04_One_Dimensional_Kalman_Filters.ipynb

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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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    "# One Dimensional Kalman Filters"
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   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "from __future__ import division, print_function\n",
    "from book_format import load_style, figsize\n",
    "load_style()"
   ]
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   "metadata": {},
   "source": [
    "## One Dimensional Kalman Filters"
   ]
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   "source": [
    "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the discrete Bayes filter - rather than starting with theory we will just develop the code step by step based on reasoning about the problem."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tracking A Dog"
   ]
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   "source": [
    "As in the Discrete Bayes chapter we will be tracking a moving object in a long hallway at work, such as a dog or robot. However, assume that in our latest hackathon someone created an RFID tracker that provides a reasonably accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
    "\n",
    "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23 m would be equally likely to be measured as 22.9 as 23.1.\n",
    "\n",
    "Before we try to implement the filter, let's start by implementing a simulation of the dog's movement and of the sensor. After all, the filter needs to filter data collected from the dog, so we need to understand this movement and sensor behavior to have any hope of filtering it."
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    "### Simulating the Sensor Measurement\n",
    "\n",
    "Simulating an RFID system is beyond the scope of this book, so we will use a simple model. We said that the sensor is equally likely to give a measurement that is too large as too small. Furthermore, it is more likely to be a small error than a large one. In the *Discrete Bayes* chapter we modelled this error with a probability. But now we know about Gaussians, so let's use them instead. We can model the error in a system with the Gaussian $\\mathcal{N}(\\mu, \\sigma^2)$, where $\\mu$ is the state (such as position or velocity) and $\\sigma^2$ is the variance in that state. So instead of saying our measurement is 22.9, we would say our measurement is 22.9 with a variance of 0.35. The variance accounts for the error in the sensor.\n",
    "\n",
    "This is a simple model, but it works very well in practice. Many sensors have Gaussian, or near Gaussian errors, and as you will see the Kalman filter is based on this assumption.\n",
    "\n",
    "In the literature you will often see this charaterized with an equation like:\n",
    "\n",
    "$$ z = h(x) + \\epsilon_z$$\n",
    "\n",
    "Here $h(x)$ is the **measurement model** - a function which describes how measurements are made from the current system state. In other words, it is the measurement we would get for the state $x$ *if* the sensor was perfect. $\\epsilon_z$ is the error that is in the measurement, and hence $z$ is the actual measurement that results. This is not meant to imply that we can somehow measure or know the exact value of $\\epsilon_z$, it is a mathematical definition that can be restated as\n",
    "\n",
    "$$ \\epsilon_z =  z - h(x)$$\n",
    "\n",
    "The utility of this equation will become apparent later in the book."
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    "### Simulating the Dog's movement\n",
    "\n",
    "Let's assume that the dog moves at a constant velocity. We can use Newton's equation to compute the new position based on the old position and velocity like so:\n",
    "\n",
    "$$ x = v \\Delta t + x_0$$.\n",
    "\n",
    "This is a model of the dog's behavior, and we call it the **system model**. However, clearly it is not perfect. The dog might speed up or slow down due to hills, winds, or whimsy. We could add those things to the model if we knew about them, but there will always be more things that we don't know. We can model this mathematically by saying the dog's actual position is the prediction that comes from our **system model** plus what we call the **process noise**. In the literature this is usually written something like this:\n",
    "\n",
    "$$ x = f(x) +\\epsilon$$\n",
    "\n",
    "Here $f(x)$ is our system model and $\\epsilon$ is some unknown error between the system model's prediction of position and the actual position. Clearly $\\epsilon$ will change over time, and as with the measurement equation in the last section we are not implying that $\\epsilon$ can be derived analytically."
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    "### Implemention in Python\n",
    "\n",
    "We will want our implementation to correctly model the noise both in the movement and the process model. You may recall from the **Gaussian** chapter that we can use `numpy.random.randn()` to generate a random number with a mean of zero and a standard deviation of one. Thus, if we want a random number with a standard deviation of 0.5 we'd multipy the value returned by `randn()` by 0.5. \n",
    "\n",
    "Our model assumes that the velocity of our dog is constant, but we acknowledged that things like hills and obstacles make that very unlikely to be true. We can simulate this by adding a randomly generated value to the velocity each time we compute the dog's position. We could write\n",
    "\n",
    "    vel = vel + randn()*velocity_std\n",
    "    x = x + vel*dt\n",
    "\n",
    "However, this could lead to velocities larger than physically realizable, so we need to ensure the velocity does not go out of bounds. \n",
    "\n",
    "To model the sensor we need to take the current position of the dog and then add some noise to it proportional to the Gaussian of the measurement noise. This is simply\n",
    "\n",
    "    z = x + randn()*measurement_std\n",
    "    \n",
    "I don't like the bookkeeping required to keep track of the various values for position, velocity, and standard deviations so I will implement the simulation as a class. "
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    "from __future__ import print_function, division\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import randn\n",
    "import math\n",
    "\n",
    "class DogSimulation(object):\n",
    "    \n",
    "    def __init__(self, x0=0, velocity=1,\n",
    "                 measurement_variance=0.0, process_variance=0.0):\n",
    "        \"\"\" x0 - initial position\n",
    "            velocity - (+=right, -=left)\n",
    "            measurement_variance - variance in measurement m^2\n",
    "            process_variance - variance in process (m/s)^2\n",
    "        \"\"\"\n",
    "        self.x = x0\n",
    "        self.velocity = velocity\n",
    "        self.measurement_noise = math.sqrt(measurement_variance)\n",
    "        self.process_noise = math.sqrt(process_variance)\n",
    "\n",
    "\n",
    "    def move(self, dt=1.0):\n",
    "        '''Compute new position of the dog assuming `dt` seconds have \n",
    "        passed since the last update.'''\n",
    "        # compute new position based on velocity. Add in some\n",
    "        # process noise\n",
    "        velocity = self.velocity + randn() * self.process_noise\n",
    "        self.x += velocity * dt\n",
    "        \n",
    "    def sense_position(self):\n",
    "        # simulate measuring the position with noise\n",
    "        measurement = self.x + randn() * self.measurement_noise\n",
    "        return measurement"
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    "The constructor `__init()__` initializes the DogSimulation class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `move()` function has the dog move based on its velocity and the process noise. The `sense_position()` function compute and returns a measurement of the dog's position based on the current position and the sensor noise.\n",
    "\n",
    "We need to convert the variances that are passed into `__init__()` into standard deviations because `randn()` is scaled by the standard deviation. Variance is the standard deviation square, so we take the square root of the variance in `__init__()`."
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   "source": [
    "Okay, so lets look at the output of the `DogSimulation` class. We will start by setting the variances to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal or in the system model, so the results should be a straight line."
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      "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
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vv/yypk2bJknq0qWLihcvrmHDhumHH35Q06ZNFRMTo08//VQRERFaunSp8fXv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\nhvoHy7kH7GbHETsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7138e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import book_plots as bp\n",
    "\n",
    "dog = DogSimulation(measurement_variance=0.0)\n",
    "xs = []\n",
    "for i in range(10):\n",
    "    dog.move()\n",
    "    x = dog.sense_position()\n",
    "    xs.append(x)\n",
    "    print(\"%.4f\" % x, end=' '),\n",
    "bp.plot_track(xs, label='dog position')\n",
    "bp.show_legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see.\n",
    "\n",
    "Now let's inject some noise in the signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yb98+wJjkY8LKldj9+CPILJl4REhwJoQQQgghHgnr1683yaiolPovqUdyMmvX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7212ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def test_sensor(measurement_var, process_var=0.0):\n",
    "    dog = DogSimulation(measurement_variance=measurement_var, \n",
    "                        process_variance=process_var)\n",
    "\n",
    "    xs = []\n",
    "    for i in range(50):\n",
    "        dog.move()\n",
    "        x = dog.sense_position()\n",
    "        xs.append(x)\n",
    "\n",
    "    bp.plot_track([0, 49], [1, 50])\n",
    "    bp.plot_measurements(xs, label='Sensor')\n",
    "    plt.xlabel('time')\n",
    "    plt.ylabel('pos')\n",
    "    plt.ylim([0, 50])\n",
    "    plt.title('variance = {}, process variance = {}'.format(\n",
    "              measurement_var, process_var))\n",
    "    bp.show_legend()\n",
    "    plt.show()\n",
    "\n",
    "test_sensor(measurement_var=4.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "> **Note**: NumPy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n",
    "\n",
    "So the output of the sensor should be a wavering dotted red line drawn over a straight black line. The black line shows the actual position of the dog, and the dotted red line is the noisy signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n",
    "\n",
    "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing CTRL+Enter. Each time it runs you should see a different sensor output.\n",
    "\n",
    "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Dx8cHCQkJiIyMpKxlhBBCSFmRmAiMHQsU8MVrvq5f50sPD+22Sd9evECdIUNQ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cYYYxrg5AygpCwoiNbcREcD48bRBaQiadK1evWoSElWE+j8JCYm4tdff1Xue3h4YOPGjUhISAAA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\n6pXcbrd27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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7138898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_sensor(measurement_var=100.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZGcmSJUuAlPelf//+vPTSS9hst+7n6qmnnmLUqFFERETYk7Mvv/yS+Ph4nn76aYe2/2Rf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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x793f9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_sensor(measurement_var=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n",
    "\n",
    "So let's first look at the plot with some process noise but no measurement noise to obscure the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MAiCJiYlZtmfuz+o5+jc8PDyyXBerVKlS2cbh6emZbWyurq7Y2tpm2e7l5UVMTAyJiYk4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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7c154a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.random.seed(1234)\n",
    "test_sensor(measurement_var=0, process_var=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will remain deviated until the random changes in velocity happen to result in the track going back to the original track. \n",
    "\n",
    "Finally, let's look at the combination of measurement noise and process noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JmYiIiIg81EzTpEGDBuzbtw8Ab29vRo0aRXx8vK1MlSpVsFgscOQIVKkCc+aA\njw/MmgVTpoCnp2PFrVvD/Pnw0ktQtizEx1uTtb1779ZTk/tMjs7WKCIiIiKSE/r27Uvr1q1p3rw5\nhmHQu3dvDh48SGhoKAAvvPCC8xMfecT6tXx5mDcPQkLSv0iePPD009YHwJ9/wsaNUKpUFj4TeZAo\nORMRERGRB97KlStJSkqiZcuWADz22GPMnz+f5s2bA9YZGDPE1xdWroQCBZy3lt1K/vzQvn3mzpGH\nipIzEREREXngxMTEcPjwYapVqwbAtWvXmDBhgi0569Wrl7Wb4p0IDs6qMEXsKDkTERERkQdCQkKC\nbWHoo0eP0qVLFw4fPoxhGDRv3pykG2ZL9PHxuXVlpgnffgtt22a+hUzkDmlCEBERERG578XFxVGs\nWDESEhIAqFSpEvXq1ePSpUsAeHh40LFjx4xVdukSdO4Mzz4Lr7ySXSGLOFByJiIiIiL3pR49enDm\nzBkA/P39KV++PDt27ADAMAymT5+Ov79/5ir95ReoXPnv2RgbNszqsEXSpeRMRERERO4Lq1ev5uDB\ng7Zt0zSZP3++bXv58uXUrl37zio3TeuU+DVqWKfLL18edu60tqCJ3CUacyYiIiIi96TExERiYmIo\nUKAAABs2bCAxMZHRo0cDMGTIENsYMwBX13/40Xb9+r8Xlf70U401k7tOLWciIiIick/66quv6N+/\nv227W7dulC1b1rYdHBxMUFBQ1lzMMOCLL2DBgvQXlRbJZkrOREREROSeEBkZaZvqHqBt27ZERUVh\nmiYApUuXpkePHtkXgK8vtGuXffWL3IaSMxERERHJEYmJibz11lukpqYCEBISwk8//cSpU6cACAwM\nZP369RiGkdUXhtOns7ZOkSyg5ExERERE7pqIiAiuXr0KgLu7O0uXLuWnn34CwM3NjX379lG4cOHs\nC+D4cahdG556Cq5dy77riNwBJWciIiIikm1M07Rb/PmDDz5gyZIltu3x48dTqFAh23ba5B/Z4ocf\noFIl2LHDupaZWs/kHqPkTERERESyzaBBg/j0009t22FhYSQmJtq2GzVqRPHixbM3iOvX4e23oWVL\niImBFi1g1y4oVSp7ryuSSUrORERERCTLbNiwgZEjR9q2mzRpwtq1a23bbdu2pXv37nc3qO+/h5Ej\nwcUFRoyAxYshd+67G4NIBig5ExEREZE7FhMTw+zZs23bBQsW5NNPPyUlJQWABg0asHTp0sxXnJoK\n4eHw8ss3VWAEAAAgAElEQVTw1wQhd6xtWxgwANasgbfeAos+Asu9SYtQi4iIiEimnDp1yjZph8Vi\nISwsjCeffJKAgABKlSrF/PnzbTMsWu4kETpxAnr3tiZTAK+95rxct27WJK5oUeujWDHr19Klwc3t\n73KGAZ98kvk4RO4yJWciIiIikmGpqalUq1aNDRs2UKpUKfz9/fnwww+5cuUKAQEBADzxxBN3Vrlp\nwvTpMHAgXL4MgYHWJO2GCUPsyi5cCH/N/Gjn7FnIzolFRLKJkjMRERERuaWwsDA6depEw4YNsVgs\ndO/enX379lHqrwk1+vfvnzUXmjMHnn/e+n27dvB//wf58zsva5rW2Rf/+MPa0vbHH9bH2bPpnyNy\nj1NyJiIiIiJ2Vq5cCUCzZs0AKFmyJHPnzqVhw4YADB8+PHsu3L49fP01dO0KnTpZuyOmx2KB+vWz\nJw6RHKLkTEREROQhFxsby/Hjx6lYsSJgneQjPDzclpz17dv3zsaOZZarK9zJ5CEiDwglZyIiIiIP\noeTkZNz+mjRj//79PP/880RGRgLQsmVLUlNTbWX9/Pyy9uKmCWfOOB9LJvIQ0zyiIiIiIg+Z6Oho\ngoODSU5OBqBGjRpUrFiRy5cvA+Dt7U2XLl2y5+J//mntvvj443D+fPZcQ+Q+peRMRERE5CHQq1cv\nzv+VDOXNm5fg4GB27NgBWKe7/+abb/D19c3eIObPh7Jl4bvvICEBfv01e68ncp9Rt0YRERGRB9Ca\nNWsIDg6mRIkSAFy9epXvvvuOF154wXY8V65cd36BPn2sX729/374+EDfvuDubl/28mV44QX49lvr\nduPG1inzixa98+uLPICUnImIiIg8AJKSkrh06RKBgYEArFixAnd3d4YNGwbAhx9+iLe3t638bROz\n69dhwwZo0MA6M+LNvv4akpIc94eFOe7z8YFFi6wJ3Jgx1kTtVjMxijyklJyJiIiIPACmTp3Ktm3b\n+OqrrwDo3r07P//8s+14SEjI7StJTYUtW2D2bJg3zzombMMGqFvXvpxpwv/+Z10A+uaHh4fzup98\n0pqY/dWSJyKOlJyJiIiIZBXTvGstQnv27GHYsGHMnTsXgHbt2vHtt99imiaGYRAaGkpoaGjGK5w8\nGT76CE6d+ntfSIi1S+LNDAOefTbjdRuGdZyZiNySJgQRERERyQrz5oGfH3Tvbm2BymLx8fEMHjwY\n0zQBa0vY6tWriYqKAiAoKIjNmzdj3GlymJJiTcyKFoU334Rdu+C33+Df/86qpyAit6GWMxEREZGs\nUKkSXLkCX30FAQHw6af/uBVtx44dhIaG4uHhgYeHB7NmzaJly5ZUqVIFDw8P9uzZQ/78+W9dycWL\ncOCANdE6cABy5YKPP3Ys16mT9TnUqKHxYCI5RC1nIiIiIpnx19pgDh59FMLDrcnPZ5/B6NGZrto0\nTa5fv27bfvPNN1m+fDkAhmHw2WefkTdvXtvxIkWKpN9SduwY5M8PefNC7drW2RXHjoUZM5yXz5sX\natZUYiaSg9RyJiIiIpIR0dHWcVkTJ8KSJVC5smOZ556zTiPfqRO89RYEBUG3bhm+xFtvvUWhQoXo\n378/AGFhYbaFoQGaN2/+d+GrV+G//4V9++DHHx0rCwqyxuztDWXKwL/+Zf1apsxdHRsnIhl3z7Sc\nDR8+HIvFwssvv2y3f8iQIRQqVAgvLy8aNGjA/v37cyhCEREReSj99pt17a4iReDdd+HsWfhrEg6n\nOnaETz6xzlro73/LqtevX8/48eNt2/Xr12fVqlW27U6dOvHcc885nvjnn9Yp7sePhzVrICbGsYyH\nh3UM2eXLsGOHder7//4Xnn5aiZnIPeqeSM4iIiKYOnUq5cuXt2uaHzlyJOPGjePzzz9n+/bt5M+f\nnyZNmnDlypUcjFZEREQeGt9+a21xmjIF4uOheXNYvRpGjLj1eQMGWMd3tWpltzsmJoaFCxfatgMD\nAxk7diypf00g0qxZMxYvXnzrug8ftnY/3L4diheHtWut64g5ExSkREzkPpLjyVlcXBxdu3ZlxowZ\n5M6d27bfNE0+/fRTBg0aRNu2bSlbtizh4eFcvnyZWbNm5WDEIiIi8tBo0gTy5LEurLx/PyxbBo0b\nZyzhKV4cwDabIkBKSgo9evSw/aM5NDSUL7/80nbcxcUFV9dbjDo5cMCamB09au1W+dNP1hY0N7c7\neXYico/J8eQsLCyMZ555hnr16tmmhgU4duwYUVFRNG3a1LbPw8ODunXrsnXr1pwIVURERB42gYFw\n+rS15exf/8r06SkpKZQrV44TJ078VV0g77zzDnFxcbYyDRs2xGLJ4EeyEiUgNNTagrd+PRQokOmY\nROTelaPJ2dSpUzl69CjDhg0DsOvSeO7cOQAeeeQRu3Py589vOyYiIiKS7Tw8MlU8LCyMLVu2ANaW\nsC5duvDLL79YD27dylsvvUShQoXuLBZ3d/j+e+sjva6MInLfyrHZGg8ePMh///tfNm/ejIuLC2Dt\nynhj61l6brW44o4dO7IsRnnw6f0imaX3jGSG3i/3D6/ISApPmsTvI0aQ4uubqXMjIiJwdXWlSpUq\nAFgsFiZMmIC7uzsAXbt2BeDI6NGUeOcdLlWvzpExY8BJ90W9Zx4upUqVyukQ5B6TYy1nP/30Excu\nXKBs2bK4ubnh5ubGxo0bmTRpErly5SIwMBCw76edtl1ATfgiIiKSRXx+/ZXS/frh9/PPPDJz5m3L\nX7lyhd9//922feHCBWbPnm3b7tChA3379nU4Lz44mBRvbwK2bKHY8OHW6exvwUhMxHL1aiaeiYjc\n73Ks5axt27ZUq1bNtm2aJj179iQkJIR33nmHUqVKUaBAAVatWkXlv9YRSUhIYPPmzYwZMybdetP+\nayVyK2n/mdT7RTJK7xnJDL1f7iPr1kH//tY1wzp2pODkyRR0MrlGSkqKrafPunXrGDVqFDt37gSs\nrR+PPvro7V/vKlWgcGFo2JB8339PvgoVYOhQwMl75uJFaNvWuqD10qXWr/LAuXHsoQjkYHLm7++P\n/01rf3h5eZE7d24ee+wxAAYMGMDHH39MmTJlKFWqFMOGDcPX15cuXbrkRMgiIiLyIFm5Etq0gYQE\n6+LR//sf/JWA3ejPP/+kRo0aHD58GBcXF+rWrUuxYsW4du0aXl5e+Pv70y2jC03XqAFz5liv++GH\nUKgQvPCCfZkTJ6wTfhw4AAULWtcqK1EiC56wiNzrcny2xhsZhmE3nuzNN9/k1VdfpV+/flStWpWo\nqChWrVqFt7d3DkYpIiIiD4RFi6yJ2fPPw4wZtsTMNE369OlDbGwsYJ2MLG/evOzatQuwTvLx3Xff\n4eXldWfXbdkSJk8GPz8oWdL+2O7d1gTuwAEoWxYiIpSYiTxEDDMjM3Dc425sEr65NU7EGXU5kszS\ne0YyQ++X+0RKCsyaBV27sm79ekqWLEmRIkUAaNOmDW3atKFHjx6AdWiFRyZnbbytqCj4a1bqHTt2\n4Hn4MGXDwuDKFevaZd99BwEBWXtNuafoM6zcLMe6NYqIiIjklOvXr3P58mVy/9UdceHCheTPn593\n330XgI8//hjfG2ZtzPLEDGyJWZr44GCoWxdy54bp063T5ovIQ0XJmYiIiDx0Pv/8cyIjI5k6dSoA\nPXr0YPfu3bbjaePf7ypXV1iwwDr5R0YXpRaRB4rufBEREXngHR8+nJc7d7Ztt23blgMHDtjWV61U\nqRK9e/fOqfD+5uGhxEzkIaa7X0RERB44V69eZfjw4daNTz6h+Dvv0GfuXKLPngWgWLFibN682W4i\nMhGRnKbkTERERB4Iv/zyC8nJyQB4enoyadIkzg0YAAMHAlBo8GDyFCiQkyGKiNySkjMRERG5b6Wm\nptq+79evHz/++CMAlqtX2RwSQoHx48EwYNo0At9/Xy1lInJPU3ImIiIi96XXXnvNNqEHwPPPP8/5\n8+etG/PmUWztWusYrpkz4V4YTyYichtKzkREROS+sG7dOiZPnmzbrl27NkuXLrVt9+jRg+eee866\n0bOntTvjzp3QpcvdDlVE5I4oORMREZF7UkxMDMuWLbNt+/r6MmbMGNsMiy1atGDBggXOTzYMGDsW\ncmJKfBGRO6TkTERERO4ZFy9etH2fkJDAs88+S0JCAgCVK1dmwoQJtuTMzc0NNzc3OHcuR2IVEclq\nSs5EREQkc377DQYPhqlTISoqy6pNTk4mJCSEs39Ndx8UFMSAAQNsCZthGDRv3hxL2jpg167Biy9C\nmTJw7FiWxSEiklOUnImIiEjGrVgB1arB0KEQFgbHjzsvd8Msirfy/PPPs3PnTsDaEtauXTt27Nhh\nOz548GAKFizoeOKvv0KVKjB5MsTHw/btmX0mIiL3HNecDkBERETuA6YJn38OAwZYE6/mzSEgAMqX\nd16+bFnw9YXKla1JVOXKULYsq9evx9vbm1q1agHwyCOPMHv2bCpXrgzAlClTbj3dvWnCZ5/Bm29C\nUpK11ezbb6Fixax+xiIid52SMxEREbm97dvhlVes37/3HgwZApZ0OuDExsLBg9ZE6sYWLU9P/hgx\ngtVbt9qSswEDBmAxDLh0Cfz8br8O2eHD8MYbkJwML7wA48aBl9c/f34iIvcAJWciIiJye2ldGUuU\ngGefvWXRVD8/LDExsGsXB2bO5NTixTTJnRssFlp36YKLn5+tbGBgIFy4AP7+1kexYtZH0aIQEvJ3\nQpgmJMTacpY/P7Rrlx3PVEQkxyg5ExERkYx5773bFjlz5gyNGzdm3759WBo04NEnnuD1c+eos2AB\nHoZBoLs7PXr0sD8pKgo8PSEuDvbssT7AeXIG0LfvP38uIiL3ICVnIiIicsdM06Rv376MHTsWHx8f\nChYsiMViYc+ePVSsWJFcuXLZLRTtVNmycPWqtQXtjz/gxAnrw9397jwJEZF7hJIzERERsffll9bF\nm6tVc3p448aNlCpViqCgIAzD4MSJE/zwww906tQJgG3btuHt7Z25axoG5Mtnffw1OYiIyMNGU+mL\niIiIVWoqvPUW9OwJrVtbJ/YAUlJSuHTpkq3YzJkzmTlzpm17xIgR1KxZ07ad6cRMREQAtZyJiIgI\nwJUr0LUrLF4Mrq7W2RgDAgAYO3YsJ0+eZMKECQD06tWLffv22U6tqGnsRUSyhFrOREREHnanTkGd\nOtbELCCAg+PH859ff7UdbtOmDbt27bJt16hRgz59+uREpCIiDzQlZyIiIg+5+K1bMX/9FUqWhIgI\nCjz7LN988w1xcXEAhISEsHnz5hyOUkTkwafkTERE5CEUGRlJSkoKALmefpq+fn78/s03ULo0/v7+\nbNu2DV9fX1v52y4OLSIi/5iSMxERkYeEaZq275977jk2bNgAgIuLC42++AJLvny242XKlMFi0ccE\nEZG7SROCiIiIPATeDwvjmVOnKJcnD8ycyfPPP8/p06dtxzt06JCD0YmICCg5ExEReSCtXbuWP/74\ngx4NGsDo0bz/5Ze4JidbDw4dSt++fXM2QBERcaD+CiIiIg+AmJgY1qxZY9t2d3fH9bXXrJN8TJyI\na3IyKa1bw88/Q4kSORipiIikR8mZiIjIferGhaEvXbpEx44dSf6rdaxmzZpUq1/fOs6sa1fYtw+X\nRYugatWcCldERG5DyZmIiMh9KCkpieDgYC5cuABAsWLF6NOnD9HR0QBYLBZCpkzBOHQIvv4aypbN\nyXBFRCQDlJyJiIjcJ55//nn27t0LQK5cuXjqqac4FB4Or70GpsmIESMoUKDA3ycEBqoLo4jIfUTJ\nmYiIyD3qxx9/ZPv27bZtf39/5syZY9349Ve+io2l1uuvw7hxsHJlDkUpIiJZRbM1ioiI3COuXbtG\nVFQUwcHBAOzfv5+dO3cSHh4OwOuvv06u48ehUyeYMwcDwNsbBgyAGjVyLG4REckaajkTERHJQTcu\nDL1y5Up69epl2+7QoQP16tWzbRcoUIA8W7fCnDmQK5c1KTt6FIYNg4CAuxq3iIhkPSVnIiIiOeSP\nP/6gSpUqtgStefPmuLq6kpSUBFiTsRuTNQBefBEGDoQjR+CTTyB//rsdtoiIZBMlZyIiIndJamoq\n/fr1IyEhAYAiRYpw6dIlIiMjAfDw8GD16tXkypULYmIgJcWxEk9PGDsWihS5m6GLiMhdoORMREQk\nG23ZsoXz588D1unt9+/fz/LlywEwDIMdO3YQGhr69wlXrsBHH0FwsLX7ooiIPDSUnImIiGSh1NRU\n4uPjbdtffPEF3377rW171KhRVKxY0bbt7+8PFy9a1yJ75RXr1PfvvgtxcbBu3V2NXUREclaOztY4\nceJEvvjiC44fPw5A2bJleffdd3nqqadsZYYMGcLUqVOJiYmhevXqTJw4kcceeyyHIhYREbm1ESNG\nsH//fgYMGABA7969OXjwoO141apVHU86fRqee+7v7Zo1ra1nDRpkd7gicp9ITU21jUeV+1euXLmw\nWNJvH8vR5KxIkSKMGjWKUqVKkZqaypdffkmbNm3Yvn07FSpUYOTIkYwbN47w8HBCQkIYOnQoTZo0\n4eDBg/j4+ORk6CIiIgD8/PPPzJkzh7FjxwLQsmVL5s6dC6YJJ09S98IF6h47Bk2bWpOwffvAMOwr\n+de/4Jln4PHH4YknoE4dxzIi8tAyTZPExEQ8PDww9LvhvmWaJgkJCbd8HQ3zxjl87wF58+ZlxIgR\n9OnTh4IFC/LKK68waNAgABISEsifPz9jxowhLCzMdk5cXJzte39//7ses9x/duzYAUCVKlVyOBK5\nX+g9I2kuX77MN998Q99u3eDMGS74+vJo6dKcOXMGb29vTNNk+/btlG/fHo+TJx0rOHUKChW6+4HL\nPU2/Yx5OGf0Mm5iYiKurKy4uLncjLMlGKSkpXL9+HXd3d6fH75kxZykpKcyePZuEhATq1q3LsWPH\niIqKomnTprYyHh4e1K1bl61bt+ZgpCIi8rA5dOgQ5iuvQKNG+FStSpf//Ad8fCAkhMCEBDZt2oSH\nhwdgneTDYrFgWiyQJ4+1xey//4WFC+HkSShYMIefjYjcb0zTVGL2gHBxceFWbWM52q0RYO/evdSs\nWZPExEQ8PT2ZO3cupUuXtiVgjzzyiF35/Pnzc+bMmXTrS/vPk0hG6P0imaX3zEPANMEwME3T1u2k\nY8eObLt+ncA//sAA/IAUNzeu58vHkYgIkkqWZPfu3XbVHPziC67nzm3fPfHcOetDJB36HfNwKVWq\nVE6HIPeYHE/OypQpw549e4iLi2PevHl06tSJdbeZnUp9bUVEJCu5nTtHntWrybt8OadeeYXBW7ZQ\nrlw5W++N1q1bsyI6mmpVqpCULx/J+fKR4ud3y3Fh1/PkuVvhi4jIAyLHkzM3NzdKlCgBwOOPP872\n7duZOHEi77//PgBRUVEULlzYVj4qKooCBQqkW5/6aktGqG+/ZJbeMw+gmBiYPx+++QZz40aMv7qZ\nhOzZQ7NmzVi2bBnvvPMOkPnXXe8XySy9Zx5ON445E4F7aMxZmpSUFFJTUwkODqZAgQKsWrXKdiwh\nIYHNmzdTq1atHIxQRETud7GxsRwaMQLCwmDDBlJdXfkxIMA6LmzCBDp16kR4eHhOhykiIg+ZHG05\ne/vtt2nRogWFCxfm8uXLzJo1iw0bNrBixQoABgwYwMcff0yZMmUoVaoUw4YNw9fXly5duuRk2CIi\nkhNiY2HWLPj9dxg2DDw9HcuMHQvJyeDiAhaL9auLC4SFcS0lBS8vLwDOnz9PixkzONisGUanTtCq\nFTFr1mC2bo1hGHjc5acmIiI5a/369TRs2JDZs2fToUOHHIsjR5OzqKgounbtyrlz5/D396dChQqs\nWLGCJk2aAPDmm28SHx9Pv379iImJoUaNGqxatQpvb++cDFtERO6mXbtg0iRrYhYfb903ZIjzskOG\nwJUrDrsTOnWi6L/+xZEjRwgICKBUqVI079yZ8//9L/nz58cFeOaZZ7LrGYiIiBO3Woz5RjNmzKB7\n9+7ZHM29IUeTsxkzZty2zODBgxk8ePBdiEZERO45bdvCokV/bzdqZJ2aPp31YXjtNWsCl5rK6hUr\nqPL44+T298fDz4/69euzbds2mjVrBsD48ePvwhMQEZH0zJw50257ypQpREREOOQID9OQphyfEERE\nRCRd5crB+vXQowf07QulS6dbdM2aNQS2bUuFChUA+D4hgYj8+XnvvfcAmDt3bob/SysiItnv5qFK\nq1at4ueff77tEKarV68+sD3p9FdKRETszZkDn34KX38Ny5bBtm1w5AgkJGTP9a5fhxMnnB977TU4\nfRo++cQhMUtISODkyZO27V27djFx4kTb9ttvv83zzz9v21ZiJiJy/+nRoweenp6cOHGCVq1a4e/v\nT4sWLQDYs2cPPXv25NFHH8XT05N8+fLRuXNnu78NaeLi4njjjTcoUaIEHh4eFC5cmGefffaW6ycn\nJyfzzDPP4OPjw5o1a7LtOd5ILWciImJvyhRwtt7kihXwV5dAO2PHwqlTEBAAuXP//bVWLcibN/3r\nnDsH06ZZr+fnB/v2Oa4b5u9vt3njwtCLFy9mxowZtkmkOnXqZPseoFChQhl7viIick9LTU2ladOm\nVK9enTFjxuDqak1hfvzxRw4dOkSPHj0oWLAgR44cYfLkyfz888/s27cPz78mjrp69Sr16tUjMjKS\nnj17UqVKFS5cuMDy5cv5/fffKViwoMM1ExMTad++PZs2bWLlypU88cQTd+W5KjkTEXlYnTkDTv4g\n0aEDlC0L0dH2j/z5ndczb561de1mmzeDsz9mzz4Lv/0Ge/ZYW80ASpWyJmtBQemGe/ToUbp3786m\nTZsAaNGiBZMmTeL69eu4urpSpEgRu5YyEZGHlWEYmH+t3Zgd23dbcnIyLVu2ZMyYMXb7X3zxRQYO\nHGi3r1WrVjzxxBN89913PPvsswCMHj2aPXv2MG/ePJ5++mlb2bS1LG927do1Wrduza5du1i9ejVV\nq1bN4meUPiVnIiIPm4QEeOklWLwYdu6EokXtj/ftm7n63ngDjh+3TnUfG2td3Dk2Nv1Ea+9e68Ni\nsU748eKL1ok+bup2mJKSwuuvv87IkSPJlSsXxYsX58SJExw8eJDSpUvj7e3Nhg0bMheriIjcl/7z\nn/847PO8YUmVK1eukJiYSKlSpQgICGDXrl225Gz+/PmEhobaJWbpuXTpEk8++SQHDx5k3bp1lC9f\nPuueRAYoORMReZgcPw7t21uTMg8Pa+vVzclZZmXgj52dRYvg/HnrdW9K4CIiIggJCSFPnjy4uLiw\nbds2fvzxR5566iksFgu7d+8m7626SoqIiEMrV1Zv320Wi4XixYs77I+JieHtt99m/vz5xMTE2B2L\ni4uzff/777/Ttm3bDF1r4MCBxMfHs2vXLsqVK/eP4r4TGR4dfe7cOXbv3m2378CBA4SFhdGxY0e+\n++67LA9ORESy0MqVULmyNTELDoaffoK/BlXfVSVKQPXqEBSEaZok3DDRyKeffsq8efNs22PGjKFM\nmTK2bSVmIiIPn1y5cjmd1KlDhw7MnDmTl156ie+++47Vq1ezevVq8ubNS2pqqq2ccfN45lto06YN\nhmHw0Ucf2dVxt2S45eyll17izz//ZOPGjQBcvHiRevXqERsbi4eHB/Pnz2fRokW0bNky24IVEZE7\ndPIktGwJycnw739bZ2LMnTuno2LYsGEkJCTw0UcfAdC7d2+OHz9uO/4wrW0jIiLOOWu5i4mJYc2a\nNXzwwQe2JVPAOpPvxYsX7co++uij7N27N0PXatGiBU899RRdu3bF29ub6dOn/7PgMynDLWc//fST\nbeFOsC4aFxMTw86dO4mOjuaJJ55wGKQnIiL3iCJFYPhwGDoUvv8+xxKzbdu28e6779q2mzdvbvun\nH0CTJk00qYeIyEPMWSuXs30uLi4ADq1bn3zyiUMy1759eyIjI5k/f36GYujUqRNTpkxhxowZ9O/f\nP6OhZ4kMt5xFR0fbTTO5ZMkS6tSpY+uL2bFjR95///2sj1BERLLGa6/d9UteunSJBQsW0LNnTwCK\nFi3KxIkTeffdd/Hw8KBy5cqa1ENERGyctZI52+fn50f9+vUZNWoUSUlJFC1alM2bN7Nx40by5s1r\nd84bb7zBggUL6Ny5M6tWraJSpUrExsayYsUKhg4dSt26dR3q7927N1euXOHVV1/Fx8fH1sMju2W4\n5SxPnjycPXsWsE4vuWXLFpo2bWo7bhiG3bgBERF5OB07dsz2RzFXrlwMHDjQtshnUFAQq1evxs3N\nDbD+7dDi0CIiAta/CTe3kjnbl2bWrFm0aNGCKVOm8OabbxIXF8fatWvx8fGxO8fLy4uNGzfSr18/\nVqxYQf/+/Zk0aRJFihQhJCTE7lo36t+/P0OHDmX48OGMGDEiC59p+gwzg9OvdOjQga1bt/LZZ5+x\nYsUKpk2bxr59+3jssccAGDBgAMuWLePQoUPZGrAzN87G4n/TgqUizuzYsQOAKlWq5HAkcr+4b94z\niYkwcKB1oo/mze/65U3TpHTp0syaNcv2s5o2bRqNGjUiODj4rseTU+6b94vcM/SeeThl9DNsQkIC\nHh4edyMkuQtu9Xpm+N+VH3/8Me7u7rRv355p06YxcOBAW2J2/fp15s2bR7169bImYhERybwLF6B+\nfZg0CXr3tq5ndhf079+fhQsXAtb/Ovbq1cvuH3V9+vR5qBIzERGRO5XhMWclS5bkt99+Y//+/fj5\n+dn9oY2Pj2fixIlUrFgxW4IUEZHbuHgRmjSBX36xrh+2YIF1HbNssHbtWmJjY2nXrh0Ajz32GPPn\nz7etIfP2229ny3VFREQedJnq6O/m5kaFChUc/gPq6+tLmzZtnC4OJyIi2Sw2Fpo2tSZmpUpBRARk\nYdeouLg4tm3bZttOTEy0m523a9euTJkyJcuuJyIi8rDKcMsZQFJSElOnTmXp0qWcOHECgOLFi9Oi\nRagFiGAAACAASURBVAv69OljG+AtIiJ30e7dsGePdXHntWshKOgfV5mYmIi7uzsAJ0+epH379pw4\ncQKLxULjxo2JiYnBNE0Mw8Db2/sfX09EREQy0XIWExND9erVefnll9m9ezd58uQhT5487Ny5k379\n+lG9enViYmKyM1YREXGmQQNYuhTWrYPChf9xdVevXqVo0aJcuXIFgNDQUJo3b25b1NPNzY0uXbqk\nO3uWiIiI3JkMJ2eDBg0iMjKSGTNmcPr0aTZt2sSmTZs4c+YM4eHhREZGMmjQoOyMVURE0tOkiXWs\n2R164YUXOH78OADe3t5UrVqViIgI2/EvvviCwMDAfxqliIiI3EKGk7PFixfTr18/unfvbrcmjcVi\noVu3bvTr14/FixdnS5AiIpK11q1bx/79+23bpmkyd+5c2/aiRYto3LhxToQmIiL/396dh1VV7X8c\nfx+QSUUkERFUcCCHHFLJKzjkhENaaZal1nWszDGtS/nLgcpwKErNtDSvmjk3X+d5QBwwpzRNydRS\nQVFBUUHknN8fR3ciqJDoOcDn9Tzn4ay11977u2UJfM/eay0psLI95iwxMZFKlSrddnuFChX0WKOI\nyP2WkgJ79sC//pWj3a5evcrZs2cpfX082ubNm4mPj+fTTz8F4P/+7/8oVOjvXwk3vxcREZEHI9t3\nzipWrMgPP/xAVmtWWywWfvzxxzsmbyIico9SU6FjR2jcGJYty9Gu8+fPp0+fPka5S5cu1KhRwygH\nBARQJhfGq4mIiMg/l+3krH///qxZs4ZWrVqxZMkSYmNjiY2NZfHixbRq1Yo1a9YwYMCA+xmriEjB\nlZYGzz8PS5eCuzuULXvH5ocPH6ZVq1ZG+emnnyYhIYH09HTA+rTDK6+8cl9DFhERkZzJ9nMrffr0\nISEhgffff5/Vq1dn2Obs7Mz777/Pq6++musBiogUeGlp0Lkz/PgjeHrC6tVQvXqGJteuXeP//u//\niIiIoFChQlSoUIG9e/dy5MgRKlSogIeHB5s3b7bRBYiIiEh25GhQwbBhw3j11VdZvXo1x48fB8Df\n35/Q0FBKlChxXwIUESnwXn4Zvv0WPDxg1Sp49FEAYmJiqFy5MsWKFaNQoUKsWbOGDRs20Lx5cxwd\nHdm1axelSpWycfAiIiKSXdl+rPGGvXv3sn37drZu3cq2bdvYvn07u3fvvh+xiYgIQJcuUKoUluXL\nuXrTOLGIiAi+++47oxwZGUlAQIBR9vHx0VpkIiJi13799VdeeOEFypcvj5ubG35+fjRp0oR3333X\n1qHZRLbvnF26dIlOnTqx7PogdE9PTywWC4mJiYwfP55WrVqxaNEiihYtet+CFREpkFq2hCNHeHfc\nOBxWrmTEiBEA9OrVi1OnThnNmjRpYqMARUREcm7Lli00bdqUMmXK0LNnT/z8/Dh58iQ7duxg7Nix\njBw50tYhPnDZTs7eeOMNli1bxvDhwxk4cKDxGGNCQgITJ05k1KhRvPHGG3zxxRf3LVgRkYJky5Yt\nrFmzhmHDhkHhwoSGhvLOO+8YyVm7du1sHKGIiMg/N2rUKNzd3YmJicHT0zPDtjNnztgoqnt39epV\nHB0dcXR0zPG+2X6sceHChfTu3Zt33303w/gyLy8v3nvvPXr37s2iRYtyHICIiFglJSWxaPp0o+zr\n68v48eNJS0sDIDg4ONOETCIiInnV77//TrVq1TIlZgAlS5bMUF65ciWPP/447u7uuLu706ZNG/bs\n2ZOhTffu3XFzc+PkyZO0b98ed3d3vL29+c9//oPZbM7QduHChTz22GN4eHhQrFgxqlWrxqhRozK0\nOXr0KM8//zwlSpSgcOHC1KtXjx9//DFDm/Xr1+Pg4MDcuXMJDw+nXLlyFC5cmBMnTvyjf5NsJ2dm\ns5natWvfdnutWrUyXbSIiNzZiRMnjPUjXdav5/GXXybpeoLm7+/PTz/9hIOD9Ue1g4ODFocWEZF8\no3z58uzcuZO9e/fesd3cuXNp06YNhQsXZsyYMYSHh3PkyBEaNWrEb7/9lqGt2WymdevWlCxZksjI\nSB5//HEiIyOZOnWq0Wb16tW88MILeHp6MmbMGD766CNat26dYVbj06dPExISwvLly+nbty9jxozB\nYrHwzDPPMH/+/EwxRkRE8P333zN48GDGjRtHkSJF/tG/SbZ/yz/xxBMsXryY1157LcvtS5YsoW3b\ntv8oCBGRgshisdCgQQP+99131FiwANdx43AFLn3zDfTqBUBISIhtgxQREblPwsLCWLVqFXXq1KFu\n3bo0atSIZs2a0bx5c1xcXADrvBf9+/enR48efPnll8a+vXr1onLlyrz33nvMmTPHqE9LS6NTp07W\nIQHAK6+8Qt26dZk+fTp9+vQBrHmLh4cHK1asuO3EWWPGjCEuLo7169fTuHHjDMcaMmQIzz77bIYP\nTJOTkzlw4ABubm739G+S7Ttnw4cP56+//qJt27YsW7bMWIR66dKlPPHEE5w8eZJhw4Zx+vTpDC8R\nEfnbwIEDjYmVTCYTg556itLPPw/jxoGjI3zwAUUWL7ZxlCIikqeZTFm/cqt9LmnatCmbNm2iXbt2\n7N+/n48//ph27dpRqlQpZs6cCcCqVatITEykc+fOJCQkGK9r167RsGFD1q1bl+m4L7/8coZyw4YN\nOXLkiFEuXrw4ycnJrFix4raxLVmyhLp16xqJGYCrqyt9+/YlLi6OXbt2ZWj/73//+54TM8jBnbNH\nHnkEgF9++cX4w+J2bW4wmUykp6ffQ3giInnb2rVruXLlivFkQaVKlViwYAFt2rQBi4XB0dEQGwtl\ny8K8edCggY0jFhEReXCCg4P54YcfSE9PZ//+/SxevJgPP/yQnj174u/vz6FDhwAIDQ3Ncv9bJ91w\ndnbOtManp6cn58+fN8p9+/Zl0aJFPPHEE/j6+tKiRQs6duzIk08+abQ5duwYzz77bKbzValSBbCO\nR3vssceM+ooVK+bwyrOW7eTsxuxgOaH1dUSkoLlw4QKxsbHUqVPHKE+cONFIznr06EH37t2tjU0m\n+Pxz+PBDmDIFHnrIRlGLiEi+cn0s831rfx84OjpSs2ZNatasSXBwMM2bN+frr7/m4YcfBmDWrFn4\n+fnd9TjZyT9KlizJrl27WL16NcuWLWP58uV89dVXtGvXjp9++inbx7lZbtw1gxwkZ+Hh4blyQhGR\n/CYtLQ0nJycADh8+TKdOnYiNjcVkMtG6dWuSkpKMtu7u7hl3DgqCBQseZLgiIiJ27cYdqVOnTlmf\nNME6Q3yzZs1y7RxOTk60adPGOP7QoUMZO3YsW7ZsITg4GH9/fw4ePJhpvxt1AQEBuRbLzbI95kxE\nRDK7cOECAQEBpKSkAFCnTh1CQkJITEwErM+nd+vWzfqp5LVrtgxVRETErqxdu9aYsfhmS5cuBayP\nELZq1YrixYsTERFhLC1zs1vXQ8vOHa9z585lqnv00UcBjN/f7dq1Y+fOnURFRRltUlJSmDJlCqVL\nl6Zu3bp3Pc8/oTmZRURyqE+fPowYMQJfX1+KFStG1apV2bp1K02aNMFkMjF79uyMOyQmwssvg7c3\nfPaZbYIWERGxMwMHDuTSpUt06NCBKlWqYDab2blzJ7Nnz8bLy4vXX38dd3d3Pv/8c7p27Urt2rXp\n3Lkz3t7eHD9+nOXLl1O9enVmzJhhHDOrZO9WvXr14uzZszRv3pwyZcpw4sQJJk2ahK+vrzEByFtv\nvcW8efNo27YtAwcOxMvLi6+//pqDBw8yZ84cY5mb3KbkTETkLjZs2MDZs2cpV64cAJcvX2bRokUM\nGjQIsH7C5+zsnPXOW7fCCy/AsWPg7g7vvAO+vg8qdBEREbsVGRnJt99+y4oVK5g+fTqpqan4+fnx\n0ksv8c477xi/dzt16oSvry8RERFERkaSkpKCn58fDRo0MKbHB+tds6zunN1a/9JLL/Hll1/y+eef\nc/78eXx8fGjXrh0jR4401icrWbIkmzdv5q233mLy5MlcvnyZGjVq8O233/L0009nOn5uMVmyk17e\nJ6NHj+a7777j0KFDuLi4UL9+fUaPHp1p1sfw8HCmTZvG+fPn+de//sVnn31GtWrVjO03j+fw8PB4\nYPFL3rVjxw4AgoKCbByJ/COnT1vvQt0n165d4/z585QsWRKwLiVy9OhRBg0aRFBQELGxsTg7Oxu/\nNLK0eDFMmgSrVoHZbB1bNn8+5NJsTmLf9DNGckp9pmDK7t+wKSkpuLq6PoiQ5AG40/fTpmPONmzY\nQP/+/dmyZQtr166lUKFCtGjRIsNUl2PHjuXjjz9m0qRJxMTE4O3tTWhoKMnJyTaMXERswmyG8HCo\nVAn27cu6TS583jRz5kz69+9vlF988UXKlCljlCtVqnTnxAxgzx5YsQIcHOCNN2DzZiVmIiIickc2\nTc6WL19Ot27dqFatGtWrV2f27NmcOXOG6OhowPrM6Pjx4xk6dCgdOnTgkUceYdasWVy8eJG5c+fa\nMnQRedAuXYJOneDdd63vt2/P3Ob3363rhQ0YAOvWZXsCjoMHD9KhQwej3L59e44ePYrZbAagcuXK\ndOzYMfOO167BTYtaZvDii9Zp8uPi4KOP4HaPPYqIiIhcZ1ezNV64cAGz2YynpycAf/zxB/Hx8bRs\n2dJo4+rqSuPGjY0ETkQKgGPHrIszf/stFCtmfWSwZ8/M7ZYuhRMnrI8TNmsGpUtD796wcWOGZlev\nXmXEiBFG8lWxYkU2bdrE8ePHAet0vdu2bct6sK/FAtHR0L8/+PlBaGjWd+v8/eHVV6FEiXu+fBER\nESkY7GpCkEGDBlG7dm2Cg4MBiIuLA8i0yre3tzcnT57M8hg3ntkWyQ71F/tnSk2leseOuMTHk1Ku\nHLGRkaSULAlZfe/q16fwrFl4rl2L57p1uB4/DtOnc+raNdb++SflypUzFomcM2cOjxYqRDVfXywm\nEz+8/TbJ69bxq4MDqWXLkl60aMZjp6fjN2UKqStX4nLqlFF9xc2N31as4JqX1/38Z5A8Sj9jJKfU\nZwqWwMBAW4cgdsZukrMhQ4YQHR1NVFRUtmY8yc1ZUUTEfllcXDj52ms8tHw5Rz74gPRixW7f2GTi\ncrVqXK5Wjb/69sU5NhavDRtIbNqUzyZOpG3btrRq1QqAwYMHEzJjBj47d2Y6zOFPPiGpYcOMlY6O\nFNu+HZdTp7jq7c25li0516oVlytXBv08EhERkVxgF8nZ4MGDWbhwIevWrcuw2raPjw8A8fHxGQbj\nx8fHG9tupVmOJDs0K9Z9dvQouLrCbf6f5lhQEAwfTu0crCkyfPhw3N3dCfviC/yAN5ycOHfunPE9\nDwoKsj4u6eZmnWgkPd361WwmMCjIes6b7Nixg7/696dy9eo4N2yIj4MDuXR1kg/pZ4zklPpMwXTz\nbI0iYAdjzgYNGsSCBQtYu3YtDz/8cIZt5cuXx8fHh5UrVxp1KSkpREVFERIS8qBDFZFbrVgB18dp\nZfCf/0BAAPTrZ03UcsNdErPo6GgiIyONctOmTVmxYoVR7tixIy+//HLGnT78EKKirGPItm2DmBj4\n+We49a7ZdRfr1YPGje8ai4iIiMg/YdO/MPr168fMmTOZM2cOHh4exMXFERcXx6VLlwDro4uvv/46\nY8eO5fvvv2ffvn10794dd3d3unTpYsvQRSQ6Gtq3h+Bg64yEN6SnWyfISE2FyZOt09536wYHDtz9\nmAcOwP/+l63TJyUl8d133xnlkiVL8tFHH5Geng5AkyZNWL58eY4uSURExF7ZcGliyUV3+z7aNDmb\nMmUKycnJNG/eHF9fX+N186ffYWFhDB48mH79+vHYY48RHx/PypUrjdW7RcQGfvsNnnwSUlKgXTu4\nedIeR0f45hvrOmQvvmit++orqFcP7rQ+4dKlUL++dbr8PXuybHL69OkM5e7du5OYmAhYB1XPmTPH\n2Obg4ICTk9M/uz4RERE74uzsTEpKihK0PM5isZCSkoLzHZbXsemYsxvTWN/NyJEjGTly5H2ORkSy\nJS4OWreGc+esCdpnn2U9IcYjj8Ds2dZ1yT78EB56CG6dARGsd9kiIyEszPr+2Wetd9syNbNQu3Zt\n1q9fT2BgIB4eHowYMYKkpCSKFy8OQLNmzXL7akVERGzOwcEBFxcXUlNTbR2K3CMXF5esl+q5zi4m\nBBGRPCIlBdq2tY4jq1cP5s2DQnf5MVKhAkyZkvW2q1ehb1+YPt1afvddGD7cSPYGDBjAM888Q9Om\nTTGZTHTt2pVdu3YZUw+/+eabuXRhIiIi9s3BwQFXV1dbhyH3mZIzEck+FxfrY4cXL1rHht3r48XO\nznDoEBQuDLNns87Tk/Q1a2jRogUAZcuWZd68eTRt2hSAcePG3esViIiIiNgtJWcikn0mE7z1FgwY\nYE2o7tGlI0dId3KiWHQ01KrF6QULmDlzppGcvfLKK3q+XkRERAoMJWciknP3kJilp6fj6OgIwO5T\np3glLo79tWoB0K5dO2O2VsAYSyYiIiJSEGixHhF5YM6fP0/FihVJS0sDIDg4mKpVq3LhwgUAihQp\nQs+ePW0ZooiIiIjNKDkTkdtbtco6JuwevPbaa5w5cwYAT09P/Pz82LZtG2Ad3PzNN99QrFixew5V\nREREJK9TciYiWYuJsS4yHRICx45le7eoqCiOHj1qlM+dO5dhseg1a9bQsGHD3IxUREREJF/QmDMR\nyez3361T5l++DM89B+XK3bZpeno6Fy5cwNPTE4Aff/wRFxcXRo0aBUB4eDhubm5Ge00DLCIiIpI1\n3TkTkYzOnLEuMn3mDLRqBdOmZb3I9HVTp05l0KBBRvnf//43fn5+Rrlq1aoEBATcz4hFRERE8gUl\nZyLyt7Q0ePJJiI2FOnVg0SJwcsrQZP/+/bz44otGuX379hw4cMCY8r5GjRq89tprDzRsERERkfxA\nyZmI/M3JCf79b6hYEZYsAXd3UlJS+OCDD4zkq2LFiixZsoRTp04BULp0aWJiYjDd4e6aiIiIiNyd\nkjORguLaNdi1C6ZMgW7drGPJstK3L/vmzyfl+hpjLi4uzJgxg59//hmwjhn7+eef8fHxeVCRi4iI\niBQImhBEJL+7eBHatYMdO6wTfNzg6GgtX19Q2mw24+Bg/bxmYFgYAwYMoEOHDphMJj755BM8PDyM\nXStUqPBAL0FERESkIFByJpLfFS0Kv/1mTcQqVYL69a2vf/0LXFwAeOedd/D29jYm9ujduzdnz541\nDvHkk0/aJHQRERGRgkSPNYrkdyYTLF4Mp0/D4cMwezZRtWoxaetW690zoEGDBixZssTYpUuXLvTu\n3dtWEYuIiIgUSErORPKLjRth0qQsNyUFBrJk+3ajXLx4ccaNG4fZbAagZcuW/O9//3sgYYqIiIhI\n1pScieQHM2ZAixYwcCBERQFw7tw5Y3NaWhpdunQhOTkZgOrVq/PFF18YMzAWKlQIl+uPOIqIiIiI\nbSg5E8nL0tMhLAx69rSuUTZoEAQHYzabqVatGseOHQPAy8uL//znPxkStjZt2uB4/bFGEREREbE9\nTQgiklclJ0PXrvDTT1CoEPMaNsT/uecIcXTEAXj22WeJiYnB398fgGHDhtk2XhERERG5IyVnInnU\nlmXLqBMVhYunJ3zzDbGbNxM9bx4hISEAfPrpp1oYWkRERCQPUXImkkdcvnyZP//8k8qVKwNw6PJl\nvqlRg8ipU+Hhh+lbq5YxhgxQYiYiIiKSxyg5E7FjNy8MvXXrVt5880127twJQPv27bl69So8/DAA\nJUqUsFmcIiIiInLvNCGIiJ1KSEigatWqpKeng9nM440a4evra8y46OHhwcsvv2zjKEVEREQktyg5\nE/kn9uyBhQth/XrYvx/OnLHOnHgPLBYL/fr1IzExEbDOsFi0aFF+3rQJOnfG8b33WLx4MUWLFs2F\nCxARERERe6PHGkX+iYULISIiY53JZK17++3M7XfuhAMHwNERHBysXx0d+fnqVUqFhFCmTBlMJhMn\nTpzghx9+oHvjxhAXx6aICAqHhUFMDBQrBv36gY/Pg7lGEREREXmglJyJ3MnJk+Drm7m+alV45hnr\nHbPTp61fz50Dd/esj/PVVzBhQqbqo40asfS33xg+fDgA77//PkWKFIHx4+HTTyl8o2H58vC//ykx\nExEREcnHlJyJZGXHDhg61Pr44u+/Z066XnzR+rpZWhqYzVkfr0YN6NyZwwcPkpSYSNCjj4LZTK0m\nTYh3dr6pWQ3rm4AAqF/ferxKlazJWsmSuXd9IiIiImJ3lJyJ3OzQIRg2DBYtspY9PKwJWsOGd9/X\nySlT1d69e/n000+ZNm0a9OqF87Fj9OnYkZhvv8VkMlEJqJTVsYYMsb5EREREpMDQhCAiN3zyCVSr\nZk3MXF0hLAyOHMleYnbdlStXiIyMNNYbq1ixIgsXLiQhIQEAf39/YmJitAaZiIiIiGSi5EzkhqAg\n69feveHwYRg7Fh566K67HTx40LreGODi4sKECRPYt28fAEWKFGHbtm08dNNxlJiJiIiISFaUnEne\nFR8PzZtDmTLw9ddZt1m/HmbMgO+/h3XrYPduOHoUU0pK5raNGsEff8C0adZj3sGNO2MAvXr1YvXq\n1QA4ODjwySef4OrqamyvUqWKsZC0iIiIiMjtaMyZ5E0XLkCbNrBrl7V8U7KUwcyZMGtWpuoSw4aR\n8PTTmduXLXvXUw8dOhR/f3/69OkDWJOzkydPGts7dux412OIiIiIiNxKyZnkPamp0KGDNTGrVAl+\n+OH2SVWjRtav589DYqL1df48acWLZ/t0UVFRHDx4kN69ewNQr149pk2bZiRnPXv2vKfLEREREREB\nJWeSFw0aBGvXWtf8WrnSugbY7fTqZX3dImnHjtvukpSUxPbt2wkNDQXAzc2NMWPG0KtXL0wmE+3a\ntaN169b3fBkiIiIiIjfTQBjJewYPtq4btmzZnROzHLhw4YLx/vLly3Tq1ImU6+PS6tSpw0cffYT5\n+hpmTk5OuLm55cp5RURERERuUHImeU/lytaJPR59NFcOd+3aNQIDA41xY6VLl6Zv377G9Pcmk4n2\n7dvj6OiYK+cTEREREcmKTZOzjRs38tRTT1GmTBkcHByYlcXEDeHh4fj5+VG4cGGaNm3Kr7/+aoNI\nxe7c4+yHH374IQcOHACgUKFCPPnkk2zbts3Y/sEHH1DmLjM2ioiIiIjkJpsmZ5cuXaJmzZpMmDAB\nNze3TOs/jR07lo8//phJkyYRExODt7c3oaGhJCcn2yhiyas2bNjA1q1bjXLRokVZsWKFUZ42bRod\nOnSwRWgiIiIiIoCNk7M2bdowatQoOnbsmGkdKIvFwvjx4xk6dCgdOnTgkUceYdasWVy8eJG5c+fa\nKGJ54KKi4OOPc7xbSkoKR44cMcq//fYbn3zyiVF+/vnneemll4yyFoYWEREREVuz2zFnf/zxB/Hx\n8bRs2dKoc3V1pXHjxkRHR9swMnlg9u2DJ5+EN96Ab7+9a/ObF4Zet24dXbt2NcodO3akadOmRvmh\nhx6iRIkSuRuviIiIiMg9sNvkLC4uDoBSpUplqPf29ja2ST527Bi0amVdl6xDB2jf/o7N4+LiqFWr\nljGjYosWLShSpAhXrlwBoESJEsa6ZCIiIiIi9ihPrnN2p0fQdtxh/SrJGwolJlK5d2/cTp7kYu3a\nHHrjDSy7dmVoY7FYiIyMpG/fvhQuXBiwjmH8+uuvqVatGgBjxoxh//79dzyX+ovklPqM5IT6i+SU\n+kzBEhgYaOsQxM7Y7Z0zHx8fAOLj4zPUx8fHG9skf/L/4APcjh3jcqVKxEZGYnFxAWDfvn0Zprc/\nfvw4mzZtMvb78ssvjcRMRERERCSvsds7Z+XLl8fHx4eVK1dSt25dwDrJQ1RUFB999NFt9wsKCnpQ\nIcr9MmMG9OmD2/TpPFy8OEWKFAGsMypWrFiRsLAwACZNmkSxYsWoVKlSjk9x45NJ9RfJLvUZyQn1\nF8kp9ZmCKSkpydYhiJ2xaXJ26dIlDh8+DIDZbObYsWPs3r2bEiVKULZsWV5//XUiIiKoUqUKgYGB\njBo1Cnd3d7p06WLLsPO/q1dh5kyIjwcXF3jmGcgqAdq1C86ft7Zxdv77a5kyULToPz9/QAAsX874\nTz7h999/Z9KkSQB0796dnTt3Gs3q1Knzz88hIiIiImJnbJqcxcTE0KxZM8D6mNrIkSMZOXIk3bt3\n57///S9hYWFcuXKFfv36cf78eerXr8/KlSuNOylyH1y7Bl26ZJwdsVq1rJOz4cNhyZLM9T/8AE8/\nnbk+LAx27IBixcDd/e+v3btDlSrs3r2b//73v0ycOBGAdu3a0blzZ2P34OBggoOD7/ECRURERETs\nk02TsyZNmhiz693OjYRNHgCLBV591ZqYeXhA377WZO12jw3WrAmXLkFqqvVuW2qq9eXllXX7nTth\n3brM9c2aQZUqlC9fnlmzZvHee+9RvHhxAgMD2b59e+5dn4iIiIiIHbPbMWdiA8eOwfffg5ub9Y5Y\ngwZ3bh8RkbPjT5jAiR078ClSBMfLlzEnJjLmnXd4wcmJCoCHhwebNm3C3d3d2OXWxclFRERERPIr\nJWfyt4AA2LgRTp26e2KWAxaLxbr8wSOP8HS3bowdO5bmzz6LAxDg5UV6mTJG25o1a+baeUVERERE\n8hIlZ5JR9erWVy55++23qVKlCt27dwegZ8+eHDt2zNiuyV1ERERERKz0zJjkqk2bNjF79myj/Oij\nj/Ldd98Z5b59+9KzZ09bhCYiIiIiYteUnBVkf/11z4e4cOECGzduNMqOjo6MGTPGKHfo0IF58+bd\n83lERERERPI7JWcF1erV1lkYJ0zI8a6XL1823icmJtKhQweuXr0KQP369RkxYoQxC6eLi4uWPhAR\nERERyQYlZwXRli3Qvr112vsjR3K0a1paGgEBAZw5cwaAcuXK0b17dxISEgDr7IrPP/+8ZlkUBSfn\n/gAAEQpJREFUEREREckh/QVd0OzdC088YV2frFs3+OSTu+4yYMAAfvnlFwCcnJwIDQ0lOjra2B4Z\nGYmvr+99C1lEREREpCDQbI0FyeHD0LIlJCZa75x9+SVkcYdr48aNFClShLp16wLg6urK/PnzqVGj\nBgCzZ8/WnTERERERkVym5KwgSUmxfm3eHObNg0LWb39qairx8fGUK1cOgD179hATE8NXX30FwODB\ng7FYLMZhlJiJiIiIiOQ+JWcFSY0aEB0N3t7g6mpUL1u2jPHjx7N+/XoAnnvuORwdHY3temRRRERE\nROT+0y2QgqZCBf5KTKR+/frG3bDWrVtjNptJTU0FwMfHh759+9oyShERERGRAkfJWX6WlgaAxWLh\njTfe4MqVKwD4+flx9uxZ9u7dC1jHlG3cuBEXFxebhSoiIiIiUtApOctvrl2Dn34isWFDroaGAmAy\nmdi1axfLli0zylu2bKFmzZq2jFRERERERG6iMWf5hOWvv7j2xRc4zZwJf/1FceBaoUJw+jR4exMR\nEcFDDz1ktPfy8rJVqCIiIiIikgUlZ/mB2Uxy9eq4JyVZy4GB/N68OesDAujl7Q1A/fr1bRigiIiI\niIjcjR5rzKN27txJWFiYteDgwJXOnVnl6Qlr1sDBg1ScMoVeb71l2yBFRERERCTblJzlhvT0+36K\nSxcvsuzNN2HVKgDKlSvHF198QXJyMgDeU6bQ7MwZaNYsy4WlRURERETEvumxxpxISwMnp4x16elQ\nty40aABvvgnly+fa6Y4dO0bZtDQc5s+n8KxZtImN5erSpTjv34+Xlxdr1qzB9ab1ym5em0xERERE\nRPIW3WLJDosFJkyAxx6DixczbtuyBfbsgcmTITAQunaFX36593OeO8e5atVwCAyE4cMxxcZyydOT\ni6Gh1hkZgaCgIAoVUn4tIiIiIpIfKDm7m9RUePlleP11axK2eHHG7Q0bwv790K0bmEwwdy7UrGlt\nn0NvvfUWCxYssBY8PQkoXJg0Z2drwrd0KUVOn6bEhAmZ796JiIiIiEiep+TsTk6fhubNYfp0cHOD\n+fOhc+fM7apVg5kzITYWBg60tq1b966H37R+PRtGjIC//rp+mGosWrTIutFkwnPdOpzOnoWvv4Y2\nbUB3yURERERE8i39tX87Z85YH2M8fhzKlIEffrh7wuXvb338cdgwKF480+aLFy+yf98+6ru5wddf\nU2/mTFzOnrUmXSNG0KlTJ5555pm/d6hePZcvSkRERERE7JWSs9vx8oKWLWHfPvj+e/Dxyf6+JUsa\nb1NTU3FxcQEg/o8/CGzQwDqGDXABLnp7U7RECUyAm5tbLl6AiIiIiIjkJUrObsdkgs8+A7MZbpoR\nMSdSU1Px9/fn4MGDFC9enEo7doDFgtnTE4cuXaBrV9zr17eeS0RERERECjSNObsTZ+ccJ2YDBw7k\n0KFDALi4uNCgQQM2b95s3ditGxw8iEN8PEyaBMHBSsxERERERARQcmZ1/DhcT6hyatOmTezduzdD\nnTHj4vX3bdu2tRYcHaFyZc22KCIiIiIimeixxs2b4ZlnwMMDtm0DT887Nk9LSyMhIYHSpUsDsG3b\nNg4dOsTUqVMBePPNNzO01zpkIiIiIiKSHQXzzpnFArt2weDB0LSpdcp8f/9s7fr999/To0cPo/z8\n889Ts2ZNo1yuXDnKlSuX6yGLiIiIiEj+VjCTszffhDp1YPx4SEuzrk22bFmWd82OHTtGs2bNsFyf\nYbFt27YkJSWRlpYGQNmyZenfv/8DDV9ERERERPKfgpmcNWkCJUpA//4QE2Ndm+z644dms5m33nqL\nq1evAtbkKzY2lgMHDgBQpEgRtmzZgpPGjYmIiIiISC7Kn8lZejqsWgUTJ2a9vU0bOHkSPv0UgoLY\ntWsX58+fB8DBwYGoqChWr15tlLdt20bVqlUfVPQiIiIiIlIA5b/kLCwMypWzLiD95ptw7lymJhZH\nR67eVB47diwLFy40ymPGjKFSpUpGuXTp0pg05b2IiIiIiNxH+W8qwQ8/tH6tUAFeesk6+cctxo4d\ny8WLF/nggw8A6NGjB4cPHza2N2rU6IGEKiIiIiIickP+u3P26qsQFQWxsRAeDiVKsGPHDsLDw40m\noaGhrFmzxii3atVKk3qIiIiIiIhN5b/k7PPPSa5Vizlz5xpVfn5+TJgwgZSUFADq1KnDpk2bbBWh\niIiIiIhIJvkvOcO68HP//v05efIkYB0ztnjxYmNBaJPJpNkWRURERETEruSJ5Gzy5MmUL18eNzc3\ngoKCiIqKumN7V1dXIiIiuHz5slHXoEEDIzkTERERERGxN3afnC1YsIDXX3+dYcOGsXv3bkJCQmjT\npg1//vnnHfd77bXXMsy4KCIiIiIiYs/sPjn7+OOP6dGjB7169aJy5cpMnDiR0qVLM2XKFFuHJiIi\nIiIikmvsOjm7evUqO3fupGXLlhnqW7ZsSXR0tI2iEhERERERyX12nZwlJCSQnp5OqVKlMtR7e3sT\nFxdno6hERERERERyX76bISMpKcnWIUgeEBgYCKi/SPapz0hOqL9ITqnPiAjY+Z0zLy8vHB0diY+P\nz1AfHx9P6dKlbRSViIiIiIhI7rPr5MzZ2Zm6deuycuXKDPWrVq0iJCTERlGJiIiIiIjkPrt/rHHI\nkCG89NJL1KtXj5CQED7//HPi4uLo06eP0cbDw8OGEYqIiIiIiNw7u0/OOnXqxNmzZxk1ahSnTp2i\nRo0aLF26lLJly9o6NBERERERkVxjslgsFlsHISIiIiIiUtDZ9Ziz7Jo8eTLly5fHzc2NoKAgoqKi\nbB2S2IGNGzfy1FNPUaZMGRwcHJg1a1amNuHh4fj5+VG4cGGaNm3Kr7/+aoNIxV6MHj2axx57DA8P\nD7y9vXnqqafYv39/pnbqNwLw2WefUatWLTw8PPDw8CAkJISlS5dmaKO+IncyevRoHBwcGDBgQIZ6\n9RuRgivPJ2cLFizg9ddfZ9iwYezevZuQkBDatGnDn3/+aevQxMYuXbpEzZo1mTBhAm5ubphMpgzb\nx44dy8cff8ykSZOIiYnB29ub0NBQkpOTbRSx2NqGDRvo378/W7ZsYe3atRQqVIgWLVpw/vx5o436\njdxQtmxZxo0bx65du/j5559p1qwZ7du3Z8+ePYD6itzZ1q1bmTZtGjVr1szw+0n9RqSAs+Rx9erV\ns7zyyisZ6gIDAy1Dhw61UURij4oWLWqZNWuWUTabzRYfHx9LRESEUXflyhWLu7u75YsvvrBFiGKH\nkpOTLY6OjpbFixdbLBb1G7m7hx56yDJ16lT1FbmjxMRES8WKFS3r16+3NGnSxDJgwACLxaKfMSJi\nseTpO2dXr15l586dtGzZMkN9y5YtiY6OtlFUkhf88ccfxMfHZ+g7rq6uNG7cWH1HDBcuXMBsNuPp\n6Qmo38jtpaenM3/+fFJSUmjcuLH6itzRK6+8wnPPPcfjjz+O5aah/+o3ImL3szXeSUJCAunp6ZQq\nVSpDvbe3N3FxcTaKSvKCG/0jq75z8uRJW4QkdmjQoEHUrl2b4OBgQP1GMvvll18IDg4mNTUVNzc3\nFi5cSOXKlY0/pNVX5FbTpk3jyJEjzJ07FyDDI436GSMieTo5E7kfbh2bJgXTkCFDiI6OJioqKlt9\nQv2mYKpSpQp79+4lKSmJRYsW8cILL7Bu3bo77qO+UnD99ttvvPPOO0RFReHo6AiAxWLJcPfsdtRv\nRAqGPP1Yo5eXF46OjsTHx2eoj4+Pp3Tp0jaKSvICHx8fgCz7zo1tUnANHjyYBQsWsHbtWgICAox6\n9Ru5lZOTExUqVKB27dpERERQv359PvvsM+N3kPqK3GzLli0kJCTwyCOP4OTkhJOTExs3bmTy5Mk4\nOzvj5eUFqN+IFGR5Ojlzdnambt26rFy5MkP9qlWrCAkJsVFUkheUL18eHx+fDH0nJSWFqKgo9Z0C\nbtCgQUZi9vDDD2fYpn4jd5Oeno7ZbFZfkSx16NCBffv2sWfPHvbs2cPu3bsJCgqic+fO7N69m8DA\nQPUbkQLOMTw8PNzWQdyLYsWKMXLkSHx9fXFzc2PUqFFERUUxY8YMPDw8bB2e2NClS5f49ddfiYuL\nY/r06dSoUQMPDw/S0tLw8PAgPT2dMWPGULlyZdLT0xkyZAjx8fFMnToVZ2dnW4cvNtCvXz+++uor\nFi1aRJkyZUhOTiY5ORmTyYSzszMmk0n9Rgxvv/02rq6umM1m/vzzT8aPH8/cuXMZN24cFStWVF+R\nTFxdXSlZsqTx8vb2Zs6cOfj7+9OtWzf9jBGRvD+VvsVisUyePNkSEBBgcXFxsQQFBVk2bdpk65DE\nDqxbt85iMpksJpPJ4uDgYLzv0aOH0SY8PNxSunRpi6urq6VJkyaW/fv32zBisbVb+8qN17vvvpuh\nnfqNWCwWS/fu3S3+/v4WFxcXi7e3tyU0NNSycuXKDG3UV+Rubp5K/wb1G5GCy2SxZGMUqoiIiIiI\niNxXeXrMmYiIiIiISH6h5ExERERERMQOKDkTERERERGxA0rORERERERE7ICSMxERERERETug5ExE\nRERERMQOKDkTERERERGxA0rOREQKqCZNmtC0aVNbhyEiIiLXKTkTEcnnoqOjeffdd0lKSspQbzKZ\nMJlMNopKREREbmWyWCwWWwchIiL3z0cffURYWBhHjx6lXLlyRv21a9cAKFSokK1CExERkZvoN7KI\nSAFx62dxSspERETsix5rFBHJx8LDwwkLCwOgfPnyODg44ODgwIYNGzKNOTt69CgODg6MHTuWyZMn\nU6FCBYoUKUKLFi04fvw4ZrOZ999/nzJlylC4cGGefvppzp49m+mcK1eu5PHHH8fd3R13d3fatGnD\nnj17Htg1i4iI5FX62FREJB/r2LEjhw8fZt68eYwfPx4vLy8AqlatetsxZ/Pnzyc1NZWBAwdy7tw5\nxo0bx3PPPUeTJk3YtGkTQ4cOJTY2lokTJzJkyBBmzZpl7Dt37lxeeuklWrZsyZgxY0hJSWHq1Kk0\natSImJgYKleu/MCuXUREJK9RciYiko/VqFGD2rVrM2/ePNq3b59hzJnFYskyOTtx4gSxsbEUK1YM\ngPT0dEaPHs2VK1fYtWsXjo6OAJw+fZr58+czdepUXFxcuHTpEv3796dHjx58+eWXxvF69epF5cqV\nee+995gzZ859vmIREZG8S481iohIBh07djQSM4B69eoB8OKLLxqJ2Y36tLQ0/vzzTwBWrVpFYmIi\nnTt3JiEhwXhdu3aNhg0bsm7dugd7ISIiInmM7pyJiEgGN99dA/Dw8ACgbNmyWdafP38egEOHDgEQ\nGhqa5XFvTuxEREQkMyVnIiKSwe2SqNvV35gF0mw2AzBr1iz8/PzuT3AiIiL5mJIzEZF87kEtNF2x\nYkUAvLy8aNas2QM5p4iISH6iMWciIvlckSJFADh37tx9PU/r1q0pXrw4ERERpKWlZdqekJBwX88v\nIiKS1+nOmYhIPvfYY48BMHToUDp37oyzszPNmzcHMi9MfS/c3d35/PPP6dq1K7Vr16Zz5854e3tz\n/Phxli9fTvXq1ZkxY0aunU9ERCS/UXImIpLP1a1bl9GjRzN58mR69uyJxWJh7dq1t13nLCu3a3dr\nfadOnfD19SUiIoLIyEhSUlLw8/OjQYMG9OnT556vRUREJD8zWXLzY1MRERERERH5RzTmTERERERE\nxA4oORMREREREbEDSs5ERERERETsgJIzERERERERO6DkTERERERExA4oORMREREREbEDSs5ERERE\nRETsgJIzERERERERO6DkTERERERExA4oORMREREREbED/w/im26Kvj2imQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7c15358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_sensor(measurement_var=1, process_var=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Math with Gaussians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9+2RZuRl8/dN7XMu+qnBmQoiKIAW4EKJCFGkLWbp1DkdO/WaI+Xn1ImzQ29Sy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\nnhAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7abe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import stats\n",
    "with figsize(y=3):\n",
    "    stats.plot_gaussian(mean=23, variance=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how this relates to the bar charts from the Discrete Bayes chapter. In that chapter we drew bars of various heights to depict the probability that the dog was at any given position. In many cases those bars took on a shape very similar to this chart. The differences are that the bars depict the probability of a discrete position, whereas this chart depicts the probability distribution of a continuous range of positions. \n",
    "\n",
    "This graph corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly speaking positions 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n",
    "\n",
    "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n",
    "\n",
    "Let's look at 100 sensor readings in a plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Zw3UIpJ7r0KEDOnToILP1eExG+0xnZWWJ/l9DQ0MWS9aKr68vvvnmG4wdOxZe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Xjz5g1yc3Olut7ExARGRkZ4/fo1q3bJgtL0kOrUqYPff/8dixcvRmZmJubNmwddXV2cP3++Utt3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\nP3HjiP835sZbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7138eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dog = DogSimulation(x0=23, velocity=0, \n",
    "                    measurement_variance=5, process_variance=0.0)\n",
    "xs = range(100)\n",
    "ys = []\n",
    "for _ in xs:\n",
    "    dog.move()\n",
    "    ys.append(dog.sense_position())\n",
    "               \n",
    "bp.plot_track(xs, ys, label='Dog position')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n",
    "\n",
    "\n",
    "Recall the discrete Bayes code for adding a measurement to a preexisting belief:\n",
    "\n",
    "    def update(pos, measure, p_hit, p_miss):\n",
    "        q = array(pos, dtype=float)\n",
    "        for i in range(len(hallway)):\n",
    "            if hallway[i] == measure:\n",
    "                q[i] = pos[i] * p_hit\n",
    "            else:\n",
    "                q[i] = pos[i] * p_miss\n",
    "         normalize(q)\n",
    "         return q\n",
    "         \n",
    "Note that the algorithm is essentially computing:\n",
    "\n",
    "    new_belief = old_belief * measurement * sensor_error\n",
    "    \n",
    "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. \n",
    "    \n",
    "If we are implementing this with Gaussians, we might expect it to be implemented as:\n",
    "\n",
    "    new_gaussian = measurement * old_gaussian\n",
    "    \n",
    "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is not particularly difficult to perform the algebra to derive the equation for multiplying two Gaussians, but I will just present the result:\n",
    "$$\n",
    "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n",
    "\n",
    "In other words the result of multiplying two Gaussians is a Gaussian with \n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
    "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n",
    "\n",
    "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Pp1mzZhiGwZ49e5SciYjcrfgEgz7jYO8xGPKEwbjnwdMjez5kWywJ/HZoA+tD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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b47c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division\n",
    "import numpy as np\n",
    "\n",
    "def multiply(mu1, var1, mu2, var2):\n",
    "    if var1 == 0.0:\n",
    "        var1=1.e-80\n",
    "        \n",
    "    if var2 == 0:\n",
    "        var2 = 1e-80\n",
    "        \n",
    "    mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
    "    variance = 1 / (1/var1 + 1/var2)\n",
    "    return (mean, variance)\n",
    "\n",
    "xs = np.arange(16, 30, 0.1)\n",
    "\n",
    "mean1, var1 = 23, 5\n",
    "mean, var = multiply(mean1, var1, mean1, var1)\n",
    "\n",
    "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
    "plt.plot(xs, ys, label='original')\n",
    "\n",
    "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
    "plt.plot(xs, ys, label='multiply', ls='--')\n",
    "\n",
    "bp.show_legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n",
    "\n",
    "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
    "\n",
    "\"Measure twice, cut once\" is a useful saying and practice due to this fact!  The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n",
    "\n",
    "Now let's multiply two Gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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It6JSqVL9FEilUmFubv5e94JnhvwWFkKI95ifnx/NmjXD3Nwcf39/8uXLZ+iQ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99HIQgE24vtAC5rEW7zzKj2SU3/g83zdnssgfbj4Iztv3BZ5kSf3/0KNs87UfvP2JbjT51LkgWS\nrZBsgyQL1O8vpbpyTVT73947glmzx+NIDrXTaEJ5eeKJIO+8447+uYkekm3R49eSk6NntdFqteGP\n9zq7//77mTVrFunp6V1ekRBCCCH+FSmKElVsn2vevHlMnz6dqqoqvv/++/DV9Ouuuy5m+85X2jvY\nbDYMCUYM9gwG2c9enDv6VS1tvr/S5oscQjzt1hksvn8R7hYXnhYnHq8Lj9fJpr9+wrYdGzufnoLr\ncsgcnIbX1xIxSuK7rxs4UP5DVPsh/zaIUYXRX7w9tqeOg9t+aC/mFRQlVNDnjU5l/KiLm9ijK4oa\n6+u97X744QdycnLYunVrxJdCn3rqKdauXUtlZWXUMbfddhu5ubm89dZb4X0nT54kPz+fnTt3csMN\nN1BQUMB9993HsmXLwm22bt1KYWEh1dXV4QK9qanpR3mRQgghhBBCxIPdbr/gY847aGbQoEFotVpq\nayOvXtfW1kZ8tH+ujIyMqKvrHcd3zETRVRudTid3PhRCCCGEEAPaeQt0vV7P2LFj2bJlS8T+0tLS\n8LeBOxs/fjzbtm2LuPNhaWkp2dnZ5OXlhduUlpZGHFdaWsq4ceNijj8XQgghhBBioDjvEBeADRs2\ncN999/H6668zYcIE3njjDf7yl79w4MABcnNz+f3vf8+uXbv49NNPgdA0iwUFBRQWFrJs2TIOHTrE\n3LlzKS4u5uGHHwbg22+/ZdSoUfzmN79h3rx5fPHFFyxcuJB169bJl+iEEEIIIcSA1u38bvfccw/1\n9fWsWLGC6upqRo8ezebNm8NT7tTU1HDs2Nm7RtlsNkpLS1m4cCHXXXcdKSkpPProo+HiHCA/P5/N\nmzfz8MMPs3r1arKzs3nllVekOBdCCCGEEANet1fQhRBCCCGEEL2nT9yKcuvWrUyfPp2cnBw0Gg0l\nJSVRbQ4fPsydd95JcnIyZrOZsWPHxpxFRly87vLgdDpZsGABubm5mEwmhg0bxksvvRSnaPuvZ555\nhnHjxmG323E4HEyfPp0DBw5EtSsuLiY7OxuTycQtt9wS8w5w4tJ0lwu/38/jjz/OmDFjsFgsZGVl\nMWvWrC7nBhYXp6fviQ7z589Ho9Hw4osv9mKUA0NPcyF99uXVkzxIn907XnvtNcaMGYPdbsdutzNh\nwgQ2b94c0eZi+us+UaB7PB6uueYaXn75ZRITEyNuHANw/PhxfvrTnzJ06FDKyso4cOAATz/9tMw7\n/SPrLg9FRUV88sknrFmzhsrKSv74xz+ydOlS1qyJnpdcXLzy8nIeeughdu7cyWeffYZOp2PSpEk0\nNDSE2zz77LOsWrWKV199lV27duFwOJg8eTJud/Sc7+LidZcLj8fDnj17WLZsGXv27OHDDz+kqqqK\nqVOndnljD3HhevKe6PDBBx+wa9cusrKyov6GiUvXk1xIn3359SQP0mf3jtzcXJ577jn27NnDP/7x\nD372s58xY8YM9u7dC1xCf632MRaLRS0pKYnYN3PmTHX27NlximhgipWHUaNGqcXFxRH7br75ZvV3\nv/tdb4Y24LjdblWr1aqbNm1SVVVVg8GgmpGRoa5cuTLcpqWlRbVareqf//zneIU5IHTORSwHDx5U\nFUVR9+/f34uRDSxd5eHbb79Vs7Oz1crKSjU/P1998cUX4xThwBErF9Jn975YeZA+O35SUlLUN998\n85L66z5xBf18gsEgmzZtYvjw4UydOhWHw8H111/Phg0b4h3agHP77bfz0Ucf8d133wGwY8cOKioq\nmDp1apwj69+cTifBYDB8l9Pjx49TW1vLlClTwm2MRiM33XQTO3bsiFeYA0LnXMTScYO187URlyZW\nHvx+PzNnzmT58uUUFBTEMbqBpXMupM+Oj1jvCemze18gEGDdunV4vV5uuummS+qv+3yBfurUKdxu\nNytXrmTq1Kl8+umnzJw5k1mzZkWN8RGX17PPPsuIESMYPHgwer2ewsJCnnvuOaZNmxbv0Pq1RYsW\nce211zJ+/HiA8E2+Ou6428HhcETdAEz8uDrnojOfz8cjjzzC9OnTycrK6uXoBo5YeXjiiSdwOBzM\nnz8/jpENPJ1zIX12fMR6T0if3Xv27duHxWLBaDQyb948NmzYQEFBwSX1191OsxhvwWAQgBkzZlBU\nVATANddcw+7du3n11VflF60XPfroo3z55Zds3LiRvLw8ysvLeeSRR8jLy+O2226Ld3j90uLFi9mx\nYwfbt2/v0XhaGXN7+XSXC7/fz+zZs3E6nWzatCkOEQ4MsfLw+eefU1JSQkVFRURbVSYpu6xi5UL6\n7N7X1d8m6bN7z7Bhw/jnP/9JU1MT77//Pr/61a8oKys77zHd9teXeRjOBes89rm1tVVNSEhQn376\n6Yh2Tz31lDpy5MjeDm/A6JyHjvFtH330UUS7Bx98UJ00aVJvhzcgFBUVqVlZWeqhQ4ci9h89elRV\nFEXdvXt3xP5p06apc+bM6c0QB4yuctGhra1Nveuuu9Thw4ertbW1vRzdwNFVHoqLi1WNRqPqdLrw\noiiKqtVq1dzc3DhF2791lQvps3tXV3mQPju+Jk2apM6ZM0c9duzYRffXfX6Ii16vZ9y4cVHTMx0+\nfJj8/Pz4BDUAqaqKqqpoNJG/MhqNRq5SXQaLFi1i/fr1fPbZZ1x99dURzw0ZMoSMjAy2bNkS3uf1\netm+fTsTJkzo7VD7vfPlAqCtrY1f/vKX7N+/n7KyMhwORxyi7P/Ol4cFCxawb98+9u7dy969e6mo\nqCArK4vFixfz97//PU4R91/ny4X02b3nfHmQPju+AoEAwWDwkvrrPjHExePxcOTIESD08diJEyeo\nqKggNTWV3NxclixZwj333MONN97ILbfcQllZGevXr+fDDz+Mc+T9S3d5uPXWW1m6dCkWi4XBgwdT\nXl7Ou+++y/PPPx/nyPuXhQsXsmbNGv72t79ht9vD49SsVitmsxlFUSgqKmLlypUMGzaMq666ihUr\nVmC1Wrn33nvjHH3/0l0uAoEAd999N7t372bjxo2oqhpuk5SUhNFojGf4/UZ3eUhLSyMtLS3imISE\nBDIyMrjqqqviEXK/1V0uAOmze0F3ebBYLNJn95KlS5dyxx13kJOTg8vlYu3atZSXl/Pxxx8DXHx/\nfVmu7V+gsrIyVVEUVVEUVaPRhLfnzp0bbvP222+rV199tZqYmKiOGTNGXbduXRwj7p+6y8OpU6fU\nBx54QM3JyVETExPV4cOHyzRml0Hnf/+O5cknn4xoV1xcrGZmZqpGo1EtLCxUDxw4EKeI+6/ucnH8\n+PEu23SeplRcvJ6+J84l0yxeHj3NhfTZl1dP8iB9du+YM2eOmpeXpxoMBtXhcKiTJ09Wt2zZEtHm\nYvprRVXlsw4hhBBCCCH6ij4/Bl0IIYQQQoiBRAp0IYQQQggh+hAp0IUQQgghhOhDpEAXQgghhBCi\nD5ECXQghhBBCiD5ECnQhhBBCCCH6ECnQhRBCCCGE6EOkQBdCCCGEEKIPkQJdCCGEEEKIPuT/AZ/R\nZZ1fxepjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b42860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(16, 30, 0.1)\n",
    "\n",
    "mean1, var1 = 23, 5\n",
    "mean2, var2 = 25, 5\n",
    "mean, var = multiply(mean1, var1, mean2, var2)\n",
    "\n",
    "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
    "plt.plot(xs, ys, label='measure 1')\n",
    "\n",
    "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
    "plt.plot(xs, ys, label='measure 2')\n",
    "\n",
    "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
    "plt.plot(xs, ys, label='multiply', ls='--')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n",
    "\n",
    "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24?  Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n",
    "\n",
    "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n",
    "\n",
    "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n",
    "\n",
    "One final test of your intuition. What if the two measurements are widely separated? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ecl9WVpaybWVlVa1+SDeVjOqofpNC+on3Uj/dunULISEhAACxWIwjR44gJydH+fqoUaOU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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7d1eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(0, 60, 0.1)\n",
    "\n",
    "mean1, var1 = 10, 5\n",
    "mean2, var2 = 50, 5\n",
    "mean, var = multiply(mean1, var1, mean2, var2)\n",
    "\n",
    "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n",
    "plt.plot(xs, ys, label='measure 1')\n",
    "\n",
    "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n",
    "plt.plot(xs, ys, label='measure 2')\n",
    "\n",
    "ys = [stats.gaussian(x, mean, var) for x in xs]\n",
    "plt.plot(xs, ys, label='multiply', ls='--')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n",
    "\n",
    "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Furthermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
    "\n",
    "Of course, this example is quite exaggerated. The width of the Gaussians is fairly narrow, so this combination of measurements is quite unlikely. It is hard to eyeball this, but the measurements are well over $3\\sigma$ apart, so the probability of this happening is less than 1%. Still, it can happen, and the math is correct. \n",
    "\n",
    "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
    "\n",
    "$$\n",
    "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
    "$$\n",
    "\n",
    "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n",
    "\n",
    "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n",
    "\n",
    "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n",
    "$\\sigma_1^2=0$, yielding\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n",
    "\\text{or just}\\\\\n",
    "\\mu&=\\mu_1\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n",
    "\\text{or just}\\\\\n",
    "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing the Update Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall the discrete Bayes filter uses a NumPy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n",
    "\n",
    "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def update(mean, variance, measurement, measurement_variance):\n",
    "    return multiply(mean, variance, measurement, measurement_variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog is with the new measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perhaps this would be clearer if we used more specific names:\n",
    "\n",
    "    def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n",
    "        return multiply(dog_pos, dog_variance, \n",
    "                        measurement, measurement_variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n",
    "\n",
    "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSimulation` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time: 0 \tposition = -0.033 \tvariance = 2.500\n",
      "time: 1 \tposition = -0.969 \tvariance = 1.667\n",
      "time: 2 \tposition = -0.985 \tvariance = 1.250\n",
      "time: 3 \tposition = -0.167 \tvariance = 1.000\n",
      "time: 4 \tposition = 0.024 \tvariance = 0.833\n",
      "time: 5 \tposition = 0.419 \tvariance = 0.714\n",
      "time: 6 \tposition = 0.190 \tvariance = 0.625\n",
      "time: 7 \tposition = 0.109 \tvariance = 0.556\n",
      "time: 8 \tposition = 0.177 \tvariance = 0.500\n",
      "time: 9 \tposition = -0.024 \tvariance = 0.455\n",
      "time: 10 \tposition = -0.042 \tvariance = 0.417\n",
      "time: 11 \tposition = 0.002 \tvariance = 0.385\n",
      "time: 12 \tposition = -0.048 \tvariance = 0.357\n",
      "time: 13 \tposition = -0.054 \tvariance = 0.333\n",
      "time: 14 \tposition = -0.002 \tvariance = 0.312\n",
      "time: 15 \tposition = -0.042 \tvariance = 0.294\n",
      "time: 16 \tposition = -0.195 \tvariance = 0.278\n",
      "time: 17 \tposition = -0.001 \tvariance = 0.263\n",
      "time: 18 \tposition = -0.020 \tvariance = 0.250\n",
      "time: 19 \tposition = -0.077 \tvariance = 0.238\n"
     ]
    }
   ],
   "source": [
    "dog = DogSimulation(velocity=0., measurement_variance=5, process_variance=0.0)\n",
    "\n",
    "pos, s = 2, 5\n",
    "for i in range(20):\n",
    "    dog.move()\n",
    "    pos, s = update(pos, s, dog.sense_position(), 5)\n",
    "    print('time:', i, \n",
    "          '\\tposition =', \"%.3f\" % pos, \n",
    "          '\\tvariance =', \"%.3f\" % s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n",
    "\n",
    "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n",
    "\n",
    "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n",
    "\n",
    "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed.\n",
    "\n",
    "Finally, look at this chart. It only displayes the "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing Predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track non-moving objects? The discrete Bayes filter used a loop of predict and update functions, and we must do the same to accommodate movement.\n",
    "\n",
    "How do we perform the predict function with Gaussians? Recall the discrete Bayes method:\n",
    "\n",
    "    def predict(pos, move, p_correct, p_under, p_over):\n",
    "        n = len(pos)\n",
    "        result = array(pos, dtype=float)\n",
    "        for i in range(n):\n",
    "                result[i] =  \\\n",
    "                pos[(i-move) % n]   * p_correct + \\\n",
    "                pos[(i-move-1) % n] * p_over + \\\n",
    "                pos[(i-move+1) % n] * p_under          \n",
    "        return result\n",
    "        \n",
    "                \n",
    "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with Gaussians?\n",
    "\n",
    "It turns out that we just add Gaussians. Think of the case without Gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n",
    "\n",
    "How is addition for Gaussians performed? It turns out to be very simple:\n",
    "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n",
    "\n",
    "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n",
    "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for Gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using Gaussians to model physical events, the results must correctly describe those events.\n",
    "\n",
    "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n",
    "\n",
    "So, here is our implementation of the predict function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def predict(pos, variance, movement, movement_variance):\n",
    "    return (pos + movement, variance + movement_variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is left? Just calling these functions. Discrete Bayes did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PREDICT:     1.0000   500.1000\tUPDATE:     1.8374     1.9920\tZ: 1.8407\n",
      "PREDICT:     2.8374     2.0920\tUPDATE:     2.6136     1.0225\tZ: 2.3996\n",
      "PREDICT:     3.6136     1.1225\tUPDATE:     3.7305     0.7190\tZ: 3.9388\n",
      "PREDICT:     4.7305     0.8190\tUPDATE:     5.0502     0.5810\tZ: 5.8309\n",
      "PREDICT:     6.0502     0.6810\tUPDATE:     5.6824     0.5080\tZ: 4.6022\n",
      "PREDICT:     6.6824     0.6080\tUPDATE:     6.3011     0.4663\tZ: 5.0469\n",
      "PREDICT:     7.3011     0.5663\tUPDATE:     7.3814     0.4413\tZ: 7.6649\n",
      "PREDICT:     8.3814     0.5413\tUPDATE:     8.6722     0.4260\tZ: 9.7468\n",
      "PREDICT:     9.6722     0.5260\tUPDATE:    10.4442     0.4165\tZ: 13.3794\n",
      "PREDICT:    11.4442     0.5165\tUPDATE:    11.4540     0.4105\tZ: 11.4921\n",
      "actual final position:    11.5300\n"
     ]
    },
    {
     "data": {
      "image/png": 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JbPoaOoVYNIuqiLhUikNY27dvT/v27QHo16+f3T7DMJg0aRJvvvkmTz75JAAzZ87E39+f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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7d25208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### assume dog is always moving 1m to the right\n",
    "np.random.seed(13)\n",
    "pos = (0, 500)   # gaussian N(0,500)\n",
    "vel = 1.\n",
    "\n",
    "# variance in process model and the RFID sensor\n",
    "velocity_variance = .1\n",
    "sensor_variance = 2.\n",
    "\n",
    "dog = DogSimulation(pos[0], velocity=vel, \n",
    "                    measurement_variance=sensor_variance, \n",
    "                    process_variance=velocity_variance)\n",
    "zs, positions = [], []\n",
    "\n",
    "for i in range(10):\n",
    "    pos = predict(pos=pos[0], variance=pos[1], \n",
    "                  movement=vel, movement_variance=velocity_variance)\n",
    "    print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n",
    "    \n",
    "    dog.move()\n",
    "    z = dog.sense_position()\n",
    "    zs.append(z)\n",
    "    pos = update(mean=pos[0], variance=pos[1],\n",
    "                 measurement=z, measurement_variance=sensor_variance)\n",
    "    positions.append(pos[0])\n",
    "    \n",
    "    print('UPDATE: {: 10.4f} {: 10.4f}\\tZ: {:.4f}'.format(pos[0], pos[1], z))\n",
    "\n",
    "print('actual final position: {:10.4f}'.format(dog.x))\n",
    "bp.plot_filter(positions)\n",
    "bp.plot_measurements(zs)\n",
    "bp.show_legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we discuss the code and results, let's try to understand this better with this chart showing one predict update cyle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KS+np6W6vL1++rPbt2yspKUnPP/+8mjVrprJly8rHx0eTJ0/Wpk2bbBkTCofD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\nAIAN/h9T1o10fD/oowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b4b400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mkf_internal import show_residual_chart\n",
    "show_residual_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This chart is very similar to one we already saw in the *g-h Filter* chapter. At each predict step we take our existing estimate and update it based on our system model. We then make a measurement. We know neither the measurement or prediction is perfect, so we choose a value in between the two. This is scaled so that the new estimate is closer to the one we trust more. We then step time forward one step, and what was the new estimate is considered to be the prior estimate, and the process repeats. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a fair bit of arbitrary constants in code above, but don't worry about it. What does require explanation are the first few lines:\n",
    "\n",
    "    velocity = 1 \n",
    "    velocity_variance = .1\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",
    "    pos = (0, 500)   # gaussian N(0,500)\n",
    "    vel = 1.\n",
    "\n",
    "    velocity_variance = .2\n",
    "    sensor_variance = 2.\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 .1 for the velocity sensor, and a higher error of 2 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. 100 m is almost as likely as 0 m with this value for the variance. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we initialize the RFID simulator with\n",
    "\n",
    "    dog = DogSimulation(pos[0], velocity=vel, \n",
    "                        measurement_variance=sensor_variance, \n",
    "                        process_variance=velocity_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, positions = [], []\n",
    "    \n",
    "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call the measurement $z$, and so I follow that convention here. When I was learning this topic I found the notations very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a more readable variable name such as `m` or `measure`. It is just something you have to memorize if you want to work with Kalman filters. As we continue I will introduce more of the standard naming into the code. The `s` at the end of the name is just a plural - I'm saying there are many `z`s in the list."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we just enter our `predict() ... update()` loop.\n",
    "\n",
    "    for i in range(10):\n",
    "        pos = predict(pos[0], pos[1], vel, velocity_variance)\n",
    "        print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n",
    "\n",
    "We call the `predict()` function with the Gaussian for the dog's position, and another Gaussian for its movement. `pos[0], pos[1]` is the mean and variance for the position, and 'vel, velocity_variance' is the mean and variance for the movement. The first time through the loop we get\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, sensor_variance)\n",
    "    positions.append(pos[0])\n",
    "    print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
    "    \n",
    "For this I get this as the result:\n",
    "\n",
    "    UPDATE:     1.8374     1.9920\tZ: 1.8407\n",
    "    \n",
    "What is happening? The dog is actually at 1.0 but the measured position is 1.8407 due to the sensor noise. That is pretty far off from the predicted value of 1. The filter incorporates that measurement into it's prediction. This is the first time through the loop and so the variance is 500.2. A large variance implies that the current prediction is very poor, so the filter estimates the position to be 1.8374 - very close to the measurement. 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.\n",
    "\n",
    "Now look at the variance: 1.992. 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.\n",
    "\n",
    "Now the software just loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 11.454 vs the actual position of 11.53. The variance has converged to 0.4105. \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 and it seems to work!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance. The variance is plotted as a lightly shaded yellow area between dotted lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HR0ceeOABQkNDJUwKIYQQN9G2bdtYs2YNY8b0RHv/fXokp8GTra97f9k5GnuP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\nomiWL19ObGwsffv2BpJp3LgCK1f+RK9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jLC0t+fbbb/Hw8ECj0XD9+nV69+6Nojzeo3jo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WDHjp+A5hiGjXr16nk7JBERERERkQtOnUsmN2/+jj597mTp0jXeDkVEREREROSCVeeGuQ4bNpx1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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7e83e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance:\n",
      "\t4.3099 2.6267 2.2812 2.1939 2.1708\n",
      "\t2.1646 2.1629 2.1624 2.1623 2.1623\n",
      "\t2.1623 2.1623 2.1623 2.1623 2.1623\n",
      "\t2.1623 2.1623 2.1623 2.1623 2.1623\n",
      "\t2.1623 2.1623 2.1623 2.1623 2.1623\n"
     ]
    }
   ],
   "source": [
    "%precision 2\n",
    "# assume dog is always moving 1m to the right\n",
    "velocity_variance = 2\n",
    "sensor_variance = 4.5\n",
    "pos = (0, 100)   # gaussian N(0, 100)\n",
    "velocity = 1.\n",
    "\n",
    "dog = DogSimulation(pos[0], velocity=velocity, \n",
    "                    measurement_variance=sensor_variance, \n",
    "                    process_variance=0.5)\n",
    "\n",
    "zs, positions, variance = [], [], []\n",
    "for i in range(25):\n",
    "    pos = predict(pos[0], pos[1], velocity, velocity_variance)    \n",
    "    dog.move()\n",
    "    Z = dog.sense_position()\n",
    "    zs.append(Z)\n",
    "    variance.append(pos[1])\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    positions.append(pos)\n",
    "       \n",
    "positions = np.array(positions)\n",
    "bp.plot_measurements(zs)\n",
    "bp.plot_filter(positions[:, 0], vars=variance)\n",
    "bp.show_legend()\n",
    "plt.show()\n",
    "\n",
    "print('Variance:')\n",
    "for i in range(0, len(positions), 5):\n",
    "    print('\\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(\n",
    "            *[v[1] for v in positions[i:i+5]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that the variance converges very quickly to roughly 2.1623 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 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 measurements means more data to work with."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animating the Tracking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n",
    "<img src='animations/05_dog_track.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
    "\n",
    "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation in a Class"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n",
    "\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance) \n",
    "    \n",
    "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n",
    "\n",
    "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n",
    "\n",
    "    class KalmanFilter1D:\n",
    "        def __init__(self, initial_state, measurement_variance, movement_variance):\n",
    "            self.state = initial_state\n",
    "            self.measurement_variance = measurement_variance\n",
    "            self.movement_variance = movement_variance\n",
    "\n",
    "That works, but I am going to use different naming. The Kalman filter literature has settled on one letter notations for each of these concepts, and so you might as well start getting exposed to it now. At first it seems impossibly terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondence with the code. Unfortunately there is not a lot of meaning behind the names chosen; you will just have to memorize them. If you do not make this effort you will never be able to read the literature.\n",
    "\n",
    "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the movement error. This gives us:\n",
    "\n",
    "    class KalmanFilter1D:\n",
    "        def __init__(self, x0, P, R, Q):\n",
    "            self.x = x0\n",
    "            self.P = P\n",
    "            self.R = R\n",
    "            self.Q = Q\n",
    "            \n",
    "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n",
    "\n",
    "    def update(z):\n",
    "        self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n",
    "        self.P = 1 / (1/self.P + 1/self.R)\n",
    "\n",
    "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n",
    "\n",
    "    def predict(self, u):\n",
    "        self.x += u\n",
    "        self.P += self.Q\n",
    "       \n",
    "That give us the following code. Production code would require significant comments. However, in the next chapter we will develop Kalman filter code that works for any dimension, including 1, so this class will never be more than a stepping stone for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class KalmanFilter1D:\n",
    "    def __init__(self, x0, P, R, Q):\n",
    "        self.x = x0\n",
    "        self.P = P\n",
    "        self.R = R\n",
    "        self.Q = Q\n",
    "\n",
    "    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",
    "    def predict(self, u=0.0):\n",
    "        self.x += u\n",
    "        self.P += self.Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Full Description of the Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the first chapter I stated that the Kalman filter is a form of g-h filter. Recall the diagram we used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EAmzfvh01NTVYunQpsrOz25w3orMoAbBROTk5OHr0KLfs7OyMxMREm3vamC1g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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7eb8c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import gh_internal\n",
    "gh_internal.create_predict_update_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what we have been doing in this chapter. But also recall this chart from the *g-h Filter* chapter, which displayed how we created a new weight estimate from the prediction of the previous day along with the current day's measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1/ZkzZx7PQRERERHVMZJki2vXGuDqVXMAQKNGD+HufguyXGDglj2ZWrdurfre0dGx2vUY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7b4f9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gh_internal.plot_estimate_chart_3()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the exception of the axis labels of 'day' and 'weight' this is the same as the residual chart I made earlier in this chapter. \n",
    "\n",
    "**This is extremely important to understand**: Every filter in this book implements the **same algorithm**. The mathematical details of the computation is different for how we calculate the values in this chart, but the process is exactly the same. We make a prediction, make a measurement, and then choose the new estimate to be somewhere between those two.\n",
    "\n",
    "It is important to see past the details of the equations of a specific filter and understand *what* the equations are calculating and *why*. This is important not just so you can understand the filters in this book, but so that you can understand filters that you will see in other situations. There are a tremendous number of filters that we do not describe - the SVD filter, the unscented particle filter, the $H_\\infty$ filter, the ensemble filter, and so many more. They all use different math to implement the same algorithm. \n",
    "\n",
    "If you understand why this algorithm works you will be able to understand most any filter you encounter.  In other words, this is not just the algorithm for the Kalman filter, it is the algorithm used for any Bayesian filter, and for many non-Bayesian ones as well.\n",
    "\n",
    "Here it is:\n",
    "\n",
    "**Initialization**\n",
    "\n",
    "    1. Initialize the state of the filter\n",
    "    2. Initialize our belief in the state - how accurate do we think it is\n",
    "    \n",
    "**Predict**\n",
    "\n",
    "    1. Based on the system behavior, predict state at the next time step\n",
    "    2. Adjust belief in that state to account for the uncertainty in prediction\n",
    "    \n",
    "**Update**\n",
    "\n",
    "    1. Get a measurement and associated belief about its accuracy\n",
    "    2. Compute difference (residual) between our estimated state and measurement\n",
    "    3. Compute scaling factor based on whether the measurement or prediction is more accurate\n",
    "    4. set state between the prediction and measurement based on scaling factor\n",
    "    5. update belief in the state based on how certain we are in the measurement\n",
    "\n",
    "You will be hard pressed to find a filter algorithm that does not fit into this form. Some filters will not include some aspect, such as error in the prediction, and others will have very complicated methods of computation, but this is what they all do. If you go back to the g-h filter chapter and reread it you'll recognize that the very simple thought experiments we did there result in this algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mathematical Relationship to the g-h Filter\n",
    "\n",
    "I state that the Kalman filter is a g-h filter, and that both are Bayesian filters. You should recognize from the algorithm above that they do indeed perform similar steps, but I did not say the KF is similar to the g-h filter, I said it *is* a g-h filter. But the KF uses Gaussians, and the g-h filter just uses the parameters $g$ and $h$. How can I assert these are equivalent?\n",
    "\n",
    "Some algebra will reveal the relationship, but it is not important to this chapter. If you are curious, I present it in *Kalman Filter Math* chapter. Here I will share the results. \n",
    "\n",
    "At each time step we can show that $g$ equals\n",
    "\n",
    "$$g = \\frac{\\sigma^2_{x}}{\\sigma^2_{z}}$$\n",
    "\n",
    "This make intuitive sense. When we perform an update we choose a value somewhere between the measurement and prediction. If the measurement is more accurate we will choose a value nearer it, and vice versa. This computation for $g$ is a ratio of the errors in the prediction and the measurement.\n",
    "\n",
    "The equation for $h$ is similar.\n",
    "\n",
    "$$h = \\frac{COV (x,\\dot{x})}{\\sigma^2_{z}}$$\n",
    "\n",
    "We haven't discussed the covariance (denoted by $COV$), so you may not fully understand this equation. Just think of the numerator as the variance between the state and its velocity. Recall that $g$ is used to scale the state, and $h$ is used to scale the velocity of the state, and this equation should seem reasonable. In the next chapter it will become very clear.\n",
    "\n",
    "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and predictions at time *n*. That is all the Kalman filter is. It is easier to think of the noise in the measurement and the process model, so we don't normally use the g-h formulation, but we could. It's the same thing written differently. The Kalman filter is a g-h filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Modify Variance Values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modify the values of `movement_variance` and `sensor_variance` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n",
    "\n",
    "    movement_variance = 40\n",
    "    sensor_variance = 2\n",
    "    \n",
    "or:\n",
    "\n",
    "    movement_variance = 2\n",
    "    sensor_variance = 40"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to Designing a Filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n",
    "\n",
    "We do not have a real sensor to read, so we will simulate the sensor with the following function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def volt(voltage, temp_variance):\n",
    "    return (random.randn() * temp_variance) + voltage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n",
    "\n",
    "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
    "\n",
    "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly  +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
    "\n",
    "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
    "\n",
    "As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change over time. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `movement_variance = .2`. This is just the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n",
    "\n",
    "Let's see what happens. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'random' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-24-3913a849411a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mN\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m50\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mzs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mvolt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mactual_voltage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvariance\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[0mps\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[0mestimates\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-24-3913a849411a>\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mN\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m50\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mzs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mvolt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mactual_voltage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvariance\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m \u001b[0mps\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[0mestimates\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-23-78e329cd0e61>\u001b[0m in \u001b[0;36mvolt\u001b[1;34m(voltage, temp_variance)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mvolt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvoltage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtemp_variance\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mtemp_variance\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mvoltage\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'random' is not defined"
     ]
    }
   ],
   "source": [
    "movement = 0\n",
    "variance = 2.13**2\n",
    "movement_variance = .2\n",
    "actual_voltage = 16.3\n",
    "\n",
    "N = 50\n",
    "zs = [volt(actual_voltage, variance) for i in range(N)]\n",
    "ps = []\n",
    "estimates = []\n",
    "\n",
    "kf = KalmanFilter1D(x0=25,               # initial state\n",
    "                    P=1000,              # initial variance \n",
    "                                         # large says 'who knows?'\n",
    "                    R=variance,          # sensor noise\n",
    "                    Q=movement_variance) # movement noise\n",
    "\n",
    "for i in range(N):\n",
    "    kf.predict(movement)\n",
    "    kf.update(zs[i])\n",
    "\n",
    "    # save for latter plotting\n",
    "    estimates.append(kf.x)\n",
    "    ps.append(kf.P)\n",
    "\n",
    "# plot the filter output and the variance\n",
    "bp.plot_measurements(zs)\n",
    "bp.plot_filter(estimates, vars=ps)\n",
    "bp.show_legend()\n",
    "plt.show()\n",
    "plt.plot(ps)\n",
    "plt.title('Variance')\n",
    "plt.show()\n",
    "print('Variance converges to {:.3f}'.format(ps[-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first plot shows the individual sensor measurements vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
    "\n",
    "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The section **Explaining the Results - Multi-Sensor Fusion** explains why this happens."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n",
    "\n",
    "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement (the innovation step)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='animations/05_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",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "variance = 2.13**2\n",
    "actual_voltage = 16.3\n",
    "\n",
    "def VKF():\n",
    "    voltage = (14, 1000)\n",
    "    for i in range(N):\n",
    "        Z = volt(actual_voltage, variance)\n",
    "        voltage = update(voltage[0], voltage[1], Z, variance)\n",
    "    return voltage[0]\n",
    "\n",
    "vs = []\n",
    "for i in range(10000):\n",
    "    vs.append(VKF())\n",
    "plt.hist(vs, bins=100, color='#e24a33')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explaining the Results - Multi-Sensor Fusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**author's note:** I am not overly keen about this explanation. It is true that multiple sensors improve results, but we get good results merely by having an accurate model of the process. I explain this much better in the next chapter. I'll leave this section here while I mull how best to explain this at this stage of learning. For now don't worry if this section is not entirely convincing; it does need work.\n",
    "\n",
    "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focused all of our attention on the position sensor. Let's change focus and see how the filter performs if the inertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30\n",
    "movement_sensor = 30\n",
    "pos = (0, 500)\n",
    "\n",
    "dog = DogSimulation(0, velocity=movement, \n",
    "                    measurement_variance=sensor_variance,\n",
    "                    process_variance=0.5)\n",
    "\n",
    "zs, ps, vs = [], [], []\n",
    "for i in range(100):\n",
    "    dog.move()\n",
    "    Z = dog.sense_position()\n",
    "    zs.append(Z)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "    vs.append(pos[1])\n",
    "\n",
    "    pos = predict(pos[0], pos[1], movement + random.randn(), movement_variance)\n",
    "\n",
    "bp.plot_filter(ps, vars=vs)\n",
    "bp.plot_measurements(zs)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.plot(vs)\n",
    "plt.title('Variance')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distinctly jagged. But, it still mostly tracks the dog. What is happening here?\n",
    "\n",
    "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43.  From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n",
    "\n",
    "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n",
    "\n",
    "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagrees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematical model this sort of reasoning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Extreme Amounts of Noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30000\n",
    "movement_variance = 2\n",
    "pos = (0,500)\n",
    "\n",
    "dog = DogSimulation(pos[0], velocity=movement, measurement_variance=sensor_variance)\n",
    "\n",
    "zs = []\n",
    "ps = []\n",
    "\n",
    "for i in range(1000):\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
    "    \n",
    "    dog.move()\n",
    "    Z = dog.sense_position()\n",
    "    zs.append(Z)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "\n",
    "bp.plot_measurements(zs, lw=1)\n",
    "bp.plot_filter(ps)\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Bad Initial Estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30\n",
    "movement_variance = 2\n",
    "pos = (1000, 500)\n",
    "\n",
    "dog = DogSimulation(0, velocity=movement, measurement_variance=sensor_variance)\n",
    "\n",
    "zs = []\n",
    "ps = []\n",
    "\n",
    "for i in range(100):\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
    "    \n",
    "    dog.move()\n",
    "    Z = dog.sense_position()\n",
    "    zs.append(Z)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "\n",
    "bp.plot_filter(ps)\n",
    "bp.plot_measurements(zs)\n",
    "plt.legend(loc='best')\n",
    "plt.gca().set_xlim(0,100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Large Noise and Bad Initial Estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about the worst of both worlds, large noise and a bad initial estimate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30000\n",
    "movement_variance = 2\n",
    "pos = (1000, 500)\n",
    "\n",
    "\n",
    "dog = DogSimulation(0, velocity=movement, measurement_variance=sensor_variance) \n",
    "zs = []\n",
    "ps = []\n",
    "\n",
    "for i in range(1000):\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
    "    \n",
    "    dog.move()\n",
    "    Z = dog.sense_position()\n",
    "    zs.append(Z)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "\n",
    "bp.plot_measurements(zs, lw=1)\n",
    "bp.plot_filter(ps)\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
    "\n",
    "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30000\n",
    "movement_variance = 2\n",
    "pos = None\n",
    "\n",
    "dog = DogSimulation(0, velocity=movement, measurement_variance=sensor_variance)\n",
    "\n",
    "zs = []\n",
    "ps = []\n",
    "\n",
    "for i in range(1000):\n",
    "    dog.move()\n",
    "    Z = dog.sense_position()\n",
    "    zs.append(Z)\n",
    "    if pos == None:\n",
    "        pos = (Z, 500)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
    "\n",
    "bp.plot_measurements(zs, lw=1)\n",
    "bp.plot_filter(ps)\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n",
    "\n",
    "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers,  laser range finders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: Interactive Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.html.widgets import interact, interactive, fixed\n",
    "import IPython.html.widgets as widgets\n",
    "\n",
    "\n",
    "def plot_kalman_filter(start_pos, \n",
    "                       sensor_noise, \n",
    "                       movement, \n",
    "                       movement_noise):\n",
    "    # your code goes here\n",
    "    pass\n",
    "\n",
    "interact(plot_kalman_filter,\n",
    "         start_pos=(-10, 10), \n",
    "         sensor_noise=widgets.IntSliderWidget(value=5, min=0, max=100), \n",
    "         movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
    "         movement_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_kalman_filter(start_pos, \n",
    "                       sensor_noise, \n",
    "                       movement,\n",
    "                       movement_noise):\n",
    "    n = 20\n",
    "    zs = []\n",
    "    ps = []\n",
    "    \n",
    "\n",
    "\n",
    "    dog = DogSimulation(start_pos, velocity=movement, measurement_variance=sensor_noise)\n",
    "    random.seed(303)\n",
    "    pos = (0., 1000.) # mean and variance\n",
    "    dog.movement_noise = movement_noise\n",
    "\n",
    "    for _ in range(n):    \n",
    "        dog.move()\n",
    "        z = dog.sense_position()\n",
    "        zs.append(z)\n",
    "\n",
    "        pos = update(pos[0], pos[1], z, sensor_noise)\n",
    "        ps.append(pos[0])\n",
    "\n",
    "        pos = predict(pos[0], pos[1], movement, movement_noise)\n",
    "\n",
    "    plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
    "    plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n",
    "    plt.legend(loc='best')\n",
    "    plt.show()\n",
    "\n",
    "interact(plot_kalman_filter,\n",
    "         start_pos=(-10, 10), \n",
    "         sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n",
    "         movement=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
    "         movement_noise=widgets.FloatSliderWidget(value=.1, min=0, max=.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise - Nonlinear Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our equations are linear:\n",
    "\n",
    "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n",
    "new\\_position &= old\\_position*measurement\\end{aligned}$$\n",
    "\n",
    "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
    "\n",
    "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n",
    "\n",
    "    Z = math.sin(i/3.) * 2\n",
    "    \n",
    "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#enter your code here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30\n",
    "movement_variance = 2\n",
    "pos = (100,500)\n",
    "\n",
    "zs, ps = [], []\n",
    "\n",
    "for i in range(100):\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
    "\n",
    "    Z = math.sin(i/3.)*2\n",
    "    zs.append(Z)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "\n",
    "plt.plot(zs, c='r', linestyle='dashed', label='input')\n",
    "plt.plot(ps, c='#004080', label='filter')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n",
    "\n",
    "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n",
    "\n",
    "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise - Noisy Nonlinear Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement the same system, but add noise to the measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#enter your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sensor_variance = 30\n",
    "movement_variance = 2\n",
    "pos = (100,500)\n",
    "\n",
    "zs, ps = [], []\n",
    "\n",
    "for i in range(100):\n",
    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
    "\n",
    "    Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
    "    zs.append(Z)\n",
    "    \n",
    "    pos = update(pos[0], pos[1], Z, sensor_variance)\n",
    "    ps.append(pos[0])\n",
    "\n",
    "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n",
    "p2, = plt.plot(ps, c='#004080', label='filter')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
    "\n",
    "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The one dimensional Kalman filter that we describe in this chapter is a special, restricted case of the more general filter. Most texts do not discuss this form of the Kalman filter at all. However, I think it is a vital stepping stone. We started the book with the g-h filter, then implemented the discrete Bayes filter, and now implemented the one dimensional Kalman filter. I have tried to show you that each of these filters use the same algorithm and reasoning. The mathematics of the Kalman filter that we will learn shortly is fairly sophisticated, and it can be difficult to understand the underlying simplicity of the filter. That sophistication comes with significant benefits: the filters we design in the next chapter will markedly outperform the filters in this chapter.\n",
    "\n",
    "This chapter takes time to assimilate. To truly understand it you will probably have to work through this chapter several times. I encourage you to change the various constants in the code and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of  the position of a dog in a hallway, the position of an aircraft in the sky, or the temperature of a chemical reaction chamber. 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 together updates your belief. \n",
    "\n",
    "Most of all, spend enough time with the **Full Description of the Algorithm** section to ensure you understand the algorithm and how it relates to the g-h filter and discrete Bayes filter. There is just one 'trick' here - selecting a value somewhere between a prediction and a measurement. Each algorithm performs that 'trick' with different math, but all use the same logic.\n",
    "\n",
    "If you understand this, you will be able to understand the generalized Kalman filter in the next chapter and the various extensions that have been make on them. If you do not fully understand this, reread this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
   ]
  }
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