eGj8sKUceGYPikKCbH6a99LbbEAq1ZB+fzziJw7F5Effojp\n8QYAYvW5qq4Jp8pqUNQZvovKa3G+obnfhzfVNMJU04ic/HP9er1SocDksXqkJY3GjTE6WW7OdCiT\nSdTirqoSX8nJwN69wLhxAzteQUHvoA0Ap08DO3cCP/uZXdMlIiIispfbhW2LRUL+W9ux/8tTyBk9\nF2avHlsvzp4VlS161MRWKhSYFD0C0ydFITkuEho/78sctR+amoAHHgA+/FA837ULWLECePFFAIBC\noUBo8BCEBg9Bclx3w546cwtOldZYV8CLympRXmMe2Bw6DddqMCtxFGYmRmO49jIdDns6cgSIiQHU\n/Vjtltuzz4oa4F1KSoBp00St6+Tkaz/evHmiS+XRo91jCQnixseuOtlEREREMnKbsH3aVIcvDhXj\nyyNnUa0eBwSbbF/grRKt1S3iZsbR4cFInWTATROj+retoi8Wi1gR7WnzZhFklyy54tuC/P2QEKtH\nQqzeOtbY3IpiU51NCD9X1YAOi3TF4ygVCiSM0eH2KaORMEbfv1XshgZxo5+fn2gqc8cdfb9HTps2\nidXtnTu7x2pqRPOboiIgNPTy7zt2TGwRurRRkVIJZGQA99wD3Hgja2YTERGR25EvbH/7Lao+3oMD\ns36G/XmnbetHD/EXwauyUgQsowGIiERYqBapkwxIjTcgPCTQsfPx9xer2VOmiDbeXR5/XNxweQ1B\ndojaB+ONoRhv7A6PrW0dOFNRZ139PlVWg3NVFxDk74vpkwyYmTgKIUFDrnLUy8jIAMrLxeM5c4D5\n84Ft29w3bKrVwPvvix9e3nije3zDhssH7WPHgDVrxHs2bAB+//ver5k3D/jsM2DGDPf9exMREdGg\nJUvY3pM8B/srW5GvCQFqDwBBQb1fFBsLGI3QGiJw08QopMYbMCZymHO7OoaHiy0N06YBjY1izGgE\noqPtPrSPtxdiIoYhJsJBNa/z8kSJu56io90/cKpU4qZXnU5sK1m9WnR37KlnyO7y5z8Djz4KBATY\nvlapFCvjRERERG5IlrD9ilkLdG1FPn0aiI+3+b6vtxemTp+E1HgD4keHOaVpzBXFx4uOlOnpQEqK\n2MM9fLjrzt8fFosInpYe9cGjomw7N7ozhUJs+Zg+HUhNtf1eQQEwcSK6y810On9etFt/8klXzZKI\niIjIbvLv2S4tBcaNg5faD/Gjw5Aab8CUceFQ+w7wRkdHmDMH+Ne/RBj09ZVvHlfy2Wei5XxPL7/c\nq4GP2+usm25j3DgRwL/4wnY8Pr7XD2VERERE7k7esB0aitiEcUi9ayqmTTIgyL9323TZzJol9wyu\nLC0N+OgjsZ/8zBmxCj93rtyzcpzMzO6wPWmSeH7XXe6/RYaIiIjoErKE7fAxUUi9+1ZMT5sK3bCA\nvt/gTiQJOHCg9/YHV0tPFzcFPvfc5bslerKbbxY3Uc6YIf6ecnXBJCIiIrKTLGH7tX+sd+6Njs7S\n1gY89hiwdavYP/zoo/LOR6MB1q6Vdw7OsmWL3DMgIiIispssS4YeGbTr68Ve7q1bxfPHHhP7uomI\niIiIroC/n++vM2eAnJzu5xYLcO+9ooOjKzQ1ueY8REREROQwDNv9NXEisH277f5hs1msdpeVOffc\n5eWig2JGBtDc7NxzEREREZHDMGxfizvvBF54wXYsKAhob3fueVesAKqqRKOX8eNF6T8iIiIicnsM\n29fq8ce7Ox7OmgVkZwMjRzrvfP/+t2jB3qWoCPj+e+edj4iIiIgcRv6mNp7ohRdE85VFiwBvJzbf\naW0VJfB6io+XvwoKEREREfULw/ZAqFSuCbybNgEnTtiOvfaaOD8RERERuT1uI3E0SQJOnnTMsebP\nF/vEuyxaBEyd6phjExEREZHTMWw7UksL8MADQGIicOyY/cczGoFdu0Rr9oQE0S2SiIiIiDwGw7aj\nVFeL9uJ//ztw4YIoCWgyOebY6enAwYPAsGGOOR4RERERuQTDtqPs3An85z/dz8+eFSHZUc1oPLHr\nJhEREdEgx7DtKI880vumyYMHgQULRLdJIiIiIhp0GLYdRaEANm8G0tJsx0tKgIaG/h3jxAmxGl5Y\n6Pj5EREREZHLMWw7kkoF7NgBTJggnt99N7B/v+gy2RdJEjW1d+0SXSKffVbccElEREREHoth29EC\nA4FPPhFh+f33AY2mf+/bsUN0iwSAixeBzExg926nTZOIiIiInI/dUZxh5EjgmWf6//r6emDZMtux\n224D5s1z7LyIiIiIyKW4su1qHR1AXZ3tWEaGbZlAb2/glVd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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "text/plain": [
- ""
- ]
- },
- "execution_count": 31,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "def plot_kalman_filter(start_pos, \n",
- " sensor_noise, \n",
- " movement,\n",
- " movement_noise):\n",
- " n = 20\n",
- " zs = []\n",
- " ps = []\n",
- " \n",
- " dog = DogSensor(start_pos, velocity=movement, measurement_variance=sensor_noise)\n",
- " random.seed(303)\n",
- " pos = (0., 1000.) # mean and variance\n",
- "\n",
- " for _ in range(n): \n",
- " move_error = random.randn() * movement_noise\n",
- " dog.x += move_error\n",
- " \n",
- " z = dog.sense_position()\n",
- " zs.append(z)\n",
- "\n",
- " pos = update(pos[0], pos[1], z, sensor_noise)\n",
- " ps.append(pos[0])\n",
- "\n",
- " pos = predict(pos[0], pos[1], movement, movement_noise)\n",
- "\n",
- " plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
- " plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n",
- " plt.legend(loc='best')\n",
- " plt.show()\n",
- "\n",
- "interact(plot_kalman_filter,\n",
- " start_pos=(-10, 10), \n",
- " sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n",
- " movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
- " movement_noise=widgets.FloatSliderWidget(value=.1, min=0, max=.5))"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Exercise - Nonlinear Systems"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Our equations are linear:\n",
- "\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",
- "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 32,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "#enter your code here."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Solution"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 33,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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A3bqp39fdu0CVKsDOneIJu+7nDZmvqVPFZ0KdOqIOuJmwvCAcECPis2cDrVop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- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30\n",
- "movement_variance = 2\n",
- "pos = (100,500)\n",
- "\n",
- "zs, ps = [], []\n",
- "\n",
- "for i in range(100):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- "\n",
- " Z = math.sin(i/3.)*2\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- "\n",
- "plt.plot(zs, c='r', linestyle='dashed', label='input')\n",
- "plt.plot(ps, c='#004080', label='filter')\n",
- "plt.legend(loc='best')\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Discussion"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "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 prediction 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": "markdown",
- "metadata": {},
- "source": [
- "## Exercise - Noisy Nonlinear Systems"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Implement the same system, but add noise to the measurement."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 34,
- "metadata": {
- "collapsed": false
- },
- "outputs": [],
- "source": [
- "#enter your code here"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Solution"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 35,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "data": {
- "image/png": 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AWrWAVavYzLjEs2esa+bw4cDixSxQJ0VeSpkymQfgkZEsDlm8mNrXk1wrXAsz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BxHRjhBEERRQJURPnq0/u+DMCwWLeKrpTx6pFoucOdOFpIiEjE1lGPHmPa8vz/rW6QlrzPICCcY\nsbFMQ1SKpSWTKSIIgiAKFxUqsCIpQUFsu1Ej9iKKLxynecl6+ZLy9vbAiBHsBVAxPx1DRjjBKFWK\naYGGhjKPeFyc5tnUBEEQhOEgErFS9YsWMW3mZctoPC9OiMVM7Sw4mL1CQlheQFKSrI25ee4cbYqV\nVok8QUY4IcPcHPD0ZC+CIAii8OLjAxw+XNB3QRQEQiEwYACQkCDbd/cuv42rK03MDAAK7CEIgiAI\ngigqCATKlTMvXuRvZxeKQugV8oQTBEEQBEEUJSpX5ksLJiYyhZzQUCAsDKhZU/35EgkQEQG8ecMK\n9nzzDeDsnL/3XAwhI5wgCIIgCKIooegJNzUFVqzQ/PyOHYEzZ2Tbc+cCCxZQyXkdQ+EoBEEQBEEQ\nRQlFLe/gYO3Ot7bmby9Zwo8xJ3QCTWkIgiAIgiCKErVqAcOGMY945cpA9eranW9hobyPKq7qHDLC\nCYIgCIIgihKVKwNbtuT+/P79WXVNKZMn5/2eCCUoHIUgCIIgCIKQ0bYt0Lcv+7+PDzBrVsHeTxGF\nPOEEQRAEQRBFleRkFtPt6gqUKQOULcsMa3UIhcDff7MS9iIRlarPJ8gIJwiCIAiCKKqEhjIjXErZ\nssD795qda2ycP/dEAKBwFIIgCIIgiKJLaCh/mwr1GAxkhBMEQRAEQRQ1IiOBX34B2rfn7y9TpmDu\nh1CCwlEIgiAIgiCKGomJwOzZyvvJE24w6NwTznEcfH19IRQKcfjwYV1fniAIgiAIgsgJd3fVMd1k\nhBsMOjfCV6xYAZFIBAAQCAS6vjxBEARBEASRE0ZGgIcHf5+NDeDlVTD3QyihUyP87t27WLNmDbZt\n26bLyxIEQRAEQRDaoli+fv164JtvCuZeCCV0ZoQnJCSgf//+8PPzg4ODg64uSxAEQRAEQeQGRSM8\nOLhg7oNQic4SM8eMGYNvv/0WHTp00NUlCYIgCIIgiNzSpQvg5ARUqsQMcnf3gr4jQg4Bx3Fcdgfn\nzZuHpUuXqr3ApUuXEBISgt9++w0BAQEwNTUFx3EQiUQ4ePAgevTowWv/5cuXrP+/fPkyj7dPEARB\nEARBEPrB09Mz6/+2trZ5upZaIzwmJgYxMTFqL+Dm5oZx48Zh586dEMqVNRWLxRAKhWjcuDGuXr2a\ntZ+McIIgCIIgCKIwojcjXFPCw8MRFxeXtc1xHGrUqIFVq1aha9eucJdb/pA3wvN680TRJSAgAABQ\nt27dAr4TwpChfkJoAvUTQhOonxCaoEs7Vicx4S4uLnBxcVHa7+bmxjPACYIgCIIgCIKgsvUEQRAE\nQRAEoXfyrWy9RCLJr0sTBEEQBEEQRKGGPOEEQRAEQRAEoWfICCcIgiAIgiAIPUNGOEEQBEEQBEHo\nGTLCCYIgCIIgCELPkBFOEARBEARBEHqGjHCCIAiCIAiC0DNkhBMEQRAEQRCEniEjnCAIgiAIgiD0\nDBnhBEEQBEEQBKFnyAgnCIIgCIIgCD1DRjhBEARBEARB6BkywgmCIAiCIAhCz5ARThAEQRAEQRB6\nhoxwgiAIgiAIgtAzZIQTBEEQBEEQhJ4hI5wgCIIgCIIg9AwZ4QRBEARBEAShZ8gIJwiCIAiCIAg9\nQ0Y4QRAEQRAEQegZMsIJgiAIgiAIQs+QEU4QBEEQBEEQeoaMcIIgCIIgCILQM2SEEwRBEARBEISe\n0akRfufOHbRr1w7W1tawsbFBkyZNEBMTo8u3IAiCIAiCIIhCj5GuLnT79m188803mDVrFlavXg0T\nExM8efIExsbGunoLgiAIgiAIgigS6MwInzp1KiZMmIDZs2dn7atYsaKuLk8QBEEQBEEQRQadhKN8\n/PgRt27dgrOzM5o2bQonJyc0b94cFy9e1MXlCYIgCIIgCKJIoRMj/M2bNwCAn376CSNGjMC5c+fQ\nrFkzdOjQAY8ePdLFWxAEQRAEQRBEkUHAcRyX3cF58+Zh6dKlai9w+fJlGBkZoWnTppgzZw4WL16c\ndaxx48aoWbMmNmzYkLXvy5cvOrhtgiAIgiAIgig4bG1t83S+2pjwqVOnYtCgQWov4ObmhsjISACA\nl5cX71jVqlUREhKSpxskCIIgCIIgiKKGWiPczs4OdnZ2OV7E3d0dLi4uCAoK4u1/8eIFfHx88naH\nBEEQBEEQBFHE0Ik6ikAgwMyZM/HTTz/B29sbNWvWxIEDB3Dnzh1eKAqQd9c9QRAEQRAEQRR2dCZR\nOHnyZKSmpmL69OmIiYlB9erVcfr0adSoUUNXb0EQBEEQBEEQRQK1iZkEQRAEQRAEQegenZat14QN\nGzagfPnyMDc3R926deHv76/vWyAMhGXLlqFevXqwtbWFo6MjunTpgqdPnyq1W7BgAcqUKQMLCwu0\natUKz549K4C7JQyFZcuWQSgUYuLEibz91E+IiIgIDB48GI6OjjA3N0e1atVw9epVXhvqJ8WbjIwM\nzJkzBxUqVIC5uTkqVKiA+fPnQywW89pRPyleXL16FV26dIGrqyuEQiF27Nih1CanPpGamoqJEyfC\nwcEBVlZW6Nq1K8LCwtS+r16N8P3792PKlCmYN28eAgMD0bhxY/j6+uLDhw/6vA3CQLhy5QomTJiA\nmzdv4uLFizAyMkLbtm0RGxub1ebXX3/FypUrsW7dOty9exeOjo5o164dEhMTC/DOiYLi1q1b8PPz\ng7e3NwQCQdZ+6idEXFwcmjRpAoFAgFOnTiEoKAjr1q2Do6NjVhvqJ8TSpUuxefNmrF27FsHBwVi9\nejU2bNiAZcuWZbWhflL8+Pr1K7y9vbF69WqYm5vzni+AZn1iypQpOHLkCPbt24dr164hPj4enTp1\ngkQiyf6NOT1Sv359btSoUbx9np6e3OzZs/V5G4SBkpiYyIlEIu7kyZMcx3GcRCLhnJ2duaVLl2a1\nSU5O5qytrbnNmzcX1G0SBURcXBzn4eHBXb58mWvZsiU3ceJEjuOonxCM2bNnc02bNs32OPUTguM4\nrlOnTtyQIUN4+wYNGsR16tSJ4zjqJwTHWVlZcTt27Mja1qRPxMXFcSYmJtzevXuz2nz48IETCoXc\n2bNns30vvXnC09LScP/+fbRv3563v3379rhx44a+boMwYOLj4yGRSFCyZEkAwNu3bxEVFcXrM2Zm\nZmjevDn1mWLIqFGj0KtXL7Ro0QKcXCoL9RMCAI4dO4b69eujT58+cHJyQq1atbB+/fqs49RPCADw\n9fXFxYsXERwcDAB49uwZLl26hI4dOwKgfkIoo0mfuHfvHtLT03ltXF1dUbVqVbX9RmfqKDkRHR0N\nsVgMJycn3n5HR8esYj9E8Wby5MmoVasWGjVqBABZ/UJVnwkPD9f7/REFh5+fH968eYO9e/cCAG+p\nkPoJAQBv3rzBhg0bMG3aNMyZMwcPHjzIyhsYP3489RMCADBu3DiEhoaiatWqMDIyQkZGBubNm4cx\nY8YAoPGEUEaTPhEZGQmRSKRUW8fJyQlRUVHZXltvRjhBqGPatGm4ceMG/P39lWKxVKFJG6JoEBwc\njLlz58Lf3x8ikQgAwHEczxueHdRPig8SiQT169fHkiVLAAA+Pj54+fIl1q9fj/Hjx6s9l/pJ8WHN\nmjXYtm0b9u3bh2rVquHBgweYPHky3N3dMWzYMLXnUj8hFMlrn9BbOIq9vT1EIpHSjCAqKgqlS5fW\n120QBsjUqVOxf/9+XLx4Ee7u7ln7nZ2dAUBln5EeI4o+N2/eRHR0NKpVqwZjY2MYGxvj6tWr2LBh\nA0xMTGBvbw+A+klxx8XFBV5eXrx9VapUQUhICAAaTwjGkiVLMGfOHPTu3RvVqlXDgAEDMG3atKzE\nTOonhCKa9AlnZ2eIxWLExMTw2kRGRqrtN3ozwk1MTFCnTh2cO3eOt//8+fNo3Lixvm6DMDAmT56c\nZYBXqlSJd6x8+fJwdnbm9ZmUlBT4+/tTnylGfPfdd3jy5AkePnyIhw8fIjAwEHXr1kW/fv0QGBgI\nT09P6icEmjRpgqCgIN6+Fy9eZE3saTwhALaKJhTyTR+hUJi1skb9hFBEkz5Rp04dGBsb89qEhoYi\nKChIbb8RLViwYEG+3bkCNjY2+Omnn+Di4gJzc3MsXrwY/v7+2LZtG5WzL4aMHz8eO3fuxMGDB+Hq\n6orExEQkJiZCIBDAxMQEAoEAYrEYv/zyCypXrgyxWIxp06YhKioKf/75J0xMTAr6TyD0gJmZGRwc\nHLJejo6O2LNnD8qVK4fBgwdTP/l/e3fIokAQhnH8XUUcLSuYNrlYtMgW7Saj2WqzmEyyBjeaRZvg\nlzDKBj+DFqugVdCwGN5LJyfHneWYE/z/YNoLM+EJTxhmICIipVJJoiiSdDotnufJer2W0Wgkw+FQ\nGo0GOYGIiOz3e1kul1KtViWTyUgcxxKGoXQ6HWm1WuTkTV2vV9ntdnI6nWSxWEitVhPXdeV2u4nr\nuk8zYYyR4/Eos9lMgiCQ8/ksvV5PCoWCTCaTn6+t/O3DLs/N53P1fV+z2azW63XdbDa2j4AX4TiO\nplIpdRznYUVR9DA3Ho/V8zw1xmiz2dTtdvtPJ8ar+PpE4SdygtVqpUEQqDFGK5WKTqfTbzPk5L1d\nLhcdDAbq+77mcjktl8sahqEmSfIwR07eSxzH9w7ytZd0u937zLNMJEmi/X5fi8Wi5vN5bbfbejgc\nft2Xb+sBAAAAy6x/Ww8AAAC8O0o4AAAAYBklHAAAALCMEg4AAABYRgkHAAAALKOEAwAAAJZRwgEA\nAADLKOEAAACAZZRwAAAAwLIPWAJSxoBEgGwAAAAASUVORK5CYII=\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "sensor_variance = 30\n",
- "movement_variance = 2\n",
- "pos = (100,500)\n",
- "\n",
- "zs, ps = [], []\n",
- "\n",
- "for i in range(100):\n",
- " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
- "\n",
- " Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
- " zs.append(Z)\n",
- " \n",
- " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
- " ps.append(pos[0])\n",
- "\n",
- "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
- "p2, = plt.plot(ps, c='#004080', label='filter')\n",
- "plt.legend(loc='best')\n",
- "plt.show()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### Discussion"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "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 practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Summary"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "This information in this chapter takes some time to assimilate. 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."
- ]
- }
- ],
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- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
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- "name": "ipython",
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diff --git a/05_OneDimensional_Kalman_Filters.ipynb b/05_OneDimensional_Kalman_Filters.ipynb
new file mode 100644
index 0000000..a5900fb
--- /dev/null
+++ b/05_OneDimensional_Kalman_Filters.ipynb
@@ -0,0 +1,2470 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# One Dimensional Kalman Filters"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "#format the book\n",
+ "%matplotlib inline\n",
+ "%load_ext autoreload\n",
+ "%autoreload 2\n",
+ "from __future__ import division, print_function\n",
+ "from book_format import load_style, figsize\n",
+ "load_style()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## One Dimensional Kalman Filters"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the discrete Bayes filter - rather than going into the theory we will just develop the code step by step."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Tracking A Dog"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As in the Discrete Bayes 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 reasonably 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. Furthermore, 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 modeling 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. We will talk about this in great detail later, but we need to model two kinds of noise. The *process noise* is the noise in the physical process. Something moving at a notionally 'constant' velocity will never maintain a perfectly constant velocity. Undulations on the ground, wind, and a host of other factors mean that there will always be slight variations in the velocity. The second noise we want to model is the noise in the measurement as no measurement is perfect."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function, division\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy.random as random\n",
+ "import math\n",
+ "\n",
+ "class DogSensor(object):\n",
+ " \n",
+ " def __init__(self, x0=0, velocity=1, \n",
+ " measurement_variance=0.0, process_variance=0.0):\n",
+ " \"\"\" x0 - initial position\n",
+ " velocity - (+=right, -=left)\n",
+ " measurement_variance - variance in measurement\n",
+ " process_variance - variance in process (m/s)^2\n",
+ " \"\"\"\n",
+ " self.x = x0\n",
+ " self.velocity = velocity\n",
+ " self.noise = math.sqrt(measurement_variance)\n",
+ " self.pnoise = math.sqrt(process_variance)\n",
+ " self.constant_vel = velocity\n",
+ "\n",
+ " def sense_position(self):\n",
+ " pnoise = abs(random.rand() * self.pnoise)\n",
+ " if self.velocity > self.constant_vel:\n",
+ " pnoise = -pnoise\n",
+ " self.velocity += pnoise\n",
+ " self.x = self.x + self.velocity\n",
+ " return self.x + random.randn() * self.noise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The constructor `__init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `sense_position()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense_position()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. and a standard deviation of 1.0. *Variance* is defined as the standard deviation squared, so in `__init()__` we take the square root of the variances to get the standard deviation. Therefore the expression `self.x + random.randn() * self.noise` computes a simulated measurement with the variance that we desire. \n",
+ "\n",
+ "Let's look at some example output for that."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 1.5537\t 0.1833\t 1.6322\t 0.4279\t-0.3008\t\n",
+ "-0.8023\t 0.6588\t 0.6328\t-1.2508\t-1.5291\t\n",
+ "-0.0836\t 0.5262\t-0.3430\t-0.0375\t 0.6807\t\n",
+ "-0.6530\t-1.1242\t-0.1033\t 0.8448\t-0.1283\t\n"
+ ]
+ }
+ ],
+ "source": [
+ "for i in range(20):\n",
+ " print('{: 5.4f}'.format(random.randn()), end='\\t')\n",
+ " if (i+1) % 5 == 0:\n",
+ " print ('')"
+ ]
+ },
+ {
+ "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 `DogSensor` class. We will start by setting the variance to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal, so the results should be a straight line."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
+ ]
+ },
+ {
+ "data": {
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jI0Pl5eVn/Hdu2LBBNptNra2tkqSLLrpIzz//vJqbm2Wz2cz/vTnjPffcM+os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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import book_plots as bp\n",
+ "\n",
+ "dog = DogSensor(measurement_variance=0.0)\n",
+ "xs = []\n",
+ "for i in range(10):\n",
+ " x = dog.sense_position()\n",
+ " xs.append(x)\n",
+ " print(\"%.4f\" % x, end=' '),\n",
+ "bp.plot_track(xs, label='dog position')\n",
+ "bp.show_legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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 position is 0.0 + 1, or 1.0.\n",
+ "\n",
+ "Now let's inject some noise in the signal."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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GowEAoFKp0axxJCJDu6BlUHs4ObrYuNVEd8dwRkRERETVRkQw/kPgZBowvDcw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\niIiIiIhIHfD/uwzs3X4GyvYAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def test_sensor(measurement_var, process_var=0.0):\n",
+ " dog = DogSensor(measurement_variance=measurement_var, \n",
+ " process_variance=process_var)\n",
+ "\n",
+ " xs = []\n",
+ " for i in range(50):\n",
+ " x = dog.sense_position()\n",
+ " xs.append(x)\n",
+ "\n",
+ " bp.plot_track([0, 49], [1, 50])\n",
+ " bp.plot_measurements(xs, label='Sensor')\n",
+ " plt.xlabel('time')\n",
+ " plt.ylabel('pos')\n",
+ " plt.ylim([0, 50])\n",
+ " plt.title('variance = {}, process variance = {}'.format(\n",
+ " measurement_var, process_var))\n",
+ " bp.show_legend()\n",
+ " plt.show()\n",
+ "\n",
+ "test_sensor(measurement_var=4.0)"
+ ]
+ },
+ {
+ "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 `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 dotted red line drawn over a straight black line. The black line shows the actual position of the dog, and the dotted red line is the noisy 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 sensor output.\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 several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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jjDFWw54j0nJUf8PUv2kvcLMI+PgH4LXHCdYWPDBPc3twIPDtHmD7QeDFaQ3n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E/LoXiX5yHbj9111WX4vWGDPEvnVujb2/N6TDZYrTp5DhatrYbSChgzpOsfJt9HX4aJiIh0yG/v\nOesOP38Q/mUV7D309dtK5zhy/BAlLifFFYVU11V522MiYxk1eAI5NgeD+w/Dau2cWQL697WQ0c+w\nuxrKKiEn+8ref+MwC8VvGqrrIDqy555QOs4LsWl9Pa9zb/BdPdL9NpbBLU/ClDHw/172dTUiIiLB\nKajD2W0TPeHs3LO6pGscPXGYkopCil1O9h/+wtseFRHDyMzx5Ngc2NJGEBLSNd3x7ilQfQTCrnL3\no20WRts6tyZ/Y8+CmCio2O95DhXAWIWzoPHZTsMtT3pe6+9dRETEd4I6nA3P8FzSuHMffNloevTI\nSFf44oDhX9eA3QYP39r+/93xU/WUVBRS4iqkqmaXtz0iPIoRGePIyXIwZMBoQkPCurzOJT/S3+vX\nCQ21MH6Y4b+2QInL05Y7xLc1SffZed4jCu+8yXd1iIiIBLugDmdRERaGXG/Yvge279E3xldqx15Y\n8Uf49nh4+FY4cfo4pZVFlLic7K7egcHzXLHw0AiGZ4zFnuXghoF2wkMjfFy5dGTSaKip90wEkj0A\nBuhxgkEjo/9XrxXKRUREfCeowxnAW/Mh6TpISdDoypU6dzloiPUAv/73lVQc3I4xngleQkPCGDZw\nDHabg2GDcokIi/RhpfJNPDMD/tdM/TsIRuOHwf+eA6OzNAmMiIiILwVlOGtuMYRYPc9vGjlYJyJX\n6sumU2yt/Dt/doYAN1F7rAjXgW2EWEO54WwgG5ExjsjwKF+XelV+9a6hrAKefRgGpARP/+jqGfrE\nf1kslh49G6mIiEigCMpw9t56+B8vwo/vM8x/WCek30Rj8xm27f6UEpeTHftKcLtb2VvzIwAy+8dw\n/y1PMDLzRqIje/m40mtz4rRh4e+gvgHuvlmX9omIiIhI9wnKcLapDE5+CdG60u6ymloa2b5nCyUu\nJ+VVxbS4mwGwWKzY0kbw2Q47APfd8l3GD/PvkNvUbHj1T/D5bnj96UvXumyNJ5jlj4SCCd1YoIiI\niIgEvaAMZ84yz9Ix0rd1+KOW1mbKq4opqXDy+e7NNLc2AWDBQma/odhtDkYPziMupjeZ/Qyf7/bc\np+LvwkJhwRtw7CQ8M8N0uE19g+GldzyvF87SZX4iIiIi0r2CLpzVNxjKqyAyHMac90DillbDmSaI\niwm+E/JWdws795ZSXOFk2+5PaWo+4103MCUbuy0fe1Y+vXsltHtfwQRLwIwuWa0WHCMNfyn0jJwO\nSbh4m6VvwYnTMHUs3GQPvn4gIiIiIr4VdOGscKtnOW4oRIR7TsBf+5PhqWXwxN3wi8d9WFw3crtb\ncR3YRrHLydYvPuFM02nvuvSkTHJsDuxZ+fSJS/JhlZ3LMQr+UggbS2HIty5e727zjLA9P6v7axMR\nERERCbpwVl0HURGeE/VzUhOguQVKK3xXV3doa3NTeXA7xS4nZZUfc7rxpHddv8SB5GTlY7c56Ns7\n1YdVdp1Joz3LTaUwq4Nw9uLjFn52vyG5j0bNRERERKT7BV04e/ROCw/f6rmE8Ry7zbMsrQBjTI+6\n16jNtLGnegfFrkJKK4s4+eVx77rkPmnkZDnIsTlI7pPmwyq7R062ZxKYXfug/kQoCXGtF22jYCYi\nIiIivhJ04QwgLNRC2HmfPC0J+sR5Zuk7cBjSk31XW2cwxlBV46LE5aSksoiGU/XedX3jU7HbHOTY\n8klNGNCjgujXCQu1sPwnhvRkiGxx+7ocEREREZF2gjKcXchisWC3Gf5rC5S4AjOcGWPYf/gLSiqc\nlLgKOXryiHddn9i+ZwOZg7S+GZ0SyP5WZPj3D+H2iXD7xMAJeA9+x1Prli0dz9goIiIiIuIrCmdn\njc6C4l2eqdYDhTGG6rq93kB2pOGQd118rwTsWfnk2BwMSM7q9BGyTz6H3/3N85Dm2yd26q67VcV+\nQ1Z64IRLEREREem5FM7Oev4RWPpYYDzbqvboAYpdToornNQePeBtj43uzejBeeTYHAzqNwSrxdpl\nNVSfvVIytYMp6QOF60AUD8yGu282vLMgMP7uRURERKTnCppw1tpq+NMmz4OnUxIuPgmPjPDvE/Mj\nxw9R4nJSXFFIdV2Vtz0mMpZRgyeQY3MwuP8wrNaQbqnnUJ1n2S+xWw7XJV59vx/GeD6DgpmIiIiI\n+FrQhLOySrj3GcjsDxXv+rqab+boicOUVBRS7HKy//AX3vaoiBhGZo4nx+bAljaCkJDu/2usDvBw\ntnVPDM7tvYmJgnk/9HU1IiIiIiJBFM42lXmWE0ddfjtfO36qnpKKQkpchVTV7PK2R4RHMSJjHDlZ\nDoYMGE1oSJgPqwzscFa+x/Dflw0B4Kl7Iek6jZqJiIiIiO8FTTgr3OpZOvwwnJ04fZzSyiJKXE52\nV+/A4JlJMDw0guEZY7FnORg6MIew0HAfV/qVlf8MB49A396+ruTK9UuE6Ag3La0Wfjq96+7LExER\nERG5EkERzowx3pEzx8hLb+d2GyoOwPGTMH54146mnDpzgrLKjylxOak4uB1j2gAICwln6MAc7DYH\nwwblEhEW2aV1XK07JgXuaFPvWAu/+8kOwkINvWMv0yFERERERLpRUISziv1w+BgkXQdZ6Zfe7rNd\nMP4RGJ4BW/9P59fxZdMptlb+neIKJ659ZbSdDWQh1lBuGDgGu83BiIxxRIZHdf7BpZ2ByU2+LkFE\nREREpJ2gCGdWKzxyO/SKuvysfMMzPNvu2AtnmgxRnTCD45mmL/l8z6cUu5zs3FuKu631bE0h3HB9\nDjm2fEZk3kh0RK9rPpaIiIiIiASuoAhng9MsvDb367eLjrQw5HpDeRV8vhvG3nB1x2tqaWT7ni0U\nu5yUV31Gq7sFAIvFii19JDk2B6MyxxMTFXd1BxARERERkR4nKMLZlbDboLwKSiuuLJw1tzaxo6qY\nYpeT7Xu20NzquWzOgoXM/sPIycpn1OA84mICcAYNERERERHpcgpnFxiVBW+thRLX12/b6m5h595S\niiucbNv9KU3NZ7zrBqZkk2NzMDorj969Erqw4u63+PeGrZUw+3tw47DAnRhERERERMSfKJxd4Mah\nkD8SstI6Xu92t+I6sI1il5OtX3zCmabT3nXpSZnk2BzYs/LpE5fUTRV3vw+LYd1m+GGBrysRERER\nEek5FM4uMHG0hU2vtG9ra3NTeXA7xS4nZZUfc7rxpHddv8SB5GTlY7c56Ns7tZur9Y1AfgC1iIiI\niIi/6vHh7ImXDKkJ8NhdEN/rm1+C12ba2FO9g2JXIaWVRZz88rh3XXKfNHKyHOTYHCT3ucQQWw+m\ncCYiIiIi0vl6dDg7cdrwyn+A1eK5P+rrGGOoqnFR4nJSUllEw6l677q+8anYbQ5ybPmkJgy47JT8\nl/JRiWHmv8Dyn0DBhMC8V+tMk+HYSQgLhYR4X1cjIiIiItJz9Ohw9vHn0NYGY4d6psnviDGG/Ye/\noKTCSYmrkKMnj3jX9YntezaQOUjrm3FVgex8n+2CqkPw3Z/CmQ2GiPDAC2iHzo6apSaA1Rp49YuI\niIiI+KseHc42lXmW+aPatxtjqK7b6w1kRxoOedfF90rAnpVPjs3BgOSsaw5k53vybnjjL56p+l/7\nMzx5T6ftutsk94EPXoLmVl9XIiIiIiLSs/TocFa41bOceDac1RzdT7HLE8hqjx3wbhcb3Rt7Vh72\nLAeD+g3BtFn48yb4wwfw8wdNpwW00FALix413PE0LPwdzPiOIS4msEafYqIsTLvR11WIiIiIiPQ8\nPTacNTUb/r797OuW/8uSP6ynun6vd31MVByjMydgtzkY3H8oVmuId52xGh5ZAsdOwozvQFonzop/\nq8MzVX/hVnhxNSx4pPP2LSIiIiIigatHhrP6E7Vs2VnIQ7ftY8eeMJzb1gEQFRHDqMzx2G0ObGkj\nCAnp+ONbLBZGZxk2FENpReeGM4vFwpIfGf5xHqQnd95+RUREREQksPW4cPbLNXPZW+MCwGqFnBui\nGJkxmRybg+zrRxEaEvaN9jPaBhuKocQF/y2/c2vMH2mh6o+GqIjAuqRRRERERES6TkCEsxUrVvCL\nX/yCmpoahg0bxrJly3A4HB1uu7fGRXhoBMMzxmLPcjB0YA5hoeFXfEy7zbMsdV1L5R6PLjX0ioaf\n3AepiZ5ApmAmIiIiIiLn8/twtmbNGmbPns0rr7yCw+Fg+fLlFBQUUF5eTnp6+kXbzyj4KcMG5RIR\nFnlNx7VneZallde0G46fNLz5N3C3wc/uv7Z9+YN7nzE0NcOrc78KmiIiIiIicu2svi7g67z00kvM\nnDmThx9+mOzsbF5++WVSU1N55ZVXOtw+x+a45mAGkH09zLrdE6iMMVe9nz9vgpZWuGk0JPcJ/DCz\n9lP4SyFEXvlgpIiIiIiIXIZfh7Pm5maKi4uZNm1au/Zp06ZRVFR0yfe1tF59mDonNNTCq3MtPHqn\n5Zqm0v+3DZ7lPVMuvY3bbfhbkbmmENgdTn1pOHHaE8x6x/q6GhERERGRnsWvw1ldXR1ut5vk5PbT\nGiYlJVFTU3PJ981cCLbvGdZ/5tuwc/ykYe2nnolJ/nFyx9sYY7j5cbj1Z7Du024t74odqvcs+yXS\nqQ/nFhERERERsBg/Hq6prq4mLS2NjRs3tpsAZMGCBaxevZqdO3cC0NDQ4KsSRURERESuWXx8vK9L\nED/g1yNniYmJhISEUFtb2669traW1NRUH1UlIiIiIiLS+fw6nIWHhzNmzBjWrl3brn3dunXk5eX5\nqCoREREREZHO5/dT6c+ZM4cHHniAcePGkZeXx6uvvkpNTQ2PPvqodxsNA4uIiIiISKDz+3B27733\nUl9fz8KFCzl06BAjRozg/fff7/AZZyIiIiIiIoHKrycEERERERERCRZ+fc/ZN7VixQoGDRpEVFQU\nubm5OJ1OX5ckfmDjxo3cdtttpKWlYbVaWbVq1UXbzJ8/n/79+xMdHc3NN99MeXm5DyoVf7F48WLG\njh1LfHw8SUlJ3HbbbWzfvv2i7dRvBGD58uWMGjWK+Ph44uPjycvL4/3332+3jfqKXM7ixYuxWq08\n8cQT7drVb0SCV8CHszVr1jB79myeeeYZSktLycvLo6CggP379/u6NPGx06dPM3LkSH71q18RFRV1\n0bPZXnjhBV566SV+/etfs3nzZpKSkpg6dSqnTp3yUcXiax999BGPP/44H3/8MevXryc0NJRbbrmF\nY8eOebdRv5Fz0tPTWbp0KSUlJXz22WdMmTKFO+64g7KyMkB9RS7vk08+4fXXX2fkyJHtfj+p34gE\nORPgxo0bZ2bNmtWuLSsry8ybN89HFYk/6tWrl1m1apX3v9va2kxKSopZtGiRt+3MmTMmNjbWvPba\na74oUfzQqVOnTEhIiPnrX/9qjFG/ka/Xp08fs3LlSvUVuazjx4+bzMxM8+GHH5rJkyebJ554whij\nnzEiYkxAj5w1NzdTXFzMtGnT2rVPmzaNoqIiH1UlgWDPnj3U1ta26zuRkZFMmjRJfUe8Tpw4QVtb\nG9dddx2gfiOX5na7eeedd2hsbGTSpEnqK3JZs2bN4p577uGmm27CnHfrv/qNiPj9bI2XU1dXh9vt\nJjk5uV17UlISNTU1PqpKAsG5/tFR36murvZFSeKHnnrqKex2OxMmTADUb+Ri27ZtY8KECTQ1NREV\nFcW7775Ldna290RafUUu9Prrr7N7925Wr14N0O6SRv2MEZGADmciXeHCe9MkOM2ZM4eioiKcTuc3\n6hPqN8FpyJAhbN26lYaGBt577z3uu+8+NmzYcNn3qK8Er127dvHzn/8cp9NJSEgIAMaYdqNnl6J+\nIxIcAvqyxsTEREJCQqitrW3XXltbS2pqqo+qkkCQkpIC0GHfObdOgtePf/xj1qxZw/r16xk4cKC3\nXf1GLhQWFkZGRgZ2u51FixYxfvx4li9f7v0dpL4i5/v444+pq6tj2LBhhIWFERYWxsaNG1mxYgXh\n4eEkJiYC6jciwSygw1l4eDhjxoxh7dq17drXrVtHXl6ej6qSQDBo0CBSUlLa9UXhiPwAAAWESURB\nVJ3GxkacTqf6TpB76qmnvMHMZrO1W6d+I1/H7XbT1tamviIduvPOO/n8888pKyujrKyM0tJScnNz\nmT59OqWlpWRlZanfiAS5kPnz58/3dRHXIi4ujmeffZZ+/foRFRXFwoULcTqdvPnmm8THx/u6PPGh\n06dPU15eTk1NDb/97W8ZMWIE8fHxtLS0EB8fj9vtZsmSJWRnZ+N2u5kzZw61tbWsXLmS8PBwX5cv\nPvDYY4/x+9//nvfee4+0tDROnTrFqVOnsFgshIeHY7FY1G/E6+mnnyYyMpK2tjb279/PsmXLWL16\nNUuXLiUzM1N9RS4SGRlJ3759vX+SkpJ46623GDBgAA8++KB+xohI4E+lb4wxK1asMAMHDjQREREm\nNzfXbNq0ydcliR/YsGGDsVgsxmKxGKvV6n09c+ZM7zbz5883qampJjIy0kyePNls377dhxWLr13Y\nV879ee6559ptp34jxhgzY8YMM2DAABMREWGSkpLM1KlTzdq1a9tto74iX+f8qfTPUb8RCV4WY77B\nXagiIiIiIiLSpQL6njMREREREZGeQuFMRERERETEDyiciYiIiIiI+AGFMxERERERET+gcCYiIiIi\nIuIHFM5ERERERET8gMKZiIiIiIiIH1A4ExEJUpMnT+bmm2/2dRkiIiJylsKZiEgPV1RUxHPPPUdD\nQ0O7dovFgsVi8VFVIiIiciGLMcb4uggREek6L774InPnzqWqqorrr7/e297a2gpAaGior0oTERGR\n8+g3sohIkLjwuziFMhEREf+iyxpFRHqw+fPnM3fuXAAGDRqE1WrFarXy0UcfXXTPWVVVFVarlRde\neIEVK1aQkZFBTEwMt9xyC/v27aOtrY3nn3+etLQ0oqOjuf3226mvr7/omGvXruWmm24iNjaW2NhY\nCgoKKCsr67bPLCIiEqj0tamISA921113UVFRwdtvv82yZctITEwE4IYbbrjkPWfvvPMOTU1NPPnk\nkxw9epSlS5dyzz33MHnyZDZt2sS8efOorKzk5ZdfZs6cOaxatcr73tWrV/PAAw8wbdo0lixZQmNj\nIytXrmTixIls3ryZ7OzsbvvsIiIigUbhTESkBxsxYgR2u523336bO+64o909Z8aYDsPZwYMHqays\nJC4uDgC3283ixYs5c+YMJSUlhISEAHD48GHeeecdVq5cSUREBKdPn+bxxx9n5syZ/OY3v/Hu7+GH\nHyY7O5sFCxbw1ltvdfEnFhERCVy6rFFERNq56667vMEMYNy4cQD84Ac/8Aazc+0tLS3s378fgHXr\n1nH8+HGmT59OXV2d909raysOh4MNGzZ07wcREREJMBo5ExGRds4fXQOIj48HID09vcP2Y8eOAeBy\nuQCYOnVqh/s9P9iJiIjIxRTORESknUuFqEu1n5sFsq2tDYBVq1bRv3//rilORESkB1M4ExHp4brr\nQdOZmZkAJCYmMmXKlG45poiISE+ie85ERHq4mJgYAI4ePdqlx/n2t79N7969WbRoES0tLRetr6ur\n69Lji4iIBDqNnImI9HBjx44FYN68eUyfPp3w8HC+9a1vARc/mPpaxMbG8uqrr/L9738fu93O9OnT\nSUpKYt++fXzwwQcMHz6cN998s9OOJyIi0tMonImI9HBjxoxh8eLFrFixgoceeghjDOvXr7/kc846\ncqntLmy/99576devH4sWLeKXv/wljY2N9O/fn/z8fB599NFr/iwiIiI9mcV05temIiIiIiIiclV0\nz5mIiIiIiIgfUDgTERERERHxAwpnIiIiIiIifkDhTERERERExA8onImIiIiIiPgBhTMRERERERE/\noHAmIiIiIiLiBxTORERERERE/IDCmYiIiIiIiB9QOBMREREREfED/x8s/SSFfQDHXAAAAABJRU5E\nrkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "test_sensor(measurement_var=100.0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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b9cFWga17gBF9gYf6AL2DAbnc9LD15ZWlOJl2EAmpGqReOgWd0AEA5HILhPhE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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "test_sensor(measurement_var=0.5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n",
+ "\n",
+ "So let's first look at the plot with some process noise but no measurement noise to obscure the results."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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mH9CEEDhXkFkfyNITUVJeqOtzsnP77yWLanR09TeYWZyouRjOiIiIiOi+o9UK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\nH+zsTWP5GojIAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "np.random.seed(1234)\n",
+ "test_sensor(measurement_var=0, process_var=0.5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will stay there until the random changes in velocity happen to result in the track going back to the original track. \n",
+ "\n",
+ "Finally, let's look at the combination of measurement noise and process noise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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CCCGEEKLO/WJV/PU1WP6awti2fgeZIzkHsNosJNosHM077Ghv5BNId0MMJqOZ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\nRESkCVA4ExERERERaQL+P08WG9h6lV0OAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "test_sensor(measurement_var=1, process_var=0.5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "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",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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F8eS0U/hxx5dQlRRXcCQR1RcswImoVhxJ2oXf9/0A7d9uGJNAgnGDp2BAz1dE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\nCCGEED+iApwQQgghhBA/+n9wJsSfsI5CQQAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import stats\n",
+ "with figsize(y=3):\n",
+ " stats.plot_gaussian(mean=23, variance=5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Notice how this relates to the bar charts from the Discrete Bayes chapter. In that chapter we drew bars of various heights to depict the probability that the dog was at any given position. In many cases those bars took on a shape very similar to this chart. The differences are that the bars depict the probability of a discrete position, whereas this chart depicts the probability distribution of a continuous range of positions. \n",
+ "\n",
+ "This graph corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly speaking positions 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 interpretation 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",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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pfXfyspP42cuKDHW5PHP+GADAx3vDWisPF/6152/4x453cz2NjOB02+H2OKFR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\n+dznPodbb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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "dog = DogSensor(x0=23, velocity=0, \n",
+ " measurement_variance=5, process_variance=0.0)\n",
+ "xs = range(100)\n",
+ "ys = []\n",
+ "for _ in xs:\n",
+ " ys.append(dog.sense_position())\n",
+ " \n",
+ "bp.plot_track(xs, ys, label='Dog position')\n",
+ "plt.legend(loc='best')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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 discrete Bayes code for adding a measurement to a preexisting belief:\n",
+ "\n",
+ " def update(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 convenience. \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 of multiplying two Gaussians is a Gaussian with \n",
+ "\n",
+ "$$\\begin{aligned}\n",
+ "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
+ "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
+ "\\end{aligned}$$"
+ ]
+ },
+ {
+ "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",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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cobhKlSrFhg0bUo5tNhuzZs3iypUrKaN2S5cuxcvLK6XNgAEDqF69OuPGjWPK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\nc8XR3hVne1cc7VxxsnfB0dbZpM9XhGgKNxScLVy4kLlz55KTk0Pbtm3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ADvRNYOrUqaxY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\nrkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "import numpy as np\n",
+ "\n",
+ "def multiply(mu1, var1, mu2, var2):\n",
+ " if var1 == 0.0:\n",
+ " var1=1.e-80\n",
+ " \n",
+ " if var2 == 0:\n",
+ " var2 = 1e-80\n",
+ " \n",
+ " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
+ " variance = 1 / (1/var1 + 1/var2)\n",
+ " return (mean, variance)\n",
+ "\n",
+ "xs = np.arange(16, 30, 0.1)\n",
+ "\n",
+ "mean1, var1 = 23, 5\n",
+ "mean, var = multiply(mean1, var1, mean1, var1)\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
+ "plt.plot(xs, ys, label='original')\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
+ "plt.plot(xs, ys, label='multiply', ls='--')\n",
+ "\n",
+ "bp.show_legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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 multiplication 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 23 meters each time, I should conclude that the length is close to 23 meters. 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",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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2zNhhCJFpLw7RmjVrFjt37sxU3Vc9T0EeDiYJuhBCFFBarZZx48Zx+/ZtvfJZ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TYzPrfbzVdffcXChQuDyidPnsyOHTvCHrNz507Gjh1LREREUPySJUs4ceIEGRkZ7Ny5k8mTJ4ec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\nSUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "xs = np.arange(16, 30, 0.1)\n",
+ "\n",
+ "mean1, var1 = 23, 5\n",
+ "mean2, var2 = 25, 5\n",
+ "mean, var = multiply(mean1, var1, mean2, var2)\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
+ "plt.plot(xs, ys, label='measure 1')\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
+ "plt.plot(xs, ys, label='measure 2')\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
+ "plt.plot(xs, ys, label='multiply', ls='--')\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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EfdeuXZg9ezYWLVqE2NhYBAUFYfDgwUhNTa3w+NOnT6Nz587Ys2cPrl+/junT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\nIYQQokKoQCeEEEIIIUSF/D8YwdxN2xDhkAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "xs = np.arange(0, 60, 0.1)\n",
+ "\n",
+ "mean1, var1 = 10, 5\n",
+ "mean2, var2 = 50, 5\n",
+ "mean, var = multiply(mean1, var1, mean2, var2)\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
+ "plt.plot(xs, ys, label='measure 1')\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
+ "plt.plot(xs, ys, label='measure 2')\n",
+ "\n",
+ "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
+ "plt.plot(xs, ys, label='multiply', ls='--')\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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. Furthermore 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",
+ "Of course, this example is quite exaggerated. The width of the Gaussians is fairly narrow, so this combination of measurements is quite unlikely. It is hard to eyeball this, but the measurements are well over $3\\sigma$ apart, so the probability of this happening is less than 1%. Still, it can happen, and the math is correct. \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": "markdown",
+ "metadata": {},
+ "source": [
+ "## Implementing the Update Step"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Recall the discrete Bayes 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 update function for a Kalman filter:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "def update(mean, variance, measurement, measurement_variance):\n",
+ " return multiply(mean, variance, measurement, measurement_variance)"
+ ]
+ },
+ {
+ "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 is with the new measurement. Perhaps this would be clearer if we used more specific names:\n",
+ "\n",
+ " def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n",
+ " return multiply(dog_pos, dog_variance, \n",
+ " measurement, measurement_variance)"
+ ]
+ },
+ {
+ "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 `update_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 `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 position 2.0, not 0.0."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "time: 0 \tposition = 1.074 \tvariance = 2.500\n",
+ "time: 1 \tposition = 1.349 \tvariance = 1.667\n",
+ "time: 2 \tposition = 0.307 \tvariance = 1.250\n",
+ "time: 3 \tposition = -0.297 \tvariance = 1.000\n",
+ "time: 4 \tposition = 0.058 \tvariance = 0.833\n",
+ "time: 5 \tposition = 0.634 \tvariance = 0.714\n",
+ "time: 6 \tposition = 0.548 \tvariance = 0.625\n",
+ "time: 7 \tposition = 0.504 \tvariance = 0.556\n",
+ "time: 8 \tposition = 0.402 \tvariance = 0.500\n",
+ "time: 9 \tposition = 0.160 \tvariance = 0.455\n",
+ "time: 10 \tposition = 0.126 \tvariance = 0.417\n",
+ "time: 11 \tposition = 0.393 \tvariance = 0.385\n",
+ "time: 12 \tposition = 0.361 \tvariance = 0.357\n",
+ "time: 13 \tposition = 0.287 \tvariance = 0.333\n",
+ "time: 14 \tposition = 0.103 \tvariance = 0.312\n",
+ "time: 15 \tposition = 0.268 \tvariance = 0.294\n",
+ "time: 16 \tposition = 0.282 \tvariance = 0.278\n",
+ "time: 17 \tposition = 0.253 \tvariance = 0.263\n",
+ "time: 18 \tposition = 0.333 \tvariance = 0.250\n",
+ "time: 19 \tposition = 0.350 \tvariance = 0.238\n"
+ ]
+ }
+ ],
+ "source": [
+ "dog = DogSensor(velocity=0., measurement_variance=5, process_variance=0.0)\n",
+ "\n",
+ "pos, s = 2, 5\n",
+ "for i in range(20):\n",
+ " pos, s = update(pos, s, dog.sense_position(), 5)\n",
+ " print('time:', i, \n",
+ " '\\tposition =', \"%.3f\" % pos, \n",
+ " '\\tvariance =', \"%.3f\" % s)"
+ ]
+ },
+ {
+ "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 initial 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 surprising. All we are doing is computing `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": "markdown",
+ "metadata": {},
+ "source": [
+ "## Implementing Predictions"
+ ]
+ },
+ {
+ "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 non-moving objects? The discrete Bayes filter used a loop of predict and update functions, and we must do the same to accommodate movement.\n",
+ "\n",
+ "How do we perform the predict function with Gaussians? Recall the discrete Bayes method:\n",
+ "\n",
+ " def predict(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 `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 `predict()` function for the discrete Bayes 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 predict function:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "def predict(pos, variance, movement, movement_variance):\n",
+ " return (pos + movement, variance + movement_variance)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What is left? Just calling these functions. Discrete Bayes did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "PREDICT: 1.0000 502.0000\tUPDATE: 5.9374 9.8047\n",
+ "PREDICT: 6.9374 11.8047\tUPDATE: 6.0781 5.4138\n",
+ "PREDICT: 7.0781 7.4138\tUPDATE: 4.6672 4.2574\n",
+ "PREDICT: 5.6672 6.2574\tUPDATE: 5.6747 3.8490\n",
+ "PREDICT: 6.6747 5.8490\tUPDATE: 6.1235 3.6904\n",
+ "PREDICT: 7.1235 5.6904\tUPDATE: 7.2806 3.6267\n",
+ "PREDICT: 8.2806 5.6267\tUPDATE: 8.4183 3.6007\n",
+ "PREDICT: 9.4183 5.6007\tUPDATE: 10.2644 3.5900\n",
+ "PREDICT: 11.2644 5.5900\tUPDATE: 13.1794 3.5856\n",
+ "PREDICT: 14.1794 5.5856\tUPDATE: 12.7885 3.5838\n"
+ ]
+ },
+ {
+ "data": {
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lGwN4YuAqOrbadCF4Zl4IoHl5uZX8KkQEFCBFRETkCmMYBl8tgdu7Ui3ClSMMw2DNtiXM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\nIlIpCpAiIiIiIiJSKf8ffy00k/BG8Q8AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# assume dog is always moving 1m to the right\n",
+ "movement = 1\n",
+ "movement_variance = 2\n",
+ "sensor_variance = 10\n",
+ "pos = (0, 500) # gaussian N(0,500)\n",
+ "\n",
+ "dog = DogSensor(pos[0], velocity=movement, \n",
+ " measurement_variance=sensor_variance, \n",
+ " process_variance=sensor_variance)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(10):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n",
+ " \n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ " \n",
+ " print('UPDATE: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]))\n",
+ "\n",
+ " \n",
+ "bp.plot_filter(ps)\n",
+ "bp.plot_measurements(zs)\n",
+ "bp.show_legend()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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_variance = 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 `predict()` step.\n",
+ "\n",
+ "For now let's walk through the code and output bit by bit.\n",
+ "\n",
+ " movement = 1\n",
+ " movement_variance = 2\n",
+ " sensor_variance = 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, \n",
+ " measurement_variance=sensor_variance, \n",
+ " process_variance=sensor_variance)\n",
+ "\n",
+ "It may seem very 'convenient' 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 `update() ... predict()` loop.\n",
+ "\n",
+ " for i in range(10):\n",
+ " pos = predict(pos[0], pos[1], movement, sensor_variance)\n",
+ " print 'PREDICT:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
+ "\n",
+ "Wait, why `predict()` before `update()`? It turns out the order does not matter once, but the first call to `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 `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",
+ " PREDICT: 1.000 502.000\n",
+ "\n",
+ "What is this saying? After the prediction, 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 prediction step.\n",
+ "\n",
+ " Z = dog.sense_position()\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 update function of our filter, save the result in our *ps* array, and print the updated position belief:\n",
+ "\n",
+ " pos = update(pos[0], pos[1], Z, movement_variance)\n",
+ " ps.append(pos[0])\n",
+ " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
+ " \n",
+ "Your result will be different, but I get\n",
+ "\n",
+ " UPDATE: 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 `predict()` and `update()` 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. The variance is plotted as a lightly shaded yellow area between dotted lines."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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GYaFziejCwkImT57M2rVrSUxMZOXKlQwfPpywsLDyKa5CCCGEEKJ2LFq0iKee+ida70Gp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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Variance:\n",
+ "\t2.5200 4.0428 3.6649 6.0266 5.8804\n",
+ "\t5.2240 6.3572 6.5137 7.9885 8.0157\n",
+ "\t9.6223 12.5884 13.0473 12.9739 12.8976\n",
+ "\t13.6351 16.7189 18.5777 18.9743 19.9421\n",
+ "\t20.6522 22.9380 24.0564 27.1851 25.4667\n"
+ ]
+ }
+ ],
+ "source": [
+ "%precision 2\n",
+ "# assume dog is always moving 1m to the right\n",
+ "movement = 1\n",
+ "movement_variance = 2\n",
+ "sensor_variance = 4.5\n",
+ "pos = (0, 100) # gaussian N(0, 100)\n",
+ "\n",
+ "dog = DogSensor(pos[0], velocity=movement, \n",
+ " measurement_variance=sensor_variance, \n",
+ " process_variance=0.5)\n",
+ "\n",
+ "zs, positions, variance = [], [], []\n",
+ "for i in range(25):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance) \n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " variance.append(pos[1])\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " positions.append(pos[0])\n",
+ " \n",
+ "bp.plot_measurements(zs)\n",
+ "bp.plot_filter(positions, vars=variance)\n",
+ "bp.show_legend()\n",
+ "plt.show()\n",
+ "\n",
+ "print('Variance:')\n",
+ "for i in range(0, len(positions), 5):\n",
+ " print('\\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(\n",
+ " *[v for v in positions[i:i+5]]))"
+ ]
+ },
+ {
+ "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 literature, 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": "markdown",
+ "metadata": {},
+ "source": [
+ "### Animating the Tracking"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
+ "\n",
+ "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Implementation in a Class"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n",
+ "\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance) \n",
+ " \n",
+ "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n",
+ "\n",
+ "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n",
+ "\n",
+ " class KalmanFilter1D:\n",
+ " def __init__(self, initial_state, measurement_variance, movement_variance):\n",
+ " self.state = initial_state\n",
+ " self.measurement_variance = measurement_variance\n",
+ " self.movement_variance = movement_variance\n",
+ "\n",
+ "That works, but I am going to use different naming. The Kalman filter literature has settled on one letter notations for each of these concepts, and so you might as well start getting exposed to it now. At first it seems impossibly terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondence with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them. If you do not make this effort you will never be able to read the Kalman filter literature.\n",
+ "\n",
+ "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the movement error. This gives us:\n",
+ "\n",
+ " class KalmanFilter1D:\n",
+ " def __init__(self, x0, P, R, Q):\n",
+ " self.x = x0\n",
+ " self.P = P\n",
+ " self.R = R\n",
+ " self.Q = Q\n",
+ " \n",
+ "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n",
+ "\n",
+ " def update(z):\n",
+ " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
+ " self.P = 1 / (1/self.P + 1/self.R)\n",
+ "\n",
+ "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n",
+ "\n",
+ " def predict(self, u):\n",
+ " self.x += u\n",
+ " self.P += self.Q\n",
+ " \n",
+ "That give us the following code. Production code would require significant comments. However, in the next chapter we will develop Kalman filter code that works for any dimension, including 1, so this class will never be more than a stepping stone for us, since we can, and will use the class developed in the next chapter in the rest of the book."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "class KalmanFilter1D:\n",
+ " def __init__(self, x0, P, R, Q):\n",
+ " self.x = x0\n",
+ " self.P = P\n",
+ " self.R = R\n",
+ " self.Q = Q\n",
+ "\n",
+ "\n",
+ " def update(self, z):\n",
+ " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
+ " self.P = 1. / (1./self.P + 1./self.R)\n",
+ "\n",
+ "\n",
+ " def predict(self, u=0.0):\n",
+ " self.x += u\n",
+ " self.P += self.Q"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "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* and *h* 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",
+ "$$ \n",
+ "\\begin{aligned}\n",
+ "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a} \\\\\n",
+ " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}} \\\\\n",
+ " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
+ " &= \\frac{\\sigma^2_{x'}}{b}\n",
+ " \\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "We can tie all of this together with\n",
+ "\n",
+ "$$\n",
+ "\\begin{aligned}\n",
+ "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x) \\\\\n",
+ "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
+ "&= x + g_n(y-x)\n",
+ "\\end{aligned}\n",
+ "$$\n",
+ "\n",
+ "where\n",
+ "\n",
+ "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
+ "\n",
+ "The end result is multiplying 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 predictions 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": [
+ "### Exercise: Modify Variance Values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Modify the values of `movement_variance` and `sensor_variance` 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_variance = 40\n",
+ " sensor_variance = 2\n",
+ " \n",
+ "or:\n",
+ "\n",
+ " movement_variance = 2\n",
+ " sensor_variance = 40"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "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-equipped 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. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "def volt(voltage, temp_variance):\n",
+ " return (random.randn() * temp_variance) + voltage"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We generate white noise with a given variance using the equation `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",
+ "\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 performance 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 $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability 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 a Kalman filter that performs well. "
+ ]
+ },
+ {
+ "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 predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict 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 known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change over time. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `movement_variance = .2`. This is just the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n",
+ "\n",
+ "Let's see what happens. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
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rzkbVVHw8AxpMIAEGxY4CYOvBNXaJSZxdjuUkkZix77R/n/Q6Pf7e1eWCuYW2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\nGVsF7NwPac9xiFPvABJG2iYI6vUEQcBvZzwCV60OXu78MkdEt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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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AAACuCr8K3zVnz6jidLmvywAAAACuCr8K3xLrvgEAABC8/DB8s+4bAAAAwcmr8P3CCy/I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\n9m3xUTUAAACA5wI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rt+E7JydHt9xyi6Rz67kXLFigBQsWaObMmXrjjTdkt9tVUFDg7B8d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\nAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Variance converges to 0.858\n"
+ ]
+ }
+ ],
+ "source": [
+ "movement = 0\n",
+ "variance = 2.13**2\n",
+ "movement_variance = .2\n",
+ "actual_voltage = 16.3\n",
+ "\n",
+ "N = 50\n",
+ "zs = [volt(actual_voltage, variance) for i in range(N)]\n",
+ "ps = []\n",
+ "estimates = []\n",
+ "\n",
+ "kf = KalmanFilter1D(x0=25, # initial state\n",
+ " P=1000, # initial variance \n",
+ " # large says 'who knows?'\n",
+ " R=variance, # sensor noise\n",
+ " Q=movement_variance) # movement noise\n",
+ "\n",
+ "for i in range(N):\n",
+ " kf.predict(movement)\n",
+ " kf.update(zs[i])\n",
+ "\n",
+ " # save for latter plotting\n",
+ " estimates.append(kf.x)\n",
+ " ps.append(kf.P)\n",
+ "\n",
+ "# plot the filter output and the variance\n",
+ "bp.plot_measurements(zs)\n",
+ "bp.plot_filter(estimates, vars=ps)\n",
+ "bp.show_legend()\n",
+ "plt.show()\n",
+ "plt.plot(ps)\n",
+ "plt.title('Variance')\n",
+ "plt.show()\n",
+ "print('Variance converges to {:.3f}'.format(ps[-1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The first plot shows the individual sensor measurements 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 `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 section **Explaining the Results - Multi-Sensor Fusion** explains why this happens."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Animation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
+ "\n",
+ "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. \n",
+ "\n",
+ "> If this is not clear, I urge you to go back and review the g-h chapter. This is the crux of the algorithms in this book. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Exercise(optional):"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "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",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "#Your code here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Solution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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ww5Ikn8+n5ORkWa3WoOdwu93aunWrtm3bptmzZ/vPk52drZ07d2rOnDnhvg4AAABgRBr0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\nAACAgQjkAAAAgIEI5AAAAICB/h/dEpsQ5+ltYwAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "variance = 2.13**2\n",
+ "actual_voltage = 16.3\n",
+ "\n",
+ "def VKF():\n",
+ " voltage = (14, 1000)\n",
+ " for i in range(N):\n",
+ " Z = volt(actual_voltage, variance)\n",
+ " voltage = update(voltage[0], voltage[1], Z, variance)\n",
+ " return voltage[0]\n",
+ "\n",
+ "vs = []\n",
+ "for i in range(10000):\n",
+ " vs.append(VKF())\n",
+ "plt.hist(vs, bins=100, color='#e24a33')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Discussion"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "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": "markdown",
+ "metadata": {},
+ "source": [
+ "## Explaining the Results - Multi-Sensor Fusion"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**author's note:** I am not overly keen about this explanation. It is true that multiple sensors improve results, but we get good results merely by having an accurate model of the process. I explain this much better in the next chapter. I'll leave this section here while I mull how best to explain this at this stage of learning. For now don't worry if this section is not entirely convincing; it does need work.\n",
+ "\n",
+ "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 focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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N6z527BhHjx4lODi4zOMUH1vWccD4POy5EbnmmmsYP348CxYs4PXXX+eaa65h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GfTA3cG6rxFqDfch/xzA6lZGbzxw2cknDhi10YRgms7adkqERro8MXexi8IvzIzPuXaQ+1URhpQ\nWqsdYO9cqdNDajKcOXXB8JWaimlXlzLrZz05BXqWv3OEq4YeRcoTWCwmPlogqTA5FwTnF9lrYH+8\n3BOZm60VVJw81nAHR7XA+73dsTw+yz7grReNNCAqLJa8O0/lRGqZzap85c7NNufCSmzcJ+l6s4W5\nVh+g5z6XbHt3Aeqdo1F/+ICfV5excV+5LVgrr6g93tkzsvjl1aOE+Gv3WX5xoU3GrxKVmdVrrx1B\nREQM+flasHLrrbfi4VFFkYqNrTLWCQoKYu7cuQihoChG3NxCeeihh1GUMBSlFXp9ONdeOwlFicJs\nDuebb9ay2KqT6OnuQXyvAQC0zS/nqmN5RB06xTs/fsVXSxaQ50DG0aCHDbMPc92IJLBOcW9+Dl79\npgizxfGKxunMM7z309d8sfgncmoEYP7evtw29lr09QTIOTkFHD+eitS7IlesQ127hd9/c7w6d+ml\nvaDU+hxxNzYqw+Lt7c1HH33Ed9+95/BZoX29IQwYMMCupqUmxKQ7oHs/xLjr7bZHRkaydu1annrq\nOaTsQK9e8aSlWVCUcBTFj9tvv4uIiE5IGU1eXik7dlRz41QtiEnjSGzXnseeeI3ExESnP1ejUZ2K\n4VW3WZpTqMNoTGZXulY2j8KIiOsN/YaDi/OUxAYRGgGKDjJT7Vfr8hq2i7eNa9BIlH+/3qhCSblx\nBZZnpqGuWoTw8NQc/kwVNlOmfywaEXi3oAXO4LxyvCsqKti5cyczZsyw2z5y5Eg2bnSsedw+p5Qj\n/u74e/syvOclbN78C+Xl9WURtaz6vHlfc+edYxh6aTe7fQUlRSzbZv/y1CkKXh6eGPR66x8DBr0e\nF53BZlFfbjZRYaqg86HTXFZhYs/vi5lzbBOWGkG7p7sH/zd6Iu1PZqEChDh+wLfLLubpTSkkBLjz\nabdgTqRk8eYP7pxIlXzwaI2Xb2WAXSlRZPSCinLtpdIMskXqG0+AqiKmzUR4Ol8B3xyQ0kKP9sls\nmF1iL48mcnlnris//BnM7eO07yA1UxLsB3qr4cs9b0iu66fg6aYipaTzDZKtn1bQKtAEWHhxjifX\n9+2Ocety5P5t1FyCrzUWa+A97pa2lCbnYHRr+AUHVKlsOBl46/73ECOP5vHm5ocZec0q/tyhBaRb\nDuzmkSm32wxsgnzNfDQjmcv6GFHVChTFg/2FHvQGyDrG6MtT6NG+xGoP7s+Up4O4ZbTC1cO06yOl\nBSHO0KNDFYVp0/5ddhPNEP9AmwxeYGAb7rlnxFlxOo1GI7feeqvt/97e3sycOROA5cuXs3z5dmbM\nmGDbP7xnf7Yf2o9XkkaBKXTRAuAdh/az7/ghRvYdzPCe/W2/P9AKT4UowWLJYOWOEP57ezkzP7aQ\nV6Qj2K8qK1dYUszvm1azKWGXwwyyh4sb/xo/GS+P+jWiV67cxY8/ruO77+YivXwRBbl4qQakhJqX\nKCamC4/c0x9552Jwb7yiQefOnVHVfKTMtet76dItZGebufbartQTcwOgDL4CBl9Ra3ulykYlbrzR\n3oWvslCzuFjHrbe+yoABHejdW7PIFgYDYsp4YifdzAqizy3f16/qWSmaGnjXpYDTzBlv5ZYHmqWf\n6hAGF8SYydrzxGyyaffLvBxtvzOBd1R7aOB5VxPy0F7Ysxm6WM2cIqI1t79Tx6FV3eoqMmGHlnzo\n1M2psV10aAm8W9DMOK+Bd1ZWFhaLpRZHMDg4uErztAYqH/Ol+YUcOHAAi6UV5eUFJCcn125sMRPz\n7VsMLypEXjeOkBBXkk8k4ePhSX49PxqLqjrMsjlCmajgMqB1dhEW1d5wJsjbjyu698dcWEL63v0E\nATkGhcwDB+zaJSRkU75jF9cDLhYtCCoqyyX5dCYdW5WwbVuO3cu3bXoavsCx0ynkb99OJ50BdyBh\n62bKguteenYW3TetRDFXsHvQeNQmGLQ0BmUVgm9XhXDHmETcXR1/98EeGTxzQzmHD7tRXh7AhGfj\neO+eg7QNLUQIE8s3X0J8lwKC/bNJTDxGmN9wduzZQkFrLZi7dnAXUjzd6QDkrl3OidC6Ofu60mK6\npZ5E1elRg45yg2U1p350IzusKxjrD9B8EncRDeSZVU5s315vW4C4wztoX1LEvdPX8unOKuWCtOxM\nvl+8kL4xVeoy4Z5w0JqAHN7ZFffATNgJFafTaOe/icJsOJgNJeU6tiaM58lJG9i718jS7WGUVJRz\n1YC9uBi0e8xkMbN61xYAwooquPZwDuY2OhITE8nNLcLLK46KirOUUKwHwcHB3H//QyhKBgcOHAAp\nCVqyjvuSUkk2uAH5tsAboMJkYtHGVazdtZVBHbvTptKx02xBn1fAS3P6sK3Yk88fWcfTU7LISoMs\nq+/H4bSTbDywizK19vK4IgRxEe3oHd2Z3PQsctPtzVvKy00sX76LsWP7A0FERQ3AaExgw4Yt9HAz\n4lGQS4ASwv79hUAqixdvZPToPkgpUZRoSCkgFigTOhKduA9qwmQysWPHb8TEBBIZqQWhZWWFzJu3\nnsxMyaBBgxrdZ2OgqiojRlzGsGF9OXDgCFRT3DGbI8/JvVEdPrkFRAPFraM5Il2RZ3ENK+HmE4bb\nNf+i1K815dX6aXM4EX8gqbCEHCf7396EcZw1elj18g9UrT6EJOylFZBWWkHaORhTu7078AaOmQT5\n27fT2sWDYOD0prWk6+pOyET9+CF+B3eSdNXt5HZ1XCR9MSPIKxBjbF8yz2RS3MB1/0vulRZccGjf\nvv5J7wWvalKpMeztYcRstgD1cLwVHZ6njuIlVbp06ILeTeOM9m/flZX7t2Fykqv26NZUdBI+6h5M\nvpv9JTpjNFCuEwSUmfGssFBkDRg6tYpicKcetqVrUWFC1esw+VcF51qFuJ7589fT10dTXzColYoC\nkpsv/4NWvoMwmeyDX8WkZSxVvZbyslg1QnVlTS++E2YTirkCVdGhGpyXTmsqLKogOcPA45914J3p\njgPv7u0qA6NC3N1z6do2kKKyM+j12vbHrttCkG8OlWoNX/97qd3xd4xOQJcbBH+A/uhRjp52ISbc\ncQFrWYnKyqAr6RaRDjoTwYtW45Gcwgw+4O6HdPgYazv5VaI8MIzUSydQ7tdwFk0pL8VQUoRq0HPS\nXFrrntyVdJj2YZH4OuCD+nmVI6xL2vr8QlAlKNoMzcPVwh8vLUSv0+6n9uGl3PLqUIZ1O0Cwr0ZV\n2pt8hBLr6olPuYXo/HIKi80k5hczbdr7dO/eiwceOAcZPOsssrzcHykzAAseR5JwO5NFR09rdtjb\ns9ZxBaXF/LF7I5fG9qZT6yhcsnNp+84c3vb9jdMz/4Ui7KlZp7MzWLl/G1MSs+iYU8aPHf1JCNT6\njwgIYWDHbvgZ616V0OtdWLRoB4GBXenWTbPknjZtGgBmTx/IOI2hKJ+C8jYsW3aMjRsPcdllPbnj\njrfp1asPD105Cqgy8qoPbhkpeB/dR1lgKAUdNKm/uXPncvLkUSIiqtwmY2K6MHNm/Hmp51AUhUGD\nBmE2gxBRJCauJD09k82bDjF02Fj69m2eItS6UBjViYTpL2Ly8kE28VlUFhxOWXBtDfCU+OvI7DOc\nCp/zlJmtXF1qhuIuQ7GWHDLXcw83Be6ZGqWk1JrMKQ3U1GBc8hy7i1bCzTrrLfub+kBk9h9JA4KR\nLWhBo3BeA+/AQE16LD3dvmI9PT2dsLAwh8eUGLQHVt+evbl96ivs23eCL774kl69ejlsb3H3gJIi\n4tp3BU8vhFCJjY1l+IDBnM44Q3Z+LtkFuWTn55FVkEd2fi5F1bi1QkpCSkzoZdW5q0NVBCe9XGif\nV05UfjkpbUO5ot9QBlpVIWyIjUXedzthFpVW1qqvZ5/9HDDy6aefY8zaCQ8/hEt1hQY3A127xqAo\n9isCliVBcOYkHbp3R3TqgeWPMDh9jE7hrRF9+ji8Ds5C5mSiAoqXD3369m2wvVN9Ssl3y6BfF4gJ\nd7w0rarlDBl4kLwiib93rMM2NfH72zlAsPUPxMbCgQNp1n/X3UfW+4vAonJV7wDcIxyvEBQUS+7Z\nPICy8hLmx57AEhIEySk8NyWdzsOubnhwo8fX2iRPHUcmH0X06I+w0lAOrdY4smV+oRTJ2soXqlTZ\nnXKMaVddX+eyvsXLiFJYTOfwcISvj8M2fsF69n17mDahmrRhfnEhn6/+1bbfzawFBN4hwQwY0JeN\nG38jMTGbPk28n+rD8uXLmTnzfZ566hZ69O6G/H0l+iLtt3f1VdcRKkpZtGkVJWX2AfWmo/sYMWAw\nPmGtUQEvWU5cF3uzKZPZzM/frQagdVEFvhUWSvQKQb7+XDN0JLFRMQghtIw7te8XKXVI2Y5XX22H\nt7c3XbrYa9qrG6KRxxOICfRF6dMHRVGYNOl6oqODWLKkP9u3J9FlyECkvzde7sYGr6O6MhW58ifE\nsDEoN9wBYH2mmREiAZOpHFWVGEQnlMPHwMuHRll4NxHJycmkfTSfOyO96dO3HxuLSs7pvXEhojJ7\n2ZTPLXdtQn3+PsSAeJTHXm3SeNTCNDC6Ezk0njZdm/e7kPk5qEX54OZB1/grEIqC7NwRrr2ZYN8A\nQup4FkmTCTU3E4Qg9vLRmj33PxCV90qvPM2RWAwZhXBtRt5/Cy4qVNZJ1YXzGni7uLjQu3dvli1b\nxsSJE23bly9fznXXXefwmFK9gpe7EVeDC3PmPEVubms8Peu2tcbdCCVFvPnSS8xftYovvniC2Ni2\neLi60SEiCiKiah1SVlFOSVkpJrMZc0YW+tWvY/YyMnXC9baMpIvegIvBBVeDAV+PlchVm7l5QDyu\nY+JR6ngoCUWxy3Tce+8NvPHG72RnZ2N01QImQ7ViwJ2Hylmy0Q1vo+T5uwQFxZLTGRA78x27fpW7\nHtcyKQHNwFO0ZlFsnMgmQkoLpWUneeidCDZ+bEZKV4QQFJVIPD0EqZmSolKICT+JopjxPw/urX6z\nHkf4eAJ1Z9E83SuY8/QhCku0gFR4eyKBjr5JVn514zNw6qznIXE34tkPobu2BOtfoqn3pOlbsf/4\nYYfHHUw+xt5jB+ke09lxx1ERUFQMJWVQR+AdFmifSV+8aQ0V1STufIWV2mH0QEoFD49w+vY9t45e\nrVu35uOPZ9Otmw42bUX+rulTizEjEK1CGBwUQM8OsSzetJr1+3ZUKxqt4KfVS7ntCitHvKiklr7w\nql2bycjNRqdKQotNqEDPkSMZfMngegsoCwqKef75L3n88ScJCPBiwIABDtuJK65B9BkCHeIA7Cb+\nwcHejB2rBepi6GinroUICNHcK7OqkhCKoiClASl9Wb9+OU8++QkvPPggl37/OvgHoft8mVN9Nwci\nIyO5ZdIk3JfNo7+vH4Nub6TEZgsAq2ulagFD/WpczkAZfiUMv7IZRuUAyVbN9jYxtsJgYfRq2PXy\nzEmwmCEk/B8bdFeH/PwNKClC9B8BLYF3C+rAeVc1efjhh/nyyy/57LPPSExM5IEHHuDMmTPcfffd\nDtuX6RQCfLRCGyEU/P2DcXWtZynXWtg0ZsSlzJ//AZ07RzU4JjcXV/y9fQnxD6SVRbsk+rAQ4qI7\n2Cyhu7RtT/vwNkSGtMLrluvQffMu7mMvqzPorgkpwc8vlpdeeong4GCWrdlBgaurHbc1PfcMEcEl\njB6Qi6rmsGl/Mfe/ZUFVy5FSZe1uyaPvS81pMiyibsOGxqBSkaMRtsKOkJgk+fcHKhZLMmY1j1fv\nOUW71glIeZSMnBzaXScpLZdsTYTBd6ss33b+pBB1fl4oikCIFLYnlvD5oqpzp+dIDiVL4CRCmPE2\nWpeGK6kPhQWUlqfx4YLa+tENQVit42U16/iAEi0jEhZnILseS/qf1yyj3OSYFqN7/lF0bz2DaOWc\nnnJKZjqbD+y229bdqi2fVlDM/v2ZCNH0wKAhxMbG0r17b6QMhEqNfBcXxNRJiCBt6d/o5s51w0cz\ncZh9keCeYwfZf+o4uLmCxQKlVYo+OQV5LN26DoDQYm21qsjXk0sHDKs36Abw8IK1lAIAACAASURB\nVHDD3z+M//zntXrbiU49EIMuRwTVXpk7q4LDyklzDWfBsrIyPv10ET//vIYPP3yfYE9rfYFHbSrO\nuYQQAv+BVp7xb/OQZ06f1/NfLJAWi+Zs+OevjhvYXCubR0WlMVDnf4blyduRibsbbty5B8qb36NM\nfbhxJ6nUQ78AbLj/ckhZJYTQMglpQT0474H3pEmTePvtt3nhhRfo2bMnGzduZPHixURERDhsryqC\nAB8/LBYLFRXQ4JCtKh+do6IID2/X6JeizNAkm0Q9VvHC1dWhXJiU0qFe9J9/bic5uQQhtAmEyWTi\nt/U7+PGy0XzYtzr1IYm7JhxmYNcTKMoJXPQp9O2ciRD7kXI3Ow6mcfikisncjEFrZDuUp95Duene\nJnUTFgCbE8p5/yc93kaVqWO1AlFFKWDDvhzGDszF1XCa8YOzWfHuIXq0r0M68RwiJVNh7KMGPNyq\nvqPtB2HwNJXfa4rqeFsnIoXFjHvUjxXbzBSW0DhYA2+qW8dfORnx7gvs7WjPhwwLCLJz1sotKmDp\nlnWNPGFtSClZuH6FHUc42C+AKKu+eHaZmX/96xlWrlzZ5HM5i9JSL2Z98yem0GCoqIBjtQulB3ft\nTZtQe1rQ/FVLkJWc8MKqYumf1iy12c5H52svPo/OztEyFCWQxx9/gbffbroNeqNQGXjnZNh9N4qi\nkJSUxi233Ey3bn2Jaxel7TjPgTcAHbtW/bv6PdyCKigK6isPI997Blnu4JlWadjkrGtlNajLf0b9\n6EVkfs7ZjS3lBCTsRKY6ECKoAWFwQUR3QnTq3rhzBIQgLr8a0fvcFv5eDBAWs5b91+sRzbDC0YK/\nL/6S4spp06bZipacQaCPL8ePpzJ27GP06NGTefPm1dlWmf6UlhELbwtIysoqcHNrBE0g06qVGty4\n4htZUIQ66ytE+7aIiWPs9p06lcljj93PTz/9TNu2bfH19eWDD2Yh5UHenJfOyfTUqrYZaXRpq1XE\nDu9dxPDeWoAhhOTqYdk8MElFiKYrmVRCeHpD78FN6kNKibcxhT/ezKis9bPD1cPyuWpIvo110+0v\nMvUKDzaR8G0C/t7eSNkWIQSj+5ew5oNkvI321AwRHobs0w1ah/LTtcfx9XRHiMZxbEV4W41OYA1a\nvlos+XW9nnsmxrAvx74QdFDX3uQU5LNy5ybbtpW7NnNJbDdCz+KlXYnE5GMcOmnv0nfV4HgUr0Do\nGUeXgNasmTnovNpCv/bam2RlpVFww9UExURCWG3KlKIoTBkxhv99/ymqNTDNKyog3cuNUO9IMGvF\nrgknjrCvGmXHt8yCVASGfj1r9Vkd8+evpHXrNgwYMBEhhE1S73xBuBu1YLqkCArzNftxwNXVlZde\neslGpZHF1gnGXxB4C3cjBIVBZhqcR355c0BKiXzzCWRhAcrT758z5zohhJbNzkyDnCwIs08gSWvG\nW5zFb1iu+AUO7UUMugK61kOvrAuVhkQZaY0/1kmIjt0QHbs13PAihszPQe7bhnA3Iup5V1aKIODW\neDnRFvyzcMGrmgD4e/vRvn0ECQmLKSmpn9csojX9WVVVmTBhAidOHGX79s9wdXUu+BbXjUWMHFpb\nqLceyD0HUN/5HHLykAlHkGNGINyr+F233HIbY8f+i8DAqiy6EAIpPYgIDrMLvE9WC7xrIiqsAikz\nkTIQIf56/lhZueT2l+GVaZmEB6fjUc+Q6nvvVZhNzFu5mANJR+kQ0ZYJQy7D10lN7MYi0NeClLkU\nlRhZti2Q8YNO0unECkhNRw7th4jUJjWiTzd0fbQXij8WpCxCymzKKwJwc7W/N9SfPofyMsSYKQjf\nai/IcOvyqzXwHjsQoICyigqOp9k7tca1bY/RzYMdh/eTX6TZzKuqyo+rlnDPNTedVWBsUVUWrltu\nt619eBRxbTto/QUFINRwDMr5zc48/fTT1vvhAEI4ptMAtA4KZXiv/jadc4DX2rryyOTbiQwJpcJs\n4sfVS+yO2Tc4jhGjrkM0MNkOCwvl/vtf48cfLyEqKqoJn+bsISbcAnq9ZpZSc5/1+5almnKR+Csy\n3oDy1g9QVIAIbF6b+HMNIQTqjg3axKakGDy9UNctQX47CzF8HMrku5rvZP6VgXdmrcDbpv18FoG3\naB2FPLQXmXICcTbFlG01ZR65exNc75jK6Qyk2QSF+Qi/uleB/9ZIPYl8/XFkx27o6gu8K1poJi1w\nDheWgX0dCLRyvHU6V3x8nCsCVBSFV199la1b5zkddIPV3tfXG+HTMOdZmkyon89FfeZNyMmDzjEo\nr8+0Bd2lpeWoqhtChGiWyNWCp1OnTjFr1lyO7LTPRpyqkZ2QUiLz8pFWTqvJLHl3fjHjZ8i/3DLe\n1QW6tSvm9pddGzNPqYUFa5axNXEvRaUl7DycwCvfzGbHof3N+vmkqiKTTiE37kAI+PcswS9riymr\nKEOu2YL8cTGkOJY1BG0e9sFP5cRMkmTn249LLpmPnPcJ1FxqDgqFngMRA+KRFjMBPnDL6FSC/XbY\nfbZWAcH4e/vi6uLCNUNH2nVx+HQSO61W9jVhMpvrdV3dtH8XZ3KqpMAEMGHIZQghyM0tZNq0N1i/\n/hw6EdYBnU6HEDqkDKG4uH7K0ah+Q/H3rjJTkVLyw8pFWFSV5ds22PHkhRBcN3w0Oh8vRH11IOgY\nOHACy5cvb9agW136E+obTyD3bnWqvTLpTpRrptZrWiU8PKFzj7+MQys8vRGhtWX5LgrY3CutCgPp\nKZrjb2nTZVjtYA2qZW5t0Tndc7NR5m6E9l1q7WsQ4VHa3ynJyOwM1EXfI3dvdvpw0Xuw5qh5aC8y\n8+yy3vLoAdQpA1FfuP+sjv9bwN1aZ9HAfSP1BsToSU4XWLfgn4uLIuMd4O1HSUkZBoPSKDlUzQ3u\nNJDeYNvGQkoJuxKQv60ARUFMGY+YOBpRrZhr+vQ38PUN47//fbHWhKGgoIC8vBJiu0WTccKeamKH\nklLU/3sEPNzRffceJrMga9dhfsh5GfXlduj+81azf7aGUGGS6HUAecy46QT3ORakcQp7jx1kw/6d\ndttKysv4askC9hw7yKThY/A8CyfAWigsRn3wWXAxoPTtxvSJmfy23kcriDmWpLVp3xaT2czizatJ\nz8licLc+xEZV8WIUxczStzIJ8KmR/avDMl4oCrpnPgDAYpEIWYgQZhJOHLFrV32Fo0dMZzpGtOVQ\ntYLMBeuW4+biSmZeDhl5OWTkZGE5nYbIzeNEoCdxUe0ZENeTTpHRNp54aXk5izevtjtP387diAjW\nigPd3V0YOnQQa9asY+jQSxtzJZsNX3zxG7NmvcvChS8TEeE4o+pqcGHS8NF89Mv3tm2nM86wcN1y\n1u/bYdd2SLc+ts/nCKWl5fz88wauvHIKiuKFX/0GuLWgznoBmXZKs+J2FCwf3INctwR69Ke5iDui\n1yB0vVr4s2cFTx/ISLUG3uFVhY7N5FpZCeEfhISq/mvuP8sMqGgVpVHVUk4gkg4jP30N2WMAuh7O\nmdQIdw9EnyHIjcuR+3cgho9z2E5aLHbvLTuEtAazGU6fQKrqOaPsXNAwWlebiut3rjQbvVH+9cR5\nGFALLnZc8IG3TlHw9fTixRe/4uuvl/Lyy6/YSRE2BCndyczMIyioiRbENaFK1B9+hdYhKPffhuhQ\nOyP17rvP8tVXqx2qsHTp0oXOoQFYirazMWkjFVLLXOYXFVJQXIR35Y+93LoUb83aG91Vnr/rDOrD\np8Dzr6Gb3PkKDO5Wwh3jkxBC1ksxqQ/5RYV8v2JRnft3H0nkWMpJro8fR1x0bY6plJLSijIKSksw\nHT1IQXER+cWFdn+rUqVvp27E9x4Aka3hZAocPkFclw7ERZch09JRi0rAzwfp78vXS35m9xEtC5yQ\ndJSHJk0lylrkd8/ELKRUUFUvsvPd8fQAN50Zyko0ukA9dICH3oVNewy8ep+RA8nH7PZVD7yFEFw7\nfBSvfDMbizWbXVBcxOxff6j+wXl17SlcVMnjQ1zZc+wge44dxM/Tm35detA/tjvr9+2w06c36PWM\nq1SpQOMST558K4ry11AYAMLCwpg3bw7h4Rag7tWN2KgYeraPZdeRKgfYNbvts8peHkbGDri03vO5\nurqzbdtJMjJ+5t1362/rCHL/Nkg9CbkZ4CDwttFCmmOi2IKmw8s6EbZOjKVVQUY0hwxrdXTshijM\nR4RFNm+/ra027SnJVXbxPo3jeosbpyP+70FEcN3mNnLex6jLFyBumI5y2QT74718wC8QcrM0Ok1I\n89UXXTRwb7GMb0Hz4oIPvP29fFEUhaeemspjj/0XIZyXvTt9+jTjxo2jffsw5s9/oVnHJXQKyusz\nQYha/Nvy8gpcXNwxGmO49964OvuQz0xHOX2CLqO7s6usasm8eoElZZorI9XpMkbtxa4W5rMrUdKn\n89nn19Qv30KeTkK5YToiumPd7VSJoghUtYIHJmXywFve3DG+bppDg+eVkq+X/UJxNbMURVFQhMBs\nqXKJLCwp5uPf5tI/tgdtW0WQlZdDZn4OWXm5ZObnUF5RN0e4Er9u+BODXs+Qrh2RJ1OQ+w4irHJ2\n8nCS1igmiu2H9tuCbtAC+59WL+GhybfZZCOFUDGbj3DdzFgmjdAzLV7jY2P0qpeH/b97ykj+7FMi\nX/+BwjAX/myjrYAY3T1sgX0lQvwCie89gGXbNjjuTAjyXHUEl5rxKzdzxupomltUwJIta1m6ZW2t\nscT3GmDjzZeVlePiEoAQxgav3bnEmDFjNCqVLCE39yCPPfYyH330GAZD7cfSNcNGcjD5GKUV5Q77\nmjDkctwd6OZu3LiP/PxirrhiDNCKO+6YhpvbWc4U/QK1wDsnCyLa1d5fOdFx/2uvaws0CE8fLWNc\nlK+tQORYpRsDmlfaTxk6Gs4FvSA0AnHDdERENDJNc2HGt5GBd+uoBtvIpCNatt5QBz0rIloLvE8d\ntwu85ZZVyJPHEX2HIqLqt8i+qFE5kS4t/udm/VvQrLjg76BKDW8pwcXFo34Nb0BdvxTLYzejLpxD\nWFgYy5YtY968+jV6KyFNZqTF+WBSKEqtACcnp4DLLnuQI0dAUep/wRdblRnKU+2DiZPV6SY1Mt4A\nWCXVirOK+WGF08N1CHlgF2xfCxV1c23TcyS9/k9SWJyOEIn06niGNbMON4nXvWrnZg6fspcoG9v/\nUh67/k7Cg0Nrtd98YDffr/iN5ds3sPtIIqczzzgVdFdiwbrlZIRbuZj7DlbtOKqNoSwyrFahXkxu\nGYF7DrNzz3a77em5go6Rudw5/jSyMFfb6FW7GHT9Hskj76qo6hlcDIeIMSRjKC3BUu26dYmKwWKR\nSGn/UxzZdwj+9Zga5bppwalfWW0rewk2JRAAbw9P4nsPtP3/mWc+I+GaWyl65CbHEmjnEUIIFMXI\nJ5+sICysLXq946DVx+jFlYPicTGrhBVVEFxcZQYUE96G3qdykTv2IU1V6jRSgru7P//971cUFQWg\nKK6EhYXh11iOSeVYrcVlMi/bcYMyKwe0JeN9QUBcdRPKzHcRXXprGyo10/2aOeN9jiAMBpRJdyIG\nxEPlPed7DqzureY5dQXPwlpfIE/ZqyPJDcuR376PPOq4BuXvAqHTIYaNQcRfpckFtqAFTcRFEHhr\nL8nc3CLACfWFgnw4sh/STqLT6QgKCkJK516Ecu1m1EnTUD/9oeHGdcDPL5AHHniAP/5Y02Bbs04L\nnjpH2Wc87Xje5dag3K3ahMPdDYTASxTz6t11BAHOorLwyNNxkCelJMi3iK7tCpi3shQhtAdPUyb9\npzLSWLTRXjc6JrwN8b0HEBYQxCOTbmNUv6FOmxM5A1VV+TxpH1IIOHQcaZ3QiCuGwb9uZEFZBmU1\nsqkTD+dwU2I2m/5cYbcvPNjE7H+fwmDIQHrmcCj+QX71u8nuWCklcdEl/LTazJ6jOQhhQZ7ROKDZ\n7lX3cSufUPr2vZ3HH//S7ngXg4F/XTWFNqGt8TF6ER0WQb/Y7lw5aAR3jLuOyDhtJWVibF/6de6O\nQV/34tXYgcNxdamauL3w7D3EUo77icS6s1znGffccw8zZjwFdEZVw3j//Z9Zvdqe+z+way8GCSMz\ntqUx/pg24VEUhesGX478Yj7q8+9QkXKG1177ltJSFSnb0KPHlbz11tsYjc2Qha40QcnNcry/MuPt\n5ty5ZFEB6vcfoX77QdPH1oJaEB26IvoMsUn5KW/PQ3l7HgSen8BblpY038Q23zrBb2TGuyHI0hKt\n4FSvr6K21EREtFa/YjbZH2sNxMU/wDxHeehFlPv+izA03sG4BS2oiQueahLg7Ut5eQUjRtyLqgr2\n7NlTv7RaZbbJSmEQQpCfb6GgIJ3IyAYksTKyNQ1w98YtRUsp2bXrMD169ACiufbarg0eA+ATHAop\nx+kc2Qr2H7Vttwu8LarmouhZ9TIXigJGdygqgeJjSJ+As9dhLnJcGPjhAklxiYWHr09BiCw+fULg\nYqhfZUSVklU7N7P7yAECff3p26mrXcEfQLmpgq+WLLDxlwE8XN24eeQEWzudTseY/sOIa9uer5f9\nQnpOHYEOYNDp8XY3EhoYjLfREx+jJ95GL3w8PckvKmLeqsW2tmcqijkYE0rnHr3AZAJXF0R4GKvT\nT7D1cO0JTJFBG48sLGLZ1vWMHxxfq43FU8eVaybz8eMmpJTMXghDuks6R6Xh45nO5k90BB/cjLoj\nBcuJU+iALHftZ6coCgN6dOePP77kyJFi8vPh9OnjdOmivcjCAoJ5ZPJtjq91+BEk2wk0qdw48mqu\nGTaSHYcS2JSwy+7+iQxpRb/OVTq7UoJSYXWCdTdeMMumnp5VXPOMDB2ff76Y33//yK6NIgSDBwyF\ntQfxMGn3z+V9BhKamo1aUgqRrcn3MLJ//2k+/ng9DzzQF4CBAwfSLPCzZhvrKKJTpj6iZcPrKfC0\ng6oi587WagNuvMdhE3l4P6hmaNOhhTveRAhvX5te+vmA/O1b5HezEJPvQrneed8Kh+jeD+Hihohs\nZhOEU9Z6k/C2CL3jxJa4/BrEFdfavWOkxQIpSbZjWwDuacmoi48jYmIRHeqmmLagBRd+4O3ji6ur\nCzt3zqO8PKrBAFO4e2i8Pmv2aeXKldx//33ceOPlPPHEzfWfLN0a4DXSPKeoqJSHHnqPO++8m5tu\ninX+QCsn1c/ViE6nw2LlNlcvsBRdOqCbU9tVT3ntSXBzpVCn543PStApHjx9WyNdOqWEokqOsneV\naYdUuaxPDsPu8ebuq3Pw9ABXl4al/X5Zt4JVuzS5q+T0VHYc2o+P0Yu+nbvSL7Y7IX6BLFi7jIxc\n+yB3Svw4/BxQNSJDWvHY9XewYvtGjqYk4+3hSZCvH4E+/gT5+hPo48eppGSEEMTGOr7uWfm5dqY0\nH4e7MCrajzHWiUxK5hkWbVxld0ynyGgigsMo3r9QuzQmC6t2b2FAXE+CamScXAySLZ8eJMDHgpTB\nqGoAd7wi2fDRGYSA0AAzlu8WQsoZKnUDsq00kZhWkbi7uuEaEk1paS4jR05h8uRhtsC7PojIVsiO\n0eCnBRLurm4M7tabwd16cyojjT1HNTrNsB6X2CY0mzcnkJNTzhW9RmmdGP+6wsr6EBISwq+//kZo\naCtU9TCKUiXjFRgejgoE6lyYPGIsA+N6Ij/6BgDRvydBQUF8+eU3pKc3cSXIAcSAeC3wqSPQED0H\nNE7NxMsHXFyhpAhZWqwZ1tSA+tFLcDwR5X/fnJ0kXQv+OlRO0LyaHuwrI8bDiPFnfbxUVTi0F8pK\nED2rJqIyPUVT5WpTN0fboeJJRipUlENAMMLofN3V3xnex/YjVy+EiVNbAu8W1IsLPvCOsmnIGpxz\nl6t0jSrTAu/Bgwezc+c2DIaD1KecACAztMC7Prt4RzAaQ/nqq29ISDjYcONqEIEh5Bt9+fyDhbj0\n9qPUUKVCcaoeIx0A0UrL3h856M7x1Aqevd0NqEMSqi6UFoNqATd3ylU9Q26H31/PI9A3lfYRpRz4\nVoenh3Oc9z93bLIF3dWRX1zIiu0bWbF9I62DQkjJtJd27N+lBz3ad66zXxe9gTH9h9W5v6GJ2JUD\nh5N8JoVjqSdt25ZuXUdUWDjtw6OYs3Rhrez7jZePx83Fld1z/wBKMJpULBYLC9Yt564rJ9c6R6Cv\nxTqWDP41IYO4dp72VJzwMJtGeIGLQoVe29mhdVsyMwsIDPSiTRtvPvvsc2JjvYC6M/y2zz2gN7oB\nvR3uiwgOcyirp9PpePfd+bhca2I4wAX8wgwP13732dkefPDBezz00GS8vY3gpQWnXhbJoK69kBYV\nuWUXAMVxnTHKViiKC2FhTmadGwERFgnNqFwhhNCk7c6c0vjHjgL60r/OubIFzkPu3IBMTUYMHmUz\n0ZJWStLZuFY2O/ZsRn32HoiMQVct8FaGjEJecmkVTcpZVGbKHRUZ/0OhVNIRW5wrW9AALox15nrg\n5+VNYWEJhYVOFtK5WYNz64PExcUFg8EdKZ3gstoy3nUH3tWNT955Zx7Fxe4IEU1UVDvGjh3r3Bit\nUO6YwZab/023224htqN9lnP9vh2s3LmZ1bu2sHbPNtbv3cHG/btq6Xz37lTK108fJyqs4WCtFgyu\niOc/QTz6Gi6GEgbE5fHJr8UoikbT8fWqXbjnCNsO7uWX9Q1XedYMuoN8/Zk49IrGj7sR0Ol0/N/o\na/DyqMomSmDO0oX88Oci0rLtaQOT48fi4+mFq4sL4e20ZV2jSbsO+48fJrGGFGDt88HQHvayUyJc\nCwJXtPHhzT5VAaGrxZ34+Pt44omZ6HQ64uLiEKIVUurPiTlS7979WLRoMcP6WAP2iyCY+89/XkBR\nPNHprI+qSq52kaYwwOFjkFdAha8PI27/H4sWbaq7swsRldJ2lYV/NVEpYXaBrk60QIM6/zPkp/+D\n09UKEG264WcfeEuTCfWD57D8d3rTnglxfTU64cmjyFP2zzDh6mbvuOsMImMQtz2KuOyqsx/T3wyK\nqVKBrMW5sgX144LPeAP89tt6Xnzxa2699f+YMWNG/Y3bxKC88qXd8p7FYuHw4TSMxnLatKmtmAFW\nzlqFCRQBgZUFnYUIAb6+Wmbw0UffJz6+P1dccRngwalTZTz55Me8/XZtKoizGDVqFKqaxeYDxew4\nvt+2PeHEkVpGK5WYNHwMg7vZZzuFSCPhuAcvf+3J1083nAkG+HKZngMnevDq9BSEOMQr08G1AR53\nTSQmH+Pb5b/ZbXN1caFrdEf2HjtIhcnk8DhFUbh11NV2RX/nCj6eXvzf6Gt4/+dvbC+vkrJSth3c\nZ9eub6eu9GxfRVkJ69ubQ8eOk+FRdS1/XruMx2+4C11dhhOOYA28A0tM5LtqP7lgvwCGDerN1q1L\nycqquuYVFSqzZi3iyJH9zJr1aKM/qyOUlZWjKHr0+jD0ej2yYxy89rVWUHWBY9asWWiXOhGoQBj0\nEBMFBoPG049ohbjv/3CVgs+C+5OZWfjXDriREIEhGjUuO90xTaXStKNForDRkNkZqB+9iPDwRDz4\nwtnXwTiBShMdmZNZ9T02Q+AtDAbUzSuhMB9yM8/a/EcYDIj+I5ArFiLXL0M0kXMuQsMR429sUh8X\nE+SxRGTSYUS7WOpSf9FVZrydWZlvwT8aF3zGG+CGG0ayd+9qHn744QbbCncjolN3RLUK7dmzZ3Pf\nfc+za9fhuo/T6djz0DQSH38QodcjJbz99o/Mn78ZVQ1FVaNp3boLCQmFCBGNooRx330P8/TTTzfD\nJ3QnIsjxhMARflm/goJaLloW7nhZcHlf5wIPKSWX9Snip9UW8otyrUY4ksbEk8lnUvns9/l2tuU6\nReGOsZO45YoJvHjHw9x4+XhiHFTLjxswnMiQuk0dmhvtw6MYN6DKQMZgUZm5KYVb92cipMTPy4dr\nLx1ld4wysA/GJx9gb3BV0JOek8W6vVXyguqytahfzEMmna7z3CJCC7xDSqomIXFt21slMgNstAqA\nkpISUlJy+c9/HBfbnQ0WLlzHmDGPsW2bNrET7kZEhzhEdKdmO8e5gl6vRwg9UoZz+PApTCYzutdn\nonv53whXV4SnESV+MIyYQNeufYmPr10AeyFDDB2NuGMGokPtgmxpqtCUJPR6jQvegsZBANvWIvds\nQb7/LJaplyM3r2rwsLOCVWqyMtiWUmrST4quat/ZolKLOyW5Sd2Iwdrqoly/rNHZc2kxI08dRx49\n0HDjvyHkmsXI9/6L3F33ilpLxrsFzuLCT3lZIYQLOt3ZDXf69OlMm3YzcJjy8gpcrZrYS5ZsJje3\nkClTrkBKV7ZuTSY9PY/YPlcBbvToEc/JkydRFE3u7+6778HFxcWWOWnTpg75pUZASsmMGc+wd+9W\nRt4ax8msVLv9biYVnZSU6RUsinbeclMFf2xZy+QRY2zthIClbx/By0NFylZAKNn5EOhrn+XZliiJ\nDIEg3wzCg1PYO0c4zeOujozcbD769ftaGe2bRl5Fx0iNq+rq4kK/2O70i+1OVn4uWxP3kpmbTYeI\ntvTv0qNWn4WFJXh5nTt+XHyfgZxIO8WJQwe5c28GAWVmynUChOCmkVc5NGCJDGlFv9gebD6w27bt\nj81r6N0xDi8PI3LzTti5HxHXEaLCax0PoIYFs7mNHyfdqr6LYGMQe/acpmtX++vg5+fH66+/jqoW\nIeVhhGg65WTSpJEEBfXCw+Pi5R5+/vlPfPjhB3z99UxiY6Ns2w8cOMGiRVu4996n8fA4dxnNhiDT\nTqJ++TYish1KHQoljiB6D667INNUAd37OzTpaoETMFoLtovykZlpmgzkuVphq8xqWwNvIQS6TxbX\nb8fuLKzfvfrbd+i69j37frr2AR8/TY0k+QhE1XYDrhMHdqM+dSd07Iru1TlnP4aLFTbb+LoTWwVt\nY/EPb+OUaVEL/tm4KALv1NRsfH2jONu4QXtpGZk7dzU7dhzi1VcfB9yowbuEjwAAIABJREFUqPBn\nzZrdTJnSDSEUhgyRJCYmoiiapvXVV19t149TxZ1nMbYRI0YwdWo8kW092XvsINn5uahSoqoqXVbv\nImbXETb3bc9czyqeu1y6hoqvV6AfOQzleo1n522sDKBT+WiBC18t9mPTJ/a0k1/XqWzcV87St06j\n14OnR+MDu4LiIj5c+B3FNQpyrhk6kt4dHVdzB/r41VskmZSUxoQJT3DbbWO5//7rGj0mZ6BYA+y3\n0tNpU6hlqDM9DIzoPYD24XVPosYNHM6uowdshj2lFeX8tnEl18ePg2LrNfCqmwpwsiCHudFVqi3u\nLq6YCiWPPPcmw4fvY+bMmbWOEcJIRoZg8+a1XHXVEIf9ysxsOHEKQoMQkfVZOYcSH9+znv0XPvr3\n78+VV44iODgLqKo9CAjw5fTpQmbP/pSHHnronI9DnfMOcv8OlLseR8RUU9LJyYQtq5AFuc12LuHh\nie7ZD5utv38ahKsbuLhBRVlVtvgsqRoNojLwzrWvGWly0A1QmXDaurpJ3QidHjHxNi0T7x+MzM4A\nV3eEpxNF1pHWGqRTJ2zqV/8oVNrGlxbX2SSn5xCi+/Q5TwNqwcWMiyLwvvfeN0hISGL16tVNUCtQ\niIkZyq+/7kSIaIQQDBkyiujorgihPRy7dOlCly7nT7JLlpZAXhaj+/VB+pWjKBkM6trLro2acAbJ\nEfr17MufGQfIshopCCnR5RZAXoHDvncftfD1M6eAcFRVsdq9l/D01GR+/TgJPvwDeecUhFvjlrBP\nZaTxzbJfyC7Is9t+We+BXNqzX6P6qo7IyAjuv/9+hg/vjpSiWTK9juDh5s7Uq6fA7xq/W7QOZUz/\nS+s9xtvoyahLhtoVkG5O2I3JbObGgiItY2l0PCu0WCxs2LfDblvnqHYMHdqT5csnYTI5vv6FhYWM\nG3cXkycPd7j/vfd+5E5vMCxYgrhuLOLGq2u12b//OPv3n+Taa+9rkuHRhYA4q2GQqhqQ8hRCaBPK\noKA2vPPOh+ekGNUR5OkkOLxPk1OrHnjb7OIv3lWFvyW8vCG7DLKthd0B5ybwFm1i4PJroFO3hhs3\nEsq0maivPYZy/d1N72t8ldGX+tZM5JrfEQ88jzJ8XL3HCR9/TQO9IE8rBA5swBPj7wZbxrsmxbMF\nLWg8LorX8U8/vUJiYiKhoc7zoGtCCEHv3n359ttvbbN1Pz8/2wv9r4DctAJ12lXIb94DPBwHD1aH\nRcXdnSsHjbBtLrFK0hVm1jbzEAJmzzhF+4gspDzKbxvMrNlVgBCH0ZemM2Hn/xB/rkMubdhd0zYM\nUwUL163gjR8+q6UEcknnbnZjawwqKkyoqgTacOONtxAV1RcpO5KdbeHJJ2fb8cedhaqqFBbWLY/V\nKjAE+eIMLCMG0n3GQ7VcH6UEKe23DetxSS0N7x2H9lOanaP9x0HG+3TmGd6Y+zlbE/fabe/StgOg\nRwhPXF0dB97e3t4sWbKEhx+egZRwzTX/4ciRNFTVC1UNZMmSHZxRNb15eSaPBx98hxMn7BVv9Ho9\nCxZs4LPPvqjzWlxsSE01cdddr7Pgh+WknswAWltt58/Po0xYTXRkDfdKac2ECSddK1twnlDdkdfF\ntZZRWHNBtO2Ics9TKPHNr/IhWrdB9848RP+ze8bWBZms1TyJVk5KZFZax3/9HuobTyB3bWzW8VzI\nqNTYl/VkvFvQAmdxUQTeUmq8ameXtywvP4zlwUnIHHuJrvr6kJlpyBqW4ecawlqEUZafx5Qp/2LC\nhCdqj8tqGS9cXegR05moMI1HXGoNvLNSU1DryfYJUcSnv5bw9CcgpRn13S8gOxc6tUOMc64QLTH5\nGK98M5uVOzfVOldsmxiujx931kuPs2f/wl13vUVOjhlXV1drEGXklVfm4+bmb1uNqA4pJQUFVQ/A\n1NRs3n13vjVghm3bDjJ16suoqieq6pgepO/SAZf7b0PxsN//ySe/Mnv2UszmNpSXm6hYvw116Rp0\nqspNI6/Cpbq7m5S4mswAbDx+yDZxMpnNLNq4itd/+IzTmWfs+nfRGyjNsvDHH7spKqr/IR4QEIAQ\nAUjZAT+/1hw/bkCI9ihKG6ZPfwD3NlrGtexUFhs3JtKqVRebFOHq1TuJienI99//yNSpU+36VT97\nHcuMW5D7tzs67QWNLVu20LdjHP22biXk/v+Q8PrL53cAddnGt2S8L0god/0bMc1K5fIP/udRJOqA\nNJvg9AntP066YVZaw8s1vyPXLUGeqbug/G+HsAjEpWMRcS1UkhY0HRd84F1UVEpqai6mOmTpHCIl\nCZKONGpZSJ1xC+qk/sis9IYbNxesxXwuUuX++x/kq6+eqd3GmvHGTQtKJwy+DKgKvEVxKbsOJ9R5\nCiHg/UdOsuzto7BoBWzfC54eKI/c1SD/sLCkmDlLF/Lhwu9qUUsAenXowtSxExsnrVcDd945hQ4d\nupGVZR/IPPDAAzzyyNNI2QFV9WD58m1IKZES9u07weTJz6CqPkgZjMkUxIIFm5CyA1LGERo6hJIS\nEKIDQsTw888b2LBhbx0jsMeoUYNZvXoPn38+l1GjHqPigznID7+G/ELahoXz2PV3EBagBV8C+KmD\nP7+082XuuqV8+cfPHDp5nP99/wnLtq2vla03unswdcxEVLPKDz8s5Y8//mhwPNpExIu3336Hyy+/\n3BY4jB07luA4rTDTLT+buXPn4eraFohj06ZsXnrpW4RohaIouNQoKJMnj2p0CZOT2vgXECZOnMid\n7dsQeiIJgOD251mZpVKhombgXXL2RjfqT59rGcScOrS8W3DWEF16o1wxEWXuJpSXPj1v55U5mciC\nvPNGgWo0UpLBbIaQcISzk8X2cRBbVStSGYj/EyDadkR58AWUcdf/1UNpwd8AFzzHe8+eIzz66If0\n7NmHWbNmOXdQpYlOWalTzWV5mfYi1embLv3UGFgDb2GqYNCgQUh5FKjB2XZ11WgMVi52dKsIusd0\nIm2PxlF2N6vM2biKbu061aJMVKJNaAXy+EnUOT8CoNw7FREUUOewVCnZlriXBeuWU+LgGvp5enPd\n8NHERTeiKt4BpBS4uLRjxox/19pXXWJv3z4TTz75KfHxkwBX2rZtR37+W0A0paV5eHt78sgjj6Eo\nWpFQmzZRLF68GIAVK9by3ns/MWvWg06MB1q37sP331/G7t27ad8+Gvdf3oXk01BQBIH+hPgH8siU\n2/l5zVI27t/FplZVhUm7jhxg1xHHclu9OnRh4rArNCWUKIVhw6YihPM/Py8vBwVQASHaPZubRVQr\nrfZBCB0VFa5Mn/6grUi4FpoQJF4QUM22fwaPmnBeTy38AjW95hqBt+h3KSI4DEIjGt2n3LoaDu1D\njJ5kV/wn005BRgqERSKCz5/05t8RwtXN9rw9H1A/ehG2rkF5/A1oZopIc0AmWz0iGiHpqsRfhRwx\nHvWGIVqR4T8o8HYGQVtWoGYnIS6/BnGxF9W04Jzigg+8Bw3qxoYNPyNEfaoNNVDDNr5BZFq5sYGh\nzVOF7iwqXwTlZQghkNIdkykHg6Hqa9E9Pr3WYVcOHMErRw/xXP/WlBoUygryWLd3GyN6Daj7XGHB\niMGXgIc7on/dChenMtKYv3oJSWm1lxEFMLTHJYwbMLxJxjdSSv7zn9lcc8119OnTsNqGr68ft912\nB6rqjV6vx8sLNm6s4he6uroybpzj4qDhw4dzySWX4OlZipSnqWul+aefVjNs2GUEBPgihKBnT21c\nlpXfAqehsGr1xEVvYEr8OGJat2HuysWU15M59jZ6MnnEGLpGd6z2+T0dUmgaC6HTIQZeBgYX+P/2\n7jy8qSr9A/j33HRJupcuUEqhlJ2q0FKQRbaRVRG3QZBBUBwBVwR/jgqoBR3U0RnHDQRmRgZFQUfH\nUURRWURGEJDFYQcBWdtSupeuuef3x03ShrZpWpLcNP1+nqdP25t7b17ogb45Oed9y8ts42nIkCGO\nL7SWxPLilvGOiK49IQEgIcm29tJjuvaA8twyINZ+k/cVtZO3JNuXN9GRm7+E/GAxxG/vhZj0UCMD\nJl24oHmOW+Vpe1NEQ0oKAtrGypJiICxC23BJGnMl2nyzGnK9AWLE7XpHQ16uibws82/Y2jxr4u3s\nRogsS+1sDzZ0AaB1o2vZBmgRg++//x4DB47DnDlL6r0sNjIK/XukIdfkh1LLkpN127eg2MEMvzAZ\noTx6L8S9E2p9/FJpCT7a+CVeWfX3WpPu1tGxmD1+Km4fPNJh0n3gwAlMnvyc3RrsGrEIgcGDB2De\nvD+jrKz+dfUJCQmYMWMG/BrRadFgMCAsLAxCxOLSpSD85z/f1zhHSonDh8/i1lsfqhGPDNXeATm6\n61CN69K6Xo3H7/w94uvY4d+3e0/Muet+u6R7xYovsWzZZ7hQy6bYxlAeewHKI/MhQuuY3a5NcdOe\n8RbdU6C8+A6Ul/7p+ecOi4C4Og2iZQMmAuq7Z5Rl/FzeNr6pvzPRzMj9u6B+/A/Io/urEm9PvoPa\nAGLk7RAPp0P8rubEjkOnj2ufOdttx2CdfDGauI+A6uX1M96nT2ciICAUMTExTlcuECaT9nZwSUnd\nzSmqkZlntes8/HauSEiCYYnWbv2q3FysWPEPJCY6ty591LWDsP3gzyi1bAgtKSvF19u34NZBwx0/\np8H+71CVEj8e2IvP/7seRSU13yHwN/hhVN9B+E1KX6fWcl+6VA6DIQT+/m2hqsUoKMjGv//9He65\n50bbOVL6YcSICRg+/K4rWh/eEKqqYuLEJ5GY2AJjxvS/7HkVPPlkOu65pxhGo/3b0ccys9EJQBhq\nX6sZGxmF2eOn4pPNX9vKBrYIDceE68ega7uav5w6dkzAmjUHkJWVhdhYN9UUro9txrvpJnSia80G\nTE2WtcTd5Wu8L1levAaxUkpTIH/cCPnZe8AkCeRd1A5GeGniHWiEaEwFls5XQUlfjCZfn9TFlPJS\n7Qsju1ZS/bw+8X7jjY+xfv1uvPXWIvTt29epa8TEByBuvQdwNpGWUpuZcOEsVkNFRkYiIiICwM8A\nKus7HSGmIAxPG4DPf9hgO7Z573YM7JGG6PBIp57z7IUMrN6wFiczztb6+FVJnXH7oBGIcvJ+UgKp\nqcMxd24fGAytIYQ/vvhiOXbsOI677/ZHWVkxNm3ajWHDxsHPz3PrLQFt5vtPf/oTOnZsA0U5CmsT\nlpMnz6Nt254QIhRxcTVLjXUcczvwv7aI6dGjznv7+/lh/G9uwNCUa5FTkI8O8W3rXG/ft29v9Os3\nWbdZESkllFdWarOpAZ79GVAdrIl3Nme8XU0e/hnq8lchOl8N5Z7Z7n0y67KSk0cAVQXCIyH8/R1f\n08SI4FCgp3O/h32NPPsr5IbPIHoPrPHCX7HNeLOqEdXP6xPvl156AFImQ1GcTxJEA9daKjeMB24Y\n7xU70EtL/aCqhQgOrv+V8+CUPtjy807kFmkbMs2qikX/XonpYyegZQvHMy3bD/6MVevXoNJsrvFY\ndHgkbh88EsntOzkZcxlWrvwGkydPhZ9fNDp2rFrX2LnzVUhOTgFwFRQlB/v3f4PNm1/FwoULnbq3\nK3Xpoi35UNUEHDu2BUIA48c/i/vum44ZM+6v9Rq/39wE/OYmqOolFBbuhpRmhIVZarr+uBty9z6I\nPikQqVchNjIKsZF1b1rVhOn6VqQQAkh07udKniG69AAefBrisrJu0pJ4CybejVdWChzcA3lwD+TY\nSRBuaqADwJZ4y7O/AnEJQJhzExbUNMjNayE//geQk1Uz8baWIuaMNzmhCbxfJCBE4zfyNeiZdF6b\n9fbbbyM19XZ8/vl/AWizkzI7B7Kw9uUnAX7+uLG/fWfD7Pxc/GX1P3D4lLYWT57PgiyvKsVoVlV8\n+v03eO/r/9RIuv0Nfrix3xA8NWmG00k3AFRUmPHtt3uxYMHSGn+HvXv3Rs+ePSGEgoCAaChKKO6+\n+26n7+0OGzfuwYQJzyIzMx+ff/4JunbtVu81W7bsxPDhj+Kbb3bYjsmDxyC/+g7yxCmnnnfmzL8i\nPf0tl63vJu+hLn0R5j89DmndL9IAomVrKMNvg+hi3/VQJHYGrkrz3g16TUH1Fy1uToSF9edkDIJh\n8Wcw6LAHgdxHDNGWS8qt67Wu09WYTcHI6jMM4rqReoRGTYzXz3gfPHgGcXHtERnp+7MH48ePx+TJ\nYxEcnIEVK77EgNTOSJz3AmAMxIIuqbjlloFISanaha6+uRy9tu5Cdt+O+ErNtx0vKS/D4k/fx2+H\njEa/P78HFBZB+dvLKAkKxPIvP8EhS1Je3TUduuDWQSMQFRbR4LiDg+PwzjsrceFCdr3nzpo1q8H3\nd7XExESsWPEeunWLh6JEonXr+jcKxcfHY9GiRUhJCQRgeSFjbYAT4twa3PvvH4f160/XWEd+JaS5\nEti2ETLnApSbJrrsvlQ39dMVkBvXQNx2D5TBowFA6+J3/jTwO9dVH1GmzHTZvZqtavsY3L7sw5p4\n5/CFtS8ScW2Bbj21d1C2rYcYepPtsfKIaJwdMR5xaWywQ/Xz+sT70Uf/grCwFfjXv/6ldyhuITPP\naWUP2ySiRYsWkLIcqmrA5s1HkBCagEQACAzCuXMlyMwMhpT+EMKS+FWageJLGNEtFXkyF9sO7LHd\nV5USX6z7HP3yCwGTERlqOf62aiUu5OfYPb+fwYA7h41B7672s23O+PjjTbj22j6Ij+8Bo9EPCQkN\nr2Gshw4dOjTymg5Q1QsoL/8FAQF+kEXarIeopV18bTp3vhpdu45t8HM7pBigvvY0UF4GOewW55th\nUOMV5gG/HgUyTlcdY+dKryTi2kJMfcylVWjqFBULMWai83uLqMkRQ8Zoy5Y2rAGqJd5EDeH1ifdX\nX/0DiuK7pYvUJyYDeRehvPMNEBkNIQIgRCtMmjQVHUIsM6OBJjz15NOWxLwCJSVHYTIFAJZ14Mql\nEtx50xi0bBGFz7ast9XfaFWsJegZQf7464fv1Kg3HR4SivvG3IG2jSyjmJNTgvHjn8S6desQEtI8\n1qEKEY25c+fh6qsTMMk64x3sOPEuK6tAVlYO4uPbuSEeAcTEad1aM8/Wu35bSqn7kqomz1oizlq5\nAqgqXerpuuJUL2XsJI88jwg0Qfz+cY88F+lDDBgB+bc/Aft2QOZmQ3hpuUjybh5d4z1kyBAoimL3\nMXFifW+PN/ztQbn/J5hn3wl1yQv1n1tWAnn6F8jLZoI9ploTneqGDBmCNtGWjXpGE5KSkhAREYE1\na7biN795BAcOnKha4lB8CUIIXN+rP+4dcwcC/LS/s1aXtMT7V3+1RtLdPq4NHp/w+wYn3VJKmM1m\nSOmHe++djXfffdenk26pqlA3roH62UpIKXHu3Dn88ksWbrvtjqqlJvXMeAshMGvWYjz88DOoqKhw\neG6jWH+GWbVXp7GS5WVQJw6E+fFJkJe1syfniUjLJjpL90pprtT+/QrBzVVEPkyEhELMfA7Kok+Z\ndFOjeXTGWwiBqVOn2lW0MJkc/6L65ZczSEiIadi62IoK4PghSGeaipw8CvWJKUCnZBhefs/553CV\nOhJvAIC1Nmi1Vsd+fn5YvPiv6N7dBPnLMe1gcdVGj2s6dMHMcVOw7PMP0bJYezGREWy/ObVvck+M\nGzK6zpJ3jrz88vsIDW2B6dMfg6JoLwh8mhCQi58HyssgRtyG+Ph4fPLJJwAAdfx0XDi0DRvX78ad\nSfaVdEpKynDuXDaSktrDz68DnnvuTygpKYG/G9aZith4rW591jnHdevPndJmZosL2dL4SkRYXhDn\nWtbyllgaV5mCG/1ugrplHeT366AMHg3R33EtfvJu8uRRbW15i1jPdkImj1CuG6F3CNTEefy3r8lk\nQmxsrO0jNNRx2+pp057EF1980bAnsc46OdMyvtCyKTGkAZ3/XMlR4i2ltmEnvKpE3Q033ICePQdA\nysiqJQ7F9n/OhNg4PDZhKkwhISgIMCAjWEv2FCHw2yGjcOf1YxqVdEtpwPjxd+HjjzehoqJ5JG5C\nCCDUsuG0INd2TAgB2XsUpqzaDkN4zRJl27cfxNSpL+HSpXZQlAh069YNqamp7gnSuqY003FFDXnG\nsqm2jY+/WHI3a6nOHMtm4sBAKPNehzJzQePvee4U8ONGyF8OAgBkySXI7ZsgD/98hcGSp6nzH4B6\n3w32S5HIp4WcPIyY7d9CHq/Z4Zjoch5f471q1SqsWrUKLVu2xOjRo/Hss886XKqwfv1nUJQGJsW2\nlvF1t1C3kpbEu0Ett10poO7EW3S5BoZ/fF3zuBAoKYnEe/vP447XnkN4fM1yY+HBoUh5/hl8tOlL\nHN6/By3CIjBx2E3onJDYoPAqK8149NHXkJ4+Cy1adEG7diZ89dVXjWrf3mSFRQAXM4GCPLuNU35+\nfnjllT8jOTkZqpqB0tJfcf78BSQlJWHgwN/illsKcPFiHoKDazbmcSXR5Rpg5O0QyfUk9qdPaOcn\ntHdrPD4vOg7Kn961VbEQ/gFA2sAru+flTXSyzkFdOAtISILhjY+v7N7kMdJcqSXcQgARLfQOhzwk\n/MhuxG5fDxkfD5HUVe9wyMt5NHuaOHEiEhMT0bp1a+zbtw9PPfUUfv75Z6xbt67Oa/buPQizuWFh\nBuReQDKAsvxcHNi50+G5MQf2oQ2AzJIynK3nXHdoawhEUHQcTh89iuIy56974403YDYXoXtqAloU\n59Z5Xkp8R1zdqj0URUFl4SUcOHCggRH6wc8vBHPmLMW0adMaeK3n7HTjz66jVBAK4MhP21GYV/Nd\nlF27dgEAvv9+E0pK8jFyZBykPIqBAwciKysLWVlZNa5xud6jtM8O/h4Sf96JSAAnK4AcHca6N3HJ\neCk4DZw8Xf95Tgi9mI+OAApOHsOxnTsRfPoYOgMoVoEjzfxnpbeGjJXQX/aho6UR20+799RzNvmK\nBEsDnV8zL+Ai/702e506OS5ycMWJ97x58+rtQrhp0yYMGjQI9913n+1YcnIyOnTogD59+mD37t1I\nSUmp9drz57MRE9OyQWsnzZblG4by+jNZg6UagVmnagSnxt7TqOumT58Oo9EfRuMJAI7/nH4NXGd4\n7txF7N17HKNGDUd5eSzGjWuL8vLy+i/0UZWWJhx+l2pvZGSVk3MJJ06cwfDh2oSXtwnI1976Lolm\nuTNvU25p7uJfqL2INpRp79aZA7lZsykJPXFQ7xDIU6RE0LmTkIpiyzVUf880+6Om7YoT71mzZmHy\n5MkOz6mrvnNqaioMBgOOHTtWZ+L95z+/im+//bZBibc0m4HW7yHAFIy0+ESH56qn90Meb4vWV6eg\nTRMsfq+q7VBUdMjWxtwVoqOL8cQTKzB69AykpHR32X3dwToblebGn52afxZITEJS/0E1ugtW584Y\nXEH2+gTIzkT3iCj3NxPxUp4YL40hLxVBfRswFhWgV69ekCXZkADC4+K9LtbmojFjRcZFQ932NcTQ\nm/hz83HqN59AvrMQ6D0I+RVa4p3UPRmCP/dmLz8/3+HjV5x4R0VFISoqqv4Ta/G///0PZrMZcXFx\ndZ7T0KQbgLaTvGOyU+cqt04Bbp3SoPt7k5Ur1+HVV1/BRx89hw4dGt8kYvPmPUhKikfr1t0QE3MN\nli5d1mQa4ribcv3NwPU32x2TR/ZBfrka6JYCZcRtOkXWMFrN71Z6h0G1EEEhEI+9oLUdlxKwvrsS\n5LulOn2RiE+E8t5mu46Z5JtE78GQykJg1w8IaGHZo2FkAy2qn8dKUxw/fhwLFizATz/9hJMnT2Lt\n2rWYMGECUlNTMWDAgDqva87NPmRhPmROFmRtFU8sYmNjsXrVcrRvb798QP58EPLkacjKSqeea/fu\nk3j22Q8AJEAIf/Tq1aveijPNmTxzHHLjGmD/Lr1DIZ3JbRtgfv4RqOv/c0X3UQaOgkjuBaEoWq3w\n1AFA+84uipI8RYSENuvfW82FiIgCUvsD5koIsxkX0oayayk5xWOJd0BAADZs2ICRI0eia9eumDlz\nJkaNGlXvjHZOjk6NbbyA/NffoU4dCbl2dZ3nDPt8CZLmTIfMV1BRUZVkq6/+Deqj84GLdW+8zMrK\nhZQKVDUOM2bMxfXXj3Rp/D6tqFD7HOreiiXOkkf3Q129BHL3D3qH0iyo362FefpNUFe+BXnmBLDz\ne617qIuIPoNheOZNKDeMd9k9ici1FEvbeDUgEGdGTYSI47vEVD+PJd5t2rTBpk2bkJ2djdLSUhw9\nehSvvvoqIiIiHF63atUqD0WoD1lUqHXOvFhL5QvrTLejDVaVlUBlBSpyA3HnnfOxbdt+yMIiIDcf\nCAwAYmpfBnTpUiluvvlJbNmSDSHiEBhoxMSJE6GwsYpziixruNxcKtBZ8uAeyA/ehtyxWe9QmgfV\nDGSeATLPsl08UXPVexAQHIqgjFMwZp3ROxpqIrw+y3rggQf0DsGt5Ib/QH34t5Cfrqj5oKWyQfXO\nlTVY1hIe2LELMTFtkZbWFzh9XnusTVydHQqNxii8+upfsW/fMb4t2hhFBdpnL5nxFpa28TKz9rbx\nMieLbeJdyK5tfImlxKSJ6zuJmhMREAhx2904O2wcKvRqwkdNjtcn3o2lLn4e5odugzxUdy1VaTZD\nHt1fZ7LiEQGB2uda1nHLUi3xFkYHM94hWuKX0rkDFi1aDIOhI9RT2saswnD7/wguXSrF4sX/RkVF\nKIToiL59r8P999/vgj+Eb5PlZVDX/QvqZ+9VHbQm3t7yn62te2XNsSxVFeoDt0CdMACynpKI5KRI\nS/fK3GzOeBM1Y8rtU5HVdwTMQdwTRc7x+sS7sfWj5cULwJkTQIGDsi4FuVAfnwT18UmNjM4FHLWM\nty01qXvGW1iWOsjiQksrcwWFB34FABSER9qdazAY8N13B/D6659DiGbUefJKSQm5+I+QK16DtDTH\nEDfcAfHgMw7LC3qUNfHOOm+L0SY7AygtAYKCIVglwzWqJd7SMuPw8ZWXAAAYmUlEQVQtrnDGW544\nDHP6A1AXP3+l0RERkZfy+uwrLy8PsbGxDb5OmEyQAGTpJdS5kMK6TjfU8TpzdxKBRi3Osprt7UVw\nCGRElOOZtGDLq2zrDCwAY4euyDt5BPGDboGUgSgvL4Sfnz/8/dtj8eK/Iy8vz8V/Ct8mAo3ai5+y\nUm12MygEomtPiK499Q7NRgSHau9+FBUA+TlARLW1/We0VvFow1bxLhMaDvj5AcWFWknSoWOATs6V\nMK2TBLBnK2TbjtomWVUFuqdecUJPRETew+sT78Yk3QCq6mmW1GzxbWOdDQ/VcblAgGU2u7zmjLfy\n2Iv1Xi7umQVx7//ZzYobb/4djDf/DgAgZQUWLHgM99wzFR06xCIyUiAyMrKu21FdwiKACxlAYb7X\n1lYWv70XMPgBfvbNceTp49rjTLxdRggB5a8fAmGRQGi4a/ZJRGnrxnExE+qSF4GM01AWfQqY2l35\nvYmIyCt4feLdaNbEu9RB4l1oSbz1XKcbGg7EJ0K0aNwLjPqWDly8mI9t2/YjMXEHOnb0nhnaJic0\nUku8C/KAlo1vVOROyi11dJC1zngnJHkumGbA5S9kwiK1F03FhUBlhXaM60aJiHyKDyfelg2JDhJv\nWagtuRA6zniLLtfA8Na/3Xb/6OhorF+/3m33bzbCLMuRCuqui+7VjEGc8fZyQgggqqVWptC6vyOI\nGzaJiHyJzybeYvQ4iIGjqjZB1cYUBCR2Blj0nuoh+l0PtO8CxMTpHUqDKQ8+A/nA01orcvJuUTFa\n4g0Afv4Q1qpHRETkE3w38W4RC9SzfEO5biRwHbs1Uv2UkbfbvpY5WVD/9jJE63ZQJj2kY1TOE0IA\nrNfu9ZSpjwF5OVCff8RWo5+IiHyH15cTbK6klJAZZyDzLjp3vqU5irr+M6jffQlpbWlOrpeTDfzw\nLeRPW/SOhHQmy0phfno61JefcMn9RMdkoGN3oN/1EKkDXHJPIiLyHj47493klZVCnXETEBAIw4fb\n6jxNZpyBOmsCEBkFw6L/QL6/CLiYCbH4P0AIN2a5hbc1z7GQUkKufAu4cB7ikQUQBoPeIfk0uW8n\n1KenaXXew1xXklRERMHwxCsuux8REXkPznh7AXnmBOQvB+0bn9jaxTvoWglo1VtKioHCAsjiQuBi\nptYNM9Y7K2/4Aull7eKthBCQ334K+d1araMiuZfRVLVu3sRlIUREVD8m3l5AffQOqI9NBCorqw6W\nWqoaGOvuWgmgqoFOcSFgqdeM+ETOdrqTpfGStWuoV2lp3zpeH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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
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AABBsLuo+3/5UVlGiZt5oBQAAAGgXLAvfHtOjiirueAIAAIDgYVn4lqSyimIrDw8AAAAE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\nfNr+vGGRKqrKLao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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30\n",
+ "movement_sensor = 30\n",
+ "pos = (0, 500)\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, \n",
+ " measurement_variance=sensor_variance,\n",
+ " process_variance=0.5)\n",
+ "\n",
+ "zs, ps, vs = [], [], []\n",
+ "for i in range(100):\n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ " vs.append(pos[1])\n",
+ "\n",
+ " pos = predict(pos[0], pos[1], movement + random.randn(), movement_variance)\n",
+ "\n",
+ "bp.plot_filter(ps, vars=vs)\n",
+ "bp.plot_measurements(zs)\n",
+ "plt.legend()\n",
+ "plt.show()\n",
+ "plt.plot(vs)\n",
+ "plt.title('Variance')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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 distinctly 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 disagrees 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 mathematical model this sort of reasoning."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## More examples"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "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 intuition 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",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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S3C3GoMDcxDYuLg6HDh3C5MmTBVXWCYODgaXpeAhqrRL1LdVO62/DXlLp0RY4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Dy/exMAgCJIfOumxxEuk+nv6G/C02/9mP07NiIRSTHKDZxXA8VZ5Yj0w1nTqxwj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\nHhyF6rp/orW9CTsPvY/un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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30000\n",
+ "movement_variance = 2\n",
+ "pos = (0,500)\n",
+ "\n",
+ "dog = DogSensor(pos[0], velocity=movement, measurement_variance=sensor_variance)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(1000):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ " \n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "bp.plot_measurements(zs, lw=1)\n",
+ "bp.plot_filter(ps)\n",
+ "plt.legend(loc='best')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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": "markdown",
+ "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",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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CaxsHBwdYWFjAyclJq71+/fparzsqKgpXr15FkyZNSnyewtuW9DyA/PeoyBeXZ555BiNH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\nUCciIiIiUqH/AFPn89MI6j9AAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30\n",
+ "movement_variance = 2\n",
+ "pos = (1000, 500)\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(100):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ " \n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "bp.plot_filter(ps)\n",
+ "bp.plot_measurements(zs)\n",
+ "plt.legend(loc='best')\n",
+ "plt.gca().set_xlim(0,100)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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": "markdown",
+ "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",
+ "execution_count": 28,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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blpAMvL8WkFIPLoQQQgixIx/8MBE7jv9g6zCIEZScW0ggYPDtXGDsAG75dzuA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omm0+rx/JL3sK1gDVxuJ0YPkfOAhgVFkgZigG+4mjNB3vRZVn+RBBfhwVEEgiCaVqPDC3f9R3kP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5XAPYfOhz+ndMZDyevv3fQ45TEe5Rm9Ntx8tfPwlO5sF9Y8Of6HvlI2djQuEszfUqSC+lAh28\nStb+yPkd+Gz7v66YCGjpqtOozdqdNtgcVlpsZRkWL3/9JPaqSv/miDiNCEugKfR8J6v2y5RmEjYd\n+pSy1oweMUlzDqlx2UMySgTalQRtAk1Rx7tzyX8BIA3mGw9+PGRGVrFAruj89NGYN36VJhlxJa2B\nsoIZmDRqjuqYHN20V864C0bdlRvkosJjaKPykQs70WvrgkHQVmPCDOFwuAbAsiy8PjcR2ZLHXZBe\nSvUaAo1jOdgGrSG1A5TM+dpNL8LS34lLjRX0+Vdn4tXZSVEUIUkiKhtOUWdq7aa/4c3vntPshz7R\nC1a1Vs8aezWaOmvAMCzizcnod/QiKzlfHmPo+ZufVoLk2AzaS3S5+Rzio1NQ1XQGlxWazgDoYkHG\nGBgN4ZhbtoK+RtluRC9RCHUPavYOZd9KNKdh3viVw/YjKRUAr1zFCpWIUZ+PMja9oJd1KULrYyyY\nsBoZCbn44x1vD8vg9cWOf+Pgue3YcWI9AOK4bT//KXW+A/fek1X7UVF9WPOaUm1UM3yobWrJQozL\nn0afX7WDt/nQ5/j3+j+iqbMGh87/hNrWi/B43eiwEAjPUAHbsRCwq0ev/SsMujCYjJF4dPULSE8Y\ngX9v+BOc7kEcubjrP3JqlePNGadlGjPqwoJUfgHI6tp+30CU+wQ5jsfoEZNg0odjZukyHDi7LeRv\nJcWka5pyAWDP6Y0a9XSHyw63x/kfZc7dHieFBS6bcgtKcspxvu44zBFxNHgMXBsV1i/F3t/8P3h/\n8//I1Zj/R5xzAJQf/GLDSXy7dy19fW7ZCozKGgeWYZGdXKBpGgOIM6fufpck8iAdOr9d02ASaDGR\nCchKKgDP8Viz+HHkpRXLjonWiZEgIdwYifSEEUgwp8k4s+AHheMEkmUKuMEer1uzuCoZI7VU7rna\nY0FlMECNu5WDgSHmYk3L+ZANI9NGL/YfK8RmmJdWjD/e8TZuW/hrxEUlod3SRFXEFAulhJaXVvz/\nsXfm8VHU9/9/zey92SSbOyQkJIFADiABgtyXyqkcEZ8boQAAIABJREFUHlWkElBR/FqRUltrW631\n22Kt1rb4a209+tUWta0nolbBW4EIhBtCSCAh932fmz3m98fszM7szs7OJpsLP88++pDszs58dnd2\n5v15f97v18vDlIEdp06yzlaIVJA4M20R5jrd3Dp72kWSlwAQpAuBilKBoijJUofMpBz+4iHMcHNw\nLrBKoCjWSY/L/guzoAA7yTl7OR+0U0t41ZzbPPaRPm6ayJpbp9GLzGe44PxcaT4/qeD0+NnaUQrf\nv/Z+bLn+YV7aDHAZJ3AoXaqlaRXsCiUT2cy5w+nA5rlvoT42ZwYhBetu6JntBIBf5P5ZlEkFgJ7e\nLhw5/7nHtt4INpo9GnNU/ISKLYlQqdSiC7hapRGVU225/mFo1FosnrYaWRPmgHM8pZzNcL4+20/y\n38Y3p12Bt9XGXhs4sx2KomCx9orKx7Reyqo4ggzBrKoRreJdUyNCYvgGSo1KI7ox+LO86/DiaOkN\njVqDMRGJfKlAV28HWjubfGa2eItsmsbRwi9hd9ixMGsVHrrtDwCAsVEpWDt/k+w+IkJjEGQI4Sdg\nKprNrN648C4szFoFBxhFPRQcQfpgxEWOw6K0G0WPc2oQczKXYmzUeNH1e+r4WV4n8kKbe3duWHgn\nZjl//w2tNahrreInOC0dDbyGvdDNlNtPREgML8vLMAwKLh9DZ4+rpEKr1mFu5lL+75aOBrR3tTqb\n5W2w222orC9FfGSSh3gCx/03/RrJY9JYrXeVBrdefS8WZV8n8pBwb/pfM28jwoKjJO99nLOo1d7H\n/uacv/kE52QsJMiMzOQc/Pbe3ZKJLQCINscjMWa8U5JUg5iweNy0aItoG+E1lDsHtRo9X/YhFTCl\nxKXBwdhxvPig7O+ksr4E1Y2lvGMldw1QCVbNhdQ0lXko+RRXnkFFfYmkwocUwkRW/oWvUFF/ybna\nyJXF0fz1U0qNDZAukdNrDQgPiXY6mbP3iMKyE7xrt6+xtXQ0Yufu+/m/x8dneNRdU4LSYSFp47L5\ne9ZvX30APX3d/KSKSybVt1bjcs0Fj9cCwBuf/42fXHKU1lwQvU+aopGTtgjXz/k+qhvL8MCudR4q\nfkKsNiuCjWbc5BTeMOiMWDFrPeIjkxATFu9sjPfM2LtnzgG2GkFFq3D7sge8Ho8fp88tRgFhpkiB\nmDwl6RfgzS73xfefwL8ENdVGvYmfAfkSiufsvYU1ou7KKA/d9gdMHT8LP7ntGei1RuQXfiV5gZmc\nnIMl09d6BOcNLdWiWeLU8bMxdfwsNjPpDJgPnt3nodvLvmex9q83GttqPfTfAbY5j0MqSKIoCuEh\n0chJW4RF2dfjid3bcP7yMQBsfeo/PnrGudyoLLALC45EW1eLZAkNh/CrdThrDDk+zX8HJQIbeo6x\nYam4eoZ45i7EZAjhVwm4Rg1acDFlGAfe+eolPLBrHd79WjrzzsEtC87JXAqKovkLC/e9cjdAOQWL\nyNBYUYNJZnIObhTotHJ13bv3/YmX/GvpqMfze3ci1BTB11S7n2dxkUm4ecndzvfEqsdwN8IX9u5E\ne5e0CRIXdCpBRauhUWsxO/NazM7wbDKmBOeD0MDH45g0DZuXZkKp8/lCBdu0qpStax/xqJtUO5cr\nF09fw9qAu11sw0OiPBQ9uno70N3bidCgcOf3YhfdHOU4XnRApADABQk6jUHU2CycUCWPSYNG5ve8\navZtmDFpoaDPhUJEaDRfZsGaGwmCc6e0phKqGst8mogJCTaaeV1fwLk66GxWlsOlTEHj1X27PHIK\nQfpg3lCIo6G1Bn955zE0t7vOgY8P/4fvWeCUZRZPWw2aViEiJMYvFZkgQ4jXUpogfTCiw+IREhQm\n0ls3ucngClGp1IgIjZGcqKTEpfNNxu6Oxxq1FmHBkVh/zX0iN1OHw4FgQyhsdiuiw+LYbfkVW9cY\nggwhIgUbu7OBTqfW8+pN3L3S1/fEna8TE6YiOiyed4TmxuP+eptNOjFlExg6dfd24v8+fIrX1Bai\nVeu8Bshp47IxK+MadnVHpYZBF4TkMZNQVHEa58tO4NntexBqcrnQ0rQKkxKyEBIUhplOU0DOuVhI\nW2czjl34BofOypd+qVUa9FktAjEIdpycYpb7b4ySuC9erDyLi5Vn2R4DBRPmPsHqKisQYec9GACI\nVs+9laBJBedckox2Ni1zRjtc9vlCxWmRwaE7DofdZ5Ltodv+AKOM34iDcaCmqRzR5ji+fIvLTrs3\nfQqR8l9o7WwU9Rdx35HKudoJwEOJRciXJ9/HFyfeQ+rYya59OBNL3Kr283t38lKhHBqVFmZTBD+e\nuMgkfvVP2FPmjSsiOBdKD1GgcPLiIY+biDflEWFWevrE+YgIicFV6UswfeICnzNEh11cC6zymWFk\njy91gQoJCkOYKdLjuY6eNpwoOsD/PXX8LGy5/mdshk5wkklpsc/KuBq/u/c1V2mFzNd9+tK3Ho8J\nJzNKm2G4i1BvXw/qWqucNdbKgnOTIQSP5P5F5EzngfM7/PkLm9DYWiOaoVc1XkaPpUu0nNnZ2wqK\noviSESluWHgn3yi1cvZ6TE6eKbqYMmCNpgDfAVfymEkICQqDWqXBk1t38/u5ceGdyJm0iL95ZYyb\nzr+mrbNZke4pB0VRWDMvFxZrr0izmqIoPH7ni15LVQy6IN4WmnHWUHLfa1ldMX8jcScxZgJWClwd\n5UiITsH2m3ciPCQK4SFRHs8LS1ncFR0A1mzm8Ve2IkgfDIqmvb6Xd7/+P6emdg32H3kT50rzFY1P\nDppiZVHnTVnO6pVLBE6VDSUixZLqxjLsOfAK+3paBbvTrEmvNfK65nIwAJrb6/GXdx9DW1czQoLM\n0Kg1Ip1g4U38xkV3iZZ9hdQ2V+DJ134IwJUZrG0qR3NHI/Y6VZW4ZiSrzYr3DvwDh85+ojhzPm/K\nct4RuD+oVRpYbL0+S6nMpnCsnpfL3vhUKg9dZUqix+T0pcO4UHFKtBricDj4m7h70/jD3/+TaBXE\nGw2tNXwvkbcbas6khVA5ZWL5rD9FIyw4Ura5Xc7W3GZnVcLUKrEUnFqlASgKoUHhou/NHByBdQvv\nQHdvJ5+t4+4lckE2NwadRs9njjl/DrnXnSk5gvzCr0T3HS5ZBXiWtbDvyYpOt1KeCU7jME4pimEY\n1DSWYVyMp/qFEtwn1Zeqz4t6Njg4+VKtWocbF96JSYlZ0Ki1/HWeo7KhBAfOfOyzDEGj0bK+EO5S\njJxjsdsUUyo4Xzt/M9bM34QnX/uhzwnz+LgM0SSLpmhesctVQsleP4XuuO5I9WBxdfbC8l4VrcZ7\nzutcZf0lr5lrQJkLd3hIlOw2PU5BiQ1L7+cnVZxRm81uhYrWoKK+xKN/xb1U0mrrQ0n1eb6p230b\nqZVyd1Q0DbvbfYpbAc47+wl0ar2zQVd8jlAUhV9u/ht/jB/d+jv88Htsf1WhjIwqfwyfWyigpaUF\n27ZtQ3p6OoxGIxITE3HfffehubnZY7uNGzfCbDbDbDYjNzcXbW3iLuby8nKsXr0aJpMJUVFR2L59\nO6xW+a5kRiTZRPH/rW+p4i8EUeY4nwHmjQvv4hUN2AyY/Par521EWIhwqUy+Npe7WEWb4ySfn5gw\n1WO59qZFWzxshrlttzkbQB/Z+Bf8eL3YlKOtsxltnU38clKw0Sw6QZVAOzVAAd/NUxwu1zybc1VB\nXErhC18mJQ6n/q7NbmV/pIKsEMM4oHGTSzxdcQDlTd4vJNwxhRMC92VFYX2zEp1ZtoaRzd4IP7fc\nFTswLXUe1CqNqDygq7fDw1jEF5xbn0alRXVjGf7x0TOob6nCq/t3KXp9n60PcYIJS0d3K746+YHk\ntsFGM17/9M+yKxpKyU6di7RxbCPQ2KgUjI1OQbdA2aexrRZNbXW46/qH8ZstL3vVn71UVYCiitN4\n/9BufJD3mt9OpVJQFMU2ktmseO2T/ycqJ+GobizDhYpT6O7txLEL34hWFYL0JlhtFlAUjczkHCyZ\n7un6K2T9NT/A9xbfA5VKjZrGcjS21XpIuQGAQ8Y6XIiKVsPiDCC5a82f3vw5KuovwWyKRE1TBdq7\nWjAtdR4e/Mv3UFh2AhqVRtJHQYqYsHiMj89QtK0UapUafX29PjOyGUkzsDTnRt6j4df/+B/R83Mz\nl4qMdQDP3g6Ac0Z1XnPD4nDbtT8QuQ8q4bevPsDqmmsNovpRIdfPvR3hIdEwGUJ4eUGKphETFo85\nk5dKvoYdn/cMINeb5N5foqbVWDX7NlFdbbelE3XNlZiZthjhodG8LCwXGAqDoAvlp0Q6+FwDnVar\nB0AhLDgKFEVhxy1PIlKmt6GmqRy1zeWYLyibY5NV7LG23fRrJLtJlU6fuIBXROO4fu7tmJQwFWMi\nEvD9pdsQFhyJls5G7LhFmUygO0adCbERrkmxt0mGe5lHfuFX2HPgFVTWl4get9r6YNSbfAfnah3b\nYCq4j0xLXIy0cdNwzYwbPO5rNEVh35E3RQnDa2asw8IsVlLV3R27vqUau/e5Vu3CQ6JF9xaKopyl\nRLS4rMXH/Tc1PhPzpqzg/37y1e1QqzRYkLUKUeY4SW361s4mFLk5yAppbKsV9cn5y78/ew4fO31C\nhBNTvcaAYEMon0Fv62zCZ8feRVHFaX4bYdkk4PoNcI6g7Dau8mPuPPClvW9xm5hzn2uQIRhp46Yh\n2hyHTSselH1fWrWOXyEaMofQ6upqVFdX4+mnn8bZs2fx6quv4uuvv8Ztt4nraTds2ICTJ09i3759\n+Pjjj3H8+HFs3LiRf95ut+O6665DV1cXDhw4gH/9619466238OCD8m86d8WP+H9zJ6aKViO/8Gvk\nX2AbHv5n3S8RERrj8Vph02NIUBjf9MF4qZkVkpmcI6phpmmVU6+cXULu7u3E/qNviZ6nKVryBgyw\nQaJ7s9ei7Otxbc6Nkttz7zUiNAYRIa73drzoAB79+52ixsidd78i2yAn9V51Gj02r/wxbl+23evr\nvO3nT28+jLLaIqhoFRraavnMcGlNoayGri/inNJTNEXD6ibT5mAcHsvArD6pf1JuG5Zuw8RElyLL\njYvu4n9UShoobXar5EoGIK0hrFap/Q4aeixdfPBvd9h4TW1fP/qK+hK0dTWjsOyEx3koV37U0Frj\nly6sNzq6W3mpvIkJU2Cz2/jMM6B8haa8/iIKLh9HqTODM5BzSkhM2FjYHFY0ttUiVLAUer7sBH76\n1w1o62yGXmNAR08bPvr2X6KbQXRYPCobShW/h7mTl2Lq+FnQa43o7evGuvl3eCzlA0BClKsR8lxp\nPt905o4wkONqmu0OG4w6E36R+2ecvHgI//ffpzBv8nJMn7gAVY2Xse/om8ieMEfZhzNA1CoNJoyd\njJxJ0l4P7nBlSk1tdbzhDsBO8NzPXakMmDB7y2VF9x7cjZqmClGTrTfeO/AKnwCYnDzTo9HMnXGx\nE7HCucL05D27fTba2t1UmIRY7RZoVBqP4FylUiMmbKxIiai5vR7vOMvtlubcxB+Xk8ATrva1djaJ\nVpW5QOeH3/stxsWmImfSQlBgy+LkJlFqlRo6jYGXRezobkVdaxWfdODudeLPJxVdPe2ikoeUuHSs\nW8Ce97MyrsGl6gKZT8w3kxKzsGq2K+7gatDdSYlLF8ml/vfbf6Gju9Wz58tuRZAu2GdwrlWzBl9a\njeu6PyVhPlS0Cmvnb/K4r7tWDz2vqSqV2uOea7P34Wjhl3xmf+PyH4quFVyZBU3RyE6di9uXbUeI\nMRwRoTGyk++rZ9yA+YLgvKWjASpahWUzb0buih0Y45zocOPUaQ2S5kFCvE1ildJt6cRXJz/AtTNu\nRIggqL5YdQ7XzLgBBaX5AEVBq9Ghub0eJy/m8du4l7VQFIWn7/u3qMQzLTGbT4JyyityyccgfbDI\nE8Fmt8LusPGy2Q7GAb3WCK2Xe74USpJJAQnOMzMz8fbbb+P6669HSkoKFi5ciKeffhqffvopOjvZ\n7NP58+exb98+vPDCC5g1axZmz56N559/Hh988AGKi9mLxf79+1FQUIDdu3cjOzsb1157LZ566im8\n+OKL/H6kEGqTcvVJapUaKpUKl2uL+MzcF8f38g0bPF5u6r4auqw29sciJH3cNMxMW4SvTrKZid6+\nHhw8/bFoG5VKLZL4GgyEetZKyEzO8Zipc9AUjavSl8i+/nzZCf4HwR3zhoV3ItgQiqnjZ2Ht/E0o\nKGVr0f/0xs/wztd/F8m5KeV3977GL6tzUns0rUJ7VwuqG8vAOBwwGUJEF2ehgYdSgo2hbpl0hyuD\noCA4j49K9lrnL7Wc2Z/Asqevi6/ZEy4/Cn/0ZbXFHis5n+S/hUtVBdBqPBsL5cbhTUHAXzp72kVL\nx3aHTbT6wTV2+8KgC0KI0cz/fqPMYxQZO/jioQ1/gFFngjk4Erdd8wP+8XOl+ejp64bF2gudVg+G\ncaC+tRo0peIzU3Y7KzU4Y9ICbBIkDHzBaS0HGYI9bnx3r/453yAKsMFVQ6unwgcgDs4nJkx1Nb05\nbxpc9ker0fFqSQ6HHd0SjriBoqm9Dv/57K8AWAWV3BU7JA07pEiISuGvPRUSEqpCXA6z7G/9UtU5\nfFvwmZupiQ3tnc34MO9VnBFIpXqD06amaBqTErMQG57gVSXJYzwqNc6XHRdZyruz/eadXgOdYKMZ\nm1Y+CKPehMzkHP53nTp2ikfQLHSYvSp9Cd+vsGbeJtyw4E5RAkmtEje3F1w+hlBTBHQaPWiKRpAh\nBJUNpThbIq3PLnVMgM3IZ4+f4yG4wHGx6hzau1pwpuSIrMykVAKgx9KNN794QWJr3/gqz+HgJmHu\n94oTxQdxoeKUqKlWimUzb8b3lmyV7LORIm3cNK/PqSQECDhZWk4Nx+P4V30PP7r1KUSZ43BV+hJc\nlb4EGrUGkaGxsqs3GUnTPa65Dz/PrtRb+nrw8PMbwTAMcpfvAADMSr/aZ9Iya8IcPLrpr7LbeKOt\nsxnFlWcBABPGZoq00E8UH4SdsaOo8gwmJ+fwanFBglWJHksX6t2uj+7la0a9iU9mcitXcvc2oz4Y\nXYJV1H1H3sQf3ngYS3NuQnt3q3PFXqtYdx6QFrZwZ9Bqztva2qDT6WA0sh9uXl4eTCYT5sxxZWnm\nzp2LoKAgHDp0iN8mIyMD8fGuQHHZsmWwWCw4duyY12Oxbnxs5nFSYpaz2Yd1LCssO8EHggVlx9De\nLZYMHBc7UVJQ//ZlP+Ql56Sw2vrwlsQFQyj3RFEUbA4bLH092PnP+9HUXuc0VBjc4FwlkUWSIyl2\noqQm9KGzn/BuanL8dc/jaHIaHM3KuAYAsGTaGt7F0253qTxQFIWzpUf7VSLB1ia6skFWGytddrHq\nHPYdeQMOxgGdxiC6GAnrQPsL6/rquWzujR23PIm65gqRSRQHRVFIT5ouekznJtHV29cjKk/p6mkX\nWYMD7Hc8ZfxVzn+7sm/cj/6jb/+NZ/7zE48ZOtcAqNXoPb4DKctu/jkZGTN/cLi59Lo394yNSvHp\nVgkAj+Q+J1r6jgiJwdQJnlnn/qJRaWAT1BByv6m2ziZoNQZe6pKmaZTXX0R53UW+JtJfKIqCTmvg\na/6/Of0Rb2A0JeUqUTOTw4t+PMAG5129Hc7aVwp/3Mau2mk0LqdFDmGDWKBWHaQoqS7ks6FB+mDR\n8rIvdFoDn+ESXsu+Of0RDrgnPdyW3zt72EyX8OZud9hRXn8Rpy8d9itBwu3zo8P/xoVa6fvQkfNf\neDTVn7l0RLaBdkxEotfAsamtDlq1DiZDCKLNcXxwunH5D0WNjYBzcm73vNlr1Bosmb5GNAFo62oR\nqVmFmSJFmtRXT1+LsVHJKPEhd+lu8sSpk3hj/9G3UNnAlozIKV9xQVLB5eP85MjhsOHAmY/xixc3\ne31dU1sdLlW5su52hx3P7Xlc1KQqhGEYUZLAZmfVZdzvFWPCEzBx7BT8cvPfvB4bYF1PU+LSERM+\nVnY7jsjQWNHnLkSqPJZ2ExZwZ/rE+UiKnehVzUYxgiC1qb0eYaZIUBSF5Lg0GLRG3Lz4bp/rpxRF\nycq9ylHZUIIuZ+O1ez08X0qiD8aYiHF8Ak0oV5qWmC0qk/TGC3t3ouDycRh1Jtx69f94nVQC7HXr\nYuVZ3u23rasZfdZe5BV8itbOJjCMA2q1tNqPNy5I6L67MyjBeWtrKx599FHcc889/ElVW1uLqChx\nUwJFUYiOjkZtbS2/TUyMuPQkMjISKpWK30aKwvIT+ERQPmJ3sLrDXKaImxlK6aTmLv8R7lz1E9Fj\nDMNAo9ZKWn9zeGv+FGZqaZp1jattrkRdSyV6LT1YMy9XMqta01Tu1YnTX1wd83aPoE6K5DFpmBA/\n2ePxk8UH0dgmb6bBcepiHn52+7OYKjAQ4i607Pfh0nv1pl/tD+wynh1GnYmVwbJbsWLWeiSPSRNt\nJ2W7K0dHd6uH5rtWo8fymd/Do5v+iqUzb5J9fXtXCwouH0dLRyOOC6Q4OXUUmqKxdc0joteYTRF4\n5gdvuN4bTeO4oAn40NlP8Pnx90SviQyN5RWKaFqFiNAY3LHqIb4UgKuXFp5rze31OHUxDzRFQesm\nW5k8Jg1RZunVE4ZhwECZqgenoPPZsT04JVhu5LA7dWv57b24xfoi2BiKIMGEMjEmFRMlzKH8paG1\nBnnnPvUwiuBuiofPfw6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7G+xzNocqeq1Ta7qhtRb/7+1HvW/nPL9jwhNg0ns2gweKCfGZ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\nwjuRqmBpc+uaRzAhfnik7Nzps1nQ0tkIlYQ2dEn1eTz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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30000\n",
+ "movement_variance = 2\n",
+ "pos = (1000, 500)\n",
+ "\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance) \n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(1000):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ " \n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "bp.plot_measurements(zs, lw=1)\n",
+ "bp.plot_filter(ps)\n",
+ "plt.legend(loc='best')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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",
+ "execution_count": 29,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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NuxoOjmcZro7wuf1FU1dg0rhZHmVw/q8/bqhmqwkVNcdx4vx+aPXyM6BdOesG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\nnGuqwMBwn0oZb7RQNs6umXejijWixH+Mcz4wMACj0QiLRbhJDh0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/EMAwDNal/myX5zyf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\nYII=\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30000\n",
+ "movement_variance = 2\n",
+ "pos = None\n",
+ "\n",
+ "dog = DogSensor(0, velocity=movement, measurement_variance=sensor_variance)\n",
+ "\n",
+ "zs = []\n",
+ "ps = []\n",
+ "\n",
+ "for i in range(1000):\n",
+ " Z = dog.sense_position()\n",
+ " zs.append(Z)\n",
+ " if pos == None:\n",
+ " pos = (Z, 500)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ "\n",
+ "bp.plot_measurements(zs, lw=1)\n",
+ "bp.plot_filter(ps)\n",
+ "plt.legend(loc='best')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "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 range finders, 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": "markdown",
+ "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 `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from IPython.html.widgets import interact, interactive, fixed\n",
+ "import IPython.html.widgets as widgets\n",
+ "\n",
+ "\n",
+ "def plot_kalman_filter(start_pos, \n",
+ " sensor_noise, \n",
+ " movement, \n",
+ " movement_noise):\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.))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Solution"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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jznms41kGn6yCb3+C0vKq+3i6w8ThcPVInfbYmrWqsG02m7FarZSUlFBaWtrS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\nHkC4GpC21ELt24LZWZ5Quvf95xDgHYJRkWmm9bA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mjnbD5DHG5e1ssWlMV4L9wrEgawlW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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def plot_kalman_filter(start_pos, \n",
+ " sensor_noise, \n",
+ " movement,\n",
+ " movement_noise):\n",
+ " n = 20\n",
+ " zs = []\n",
+ " ps = []\n",
+ " \n",
+ " dog = DogSensor(start_pos, velocity=movement, measurement_variance=sensor_noise)\n",
+ " random.seed(303)\n",
+ " pos = (0., 1000.) # mean and variance\n",
+ "\n",
+ " for _ in range(n): \n",
+ " move_error = random.randn() * movement_noise\n",
+ " dog.x += move_error\n",
+ " \n",
+ " z = dog.sense_position()\n",
+ " zs.append(z)\n",
+ "\n",
+ " pos = update(pos[0], pos[1], z, sensor_noise)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ " pos = predict(pos[0], pos[1], movement, movement_noise)\n",
+ "\n",
+ " plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
+ " plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n",
+ " plt.legend(loc='best')\n",
+ " plt.show()\n",
+ "\n",
+ "interact(plot_kalman_filter,\n",
+ " start_pos=(-10, 10), \n",
+ " sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n",
+ " movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
+ " movement_noise=widgets.FloatSliderWidget(value=.1, min=0, max=.5))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Exercise - Nonlinear Systems"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Our equations are linear:\n",
+ "\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",
+ "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "#enter your code here."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Solution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 33,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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IbkCN4AY57vdsFwW9TmXglPSHNo1GGDQFjEaVgV1lttRRNu5fxertSzRtri5u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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30\n",
+ "movement_variance = 2\n",
+ "pos = (100,500)\n",
+ "\n",
+ "zs, ps = [], []\n",
+ "\n",
+ "for i in range(100):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ "\n",
+ " Z = math.sin(i/3.)*2\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "plt.plot(zs, c='r', linestyle='dashed', label='input')\n",
+ "plt.plot(ps, c='#004080', label='filter')\n",
+ "plt.legend(loc='best')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Discussion"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "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 prediction 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": "markdown",
+ "metadata": {},
+ "source": [
+ "## Exercise - Noisy Nonlinear Systems"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Implement the same system, but add noise to the measurement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 34,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "#enter your code here"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Solution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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iYOvMoM4jTNRSUZUszC3o2rIfugwH0rKT8PR1wUpWSRXVoNYF4efCj+PvHVTh\nMsJuTgor3lG571VILVroigNnoPPT8MsclR4yWNOkrC1tsbSwJjcvG4C8glwys9Ows3E0cctEbRaX\nck2z7eHsXan9bKxs6dayP/a2jv+OW/DDTFfrPiJFJWXmpLNm1/fk5GXz8c8v80CfcfRsM8TQCRCT\nFMnidXMM9X09GksQXg84WLtoZsgpKS0zhaj4K0TFh5GQGsNDdz5bja0TdU2t+oZJSovn63XvYW1h\nw7AeY+jeaiBmuhsPlejbQWHfYpX7X4XzxaYQv5YA/abAgpdUxg2XQLw6xSRG8suOb3C0c8HRztUQ\ngF+XnJ4oQbi4ZRnZaWRmpxm2zc0scLKv/OC6Rwf/X1U0S9RA58KPk1OsA2DNru9p3aSLYXyAq6On\npn5iSky1t1HULAUF+cz67mnDyrsAQ7uNwl6+s8QtqlVB+F97l5OXn0tefi4rti7kyPndPP/gO+Xu\n08JfH4g/OhvW7ysqz82DZ+bC3lMq/TqCsz04O4CLQ9H/bSR33OjiU64REn7sho+nZCTg6xFQfQ0S\ndUp8crRm293JWwbXiTKdjzip2e7eaqBmgK6jrQsWZpbk/TsVblZuJpk56bKoWD1mZmaOt2sjzQqq\nUfFXZM5wcctqTRAeGRfKgbPbNGUdg3qVqldYWEBM0lXcHL2wtNDncjo7KKz9UGXm1/DBUm39b9fp\n/5XFz0vlof4wZhB0CEJylY0gNTO53MdloRRxO+JKBuEV5IKL+ut8xAnNdnBAR822oii4OHoQm3TV\nUJaYGouthwThdUVqRtK/aZGVH/fh6x6gCcKvxkkQLm5drQjCVVVlza4fNHN4ers2onurgYbtbUfW\ncuLSPiLiQsnNy2byA2+XmONTYe5EaNdM5ek5kJVT8XnDY+CTn/T/WvjD6EEqowdB04YSjN+q1BJL\n1rvYu9OuaQ+cHdxwsnMjoEGQiVom6oL2ze7Az6spccnRxCVH4+LgbuomiRooKS2OuOQow7ZOZ0ag\nT3Cpeq6OnqWC8IYeTaqljaLqrf3nf5y4tJ+OQb3oFjwAVVUr7GwrOYBXlq8Xt6NWBOERsZdK9Vrc\n1+sJTT54dEIYl6LOGLbDYy5qgvDrHhmo0NxP5YHX9EF2ZYWEwVvf6P91DVZ5+h4Yd7c+uBeVVzII\nv7PDvfTreK+JWiPqGnMzCzxdfPF08TV1U0QNZm/jzKT7Z3M+4gTnI05gaWFV5mwYLf074GTniquj\nJ26OnjRABNwGAAAgAElEQVTyDCzjaKI2ysrJ5OiFf8jLz2XPqU3sObWJwa3H4u0UUO5+vu6NNdtX\nE65UXSNFnVcrgnA/r6Y8/+C7/L7rB8JjLxLUqC3BAZ00dRp5NWXfmb8N2+GxF294vA5BCseWqPy4\nQb+QT0o6JKdDchpEJaSTkJJHdo4DhWrZf54DZ/T/1uyAZbNVnB0kEK+s1IxEzbYsDS5qmuMX93I5\nOoRrCRFEJ0Yw/p438PVoXPGOotawMLeghX97Wvi3B6CgsKDMev063HwHwcGQ7Zy5fJg2gd3KTJkU\nNcPRC7vJy881bLvYu+Pp6Ffhfj7u/ni5NsTXPQAfN38ayg8zcRuMGoTPnTuXX3/9lfPnz2NlZUX3\n7t2ZO3curVq1uu1jN2vYmumPfMiRc7to4OZX6paRn2dTzXZEzI2DcNDniT8/UltWUJDPf36YRlJ6\nPHn5VlyO6sL58N6ER3csMyBfvw+6PQu/f6DSwl8C8coY1mMMXVr2IzUjidSMJPkAEzXO3tNbOHPl\nsGH7WmKEBOF1XHmzbN2M8xEn+XHjfAAOn9+Fg60zzRq2NsqxhXEV77QD6Brcv1KDuB1snZnx2JdV\n1SxRzxh12oAdO3YwZcoU9u7dy9atWzE3N2fgwIEkJSVVvHMl6BQdnVv0LfML0cc9QDOnb2JaHGmZ\nKTd1/EJVpV/H+wCwMM8hyG83w3vNZfd/z7HoFejbofQ+FyKg+7Pwxz9q6QdFKQ3c/Ggb2I1ebYcy\nrMdovKopbUBVVWISI4kplt8pRFm8XRtptqMTIm5Qs0hefh4Xr54mOzerqpolaoFdJ/7SbK/dvcRE\nLRHluZYYwZXoc5qybsH9TdQaUZ8ZtSd8w4YNmu0ff/wRJycn9uzZw913323MU5ViYW5BA3c/ImND\nsbSwppFnIJk56TjYOt3UMe7scA+9297Fsi1fcChkB2+P+wYXB3e6t4Lx98HlKJUxb8H+ovRzUjPg\nvlfh3fEqrz0ms6jUNImpcfywYZ7hQ/e+Xk8yoNP9N7W/g60zFuYWVdVEUQl5+blk5WTgaOdS5uOF\naiEKym2//xq4aYPwa4nlB+HZuVm8v/T/SEyLw8bKjlfHzMfV0eO22iBqp+MX92q2w2IuUFhYgM5I\nPe3COFRVpW1gd05dPkhhYQFNG7bG3cmbK0SaumminqnSnPDU1FQKCwtxcSn7S/NGzkec5HJ0CIO6\nPHhTc/yOvPM5bKxs8XT2ua0PPTMzcx4fMo3HBr9Q6gu9sY/Cti9VJs2DH4p1eqgqzPgvnLgI37yu\nYmcjgXhlHQzZQUxiJMnp8aSkJzJ64BSjHt/B1omU9KJc9A37f+bO9sMxM6v48l+66TMOnN2GjZUd\nkx94Gz+vphXuI4wnJjGSv4+sISL2EtEJ4QT7d2T8vTPKrHv0/D+s3LYID2cfPJy8adW4M51b9L3p\nc5bsCa8oCN9zahOJaXEAZOVksOngKh4ZMOmmzyuqR25+DpbmlZ+S7maMHTyVpZs+05SFxVykcYPm\nVXI+cWsauPnxzPDXSMtM5lDITjxdfEzdJFFPKaqqVlkexcMPP8ylS5c4dOiQIZhNSSlKEblw4UKp\nfdKzk/nz+Hfk5Gfi59aCnk3vwaKKPjBvh6rCyp0ezF/TiIJCbcDt5phHkG8mAV7ZNPbKxt8rm8Ze\nWTjblz34p7776/j3xKcXpYkMaf0YXk7+5exx81bs/4Sc/EzD9t3tnsbNvvw5pOPTrvLXie8BMNOZ\n06JBFzoFDDBqu0T5EtOv8cfxbwzbNpYOjOwytcy6JyJ2cSx8h2G7pU83ujQedNPnzMvP4af9Hxm2\nFUXHmO6v3jBv+JdDX5CRo019e+yOGXJHrAYqVAtZdeBT7K2d8XYKoIFTAN7Ojcvt7LmadImkjBjS\nc1LIyEmmU8BAnG1vfKdjR8ivXE26QAPnJvi6BOLn1gJrC9uqeDpCCBNo1qyZ4f9OTpXPtihLlfWE\nT58+nT179rB79+5KfxnlF+SxPWS1IVgKTwghNSuBu9s9rcn3NrWo5FDsLJ0Y1Rcae2fzxg9NSM0s\nal9CqgV7U53Ye1b74rjY5zG4YyJT74/EXO5OGthaOUB60XZmbtqNK5ejUC0kLSsJJ9vSy5R7ODYk\nMvG8YTs+LarCIDwiUf8jUUHB0cYNc52ko1Sn4+E7iUzSDrDOyk0jMzcNW0uHUvXTsrVjTxysb+4O\n3HUW5la09+uLnZUjTjYeONm63zAAV1WVnLxMTVkTjzYUqgWYKTXnM0voJaZfIyc/i5z0LBLSo7kQ\nc4xRXaeXu8/ZqANEJV8ybDfz6lBuEN61yWAsze+tUd9ZwvhiUsNJTI8hKSOGpMxYBgQ/Ij+2xE2r\nkk+JadOmsXLlSrZt20ZAQMAN63Xu3Nnwf1VV+XHjfBIzrmnq9Gw3iG5du1dFMw0uXj1N4wYtKhwh\nX6gWsunAKv4+/TPebo2YPupDOne2ZuidKve/BqdCyz9PUroFK3Z64eHpxefT6l8v2anQg2w5/CuO\ndi442bnSrGFr2gZ2JyzjGOEJIYZ6rp5OXF+Xqfg1UpEVWxdxNuwIMx77qlT+dpIaRuSeoiBctcqu\n8NjHrm3W10UlKSOGAV3uo3O7yrdH3J4DkX+SkB5VqtzV257WTfSvw6FDhwD9dbIrdLWmXqe23Wjp\nX8Zo6kqo7HUXn3KNgr1Fd7isLW35v0dmSw5wDXP9OjFzyNeUtwxoT5cuXcrd91LqIU0Q7uzhQOeO\n8jlQFxX/PKnI+8uWahbq8WzoQlCjNlXVNFGDFM/ouF1GnR0FYOrUqaxYsYKtW7cSFFT51Q/3nt7M\noXM7NGVtA7szqMtDxm6iRkzSVb5YPZN3l0xi5/G/yM0reynN3Pwcvv79Xf7a9xMqKtEJ4WzY/zMA\nTXwV9vwXnr4HLCrxs+bL1bB8U/2bTSU2+SqhUWc5dmEPO479wfmIkwA42blq6t3K0vUXIk/yz8kN\nJKbGsuvEn6UeL74Sp52NI5YW1uUeT1VVLpcYPS95ndUrOj6szPKI2EtllseXWLLeoxqWrHd38uaD\nCcuYeP9bDOn6ML3aDJUAvAY7H3Fcs12Z5cbdHD0124mpsUZtk6g+hTeYD/5W+LoHaLZl5UxxK4za\nEz558mSWLl3KmjVrcHJy4to1fa+2g4MDdnZ25e7r5dIQTxdfwxLBXq4NGTt46k0NzLxOVVUS02IJ\nj7mEjaWtYUGGsmw9vAYVlYTUGFZv/5qTl/YzecTbpepZmFliY6V9Dv+c3MTQrqOwsrTB3lZh8Wvw\nxTSV8xFw9gqcDYOQKxASrl9xMzevaN/xH0Dbpiqtm9SfHvGSq2U62uoX6nGy16aPpKQnQvmXi0ZB\nQT6rtn1t2N54YBXtm/bUzFDh59WMx4dMI6BBc9wcvSpMkUpMjSUtM9mwbWluhU+JD11RdTKy00gp\nsbATgL1N2fl3OXnZZOZkGLZ1OjNcHKpnhhJrSxta+ne45V53UT0KCvMJjTqrKWteiSDcVYLwOqFQ\nLeSjn17Ew8WH7sEDaeHXrtI/mA+dVVm5Fcx04OsBDT0hLaM96VnHsbVKQacrlCBc3BKjBuELFy5E\nURQGDNAOXps9ezazZs0qd99A32BeHfMpmw/+ws7jf/Ls8NexLmMZ4YqcDTvK/zZ+SkZWKgDBAZ1u\nGISnZCRyIGSbpqx7q4Fl1lUUhUcGTOJcxAnSs/S3IrJzMzkQsp3ebe8y1LO2UmjbFNqWmETjcIhK\nr4mQ8+8CXZnZ8OAbcOAbFSf7+hGIp5QMwv/tAW/k2YTBXR7Cyc4VJ3s3PF18iAyNqfRxtx/7QzOD\nRVZOBolpsZog3MrC+qZmyrha4gPVz7uZ0Rb0EBWLKqMX/O1xi3G2dy/zB5SVhTXzJq8gOS2euORo\n0rKSb/r1UlWVb9fBwt+gcQN462loE1g/3pv1QXp2CnbWDoY7bc72bng4VzwrRmV6wnPysvnhr3n4\nuPvj4x6Ar0eAZpadgsICFJC7JCa08cAqrsZf4Wr8FY5d2IOrgwczHv8KC3PLcvc7eFalz6Si7+4i\nfYG+KEoBdjaJ7Dkehp+nSs+2Mk2xqDyjBuGFhYW3tb+FuSXDeoymf6f7bykAB31qw/UAHPQrZ6qq\nWuabYvvRdRQUFOUIujl60b7ZHTc8tpWlDXe0Hsymg6sMZbuO/0WvNkMrfNN1aqHwxTSV8R8UlV2I\ngKfeg1/mlN2+uiatVBCu7wn3dm3E8DvGah6rbBCelBbP+n/Tgq7rFjyApr63t0pr28BuzH3uR65E\nn+PKtXO4OXqTlBZPeMxFWjXuhLmZDNKsStEJ4ZrtTs37VNizbaYzw83JCzcnr5s+X16+ftrRb9fp\nt4+ehz/3wvsTVf5vpD7IsjS3lCCqFnOydePtcd8QlxzFuYgTN/xeKMnduQG92gzF1dETV0fPMtOc\nriWEc/rKIU5f0ecUezg1YNqoDzgbdoTTlw8TEnaUp4a9THO/dkZ/XqJiIWHH2LBP+z3RyKtphQF4\ndo7Kk++WFYAXUVUz0jM9OHLOgz6TIDgAnr1P5bGh4OpY97/Xxe2pkcO3bzUAB30ai6W5Fbn5+tzu\ntKwUktPjS32BZ+Vk8M/JjZqy/h3vq7D3rGebIWw59AuFaiEt/DvQp+0wVFQUbvxmKyjIJzoxnFaB\nofTr5Mu2wy0Mj63ZCR8ug1fH3nD3OiMls2QQfmuzVxQXnxKtf73zsgGwsbLj3p6P3fZxAeysHWjV\nuDOnQg+y9/QWlm/5AoCXHpkn84VXsV5thtDcrx1R8WFEx4dV6bLxSakqI2fC1sPa8pxcmPYZfPnL\nKfp0+Jh3npldZkrSlWiVb9bBnhPQrlkBQ7qdJiVjDxejTvPK6E9lkacaRFEUPF188byJlXrtrB14\nuP+EcutcLXHnxsfdn7W7l2iWRj995bAE4SaQlBbPko2foFI0DsvOxpERfZ6ucN9Z3+hTS2/GmSv6\nz43XF8LI/irP3ov0josbqpFB+O0w05nR0KMJodFFuX/hMZdKBeGWFtY8MmASWw79SmRcKHY2jnQL\nrngOaBcHd0YNmEQTn5aVXnI9KiGMj356EYDmARacvfIR1xKK5sGe8V/o0lKlf6e6/SZ9+u5XSU5L\nIDUzidSMJNwcb77HsqRmDdsw8/Gv+HPvcnaf3MDwO8bi8G+uubGkZ6Vo8tnDrp2XILyK6XRmeLn4\n4uXiS4dy7k7drouRKsNfgvPlrMdzKbI1UXHzadvkKlMf1pfl56ss35zA8s3ObD5gxvXVFrYfNePz\nVa0I9E2jffNQQqPOSOBVD5TMB/ZxD6CBm58mCD9z+RAj+oyr5pbVLYVq4U2PE7t49RSZ2UVz4Coo\nPDFkOi4O7uXut+ekysc/acsGdIaABhAVB1fjITIWElPL3j87F37coP/Xsy0smanSxLduf8eLm2fS\nIPyXHd9wd49Hb6vnuyyNvAI1QXhE7EXaNdVOc2imM6NjUC86NOvJufDjZGSnYmlRuUWBetwgb/xG\nvF39MNOZU1CYj7lZHoO7v8e6nYtIStN/mBQWwuhZcPh7lYaedfdN6u3aqNRqhMZga23PyH7j6dlm\ncKWOX6gWEpt0lSvR52np3wEne9dy6/t5B3H80j7DdnjMxXJqi9pix1GVB98o/SXq7w3J6ZBSbO76\nrBwnpn3mxPkIFS8X+GYdRMaWno8e9LenL0b25GJkT05dvMacCSr39AQzs7r73q7vygrCgxq1NXzu\nA8QmRxGXHF0ts/bUNVk5Gfyy4xtsrewZ0bfiHuziurS4Eyc7V5as/5i0rBTu6v5IuZM1AGRmqzz1\nHhRfyrCRF6x+j1JjuLJyVHYeg8W/w++7oaCMCVj+OQEdnoRFr6iMHiSfA6KI0acovBk7jv3B3B+f\n51ToQaMe18+rKWY6cxp5BtKz9RCa+ATfsK6iKLTwb0+n5n2M2gaAC5GnyMvPw8LcggbufoZyR7s4\n5k66TPG7U3HJMHIG5ObVv6kLjcXHPaDCnN21u//H64vGMufH51m+5QvOR56o8Lj+JXq9w2JKr/Qq\nqkdBYQFR8WEcPrdTU56akczNLP77w58qg18oHYD3bAsHvoFjS6Bt06RS+y38FWZ/q+8Bq4yQMG9G\nvA7Bj8L/1qs31UZRO6iqWmogsY+7PzZWtgT6tNSUn7lSIudJlHLp6hnCrhWt6XAu/DjvL53KgbPb\n2H5snWFq25sR1Kgtr4z5lIGdH2Rw15EV1n9jkX7MVnHfvl46AAewsVIY0k1h9RyF8F/hveegcRnj\nfdMy4dHZMO49lfRM+RwQemazZ8+eXZ0nzMkpmod727E1ZOdmcvj8LtoGdjcM1Ltdns4+DOryEL3b\n3UXrJl1M0vOQlBbHvJ9fZt+ZLZibWVBYWKCZcaNrSw+a+gaz/WjRPlfjwNYaerWrf7+Uz4YdZdeJ\n9ew7vUU/YDavABc7L3x8Kp694GZciDzJuWJzBTvbuxIc0ElTJzohAitLa8OKd7bW9vx96DfD4xlZ\nafTreJ8MzqxGqqry1W9vsXrb1+w4/gfHL+7ljtaDSYxPIq8gl8/XvszWI79z9PxuLl49RbumPW6Y\ngzlnicrU+fo7UMWNHaLv6XK0V3C2VxjYJZwDIRuIimtFRf0Vvh4RvDjaibjkQuKSS583MVU//uPY\nef0tbTub+vceN6Vdx9ajoKOJf9Mqyc1t1qgN/t7NcHX0wNrKlj7t70ZRFNKzUwkJPwaAmZk5Pm7+\nkp5UjsLCAr5e9x6bDq4mIvYS7k4NWLrpMxLT4gx1LkSeonvwgAoHVZZkbWlDc7925b7+UVFRHLlo\nz5vfa1NVnrsf/m9kxdeNg61CpxYZPNDnCnf3cCMmEUJLrDd27AKs3g53tAYfd/kcqEqJqXEcu7CH\n5PQEPJwbGO29XzyOtbYuf82RitSInPCuLfvh6xFgtOOV9eaMig/j991LeHzoNOysSy95fbsyslJJ\nTk80PI9NB3+hoDCf5PQEVm3/ulT9iLhQZj4JB87AX3uLyt/5HkYNUGnsU7/enJejQth+dK1h267h\njVNEToYeIDig0y1NGejvrV1A6kr0ec22qqp8/ssMsnIyaOjRhMYNmnN3j0fxdPElLjkKbzc//L2a\nkZuXbfQ0KqGXm5eDhbml5gNTURRy8rINA64BwmMvAjrSshL/3S+bq/FXyM3LueGH7ab9KjNLvx35\nz7Mw4wnt4Clfj4Z0CX6VRl7H2bRvOqkZ3pp9zM2yCfLbRavAjTx0Z3NG9hvPm0/pmDp/Gb/vakVE\nTOlb3mt3w/7H4dvXVYbdUb/e46aSlpnMPxf0095sP7eC5n7tGTuk4jUo0jNVdp+A5n7gaB/LgTPb\nSEyNJSEtFk/nBjwyYDKgv2YCvIMI8A5CVVV+3wVTP4WABipBjXrSKSiGDkHtad6oLVbymVGuoxf+\nMcyMdOryQc5cOczYwVP5ceN8w8DKpLQ4ft35HY8Oer7MY1y/23QrAVdmjo7/LA/QlDX2gY8mV27/\nS1dP87+N88nJy+a1R+ez4VNXvvoFXv5KO8PKhQi44zmYM0Fl2ijQ6eSzwFgystM4dmEPh0J2cCnq\njKF8UOcHucdIkzYYk8mDcDsbRx7o/VSVnuNaYgRf/TqLtKwUvvzlTSaP+A/2No5GOXZEbCi7jv/J\n4XO78HJtyMujPyYpLZ59p7do6vVpN4xriZE08gykkWcg/l7N0OkUfpip0mJ00W3xrBz4v09h7Yf1\nY9rC60rmZWfmpJVZ78yVwyxeNwcf9wAe7vccTUrc7q2Iv5c2CI+Mv0xufg6W5vrxAHHJ0YYpLsNj\nLhCTFMkDvZ/i2XvewNnerdLjBsStW77lS86GHcHHzZ8G7v70ajMUH3d/GnkGam5TR8RewtO8GWnZ\n2rQR9xvc+YpLUnnyPW2ZtSX8MBMeHlDWbWY7nrzrJdydvLGd7sysb+DnLfo5xAN81uLuvAIry0wA\nmvjcD+i/+McMbkD7oM1YWeSyfk97Vm2zJK/YaukxiTD8ZZjwgMq8KWBrXX/e56ZQPH0hLSuFmKTI\nCgPw5DSVvpPh5CVQFHj6HgvMLX7B3Ey/4lrxaXCvS0lXmfiR/hop4o6Z2XjaNIEuwdAtWKV7K2gZ\nILNllFRQWMD6EtMIdmzem84t+hIRe4ltxTpp9p/5m/ZNe9CqcdHy8qqqcjbsCBsPrGJot1G3tHjW\nF7/7EpWg/Yz/7g2wt634tdqwfwXr969AVfW32JZunM+kEW8z5SEdfdqrjH5LO9NKXj68/CXsOgYr\n31WxtJDr4XZdjg7h89UzDeMwijtyYTdDu4266TsoVc2kOeEAI/o8jZ2RAuKyxCZd5ctf9AE46Bdh\n+eKXmWTlZN72sZPTE5j304vsO/M3eQW5RMaFcjn6HJsP/aK5CNwcvXig9zimjPgP9/V6go5BvQxz\nGbs7K3wwSXvcP/fob13XJX8fXsOHy6ez6Pd3WL7lS86Fa5ePdi6xamZmbtlB+OaDvwD6gVDzV73O\n5kO/3lQ7HO2cNSvgFRYWEBl72bB9OTpEUz8j424ena3j458akJBSs968dVV0QhhZORlcijrD7hPr\nyczRj5D089Tm5kfE6JevT83WrqxZVvqZqqo8PReuJRSV6XTw57yyA/DrOgb1ws+rKe7ONix4SSFx\ng8Kh7+D+PpfxcCn6sg70LRp30r3VAMbd/QqPDu7G0tlWnF4G3cuYtn7Rb9DpKf1CXqLqnI/Qjvuo\nzFL1//epPgAH/eC8b9a6sHLLR8QlBQCQkBqrye8/cEal41MlA3C9ggJ9CsLi3+GZudB6LPSbAuHX\n5HUv7lDIdmKTi3I3dIqOu7o9AsDwO8ZqBt33bD3EsBaEqqqcDD3Axz+/zKLf3+FydAiL1vyHv/b9\ndFPL1G85qPLLP9qFmZ4fCX07VC44NjezMATgAOcjT7LtyO8AtG2qcPBbGH9f6f3W7oZx70FhoVwP\nt6uhRxMsSwTZOp0Z99zxGK+P/bzGBeBg4iC8hX8HOlfBgMjrUjOS+OLXWaSWmJ+6WcPWRkklcLZ3\n0/wSB1i358dSveCDu47EzOzGNx2euls/IKy4qfOpU4M3YpOuEhkXypkrh9l3eguxSVc1j5cMwrPK\nCMIzstMILREkt6hkfqWqquw7pbL/tIqfV3MszCxp4tOS/h3vw96mKD3pSvQ5/flzHNi4dzqLfnuU\nFX/DR8ug+SMw938q2Tl153WpafIL8ogpcW34uOmn82zkGagpj4jVR0lpWdr3d1lB+MLf4I9/tGVv\nPA79bmFaUEVReGzIC7zz9HfMenIRT971Uqnrt7imDRV2LoDZT4NZiQyqc+HQYzx8sUquqapSMghv\n3qj8z4zV21SWbixdnpjiz6q/P+TQ2RFk5+SSkZ1GYaHKh8tUek2Ay1Gl97mRnceg41Pw1x553UH/\n+bzj2J+asq7B/Q3vZQtzS8YOnoqLgwcT7nuTUQMmGlJ7lm/5ksXr5vybnvbv8VDZsH8Fq7cvrtT5\n45P1P9KLa9YI5pY/PbxG/073E9Swjabsjz3LDJ9TttYKi15RWP0euJTIiF2+GV5ZUPlzibJZmFvS\nrsSUtj7u/nRpeafhbndNY9IgfOygqVV6S05RFIZ2fRgnu6JUh56th/Bg32eNdt7e7YZpti9HhzCy\n33OGXjs3Jy+6triz3GPodAoLXgLzYl/QkbEw+zujNLFGSL3BkvXXOVWiJzwk7Kimp8HHzb9UYFaW\n2CSVodP0OXg9xsP7S16gme9PTLh3Dvf3fkqzcMfl6BAuRtzB8g1fcCGit+Y46Vn6Od1bjYVft8tM\nF1UhJvGqpvfK2d4NW2t7ALzdGmFhZomVpQ1NfVvRqXlvCgoLUFE1PRzuTtrc7dOhKi99oT1P91Yw\n6zaz4BRFwd3Jm45BvSqsa26uMGucwu6F0LSh9rH8Av2P7r8P1e/rqSreT3HJ0SSkFq2+a2ZmXm4K\nW3S8yoQPb3y8wkIL9p18jF+3vcvmAyncNR1eW6B/DYtr2xTGDCr9WheXmKpPS3pjkUp+fv1+7RVF\nYcqI/zCk60isLPSD4od2fVhTx8+rKbOeWFhqIH37pj3KPGbrJl0Z0u3hMh8rLi9fZdSbEFFskWad\nDr6fcXOpYjpFx9ghL2BrZW8oKyjMJyTsmKbeiDsVji3RB/nFffITfPxT/b4OjKFz8754OvtwV/fR\nvPnEQl4Z/Um5nSSmpqjVHEmkpKQY/u/k5FRl51FVlRmLnyQ9q+h83YMH8MjAyTc92X95CtVC5vz4\nvKZn965ujzC02yhOX9YvYdy6SZdKHeuVr1TmLS/aNjODw9/pb2XVdh/+NJ3I2FDD9rSHP6Bxg+aG\nbVVV2XxwNU72rjjZuREZFo2TjTtduhT97f638VMOhewwbA/sNIJ7ez1e7nn/OaH/gI2KL/2Yp4v+\nduPEB/TLC0cnFHLPy+c5cq556cpluLMDfDoV2jWr/a9PTXEwZAc/bvzUsB3s35EJ988ybCemxuLs\n4G54Dx86pH+PdezUkdSMJOKSo/F1DzAE7jm5Kt2ehRPFpnZ3sIWjP2CyhTPSM1WmfwHfrNWWdwiC\ng9/W30Faq7Z9TWJaLF1a3EmbJl0NP6zSMlOwt3G8pY6T1Ixk9p3ZwoFTO4hLjaRZw9ZMefCdMuuq\nqn7hpvVFSwJgYQ739IRfd5S5S5mmPAQfTgJrK317E1JUDpyBA2dh475C9p0u/f3TtwMsnw0NZLYM\n0rNSuXT1TKm1PW5EVVXm/fySoce5XWB3Bnd9mEaeTSq1/9T5Kl+s0pa9NAY+nHxrr8Xxi3v59s8P\nsLNx5NGBz9/w+z/0qkrPCfoxIsUtfQvGDK5/10FmdjrWVra3HZ/dzsDcyjJmHGvSKQpvd2qX8iiK\ngrWlLWeuHAFUerYZyqj+EyqcR/pWzgNw5soRzMzM6dy8D12D++Fk71rh8siqqh18eUcbWLYRUjKu\nPw7HL+rTVWr7IJ71+38m59+l5QGGdB2p6TFQFIVA31Y09GiCu7M3iXEpKIqimaIwJPw48clR5Bfo\nB7/Gqr8AACAASURBVEcN7zlWk99dnKqqfLoCxr4NqRlltykjG7Ydhq9+hYsR8MJ8hdCo0quotW6i\n7+nKytGWX7kGi9dCbBL076Tv7bxVBQX5vLNkIscv7uV85AkiYkNp9u+tzdr+2t+M8xEnuBB50nDH\no23T7rTwK5plxMbKTvP3iIrS5wD4+vpibWmLm6Onplf8la/g913acyx+De7sePN/0+zcLK7GXcbB\nxgmdrvJfFPkFeVyIPEVhYSF2Ng5YWijc00uhVRNYtbWo3rUEaNqobvzovll5+bks3fwZUfFhHLu4\nh53H/6S5XzsOn9/Jt39+gLuTNw3c/Co+UAlWltYE+gZjW+BJiwZd6N1l0A0H5f93DXy2Uls2ZwJ8\nNk2hdRPYfCCP7Nwbf39YWabx7H2/8+X01prPAltrBTubMMKufYKNzSLMzDK5GtsGtdiN6LBrsGwT\ndGpOvZsZqyRLCyu8Xcu5hVCCoig42rmgqoU8edeL9G0/HCc7l0rt+90fKjP/qy3rEJjGT+9YYXaL\nP4a9XRthZ+PIyDufpZHXje/UujgqDOgMP22G3Lyi8nX/6O/UBdaz1TXfXTKJP/Ys5cCZbZy8tJ+W\nAR2xsrj5GFFRlAq/M/Py81DVwluOB40Zx9bZnvDrktLiyC/Ir9K5wrNyMtl1/E96tB5U4ZLpR87v\nJjzmAuGxl7gad5nZT32NjZWd4fHfd6k88Jp2n/++Cs/eW3vfkIWFBUz7cqQmleTjySvLHSRxvYez\nc2dtzn1BQT6Xr50jJOwod3V7pMxc+5R0lXHvwW+3ObjVwhxmjYNXHtUvtDD542hW/u2JqpZ+447o\nCyveufVVERNTY5n9/XhNmauDB+PufhW/EosF1XUFhQXEJUcRFR+Gp4sPDT1u3KN1o+sE9NMRDp2u\nLXtkICybfXM/bJZu+owLESdJStffTnl97OeVCggvXT3NjmN/cjb8KDm5WWXeuRnzlqoZzOfnBSE/\nFfWi1hfHLuzhu7+0eSAezj7E/TtQz9nejRmPfXnLU/yVd50AXIhQ6fAkZBb1E9C7HWz9oug9fS1B\n5Zm52illr/PxOMXgbvMZ0bcfw+8YW+rxpLQ43vruWcN2VFxr9px4m2sJ2h9zOh28PxFeGlO/Xn9T\n2HtKpd8UbQDs7ZLDkpdCGHRn+StqGtOWgyp3v4RmBiV7G9j+FXRsXj+ug4LCAqaXiBHmTV5RYR73\niq2LSM9Mxsc94N9Vatto4qmSVFXl6IV/WPfPj/RqexcDOt1/S+01Zhxr8tlRqpqLg0eVL9ZjY2XL\n4K4jKwzAQT+N0dYjv3Mx8hRZORlExoVqHr+vt8K9JVJMX1ugn16ttlIUHW8+sYAXRr7PuGGvMKr/\nxFsepWxmZk5T31YMv2NsmQH4sfMqnceVHYC/MhZCV8P00fqUhPJ0aQlHvocZTyhYmCu4Oip88n8F\njB78Ao28jpaq/+sOmPLJree1JhVbjOK6xLQ4zTyn9YWZzuz/2Tvv8CiqNQ6/s5veOymEkEAgEHrv\nXQQEBAFBhYsiAnbhXhVsKKJiA0SlKCiCNBHpXTqEXgKhB0hI771nd+4fQ7KZ3U2yCUlIQt7n2Qdm\n5szsZPfszDfnfN/vh6uDJ+2a9CgxAC8JfXKEXq6w+H9ln1lIyUgsDMABNh5aRkRcCGpRXcJekJye\nyKXgAHJyswC4GnJOp83cKdLDXgH3Y+DHv8t0erWCszcOy5b9GrQhMVVjS5qcnsDes5XzweTni/xn\njjwAtzKXpCuLPlS7Ogps/xaWvgeWD54FBEFNZ/+1jOg9GyuLBNydGup9D3trZ9k2d+cgls86QX+t\nZwK1Wpq9Wbq55l7vawIRcSKjPpAH4Oam8O3kO9hb6crbVSYDOgr88bF8XXoWDPkv3Al/PPpBSnqi\nLAC3Nrc1qJDyWsh5Au+cYvfp9azYOU9W/6FNbFIEC/6aycrd35GQGsO+sxv1So1WNbU+CK9u6Co8\n3NVp88N0yTmzgKQ06cL8KLkXdZPVexey+/QGmWGKIRQUsPm4+9HGtxvdWz5ZKee4eo9It6lwRy6u\ngZ01bP0a5r0q0NBN4Ls3BEL/gU9fzsTZLlfW1tQE5r0GJ5aCv488WKtn746bUzzDe83hqR5fYGMZ\nLdu+bItktlQeEvUE4SCZGNVRdqZ9oytHuPoTsLMu+8iSm4N81Ds44ipfr32HWcsmEBisZ1j0Ac28\n2sryG6MS7pOQIr9J+HgIvD5Kvt+Xq6Q84seFjKzUB2mDGp7q+gJ92w6XrTt0YauOqlJFMO9POK31\nrLvwHf1pIYIgMOVpgXt/w8a58Oqod+novxGFQgog3J28in2fFt7y3ODb4XvYMx8+fknSIi/KG/Nh\n+/Ha3weiE8MKJUiriuwcKQAven0ASQ+8af2sSn3v9KxU8vJzddaPGyAw/y35utgkGDgdwmJqfz/Q\nHoSyt3YudZ/M7HTZfgqFknr2nsW2tzCzJjoxrHA5KyeDvWc2Ftu+qqgLwquY+lrFIgXFJEXxchX4\nZJJ83R+7pWmrR0FmTjo///MJZ28cZvepdfx7tmza3JWNSiXy/mKRiZ9Dttb1rV1Tqbh1WA/5XU6l\njiU+7QVG93+B/h0X4e1+kfFPilxcCe+9IOjN71YolHjWa4wggLf7OUb2/Yh69vIHkk9XwLItZf+e\nklL1B+F3I6/XqbBoIYoi8SnRXLx9gkPX/+Je3FXZqPSuAFFnJuSD/0CP1uXM8XTUf2HPyskosere\nwsxKR4nj4APd4KJ89KL0oFhASjrMXVmeM62ZRCaEykywXOw9aFCvMU92GiNTtlKp89l81LCnXFE0\nTL3o/A2ROVoqVE/3lOpwSsLJTuDJLmkoFJpBFCOlMc527sXu06lZH9nynchrJKZF89lkgV3fywde\n1GoY94mkP16b+emfT5i5dDwf/DKRhX/NIi0zuVLfTxQlQ6UzWg9d74+HsQMqL/UjNy+HfWf/Zs7K\naRy7vEtvm3fGCvzvefm6e5HQ701p5L42oxuE69ZmaROZECpbrmfvgbGRcbHtrcxtGNhxtGzdscu7\niUuOKsOZVjx1QXgV00BrJDxcz0g4wPSx4O8tXzf5K0jLqPof47V752Wj33vObKiU94lODGPDgSUs\n2zqX7Zd+5cTtbaXuk5ohMnKWpOOtzdQRcHyJ/hEtBxsXLM2sUSrzaeZ9iKd6zGFE79+xtQovMc3A\nq0h+trVFAh+8uEtH8/X172HL0bJ9T0lpeuRbgNTMJOJTovVue1zZcux35qycxu+7viUs8RbHbm3m\nfz+P5YvVb3DrfjBvL5S379T84eQIXR3053+bGJmWmi7TWks+7dLtEzojfw42ArO03JQX/yOpJzwO\n+NZvydzJvzNpyHu09OlEV/8BCIKAqYk5I4q4KTf28GdYd918a31EJYQy549p/H34V66FXNDroJeV\nI/Kfz+Xygi72Ug2OISlLVuY2fD1tLe+MmcezfacxqNOzKEso9HKx98DHvRkmRqZ0ataXN0fNLTRt\ne7KzwPo50oyN5vxg2LsQXEtTErJzswqla9OzUgiJvikr1q8MvlsrDWgVZUhXKS2ssgiJvsXnq6Si\nw+zcTPae2UhGtn4zunmvwnitieI7EVIgHlmLA/GcvGxMihRhhsTcZvuJ1YRG3y52n8j4ENlycalg\nRendZqhslF2lzmf7idVlPt+K5JHb1j9ueDj7ICAgIv2gktLiyMvP1cmRNjYS+GWmZAJRMKBzP0YS\n9F/ybtWecz0H3ZHArJyMEgsgykNmdgYngjQuGQLSjfDQxW2Ym1jSrGFb2cjY3QiRp9+Hq/fkxzE1\ngV/ehwmDir+RCoKAl2sTroWcL1x3+NJ2Dl/ajrmpJaP7TKGjX2+d/RrUa4KjbT286vnSoF5jmni2\non1TGPCWZhRerYbnZsPeBSK92hg2uvJ0zxfp2XoISWlxLNs2V/YZRMaHVHpdQ3UgOjEMMxMLbC0d\nSgyC3Bx1p/zzVXnEJIazcpeTLB1JEKTfy8Mo17g66ldqaOjapEQTLoCu/k9w5NIO4lOi6ejXh5G9\nJukNNN4cDT9vkn7jIBVpfbgM1s0p92nXKIyNTGjj2402WkYb7Zr0IOjeWVp4d6Rdkx4G5/NfDblA\nQkoMRwN3cjRwJ54OTenbbIyszYfL5DbiIF03XOyLf48jl3ZwL+omiamxJKbG8sqwD/Bx98PH3c+g\n83p+wBvYWDroNYsb2l3g5/9KI7UFxCVLucEnloo4l3BeNRHt1CJHW9dSf0/lJT9f5H8/wSKt7IOm\nDaRC7fIW1BuCk61rYV0ISPfO/Wc3MaLnizptFQqBFR+IZOXApsOa9bfDpED80E9irZSx7N7ySbq1\nGMiqvQs4f/MoKekJ7D+3CRNjM7xcffXuox2EexgQhBsbmTCs23hWPZDBdbFzp4Nf5RlGGkJdEF7F\nmJmYM6jLOBysnfF08aGeg2exoyddWwi8M1ZkwXrNumVbYHRfkf4dqu6H6Onig6uDpyyf6n5MME0N\ndKs0FDsruYFPZm4aKrWKPafWk5WbCUjpPFOHfcTFW/aM+QgSUuTHcHOEzfOgU/PSP5+GWkF4AVk5\nGVib6694btO4K221AoX6zrB+jsgzH0gBOEBOLjz9PhxdLNKyUennYmZijruTF+5OXrzwxJvEJkXi\n494Mbze/Qs3r2s6GA0u4E3kNCzNr3B0bMLrPK3pHN4ozaErPdGHFVrn83NQR0LbJw/1WLEytePe5\n+Rw4v5kLtzR6hz5FrOqLw8TYlBeeeJPc/FyaebUttp2ZqcDcqVKBYAEbDsD0caJBfbm2IggCE7Ul\nbgzg2j15Eay7nXzG4shFUUeOcNJQGN6z5M/6xv1Lhf4PAIlpscUGCfooSbIWYOoIgfsxIl+t0qwL\nDofh78GBH8UymcdUd+KS5RajLvbFp/I8DEmpIs/Nhn1n5OttLGHLPLC1qtzP1Mrchic6jGJ7gGbE\n9UjgDnq2HoyjTT2d9sZGAms/Exn3sVxg4FYY9H8LDv4o4upYe/pBAYIg0Mi9Oedvav5obeGKogzv\nMZGOfn2IiA8hMj6ERgZcjwHaNe3JuZtH8W/Ynm4tBlbag5+h1KWjPAIGdx5L5+b9cHdqWOL0JcDn\nr+g6az2KtBSvevIbTWhM8dNE2qzZt4i5q15n0aaP+GP393qLUQFsLO0LR78BsvMyuBNxtTAABylt\nY/2/tgx8RzcA7+AHZ1YYFoADeLk20bteQCh+WzEjccN7CizVmqFISYfBM8o+jdi5eX+GdZ+Av3eH\nxyYAF0WxMMcvMzuN4IirsunJohQ4Z2pz5uorZOVovh9H24qbZvZ08aFnq8EM7DiGRh7+GCmNaeRu\n2EW/kYd/iQF4Ac8/IRn2FOW9nyvHSbI2k5mdzr0oeUGzh73mwS0tQ+SlLzQzjAAN3WCBVmGcPhy1\nfAm0C20rgrlTYMIg+brT1+D52VL9S20hNkkrCC8hn7683AwV6TpFNwA3N5UkZZt6VU0w27vtUFn9\niEqVz86Ta4ttb2wksG6OVJ9QlBuhUiAek1h7+kFRtGvmSgrCLUytaOThT6/WTzGu/+t4uxk2G6UQ\nFEx7+mN6th6iNwDPycsmJjG8bCf+ENQF4dUcCzOBFbPk1fOh0TBzadWeR0FQamFmTTOvdnqf4Isj\nNjmS2KQIgsODOH/rGFk5+t1zjJTGWFnIR6BPXtWIKCenubEnYDavfqvQsYkeNwCOLAYPZ8Mvql6u\nvrg5NtAprnNzbIC5aSkahnqYPFxgzivydZHxMO3bukCqNJLTE2T9wsTYrFgjJqVCiYezvGAiLKYV\n1+7J9d6+nCblW1cUjTyaM7TbC7w9+gu+nraWxh7+FXZskKaiv3ldvu7oJdhxokLfptZz4/4lWV2H\nm2MDrMw08rH//QlCtGqxfvsArC1L7ysOWte9ojKKFYUgCPw6Ex35wm3HYcDb8NcBkZzcmn89MTE2\nxdnWrVBBqLRZgrKy77RIlynSCHJR6rvAsSVSHn5VYWJkylNdNVWXTTxb0bft0yXvYyyw4XPJsbUo\n10Ok9MfYGixbXBzujl4IRRSlElJiio0XKouDF7by1Z9vseHgUlIzKrdQGOrSUWoEPVoLvDVGPn26\n5B8Y3Uekb/uquZC09e1G0watcbJ1LbPOckHxTQEFbmYqlUhCKjjZaqy6ba0cZBXy528eJTfPnLPX\nxhB4eyhqtW718+dTJPWLsp6XhakVs8YvYtfJdbJi04ZuhtnW6+PDiZL01eIiAjI7TkiuaM8PLPdh\naz1RWpXubo4NSrQv9nH3IyT6JgAqlRFHL8iffjr4waRSFC4ehpKq8A1FpVYRlRAqK+7s30FgcBdR\nZp3+7k/Qu62IjQFBYk3i8MXtmJqY06ZxtzI/9KZlJrPv7N/0av2UTr1EZLy8LzVv2K7w/7sCRJZr\n1Xu//azhDqraI+EVEYQnpcWTmpEkS2sxMRb4+wuR3q/D5WBN2yMXpZejLYx/UuTlYdDCp2b2i/7t\nR9K//UjyVXkkpMRgWYyTaVkRRZFFG+G/P2rSAwvo2gI2fckjSefo6NeHG6GX6NS8H34N2hh0vzIx\nFvhrrsjoD2FngGb91XvQ7w3Yt1DEvQwDT9UdE2NT6tl7yFJfI+JDKnzAozhSM5I4cH4zalHNiSt7\naOTejA56asMqklprW1/b6NUG/joIiUW05Y8FwstDpR9qZWNibIqlmXWZA11RFNkesBq1WjN0PbTb\nCySkGNN5MsxaItnGn7sO8SnQyM2Nnq074Gbui49zG3acdWDXiZmExbTTcaq0NIf1c2DK06Xb1JaE\nUmmEpbk1AgJpWSn0aDWY+lojrYYiCAJPdoYD5yCsyP358EWYOASszHXPUxTFx8qaXh+Bwae4GRZY\nuNzcqx0tfToV297Pqy2Du4zD2agxV+88w5HL8pytTV+CZ73q+5lGxN3j1+1fcuD8Zjr69ZYVObf2\nhWVbNekSCalwPBCe7V81v/WqIC8/l1+2f8HF2yc4cnE7UQmhNPLwL9WmOjMnnX1nN7Jyz3zuRl4j\nMztdR4GmiWcrurZ4gnoOnigUSro0709WWh4pGUomfetKehEpaD8v+GuuNP1v6HkHBO0rXI5LiSIi\nPgSVOt+gwjDNcfIIDD7JlmMr+fvIr4TG3KZHS3kOipmJwLAesPEgpGoNBmblwOmrsGQz7D4lqaq0\nblz2gYjqgEKhxMrcRiZTWV6SUkUmz5NUULQnHycOho1flOwVEBkppci4u1d8aowgKGjj2w1nO7cy\nfU9GSoFnesOFm1J9QAFxybDlKAzrAfbl8D+oLuTkZZOakYiJkSkKhYKI+BCUCiNaeHekW8uBNHRr\nqreQuTLYcmxl4eCOp0sjRvWZrPe7qsg4tsJHwhcvXsy3335LdHQ0/v7+LFy4kB49epS+42OKKIqk\nZCRibGSCpZl1se2ktBSRPm9oLi73ImHmEvjpv5V3fhlZqWw6ugJ7KyfsrJ1wtnXDz8twS9/s3EyZ\nOYGxkQlmJha8vRxu3pfWJaTA34ekF7TCwxlaN0wgNNaUq6H6c6J7tJJUL7QNdcqDj3uzQj3nfFWe\nQakjIdG3CI2+xf2YYMLj7vLfcd8WOnwplQLLZ0k22DkP/vTEVHhzvnTD1+bY5V3sPbMRe2tn7K2d\naOvbnXZNNL+Z3LwcohPDarV9vZmJBe5ODYlJDEelzi/R9KQo8SlGLN8jv2FOGgqd/avvTWnvmY3s\nPrWuMGXir0PLmDLsw8KLfQsfgUlD5SO2xy/DyJmw7RuxVljaX713rnCaOU+Vy62wK1gYoLZ0PeSC\nzGDj/M2jDOgwUqeA187KkW4tnqBbiycASIw8x7d/NyCqiEGLUim5YpqX4fN0tnNnbL9XORm0n/ux\n0hD15TuncLJ1paNhKakAZGSn8see+YUugRFx9wiLvYunVk6sh7PAgUUik76EE5f1H+vMNel16Dys\n+uTxfaDfe1rk5S+lFMCiKBTw9WswY1zNfEgBqXB705eSHO/e05r1dyOh56uw/weRZg1r5t8WHB7E\nsm1zEQQFNpb2tG7UmRljvy5xH5VaVWo9XXnw82rDzbBA4lOiGdHzxRJnYyuKCg3CN2zYwDvvvMOS\nJUvo0aMHP//8M4MHD+batWt4ehbvZPQ4cuHWcc5cO0hY3F3SMpMZ3WcKvVoPKXGfnm0E3hwtymSW\nFv8jqaUYOp1aVhJSYzl340jhsptjA2Z5LTJ4f+1UFBtLe1LSYe2+YnYAIuIgIk6/CYqHM3z7Bozt\nXzkXVCOlYWkGf+z+XmaRGxF3T1YY4ucl8OnLIrOWaPaRHjRERveVn3diaixpmckkpGRz8WYHjJVe\njOqrwsluHbFJgYTF3UVA4OtX1xhk5VsT6dFqED1aDUKlyic2ORJLM8Ompn/cVp/MHM3F2M4avppW\nWWdZMViYWspylq/eO8fF2ydkD17z34Srd+FkkGa/f8/B2I/h7y9Fg0duqyvaNvXtmvQwSKWgbZMe\n7D+7qbCIV0Rk58m1vDLsgxL323/Rnn0X5OpLM8cbXsRdgJmJOd1bPknQvbOy9YY+NBZgZ+VIswZt\nuBaqcQo9fe2AThAO4OspcGwJBN4WWbED1uyVXJS1WbMPRvaGZ/qU6VRqPOmZkvzgL7o+WNhYwrrP\nYHDXmv17ASkQ3/yVpPSyVSPSRGQ89H4d9swXade05v2dyenSk7EoqklJTyA7t3TX0i9WvY5CocTd\nyQsPp4b0aj20XHVc2rRu3BV/7w5cCzmPb/2WD308Q6jQMH/+/Pm89NJLvPzyyzRt2pRFixbh5ubG\nkiVLSt/5MSMhNZZroRcK85/D9Thn6uOLqdBIq35l0peVZ3OtbSJjZ1W6k1VRnO3dmTt5Je89P59p\nT3/MqF6TWbUHMrPLdh6mJlK+9Y11ksXvox7R0JYlux8TrNPmv+Ok3OSivPG97neVmBZHXFJDNuz/\nnrPXniXgSn3+u0jBy1+MYfm2wUTE+pKvyidMz3vUNpRKI9wcG2BjqSmky80TuXJHZO9pkd92iMxd\nKfLadyLD3xPZfU7+sDZnMtVeT7l7q0E6lfybDv8qu/lYWQjs/E5yfC3K9hMw4bOarZKRnpXKVS1p\n0I5+fQzaVyEoeKrbC7J1V+6eIST6VrH7RMWLfP2X3HCpbRPJLr68aOedlyUVpYDO/v1ly+duHiUv\nP6/Y9q19BRZNF4jYKmlbaxduAsxYBJnZNbdvlJXjgSJtJuoPwFs3hpO/VP8APDs3iyt3z5TeECkQ\n/2uupKRUlPhkSUf8eGDN++7LalmflZNBfEo0sUkRXLodwO5T6zF6SJnBtAyRk0EiSzeLvLXAiNe+\n7czGg1XzWVZYEJ6bm8uFCxcYOFBefTZw4EACAgKK2evxxdO5dPt6fViaC6zQGvQJiYJnP4K8/Irv\nNMnp2kG4IzGJ4Zy5fohNR5bLcr31oRAU2FjaUd/Zh+YN2+Pv3YGlm+Vtpo6Ar16FgZ0k6ShtRvaC\na2vg8ykClnpyqh8FDbQkG2+HX9FpY2Qk8NuHYFzk+hCbBO8UcXQURZEdx33ZeOAbUtLlaRX5KhNu\nhvZl08GvWLdvIfPX55KcVvMusg/D6asi9UdA6/9Ico+Tv4JPfoWlm3VVQ1o1hmkjHs15lgWFoGBc\n/9dlI79pWSk6mvV21gJ75us65/51UPoc1Oqa2Rcu3Douu24U2NQbSgvvjjIJUQGB4PAgvW1jEkXG\nfASpmZrP2sQY/vi4/Pn1mTnpssBBoVDiYq/f0KkkWnh3wqJICmJmdhpB90oPxsxMBZ57QmD/DwJn\nV4BRkVn5+zEw79EaABpEaPRt7kZeJz0rtVzKUTm5Iu/9LBWu3pUrHaJQwKz/wOnlVOsUjYi4EDYc\nXMrHy1/i1+1fGmyfbmwksOoTmKIlrpKaAU9Ol1RhahKJZQzCtR+AXew9dMwOSyMnV2T9vyLPfiTi\n+6yI7UDoPhVe+066twRckVK8qoIKS0eJj49HpVJRr55cwsnFxYXoaP222+fOndO7/nEgOy9TthyZ\ncJ/TZ06hVJT+lVgA43rXZ/0RzWd96AKM/yiWd0eHFb9jObh+T35zO3l1Pyev7i9ctsEde0v9UnL6\nOHfbihuhmuE9pULk6faXcbLJp78f5I4VCAqx5NxtaxLTjBnQNpEOvukkREJCZAkHrmJy0+QX96C7\n5wg4dUJvusikga4s26WZvlizD9p53aa1Tzpz13lx+HLpkWNiihdL/vHit+1qJg2M4sUnoqmh6Y0G\nk50rMPYrf+KTDUvBeWPIDS5dqlo5q4fB27EFwbGXMDe2ws7ShbDQcNSputfEb18yYuqipoTFawqA\n/tgN6amxvDcmrMb1A6N8W3o3HUVY4i0ikoLxsPbl/Hld06ySaOLYkdDoW3g6NKFNgz7Y4cLew9vJ\nV+XhbFMfhaDg0h1LPljpQ3yq/AY9ZXA42YkxnEss3/knZ8ZhaWpDRo5UJW9j5kDgpcBS9tJPA3s/\nbkSdxdTIHB/nliRFp3MupWz3xWd71mftYc294Js/1bT3vIqHU24Jez1aDl7bQHiS5DVhYmRGzyYj\nZVruJXE/1pQP//DhZrhu+oGnczafjg+hZcMMLpfvKwGqJjbZGfgbCemam9o//66ifcP+Jewh5+W+\nkJnmwZ8HXQvXZeXAsHfVfPfKHbo2Sy1h7+pDWKTc8jo+KpFz2cV//jei5NvMFNYGf18hMaZsCXBm\n51lHUjJKjrWOX0jl3Dn9fii+voYbdJVGnUThI8LM2AJLU1syciTHGVFUk5QRi5O1YVXZbw6P4HqY\nBYF3NSMpG4+50Ng9i5Hd4kvYs2xk5pb8Q45PjyhTEP73cXnbvq2TcLLJL1w2UuSTqV6Dh3s8Lqpc\n7iRm0V6c/sjTT7RxtHLDytSO9BwpncjEyJSUrHicrXW1bicOiOZgoD23IzQ3ja82NMBIKRKdpBtg\n9mqRxO1IC6ISdbfl5ClYstODu9FmfPx8KCZGNWvUQ5vMnDTOhezHy6k5Xo7yFI3le9z1fgbaVEMo\nMAAAIABJREFUKASRSQOjaNOo5gTgAG29+tCuYT/MjEvOZXSyzefn128xZVFTWX/ZdMIFpRKmjwxD\nWYMcH0yMTPFyaoaXUzPUorrU2TR9uNl5M7ztVOwsNKNmQeEBhCZcx1hpxu3QCew6NQi1Wv7BtPZO\n54W+D2ewY2fhzKgOb5GTn0VyRhwqdfEpJKXR1LUD9WwaUN/B16ABGH1MHhzJnvMOJKZJ9Sy5+QoW\nbPbku1cMm119FKRkaSpkc/OzS/0NFLDnnD3z/vKS1YEU8GyvWN4YFo6ZSc24JjZ1bUdAsCYID465\nRJsGvQ3uB4IgxQFW5iqW7tTcd/JUCuasbcjW2VdqxP3B2MgMM2OLwoFJS1NbcvKyiEm9T2JGNIkZ\nMThautK6gWQvn5whlwW1tyzZsyQnT+BQoD2bA5y4eKd48QttbkdWjSJLhQXhTk5OKJVKYmLkF7iY\nmBjc3Nz07tOhg56ktseIwOhmBN45hUKhxM3Bk0a+3mUqBtjbVKTTy9IUZAHf/u3Fk7286NWmYoJW\nB3crIuNDSE6PJyktnuzcTFn+mmCWa/D3GBknckQra+PDlx3o0Fae1/vnya9ky3ZuZlVWJFEWkhlG\nXEoU7Xx74OvZssRq7XWfi3R+BVQP4g3t0TkAK3MVsybeZtaEZqjVInvPiLyz8BzB4bryjHvPO5KZ\n78g/X4GjbfV6QDEElVrFscBd7Ly8lpzcLJKzYxjadxSmD6SoLgeLrDks36dlI2jpA+7O4O4kFemm\nxt+ggUsOT/RpA1Ss2Ud141hzkV6vIVP4+OuoC1kqF9Z8KuWRP66oVPn8dXY+ObkW7Dr7Bncjuuq0\n6eCbyq6FNjjZ1b77zvy3RV4sorx0NMiOuLz21TIfWqXK588AuQlK724DSpShy8gSeWsh/L5Dd5tn\nPclsqX+HeoDhJnL6KBhRrYrYpFVeSy6GHSpUCcrJz0Jhk00HA+sjCujYEZr5irxdJM0xIdWYmwnt\neOmp6vf9a1PwWefm5ZCcHo+jTT2uhV5gQxEVJGNTRWG7C5F7Zft3at0df2/939efe0XeWSiXdtaH\nIEATTymlsVVjqZ6gdWNj6ru01zsAmJKSouco5aPCgnATExPat2/Pvn37GDVqVOH6/fv3M2bMmIp6\nm1rFwE5jGNBhFO5OXmXOaQJwsRfYMk+kx6uaQsd8FYz+EM6uEPFyrQj5Pj983DUjlNdDL8qC8NDo\nku3ri2pgL9+uCUIBmjeU9M9LY8XOb5g3tfolOj7RcVTpjR7QrqnA++NFvvxD//YOfrB+jhIfD0kq\nUaEQGNxFwPtrE3Lz4tl2rB4/bJTkHAs4FgjdpsLO70Qa16/+F9sC7kXd5K9DS4mI00xDJqcnsPv0\nBkb0fBG1WmTq1/K+Ut8Fji/RdTU8d65mjX4/DI3qC+z/QZIpjS8Sw2w/IcmUbftGrNba6BWBWi0S\nmyTl/SqLvO5F3yAsxoU9J9/Vqa0AePGJKKYOiayVATjA+Cel4sSAIoMc7/wA/dqLmJpUrz4Rnxoj\nUweytXQoMQAPuisy7mO4FqK7bUw/WPZeydrf1RUTY1M6N+vH4UvbC9cdv7zH4CLlorw5RuB2uMhP\nf2vWLVgPLw6pOZKVJsamha6p2j4dEfEhqNUqFAolU4Z/SHpWKpHxoUTE39Opzyrgtx0ik7/SuwmQ\nlLQmDJLctls3lmSgHwUVOok5Y8YMVq5cyYoVK7h+/Tpvv/020dHRTJtWzTXDHhGeLo3wcvUtVwBe\nQJsmAn98JF8XnwxPvy9JN1U02gVUkQn3yckrXurkm3UzmL1iMl+veZ8FG+S6WtNG6pcZdLSVj2a0\nbdztIc64+vDxi9Csoe766ePg+FLw8dD9LPy82tCqsSsfvSRw+ldoKhd54HYYdJ0CAVeq/7QjgFqt\nYs3+RbIAvIA7kddQqVUs2wqntYpifpxhmK14bae5t8D+hdJMQFECg6HzK3DmWs3oB2UlI0tSxXF5\nCtyHg+tQcB4CDoPAdiC0+Y8/G/Yv0AnA7axh69fw2tDIGpWyU1YUCoEfZyCrD7gdBgs2FL/PoyI2\nKUK27GyvPwVTFEWWb5Nme7UDcFMTySdi/ZyaGYAX0L2VZNCkUChp07ibzNq+rEwfKz2cFhB0F/Yb\nJrpS7bCzcpL5puTmZROXoqkttDK3oYlnS/q2HY61ha3O/uv/FXllnv5j92wNqz6BiK3wwzsCXVsI\njywAhwoOwp999lkWLlzI3Llzadu2LQEBAezatatOI7ySGdVXYPbL8nWXg+HFuRWvoGBpZo27U0N8\n3JrRp+1wJg6aUeKTdlJqHEnp8Ry9ZE9KuuZHZWkuPYXqo0+bYYX/NzUx54mOoyvs/B8lpiYCqz8B\n+wcfg6MtbP8Wvn9TMEipwcdD4MQy6N1Wvj4hBfq/BRv+fTQBWFnUDRQKJaN7yy3mzUwsGN3nFaaP\n+YrYRIVMWx1gRC94umfNvdFWNK19BU4vl2T2ihKdAH1eh78OVM9APD0rlRwDNICLkp8v8stWkSZj\nJVWc0qaVi9K2CZxbAcN61Ky+I4oisUllr0Jv20TQUcyYuxLCY6tXfzAzsaClTyfq2ddHqTCinp3+\nNLKvVsGUryFbq77UzwtO/wpTRzx6qdqHpZ69By888RafTfqVSU+9RxPPVuU+lre75KxZlLI+hJVH\nqaYyEAQBD63R8PDYuwbtu/WYyIQ5csdUE2N4ZyxcXQNHFguMf1Iok0lXZSKIVfypF82lsbXVfYKp\no3yo1SJjP4ZNh+XrmzeEbq2giz90bSGNpCoUD9f5DLVZz8vP5b8/PwvAlsOfEh7bunDblKdh6Xv6\nj5GXn8e6nctIzIhmSM+xNPGsfvngD0NMokjQXek7KY/kYk6u9JT/517dbZ9PgQ/+UzXOcKIocu7m\nUQ5d2Mqbo+aWySxh5e7vuHDrOO2b9mJEzxextZSMVMZ9LPLXQU07K3PpwllcmkVV5nBWFnn5ecQk\nhREZH4qJkSltfA2b+cnIkm42W47qbpvziqSrX52ClM1Hf+PY5d00qd8Sf5+OtG7UVaYHXxRRFNl2\nHGYtgRuhepuUyItD8lj8P+NCd9Ga0E9y83I4f/Moxy7vJjIhlM9e+hVbK4fSdyxCQopI03Hyh5Vx\nA2DtZ9WnHxRFpVaRm5ejc+04dkmk75ugVsvbTxwszYpVVv1DTegnJXEqSKTbVPm6y6slF159pGQk\nsufUBuJTo4lPicbS1Jr/PfddFZxp6Ww5tpKDF7YULvdvP5Kne0wscZ+9p0Wefh9yi9RKK5Xw9xcV\nO5BTkXFsnTpKLUGhEFj5kUhwuDQ1XcC1EOlVYIFtZw2dm4v0aQevP1O+i5mhN/bUTMktMynVXRaA\nA7w6svj9jI2Mae7RBaBGBeCpGclcCg7A1tKB1o27FNuunoNAvQf31ty8HIyNTMoULJmaCPzxsYiP\nB8z5Tb7t41+kWZDfPhArXFO96MNXbFIkGw8t42aYpAO28+QaRvd5paTdZYzsOYmu/k/QtIGmX+wK\nkAfgID1U1OY851thV1i8eXZhjqy3m5/BQbilucDfX4h8sAy++VO+7ZNf4ew1WPyuiIfzo//8RFEk\n6O5Z8lV5XAu9wLXQC1iZ29JWz996KkjkvZ/heDE27eam0kyaSgUqtfTKy1eRr1Jjbx3Bi0/F8u3r\nnSv5L6p4ft48m3tRNwqXA4L2MbjLuDIdw9FW4IupIq9+q1m3/l+YPFykX/tH3w+0USqUOgF4UqrI\n+DnyANzSHBb/DyYMqn5/Q3WiSwuBri1EmdPugg2wYpb+9gIKTgRpRnPSjVMMHmSrCGISwxERsbd2\nxtTYTLataYPWZGanUd/Fh/rOPriXYoh15KLIM7PkAbggwOpPqvdMal0QXk3IzE7nUnAAYbF3Gduv\nfDn0luYCW76WcujikvW3SU6Dvael1/4zsHeBiFKpv4Oev3mMS7dPYGfthL21E409WpTJVCM1QzqJ\noDtPytZ3aylNqdcWIuLuseXYSm6FX0EU1fi4NSsxCC/K12unk5qZhIO1M/bWzjzX/3W9o19qUU1s\nUgR3I69jbGRCR78+fPoyeLuJTPka8jQqj2w8CDfvw+avRLzdK+5zDgjax+FL22nm1Y67kde5H6Mp\nyj0WuIuOfn10nESLu6DbWjnI/s6MLJHXv5e3ad8U3jC89rVG4mTrKitSi0wILdNNUKEQmPcqNG0g\nMu0beT/YfgKOBsL3b4q89NSjHRWPTYogLkVjRqJUGtHMq61Ou993SsVU+uZnzUykKeX3x4Otlfbf\nYkRiahwqtRnOdjUvAAdo37SnLAg/EbSXgR1Hy0ydCsjMSWdHwBr6tBmGi1ZO9eRh8Os2uHBTs274\ne7DkXbHaB7GiKDL1GwjTUpHc9AUM7Fy9z726MGMcjClSJ7ZmL3w5VaSeg+7nZ21hi4mxGbkP6rpy\n8rJJz0rVm2ddGWw9sYqgB0IPFmbWTBw0o/C60Myrrc41IjI+FGc7N506ulNBIsPelXTSi/LrTMlh\nuzpTi0tVagYqtYoVO+bx4fIXWX9gMSeu7ClXPmABXq4CB380THXk4Hn4fGXx20OjbxF45xRHLu1g\ny7GV3Lh/qUznkpaZRF6+CTdC+snWlzQKXhMxM7XgZlgg4oNg6m7UdR0rXn2IokhSWhw5uVlEJdzn\nWsh5jI11i3RDo2/xwS8T+XL1m6w/sJiDFzQezROHSK6KDjbyfS4HQ6fJcOh8xWWbXQ+9SExiOIcv\nbpMF4AAiIhsOLkFVRPM5PiWaBRtn6jic6WPO7xBaxNNLoYBl71PsA2Jtwd7aCXMTzUhgTm4WiWmx\nJeyhn5eeEti3ULcfpKRL7pqDpkNo9KPL9wy6d1a27OvRQkcR49B5SRVHOwBXKOCloXBrA3w5TdAT\ngEs42DjjbKdfDrcm0NGvDyZFRgNTM5K4XIyd+fHA3Ry/vJsvVr3Obzu/ITT6NrFJkUQlhKFUCiya\nLm+fmQ0TP4fJX4lk5VSPvF99rNgOfx+Sr/vvc49fAJ6SnkhCSvn07Ef0Au8iz2W5ebD4H/1tBUHA\nyUYuhBCfot9csTIoep/MzE7DzKT4lMbs3CzmrXmbdxeP48vVb7Jq7wJEUeTSLZEh/4N0rXKTRdNh\n0tDq32/qgvBHjFKhJCMnHZVKM4R17uaRhzqmv4/A4Z8FEvfAnvkw+2V4srOUiqLN57/DwWICtaQH\nlvWiCOevP8OEz4bSZqLIR7+InL8hllrE0apRF9o0+pOcPKvCdU52MLpv+f+26oijTT0aujaVrbt4\n+0QxrTWkZ6WQr9LMnZmZWGBhaqXTzsnWlcxsjbJMZFxIobYsQN/2AmeWQwsf+X4JKTBwOvy4sfTv\nqjRUqvzC1JMChnWbIFsOj7vL0cCdAOSr8li5+3tCom7y/fp3CQjar/ccbt2X7Kfnr5evf2uMJOtY\n2xEEATcnL9k6Qx5a9NG7raSg07WF7rb9Z6HlePh5k/hI7O6vaAWTLXw6ypaDw0VGfyhJrBblqW5w\n6Q9YMUugvkvt7g/mppY68nTHLu/SaZebn8ORS5JgtojIpeAAvt/wLnNXvcb2E6sA6NZS4P3xuu/x\n2w5JTenW/eoXiN8IFXnnB/m6dk3hi6n629c2RFHk5v1AVuz8mtm/TWbHyTXlOo5SKfD2s/J1SzZT\n7MOXk52rbLlqg3C5saBDCZb1UQnSdVEtqolODON+TDAxiTD0XWmGvyhfvQpvjK4Z14u6ILwa0KGp\nvKT53I0jFVKlbGctMLCzwOxJArvnC8TvgosrKcxHBinAHv+ZVCyoTXJ6AqIocOTCFE5emUBckimX\ng+HLP6Djy1D/6Ryefv8ab/+wgj2nNz04nkhCikjQXZF/z4os2WwsO+akoVQ73dqKoF2THrLlCzeP\nl7pPYqp8tNze2klvO0tzG1wdNApDIiIXbsmP7+MhELAMRvWR76tSwdsLYfI8yH6IEbB70TdlyhbW\n5rb07zCSdk16Fq5zc2yA1wPN1u0nVheOluepcll/4GeuhUjW5Nk5Iuv2i/R7Q8TvOfhurVwT3LMe\nzJlc7lOtcbg7VkwQDpKW+NHFsOBtsJCnWJKeBW/Oh75vQEhU1QVhalGNvbWzbMS/hbcmCE9OExn+\nHiRp3UjXfgbbvxWKLSqrjfRoqZGMcrJ1pYV3R517wZlrh0jL0m8WEp0YVvj/L6dJ0/FmWpNrl4Oh\nwyRJxq2qCYu9Q0DQPm6HB5GakVT4t+Xkijw/W+N3AVIe+NpPMUg5qjYQHBHEz5tnExh8ErWo5tLt\nANIyi8krLYWXhoBtkfGc+GRYvUe33b2oG6i1ql+T0xN0G1YCOblZssElpcII62IKtUH3uuhi782Y\njyBSyyD8oxfh/fE1p8/U5YRXA9r4dmXj4WWFo+HxKdGExtymoWuTUvYsGwqFQGtfWP2JyJPTNdO+\n0Qnwnzmwe74oU05JTEng4LnXuH5vgN7jRSWYsv14M6AZv23PxMFGJDpBnpdaFEGAqU/r31bTaevb\nnc1Hf0NE+lDvxwYTlxxV4vS4dsqKg7VLsW1bNeosu8Eev7KHbi0GyvJ8rSwENnwu8sUfMHu5fP/f\nd0iFeis/Ess1wnw95IJs2c+rLQpBwTO9JhEcEUTv1kPp2244Rkpjrtw9w6GL22Tt/b07oVK1Z8Yi\nkdV75KZD2iya/ni5P7o7NcTa3BY3Jy9J/rOIOVZ5KBgJG9ZdUtE5JP/qOBYoPUSv+0xkQMfK/5wV\ngoKJg2agUuVzJ/IaIdG3cLCR+np+vsi4T3QVUOZOqf65nJWBh3NDBnQYRWMPf/y82qAQ5ONkarVK\nphihTUJKDLn5OZgYmSIIAi8Pg47NRJ79CG5pLh+kZ8Hzs6VitoVvV93AyJU7Z9hzRqObN6DDKIZ3\nn8CspXBJy/dt0XRo0uDx6QONPPxxtnUrrJ1QqfM5dfVAmUzhCrC2FHhluMh3azXrFqyHycM093hR\nFPlp0yfk5ueSrzJFIaiY+8rSYgeDKpqCmfYC7Kwcdfp7UbS9JbYdHcEJreLtN8fAZzVsAKduJLwa\nYGFqRYuGckmkwOCTlfZ+AzoKfPAf+br9Z+HrIgoLOTn5/HNoQrEBuDYZWRaExRQfgAMM7kKFFgpW\nJ2ytHGjk0Rwrc1t6tBrMW6O/0DEd0iYzJwOlQvMcXNLFr1uLgQhoPruohPvEJUfptFMoBD5+SWDL\nPLDWSq8LuisZunzyq0huXtlGwbTfq6BgxsbSntkvLuOJjqMwUhqTkZ3Gmv0/AtJDXkJKAwJvTWLB\nuvdpMxEWbig+ALe1gl/er96V7JVBtxZP8MWUP3jjmTk802sSvvUrRhHIx0Ng/w+SqYl2X0hIgUEz\n4Ns1D5+qZChKpRFNPFsxsIju/39/gn1aac8vDIRZWtenx4nh3SfQvGE7vQFJWOwdEos8vCsVRrJr\niIhInFZNUavGAmdXSFKF2izbIs2MRMVXTR+ITZafm5NtPfacElmopWc9tj+8OKRKTqnaoBAUdG8l\nFzHYHrCaqISwYvYombfGgJFSs3zzPuw+pVm+G5nB6auDWbf3B5b9s54/dy8mONyxXO9VHtRqFT7u\nzbC3dkYhKLDTc//Lzs1i39m/+W3XNxy/ohnKv3p3ALsCGsnaPtER5r9ZvWRZDaFOJ7yaEBh8ij/3\n/0CbRl3p4Ncb3/otUCiUpe9YTpLSkhn4jpLzNzRzVkolHPoROvvD87NFNh2Wd2ZXR2mq58BZ2HNa\nJCvH8M6uVMKRn6VcRUOoiXqtKemJWFnYoizD96YW1aRlJJOYFoe5qYUs7USbZdvmEhF3j24tBtK1\nxROF2trFce2eyIiZEByuu61VY1j5oeS4aiiJqbFcD73I9dCLjO33qk4FvVotkpUDW46d4edN97l5\nvzNJqaUbdXVvBa8Ml2oFyupcVhP7yaMgLEZSndhzSnfbs/1g+ayqn31YulnkNS1J4i7+cPBHCvW9\nK4ra1E8SU+M4fHEbAVf30863O6mZyYWpXgATB82gfdNeOvuJosiyLZKdfVEZN5AcWP/5Cjo1r9w+\n8M3aGYTHaUxXnuv/FSNn+hGbpGnj5SqlTT4KJ8xH3U8yslL5eMXLhbVC9tbOzHzhhzJ5MBRl/Kci\na/drlnu3lYQRVu2W7uFqtfwzru8i1WA42FTtZ69Sq8jJzcLCTF4TlZefy7uLx8kUpKLim7L58Oeo\n1ZpUV293OLui6s67IuPYuiC8mqBS5aMSVZgYmVbq+6zZ/yM37l8iJT2B9ExHth5ZRlKaJmis7wKt\nG8POAPl+9V3gwCLw9ZQ6eWa2yDuL1nPskishkR1kxZfGRpnYWKbTyMMKbzcL3J2lAKtrC8N/II/6\nYlgdSctMxsLMukxBfnKayPQf4I/dutuMlPDhi5K5j7GRYd9NeqbIj3/D1mPSaGpmNmTlStJQObml\n71+AvTX8Z7Akp+b/EDm/df3EcNRqkXmr4eNfdRVIWvhIQVjj+lVzEzt4XkqJ064FOP0ruDpW/DnU\nxn6SkZ1GviqPQxe2cfDCFsxNLKjn6En/diNLlEi9cFMydrsjd4/H1ESaiaosGUNRFHl3yXOFcngq\nlRGBt9YRcEUzkq9QSIM13Vs9mtHM6tBPNh/9rTCd77URn+LnZYDUWTGcvyHS8eXS2xXlmd6w8Yvq\nM6I878+3iXxQlJmeZc+Oo0uIT9HESRZmELBMmvGpKurMemohSqURyir4OlIzkkh5UHhhZZHAxy9d\nZcYijVVueKz0KkpDNykAL5pKYmEm8HRPNWamP6BSK0lO88DGwhSRMEyMpYusgMDrz8ypUYY71Rlr\ni+KLVorDzlrg94/gmT6SjnRUkZqbfBV8tgK2HIEZz4k807t4B8+sHJElm2HeaqnIpzwYKWFARynd\nYFSfih/trKNkFAqBDyZCu6Yiz38qVxQIuivlif85W+SpbpX7vZwMEhnzoTwAtzCDrfMqJwCvDajV\nKrJyM7E000hcFfy/b7vh9G03HBsLe4MCp3ZNBc4sl/rA3tOa9Tm5koxhYLDIvGlgZOCDuaGkZCQW\nBuCiCCcCp3E5WH7P++SlRxeAVxeGd/8P+ap8VOr8hwrAAdr7CfRuK3LkouH7/HNEkoqcPPyh3rrC\nqO/iQ2RCKCqVEXsC3pMF4AC/fVC1AXhFo/z0008/rco3zMnRqKmbmZmV0LKOyiAmMYw7kdcKl1s3\ntqZBvbYEXNHfvnF9aXq4oZtuJ1colAgI9Gw1kEGde3I9dA8iGgUNr3q+DOn6XInFFsURGSnlDrq7\nu5fSsg5DaNpA4KWnpEryy3fk22ISJevzHzdCcAQ4WEODetJISF6+yPJtkvnDpkNy9QJDMFLCwM5S\nju/yWTB5uECrxkKF3eDr+knZaVxfYHQfOHwRWRpATi6s2w87Tkjfc0O3h0tREUWR9QcWk56Viq2l\nA8ZGpny7FibM0e1HGz6HPu0q70ZaU/tJWmYKRy7tYPW+H4iMD9HrpmpmYo6ZiXmZRi7NTQWeGyDN\nYGlf+08GwelrkjykeQU+KOfm5WCkNMbKwpYz13px7NJQ2fa+7aSR+KLiAFVNdegnCoUCf+/2NPdu\nr/c7zcvP5dftX2Jr5YCjTcl1RwCONpJrqj7cnCLp0mIX6ZlmZGRr0hsPnBd5pg842VXtd5GeKRJ0\nF6ITITZRMh0Mj8vkWkgEp4Oe516k3Ijr3RfgnbFV318qMo6tS0d5zLh0O4Dfdn1TuNzYw59XR8yl\n92tw6qq8rZ8X/PsDuBtge/3bzm+4FKzJYVEqjXjvuQW4OZaeE6yP6jAtWBEkpcWjEBR6XTAfFVuP\nSaPiMYnFt2nkAU/3kkbJ75bBO6rAUryDH4zpB0/3rNw8vdrST1SqfGKSwomIDyUqPhSlUslTXV+o\n1PfMyJLUU4q7QSsUMLCTNHMxolfxsyTFERkfyrw1bwOQnW3LicsfcD1EV/Hpy2kwc0Ll3khrYj+J\nSrjPN+tmFKpmKRRK5kxajo2lfYW+z597pX6gnU5mbiqZP1lbSC8bywf/WoBfQ+jeEjo2K/uM1qHz\nIgO1UpG83eHMcnC0fbQjmjWhn2w/sZr95zYhIDCgwzMM6fKcXlfVAtRqkQFvSQ/dIHl1vDAQJg7W\n1ARtOHCCiZ+3JzdPM8rctomU5lFVyjl7TomM+kDX9bI4BnaCnd89GkO3unSUx4SUjETuRt6grZ7R\nj7JyNHAn9tbO1NMq/AuPu4dSKbL2M4H2L2m0elv4wP4f0Gt1q01efl6hNF8BgzuPK3cAXtNJy0zh\n4u0TXLh1jLuR1+nffgRP93hR1iY3P4esnAysLezKNVMAUlHn7bArhMfdo3/7EQbv93RPgR6tRN5e\ngKxopyh3ImD+Ov3brMzh7Wdh/JNSwG1hJt2wzUyqTx5hTSM2OYp5a94pXLaxtK/0INzSXGDNpyId\nmsH7i+VBEYBaLRVy7jklfc9Duor0bSeNWDZpUPp3XeCSGRHrz77T08nI0lVeeG88ek1l6gBXB08c\nbeoRmyQlb6vVKgKC9jGo89gKfZ/xTwr4NRAZOQsiiqimZuXIl/VhYgwd/ES6tYQeraBby5JHT+9G\niDz7sbyvWZnD1q8ffQBeE7gfE8yB85sBSQln/7lN3Ay7zMRBM4qVw1UoBHZ9L7LrpPQQ1butrva6\ng000Pdr8wsGzbxauu3gLPvwFvnuj4v8Otagm6O4Z7K2dsbd2JiPLmglzDA/AfdwlH4Ha4KhcF4RX\nM9SimnM3jnD2xmFuhUnzhI3cVzzU6EduXg5bj/9BXn6urPCznkN9PJ0bkZuXQ0M3c07+IvLdOnC2\nAw+Xn9h8NAk7ayfsrZ3o1uJJHTWMAoyNjHn5qfe5ePsEfx1ahoO1M/3b1zJv+jJw8/4l/j78S+Hy\nxVsnGN59oixouRNxjSVbPkOpNMLeyokW3h15prdhFTQqtYojl3Zw4spe4pIjUQgK2jXpUSZ9V0db\ngT8/hQ9fFPljN6zeLc8X14eRMp+Xh2UzZ7IVzvY1/+JXnXCxc0OpNCoc9UzNSCI9KxXZodN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QUFeOeddxAZGYn8/HzMnDkTU6ZMwY4dO259AWqVKIrYsHM1DmXvBtD4UOVH3y3DvMlvyz4Qr9l7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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sensor_variance = 30\n",
+ "movement_variance = 2\n",
+ "pos = (100,500)\n",
+ "\n",
+ "zs, ps = [], []\n",
+ "\n",
+ "for i in range(100):\n",
+ " pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+ "\n",
+ " Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
+ " zs.append(Z)\n",
+ " \n",
+ " pos = update(pos[0], pos[1], Z, sensor_variance)\n",
+ " ps.append(pos[0])\n",
+ "\n",
+ "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
+ "p2, = plt.plot(ps, c='#004080', label='filter')\n",
+ "plt.legend(loc='best')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Discussion"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "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 practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Summary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This information in this chapter takes some time to assimilate. 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."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.4.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/13_Particle_Filters.ipynb b/_13_Particle_Filters.ipynb
similarity index 100%
rename from 13_Particle_Filters.ipynb
rename to _13_Particle_Filters.ipynb
diff --git a/pdf/merge_book.py b/pdf/merge_book.py
index 9a630f4..7808ec4 100644
--- a/pdf/merge_book.py
+++ b/pdf/merge_book.py
@@ -39,7 +39,7 @@ if __name__ == '__main__':
'../02_Discrete_Bayes.ipynb',
'../03_Least_Squares_Filters.ipynb',
'../04_Gaussians.ipynb',
- '../05_Kalman_Filters.ipynb',
+ '../05_One_Dimensional_Kalman_Filters.ipynb',
'../06_Multivariate_Kalman_Filters.ipynb',
'../07_Kalman_Filter_Math.ipynb',
'../08_Designing_Kalman_Filters.ipynb',
diff --git a/table_of_contents.ipynb b/table_of_contents.ipynb
index 845042c..19f415c 100644
--- a/table_of_contents.ipynb
+++ b/table_of_contents.ipynb
@@ -35,7 +35,7 @@
"Introduces using Gaussians to represent beliefs in the Bayesian sense. Gaussians allow us to implement the algorithms used in the discrete Bayes filter to work in continuous domains.\n",
"\n",
"\n",
- "[**Chapter 5: One Dimensional Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/05_Kalman_Filters.ipynb)\n",
+ "[**Chapter 5: One Dimensional Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/05_One_Dimensional_Kalman_Filters.ipynb)\n",
"\n",
"Implements a Kalman filter by modifying the discrete Bayes filter to use Gaussians. This is a full featured Kalman filter, albeit only useful for 1D problems. \n",
"\n",