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      "Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
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     "source": [
      "One Dimensional Kalman Filters"
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     "metadata": {},
     "source": [
      "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style."
     ]
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    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Tracking A Dog"
     ]
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n",
      "\n",
      "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Futhermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n",
      "\n",
      "Implementing and/or robustly modelling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. "
     ]
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     "input": [
      "from __future__ import print_function, division\n",
      "\n",
      "import numpy.random as random\n",
      "import math\n",
      "\n",
      "class DogSensor(object):\n",
      "    \n",
      "    def __init__(self, x0=0, velocity=1, noise=0.0):\n",
      "        \"\"\" x0 - initial position\n",
      "            velocity - (+=right, -=left)\n",
      "            noise - scaling factor for noise, 0== no noise\n",
      "        \"\"\"\n",
      "        self.x = x0\n",
      "        self.velocity = velocity\n",
      "        self.noise = math.sqrt(noise)\n",
      "\n",
      "    def sense(self):\n",
      "        self.x = self.x + self.velocity\n",
      "        return self.x + random.randn() * self.noise\n"
     ],
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     "source": [
      "The constructor `_init()__` initializes the DogSensor class with an initial position `x0`, velocity `vel`, and an noise scaling factor. The `sense()` function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for `sense()` you will see a call to `numpy.random.randn()`. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i in range(20):\n",
      "    print(\"%.4f\" % random.randn(),end='\\t')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-0.2093\t1.0177\t-0.1450\t-2.2557\t0.2699\t0.2095\t-0.4464\t-0.3039\t-0.4437\t-0.3667\t0.7999\t0.6447\t1.9560\t0.1862\t2.2909\t-0.3298\t0.5015\t0.4101\t1.3123\t-0.3362\t"
       ]
      }
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     "cell_type": "markdown",
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     "source": [
      "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n",
      "\n",
      "Okay, so lets look at the output of the `DogSensor` class. We will start by setting the noise to 0 to check that the class does what we think it does"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.pylab as pylab\n",
      "\n",
      "dog = DogSensor (noise=0.0)\n",
      "xs = []\n",
      "for i in range(10):\n",
      "    x = dog.sense()\n",
      "    xs.append(x)\n",
      "    print(\"%.4f\" % x, end=' '),\n",
      "plt.plot(xs)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 "
       ]
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EO52Udluffc7SeHzdUKx+cn10Th+Oq887MbatWxvb1r8aa9aXv78qr/v7++Oq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\nAAAtzYEXAICW5sALAEBL+/+lZAtqwGoXsAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa234128>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that `sense()` returns the dog's position *after* updating his position, so the first postion is 0.0 + 1, or 1.0.\n",
      "\n",
      "Now let's inject some noise in the signal."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def test_sensor(noise_scale):\n",
      "    dog = DogSensor(noise=noise_scale)\n",
      "\n",
      "    xs = []\n",
      "    for i in range(100):\n",
      "        x = dog.sense()\n",
      "        xs.append(x)\n",
      "    p1, = plt.plot(xs, c='b')\n",
      "    p2, = plt.plot([0,99],[1,100], 'r--')\n",
      "    plt.xlabel('time')\n",
      "    plt.ylabel('pos')\n",
      "    plt.ylim([0,100])\n",
      "    plt.title('noise = ' + str(noise_scale))\n",
      "    plt.legend([p1, p2], ['sensor', 'actual'], loc=2)\n",
      "    plt.show()\n",
      "    \n",
      "test_sensor(4.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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tp8SjWYsWZPXsqSRbvManM9oVKlQgPj6eW2+9FbfbzWOPPcaxY8eIjo5m7ty5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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa362748>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n",
      "\n",
      "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n",
      "\n",
      "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n",
      "\n",
      "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(100.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qeEyfHotjx5r9FoTaW78+Eh0dwP/9X4es+0+ZEotXXmnH6NHS5To7doTh3XfD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1pGW4uNRHryJREREVG8SdBCO3C8wUihvXu3hJkzXSgrk6Oa045WoZ2VpSApScGJlV8KWGBr6utF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\npOWF+cxj+wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3d7ecf8>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_sensor(0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3xlW1KgcPmujcuQytWxcwfPhxTCZvVylybmq0JWBotk6MKBdiRLnwTebt2//X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\ngv8D7tBI5OsGvIQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa353da0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply `randn()` with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution  $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. `DogSensor.__init__()` takes the square root of the noise setting so that the `noise * randn()` call properly computes the normal distribution."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Math with Gaussians"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import stats\n",
      "stats.norm_plot(23, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FD7wzkZVW7axEUoQfslMiZJdCRJLZdCSDiMhRyhvPQNdpxDVxQbJLISc1J1mL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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa3669e8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n",
      "\n",
      "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpertation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n",
      "\n",
      "Let's look at 100 sensor readings in a plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(23, 0, 5)\n",
      "xs = range(100)\n",
      "ys = []\n",
      "for i in xs:\n",
      "    ys.append(dog.sense())\n",
      "               \n",
      "plt.plot(xs,ys)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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abtNwGm+7cgp/+aNzsR4PFcI+qcgaxjJ8oELYMAxIqo6hFIerNuRx5Hywk4as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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa76bd30>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n",
      "\n",
      "\n",
      "Recall the histogram code for adding a measurement to a pre-existing belief:\n",
      "\n",
      "    def sense(pos, measure, p_hit, p_miss):\n",
      "        q = array(pos, dtype=float)\n",
      "        for i in range(len(hallway)):\n",
      "            if hallway[i] == measure:\n",
      "                q[i] = pos[i] * p_hit\n",
      "            else:\n",
      "                q[i] = pos[i] * p_miss\n",
      "         normalize(q)\n",
      "         return q\n",
      "         \n",
      "Note that the algorithm is essentially computing:\n",
      "\n",
      "    new_belief = old_belief * measurement * sensor_error\n",
      "    \n",
      "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convience. \n",
      "    \n",
      "If we are implementing this with gaussians, we might expect it to be implemented as:\n",
      "\n",
      "    new_gaussian = measurement * old_gaussian\n",
      "    \n",
      "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n",
      "$$\n",
      "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n",
      "\n",
      "In other words the result is a Gaussian with \n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n",
      "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
      "\\end{aligned}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n",
      "\n",
      "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "def multiply(mu1, sig1, mu2, sig2):\n",
      "    m = (sig1*mu2 + sig2*mu1) / (sig1+sig2)\n",
      "    s = 1. / (1./sig1 + 1./ sig2)\n",
      "    return (m,s)\n",
      "\n",
      "xs = np.arange(16, 30, 0.1)\n",
      "\n",
      "\n",
      "m1,s1 = 23, 5\n",
      "m, s = multiply(m1,s1,m1,s1)\n",
      "\n",
      "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
      "p1, = plt.plot (xs,ys)\n",
      "\n",
      "ys = [stats.gaussian(x,m,s) for x in xs]\n",
      "p2, = plt.plot (xs,ys)\n",
      "\n",
      "plt.legend([p1,p2],['original', 'multiply'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sxBBMmBqGESPd4OnlCon05rvJug49mq62o76uBQW5l3FgVwHCo30xbmIwYsYGwEUhE/Sn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\ndxcWty2znZuba1P1cNu5tg8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ZGtxvs9zZ2YVTR8ox49YYK1ZHZB/Co3zh7qnApdy+V/lz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\nwiyEEEIIIcQw/j/5tHu9tGWWPAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa78ef28>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplation is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n",
      "\n",
      "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. So the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n",
      "\n",
      "\"Measure twice, cut once\" is a useful saying and practice due to this fact!  The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n",
      "\n",
      "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.arange(16, 30, 0.1)\n",
      "\n",
      "m1,s1 = 23, 5\n",
      "m2,s2 = 25, 5\n",
      "m, s = multiply(m1,s1,m2,s2)\n",
      "\n",
      "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
      "p1, = plt.plot (xs,ys)\n",
      "\n",
      "ys = [stats.gaussian(x,m2,s2) for x in xs]\n",
      "p2, = plt.plot (xs,ys)\n",
      "\n",
      "ys = [stats.gaussian(x,m,s) for x in xs]\n",
      "p3, = plt.plot(xs,ys)\n",
      "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jupR6J23jHqSu3oauO1ZAJpOJLoeIaokzzEREDVDe0TMoupYMn/HDRZdSL3mO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SunTp3q9jCWLYl/d0n8u0di313LMv4GULAaG4V5P0xrbrfr79ThplhXq9UFnWPOhHnTpk2cO3eO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\nIYQQc5CEWQghhBBCiDn8A+JlI6Hm3vVIAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa78e4e0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n",
      "\n",
      "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24?  Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n",
      "\n",
      "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n",
      "\n",
      "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n",
      "\n",
      "One final test of your intuition. What if the two measurements are widely separated? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.arange(0, 60, 0.1)\n",
      "\n",
      "m1,s1 = 10, 5\n",
      "m2,s2 = 50, 5\n",
      "m, s = multiply(m1,s1,m2,s2)\n",
      "\n",
      "ys = [stats.gaussian(x,m1,s1) for x in xs]\n",
      "p1, = plt.plot (xs,ys)\n",
      "\n",
      "ys = [stats.gaussian(x,m2,s2) for x in xs]\n",
      "p2, = plt.plot (xs,ys)\n",
      "\n",
      "ys = [stats.gaussian(x,m,s) for x in xs]\n",
      "p3, = plt.plot(xs,ys)\n",
      "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sXbsWALB3715oNJqY13q9Xvz617/G73//ewCYvj6RexARZSIxe5iBqSOy3TBY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\n4v8DO365XXzAG7oAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa96f6d8>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n",
      "\n",
      "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Futhermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n",
      "\n",
      "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n",
      "\n",
      "$$\n",
      "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
      "$$\n",
      "\n",
      "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n",
      "\n",
      "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n",
      "\n",
      "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n",
      "$\\sigma_1^2=0$, yielding\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n",
      "\\text{or just}\\\\\n",
      "\\mu&=\\mu_1\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n",
      "\\text{or just}\\\\\n",
      "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing the Sensing Step"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n",
      "\n",
      "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the sense function for a Kalman filter:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sense(mu, sigma, measurement, measurement_sigma):\n",
      "    return multiply(mu, sigma, measurement, measurement_sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sense_dog(dog_pos, dog_sigma, measurement, measurement_sigma):\n",
      "    return multiply(dog_pos, dog_sigma, measurement, measurement_sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "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 `sense_dog()` function should make what we are doing very clear. \n",
      "\n",
      "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSensor` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at postion 2.0, not 0.0."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dog = DogSensor(velocity=0, noise=1)\n",
      "\n",
      "pos,s = 2, 5\n",
      "for i in range(20):\n",
      "    pos,s = sense(pos, s, dog.sense(), 5)\n",
      "    print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "time: 0 \tposition = 1.524 \tvariance = 2.500\n",
        "time: 1 \tposition = 0.607 \tvariance = 1.667\n",
        "time: 2 \tposition = 0.647 \tvariance = 1.250\n",
        "time: 3 \tposition = 0.667 \tvariance = 1.000\n",
        "time: 4 \tposition = 0.654 \tvariance = 0.833\n",
        "time: 5 \tposition = 0.596 \tvariance = 0.714\n",
        "time: 6 \tposition = 0.619 \tvariance = 0.625\n",
        "time: 7 \tposition = 0.662 \tvariance = 0.556\n",
        "time: 8 \tposition = 0.733 \tvariance = 0.500\n",
        "time: 9 \tposition = 0.865 \tvariance = 0.455\n",
        "time: 10 \tposition = 0.869 \tvariance = 0.417\n",
        "time: 11 \tposition = 0.826 \tvariance = 0.385\n",
        "time: 12 \tposition = 0.676 \tvariance = 0.357\n",
        "time: 13 \tposition = 0.567 \tvariance = 0.333\n",
        "time: 14 \tposition = 0.660 \tvariance = 0.312\n",
        "time: 15 \tposition = 0.712 \tvariance = 0.294\n",
        "time: 16 \tposition = 0.695 \tvariance = 0.278\n",
        "time: 17 \tposition = 0.607 \tvariance = 0.263\n",
        "time: 18 \tposition = 0.545 \tvariance = 0.250\n",
        "time: 19 \tposition = 0.582 \tvariance = 0.238\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the intial value of 5.0 to 0.238.\n",
      "\n",
      "By now the fact that we converged to a position of 0.0 should not be terribly suprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n",
      "\n",
      "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n",
      "\n",
      "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementing Updates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track nonmoving objects? The histogram used a loop of sense and update functions, and we must do the same to accomodate movement.\n",
      "\n",
      "How how do we perform the update function with gaussians? Recall the histogram method:\n",
      "\n",
      "    def update(pos, move, p_correct, p_under, p_over):\n",
      "        n = len(pos)\n",
      "        result = array(pos, dtype=float)\n",
      "        for i in range(n):\n",
      "                result[i] =  \\\n",
      "                pos[(i-move) % n]   * p_correct + \\\n",
      "                pos[(i-move-1) % n] * p_over + \\\n",
      "                pos[(i-move+1) % n] * p_under          \n",
      "        return result\n",
      "        \n",
      "                \n",
      "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n",
      "\n",
      "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n",
      "\n",
      "How is addition for gaussians performed? It turns out to be very simple:\n",
      "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n",
      "\n",
      "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n",
      "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `update()` function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n",
      "\n",
      "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n",
      "\n",
      "So, here is our implementation of the update function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def update(pos, sigma, movement, movement_sigma):\n",
      "    return (pos + movement, sigma + movement_sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What is left? Just calling these functions. The histogram did nothing more than loop over the `sense()` and `update()` functions, so let's do the same. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# assume dog is always moving 1m to the right\n",
      "movement = 1\n",
      "movement_error = 2\n",
      "sensor_error = 10\n",
      "pos = (0, 500)   # gaussian N(0,50)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(10):\n",
      "    pos = update(pos[0], pos[1], movement, movement_error)\n",
      "    print('UPDATE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n",
      "    \n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "    \n",
      "    print('SENSE:  %.4f,\\t%.4f' % (pos[0], pos[1]))\n",
      "    print()\n",
      "    \n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "UPDATE: 1.0000,\t502.0000\n",
        "SENSE:  0.8308,\t9.8047\n",
        "\n",
        "UPDATE: 1.8308,\t11.8047\n",
        "SENSE:  3.0009,\t5.4138\n",
        "\n",
        "UPDATE: 4.0009,\t7.4138\n",
        "SENSE:  4.1303,\t4.2574\n",
        "\n",
        "UPDATE: 5.1303,\t6.2574\n",
        "SENSE:  4.0626,\t3.8490\n",
        "\n",
        "UPDATE: 5.0626,\t5.8490\n",
        "SENSE:  4.5662,\t3.6904\n",
        "\n",
        "UPDATE: 5.5662,\t5.6904\n",
        "SENSE:  5.1264,\t3.6267\n",
        "\n",
        "UPDATE: 6.1264,\t5.6267\n",
        "SENSE:  7.5146,\t3.6007\n",
        "\n",
        "UPDATE: 8.5146,\t5.6007\n",
        "SENSE:  6.9139,\t3.5900\n",
        "\n",
        "UPDATE: 7.9139,\t5.5900\n",
        "SENSE:  6.8968,\t3.5856\n",
        "\n",
        "UPDATE: 7.8968,\t5.5856\n",
        "SENSE:  9.1777,\t3.5838\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kqYDRaESxYsWULoOIiIj8TFi3brC3bw/b88/n+70iM7y6ghZWUAaDgV9qIiIiIiIAgObc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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa6fb7b8>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n",
      "\n",
      "    movement = 1 \n",
      "    movement_error = 2\n",
      "    \n",
      "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the `update()` step.\n",
      "\n",
      "For now let's walk through the code and output bit by bit.\n",
      "\n",
      "    movement = 1\n",
      "    movement_error = 2\n",
      "    sensor_error = 10\n",
      "    pos = (0, 500)   # gaussian N(0,500)\n",
      "    \n",
      "  \n",
      "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we initialize the RFID simulator with\n",
      "\n",
      "    dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
      "\n",
      "It may seem very 'convienent' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n",
      "\n",
      "The next code allocates an array to store the output of the measurements and filtered positions. \n",
      "\n",
      "    zs = []\n",
      "    ps = []\n",
      "    \n",
      "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we just enter our `sense() ... update()` loop.\n",
      "\n",
      "    for i in range(10):\n",
      "        pos = update(pos[0], pos[1], movement, sensor_error)\n",
      "        print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
      "\n",
      "Wait, why `update()` before sense? It turns out the order does not matter once, but the first call to `,DogSensor.sense()` assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the `sense()` first.\n",
      "\n",
      "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n",
      "\n",
      "    UPDATE: 1.000 502.000\n",
      "\n",
      "What is this saying? After the update, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the update step.\n",
      "\n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    \n",
      "Here we sense the dog's position, and store it in our array so we can plot the results later.\n",
      "\n",
      "Finally we call the sense function of our filter, save the result in our *ps* array, and print the updated position belief:\n",
      "\n",
      "    pos = sense(pos[0], pos[1], Z, movement_error)\n",
      "    ps.append(pos[0])\n",
      "    print 'SENSE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n",
      "    \n",
      "Your result will be different, but I get\n",
      "\n",
      "    SENSE: 1.6279 , 9.8047\n",
      "    \n",
      "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n",
      "\n",
      "Now the software just loops, calling `update()` and `sense()` in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n",
      "\n",
      "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%precision 2\n",
      "# assume dog is always moving 1m to the right\n",
      "movement = 1\n",
      "movement_error = 2\n",
      "sensor_error = 4.5\n",
      "pos = (0, 100)   # gaussian N(0,50)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "vs = []\n",
      "\n",
      "for i in range(50):\n",
      "    pos = update(pos[0], pos[1], movement, movement_error)    \n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    vs.append(pos[1])\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "    \n",
      "#plt.subplot(121)    \n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()\n",
      "\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()\n",
      "print ([float(\"%0.4f\" % v) for v in vs])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R3nknjAULHEydmndWxe/ZOGMB7HK56Nq1Kz179uTbb7/l4MGDJCYmMn36dBYsWEBiYiIH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\nL4e77nIT/fzzOrFNREREgGtogGfPnk16ejqDBw+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dgoQh5UKMKBdiRLmQQKhRA5yUlERB\nQUHldUFBAUlJSVUe43Q6yc3NrV110uDcfvvtyoVcQbkQI8qFGFEuxIjT6azW42vUAKelpXHs2DHO\nnz+Py+Xi7NmzV4w/tG/fvia3FhEREREJqho1wHa7nezsbEaNGgXAlClTAlqUiIiIiEiwmI4cOeIP\ndREiIiIiInUlpEchi4iIiIjUNTXAIiIiIhJRarUN2k85cOAAmzdvxmQy0b9/f+0PHKHWr1/PF198\nQWxsLBMmTACUDYHCwkJWrFhBWVkZVquVjIwMbrrpJmUjwpWUlPDGG2/g9XoB6NWrF2lpacqF4HK5\nWLBgAenp6dxxxx3KhPDUU0/RpEkTAG644QYGDhxY7VwEvAH2eDxs3LiRP//5z7jdbl577TWFM0J1\n6NCBjh07smrVKkDZkApms5khQ4bQpEkTLl68yOLFi8nOzlY2IlxUVBT3338/drudkpISXnzxRdq3\nb69cCNu2baNZs2aYTCb9HBEAbDYbDz/8cOV1TXIR8BGI/Px8kpOTiY2NJTExkYSEBM6cORPol5F6\noGXLljgcjsprZUMA4uLiKn9zT0xMxOv1cvLkSWUjwlksFux2OwClpaVYLBZOnTqlXES4goICiouL\nadq0KX6/Xz9HxFBNchHwFeCioiLi4+P57LPPcDgcxMXF4XQ6SUlJCfRLST2jbMiPHTt2jKZNm1Jc\nXKxsCC6Xi8WLF3P+/HmGDx+u7xnCpk2buPPOOysPvlAmBCpWfBctWlQ5RleTXARlBhiga9euABw6\ndEjHJEsVyoZAxak9GzZsYMyYMXzzzTeAshHpoqKimDBhAgUFBSxbtow+ffoAykWkysvL47rrriMx\nMRG/v+qOrcpEZJs8eTJxcXGcPn2aN998k4yMDKB6uQh4AxwfH1/lOLrLXbmIsiGXud1uVqxYQf/+\n/WncuDFOp1PZkEpJSUkkJiaSmJioXESw/Px8Dh8+TF5eHsXFxZhMJrp166ZMCHFxcQA0a9aMRo0a\n1eh7RcAb4GbNmnHu3DmKi4txu90UFhZWzvtJZFM2BMDv97Nq1So6duxIamoqoGxIxe4gVqsVh8OB\n0+nku+++4/rrr1cuIljfvn3p27cvAFu2bCEqKoru3buzYMECZSKClZaWYrVasdlsXLhwoTID1f1e\nEZST4C5vRQFw55130rZt20C/hNQDa9eu5fDhw5SUlBAbG8uQIUNwu93KRoQ7ceIEr7/+OsnJyZVf\nu+eeezhx4oSyEcFOnTrFe++9V3ndu3fvKtuggXIRyS43wOnp6cpEhDt58iSrVq3CarViMpnIyMgg\nNTW12rnQUcgiIiIiElF0EpyIiIiIRBQ1wCIiIiISUdQAi4iIiEhEUQMsIiIiIhFFDbCIiIiIRBQ1\nwCIiIiISUdQAi4iIiEhEUQMsIiIiIhHl/wP4/6Zy2vjzcwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa96d828>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ATPNdKc7JYlIcNOyCwUIuYCEXsJALuMF3pZhJMQAAADLNf6U4wiXZgoZdMFjI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\nAACB9/8BRDi4tembSfcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa992f98>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literatue, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\""
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Relationship to the g-h Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n",
      "\n",
      "The equation for our estimate is:\n",
      "\n",
      "$$\n",
      "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n",
      "$$\n",
      "\n",
      "which I will make more friendly for our eyes as:\n",
      "\n",
      "$$\n",
      "\\mu_{x'}=\\frac{ya + xb} {a+b}\n",
      "$$\n",
      "\n",
      "We can easily put this into the g-h form with the following algebra\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n",
      "\\mu_{x'}&=x-\\frac{a+b}{a+b}x  + \\frac{ya + xb} {a+b} \\\\ \n",
      "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n",
      "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b}  \\\\\n",
      "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "We are almost done, but recall that the variance of estimate is given by \n",
      "\n",
      "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} +  \\frac{1}{\\sigma_2^2}}\\\\\n",
      "= \\frac{1}{ \\frac{1}{a} +  \\frac{1}{b}}\n",
      "$$\n",
      "\n",
      "We can incorporate that term into our equation above by observing that\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n",
      " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n",
      " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n",
      " &= \\frac{\\sigma^2_{x'}}{b}\n",
      " \\end{aligned}\n",
      "$$\n",
      "\n",
      "We can tie all of this together with\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n",
      "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n",
      "&= x + g_n(y-x)\\\\\n",
      "\\blacksquare\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "where\n",
      "\n",
      "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n",
      "\n",
      "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n",
      "\n",
      "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n",
      "\n",
      "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#####Excercise:\n",
      "Modify the values of `movement_error` and `sensor_error` and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n",
      "\n",
      "    movement_error = 40\n",
      "    sensor_error = 2\n",
      "    \n",
      "or:\n",
      "\n",
      "    movement_error = 2\n",
      "    sensor_error = 40  "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction to Designing a Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equiped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n",
      "\n",
      "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "temp_variance = 2.13**2\n",
      "def volt():\n",
      "    return random.randn()*temp_variance + 16.3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We generate white noise with a given variance using the equation `random.randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n",
      "\n",
      "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performace will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n",
      "\n",
      "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatibility is nearly 0.0% at low temperatures, and always nearly  +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n",
      "\n",
      "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `sense()` function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n",
      "\n",
      "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = temp_variance\n",
      "movement_error = 0\n",
      "movement = 0\n",
      "voltage = (25,1000) #who knows what the first value is?\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "vs = []\n",
      "N=50\n",
      "\n",
      "for i in range(N):\n",
      "    Z = volt()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n",
      "    ps.append(voltage[0])\n",
      "    vs.append(voltage[1])\n",
      "\n",
      "    voltage = update(voltage[0], voltage[1], movement, movement_error)\n",
      "\n",
      "plt.scatter(range(N), zs, marker='+')\n",
      "p1, = plt.plot(ps, c='g')\n",
      "plt.legend([p1], ['filter'], 3)\n",
      "plt.xlim((0,N));plt.ylim((0,30))\n",
      "plt.show()\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()\n",
      "print('Variance converges to',vs[-1])\n",
      "print('Last voltage is',voltage[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YxLYTp2LPb5RwuVx64eAL+re//psmZU7SS199SeMzxvv1mpMzJ+vZBc9qb9Ve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\nuueee7wa4MZ3NurbF3+bwhc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DZxnyAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa36da58>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gTz3DnNUtVsxWwYRcwIRcwIRcwAkZKbpS/KwuX0gDAACAWzJXdLmWblFjtgom5AIm5AIm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\nnTlmpnIRs+MlOFWco7YiibP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       "text": [
        "<matplotlib.figure.Figure at 0xa986f98>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Variance converges to 0.0907297673624\n",
        "Last voltage is 16.3277712404\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n",
      "\n",
      "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n",
      "\n",
      "##### Exercise(optional):\n",
      "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n",
      "\n",
      "> use plt.hist(data,bins=100) to plot the histogram. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Solution\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = temp_variance\n",
      "\n",
      "def VKF():\n",
      "    voltage=(14,1000)\n",
      "    for i in range(N):\n",
      "        Z = volt()\n",
      "        voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n",
      "    return voltage[0]\n",
      "\n",
      "vs = []\n",
      "for i in range (10000):\n",
      "    vs.append (VKF())\n",
      "plt.hist(vs, bins=100)   \n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jKIZr9FWZjfwAIH6cO+1BUQwAAADrURTDNfqqzEZ+ABA/zp32oCgGAACA9Vin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\noygGAACA9SiKAQAAYD2KYgAAAFjv/wPyHcSrvv9pAwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa714b00>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Discussion\n",
      "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Explaining the Results - Multi-Sensor Fusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focussed all of our attention on the position sensor. Let's change focus and see how the filter performs if the intertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30\n",
      "movement_sensor = 30\n",
      "pos = (0,500)\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "vs = []\n",
      "\n",
      "for i in range(100):\n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "    vs.append(pos[1])\n",
      "\n",
      "    pos = update(pos[0], pos[1], movement+ random.randn(), movement_error)\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()\n",
      "plt.plot(vs)\n",
      "plt.title('Variance')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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d7v+JwNhs4AVaTUuBxkXo2B55BLYHHvB53LFjLEwmBjfeqJwt3aQeF48/bsXc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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa96a7b8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pO6tG0BoBAAAAh+FhOWQVvV0wIRcwIRcwIRewEw/LAQAAIC9l6WE5CmHE0NsFE3IBE3IB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\nACAvUQgDAAAgL1EIAwAAIC/9f66CKC7iPIfWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1520ce10>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distintly jagged. But, it still mostly tracks the dog. What is happening here?\n",
      "\n",
      "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43.  From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n",
      "\n",
      "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n",
      "\n",
      "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematicall model this sort of reasoning."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More examples"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Extreme Amounts of Noise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intution tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30000\n",
      "movement_error = 2\n",
      "pos = (0,500)\n",
      "\n",
      "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(1000):\n",
      "    pos = update(pos[0], pos[1], movement, movement_error)\n",
      "    \n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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F+/jx4wCAyy+/3L+N53kMGjQo4LhmzZrFXrg4Q3zlCGokrF9QFKgU/hDElCTIdJHy4wWZ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Xwcx5YtyHzpJbS/9pruMWX+5CdAIICuZct0H2sw29krQYkkZ/Fi+ObNg/+mmyK/5o474Fuw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\nIiJB/h9bb34+caO4SQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa963f98>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Bad Initial Estimate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30\n",
      "movement_error = 2\n",
      "pos = (1000,500)\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(100):\n",
      "    pos = update(pos[0], pos[1], movement, movement_error)\n",
      "    \n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yb0RERERUt3CradKE0s31RCWYCxJhLkiEuSAlcQaZiIiIiKgUFsikCbzzmESYCxJhLkiE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       "text": [
        "<matplotlib.figure.Figure at 0xa977080>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example: Large Noise and Bad Initial Estimate"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What about the worst of both worlds, large noise and a bad initial estimate?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30000\n",
      "movement_error = 2\n",
      "pos = (1000,500)\n",
      "\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(1000):\n",
      "    pos = update (pos[0], pos[1], movement, movement_error)\n",
      "    \n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense (pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2VOwYpPax3Hkn+GbNIt0MQgCLBerNm2Ht2zcsh2MLCsD+/ntYjkVINFLv3g3N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Dp2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\nat4cZuvWsCKRYOMPSSLqHs2bo+T00xF96KG8MgB+zxSH8P2cHEc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5ZgHHJnLZjL59PVJC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       "text": [
        "<matplotlib.figure.Figure at 0xa7718d0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n",
      "\n",
      "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30000\n",
      "movement_error = 2\n",
      "pos = None\n",
      "\n",
      "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "for i in range(1000):\n",
      "    Z = dog.sense()\n",
      "    zs.append(Z)\n",
      "    if pos == None:\n",
      "        pos = (Z, 500)\n",
      "    \n",
      "    pos = sense (pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "    pos = update (pos[0], pos[1], movement, movement_error)\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dUiI62HBNm6ovnFLTyyQyAyDFsoqqVsUNnk6vwE+dLihAysCBkvuZvXtFy4VS\nFy/Wrowm8YjWuYvlFAmlCprW1roYgW/UCOxVV+kthizmzz/XvbSvUpL/9a9qK6xatFQ0PW3poET7\nBXp5xlKdlehLfbLsC3vVVQDPI2nkSNDHj+stjmLM8+YF9dWEp58WzR8ti6cfaJR0IaaUaF6FxSFh\n6lQkvPpqtc+VD4bff1enkEPIJxu0zWwGqzYwL4pKNH30KKjTpxUfX/XMM9oFaOmEn4+j5wHy/K2q\nkqzgSJ05A4OM35MxPx/MoUNB21Ouu+6SWDqOeUIo0Yp9X0MUnTCuXy9EfYcgo3FjGBQEasUbzKZN\nMe8rSjkcwuRWAXr7RNNnzoAOyGWrFLZtW7i6dtVEDq55c+EfJQpyQoIm1/TAtmwJh8fKyXHgGjWC\ns39/Ta+hlsNHjuiuyMcK5T/9BJjNYI4cAVQUb9MVnhcNgDVs3qxex/H469dGJRoGg7KZM3zKfosM\nEqYff1R+Tc/5YmlSwqnLHsUKYOZ582D64Qf/jTLXYvbsgXHt2qjIogue38pt3Ujr1g1pEv5QiqwO\nIscwBQWgjx4NW0RC5LBt22o2EeVD+PxaXn8dlR9/rKgt7xJ1LSJh+nQwe/fqLUatgpKY2IfC1aOH\nJvUNAIDPzASfkBBSieYTE1Hx2WeaXNMLy3qfX65JE1R8/rn+qdRqW80ELYiDoGIvHCcEygbqO+Hq\naCBKdPUDEelSFM9Llnl23H03rK+/rqo556BB4Fq2jEwmMXgextWrg7+v3PevBQOHn4+j54H3+NmV\nlYFWaKESQ8rVxbB+fdhtEiKHKikBfeqU7DFKfV8pnpdcrQCgLvi2Nrp0xEHZbwBw3HKLouP09omO\nBPuDD8Jx663aNahASar47DPNLdHg+epYnKSkmHAXurx9e/A1UagrxqEKC8Fs3+7+EPtBxV44TjCM\nBaYiDmf88jwTGo17saVEM4xyJVrGEq0KuZmMREVEOajychg1yvXpB8eBOXYs6PtWvfgiKufNEz9H\nruy3wwGqpERbGaON+7s77rpLm/ak/MXjQKmo1Wg4uBt/+klYtpRCoSXDNnYsnDI+9nFLHCjRXP36\n1e4JtRiuRQvwWmZMUPAcuW68Ufvg84QEcFlZ2rYZIVyjRnDedpveYuiOYds2WGbOBL1/P6jCQr3F\nUY5b8Q10taTPnAGzb5+6tngerm7dNKsHEVtKdGUlKKWWUxlLNFe/PpxKLRJav0Rstuj4IXu+Z4Bl\nwXnTTXBQ8f78AAAgAElEQVQMHy5+jkzWEdPXXyO9ZcuYd13w9XHkGzVCydmzmg2Grm7dNGmHoDEK\nLGhKfV/ZnBw45AoU8bwi15GqWbPAqU2lFAcYduyAZfZsvcWQR0Wcid4+0QBiJq2o7dFHdXGjcObm\nourVV2v8unKcWbCArDAC3mfJ8uaboIuLZeNFYgX60CEhqBAI0vfokhKY33tPVXtst24o//ZbrcSL\nLSWabd8efEaGsoMNBri6dAGfmBi0i09Ph+POO5W1Q9OwPfWU6C6qsBBJo0cra8d7UpSWSMLIt8kz\njPSkxN0Os39/pJLVHBTl/1KQmfywIUp3c1lZ0uWOdbTMMZs2XZKp95Jvuql6qU7LZ4jn5VeTwvGp\nq0VQVqt0iswYwT52rOg4H4uwbdqAS0vTWwwAgG3SpKAyyTVCWRkMGzfW/HVloOKxQl80YFkwu3eD\nstlQNWlSXKT9o8+cgemnn4QPAcYV+5gx4Jo2Vdcgw2jqwhRTSrSal5n13XdR/ssvQEpK0D5nv35C\ncBIA8DzS5JYCGQZsTo64a4PLBcO2bYpl8hINJdrdJtewoeJTEt54A6zEd3deey3YZs1iPrBAzsdR\nLKOKd19mpmxJ8LK1a8GLZGWwjR0LPkS1PC9WK6gLF5Qdq5CEV16Bef58TduMBww7dlS7aCkogKLY\n9zWEFdN1ww2qMt7UNlwdOoCPEaVPCtukSYDC3Pt6+0RXLFwILkzFhN63D4bff9dEDnrvXljmzAl9\nIMsCZWWaXNMDc+wYEp55xvs58YknYJQreFQDNGncOEiJThw3DozMO6JWwnFgTp4Edf482Jwc7f3h\nowFNg2cYsK1aBekrrquvBp+UpJNgArGlRGsUke8cOhRsly7CB5YFHWKQSJg1C9TZs+LyqA3Mi5Yl\nmufBm81w3n674uMB4V6I7m7cGK7u3eOu9KcvpX/9hdKtW8V3MoxsSXC+USNRywTbpYtQXlQBxp9/\nRqLEKka4GNevh+GPPzRtU08MSrPD+LgeMdu3a2c1CuGuYX3pJaQoXbWqhVRNmya8TAmawDVvDshM\n7uUwbNkCk0bVWOmzZ2FQ4NpCHzqE1Btv1OSaXnzegfTevTDPnw8qMCCshqFYNqgMunnZMiFY/1LC\nE5TvctV4PQsq3PLynneDmHElBoIjY0uDisaPGphbWOK6YinRzB9+CFql873p++9BFxSoOkcRFKUu\n16YnJYycAjFvHpy5uRoIFz1kfRxTU8G1aKHp9RwjRsB1ww3KDo5WyegYXx1QTFkZUpRM+ux2UBUV\n1c9gcnJIa54a31dezi80ntI8RYMYeAmFwrhsGUz/+5+iY2PCJzpMLHPmwLhmjTaNKfEjr6oSSmEr\nDeZXiq8S7SmSo/MzdvrYsSBF3nnNNXD17KmTRPrgXWWtaSXa5UJahw5hncpTFCiWBduiRbBrXpjj\nF338uGb1IGJLiY6GbyLPgzcaZdvmJbJYhFXhiKK0yx7hi9mMyi+/DNpsefllpIgtYdaCkt9i0CdO\nwPzJJ3qLIRAtBexSU+oCUhfKpZ1Ui/P222F9/33pAxROhFIGDYJl+nRNZIopojUR1BDmn39AHz6s\n/PhNm+Ir84Ab5vhx7eRWEDBLORzKS4OroaICtMfNLfDZFsEyfbrmLiWBMHY7zIH5sC/BeAhXr15g\nmzUDm5Oj3G1RCyIoQkdxHKiyMlQuWAAuYNWMa9Cg2nVXBczeveorHUoQU0o0n5amiQJBFRYKJcEB\nZQ+KTBYLtfAWC3gRP+1oYfrhBxjEiiWoyX8bw/j6ONJHjyKtUyeYFi+OuN2EF18Es2lTZI1EaSZ/\nyZWnDSznriBjjlLfV7qgAKke1y7RA2hFz75h82YYNm9WdM14gm3bFlUilcBiChXWpt69eyM1NxcJ\n06ZFVyYJmJ07I8vNr5FSR7EsjL/8AshlinLLSWmsRJv/9z/QnqV7BWW/LXPnRl2ZrTN6dHA1SIWZ\neWodNA3bpEk1a4XnOFAOB+BwqD6V3r8fzIEDovtcffrA/vjjqtoz/PEHzPPnw3XddaplESOmehB9\n+jRopdkiKithfvttUJ7lIh+osrJqRctkQpmcsmS3CyXCRQY+PjFReao8D1Es+62K2miJVpGhhNm9\nG8lSqf8A0AcOgBYJJqVKShRPqJidO2FYt07RsUrh6tbVrPSv7qSkoNST2F8O9/32BrhpbRmVUxIU\nKtEAQNXCYit83bpgr75abzFkMc+dq8qn1tm3r3TazyiTkpsbWSllrZRJj++rnBLteS7CrLAohV8m\nlVBjtsMh3C+FgaNhI/Kcu66/PubyWdcEbPv2gMkkBFbu2VMzF/Xc+zCeDb5uXThvuAGmL74I2pc4\nfrz6wHCXKyxlXooY0Paq4Q0GxXmik0eNQuK0aaJKtPGnn6pL9NK0fKJ+9+AslqkBNC0E36khiko0\nXVCg3I8nMRGVc+aA2b1bdLchLw/mjz7SULro4OfjGFD2G1VV0i8Aq1Xav9Buh+nnn0WVp9QuXUT7\nlBiGLVuqff40wvbUU7A9+KCmbeoGRSlLaM/zwuqNx99NgSVase8rRcnmQjXm5YFr0kRZW5EoRyLQ\ne/fC+PPPmrapFsP69aAiqPqpCpcLTBjp9OjiYsWKXn5+PiirVSh5rQNUVVXYZdTZJk3gVBqPEQJX\np07CP3ITUpYFbzaHnz7QbhddEucaNYLtP//xXsPVowccI0eKNkFdvAg+PT3qlui9+/cHjfe2p58G\nFyIVam2k8vPPwTVtKuhI0ahpIYZn1SOcVVaOA1VejoQZM4J2GTZuVB+0qnFtkJhSolWV/ZYJGFQb\n4cwnJ4sr2mH4TFEcF9Kfkzp5MqzZv+nLL5W7MhgMoEtKYPr8c9HdzIkTQnofDWdkUSeg4Exat25I\nC6cAhky1S7q0FLTE0lFQM336oGriRPXXl8E+blzMWwa1hvIEwbpx9ewJqqJCk7b5EK4AiY8/jvJV\nqxS1RWmsRBt274bxm280bVMtCc8/D9pjcIgyVHk5UgcMiP6FrFZAx7RX4WaiYDt1klQ21cI3bgyu\nfv3QSnRmJsrCTPNmeeMNpIkVrGJZryGJ7dIF1tdfl8xXTZWUKK8NEQE8RQUpcNTp00B5edSvHbPo\nEVQcjquT53cTM06G49eusRtPbCnRasp+y2XdCNiWfMcdwsAqAsXzQalvPNgmThRylKrAMWwY+BC5\nnFOGDAF98qSqduF0wrh2rabFVsyLFsG0aJE6OTTG/PHHgIzC5Of7Gli1sbISdBhWNCpEyXjFEfK1\n0WVGB/i0NJTu2lW9wW4Hc/Cg7DlKfaIpjpMfUwIGVOriRWmLs8buHDzD6O//XoNlvyPJWuRQWPSq\nd+/eoKqqdLNEAwj7flY99xxcvXppK4dM/+IzM1GpstqbX/NSwYA87x0X+YwMsO3aSbdRUiJYoqNM\n286dwQco8olPPw2jzulEjcuXaz6uyEGdPAnas1JSk0HFqang6tYNT4n2ZHo5fTpYjwtn/Kr1lmil\nN1mFf6xh82bpF6ncTMZgkK92JgKfmBg6e0QYQX9URYVQ+CXg+1Y98wwqAqOOPcjluQ6jAmIkUOfP\ni25PnDRJ0uUkCJ4Hl5kJ+7h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XrJloTlDFSEwuzO+8I2tl6t27t6A4u1zCd/f9TjYbaE8A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\nag44ANKWLYjNn4/UDTdUTOUXZXZVFVWnTj3VffYREEJtxgzEZs8uSS0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r9pn6zTc8aVB1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dasIBRP11E866zyzEOKAmO//ZBjHfP+zc75v1UBK0q7VIo+H7Lmxx97DNorr6BYISUXM+nXX6EJ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6cmLjufCl5v2mW/Q9OmySFRqjNu+HAIRx2FOpNn/eCBAxDVvitICewDgzFsZURb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\nULBCvakE38kAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa23b518>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n",
      "\n",
      "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers,  laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise: Interactive Plots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.html.widgets import interact, interactive, fixed\n",
      "import IPython.html.widgets as widgets\n",
      "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n",
      "    # your code goes here\n",
      "    pass\n",
      "\n",
      "interact(plot_kalman_filter,\n",
      "         start_pos=(-10,10), \n",
      "         sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n",
      "         movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n",
      "         movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n",
      "         noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<function __main__.plot_kalman_filter>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Solution\n",
      "One possible solution follows."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "zs = np.zeros(100)\n",
      "ps = np.zeros(100)\n",
      "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n",
      "    dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n",
      "    random.seed(303)\n",
      "    pos = (0,100)\n",
      "\n",
      "    for i in range(100):\n",
      "        Z = dog.sense() + random.randn()*noise_scale\n",
      "        zs[i] = Z\n",
      "\n",
      "        pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "        ps[i] = pos[0]\n",
      "\n",
      "        pos = update(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n",
      "\n",
      "    p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "    p2, = plt.plot(ps, c='b')\n",
      "    plt.legend([p1,p2], ['measurement', 'filter'], 2)\n",
      "    plt.show()\n",
      "\n",
      "interact(plot_kalman_filter,\n",
      "         start_pos=(-10,10), \n",
      "         sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n",
      "         movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n",
      "         movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n",
      "         noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QExMDpBfGtWvXpmHDhjidTvbu3YvJZMoops6dO5dxnLYL57ZhGJQpUwaHw5HxE37Dhg0B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\ngrN796DoL86N1q3dVK+eSI8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ybvduXD175lNwRUtQ5YUEDeWFBJJGkEWkQPl88PbbIUyd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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa79b048>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<function __main__.plot_kalman_filter>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise - Nonlinear Systems"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our equations are linear: \n",
      "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n",
      "new\\_position &= old\\_position*measurement\\end{aligned}$$\n",
      "\n",
      "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
      "\n",
      "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n",
      "\n",
      "    Z = math.sin(i/3.) * 2\n",
      "    \n",
      "Adust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#enter your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30\n",
      "movement_error = 2\n",
      "pos = (100,500)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "\n",
      "for i in range(100):\n",
      "    pos = update(pos[0], pos[1], movement, movement_error)\n",
      "\n",
      "    Z = math.sin(i/3.)*2\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['input', 'filter'], 2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+ppX28LM6n/P+Oy0tDQAwbNgw+ENITU0tvku3CB9++CFiYmIwZMiQAj9PT09H/fr18z9X\nrZqAH3/MQMmSAZ2OiIiIiKiAAwcOoEqVKj7vp1i9AuuECSj4JEeUh3FBUhgXJIVxQXIyBHqAMWPG\neLUdZ44gIiIiIi1RrEeYcwkTULDGiygP44KkMC5ICuOC5KRYIhwfz0SYiIiIiLRD0RphlkYQa7tI\nCuOCpDAuSArjguTE0ggiIiIiikiK9ghnZDARjnSs7SIpjAuSwrggKYwLkhNLI4iIiIgoIrE0ghTF\n2i6SwrggKYwLksK4IDkp2CPsxrVrip2OiIiIiKhIik6fxtIIYm0XSWFckBTGBUlhXJCcWBpBRERE\nRBGJs0aQoljbRVIYFySFcUFSGBckJ0V7hFkaQURERERaIaSmporBOHB6ejrq16+f/1kUgQoVSuCv\nv67CYgnGGYmIiIgoEh04cABVqlTxeT/FeoQFgeURRERERKQdis5nxvIIYm0XSWFckBTGBUlhXJCc\nFE2E4+M5cwQRERERaYOiiXBCAhPhSMf5H0kK44KkMC5ICuOC5KR4aQQTYSIiIiLSAvYIk6JY20VS\nGBckhXFBUhgXJCeFE2E3rl5V9JRERERERJJYGkGKYm0XSWFckBTGBUlhXJCcOGsEEREREUUkxWuE\nOY9wZGNtF0lhXJAUxgVJYVyQnFgaQUREREQRSfEeYS6xHNlY20VSGBckhXFBUhgXJCeWRhARERFR\nRGJpBCmKtV0khXFBUhgXJIVxQXJSfNaIjAwBoqjkWYmIiIiIbqVoImw0AhYLkJWl5FlJS1jbRVIY\nFySFcUFSGBckJ8WXeeNcwkRERESkBYonwpw5IrKxtoukMC5ICuOCpDAuSE6KJ8IlSrhx9aripyUi\nIiIiKkDxjLRqVTd+/ZWJcKRibRdJYVyQFMYFSWFckJz8ykivXLmCpKQk9OjRA927d8e6deu83rdR\nIyf27jX4c1oiIiIiItn4lQjHxcVhwYIFWL16NebNm4fJkyfD7XZ7tW/jxk7s28dEOFKxtoukMC5I\nCuOCpDAuSE5+JcIGgwFRUVEAgIyMDJhMJq/3rVbNjdxcAadOccAcEREREanH767Z7Oxs9O/fH2lp\naXjnnXeg03mXUwuCpzxi3z4DKld2+Ht6ClGs7SIpjAuSwrggKYwLkpPfo9ZiYmKwdu1arFixAtOm\nTUNOTo7X+zZs6MT+/SyPICIiIiL1BJyNVqtWDRUrVsQff/yB2rVrF/hu1KhRSExMBAAkJCSgdu3a\naN68ORo3dmLkSBHJycn5T3Z5NT/8HN6f836mlfbwszY+f/LJJ/nXBy20h5+18TnvZ1ppDz9r4zOv\nF/ycJzk5GWlpaQCAYcOGwR9Camqq6OtO586dg8lkQsmSJXHhwgUkJSVh9erVKFmyZP426enpqF+/\nvuT+djtQrVoJHD16FfHxfrWbQlRy8j8PP0R5GBckhXFBUhgXJOXAgQOoUqWKz/sZ/DnZmTNn8PLL\nL+d/fv755wskwcUxmYA6dZz44QcDWrd2+tMEClG8eJEUxgVJYVyQFMYFycmvRLhu3bpYu3ZtQCfO\nGzDHRJiIiIiI1KDaEm+cTzgy3VjbQ5SHcUFSGBckhXFBclItEb7/fhcOHDDAwRnUiIiIiEgFqiXC\nJUqIqFLFjSNH9Go1gVTA2i6SwrggKYwLksK4IDmplggD/9QJExEREREpTdVEuHFjJ/buZSIcSVjb\nRVIYFySFcUFSGBckJ030CIs+z2RMRERERBQYVRPhxEQ3dDrg5ElVm0EKYm0XSWFckBTGBUlhXJCc\nVM1ABQFo2JDlEURERESkPNW7YjmfcGRhbRdJYVyQFMYFSWFckJxUT4QbNWKPMBEREREpT0hNTQ3K\nULX09HTUr1+/2O2cTqBq1RI4fPgaSpbkqDkiIiIi8s2BAwdQpUoVn/dTvUfYYADuu8+J/fvZK0xE\nREREylE9EQbyplHjCnORgLVdJIVxQVIYFySFcUFy0kQizIU1iIiIiEhpqtcIA0BmJlCjRgn8/vtV\nmM3BaA0RERERhauQrREGgLg4oHp1Fw4dYnkEERERESlDE4kw8M9yyxTeWNtFUhgXJIVxQVIYFyQn\nJsJEREREFJE0USMMAKdPC2jRIh6HDl1DXFwwWkRERERE4Sika4QBoGJFEZ06OfDSS9FqN4WIiIiI\nIoBmEmEAmDo1Bzt3GrB+vVHtplCQsLaLpDAuSArjgqQwLkhOmkqE4+KATz7Jxvjx0Th/XlC7OURE\nREQUxjRTI3yjyZMtOHZMj0WLsiEwHyYiIiKiIoR8jfCNnnvOirNndZg3z6R2U4iIiIgoTGkyETaZ\nPCUSb7wRhT/+0GQTyU+s7SIpjAuSwrggKYwLkpNms8x77nHj2WetGDkyBk6n2q0hIiIionCjyRrh\nPG430KdPLBo3dmLiRKtMLSMiIiKicBJWNcJ5dDrgww+z8cUXZvzwg17t5hARERFRGNF0Igx4Ftp4\n550c9OsXi6eeisZvv2m+yVQE1naRFMYFSWFckBTGBckpJLLKrl0d2L8/AxUquNG1axweeSQGe/ey\nh5iIiIiI/KfpGmEpOTnA4sVmfPSRGbfdJmLsWCs6dnTAYJD9VEREREQUAsKyRlhKdDQwdKgN33+f\ngVGjrPjgAwuqVi2BpKRYvP22BSkpBuTmqt1KIiIiItK6kEuE8+j1QI8eDmzcmIlDh65h6FAbrl0T\n8OqrUbjrrhLo2DEOb7xh4TzEGsPaLpLCuCApjAuSwrggOfldUHDu3DmMGzcOmZmZMJlMmDBhApo2\nbSpn27xWqpSIzp0d6NzZAQDIzgZ++MGAbduM6NQpDvXrOzFihA2tWjm5ZDMRERERAQigRvjSpUu4\nePEi7r77bpw+fRr9+/fHzp07878PVo2wr3JzgeXLTfj0UzMcDgEjRljx0EN2xMSo3TIiIiIikoPi\nNcKlS5fG3XffDQCoWLEiHA4HHA6Hv4cLmqgo4NFH7di5MxNvv52D7duNqFMnAdOmWeB2q906IiIi\nIlKLLAW0u3btQs2aNWE0GuU4XFAIAtC8uRPz52djy5ZMJCcbMHhwDHJy1G5ZZGFtF0lhXJAUxgVJ\nYVyQnAKedOzChQuYPn06Pv7441u+GzVqFBITEwEACQkJqF27Npo3bw7gn0BW4/Ptt7sxfvxGzJhR\nB927l8fixVlITd2lWnsi6XOeoJ2vYUMIFy/i0LZtyKxcGc1bttTUn5+fpT///PPPPm2fsn07Sh89\nihqtWsFdpQqSDx/W1J+Hn0PkesHPIfW5ZXw8YgYNQg2TCT+NGYN/P/aYptrHz8pfH5KTk5GWlgYA\nGDZsGPwR0DzCNpsNQ4YMwahRo/IbmEfRGmG7HYa9e2HcuBHuSpVge+IJr3YTRWDqVAuWLTPhq6+y\ncNddrJUIZZYpU2B5/32IpUsDggB7167InT5d7WZREEQ/8wwMu3YBOh10p04he8YMOHr1UrtZpILo\n8ePhvu022Hv0gPvee8ER0eHJ+M03iH76aeS8+SZ0ly7B8u67yPr6a7j+/W+1m0bBlJEBxMV59Xut\neI2wKIp44YUX0LVr11uSYCVZ3n0XCXfdhajXX4cYFwfH9R7AG+n+/BPIyrrl54IATJpkxTPPWNGt\nWxx27zYo0WQKEuuECbh69iyu/fILMvbsgXHrVpiWLFG7WSQz09y5MKSkIGPzZmTs3Yur6elwdO+u\ndrMoyISrVyFcu3bLz20PPwwhKwtxDz2E+MaNYZo/X4XWUVC53TCtWIGspUvhSEqCbcQIXPvhB7hq\n11a7ZRQsogjjsmVIaNQI+utv/ILF70T4xx9/xMaNG/H111+jZ8+e6NmzJy5cuCBn24qlP3gQ5s8+\nQ0ZyMjI3b4b1uefgrlHjlu3Mc+Yg9rHHAJtN8jiPPGLHZ59lY/DgGCxbpt0653Bw8ytPv4gihPPn\nb/252QzoPCEtJiQga/58iCZT4OejoPMlLoSrV5G1YAEQH3/9B4JnYvGb6P74Q67mkUry4yIjA7F9\n+sC0aNEt27juvx+5U6bg2k8/IXvGDERNngzdsWMKt5SCSqdD9uzZcNWtC+B6XMTGsvc/TOlOnkRs\n376wvPcesr78Mv/fPVj87gJt0KABjhw5ImdbfKY7cwY5//0vxMqVi9wu99VXETNsGGKGD0f27NmQ\nWo+5ZUsnVq3KxMMPxyInR8DAgfZgNZsCZFq6FOYvvkDmhg1FXgjdNWpIPhhRaLONG1f8Rk4nYvv3\nR+7rr8PRqVPwG0XBk52N2IcfhrNuXdhGjix8O0GAq2FD5EybBoHLi0au7GxwftTQpT98GLFJSbCO\nGQPb6NGAApMwBFQjXBStzCOcz2ZD7IABcFeogJwZMwpNoH7/XYdOneLw7beZrBnWIOHUKcS3bo2s\n5cv5WoyKZNizBzHDhiFj1y6IpUqp3Rzyh9WK2IcfhrtiRc91W8eVQqlwht27EfXSS8jcvJmxEqKi\nx4+Hs3Zt2IcM8XlfxWuEQ47ZjKz586H/7TdEvfJKoZtVr+7Giy/m4vHHY2Bnp7C2uN2IGTUK1tGj\nmQRTsZxNmsDeuzein31W7aaQPxwOxAwZArFUKeR88AETmwhi/vRTCJcv+7yfs3FjQBBgXLUqCK0i\nJeS89Rbs12cDUUpkXVliYpC1ZEmxo0wHDbKjfHk3pk+3KNSwyBFIjbD5k08ApxO2MWP8bwAnjtak\nIuPCavX7uLkvvgj90aMwrljh9zFIJTodfr3zTmTPnClZA07hSX/0KCzvvQcxOrrQbQq9Xuh0yH31\nVURNmQL2ZIUovV6yfDWYIisRBiCWLAl7375FbiMIwPvv52DhQjP27OFMElogXLsGy8cfI+eTT/y+\nKQqXLyO+cWPo/vpL3sZR0BiSkxHXvj38XgbSYkH2xx/D8u67gMslb+MouPR6nOzcWZEaQdIO8/vv\nwzpyJGDxryPK+cADcN95J8ycPYS8FFo1wjYbTCtXwv7QQ4qMFt2wwYjnn4/Czp0Z+QPUSUWZmZ75\nBANg/uwzmBYuROa2bXzVqnV2OxLq1UP2Rx/B+eCDgR3LavX7xkohzGqFef582IYP5wwDIUD311+I\na9sW1w4cQCA3Xf3PPyO2Xz9c278/4HsGhY6IqBG2zJgB49q1il3QOnZ0oFUrJ154ofBXNKQgGS5o\ntuHDAZ0Ohm3bZGgQBZPx22/hql498CQYYBIcqYxGmBYvhmnpUrVbQl6wzJgB26BBASXBAOCqXRs5\nU6fy4Ye8EjKJsO6vv2CeORO5U6cqet433sjB/v0GrFrF13NykGUe4UAIAmyDBsE8b5667aACpOLC\nPHcubIMHK98Y0oyArxd6PXLeegtRr73mWaGKtCs7G8Zvv4Xt8ceL3dSbuHD07OmZa5i0ze1GbFKS\nqiWLoZEIiyKiJ06EdcwYuBMT5TtuTg6My5cXuUlMDDBzZjaeey4ap0/z6TIc2JOSYNi1C8LZs2o3\nhQqh++036FNT4ejSRe2mkJJEEcYNG2St53Y1aABHu3aIUrgThXwUE4Nr338PsWxZtVtCCjKuXQvh\nyhW4b79dtTaERCJs2LwZurQ02EaNkvfAej2iX3oJul9/LXKz++5zYehQG0aPjvF7zA55qLkcd764\nOOS8/z5rhDXklrgQBOT8979AMFYGdLsBMShDIyhAhj17PNNbXn+lLdf1IveVV2Bavhz6o0dlOR4F\niZflb5q4j1DgXC5ETZ2K3BdeULWMJSQyAeP27bA+8YT8N0WzGbZBg2CZNavYTcePt+LqVQFr1rBE\nQimGjRsRPX58UI7t6N6dPQ8a5v7Xv+Do3Tsox47t0wf6778PyrEpMOaZMz2vxmV+SBVLl4b1ySdh\n2LVL1uMSkf9My5dDLFECzrZtVW1HSCTCuVOmBG2CZdvgwTCuWAHh6tUitzMYgEmTcjF9ehR7hQPg\nS82fecECOOvUCWJrSCuUrB13PPAAzIsWKXY+8o7u5EkYdu+G7aGH8n8mZ1zYxowpeolmChm+xoVh\n+3bojxwJUmvILw4HLNOmIffFF1Uf1BgSiTCAoL3GFsuXh6N9e5gWLix227ZtnYiOFrF6NXuFg024\neBGGnTth79VL7aZQmLH36wfjmjVcXEVjzLNmwT5gAAc4kex0J07AMm2a2s2gGwgXL8LRuTOcLVqo\n3ZQQSoToSEvLAAAgAElEQVSDyDZiBMyzZhU7QEMQgOeeY69wILyt7TItXQpHx44BT6NDoUHJmj+x\nYkW46teHcd06xc5JxcjKgmnxYs/0hjdgLWiYczoR/eSTPj+U+hoXjqQkGHfu5MwhGiJWqIDcyZPV\nbgYAJsIAANd99yF74UKvVixr29aJ2FiR06kFkyjCtGgR7I88osjphIsXFTkPeSErS5HT2AYMYHmE\nllgsyFq0CG4/JsOn0GVauRK6P/8EilhOWQ5iQgIczZrBtH59UM9DoYmJ8HWumjW92i6vV/itt6K4\nYqsfvKntEi5ehJiQAGezZkFvj+7XXxHXpg2X31VZcnIykJWFhPr1i63Xl4Ojc2dPuZXdHvRzkRcM\nBrgaNbrlx6rPO07B43bD8t57sI4b5/Ou/sSFo1cvGFet8nk/Cn+aToTNH36oyTq+Nm3YKxxM4m23\nIeubbxSZ3sx9zz0Qy5SBYevWoJ+LimZasQLOhg0hligR/JNZLMhatiw407ORpgnnz8P83ntqNyPi\n6ffvB9xuOFu3VuR89g4dYNy9G8K1a4qcj0KHZhNh/dGjsHz6qSaXRmWvsP+0WPNnGzQI5vnz1W5G\nRGvevDlXkqNbBON6IcbHw/LBBxDOnJH92OQ90zffwN6jh18zBvgVF/HxyFy2DKIGcwpSl2YTYdPX\nX8PWt69mFz1o08aJ+Hj2CocDe+/eMKSk8MaoIv3BgxAuX1asd4gimMUCR+fOMK1YoXZLIpph1y44\nunZV9Jyu++8HzGZFz0kFWaZOLXZFX6VpM8t0u2Fatgz2vn0VP7UuLQ36H34odrsbZ5Bgr7D3NFnz\nFxsLR69eMHsxhR4Fx5U334R90CDNPvhScOgPHYJw5Uqh3wfremHv2xemZcuCcmzyTubGjV6PzbmZ\nJu8jVDxRhOmrr+C+5x61W1KAJu86hpQUuEuXhvveexU/t/7YMUS9/rpX27Zu7USJEuwVDgfWoUPh\n5kpzqrHHx8Om0CwhpB3RY8ZA99tvip/X2bw5dOfPq3Juus5sVn0hBVKW/tAhwGSCq0YNtZtSgCYT\nYdPXX6vSGwx4Vp0yHDrk1ch19gr7rqjaLtPChaoNWnPXqAH7wIGqnJuAMrNmqbbktWnePBjXrlXl\n3JFMl5YG3fnzcDVoUOg2QRtToNfD3qsXTEuXBuf4FFRaHGtCxTOtWeN3XXgwaTIRtj7zjGJzyN4i\nOhqOZs1g2LLFq81btXKiZEkRK1eyVzggogjL//4HMS5O7ZZQhBHj42GePVvtZkQc44YNcLRr59X8\n7cFgHTcO1rFjVTk3qSwjQ7E5y+k6UYRx9Wo4undXuyW30GQi7L7jDoilSql2fkeHDjBt2ODVtnm9\nwm+/HQVRDHLDwkBhtV36ffsAvb7I3iEKX2rW/Dk6dYL+55+hS09XrQ2RyLh+PRydOhW5TTDjQixT\nhitXhqhA4yJm/HjWiCtMl54OMSYGrtq11W7KLTSZCKvN0aGDp0fY4fBq+wcfdAIAdu82BLNZYc28\nYIGnRlRjr0woAlgsntfkX32ldksiR0YGDD/+CMeDD6rdElKYYeNGwGpVtQ327t1h4uIainInJiJz\nxw5N3uOZCEsQK1RA7iuvADabV9sLAjB4sA1z5nBaluJI1nY5nTCuWwd7UpLyDSJNULvmz96/P0xL\nloCvdZQh5OYi9+WXgdjYIrdTOy5IXsKFC4gZMSLg4wQaF4527Twzlpw/H3BbyAcanRVIm63SAPvg\nwcVepG/Uv78dmzcbcOGC9p52tE5/6BDclSpBrFRJ7aZA+PtvxKo0UDPiuN2IfeghIDtb7ZbAVb8+\nBJsNwt9/q92UiCCWKwfb8OFqN4MUZly/3jNXuNqLWkRFwdmuHYzffKNuO0gTNJUI6375JWR7ZEqU\nENGliwOLF3PJ1qJI1Xa57rsPWatXq9CaW4kVKkD/00/QnTypdlPCnv7AAejS0oCYGPXnBRUEXPv+\ne4iVK6vbDipAkbiw2aA/cCD45yGYvv0W9i5dAj6OHHFh79ULppUrAz4OhT7NJMLCmTOI69LF67pc\nLRo82IZ588xwu9VuSYgRBNUGRzocwL59ekyfbkGXLrHo1CUBO+qMgnHTJlXaE0mMmzbB0b69aucX\nReDCBQF79+qxaJEJsxfFe1sNRSFIFD0vHzIygEuXBJw9K+DUKQF/HcnFxZ7jNPFmIqxlZsKwZ49n\nphCFpafr8NVXJmzfbsBvv+mQmQk4WreGu3p18IZNmhndZdy2Dc4HHgBModuj2qCBC9HRInbuNOQP\noKOCtFDzd/y4Dlu2GLFjhwG7dxtxxx0utGzpxPjxVly6pMNjLzyL5kf24cWOAipXDs03FKHAuGkT\ncq8vXqNEXIgiMG+eCSkpRpw4ocMff+ig0wHVqrlRrZoLly7pMGeOGZ9+mo0aNXhz1AK54uLsWQGP\nPhqLY8f0MBoBg0G8/v+A0RiHTGsykoaexxtfxsDImTCDwrh5M5yNGskyU4cvcbFqlRETJ0ajWTMn\nrlwRcPq0DqdP66DXAxUrfoGKfd0YO9bKe3aQ6P76C/rUVDg6dFC7KYXSVCLsaN1a7WYExDNozo45\nc8z8pdKo5cuNeOGFaHTu7EC/fnbMmJGDMmUKJrtdW2RgZt39aPnAgxjxuA1jx1oRHa1Sg8OUcPYs\ndH/+6bkxKkAUgZdeikJKigEjR9owYoQL1aq5UaqUWGCbxYtN6NEjDk8+acWoUTa1prglGR05oseA\nATEYONCOTZsyJQet26Z+jCFfdUdSUizmzMlG6dJ8AJabu2pVWJ9+WrHz5eQAL7wQjZQUA5YsyUK9\nev+seiWKwLVrAk6fFvDLL3o8/ngMpk/PQY8eoftGWqtMixdDyMrSdCKsjdIItxuG7du1lwiLIuLa\ntIFw+bLXu/Tta8POnQacPctBc1LUrAXduNGAF1+MxurVmXjvvRz06uW4JQkGgOgK8Xil0bfY9e52\npKbq0bhxPJYvN4Zq+bomGXfsgPPBB5HX/RbMuHC7gWefjcL+/QasXp2F/v3tuP9+V4EkGPA8yA4Y\nYMfmzZnYsMGInj1jkZ6ujUtkuND9/jtihg71evtA42LjRgN6947Fa6/lYsIEa6EzN0V3aorV5r5o\n0MCJtm3jcOwY/93l5qpTB86mTWU5VnFxcfSoHq1be0qdtm3LKJAEA57f9RIlRNSo4UZSkgPLlmXh\nhReisWBB6L6R1qr81eQ0TBO/7fqffoJYqpT2BqoIAtwVKsC4ebPXu8THA927O7BwIadSK5bb7Rkg\nqYA9ewwYMyYGCxZk4d57i3/tnbV0KSr2rIfZs7Mxc2YO3n03Cm+8ofJI5zBi79cP2e+/H/TzuFzA\nuHHROHZMj+XLM5GQUMzTjMuFaqdTsGZNFtq1c6B16zgsXmziQ5BMjOvXQ0xIUORcn31mxlNPeX7n\ne/cuuqfP9e9/w3DlIl79z+946aVc9OgRh7VrWSMRakQR+OILM3r2jMXTT1sxc2YOvFmstHZtF9as\nycT06RZ8/DHv3XLR/forhIwMzS+U5XciPG3aNDRr1gzdunULvBV2O2wyzC0YDI4OHWD0cpW5PEOG\n2DB/vgkuV/HbRpoba7v0hw4hdsiQoJ/zp5/0GDQoBp99lo0GDbz8RzH/czFs2tSJVasy8dVXZmzb\npplqotAmCAVqBYNRI+x0AqNHRyMtTYelS7O8K00UBMQMGgTDmVN48kkbVq7MwkcfmTFpUpTs7YtE\nxg0bYC9mNbkb+RMXTifw3HNRmDPHjA0bMtGwoRe/8zodrBMnQrDZkJTkwNKlWZg0KRpvvmnhWCoN\nkooLux0YNCgGCxaYsGFDJh56yO7TMatXd2PdukzMnWvG1KkWPvzKwLRmDezdu2t2/uA8freuffv2\n+PTTT2VphKthQ9h8eF2mJEf79jBs2+b5LfNS3boulC4tYutWJk1FMW7ZAkebNkE9x++/69C/fyze\neScnoLrt224T8ckn2Rg9OgbnzrHsRescDmD48BhcvKjD4sVZiInxckedDo5WrWDcsgUAUKuWC+vW\nZWLdOiM2beLvcyCES5dgOHIEzhYtgnaO7GxgwIBYHD+ux3ffZeD2273PYm3Dh8NdrRoAzzV88+YM\nbN9uxBNPRDMpCgFvv22B1Spgw4ZMVKvmw9OL3Y6YQYMAlwuVK4v49ltPadQLL0TxIShAxs2b4ejY\nUe1mFMvvRLhevXooUaKEnG3RJLFcObirVYNhzx6f9hs0yIa5c/mK5WY31nYZt2yBo23boJ3r1CkB\nSUmxmDQpF926BT4I4oEHnHj0URtGjozhBVJmctYI22zAkCExsNmABQuyEOVjZ66zTZv8RBjwdFx/\n+GEOxo2LwZUrfAjyl3HTJjgeeMCnxRR8jYvXX49CbKyIJUu8fANQhHLlRKxenYmjR/VYsYJlEn4L\nwlPEzXFx6JAe8+aZ8cEH2Te+zPOOyQT98ePQHzoEwNPpsWZNFg4fNmDs2Ghe6wNgHT8ezoYN1W5G\nsbTdX60Rjk6doD940Kd9kpLs2LPHgL//5o1TinDlCvTHjsHZpElQjn/xooCkpDiMGGHDo4/69oqs\nKBMnWmG3A++/z3phrZo0KRqCAMydm+3XAlaOVq1g2LWrwJzmLVo40b27Hc8+y+lD/GVITg5q79AP\nP+ixZo0J77yTI9sUaGYz8P77OXjxxWhcusRruT8skyfDtGBB0I5vswGjRsVgypQclC/vX9LtaNkS\nxh078j8nJIhYvjwTv/yix5IlHEDnL0fHjvC5J0IFTIS9YH36adjGjfNpn9hYoHdvO778kr3CN8qr\n7TJs3+5JgoOw1KYoenoEu3a1Y/TowFZI0O/dC2Rm5n82GIDPPsvGp5+asXcv59bylXD5MnR//nnL\nz+WqET50SI9164z48MMcv6ckF2+7De4774Thhx8K/PyVV3Lx88/sHfRXzgcfwO7j8uXexoXDATz9\ndDQmT85ByZLy9kDed58LvXvb8fLL2r+ha5Hp22/hqlVL1mPeGBfTp1tQvboLSUn+v/VzPvggDDck\nwgAQHQ28/XYOXn89Cteu8SEonAW16G3UqFFITEwEACQkJKB27dr5AZz3aiMkPut0fu1fp0483nyz\nBSZMsGLvXg39eTTw+dgff0B3333wVOTJe/zVq404fToHDzywE0Bgx+v43nuwDRyIbddXvmvevDkq\nVRIxYsQPGDSoFvbudaNkSVH1v89Q+dzm2DHof/oJG/v3l/34bjfwxhud8NJLufj5510BHe+nNm2Q\nfewYal1/Y5H3/SeftMTDD8dCr9+M0qVtqv998rPn88SJZ2AyOZCUZJTleDd/btVqK8aOfRBbtxrQ\nurVT9T9vqHxuceedEC5fxo6MDCA5WfbjR0W1xMKFZrz11iakpNj9Pt5OQUD777/3TD4cHV3g+06d\nHBg9+gpGjjyi+t8nPxf8nPffaWlpAIBhw4bBH0Jqaqrfj8+nTp3CE088gbVr197yXXp6OurXr1/0\nyU+dgnnePFhffNHfJmhe+/ZxGDfOis6dOVE34AnavGAOBqsVaNw4HjNm5KBFC2fAxzN/+in0R44g\nZ8aMW76bNCkK6ek6zJ+fXej8pFRQbJ8+sA0cCEf37gV+LkdcLFpkwpw5Znz3XWZQBylPnWrBwYOe\nSfr57x5c3sTFyZM6tGkTh82bM3HHHQEWdIoioh9/HDnvvIOb593avNmACROikZKS4f3gywhn+uor\nGL/7Dtlz5sh63OTkZDRo0BwtW8bj+edz0atX4PfX2M6dPTWtN41buXJFQOPG8fj66yzUqcOpoLTs\nwIEDqFKlis/7+X27+L//+z/0798ff/75J1q2bIlt27b5fAzjli3QnTzpbxNCwsCBNixaxBojpXz2\nmRm1arlkSYIBwNGunWceaYkBH6++mou//9bh889Z/uKV7GwY9u+H48EHZT90RgYweXIUpk3LCfpM\nPRMmWHHhgoB58/h7rTZRBJ55Jhpjx1oDT4IBQBCgO38expSUW75q29aJxo2dmDqVJRLeMuza5Rkg\nGQRTp0ahRg2XLEkwAGTPmgVny5a3/LxkSREvvZSLZ5/lwDmvhdg0K37fMl599VUkJyfjyJEj2LFj\nB1q1auXzMYxbt8KptdXkZNa9ux27dhk52vy6YPYGX7gg4IMPLPi//8uV7ZjuqlUhxsZC/9NPt3xn\nNgNffJGNadMsOHmS5fbFMe7aBWe9epAazh9oXLz5ZhQ6dHCgfv3g99gYjcDHH2djypQo/PUX/92D\nqbi4WLHCiHPnBIwaFdhYgBs5WrWCYft2ye+mTMnFsmUmHDjA8QHe0B89GpTp8ozGlvj6axPeeitH\ntmOKlSqhsFGWjzxihyiCnVpeih4/HkaJSoFAHTmix/Hj8l9z1buKO52ep8Ug9A4Fi+7YMZ9XQouP\nB1q3dmD1ag6wCbapU6PQr5/dtzkkveBo1w7GTZskv7vzTjeGDLHhnXc4i0RxjBs3wtGunezHPXZM\nh2XLTHjpJfkegIpz771ujBtnxahR0Vw4pxi6X36B8Pffsh/3yhUBL70Ujf/9T75ZIgDA2aoVjIW8\n4SxdWsTkybl46qnoGycVoUJkbt2aPzezXHJygDFjYjBtWg7KlFGm51Gn8wyce+ONKHZqFUcUYdy0\nCa5775X7sHjuuSgcPGiQ9biAiomw/uBBuCtVgli+vFpN8JlxyxaYZ8/2eb9+/ez4+ms+SQIFi9zl\ndOyYDt98Y8TEiVbZj23v1w+uu+4q9PvRo21Yt87I3sFiuKpXh6NzZ8nv/I0LUQSefz4aEydaFbsp\n5nniCRtEUWAvUTGipk2Dcdcuv/YtKi5eey0K3brZvV8t0kuuWrUgXLkCXXq65Pd9+thRvryIGTP4\n8FssnQ5yF9JPnRqFSpXOoHt3ZZ9E6tRxoXt3O954g6UxRdH98QcAyP4AlJxswPnzOvTuLd90qHlU\nu3Mbt26F049yCjU5W7Tw64Lepo0Dv/2mR1oaE6XShw/DNH++rMcUReCll6IxYYIVJUrInwy56ta9\nZXDXjUqUEDF0KHuFi2MbNQruqlVlPebKlUZcvSpg8GD5Xo3fyPLGG9AfPiz5nU4HvPxyLt57zwKn\nPCXp4cfthiElBQ6ZS6L27DFg82ZjcN4C6HRwPPggDFu3Sn4tCMC77+bg44/NQXlNS4U7fVrAwoUm\nDBt2VJXzT5pkxbffGnHwIEtjCmPcsQOOli1lfQASRWDaNAsmTLDCIH+HsHqJsG3wYFifeEKt0/vF\nVbs2hHPnIJw/79N+JhPQs6cdy5ax5+i+33+HkJUl6zE3bTLg7791GDIkOMmQN0aNsmH9eiP+/JM3\nRn/4UyOclQW88ko0pk3LDcrFEQAEmw3G774r9PumTZ0oX96NlSv5uy1F9+uvEOPjIVau7Nf+UnHh\ndHrmDH7zzZyAV48rTO7kybA/9FCh31ep4saTT1oxeTJ7B5X00UcW9O9vR9euwVutTDh/vtDBXiVK\niHjlFQ6cK4phxw7JQYeBSE424OxZHZKS5O8NBlRMhMVy5SBWqKDW6f2j18PZpAkMfrzG7dPHjiVL\nTKE2mFJeouhZe7xNG9kO6XAAL7/smUhfzjpBXyUkiBg2zIa332avsFL+9z8LmjVzoEmT4HXHOm5a\nblnKM89Y8c47Ft4YJRh37YJT5t7g1auNKFlSRNeuwXs1LpYrV+xiP0OH2rB3rwG//caHXyVcuiRg\n8WITxoyRv/wtnygivnVryUV/8vTvb4fBAMyfz4ffW4gi9L/8AofMAySnTw9ebzDAleV85mzeHEY/\nEuFGjVyw2YCfforcVyq61FRYHQ64i6i39dWcOWZUquRGu3bqv5t+4gkbNm404sQJ/lr5ytca4ZMn\ndZg3z4zXXgvuADln48bQ//ILhCtXCt2mVSsnYmNFrF3LAbE3MyQnB3RTvDkuRBH44AMLnnrKqvoc\nzjExnmSYtcK30h07BuH0aVmPOXOmGT16OFCxohi0sSYQBDhatix01hDAUxI1bVoO3norCjb1XkJq\nkyAgY98+WTs5k5MNOHNGhz59gtMbDDAR9pmjY0c4GzXyeT9BAPr2jexBc8YtW3C+fn3ZaoeuXhXw\n9tsWvPFGjuo3RcDTKzx8OHuFlfDxx2YMHGhDhQpBfsViscDRtGmRN0ZB8Mwt/M47lsh+4yPBVa+e\nrNNnbdtmgN0uoH17bUzZMHy4Dd9+a8Tff2vgAqQhUVOmwLB3r2zHy8jwdHo89VQQe4Ovc7ZsCWMR\nv++AZ+Dc3Xe7sHx55N7PCyXzRO7Tp1vwzDPB6w0GmAj7zF21apG1Y0Xp29eOFStMETvdkiE5GWX6\n9ZPteB99ZEanTg7UqKHMO2nzZ5/BuGFDkduMHGnFpk1G/P47f7XyGFesKHZOSV9qhK9cEbB0qQnD\nhyvTHeNs3RrGQgZO5enQwZOYbdzIXuEbWceP95QZ+OnmuPjgAwuefNIa9EVTvFWqlIj+/e345BM+\n/OZzOmFISZG1JObzzy1o29aRv2hKMOejdzzwgKf8sZgb9dixVnz4IR9+gyk52TP+p2/f4PUGA2ok\nwrm5iNQJGO+6y42KFd3YuTOIjzYaljttmmz1wTk5wNy5ZowdG/wegnyiWGwiHB8PPP44e4VvZFq+\nHLDLdyGbO9fzABT03uDrbA8/jJz//rfIbQQBGD/eirfe4o0xWA4e1OP33/VBGzAjRbh82bNuexFG\njbJi0SIT55e9Tn/4MMRKlSCWLSvL8bKzgU8/NWPcOGWu9WL58hArVCh0tpg8Dz7ohMEgYvPmyLyf\nK0GJ3mBAhUTYvHAhop99VunTakafPnYsXRqZr1PciYlILubi4q2vvzbh/vudqF5duRFKzubNYZBY\nevVmI0ZYsWWLkVMrAYDLBcPu3XA2a1bkZt7W/NlswKxZZowereADUFyc53/F6N7dgawsAdu388Yo\nlxvj4oMPLBg1ygqTgpfPmGHDin0bULmyiE6dHFxq/TrDrl2yDpaaP9+MRo2cuOeef671QasRvs72\n0EOeh6AiCAIwZowNH33ETo9gSEnx9Ab36xf8B1/F79SGbdtkH1EYSnr3tmPdOiOys9VuSehyu4FP\nPrHgiSeUHanguvdeCJcvFzsIJD4eGDnShrfe4gVSf/QoxLJlZVs4Z/lyE+6916VYOYwvdDpPrzDn\nk5bfiRM6JCcbMHCgsr/zjlatYChklbkbPfmkFbNmmXldB2DcuRPOBx6Q5Vg2G/DhhxaMH6/ggy8A\n25NPwtm2bbHb9eplx++/63H4cOQOgs+jP3AAwoULsh1Pqd5gQOlEOK93KIj1PVpXrpyIBg1c2LAh\nMmsJ5ajt2rLFAItFRPPmCs8UodPB2bQpDLt3F7vp8OFWbN9ujPiplbytFfQmLkTRM4+oor3BPurd\n247Tp3XYvZu9wnLIi4sPP7Rg8GAbYmOVPb+zVatiB04BwN13u9G4sRMLF7JX2NmwIZxNm8pyrMWL\nTahRw4W6dQvW6wazRtgXRiPw+OOeWuFIFz1xIvSpqbIca/duA9LTlekNBhROhPW//ALxttsCGjyh\nFabZs2Fct86vffv1i9zyCDl8/LGnN1iNmSKczZp5NX1efLxnOrVIrxU2pKTAUUxZhLe2bjVAEES0\naqX+VHmFMRiAceOsEf/vbly+HMb162U51rlzAlatMmLECOXnqnLVqAHh0iUIZ88Wu+2TT1rx0Ufm\nSB0Ck8/6/PMQS5QI+DhOp6cc5plngjtFYqAGDbJh61ZP4haphKtXof/tNzjvv1+W4ynZGwwonAgb\nUlLgbNJEyVMGjSCKfifCnTvbsXevARcvRsjgCqsVeasNBFrbdeyYDqmp+qCsN+4N+8MPI/e117za\nduhQzwwSZ89GyL+zhNzXX4fDi1eM3sSFpzdYnQcgAEBmpmewbzH697fj+HE9fvghcl+XmpcsgRzr\nTicnJ+Ozz8xISrLjtttUGIWo03kWUdqzp9hNGzRw4Y47uMqgXFauNKFiRTcaN7519oZg1wj7Ij4e\neOQRO2bOjNy3AYbkZE8SbA7872D/fj1OnlSuNxhQOBEWMjPhaN1ayVMGjaN5c79WmAOA2FigfXtH\nxFwwzfPmIer552U51iefWPCf/9gUHTBzIzEhwevejvh4oFcvB+bPj9wLpLtqVcixDu7Ro3qkpio7\nY8DNYkaO9KqX02QCnnrKinffjdBeYYcDhn37ih0g6Y2cHAPmzTNj9Gj1Vi5wdOkCwctZT556yor3\n3uMqg4Fyu4F337Xg6ae1WwZ1oxEjrFi82IRr1yKz08OwcyccMi2r/MUXZgwfblN0pVhFE2HrhAlw\n9Oih5CmDxn3XXRCsVujS0vzaP5IW1zCkpMB1/ZVJILVd588L+OYbI4YMCZ3lfIYOtWHePL4uLU5x\ncfHRR2YMH67sjAE3czZp4lV9OAA8+qgNP/5oiMiZQ/SHDsF1++0QS5UK+FipqS3x4IPO/Plj1WAf\nMMDrueNbtXLCZBKxaVNkjgGRy/r1RkRFiWjdWvqtglI1wuaZM4udPQLwzBzSoYMDc+dGxj39ZsYd\nO+CUIRG+cEHAxo1GDBigbIdH5F2l5SIIcDZrBsOuXX7t3qqVE2lpuvBfjlcUYdizBw4ZBk/Mnm1G\nz54OlC4dOhO11qzpwu23u7BuHW+M/jpzRsCGDUYMHqxebzBwvT7ci+nzAMBiAQYMsGPu3Mh7G2BM\nTpZlQLTNBsyc6VlAI1QIwj+9wuS/vCkS1V4x1Lh5s1dlMQAwerQNn31mkXPK9NDgcsHepQtctWsH\nfKgFC8zo2tWBEiWUvceHeRYWXI4WLfwujzAYgJ497WG/RKPu118hxsVBrFQJgP+1XVarZ4nNkSND\n56aYZ+hQG2bPjryEyBdFxcWsWWb062dX/OJ4M1ft2tCdPg3h4kWvth882IYlS0zelBWHFcOuXbIs\nq7x0qQnlyl3Cv/8dWktxdu/uwPnzAvbvj6wacdPs2UUuRe6t48d1+OUXPbp2Lfw1mlI1wt7OEgQA\ntRm8m8cAACAASURBVGp5ll1etiy87+m30OthfeWVgJdWdrmAOXNMGDZM+Te+TIQDYO/dG7lTpvi9\nf+/enkQ4nFeiMu7eLctUOkuXmq6v766R4rucHK8GTgFAt24O/PabHr/+GkG/bjYb5AjsrCzPhPpK\nzxktyWCAs1Ejr2+Mt9/uRv36rogZC5AnZ/p0OAKcR1YUPauJ9er1h0ytUo5eDwwZYou4twHmhQsh\nR+3S3LlmPPKITY5xVwFzNG3qdY8wwGWXA7FpkxHlyomoU0f5B98IujMHQXx8QHVwDRu6kJvrGQgU\nroSLF+Fo1Sr/sz+1XaKYt4CGdnqDY0aO9HrWEJPJUzM6Z44GruwKMX/xBaImTfJ6+8LiYuFCM5o3\nd+L227XxAGTv3BlCVpbX2//nP5H3NsBdvToQExPQMX74QY/cXAGjR98tU6uU9fDDnoWTImXZZeHq\nVeiPH4fzvvsCOk5uLrBkiQmDBhVdX6BUjbCrXj3ojx8HMjK82p7LLvvviy/MGDpUnQ4PRRJh4cwZ\nGDdsUOJUIUUQgN69HWFdHmF97jk4kpICOsb27QYIgucioxXOJk28rhcFPK/Jly41ITMziI3SEENK\nCpwNGgR0DLfb0yuopQU07IMHwz5ggNfbt2vneU3Olad8M3euGQMH2gJ92yor8xdfeJ0QlS7tGTy1\neHH4XttvlP/7HmA37qpVJtSv79LMgy/MZjjr1YNh/36vNhcEYMSIyOr0kMOJEzocPqxHz57qFFgr\ncpkxbt4M0/LlSpwq5CQl2bFihTFiXqX4U9uV1xus9sCJGzmbN4fBh0S4UiXPSngRsZBK3gqSPkyf\nJRUX27YZkJAg4v77Q6tG9EZ6PTBokD3ieoUDcfWqgG+/9Ywc19J8scY1a2DYu9fr7YcM8cwYEwnX\ndsOuXQGXwwCeAdH/+U/xvYJKxkXupElw33WX19v36uVZJ+DUKQ3dsDRuzhwzBgyww6LSGFNFEmHD\nnj2yrS4VbmrWdCEqChE3sMJbx497nhT79NHWUFxXzZoQLlzwasWpPEOH2vDFF+FfP6Y/dgxi2bIQ\ny5cP6Djz5pkxaJAGaoMD9OijNqxZY/S2MzHiLVliQtu2TpQpo61fFGfTpjB6WR8OAI0auaDXAykp\n4f+a3LBnT8BjQX76SY+zZ3Vo105bc026GjeGOzHR6+1jYjwdXJGw3Lb500+9HjNRmNxc4KuvTBg8\nWL1rvTKJcBitKCcpNxfIzvZrV0HI6xWOgJ5C+F7bNX++uk+KhdLpfBpRDAAPPOCE0wns2RPeN0aD\nH9Nn3RwXZ88K2LXLoOoCGnIpV86zLPRXX4X5jdFqDXiApCh6yiLy5gpXqhbUG86mTX16CyQInpKo\nSHhNnv3553DVqxfQMebM8Tz46r3oE9JSXEgZNMiOL780wxW6L7O8Ylq4EGKAAyRXrvSUw6g5V3jQ\nE2FdejoEq9WnVwuhJnrCBJiWLvV7/6QkO1atMsmxImlYsdk8vUOPPabNXkFHhw4QfOjmEwRPr/Dn\nn4f3jVF3/nzAqwwtXmxGjx4OxMXJ1CiV5Q2aC+e3AZb//Q+WadMCOsa+fXq43UDTptq7GDobNID+\nl188U5l46aGH7Ni61YALF8L7Nbn7X/9CIEuBZWQAq1YZ8eij2rzW+6pWLRcqVHBj8+bwnT9euHoV\n+r/+gqtOnYCO4xkkp+44kKAnwobduz29wVoq8JSZs2lTGP1cWAMAqlZ1o3JlN3buDJ+eQuHsWRi2\nbr3l577Udn3zjRE1a7pQtapGBk7cxP7YY7APHuzTPv3727BtmwFnz4bv70Puq6/C0b27T/vcGBdu\nNzB/vknTZRGmBQu8HjgFAM2aeRK7cH5NbkhJgfP6CpL+yusVzLtdaKlGGFFRcNWuDcMPP3i9S0KC\niC5dHFi0KDLe+Plr6VIzWrZ0onx5754UNRUXhRg0yIZ588L3392wb59nlpAAHoAOHNDj8mUBbdqo\n++Ab9ETYVb06bMOGBfs0qnK2aOF5ZRZAd0/enMLhwvjddzAtWRLQMcKlRvRG8fFAr14OzJ8f3r3C\ngdi+3TNIrm5d7b5XNC1bBqMP84sKgmfwVNgOmrNaYTh8GM6GDf0+xOXLAr77zoiHH9ZuOUzupElw\n33GHT/vkDZpza/N5XnWi6P0guVAS7oPmDDKsEfDFF54yKG/KYYIp+InwfffJstymlrmrVAEMBuhO\nnPD7GL162bF+vRFW7cwUFZDCfkm8re36/XcdUlP16NxZWwMn5DB0qOfG6Ai/P5rfboyLefPMGDzY\npumXSL7WiwJA//6e1+Tnzmn4D+Ynw8GDcN19NwKpZVm82IROnRwoWfKfDgWt1YI6W7TwORGuX9+F\nuDgR27eH79uAQOzbp4fDAbRo4X2voOJxYbcjrmVL+LJ+crgPmgs0Eb58WcC6dUY88oj6D74amqUx\nhAmCZwWaAEZPVqwoomZNV3jUFIkijCkpPk2fdbN588x4+GG7HAsVaU7Nmi7cfrsL69eHwb+1zM6d\nE7BzpwG9e6t/cSyKs1kzn3/fExJEdO/uwIIF4XdjNOzeDWfjxn7vL4qegbHh9gYI+OdtQFiuNCfD\nAMk5c7T/4Jt3I9IfOuTTbuE8aC57xoyA5opftMiEjh0dKF1a/YETTIRl4mzXDoKfM0fkSUoKj/II\n3cmTgMsFd7Vqt3znTW1X3iC5gQPD76aY5z//8fQKk0deXCxebEL37g7Ex6vcoGI477sP+tRU+LpC\niuff3RR2N0bh0iU4W7Twe/+UFAP0es+UYzcKhVpQbyQl2ZGcbMCZM1rO9nxnef99WKZO9Xv/ixf9\nK4dRIy6cTZr4tNwyEN6D5tz33OP3Aiput+cBSCvlMEyEZWLv2xe2kSMDOkb37g5s3WoM+dXHDCkp\nnlcmfj7ia32Q3M2My5ZBuHTJp326dnXg8GE90tLC51dQOHUKhgBuUJ5BciHSK2ixwFm3Lgz79vm0\nW926LpQtK2LTpvC6Meb+979wdOjg9/5z54ZAr2AA4uKAnj3D722AYe/egHsFu3QpWA6jVc5mzXya\nRzrP4MHhPWjOH7t2GRAdLaJBA230CITPXTgMlColonFjJ9avD+1fGle1arAVMpuCN7Vd8+aZQ6o3\n2LR8uc8JoMUC9Oljx4IFof1vfSPT+vV+TyPYvHlz7NhhQFyciHr1tHFxLI51wgS4b7/d5/2GDImM\nuWW9deGCgC1bDHjooVt7BbVWIxyIwYNtmD8/jF6T2+0w/PgjXI0a+bW72+251ufNGe0LNeLC2aQJ\n9Pv2wdd/wJ497di3L3wHzfnjyy/NGDjQrpkH36AmwjEDBwbz8GEpHMojXI0b+/2aNG+QXJcuoTOS\nzJ9XZgDw2GOegRThcmMMdPBE3iwhWrk4FsfZsqVn/lQf9expx/ff63ljvG7xYk+vYEKC9nsFAQAO\nB+LatfNp4BQA/PvfLpQrFz6vyfWHD8N1xx0QExL82n/HDgNiYkTcd19oXADFMmUgli8PXWqqT/uF\n+6A5X126JGDzZgP69tXOOBC/E+F169ahQ4cO6NChA7Zt2ya5jRAuUyAoqFMnz5Qrly+H502yuNqu\n+fNDb5CcryvM5alZ01M/tnVrGIwmF0XPMqt+riC5du1+7Nhh0NxS2sEQE+OZLnHRIt4Y83oFC1te\nVZM1wkYj8P/tnXd8E/X/x193ySXppIwiG1GQPSwgoy1lTylDZG+QpQxB+Cq4kKGAAxCUDaWMQgWZ\nspRZkL3EMhysMsvqSDPukvv9cZYfo7TJ5S53l3yejwePB2nvM9K8c/f+vKfdDt2ZM24PFbwBGrq5\n5YKnbZWFMChxVkGl5CJ9zx44K1Vye1zv3j6UNGe3e5QguXatkCQXFqaeg68oRdhut+Obb77B6tWr\nsWzZMkydOjXH61gPa8z5IyEhQOPGLDZt8g2rgTvYbELPcS2FRQCAo3p16K5cAfXokdtje/e2+URN\nYfqffwCGEUoJimD37pJo21b9SXJS0auXEBbjEw9GD9i/X1tWwWy4evVEHX47dLDj6FHfcJPTqami\nS6Peu0dhzx4NHnwDAkQN86WkOdOcOTBNmSJqbHZ1mF691PW5i1KEz549i3LlyqFAgQIoWrQoihQp\nggsXLjx3nVjrkJZh1q0D9fChR3N06qT98IgXkVtsl9aS5B7DMOBq1nQ7cQoQHoxJSdqvLas/dEg4\n+Iow7zidwL595bWRJCcR1as7ULCg9mvLUjdvepQgmVfNaLXGCHORkWDcrCMNAIGBgjfAF9zklkmT\nwL75pqixCQkGtG4tPhxGrXKRG76SNKc/dAiO118XNfbYMR04Tn0t1EUpwvfu3UN4eDgSEhKwbds2\nhIeH4+7du89dJ/aPpWWMCQluF9p/lqZNWSQn+18M4fLl2kqSexLryJFwlCrl9riQEKFayOrV2r5B\nOl99FfaePUWN3b9fj+BgHhER2rIKekqvXtr3BjDbt8OwerWosffuUdi7V4NWQfyXOHX0qNuJU4Dg\nJl+xwkfc5CLg+exkKW3e68XiE0lzHAf9sWOia4YL1mD15YF4lCzXtWtXtGrVCgBA5fTOtBToKRFc\n/fqiEqeexGgUSu2sXauthyR15w4C8ygh96LYrr//pnHhgraS5J6Ea9gQzooVRY3t1cuG+Hijp3Xp\nFYWLjBSdIBkXZ0Rk5HnV3RxdwuFAcJs2ENMSslMnO/bt0yM1VYtvXIDxIE509WrBKphbOIwqY4Tx\nX+JU0aLQnT/v9thq1RwID/eR3AARHDki9NN9tma0O6hVLnLDF3IDdOfOwVm8OPiCBd0em54ueH27\ndlXfwVfUNzE8PBypqamPX6empiI8PPy564YNG4ZS/1nJ8uXLh6pVqz52aWQLsq+9jqlXD4Hjx3s8\nX8WKxzBrVg28/77gbVbL+8vtddGkJFRLT8/1+mye/f2XX6YiOjoVBkNB1bwfb72uWdMBp9OMefPO\nY+jQiorvx5uvy5ePxp49eowcuRNJSa8pvh8xrymrFclxcXhQubLb49u0aY7Vqw2IiPhNNe/H5dc8\njzaHDsHy0Udujz9wIAkLFjTCwoVcrtdno4r3+8xr3cSJqFeliqjx9esn47vvwtGsmUk178dbr5cv\nNyIq6gIOHvxX9Hx//PGHcu/Hbsepn3+GuXhxt8f36RODbt2CUafOr9Dp1PF5uPO6ydmzYOvXFzV+\n+/bSaNAgCIUL85LtJ/v/165dAwAMHDgQYqAuXrzoth3KbrejVatWSExMhM1mQ58+fbBz586nrrl+\n/ToiIiJEbUrT2GwIK1sWj/78E55k/vA88MYbofjxR7Nqik7nRcC4cXCWLAnb8OFujbPZgKpV82Hb\ntgy8+qrG4oMlYv58I06c0GHBgiylt+JVZs824tIlHebM0e77Dvj4Y/D588M6ZozbYw8f1mHEiCAc\nOZKuOYs4feUKQlq3Rtqff7odG37okB6jRwfi99+1976lID0dqF49Hw4fTsdLL2nYFeQmaWkUqlcP\nxfHj6ShUSJvvm/73X4S0bYu0c+dE5UQ0bRqC//3PgmbNOBl2Jy8Bn34KLiICbPv2bo9t3DgE48db\n0LSpfO/75MmTKCkiYVtUaITBYMCYMWPQrVs39O3bF+PHjxczjW9iNAodp44d82gaigK6dLEjIUE7\n4SVi68hu3iwkyfmrEgwAnTvbsXMng4cP/UcryM4g1nqsIBcZKaqCACC4h2ka+P13vcS7kh/9oUNC\nQrQIZWD5cqE6jD8qwYBgI3nzTVZT9/dsqDt3RCdI/vSTAY0acZpVggHAWaYMwPOgr14VNV7LlYIs\nX3whSgk+e1aHe/coNGqkTuVfdIxw69atsWPHDuzYsQMNGzaUcEvaxzpyJJzFi3s8T5cudmzYYIBN\nA3oC9fAhdNeuwVGtWq7XPevyBISe42K6C/kS+fPzaN6cxdq12nswiiUpSQ+jEahd25GjXGgFrm5d\n4eDLuX+Tp6jspDntfe7Ol1+GrVcvt8c9ekRh+3Ymx05yz6JluciL3r21mRvA7NwJQ3y82+OEg680\n5TEVlQuKEl0+DxDihA8e1OP2bf85BcbHG9Cjhx06ndI7yRnSYlkGuKZN4axQweN5SpZ0olIlB3bs\nUH/twcc95xn39nr+PI3Ll3Vo1UqbSXJP4XAguH17iD259Oplx/Ll2nowUqmpCHz3XVFjhYL62rcK\n8vnzw1GqFHT/xS26S9eudmzfzuDRI239Ibj69cGJMIKsXWtA06YcChbUkKDLQK1aDhiNwoFQS4ht\nnHP6tA5paRRiYtRpFXQHNjJSdHWo4GChUpCWk+bcISsLWL/egB491GvsIoqwyuna1Y41a9RvLWIb\nN4Z5zpw8r8sOds8mLs6IHj1s7urP6kSnA5WeDt2pU6KGR0ZysFqBkydVemzOAf3vv4O+d8/tcffv\nU9i1S4/OnQWr4LNyoTUyt2yBo0YNUWMLFuTRuDGHxET1f889xV2roOrlguNAX7kiaihFadNNLjYE\nLj7eiJ497aAl0DqUlguuXj2PqkP16WNDfLwBTj+IBty0yYCaNR0oUUK9B1+iCKuctm0FN8q9eyq3\nFhmN4IsVc2uI2QwkJhp8qpECV7cuGJE3SJrWXm3Zx4003CQhwYBWrdTVZtMT+LAwUbGy2QgKkUFT\n3gAxnDihg8VCISpK+1ZBAKBv3UJIixaiW8527mzHrl16PHig8vv7f1ApKaCysuAsV86tcZmZwIYN\nDLp39417vbNCBTgiIgCLRdT4GjUcCA3lsW+ftrwBYoiPN6BXL3V/7kQRVjkhIUDLlqzPdJp7Mrbr\n558NeOMNTtUnRXfh6tcXHTsGCB6ATZsYZGRIuCkZEeMmzU6Se/IA5MuxoK7QoAGHzEwKp05pxxsg\nhuyC+q5aBdUuF86SJcGbTKD/+kvU+Pz5ebRowWrC6wf8Vze6bl23D30bNhhQty6HYsWkudcrLhcU\nBfOiRaJbLlOUYBXWitGDuntXVCjIpUs0/vlHh5Yt1R36SBRhDaC16hGusmyZ7yXJcXXrQn/0qKjE\nKQAoUoRHdDSniYMPlZYG3eXLbocEHD6sB0V5VlDf16BpoGdPO+LjtfFgFEN6OrBpE4Nu3dRXUN8T\nPD389u6tndwAZ4kSsPXp4/a4+HgjevXyrc/dUzp1smPvXm001GG2b4dh+XK3x8XHG9G1q131oY9E\nEZYLlkVwx46iFaInadCAw927NJKTtf9xZcd2nTmjw927FJo08Q0XaTZ8oUJwFisG3blzoufo39+G\nxYvV/2DUHTkCLiLC7Q6ScXHPl85SOuZPDXTvbsOGDQwyM5XeSe5QDx8icNgwt8etX29AgwacW3Vz\ntSAXnirC9etzcDiAo0fV7w3g6tUD16SJW2POn6eRkkKjWTPprIJakIu8CA0F2rRhsXq1+o0e+kOH\nwEVGujXGYhFC4LQQ+qh9zUqtMAyou3ehO3vW46l0OiGWbM0alVqL/usm5w7LlhnRp496y6l4Qsam\nTXBUry56fIMGHGw26nErUrXCRUcj6/vv3Rrz8KFQOkuNbTY9xukElZIienjRojzq1eOwfr26H4z6\nI0dA377t9rjssAhfg4uMBHPwoOg4YYoCevbUjpvcXeLjjeje3Qa974fDuk12sqSqjR48DyYpCZyb\nh4+ffzbg9dcdKFNG/RmBRBGWEU8tBU/SpYsNiYkGONTmTbZYEFalilAjxQWSkpKQni4kTqi5nIon\n8OHhHiVO0TTQr58NS5ao/MEYEACnm1181q41oHlzFgUKPH3nVzzmTwLoGzcQ2qSJaIUIAAYMUL83\n4HEjDTfILqjfuLF7HiAtyIWzTBlwderAE1N+1652bN3KiLEpqJqsLCEhukcPaQ++WpALV6hdW/0l\n9OgrVwCeFxqJuMGSJUYMGKCNZzxRhGXE0xIrT1KhghNFizqxd6+6vjD6kyfhKF8eCAx0ecxPPxkQ\nE8OhSBEVP+0Vpls3O3btYjQRP+YqPC+Uy+vd2wetwfgvccpoBP3336LnaNSIg9msbm+AmPJZy5er\nu6C+R1AUzEuWCJnNIilcmEdMDIefflK3N8BdfvrJgFq1OLz8svqtgmKgL1yAISFB9HgtlNDTJyWB\njYx0y7hz8qRw8G3aVN1JctkQRVhGuHr1oD98GFIVC1RjTWF3H4qRkVFYssT3kuSkJiyMR9u2LFas\nUO8N0l2OHtWBZYV6yc/iCzF/wH/tlkUW2gcEb8CAATYsWmSScFcSkpkJ3cWLQmy4i5jN4gvq+4pc\nuEK/fjYsXmxStTfAHXgeWLTIiHfekf5erxa5oFgWpu++82iO7BJ69++r0+jhLF0a9h493BqzeLHw\njNfKwZcowjLCFykCPn9+0BcuSDJfx4527NypLveZu4rwsWM62GwUoqN9K0lODgYMsGHZMhWGw4hk\n+XLjc0lyvoYUXqDu3e347Td1tmDVHz8OR5UqbpWNWrPGgPr1fatMohzExAhJc2p0k1OpqQgcPtyt\nMUeO6GC1UmjY0Hfv9Y5KlUClpoK6c0f0HPnz82jZUr0l9LgGDcDFxLh8/YMHFH75hUHPntrx/BFF\nWGYytm6VpN0yIHSgio7msGmTSr4wdjv0J04I8XEuMm1aGvr0cb2OqGbheVB373o0RfXqDhQuzOPX\nX1VYe8ZsduvytDQKW7e+uHSWr8T8cfXre5Q4BQD58vHo0IFVpbuUe+MNmOfNc/l6pxOYP9+EwYPF\nWQV9RS5cgaKAwYOtWLBAfZ+7PikJlJsdJBcsMGHgQHnu9aqRC51OKJnpgRcIAPr0sSMuzugTneZW\nrjSgZUtWUy3UfV0dURz+pZcg5Z2gRw87li1Tx42SvnULbIMGQlctF3j4kMLRo0V8ro5oTtBXriC0\nUSOPFCLg/0upqQq7HWEVK8Kdrh+rVhnQpAmHQoW0c3MUg/PVV8FVr+5R4hQADBxoRVycEazaQuwC\nA+EsXdrly/fu1cNg4H2mk5zcdO5sx6FDely9qq5Hs/7gQbeqBty8SWHvXj26dvX9EDgpkuLr1uVg\nMvH47Tf1eQPcwekEli7VTpJcNur6thHypFkzFg8eUDh2TPngG2fp0jCvWOHy9StXGtC6tVNTJ0Wx\nOF9+GeB50FevejRP+/Z2nDqlw+XL6vmq6k6fhqNMGZeTgxwOYP58I4YOtb7wGrXE/HkMRcG8cqVH\niVMAUKmSE6+84sCWLSr0BrjB/PkmDBokPhxGS3JB//03mJ9+8miOoCAhNEZth1/mwAFw0dEuX79s\nmRGdOtkRGirPftQkF1xUlOAF8gCKAoYOteHHH1WaG+Aiv/2mR758PGrW1FY8n3qergSX0OmAQYNs\nmDdPW18Yux2YN8+EIUO0dVIUDUVJEi8aECBUkFCLFwBwv63y1q0MihThUauWtm6OSjNwoA2LFqnn\nc3eXv/+mceqUDp06+b4HCAAoqxUB06d7PM/AgTasWmVwN/pINqjbt0GlpsJRubJL19tsQj6A1qyC\nYnFUrQrLhAkee/86dLDj/HmdphtnLV4sfO5aywPR7l/cj+ne3YY9e/RISdGOtK1bZ0DZsg6YzfuU\n3orXkKqOdL9+woPR+mKDqldhDh50K0Hyhx9MGDYs982rJuZPRbRuzeLKFR3OnVPe+yOGhQuF5Eg3\n8uqeQ0ty4ahUCdS9e6BENBt5ktKlnahXj8PaterIBdFnf99dLAGwaZMBFSs6UL68fAGvqpILnQ7s\nm296VDseAIxGIRROLUYu+vp1BIwb5/L1V6/SOH5cj44dtXfwJYqwN+B5j2+OTxIaCnTpYsfixer4\nwuSF0wnMnm3CyJEq0eS8BFu/PvQS3LDLlHGiRg0HNm5UwYPRbof+8GGX3aTHj+tw5w6FNm3UFuyq\nfhhGOASpxirsRkx4errQSKF/f/+wCgIAaFrwAklw+B00yIb589VRSo1t1QpZ06a5fP3ChfKUTPMH\n+vWzYfNmBvfuKW/k0h84APr+fZevX7bMiK5d7e60FFANRBH2AtS9ewitWxfgpEsYGTTIhhUrDK42\ndFOUnTsZGI08GjbkVBXbJTfOChXgLFdOVAvqZ8nuOKY0dEoK2Oho8Pnzu3T9jz8KMaJ5GZP8SS7c\noXdvGzZuZPDokbIPRurRI+SrWtXle9iKFUY0bsyhWDHPNDmtyYVUTZSiojjodMC+fSpIngoMBF+8\nuEuXnjolHHxbtJD34Ks1uXCVQoV4xMayWLpU+Xu9/uBBsC7+na1WIQdIq/0BiCLsBfjwcPDFi0N3\n5oxkc5Yp40SdOsq5z5gtW0Clprp07axZJowYYdVc3JDHUBQy166FFBkjzZqxuH2bwpkzyrrJna+8\nIiSDucD16zT27tX7bCvt3KD//RfMpk0ez1O4MI9mzVisWqWsN0B/6BAcNWsC+rwVM4dDsAoOHuxf\nHiBAaKjiaeIUIHjZBw1SZym13Fi0SIgR1UojBTUyZIgVS5YYYVP4tqlPSnI5BG7jRgOqVXPg1Ve1\nWf+NKMJego2Ohv7AAUnnHDxYyDL1eu1BpxOB778PV76phw8LFoLYWMFCoKrYLg2h0wF9+6ovmzw3\nFiwwont31zLHfU0uqLQ0BHz1lSRzDRwoeAOUrDGq378frIvhMDt2MChYUJrkSK3JhaNqVVjGjPE4\ncQoA3n7bjmPH9KqqGJMb9+55r5GC1uTCHSpWdKJSJQfWr1fu8EtfuwbKaoXztddcuj77AKRVtPEN\n8wG4Bg3ASKwIR0VxMBh47NnjXfeZ7s8/wefPD75EiTyvnTXLhPfes7piSCLkQa9eNmzZwqiy49iz\nZGQItYMHDdLuzdETHFWrgrp50+OmKgBQu7YDoaHK1hh1p3zW/PlGDB6svcxxSdDrwb71lseJUwAQ\nGCjUjV+4UBuH3/h4I958k0WBAioIbFYAQ2IiAiZOlGSuIUOsmDfPqFiMuP7gQXCRkS7JcXY4TPPm\n2s0DIYqwl+AiI6E/dkyoIyYRFAUMGeL9LFP9nj1gGzbM87rkZBqnTumfaqDhq7Fd3iA8nEfXnM8+\nxAAAIABJREFUrnbMnq3+JMmVK42IieFQsqRrZkyfkwu9HlxUFPT793s8FUVll1JT5nOnUlNB3bgB\nR/XqeV6bnEzjr790aNdOmvucz8mFmwwYYENCgsGdPEVpcTG/geOAJUu8lySnRrlwvPwy9L/9Jslc\nTZpwsFopHDyozOHXHhuLrMmTXbr2229NGDpU2+EwRBH2Eny+fLC3bQvag57kOfHWW3b88YcOly55\n76Nk9u1zqff4nDkmvPOOZ+WTCE8zYoQVCQkG3LmjXnObwwHMm2fMs2Sar8M1bAhmzx5J5urY0Y7T\np3W4cMH7t2z62jWwHTq4FB88f74J/frZYFBBgRNfoGRJJ6KjOaxZ432rMJWSgny1a7sU5rFtG4MS\nJZyoVs1/a4U7atSA7soVUI8eeTwXTQNDh1rx448KeQOCgsAXK5bnZWfP6nDihB59+2rb80cUYS+S\nNXcunCVLSjqnySRklnstqcJqhf7YsTzjBVNSKGzfzjwXN+TLsV0vgrp7F4b4eEnmKlKER+fOdsyZ\n433roGHVKrhS5V9MAw1flAu2YUMw+/ZJEi8aEAC8+64VX33l/VOlo2ZNZH33XZ7X3b9PYdMmRtKH\noi/KhbsMHmzDwoXejxFnDh4EV7dunu5xnhesgt48+KpSLhgGXK1aklQNAYR228eO6fHvv+pV02bM\nEBLhtW7sUu9fmOAy/fvbsG6dAQ8fesFKaLcja+rUPCsh/PCDCT162BEW5p/xYk+h1yPw448BVpoY\nqhEjrFi50oDUVO9Zhan79xH40UdwxdT344+mXNsp+wvOV1+F5bPPBBO5BAwcaMPRo3qcPatOH+Ty\n5Ua0bs0iPJx856WkXj0ORiOPXbu8225bn5QEzoUQhM2bGVAU8Oab2o0RlQouKkqS2vGAECPeu7cN\n8+erM0Y82xrcp4+2rcEAUYR9giJFeLRsySI+3gv+yNBQ2Hv2zPWShw8pJCQYclSG1BjbJTd8gQJw\nlCkD3YkTksxXrBiPTp3smDvXe1Zh/YEDgnWIyf1hfPy4Drduud9AwyflgqJgf/ttl0IKXCEwEBg1\nyoovv1RfjHhGhlAlZNgwaR+KWpULZtMmBHzyiSRzURTwv/9ZMWmSSaozlUvok5LyrCPrcABTpgRg\nwgSLV5Mj1SoXbP360J09K9l8AwbYkJhoQFqa+kLhfMUaDBBF2GcQ3GcmqYyOHrFokWAZ8rSYvi/B\nNWgguMklYsQIK+LjDbh/3zs3SGb/frANGuR53Y8/mjB4sI1UCZGJPn1sOHdOj2PH1GUVnjPHhJgY\nFpUr+2+M6JM4ypYFs3WrZPO1bs0iKAj46SfvBF/T16+DMpvhrFAh1+vWrjWgUCEnGjeWrlmUlnG8\n8QYyN2yQbL6iRYU64kuXejHo3oXMTF+yBgNEEfYZatRwoFQpBxITlc1SycoSFOHhw3N2jasytssL\nsDExklQQyKZECR7t27OYO9c7bjP9/v15JkieP0/jwAFxDTT8VS7cxWgEPvjAgqlT1WOGuX2bwqJF\nRkyYIH04jFblwlmxIiibDfS//0oyH0UBn39uwdSpJli9EHVE3bgBe8eOucYH2+3AtGkmfPyx95sl\nqVYuaBpSl08YO9aKuXNNXmm7TKWkIN8bb+SZ1zB9uu9YgwGiCHsdKi0NxgULZJl74kQLJk0KUNSN\n8u23JkRFcShfXpsdZuSCq1sX+rNngcxMyeZ8/30L4uKMePBA3s+bSkkBlZYGR6VKL7yG54EJEwIx\nZoxVikZ6hFzo3t2Oq1dpJCXJbHbneRiWLcsztn3atAD06GF3uVSeX0BRQrKkRFVDACFWuHJlB5Ys\nkf/w66hbF5Y8GsLExxtRrpwT9eoRa7CclC3rRKdOdnz1lfwhUczBg+Dq1Mn1AHT2rA6nTvmONRgg\nirDX4Y1GBEya5HJ9RneoVcuBFi1YxWIIk5NpxMUZMXly1guvUWtsl+wEBcE8b56kU5YowaNtW1b+\nEjsMg6wZMwRrxwvYvp3BzZs0+vcXd3P0W7kQAcMIMaNTp5pkLbhPX72KgOnTc41xvniRxpYtDEaP\nlsdMqWW5YBs3hn73bknn/PhjC2bONCkeM5qVJRg9JkywKLK+luVCDOPGWbFpkwHnz8ursukPHswz\nQdLXrMEAUYS9j8kErlYtMIcOyTL9J59Y8PPPBlkyy4M7dnxhpyynExg9Ogjjx1tQtCiJDc4Jtk0b\nIDhY0jlHjxb60stZMYR/6SWw7du/8Pc2G/DJJwGYMiUrr1w6v0R37hyCunaVdM5Oney4f5/G7t3y\nWYX1+/cLyVK5WIe++CIAI0daSXWYHOAaNoT+zBlIWfesUiUnmjdnMXu2spUEFi0yonZtDjVqkJhw\nb5A/P48xY6z45JNA+RbheTC7d+eaC5JtDe7d23eswQBRhBWBi46WNF70SQoW5DF+vAVjxwZKWneS\nvnwZuvPnwYeH5/j7uDghNrlPn9w7Sqk2tkujlCrlROvWLObNU+7BuGCBEWXLOtCkiXgXqS/LhePV\nV4WDr4ReIJ0O+OgjIVZYLquwPikp17bKhw7pce6cDgMHyvdQ1LJc8AULIu306Vw9KWL48EMLli41\n4uZNZazC6elCcuRHHyljDQbULxfUnTugz5+XdM7+/W24fp3Grl3yHH7p8+fBGwxwliv3wmt80RoM\nEEVYEdjoaMlqDeZEr152OBzAqlXSJc7p9+0DGxOTo3Xo9m0KU6cG4NtvzVLf8wkuMGaMFYsXGxVx\nl969S2HWLBMmT1buoah6AgLA1awJRuLvfGwsC5YVunpJDs+DOXAA3AusQzwPfPppAD7+2AqT+qq5\nqQcZyqeUKMGjVy87pk9XRhv54QcTmjVjSR5ILuiTkhDwxReSzskwwBdfWPDJJ4GyVIeiU1Jg79z5\nhR4gX7UGAyIV4WnTpiEyMhJt27aVej9+geP116G7ehXU/fuyzE/TwNdfZ2HSpADJXObMnj3gGjbM\n8XcffRSIPn1sqFQp7xujv8V2eYOXX3aiRQsWs2Z53yo8ZUoAuna1o2xZzx6Kvi4XbKNG0O/dK+mc\nNA2MHy/ECkvddYy+dAm80Qhn6dI5/n7jRgYcJ7R4lxNflwuxjBplxdatDC5dktjywPMwLF36wgTJ\n+/cpLFxoxLhxyjbMUbtccI0bgzl4EFKX+GjenEXRok7ExUl/r+eaN4f1ww9f+Ptp03zTGgyIVISb\nN2+O+fPnS70X/0Gvh3nBAvAyBlTWqOFAbKwdkydLILUOB/QHDggW4WfYuVOPP/7QYcwY0klMST79\n1ILVq404fNh79WXPntVhxw4GY8eSzz4vuIYNwUisCANAixYsTCZgwwZp7yV8cDAsU6bk+Du7HZg0\nKQATJ1qIB0gh8ufnMXy4VZr7+xPokpNhmj37hZbsmTNN6NjRjtKliTU4N/j8+eGoWFGydsvZUBQw\nZUoWZsww4dEj73kAt25lkJys80lrMCBSEX799dcRFhYm9V78CrZFizzbFHvKhAmC1eDkSc+UI92F\nC+CLFAFftOhTP8/MBMaODcQ332S5fEpUe2yX3FApKQhp3lzyeV96icfMmVkYMiRIuhAJhwMhLVsK\nKeLPwPPARx8F4MMPLciXz/MgVV+XC0eVKqAsFlD37kk6L0UJCbITJ0rn/QEAvnhxIbkzB5YtM+KV\nV5yIiZG/bJavy4UnvPOODSdP6nH0qHSHX2bHDuHZlIN7/Pp1GqtWGVRh9NCCXLBNm4L59VfJ561U\nScgLmTHDOzFJKSkURo8OxIIFZp+0BgMkRtinCQvj8emnQuKcJ605HZUrI33Xrud+/tVXAahfn/PK\nA9FX4IsVA331Kuhr1ySfu0ULFs2asRg7Vpq7le70aVDp6UJv32fYuJFBRgaFXr3kdY37DDSNtNOn\nwRcqJPnUMTEc3nyTxZAhQZKHSDxLejrwzTcmTJz44hKJhGdIT4fu8GHJpw0IEBLnPv88QLLPndm+\nXVCEn8FqBfr2DcKoUVYUKUIqhLgC26SJLIowICTKrlljwD//yKvCcRwweHAQhgyxoXZt360Qkutf\ncdmyZWjbtu1T/2bNmuWtvREkoGtXOwwGID7ew8S5oKCnXp45o0NiogGTJrmXJKX22C7ZoWmhaoiE\n7ZafZOJEC86e1WPtWs8TJfUHDuRYSsdiAT77LABTp1oka6LkF3IhccepJ/n8cwvS0yl8+618ViLB\nCxCI5s1Zl/IBpMAX5IK+dw/B/fvn2a1LDN262cHzFKZO9fxzp1JTQV+6BC4y8qmf87zg+Std2on3\n3lOHa1wLcuGoUQP2Nm3ybEgjhsKFhdCYzz6T10T79dcmGAzAyJHKewHkJNeU1r59+6Jv376iJx82\nbBhKlSoFAMiXLx+qVq36WICzXRvktfyvv/46C23aGMHzJ9CvX1WP57t/n0L//jy6dz+DQoVeVvz9\nae01GxODh+vW4VSZMrLMv3ChGW3bGkHTh9GpU4To+epu3IiAceOe+/3MmSaULHkHwAkAyv89yWvg\nyJEkDBlixEcfNUXNmhwYZq/k661ZUw7JyWWxeXOG4u9XS6+dr7wCC4AzK1eies+eks8fH5+J6GgG\nDscVfPbZy6LnK/Hbb6jcsCFgMDz1+2XLDEhKsmH69CRQVD3F/56aev3pp7LNX7Uqjbi4lkhMNKBo\n0d2i56P/+gt/JybiZoMGT/3+3LkCiIurhz170nHokEr+ns+8zv7/tf88rAMHDoQYqIsXL4o6pqak\npGDo0KHYvHlzjr+/fv06IiIiRG3Kr+D5XAvWS8XWrQxGjQrE7NlZaNVK/An10iUa3boFIzaWxaef\nWtzeelJS0mNh9lfoa9cQ0rw50s6fl+2znzvXiE2bDNi6NUNcBSerFWGvvYZH5849FcseF2fAN9+Y\n8MsvGShRQjoLF5ELaUhK0mPgwCD8+mu6pJ/P2rUGTJliwo4dGV51jfuKXAR88AGcpUvDNny4LPNf\nuEAjNjYEy5aZUb8+J2oO+sIFUFYrHDVqPP7Z0aM69OoVjG3bMvDKK+pJkPMVufCU5GQaHTuGYObM\nLLRsKe65bpoxA9SjR08lxz54QCEmJhTffmtGs2bi5EkJTp48iZIlS7o9TlSAycSJE9G1a1dcvnwZ\nMTEx2CNhP3W/gmURWrs2kJEh+1Jt2rBISMjEmDGBmD9fXOmVffv0aNs2BKNHW/HZZ+4rwQQBZ6lS\n4PPlA331qmxrDB1qQ1AQj6+/Fucy1Z09C0f58k8pwQkJBkyfHoCff86UVMkiSEdUFIdhw6zo2zcY\nNhFebPrKFQR36PDUzw4c0OPjjwOQkJBJ4kNFwjVqBEbidstPUqGCE/Pnm9G/fxD+/Vdc3KizQoWn\nlODbtyn06xeM7783q0oJJvw/lSo5sXJlJkaMCERSkhiLB8Ds2gW2WbPHr3keGDEiEO3a2TWlBHuC\naItwXhCLsGsEd+oEW8+eubawlZKrV2l06RKMRo1YTJ6cd4yn7swZOKpUwbL4AHz5ZQAWLzYjKso/\nvhyywnGyFNt/klu3KDRqFIplyzJRt66IRIeMDCAkBACwfj2Djz8OxM8/Z5BC+p5gtUJ/4sRzcZhS\nwvNA795BKFrUienT3YvhN/7wA3QXLyLrv1yQbEvjokVmNGhAvveiSU9HWJUqeHThQo7Jp1KxdKkB\n8+YJlntP2l7b7UC7diFo1IhVvGYwIW8OHNBjwIAgJCRkIiLC9Xs9df8+8kVE4NGlS4BRMJAtWmTE\nypUGbN+ekf0jzeBVizBBOuxt2oD55RevrVe6tBPbt2cgOVmHPn2CYDa/+FoqNRUBsR3w8SeBmDtX\ncIcTJVgiZFaCAaBoUR7ffiuUVLt7V4T5/j8leMsWBuPHB+Knn4gS7DF2O4K7dRMyDmWCooC5c83Y\nvZtBYqJ7SZPMtm1gW7cGANy5Q6FLl2B88YWFKMGeEhoKy9ixoHK74UpAv352NG7Mom/fII9ytCZM\nCECBAk588AFRgrVAdDSH2bOz0L17MM6fd12t0+/ZAzY6+rES/OefOkybZsKiRWbNKcGeQBRhhWFb\ntgSza5dwBPcSYWE8EhMzERrKIzY2BNev08jIwON/mZnCv0dbj6BDwDb88SeDnTsz8OqrnitBTwa5\nE+SndWsWPXvaERUViuXLDW6XWdq1S48xYwKxZk2mrJUC/EYuQkOFQvtHjsi9DOLizBg/PsDlOrPU\n/fvQnz0LtkEDZGYC3boFo2dPO7p2Va5Eni/JhW34cPDh4bKvM3myBSYTj7FjA0UVqli1yoB9+xj8\n+KNZtQ1TtCQX1J07CBw0SPZ1WrZkMXlyFjp1CsGVK659cMyuXWCbNoXTCSxfbsBbbwVj6lSLJM96\nLaFSMfcf+KJF4SxXDnovf7ENBmDu3Cy0aMEiKioUlSuHoXLlMFSqFIaKFYV/lce+jZdeNiExMRP5\n85PYQK3ywQdWrFuXieXLjYiNDXa5LevevXq8+24QVq7MRPXqvltD0tuwMnWZe5bKlR2YOTML/foF\no3fvIJw7l7tCzOzYAbZhQzy0BuKdd4JQubKDWAQ1iE4HLFxoxokTOnz6aQDu3MnDG/Tf6fjYMR16\n9QrCF18EYPnyTLn7PfkNfHg4mD17QKWkyL5Wp04sxoyxoGPHYNy8mbcX0DZgAH4v+RaaNQvBqlVG\nrFmTibff9r/a8CRGWAUY58wBaBq2YcOU3sr/Y7MhX8WKSD948LmOcgRt4nAAixcbMX26CQMH2vD+\n+9bn3F/371M4eVKHY8f0WLbMiLg4M+rVI25xKdEdP46gd99F+uHDXqkYY7EI3eBmzzahdm0OH35o\nec66n54O/NrnZyTeb4JDV0shNtaOb7/Ngoxd4Akyc/MmhalTA7B1K4O6dTl0725HixYsDE9Ey/A8\nsH/EVnx7IBJX+FJ47z0bevSwyRnG7JcEDhoErn592D0oR+sOM2casXSpEe3asYiOZlGnDvfcwSY1\nlcLEiQHYvZvBZ59Z0LmzXfMJ8GJjhIkiTMgRZts2GOfOReaWLUpvxafR//orHK+/Dr5gQa+teeMG\nhQ8/DMSlSzp8+KEFd+7QOHFCj5MndbiXCrz+WgZqxhgRG8sSS7Ac8DxCX38d5hUr4KhSxWvLZmUB\nS5caMWeOCXXqcBg50orLl2n8/LMB+/cziIpi0aGdDS1acdnh4QQfIDMT2LTJgFWrDLh4UYe33rKj\nWzc7/v6bxqxZJuCfKxj5zn3ETniNHHxkwrB2LZjNm2GOj/famocP67B/P4OkJD1OndKjfHkHoqI4\nREay+OcfHb75xoQuXewYN87iM9Z/oggTJEW/dy8oiwVsq1aSzkvqPz5N0IABYKOjvWYpeJKtWxks\nWGBE2bJORERwqFmTQ7X1U6HLyoRl8mSv7sXf5IJZvx6OChXgrFTJ62ubzcCSJUYsWGBChQoOdOhg\nR5s2LPLlU1/4k7/Jhdxcvkxj9WoD1q41oHhxJ0b1T0Wn9ysg7dJFwCRfV0Kp0ZpcUPfuIbRWLaRd\nuoSnTPJewmoFTpzQIylJ+BcYCEycmIUKFXwrFlisIix/6jpBk3ANGyq9Bb/AHhsLY1ycIopwmzYs\n2rR5OrXctGUTzN995/W9+Btsx46KrR0UBAwfbsPw4epol+tX2GwI6tcP5qVLoURafpkyTowfb8X4\n8ULst2HNJnANYzSlBGsRvlAhOMuWhf7YMVlLJ74IkwmIjOQQGcnhf//z+vKqhyTLEbyKlk7x3oBt\n2hT6EydAPXig9FZA//UXqLQ0OGrX9vraRC4IOeFzcmE0gsrMBLNzp9I7AQAw27eDbdFC6W24jRbl\nIjMhAVz9+kpvQ4AjeR9PQhRhAkFJgoLAxsSA2bZN6Z3AsHkz7G3aQLU1kwgEH8D+9tswJCYqvQ2A\n50Ffv/5UVzGCfPCFCnklOdYVggYNAkPyfx5Dnngqgk5Ohv6335Tehqxoqf6jt7C3awfDpk1KbwPM\n5s1g27ZVZG0iF8qh370b1I0bSm8jR3xRLuzt2kG/fz+ohw+V3QhFIePXX8EXLqzsPkTgi3LhNVgW\n+j17wNWqpfROVANRhFUEffs2AqZNU3obBC/DNmsGW5cuym7C6YS9c2dw9eopuw9/REzXAwnXDhw7\nFrQKQnP8htBQcI0bg9mwQemdEPwQ/bFjcL78MvgiRZTeimogirCK4KKihDjN27cV20PgiBHQHTsm\n2/xajO2SndBQRZOnAAh1rIcO9Urr55zwV7lgNmxAwEcfKbY+ff48wHFeLePmDr4qF/bOncH4uPdP\nTnxVLryBYd06sG3aKL0NVUEUYTVhMIBr2hTM9u2KLE+lpcGwYQMc5csrsj6B4G84IiJgWL8eYNm8\nL5YBw7ZtQolElcQu+gtss2Ywx8UpvQ2CAtBXr4L+5x9lFs/MBLN+PWzduimzvkohirDKsLduDcPW\nrYqszfzyC9joaMhZXZvEdhFywl/lwlmqFJylS0O/f78i6zO//AK2dWtF1nYFn5ULnU74RxCFluWC\n2b4dJoVCIHX//gu2fXvwxYsrsr5aIYqwymCbNIH+yBGh56mXMfz8M+wdOnh9XQLBn7F37ChYhb0M\ndeMG6CtXSFy4v8HzMP7wg9BlgeB17G+/DWbnTlCPHnl9bUe1asgideKfgyjCaiM0FJlLl3o9VpN6\n8AD6I0dkrylJYrvyQIn6jkoma/2HP8uFvV07oXyezcsNLoxGZM2ZAzX31fVnuZALfVISjPHxijT0\nkAotywVfoICQLKnA4ZeQM0QRViFckyZAYKBX19QdPw62aVMgJMSr6xKeICsL+apXB7KyvLYklZqK\n0KgowOlbrTa1BF+sGLj69aG7eNG76xYqJHkLdYL6MS5cCOs775C4cAWx9egB44oVSm+D8B9EESYA\nALjmzWFeuFD2dbQc2yU7gYFwvPaaV7PJmV9+EZIjFW6i4e9yYV6xAo5q1ZTehurwebngeRgXLgTs\ndq8sR6WkQH/wIOydO3tlPbnQulxwDRuCTk2F7tw5pbdCAFGECU9COoopjrebaxg2b4Y9NtZr6xEI\nhCegKBjWr/fa4de4ZImgBAcHe2U9wgvQ6WCePRvOAgWU3gkBRBEmeBktx3Z5A7Z1a+h37QIsFtnX\nou7ehf7YMSEkRmGIXBBywh/kwtalCwxr18q/EMvCuHIlbAMGyL+WzPiCXHCNGoEvVswrawWOGAH6\n8mWvrKVFiCKsZmw20H/9pfQuCF6EL1wYjjp1YFi9Wva1TN9/L9STJNYhv4K+elUVCZIEAbZ9ezC7\nd4NKS5N3IYZB+m+/wVm2rLzrEFQFfekSmF274CxRQumtqBaiCKsY/cmTCO7WDXA4lN6KZGg9tssb\nWMaNg07u0zvPg/7nH1hHjJB3HRchcuElMjMR0qQJ6OvXld6JS/iDXPBhYWBjYsBs3Cj/Wj6iDPmD\nXEiFMT4e9q5dVV0dRmmIIqxiuLp1wefPD2bLFtnWMKxYQVwmKsNRsyYskybJuwhFwbxqlddccwTX\n0O/fL5RSkwnjihXgIiPhLFVKtjUI7mPv3BmGxESlt0HwNWw2GNasga1XL6V3omqIIqxmKArWkSNh\n+v57WVyZ9LVrCPjsM/ABAZLP/SJ8IbaLID1ELgT44GAEjhkDZGZKPznHwfjjj7AOHy793DLhL3LB\nNmsGy6efKr0NzeBTcsHzoO7dk2VqZutWOCpVgvOVV2SZ31cgirDKYVu3BpWRAb0MriDTlCmwDRwI\nvkgRyecmEAju44iIABsdDdPs2ZLPzWzcCGfJknDUqiX53AQPMRrhqF1b6V0QFECXnIyQ5s1lqeXO\n7N1LrMEuQBRhtUPTsL73HkyzZkk6re70aTD798P63nuSzpsXJLaLkBNELv4fyyefwLh4MagbN6Sb\nlOeF5EgNWYMBIhdSoN+5E/S1a0pvQ1J8SS4clSqBDwyE/tAhyefOmjULbIcOks/raxBFWAPYO3eG\n7Z13pJuQ5xHw2WewjBtHOslpgfR06ebydhtfgtvwJUrA1rcvAqZMkW5SpxO2wYPBNmsm3ZwE9WO3\nI2jUKHlCbQjSQFGw9+gBQ3y8LHOT/gB5Q/5CWsBoBNuihWTT0devgzKbYVfAZeJTsV1egLp5E/nq\n1pXkQUalpiK0dm2vtnB2FSIXT2MdOVKoHGI2SzOhTgd7t26aeygSufAMZvNmOMqWhbNSJaW3Iim+\nJhf2rl3BHDggSwgkIW+0dVckSIKzVClk7NoF6PVKb4WQB3yxYuDq1YNx8WKP5zJ9/z3YVq2AwEAJ\ndkaQldBQZGzbBgQFKb0TgrdxOBAwfrwkh1/TwoXSehMJssDnzw/zrFkIGjoU1KNHSm/H7yCKsL9C\nUYos60uxXd7CMm4cTHPnAhkZouegUlNhWLFCNXWDn4XIBSEn/FIudDpQDx8i4KuvPJvmyBHQKSnC\n4dfH8EW54Jo1g3nmTPCeNjhSocdP7RBFmEBQOc7y5cE2agTTwoWi5zDNmQN7p07gixeXcGcEAkEO\nLJMmwZCYCN3Zs+ImcDgQNHo0sr78knj+NATXpIlHnxd98SJC69UjMeFuQl28eFGWXpvXr19HRESE\nHFP7N+npYA4cANu6tWJWXYL3of/+GyGtWiHtxAkgNNStsVRqKkLr1EH6gQNEEfYnbDYYNmyAvUsX\npXdCEIFh5UoYlyxBxs6dgE7n/gTp6W7fKwgaxmxGaNOmsA4bpkj+jxo4efIkSpYs6fY4YhHWGJTV\nCtOMGQgcNQpgWdcHWiyyNOUgeAdn2bLI+vJLUCJqTVJWKywTJxIlWMtYLO5ZedLTEdy5s9CljuPk\n2xdBNuzdu4MPCBCfH0CUYP+B5xE4Zgy4iAjYe/ZUejeaw21F+M6dO+jWrRvefPNNdOzYEYdkqH1H\neDF84cLI2LwZ9M2bCO7e3eW40YBPPoHxhx9k3l3e+GJsl7dgO3UCHxbm9jhnyZKqtxAQucidgK++\nQsC0aS5dS929i5DYWDjKlYN58WJNu8b9Wi4oClnffgsqNVXpnagOv5ELq9WlywxxcdBcLmi6AAAH\nR0lEQVSdO4esGTOIp1gEbivCer0en3/+ObZs2YI5c+bgww8/lGNfhNwICUHm6tVwFiuGkDffBHXr\n1gsv1Z05g6AePcDs3CmUT1KY27dvK70FggohcpE71mHDYEhIQMCECaBSUl54HX3lCkJatQLbqhUs\nM2aIc6mrCH+XC+drr8E6YYLS21AdfiEXTidCmjfPu9FGejpM330H89KlpCKQSNxWhAsWLIjy5csD\nAIoVKwaWZcG646InSINej6yZM8G2a5ejpUh39iyCevRAcPfu4GJikH70KPgCBRTY6NMYjUalt+BT\nUCkpgN3+/z+w2aRtwOEliFzkDv/SS0jfswcAENqgAQLffRf0338/d13gqFGwvvcerP/7n09Yhohc\nuIZp8mQw69crvQ2v4RdyQdOwTpiAwCFDci+pFhqK9N9/h7NcOe/tzcfwyGd24MABVK5cGQzDSLUf\ngjtQFKyjRwMOx3O/0h0/Di4mRnCNmkwKbI7gDUzz50O/dy+yfvgBvE6HoEGDYO/RA7ahQ5XeGkFi\n+BIlYJkyBdaxY2FcvBj0jRtwli371DWZa9YA/qAk+DlBvXsDTie4qChQ6ekwbN6MDPKd9znYFi2g\nT0pCvrJlAaMRfHAw0n/7DXyJEk9fSCzBHpGrIrxs2TKsW7fuqZ81bdoUI0eORGpqKqZPn44fVBB3\n6vfk4P609++vwEby5pqP9bxXGssXX8CwZg2C33oLcDph+fxz2Hv0UHpbbkPkwnX4sDBYx4zJ+Zc+\npgQTuciZrBkzoE9KAnPgAOjLl5GZmAi+YEGlt+U1/EkuLJMmwfLFF0BWFiizWRWeXV9DVPk0m82G\nfv36YdiwYS9sdZicnIyQkBCPN0ggEAgEAoFAIORGRkYGKoloJ+62IszzPMaMGYNatWqhe/fubi9I\nIBAIBAKBQCCoAbcV4ePHj6Nv374o+0Rs2sKFCxEeHi755ggEAoFAIBAIBLmQrbMcgUAgEAgEAoGg\nZkhnOQKBQCAQCASCX0IUYQKBQCAQCASCXyJL780//vgDv/76KyiKQsuWLVGhQgU5liGonPT0dCQk\nJMBqtUKv16N58+YoW7YskQ8CbDYbZs6cicjISERFRRGZIOD69evYsGEDnE4nihQpgi5duhC5IGD3\n7t04d+4cAKBKlSpo3LgxkQs/Zdu2bThz5gyCgoIwfPhwAC/WN92REckVYY7jsHPnTgwZMgQsy2LJ\nkiVESP0UmqYRGxuLIkWK4NGjR1iwYAHGjBlD5IOAvXv3onjx4qAoitwzCHA6nVi3bh06duyIUqVK\nISsri8gFAQ8ePMDp06cxatQo8DyPmTNnolq1akQu/JTKlSujWrVqWP9fF8UX3SPcvXdIHhqRkpKC\nwoULIygoCGFhYciXLx9u3bol9TIEDRAcHIwiRYoAAMLCwuBwOHDt2jUiH35OamoqzGYzihUrBp7n\nyT2DgJs3byIwMBClSpUCAAQGBhK5IMBkMkGn04HjOLAsC71ej4yMDCIXfkqpUqUQ+EQXvRfdI9y9\nd+iGDx/+uZQbTUlJgdlsRnp6Oh4+fIi0tDQUKFAABf2o6w3hef766y88evQIhQoVIvLh52zcuBHN\nmzfHrVu3oNPpQNM0kQk/5/r160hNTcXp06dx8OBB8LxQzIjIhX/DMAxomkZ8fDwOHTqExo0bg+d5\nIhd+jNVqxdmzZ1GnTp0X6psWi8UtGZEtWe6NN95AlSpVAAAURcm1DEEDZGRkYPv27Wjbtu3jnxH5\n8E8uXLiAggULIiws7LGykw2RCf+FZVlcu3YN7du3x8CBA/H777/j4cOHAIhc+DMPHz7E0aNH8cEH\nH2D06NFISkoCx3EAiFwQ/p8nZeFFP89NRiSPEQ4JCUFGRsbj15mZmaTVsh/DsiwSEhLQsmVLFChQ\nABkZGUQ+/JiUlBQkJyfjwoULMJvNoCgKderUITLh54SEhCA8PBz58uUDABQrVgwcxxG58HNSUlJQ\nvHhxGI1GAEDRokXx8OFDIhcEADnrm6GhobDZbG7JiOSKcPHixXH37l2YzWawLIv09PTHcaIE/4Ln\neaxfvx7VqlVDuXLlABD58HeaNm2Kpk2bAhCywY1GI+rWrYuZM2cSmfBjihcvjrS0NFgsFjAMgzt3\n7qBBgwY4efIkkQs/pkCBArhx4wY4jgPP87h16xZiYmKIXBAAvFif4DjOLT1Dls5y2WUrAKB169Yo\nX7681EsQNMCVK1ewdOlSFC5c+PHPevfujStXrhD5IDxWhCMjI8k9g4Bz585h3759cDgcqF69OmJi\nYohcEJ4qnxYREfFUuUWAyIU/sXnzZiQnJyMrKwtBQUGIjY0Fy7I5yoI7MkJaLBMIBAKBQCAQ/BLS\nWY5AIBAIBAKB4JcQRZhAIBAIBAKB4JcQRZhAIBAIBAKB4JcQRZhAIBAIBAKB4JcQRZhAIBAIBAKB\n4JcQRZhAIBAIBAKB4JcQRZhAIBAIBAKB4JcQRZhAIBAIBAKB4Jf8H85uymGylLGsAAAAAElFTkSu\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa78a630>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Discussion\n",
      "\n",
      "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n",
      "\n",
      "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the predition and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n",
      "\n",
      "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Exercise - Noisy Nonlinear Systems"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement the same system, but add noise to the measurement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#enter your code here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "######Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sensor_error = 30\n",
      "movement_error = 2\n",
      "pos = (100,500)\n",
      "\n",
      "zs = []\n",
      "ps = []\n",
      "\n",
      "\n",
      "for i in range(100):\n",
      "    pos = update(pos[0], pos[1], movement, movement_error)\n",
      "\n",
      "    Z = math.sin(i/3.)*2 + random.randn()*1.2\n",
      "    zs.append(Z)\n",
      "    \n",
      "    pos = sense(pos[0], pos[1], Z, sensor_error)\n",
      "    ps.append(pos[0])\n",
      "\n",
      "\n",
      "p1, = plt.plot(zs,c='r', linestyle='dashed')\n",
      "p2, = plt.plot(ps, c='b')\n",
      "plt.legend([p1,p2], ['measurement', 'filter'], 3)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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n8Q7zo4/C/NhjHnv/O3cYbNqkwYsvGvD77zk4fpzH888HwlQ1nFaGyzHu/HnZ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\nO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       "text": [
        "<matplotlib.figure.Figure at 0x2252048>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Discussion\n",
      "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n",
      "\n",
      "Very shortly after practioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This information in this chapter takes some time to assimulate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n",
      "\n",
      "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "author notes:\n",
      "    clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end.\n",
      "    \n",
      "    "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}