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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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     "source": [
      "Kalman Filters"
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     "input": [
      "#format the book\n",
      "%matplotlib inline\n",
      "import sys\n",
      "sys.path.insert(0,'../code') # allow us to import book_format\n",
      "import book_format\n",
      "book_format.load_style()"
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     "source": [
      "One Dimensional Kalman Filters"
     ]
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     "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": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking A Dog"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
      "\n",
      "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. 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. "
     ]
    },
    {
     "cell_type": "code",
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     "input": [
      "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, variance=0.0):\n",
      "        \"\"\" x0 - initial position\n",
      "            velocity - (+=right, -=left)\n",
      "            variance - variance in measurement\n",
      "        \"\"\"\n",
      "        self.x = x0\n",
      "        self.velocity = velocity\n",
      "        self.noise = math.sqrt(variance)\n",
      "\n",
      "    def sense_position(self):\n",
      "        self.x = self.x + self.velocity\n",
      "        return self.x + random.randn() * self.noise"
     ],
     "language": "python",
     "metadata": {},
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     "prompt_number": 2
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     "source": [
      "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and an noise scaling factor. 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 variance to get the standard deviation. Therefore the expression `self.x + random.randn() * self.noise` computes a number with the variance that we desire. \n",
      "\n",
      "Let's look at some example output for that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(20):\n",
      "    print('{: 5.4f}'.format(random.randn()), end='\\t')\n",
      "    if (i+1) % 5 == 0:\n",
      "        print ('')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 1.2921\t 0.1444\t 0.7473\t 0.3516\t 0.4305\t\n",
        " 1.8350\t-0.1108\t-0.1800\t 0.3818\t-0.2313\t\n",
        "-0.2557\t 1.3211\t 0.1475\t 0.9038\t-0.1875\t\n",
        "-0.3380\t-1.1683\t 0.6501\t-1.3499\t-0.9251\t\n"
       ]
      }
     ],
     "prompt_number": 3
    },
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     "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",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.pylab as pylab\n",
      "\n",
      "dog = DogSensor(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",
      "plt.plot(xs, label='dog position')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "stream": "stdout",
       "text": [
        "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
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hnTbapaFZqSorO6qysqMmT2ldvKaMYU/GsStj2JNx7Kp26enpSk9Pl/TDnoqL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\n3DwMKqfFQmYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce7e0e9978>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "def test_sensor(variance):\n",
      "    dog = DogSensor(variance=variance)\n",
      "\n",
      "    xs = []\n",
      "    for i in range(100):\n",
      "        x = dog.sense_position()\n",
      "        xs.append(x)\n",
      "\n",
      "    plt.plot(xs, label='sensor')\n",
      "    plt.plot([0, 99], [1, 100], 'r--', label='actual')\n",
      "    plt.xlabel('time')\n",
      "    plt.ylabel('pos')\n",
      "    plt.ylim([0,100])\n",
      "    plt.title('variance = ' + str(variance))\n",
      "    plt.legend(loc='best')\n",
      "    plt.show()\n",
      "    \n",
      "test_sensor(variance=4.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OoUujari75o9uo79ez/ZDpwiuGEDHuIMA9uB9pSXjxXEUwEuw5ORk9u3bx6RJ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\nuIiIiIhIIVIAFxEREREpRP8PILSctx3Ibi4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce7dc2d3c8>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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 blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n",
      "\n",
      "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n",
      "\n",
      "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(variance=100.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pnu31GEII+V+hM5jw+N9/xp03ZeLesdntfTmkBZwz4AzDoFdKLI5drsClkto2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OuV+ZhNvn8kLM5NYtncZDp6Bzh+phWAvFkSgAshhBCjJQG4CBp/NeDgKkMJVgDe2dtP/6DaGBkZ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\n/wNXTQofztHuLQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce7e0e9278>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(variance=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YcBEREZESJN9q47uNh3nvu5188tWr3JpxgnyTmTWN2uHxwr+p31TjuEs7FXAR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\ncpmgsHPuuwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce7dd79470>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Math with Gaussians"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "stats.plot_gaussian(mean=23, variance=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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jo3tjsVgMJxKpHDHX9MDNxcrna/4kLlkLlYjUZirLIlJlXlq0mbz8Iob1aE3P\nto1NxxGpNC0b+XHzxe1xOGDKnA2m44hIFVJZFpEqkbj/CHNX7MDFaiEmuqfpOCKV7l9XdKWetzur\n4lJZ8cde03FEpIqoLItIlXhu3q8UlzgYExmqBUikVqrv48mEy7sA8MycXykuKTGcSESqgsqyiFS6\njTsO8P2mFLw8XLn/qu6m44hUmVsu7kDzQB8S9mSwcHWi6TgiUgXOqCzv27ePyMhIbDYb3bt3Jz4+\nvtzHOBwOoqOjadGiBVarlT179hy/7c8//2To0KEEBgbSuHFjbrrpJrKysir+LETEaTgcDqbM/RWA\nOy/pSOP63oYTiVQdT3dXHrmmBwDTFmwiL7/IcCIRqWxnVJbHjh1Lp06dyMjIIDo6mujo6DPaeL9+\n/Vi4cOFJ12dnZ3PdddeRnJxMcnIydrudBx544OySi4hT+nFzCht3HiTA15O7LulkOo5IlbvywhDC\nWwdyIDOXd7+PMx1HRCpZuWU5KyuLpUuXEhMTg4eHBxMnTiQlJYW4uLJ/IVgsFiZMmED37if/CbZb\nt27ccMMN+Pr64uXlxZgxY1i3bl3Fn4WIOIWi4hKenbcRgPuu7Iqvt7vhRCJVz2r970Ilr3+5hfSs\nPMOJRKQylVuWExMT8fT0xGaz0b9/f5KSkggODmb79u2VFmLdunV07ty50rYnImbMW7nz+LLW1w9q\nZzqOSLXpH96cgZ1bkGMv5JXFv5uOIyKVyLW8O+Tm5uLj40N2djYJCQlkZmbi6+tLbm5upQTYvHkz\nH3744Wm/WQ4MDKyU/UjZ3NzcAL3eJtX0Mci1FzD975Iw+dYomjZuZDjR2avpY1Ab1OQxeGHcxfQc\n/z4fL0vg/ui+hDQPMB2pQmryGNQWGgPnUm5Zttls5OTkEBQURFpaGlB6zLGPj8857zw5OZmrr76a\n2bNnc/7555/yPpMnTz7+84ABA4iIiDjn/YpI5Xv9i038lZFD9zZNGNk/zHQckWrXoXVDbhjckY9+\n/IP/fLCSzyZdaTqSiJzGypUrWbVq1fHLUVFRp71vuWU5JCSEvLw8UlNTad68OQUFBezatYvQ0NBz\nCnno0CGGDh3KlClTuPjii097v/Hjx59wOT1dy4pWhX/+96rX15yaPAYZ2XZenFf616GHR3UjMzPD\ncKKKqcljUFvU9DGYcGk481bEs2jNDn5Yv40ebWreypU1fQxqA41B1QsPDyc8PPz45YSEhNPet9xj\nlv38/BgMTW3RAAAgAElEQVQyZAhTp07Fbrczffp0WrVqdcIOIiMjiYmJOemx+fn52O12AOx2+/Gf\njx49ytChQxk3bhzXXnvtmT8zEXFKr3zxO9l5hUR1CqJfh+am44gY0zTAxthhHQGY/OkGHA6H4UQi\ncq7OaOq4WbNmERsbS0BAAPPnz2fevHkn3J6SksKhQ4dOelxoaCh+fn5YLBbCwsKw2WwAfPHFF2zZ\nsoVJkybh6+uLr68vfn5+lfB0RKS6pRzK4uOl27BY4LExvUzHETFu/IjOBPp5sunPg/ywOcV0HBE5\nR+UehgEQFBTEihUrTnt7UlLSKa9PTk4+5fU33XQTN91005nsWkSc3LT5mygsLuHq/m1o31Ino4j4\nertz35XdmPTRLzw791cGd22Jq4sWzBWpqfTuFZEK+yPpMF+s24WHmwsPX93DdBwRp3HdwDBaN/Zj\n119HmbNih+k4InIOVJZFpMKenVu6AMnNF7WneYNznyFHpLZwd3UhJronAC8v2kyuvdBwIhGpKJVl\nEamQlX/sY3VcKvW83ZlweRfTcUSczohe59E1uCGHjuTx9rexpuOISAWpLIvIWSspcTBl7q8A3HNZ\nF+r7eBpOJOJ8LBYLj/+9DPab3/xB2lEtgy1SE6ksi8hZW/xLIvEp6TQNsHHLkA6m44g4rT7tmjK4\na0ty7YVMX/yb6TgiUgEqyyJyVuwFRUxbsAmAh67ugZf7GU2qI1JnPTa6J1aLhU+WJ7D7wFHTcUTk\nLKksi8hZ+XhZAvvScggLqs/V/UNMxxFxeqFBAURHtKWo2MHUeRtNxxGRs6SyLCJn7GhuPq9+8TsA\nj47uhYtVv0JEzsQDI7vj6e7CN78m8VviyYt4iYjz0iediJyxmV9t5UhOPn3aNWVQlxam44jUGE0D\nbNzx9zLYz3ymZbBFahKVZRE5I/vTc3j3+zgAHh/TC4vFYjiRSM0yfkRn6vt4sGHHAZb+vsd0HBE5\nQyrLInJGXvp8M/bCYkb0Po+uwY1MxxGpcfy83Zl4ZTcAnp3zK0XFJYYTiciZUFkWkXLt2JfB/FV/\n4upi4ZFrepqOI1Jj3Ti4Ha0a+fLn/iPMX7XTdBwROQMqyyJSrufmbaTE4eC6qHac36Se6TgiNZa7\nq8vx/3C+9PlmjmkZbBGnp7IsImXasP0vlv62B5unG/dd1dV0HJEa79Le59P5/AYcyDzGO3+fByAi\nzktlWUROy+Fw8Myc0mWt77qkIw3reRtOJFLzWa0WHh9dugz2zK+2kp6lZbBFnJnKsoic1rcbk/kt\n8RAN63lx5/BOpuOI1Bp9OzRjYOcW5NgLj89dLiLOSWVZRE6psKiE5+aVfqt831XdsHm6GU4kUrs8\nNroXFgt8/FMCyQezTMcRkdNQWRaRU5qzYjtJB7I4r4kf10aGmY4jUuu0axnAqP5tKSwu4fn5WgZb\nxFmpLIvISXLthby86DcAYq7piZurflWIVIUHr+6Op5sLX67fzZZdh03HEZFT0CegiJzk7W9jOXw0\nj67BjRje6zzTcURqreaBPtw2NByAZ+ZoGWwRZ6SyLCInSDuax5vf/AHAJC1rLVLl7r60M/4+HqxL\n+IvlW/eajiMi/0NlWUROMH3xb+TaCxnctSUXtGtqOo5IrVfP5sG9l3cBSpfBLi7RMtgizkRlWUSO\n233gKJ8sT8BqsfBotJa1FqkuN1/UgRYNfdi+L5OFq/80HUdE/h+VZRE5btr8TRQVOxg1oA1hLQJM\nxxGpMzzcXHh4VOl/UKct2ExeQZHhRCLyD5VlEQFgy67DfLVhN55uLjw4srvpOCJ1zhV9gglvHciB\nzFze0zLYIk5DZVlE/l7WegMAtw0Np1mgj+FEInWP1Wrh8TGly2C//uUWMrLthhOJCKgsiwiwfOte\n1iX8hb+PB3df2tl0HJE6a0B4cyI6Nic7T8tgiziLcsvyvn37iIyMxGaz0b17d+Lj48vdqMPhIDo6\nmhYtWmC1WtmzZ88Jt69YsYLQ0FB8fHy48sorycrSMp8iphSXlPDc3NLVw+69vAv1bB6GE4nUbY+N\n7o3FAh8t3caeQ/p8FDGt3LI8duxYOnXqREZGBtHR0URHR5/Rhvv168fChQtPuv7YsWOMGjWKp556\nisOHD2OxWHj00UfPPrmIVIqFqxNJ2JtB80Afbhrc3nQckTovvHUgV/UNobC4hGkLNpmOI1LnlVmW\ns7KyWLp0KTExMXh4eDBx4kRSUlKIiyv7xAOLxcKECRPo3v3kk4R+/vln/P39GT16NF5eXjz44IPM\nmzfv3J6FiFRIXkERLyws/TB+5JoeeLq7Gk4kIgAPX90Dd1cri3/ZxR9JWgZbxKQyy3JiYiKenp7Y\nbDb69+9PUlISwcHBbN++vcI73LFjB2FhYaxdu5YhQ4YQEhJCRkYG6enpFd6miFTM+z/E8VdGLh1a\nBXLlhSGm44jI34Ia+nLrkNJlsKfM+VXLYIsYVObXSLm5ufj4+JCdnU1CQgKZmZn4+vqSm5tb4R0e\nO3YMHx8fDhw4QEJCAh4epcdH5uTkEBgYeNL9T3WdVD43NzdAr7dJ1T0G6Vl5vPFV6bLWz985mIYN\nG1TLfp2Z3gfmaQz+6z83RzF35Q7WxO/n9+QsLupxfrXsV2NgnsbAuZRZlm02Gzk5OQQFBZGWlgZA\ndnY2Pj4Vn1bqn22OHDmSkSNHkpmZCXDabU6ePPn4zwMGDCAiIqLC+xaR/3p+zi8czc1nULfWDO52\nnuk4IvI/Any9eDj6Qh5772cee+9nBnZtjYuLJrESqQwrV65k1apVxy9HRUWd9r5lluWQkBDy8vJI\nTU2lefPmFBQUsGvXLkJDQyscrm3btsycOfP45W3bthEQEHDa/z2NHz/+hMs6XKNq/PP66/U1pzrH\nYO/hbN76ajMWCzw8sqvG/W96H5inMThRdL/WvPGFD7FJh3nnqw2M6t+2yvepMTBPY1D1wsPDCQ8P\nP345ISHhtPct87+ofn5+DBkyhKlTp2K325k+fTqtWrU6YeORkZHExMSc9Nj8/Hzs9tIJ1e12+/Gf\no6KiOHr0KHPmzCE3N5cXX3zxjGfYEJHKMW3BJgqKSrjywhDCW+vwCxFn5enuykOjSk+Wn7ZgE3Yt\ngy1S7cr9e86sWbOIjY0lICCA+fPnnzRzRUpKCocOHTrpcaGhofj5+WGxWAgLC8NmswHg7e3NggUL\nePLJJ2nUqBEAU6dOrYznIiJnIDYpjUVrE3F3tfLIqB6m44hIOa7qG0L7lgHsT8/lgx/LX+tARCpX\nufNEBQUFsWLFitPenpSUdMrrk5OTT/uYiIgIduzYUW44Ealc/39Z61su7kBQQ1/DiUSkPC5WK4+P\n6cV1z3/Pa0u2MDoylPo+nqZjidQZOlNApA5ZGbuPNfH7qeftzoTLu5iOIyJnKKJjEP06NOPosQJe\nW7LFdByROkVlWaSOKClxMGXOrwBMuLyLvpkSqUEsFguTxvQG4IMf49l3ONtwIpG6Q2VZpI5YtDaR\nbXsyaBZo45aLO5iOIyJnqeN5DbjywmAKikqYtlDLYItUF5VlkTrAXlDEtAWlH64Pj9Ky1iI11cOj\nSpfBXrQ2kbhkTSsmUh1UlkXqgA+XbiM1PYd2LQO4qq+WtRapqVo28uOmi9rjcMCzczeYjiNSJ6gs\ni9RymTl2ZnzxOwCTxvTCxaq3vUhNdu/lXfHzdmdlbCqrYveZjiNS6+lTU6SWe/3LrRw9VkC/Ds2I\n6BhkOo6InKMAX0/uvrQzAFPm/kpJicNwIpHaTWVZpBbbdzib93+IA+DxMb2wWCyGE4lIZbhtaDhN\nA2zEJafzxbpdpuOI1GoqyyK12LSF/yxrHUyn8xqajiMilcTL3ZWHri5dBvv5+Ru1DLZIFVJZFqml\n4pLTjy9r/bCWtRapda7u34awoPrsS8vho5+2mY4jUmupLIvUQg6HgylzNuBwwE0XtadlIz/TkUSk\nkrlYrTw2phcAM77YwpHcfMOJRGonlWWRWujnrftYFZdKPW937r28q+k4IlJFBnZuQZ92TTmSm88b\nX2oZbJGqoLIsUssUFZcw+bP1ANx7RVcCfLWstUht9f+XwX7vh3hS03IMJxKpfVSWRWqZOSt2sDP1\nCK0a+WpZa5E6oEtwQy674HzyC4t5Qctgi1Q6lWWRWiT7WAEvLtwMwKOje+Hh5mI4kYhUh0eu6Ymb\ni5WFa/5k2x4tgy1SmVSWRWqRN77eSlpWHj3aNGZEr/NMxxGRatK6sR83Dm6HwwHPzd1oOo5IraKy\nLFJLpKbn8M63sQD857reWoBEpI751xVd8fF0Y/nWvayJTzUdR6TWUFkWqSWmztuIvbCYyy44n+5t\nGpuOIyLVLNDPi/H/LIM9R8tgi1QWlWWRWmDr7sPHFyB5NLqn6TgiYsjYYR1pUt+bP5LS+GrDbtNx\nRGoFlWWRGs7hcPD0p6VTxd02JFwLkIjUYV4erjwwsnQZ7KnzNpJfWGw4kUjNp7IsUsP9sDmF9dsP\nUN/HgwmXdzEdR0QMu2ZAW9o292fP4WxmL0swHUekxlNZFqnBCoqKeWbOBgAeGNmdejYPw4lExDRX\nFyuPji5dBvuVxb+RdazAcCKRmk1lWaQGm/1TAkkHsghuWo/rB7YzHUdEnMRFXVvSO7QJmTn5vLbk\nd9NxRGo0lWWRGupIbj4vL/4NgEljeuPmqreziJSyWCz857oLAHj3+zhSDmUZTiRSc+nTVaSGmvHF\n7xzJyadPu6Zc1K2l6Tgi4mS6BDfk6v5tKCgq4ZnPNpiOI1JjqSyL1EAph7L44Md4QAuQiMjpxVzT\nEy8PV77dmMwv2/abjiNSI6ksi9RAz3y2gYKiEkb2C6HTeQ1NxxERJ9U0wMbdfy9U8sTsdRSXlBhO\nJFLzlFuW9+3bR2RkJDabje7duxMfH39GG54xYwZNmjQhICCAxx577ITbFi5cSNu2bfH392fAgAFs\n27atYulF6qC18fv5dmMyXh6uPBrdy3QcEXFydw3vRLNAG9v2ZDBv5U7TcURqnHLL8tixY+nUqRMZ\nGRlER0cTHR1d7kY3bNjAU089xc8//0xcXBxz585lwYIFABw8eJAbb7yRd999l8zMTKKiorj55pvP\n+YmI1AXFJSU88ck6AO65tDNNA2yGE4mIs/Nyd2XSmN4APD9/E9maSk7krJRZlrOysli6dCkxMTF4\neHgwceJEUlJSiIuLK3OjCxcuZOTIkbRr145mzZpx++23M3fuXAB2795NvXr1GDBgABaLhauvvlrf\nLIucoc9+3kHCngyCGvhw5/BOpuOISA1x2QXn06NNY9Ky8pihqeREzkqZZTkxMRFPT09sNhv9+/cn\nKSmJ4OBgtm/fXuZGd+7cSWhoKK+++ioPPvgg7du3Z8eOHQB06tQJNzc3VqxYQXFxMQsWLGDEiBGV\n94xEaqmjuflMW7AJgEnX9sbL3dVwIhGpKSwWC0/d0AconUou+aCmkhM5U2V+2ubm5uLj40N2djYJ\nCQlkZmbi6+tLbm5umRv953Hbtm0jJSWFYcOGkZOTA4DNZmPmzJkMHz6cgoICWrduzfLly0+7rcDA\nwAo8LTlbbm5ugF5vk8obg+cXLiMj206/ji24aVgPzYBRBfQ+ME9jUHUGBQZy3eBwPv0pjhc+/525\n/77qlPfTGJinMXAuZZZlm81GTk4OQUFBpKWlAZCdnY2Pj0+ZG/3nca+++ioAixcvPv6YLVu2MG7c\nODZt2kRoaCivvfYal1xyCbGxsafc1uTJk4//PGDAACIiIs782YnUEjv2pjPzy81YLPDinYNUlEWk\nQibfEsHi1Tv4Yu1OVm5NIaJzK9ORRIxYuXIlq1atOn45KirqtPctsyyHhISQl5dHamoqzZs3p6Cg\ngF27dhEaGlpmgLZt255wqMa2bdsICwsDYOnSpfTq1Yt27UqX5r399tu57777OHjwII0bNz5pW+PH\njz/hcnp6epn7lor553+ven3NKWsM7nvje4qKS7guKowW9d00TlVE7wPzNAZVywO4+9JOvLBwM/e9\n8QPfT7kSF+uJR2RqDMzTGFS98PBwwsPDj19OSEg47X3LPGbZz8+PIUOGMHXqVOx2O9OnT6dVq1Yn\nbDwyMpKYmJgTHjdq1CgWLVrEtm3bSE1N5f333z8+i0b79u1Zu3YtO3fuxOFwMHv2bBo0aECjRo0q\n9GRFarvlW/ayfMtefL3ceHhUD9NxRKSGu3N4J5oH+mgqOZEzVO7UcbNmzSI2NpaAgADmz5/PvHnz\nTrg9JSWFQ4cOnXBdr169eOKJJ4iKiqJjx45ER0czatQoAIYPH869997L4MGD8ff354MPPmDx4sX6\ns7LIKRQWlfDk31PFTbyyGw3qeRlOJCI1nZe7K4+PKZ2jXVPJiZTP4nA4HKZDnM6yZcuOH64hVUt/\n8jHvVGPwznexPPnJes5r4sfy56/G3dXFVLw6Qe8D8zQG1cPhcHDFU1+x6c+D3DW8E/++tvfx2zQG\n5mkMql9CQgKDBg065W1a7lrESaVn5fHyot8AeOK6C1SURaTSWCwWJt/UB4sF3v0+lsT9R0xHEnFa\nKssiTuqFhZvJOlZARMfmDO7a0nQcEallOp3XkGujwigqdjDpo19w4j80ixilsizihGKT0vhkeQIu\nVgtPXt9Hx/SLSJWIuaYn/jYPVsel8t2mZNNxRJySyrKIkykpcfDYh2txOOC2IeG0DapvOpKI1FIB\nvp48fE3pLDtPzl5PXn6R4UQizkdlWcTJLFi9k98SD9HI34v7r+pmOo6I1HLXDwyjQ6tAUtNzeP2r\nLabjiDgdlWURJ3Ikx86Uub8CMGlMb3y93Q0nEpHazsVqZcpNFwLw5td/sGt/puFEIs5FZVnEiTz9\n8WrSs+z0Dm3CVX1DTMcRkTqiZ2gTRvYLIb+wmIdnLTMdR8SpqCyLOInY3Yd46+vfsFosPHPzhTqp\nT0Sq1eOje+Pj6cY3GxL5bkOi6TgiTkNlWcQJOBwO/vXGj5SUOLj5ova0bxloOpKI1DGN63tz/8jS\n8yQeeOsn7AU62U8EVJZFnMKitYn8Er+PRv7ePHh1d9NxRKSOuvXicMJaBrL7ryO8/V2s6TgiTkFl\nWcSw7GMFPDNnAwDP3BpJPZuH2UAiUme5uVp5edxFAMxYsoXU9BzDiUTMU1kWMezlRb9x6EgevcOa\ncf3gjqbjiEgdN7Bra67qF0pefhFPf7redBwR41SWRQzasS+D936Iw2KBV+6+GKtVJ/WJiHlTxw7E\ny8OVrzck8fPWvabjiBilsixiSEmJg0ffX0txiYMbBrWja5smpiOJiADQslE97r+y9GS/xz9cS55O\n9pM6TGVZxJD5q3ayYccBGvh58cg1PU3HERE5wR3DOhIWVJ+UQ9m8tkQr+0ndpbIsYkB6Vh6T/z6p\n78nrL8BfJ/WJiJNxc7Uy9dZ+AMz8aiuJ+48YTiRihsqyiAHPzPmVIzn59A9vzhUXBpuOIyJySj1D\nm3BtZCiFxSXEvL8Gh8NhOpJItVNZFqlm6xL+Yv6qnXi4ufDsLX21Up+IOLVHR/ciwNeTdQl/8fka\nrewndY/Kskg1yi8sJub9NQBMuKwL5zepZziRiEjZAnw9+fe1vQF4+rP1ZObYDScSqV4qyyLV6M2v\nS4/7O79pPcZf2tl0HBGRMzKqfxv6tGtKepad5+ZtNB1HpFqpLItUk6QDR5nx9xnlU2/ph4ebi+FE\nIiJnxmKx8NwtfXFzsfLp8u1s3HnQdCSRaqOyLFINHA4Hj3+4lvzCYkb2C6Fvh2amI4mInJU2zesz\nbkQnAB59fw2FRSWGE4lUD5VlkWrw5frdrIxNxd/mwX+uvcB0HBGRCrn3iq60auRLwt4M3vku1nQc\nkWqhsixSxY7k5vPkJ+sAeGx0LxrU8zKcSESkYrzcXXn2lr4AvPT5ZpIOHDWcSKTqqSyLVLFnPtvA\noSN59GzbmDGRoabjiIick8hOLbiqbwj2wmIe0dzLUgeoLItUodVxqcxZsQN3Vysv3jEAq1VzKotI\nzffUDX0I8PVkbfx+5q7cYTqOSJVSWRapIsfshTz87moAJl7ZjZBm/oYTiYhUjgBfT56+oQ8AT3+6\ngYOZxwwnEqk65Zblffv2ERkZic1mo3v37sTHx5/RhmfMmEGTJk0ICAjgscceO+G2pKQkhg4diq+v\nL02bNuWjjz6qWHoRJ/bCws3sOZxNu5YBjB+hOZVFpHa54sJgBnZpQdaxAiZ9tNZ0HJEqU25ZHjt2\nLJ06dSIjI4Po6Giio6PL3eiGDRt46qmn+Pnnn4mLi2Pu3LksWLAAgOLiYkaMGEGXLl04ePAgu3fv\npm/fvuf+TEScyG+Jh3j3+zisFgsv3TEAN1f9EUdEaheLxcLUW/ph83Tj243JfLsxyXQkkSpR5id4\nVlYWS5cuJSYmBg8PDyZOnEhKSgpxcXFlbnThwoWMHDmSdu3a0axZM26//Xbmzp0LwOrVqzly5AhT\npkzB29sbLy8vQkJCKu8ZiRhWUFTMQ++sosTh4M5LOtL5/IamI4mIVInmDXx4LLonAJM+/IWjufmG\nE4lUvjLLcmJiIp6enthsNvr3709SUhLBwcFs3769zI3u3LmT0NBQXn31VR588EHat2/Pjh2lJwBs\n3bqVsLAwrrvuOho2bEhERAQJCQmV94xEDHvjy61s35dJ68Z+PDCyu+k4IiJV6sbB7enRpjEHjxzj\nmc82mI4jUulcy7oxNzcXHx8fsrOzSUhIIDMzE19fX3Jzc8vc6D+P27ZtGykpKQwbNoycnByg9Nvq\n1atX8/bbb/PJJ58wbdo0xowZw5YtW065rcDAwAo+NTkbbm5ugF7vc7Ut+TCvLvkdgFn3DyeoWeMz\nfqzGwDyNgXkaA/MqMgbvPnQpve7+gM9W7OCGoV2J6tK6itLVDXofOJcyy7LNZiMnJ4egoCDS0tIA\nyM7OxsfHp8yN/vO4V199FYDFixcff4y3tzcBAQHcfPPNANxzzz1MmjSJo0ePUq9evZO2NXny5OM/\nDxgwgIiIiDN/diLVqLi4hHGvfEdhUQm3DetCROdWpiOJiFSLsJYNiBl9IU/PXs1d079j81u34ePl\nbjqWyGmtXLmSVatWHb8cFRV12vuWWZZDQkLIy8sjNTWV5s2bU1BQwK5duwgNLXthhbZt255wqMa2\nbdsICwsDIDg4GIvl5LlmTzep+fjx40+4nJ6eXua+pWL++d+rXt+Ke/PrrWzYvp8m9b158KrOZ/1a\nagzM0xiYpzEwr6JjcOvgtny+ahvxKenc/8Z3PHdLv6qIVyfofVD1wsPDCQ8PP365rEOCyzxm2c/P\njyFDhjB16lTsdjvTp0+nVatWJ2w8MjKSmJiYEx43atQoFi1axLZt20hNTeX9998/PovGwIEDsdvt\nzJ49m+LiYmbOnEnnzp3x99cctFJz7dyXyQsLNwMw7fb++HnrGxURqVvcXK28clcEbi5WPv4pgVVx\nqaYjiVSKcuezmjVrFrGxsQQEBDB//nzmzZt3wu0pKSkcOnTohOt69erFE088QVRUFB07diQ6OppR\no0YBpQV8/vz5TJkyBX9/f7755hvmzJlTiU9JpHoVFZcwcdYK8guLGRMZyqAuLU1HEhExon3LQO67\nqhsAD769iuxjBYYTiZw7i8OJF3VftmwZ7dq1Mx2jTtCffCrulcW/8cLCzTQP9GHZ1JH4VvBbZY2B\neRoD8zQG5p3rGBQVl3DZk0vYujuNayNDeeGOAZUZr07Q+6D6JSQkMGjQoFPeppUSRM5BXHI6rywu\nnf3ipbEDKlyURURqC1cXK6/cGYmHmwufrdjBz1v3mo4kck5UlkUqqKComImzVlBYXMLNF7Wnf3hz\n05FERJxC26D6PHR16TzzD76zWouVSI2msixSQdMX/UbCngxaN/bj8dG9TMcREXEqYy/pSLeQRhzI\nzOWJ2etMxxGpMJVlkQrYsuswb3y1FYsFpt8Zgbenm+lIIiJOxcVqZfqdEXi6ubBg9Z/8+FuK6Ugi\nFaKyLHKW8gqKmPjWCopLHIwd1pFeoU1MRxIRcUohzfyJie4JwEPvrObw0WOGE4mcPZVlkbP07Jxf\n+XP/EUKa+fPQqB6m44iIOLXbhoTTt0Mz0rLyuP/tVaddhEzEWaksi5yF5Vv28v6P8bi5WHl9fBRe\n7mUugikiUudZrRZeuTMCf5sHy7fs5aOfTr9SmogzUlkWOUNpR/O4/+2VADw0qjsdz2tgOJGISM3Q\nLNCHqbeVLn89+dP1/JmaaTiRyJlTWRY5Aw6HgwffXcXho3n0adeUu4Z3Mh1JRKRGubT3+Yzq3wZ7\nYTH3zPyZgqJi05FEzojKssgZmL0sgaW/7aGetzuvjovExaq3jojI2Zp844W0bOhLXHI6LyzYZDqO\nyBnRJ75IORL3H+GpT9cD8Nyt/Wge6GM4kYhIzeTr7c6M8VFYLRbe/OYPftm233QkkXKpLIuUoaCo\nmHve+Bl7QTFX92/D5X2CTUcSEanRerZtzL+u6IrDAfe+uYIjWt1PnJzKskgZnp+/idjkNFo29OWZ\nGy80HUdEpFaYeGVXugY34q+MXB5+d7WmkxOnprIscho//b6Ht775AxerhRnjo/D1djcdSUSkVnB1\nsfL63VH4eLrxza9JfLxM08mJ81JZFjmF/ek5THxrBQCPXNODnm0bmw0kIlLLtG7sx7Tb+wPw1Cfr\niUtON5xI5NRUlkX+R1FxCXe/sZzMnHyiOgUxbnhn05FERGqly/sEc93AMPILixn3+jJy8gpMRxI5\nicqyyP946fPN/LrjIE3qe/PquEisVovpSCIitdZTN/ShXYsAdv91lEc/WKvjl8XpqCyL/D+rYvfx\n2pdbsFosvH73QAL9vExHEhGp1bzcXXnr3kF4ebiyaG0i81buNB1J5AQqyyJ/O5h5jAkzV+BwwP0j\nu9GnXVPTkURE6oSQZv48d0tfAB7/aC079mUYTiTyXyrLIpQep3zPzOWkZeXRt0Mz7r28i+lIIiJ1\nyvMxW+AAACAASURBVKj+bUuXwy4o5q4Zy8i1F5qOJAKoLIsA8Pz8jfyy7S8a1vPitXFRWs5aRMSA\nZ2/uS5tm/uxMPcKD76zS8cviFNQIpM775tf/a+/O46qq8z+Ovy6LLBeQTUFAARVBRFzDMTfMvTRL\nJdqtxrGyZcqsbJkxMx0bawyrn+Oak/1Ms1zKpXJJzV0zEwQRF1BBRfZ9Efj9QfHLEtRGPSzv5+PB\nA+499xzf53zA+7nnfu/3nOR/1lTOpzz7mX54uNgbHUlEpEGyt7Vm/vMDMNta8+XuE8z/OsboSCJq\nlqVhO5aSxfg5WwF4/f5uGqcsImKw1l7OzHy8DwBTluxhz5GzBieShk7NsjRY+UWljJm5gbyiUoZ1\na8lfBocYHUlERIA7wvx58o5QysoreOL9TZzPLDA6kjRgapalQaqoqGD83K0kpGQR4OXMu2N7YzJp\nPmURkdpiYuQtdG/bjNSsQh6ftZGSi2VGR5IGSs2yNEhz10ezZs9JHH41Pk5ERGoPK0sL/v1MPzxd\nzOw7ep63luwxOpI0UGqWpcHZfjiZqZ/uBeC9J/rQ2svZ4EQiInI57o3tmPvXflhbWrDgm8N8/n2C\n0ZGkAVKzLA3KyXPZPB61ibLyCp4e1oEht/gbHUlERGrQJcCDNx/uDsBLC77nh4TzBieShuaKzfKZ\nM2cIDw/HbDbTpUsXDh8+fFUbnjVrFp6enri6uvLqq69e9jFTpkzBwsKCEydOXFtqkT8gp6CER9/9\nlqz8Yvp3asFL93Q1OpKIiFyFh/sH83D/thSXlvHnmRtISc8zOpI0IFdslseOHUtoaCgZGRlERkYS\nGRl5xY3u2bOHyZMn89133xETE8PSpUtZvnz5JY9JTExk8+bN+lCV3BRl5eU89eFmElKyCPRx4YNx\nuvCIiEhd8uZDt3JrcDMuZBfy2L82UFh80ehI0kDU2C3k5OSwYcMGJk6ciI2NDc899xxJSUnExNQ8\nSfjnn3/OyJEjadu2LV5eXowZM4alS5de8pjnn3+eqVOn6uo8clP8Y+k+Nh88jYuDDR+9MBBH+0ZG\nRxIRkWtgbWXBnGf749vUkejENJ6fs1U9hNwUVjUtPHbsGLa2tpjNZnr16sX8+fNp1aoVR44cISSk\n+jlpjx49Su/evYmKiuL06dP07NmTJUuWVC1ft24dtra23HrrrVcM6Obmdg27I3+UtXXlbBD18Xgv\n3hDN7LWHsLK0YOnfRtC5ra/RkS6rPtegrlANjKcaGK8218DNDVZNiaT38x/z1Z4TdGrjzasP9DA6\n1nVXm2vQENXYLOfn5+Pg4EBubi5xcXFkZmbi6OhIfn5+jRv9Zb3Y2FiSkpIYMmQIeXmV44uKi4t5\n+eWXWbt27VUFnDJlStXPvXv3pk+fPle1ngjA7thknpr1NQAzxw2gT4fa2SiLiMjVaevrzscv38mI\nNz7nzcXf09bXjbt7BhkdS+qYrVu3sm3btqrbffv2rfaxNTbLZrOZvLw8fHx8SEtLAyA3NxcHB4ca\nA/yyXlRUFAArV66sWuedd95h6NChtGjRourtk5reRhk3btwlt9PT02v8t+WP+eXVa306vifPZTPi\njS8pKS1jdP9gRvypRa3ev/pYg7pGNTCeamC8ulCDsNYuvHZvGG99updH3/4Ks1U5XQI8jI513dSF\nGtR1ISEhl4ySiIuLq/axNY5Zbt26NYWFhSQnJwNQUlLC8ePHCQwMrDFAmzZtOHLkSNXt2NhYgoIq\nX/Xt37+ft99+GwsLCywtLQEICAjgyy+/vMJuiVy9jNwiHvzn12TkFtE31IfJD3U3OpKIiFxHT9wR\nyv3hgRSVlvHIu9+SeD7H6EhST9XYLDs5OTFo0CCmT59OUVERM2fOxNfX95JOPDw8nIkTJ16yXkRE\nBCtWrCA2Npbk5GQWLlxYNYvGypUrKS8vr/qCyrHRd9555/XeN2mgCksu8si735B4Pod2vm78+9l+\nWFtp5gsRkfrEZDIx7dGehIf6/HyCZD0ZuUVGx5J66IodxJw5c4iOjsbV1ZXPPvuMZcuWXbI8KSmJ\n1NTUS+4LCwtj0qRJ9O3bl/bt2xMZGUlERMRlt6+p4+R6Kisv59n/+Y4fElLxcjPz8YuDcLDTzBci\nIvVR5QwZ/Wjn68bJczk8+u63FJZoSjm5vkwVtXjelU2bNtG2bVujYzQI9WV81Buf7GLe+hic7Bux\natIwAn1cjY501epLDeoy1cB4qoHx6mINzmXmM2zSalLS87n9Fn/mPNsPC4u6ezKuLtagrouLi6Nf\nv36XXab3pqXeWPB1DPPWx2BtacG85/rXqUZZRET+OE8XM4tfHIyjnTXr9p1kypI9RkeSekTNstQL\nK3ccY9InuwB4d2xverbzNjiRiIjcTEHNXZn//ACsLS2Yuz6aD786aHQkqSfULEudt/HHUzw3ZwsV\nFfDavWGM7BlgdCQRETFAz3bevPdEH0wmmLZ0H/+7+ciVVxK5AjXLUqftOXKWx6M2crGsgqeGdWDc\nsA5GRxIREQPddWtrpj5SeVW/lxd+z5e7jxucSOo6NctSZ8UkpjH6nW8oKi3jgb5BvBJ5i9GRRESk\nFhjdP5iXIrpSUQHP/s8Wthw6bXQkqcPULEuddPxsFve/vZ7cwlKGdvPnH4/10DSEIiJS5dnhHRk7\npD2lZeWMeW8j+46eNzqS1FFqlqXOSU7L475/rCc9p4g+7b15f1xfLC30qywiIv/PZDLx9we6cU/v\nNhQWX2T0jK85nKSp2OTaqcOQOiU5PY+IqWtITs+jc+umzH9uAI2sLI2OJSIitZDJZGLGmF4M6epH\ndkEJkdPWEntKDbNcGzXLUmekpOdxz9S1JKXm0qGlO5+8NBh7W2ujY4mISC1mZWnBh0/fxm0dm5OZ\nV0zktHUcOZ1hdCypQ9QsS51wNiOfe6atJfF8Du393Fky8XYam22MjiUiInWAjbUl8/7an76hPmTk\nFnHPtLXEn1HDLFdHzbLUeuczC7hn2lpOnsshxM+NT18ZgrMaZRERuQa2jayY//wA+rT3Jj2niHum\nriMhOdPoWFIHqFmWWi01q4CIqWs4cTab4BaufDrxdlwcbI2OJSIidZBtIysWjB9I7xBv0nIKiZi6\nlmMpWUbHklpOzbLUWsnpeYx8aw3Hz2bTtrkry169A1dHNcoiIvLH2TWyYuH4gfRo58WF7EJGvbVG\nH/qTGqlZllrp5LlsRrz5VdUZ5WWv3q5GWURErgs7Gyv+88IgeoV4VzbMU9Zw4Fiq0bGkllKzLLXO\nkdMZjJjyFWfSKqeHW/76UNyc7IyOJSIi9YidjRWLXhjIoC6+VdPK7TicYnQsqYXULEut8tOJC4x8\naw2pWYX0aOfF0ldu14f5RETkhrBtZMWcZ/szokdrCoov8tCMr9lwIMnoWFLLqFmWWmNnbAr3TF1L\nVl4x/Tu14OMJgzBrHmUREbmBrK0siHoinIf6taW4tIwx721g9a7jRseSWkTNstQKq3cd54G315NX\nVMqdf2rJ/OcGYNvIyuhYIiLSAFhYmPjHoz14algHLpZV8NSHm1nwdYzRsaSWULMshpu3PppxH2ym\n5GI5jw1sxwdP9cXaSr+aIiJy85hMJl69N4xX772Figr4++JdTP5kN+XlFUZHE4Pp1J0Ypry8grc+\n3cOcddEAvHZvGE8ODcVkMhmcTEREGqqnhnXE08XMC3O3MXd9NCkZeUQ9Ea53OxswVV4MUVRykfFz\nt7F613GsLE28+5c+jOoVYHQsERERRvYMoKmzPX95bwNr9pwkNauAheMH6qJYDZTe65ab7kJ2ARFT\n17J613HMttYsfnGwGmUREalVeoV4s+Lvw/B0MbM3/jzD3/iSpNQco2OJAdQsy00VeyqdO/62mgPH\nUvFyM7Py78Po3d7H6FgiIiK/E9zCja8m30mQjwvHz2Zz+99WaS7mBkjNstw03x5IYvgbX5KcXnmx\nkbVv3kU7XzejY4mIiFTLy82BlZPu5LYOzcnKK+a+6etYtCGWigp98K+hULMsN1xFRQUffnWQx/71\nLQXFFxnRozXLX7uDps72RkcTERG5Iif7RiyaMJBxQ0MpK6/gtUU7mLhwOyUXy4yOJjeBPuAnN1Ru\nQQnj525l3b5EAF6K6MqzwztqxgsREalTLC0seO2+bgQ1d+XF+d/zyeYjJCRnMe+5/rg52RkdT24g\nnVmWGyYhOZOhk1azbl8ijnbWfDR+IH+9q5MaZRERqbNG9gzgi78NxdPFnj3x5xj02kr2J5w3Opbc\nQFfVLJ85c4bw8HDMZjNdunTh8OHDV7XxWbNm4enpiaurK6+++mrV/QkJCQwePBg3Nzc8PDwYPXo0\nOTn6hGl9smbPCe74+2qOpWQR5OPCurfuZmAXX6NjiYiI/Nc6tWrK2il30SWgKWcz8hk55Svmro/W\nOOZ66qqa5bFjxxIaGkpGRgaRkZFERkZecZ09e/YwefJkvvvuO2JiYli6dCnLly8HIDc3lwceeIDE\nxEQSExMpKirihRde+O/2RGqFopKL/P3jnTw+axP5RaXc1b0VX00eTkvPxkZHExERuW48Xcx8/vpQ\nxg5pz8WyCiZ/spsx720gO7/Y6GhynV2xWc7JyWHDhg1MnDgRGxsbnnvuOZKSkoiJqfma6Z9//jkj\nR46kbdu2eHl5MWbMGJYuXQpA586deeihh3B0dMTOzo777ruPXbt2XZ89EsMcS8nizje+ZME3h7G2\ntGDyQ9354Km+2NtaGx1NRETkumtkZcmkB//E/Of642TfiK/3JzH4tZUcOnnB6GhyHV2xWT527Bi2\ntraYzWZ69erFyZMnadWqFUeOHKlxvaNHjxIYGEhUVBQTJkwgODiY+Pj4yz52165ddOjQ4Y/tgRiu\noqKCZVvjGfz6Sg4npePn4cTqN+5kzOAQjU8WEZF6b8gt/qx/627a+7lz6kIuw9/4kn+vPUR5uYZl\n1AdXnA0jPz8fBwcHcnNziYuLIzMzE0dHR/Lz869qvdjYWJKSkhgyZAh5eXm/e9wPP/zAokWLqj2z\n7OameXhvBmvryrO/13q8s/OLeOb9b/lsSywA9/Ztx6ynB+JktrnuGeu7P1oDuX5UA+OpBsZTDf4Y\nNzc3vp/1CC/P3cycNQeYsmQP2w6fZf6EoTRv4nRN21INapcrNstms5m8vDx8fHxIS0sDKsccOzg4\nXNV6UVFRAKxcufJ36yQmJjJq1CgWL15My5YtL7udKVOmVP3cu3dv+vTpc6XIcpNs/jGRx2eu43Rq\nDmZba957aiAP9tfZZBERaZhsG1kR9fRABnb158n31rP1p1N0fWIBs54eRGTfYKPjya9s3bqVbdu2\nVd3u27dvtY+9YrPcunVrCgsLSU5Oxtvbm5KSEo4fP05gYGCN67Vp0+aSoRqxsbEEBQVV3U5NTWXw\n4MFMnTqVgQMHVrudcePGXXI7PT39SpHlD/jl1evVHN/8olLe+nQPH2+MAyDU350PnupLq2bOZGRk\n3NCc9dm11EBuDNXAeKqB8VSD/96fAlzZMG0EE+ZvY8OBU4x++0tWbjvM1Ed74HwV77yqBjdeSEgI\nISEhVbfj4uKqfewVxyw7OTkxaNAgpk+fTlFRETNnzsTX1/eSfyA8PJyJEydesl5ERAQrVqwgNjaW\n5ORkFi5cWDWLRnZ2NoMHD+bJJ5/k/vvvv+YdFOPsjE2h/8Qv+HhjHNaWFrw4qgtfvjGcVs2cjY4m\nIiJSa7g3tuOj8QP55597YWdjxapdx+n70nLW7j1pdDS5Rld1Bb85c+bw4IMP4urqStu2bVm2bNkl\ny5OSkn43jCIsLIxJkybRt29fSktLeeKJJ4iIiABg1apVHDx4kISEBF5//XUATCaT5lquxfIKS3j7\ns/0s/LZyju12vm7MfLwP7Xw1nkpERORyTCYTD9wWRPfgZoyfs5V9R88zNmojt9/ix1uje+DhYm90\nRLkKpopaPIP2pk2baNu2rdExGoTq3vKpqKhg/f5E/vafXZzLzMfK0sSzwzvxzPCONLKyNCJqvaW3\n3YynGhhPNTCeanBjlJdX8PGmOKYt3Ut+USmN7Rvxtwe6cW+fwN991kc1uPni4uLo16/fZZdd1Zll\naZhOX8jltUU72HTwNAAdWzbh7T/3JMTP3eBkIiIidYuFhYlHBgQzoFMLJn60nc0HTzNh3vd8sf0Y\nUx+5lUAfV6MjSjXULMvvlFwsY976aP614gBFJWU42lkzMTKMh/oFYWlxVRd9FBERkcvwdnfg4wmD\nWLXzOH9fvItdcWcZ8MoKHhvUjvEjuuBk38joiPIbapalSkVFBd/+kMSbS3Zz8lzl+PHh3Vsx6YE/\naVyViIjIdWIymbi7R2vCO/gwY/kPLN4Ux7z1MazaeZxX7w3j8eF/wsJC07DWFmqWBYDoE6m8OHcT\nWw4mAdCqWWOmPHwrfUJ9DE4mIiJSP7k42DLt0R7c3zeQ1xbtZH/CeZ6fs5Vl244x/S+3EeBha3RE\nQc1yg3chu4AZy3/g063xlJdX4Gy2YfyIzjzcPxhrKw25EBERudFC/NxZNWlY5fjlpXvYHZdM+PjF\nDOnqx8TIW2jtpelZjaRmuYHKyi9m9ppDLPgmhsLii1hZWvDk8M48eXswLg56JSsiInIzmUwmRvUK\nYFAXXxZtTiBqxV7W70/k2wNJ3BceyPgRXTQk0iBqlhuYvMIS5n0dw9x10eQUlAAwoHML3nlyEIHN\n3TRNjYiIiIEc7RvxxujejB3aib8t2MTSLfF8svkIX+w4xmMD2/H47e1xc7IzOmaDoma5gcgvKmXx\npjg+/OonMnKLAOgV4s1LEV3p3Lpp1ZyOIiIiYjwvN0f++edejB3Snn8s28vX+5P48Kuf+Ojbw4zu\nH8wTd4Ti3lhN882gZrmey8wr4qNvDrPg28Nk5RUD0DXAg5fv6cqtwV4GpxMREZGatPZyZsHzAzlw\nLJWZKw+w+eBpZq89xEcbDvNwv2CeHBpKU2cNz7iR1CzXU2cz8pm7LppPNsdRUHwRqGyS/3pXJ/p2\n8Pnd1YJERESk9urcuimLXxzMweMXeG/VATYcOMXc9dH8Z2MsI3u0Zuzt7QnwdjE6Zr2kZrmeOXTy\nAgu+OczqnccpLSsHIDzUh2fu7Ei3IE81ySIiInVYx1ZNWPTCIKJPpvHeqgN880MSS7bEs2RLPP06\nNueJO0Lp3raZnu+vIzXL9UDpxXLW7TvJwm8Osz/hPAAmEwzt5s/TwzrS3l+XpxYREalP2vu7s+D5\ngRw/m8W89TEs33aUTQdPs+ngadr7ufPIgGCGd2+FnY1avf+WjmAdlpyex2fbjvLJpiOcy8wHwMm+\nEfeFBzJ6QDC+TZ0MTigiIiI3Uqtmzkx/rCcvjurCfzbEsmhjLNGJabwwbxtv/u9uRvVuw8P92mqu\n5v+CmuU6puRiGd/+kMTSLfFsiT5DRUXl/QFezjw2qB0jewZgtrU2NqSIiIjcVG5Odowf2YUnh3Xg\ny10nWLwplh+PX2DB1zEs+DqGW4ObcX94EIO7+uls8zXS0aoj4k5l8Nm2o3y+PaFq6rdGVhYM6uLH\n/bcF0audl8YniYiINHB2jayI7NOGyD5tiD6ZxuJNcazYeYydsWfZGXsWB1trhnbzZ1SvNnQL9MTC\nQr3DlahZrsVOnstm9a7jfLn7BPFnMqvub9vclXvDAxnRozWujrranoiIiPxee393/jmmF6/f340V\nO47x+fcJ/Hg8laVbj7J061GaN3FgZM8A7r61tYZp1EDNci2TnJ7Hmj0nWL3rOD+dSKu639nBhqFh\n/twXHkSHlu46iywiIiJXxcm+EY8MCOaRAcEcS8nii+0JfLH9GKcv5PHeyh95b+WPBPq4cEeYP3eE\n+RPo46I+41fULBusoqKCw0kZfPtDIt8cSCIm8f8vN+1ga82grr4M796K3iE+WFtZGJhURERE6rrW\nXs68fM8tvDiqK7vizvLFjgS+2Z9E/JlM4s9k8q8VB2jZrDF3hPkzuIsfof7uDX6ohpplAxQWX2RP\n/Fk2/niKb384RXJ6XtUyexsr+nZozvDurbitY3PsGqlEIiIicn1ZWJjo0c6LHu28KH2snJ2xKazd\ne5L1+xM5cTab91cf5P3VB3F3sqNvBx/6dWpB7xBvGpttjI5+06kTuwnKyys4nJTO1ugzbItJZl/8\nOUoullct93C2p3/nFgzq4kuPYC9s1SCLiIjITWJtZUGfUB/6hPow7dEe7D5ylnV7E9n4Y+UJveXf\nJ7D8+wQsLUyEBXrSu703PYK96NCyCVaW9f9db3VlN0B5eQUJKZnsOXKOXXFn2X44pWoGC6i8YEio\nvzt9Qn0Y1MWXDv5NGvxbHCIiImI8K0sLerbzpmc7b6Y+citHkzPZ9ONpNv90mr3xlX3NrrizAJht\nrekW5EmPYC9uDW5GO183LC3qX/OsZvk6KC4t49CJC+w9eo698efZf/Q8WfnFlzzG282BPu296dW+\n8hdQs1iIiIhIbWYymQj0cSXQx5VxwzqQnV/MtphkdhxOYUdsCifOZrP54Gk2HzwNQGP7RnRu3ZQu\nAR50CWhKp1ZNcbRvZPBe/PfULF+j0ovlHE3O5NDJCxw6mcahE2nEnkq/ZFgFQDNXM90CPbkl0JNe\nIV609GysT5aKiIhIndXYbMOwbi0Z1q0lAGcz8tkZm/Lz11lOXcjlu0Nn+O7QGaDynfRAbxe6BHjQ\nqXUTQnzdaePjgo21pZG7cc3ULNcgp6CEo8mZxJ/OJPZUOj+dSCPuVDpFpWW/e2yQjwu3BHoSFuhJ\nWBsPfJo4GpBYRERE5OZo5mpmZM8ARvYMACA5LY/9Cec5cCyVHxJSiUlM48iZTI6cyeR/vzsCgLWl\nBQHezoT4uRPi60a7n79q8xloNctAXmEJx89mV02bEn86g/jkTFLS8y/7eD8PJ0L93enQsgnt/dxp\n7++OUy0usoiIiMiN5u3ugLe7A8O7twKgqOQi0Ynp/JBwnkMn04hJTOPEuWxiT2UQeyqDz361rpeb\nmQAvZ1p7uxDg5Vz55e2Mm5OdMTvzKw2mWc4tKCHxfA4nzmWTeD6HxPM5nPz55wvZhZddx8baktZe\nzgT6uBDU3IVQ/ya093fHuQFOmyIiIiJyLWwbWXFLGw9uaeNRdV9+USmxpzI4nJTO4cQ0YpLSOXI6\ng5T0fFLS89kanXzJNlwcbAjwdsbPozEtmjjSoqkjLZo64dvUkSaN7W7KENd60SyXXiznfGY+KRn5\nJKflkZKRR3Ja/s/f80jJyCcrr7ja9W2sLfHzcKKNtwuBzV0I8nGhjY8Lfh5O9fJTnSIiIiJGMNta\n/66BvlhWzqkLuRxLziIhJZOE5CyOpWSRkJxFZl4xe+PPszf+/O+2ZdvIEt+mTrRo6khzd0eauZrx\ndDXj6WJf9fP1uF7FFbdw5swZHnzwQfbt20dQUBAff/wx7dq1u+KGZ82axbRp0ygpKeGJJ55g2rRp\nVcu2bNnC448/TnJyMgMGDOA///kPTk5Ol91O/JkMLmQXkpZdSOrP3y9kF3Ihq4ALOT/fn1VIeUVF\njXlsf26I/Tyd8PNojL+nE34eTvh7NKaZq1lTt4mIiIgYwMrSgpaejWnp2ZiBXXyr7q+oqOBcZgHH\nUrI4lZrLqdQcklJzOXWh8ntWXnHVENrqOJttLmmemzS2w93JDvefvzdpXPlzjfmutANjx44lNDSU\nb775hqioKCIjI4mJialxnT179jB58mS2b99O48aN6dmzJ506dSIiIoKCggIiIiJ4//33GT58OA88\n8ACvvPIKH3744WW3ddvLX1wpIiZT5YU9vNwc8HY34+VaOWbGy82Mt1vldzdHOzXEVxAXF0fTpk2N\njtGgqQbGUw2MpxoYTzUwnmpQOXVdM1czzVzNl12eU1BS2URfyOH0hVzOZRRwLjOfsxn5nMvM53xm\nAVn5xWTlF3OkhoYaYOPrPatdVmOznJOTw4YNG5g/fz42NjY899xzTJkyhZiYGEJCQqpd7/PPP2fk\nyJG0bdsWgDFjxrB06VIiIiL47rvvcHZ25t577wVgwoQJ3HnnndU2y62aNa7q+ps2tse98f+/CmjS\n2I4mTnY0dbGnkVXdmoakNtIfpvFUA+OpBsZTDYynGhhPNbgyJ/tGhPi5EeLndtnlFRUVZOQWcTbj\nlwa6gLTsQtJyKkcppP/8Pa2az679osZm+dixY9ja2mI2m+nVqxfz58+nVatWHDlypMZm+ejRo/Tu\n3ZuoqChOnz5Nz549WbJkCQDx8fEEBQWxY8cO3nzzTRYvXkxGRgbp6em4uf1+Z7e9c0+NOyAiIiIi\n8lsmkwk3JzvcnOwI8XOv8bFxcXHVLquxWc7Pz8fBwYHc3Fzi4uLIzMzE0dGR/PzLT6n22/ViY2NJ\nSkpiyJAh5OXlXbLs3LlzxMXFYWNTObNEXl7eZZvly90n15+1tTW33XYbzs7ORkdpsFQD46kGxlMN\njKcaGE81qF1qbJbNZjN5eXn4+PiQlpYGQG5uLg4ODjVu9Jf1oqKiAFi5cmXVOr8sGzlyJCNHjiQz\ns3IMSXXb3L59+7XtkYiIiIjIdVJjs9y6dWsKCwtJTk7G29ubkpISjh8/TmBgYI0bbdOmDUeOHKm6\nHRsbS1BQUNWy2bNnX7LM1dX1smeQ+/Xrd007IyIiIiJyPdU4ibCTkxODBg1i+vTpFBUVMXPmTHx9\nfS8ZrxweHs7EiRMvWS8iIoIVK1YQGxtLcnIyCxcuJDIyEoDbbruN7OxsPv30U/Lz83nnnXeqlomI\niIiI1CZXvOLGnDlziI6OxtXVlc8++4xly5ZdsjwpKYnU1NRL7gsLC2PSpEn07duX9u3bExkZSURE\nBAD29vYsX76cN954o+pTntOnT79e+yMiIiIict2YKiqucDUPEREREZEGStdyFhERERGphpplERER\nEZFqXPFy11L/7Nu3j1WrVpGYmEiPHj0YN24cUDkH9ty5c4mJicHKyor+/ftXjTWX66usrIzZLVzB\ntwAABYdJREFUs2cTHR1NcXEx/v7+/PnPf8bHx4eLFy8yb948du/ejdls5qGHHqJ79+5GR653aqrB\n6tWr2bx5M1lZWbi7u3PffffRtWtXoyPXOzXV4Bd5eXn89a9/pWPHjjzzzDMGpq2frlSDtWvXsnbt\nWvLy8mjWrBnTp0/HZDIZnLr+qOn46zm59lCz3ACZzWaGDx/OoUOHKCkpqbp/+fLllJSU8O9//5vs\n7Gxee+01WrVqRefOnQ1MWz+Vl5fj6enJ/fffj6urK2vXrmXGjBlERUWxdu1azpw5w+zZs0lMTGT6\n9Om0adNGF+i5zmqqgaWlJRMmTKB58+bEx8czbdo0ZsyYoUvPXmc11eAXn376KR4eHmrQbpCaarBj\nxw7WrFnDSy+9hL+/P6dOnVIdrrOajr+ek2sPDcNogIKDgwkLC/vdhWCSk5Pp0qUL1tbWuLu706ZN\nG5KTkw1KWb9ZW1szatQoXF1dgcopGM+dO0dOTg67d+9myJAh2NvbExwcTJs2bdi7d6/Bieuf6mqQ\nm5vL0KFDad68OQCBgYF4eHhw4sQJI+PWSzXVAODEiRNcuHCBTp06oc+i3xg1/V+0YcMG7r77bvz9\n/QFo0aKFkVHrpZqOv56Taw81y1KlY8eO7N+/n+LiYlJTUzlx4gShoaFGx2oQjh49iqurK46OjqSk\npODl5cWsWbPYuXMnPj4+pKSkGB2x3vt1DX4tLy+Ps2fPqlG4CX5dg4qKCj766CMefvhhNco30a9r\nkJSURHZ2Ns888wzjxo3js88+Mzpevffr46/n5NpDwzCkysCBAzlw4ACPPPII5eXlREZG4uvra3Ss\neq+goIBFixbx8MMPYzKZKC4uxtbWltOnT9OyZUtsbW1JT083Oma99usa/NbcuXPp06cPXl5eBiRr\nOH5bg82bN+Pr64uPj4/e+r9Jfvt/UUFBAQcPHmTq1KmUlJQwadIk/Pz8CAsLMzpqvfTb46/n5NpD\nZ5alyvvvv4+vry+LFy/mww8/ZPv27ezatcvoWPVaaWkpM2bMoEePHlUf4rOxsaGoqIgZM2YwdOhQ\nCgsLsbOzMzhp/XW5GvxiyZIl5Ofn8+ijjxqUrmH4bQ0KCgpYtWoV99xzD4DOLN8El/s7sLW1JTw8\nHCcnJ9zd3enWrRuxsbEGJ62fLnf89Zxce6hZlio//vgj4eHhWFlZ4e7uTufOnYmOjjY6Vr1VXl5O\nVFQUzZo1q2oKALy8vC4Zl3bmzBmd1bxBqqsBwJo1a4iOjubFF1/E0tLSoIT13+VqkJqaSmpqKn/5\ny1+IjIzkiy++YPv27bz88ssGp62fqvs78PDwuORxetFyY1R3/PWcXHuoWW6AysvLKSkpoby8nPLy\nckpLSykrK8PHx4dt27ZRVlZGVlYWP/30U9WHnOT6mzt3LiaTiTFjxlxyf/fu3Vm/fj0FBQUcPnyY\nhIQEve15g1RXgy1btrBx40ZeeeUVbG1tDUrXMFyuBn5+fixbtqzqa9SoUfTq1Yu3337bwKT1V3V/\nB2FhYWzevJm8vDwyMjLYt28f7dq1Myhl/VXd8ddzcu2hy103QFu2bGH27NmX3BcREUH37t1ZsGAB\nJ0+exNramu7duzN69GgsLPSa6nq7cOECTz/9NI0aNbpkPOarr75KQEAAc+fO1TzLN9jlamAymXjl\nlVf44IMPyMzMvOSM8ogRI7jrrruMilsv1fR3EBQUVHV7+fLlnD9/nqefftqImPVaTTVo1aoV8+bN\nY+/evdjY2Gie3xugpuPv6Oio5+RaQs2yiIiIiEg19PJERERERKQaapZFRERERKqhZllEREREpBpq\nlkVEREREqqFmWURERESkGmqWRURERESqoWZZRERERKQaapZFRERERKqhZllEREREpBr/B8pwtpUG\nSRZ4AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce7dae7518>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n",
      "\n",
      "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical 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",
     "collapsed": false,
     "input": [
      "dog = DogSensor(x0=23, velocity=0, variance=5)\n",
      "xs = range(100)\n",
      "ys = []\n",
      "for i in xs:\n",
      "    ys.append(dog.sense_position())\n",
      "               \n",
      "plt.plot(xs,ys, label='dog position')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cc7Fr1y7x8R/96EcYGBhAa2srTj/99LoRTpuBFd8xKUWtAhM2Oeg42lpYQFyr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AWp9r2frdkoNrSxcYo132U0qk13eIxr/niXrRSPHDqNpdUC7vj3x/HGi3Zgx1hzvrbqL3a/8Y7x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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79cf12b0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "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 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",
     "collapsed": false,
     "input": [
      "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')\n",
      "\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZQnBwMF26dOHxxx+vcnzVqlXExsYSEBDAlVdeSU5OTv2fgYhIA2UWJnE090fs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\noqNP9D0oaDhctJyCykMNXqeiKDx2Sx9m3XwNqgpz3tvIi19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eU8qt85dy/79Xk1dSRa/2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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79d0dc18>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "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')\n",
      "plt.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uAksrDI/+A828bn/hNFbaLSNQ0Qfg192Y/vsehplvozXC3dFE3XB2dtY7hKtq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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79c932e8>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n",
      "\n",
      "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24?  Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n",
      "\n",
      "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n",
      "\n",
      "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n",
      "\n",
      "One final test of your intuition. What if the two measurements are widely separated? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.arange(0, 60, 0.1)\n",
      "\n",
      "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')\n",
      "plt.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EZNCURIuIhDmzvHPG2DeDPEhG5zim6qJFRAZMSbSISLirLgfAcI4KznjOTO/H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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce74a743c8>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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",
      "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
      "\n",
      "$$\n",
      "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
      "$$\n",
      "\n",
      "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n",
      "\n",
      "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n",
      "\n",
      "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n",
      "$\\sigma_1^2=0$, yielding\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n",
      "\\text{or just}\\\\\n",
      "\\mu&=\\mu_1\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n",
      "\\text{or just}\\\\\n",
      "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing the 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",
     "collapsed": false,
     "input": [
      "def update(mean, variance, measurement, measurement_variance):\n",
      "    return multiply(mean, variance, measurement, measurement_variance)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:\n",
      "\n",
      "    def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n",
      "        return multiply(dog_pos, dog_sigma, 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",
     "collapsed": false,
     "input": [
      "dog = DogSensor(velocity=0., variance=1.)\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)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "time: 0 \tposition = 1.848 \tvariance = 2.500\n",
        "time: 1 \tposition = 1.440 \tvariance = 1.667\n",
        "time: 2 \tposition = 1.032 \tvariance = 1.250\n",
        "time: 3 \tposition = 0.551 \tvariance = 1.000\n",
        "time: 4 \tposition = 0.504 \tvariance = 0.833\n",
        "time: 5 \tposition = 0.379 \tvariance = 0.714\n",
        "time: 6 \tposition = 0.244 \tvariance = 0.625\n",
        "time: 7 \tposition = 0.321 \tvariance = 0.556\n",
        "time: 8 \tposition = 0.381 \tvariance = 0.500\n",
        "time: 9 \tposition = 0.305 \tvariance = 0.455\n",
        "time: 10 \tposition = 0.435 \tvariance = 0.417\n",
        "time: 11 \tposition = 0.423 \tvariance = 0.385\n",
        "time: 12 \tposition = 0.445 \tvariance = 0.357\n",
        "time: 13 \tposition = 0.404 \tvariance = 0.333\n",
        "time: 14 \tposition = 0.397 \tvariance = 0.312\n",
        "time: 15 \tposition = 0.282 \tvariance = 0.294\n",
        "time: 16 \tposition = 0.239 \tvariance = 0.278\n",
        "time: 17 \tposition = 0.161 \tvariance = 0.263\n",
        "time: 18 \tposition = 0.204 \tvariance = 0.250\n",
        "time: 19 \tposition = 0.160 \tvariance = 0.238\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "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": "heading",
     "level": 2,
     "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 sense and update functions, and we must do the same to accommodate movement.\n",
      "\n",
      "How 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 `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n",
      "\n",
      "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n",
      "\n",
      "So, here is our implementation of the predict function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def predict(pos, variance, movement, movement_variance):\n",
      "    return (pos + movement, variance + movement_variance)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "# 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(0,50)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, 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",
      "plt.plot(ps, label='filter')\n",
      "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "PREDICT:     1.0000   502.0000\tUPDATE:    -2.4457     9.8047\n",
        "PREDICT:    -1.4457    11.8047\tUPDATE:     0.7765     5.4138\n",
        "PREDICT:     1.7765     7.4138\tUPDATE:     1.4225     4.2574\n",
        "PREDICT:     2.4225     6.2574\tUPDATE:     2.3347     3.8490\n",
        "PREDICT:     3.3347     5.8490\tUPDATE:     4.8032     3.6904\n",
        "PREDICT:     5.8032     5.6904\tUPDATE:     5.4486     3.6267\n",
        "PREDICT:     6.4486     5.6267\tUPDATE:     6.5119     3.6007\n",
        "PREDICT:     7.5119     5.6007\tUPDATE:     8.9309     3.5900\n",
        "PREDICT:     9.9309     5.5900\tUPDATE:     9.5451     3.5856\n",
        "PREDICT:    10.5451     5.5856\tUPDATE:     9.8194     3.5838\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XtEJg6pQpmE6cKAzLxsRETAkJ2OrWLXF/33nzMP35Z7HnT23YgK1x42LP+8yf\nj8PdvUgPs91sBpPJ6RovRAFYRESkBnB4e+Pw8CBl1izsoaGVfv3Vv8cxds46/kzJwsvDxHP3deaf\nvVrVzDl7hfzu3S9p/4yxYzGdPInx1KmCsHwmOJf2Xg34z38wpqUVec5hNHJq27YSj/FcvhxDgwZO\nf/BTABYREakBsoYNI6dvX+z16lXqdTNz8pn8+Rbm/7gPgI7Nw5gxrAdNrgis1DqkasseOND5nR0O\nsgcOLNKzbExIwJiWhj0kpMT9Q4YOxZCfDytXOnUJBWAREZEaorLD7+a9Jxnz3hpiEzPwcDPy9N3X\nMPS2NphcMPxCahCDgfTnniv+vMVS8hCIvDxye/fGMznZ6UsoAIuIiMglycm38urXP/PB/+3C4YCo\nxmZmDutBy4Yl9M6JlBd395Kf9/IiZc4czGYzrF/v1KkUgEVERKojF630tf1QAqPfXcPBE6mYjAZG\n9mvPyH7t8HArn5uTRCqDArCIiEg1Y8jMxDxwIBlPPEHeTTdVyjXzrTZmLN7OW9/uwGZ30Lx+EDMf\n60HbJpV/w51IWSkAi4iIVDOBzz6Lx6+/EjB1Kok33ljh86juiU1i1Dur2RObjMEAw267mqfv7oiX\nh2KEVE9654qIiFQj3gsW4PPNN9i9vUl5550KDb9Wm513vvudaQt/xWKz0yjMn+lDY+jcsnJvthMp\nb2W+TXPnzp1cd911BAYG0rJlS5YsWVIedYmIiMh5TIcOEThhAgBpL72EtXnzCrvWwROp9Hvxv0z5\n+mcsNjv/6BXJilfuUviVGqHMHxsffPBBBgwYwIYNG1i5ciV9+/YlLi6OkJLmaRMREZHL43AQPHIk\nxuxssvv1I+eeeyrkMna7g4+W7+Y/X20lN99GvRBfpg2JJubqkpfEFamOyhyA9+3bx9133w1Ar169\n8Pb25siRIwrAIiIi5clgIG3SJAJee420KVMqZAaIuMQMxry3hk17TwLw9+ub8+KDXQn09Sz3a4m4\nUpmHQNxyyy0sWLAAm83G8uXLCQgIICoqqjxqExERkXNYrr2WpK+/xuHvX67ndTgcfP7TPno+s5BN\ne09SJ8CbuWN6M2NYD4VfqZHK3AM8bdo0evfuzaRJk/Dy8mLRokV4ehb/x2I2m8t6qRrN/czkzmqn\nC1M7OU9t5Ry1k/PUVs6pbu10IimD4TP/j//7+RAA/bu3YNYTNxMa5FOh161u7eRKaivnuJe2UEYJ\nyhSAc3LoXkPSAAAgAElEQVRy6NmzJ9OnT6dfv35s3LiRvn37sm3bNiIiIorsO3ny5MKvo6OjiYmJ\nKculRUREpAwcDgdfr97L6NnLScnMJdjPixmP38SAHpEYXLDAhsjlWLNmDWvXrgXAZDIRHR3t1HFl\nCsC7du0iIyOD/v37A3DdddfRpEkTNm3aVCwADx8+vMjjpKSksly6xjn7qU7tcmFqJ+eprZyjdnKe\n2so55dlOpsOHsTVpUubznC8pPYd/fbSBZVuPAHBj24a8NuR6rgj2JTk5udyvVxK9n5yntipdVFRU\n4dBbs9nMeieXQi7TGOArr7ySnJwcli5disPh4JdffmHv3r1ERkaW5bQiIiK1nsf69YTFxBDw738X\nLHtcTv73y1FuHL+QZVuP4OvlzmuPXM+8p2/mimDfcruGSFVXph7gOnXq8NVXXzFhwgQefPBBwsLC\nmD59OldffXV51SciIlLrGJOSCB45EoPdjsPbu1xmfEjLymPip5v4Zt0fAHSNrMf0oTE0DC3fG+pE\nqoMy3wTXp08f+vTpUx61iIiIiN1O0OjRmE6dIq9zZzLGjCnzKdfujOfJOWs5mZyFl7uJCfd2YvBN\nrTEaNdZXaicthSwiIlKF+L7/Pl4//og9KIiUN98s01LHWbkWXvpiC/NW7gWgfdMwZgyLoVn9oPIq\nV6RaUgAWERGpKvLy8J03D4CU6dOxN2hw2afasu8kY95bw7GEDNxNRsbe1ZHHbr8aN1OZlwAQqfYU\ngEVERKoKT08Sv/sOr+XLybvppss6RW6+lakLfmHODztxOKBVRAgzH+tBqwjNIStylgKwiIhIFeII\nDibnnnsu69jfDicy6p3V/HEiFZPRwBN92zG6f3s83EzlXKVI9aYALCIiUs3lW23MWrKDWUu3Y7M7\naFY/iBnDYmjfNMzVpYlUSQrAIiIi1di+uGRGvbuaXUeTMBhgyK1RjB9wLd4e+hEvUhr96xAREXGV\nnBx8P/6YrIcfBg+PSzrUZrfz3rKdvPbNL+Rb7USE+vPG0Bi6RtaroGJFag4FYBERERcJfPFFfD/9\nFPfdu0l96y2njzv8Zxqj313Nr38kAPDAjS15fmBn/LwvLUSL1FYKwCJSezkcuA0dimHfPtyffx5L\n+/aurkhqEa/vvsP3009xeHiQOWyYU8fY7Q4+WbmHl77YQm6+jSuCfXh9SDQ3tG1YwdWK1CwKwCJS\na/l88gmmTz4BoE7fvmQ89RSZI0e6uCqpDUxxcQQ9/TQAaRMnYo2Kuugx8YkZPPn+WjbsPgHAndc1\nY/I/uxHk61mhtYrURArAIlIrmQ4eJGDyZABst9+O6bvvwGZzcVVSK1gsBA8fjjE9nZybbyZ70KAL\n7u5wOPh67QEmzttEZq4Fc4AXUx7qzt+uvbJy6hWpgRSARaRWMuTnYwsPx9GpE9YPPyT5f//D0q6d\nq8uSWsCQk4M9JARr/fqkTpsGBkOp+55KyWbc3HWs3B4LwK3XNGbKQ92pE+hdWeWK1EgKwCJSK1lb\ntSLx//4Pc2AgAJZrrnFxRVJbOAICSP74Y4wnT+IIDi51v6WbDjHh4w2kZuYR4OPBS//sxp3XNcNw\ngcAsIs5RABaR2svbG/z9L7iL5+rVYLWS16tX5dQktYPBgL1+/RI3JWfkMuGjDfx3y2EAelwdzmuP\nXE99s19lVihSoykAi4iUwpCcTNCoUZhOnybrgQdIf+EFHD4+ri5LarDl244x7oN1JKbl4OPpxgsP\ndOH+G1qq11eknBldXYCISFXlCAoi87HHcHh44Dt/PqE33YT79u2uLkuqI4fjgpvTs/MZ894aBk9b\nTmJaDl1aXsHKKXfxwI2RCr8iFUABWERqBc/VqwkcNw5DVpbzBxmNZA0bRuKyZVhatsTtyBHq9O2L\nz8cfV1idUvO4//IL5rvuwhQXV+L2dbuO0/OZb/h67QE83U288EAXFjx7O43CAiq5UpHaQwFYRGo8\nQ3IyQU8+ie9nn+H99deXfLy1VSsSly0j89FHCx63aFHeJUoNZUhLI/jxx/HcsgWf+fOLbMvOtfDs\nxxu495XvOZGURbsmofzv5f48emsbjEb1+opUJI0BFpGazeEg6JlnMJ06RV6nTmT/4x+Xdx4vL9Jf\neIGsQYOwNWpUvjVKzeRwEPTUU7jFx5Pfti0ZY8cWbvr5wClGv7uao6fScTcZGXNnBx7v0xY3k/ql\nRCqDArCI1GjeixbhvWwZdl9fUmfMAJOpTOdT+BVn+Xz6Kd7ff4/dz4+Ut98GDw9y861MW/gr7yz7\nHYcDIhuGMGNYD6Iam11drkitogAsIjWW6fhxAp97DoC0f/+7QsOr36xZWCIjyevdu8KuIdXIoUME\nTpoEQOrUqdgaN2bnkdOMenc1++NTMBoMPH5HW568swOe7mX7UCYil04BWERqLHtAALm33IIhLY2c\ne+6psOu479iB/9SpGBwOTZcmBa68kvRx43A7epSM2/rw5sJfmbl0O1abgyb1ApkxNIaOzeu6ukqR\nWksBWERqLIe/P6nTp0N+/gWXmy0ry9VXk/7ccwS8+iq+8+fjuWEDKW++iaV9+wq7plRxZ2YQ2R+f\nzKgXlrLz6GkAHr4lin8NuBZvT/34FXEljbYXkZrPw6Niz1/KdGle331XsdeVKstms/Pust+59bkl\n7Dx6mvA6fnw94Tb+/WBXhV+RKkD/CkVEysnZ6dICpk7Fe+lS8rt1c3VJUtHy8/H58ktMiYmFszwc\nPJ7MkGnfs2lPPAADe7Rg4v1d8Pep4A9iIuI0BWARqVnsdjC68JdbXl6kT5xIxpgxOPz9XVeHVCyL\nBZ+vv8Zv5kzcjh/H7ubGrKDWLDyWy/ZDiQDUDfLhtSHX07NdhIuLFZHzKQCLSI3hsXUrgRMmkDJj\nBtaoKJfWovBbc3l//TV+06bhHl/Qw7svoC7PhUezaNUxHAYjnu4mBvRoxfi72xHs5+XiakWkJArA\nIlIjGDIzCRo1CrfYWLy/+44MFwfgElksBD/6KNkDB2q6tGroVEo2K7fH0uaDRdwSH89enzpMatyD\nBaGtCAv2Y2D7CHq1j+CO6Ch8vTxISkpydckiUgoFYBGpEQImTcItNhZL69ZkPPmkq8spkffChXgv\nX4738uVk3X8/6ZMmabq0KszhcLDraBIrth1jxfZYfj9SMJNDI78OdIsMZc+1Peh5TWOWtY+gTeM6\nhcsX+3pprK9IVacALCLVntf//ofvF1/g8PQk5c03K37Wh8uUM2AAxtTUgunSPvvsr+nSOnRwdWly\nRk6elXW7j7Pq16NkrVrDYlO9wm1eHiauj2pAr/bd6dkugnohvi6sVETKQgFYRKo1Q2oqgU8/DUD6\nM89gbdHCxRVdwJnp0vKiowkeORL3vXup068fp5csUQh2oRNJmazaEceKbcfYuCue20/sZNLR1bTK\nPk2vG0ZT74Yu9O7QiOta1dcUZiI1hP4li0i15ggMJP255/D63//IeuQRV5fjFGurViR+9x0BU6fi\ntn8/lnbtXF1SrWK3O/j9yGlWbD/Gyu2x7DqahMFhp//pfWw5upo2WQkA5FxRny+HdCI/5noXVywi\n5a3MATgnJ4fRo0fzzTffYLfbGThwILNnzy6P2kRELs5gIGfAAHIGDHB1JZfmzHRpWK2unbatlsjO\ntbBu13FWbI9l1Y5YElJzCrd5e7oxI3cnj+7+GgBr/fpkjhpF9oABVXY4jYiUTZkD8JgxYzh8+DB7\n9uwhLCyMPXv2lEddIiK1g1sp/w3bbGAyVW4tNczx05kFgXd7LBv2nCDPYivcVt/sS6/2EfRu34hu\nrerhk5mOpf+vZD30ENn33gueni6sXEQqWpkCcE5ODvPmzWPbtm3UrVsXgNatW5dLYSIitZXp+HHM\n995L2vPPk3fTTa4up9qw2x1sP5TAyu2xrNgey97Y5MJtBgO0bxpG7/YN6dU+glaNzBgMhr+ODQkh\ncfXqgh1FpMYrUwA+cOAABoOBxYsXM3PmTMxmMy+//DL9+vUrr/pERIoxZGTU6IUmfD75BLfDhzEP\nHqzp0i4iMyeftbuOs3J7LKu2x3E6/a+hDT6ebsS0Cad3hwhubBtO+I6f8X99IunjxpHfOLr4yRR+\nRWqNMgXg9PR08vPzOXLkCLGxsWzcuJE+ffrwxx9/cMUVVxTZ12w2l6nQms7d3R1QO12M2sl5NbWt\nDDt24H7LLVgnT8Y+ZEiZz1cl2+m117BGRGB6/nl8P/sM782bsX70EY5OnVxaVlVpq6N/pvLD1kMs\n23yQtTtjyT9naENEWAC3dWnG3zo1I/rqCDzdTRh+/BG3h/+BcfNmAILnz8fav3+F1VdV2qmqUzs5\nT23lnLPt5IwyBWAfHx9sNhtjx47Fw8ODHj16cNVVV7F58+ZivcCTJ08u/Do6OpqYmJiyXFpEaqPc\nXNwGD8aQmopxzx7srq6nohiN2EaNwt6zJ26DBmHctQv3m24i/8ABCAtzdXWVzmazs3X/CZZtPsgP\nWw+x+2hi4TaDAbq0asDfOjXjti7NaNWozl9DG44exf3hhzFu2ACAw2zG9uST2IYNc8XLEJEKsGbN\nGtauXQuAyWQiOrqE3+6UoEwBuEmTJkXGUF3I8OHDizzWEpFFnf1Up3a5MLWT82piWwVMmoTn3r1Y\nmjbl9NixOMrhtVXpdqpXD779loCpU7EHB5NpMoEL66zMtsrIzmf1znhWbo/lxx1xJGfkFm7z83In\n5upwerWPoGe7hpgDvAu3JSefM+7XZCJs/37sQUFkDhtG1uDBOPz8IDe34E8FqdLvqSpE7eQ8tVXp\noqKiiIqKAgraaf369U4dV6YAHBwcTExMDG+88QazZ89m06ZNHDhwgC5dupTltCIixXisX4/f++/j\nMJlInTULh7f3xQ+qCTw9SX/+eVdXUSmOJaSzYlssK7fHsnnvSSy2v/r4I0L96d0hgl4dGtGl5RV4\nuF18hgyHjw/JH32EtXnzGj1mXEQuXZmnQfvwww8ZNGgQQUFBhIeHM3/+/GLjf0VEysRmI3DCBAAy\nxozRwhHnMGRmFvRqVkNWm51f/zhVMGvDtlj+OJFauM1oMNCpRd3CqcqaNwgq9TeO7r/+iiE3l/zr\nriu2TSvsiUhJyhyAGzduzOrVq8uhFBGRUphMpHz4Ib5z5pA5YoSrq6kyPJcvJ+ipp0h9/fVqM11a\nenY+P/0WVzC04bc4UjPzCrf5e7vT4+qG9O4QwQ1tGxLi73XBc7nv2IH/tGl4/fgjlmbNSPzxR82d\nLCJO0VLIIlItWJs1I23qVFeXUaX4LF6MKSnpr+nSXngBh6+vq8sq5vCfaWd6eY+xdf+fWG2Owm2N\n6wYUDG1oH0HnFvVwd7v4qnjuO3fi//rreK1cCYDdx4fcW2+F/HyoLUNjRKRMFIBFRKqplNmzyW/X\njoApU/D97DM8N2wgZdYsLB07urQuq83OzwdOsWLbMVZuj+XQybTCbSajgS4tr6B3h0b0ah9B03qB\nTt9MDYDdTvDw4bgdPozd25ushx4ia9gw7CEhFfBKRKSmUgAWEamujEayhg4lLzqa4BEjcN+7l+CR\nI0lYs6b0JZYrSGpWHqt/i2PFtlh++i2OtOz8wm2BPh7c0LZgBbYebcMJ9rvw0IYLMhpJf+opPH7/\nnczHHsNep045VC8itY0CsIhUSabDh7FdeaVW53KCNTKSxGXLCJg6ldybbqq08HvwRCortxfM2rB1\n/5/Y7H8NbWhSL5De7SPo3aER1zSv69TQhvOVdoNfbt++5PbtW6baRaR2UwAWkSrHdPAgoTffTF6v\nXqS89RZcwuo+tVYlTJdmsdpYvyuORWt2sXJ7LEf+TC/cZjIa6NaqHr3aR5wZ2hB02ddx++MP/KZP\nx3PLFk6tX69xvSJS7hSARaRqsVgIHjUKY24uDi8vhd/ykJuLMSMDe2io04fk5Fs5EJ/Cntgk9sYm\nsyc2md3HkknP/mvWhiBfT25sd2Zow9XhBPp6lqlM06FD+M+YgffixRgcDhweHnj8+iv53buX6bwi\nIudTABaRKsV/1iw8duzA2qABaecsoS6XL+DVV/FeuLDE6dIcDgcnkrPYcyyJvXHJ7DmWzN64ZA6f\nTMPucBQ7V8sIMze0aUDvDhF0bF4XN9OlD20oid9bb+H/6qsY7HYc7u5k3XsvGSNGYG/QoFzOLyJy\nLgVgEaky3Ldtw2/mTBwGA6kzZuAICHB1SdWf1Yr73r2F06XF3t6fxf0e5veEHPbGJbM3NpnUrLxi\nh5mMBq6qH0SrCDORESG0ijDTrW1TGtTxr5DlWC1RUQU39d13H5kjR2ILDy/3a4iInKUALCJVht9b\nb2Gw2cgcOpT8bt1cXU615XA4OJGUxe4zwxf2dn2IzpkhjP1tGRHfLea2lav5IvJOtgQ2BCDYz5NW\njcy0igghsqGZ1o1CaFY/CC+Poj8izOaKW044LyaGU5s2Ya9fv8KuISJylgKwiFQZKbNnY/ngAzKH\nDHF1KdVGTp6VffHJZ8bpngm8sclFpiED+G9gexZc04CvDiymRepJ5hgPsHPcECIjQqgb5HNpc/Fe\nJtPx4/i+8w4ZY8fiCA4uutFgUPgVkUqjACwiVYe3t5Y6LoXD4eD46Uz2nA26cQU3ph35M40ShuoS\n4u9V0KN7ZvhCq4gQmjcIxtP+FBlvvUXo4MHcUEmLRxhPnMD/rbfw+eILDPn5OPz9yRg/vlKuLSJS\nEgVgEZEqJjvXwr74lKK9unHJpJ/XqwvgZjLQrF4QrRqZiWwYQqtGBcMYwoK8S+nVNZExdmzFvwjA\nmJCA35tv4vvZZxjy8nAYDGT360fOXXdVyvVFREqjACwi4iIOh4P405nsjU0uHK+7JzaJo6fSS+zV\nNQd4FdyUdk7Qbd4gCE93U7nUY4qNxeHtfUnTpV3wfH/+id+HHwKQ06cPGWPGYG3RolzOLSJSFgrA\nIuIyHj//jCUyssTVvmqas726e84Juntjk8nIsRTb181koHn94DPDF/4axhAaWFqvbjmwWAh+7DFM\ncXElTpd2Wae8+mrSn32W3BtuwBoZWQ5FioiUDwVgEXEJ0/HjhDz4IPbgYE5/+2259Tq6msPhIC4x\no3DxiD2xyeyNu3iv7rlBt1n98uvVdZYhMxOHr2/hdGlZAweSPmkSDl/fix5rTE4Gux17nTrFtmUO\nH14R5YqIlIkCsIhUPrudoFGjMGZkkNetW4nBqTrIyrWw78zNaGd7dffFXaBXt0EwkQ1DaH1mvG5k\nRAhhQT4uqLw4R3AwSV9+ie8HHxAwZQq+n3+O58aNpMyahaVjxxKPMaSk4Pfee/h++CE5/fqRNnVq\nJVctInJ5FIBFpNL5vv8+nps2YatTpyA0VcIUXGVhtzuIP51RJOjuiU3mWELJvbqhgd5nxun+NV63\nWf0gPNwqt1f3khmNZD36KHnR0QQ/8QTue/fivnNnsQBsSE3Fb84cfOfOxZiZWXDo6dNgt4OxfFaG\nExGpSArAIlKp3PbtI2DKFABSX3utyvX+ZubkF4zVPbM08Nl5dTNzi/fqupuMNGsQRKtzphqLjAgh\nNLBq9OpeLmvLliQuW4bPN9+QPXBg0Y2ZmYR1744pJQWA3JgYMsaOLbWXWESkKlIAFpFK5bV8OYb8\nfLLuv79cbrQqq98OneK/m/7g133x7I1L5uip9BL3Cw30PhNw/wq61aJX93J5epJ9//3Fn/fzI/eW\nW3CLiyPjqafIv/bayq9NRKSMFIBFpFJljhyJpVUr8rt2dWkdFqudGUu28ebSHdjsf41jcDcZad4g\nqMgCEjWhV7c8pf3nP+Dh4eoyREQumwKwiFS6vF69XHr9gydSGfH2T/x+5DQGAwy+pS0dmoQQ2bCg\nV9fdTeNYL0jhV0SqOQVgEak17HYHn6zcw0ufbyHXYiO8jh8fjruD6KsjSEpKcnV5IiJSSRSARaRW\nOJmcxZPvrWHtruMADIi+in8/2JXGDeu5uDIREalsCsAiUqE81q7FHhKCNSrKZTUs3XSICR9tIDUr\njxB/L6Y+3J1br73SZfWIiIhrKQCLSIUxJiYS/MQTGNPTOb10KZa2bSv1+qlZeTz70QaWbDoEQM92\nDXl9SHSVWXxCRERcQwFYRCqGw0HQ009jSkoir3t3LG3aVOrl1+46zph31/BnShbenm5MeqAL99/Q\nEkMVX3RDREQqngKwiFQIny+/xGvFCuwBAaS88UalrRCWk2/lla9+Zu7/7QKgQ7MwZj3WgyuvCKyU\n64uISNWnACwi5c509CgBEycCBXPG2hs0qJTr/n4kkZFvr+aPE6m4mQw8eWdHHu/TFjeTpjUTEZG/\nKACLSLlzO3IETCZy7riDnH79Kvx6Vpud2f/9jTcW/YrV5qB5/SBmDe/B1VeGVvi1RUSk+lEAFpFy\nl3fDDSSuWoXdxwcqeMztkT/TGPnOarYdTADg4Vui+Nc91+Ltof/eRESkZPoJISIVwlbBwx4cDgef\n/bSPSfM3k5Nn5YpgX6YPiyE6qnKGW4iISPWlACwi1U5CajZPvb+WVTviAOjXtSkvD76OIF9PF1cm\nIiLVQbndGbJu3TqMRiNz584tr1OKiBTz/c9HuHH8N6zaEUegjwdvP3Ejs5+4UeFXREScVi49wFar\nlWeeeYbIyEjNsSlSC3msX4/bwYNk//OfFTbmNz07n4nzNrJg3R8AREc14I2hMdQL8a2Q64mISM1V\nLgH4zTff5Pbbb2f58uXlcToRqUYMaWkEjx6N6eRJHH5+5Nx9d7lfY/Pek4x6dzXxpzPxcjfx7H2d\nGNS7NUajPnCLiMilK3MA/vPPP/n444/ZunXrBQOw2Wwu66VqNHd3d0DtdDFqJ+dVVlu5jR2L6eRJ\n7J064fPww/i4ld+tBXn5Vl6ct47pC7fgcECH5lfw0bg+tGhYfq9J7ynnqa2co3ZyjtrJeWor55xt\nJ2eU+SfVU089xbPPPoun54XH302ePLnw6+joaGJiYsp6aRFxMeOCBZi+/BKHjw/WuXOhHMPvzsMJ\nDJ76X3YdTcRkNDB+YDf+dV833N1M5XYNERGp3tasWcPatWsBMJlMREdHO3VcmX5abdiwgSNHjjBg\nwIDC5xwOR4n7Dh8+vMjjpKSksly6xjn7qU7tcmFqJ+dVdFsZT54kbMQIANKef57skBAoh2vZ7Hbm\nfL+TqQt+Id9qp3HdAGY91oOOzeuSnpZa5vOfT+8p56mtnKN2co7ayXlqq9JFRUURFRUFFLTT+vXr\nnTquTAH4l19+YdOmTRiNf00msWbNGnbv3s0bb7xRllOLSBVnyM/H2rgx9pAQsh98sFzOGZeYweh3\nV7N5358APNgzkokDO+Pj5fyvtURERC6mTAF41KhRjBo1qvDxDTfcwIMPPshDDz1U5sJEpGqzNWrE\n6SVLMGRllXnmB4fDwddr/2DivI1k5loIC/Lm9SHR9GwXUU7VioiI/EULYYjI5XN3xxEUVKZTJKXn\nMH7uen745SgAf7v2Sl59uDsh/l7lUKCIiEhx5RqAf/rpp/I8nYjUcCu2HePpD9aRmJaDv7c7L/3z\nOu7q3kzziYuISIVSD7CIVLqsXAsvfraZz37cB0DXyHrMGBpDeKi/iysTEZHaQAFYRJzivm0bfu+/\nT+rLL+MICbns8/zyxylGvbOao6fS8XAzMn7AtTx6axstaiEiIpVGAVhELsqQnU3wyJG4HTmCtVkz\nMsaOveRz5FttTF+0jbe+/Q27w0GriBBmPXYDkRGXH6ZFREQuhwKwiFxUwOTJuB05giUykownnrjk\n4w/EpzDyndXsPHoagwEe79OWsXd1xNNdi1qIiEjlUwAWkQvy/PFHfOfNw+HhQcqsWXCRVR/PZbc7\n+HD5bv7z5VbyLDYahvoxc1gPOresV4EVi4iIXJgCsIiUypicTNCZ4Q4ZTz+NtVUrp489kZTJmPfW\nsH73CQDujbmKSQ90xd/Ho0JqFRERcZYCsIiUyu7jQ07fvrjv2kXm0KFOH7dk40EmfLSBtOx8zAFe\nvPbw9dx8TeOKK1REROQSKACLSOm8vEifNAksFjBdfLxuSmYuEz7awLebDwPQq30Erw+5ntBAnwou\nVERExHkKwCJyce7uF91lze/xPDlnDX+mZOPj6caLD3blvh4ttKiFiIhUOQrAIlImOXlWXv5yCx8t\n3wPANc3rMvOxHjSuG+DiykREREqmACwiRdntYDQ6tetvhxMZ8fZPHDqZhpvJwFN3XcPwPldjcvJ4\nERERV9BPKREp5LZvH6E33IDHli0X3M9qszN90TbumLSUQyfTuKpBEMv+3Y8Rfdsp/IqISJWnHmAR\nKZCXR/CIEbgfPIj3woXkd+5c4m6HTqYy6p01bD+UAMAjt0TxzD3X4u2h/05ERKR60E8sEQHAf9o0\n3Pfswdq4MekvvFBsu8PhYN6qvUz+fAs5eVbqhfgyfWgM10c1cEG1IiIil08BWETw2LIFv7ffxmE0\nkjJjBg5f3yLbT6Vk89T7a/nxtzgA7ryuGS/9sxuBvs6vCiciIlJVKACL1Ha5uQSNGoXB4SBjxAgs\n115bZPOyrUcYP3cdKZl5BPl68spD13FHl6YuKlZERKTsFIBFajsvL9JffBGfTz8lY8yYwqfTs/N5\n7pMNLFx/EICYNg2Y9mgM9UJ8SzuTiIhItaAALCLk3nwzuTffXPh4454TjH53DceTMvHyMPH8fZ35\nZ+9WWtRCRERqBAVgESmUm29l6oJfmPPDThwOaNcklJmP9aBZ/SBXlyYiIlJuFIBFBIBdR5MY9c5P\n7ItPwWQ0MKp/e0b2bY+7m+b1FRGRmkUBWKQWMqSn4wgoWKrYZrfz7rLfeW3Br1hsdq68IoA3h99A\n+6ZhLq5SRESkYigAVyUWS8Efd3dXVyI1mOnoUUJvu43MRx9l9z3/ZPSctWzdfwqAf/ZqxXP3dcLH\nS+9BERGpuRSAqxDjp58S9sorZA4fTvaAAeDl5eqSpKaxWgkeORJjaion1v1M798Dycq1UDfIh2mP\nRphkSCUAACAASURBVHND24aurlBERKTCaXBfFWJcuhS3uDiC/vUv6nbrhu+cORiys11dltQgfm+/\njcevv5LoF0w347Vk5Vq4rdOVrJxyl8KviIjUGgrAVYh10SKS334bS2QkplOnCHzxRcI6d8Z05Iir\nS5MawH3nTvxefx2AgU1uxxoQyKzHevDeyJ6E+Ou3DSIiUntoCERVYjKR27cvuXfcgeeKFfjPmoUh\nNxdbo0aurkyquczsPHhkBKE2G7MadCK7e3dWDe1Bgzp+ri5NRESk0ikAu4jp2DE8N24k+9574fzF\nBQwG8m66ibzevTEmJ4NRHfVy+X7e/ycj31mNI/w2XrSvI2PCBL664xqMRi1qISIitZMCsCvYbASN\nHo3n1q0YUlPJeuyxkvczGLCbzSVu8n33XdyOHSNz+HBsDTV2U4rLt9iYPH89077ejN3hoHWLpjSe\n+TA3h4e4ujQRERGXUgB2Ad85c/DcuhVbWBjZ99xz6SfIz8fv7bcxJSXh8/nn5Nx5JxlPPIGtadPy\nL/b/27vzsCjL/Q3g9zA7u6CgIOKWApqilqYobqdc0tKs6JhouWSZmktGeU6lmUfSzPXoz4wyU0/m\npVKZ2oIK4l6WpOAeoCCy77PP+/sDpUjQkZlhZpj7c11dl8687/t8+ap58/jM85BD0emNOPNHHo6c\ny8Z3pzJwLj0PLiIRpj8RjrljukMmEdu6RCIiIptjAG5gkrQ0eC5dCgAo/vBDCD71mI2TyVCwYwfc\n166FMj4erl99BeWOHVCPHImilSsBudzCVZO9MhiNSM0oxJHUbBw5l40TF3JQodZVv9+mhTdWTOmH\nhzs2t2GVRERE9oUBuCFptWgycyZEWi0qnn8emsGD6/0ofceOKF6zBmVz5sB93Tq47tgBl4ICht9G\nThAEXLhehKOp2TiSmo1jqTdQUqmtcU27Fl7oExaAp1vK0ffJAVCrKmxULRERkX0yKwDr9XpMnDgR\nP/30EyorK9G9e3esXbsWYWFhlqqvUXEpKABEIuiDg1H67rsWeaahTRuULFuGslmz4MI9gxsdQRDw\nx81SHDmXjaOp2TiaegP5paoa1wQ1c0dEWAAiOgWid2gLBKpLoPzmG3jOXgNhSw/cXLcOgjt3eyAi\nIrrNrABsMBjwwAMPIDY2FgEBAVi5ciVGjRqFixcvWqq+RsXYogXy9uyBODsbgpubZZ8dGAhjHe+5\nbtoEQ3AwNAMG3LnjBNmd63llOJJ6A0dSs3A09QZuFNacwfX3dkVEpwBEhAWgT1gLtPLzBDQauO7Y\nAeWKeMiOH4dIEAAARqXS4r/XiIiIHJ1ZAVgul+Ptt9+u/vkLL7yAOXPmoKCgAL517F7g9GQyGFq3\nbrDhXPLy4LVoEURqNbRduqB85kyohwzh1mp2JLe4smpJw7mqZQ0ZuWU13vfxUKB3aIvq0NuuhRdE\nf/9GRiyGx4cfQpyXB0GhgOof/4Bk/HgYhw0DSksb8KshIiKyfxZdA3zs2DEEBgYy/NoRwdUVZXPn\nwm3DBshSUuAzeTJ0HTui7LXXoH7ySVuX55QKy9Q4lnajOvReyi6u8b6HUoreoVWzuxGdAhDS0ufP\nPXt1OkCtBpTKmg+VSFA2dy4EuRzqYcMgeHjwzyEREVEdRIJw699KzVRSUoKePXvi/fffxzPPPFPj\nvYSEBPTt29cSwzRaUqkUAKDT6e5xZT2pVHD57DNIli+HKCsLhmefhX7zZuuMZUVW75MVlFZokHz2\nGhLPZODQmQykXM3FX//UucqliOjcEgPCg9G/SzDC2/tDIv7LDL3RCNHRoxBv3w6XXbug/9e/YJw2\n7Z7jOmKvbIF9Mh17ZRr2yTTsk+nYK9NIpVIcPHgQg03YZMAiM8AajQajR4/Gc889d0f4vW3RokXV\nP46MjET//v0tMbR9KyqCeNEiGN5+G2jSxLa1KJUwTpsG7eTJcNm6FcIjj9i2nkasUq3D0dTrOPRb\nBpJSMvHLxRswGP9MvHKpGL1CAzGgazAGhAfjoQ4tIJPWsj9vejrEGzdCvH07RNevV7/scuKESQGY\niIiosUtMTERSUhIAQCwWIzIy0qT7zJ4BNhgMeOaZZ+Dn54f/+7//q/WahIQEhIaGmjOMQ/KeMQOu\nu3ZBNXw4ijZuvOu1t/+5uqCgoCFKq5Pi+++hiYiw210D7KVPf6XRGfDr5dzqvXhPX86FzvDnRxLF\nLiKEt2t2a6eGAPR4wB9K2b2/95SdOoWmo0YBAPSBgVCNGgXVqFHQh4aa9GFGe+yVPWKfTMdemYZ9\nMg37ZDr2yjS+vr5ITk5umBngqVOnwsXFBevWrTP3UY2K4ttv4bprF4xKJUrfesvW5ZhEfPkymkya\nBMHLCxUTJ6J84kQItp65tkN6gxFnrubhaOoNHEnNxqmLOVBrDdXvi0RAlzZN0Ses6kNrPTv6w10p\nq/N5ouJiCN7ed7yu7dEDZa++Cs0//gHtQw/xg4tEREQWYlYAzsjIwKeffgpXV1d4eXlVv75//35E\nRESYXZyjcrl5E163Qm/p22/D0LatjSsyjUijgfbhhyE/eRIeH30Etw0bUDFhAipeegnGZs1sXZ7N\nGI0CUjMLkHxrL94T53NQrq65DiukZRNEdApAn7AAPBLaAt5udz+QRFRWBsW+fVDGx0N+5Ahyjx6F\nITCw5kUuLiibP9/SXw4REZHTMysABwcHw2isa/dZJyUI8J43D+KiIqj790fl+PG2rshk+k6dULB7\nN2THj8N99WooEhPhsW4dRDodShcssHV5DUYQBFzKKq5e0nDs/A0Ul2tqXNOmuWf1koY+oQFo6qWs\n42k1yRMT4bp1KxQJCRCp1VXjSSSQ/vrrnQGYiIiIrIJHIVuaTgdDUBCM3t4o/vBDhzx4QvvIIyh8\n5BFIf/sN7v/9L8qnTrV1SVYlCALSb5ZWL2k4mpqNvJKap60F+rrXOHwiwLd+a6TliYlQfvcdBJEI\nmt69q9b1Dh8OwcfHEl8KERERmYAB2NJkMpQsXoyyOXNgdPB9WHXh4Xf98J44MxOGVq0asCLLySoo\nrz5e+EhqNrILap625uetRJ/QqhneiE4BaNXM487DJ+oiCHApLKz1178yKgoGPz+oRo6EkTO+RERE\nNsEAbCWOHn7v5fYOBarhw1E+cyZ0Dz5o65LuKq+ksnqG98i5bKTfrHk6mre7vCrw3jp8on2At+mB\n9xbJpUtQxsdDGR8Po6cn8vftu+MafceO0HfsaNbXQkREROZhAKZ6kZw/D0Euh3LvXij37oV64ECU\nv/YatA8/bOvSAABF5WocT7u9pOEGLlwvqvG+u0KKR24dL9wnNABhrf5y2tr90Grh9umnUO7eDdnZ\ns9UvG/z8ICoq4i4aREREdogBmOqlMjoa6sceg/uGDXD94gsoDh6E4uBBFK1cCVUdh6FYU7lKixMX\ncnDkXNWShnMZBTVOW1PIxOjZoXn1koYHWzetedpafUmlcPviC0jS02H09IRq+HCoRo2Ctk8fQFzL\n4RZERERkcwzA5tJq0WTGDJS/9BJ0PXrYupoGZfT3R+k776Bs+nS4x8VBuXMn1EOHNsjYKo0epy7d\nrFrDey4bZ67m1ThtTSZxQff2ftU7NYS384O8ttPWTCSqrAT0egienn97Q4TSmBhAKoV64EBAoaj3\nGERERNQwGIDN5LFyJZR79kB67hxyDx0CJM7XUsHHB2Xz5qFszpzaZz2NRkAQ6j0jqtMbcTm7GGnX\nCvFHbgpOXcjGibQsaPU1T1vr3t6v6vCJTgF4+AF/KOVm/lrodJAnJUEZHw/F/v0of/VVlM+adcdl\n6ieeMG8cIiIialDOl9YsSPrLL3BfswaCSITi5cudMvzWUEfAVezfD88lS1A2fTpUTz0FSKV1PiK/\nRIXUzAKkZhYiNbMAaZmFuJRVXONoYaBqd7nOrX1vbUsWgF4dm8PDte7T1u7ry0hPh/uGDVB8+y3E\nRX+uHZZcvWqR5xMREZFtOXliqz+RSoUmr70GkdGI8ldegbZXL1uXZLeUu3ZBcvUqmsyZA4+PPkL5\ntGkoGfM0LhdqqkNuamYB0q4VIrdYVeszgv08ENbKF907BiK8vT9CA9zQxN06yw1EKhXcNm8GAOg6\ndIBq9GionnwShuBgq4xHREREDYsBuJ48Fi+G5I8/oAsJQenrr9u6HLt2KfYjVHbqiXZbPkWz69fg\nPX8+Khcswcyu0Uh186txrZtCitAgH4S28kFYKx+EtvJFaFATuCurZnd9b20vV1BQYHZdLllZte7F\nqw8NRcm//w1NZCT0YWEOeZgJERER1Y0BuJ60vXrB8N13KFq1ih98ukWrN1St1c0sRGpmIdJuLWWo\nOlVNBJeOL2K0Txr+nZEEH70KuuDWGNba71bQ9UFYsC+CmnrUbzsyE7nk5UH57bdV25adPo3chATo\nQ0LuuK7ilVesVgMRERHZFgNwPalHjoT60UedNvzmlVRWB93ba3Yv17JWF/hzVjcs2AehQf2Q2epN\neIrVONSudYPVK//hB7ht2gT54cMQGatqNLq6QnLhQq0BmIiIiBovBmBzOEH4vT2rm5pRiLRrhUjN\nqFqrWzWre6fW/p5VM7pBVTO6oa187mtWV7l9O6RpaSh/+WUYmze32NchPXcOisRECBIJ1IMHo3L0\naGgefRSCq6vFxiAiIiLHwABM1e5nVtddIUXo7aULraqCbmiQD9wUde/wcE8GAzxWroQkMxNun3+O\nyqgolL/6KgxBQSbfL87OrvV61dNPw9isGVTDh0Pw8al/jUREROTwGIBNJQiN5sNQ9Z3VvR10w1r5\noKU11uqKxSjcuBEeq1dDsXcv3L74Aq7btkH11FMoWbwYgpvbnfcIAqS//Qbl7t1QfvstBFdX5CYn\n3/FrZQgKQuW4cZatl4iIiBwSA7ApBAFNpk6Ftnt3VEyZ4lBH3OaVVFYH3XO3gu69ZnX/GnRDzJ3V\nvU/6zp1R9PHHkFy6BPc1a6CMj4c0NfXOpQoGAzw++gjK+HhI0tP/vL91a7jk5cHoV3N3CSIiIqLb\nGIBN4Prll1B+9x3kyclQjR4No7+/rUu6g1ZvwKWs4j/31L21lCG/9M5ZXZHo9qyu762Z3aqlDEHN\nPCCyk1lu/QMPoHj1apTNnQuXoqI7Z9/FYsgTEiBJT4fBzw+qJ56AavRo6Lp2bTQz9URERGQdDMD3\nIM7MhOe77wIAShYvtovwm1tcWR10q7YbK8Sl7CLoDcId13oob63VDfK9tQtDw8/qmsMQHFznARRl\nb74JQSyGtk8fh5qVJyIiIttiAL4bgwHes2bBpaICqhEjoBo1qkGHvz2r+9cZ3TRTZnWDfRB2axeG\nlk3d7WZW19I0AwbYugQiIiJyQAzAd+EWFwf5iRMw+PmhZMkSq/7TenG5Gqcu3MCJs380+lldIiIi\nIltiAL4L9ZAhUOzfj/Jp02C04tZZR1OzMXnlTyip0NR4XSQC2jT3rA66zjCrS0RERGRtDMB3YQgO\nRsHOnVad+d1z4ipmrDsIrd6I8Hb+CG/rW70TQ8eWTTirS0RERGRhDMD3YsXw+/lPqfjXpiMQBOCV\nJ7pj+cuPoqio0GrjEREREREDsE0IgoDlO09jxe7TAICYZx/CghcHc1kDERERUQNgAP4rnQ6QSKw6\n62swGvHWZ0ew9cB5uIhE+GBSX4wdGMLwS0RERNRAXGxdgD3xXLgQPhMmwCU31yrPV2v1mLoqAVsP\nnIdCKkbc7EcxdmCIVcYiIiIiotpxBvgWWVIS3D/7DIJEApfcXIsfpVtSocHEj37A8fM58HKVYdPr\nQ9CzY3OLjkFERERE98YADEBUUoImc+YAAMrmzIG+c2eLPj+nqALjPtiPtGuFaN7EFVtjhiEkyHrb\nqhERERFR3RiAAXi9/TbEN25A260byl991aLPvnKjGGNj9+F6fjnatfDCtphhaNnMw6JjEBEREZHp\nnD4Ayw8cgOvOnTAqFChatarqQ3AW8tuVPEQv24/CMjW6tfPD5nlD4OOhsNjziYiIiOj+OX0A1vTt\ni7KZM2Fo3hyGdu0s9txDKdcwZeVPqNToMahrEDbMHAxXHmpBREREZHNOH4Ahk6EsJsaij9x15DJm\nbzgEvUHAmL7tsXxKf0gl3HCDiIiIyB6YncquX7+OAQMGwM3NDT169MC5c+csUZfD+njf75ix7iD0\nBgGvPN4FK6cOYPglIiIisiNmJ7OXXnoJXbp0QWFhIaKiohAVFWWJuhyOIAhY/L8TWLjlOADg7bG9\n8O+xveDiwgMuiIiIiOyJWQG4tLQUP/74I958803I5XLMmjULGRkZOHv2rKXqszyjEaLSUos+Uqc3\nYvaGRKzbkwKJWITVrwzAy493segYRERERGQZZgXgy5cvQ6FQwM3NDf369cMff/yBdu3a4fz585aq\nz+LcNm6E38CBkCUnW+R5lWodJq74ATsOX4JSLsGmuUMwpu8DFnk2EREREVmeWR+Cq6iogLu7O8rK\nypCWloaioiJ4eHigoqLijmt9fX3NGcoiRKmpkH7wAUQaDbwkEhjNrKmgVIVxi3bgxPls+Hoqsfu9\nZ9AzJKBez5JKq3aIsIc+2TP2yXTslWnYJ9OxV6Zhn0zDPpmOvTLN7T6ZwqwA7ObmhvLycrRs2RL5\n+fkAgLKyMri7u99x7aJFi6p/HBkZif79+5sz9P3TaiGZOBEijQaGF16A8fHHzXpcZm4JRv7rK1y4\nVoAgP098tzgKHYL4G5OIiIiooSQmJiIpKQkAIBaLERkZadJ9IkEQhPoOWlpaCh8fH2RkZCAwMBBa\nrRa+vr44duwYOv/lOOGEhASEhobWdxiL8Fi2DB4rV0IfFIS8H3+E4FH/09guXC/E2Nj9yCmqQEjL\nJtgSMwwtfNzMqu/2d3UFBQVmPaexY59Mx16Zhn0yHXtlGvbJNOyT6dgr0/j6+iI5ORmDBw++57Vm\nrQH29PTEkCFDEBsbC7VajRUrViA4OLhG+LUH4qwsuK9dC0EkQvGKFWaF31MXcjB64bfIKapAr47N\nsfOdkWaHXyIiIiJqOGYfhLFhwwaMGzcOPj4+CA0Nxfbt2y1Rl0UZAgNRuHkzpL//Dm3v3vV+zg+n\nM/DK6gSodQYM6RGM/04fBKWMZ4kQERERORKz01vLli1x6NAhC5RiXZr+/aExY93xl4cu4I24wzAY\nBTw/MAT/eTECEjEPuCAiIiJyNJy+vAdBELD2mzOI/eoUAGDW6G54fUwPiEQ84IKIiIjIETEA34XR\nKGDBlmOI+/4cRCLg/fF98MJjnWxdFhERERGZodEGYHF6OgytW9f7fo3OgNkbEvH1sSuQSVywetpA\njOzV1nIFEhEREZFNNMpFrIq9e+EXGQn3VavqdX+5SosJH36Pr49dgbtCii/eGMrwS0RERNRINLoZ\nYJe8PHjFxEBkMMDo6Xnf9+eXqBC9bD9S/shHMy8ltrwxFJ1bN7VCpURERERkC40rAAsCvOfNg7iw\nEJp+/VA5YcJ93Z6RW4qxsfuQfrMUrf09sTVmGFr733+IJiIiIiL71agCsPKrr6D48UcYPT1RtHw5\n4GL6Co+z6QUYt3Qf8kpU6NzaF1veGIpmXq5WrJaIiIiIbKHxBGCdDh4rVwIASt5/H8bAQJNvPXIu\nGxM/+gHlah36dgrAJ7MehYerzFqVEhEREZENNZ4ALJUiPz4erjt3QvXUUybftufEVcxYdxBavREj\ne7XFqlcGQC4VW7FQIiIiIrKlxhOAARj9/VE+bZrJ13/+Uyr+tekIBAF48bEwvBfdBy4uPOCCiIiI\nqDFrVAHYVIIgYPnO01ix+zQAIObZhzDjiXCe7kZERETkBJwuABuMRrz12RFsPXAeLiIRPpjUF2MH\nhti6LCIiIiJqIA59EIbs1CnAYDD5erVWj6mrErD1wHkopGLEzX6U4ZeIiIjIyThsAJb++it8x4yB\nb1QUoNPd8/qSCg2e/2Af9v2cDi9XGf731nA81iO4ASolIiIiInvikEsgRCoVvF97DSKDAbouXQCp\n9K7X5xRVYNwH+5F2rRDNm7hia8wwhAT5NFC1RERERGRPHDIAeyxZAumVK9B16IDSN96467VXbhRj\nbOw+XM8vR7sWXtgWMwwtm3k0UKVEREREZG8cLgDLDh+Ge1wcBIkExatWAQpFndf+eiUX45d9j8Iy\nNbq188PmeUPg41H39URERETU+DlcAHb98ksAQNmsWVXLH+pwKOUapqz8CZUaPQZ1DcKGmYPhqrj7\nUgkiIiIiavwcLgAXr14NTWQkVGPG1HnNriOXMXvDIegNAsb0bY/lU/pDKnHYz/sRERERkQU5XACG\nWAxVVFSdb3+873cs3HIcAPDK410w/7mePN2NiIiIiKo5XgCugyAI+M+XJ7FuTwoA4O2xvfDy43Uv\nkSAiIiIi59QoArBOb8S8T5Kw4/AlSMQifPRSf4zp+4CtyyIiIiIiO2T3C2NlSUlwyc2t8/1KtQ4T\nV/yAHYcvQSmXYNPcIQy/RERERFQnu54BFl+/Dp8pUyBIpcj//nsYAgNrvF9YpsaED7/H6cu5aOIu\nx+Z5Q9G9vZ+NqiUiIiIiR2C/AdhohPesWXApL4dq+HAYAgJqvJ2VX46xH+zD5exiBPq6Y9ubw9A+\nwNtGxRIRERGRo7DbAOwWFwf5sWMwNG2KkthYQPTnTg4XrhdibOx+5BRVIKRlE2yJGYYWPm42rJaI\niIiIHIVdBmDJxYvwXLIEAFC8bBmMvr7V7526kIMJH36PkkotenVsjk/nPgZvN7mtSiUiIiIiB2OX\nAVh28iSg06Hiueegeeyx6td/OJ2BV1YnQK0zYEiPYPx3+iAoZXb5JRARERGRnbLL9Fg5bhx0YWHQ\nP/Dnbg5fHrqAN+IOw2AU8PzAEPznxQhIxHa/iQURERER2Rm7DMAAoOveHUDVARdrvzmD2K9OAQBm\nje6G18f0gEjE092IiIiI6P7ZbQAGAKNRwIItxxD3/TmIRMD74/vghcc62bosIiIiInJgdhuANToD\nZm9IxNfHrkAmccHqaQMxsldbW5dFRERERA7OrEW0S5cuRYcOHeDp6YkHH3wQ33zzTb2eIzt+HPKk\npOqfl6u0mPDh9/j62BW4K6T44o2hDL9EREREZBFmzQBLpVLs3r0bnTp1wtGjRzFs2DD89ttvaNOm\njcnPEJWWwnvmTEiyslCweTOyHuqD6GX7kfJHPpp5KbHljaHo3LqpOWUSEREREVUzKwDPnj27+sd9\n+vRB27Ztcfr06fsKwF7vvgtJVha04eG4FBKOfy78Buk3S9Ha3xNbY4ahtb+nOSUSEREREdVgsTXA\nRUVFuHjxIjp37mzyPYr9++H61VcQFAqcfGMhnlq8D3klKnRu7YstbwxFMy9XS5VHRERERATAggF4\n6tSpeOGFF9CxY8da3/f9y2luAIDcXMjefBMAcH7aXAzfcg5llVoMDA/G9refgqeTne4mlUoB1NIn\nqoF9Mh17ZRr2yXTslWnYJ9OwT6Zjr0xzu0+muGcAXrBgAd577707Xh81ahR27doFAJg/fz6Kioqw\nbdu2Op+zaNGi6h9HRkZigLs7IJMhJ7wnuqXIoNFr8XRkCOJeHwE5T3cjIiIiontITExE0q2NFMRi\nMSIjI026TyQIgmDOwCtWrMC2bdtw6NAhuLm51XpNQkICQkND73h9+9cnsGzLEdyQeeDFx8LwXnQf\nuLg45wEXt7+rKygosHEl9o19Mh17ZRr2yXTslWnYJ9OwT6Zjr0zj6+uL5ORkDB48+J7XmjXV+vnn\nn2PDhg04fPhwneG3NoIgYPnO01ixOwWQeSDm2Ycw44lwnu5GRERERFZn1j7ACxcuREZGBtq2bQsP\nDw94eHggNjb2rvcYjEbEfJqMFbtPw0UkwrLJ/TDzyW4Mv0RERETUIMyaAb569ep9Xa/W6jH9vwex\n7+d0KKRirJ8xGI/1CDanBCIiIiKi+9JgnzZTnTmHpH+vxE/u3eHl7opNrw9Bz47NG2p4IiIiIiIA\nDRiAK6Mn48WCTBSGaNFt6QqEBPk01NBERERERNUaLAA/WJCJ625N0P+TWAQw/BIRERGRjZj1Ibj7\npVu3FgFtWjTkkERERERENTRYAC6eOAnyfwxoqOGIiIiIiGrVYAG4cv5bDTUUEREREVGdGm4JhFLZ\nYEMREREREdWlQdcAExERERHZGgMwERERETkVBmAiIiIicioMwERERETkVBiAiYiIiMipMAATERER\nkVNhACYiIiIip8IATEREREROhQGYiIiIiJwKAzARERERORUGYCIiIiJyKgzARERERORUGICJiIiI\nyKkwABMRERGRU2EAJiIiIiKnwgBMRERERE6FAZiIiIiInAoDMBERERE5FQZgIiIiInIqDMBERERE\n5FQYgImIiIjIqTAAExEREZFTYQAmIiIiIqfCAExEREREToUBmIiIiIicitkBuKioCM2aNUN0dLQl\n6iEiIiIisiqzA/D8+fPRtm1biEQiS9Tj1NLS0mxdgkNgn0zHXpmGfTIde2Ua9sk07JPp2CvLMisA\n//LLL0hPT8fw4cMhCIKlanJa/M1tGvbJdOyVadgn07FXpmGfTMM+mY69sqx6B2BBEPDaa69h+fLl\nDL9ERERE5DAk9b0xLi4OXbp0QVhYmEnLH3x9fes7lFOQSqUYNGgQvL29bV2KXWOfTMdemYZ9Mh17\nZRr2yTTsk+nYK9NIpVKTr71rAF6wYAHee++9O14fMGAAMjMzcezYMQAwaQY4OTnZ5KKIiIiIiKxF\nJNRj/cKZM2fQrVu3O14PDw/H6dOnLVIYEREREZE11CsA/93ChQtx5coVbN682RI1ERERERFZDQ/C\nICIiIiKnYpEZYCIiIiIiR8EZYCIiIiJyKgzARERERORU6r0PsCkKCgqwZs0aXLlyBQEBAZg+fTqC\ngoKsOaTDOXXqFOLj45Geno6IiAhMmzbN1iXZLYPBgPXr1+P333+HRqNBmzZtMGnSJLRs2dLWw0MT\neQAABvdJREFUpdmd1atX4+zZs9BoNPDz80NUVBQeeughW5dlt9LS0rBgwQJMnToVgwYNsnU5dmnB\nggW4dOkSxGIxAKBnz56YPn26jauyP1qtFps2bcLx48chCAIiIiIwefJkW5dld/Lz8zFnzpwar2k0\nGsydOxc9e/a0UVX2KTMzExs3bkRmZiaaNGmCsWPHske1OH/+PD799FPk5OQgICAAL7/8Mlq3bl3n\n9VZdA7xkyRL4+/sjOjoae/fuRVJSEpYvX26t4RxSamoqysvLkZKSAq1WywB8FzqdDl9//TUGDRoE\nHx8ffPfdd/jhhx+watUqW5dmdzIyMhAQEACpVIqUlBTExsbis88+g1wut3VpdsdgMGDBggWoqKjA\niBEjGIDrsHDhQvTr14/9uYePP/4YN2/exIwZM+Dl5YXr169z4scEOTk5iImJwcaNGyGTyWxdjl2Z\nN28eevfujaeeegopKSlYtmwZ1q9fD3d3d1uXZjd0Oh1effVVREdHo2/fvti9ezcSExPvmg+stgSi\nsrISKSkpGDVqFKRSKR5//HHk5eUhMzPTWkM6pLCwMPTs2ZO/kU0glUrx9NNPw8fHB0DVgSw5OTko\nKyuzcWX2Jzg4GFKpFIIgQK/XQ6FQmHRiozPat28funfvDi8vL1uXQg5Oq9UiKSkJEydOhLe3N0Qi\nEcOviQ4cOICePXsy/NYiOzsbjzzyCACgS5cukMlkyM3NtXFV9iU7OxsajQb9+vWDSCTCiBEjkJOT\nc9fMabUAnJOTA6lUCoVCgXfeeQe5ubnw9/dHdna2tYYkJ3Px4kX4+PjAw8PD1qXYpU8++QTjxo3D\nmjVrEBMTw79YalFcXIzExESMGDHC1qU4hG3btmHSpEl4//33kZWVZety7E52djZEIhFOnjyJKVOm\nYM6cOTh58qSty7J7RqMRhw8fRv/+/W1dil3q2rUrjh8/DqPRiDNnzkCpVPIbq7+pazFDTk5OnfdY\nLQBrNBooFAqoVCpkZWWhvLwcSqUSarXaWkOSE6msrMSmTZswfvx4W5dityZPnozNmzcjKioKa9as\ngVartXVJdmfz5s0YPXr0fZ0f76yio6Oxfv16rFu3Dm3btsXSpUthMBhsXZZdUalU0Ov1yM3Nxfr1\n6zFp0iSsXbsWxcXFti7NrqWkpAAAOnfubONK7NP48eNx4MABPP/881i+fDleeukl/j/rbwIDA6FQ\nKJCUlAS9Xo9vvvkGLi4ud/17z2oBWC6XQ61Ww9fXF3FxcejQoQNUKhUUCoW1hiQnodPpsGzZMkRE\nRKB37962LseuicViDB06FFKpFGfPnrV1OXbl/PnzyMvLQ58+fWxdikNo27YtpFIp5HI5/vnPf6K4\nuJizwH8jl8thNBoxcuRISCQSdOrUCS1atMDFixdtXZpdO3jwIPr162frMuySVqvFokWLMH78eGzb\ntg3z58/HqlWrkJ+fb+vS7IpUKsXs2bOxd+9eTJ06FaWlpfD394dSqazzHqvtAtG8eXNotVoUFhbC\nx8cHer0eN2/eREBAgLWGJCdgNBqxatUqtGjRAs8++6yty3EYPO/mTlevXsXFixcRFRVV/Vpqaiqu\nXbuGCRMm2LAyclR+fn62LsHhlJeX4+eff8bSpUttXYpdyszMhEqlqt71ISQkBH5+frh48SKaNm1q\n4+rsS0hICGJjYwEAZWVlSEhIQHBwcJ3XW20G2NXVFV27dkV8fDy0Wi327NmDZs2aoVWrVtYa0iEZ\njUZotVoYjUYYjUbodDoYjUZbl2W3Pv74Y4hEIm4rdBfFxcU4cOAAKisrYTAY8OOPP6KkpAQdOnSw\ndWl2Zfjw4di+fXv1f2FhYZg6dSrDby0qKyvx66+/QqfTQafTYceOHfD29uYWhH/j7u6OsLAw7Nmz\nBwaDAWlpabhx4wb/7N1FcnIyWrVqhcDAQFuXYpf8/Pyg1Wpx6tQpCIKAK1euICsri/2qRXZ2NnQ6\nHcrLyxEXF4fOnTvf9ZsEq26Ddnsf4MuXLyMwMJD7ANfi0KFDWL9+fY3XnnnmGTz99NM2qsh+5eXl\nYfr06ZDJZDV2NJg/fz5CQkJsWJl9KS0txcqVK5GRkQG9Xo+WLVsiOjqaPboHbvNVt9LSUixevBg3\nbtyAWCxG+/bt8eKLL/Jf9GqRm5uLdevW4cqVK/D19cXzzz+Phx9+2NZl2a233noL/fv3x9ChQ21d\nit36+eef8b///Q/5+fnw9PTEqFGjMHjwYFuXZXfi4+Px9ddfw2g0Ijw8HFOmTLnrDltWDcBERERE\nRPaGRyETERERkVNhACYiIiIip8IATEREREROhQGYiIiIiJwKAzARERERORUGYCIiIiJyKgzARERE\nRORUGICJiIiIyKkwABMRERGRU/l/J5qzddoqtZkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79c8bfd0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "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, noise=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."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%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(0,50)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, variance=sensor_variance)\n",
      "\n",
      "zs, ps, vs = [], [], []\n",
      "for i in range(50):\n",
      "    pos = predict(pos[0], pos[1], movement, movement_variance)    \n",
      "    Z = dog.sense_position()\n",
      "    zs.append(Z)\n",
      "    vs.append(pos[1])\n",
      "    \n",
      "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
      "    ps.append(pos[0])\n",
      "    \n",
      "#plt.subplot(121)    \n",
      "plt.plot(zs,c='r', linestyle='dashed', label='measurement')\n",
      "plt.plot(ps, label='filter')\n",
      "plt.legend(loc=2)\n",
      "plt.show()\n",
      "\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()\n",
      "\n",
      "for i in range(0,len(vs), 5):\n",
      "   print('{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(*[v for v in vs[i:i+5]]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TRlAYFhEREWkCy+7dRN10E6baWor/3/V8km5mb84/AegeMZoergvat0BpFIVh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\nbR0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce74a4a710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KNm7cKM8l6Uof7LFqCjAM/1WGcNQEIqEuEAl1gUiC7RaTJ0/u1vssP5a6saXN6ikAAAAA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\nSAYAAADC/H/iqkPzRLrR2AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79d0d320>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "102.0000 6.3099 4.6267 4.2812 4.1939\n",
        "4.1708 4.1646 4.1629 4.1624 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n",
        "4.1623 4.1623 4.1623 4.1623 4.1623\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "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": "heading",
     "level": 3,
     "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",
      "<img src='dog_track.gif'>\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": "heading",
     "level": 2,
     "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 impossiblely 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 correspondance with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them.\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, R, Q):\n",
      "            self.x = x0\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 signficant 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",
     "collapsed": false,
     "input": [
      "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",
      "    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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Relationship to the g-h Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* 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",
      "$$ \n",
      "\\begin{aligned}\n",
      "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n",
      " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n",
      " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
      " &= \\frac{\\sigma^2_{x'}}{b}\n",
      " \\end{aligned}\n",
      "$$\n",
      "\n",
      "We can tie all of this together with\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
      "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
      "&= x + g_n(y-x)\\\\\n",
      "\\blacksquare\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "where\n",
      "\n",
      "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
      "\n",
      "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n",
      "\n",
      "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n",
      "\n",
      "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#####Exercise:\n",
      "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": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction to Designing a Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-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",
     "collapsed": false,
     "input": [
      "def volt(voltage, temp_variance):\n",
      "    return random.randn()*temp_variance + voltage"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "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 good Kalman filter. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of 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",
     "collapsed": false,
     "input": [
      "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",
      "plt.scatter(range(N), zs, marker='+', s=64, color='r', label='measurements')\n",
      "p1, = plt.plot(estimates, label='filter')\n",
      "plt.legend(loc='best')\n",
      "plt.xlim((0,N));plt.ylim((0,30))\n",
      "plt.show()\n",
      "plt.plot(ps)\n",
      "plt.title('Variance')\n",
      "plt.show()\n",
      "print('Variance converges to {:.3f}'.format(ps[-1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cmKFdvRjd0xsvN3uN12JlbkKnpi50auoCQFGRiv8FX2T+uiMcOn+Tvu9tZkzv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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce7dd40780>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZwdILAAAAdJKuFZR7B0viNtYAAADoeF0qKHMxHwAAADpLlwrKXMwHAACAztK1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\n1mubduvvG3dpw7aD+tcnTY9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       "text": [
        "<matplotlib.figure.Figure at 0x7fce74adaa90>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Variance converges to 0.858\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `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": "heading",
     "level": 3,
     "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 inital 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": [
      "<img src='volt_animate.gif'>"
     ]
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "#Your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Solution\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variance = 2.13**2\n",
      "actual_voltage = 16.3\n",
      "\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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZAAAAMCAoAwAAAAYEZQAAAMCAoAwAAAAYEJQBAAAAA4IyAAAAYEBQBgAAAAwIygAAAIBB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\nZptuL2gAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce74aac3c8>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Discussion\n",
      "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Explaining the Results - Multi-Sensor Fusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**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",
     "collapsed": false,
     "input": [
      "sensor_variance = 30\n",
      "movement_sensor = 30\n",
      "pos = (0,500)\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, variance=sensor_variance)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "vs = []\n",
      "\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",
      "plt.plot(ps, label='filter')\n",
      "plt.plot(zs, linestyle='dashed', c='r', label='measurement')\n",
      "plt.legend()\n",
      "plt.show()\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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w4cP89ttv/Pvf/2bWrFlFigeyvzYbNmzg5MmT2Gy2PF+XK+mSiXO3bt3o379/np8yFixY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\nTPkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce74aa2358>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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T5Ds2+AAAAIC1hXeDD8YYAwAAwKLCvCoFwRgAAADWFN7Jd26GUgAAAMCawjv5jh5jAAAA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\nAEASwRgAAACQRDAGAAAAJEn/P1yM9AhuPJa/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79d25080>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "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": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More examples"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Extreme Amounts of Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your 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",
     "collapsed": false,
     "input": [
      "sensor_variance = 30000\n",
      "movement_variance = 2\n",
      "pos = (0,500)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, 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",
      "\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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RAPkBZlJzp08nc/VqTnzwQXBlFbUA2+n0pqAESo8wZmQQ/tFH7nE2b175gswa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QAsFg7oCbEk0eDUvyBEoyxa+h0lgQjnnt4Ys470ORcsiJFoNXTF6ZT/iyON+iqt/vg4VqxAMpsx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\nERFRAP0/xSigF/9eFOoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce74a748d0>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Bad Initial Estimate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30\n",
      "movement_variance = 2\n",
      "pos = (1000,500)\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, 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",
      "plt.plot(ps, label='filter')\n",
      "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hhBAVZP/LL4Wf25QWnM1m8jp1QpOYiNVgKNxssVr58Mf9zP75CAD9QhvzyTPd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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce749750b8>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Large Noise and Bad Initial Estimate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What about the worst of both worlds, large noise and a bad initial estimate?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30000\n",
      "movement_variance = 2\n",
      "pos = (1000,500)\n",
      "\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, 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",
      "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
      "plt.plot(ps, c='#004080', label='filter')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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P9wlpx3nnAZCxdCm5Tz+NvWPHSs25OjhrfbCNRiNms5mMjAxJhvIPwqAeXAiW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\nYEE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TJ8vuCiQCffui4oMPNLcvIdSzp5JgJ7pfaBHs85XMSeusZtbF368fwm3byoMb3cGD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\naGgwiKKk8l//gva336A7dQq+li3Fzy2QlMQ9KVDbP+Q3P6zNJmtU4uneHf7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C+vbbSBs4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SPSZMuQbQFhz6uAYe9eWN94A/oonu6knBxkZmUhYcaMiOtFgiqIRIPSBNJrCIIgiJrT6FVF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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce74943a90>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
      "\n",
      "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_variance = 30000\n",
      "movement_variance = 2\n",
      "pos = None\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, 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",
      "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
      "plt.plot(ps, c='#004080', label='filter')\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hV/xNN1G7TRsKunbl2F9/kTl2bKWGENBxsRIpK95Fl5q8PN9juffcU+L+8bfd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j7Tgt+Pc9EiIqomVPB69UTBgCFO2T9uHMHBg3UttZSXR7nBZi4RstuNFInoY03UqGp2a5LbbfaH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F1D7Q4gNIIELuYcMiJkZKcejQeMiWY40VLUSSZvnvf2H45Rd4Bg0CLURGXxbERMIRI2CV6Y9F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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce748d07b8>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n",
      "\n",
      "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers,  laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise: Interactive Plots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `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",
     "collapsed": false,
     "input": [
      "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",
      "                       noise_scale):\n",
      "    # your code goes here\n",
      "    pass\n",
      "\n",
      "interact(plot_kalman_filter,\n",
      "         start_pos=(-10,10), \n",
      "         sensor_noise=widgets.IntSliderWidget(value=5, min=0, max=100), \n",
      "         movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
      "         movement_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.),\n",
      "         noise_scale=widgets.FloatSliderWidget(value=1, min=0, max=2.))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<function __main__.plot_kalman_filter>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Solution\n",
      "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",
     "collapsed": false,
     "input": [
      "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, 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))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/m7fLk1ZEYVhERERaBcMw2JtTyvLN2WRsOojLbWC1mLigT0fGDkkiLND32Img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\n7pkzadO/P1mPPGJ1FMukTZtG9kMPkXfDDVZHERERkWau6Vz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rGD58OFOmTNE8w2KZo52b\nI0aMYNeuXaxcuRLDMGjXrh2jRo3i9NNPtyilJKOSkhJuv/12XC4XNput7vH777+fk046qd7vnXEr\nwyIiIiIiTZ2WYxYRERGRpKUyLCIiIiJJS2VYRERERJKWyrCIiIiIJC2VYRERERFJWirDIiIiIpK0\nVIZFREREJGmpDIuIiIhI0lIZFhEREZGk9f8B69+n+CAc8V0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79c68c88>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<function __main__.plot_kalman_filter>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise - Nonlinear Systems"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our equations are linear: \n",
      "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n",
      "new\\_position &= old\\_position*measurement\\end{aligned}$$\n",
      "\n",
      "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
      "\n",
      "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n",
      "\n",
      "    Z = math.sin(i/3.) * 2\n",
      "    \n",
      "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",
     "collapsed": false,
     "input": [
      "#enter your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uj7Ye9rC1EmDf+dv4YX88Tl27h+9fGYj23s7sBUx0Ir+0GnO/OYartwvA5XAgFvHB53PB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\n3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s8Pa3IyiqoSPnUqwRkZBK1YgX7//ovepoWFUbl5M1Vr12K/6SY3JXt98HfEImfOnKGo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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fce79c28ba8>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Discussion\n",
      "\n",
      "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n",
      "\n",
      "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the 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": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise - Noisy Nonlinear Systems"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement the same system, but add noise to the measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#enter your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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lSgYGNqdza9OvFmtpyyk2HkwQq5VGpFarWbRO08Xg7Ynd+OHFAbg72RIRnczA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\nIj09HavVyurVq2lvb6e+vj5QS8o4ZLVaycjIwGazAbB06VJaW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       "text": [
        "<matplotlib.figure.Figure at 0x7fce749f6128>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Discussion\n",
      "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
      "\n",
      "Very shortly after 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": "heading",
     "level": 2,
     "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": {}
  }
 ]
}