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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
     ]
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     "source": [
      "Unscented Kalman Filters"
     ]
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     "input": [
      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import sys\n",
      "sys.path.insert(0,'../code') # allow us to format the book\n",
      "import book_format\n",
      "book_format.load_style()"
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     "language": "python",
     "metadata": {},
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     "source": [
      "In the previous chapter we developed the Extended Kalman Filter (EKF) to allow us to use the Kalman filter with nonlinear problems. It is by far the most commonly used Kalman filter. However, it comes with a lot of difficulties and limitations. For example, it requires that you be able to analytically derive the Jacobian. However, for many problems this is either very difficult or impossible. Furthermore, being an approximation, the EKF can diverge. In this chapter we will use the unscented Kalman filter (UKF) to tackle these problems.\n",
      "\n",
      "I particularly like the following way of looking at the problem, which I am borrowing from Dan Simon's *Optimal State Estimation* [1]. Consider a tracking problem where we get the range and bearing to a target, and we want to track its position. Suppose the distance is 50km, and the reported angle is 90$^\\circ$. Now, given that sensors are imperfect, assume that the errors in both range and angle are distributed in a Gaussian manner. That is, each time we take a reading the range will be $50\\pm\\sigma^2_{range}$ and the angle will be $90\\pm\\sigma^2_{angle}$. Given an infinite number of measurements what is the expected value of the position?\n",
      "\n",
      "I have been recommending using intuition to solve problems in this book, so let's see how it fares for this problem (hint: nonlinear problems are *not* intuitive). We might reason that since the mean of the range will be 50km, and the mean of the angle will be 90$^\\circ$, that clearly the answer will be x=0 km, y=90 km.\n",
      "\n",
      "Well, let's plot that and find out. Here are 300 points plotted with a normal distribution of the distance of 0.4 km, and the angle having a normal distribution of 0.35 radians. We compute the average of the all of the positions, and display it as a star. Our intutition is displayed with a triangle."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "import matplotlib.pyplot as plt\n",
      "import math\n",
      "\n",
      "xs, ys = [], []\n",
      "N = 300\n",
      "for i in range (N):\n",
      "    a = math.pi / 2. + (randn() * 0.35)\n",
      "    r = 50.0         + (randn() * 0.4)\n",
      "    xs.append(r*math.cos(a))\n",
      "    ys.append(r*math.sin(a))\n",
      "\n",
      "plt.scatter(xs, ys, label='measurements')\n",
      "plt.scatter(sum(xs)/N, sum(ys)/N, c='r', marker='*', s=200, label='mean')\n",
      "plt.scatter(0, 50, c='k', marker='v', s=200, label='intuition')\n",
      "plt.axis('equal')\n",
      "plt.legend()\n",
      "plt.show()"
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4aw9RWFiIWbNmQa1WY/To0Rg+fDh2797dogMkIgpUc4I098e4fq6svHXbkSMq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\nEEv4AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fadfd2a7908>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that out intuition failed us because the nonlinearity of the problem forced all of the errors to be biased in one direction. This bias, over many iterations, can cause the Kalman filter to diverge.\n",
      "\n",
      "For all these reasons there is a need for a different way to approximate the Gaussian being passed through a nonlinear transfer function. In the last chapter I showed you this plot:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from nonlinear_plots import plot_transfer_func\n",
      "from numpy.random import normal\n",
      "import numpy as np\n",
      "\n",
      "data = normal(loc=0.0, scale=1, size=500000)\n",
      "\n",
      "def g(x):\n",
      "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
      "\n",
      "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VSCuxACaqApamqn3oWJsZ4TsVbizMysnHzzvP4eKtRzAxLRxqkZWZWWK/9Mxc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\nARgAAABehQEYAAAAXoUBGAAAAF7l/wEJ4HV52PAreQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade46d2d68>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I generated this by taking 500,000 samples from the input, passing it through the nonlinear transform, and building a histogram of the result. From that histogram we can then compute a mean and a variance that we compared to the output of the EKF.\n",
      "\n",
      "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a 'monte carlo' approach, and it used by some Kalman filter designs, such as the *Ensemble filter*. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the transfer function is, as long as we sample with enough points we will build an accurate output distribution.\n",
      "\n",
      "\"Enough points\" is the rub. The graph above was created with 500,000 points, and the output is still not smooth. You wouldn't need to use that many points to get a reasonable estimate of the mean and variance, but it will require many points. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you only needed $50$ points for 1 dimension, you'd need $50^2=2,500$ for two dimensions, $50^3=125,000$ for three dimensions, and so on. So while this approach does work, it is very computationally expensive. The Unscented Kalman filter uses a somewhat similar technique but reduces the amount of computation needed by a drastic amount by using a deterministic method of choosing the points."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Choosing Sigma Points"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at the problem in terms of a 2D covariance ellipse (2D only because it is easy to plot, this extends on any number of dimensions)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ukf_internal\n",
      "ukf_internal.show_2d_transform()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ayWRCfUs3ksd5GSuWVPo0h2MICimg4jqsAUsiCIIw2pWbN29GZqY4k+THkj09\nF0l3PAdVZLzYUbxOcLkwcKoSvZU70Vu1C/buljHHqyITEJa9AGHZ86FLyYJEygLlaS67FU2v/wDz\nMpLx8m9+zV1XKGiV7t6LfmUEomJiL/u+WFJpLAN9ZqCnCUvz88SOQpehuroay5Yt+8zr/O43aVtb\nG4aGhqCMiBM7iigkMhn0adOgT5uGxKvugq39FHqrdsJUuROWpmPnjbd3N6N9+1to3/4W5CFhMGRe\ngbDs+QhNn8WtbD1EptIgef1TKPvrD/DIY9/BL599hke5Kej09PSgxTSI1JxLP+jBkkoXyma1IE7P\nDRsCmd8V1oqKChiSp7AAAJBIJNDEpkITm4q4pTdhyNyF3qrd6K3aif66gxBczhHjnYO96N63Ad37\nNkCiUMGQPgth2QtgyLwCCl2YSM8iMEkVKiTe+ENs/MOD+NULL+Bb3/ym2JGIvKryWC30MUkX/VrN\nkkqXYshqRVhCqNgxyIP8rrAePHQI0thJYsfwSUpDFIx5a2DMWwOXbRDm4/vQW7kT5pq9cFkHRowV\nHHb0Vu1Cb9UuQCKFLiXrzNSBrPlQRyeK9AwCi0ytRdItT+F3v3sASQkJuPbaa8WOROQVF3t0lSWV\nLpd7yIqQkOD85DVY+F1h3bv/ENQTP3t+A/2PTB2CiGkFiJhWALfLiYETFWcKauVODPV2jBwsuDHQ\ncBQDDUdx+sPfQW1MHi6vIUlTgmatW09QGqKQvP4pfPcHjyAmJgYLFy4UOxKRxx2pOY7Q2OQxj66y\npNJ4cg1ZuUJAgPOrwioIAqqOHsGEgrvFjuJXpDI5QtNnIjR9JpLW3gtraz16K8+UV0tL3XnjbR2N\naOtoRNvWv0Ohj4AhKw9hWQsQOikXUgW3vbtYmthUJF7/OL561z147+23fPJERqLx0t3djbZeC1Jz\njOddx5JKnuB2uyE4hrgGa4Dzq8La2toKNyRQhEaJHcVvSSQSaOMnQRs/CfEr1sNuaoe5ajdMlTvR\nf+Iw4HaNGO/o70HX3g/RtfdDSJVqGDLmICxrAQyZ8yDXcr7QhdJPnA7j6rvx5ZtuwYYP3kd8fPCt\ncEHB4eix2hFHV1lSydNsFgsMOi3PbQlwflVYu7q6oAmL4j/KcaQKj4FxwdUwLrgaTusAzDV70Vu5\nC+ZjZXDbLSPGuodsMB0phelIKSCVQp+aM7xklipIV224GBEzlsJp7sR1N96Mkv9+wKMBFHC6u7vR\nZrYiJTEPfDnmAAAgAElEQVQa9TWVLKnkFQP9ZiRG8sThQOdXhbWvrw9yNeeoeIpco0Nk7jJE5i6D\n2zmE/vrDw/NeHX3dIwe73eg/cRj9Jw6j6T8vQxOX9slmBQugTUjnm4pRRC+6Di2dp/DgI4/ilRdf\n4H8nChiCIOD9Dzdg5/5DOPDD77CkktcMDfYjmp9aBTy/Kqz9/f2QqnhUyhukciUMGXNgyJiD5HX3\nwdJ8/My816pdsLadPG+8tfUErK0n0Lr5dSgM0QjLykNY9gLo06ZDKleI8Ax8k0QiQeza+1D6yv14\n429/w8033SR2JKJLJggCjh49iv/85z/497//jdOnT486liWVPMVp7UdYGI+wBjq/K6wSFY+weptE\nKkVI0hSEJE1BwsrbYe9ugemT8jpw8ggguEeMd5g70bn7fXTufh9SlRZhU+ad2awgYy7kGi7sLFNq\nkHD943jiqYcwY/p0TJ06VexIRBfs3JL6wQcf4NSpU6OOZUklT3MMDUEBF1cICAJ+V1jBI6yiU0XG\nI3bRtYhddC0cg2aYq/egt2oX+o6Vw+2wjxjrtlvQc3greg5vhUQmhz5tOsKy5yMsaz6UYeefRRws\nNDEpMK7+Ou648y58vHkjNBr+IiffxZJKvmqg34yYyAixY5AX+FVh7evrg6BkYfUlihADomYXIWp2\nEdwOO/pqDwxvSOAc6B0xVnA50Ve7H321+9H43m+gTUg/M+916gJoYtOCbj5n5MwVaK7bj+99/4f4\n5S+eETsO0QgXVVJVKuTMzsPSq77AkkpeZenrw6R4TgcIBn5VWK1WGyDnOqC+SqpQnZm7mpUHwf0t\nDDZVo7dyJ3ord8HWef4JGJbmWliaa9Gy8TUow2OHj7zqJ0yDRCYT4Rl4X8yab+C/L96FouJiFBUV\niR2HgtzFlFSNRoPly5ejqKgIA4ICk2blQxYkP7fkO1zWAYSHJ4sdg7zArwpreHgYYGsXOwZdAIlU\nCl1KNnQp2UhcfSdsHU0wVZ0pr4ONVYAgjBg/ZGpDx4530LHjHcg0ehgy5yE8ewFCJ8+BTBW4R2vk\nGh3iv/QYHnj4EeycMwcREfxoi7zrUkrqmjVrsHTpUmg0GlTXHMOxLhvLKnmd2+2Ge2gQBoNB7Cjk\nBX5VWCMiIiCx9Ykdgy6B2piEOOP1iFt8PRz9Peit3oPeyl3oq90PwTk0YqzL2o+eA5vQc2ATJHIF\nQifNRFjWfBiy8qAMjRTpGXiOPnUqBrIX4cmf/BTPP/es2HEoCFxuST3L5XKh5mQjotJneCM20QiD\n/X2INOj5ZilI+F1hdVtYWP2dQh+B6LmrET13NVxDVvQd34/eyp0wV++B81P/fwWnA+aavTDX7AXe\neR4hyZmfrPc6H2pjSsDMe41efis+fP523Lr+ZkyfPl3sOBSAxquknqulpQUulR4qtdpTsYlGNdjf\nj4mR4WLHIC/xu8LqHDSLHYPGkUypQfjUfIRPzYfgcmHgVOWZea9Vu2Dvbjlv/GBjNQYbq9G84VWo\nIhOGd9rSpWRBIvXfd9lyjQ7Gwtvx4Le/g40ffQCpVCp2JAoAniip56qqPYnwmAnjGZnogjksfYhM\nTRU7BnmJ3xXWIRbWgCWRyaBPmwZ92jQkXnUXbO0Nn6z3uhOWpmPnjbd3N6N9+1to3/4W5CFhMGRe\ncWa91/RZkCn974hPxMxCNOz/CH//+99xEzcUoEvk6ZJ6Vnd3N8wOAakGnqFN3ud2u+Gy9HHefxDx\nu8Jq62dhDQYSiQSa2AnQxE5A/LKbMGTuQm/VbvRW7UR/3UEILueI8c7BXnTv24DufRsgUahgSJ+F\nsOz5MGTmQaHzj1+oEqkUMVd9A0/99LtYvXo1wsP5URddGG+V1HMdqz8JXVTcpUYmuiz95l7EhIdC\nqeTKQcHCrwpraGgoILjhtPRDrtWLHYe8SGmIgjFvDYx5a+CyDcJ8fN+Zea81e+GyDowYKzjsw2vB\nQiKBLiX7zNSBrPlQRyeK9AwujDYhHfrshXjqpz/Hc8/8TOw45MPEKKlnDQ4OoqnDhJRp6Zd1P0SX\nasDUjemJwbv5TDDyq8IqkUiQkTUVg6ePwTB5tthxSCQydQgiphUgYloB3C4nBk5UnCmolTsx1Nsx\ncrAgYKDhKAYajuL0h7+D2pg8XF5DkqZA4oNzRaOX34b/PH87vv7V2zF58mSx45APEbOknutkwymo\nImI415pE4xgwwWjk62Mw8avCCgDzZuXio0YWVjpDKpMjNH0mQtNnImntvbC21qO38kx5tbTUnTfe\n1tGIto5GtG39OxT6CBgy8xCWvQChk3IhVfjGR0tyrR4R87+A5194Ea+8+ILYcUhkvlJSz3K5XDh2\nqhkxGbnjft9EF8I6OIAQpQw6nU7sKORFfldYZ83MxQd7Xxc7BvkgiUQCbfwkaOMnIX7FethN7Z8c\ned2F/hOHAbdrxHhHfw+6yj5EV9mHkCrVMGTMQVjWAhgy50GuDRXpWZwROW8NNj73FTQ3NyMhIUHU\nLOR9vlZSz9Xe3g5BFQKlSuXRxyEajbmnB2lxnA4QbPyusObm5qLv1PcQLwgBswYneYYqPAYxC76A\nmAVfgNM6AHPNXvRW7oL5WBncdsuIse4hG0xHSmE6UgpIpdCn5gwvmaWK8P6JJXKtHhGzVuKl3/4O\nTz/5hNcfn7zPl0vquU42NUMXwbJA4hkaMCE2fYrYMcjL/K6wJiQkQCYBHOYuKMOixY5DfkKu0SEy\ndxkic5fB7RxCf/3h4Xmvjr7ukYPdbvSfOIz+E4fR9J+XoYlL+2SzggXQJqR77Y1S5IIv4J+/vhMP\nf+sBLt0SoPylpJ5ls9nQ3NmLpByebEXicDiGgCELXxODkN8VVolEguycaehoqmFhpUsilSthyJgD\nQ8YcJK+7D5bm42fmvVbtgrXt5Hnjra0nYG09gdbNr0NhiEZY1pl5r/q06ZDKFR7LqTREI2xqPv74\npz/j4Yce9NjjkHf5W0k9V2trK2T6cG6FSaLpM5mQGBPFE/6CkN8VVgAoWHAF/rL9IMJzFoodhfyc\nRCpFSNIUhCRNQcLK22Hrbhk+aWug4SgguEeMd5g70bn7fXTufh9SlRaGKXMRnr0AoRlzIdeM/wkA\nEfnX4Q9/eBD33H0XtFrtuN8/eYc/l9Rz1Z46jbDoVLFjUBCzmHswbTLn9Qcjvyysa666Ci+8/DvE\nXXUvJHynT+NIHRmP2EXXInbRtXAMmmGu3oPeql3oO1YOt8M+YqzbboHp8McwHf4YEpkc+rTpCMue\nj7Cs+VCGjc8cP7UxCSEp2Xj77bexfv36cblP8o5AKaln9fX1odcyxJ2tSDSCIMA5aEZk5DSxo5AI\n/LKwpqamIj4+Hv0nKxA6iUureFP/iQoIbhdkKi2kKg1kKs2Z75Uan1zT9HIoQgyIml2EqNlFcDvs\n6Ks9MLwhgXOgd8RYweVEX+1+9NXuR+N7v4E2If3MvNepC6CJTbusea8hM1bgH/96l4XVDwRaST3X\n6eYWKA1RYsegIGY29SAmTAe12v+23qbL55eFFQC+9IW1eO3jbSysXnbqnedh62j8zOukCvUnJVYL\nmUoD6fDXT12m/N915xbfEZf5WAGWKlRn5q5m5UFwfwuDTdXordyJ3spdsHU2nTfe0lwLS3MtWja+\nBmV47PCRV/2EaRf9qYBh8hxUvf0s2tvbERMTM15PicZJIJfUswRBQF1TC8JTs8SOQkGsr7sdV6Qn\niR2DROK3hXXd2rX49YsvI3bNNyCV+e3T8DuuTy0HdS63wwa3wwbngGlcHstXC7BEKoUuJRu6lGwk\nrr4Tto4mmKrOlNfBxipAEEaMHzK1oWPHO+jY8Q5kGj0MmfMQljUfhslzIFN//rxUqUKJiKw8fPDB\nB7jjjjvG5TnQ5QmGknqunp4e2KGARhsidhQKUi6nE4LFDKORB6mCld82vaSkJCQlp6C//hB3vfIi\nt93qvcfykwKsNiYhzng94hZfD0d/D3qr96C3cif6ag9AcA6NyOCy9qPnwCb0HNgEiUyB0PSZZ8pr\nVh6UoZGjZtdOLcBb777LwiqiYCup52poPA0NV2UhEfV0dSAlLhpKpW/sSEje57eFFQCu++I6vFqy\njYXVi6Y9/ibcditcdivcdgtcditcdss53//vcrfdAteQ9ZPxn33Zp49GepI3C7BCH4HouavgGOiF\nvbsVts5GuIdsI24vuBww1+yFuWYv8M7zCEnO/GS91/lQG1NGzHsNTZ+F6refQUtLC+Lj48clP32+\nYC6pZzmdTjS0diA2c6bYUSiIWXo6kTpjstgxSER+XVjXrV2LX/zyVzCuvBNyrV7sOEFBptRAptRA\nMQ7/uQVBOFMiWYABAION1RhsrEbzhlchkSkgDzFAGRYNRZgRcnUIpCHheOjhh7Fo4UKEhIRAp9NB\np9MhJCRk+O/nfuU6hZeGJXWk7u5uCEotFAoe2SJx2G02yF1WREXxpL9g5teFNS4uDstXLMehvf9B\nzJIbxY5DF0kikbAAj/ZcXA44+rrg6OsCGquHL9/e1oDt27Zd0H1oNJrzSuznFV2dTgetVjtizNnL\nAnmxeJbU0bV1dEIdyl2FSDymznZMSk7gm/Ag59eFFQC+dd83sOaLX0J0/jWQKlRixyERebcAf6rk\n2q1wD33GdZ+6zJsF2Gq1wmq1orOzc1zuL9AKMEvqhWloaUfExByxY1AQs/V2IIlTUoKe3xfWjIwM\n5M6YjqZ9xYjOWyt2HAogYhRgx4AZ1pY6WNtOwt7TCsHluPwHHieBUIBZUi+O2WyGXZBCpQ6+506+\nYbC/D3qVDGFh3LAi2Pl9YQWAhx+4H+vvvBdRc6/kzlfksy62ALtdTgycqDizWUHlTgz1dow5Pjk5\nGbNmzcLUqVMRExMDq9WKgYEBDA4ODn89+/2n/372e7fbPeZjjCdvFeCQkBA4HA60traioaEBZrN5\n1PtQq9VYsmQJ1q1bh+XLlwdlST1XR2cnlDpOByDx9Ha2IyclUewY5AMkgjD6Z5SbN29GZmamN/Nc\nsqIr18KStRIRM5aKHYVo3AmCAGtrPZo3/BFoOwZzb++Y441GI1asWIHCwkLk5+df0M4wgiDAarWO\nKLGjlVtfLMDj7dwCfKFHekc7ShwSEjLmEeCXX34Zf/jDHxAZGYno6GhERkYiKipq+Pvo6GhERUUh\nKioKkZGRUKm8M/1p8/adQGQy9NyOlUQgCAIaDu/F2mX5Qf/mMVhUV1dj2bJln3ldwBTWkpISPPTD\npzHh3lcuaxtMIl822HQMlo9+jbfe+AtKSkpQXFyMPXv2wOl0jnobrVaLxYsXo6ioCMuWLUN4eLhX\nsrIAjzRWAX7//fcv6r4MBsNwqT3757PKbVRUFPR6/SW9JtpsNvx7UylSp8/jayqJoqerA1prFxbl\nzRM7CnlJUBRWt9uNxcsLIcz6Io+yUsByOx048uOrUXX0CLTaM7tk9fb2YuvWrSguLsaWLVswODg4\n6u1lMhnmzp2LoqIiFBUVITk52VvRL5sgCLDZbCMKbX9/PyorK7Fz507s27cPPT09o95eKpVCq9VC\nLpfD6XTCYrH4dQG+UCqVatRy++miGxERAbn8zEyx5uZm7DnejKR0//gdQIHnVNVhLJqezi2pg0hQ\nFFYAKCsrwy13fB3pD7x6QVteEvmjhlfuxau/+jlmzz5/wwy73Y5du3ahuLgYGzduRFtb25j3lZmZ\nOVxec3Jy/OJImiAIOHLkCD744IPLOnHqswrwaF8/6yixxWI572iwvxdgiUSC8PBwREVFQalSQxMW\nBWNcPAwRUTCERyDs7NfIM1/VGr7OkmcMDvTD0nQMq5cv9ovXJRofQVNYAeCue+/DQbMSsau+JnYU\nIo9oeeOHePL+27By5coxx7ndblRUVKC4uBglJSWoqakZc3xcXBwKCwtRVFSEvLw8n9oCcbxKqqcz\nXmoBLikp8UrG8abWaGEIj4AhPBKGiDN/wiIiR5TbrNw5oi9hRv6nqa4GucmRSEtLEzsKeVFQFdaO\njg4sXLwUKV/7JTRG//m4k+hCtb77HB744hLceOPFbZbR0NAwPO+1rKxszKOBer0eS5YswcqVK7Fk\nyRKEhoZebuyL5g8ldbxcf/31KC0tFTuGR7y98yhk8oBYkIa8xDE0hNbqA1hXuBgKhULsOORFYxXW\ngHsVMRqNePCBb+KVt15C8q0/40cJFHAEdeiYczVHk5qaijvvvBN33nknenp6sGnTJpSUlODjjz+G\n1WodMba/vx/vv/8+3n//fSgUCuTl5aGoqAgrVqxAQkLCeD2V8wRTST3Xiy++CJvNBpfLdd4ft9sN\nl8sFp9M5/P2FjnG73XA6nRc9prOzE90WJzQhIXAPX+6E2+WG233m7+7h27uGL//036VSGcsqXbSu\nthZMTolnWaURAu4IKwA4nU4ULF0Bad71iJhWIHYconHVtu0tFMULeOJHPxyX+7NardixYwdKSkpQ\nUlKCrq6uMcfn5OSgqKgIhYWFyMrKuuw3hcFaUn3Z1h274QpPQKjBOytKEJ3ldrvReKQcqwuugE6n\nEzsOeVlQTQk4a8+ePbj1znsw6VuvQqbkLzUKHF37NmDqUD1+99Jvxv2+XS4XDhw4MDx1oL6+fszx\nSUlJw/Ne582bN3yG+edhSfVdLpcL73y0GYk5czn3lLyuu6MdoQ4TFsybI3YUEkFQFlYAuPu+b2J/\n+xDi1n1T7ChE46a3ajei6jfhX/94w+OPVVdXN1xe9+/fjzFeLmAwGLBs2TIUFRVh8eLF5x0dYUn1\nDyaTCZvKjyAlK1fsKBSEGioPYMnMLERHR4sdhUQQVHNYz/XM00+hYOlymCp3Ijx7gdhxiMaFTB2C\n/v5+rzzWpEmTMGnSJNxzzz3o7OzEpk2bsGHDBpSWlsJut48Yazab8c477+Cdd96BUqlEfn4+CgsL\nkZiYiN27d7Ok+gmz2Qy55gL2DiYaZwN9ZoQqgKioKLGjkA8K6MKq1+vxu5dfxE233oGQpClQhkaK\nHYnosrnsFoSJMLcrOjoaN9xwA2644QZYLBZs27YNxcXF2LRpE0wm04ixQ0ND2LJlC7Zs2TLmfbKk\n+p62rh5odN5fFYLI1N6C2RNTebI0faaALqwAMGfOHNxx63r8/e1nkHzr05BIOSeL/JvLZoFeL+4R\nMK1Wi1WrVmHVqlVwOp0oLy/H66+/ji1btqCvr2/M20okEkyYMAHXXHMNvvrVr/LECh/T3mVCZDqX\nBCTvsttskFjNSEiYKXYU8lFSsQN4w0PfegCJehk6tnh+zh+Rp7lsgwg3iH8ETBAEVFRU4JlnnsFD\nDz2E995773PL6tnbnThxAs8++yzmz5+PBx98EMXFxectrUXeZ7FYYHcDSpVK7CgUZDpbGpE9KfWC\nT9yk4BMU/zLkcjle/d0rWLqiCJqUbISmzxI7EtElc9kGEG4Up7Be7IlT+fn5MBqNaGpqwp49ezA0\nNDRiTHd3N9588028+eabUKvVWLRo0fB6r5GRnMLjbSaTifNXyevsNisw0IMJqTliRyEfFhSFFQBi\nYmLw+1dewm133g31PS9BGcYzEMk/CfZBhBmSvPd443R2f39/P7Zu3YqSkhJs3rz5vKOxNptteC1Y\niUSC2bNnY+XKlSgsLOT2jF7SbeqFIoSFlbyro7kRUyel+tR20OR7gqawAsCCBQtw/z134bd/fRyp\nX/slZOoQsSMRXTTJkNXjc1g9sQSVXq/H2rVrsXbtWjgcDuzZs2d4yazm5ubzHr+8vBzl5eV48skn\nkZ6ePrxZQW5uLqTSoJjN5HWtnT3QxU0UOwYFEbvNCsmgCWkTposdhXxcUBVWALj3nrtxqrEJG//2\nBJLWPwWpnFu/kX9xm9sRFxc37vfrzXVSFQoFFi5ciIULF+KJJ55AZWUliouLUVxcjMrKyvPG19bW\nora2Fi+++CKMRiNWrFiBwsJC5OfnQ61WX/RzpfO5XC6YByxICeFJcOQ9nc2NmJo+gduw0ucK6I0D\nRuNyuXDLrbfj+IAM8dc8wiU0yG8IgoDqp6/Dtk3FiI+PH5f787XF/E+fPj185HXPnj1wOp2jjtVq\ntVi8eDGKioqwbNkyhIdzK9FL1dfXh5LdB5GczbO0yTtsVgu6aiuwZsViFlYCEMQ7XY3FarVizdXX\nYCAuBzErbhM7DtEFsZvaceq396HqyOFLfqPliyV1NL29vdi6dSuKi4uxZcsWDA4OjjpWJpNh7ty5\nKCoqQlFREZKTuTTTxWhtbcXumiYkpgfmaz75nqa6GkxLjED6JE5DoTNYWEfR1dWFoivXQH3FtYia\ne6XYcYg+l+lIKYyntuHtv79+Ubfzp5I6Grvdjl27dqG4uBgbN25EW1vbmOMzMzOHy2tOTg4/Sfkc\ndXV1qOywIi45VewoFARsVgu66ypw1XIeXaX/YWEdw4kTJ3DVui8get2DCMucJ3YcojG1Fr+KL02L\nwSMPP/y5YwOhpI7G7XajoqICxcXFKCkpQU1NzZjj4+LiUFhYiKKiIuTl5fFs5M9QfuAQuiU6RETH\niB2FgkBTXQ2mJ0Vg0kQeXaX/GauwBt1JV5+WlpaGv/75j7jh5q9AesPjCJ04Q+xIRKNytdZixi2F\no14fyCX1XFKpFDNmzMCMGTPw6KOPoqGhYbi8lpWVwe12jxjf2tqK1157Da+99hr0ej2WLFmCoqIi\nLF26FKGh4m/C4AtMfQNQx7KskufZrBbIbGakpuSKHYX8SNAfYT1rx44duOPOuxB37aMwZMwROw7R\neQSXC5U/uRa7S7fBaDT+7/IgKakXqqenB5s2bUJJSQk+/vjjMXfQksvlmD9//vBmBQkJCV5M6jsE\nQcDbH5YgMWceZDJuX02e1VRbgxnJEZjIo6v0KZwScIHKy8tx8623IXbdgwjLni92HKIRzMf3Qbr7\nDWwp+Ygl9QJZrVbs2LFjeEOCrq6uMcfn5OQMr/ealZUVNPNerVYr/rN1F1KnzRU7CgW4wf4+DDQd\nw+plBXxzROdhYb0Ihw4dwvU33wLjld9A+LQCseMQDWt+5zmszo6HWq1iSb0ELpcLBw4cGF4yq76+\nfszxSUlJw/Ne582bF9B7nHd1dWHb4eNIyuDWmORZDVWHsCA7LWg/zaCxsbBepMrKSnzp+hsRWfhV\nRMxcIXYcCmKCIMDSXIueQ1vQUfovCIJ71LEsqRenrq5uuLzu378fY7wUwmAwYNmyZSgqKsLixYuh\n0wXW4vqnTp3CgcYeJEyYJHYUCmA9XR1Q9rdjSX5e0Hx6QReHhfUSHD9+HNdcdz0MBTchkktekRed\nLammim0wVWyDvad11LEsqeOjs7MTGzduRHFxMUpLS2G320cdq1QqkZ+fj8LCQhQWFiImxv9PVKo4\nWolGqwzGOB71Is9wu91oOLIPhXm5iIiIEDsO+SgW1kt08uRJXH3tddDOugrRi67jO0LyGJZU32Gx\nWLBt2zYUFxdj06ZNMJlMY47Pzc0dXu81PT3dL18ntu8uw5A+FqFh3CmMPKO9uQkxchvmzuJOajQ6\nFtbL0NzcjBtu+QoshmTEXf0ApHKu30jj42JKKgCsXr0aV199NUuqFzmdTuzbtw8bNmxASUnJmPOG\nASA1NXW4vM6ePdtvTiop3loKdfwkaEICa6oD+QbH0BCaqw/gqiULoNVqxY5DPoyF9TJZLBbc/Y37\ncbDuNBJv/AEUen6cQZfmYkqqVKGCITMPwmAPri9aiO9/77teTEqfJggCjh07Nrze66FDh8YcHxER\ngRUrVqCoqAiLFi3y6TcZ/96wGVGTZ0DBDRXIA5rqapAdZ8CUjMliRyEfx8I6DtxuN575xXP48xv/\nQNLNP4Y2nicn0IW5lJIaMb0AoRlzYe9sQvNfH0fZ7p0Bd6KPv2ttbR2e97pz5044HI5Rx6rVaixa\ntAhFRUVYvnw5oqKivJj08731/gak5M73y+kM5NsG+sywNNdi5ZKFAb3SBo0P7nQ1DqRSKR779iPI\nmpKBhx99DLHrvonwnIVixyIfdTklVaZUD1/XtfFVPPytB1hWfVBcXBzWr1+P9evXo7+/H1u3bkVJ\nSQk2b96Mvr6+EWNtNtvwWrASiQSzZ88enjqQlpYm0jM4Y2hoCIJEyrJK404QBHQ11mPh9Cksq3TZ\neIT1ElRUVODmW2+HNncljEtu4gs9ARi/knpWX+1+9H/0Enbv2AaFQuHJ6DSOHA4H9uzZM7xkVnNz\n85jj09PThzcryM3NhVQq9VLSMwYHB/Hh9r1IzeEOfzS+utpaoXeYsDBvnthRyE9wSoAHtLe34+av\n3I5uqR5xV38L8hCD2JFIBONdUofv1+3GyZfvxdPffRBr1qzxRHTyAkEQUFlZieLiYhQXF6OysnLM\n8UajEStWrEBhYSHy8/OhVo/+b2S8mEwmbNlXiaTM6R5/LAoeDscQTlcewOqCK6DX68WOQ36ChdVD\n7HY7nvzJT/HP9/6N+C8+gtB0LtcRDDxVUs/VXf4RVNUbsWnDhzyCH0BOnz49fOR1z549cDqdo47V\narVYvHgxioqKsGzZMoSHe2bJqY6ODuw4egKJk7M9cv8UnBprq5EdZ0DmlAyxo5AfYWH1sG3btuHe\n+x9ASM4SGFfcyqWvApA3SupZ1o5GNPz+Qfz7nX/y5y+A9fb2YuvWrdiwYQO2bt2KwcHBUcfKZDLM\nnTt3eN5rcnLyuOVobm7G3rpWJE5ksaDxYeruhNDdhBUF+X6ztBv5BhZWL+jp6cF9DzyIw7WnEP+l\nx6CJSRE7El0mb5bUs9wOO06+ch8eve9O3HLzzZcanfyM3W7Hrl27UFxcjI0bN6KtrW3M8ZmZmcPl\nNScn57KOwp88eRKHmvuQkCruyV8UGJxOB5qOHkDhglke+1SAAhcLq5cIgoC/vv46nnz6ZzAuvxWR\n867ix7l+RoySeq6Wd5/H9Egp/u+3L/PfTpByu92oqKgYXu+1pqZmzPFxcXEoLCxEUVER8vLyoLzI\nte3TBEsAABiXSURBVFSrqmtQ1+dGbELS5cQmAgCcrj+GjOgQZGexO9DFY2H1srq6Otzx9bvRrwxH\n7LoHuNGAjxO7pJ7Vc3ALbDvfwNaNxVzGioY1NDQMl9eysjK43e5Rx+r1eixZsgRFRUVYunQpQkND\nP/f+Dx+txGmbHNGx8eMZm4KQ2dQDZ8dJFC5eyKkAdElYWEUwNDSEnz/7C/zl9TcQvfQWRF2xBhIp\nf4B9ha+U1LNsHU048fsH8O4/38TUqVPH/f4pMPT09GDTpk0oKSnBxx9/DKvVOupYuVyO+fPno6io\nCCtWrEBCQsJnjjt4+AhanSpExcR5KjYFAZfTicbKA1iRl4uICB6koUvDwiqi48eP48FHHsOpzl7E\nrL0fIUlTxI4UtHytpJ5l727ByT88jB9/91Fcf/2XPfY4FFisVitKS0tRUlKCjRs3oqura8zxOTk5\nw+u9ZmVlDU85OXCoAm0uDaJiYr0RmwJU88laTAxXYdpUrjZBl46FVWSCIODtt9/GD554ErrMfBhX\n3Aa5luvSeYOvltSz7D1taPjDw3jsW/fh1lu/4vHHo8Dkcrlw4MCB4SWz6uvrxxyflJSEwsJCFBYW\nQqHWokcaikhjjJfSUqDpM5tgb6lHEbdfpcvEwuojent78cRPfooP/vsRjEVfQ8TM5TyxxgN8vaSe\nZTe149QfHsaD992Fr91xh9celwJfXV3dcHndv38/xniZh06nw9Q5eVi44krkXpEPTQjnT9OFc7lc\naKw8gKVzchAdHS12HPJzLKw+5sCBA/jWI4+i162E8cp7oI2bKHYkv+cvJfWsIXMnGv7vYdx/1x24\n++t3ev3xKXh0dnZi48aNKC4uxvbt2zE0NDTqWLlCgWmz8zB30VLMWbQUEVFGLyYlf9R8sg6poTLk\nTp8mdhQKACysPsjlcuG11/6CZ59/HiETZiBy6XqooxPFjuVX/K2knmU3taPxT4/hnttv+f/27jwo\nzvy+8/inm6s5m0sgQBwCCYSYkQAhrkYnMCMmW4ljbybZqk3FKXsTb5yrKqnaP7Ne17qSde1WdpPN\n2Jls7SZrJ/bu2E482cwoY81YQjMICXFJCAkd3Iibbq5u+tw/NDNlWScy8DwN79c/8MfzPP3RH01/\n9PTv+f7021/+LcNyYOdZXV3V+fPnP5336nQ6n3p8cdlhVR8/rerjjdqzt4hvhPAQ18K8vJP31HzC\nse5xasDjUFhNbGVlRX/55pt645tvyl7mUPqpf63oZO5qPEm4ltRPuAY6NPHWf9If/v7v6jf+zReN\njoMdzO/368qVK/rf3/q2PrrUrpnJiacen7Un/9PyWnKo4qGxRYuuBSXZGRK/k3jX1jRxs1tNdZVM\nBcCGobCGgYWFBf33N97QX//Nt5RS2az0E7+iqAQ+AKTwL6nSg3/DzPnvaLH9H/TmN/5C9fX1RkcC\nJEndvdc17o3S6sqyLl94X5cvnNOdG9eeek5ScoqqHCdVfaJJJS+X6zc/c1p7i0vlaGxRfeMZHuDa\n5kKhkIb6e3WkKEv7iljSho1DYQ0j09PT+i9/+l/11vd/oLSaf6H0Y68rMnbnPQSxHUrqJwKeFU18\n7+tKDy3rf/2Pv1R2NgPaYR6P2zhgbnpKVy5+oMvnf6TejksK+P3rumbp4SNqaG5R7alXWAe7DU2O\nDCk9Yk111UdYJoINRWENQ2NjY/rjr/9nnT37z0qpOqO0ul/Y9ksFtlNJ/YR7akhj3/6KWhpP6Gtf\n/YpiYmKMjgQ8pO9Gv+4tS5nZj19Dv7q8rK5Lrbp84Zw6Pjyv1eWl5762xWLRwYoqNTS9ptpTryg5\nNW2jYsMgi84FrU7c0asnHPw9w4ajsIax4eFhfePNv9Jbb70le3GV7HWfU0Le9tl8YDuWVEkK+rya\nufBdzbf9vb76lT/SL7/+utGRgMe6d++eeu8vKTu/8JnH+v0+3ejq0OUL59R+/pxmp578fv1pFqtV\nLx+pkaOpRbUnm5WUzJKncOPzejV2o0vN9axbxeagsG4Di4uL+tu//Tt9482/UighTUm1v6iUsgZZ\nwni/5rWFKQ188w+2TUn9hOvWFU3/45+r8lCZ/uQ/fvWJW2ICZjA+Pq72O/e1p6hkXeeFQiG9/Z2/\n1v/80z9e92taIyJ0+Gid6htbVHOiUYn25HVfA1tvsL9X5fkZKineb3QUbFNPK6xsSREmkpKS9KUv\n/aa++MUv6OzZs/pvf/FNDbz7ppJrf15pR18Ly3Wu0fZdCvoenQkZjiVVkrzOGU2/84ZC0/f0Z1//\n2hPfdICZREdHKxTwrfs8i8WilLRdSt2VofmZ6XWdGwwE1HXporouXdQ3/uSPVF7tkKO5RdXHGxWf\nwC6AZjQ1NqKcxEgV799ndBTsUNxhDWPd3d36sze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FbBUKKwBgS6SmpurksXpNTU2pt39A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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fadfd2a49e8>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here on the left we show an ellipse depicting the $1\\sigma$ distribution of two state variables. The arrows show how three randomly sampled points might be transformed by some arbitrary nonlinear function to a new distribution. The ellipse on the right is drawn semi-transparently to indicate that it is an *estimate* of the mean and variance of this collection of points - if we were to sample, say, a million points the shape of the points might be very far from an ellipse. \n",
      "\n",
      "Let's look at that by running a bunch of points through a nonlinear function.\n",
      "\n",
      "###### Exercise: Plot 2D points\n",
      "\n",
      "Write a function to pass points through the state transition function:\n",
      "\n",
      "$$\\mathbf{Fx} = \\begin{bmatrix}1 & 1 \\\\ .1x &y\\end{bmatrix}\\begin{bmatrix}x\\\\y\\end{bmatrix}$$ \n",
      "\n",
      "for the mean $$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}$$ and the covariance\n",
      "$$\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$\n",
      "\n",
      "Plot both the original points and the converted points. Plot the mean passed through the function vs the calculated value, and print the difference between the two."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your answer here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution\n",
      "\n",
      "Here is my answer."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "import numpy as np\n",
      "from numpy import sin, cos, tan,log\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "from numpy.random import multivariate_normal\n",
      "\n",
      "\n",
      "def f(x,y):\n",
      "    return x+y, .1*x**2 +y*y\n",
      "\n",
      "mean = (0, 0)\n",
      "p = np.array([[32, 15],[15., 40.]])\n",
      "\n",
      "xs ,ys = multivariate_normal(mean=mean, cov=p, size=5000).T\n",
      "fxs, fys = [], []\n",
      "for x,y in zip(xs,ys):\n",
      "    fx, fy = f(x,y)\n",
      "    \n",
      "    fxs.append(fx)\n",
      "    fys.append(fy)\n",
      "\n",
      "# Compute mean\n",
      "mean_fx = f(*mean)\n",
      "\n",
      "computed_mean_x = np.average(fxs)\n",
      "computed_mean_y = np.average(fys)\n",
      "\n",
      "plt.subplot(121)\n",
      "plt.scatter (xs,ys, marker='.')\n",
      "plt.axis('equal')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.scatter(fxs, fys, marker='.')\n",
      "plt.scatter(mean_fx[0], mean_fx[1], marker='v', s=120,c='r')\n",
      "plt.scatter(computed_mean_x, computed_mean_y, marker='*',s=120,c='r')\n",
      "plt.ylim([-10,290])\n",
      "plt.xlim([-150,150])\n",
      "plt.show()\n",
      "print ('Difference in mean x={:.3f}, y={:.3f}'.format(\n",
      "       computed_mean_x-mean_fx[0], computed_mean_y-mean_fx[1]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2YuPGjQCAnTt3wuPxOB67pqYm6vuurq6xmsaYwSNomTh2O+k2j1BIwiefsLXl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\ncfjCF5L82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qWuro4///nP/Pu//zsACxcu5LbbbqOqqorCwkKefvppHn744Qt7Iop+TaYN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\nlSTOQgghAHC73eTn54d6GOIKpDud+B58MPhYiK5KEmchhBBChJyalWU98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       "text": [
        "<matplotlib.figure.Figure at 0x7fade43109b0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Difference in mean x=0.070, y=43.905\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This plot shows the strong nonlinearity that occurs with this function, and the large error that would result if we linearized the function at (0,0). We would reasonably expect an EKF to diverge rapidly with this function.\n",
      "\n",
      "In the chart above we used 5,000 points to generate this solution. While the answer is quite accurate, computing 5,000 points for every update would cause our filter to be very slow. So, what would be fewest number of sampled points that we can use, and what kinds of constraints does this problem formulation put on the points? We will assume that we have no special knowledge about the nonlinear function as we want to find a generalized algorithm that works for any function. For reasons that come clear in the next section, we will call these points *sigma points*.\n",
      "\n",
      "Let's consider the simplest possible case and see if it offers any insight. The simplest possible system is *identity* - the transformation does not alter the input. In mathematical notation this is just $f(x) = x$. It should be clear that if our algorithm does not work for the identity function then the filter will never converge. In other words, if the input is  1 (for a one dimensional system), the output must also be 1. If the output was different, such as 1.1, then when we fed 1.1 into the transform at the next time step, we'd get out yet another number, maybe 1.23. The filter would run away (diverge). \n",
      "\n",
      "The fewest number of points that we can use is one per dimension. This is the number that the linear Kalman filter uses. The input to a Kalman filter for the distribution $\\mathcal{N}(\\mu,\\sigma^2)$ is just $\\mu$ itself. So while this works for the linear case, it is not a good answer for the nonlinear case.\n",
      "\n",
      "Perhaps we can use one point per dimension, but altered somehow. However, if we were to pass some value $\\mu+\\Delta$ into the identity function $f(x)=x$ it would not converge, so this is not a possible algorithm. We must conclude that a one point sample will not work.\n",
      "\n",
      "So, what is the next lowest number we can choose? Consider the fact that Gaussians are symmetric, and that we probably want to always have one of our sample points be the mean of the input for the identity function to work. Two points would require us to select the mean, and then one other point. That one other point would introduce an asymmetry in our input that we probably don't want. It would be very difficult to make this work for the identity function $f(x)=x$.\n",
      "\n",
      "The next lowest number is 3 points. 3 points allows us to select the mean, and then one point on each side of the mean, as depicted on the chart below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ukf_internal.show_3_sigma_points()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1T8JCLAYnkqbmz3+8lOAAXzbvPMDn3514Bl4RkTOhIi0ibueD9b+wLbuQ0Fb+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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade42d74e0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For this to work for identity we will want the sums of the weights to equal one. We can always come up with counterexamples, but in general if the sum is greater or less than one the sampling will not yield the correct output. Given that, we then have to select *sigma points* $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the input Gaussian. So we can write\n",
      "\n",
      "$$\\begin{aligned}\n",
      "1 &= \\sum_i{w_i}\\;\\;\\;&(1) \\\\\n",
      "\\mu &= \\sum_i w_i\\mathcal{X}_i\\;\\;\\;&(2) \\\\\n",
      "\\Sigma &= \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\\;\\;\\;&(3)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "If we look at this is should be clear that there is no one unique answer - the problem is unconstrained. For example, if you choose a smaller weight for the point at the mean for the input, you could compensate by choosing larger weights for the rest of the $\\mathcal{X}$, and vice versa if you chose a larger weight for it. Indeed, these equations do not require that any of the points be the mean of the input at all, though it seems 'nice' to do so, so to speak.\n",
      "\n",
      "Methods for selecting these sigma points is it own topic. In the next section I will develop the two most typically used methods. They have the virtue of requiring only 3 sigma points per dimension, which is far lower than we might expect to provide good results. Despite the low number of points, the computations for the weight selections are very easy and efficient, and the numerical performance of the filter is as good as, and usually better than the EKF.\n",
      "\n",
      "But before we go on I want to make sure the idea is clear. We are choosing 3 points for each dimension in our covariances. That choice is *entirely deterministic*. Below are three different examples for the same covariance ellipse."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ukf_internal.show_sigma_selections()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DkrgrxApwhHUFZmdnEU6qYS4sEh1lXYTD4YfKKgAEgwF0dnYqZqRVpVLB4Kzg\n65w0jY+PQ1fkglbHuXlKodXpoCly8kSfNI2MjMBQXMHioiDmQitCSTW8Xq/oKDmJhXUFxsbGYChW\nznSAQCD4UFm9JxgMIBAICkgkRqGrEr0DnKOXjqGRURgc3PJNaYzFFRga4UNdOm4PjqDQpZz7CC3T\nO8o58LFCLKwrMDw+BYvDJToGrTOrsxQjE27RMXLC0PgUrK4S0TFonVmdJRge5+bo6RiZmIKVu8wo\njsXh4n1khVhYV2BkYgpFCiqsNpsVVqvtsX9utdpgs1kFJBLDVFCIhXAUi4uLoqPIWiqVwrh7GkV2\n5VwjtKzI7sKEZwapVEp0FFlbXFzEQjgGUwG3fFOaouISjEyysK4EC2uGwuEwfPOLMBc9XuDylclk\nQkdHx0Ol9d6iK5PJJDDZ+lKpVDBYnZienhYdRdZ8Ph9UBgu0XHijOFq9HtCb4fP5REeRNY/HA4PV\nyfmrCmQpssEXmOdBNCvAXQIyNDMzA31RMdRqZXV9p7MYH3zw/v05qzabVVFl9R5tYTHcHg8aGxtF\nR5Gt6elp6IqUsXsEPU5XVIzp6Wm4XBxhfxq3xwNtIa8RJVKr1dAVOjAzM4OamhrRcXKKslpXFng8\nHugU+kNjMplQXl6G8vIyRZZVAChwODHM+UfPND7phoGFVbH0RcUY5yvPZxqecKPA4RQdgwTRFRbD\n4/GIjpFzWFgzNDzhhsXOHxqlKip2YXTCzQMEnmF4YgpFxRxdU6qiYheGJ7jw6mkkScLYpIfXiIKZ\nHU4uvFoBFtYMjU66UcQnY8UymguwFEty4dVTJJNJTHpmUciHOsUqtDsxOT2LZDIpOoosLS4uYimW\nhNFcIDoKCWJ1uDDCh7qMsbBmIBwOI7AQUtSCK3oYF149m9frhdpUwAMDFEyr00FlsHBz9KeYnp6G\nwVrMBVcKZi6yYW4hpJiDd7KFhTUDHo8HequDPzQKpy1yYMrN+UdPMj09zcUkBF0RH+qeZsrtgZZz\nvBVNpVJBb3XwGskQC2sG/H4/NBae+6x05iI7pmY4evQkM14fdAXK2ZuXnkxXYMWMl1tbPcnUjBcW\nK+8jSqcx2+D3+0XHyCksrBnwzQWg47wjxTMXFGLW//hRtQTM+OZgKigSHYMEMxUUYcY3JzqGLM34\neY0QoDMXwDfHayQTLKwZmPbNwcwfGsUzFRTB6+cPzZPM+udgLuQ1onTmwiLM8hp5jCRJ8Pl5H6Hl\n+8i0jwMPNRZOAAAgAElEQVQfmWBhzcAsn4wJgM5gRCyR4oT5R0iSBK8/wGuE7j7UBbj92yMikQhi\nSUCrN4iOQoKZCvhQlykW1jRJkgT/XBAmC89+VjqVSgWtuRDBYFB0FFkJh8NISCroeDNWPJ3egISk\n4kPdI4LBIHSmAi7cJZgLiuDjQ11GWFjTtLS0hJRKy/PRCQCgNRWwsD4iEAhAZ+YDHS3TmQsRCPCV\n54MCgQA0vEYIgFavR1KlQSgUEh0lZ7CwpikYDELLHxq6S8XC+phgMAiNiYsSaZnGxLcQjwoGg1Ab\neY3QMp2JD3WZYGFNUyAQ4M2Y7jNauAr6UcvXiLLnr4bDYbjdHrjdHsW/DlcbC3gzfsSMzw8Dp5XR\nXRpOLcuIVnSAXMHCSg8yFRRhxtsnOoaszPgCMBQo92bs9frQ2dmJYHC5pFmtNnR0dMDpVOYm8UZu\n//aYGV8AJlep6BgkExoTH+oywRHWNM3OBflkTPeZCgq5tdUjZucCil2UGA6HHyqrABAMBtDZ2anY\nkVajhYX1Ub65AEwKfqijhxkshZjhNZI2FtY0LSyFoDcYRccgmdAbjFgKR0THkJXFUAg6hV4jgUDw\nobJ6TzAYQCCgzFd+eqMRi1xQ8pClcJj3EbpPbzBiMaTMB9qVYGFNUygc4d55dJ9Gp0ckGkUqlRId\nRTZCoQh03EWD7tLpDQiFo6JjyEYqlUIkGuN9hO7T6vVYYmFNGwtrmpbCYe4vSfep1WqotXpEo7wh\n3xOORKDTK3P0yGazwmq1PfbPrVYbbDargETiafUGhBQ6HeJJotEo1Fo992Cl+3R6I0IRvqlLFwtr\nmsLhKAsrPUStY2G9J5lMIhZPQKPTiY4ihMlkQkdHx0Ol9d6iK5PJJDCZOFqdHrF4AslkUnQUWYhE\nItDwHkIP0Or1CHFqWdq4S0CaQuEwX+XQQzQ6AyJ8OgawPHqk0Sl79MjpLMYHH7x/f86qzWZVbFkF\nlk+EU2t1iEajMJvNouMIF41GodYo84GOnkynNyLMwpo2FtY0JBIJJFISNFr+56If3LsZ0/LokVrH\n+asmk0nRJfVRGv3yQx0L691rhIMe9ACNVot4IolEIgEt+8WP4pSANEQiEWg494geodLqOcJ613Jh\n5c2YHqbmNXJfNBqFSsuHOvqBSqWCRmfgwEeaWFjTEI1GOfeIHqPiHNb7IpEI1LwZ0yPUvBnfF4lE\noNJySgA9TK3nQ126WFjTsPxDw5sxPYKjR/dFo1GoOCWAHsG3ED9YHmHlwAc9TK3lWoh0sbCmIRqN\ncn4ePUatXd6LlYBYLAYVF5TQI9Q6HWKxmOgYshCORDnCSo9Ra3mNpIuzfNOQSqWEz18Nh8PCVx/L\nIYOccqhVaiSTPDgAWL5GoMqv59+VfM/W6+/kCkml5uEad6VSKagzuEby9XuRj59rVZ+J10jaWFjT\nJEFcYfV6fQ+dU35vf0ens1hRGeSUAwCgAlKStP7/XhmSw0NdNq3ke7Zefye3qCDxGgEAJFMpqNTp\nXSP5+r3Ix8+12s+kUvMaSVd+DYmsEZE343A4/NDFACyfT97Z2YnwOp0iI4cMcspxj0qtRirFTdEB\n3P3BzY/CupLv2Xr9nVyjUqk4enSXJKWANO4j+fq9yMfPla3PxMKaHhbWNEiSlNYPzVoIBIIPXQz3\nBIOB+68glJBBTjnuUUEF3ouXSZIEpDl6JHcr+Z6t19/JNRJ4M74nlQJUaUwJyNfvRT5+rqx8JpWa\n10iaWFjTkE+jR5RFKr7KeRD/S9Bj8miayGrxt4KejPeRdLGwpmF5OoCYL5TNZn3ofPJ7rFYbbDar\nYjLIKcd9kgR1nowqZkWe/Oiu5Hu2Xn8n16jy4yuRFSqVKq1rJF+/F/n4ubLymaT8mv+/llhY06BW\nqwFJzLtfk8mEjo6Ohy6Ke5O612t1pRwyyCnHPZKUYmG9S6VS5c07iJV8z9br7+Sa5WuEtxkAUKsB\nKY2Bj3z9XuTj58rOZ5JYWNPEXQLSIPrL5HQW44MP3he6FYgcMsgpB7D8ii+TbWrymVqdX/OwVvI9\nW6+/k0tUEP/7KRdqtQZSKr39NvP1e5GPn2u1n0mSWFjTxcKahnRf5awlk8kk/MKWQwY55YAEjh7d\nJYdrJNtW8j1br7+TKyRIvEbuUqtUGc0sy9fvRT5+rlV9JokPdeniL0ka1Go1JC4Hp0ekUkloNLyE\nAECj0QASt/iih6lSnBJwj1ar4TZ49LhUcvn3k34Uf0nSYDAYkErw6DR6mJSIw2jg2eDA8jUiJeKi\nY5DMpBIxGHiNAACMvI/QE/AaSR8LaxqMRiNScZ4ZTw9LJaIwGo2iY8jCcmHlzZgeJsV5jdxjNBoB\nPtTRI1hY08fCmoblwsqbMT0iEePN+C6j0YhUjA919LBUIs6b8V3LD3W8RuhhyVg07+b0rhUW1jQY\nDAYk47G8WgVNq5eK88n4HoPBgFSSo0f0sCRHWO8zGo18C0EPkSSJD3UZ4C4BadBoNNDrtEjG49Dq\n9aLjkEykOMJ6n9FoRJIjrAiHw3m1Zc9q8aHuB/cGPojuScRjMOh1XJiYJhbWNJlNJsRjERZWui8V\ni/JmfJfBYICUjCt6T0Gv14fOzs77Z4vf20Dc6SwWnEyMVCoFKRnnQ91dRqMREgsrPSARi8LE6yNt\nrPVpMpsMiMf4Y0M/4AjrD9RqNQx6PRIKHWUNh8MPlVUACAYD6OzsRDgcFphMnGQ8BoNer9gHmEdx\nhJUeFY9FYTHxHpIuFtY0LY+wKvNmTI9LJZNAKgk9R9zvM5uMin2oCwSCD5XVe4LBwP0pAkoTj0Vh\n5s34PoPBAKQSSHFPb7orHovxGskAC2uazCajYkeP6HHx+PLoKkePfmAyGRGPRUTHIJmIx6Iw8WZ8\nn0qlgtFg4H2E7otHI7CYlT3PPRMsrGkqKjAjGg6JjkEyEYuEUWA2i44hK4UWM2IRZb7+ttmssFpt\nj/1zq9UGm80qIJF4sXAYRQUW0TFkpcBiQVSh1wg9LhYJo9DC+0i6WFjTVOKwIxZaFB2DZCK8OA+X\n4/GComSlxXaEF+dFxxDCZDKho6PjodJ6b9GVUncKCC/No9RhFx1DVlwOGyKLC6JjkExEQwsoKeY1\nki7uEpAmm82GVGRIdAySifDCPDbwh+YhLocdUfeU6BjCOJ3F+OCD97mt1V2xpUU468pFx5CVkmI7\npgLKfKijx0nhRVitynwDsxIsrGmyWq1IhvhkTMtioQU4G6tEx5AVq9UKKdInOoZQJpNJ0SX1QanI\nAmy2VtExZMXpsCE+NSk6BslEgoU1I5wSkCar1YpYaIGnXREAIBVZhM3GKQEPslqtSIQ5bYaW8Wb8\nOJvNhmSYAx+0fMpVIrTAayQDLKxpMhqNMGjViEe5CpqAZJg/NI+yWq2I86GOsHwzjocWUFRUJDqK\nrFitVhZWArC8Q4Beq+YbmQywsKZJpVKh2GFT7KIS+oEkSYgvcfToUUajESadFjE+1CleLBKGWa/j\nwRqPWH6oW+JDHSG8OA8nFyVmhIU1AyUOO0Jc4al40XAIFrORhwY8QbHDhvACH+qUbvlmzCkzj9Lr\n9bAY9dwikRBaXOBOMxliYc2AkrftoR/wZvx0JQ5eIwSEFufh4ujREzn5po4ARBYXUMqdZjLCwpoB\nh50T5gkILQThsrOwPklJsZ0jrITIAkePnsbFhzoCEA/Nw8H7SEZYWDPgdDqRWHj8vHBSlvD8HKrL\nS0THkKUSlxOJJV4jSpdYmkNpiUt0DFmqKnMhFPSLjkGCJRcDcDqdomPkFBbWDLhcLsSXAkglk6Kj\nkECJBR9KS0tFx5ClsrIyxOd9omOQYLEgr5GnKSsrQ2KB14iSpZJJxJcCcLn4UJcJFtYM6PV6lDis\nWOTTsWJJkoRY0M+b8VPY7XZoUlHEeF66YsUiYWilGOx2zs97ktLSUsSCfu4UoGCLQT9Kim1cuJsh\nFtYM1VVVYN43KzoGCRKaD8BeaObeeU+hUqlQXVGGeb9XdBQSZN4/i+qKMqhUKtFRZMlkMsFeaEZo\nnlNnlGreN4v6qgrRMXIOC2uGaivLEQrwZqxUQf8s6vhD80z1VRVYYGFVrHm/lzfjH1FXVYGgnwMf\nShUKeFFbWS46Rs5hYc1QaWkpEgqdoxcOh+F2e+B2exAOK/OVb8jvRV0Vf2iepbK8DLF5Flalis97\nUVleJjqGrNVVlSPEhzrFSsxzjvdKaEUHyDUlJSVIhOaRTCag0SjnP5/X60NnZyeCweXXWFarDR0d\nHXA6iwUnW1/xBR/KyraLjiFrpaWliCn0oY6A+DzneP+Y0tJSxM93i45BAiSTCSRC81xwtQIcYc2Q\nTqdDmdOOxYByFl6Fw+GHyioABIMBdHZ2KmqkNZVKIb7gR0kJt7R6FpvNBp2UQJQLrxQnGg5BJyVg\ns3F/yWcpKSlBfMGPVColOgqts8U5H8pdDuh0OtFRcg4L6wrUK2zhVSAQfKis3hMMBhAIBAUkEmNp\nPoBiWxHPR/8RKpUKtZXlmPfNiI5C62zeP4vaqnIuuPoRJpMJDmshlrjwSnGCvlnUc1rZirCwrkBd\ndSVCft6MlSYw40ZDNReTpKOxphIL3mnRMWidzc9Oo7GmSnSMnNBYU4ngrEd0DFpn4blZ1FZVio6R\nk1hYV6CmpgZR/5Ri9tGz2aywWh9/xWe12mCzWQUkEiPkncKGxnrRMXJCQ30doj636Bi0zqL+KdTX\n1YqOkRNaGuqw5J0UHYPWkSRJiPqmUFvLa2QlWFhXwGazwVloxsKcMhaWmEwmdHR0PFRa7y26Usp+\npKlUClG/B3V1daKj5ISKigpIkXkeIKAgsUgYqsgCKir4FiIddXV1iPo8nMeqIAtzXjiLzLBalTPQ\nk03KWeaeZW3NDbg6NY4ihzLOAnY6i/HBB+/fn7Nqs1kVU1YBYN43g3KnHRaLRXSUnKDRaLCxoRbT\nnkmU1zWJjkPrwOeewIaGWmg0GtFRckJBQQHKim2Y983A5uI2YErgc09gZ0uj6Bg5iyOsK9TUUIeI\nf0p0jHVlMplQXl6G8vIyRZVVAPC5x9He3CA6Rk7Z1NyAhZkJ0TFonSzMTqKNN+OMbG5phN/Na0Qp\nIt5JNDXUiY6Rs1hYV6impgaJeS8S8bjoKLQOYj43GvlDk5Ha2lpEvcqZ661kkiQh6uXcvEw1NtQh\n6lPWwIdSJeJxJBd8qK6uFh0lZ7GwrpBer0dDdQXmpvljk+/i0QikUBCVlVzZmQm73Q6bxYDF4Jzo\nKLTGFgN+2CwG2O120VFySmVlJaRQEPFoRHQUWmNz01Oor66AXq8XHSVnsbCuQltzAwLTfJ2T73ye\nCbTUV0Or5ZTvTKhUKrS3NMA3NS46Cq0xn3sCmzkdIGNarRbN9dXwebhbQL6bm55AO6+RVWFhXYWG\n+npEvRxhzXfz05NobeJ2VivR3FCPCF955r2IdxLN3PJtRTY11WOeAx95L+abQj13mVkVFtZVKCkp\ngVmTxBJfeeatVCqFqHcSDQ1ccLUSy3O9ZxGPRUVHoTUSj0WRWPBybt4KNTQ0IOqd5PZWeWwpOAez\nOsljvVeJhXUVVCoV9mzdhOnRAdFRaI3MTU+hstgKh8MhOkpOMhgMaG9uwMzYsOgotEamx4awuaUB\nBoNBdJSc5HA4UFFs5XqIPDY9OoA9WzfxyOJVYmFdpfZNmxByD3MldJ7yjQ9g7/Z20TFy2s4tbZif\nHBQdg9bIwtQQdm7hNbIae7e3wzfOayQfSZKEpakhbG5rEx0l57GwrlJZWRkcZh2C3hnRUSjLkok4\norPj2Lhxo+goOa2hoQHqcACRpUXRUSjLIkuLUIcCqK/n/NXVaN24EdHZMSSTCdFRKMuC3hk4LXqU\nlpaKjpLzWFhXSaVSYe+2NsyOcVpAvpmdHEVzTQUKCgpER8lpWq0WO9o2wDPGEaR84xkbxM72jdxB\nY5UKCgrQXFOB2YlR0VEoy2bHBrB3WzunA2QBC2sWtG3ahLBnhJPm80xgYgi7t/JVZzZs29yGpakh\n0TEoy5YmB7G1fZPoGHlh99Z2BCb4UJdPUskkwp4RbNrUKjpKXmBhzQK73Y7aMgf8Hm5Nki/i0QiS\ngWk0NzeLjpIXqqqqYEYMiwG/6CiUJYsBPyzqBHcHyJKmpiYkA9M8RCCP+DwTqC1z8ECNLGFhzZLd\nW9rg4yvPvDE9NoStGxu58jlL1Go19m5rwwynzuSN5ZXPbXzVmSVGoxFbNjRgeoxvIvKFf3wIe/iW\nLmtYWLOktbUVMd8EEvG46CiUBQuTQ9i+mas6s6l90yYsTQ1xR408IEkSQu4hbG7jdIBs2rGlHfOT\nLKz5IBGPI+ab4KLdLGJhzRKz2YzNzfVwD/WJjkKrtDDngzG5xJXPWVZSUoJKRyG8U2Oio9AqeSfH\nUOkohMvlEh0lr9TX18OUXMICp87kPPdQH7a21MNsNouOkjdYWLPouX27ERjp4QhSjnP3d+PFfbug\n0WhER8krKpUKLx3Yg9mBbtFRaJVmBrrx0oE9nA6QZRqNBi/u3Ql3303RUWgVJElCYOQWDu7dLTpK\nXmFhzaLKykpUOcyYneTWJLkqGg4h4R3H9m1bRUfJSxs2bIApsYh5v1d0FFqheb8X5uQiNmzYIDpK\nXtq+fRsS3nFEwyHRUWiFZidHUeWwoLKyUnSUvMLCmkXLI0h7OYKUwyb7b+HA9naYTCbRUfKSRqPB\ni/t2wcNrJGd5Brrx0v7dfAOxRkwmE/Zvb8Nk/y3RUWiFvAPdeOnAXr6ByDIW1ixraWlBQSqEef+s\n6CiUoWQijsXxPuzdvVN0lLy2fdtWJLwTiISWREehDEVCS0j6JrBt6xbRUfLavt27sDjeh2SCi3hz\nzbx/FpZUCC0tLaKj5B0W1izTaDR4cf9uePh0nHPcwwPY3FgFh8MhOkpeM5lMOLC9HVMDvEZyzdTA\nLRzYvplvINaYw+FAe2MVPCPcKjHXuPu68SLfQKwJFtY1sHXLZiR9Ezw7PYdIkoS54Vs4tG+P6CiK\nsHf3TiyN93MEKYfcewOxZ9cO0VEU4bl9e+Af6uYi3hwSWVpEam6SbyDWCAvrGjCZTDiwYzOmBnpE\nR6E0eafGUGE18tSedeJwOLC5sRruoX7RUShN7qF+bGmq5RuIdVJdXY1yqxE+97joKJSmyf5bOLhj\nC4xGo+goeYmFdY3s27MLocl+RCNh0VHoR0iShOk713H40D5Okl9Hzx/cB/9QF5LJhOgo9COSyQTm\nhrrw/IG9oqMohkqlwpFD++C5fY2jrDkgGgkjPDXANRBriIV1jdhsNjy3ox3jt66KjkI/YnpsCJUF\nWp5Iss4qKyuxpb4Sk318EyF3E323sLm+ktv0rLONGzeiokDL41pzwPitq3h+52bYbDbRUfIWC+sa\nev7QASRnRxBaCIqOQk+RSiYxe/sK3nzlJY6uCvDqyy8gOHwT8WhEdBR6ing0gvmhm3j15RdER1Ec\nlUqFt155CTO9l5FKJkXHoacILQSRnB3Bcwf3i46S11hY15DZbMarh/ZirPuS6Cj0FJODvWitdqG2\ntlZ0FEUqLi7GwW2tGOu5IToKPcVYz3Uc3L4JxcXFoqMoUm1tLTbVlGBysFd0lKwIh8Nwuz1wuz0I\nh/NjytxY9yW8+tw+HsO6xlhY19ju3btgDPsRmJ0WHYUekYjFEBi4gZ8cfkl0FEV74dBBxDz9CC/O\ni45CjwgvziPmGcALhw6KjqJor738IuYGbiARi4mOsiperw8fffQxPv74I3z88Uf46KOP4fX6RMda\nlcDsNExhP3bv4tzVtcbCusZ0Oh3efPk5THRf5MR5mRm7fR1721vgcrlER1G0goICHDm4G2O3roiO\nQo8Y676CIwd3o6CgQHQURSspKcHetmaM3b4uOsqKhcNhdHZ2IhgM3P9nwWAAnZ2dOTvSKkkSJm9d\nxJuHn4dOpxMdJ++xsK6D9vZ2lBoleCfHREehuyJLiwhP9OGl5w+JjkIA9u7eDe3CNOb9XtFR6K55\n/yy0i9PYu3u36CgE4OUXnkN4oi9nT4gLBIIPldV7gsEAAoHcXOcxOzmKEoOEtrY20VEUgYV1HajV\narx55EV4ei5x4rxMjN26gpf37kBRUZHoKATAYDDg9RcPYvzmBb6JkAFJkjB+8yLeeOkQDAaD6DgE\noKioCC/v3Y6x7suioxCWF+xO91zGm0dehFrNKrUe+F95nTQ0NKCt2oWxXi4uEc3nmYRhcRoH9nNP\nSTnZtnUryo0SPCMDoqMonme4HxUmCVu38MQeOTmwfx8Mi9PwT0+KjpIxm80Kq/XxLZ+sVhtsNquA\nRKszdvsG2qtdaGhoEB1FMVhY14lKpcLbr7+KyEQvFgN+0XEUK5mIY/L6afzirdd4GonMaDQavPv2\n6/D2XuSBGwJFI2F4b1/Cz996neehy4zRaMQv3noN49dO59yxxiaTCR0dHQ+VVqvVho6ODphMJoHJ\nMrcY8CM63ou3Xn+V2yGuI63oAEpSVFSEnx55Hn88dRptL77NL7oAIzevYldLDZqamkRHoScoKyvD\n4b1b8f21s9i4/7DoOIo0fO0sjuzdhrKyMtFR6Amampqwq7kat29eReP23HpL5HQW44MP3r8/Z9Vm\ns+ZcWZUkCSNXT+HnR57nlLJ1xhHWdbZj+3Y02I0Yv9MtOoriBGanIc0O4fVXj4iOQs/w/KFDsCaC\nmBkfFh1FcabHhmBNBPEct7GStddfPQJpdghBb+5tl2gymVBeXoby8rKcK6sAMH6nGw0OE3Zs3y46\niuKwsK4zlUqFn7/9BpaGuzg1YB0lE3GMXT2J9376E27uLHM6nQ7vvfMWPDfPcmrAOoqGQ5jpPof3\n3nmLW/TInMViwa/efg2jV77PuakBuWwx4EdouAs/f/sNviEVgIVVALvdjp+99iKGL5/krgHrZOjG\nRezZWIuWlhbRUSgNlZWVeHXfDgxdPsVdA9aBJEkYunIKr+7ficrKStFxKA0bNmzA7g3VGL5xUXQU\nRUglkxi+fBLvvPYi7Ha76DiKxMIqyLatW7Gp0o4Rbpa+5rxTY9AHJ/GTI5wTmUuef+4gyvQxTA3e\nER0l700N3kGZPo7nDh0QHYUy8PorR6ALTsI7xT2+19rIrStoq3Rg29atoqMoFgurICqVCj976w1o\nvCOcq7eGQgtBuK+fwofv/jQn50spmUajwXs/+ykWB6/yaOM1FJidxuLgVbz3s59yV4AcYzKZ8OG7\nP4XnxmmEFnJz8/1cMDM+DK1vFO+89TqnAgjEwiqQxWLB3773c3i7z2GB81mzLhGLYeDcUfzitRdQ\nXV0tOg6tQHFxMf7qZ29i7PLxnD3hR84ioSWMXz6Ov/rZmyguLhYdh1aguroa7776PAbOHUUiFhMd\nJ+8sBPzwdp/D3773c1gsFtFxFI2FVbDy8nL8+q0jGD5/FPFoRHScvCFJEvoufofn2huwfds20XFo\nFZqamvDWc7sxcO5bJJMJ0XHyRjKZQP+5o3jr+T3c5i3Hbd+2Dc+1N6Dv4nec851FsUgYQ+eO4tdv\nHeE2bzLAwioDbW1tOLK7DX3njyGVSomOkxdGbl5GfQHw2itH+AonDxzYvw876l0YuHyaN+QskCQJ\nA5dOYWd9Cfbvy629POlxKpUKr71yBHUFy799tHqpVAr9F47jlT1taGtrEx2HwMIqGy+98AI2uMwY\nun5edJScNz06BI1/BO+9+w7n5OUJlUqFt994HSWqRe5hnAXjt2+iRL2Et9/gnLx8odFo8Ot334HG\nPwLP6KDoODlv6Pp5bHCZ8dILL4iOQnexsMqEWq3GLzreRsGSB5MDt0XHyVnzfi98Pefwm/fe5Xyj\nPKPX6/HhL3+O+MQteKfGRcfJWd6pccQne/DhL38OvV4vOg5lkcViwd/+6ufw95zHvN8rOk7Omhy8\njYIlD37R8TbUatYkueD/EzJiMpnwN7/+BSLD1zE9OiQ6Ts5ZDPgxev4bfNjxE5SWloqOQ2vAarXi\nN7/6GWa7TsE/PSU6Ts7xT09htusUfvOrn8FqtYqOQ2ugrKwMH3b8BKPnv+HhNCswPTqIyNB1/M2v\nf8GdZWSGhVVmiouL8T//+j0s9F1kac3AYsCP4bNf4cO3j2Djxo2i49Aaqqqqwn977x1MX/uOpTUD\n/ukpTF/7Dv/tvXdQVVUlOg6toY0bN+LDt49g+OxXLK0ZmB4dxGLfJfzPv36Pu2bIEAurDJWUlODv\nWFrT9mBZ5eR4ZaitrWVpzcCDZbW2tlZ0HFoHbW1tLK0ZeLCslpSUiI5DT8DCKlMsrelhWVUultb0\nsKwqF0trelhWcwMLq4yxtD4byyqxtD4byyqxtD4by2ruYGGVuXuldbHvIiYGekXHkY25GTeGz7Gs\n0gOl9eoJzEyMiI4jGzPjw5i+eoJllX4oree+wtyMW3Qc2ZgY6GVZzSEsrDmgpKQE/+u/fAjDbB/6\nLn6v6NN+JEnCRH8PZq9/h//+y7dZVgnAcmn9P/76Vwj3XcTwzcuKPlxAkiQMd11CpP8S/s+/eY9l\nlQAsl9b//su3MXv9O0z094iOI1QymUDfxe9hmO3D//ovH7Ks5ggW1hzhcDjwd7/5a2y0q9F78nNF\nnqueTCbQf+l7GLz9+Pv/+ldoaGgQHYlkpKKiAn//P36DsqQft898g3gsKjrSuovHorh95huUpebw\nf/2P36C8vFx0JJKRhoYG/P1//SsYvP3ou6TMwY9IaAm9Jz9Hq0ONv/vNX8PhcIiORGliYc0hBoMB\nv/r5O3h99yb0nfwzArMe0ZHWTWRpET3ffYZWh4Y/MvRUFosFf/vhr7G/sRS9J/6MpeCc6EjrZik4\nh94Tf8b+xlL87Ye/5sEZ9ET3Bj9a7Wr0fPeZogY/ArMe9H3XiTf2tOGXP3sHBoNBdCTKgOa3v/3t\nb5/2h8PDw3C5XOsYh36MSqVCTU016sudOHf8G4QlDQodzrw+XnF5vurXePvQDrz2yhFotVrRkUjG\n1By/RHYAAAkbSURBVGo1mpsa4So04NyJo5CMBbBY7aJjramZ8WFMXT6OX7/xIg4d2M/TeeiZtFot\nNm3cCJMUw7mTx6G3OmGyFIqOtWYkScLkQC8CPefxm1+8ha1bt+T1PTOXeb3ep749VUnPmOx17Ngx\ntLa2rlkwWh2/34+PP/kT3BEN6ncchLkwv06uiceiGLl5Geq5cXzwzpucAkAZm5qawr990oklvQN1\n2/bBYDKLjpRV0XAIw9fPoSA2hw/f7UBFRYXoSJRjBgcH8XHnF0jZq1G3eRd0+vwadQwtBDF89QzK\njUm8/+47fDsnc729vTh8+PAT/4yFNcclk0lcunwFX3x3FqbqVtS0boVaoxEda1UkScL02CBmbl3E\nwa0bcPjFF3hEHq1YLBbD6TNncezCNdiad6CyqTXnR1fuLT4MDlzDkX07cOjgAeh0OtGxKEeFw2Ec\n++4kznb1wbVpN0prGnP+GkklkxjrvYHIeC9ef/EAdu/aCU2O3xuVgIVVAYLBID7/+lvcHJtB1dYD\ncJTm5khLaGEeI9fPwKWN4923foLKykrRkShPzM7OovOLrzHsj6B2xyEU2nPz6MV5vxdj186g3mFE\nxxuvcdoWZc3k5CQ++ewrzCZ0qNt2EObCItGRVsQ/PYXJG2fRXlOCN187Aqs1v94+5jMWVoWQJAn9\n/f344xdHEbGUoHrTjpz5wYnHopjsu4XweC9ef2E/9uzexadhyjpJktDV1YU/HT0JtbMO1a1bc2aa\nQDQcwnjvDaS8I3jnlRewZQvn4VH2JZNJXLh4CV99fx6m6lZUtrTlzDSB0MI8xnuuwrg0g3fffBVN\nTU28RnIMC6vCRKNRnDt/EScvXkWqqATlLVtgLZbnPnPhpQVM3ulGxD2IXe3NeOm5Q7DZbKJjUZ5b\nWlrC96fP4uy1bmid1ajcsEW2C7OWgnOYvNOFhHccB7a34/lDB7gDAK25QCCAE6dO43J3P4zljajc\n0C7bhVlB7zTc/Tehnp/BC3t2YP++PdwBIEexsCpUNBpF182bOH7mIhZUJpQ0bYazskYWT5zzfi/c\nfTchBSbx3K6t2LNrF4qKcmM0mPJHKBTC1WvXcOLcFcTNDpQ2b4a9pFz4NSJJEuZm3JjuvwldyI+X\n9+/Cjh3bOZeb1t38/DwuXr6MU5duQGWvRHnLZhQ5nKJjQZIkeCfHMDNwE4VSGC8f3IMtmzezqOY4\nFlaFSyaT6Ovrw/HT5zEZjKCgshGuylpYrPZ1vTFHQkvwTo5iwT0MY3wRLx/Yg21bt8BoNK5bBqIn\nicfjuHXrFo6dvoC5hBqFFY1wVtau+5Sa0ML88jUyNQi7NoXDh/aira2NC6pIuEgkgus3unD87EVE\ndAUorGiAs6IGRvP6jfZLkoSl4BxmJ0exODmISqsRLx/ah5aWFk4hyxMsrARg+WIfHx/Hrd47uHG7\nHwuxFAzOKjgqamEvKc/67gKSJGFhzgvv5Bgis+PQxJbQ3tyA9tYWNDc38weGZCeVSmFoaAg9d/px\no7cfUbUeBmcViitqYHWWZn1/01QqhaB3Gr6pMUS9EzBKMWzZ2Iy2jS2or6/nfqr/f3t309TGkcBx\n+D8SL0ZYyBLIhqK8e7Bxkt2qJN//UyS1W8sW4MOmQpANSBZYYF5GkwOnlNcJh6zd9j7PUTWHufTM\nr9Q93RSnruvs7+/nn7t7+cfey8yXH+bB8Gk2tv+Sbv/P3xN8XteZvD7K+Jf/5Ork53SXWvnu6538\n/Zuv8vTp008+G8KfS7DynqZpcnx8nIODl/nx33v5aXSa5UeP017t5UG3l063l9W1R1l6sHKvB8LN\n9VUuzt5kdj7N5fk09cVZriavM1hdzvd/28mL58+zvb0tUvlsNE2To6Oj7B28zI+7+xmNp1nuP0m7\n08tKdy2ra4/S6fay9OB+0/TX7y5zcT7N7OxNLs/PUl9MczV5lc1BL99/s5Od58+ytfXplyPAfdV1\nncPDw+wdHOSHf+1nPLvKcv9x2p21rHR7We320ll7dK+PtpqmyfW7y8zO3uTifJp359PUs2mu3rzO\nX7c28u3XO3n+7FmGw6Ex8gUTrPyh2WyWw8PDjMfjjE7GGR2f5vXJOJfXt1lcXUtrcTlVq5VUraSq\n0szrZD7PvL7NzewsC6kzXO9na7iRreEgg8Egm5ub6fc/7rID+F+ZTqc5OjrK6XicV8fjjE5O8+rk\nNNd1srjaS2thMWm1UlV3/4o2zfxujNze5GY2zVI7ebKxns2N9TwZDrI+GGRra8uWO3wRmqbJZDLJ\naDTKeDzOL8enGR2f5vh0krpqZ6GzllZ74W6MtNpJ0yTNPM18nvnNVW5mZ1lZWsjjjUE2h+vZ3Lh7\nj2xvb/vI8P/I7wWrMy5JcncG+4sXL977/fLyMpPJJNfX17m9vc18Pk/TNGm322m321lcXEyv18vD\nhw+FKV+0Xq/3Xlw2TfObMVLXdebzeZK7I2Lb7XaWlpbS7/ezsnK/2Qr4HFVVlcFg8N5JUk3T5O3b\nt5lOp7m5uUld16nrOlVVpdVqZWFh4TdjBD5EsPK7VlZWPETgA6qqSqfTSafzeezlCh9bVVXpdrvp\ndsvcEovPhxX9AAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbAC\nAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROs\nAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEE\nKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0\nwQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAU\nTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAARROsAAAUTbACAFA0wQoAQNEEKwAA\nRROsAAAUbeGPLtjd3f0Y9wEAAP9V1TRN86lvAgAAPsSSAAAAiiZYAQAommAFAKBoghUAgKIJVgAA\nivYrRVMNT18SlH8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade432add8>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that while I chose the points to lie along the major and minor axis of the ellipse, nothing in the constraints above require me to do that; however, it is fairly typical to do this. Furthermore, in each case I show the points evenly spaced; again, the constraints above do not require that. However, the technique that we develop in the next section *does* do this. It is a reasonable choice, after all; if we want to accurately sample our input it makes sense to sample in a symmetric manner.\n",
      "\n",
      "There are many published ways for selecting the sigma points. For now I will stick with the original implementation by Julier and Uhlmann [2]. This method defines a constant kappa ($\\kappa$) which controls how spread out the sigma points are. Before we work through the derivation, let's just look at some examples. I will use the class UnscentedKalmanFilter from FilterPy to generate the sigma points for us. It is convention to write\n",
      "\n",
      "    import UnscentedKalmanFilter as UKF\n",
      "    \n",
      "because UKF is the standarized shorthand used in the literature for this filter.\n",
      "\n",
      "I will plot the sigma points on top of a covariance ellipse showing the first and second deviations, and size them based on the weights assigned to them. I am using the covariance ellipse\n",
      "\n",
      "$$\\mathbf{P} = \\begin{bmatrix} 4&2\\\\2&4\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import array\n",
      "import matplotlib.pyplot as plt\n",
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "from filterpy.common import plot_covariance_ellipse\n",
      "\n",
      "x = array([0, 0])\n",
      "P = array([[4, 2],\n",
      "           [2, 4]])\n",
      "\n",
      "sigmas_kp5 = UKF.sigma_points(x=x, P=P, kappa=.5)\n",
      "sigmas_k2 = UKF.sigma_points(x=x, P=P, kappa=2)\n",
      "W0 = UKF.weights(2, kappa=.5)\n",
      "W1 = UKF.weights(2, kappa=2)\n",
      "\n",
      "for i in range(len(W0)):\n",
      "    plt.scatter(sigmas_kp5[i,0], sigmas_kp5[i,1], s=W1[i]*500, c='g')\n",
      "    plt.scatter(sigmas_k2[i,0], sigmas_k2[i,1], s=W0[i]*500, c='b')\n",
      "\n",
      "plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, std=[1,2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VkjTH2Y0BLnTbuORfRL0msLZoQlH2b5GSJEl4cv3Jq/78ifUnuNHFDHMsFX7iYzCKpj0U\nInoDLG8gInqZHyY4vz3EprcNNxns62I1Kg/bVLDdHcELYmR5zh3aiGYUH5lERADagwDfX+/i/OAl\nRBiXMxxU4BVC4I61O67683euvRNCiAMZC904RZZgGjL8xMdwxBIHolnF0EtEcy3PBV7acfHidgcX\nhhdgmCkOL+1vOcOVnKqfwpkTZ173/TMnzuBk/eSBjoVunGMpDL1EM47lDUQ0t+I0w/mtIbbcHtrh\nDpYWNFTt6ZwWq2oV95++H/ccvedyfe8da3fgZP0kOzcUQMVS0On7cEcxhBCswSaaQQy9RDSXvCDG\n+W0Xm942/GyAI8smdG26b35V1Sre1nob3nnLOwEA7tCd6njo+qmKDFUVCJIQQZTCNrVpD4mIXoOh\nl4jmzs5ghIudITa8DchqgqMrFpQZ2kJW5kKoQjI1BWEWIUwyhl6iGcTQS0RzQwiBi20Pm/0B1v0N\n1CsSmnVz2sOiktA0CUkUI4zTaQ+FiK6AoZeI5kKeC5zbHmJz0MVOsI3lpgbH4imQJkdXZQxGMaIk\nm/ZQiOgKeMYnotJL0hzntgbYHHbQjds4xP67tA90XUaSxQhjhl6iWcTQS0SlFsYpzm0NseFuw0v7\nOLJsQlNZM0uTp6syMmSI0hR5LiDPUJ04ETH0ElGJjcIEL24Nse5uIIaPI8vWgfffpfmiKkCSjUsc\nLINPsUSzhI9IIiqlgR/h/PYAl7wNSGqEw02TM2+07wxNRpTFCOKUoZdoxvARSUSl03VDnN/pY93b\ngGGmWF5ghwY6GLoqI4m5mI1oFjH0ElGpbPZ8XOwMsO5dQq0ioVk3pj0kmiOKIiHMM2RZPu2hENFr\nMPQSUSns9uDd6Pex7q9jsaGi5nCDADpYsiRBiBy5ENMeChG9BkMvERWeEALnt11sDLrYGm1hhT14\naUokCYC0+wkRzZI99e1J0xS/8Ru/gbW1NTQaDdxzzz149tlnJzU2IqJrEkLg3NYQ6/0OtoNNrC3p\nDLw0FZubOp580sZ/+3MH/+W/1PG1r1Vx4QLryYlmxZ5Cb5ZlePOb34xvf/vb6Pf7+IVf+AXce++9\nkxobEdEbEkKMW5INutgJt7C2aHLTCZqK579v4j//5yr+n884+Od/VvDYYyo+8pEqfvZnG3jmGXva\nwyMi7DH0GoaBP/zDP8Ta2hoA4L777sMPfvADdDqdiQyOiOhq8vzlwNvvoB1u4fCSCUPnphN08DY3\ndfz+f3Xg+zIACZByQBrX9A6HMj7wgRpnfIlmwETfA/zWt76Fw4cPo9VqTfJqiYheZRx4B1gfdNCN\ndnB4yYSuMfBej1wIpFkOIYA0y5GJ8ecAIMsSZEiQJEBRZOiqDAmsTb2Wf/s39eXA+zJJAPjhQrbh\nUMY//7OGY8fCgx8cEV02sdA7GAzwsY99DJ/+9Kev+PMyBmFNG68ML+N9o8nj8TIZeS5wdr0HTyRI\n9BA/emyldIFXVcen5nqjftPXIYRAFGeIkgxRko4/xiniLEMucuQiQ5ZnyIVAjny89moceSFLEhRF\ngSZr0FUFuqbA0FQ4pgbbZEeMV8qzHI8//oqSGvHqmd5dX/+6gd/8TQWKMvnyG55b6HrN+7EykdAb\nRRF+6Zd+CR/4wAfwy7/8y1e8zAMPPHD58zvvvBN33XXXJG6aiOZIngu8sNHDxf42OuE2jq7apQu8\nexHFKfwwwShKMIpShEmIJEsQZTHSPEGcxciQQZElyLIERQJkRXq5zdZ4Fhgvf8xigSwFFEmFpqow\nZAOWZsHWTDiWjqqto2Lp077Ls+k1M71EtH8effRRPPbYY5e/vvvuu6962T2H3izL8Ku/+qu49dZb\n8clPfvKql/vwhz/8qq/LUPe7+0qpDPeF9h+Pl725vGit30En2sbhZROB7yKY9sD2we4M76A/uOZl\ngziFO4rhhQnCNEaUhgjSEFEWQVEEdFWGpkrQVBkVU4KqyrjeQCaEQJKmSDOBYdTH1jAHchmmaqGi\nOagYJhoVEzVbn+syiHe9y8ZTT73xDPjP/3yEft/dl9vnuYWuVxmPldOnT+P06dOXv37uueeuetk9\nh94PfvCDkGUZf/EXf7HXqyIiuqLdtmQbg+448C6Z0NX5neGN0gzuKIY7ijFKQozSEUbJCJBymLoM\np6KgqWlQlL39jSRJgq5J0DXANhUsVIEkzRGEIdqhj36kYxjWUTUsLFRN1O353P3uR34khePk47pe\nSQC5Aogf/u1rtRw//uPJFEdIRMAeQ+/58+fxhS98AbZto17/Ye3ZN77xDdxxxx17HhwR0Ss3ntjt\n0jCPJQ0CAsNRjIEfYRTF8NMR/MSHQArHUrBYUQ/k76KpMrSKjFpFwyjI0PN3MIh1+HEDXuBgdcGG\nIs/X/8/qaow/+VN/3MFh9OrQW6vl+PKXh1zERjQD9hR6jx8/jjzn/uJEtH8utj1svKIP77wF3izP\n0ffHYdeLfbixi1TEMA0ZzboKQ59eKyzbUmBbCkZBhra3jTCrIUoyrDRsOHO24O3WN4f47GdzPPNd\n4NFHDFSTDB/4RRc//uMJAy/RjOC2RUQ0szZ7Pjb6fWyNtrC2ZMxVH944ybDV98dlDLEPNx5CknPU\nHBWWaUCaoW1ubUuBoUvoDFyseyHitIXVRhWNynyVO6yuxrCrCd7+1gy3rwxwZDGb9pCI6BUYeolo\nJnWGAS52Blj317HS0uZmp7Uky7DR8dDzAmz0duAlHnRdQrOhwtBnd/ZUUWQsNw0MvQRboy3kEBCo\nYqEym5sy7L5oEGKyXRayHJAhQ56d1yRE9DKGXiKaOQM/woX2AOveJSw2VDhm+U9VWZ6j64bo+yEy\nNccgHgBKiOWqBq1Ai/ZqFQ2KkmLH3QYAyJKEujM7M75u6uLs4CyeXH8SAHDH2h04VT+FqlqdyPXn\nuYAiK1D3uIiQiCav/M8kRFQofpjg/PYAl9x11KoSas7szm5OQi4Eel6EvhdiGLkYREM0WzYOLZqI\nwmKumXAsFUKk2PG2oUgyDE2BqU//6cZNXTz43Qfx8LmHL3/vobMP4cyJM7j/9P0TCb5ZLmBIChRO\n9RLNHL4UJaKZEcYpzm0OcMlbh2llaNbKvfmBHya4sD3ExW4HF91LCMQQS00VSw2zULO7V1KxVdiW\nhE7QxWbPH298MWVnB2dfFXh3PXzuYbwweGEit5FlArIk77ldHBFNHh+VRDQTkjTHi5tDrHubkNQY\nywuz85b4pCVZhvWuj/PtPi65mxgmPbQaKpYW9FJ1p6hXVGSI0Atc7AxGUx2LJEmXSxqu5In1Jyay\nODAXgCIpUDnTSzRzpv9+ExHNvSzPcW5rgA1vCwl8rDVnc/HTXgkI9L0IXTdEL+zDTzxUHQXVGap5\nnSRJktBqaNju9mF4BqqWDtsod7lKnOTQdA2aOh8LL4mKpDxTCkRUSLu7rW0OO/DTAQ4tmZBLOEsW\npRkutj281O3honsJieRjpaWh6pR77kFTZVRtGW40RNedXr9aIQTuWLv6pknvXHvnnjs5ZLlAngOG\nqsHQGHqJZg1DLxFN1Us7LraGPXTjNtaWzFIuABr4ES5sD7A+3EEvbmOhrmCxoc9N3WfFVhFkI7hh\nhDBOpzaOU/VTOHPizOu+f+bEGZysn9zz9SdJDl0xGHiJZlS5pxiIaKZt90fYHAywE2xjban4i7de\nK8tzbPZG6I98dIIODF1gtWGUcib7jciyhIqtYBgP0XFNHG5VpjKOqlrF/afvxz1H78ET608AGM/w\nnqyfnEjnhijJocvmTHSqIKLX4yOTiKbCHcW41B1iw9/AclMr3W5rfphgsz96uXZ3iEZNg23O7wxg\n1VaxMRrBCyKkmT21PrZVtYq3td6Gty++HcBkN6eIkxyGos/NRipERcPQS0QHLkoyXNgeYt3bQL0i\nw7HKdSrquAG2Bz46YQeSkmKlOT+lDFcjyxIMXUKQhvDDZOobVkx6JzZgPNPraAZMrVzHM1FZ8JFJ\nRAcqzwXObw2x4W9D0RI06+Xp1JCJHJvdEbq+h07YRtVRUHPK3Wv4RliGjMAP4M1A6N0PcZLDMHWW\nNxDNKD4yiehAXWy72PK6CLIhjixa0x7OxERpho2Oh04wgJcM0KrrMI35nt19LctQ0HMDjMIEmcih\nSOX5+6RZDggFulqsbaOJ5glDLxEdmPYgwNZgiG7YxuHl8nRqGAYRtno+OqMuUinE8oIOlcHndWRZ\ngq5ICLMIYZTBMcvzN4oTAV1hqzKiWcbQS0QHwgtivNQZYN3fwNKCVpqdxzpuiO2Bh51gB4aeY7mm\nT2Rnr7LSNAlJHiNJ82kPZaLiJIeuWLBY2kA0s/joJKJ9F6cZzm+72PA2UKtIqNjlOPVs90fYcV20\ngzaqjowq63evSVVlJGGKKE0BlKeuN4wzWIoByyjHsU1URuWYaiGimSWEwIVtF5veNmQ1Qate/GCY\nC4H1ro+t4RA7wQ4aNaX0O6tNiqbISPMEcclmeoMoh63acMxyb7NMVGQ8SxPRvrrU9rDl9uBnAxxd\nKf7CtUzkWO/46HhDDJIulho69JL1GN5PuiohycoVeuMkhyQUWLrOml6iGcbQS0T7puuG2OiPd1w7\nXIIthtMsx6WOi/aoDy8ZYmlB50r9GyTJQI4MIp98n9xpGUUZLNVGhbO8RDONoZeI9kWUZFjveNgc\nbWGpUfwd15Isw6W2h51RF0HmccOJmyRJEiDGJSICAhKK/UIIAIIwg6NaqFjFL90hKjOesYloX7y0\n42LT34ZhZIWvd90NvNt+F1HuY6VpMPDugSQBQuTI92FXtGkIogy2ZrGel2jG8axNRBO31Rthxxtg\nlLlYWij2Cv3dwLvldxALH0sLOuSCl2lMmyxLEBAQJSjrDeMMiqTD1g3W8xLNOIZeIpqoIEqx0XOx\nPdrG8oJe6DreNMsvB95EjBh46XVGQQZHs1FlaQPRzGPoJaKJyXOBCztDbPnbqDiAbRZ35ivLx4vW\ntv0uA++EZbmALCml+HuOwgy26qBqM/QSzTqGXiKamI2uj22vhxg+Fgvcj3e3D2971EeUs6RhkvJ8\nvHhNkSXIBd+5LssFolTA0Sx2biAqAIZeIpqI4SjGZt9FJ2xjtWkWeiveja6PtjeAlw6xzMA7UUII\nyJJc+MALjEsbLMWGY/EYISoChl4i2rM0y3Gx7WJztIlmTS10e7Ktvo+O72KY9LDU0CErDDOTlOWA\nJMmlCIlukKKiVVBjPS9RIRT3mYmIZsbFtodtvwNZTdCoFvdt3o4bou166IYdLNa58cR+yDIBRVKg\nFrzlW5YJBGGOql5Bo1LsDiVE86LYZx0imrquG2JnOMQg7mKlWdwZr2EQYXvgoR200ayp3Fp4nyRp\nDl3RoBf8BYUbpHBUBzXbKHyAJ5oXfKQS0U1L0vzyrmuLDb2wT/5RkmGr52Mn2EG1IsMqcNeJWZek\nApqkQy94T1vPT1E1qpzlJSqQYj5DEdFMWO96aAddaHqGql3MXdeyfBzc26MuDCMv7P0oijjNoSkq\nTK24f+ckzREnEqp6BXWboZeoKBh6ieimuKMYO0MP/Wi84KuoNnsjdMM+MinEQoHrkYtACIE0AzS5\n2PXS7ihFRa+g7hilWJBHNC+Ke9YhoqkRQuBSx8NOsIOFmlrYANMeBuj4LrxkiMWGVug2a0WQpAKq\nrMLQit2yzPVT1PQqGg5neYmKpJjPVEQ0VVv9EbqjAVIEaFSK+Ta1F8bYGfrohh206jqUgtYjF0kY\n5zAUA6ZezGMGAMI4g8gVVAybu7ARFQzP8kR0Q6Ikw3bfx07QxvKCUcjZ0TTLsdUP0Ak7qDlKofsK\nF0kU5zAVA5ZR3NDrjlJUjRrqnOUlKhye6YnohlzqeNgZdWBbgGUUcwX+Vn+EXtCDrKSoOsUNYEUi\nhECU5DAVE7Ze3Nppb5ShqlXRrJjTHgoR3SCGXiK6bn0/Qsd14aUDLNaL+dZu34vQH/nwUxetWnHD\nV9FEsYAm67AMrbCt7fwghSoZqJpmoWerieZVMc88RHTgdlt7bQc7aNU1KAXcnjdKM+wMfbSDNhaq\nGrcYPkBBlMJSTdhGcV9o9L0Udb2OZpWzvERFxNBLRNdlszdCZ9SHJMeoOcULLgICWz0f3aAH0wQ3\noDhgQZQQFI6mAAAgAElEQVTDUm1UrWK+QxDFOeJYQt2oMvQSFRRDLxFdUxCl2B546IRtLC0UcwFP\n143QDzxEYoRGpXihvciCKIMi6XB0HUZBd2LrewnqRh3NmgVF5lMnURHxkUtE17Te9dAJuqg6ciE7\nHcRphq47Qi/soVnTZ35DgVzkyEU+7WFMTBBkcFQbFauYL5iyTMAPcjSMOhZr1rSHQ0Q3iZX4RPSG\nvCBGzx/BT4c4tljMJ/ydQYB+NICpY2ZDeyIS7AQ7OD88j3bYBgAsmos4XjuOJWsJmlTM2ek8Fwji\nHA3bRtUq5n0YeAkqWhUNxyrsTDURMfQS0TVs9kboBB00qhqUGZ8hvRI3jNEfjTBKPaw2Z3Om8aJ/\nEd948Rv4Tvs7V/z5Wxffivfe8l4ccY4c8Mj2LoxyaLIB29Shq8ULjEIIDPwUh50GlurFfNFHRGMM\nvUR0VQM/Qs/3EOY+VpziPeHnQqDdD9CLeqg56kx2a3i+/zw+98znkIoUAGAoBtYqawCAS94lxFmM\n77S/g2c7z+JDb/sQbm3cOs3h3jBvlKKiLaBW0N3Lhn4KXbZQtyw4ZjFnqolojKGXiK5qs+ejHbax\nUNNmvg72SrpuiH7oAlKCij17s7wX/YuXA6+lWnhP8z8h757E+f93CQDwMz+6A3n5BXyz+zcI0gCf\ne+Zz+J2f+p3CzPjGcY40k1BxKoXt2tD3EiwZS1jkLC9R4e25uO3ixYt497vfDcdx8JM/+ZP43ve+\nN4lxEdGUdd0Q/cBHIkLUC7hrWZrl6HkBBtEACzO4CUUiEnzjxW9cDry/2Pxd/J8vvgv/82+P4nv/\nauJ7/2rif/7tUfyfL74Lv9j8XViqhVSkl3+nCIajFFW9ioajQy7gdtV+mELKddTNChrcdpio8PYc\nen/7t38bb33rW9HtdvH+978f73//+ycxLiKaIiEEtnojtIM2WjUdUgEDS9cNMYxdGAaga7O3eG0n\n2Llcw/ue5n/C1774ZoTB68cZBjK+9sU34z3N/wgA+E77O9gOtg90rDcjTXNEsUBFq6A+g7Ps16Pv\npqgbdbRqZiEfA0T0ant6JhgOh/j7v/97fOITn4BhGPjYxz6G8+fP47vf/e6kxkdEU9AZhuiHQwgp\nRrWAs7xxmqHnB3BjF/XKbI7//PA8gHENb949ecXAuysMZIjuKeiK/qrfnWVukMLRHNQdo5DbDodx\nhjiW0DBqaNW4GQVRGezp2eAHP/gBTNOE4zh417vehQcffBCnTp3Cv/3bv+H06dOvumyr1drTQGeR\npo3fMi3jfaPJK8rxkucClwbbiNQYt6y0ULFnrzTgWtbbLlI1Q6tZwUJj9mYZc5Ffbku2Vlm7XMP7\nRs49u4S1/7CGc4NzaIdt2I4NWZrNMJnlOXqejEMLazh2qAnTmM0XHm/E3Rrh+HILb1pdw/JSbdrD\neUNFObfQ9M37sbKnM5Hv+6hUKnBdF8899xx6vR6q1Sp833/dZR944IHLn995552466679nLTRLRP\ntno+uqM+ZDVFxXamPZwbFsUp+l4AL3FxuMEZumkYeCkcrYK6YxYy8I7CFHEk4VhzAYealWkPh4je\nwKOPPorHHnvs8td33333VS+7p7OR4zjwPA9HjhxBuz2etXBdF5XK608SH/7wh1/1dafT2ctNz4Td\nV0pluC+0/4pwvKRZjudf6uLF/otYWVQx6BdjwdQrbfZ8XOptQ9JCBMHs7mq2aC4CGLcl+5kf3cH3\n/vXoG17+xI/u4O+99cu/O/JH+z7Gm5GmOXa6CQ7ZFehSikF/MO0h3bCLWwFq6hJ0JOj3e9MezjUV\n4dxCs6GMx8rp06dfVV3w3HPPXfWye3pv7E1vehOCIMClS5cAAHEc4+zZs7jtttv2crVENCWdYYhe\nOICuC1hG8TYSSLIMg1EIP/VQs2d7hvF47TgAIM5iyM0XYFpXD+imlUNqnkWcxa/63Vk09NPx4jXH\nhFHAzSj8IEWeaWjadW5GQVQyewq9tVoNP/uzP4tPfepTCMMQn/nMZ3D8+PHX1fMS0ewTQqDjBuhH\nfTSqxavjBYC+F8FLfFi6DGXGF08tWUt46+JbAQDf7P4N7r3v+1cMvqaV4977vo9vdr8EYLw727K1\nfKBjvV5JmiOIBKp6Fc1qMUtL2oMYLauJ5bpdyN7URHR1e54K+fznP49f+7VfQ7PZxO23346//du/\nncS4iOiA9bwIg9CDJKewzeLNcOVCYDhK4MUuFhdme5YXADRJw3tveS+e7TyLIA3wP7r/N37mvv8I\n0T2Fc8+OF7ad+NEdSM2z+B/dLyFIA6iSivfe8l6o0mzev76XoqrXsOBYhdxy2PVTyMLAgsWODURl\ntOcz55EjR/DII49MYChENE3tQYB+1MNCQWd5h34ML/agqmIm+/JeyRHnCD70tg/hc898DkEa4KHt\nv4ShGDj0Hw4BAP7eW0e8PS5pUCUVH3rbh2Z2N7YgzJDGElaqtULO8goh0BnGWLEOY7lhsy8vUQnN\n5nQBER0oL4gxCEaI8xAVu3izvADQ90O4iYfqjPblvZpbG7fid37qd/CNF7+B77S/gyiLcG5w7lWX\neeviW/HeW947s4E3zwV6XoKmuYRW1SpkX96Bn0KTLCxYlUKGdiK6tmI9OxDRvtgZjGt56xW1kDNc\nYZzCjyNkIoZtFi+wHHGO4Dff8pvYCXZwfnj+cg/fRXMRx2vHsWwtz2xJAwC4oxQGLNQtG43K7PVF\nvpY8F+gNE6zZK1hZsKc9HCLaJ7N7FiWiAxHGKfp+AD/1cNwpXmAEgGEQI0hHsM3i1ZHu0iQNa/Ya\n1uw12M44eM1qW7JXStIc7ijDIbuB5XoxA2PfS2DJDhacCupO8UI7EV2f4r0HRUQT1RmG6McDVGwZ\nilK8WV4BATdI4Cd+oUPvK8mSPLO7rb1Wb5igoTfQrNgw9eLNo6RZjoGboWm1sMpZXqJSK8ZZlYj2\nRZrl6LoBBuEAjUoxF7CNwhRBEkKS88IsYCsLd5RC5BpqZg2tejHfJWj3Y9T0OharFVQsfdrDIaJ9\nxGcIojnWGYboR0OYBgobGN0ghp/4cEoyy1sUSZpj6GVomk2sNCwoBZmZfiU/TBGGEhatFtZaxdty\nm4huTPHOUkQ0EWXYjEJAwA9TBElQmtKGIhBCoNNPUNcbaFVsVMzizZAKIbDTi7FkL2O16RSyrzAR\n3RiGXqI55QYJ3GgEyElhA2MYZwjTELKSQ1V5OjsoAy+FAgMLVhVLBV281hsmMCQHLbuGxVox2/QR\n0Y3hswTRnOp7IdzYRc0p5iwvAPhhgiALYRo8lR2UKM4xCgRaVhMrCw7kAra4i9McfS/Dkr2Iw4uV\nQrbpI6Ibx2cKojmU5wIDP4Ibu6hYxZzlBYAgThGlIUy9uPehSPJMoDNMsGA2sVizYRWwWwMA7PRi\nNI0mlmsVOGZxX/QR0Y1h6CWaQ30/ght7MHRAK2hZQC4EwihFnMUwCroIr2jagxiOUsGCXdxdy9xR\niixR0bKbWG1y8RrRPOEzBdEc2g29VbuYM3UAEEQpojyGrkqQZb49vd96bgzkOprWAg4tOJBQvL95\nlgu0+zGW7SUcajqF3C6ZiG4eH/FEcyZJcwxHIYJshEqBQ2+cZoizCJpWvPBVNKMwQxAAi1ar0GGx\nO4jhqDU0nWphZ6qJ6OYV88xFRDet74dwYw+WIUEp8AxpnGZIsoRdG/ZZnOToDVMsWotYbVQKW8cb\nxhm8kcCi1cLhxcq0h0NEU8BnC6I50/ciuPGw0KUNwHgFfiJS6Ay9+ybPBNqDGAvGAharFdQdY9pD\nuilCCGx1I7TMRSzXncIGdyLaGz5bEM2RME7hhiESEcEpcNcGAIiTDEkWQ1OLO1s9y/JcYLu3Ww5Q\nw3KjmP14gfECPAMOlioNrC5w8RrRvGLoJZojuwvYbFMpdG/SJMsQZylkGVzEtg+EEGgPEuiyjSW7\ngbVmMReuAeN6ZM8Hlp1lHFuq8XghmmMMvURzZFza4KLmFPvt3SwTyEVW6JrkWdYbJJAyHUt2C4ea\nFShyMZ8qspdnq1fsFaw1q7CMYh/3RLQ3xTyTEdENC+MUfhQhQwzLKHZpQ5YLZCLnrN0+GHgJklTF\nirOEw60KdLW4x8p2N4Kj1LBYKXZ5BhFNBkMv0ZxwgxijxIdd8MALAJnIkec5mHkny/VTjEbAkrWI\n1QUHhlbcY8X1U8SxghVnCceWq9MeDhHNAIZeojnhBgn8dAS74AvYACDPgBwZCvqu+0xy/RSun2PZ\nXsbqQrG3503SHO1+glV7BWsFn60mosnhUwbRHMhzAW8UI8hGsM3iB4BMCOQQLG+YEHe0G3hXcKhZ\nRd0uZmuyXVudCA2jieV6jZtQENFlDL1Ec8ALE4zSAIZa7A0pdkkSIAEQYtojKT7XT+F648C7tlD8\nwNsdxpCEgSWniSPchIKIXoGhl2gOuEGMUeqXYpYXAGRIkCBBMPXuydD/4Qzv2kK1sJtP7ArjDH03\nw4q9gqOL1cJ2nSCi/cEzAtEc8IMEQRrCKknolWRAgsyZ3j0YeAl8X1xu51X0wJvnAludCEvWMlYa\nVVRtfdpDIqIZw6aFRCWXZjlGcYI4j2Dq1rSHMxGyLEGWJIbemyCEQG+w25ZsEasLlcKXNADAVjeC\npdSw5Iw30yAiei2GXqKS88IEQTqCqcuF3oXtlWRIkCUFWcbUeyPyXKAzSIBMx4rdwlqzWuguDbu6\nwxhpouFwbRnHV2qlOc6JaLIYeolKzg8TjJIAllmeaiZdk6HJKlKG3uuWZwI7/RiaZGOx0sKRVqXQ\nfXh3+WGKgZvjaPUwji3XSnGfiGh/lOdZkIiuyA8ShFlY+F3YXklTFGiKhjwfz17SG0vSHJu9CKZS\nxYrTwtHFcgTeJM2x3Y2x6hzC4WYdNdbxEtEb4EwvUYkJIRAlGeIsgqGVo553l67J0BQdSSpg6Hw7\n+2pGYYb+MEVdb6JVqWGt6ZSiq0GeC2y0IzT1RazU6lhZ4DbDRPTGGHqJSixMMoRpBFVB6TZy0FUZ\nmqwhTiIYevFD3H7ouwlGgcCitYTFagVLdRtySepdt3sRDMnBcrWJo0vsx0tE18ZnCqISi5IMSR5D\n08r3ULcMFZZqIoiyaQ9l5uS5wHYvRhwpWHVWcXihgZWGU5rA23cTxJGKQ5VVHF+ulWLmmoj2H2d6\niUosjFNEeQyjhKHXMTVYioVOKJDn3JJ4VxznaA9j2EoFrUoTh5oOLL08p/pRmKE7THG0cgxHl6ow\nS3TfiGh/8WxBVGJhnCFOY1Ts8oVeRZJhmxrMwEIYpbCt4i/M2gshxHhL4VGOBaOJplPDoQUHqlKe\n//s0y7HVjbBqr2GtWSv8hhpEdLAYeolKLIzTlxexTfahvtsHddrbAFdMDbZmwQt6cx16kzRHd5BA\nEjoOOS20qjZaNRMSyjP7LcR44VpDb2G5VschbkBBRDeIoZeopPJ83LkhRQpNncwGBG7q4uzgLJ5c\nfxIAcMfaHThVP4WqWp3I9d+oiq2holfQd/uI4xz6HC5o80YpBl6Gul5Hw6xhZcGGbRR/w4nX2uhE\n0OFgpdLC8eXpHG9EVGwMvUQltduqTFOkiexQ5aYuHvzug3j43MOXv/fQ2Ydw5sQZ3H/6/qkEX0WS\n0ajoGEZ1DPwBlvT56dOapDn6boosVbBkLaNVcbDUsKBI5Qv+O70IItWxVl3FiRUuXCOim8MzB1FJ\nBXGKMIsmtojt7ODsqwLvrofPPYwXBi9M5DZuRsMxUDMqSJLxIq6yE0Jg6CXY7iYwpCrWqodwdLGO\n1QWnlIG3O4wRBAoOV9ZwYrXOhWtEdNPKd4YkIgDjet5xu7K9z/JKknS5pOFKnlh/YiKzyTdDkWU0\nKgYaRgOdYVzqHdrCKMdmJ0IUalixV3Gk0cKJ5SpqVjkXdA39BENX4HB1DceX63DM8pVtENHB4Utm\nopJKsxxplsJRy//atlk14QVVhGmIvheiWStXmUOa5hh4KaIYWDBbqJsOlhvlakX2Wn6Yot1PcaRy\nFMcW6+zUQER7Vv5nQ6I5leYCGTJMovxRCIE71u646s/fufbOqXZykCBhtemgaS0gDMe9XMsgzwR6\nwxib3RgqKlirHMKRZhPHlmulDrxhnGG7k2DNWcPhZh2tWrm20Cai6WDoJSqpLMuR5TmUCW3acKp+\nCmdOnHnd98+cOIOT9ZMTuY29MFQFSzUHi9YiesMUUYHre3Mh0HNjbHRiILWx5qzhaGMRJ1bqaFbK\n1YrsteI0x0Y7wrK9gkONBluTEdHElHeqgGjOZblALjIo8mTqIKtqFfefvh/3HL0HT6w/AWA8w3uy\nfnJqLcteq1ExEKdV5EKg02+jWddgGsV5bZ9nAl6QoucFsFQHq7aDmm2hVTNhqOXvQ5xlAhs7IZrG\nElZqCziyWJn2kIioRBh6iUoqzQQykUGWJ1ffWlWreFvrbXj74tsBTH9ziitZbtgQEJAkCe3BDuoV\nBRV7tk91cZLDG6UIIgFLtXGoeQh1y4YhJXPTrSDPBdbbISpqA6vVJk4s16a2OJKIymk+zqZEc0YI\nMf4nYWLlDa+9/lm20nAgSRIkSOj6XQRxjFZVg6zMTogSQiCMcrhBhjQBKnoFh5wKqpaJ46st2KaG\nQX8w7WEeCCEENjsRdFRwqLqMW1brkPfhuCWi+ban9/3+7M/+DLfeeitqtRp+7Md+DH/3d383qXER\n0U26cMHEV75awR89UMGD/72KRx6xsblZrm4G12O5buPoYh1rlVVowsZmN8IomP4CtzjO0RvG2GhH\nGHoSHKmBI9XDOLqwhFtWGlhrOrDnrDXXZicCMhNr1VXcslqHqhSnJIWIimNPM72apuGrX/0q3vKW\nt+Cpp57Cz/3cz+Ff/uVfcMstt0xqfER0A555xsYHPlDD0MuBag9oaHjmnxw4To4/+VMft745nPYQ\nD1TNMmDpKvSegkFgo+/3MfBD1BwVtqkc2NvncZIjiDL4YQYpV+DoFSxbDmxdR83WUXP0Um4scT02\nOyHy1MDR6hpOrtZhaOWvXSai6dhT6P34xz9++fN3vOMdOHnyJJ5++mmGXqIpuHDBHAfeoQwoKSBn\ngBiHOt+X8fv/1cFnP5tjdTWe8kgPlqYoOLpYRW2ko+Ka8OIQA7+PgRfBMmRYhgpDn8xWzbuSNEcU\nj/+FcQZZ0mAqFhYNG7ZmomJpqDnGXCxOeyNbnQhZouNo9TBOrtZhGay4I6L9M7EzTK/Xw/PPP4/T\np09P6iqJ6AY8/bQ2DrwAgByQMuAVra18X8a//7s6d6F3V902ULcNDAMTPdeEF0UIswADN0Qmxts1\na6oEVR1/1K6xqYcQAnkukGXjNltJmiNJBZI0hwQFpmLCUAzUbROmqsExNVQsDbYxX6ULV7PVjZAm\nGo5Wj+Dkan3uSjqI6OBNLPR+8IMfxH333Yfbbrvtij9vtVqTuqmZoWnjk3QZ7xtN3n4eL1mW4aGH\nXvlwvvKs5WOP6Xjf+xTIc1wzWW8ARw8BQZTADRJ4owhBnCBMA0RZjDRPMAoTZCIDJECWAEkGdieC\n8wzIhIAkZEiSDFVWoMk6bEuDLuvQFR2aqsI2xwHXMTXoN/iWvaqqL4+1Pum7PxM22gFM3cGxpaO4\n9UgLFWv+as4nic9FdL3m/Vi5Zuj9oz/6I/zxH//x675/77334itf+QoA4Pd///fR6/XwpS996arX\n88ADD1z+/M4778Rdd911M+MlousiAUIBMNtdFqbJMjRYhoblho04yRBEKaIkRZxmiJMMUZJBiBwC\nQI4cQow3u5AlBbIkQ5FkKPJ4ZlhXFZi6CkNTYGgq1DnY+vlmbbQDJKGGY/WjePPhJgMvEe3Jo48+\niscee+zy13ffffdVLyuJPfYe+sxnPoMvfelLeOSRR+A4V94555vf/CZuv/32vdzMTNp9pdTpdKY8\nEiqC/T5evva1Kj7ykZc3iZAToPYSUH8JiH/Y4P8Tn/Bx112jfbn9shEQyIWAyMc7pInxNyHLgCLL\nkPdxEdzuDG/ZWpZtdSIksYoj1cM4udpg4J0QPhfR9ZqHY+W5557De97zniv+bE/lDX/1V3+Fz3/+\n83j88cevGniJ6GD8xE8kqNXyl+t6JUDIeOVMr+PkuO22dGrjKxoJEhRJAuZ7rdnEbHZCZImOY7Uj\nuGW1Doc1vER0wPb0HtwnP/lJnD9/HidPnkS1WkW1WsWnPvWpSY2NiG7AsWMhvvzlIWq1/OWuDRJ2\nQ+9uy7J5XcRG0yOEwEY7RJYYlxetMfAS0TTsaab3hRdemNQ4iGgC3va2Ef73/87x7f9Pwd98PUNg\npvi5e3zcdlvKwEsHLs8FNrsRkJqX+/CySwMRTQubIhKVzLFjIY4cETj1dhcvDlycPDz9Xcho/mTZ\neIZXg4O16ipOHmqwDy8RTRXPQEQlJEnj4oY8Z/cGOnhJmmN9J4Sj1nGosoJbVmswdT7dENF08SxE\nVEKSJEHCeJcxIcSBbbdLFMU51tshmvo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       "text": [
        "<matplotlib.figure.Figure at 0x7fade41ab4a8>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that the sigma points lie between the first and second deviation, and that the larger $\\kappa$ spreads the points out further. Furthermore, the larger $\\kappa$ weighs the mean (center point) higher than the smaller $\\kappa$, and weighs the rest of the sigma points less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know *how* these weights and sigma points are selected yet, but the choices look reasonable."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Choosing Sigma Points\n",
      "\n",
      "As I already said there are several published algorithms for choosing the sigma points. I will present the method first chosen by the inventors of the UKF. \n",
      "\n",
      "Our first sigma point is always going to be the mean of our input. We will call this $\\mathcal{X}_0$. So,\n",
      "\n",
      "$$ \\mathcal{X}_0 = \\mu$$\n",
      "\n",
      "Tne corresponding weight for this sigma point is\n",
      "$$\n",
      "W_0 = \\frac{\\kappa}{n+\\kappa}\n",
      "$$\n",
      "where $n$ is the dimension of the problem, and $\\kappa$ is a scaling factor that will be discussed in a moment.\n",
      "\n",
      "The rest of the sigma points are defined to be\n",
      "\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "\\mathcal{X}_i &= \\mu + (\\sqrt{(n+\\kappa)\\Sigma})_i\\,\\,\\,\\, &\\text{for}\\text{ i=1 .. n} \\\\\n",
      "\\mathcal{X}_i &= \\mu - (\\sqrt{(n+\\kappa)\\Sigma})_{i-n}\\,\\,\\,\\,\\, &\\text{for}\\text{ i=(n+1) .. 2n} \\\\\n",
      "\\text{and the corresponding weights are} \\\\\n",
      "W_i &= \\frac{1}{2(n+\\kappa)}\\,\\,\\,\\text{for i=1,2..2n}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "$\\kappa$ (kappa) is a scaling factor that controls how far away from the mean we want the points to be. A larger kappa will choose points further away from the mean, and a smaller kappa will choose points nearer the mean. Julier and Uhlmann suggest using $\\kappa + n = 3$ if the distribution is Gaussian, and perhaps choosing a different value if it is not Gaussian. \n",
      "\n",
      "It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to 1 standard deviation. However, there is an $n$ term in there - the more dimensions there are the more the points will be spread out and weighed less."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Unscented Transform"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The unscented transform is the core of the algorithm yet it is remarkably simple. Given a set of sigma points and a transfer function we need to compute the new mean and covariance of the points after they have passed through the function. In other words, loop through the sigma points and compute their new position after passing through your nonlinear function. Then just compute the mean and covariance of these points.\n",
      "\n",
      "In other words, we just compute the mean and covariance from the equations above:\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mu &= \\sum_i w_i\\mathcal{X}_i\\;\\;\\;&(2) \\\\\n",
      "\\Sigma &= \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\\;\\;\\;&(3)\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Unscented Filter\n",
      "\n",
      "Now we can present the entire Unscented Kalman filter algorithm. Assume that there is a function $f(x)$ that performs the state transition for our filer - it predicts the next state given the current state. Also assume there is a measurement function $h(x)$  - it takes the current state and computes what measurement that state corresponds to. These are just nonlinear forms of the $\\mathbf{F}$ and $\\mathbf{H}$ matrices used by the linear Kalman filter.\n",
      "\n",
      "### Predict Step\n",
      "For the predict step, we will generate the weights and sigma points as specified above.\n",
      "$$\\mathcal{X} = sigma\\_function(\\mu, \\Sigma) \\\\\n",
      "W = weight\\_function(n, \\kappa)$$\n",
      "\n",
      "We pass each sigma point through the function f.\n",
      "\n",
      "$$\\mathcal{X_f} = f(\\mathcal{X})$$\n",
      "\n",
      "Then we compute the predicted mean and covariance using the unscented transform. I've dropped the subscript $i$ for readability, and switched to the roman letters x and P for the mean and covariance.\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{x}^- &= \\sum W\\mathcal{X_f} \\\\\n",
      "\\mathbf{P}^- &= \\sum W{(\\mathcal{X_f}-x^-)(\\mathcal{X_f}-x^-)^\\mathsf{T}} + \\mathbf{Q}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "This corresponds with the linear Kalman filter equations of\n",
      "$$ \\begin{aligned}\n",
      "\\mathbf{x}^- &= \\mathbf{Fx}\\\\\n",
      "\\mathbf{P}^- &= \\mathbf{FPF}^T+\\mathbf{Q}\n",
      "\\end{aligned}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Update Step\n",
      "Now we can perform the update step of the filter. Recall that Kalman filters perform the update state in measurement space. So, the first thing we do is convert the sigma points into measurements using the $h(x)$ function.\n",
      "\n",
      "\n",
      "$$\\mathcal{X_z} = h(\\mathcal{X})$$\n",
      "\n",
      "Now we can compute the mean and covariance of these points using the unscented transform.\n",
      "\n",
      "$$\\begin{aligned}\n",
      "\\mathbf{x}_z &= \\sum w\\mathcal{X_z} \\\\\n",
      "\\mathbf{P}_z &= \\sum w{(\\mathcal{X_z}-x)(\\mathcal{X_z}-x)^\\mathsf{T}} + \\mathbf{R}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The $z$ subscript denotes that these are the mean and covariance for the measurements.\n",
      "\n",
      "All that is left is to compute the residual and Kalman gain. \n",
      "\n",
      "The residual is trivial to compute:\n",
      "\n",
      "$$ \\mathbf{y} = \\mathbf{z} - \\mathbf{x}_z$$\n",
      "\n",
      "\n",
      "The Kalman gain is not much worse. We have to compute the cross variance of the state and the measurements, which we state without proof to be: \n",
      "\n",
      "$$\\mathbf{P}_{xz} =\\sum W(\\mathcal{X}-x)(\\mathcal{X_z}-\\mathbf{x}_z)^\\mathsf{T}$$\n",
      "\n",
      "And then the Kalman gain is defined as\n",
      "$$K = \\mathbf{P}_{xz} \\mathbf{P}_z^{-1}$$\n",
      "\n",
      "Finally, we compute the new state estimate using the residual and Kalman gain:\n",
      "\n",
      "$$\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n",
      "\n",
      "and the new covariance is computed as:\n",
      "\n",
      "$$ \\mathbf{P} = \\mathbf{P}^- - \\mathbf{PKP}_z\\mathbf{K}^\\mathsf{T}$$\n",
      "\n",
      "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. We convert the mean and covariance into measurement space, add the measurement error into the measurement covariance, compute the residual and kalman gain, compute the new state estimate as the old estimate plus the residual times the Kalman gain, and then convert both back into state space. The linear algrebra is slightly different from the linear Kalman filter, but the algorithm is the same."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using the UKF"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We are now ready to consider implementing a Kalman filter. All of the math is above is already implemented in FilterPy, and you are perhaps a bit lost at this point, so lets just launch into solving some problems so you can gain confidence in how each the UKF actually is. Later we will revisit how the UKF is implemented in Python.\n",
      "\n",
      "Let's solve the 'bearing only' target tracking problem. Here the idea is that we have a ship or other platform tracking a moving target. Our sensor only provides the bearing to the target relative to the ship.\n",
      "\n",
      "This is a nonlinear problem because the conversion between a target position and the bearing is:\n",
      "\n",
      "$$\\theta = \\tan^{-1}\\frac{y_{ship} - y_{target}}{x_{ship} - x_{target}}$$\n",
      "\n",
      "If we were solving this problem using and EKF we would need to compute the Jacobian of this transform to linearize the filter. With the UKF we do not have to do this - we will see how this works as we work the example.\n",
      "\n",
      "\n",
      "### Define State\n",
      "\n",
      "First, lets define our filter state. Let's assume a constant velocity model for the target, so a reasonable state would be\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x} \\\\ y \\\\ \\dot{y}\\end{bmatrix}$$\n",
      "\n",
      "\n",
      "where $x$ and $y$ are the position of the target, and $\\dot{x}$ and $\\dot{y}$ are its velocity. \n",
      "\n",
      "### Define State Transition\n",
      "\n",
      "Now we need to tell the filter how to perform the state transition - how to predict the next position from the current position. In the linear Kalman filter this is the equation $\\mathbf{x}^- = \\mathbf{Fx}$ but the unscented Kalman filter is intended for nonlinear problems. We cannot implement nonlinear behavior using linear algebra, so instead of providing the filter with a matrix we need to provide the filter with a function that computes the transition.\n",
      "\n",
      "As it turns out our state transition is linear. We model the target movement using the standard Newtonian equation\n",
      "$$x_k = x_{k-1} + \\dot{x}\\Delta t$$\n",
      "\n",
      "However, the UKF code in FilterPy does not differentiate between linear and nonlinear versions, so we will need to write a Python function to perform this computation. The signature of the function required by `filterpy.UnscentedKalmanFilter` is\n",
      "\n",
      "    def fx(x, dt):\n",
      "       return x\n",
      "       \n",
      "The filter implements the state as a one dimensional array, so our function can be implemented as"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def fx(x,dt):\n",
      "    # pos = pos + vel\n",
      "    # vel = vel\n",
      "    x[0] += x[1]\n",
      "    x[2] += x[3]\n",
      "    return x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "> FilterPy's KF and EKF code uses a 2D array to store the state. Due to implementation details the UKF uses a 1D array. I am not enamored of this inconistency, but for now this is how it is."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Define the Measurement Function\n",
      "\n",
      "Now we define our measurement function. In the linear KF this is implemented with the $\\mathbf{H}$ matrix, but because the UKF is nonlinear we need to provide a function. We have already given the computation of the bearing from position as\n",
      "\n",
      "$$\\theta = \\tan^{-1}\\frac{y_{ship} - y_{target}}{x_{ship} - x_{target}}$$\n",
      "\n",
      "so all we have to do is compute that in a function. The signature of this function is required to be\n",
      "\n",
      "    def hx(x):\n",
      "       return measurement\n",
      "       \n",
      "The filter state does not includes the ship's position, so we will assume a global variable `ship_pos` is defined that specifies the (x,y) coordinate for the ship."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "def hx(x):\n",
      "    \"\"\" measurement function - convert position to bearing\"\"\"\n",
      "    return math.atan2(ship_pos[1] - x[2], ship_pos[0] - x[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And those two functions are the crux of the problem. All that remains is defining the noise in the system, and running the filter.\n",
      "\n",
      "**Important Note**: There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Design Noise Parameters\n",
      "\n",
      "We have spent a lot of time designing the $\\mathbf{R}$, $\\mathbf{Q}$, and $\\mathbf{P}$ matrices in past chapters, and nothing changes for the UKF filter, so I will just choose some arbitrary values without much discussion. Let's assume the standard deviation in the bearing measurement is $\\sigma=1^\\circ$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Implement the Filter\n",
      "\n",
      "So let's implement a filter given the design above. I'll just present the code; it should look very similar to the linear KF to you. The main difference is how we construct the filter:\n",
      "\n",
      "    f = UKF(dim_x=4, dim_z=1, dt=dt, fx=fx, hx=hx, kappa=0.)\n",
      "    \n",
      "When you construct the filter you have to provide the state transition function, the measurement function, and the value for $\\kappa$ along with the usual dimension and time step values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "\n",
      "\n",
      "def fx(x,dt):\n",
      "    # pos = pos + vel\n",
      "    # vel = vel\n",
      "    x[0] += x[1]\n",
      "    x[2] += x[3]\n",
      "    return x\n",
      "\n",
      "def bearing(ship_pos, target_pos):\n",
      "    return math.atan2(target_pos[1]- ship_pos[1], target_pos[0] - ship_pos[0])\n",
      "\n",
      "def hx(x):\n",
      "    \"\"\" measurement function - convert position to bearing\"\"\"\n",
      "    return math.atan2(x[2] - ship_pos[1], x[0] - ship_pos[0])\n",
      "\n",
      "\n",
      "dt = 0.1\n",
      "ship_pos = [-40,20]\n",
      "target_pos = [0,0]\n",
      "\n",
      "std_noise = math.radians(1)\n",
      "\n",
      "f = UKF(4, 1, dt, fx=fx, hx=hx, kappa=0.)\n",
      "f.x = np.array([target_pos[0], 0., target_pos[1], 0.])\n",
      "Q = Q_discrete_white_noise(2, dt, .01)\n",
      "f.Q[0:2,0:2] = Q\n",
      "f.Q[2:4, 2:4] = Q\n",
      "\n",
      "f.R *= std_noise**2\n",
      "f.P *= 100\n",
      "\n",
      "N = 300\n",
      "xs = []\n",
      "for i in range(N):\n",
      "    target_pos[0] += 1 + randn()*0.0001 # add some process noise\n",
      "    angle = bearing(ship_pos, target_pos) + randn()*std_noise\n",
      "\n",
      "    f.predict()\n",
      "    f.update(angle)\n",
      "    xs.append(f.x)\n",
      "\n",
      "xs = np.asarray(xs)\n",
      "plt.plot([i/10 for i in range(N)], xs[:,0])\n",
      "plt.xlabel('time')\n",
      "plt.ylabel('target X position')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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u13WF7sLCQiZPnqwn4SIiIjbmeF4RH61O55O16Zwr+vXlyFt6tGZo73YM7NYK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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fadd8cd6d30>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we look at only the target's estimated position in x, the results look very good. After running for several seconds the filter appears to settle down and produce a reasonably linear output for the target's position. However, let's look at the 2D plot of position. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "book_format.equal_axis()\n",
      "\n",
      "plt.xlabel('target X position')\n",
      "plt.ylabel('target Y position')\n",
      "plt.plot(xs[:,0], xs[:,2])\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7EP7B49UKC/JTfGSQXt68/1s/1/ycdNm+cdjdz2aVn7Xtyv/237fW9jDfPr+n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\n/AxpwdVW1doAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade415e978>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we can see the actual performance is abysmal. This is not an indictment of the UKF, but of the difficulty of the problem we are trying to solve. There are an infinite number of solutions for each measurement. For example, if our ship is at (0, 20), a bearing reading of 0 could reflect a target position of (0, 20) or (100, 20), or (1e300, 20). The Kalman filtering literature has many treatments of this problem; a common solution is to have the ship perform manuevers while tracking. This allows the filter to reduce the range of possibilities to something managable. This is rather outside the scope of this book so I will leave it to you to search the literature if you are interested in this specific problem.\n",
      "\n",
      "Instead, I will make the problem tractable by introducing a second sensor. The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. In the chart the width of the circle is intended to denote a different amount of sensor noise."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "circle1=plt.Circle((-4,0),5,color='#004080',fill=False,linewidth=20, alpha=.7)\n",
      "circle2=plt.Circle((4,0),5,color='#E24A33', fill=False, linewidth=5, alpha=.7)\n",
      "\n",
      "fig = plt.gcf()\n",
      "ax = fig.gca()\n",
      "\n",
      "plt.axis('equal')\n",
      "plt.xlim((-10,10))\n",
      "plt.ylim((-10,10))\n",
      "\n",
      "plt.plot ([-4,0], [0,3], c='#004080')\n",
      "plt.plot ([4,0], [0,3], c='#E24A33')\n",
      "plt.text(-4, -.5, \"A\", fontsize=16, horizontalalignment='center')\n",
      "plt.text(4, -.5, \"B\", fontsize=16, horizontalalignment='center')\n",
      "#plt.scatter ([-4],[0], 'r')\n",
      "\n",
      "ax.add_artist(circle1)\n",
      "ax.add_artist(circle2)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9L3i7WGckRuO/f3Yz1i7OCNo1ie5mw9JM/MVnNyItIXjp67beYXz/jROY8Ny7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\no835jvgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fadd6d38940>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can compute the bearing between a sensor and the target as follows:\n",
      "\n",
      "    def bearing(sensor, target):\n",
      "        return math.atan2(target[1] - sensor[1], target[0] - sensor[0])"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So our filter will need to receive a vector of 2 measurements during each update, one for each sensor. We can implement that as:\n",
      "\n",
      "    def measurement(A_pos, B_pos, pos):\n",
      "        angle_a = bearing(A_pos, pos)\n",
      "        angle_b = bearing(B_pos, pos)\n",
      "        return [angle_a, angle_b]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The design of the measurement function and state transition function can remain the same as nothing has changed that would affect them. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from filterpy.kalman import UnscentedKalmanFilter as UKF\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "\n",
      "\n",
      "def bearing(sensor, target_pos):\n",
      "    return math.atan2(target_pos[1] - sensor[1], target_pos[0] - sensor[0])\n",
      "\n",
      "\n",
      "def measurement(A_pos, B_pos, pos):\n",
      "    angle_a = bearing(A_pos, pos)\n",
      "    angle_b = bearing(B_pos, pos)\n",
      "    return [angle_a, angle_b]\n",
      "\n",
      "\n",
      "def fx(x,dt):\n",
      "    x[0] += x[1]\n",
      "    x[2] += x[3]\n",
      "    return x\n",
      "\n",
      "\n",
      "def hx(x):\n",
      "    # measurement to A\n",
      "    pos = (x[0], x[2])\n",
      "    return measurement(sa_pos, sb_pos, pos)\n",
      "\n",
      "\n",
      "def moving_target_filter(std_noise):\n",
      "    dt = 0.1\n",
      "    f = UKF(dim_x=4, dim_z=2, dt=dt, hx=hx, fx=fx, kappa=2.)\n",
      "    f.x = np.array([target_pos[0], 1., target_pos[1], 1.])\n",
      "\n",
      "    Q = Q_discrete_white_noise(2, dt, 1.1)\n",
      "    f.Q[0:2,0:2] = Q\n",
      "    f.Q[2:4, 2:4] = Q\n",
      "\n",
      "    f.R *= std_noise**2\n",
      "    f.P *= 1000\n",
      "    \n",
      "    return f\n",
      "\n",
      "\n",
      "def plot_straight_line_target(f, std_noise):\n",
      "    xs = []\n",
      "    txs = []\n",
      "\n",
      "    for i in range(300):\n",
      "        target_pos[0] += 1 + randn()*0.0001\n",
      "        target_pos[1] += 1 + randn()*0.0001\n",
      "        txs.append(target_pos.copy())\n",
      "\n",
      "        z = measurement(sa_pos, sb_pos, target_pos)\n",
      "        z[0] += randn() * std_noise\n",
      "        z[1] += randn() * std_noise\n",
      "\n",
      "        f.predict()\n",
      "        f.update(z)\n",
      "        xs.append(f.x)\n",
      "\n",
      "    xs = np.asarray(xs)\n",
      "    txs = np.asarray(txs)\n",
      "\n",
      "    plt.plot(xs[:,0], xs[:,2])\n",
      "    plt.plot(txs[:,0], txs[:,1])\n",
      "    plt.show()\n",
      "   \n",
      "    \n",
      "np.random.seed(123)\n",
      "\n",
      "sa_pos = [-40, 0]\n",
      "sb_pos = [40, 0]\n",
      "target_pos = [40, 20]\n",
      "\n",
      "std_noise = math.radians(1.)\n",
      "f = moving_target_filter(std_noise)\n",
      "plot_straight_line_target(f, std_noise)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MSJ3bSTn55Vq+Mcvo8YAq41QjAMBjrd68X28v2qTrr4jUA3dulincLt/yi5Ty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\nXbMoogsAPAxHvAAv9tvNUdf/eLVe/eR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AAPgdl2a8Bg8eLH9/f5lMJplMJt19992SJIfD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\nluiQgCnNwkMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade425b5f8>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This looks quite good to me. There is a very large error at the beginning of the track, but the filter is able to settle down and start producing good data.\n",
      "\n",
      "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors with the same y-coordinate. This will cause a nonlinearity in the computation of the sigma means and the residuals."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(12330)\n",
      "target_pos = [0, 0]\n",
      "f = moving_target_filter(std_noise)\n",
      "plot_straight_line_target(f, std_noise)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5eYqOjlZMTIzOnj0ri8WiiRMnln/dESNGqFWrVkpPT9eAAQM0YMCAipwXAGCQ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade432a2b0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we seed the random number generator just right we can get the filter to eventually lock onto the signal and converge to a solution, but of course this is untenable behavior for a real world filter. I will deal with this nonlinearity later; I bring it up now in case you are experimenting with the code above and you start to see this sort of behavior."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Exercise: Track a target moving in a circle\n",
      "\n",
      "Change the simulated target movement to move in a circle. Avoid angular nonlinearities by putting the sensors well outside the movement range of the target, and avoid the angles $0^\\circ$ and $180^\\circ$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your solution here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution\n",
      "\n",
      "We have a few choices here. First, if we know the movement of the target we can design our filter's state transition function so that it correctly predicts the circular movement. For example, suppose we were tracking a boat race optically - we would want to take track shape into account with our filter. However, in this chapter we have not been talking about such constrained behavior, so I will not build knowledge of the movement into the filter. So my implementation looks like this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_circular_target(f, std_noise, target_pos):\n",
      "    xs = []\n",
      "    txs = []\n",
      "    radius = 100\n",
      "    for i in range(300):\n",
      "        target_pos[0] = math.cos(i/10)*radius + randn()*0.0001\n",
      "        target_pos[1] = math.sin(i/10)*radius + randn()*0.0001\n",
      "        txs.append(target_pos.copy())\n",
      "\n",
      "        z = measurement(sa_pos, sb_pos, target_pos)\n",
      "        z[0] += randn() * std_noise\n",
      "        z[1] += randn() * std_noise\n",
      "\n",
      "        f.predict()\n",
      "        f.update(z)\n",
      "        xs.append(f.x)\n",
      "\n",
      "    xs = np.asarray(xs)\n",
      "    txs = np.asarray(txs)\n",
      "\n",
      "    plt.plot(xs[:,0], xs[:,2])\n",
      "    plt.plot(txs[:,0], txs[:,1], linestyle='-.')\n",
      "    plt.axis('equal')\n",
      "    plt.show()\n",
      "\n",
      "sa_pos = [-240, 200]\n",
      "sb_pos = [240, 200]\n",
      "\n",
      "np.random.seed(12283)\n",
      "std_noise = math.radians(0.5)\n",
      "target_pos = [0, 0]\n",
      "f = moving_target_filter(std_noise)\n",
      "plot_circular_target(f, std_noise, target_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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le5m9bD/Ldybxwf296BbVqK6rV8WgDsFs+nACfZ5fZCrbd+IsgZO/Ie7b+3B2\nqP8rWgjrVq15yn744QemTZtmVvb666/zyiuv8PDDD191nrJ33nnHNJ+ZzFNmHeSb1Y2JPZnNz+uP\nsSQmnsLSiss+p0WTyt6tUV3DKNcZ+HFtLN+tPnLZ557n7erAqK5hjO4eToemvvVm0HlJRTYHMxaR\nkr/VVNax0TT8nKP5K/65Ks+P8h5FM68hqBQbdAYtDhqPWqlnbZ/n+do0crRJ7EybQ4BLO7S6fG4L\ne4N/Tv2Hk/nmg8wVFJp7j6S13wTislbibt8EL8cIU4Csr7y8vNh25BQPf7zcNGHt5H7NmXFnZ9ys\ncN3J7IJSbn97OcfTzAP1Ty8MoV+bq4d9ayGf57WvziePrWkSymqXvImvraCknGX/nGD+xjj2J1Yd\nfwQQ6u/KmG5NGdU1jGA/V1buSuKprzai01/5reZsr2FY51DGdAunR7T1T2FRri9hW+oX5Jel4qjx\npmvgIxSUpxFz0nw8XGPXLnQNepSskuM4ajxw1HihUur20pW1nOcVei252iQ2JJt/KY32GUO0zzgW\nxpr3yoW496RL4MO1WUWLOd/m6Wcy+fKP/XyxbD8VegN+7o68PaW7VU7Yqi3X8cycTfyxPdGsfEKv\nCD54oJfVr5VpLef5raTOJ48V4lZgNBrZcewMv26Ku+xyLQABXk6M6hrOmG7htAzx4uTZQv7vjwP8\nvOHYZZ9/XttwPx4b05F+LX1xsMJxNpdKyothZ9ocszKtLp/TRfsJ9+gHgJtdEI4aT7oFPW665Ojr\ndOVxo7cqjdoeX6coJkXPM5WVVGSjoK5ydyhAcl4MXQIfZlf6dyioyNWm0LPx09jbuNWb3lQ7jZrn\nxndgRJdQnv92C3viM3nws7UM6RjM2/f1sKq5wextbfjP4/1p5OlkNi/goi3xuDra8ua93euwdqKh\nsv6/AkLUkYzcEhZtOc6Hi3dftpfL2V7D7b0iGNMtnA4RfhiMRtbsTWHsW39SWqa74n7VKoVhnUK5\nf3A0g7u1QFEUq/w2W64vYXf6dxSUncZO7Uy/0FeIz15T5Xk9mzyDr2ML1Cpbs4Ahbpyj5sL0BZOi\n52E0GsgsPsrRrOU0cetChb6UpNzNprtO/zj+BAAtvEcT7tkfR039GHfYLMiT318bxY/rjvLu/J2s\n2p3C1iPpvHJHZ+7uH2U101AoisJrk7vi6WLPewt2mcq/W32Ezs38GdElrA5rJxoiCWVCXKRCZ2D9\n/pP8sjHxy4t2AAAgAElEQVSOtftOXvY5d/SJZHT3pnSPaoSNWkVadhGvzdvG92uuPrmrh7Mdk/tH\ncd/AKAK8KqdnsLYeDoPRgEpRseDIPVUeMxqNRHjdRrm+GFfbAPydW6Io1n2Ztb5TFBV+ztH4OUcD\noDfo6BX8HJtTPjR7XmzWMoJcO1FSkcW6pLdo63cXoR59sFU71kW1r4tKpTDlthbc1r4JM37Yyt97\nT/Ly91uZt+4oz0/oyG3tmljN++PxUW3xdXfkmTmbTGUPz15HzMdehPq71WHNREMjoUwIICE9j/kb\n41gcE8/Z/KoTvI7oEsr4HhH0aR2EnUaN3mBg48FTPPmfjVec+uK8qCaePDC4JaO7h1vlJcqi8gz+\niv8X7vZNcLBxp3fw81WeE+E5CDAS6t6r9isoTNQqGxo5tzb1SOaWJpNXlkph2Wnc7ZuwLqlyXsf9\nGb+wP6NypZSRkZ9bdQ9aoJcz3z87iOU7k3h93nZiT+Yw9eM1tG/qy4sTO9IzOrCuqwhULlvWyNOJ\nO95bYSrr+dxCTnw/1Sqn+BD1k5xJ4pZVoq3gzx2J/Loxjl3Hq05loVIU3pvWg3Hdm5qWW8nMK+Gn\ndUf5eOneq+5bpSgM6RjMtMEt6drc32q+8Z9nMBo4W3yUjSkXpqPJ056kSJWJ3lBxbh4tW1ztrG/a\nAnGBh0MIHg4hpu3WfhOJy15JeuGF89NGZUdG0REyig/jqPEh1L0XapV1LR+kKAoju4RxW7smzFt3\nlC/+2M/ehEwmvbuCntEBvDixE+2b+tZ1NenVMpA1745j0CtLTWXDX/2dde/fXoe1Eg2JhDJxSzEa\njexNyGT+xjiWbU+kWFt1KgsHOxseG9GGh4e1wtFeg8FgZMvhNOauPsKavVVnir+Ym6Mtd/Vrzn23\ntaCxla35ZzDqOZy5hAjPQRRXZJoFMgB3+2D6h8xArdLg4RBcR7UU1eHr1Bxfp+YYjHqScjdzqnA3\ntmonEnLXcaqgckzUntOVqxH0C3kFH8fmVvWFwd7WhgeHtuKufs35dtVhvvrrIDFH0omZuYzb2jfh\nhQkdadGkbpcNig724qcXhnD3B6sAOHYqlzd+2s7Mu7vWab1EwyChTNwSsgtKWRwTz/yNcVXmHjpP\npSjc2bcZz43vgJ+HIzmFWn5cd5S5q4+Qln3l9VkBmgV5MG1wtFmvmjUwGo2kF+4lJvUzU9nZkjj6\nh/wbP6doHDQeeNiHEOk1uA5rKSxNpagJ9+xHuGflHbHNvIZQUpFNTumF6R02JL9Lc69htPG/0+oW\nYXey1/DUmHbcOzCKr/46xHerD/P33pOs3XeSUV3DeW58e8IbuddZ/fq1acy9A6P4ce1RAL5eeYj2\nEb6MlIH/opoklIkGS28wsOlgGr9ujOPvvSlU6CvvWPNwtkOlUsguuDDtQP+2jfn3nZ2JDPRg9/EM\n3v51B0u3Vp2B/mKKAre1C2ba4Gh6RgdY1R81o9GI3liOzqA1C2QAasUWRVHoG/JSHdVO1DZvx0hu\nC3sDvaGcQ5lLiMtegZ3aFV+naEor8vjj+BO42PrTwmcMIe496rq6Jh7O9rw8qRMPDInmi2X7mbfu\nKMv+OcHyHYlM7B3JM2PbE+h95bWTa9Lb93Vn+Y4kcgorP0emz15Hk7dcaBPmUyf1EQ2DTB4rTBrK\nZIOnc4qZt+4oCzcf53RO5TqFKkWhb5sgGnu7sP3YaeJO5QKVlyJevasLbcJ8WBITz7x1R02PXYmL\ng4Y7+jZjym3RhPi5Vquulm7z84P2Xe0C8XIIp3Pggyw4cg82KntC3HrQvtG9t/wdkw3lPK8ug7Hy\nS8rOtDmk5G8ze6xv8EumOz4twVJtnpZVxKe/7WXh5uPoDUZsbVTcMyCKJ0a3xcet9u80TTyTT6/n\nFpqVbfzgdiICa2d1iquR87z2yYz+wqLq+5vYaDSyYNNxZs77h6JzY8WCfV2Y1KcZbcN8+Hb1Ydbv\nr1zgupGnEy9O7MjgDiF8t/owc/46eMWlks4Lb+TGtEHRTOgdiZOFLlFaqs1zShP5O3GmWZmTxpth\nER81qLUULaG+n+eWZjQaSC3YxT+nvjSVDWv6AQajnoSctUR43YarXfXugLR0m584ncfHS/ay7J8T\nQOU40PsHt+SREa1xr+Vlm75bdZjX5pkvl7X+/fE0C6rbO17lPK99EsqERdXnN/HZ/BKe/3YLf++t\nnFtsYLsmPDS0FeEBbnyyZC+/bozDYDTibK/h8VFtuXtAcxZsOs6Xf+wnt+jqU1qEN3Lj+QkdGd4p\n1OKTWlanzXWGMhTUZJbEVpm3ytcxit7BL6BWyQiFS9Xn87ymFZadISF3He38J1dZm7ON35008xp6\nU5fpa6rNj6Rk8+Hi3ab3vaujLc+Ma8+DQ1rW2nACg8HIxHf/4p+jp83K17w7jujgurspQc7z2ifL\nLAkB/LUziZfmxpBTqMXV0Za37+vO0I4hzFlxiCkfr6akTIdapXDfgBY8PqoNa/aeZMCLS8jIK7nq\nfgO8nHhuXAdu7xVhVWtRllbkEpP6OTmlJ2jqMYB2je7Gza4xLnb+eNiH0MJnVF1XUdRTLnb+tPOf\nDFSuEpBTmkhReeV0MQcyfiWnNJGWvuNwtQuoy2qaRAd78cNzg9kTn8EHi3YTcySdN37aTuLpfN6Z\n0h21qubftyqVwscP9WbgS0souWglj0GvLGXl22NoHSpjzMT1k54yYVLfvlnlF5fx7/9tMw3I79Uy\nkI8f7M3W2HRmLdhlCl2DOwTz4sSO7D9xlk+W7uVU1tXvpPRyteep0e24e0AUdpqavfR3I21uNBrY\nmjqbtMI9ZuXnl+O51ceKXa/6dp7XtcziY2xIfse03S3ocQJd2pNWuJcmbl2uax+11ebLdyTy5H83\nUlahZ1inUL54tG+tTez649pYXv5+a5XyP98YXSdzrMl5Xvukp0zcsjYfTuPZOZs4nVOMva2aV+/s\nQs+WgTw9ZyPbYisvI7QJ82bGHV3IKijlwc/WcuJ0/lX36eKg4ZERbXhgSEuLjRmzBINRT2HZGVzt\nAswCWbBbd7oEPgwggUzUGF+n5kyKnkdhWQZJeZsJcu3IrrRvSc6P4Z9TX+LnFE3v4OetYuziiC5h\neLs6MPWTNazYlUTuB1q+f3YQLo62NX7sewZEsXJXMpsPp5mVT35/JZs+nICvu/UueSWsh/SUCZP6\n8M2qtEzHO/N3mNaZbBfuy0cP9mLl7mS+WLafsgo9Hs52vHpXV9ydbPlwyR6Onsy56j7tbdWmQcIe\nzva18WuYXK3NK/Ralh57EABbtTMjIj7hZMEOTuZtk/Fi1VAfznNrtyL+RQrL083KRkV+gYPm8nOH\n1Xabx57MZvL7K8nMKzVN9loboSgtu4gBLy6uctNQ75aB/Pzi0FpdaF3O89onPWXilrI3IZOnvtpI\n4ul8bNQKz47rQKdIP6bPXkd8euWEsBN6RdCvTWO+WXmIfSfOXnV/NmqFyf2ieGpMO/w8rOdbbIW+\nlKXHHjIr06gcKarIJNyjL+EefeumYkKcMyzifYrKM/kr/jlTmb2NG8l5MThqvPB1qtsv0y2aeLFs\n5ijuen8lR1KyGfPGH/zy0rBqT2FzLYFezrx+dzee+2azWfnmw2l89ddBHh3ZpkaPL+o/CWXC6pXr\n9Hy6dC9f/nEAg9FIsyAP3ry3G8u2neCDRbsBCPV35faeEcQcSefRL9dfdX+KAuN6NOW58R0I9q3Z\nD+kbZTDqWXXiFbMytaJhWMT7qBR5uwrr4Wzry6ToeVTotWh1+VQYSth7+kcqDKUADAx7Ay+Hupvh\nvomvK7+/Nop7PlzFwaQsxrzxBz+9MISWId41etxJfSL5a1eSafqd896Zv5OuUY2sYg1PYb1kIIqw\nasdScxjx2jJmL9uPESMPD2vFw8Na8diXG/hlYxwatYoBbRvTyNOJDxfvqXJb+qWGdAxm3azxzH6k\nn1UFsrSCPayIfwGVoqaJaxe8HSMJde/DhBb/4/YWcyWQCaulUdvjYueHgopmXkNN5WsTZ7LgyD1U\n6LVXeXXN8nZzYNGM4fRqGcjZ/FLGv7WcrUfSr/3CalAUhQ8f6HXZ+dLGvfknBSXlNXp8Ub+pX3/9\n9dfruhJXkpSUhI+P3E5cWxwdKy/hlZaW1nFNKpdI+nrFIR75Yh1nckto4uPC63d3Y2tsOnNWHKKk\nTIeHsx0BXs7sjs8k9ezV76js1TKQ/zzen4eHtcbb1aGWfotrU2n0fL11LCcLtlOuL8LVLpAIr4GE\ne/Qj0LW9VS3d1FBY03nekKhVGnydonCzCyS1YKep/FTBHloFDkdRVHXS5rYaNSO7hpF0Jp9Dydks\n++cETQPciQyquVn3nR1saeTpxMpdyWblBqORw8lZjOvRtMbf23Ke1z5HR0dOnjxJWNjN9xDL129h\ndbILSnl49jpTr9fE3pH4ezjy8vcxaMv1puflFpVdc+LXduE+vDSpEz2jqzcjeU04VbCbrUc+N23b\nqp1xt28svWKiXmvs1oVJbl2Iy1pJSv4/NHbtjIKK/2weRoTnbbT1n1zrd2raadT832P98XK15/s1\nsUz/Yh3vFmq5d2CLGjvm2O7hrNiZxMrdyWblmw6l8f2aI0wb3LLGji3qL/n0F1Yl6Uw+d3+wiuSM\nAnzcHJjcvzmr96SwcPPV76B0tLPBx82BU1lF6A1GvF0deGdKd4Z3DrWq3iaj0UhK/jYcNV74O7cy\nlUd5j6K134Q6rJkQltXMeyiRXoMxYuBw+nIA4nP+Jj7nbwaGzsTLsWmt1kelUnjr3u54uzrw4eI9\nvPz9VrLyS3lmXM30SCuKwqxpPdl5/AzZBeaXcF/98R+6RQUQ1aRul2IS1kfGlAmrsTchk1Gv/0Fy\nRgHBvi50jPDj89/3cfRkDj5uDvhf5g5JtUphWKcQmgV5kpJZiN5gZGjHENa/P54RXcKsKpCdyN3I\nwth72ZH2FbvSvwEU7ur0DY/0+ksCmWiQFEWFSrGhRaMhtGw03FS+NukNEnM3X+WVNVUfhafHtueD\n+3uhUhQ+XrqXGT9sQ28w1MjxvN0c+OqJAagvMxXGwJeXUFquu8yrxK1MQpmwCqt2JzPhneXkFFZ+\no8wu0LJydzIqRWFA28ZobFScyTVfFmlQ+2D+dXsHth87w74Tmbg4aPhseh++eXogXlY0bsxoNLDg\nyD3sTv/OVBblPRq1osHdIdCqgqMQNUGt0tA74jEGh7+LRlX55SrYrTuZxUfJ1abUen0m92/O108N\nwE6j5n9rY3nki/WUVeiv/cKb0L1FAK/f3fWyjzWd+n2NHFPUX3L5UtS579cc4dUft3HxNMZF2gra\nhfvSLtyHuWuOmD2/bZgPT41px1+7knh/YeWUGD2iA/j0oT4EejvXZtWvSW8oZ2PK+2ZldT1VgBB1\nxd2+MeOi5qAzlGEw6tiRNoeSisrJTUdFzsZBU3OD7y81tFMoP79oz9SPV/PXziTyisv4/tlBNbKa\nx9RB0RxKzmbh5uNVHhv/1p8seXWkxY8p6ifpKRN1xmAw8tYvO/j3/8wDmYuDhlfu6ER+SZlZIPNy\ntef/HuvHi5M6MeN/W1m8JR57jZq37u3G/JeGWVUg0xt0JOXFoFbZ4qzxxd7GjVD3Pkxs8aMEMnHL\ns1FVThcR6NLBVPbH8SdZEf8CtbnITLeoRix5dSS+7g5sPZLOtE/W1EiPmaIovDe1B23Dqs4msP3Y\nGb78Y7/FjynqJ+kpE3VCW67j6a828eeORLPyIR2D6d0qiFcuWdj31bu6cEffZnyyZA/fra4Mam3D\nfPj8kb40Dbj80i51ZVf6XBJzNwDgaONBW//JKIoKW7X1rBogRF3TqO1p3+gedAYtSXmV48sKy0+z\nNXU23Rs/Xmt3aEYHe7Hk1ZGMe/NPYo6k89iX6/nqyQHYqC3bZ2Fva8M3Tw9k2Ku/czbffJqK9xbs\nonljTwa2a2LRY4r6R3rKRK3LLdJy56wVZoHMzdGWd6b0YMvhdLNANqBtYw7PuYeuzRsxauYyvlt9\nBBu1wr9u78Cy10dZVSAr0xWyKHaqKZAB5GlPYmfjLIFMiCvoHPgg46O+w8W2ERqVAw4aD1SKmpS8\nbRiMNTPO61Jh/m788tJQ3BxtWbk7mee/3YLBYPkeuwAvZ755auBlB/7f99Fq9iZkWvyYon6RnjJR\nq05mFjD01d/Ju2h+sf5tGjO6WzhPfbXR7Lkb3r+dUH83Pv99H7OX7UNvMBIZ6M7nj/Sldah1TSps\nNBoo0xdiMF64m2p0sy+xt3Grw1oJUT/YqGwZFvEBxeVnsbNxI61wL9vT/sv2tP8ytOksXO1qfp7B\nFk28+N/zQ7hz1goWbj6Om5MtMyd3tfiNOJ2a+fPOlB68NDemymPj3vyTtbPGW9WXTVG7pKdM1JoD\niWfp9swCs0D20YO9CPJxNgtk04e3Ju3nBwEYOXMZn/62F4PRyENDW7Hy7bFWFcj0hgoOZSxi88mP\ncLFtRBu/O+kSOJ1J0fMkkAlxg5xsfbBR2ZJdkmAqW5nwEumFtTPmqlOkH98+PRCNWsU3Kw/z2e/7\nauQ49wyIYnK/5lXKK/QG7pq1kkJZiumWJT1lolYs3hJvFrzahvkw+9G+9P7XIrPnbXj/dpoGuPP1\nykPMWrCLsgo9Qd7OfDa9L92iGtVyra9Oq8tnWdzj57YUskvjae49rE7rJERD0NpvIm52QWxP+y8A\nW05+zO1Rc1GrLH9n5KX6tm7Ml4/145Ev1vPR4j24O9kxdVC0xY/z1n3dOZqaU+WSZVp2ET+tP8oj\nI9pY/JjC+klPmahxUz5ebRbIXr+7Kx880MsskDnZa0j8YRquTrZMeu8v3vhpO2UVeu7s24y17423\nukCWmLv5okAGvZs8h7djZB3WSIiGJdi9O+Oafw1AK98JKIqaw5lLKdcX1/ixR3QJ4/37ewLw7/9t\nY0lMvMWPYadR8+3Tt132sW9WHq6xedOEdZNQJmpMfnEZgZO/4e+9J01lMR9PRFuuZ9ArS01lT41p\nx/HvprD1SDq3vbyUbbGn8XZ14PtnB/HRg71xcbSti+pfUWr+Dnalf2va7hcyg0Yu8q1WCEvTqB2Y\nFD2PFj6jOHr2D46c/Y3fjk1nzYnXavzYd/Vrzqt3dQHgmTmbWLPH8pPc+nk48sfro6qUZ+SV1EgQ\nFNZPQpmoEWv3naTFQz+atpsFeZDy4/2Me+tPZi3cZSpf+fYYnh7bjjd/3s49H64ip1BLn1aBrJ01\njkEdguui6leUpz1Jub4YN/sm2Kjs8Hduxehm/4evU9WxIUIIywpx72H6OVebxIIj91ChL73KK6pv\n+vDWPDG6LXqDkelfrGNbbLrFj9Ehwo/3pvaoUv6f5QdqbPknYb0klAmLKtZW8MR/NnDfR6tNZa/f\n3ZV5Lwwh+N7vyMy78CF64vupuDnZMfaNP5mz4hBqlcIrd3TipxeG4uNmXVNI7D/zC6tPzOC3Y9Nx\ntvVjaNNZ9Al+AXsb17qumhC3BCdbH8ZHfWtWti7pLYrKM2r0uC9O6Mi9A6Moq9Az5eM1HEg8a/Fj\n3DuwBS0uWZw86UwBK3clW/xYwrpJKBMW88/R07R77GeWbr1w59TyN0fj6WJP5yd/NZVN7B1J2s8P\nsmZvCoNfWcr+xLMEeTuz9LWRPDayLarLzOFTVwxGHWtOvEpc9kpTmc5QiqPGqw5rJcStyUZlx6To\neYR79EelqCmpyEKp4T9jiqLwzn09GNMtnGJtBZPfX8nxU7kWP86Kt8ZWKfvP8gO1usKBqHty96Wo\nttJyHbMW7OLbVYfNymM+nshLc2OIOXKhy3/e80PoFtWIF77dws8bjgEwrFMIHz7YG3cnu1qt9/XY\ncvITcrXJpu0JLX6otZnGhRCX1zFgKq39JpGvTcVB48WCI/fQ3GsYbfzvrJHjqVQKn03vS2FpOev2\np3LnrJX8PnMkjX1cLHYMjY2KTR9OoM/zF26AOpCYRcyRdHq1rPl52oR1kJ4yUS2lZTru+2i1WSBr\nHuTBhvdvp+dzC80C2aGv7iHQ24nhr/3OzxuOYadR8+7UHnz91ECrC2QV+lLytKn0bPw0AC19xjMp\nep4EMiGshK3aER+nZhzIqOyFP5a9ggVH7qmxniWNjYo5Tw6kSzN/zuQWc8d7K8jMK7HoMZoGuDOi\nS6hZ2f/9ecCixxDWTUKZuGnach3TPlnD1ouCV8/oAP51ewf6vbjYVNY2zIfUeQ+wancyw179nbhT\nuYQ3cuPPN0Zz38AWFp8xu7qS82JYmfAim1I+oFxfzKToeUT7jqnragkhLqOt3514OTQ1bS+MvRed\noewqr7h5DnY2/PCvwbQK8SY5o4BJ7/5FdoFlbzb46okBZttbDqdxMMny49iEdZJQJm5KWYWeBz9b\ny+bDaaayUV3DaOzjwgOfrTWVvTu1B7++PIzH/m89z3+7BW25nom9I1n19liig61vXNahzCXsSJtD\nqS4XjcoRvbGirqskhLgKRVExMGwmjZzbXlyKwVgzdy66Otry84tDaBbkwfG0PCa9t4KcQq3F9q8o\nCp9N72NWJr1ltw4JZeKGlev0PDx7LesPpJrKJvSKYHd8Br9ujDOVbfzgdtqE+jBkxlL+2J6Ik72G\n2Y/05dOH++BoX/Mzc9+oHWlziD37u2m7X8hLONv61mGNhBDXq3fwc3QPepxRkV9Qri9kzYkZZBTH\n1sixvFwdmP/yMMIbuXH0ZA53zlpBXrHleucm9DKfiHr5jiQSz+RbbP/CekkoEzekQmfgkS/WmU0I\nO6JLKIu2xJOefWGm7ePfTWH9gVTGvPEHKZmFtAzxYuXbYxjfM6Iuqn1NyXkxJOddWCB4QosfcNB4\n1GGNhBA3qrFbFxw07iTkrCO/7BQbk99jwZF7auRYvu6OLJwxnBA/Vw4nZzN51koKLLhm5ffPDTLb\n/mr5QYvtW1gvCWXiuun0lYFs1e4LM1u3C/dh+Y6ki7Z92fvlZKZ/sY43f95Bhd7A/YOj+eP10YQ3\ncq+Lal9VcflZckoTCXLtjJ9TNF0CpzOxxY8yoF+IeqyV7+1m2zV1A4C/hxMLZwyniY8L+xPPcs8H\nqygqtUwwu61dE7PtnzccIyPXsjcWCOsjoUxcF73BwEOfr2Xl7mRTmbO9hn0nLgxAvatvM16e1Ilh\nr/7G+v2puDvZ8f2zg3jz3u7Yaawv5ORpT7I8/ln+TpxJaUUOfYJfJMS9h9XdeCCEuDGKomJiix+x\nU1+Y3Dkhd12NHCvQy5mFM4YT4OXE7vgM7vtoNSXa6o9FVRSFTx4yH1v2n+Uytqyhk1AmrklvMDD1\n4zWsvmTtt6KLPnieHtuORp5O3PHeCs7kltC5mR9r3rO+pZLO0+ryWX1ihmm7TF8gYUyIBkRRFEY3\n+9I00XNy3hYMRl2NHKuxjwuLZozA38OR7cfOMOWTNZSWV/9YY3uEo75oMu1vVx0m34Jj14T1kVAm\nrspgMDL5/VWs2596xee8fndXCkvK+XjpXowYeWpMOxbNGEGgl3Mt1vT66QxlLIt73LTdP/RVvB0j\nr/IKIUR9pCgKIyM/o2vQo/Rq8ixaXT4r4l/EWAN3Zob4ubLgleH4ujuw9Ug693+yBm01g5mtjZoX\nJ3Y0K3vn153V2qewbhLKxBUZDEZGzPydLRdNe3GpTx/uw5ncEr5bfQRbGxU/PDeYFyZ0xEZtnaeW\nwajDRmWHh33lBI0jIj7BRwKZEA1asFs3bNUu/Hn8aQrL01kYex9lukKLH6dpgDsLXh6Ol6s9mw6l\n8dDnaynX6au1z7v7R+F00d3qP284ZpFeOGGdrPMvp6hzRqORzk/9yoHErMs+bqdR8/2zg0g6k89X\nfx3ERq0w56mBDLxkcKo1KS7PYlXCDE4V7Oa2sDcY0+y/ONn61HW1hBC1QKWoiPIeadr+Pe5RCstO\nW/w4kUEeLHh5OB7Odqzbn8ojX6yjQnfzPXNuTnbcNzDKrOzBT/+ubjWFlZJQJqowGo0E3f0tp3OK\nL/u4s72Gn14YwpGT2cxeth+1SuG/TwxgUHvrHD8GEJe1kuXxz1BYns6xrL8AI3Y21nl5VQhRM1r7\nTSTco79pe0fa1zVynKgmnsx/eRhujras2p3C4/9Zj05/88Hs4WGtsbe9cLPUhoOnqn1pVFgnCWXC\njE5vIOjub6/4uIezHQtnDGf/ibN8tHgPKkXhi0f7MaxT6BVfU9diTn7G/oxfTNu9g/+FosipL8St\nqGPAVAaEzsTdvgkDQl8luySBCr1ll0oCaBnizS8vDcPFQcPyHUk8/dVG9IabC2bebg5M7m/eW9bj\n2YWWqKawMvKXSZgUlpThPPyDKz7eyNOJ314byc64M7wzfyeKAp883JvR3cJrsZY3Jq1wL2mFe0zb\nIyI+xVbtVIc1EkLUNW/HpgwOf4ec0kQ2psxiTeK/KanItvhx2ob78NOLQ3Gy1/DbthM89/VmDIab\nmy/tkeGtsbW58Cf7TG7xFa9miPpLQpkAID27CJ9xn17x8bBGbiybOYqtsad5/aftAHxwf68qy4FY\nm4yiIwA4aXwYH/UNTrbedVwjIYS1sLNxBRSKyjP58/jT6A2WX+u2Y4Qf854fjIOdDYu2xJstRXcj\nGnk6MalPM/N9P/HLFZ4t6isJZYLDyVkM/ffvV3y8ZYgXv706kk2HTjHjh60AvHNfd+7q17y2qnjD\nzhbHkZS3hXb+d9Mn+AWGR3yMjcq+rqslhLAizra+tPadaNpefHRajUyX0aV5I2ZN7QnAf/86cNO9\nZY+NbION2nw+xavdHS/qHwllt7g1e1MY++afZBVcfkxF1+b+LJoxgg0HU3nhuy0AzLy7K1MGRddm\nNW9IVkk865PfZmfa16Tkb8PfuZVMDCuEuKwIr9to43enaXvvmZ9qZEmmMd3DCfRyJulMAX/vTbn2\nCy6jsY9LlfWD73hvRbVuIhDWRULZLey7VYe5/5O/KSm7/F08A9s14acXh7LhQCrPztmM0Qiv3NGJ\nhyJSj+0AACAASURBVIa2quWaXr8KfSnrkt40bfs4NrvKs4UQApp7D6Nr4COoFBvK9UUYsXzIsVGr\neHBoSwDmrDh00/t5fFRbVJd8yVyw6Xi16iash4SyW5DeYODV/23jtXn/YDAacb5oYsLz2oX78PVT\nA9lwIJUn/rMBg9HIv8Z34LGRbeugxtfHaDSy9NhDpu0+wS/IGDIhxHUJdu/OwNCZdA2cTmbxUZYe\nfdjiPWZ39m2Gq6MtO+LOsDch86b2EebvxuhuYWZlL3y3hdIrfLkW9YuEsltMsbaCqR+vYe6ayhn4\n37q3m9kalgBervbMeWogmw6d4tEv1qM3GHlidFueHtuujmp9bQajAUVRaO03CYBBYW/h72y9PXpC\nCOvj4RBChUHLppT3qTCUsDD2XosGM2cHW+4ZUDm1xZwVB296P0+OrvpZ/M2qm+99E9ZDQtktJD27\niLFv/sm6/al4ONvx4/NDePXHf8yeo1Ip/PfxARw/lcvDn6+lQm/g4WGteHFCR6sdl2UwGog5+QmH\nM5fS3GsYt0fNxcMhpK6rJYSoh2zVjrTynWDa3pE2x6L7nzooGo1axYqdyaRkFtzUPiKDPKrMDfn+\nwt3kFGotUUVRhySU3SIOJ2cxcuYyjqRkE+rvyqIZI3h3ftWFbd+9vy8Go5EHPv2bcp2BaYOiefWu\nLlYdyBbF3sfpogPE5/yNVleAWlX1cqwQQlyvFj6jUCk2AKTkbyW75ITF9t3I04kx3cMxGI18u/Lw\nTe/nqTFVe8s++31fdaomrICEslvA3oRMxr75J2dyS+ja3J/fXxvFO7/u4GCS+bqWt/duTp/WwUz7\nZA3aCj2T+zfnzXu7WW0gMxqNLIq9z7TdJfAhHDTudVgjIURDMaHF99iqnQn3GICXYzh6g+XGbD00\nrHJoxa+b4sgturnerZYhXlXWGv5u1WFOnbX8Quui9kgoa+B0egMvfLuFkjIdY7qF88tLw/jij/1s\nOHjK7HmRge68dk8vxr++mJIyHeN6NGXW1J5WG8gAkvO2mH4OdutBgIv1jnkTQtQ/Y5v/l44BU4jL\nXsXapNctthxTiyZe9GkVSGmZjnnrjt70fi7XW/bugl3VqZqoYxLKGrh5645yNDXn/9m77/i2ynMP\n4L+jLcuS994jdpw4exOyIYSwQ0NCS6CUWdrLaGlLS7kFci9dtBRaKJQNtyUhCSMbQiBOQsiejh07\n3jPetmRLsta5f8g+kmw5li3rnGPn+X4+/dxzjo7e81zFRo/f8bxIigrGiw8uxKffluCt3Z5d5lq1\nHK/8eAnW/eFz1LV0Yu74WLz4wEJIJOJNyCz2Lo/9LOckPCRgNISQscrm6EZp69doN1fikwsPwuYY\nmXlbD98wGQDwzhfn0W21D6uN6ZnRWJib4HHt8+9KUVA18ltGEX5QUjaGtehN+POm4wCAZ++ah/zy\nZjz1zsF+9/31oUV4ccsJnCltRGZCGN58/Foo5VK+w/UZyzqgkGowM+5HSA6Zh9UT3hd1jx4hZPSS\nSZS4OvkJ7nxL4QNwsMNLotwtyE1ATnI4mjpM+PTbkmG3421V/O+pt2zUoqRsDPvDxmPoMFqwaFIC\nJqVG4v6/OVdTunv0lqk4fOESvjpVhXCtCp89vxrhWvFuR8SyDnxccA/2lq9Hom4m5iU+AglDP8aE\nkMDRKeMwMeo27vxwzWt+t8kwDB5e6ewte33H2WFvvTRnfBzmjo/1uPb16WrknRnergFEWPRtNkad\nKWvCR3lFkEkZ/HrNbNz71y/RrDd59IDlJIcjUqfG27vzIZdKsPG/VyEzIVzAqC+PZVl83DOxv9lY\nDIOlQeCICCFXitzoVQhRJgEAqvVH0W6u9rvNm+elIzZMg4t17fjm7PDbe+y26f2u/fadfQHZLooE\nFiVlY5DDweLp9w6BZYH7V0zCP7adxvnKFqTG6DzmLvz4hsl49v8OAwD+/MACLJiUPFCTonCo5u/c\n8eyEh6BTxgkYDSHkSrMi8wVMibkTcxIeRqgqCTZHt1/tKWRS3L/CuY/w6zuGX0x2wcR4TE2P8rh2\nrKgenx4s8is+wj9KysagTQeKcaq0ETGhQZAwwPYj5QhWyaFWyLh7nr1rLn797rdwsCwev20aVi/I\nEjDiwVnsXajRO+dJxAVPQVro1QJHRAi5Eo2PXImUkKvwXfWr2FJ4P7osTX6194OlOQhWyXGooB7n\n+pQp8hXDMLhvRW6/6//9Xh6sNtqsfDShpGyM0RsteGGDM3mZMS4Gr20/C4YBfrh8IgqrWwEAuiAF\n3th5Dl1mK26dl4Enb58hZMiDMtv0kDJK3DDuL0jQzsTClCeFDokQcgVzsFZU6Z2jDNsv/syvGma6\nIAW+v2Q8AP+2XrpxThqiQ9Ue10pq2/DRvgvDbpPwj5KyMeYvW06gWW+CVi3n5ig8dus0/GPrae6e\n6NAg1Ld2YVZWDP7y4EJRr1y0Obqxv/JF5FX+AXKJGlcnPyZ0SISQK5xUosDyjP/hzs82fuxXe/ev\nyIVUwmDr4TLUNncOqw2FTIp1S3P6Xf/rJyfR1Wd/YyJelJSNIUU1rXj3y/MAAIPJClNPEdgD+bXc\nPUFKGUrq2pESrcXbT1wLlduQptiwLIsthfejzVwOo5Xq7hBCxCNMlYLYYOfqyeKWXbA5LMNuKyEy\nGDfPTYfdwfarIzkUdy3LgVzq+bXe1GHCm7tos/LRgpKyMYJlWfz2/UOwuy2rnpYRhbWLsnHiYiN3\nzdhtQ0iQAh/8YgUidGpvTYnG6Uv/5o6TdHOglGkFjIYQQjwtTH4SSqkOyzP+B1JG7tcw5kM95TH+\n/c0FdHQNbwFBdGgQbpqb3u/6P7efRYt+ZHYjIIFFSdkYsf1oOQ4V1HPnMaFBePPxa3HHCzs87pNJ\nGbz5+LXIjBf3HpE2hxnFrV9w51Ni1woYDSGE9McwDG4d/ypU0hAcqHoRpy/937DbmpQWifkT49Fl\ntuI/3wx/Hth913lO+B+fGIZOsxUvf356gHcQMaGkbAwwmq14/t+HuXOlXIq3f3Ytfvn2gX73/um+\nBZg/MZ7P8IblTINrjsYt2f8QMBJCCLk8s60dlzrPo6RtLzaeXzfsdh7q2aj8rd3nYbENb9eAqRlR\nmJbhKo8hkzm/5j/OK4LZMnKbqpPAoKRsDPj71tOoa+nizl98YCGUcim+Pu1ZjPCnN0/FmkXZfIc3\nLOMjrkeMZiKuy3gBKlmI0OEQQsiAwtSpCJJHcOdnGjYOq50lk5OQlRCKS21d2Ppd2bDjud+tPEZ+\nRQsmpUbCYLLi6zP+F7wlgUVJ2ShX0aDHK27d0j+5aQpumZeOa3/9icd9N85Jw69Wz+Q7vCGr7jiC\njefXgYUDi1OfQqgqSeiQCCFkUDeM+zN3fKF5+7A2LpdIGG5u2es7zw67Iv/K2Wke56kxOgDAZ4dK\nh9Ue4Q8lZaPcb951bTC+bGoSfnXHTPz471973JMeF4K/PbwYEol4S18AQKelEYdqnEOVOy5SLTJC\nyOjBMBLclPUyd37KbaHSUNw2PxNRIWoUVrV6rJwfCoVMiruXT+LOzVbnsOXeU1UwGIe/SpQEHiVl\no9j+/FrknXP+0mpUcrz6k6U4W96MHUfLPe5btyzHo5q/WO24+HPu+NZs/zf8JYQQPgXJw7Ei4w8I\nV2cgO+L6YbWhlEvxo+v833pp/b2LueM9J6swPTMaZqsdu09UDLtNEniUlI1SLMviTx8f486fXzcP\nUgmDG//7c4/7ZFIGt8/P5Du8IbvQ7FolmhN5M5W/IISMSiGqBFyT9jsopBpsLXp0WPtjrluWA7VS\nhrxztSioGl6NxpgwjWdcQQoAwOc0hClqlJSNUntOVuFUqXPPNZVciluuysBjr+/jXs+Ic06OXz49\nRfT1yAAgM/xahKnSoFXEYnLMaqHDIYQQv3xe9FOYbG3Iq/zTkN8bFqzCnT2Lst7YOfzCrz9fPYc7\nbjGYIZMy2J9fSzXLRIySslHI4WDxp83HufP7VuQi72wNdh6rAABE6FRw9EwQHQ2rLcva9qOpqxDL\nM57HSrfJsoQQMhoxDIPpcfcAAJqNxag3nBlyG/dfnwsJw+DzQ6Wob+0a/A1ePPE9V1J2trwZk1Ij\nYXew2N5nigsRD0rKRqFtR8pQWNXKna+YmYr7XtrDnT91xyyUX9IjNiwIiycnChGiz2r0x3Gs7k3s\nr3oRbaZKocMhhJARMS78Gu54f9WLcLBDqzuWEq3DytmpsNod3PZ5QxUZEtTninOxFw1hihclZaOM\nze7AX7ac4M5XzkrFS5+e5M5/etMUHCtuAAB8b0EWZFLx/hOzrAPfVrtWK4WpUwSMhhBCRlZv4Wu5\nJAjsEJMywLX10od7C9FpGt6qSfeaZadKG6GSS3Gk6BJqW4a38TkJLPF+YxOvthwsQWl9B3e+eHIS\nVyRWLpXg/utzse2Is+jgmkVZgsToq48L7uGOl6Q+LWAkhBAy8lSyENw2/g2synkD7eZqtJoqhvT+\n6ZnRmJMdC73Rgo/2FQ0rhqVTPGs9pvXMN976HfWWiRElZaOIxWbHS5+6esnGJ4bhSJFrv8s3Hl2G\nr05VwdRtw5zsWKTHircSvtHqWlEkZRSI1owXMBpCCAkMhTQI1R1H8VX5szhS+0/YHUPr8Xr4Bmdv\n2Zu78mGzO4b8/NnZsR7nbQbnatDPKCkTpYAmZYsXL4ZarYZWq4VWq8U99zh7RqxWK+677z7odDqk\npKRg06ZNgQxjzPhoXxGqm1xdzuuW5WDLwRIAQFiwEstnpGDDvmIA4p/g3zvxNS54Mm7PeVPgaAgh\nJHBig52Jlb67DpsL7xvSe6+Zloz0uBDUtnT2q0HpC7VShqsmxHHnl9q6oFXLkV/RgpK69iG3RwIr\noEkZwzB49dVXYTAYYDAY8P777wMAXnrpJZw/fx41NTX44IMP8KMf/Qg1NTWBDGXUM1lseOWzU9x5\nqEaJArfJ/jvW34qSunYcv9gAjUqOm+akeWtGFKx2EzLCl+Ka9OcwI+5eMAx12BJCxi65VAWF1FU3\nbCjDmBIJgwevd1bn/+f24W29tCA3weN8akY0AOBz6i0TnYB/G3r7Adq0aRMeffRR6HQ6LFq0CPPm\nzcOnn34a6FBGtQ++KsClNiN3vnZxNv79zQUAQLBKjpRoHTbmOXvJbpmbjiCVXJA4B2OytuGTCw9i\nS+EDCFEmQqOIFDokQggJuFuz/8kdf1fz9yG993sLxiFcq8K5imZ8V1g/+Bv66JuUBfd8P3z2Xemw\n99ckgRHwpOzXv/41oqKisHz5cly44EwiiouLkZ2djbvuugsbN27EhAkTUFQ0vEmMV4JOkwX/2Oqq\ncyNhGExOcyUzn/3uZlhtDmw+eBEAsGaxeIcutxY/CgCwOcyQMOLf+okQQkYCwzCYHns3AMBobYPJ\n6vvQoVohw73XTgAwvK2X3L8vAMDYbUWkTo2y+g7kVwxvxwASGAH9VnzxxReRm5sLu92O9evX4+ab\nb0ZBQQG6uroQHByM/Px8zJgxA1qtFtXV1V7biIiICGSIo8KbHx1Cq8HMnd8wNxNPvJHHnV89bRy2\nf3cRTR0mZCdFYPmcHDDM0Dcfl8udfz0F6jM3mBu445nJ30dUZFRAnjOaBPozJ/3RZ84/+sydIiLW\ngpWbEKebiMSIjCG99/E7rsar289i7+lqNHayyEm5/ChD38/82hlp2HPCOSct71wt7l4+CR98eQ67\nT9Vi8Uzx/iE/mvR+5v4IaFI2Y8YM7viFF17Aq6++isLCQmg0GnR1deH06dMAgMceewxarfe9Dtev\nX88dL1y4EIsWLQpkyKLTZjDjpc1HPK49eMM0bPvO2Sv2+O2zAQDvf+n86+mH100eVkLGhw+P3ssd\nz0r5gYCREEKIMOal3Qur3YxPT/8CGVELMDnhZp/eFxUahHXXTsKbO07h758dw2uPDW3D85uvyuKS\nMgCI1DkLy27KK8QL9y2BRCLO7w2xy8vLw/79+wEAUqkUCxcu9Ks9XsePGIYBy7LIyspCYWEhpk+f\nDgAoKCjALbfc4vU9jzzyiMd5S8uV1dX6x4+PoaPLtaFtVkIoth8q5M4fv3kSCkursfNICaQSBtdP\njx/2Z9T7F1WgPuObs/6OrcX/hdkJD6G1tXXwN1wBAv2Zk/7oM+cffeaedl78BQyWS6jXn0eUfKrH\nIoDL+cGiDLy54xQ2fH0ev1w1FdqeTca96fuZzx0X7vF6TWMbwrUq1DYbkH+xCgmRwcP8/+bKlpub\ni9xcZ4HeiIgIHDx40K/2AjanrKOjA7t27UJ3dze6u7vx3HPPISYmBhMmTMAdd9yBV155BR0dHdi3\nbx8OHz6M2267LVChjFrNHSa8tTsfANDb+XXv8oncBrUKmQRymQRbDl6E3cHimmnJiOq3rYY4FDZt\nh9nWjjUTP0Ra6NVCh0MIIYJZmvZb7vjTCw/7/L5xCWGYlxMHY7cNnxwqGdIz4yM8k669p6uQEu0c\noapuMgypLRI4AUvKrFYrnn76aURGRiIuLg6HDx/Gtm3bIJPJ8MQTTyA3NxdJSUm455578M477yAh\nIWHwRq8wr247A2O3DdGharAsoAtSIDfVNY9g829vBMuy2NCz6nKtSGuTVbQfxNnGjdhbvh4W+/A2\n1iWEkLFCJQuBRu6aU9s2hBIZdy11Ftr+cG/hkFdOTk13PbNFb0az3gQAqKKkTDQClpRFRkbi5MmT\nMBgMaG1txe7du5Gd7UwaZDIZ3n77bej1elRWVmL16tWBCmPUqm/twvtfFQAAInVqAM5tk+576Uvu\nnhnjYnCooB4lde2IClFjSZ/tNMTAwdpxpPYNAECYOtXnbnpCCBnLbhj3F+6YYaQ+v+/6WWkI16pQ\nWNWKkyWNQ3rmY7dN8zjvLUZOPWXiQVU7RepfO8+h22rH/InxKKlrB8MAd18zAY3tzr9s7lycDZvd\ngd/933cAgLuX5UAuE98/56aCH3LHcxIeEi4QQggREYZhcHvO21gz8UPIJWqYbR2DvwmAUi7F2p59\njT/cWzjI3Z6umZrs9Tr1lImH+L7FCViWxRcnKgA4e8ksNgcW5iZg2+Ey7p71d1+F9/cUoLCqFUlR\nwfjxjVMEinZg3TbXL7pcEoRgRbSA0RBCiLjIJApUdXyHXSW/xNmGj31+3/eXOIcwtx0uQ7vbQrDB\nDLTCsoaSMtGgpEyESus7UNloQFiwEkXVzlWKaxdn40+bjnP3GEwW/Hmz8/y5u+ZBrRRfIdbStq8B\nABHqTNw6/lWBoyGEEPEJU6XDzlpR3r4f5e2+rdxLiw3BwtwEmK12bD5wcUjPy4wP7XeNesrEg5Iy\nEdp7ugqAs5fsQk0bwoKVyElyLWf+6Knr8b8bjsJgsmLp1CQsn5EiVKiXlRN5ExYk/xyzE+6n6v2E\nEOKFVhnDHR/tmX/ri7uW5QAY+oT/B67P7XetvrULFpvd5zZI4FBSJkJ7Tzt3N2jqcM4fW3X1ONz/\nt6+411UKGTYfuAilXIr1d18lymKxR2vfxIGqvyJakwOdklbWEkLIQOYkuMpidFmafXrP8ukpiA5V\no6SuHUcuXPL5WTMyY/pdY1mgtrnT5zZI4FBSJjIGowVHe37BeucK3LEgCyV1zn3SrpuRgt+89y0A\n4Mc3TkZqjE6YQC/D7rChvH0/6jvP4ET9+0KHQwghopYaOp87Lm/f79N75DIJ7lzsKo/hK2/DlwBQ\nTUmZKFBSJjIHztfCandw51PSI3G82PVX0KS0SG5y/09vmipEiIPaWfIkdzwz7kcCRkIIIaPD0tTf\nQiULhVoW5vN7vr84GwwD7DxWjpaemmODkcskiApR97te3UjzysSAkjKR+fq058bsaxZl4+n3D3Hn\nb+xw7nEp1sn9LMvCaHVtpSKViC9GQggRmyhNNm4c9xLSwxah2ejb5P3EKC2WTkmCxebAx/uLfX6W\nt5qW5Zd8K8lBAouSMhFhWdYjKVPJpVjm9ssjlTCin9zfbXf9tbVq/L8EjIQQQkYXB2vFxwX3YG/5\n8z7PLeud8P9/X1+Aw+HbhP8JyeH9rn3y7dC2bSKBQUmZiJyvbEFDu5E7Xzk7Des/OsKd2x2sqCf3\nO1g7JIwMayZ+iFuyX4Vc2r+LnBBCiHfu/83cfvEJn96zbGoS4iM0qGjQ42BBnU/vmZgS0e+a+3cP\nEQ4lZSLy1akqj/O1i7Kx/Ui5xzWxTu4HgHrDaWwrfhTnGz+DSibOGAkhRMzGhV/HHZusbYPeL5VI\nuGKyH37l24T/CV6SMiIOlJSJyNdnXEOXKdHafsmXmCf3syyLg9V/g83RDZlEKXQ4hBAyKk2L/QF3\nfMTHumV3Ls6GVMLgy5MVaGgbvMcrVKNEfET/fYjLaF6Z4CgpE4lWg9ljc9k7Fmbh2Z59LXuJdXI/\nAJS27eWOk0LmCBgJIYSMXgzDYEbcDzEx6jYsTPmlT++JDdNgQW4CbHYWR4t9q1nmbQjz319fGFKs\nZORRUiYS35ypRm9RZoZxJmU7j1Vwr4t5cj8Aj3pkQfL+k0gJIYT4JjN8GcZHrkRZ29doN1cN/gYA\nCRHBAIA2g9mn+6ekR/W79u+vh7bBORl5lJSJhPuqy8WTEj1qlQEQ7eR+ALDaXfVxZsbfJ2AkhBAy\nNhQ0fY4T9e8jv/ETn+4PC3ZOG2nr9G2D8nnj4/pdM5issDscXu4mfKGkTARsdgf2na3hztcuzsbb\nX5znzh9aOUm0k/sBQN9dC6VUi6igbGSELRY6HEIIGfUywpYCAGoNJ3CpM3/Q+0O5pMy3nrKpGVFQ\nyqX9rudXtHi5m/CFkjIROFXSyG2pFK5VYfmMFLy92/VL+IvvzRQqNJ9EBGXipqy/eezfRgghZPg0\nCtfwYl7lHwe9PyxYBcD3njKVQobpmdH9ruedq/FyN+ELJWUi8JXb0OWq+Zm4UN3KnasUUtFO7geA\n0tavsfH8Opxv+gwaRaTQ4RBCyJjR21sGAFb75XvAuOFLH+eUAcBcL0OYeWcpKRMSJWUisNetPtma\nRVl4fcc57vy1nyz19hbROF7/LgCgsHmbwJEQQsjYMj3uHjA9X9M1huOXvTdMO7SeMgCYmxPb79rx\niw3oNFmGECUZSZSUCay+tQuFPT1jEToVshPD8Pl3pdzry6YlCxXaoDotDdzxsrRnBIyEEELGHgkj\nwdzEHyMn8kZEqsdd9t6wIc4pA4AZmTGQSz3TAJudxaHC+qEHS0YEJWUCO37RldgsnZKEg/mubTLk\nUglkUvH+E31V9jx3HBmUJWAkhBAyNiWHzMXkmDXotuvRbBx4f8reOWXtQ+gpUytlXktj7Kd5ZYIR\n7zf+FaKwyjV/bP7EePzirQPc+dN3zhYiJJ+lhl4NAMiNWiVwJIQQMnbtLV+PveXPY2/5cwPe07v6\nsqPL4vPG5AAwN6f/vLJ9NK9MMJSUCexcRTN3PD0zGrUtndz54smJQoTkE7OtA5OiV2PNxA8xIepW\nocMhhJAxa6Lbf2O7bZ1e75FJJdAFKeBgWXQYfe8tm+dlXln5JT2qGvVDD5T4jZIygbkXjT3gNnQJ\nAJnxoXyH47MTde9h+8XH0dBVINqitoQQMhZEBY3nji834X+oBWQBYOa4GEgl/f8bvj+/dggRkpFC\nSZmA9EbXCpc7F2fj6fe+5c5vvzpTtMmOofsSagzHYbZ1QKeIFzocQggZ06QSObQKZ4/W8bq3B7wv\ndBhlMYLVCkxO61/OKO8sJWVCoKRMQEVu9cgW5CZ4vNb3XEzONn7MHatk4t1pgBBCxoppceuQGX4N\nVo3/14D3DLWAbC9v9coOnq+FzU5bLvGNkjIBnS5r4o5Vfba7uHqieJOyGv0xAAADBgxDP0KEEBJo\nccGTMSVmLS515aPVVOH1nuGUxQC8T/bXGy0e31GEH/SNKqB/f32BO/7MrTZZelwI4sI1QoQ0KAdr\n545zo78nYCSEEHJlKWrZhUPVr+Bi6xdeXx9uT9msrBh4my2zn1Zh8o6SMgFdrGsHAMRHaLD1cBl3\nfdEk8faS6bvrIGUU0CpikRN5k9DhEELIFSNROwsAUNF+EPruun6v9/aUDaVWGQCEaJSYmBLR73re\nOZpXxjdKygTCsq46MlEhao/XFoh46DJUlYRbsl/FVUmPinYhAiGEjEUhKtd3w8Gqv/V73bXV0tCG\nLwHv88pOlTaio2toCR7xDyVlAimubeOOO7o89xnzNr4vBmZbR8/m458iVJUkdDiEEHLFkTDO+ccG\nS/+tkFybkg89kZrn5XvH7mDxbUH/HjkSOJSUCeSDrwq544oGzyJ9IRol3+H4pLhlNwCgqGWnwJEQ\nQsiV6bqM33PHXZZmj9dcc8qG3lM2O7t/EVkAyK9oGXJbZPhkQgdwpXpvT4HQIQxZYfN2AIBaFi5w\nJIQQcmXSKeOQHrYEYFkAntsphWmHXjy2V7hWhZykcBS6lWoCgIu17cOOlQwdJWUi422ypRgYra5f\n1FkJ9wkYCSGEXNlmxf8IAGB3WD2uh/aMsrQOoXisu7k5sf2SspK6tgHuJoFAw5cC6DtxMrxnciYA\nXDVBnPPJWkyukh1xwZMFjIQQQq5snZZGbDy/DpsLfwQH6yrwGhuugVYtR31rFwoqhl5jLDelf2X/\n8kt6KiLLI0rKBLCvT+0XXZCCO85JEmdPWZJuFtZM/BC35wy8xQchhJDAC5K7vieqOr7jjhUyKW69\nKhMA8N4XZ4fcboaX/Zatdke/ec8kcCgpE8C7X573OHffDDYxMpjvcHxytPYtnGvYBLuDlkcTQoiQ\neldgAsCR2tc9XrtzcTYA4N9789FtsQ2p3cz4EK/XL9bSECZfKCkTwLHiBo9zudT1z5AUJb6krNPS\niPL2PFxo2QEJQ9MQCSFEaOlhi71en5wWiZzkcLToTdh+uGRIbYYFq7hNzd31FjongUdJmcjEhYsv\nKfui9DcAnFssyaXqQe4mhBASaNkRKwAAscGTPK4zDIM7Fzl7y9774syQ2x2fGNbvGq3A5A8loYz3\nJQAAIABJREFUZTzzNmGySW/ijuUy8f2T2GjIkhBCREWnTMCaiR9iYfIvYLV7rra8bX4mFHIpvjpZ\njtrmziG1621eWQn1lPFGfBnAGGex2j3OZVIGLfrhLV/mA+u2smd8xEoBIyGEEOLuUuc5fF70Exyr\ne9PjerhWhVuuygLLAh/vLx5Sm5kDJGUOB+vlbjLSKCnjmblPUpYcreOO5wxQUVlI+m7nVh4KaTAm\nxawROBpCCCG9VLJQdNsNqNYfhc3huV3fPdc5Sxdt3F80pIQqM65/UmbstqGuZWg9bmR4KCnjWXOH\nyeM8IcI1h2yWCJMypUyL6bF3Y2LUbZAw9ONCCCFioVPGc8c1+mMery2dmorkaB2qmzpxcAj7V45L\n6J+UATTZny/0Lcuz6maDx7n7HLKUaC3f4QzKaG1GetgSZEUsFzoUQgghbi5XGkMiYbjesg37inxu\nMyEiGCq5tN91Ssr4QUkZz2r6TLpUylw//GKrUWaxG7Gn7HfYXHgvLHaj0OEQQggZgErWv8bYumsn\ngWGAXcfKfd56SSJhkB7Xv60SWoHJC0rKeFbT5NlTFhMWxB0nRomrp+xiy5fcsUIadJk7CSGECGFR\nyi8BeFb575UcHYJFkxJhsTnw6be+1yzzNtn/Iu2ByQtKynhW3eTZUxYXruGO492OxaC8PU/oEAgh\nhFxGZFAWFiT/HItTnvL6+tqeCv+fHir1+ro33pKy4tp2sCytwAw0Ssp45j58GRKkQJfZyp2rFOKq\nlt9lbQYAxNIG5IQQIkoyiRI6ZTwuNG9Hs7F/+YvexWUqRf95YgPxlpS1d3aLunzTWEFJGc9q3Cb6\nZ8SHouxSh4DRXN68xJ8gSB6BlJCrhA6FEELIAHZc/DkKmrfifNPnHtftdgfe2p0PALh3+USf2/OW\nlAE02Z8PlJTxrMmtJEZGXAjK6sWZlDlYB6I1Obgp629IDZ0vdDiEEEIGkBwyDwBwqfOsx/UdR0pQ\n0aBHcpQWK2am+NxeeixtTC4USsoElBEXKtqkTN9di8+Lfoqvyp4XOhRCCCGX4b7/pd1h447/tuUo\nAOC+FbmQSnz/ulcrvU+loe2WAo+SMgFlxIdwFf5DNUqBo/H0Xc2rAACzjf4yIoQQMUsLXcAd1xlO\nAACOFdXh0Pka6IIUWLsoa0SeU0xlMQJOXDPLx7juPlssZbjVgtEGyfkO57L03bUAXJP9CSGEiNe8\nxJ9Aq4hDiCoRAPDKJ84K/z9YMh7BasWIPKOyQT8i7ZCBUU8Zj/pusZTitu/lSP3SjAT3Zc/zEn8i\nYCSEEEJ8Ea+dDpvDjGZjMWqbO/HJgQuQShjce53vE/zdTUmP7Hetvavb3zDJIKinjEeNHZ5V8d1L\nYGjV4ukp67I2csdxwVMEjIQQQogvGrrycbDqJUQFZePb766F3cHijsUTPPZXHorJaVE4U+Y5UqI3\nWmB3OIY0P40MDX2yPGpsG3irIjH1lLWaKgAA8cFTIZeqhQ2GEELIoNSyMABAk7EIH31zHgDw2KpZ\nw27PW08Z4EzMSOBQTxmPGvsMX7rTiigpS9LNQlTW3+FgbYPfTAghRHAaeRR3zEqMmJ+bgRlZcWhp\naRlWe0kDbPvX0WVBWLBqWG2SwVFPGY8a2y/XUyae4cvStm9Q0XEQEsb3CtCEEEKEo5S5hilnTGzE\nY6tm+9VesMp7R0EHzSsLKOop45F74VgJw3i8FqwST1J2ov49AECzsRgLkn8mbDCEEEKGRC4JxQ1z\nMv1qQ6Pynh5QUhZY1FPGI4XM9XEnRXlOvhTT8GUv2vOSEEJGj6KLGTCaZFg6JQFSqX9f75oBOgpo\nBWZgUU8Zj3RBrgKx45PCPV4Ty/ClezmMcFWagJEQQgjx1fGLDXhrSxy06jQce2WV3+0NlJR1dNFE\n/0CinjIe6TSu3rCJKREer4klKWs31XLH4ep0ASMhhBDiqzd3nYNKZcNTDx3HFxWP+t1ekHKgpIx6\nygKJesp4FBJ0uaRMHMOXOlUslqb+Fh3dtWD6zHsjhBAiPlWNeuw8WoFQHaBQtcNid+6BKZUM/yte\nLvPeZ0NJWWBRTxmPdG5JWW6fpEwsxWP15nowDIMk3fDr2xBCCOHP21+ch4NlsTh3AnftXN3WgDyL\nhi8Di5IyHllsDu44IdJzor9mgOXHfDtXtw17y9ejsuOQ0KEQQggZhN5owUf7igAAD62cxF232QPT\no0UT/QOLkjIe1TQbuOO+Q4Ni6SnLr9sOADBZ2wSOhBBCyGD+880FdJmtuGpCHHJTXVX4mzpLA/I8\nGr4MLJpTxqOqRsOAr4mtJIZS5r2aMyGEEHGw2R14+4t8AMCD1zt7yW7Nfg0SRo7Y6AS/2w9WydFp\ntnpco+HLwKKeMh7VNHcO+JoYVl9a7a7ittGaHAEjIYQQMpgdR8tR19KF9LgQLJuaDACw2DtR1XEI\n1W2n/G4/NlzT75reSD1lgURJGY8qGvTcsd3hgMVm587F0VPmGlLVKuIEjIMQQshgDl+oBwCsWZgF\nicT53+9GYxGO17+L4sZv/G4/OlTd7xr1lAUWJWU8ck/K9EYL2jtdf3H0/kIJyebohkyihFKqhVza\n/5eREEKIeHjbnq/V6JxLVtTwld/te+ss6DB2w+FgvdxNRgLNKROI3miBqdsmdBge1PIQPDD/E1xq\nqhY6FEIIIYMI0Th3iXH/Az9ElTRi7asU/VMElgUMJgv3bDKyqKdMIPouC9o6xTU236C/gM/P/gpl\nbfuEDoUQQsggQoOdiZH7ikj3+cB2h7Xfe4ZCKZd6vU4rMAOHkjKBdBi7YbHaB7+RR5Wtx1HXkY8z\nDRuEDoUQQsgguJ4ytyRJp3TNB3ZfvDUcKsVASRnNKwsUGr4UiN5o8RivtzsckEqEzZGPV/1H0OcT\nQgjxXaiXpEzCyBAdlANWYoWD9W+KjEruPUWgArKBQ0kZT1jWc2JkR1c3ZG5JWEeXBeFaFd9heVDK\ntOi2DVxLjRBCiHiEeplTBgBL0n6DiAjnVn4mtAy7/YF7yigpCxQavuRJl5cCfO5F+cTwl0dvQhaj\nmShwJIQQQgbjmlPmOZx4uOZ1vLZ/Jc7UfOZX+wPNKXPfMpCMLOop40lTh+fYvt5oQZDS9fH3/UtH\nCPfO/QgmawfMnfQLRwghYudtThkAXOo86/y/+gIkqhcMu31vqy8B8WwLOBZRTxlP+idl3R69Z2JI\nypo6S2G0tEIqoV84QggRO61aDqmEQZfZCqtb71W33TnqUdp80K/2B0rKqBxG4FBSxpPGdqPHeUeX\nBV1m1yRMMQxf7i95FVvP/QZG2oycEEJEj2EY6IKcC8a8zfNKDpvpV/vqAeaUiWMHmrGJkjKeNPfp\nKevo6kan2eJxLjS92bllh8naKnAkhBBCfNE7r8zbH/YWe5dfbQ80p0ynoaQsUGhOGU+a9P3nlHWZ\nxDV8SQghZHTxVhbjeznvIioyCgwjQUuLP6svvacIOuopCxjqKeOJQub5F4fB6Ln6sk0EPWW9Orpr\nhA6BEEKID3qTMvfRlnZzJU7XfILa9rN+tT1QSQyNlz03ycigpIwnceEaj/OqJoNnSYxOM98hDShC\nnSl0CIQQQnzgbf/LRmMhvit/B5Wtx/xqe6DisRIJ41e7ZGCCJWU1NTVYvHgxNBoNZsyYgfPnzwsV\nCi/6JmXGbpvH8KUYtq0IVSdBwsigkoUIHQohhBAfeNv/sqDpcwDA6ZotfrWtHKCnjASOYEnZgw8+\niMmTJ6O1tRVr1qzBmjVrhAqFF32TMgDo6hbXnLLvz3oDDy/YCo0iUuhQCCGE+MBbT1mYKmVE2h6o\np4wEjiBJmV6vx549e/DUU09BqVTi8ccfR2VlJfLz84UIhxexYUH9rnWaxFPR38Ha8NmZX2HLqZ/B\nwYpro3RCCCHecasvja7RFovdONDtQzLQnDISOIIkZSUlJVCpVNBoNFiwYAHKy8uRkZGBCxcuCBEO\nL4LVCq6eTC8xFY9lWaCu4xwaDBf83sSWEEIIP0KCenvKXPOSp8SsBQAEKcL8anugkhgkcATpm+zq\n6kJwcDAMBgMKCwvR1tYGrVaLrq7+NVV6N1UdCxIiddBXNXPnfYvHhoeHg2GEmUCpN13ijqMjY8Ew\ntAaED3K5cxXTWPo5Fzv6zPlHn3ngJMc5p5uYrCz3+UrU4xDZmo7I4HT/PnN5/xEegP4dB9L7c+4P\nQZIyjUaDzs5OJCYmornZmaQYDAYEBwf3u3f9+vXc8cKFC7Fo0SLe4hxpCZFaFLolZcaeOWUqhQxm\niw1dZiuCBar/4oBryJIFC1pbQwgh4heqVQEAWg2unrKwoET8YM4bAACr1er1fb5QD1CnjLjk5eVh\n//79AACpVIqFCxf61Z4gn3hmZiZMJhNqa2uRkJAAi8WC0tJSZGdn97v3kUce8Tj3pxCe0CK13rNo\nlmUBAGVV9UiI7J+Y8qHD7EoW21rbBYnhStT7F+do/rkebegz5x995oEjsTuTsZb2Lu7zLW39Gsfr\n30Vy+CzMi3t02G2bLd6nstC/o0tubi5yc3MBOH/ODx70b79RQcaodDodrrvuOvzhD3+A2WzGSy+9\nhJSUFO7/sbEq1ssKTADotjp7qdoEnFcWrIjFmhmv4e45HwgWAyGEkKEJ8VLRv81cCQCoaTvlV9sG\nk/Clmq40gk0ceuONN3Du3DmEh4fj448/xsaNG4UKhTd9y2LIpZ4ff3uXcAVkpRIZjJY2NHeWwu6g\nX0RCCBkNQtwq+veOupS2fQ0Afi/a0hvpu4Bvgg0YJyYmYt++fUI9XhB9kzJtkMJjHoDQKzD3Fv0F\nRksrbsp6GUGScEFjIYQQMji1QgaVXAqz1Q5Ttw1BKjmSdHNQrT8CrTLGr7YNRud8tNQYHSoa9CMR\nLhkELbHjUWxYn6RM7TnHTOhaZUZLKwCgzVQuaByEEEJ8x9Uq6/kOCVOnQsLIMC56sV/t6nuGL+Mj\nvE+9ISOPllbwqN/wpUwKpVzKzSnTi2CrJQCwOEam8CAhhJDAC9EocanNiPaubsRHBCMn8kZcnX0P\nWJZFa2vrsNvt7EnK+tbYJIFDPWU8Cuv5a6ZXbUsnxie5ivt1iGT8vsNcLXQIhBBCfBTKzStzfoc0\nG0twomoj6vX+7Slt6PlOEqpU05WIkjIe9S0Ma+q2ISbU1XumNwq//yUARGtyhA6BEEKIj1z7Xzrn\nKDd2nceRivdR2XrMr3Z7J/rrKCnjDSVlAtMGueaVCT18mRg6DUpZMGQStaBxEEII8V3fOWXnGjcD\nAE5Vb/Kr3d6eMi0NX/KG5pTxTKWQwmxxVc/XqFxJWYfAE/1vmrQeDCOhwoCEEDKKhGicSVNHnz/s\nNQr/tkPqnejft3wTCRz6pHnWdwWmXOba8PVSm7AT7I9XbcCGE4+gvvOsoHEQQgjxXe+csr4FyHWq\nWL/aNYhknvOVhHrKeBYTGuRR76WmyQCZlIHNzqKwevirZEbCscr/AwA0qM4jLniyoLEQQgjxTahb\nAVkAWDX+X5BrrFBIg2HpGn67BpOzThlDmyHzhnrKeNa3LEZpfQfmT4gXKBrvilp2Ch0CIYQQH3Fz\nynp6yuRSNSI0adCqovxqt7enTEbDl7yhT5pnC3ITPM4rG/SYMz5OoGg8BSnCBr+JEEKIqIT06Skb\nKb17X1JSxh/6pHm2cJJnUma1OzzmmZkt/u1V5o/U8DmCPZsQQsjwuK++NNs6sPH8Ory2f6Xf7faW\nxJBKaPySLzSnjGcxYUH9rqkUrsn+LXozEiKD+QyJc1X6/ZiWtBpGg1WQ5xNCCBk6954yo3Xk5iZT\nTxn/6JPmmVTS/yOvb3XNxDxadInPcDzIpEq0GatRqz8hWAyEEEKGJlTjmlNW2f7tiLVLPWX8o6RM\nAIl9esLK6ju4428L6vgOx8Ou88/jaN2bsDuEG0YlhBDiu946ZXqTBeHqcSPSptXmgNlih4RhwI5I\ni8QXlJQJYOnUJI/z0vp27vjb88IlZQwkYOEAALSZywSLgxBCiO+kEgl0QQqwLGC2sFBIg5EVvcSv\nNnuHLrVqOUzd9Ec6X2hOmQBSY3Qe52WXOhCuVaHVYEZVk0GgqDz35uy0NCEyKEuwWAghhPguRKOA\n3miBkp2A28b/E6FhIX61xyVlQQpKynhEPWUCSI32TMoa202YkhbJndvsDr5D6qfOcFLoEAghhPgo\nVKMCAFR3HMG5xi1oNVb61Z77vpfGblr8xRdKygSQ0qenDAAsbomY+3CmUJJD5godAiGEEB/1zitr\n7T6DgqbP0NJV4Vd7vfto6tQKGN16yvpuFUhGFiVlAkiJ7p+UNXeYuOOz5c18huMhK3oJ1LIwSBmF\nYDEQQggZmt5aZWbJGQCAyeLfH/ctBud3UoRO5ZGU9d2VhowsmlMmALVShpjQIDS0uzYgb3JLys6U\nNWH1AmHmcy3JegLtbR2D30gIIUQ0QjRKKBWu5CkpbKpf7bXqzQCAcK0K7W47BcSF96+1SUYO9ZQJ\nJCVG63HeajBzxycuNvIdDsdoacHWokfxSeFDgsVACCFkaMI0SiTHuxaKRQZn+NVeS893UoRO7dFT\nluxlpIeMHErKBOJtCLNXQVWLYKtd7A4rTLY2WB1GOFi7IDEQQggZmtBgJS5WhKH4zIO4cdxLfrfX\n0tNTFqFVoandNZIzPon2SA4kSsoE0rcshjubncXZ8iYeo3EJDUrkjsva8gSJgRBCyND0brXU1umA\nRhE5yN2Dc59TVtWo5673rR5ARhYlZQK5XFIGACdLhBvC7GW2Cb8KlBBCyOB6J/p3uM3/8kdvT1m4\nTo2OnvIYgPfqAWTk0ER/gQz2gy3kvLJebeYKoUMghBDig5AgJf76m/0AgBp9OCIirvOrvd55zhFa\nlcf1qBC1X+2Sy6OkTCCXm1MGACdKGsCyrEeVfb6sGv8vSCVySBj68SCEkNEgNFiJmk7nsVzif+LE\nzSnTeSZlQnwnXUlo+FIgYcFK6IIGrgXW2G5CbXMnjxG52FkrSlu/QVHLbkGeTwghZGg0alfVfa0y\nzq+2HA4WbZ2ukhiEP5SUCYRhGB96y4QZwrTajTh56QNcaN4OlmUFiYEQQojvNGrXrjBB8nC/2mrv\n6obdwUIXpIBM4koTFDJKGQKNPmEB9dYqmzkuxuvrQiVlGkU0AMBs64C+u1aQGAghhPhOqZCgrDoE\nReWh6Lb6V86odz5ZuFYFk8VVnmlWdqxf7ZLBUVImoN6lxbmpEV5fP3mxgc9wOBLG9WNRSxuTE0KI\n6OmUsdjw+Vy88dEkv1dgtujdt1hyDYsO1IFARg4lZQJKjXUmZXq35cYAoFJIwTBAfkULzBZhisj2\nOte4SdDnE0IIGVxe5Z/wyi9bUfzOWkSH+rcVElfNX6vmNiYHKCnjAyVlAkqNCQEAlF/y3GvSbLEj\nKVILq92BcxUtQoSGCZG3AADig/3bP40QQkhgGa0tuNR5Dg3G41Ar/N+bkiuHoVN5fD9NzYjyu21y\neZSUCah3u4rCqlasnJXq8VqEzrmk+YRAQ5ipoVcjKigbYeo0QZ5PCCHEN0dq/wUAYMGOSCkj9y2W\nvjlTw10P6ylQSwKHkjIBhQWrkBylhdlqx/yJCR6vRYY4lyELVdlfq4zF0rTfIjd6Fa3AJIQQEbM7\nLIPfNAS9w5fhOhU+PlDMXacaZYFHSZnAclOde5TJpZ7/FL1VlIWs7J9X8SdsPL8OB6r+KlgMhBBC\nLo/pWZyVqJs1Iu219k7016ph6hZ2XvOVhkq2C2xyWiR2HivHhepWj+syqQQhQQpcautCbUsnEiKC\neY+t9xe9vvM0788mhBDim2VpzwDAiI1qDFTNnwQe9ZQJbHKas6fsbHkzNCo5d72q0YBpmc56YUIN\nYbKgYUtCCBktRmp4scXQPykbFx86Im2Ty6OkTGCTepKy81UtuHtZDnf9Yl07pvckZUJN9p8Zdy93\nbHOYBYmBEELIwIzWVphtHYPfOASuif6uPTR/uHziiD6DeEfDlwIL16qQEBGM2pZOxIVruOv1rV1c\nL5pQPWVBcldR226bATIFdWUTQoiYfFX2LEy2Nqhl4bg5+2W/22NZFq0G55wy92r+N89N97ttMjhK\nykRgclokals6YXM4PK7HhDnrzZwrb0a31Q6lXMprXAzDYM3ED3l9JiGEEN+ZbG0AgJSQuSPSXqfJ\nCovNgSClDJ8dKuWu08bk/KDhSxHoHcKsbenyuN5m6Ma4+FBYbA7kVzQLERpajCX4uvx/cazubUGe\nTwghxDuj1bVALClk3oi06T6f7N0950ekTeI7SspEYFJPWYz88mZMSA7nrpfUtWNmlnNbi28L6gSJ\nTSKRo8l4AWVt+9BtMwgSAyGEkP6ajEUAgAj1OISpUkakzYY2Z+dApC4I7Z3+7aFJho6SMhHonTuW\nX9mChZMSuevbjpThmmnJAIAvjlcKEluI0hXPheYdgsRACCGkvwh1BqbG/gDjI1eO2MrL0nrnooH0\nON2ItEeGhpIyEYgMUSMuXIMusxUqhWve2LHiBiyalAiVQorTZU2oa+nkPTYJ44rnQgslZYQQIgYs\n64DJ2oZx4dciUTdzxNq9WNsOABgXH8ZdS42hBI0vlJSJRG9vmc3uWRuMYYDFk529VV+eEKa3LCVk\nPndMWy4RQojw2sxV+Lrif/Bl6W9HtN2SemdSFhXiKofx8A2TR/QZZGCUlIlE77wyo9nqcf1YcQNW\nzEwFAOwWKCmbk/AglFItAEDfLczcNkIIIS57ypxV/B2sY5A7h6a0zpmUVTbquWsLJyUMdDsZYZSU\niUTvCszC6lZMTHHVB3trdz6umZYMqYTBd4V1aO/if+Ilw0gwK/5+LE9fD50yjvfnE0II8c5gGbk/\nlE0WG6qaDJBJGRzIr+Wuu9fQJIFFSZlIcJP9KzxXYH51qgphwSrMzYmDzc5i76kqQeKL106DnbXh\ndMMGQZ5PCCHEyX2Hlesy/nfE2i2/1AGWBVKidThV2sRdV8j4rZF5JaOkTCSiQ4MQGxYEg8mKzD57\njJksNqyY4VzuvPt4hQDRAe3mKuwtfw7FLbtgd1gEiYEQQgggYeSYnfAQguSRHivk/VXSM3TZ9zuI\n8IeSMhHJ7ZlXFqlTe1w/VtyA63rmlX1ztsZj6wu+hKldNXCO1P6L9+cTQghxkjBSpIVejZuyXgLD\njNzXeEnPysvEKC13bXxi2EC3kwCgpExEeocwS+raccPsNO76u1+cR0JEMCanRcLUbcOBc7UDNcEL\nmuxPCCFjT0lPjbIqt0n+C2iSP68oKROR3sn+ZyuaPZKyL086V126VmFW8B0aAGBy9B0AgI7uakGe\nTwghV7oLzTuw8fw6FDRtHfG2e4cvj164xF1LjNQOdDsJAErKRGRqehQA4MTFBsyfEO/xmqnbhhUz\nnUOIX56ohM0+ssugfZEZfg1yIm/EqvE0fEkIIUI407PYqrB5ZJMyh4NFaU+Nsg6ja95wfAStvOQT\nJWUiEh0ahGkZUTBb7DhWfIlL0gAg71wNshLCkBarQ1tnN44VN/Aen1yqxoSoW3Gp8yxKWr/m/fmE\nEHIls7ktspqd8NCItl3b0gmzxY7oUM85zQkRwSP6HHJ5lJSJzPWzUgEAO49V4L4Vudz19f85AoZh\nsGKG83WhVmEarc04VPMPnGn4j8d/IAghhARWQ2c+d5yoHbmtlQDX0GWQUu5xPYW2WOIVJWUic/0s\n51yyPScrschtgmVFg3Pi5YqepG338QpBtjzSKZ0x2Rzd2HnxSd6fTwghVyoH7AhWxGJy9B0jtgF5\nr4s9SZl7gfIJyeEI1ShH9Dnk8mRCB0A8pceGICcpHIXVrThT1ozkKC2qmgwAgKYOI6ZnRCM6VI2a\n5k6cr2xFbmrEIC0GjsnWJtizCSHkSsKyLBK0M5ConQkW9hFvv7enrL3TlZTdfc2EEX8OuTzqKROh\nlT29YbuOleOJVdO563/8+DgkEgbLpwtbSHZOwsPcsXtlaUIIIYHRYrqIHRd/jpK2vZAwI9+f0rvn\npbvre1b8E/5QUiZCvUOYu09U4pppydz1j/YVARC+NEZKyFXcca3hlCAxEELIlWRv+XoYrc0wWlsC\n0v5FL0lZZIjay50kkCgpE6HxSc5Vlq0GMwqrWj1eM5qtmD8xHlq1HIVVrah0K/LHF4ZhMDv+AaSH\nLUaoMon35xNCyJXEfWs7jTzqMncOT6vBjBa956jHtIyRfw4ZHCVlIsQwDG7o6S3bdbwcv7trLvfa\ntiNlUMikWDrV2YO261iFECEiLWwhZsXfB6lEAYvdKEgMhBByJTjd8BF3nBG2ZMTbL+2p5O/uZ6tm\njPhzyOAoKROp3iHMXccqcPv8TO76z/61HwBw4xzn61sOXuQ/uB6bC36EHRd/jlOXPhQsBkIIGeti\nNBMBAFpF/IivugSAkrr+i7YWTabtlYRASZlITUmPRHyEBpfajFw5jF5GsxXLpiYjNFiJgqpW5FcE\nZo7BYOK0UwEAFe0H4WD532GAEEKuBIm6mVgz8UNcn/n7gLRfUte/p0wqofRACPSpixTDMFxv2c5j\nFbhuRgr32tdnqqGUS3HrvAwAwKYDxYLEODXm+9xxtf6IIDEQQsiVgmEC85VdVO05d3n93fMC8hwy\nOErKROwGt9IYz69z/ZI8/29nAnTHwiwAwKeHSmC18d9TpVFEIiooGwBwuOY13p9PCCFjmaG7ARvP\nr0NVR+D+6GVZFmcrmj2u3X71uIA9j1weJWUiNjMrBpE6NSobDWjvcq2+qW3phKnbhslpkchKCEWL\n3oxvzlYLEuO02HWIDZ6Mm7NeEeT5hBAyVvXO1/2u5h8Be0ZdS1e/lZchVMVfMJSUiZhUIsGKmc5h\ny13Hy7nhSgDYc6oSDMNg9QJnb9mm/cIMYYapU7Aw+Ul0dNeivP2AIDEQQshYw7Is6jvPAADSA7Di\nstfZ8iaP85zk8IA9iwyOkjKRW9k7r+xoOZ75wRzu+n+99g0AYNXVmZAwDPacrEKrQZjV5TH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2DBulgycovNEaqeQqGgX9hHhLh2ZWCjzyipyEGn05k1JiGE+C/SCo9x9NISAOIzV5ktjt93nyIj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\n9wvrD53FguswC1HrxZ7NImDMN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       "text": [
        "<matplotlib.figure.Figure at 0x7fade4135eb8>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Discussion\n",
      "\n",
      "The filter tracks the movement of the target, but never really converges on the track.  This is because the filter is modeling a constant velocity target, but the target is anything but constant velocity. As mentioned above we could model the circular behavior by defining the `fx()` function, but then we would have problems when the target is not moving in a circle. Instead, let's tell the filter we are fare less sure about our process model by making $\\mathbf{Q}$ much larger."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def circular_target_filter(std_noise):\n",
      "    f = UKF(dim_x=4, dim_z=2, dt=0.1, hx=hx, fx=fx, kappa=2.)\n",
      "    f.x = np.array([target_pos[0], 1., target_pos[1], 1.])\n",
      "\n",
      "    Q = Q_discrete_white_noise(2, dt, 10.1)\n",
      "    f.Q[0:2,0:2] = Q\n",
      "    f.Q[2:4, 2:4] = Q\n",
      "\n",
      "    f.R *= std_noise**2\n",
      "    f.P *= 1000\n",
      "    \n",
      "    return f\n",
      "\n",
      "std_noise = math.radians(0.5)\n",
      "cf = circular_target_filter(std_noise)\n",
      "target_pos = [0, 0]\n",
      "plot_circular_target(cf, std_noise, target_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2ujOAxIx8TqSUr+Y/smcor49oV+FJSoOiJ6/kHK529Vkc9YgxPdCtM+39Hpdg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OjYEJstbjESyoRVmzwg7IpDlOiNJmZ+sY35q6Ixm2t/MlOpUHK7773YadxZdfoxTuesZ2P8q7WW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\nAEhAlAEAJPACFh/ejO9aHuAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade42a7320>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The convergence is not perfect, but it is far better. \n",
      "\n",
      "###### Problem: Sensor Position Effects\n",
      "\n",
      "Is the behavior of the filter invariant for any sensor position? Find a sensor position that produces bad filter behavior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your answer here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution\n",
      "\n",
      "We have already discussed the problem of angles being modal, so causing that problem by putting the sensors at `y=0` would be a trivial solution. However, let's be more subtle than that. We want to create a situation where there are an infinite number of solutions for the sensor readings. We can achieve that whenever the target lies on the straight line between the two sensors. In that case there is no triangulation possible and there is no unique solution. My solution is as follows."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "std_noise = math.radians(0.5)\n",
      "sa_pos = [-200,200]\n",
      "sb_pos = [200,-200]\n",
      "plt.scatter(*sa_pos, s=200)\n",
      "plt.scatter(*sb_pos, s=200)\n",
      "cf = circular_target_filter(std_noise)\n",
      "target_pos = [0, 0]\n",
      "plot_circular_target(cf, std_noise, target_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jy/H+Z8k4cjoCPafYAICf/+UA3v06B5vWzsOYiADfV5yI+oXBjGiAHThbigde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\nRERMQsFMRERExCQUzERERERM4v8Di1vz8YTpEEoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade41e8da0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I put the sensors at the upper left hand side and lower right hand side of the target's movement. We can see how the filter diverges when the target enters the region directly between the two sensors. The state transition always predicts that the target is moving in a straight line. When the target is between the two sensors this straight line movement is well described the bearing measurements from the two sensors so the filter estimate starts to approximate a straight line. \n",
      "\n",
      "\n",
      "###### Exercise: Compute Position Errors\n",
      "\n",
      "The position errors of the filter vary depending on how far away the target is from a sensor. Write a function that computes the distance error due to a bearing error. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# your solution here"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution\n",
      "\n",
      "Basic trigonometry gives us this answer."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def distance_error(target_distance, angle_error):\n",
      "    x = 1-math.cos(angle_error)\n",
      "    y = math.sin(angle_error)\n",
      "    return target_distance*(x**2 + y**2)**.5\n",
      "\n",
      "d = distance_error(100, math.radians(1.))\n",
      "print('\\n\\nError of 1 degree at 100km is {:.3}km'.format(d))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Error of 1 degree at 100km is 1.75km\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Discussion\n",
      "\n",
      "This is an inherent physical limitation that is extremely difficult to deal with when designing filters. We can see that a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. For example, here is a scatter plot that shows the error distibution for a $1^\\circ$ standard deviation in bearing for a $30^\\circ$ bearing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = 100\n",
      "xs = []\n",
      "ys = []\n",
      "\n",
      "for i in range (3000):\n",
      "    a = math.radians(30) + randn() * math.radians(1)\n",
      "    \n",
      "    xs.append(d*math.cos(a))\n",
      "    ys.append(d*math.sin(a))\n",
      "    \n",
      "plt.scatter(xs, ys)\n",
      "plt.show() "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Sa6/ZdOKEWQsWnNILL9hVUeFQVZVV773HmSoASAQdKiBLDB5co0AgT5ddFtLN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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade4326470>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Exercise: Explain Filter Performance\n",
      "\n",
      "We can see that for even very small angular errors the (x, y) positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer this for the one sensor problem as well as the multiple sensor problem. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###### Solution\n",
      "\n",
      "> This is **very** important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you really need to revisit some of the earlier Kalman filter material in the Multidimensional Kalman filter chapter.\n",
      "\n",
      "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible psoitions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target to form an intuition."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pos = [5, 5]\n",
      "for i in range(5):\n",
      "    pos[0] += 0.5\n",
      "    pos[1] += 1  \n",
      "    \n",
      "    actual_angle = math.atan2(pos[1], pos[0])\n",
      "    d = math.sqrt(pos[0]**2 + pos[1]**2)\n",
      "\n",
      "    xs = []\n",
      "    ys = []\n",
      "\n",
      "    for i in range (100):\n",
      "        a = actual_angle + randn() * math.radians(1)\n",
      "        xs.append(d*math.cos(a))\n",
      "        ys.append(d*math.sin(a))\n",
      "    plt.scatter(xs, ys)\n",
      "\n",
      "plt.axis('equal')\n",
      "plt.plot([5.5, pos[0]], [6, pos[1]], c='g', linestyle='--')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6s8/WaPjwGjNLBPB/2PQNIOEYhqH7Vt6n17e8rsZgo9nlhHQwOFVX21VU5Gq+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\nAAAADP4HF1CTyUoO+XQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade41245f8>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that each individual measurement has a very large position error. However, when we plot successive measurements we suddenly have a clear trend - the target is obviously moving towards the upper right. When the Kalman filter (whether a linear KF, an EKF, or UKF) computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately $45^\\circ$ degree line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this sort of noise distribution. Of course, this graph makes it look easy because we have computed 100 possible measurements for each position update and plotted them all. This makes it easy for us to see where the target is moving. In contrast, the Kalman filter only gets 1 measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n",
      "\n",
      "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose in the example above we told the filter that the initial position of the target was 1000km away from the sensor (vs the actual distance of 7.07 km), and that we were highly confident in that guess by setting $\\mathbf{P}$ very small. At that distance a $1^\\circ$ error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's consider the effect of adding a second sensor. Again, I will start by plotting the measurements so we can form an intuition about the problem."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sin, cos, atan2, pi\n",
      "\n",
      "def isct(pa, pb, alpha, beta):\n",
      "    \"\"\" Returns the (x, y) intersections of points pa and pb\n",
      "    given the bearing ba for point pa and bearing bb for\n",
      "    point pb.\n",
      "    \"\"\"\n",
      "    \n",
      "    B = [pb[0] - pa[0], pb[1]- pa[1]]\n",
      "\n",
      "    AB = math.sqrt((pa[0]-pb[0])**2 + (pa[1] - pb[1])**2) \n",
      "    \n",
      "    ab = atan2(B[1], B[0])\n",
      "    a = alpha - ab    \n",
      "    b = pi - beta - ab\n",
      "    p = pi - b - a\n",
      "    \n",
      "    AP = (sin(b) / sin(p)) * AB\n",
      "    \n",
      "    x = cos(alpha) * AP + pa[0]\n",
      "    y = sin(alpha) * AP + pa[1]\n",
      "    return x, y\n",
      "\n",
      "\n",
      "def plot_iscts(N=4):\n",
      "    for i in range(N):\n",
      "        pos[0] += 0.5\n",
      "        pos[1] += 1  \n",
      "\n",
      "        actual_angle_a = math.atan2(pos[1]-sa[1], pos[0] - sa[0])\n",
      "        actual_angle_b = math.atan2(pos[1]-sb[1], pos[0] - sb[0])\n",
      "\n",
      "        da = math.sqrt((sa[0]-pos[0])**2 + (sa[1]-pos[1])**2)\n",
      "        db = math.sqrt((sb[0]-pos[0])**2 + (sb[1]-pos[1])**2)\n",
      "\n",
      "        xs, ys, xs_a, xs_b, ys_a, ys_b = [], [], [], [], [], []\n",
      "\n",
      "        for i in range (300):\n",
      "            a_a = actual_angle_a + randn() * math.radians(1)\n",
      "            a_b = actual_angle_b + randn() * math.radians(1)\n",
      "\n",
      "            x,y = isct(sa, sb, a_a, a_b)\n",
      "            xs.append(x)\n",
      "            ys.append(y)\n",
      "\n",
      "            xs_a.append(da*math.cos(a_a)+sa[0])\n",
      "            ys_a.append(da*math.sin(a_a)+sa[1])\n",
      "\n",
      "            xs_b.append(db*math.cos(a_b)+sb[0])\n",
      "            ys_b.append(db*math.sin(a_b)+sb[1])\n",
      "\n",
      "        plt.scatter(xs, ys, c='r', marker='.')\n",
      "        plt.scatter(xs_a, ys_a)\n",
      "        plt.scatter(xs_b, ys_b)\n",
      "\n",
      "    plt.axis('equal')\n",
      "    plt.show()\n",
      "\n",
      "pos = [4, 4]\n",
      "sa = [0, 2]\n",
      "sb = [8, 2]\n",
      "\n",
      "plt.scatter(*sa, s=100)\n",
      "plt.scatter(*sb, s=100)\n",
      "plot_iscts(N=4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uLlb64sVSJKKt143VqrUZKv63ZNVo9uzaQ96TmekoL89WWVlYXbo4ys6WciKV\nSps5U3Z+vtKfey65EW/PnoQltFkEJgBoQQ5eSuBwrGBQ6weOVn29Ie2Siov3VZQefDBN06aFNWFC\nMkBNnx5W166Wbrghqk6dHD32WHIByqFDu2robbfJs2GDfEuXSnurV4QltFUEJgBoYdxCy3vvZaiu\nztSyZV4Fg84Br23e7NXGjXE980yNfD5HGRnJ1+fPD6hTJ0fl5QFJUs+ettq376WBXWoUvfNOWRnJ\ngGXG44QmtEmswwQArcjatRn64guPxo/PUHl5QB07Ovr5z/et9P3QQ3W66KKE8vJsnVVQo17ORlVX\nmxo69MD1maZODSqRMPRRcKDSy8vliUSUU1qqnNLSQ/auA9oCKkwA0MJVVfllmtK2bT59+qlHP/95\nemoI7ne/C+oHP6hXaWmt8vMdeb22zgp9rrSyMskwZHfrpnO/207/2tjxkM9dutSr4cMT2nnTfyj0\nfy+f6ssCmhUCEwC0ULt3+/Xhh36NG5epwsLkLruBgHPIcYMGWfJ4pIKOVWr/0guKDxkiw7Ikw1Ci\nf3+llZbqwv/4Dz32WG/ddVdy6G3SpIj+8hefzjvP0seJbJ0/cKDqhg2j6RttFkNyANACLV+eof/8\nzwyNG5epykpTtbWGFizwqWtXR/fdF0kNwT32WFi9Ou/RcHuh0pyIvOvXy9izR1aPHrK6d5e5bZsM\n21bak0/qsgHb9dRTtSosjOovf/Fp/Pio7r03XS++6NdbO/vICgYPCEtmPM7wHNoMAhMAtDBVVX4V\nFWWpttZIPffss34VFUX1+OMBbd9u6C9/qdYr/9yhby1/SH2W/UXxfv1kBwKyevZU2v/+r6zevRUb\nNkySVD9mjOz8fKXNmKGLem7TqFEx3XtvvR58MKixY2MqLw/ottsy9cYbWanva1gPip4mtBUEJgBo\noZ591q8JE+qVl2fL75fOPDOuefN269//vU59+tSpfSdbtbfeKnPzZmXNmCHDsmSdfroc05R/8WIZ\ndXWyeveW4/fL3LFDdo8e8qxcqd65O5SV5WjkyLimTUtLNYLffXeGPvwwo6kvG2gS9DABQAsTCsU0\na1aNioqyNHu2X3Pm1KhLl7hCodghxzoejwzbliQZti3Ppk1KXHCBnOxseTZulHfVKsnjUe0ddyjz\niSdkbtminEhEXS++SldeaaSWGWgQj0ubNwdV0DXBqt9oU6gwAUALNGhQWAsXVmnevN3q1y+sDlnh\nww6NWcHuwXzBAAAgAElEQVSg9vzkJ6oZPz4ZiCoqFLnkEhnV1ckDHEdKJJT2xhvJxz6fooMHq+vi\n/1VORlRlZeFUP9TPf16n117zac8ejyL/+ji5BQvQRlBhAoAWqqGidLT95STJ8XqVPn++jGhUTiAg\nx+OR94MPpHhciXPOSR5kWar90Y+SFaNAQE6HDjr3b1Plv/5ePfigoU2bTNXXG3r66TQ9/bT0WNkF\nGhn6v1N6vUBTIjABQBtgVlTIKihQ7ZgxcrxeyTAkn09O+/byL1qUDFVffCHP1q2qLimRZ9MmxYcN\nU+/Eh/qi2wCtXevR736Xllrf6a7iLM15+m7189U18ZUBpwaBCQBaOLf95Q73enVxsTLnz5dn0yY5\nHk9yaG4vw7Zlh0LyrlwpGYYG994q45vfOqSf6R//DKhLfuKwvVNAa0MPEwC0ArbPd9Tm64Nfd7xe\nmRUVMrdvV+K882T36KHw9deruqRE6X/7m3zLl8vctk12587ybd6sb3zwhB57bF8/04QJ9VqwgGZv\ntB1UmACgDWqoOhmJRKp52w7sV0HaO2TXsLq3JA321WjOHFv/+Idfs2f7NXVqmOoS2gwCEwC0UbbP\nJx1muK7mxhtlJBKHXTKgX7+wunSJa+xYEZbQphCYAKCNaFh24OAQdNjHRxneIyihLaKHCQDaALYy\nAU4MgQkAAMAFQ3IA0Aa4LT0gHXnIDgCBCQDajKMFIbfVwoG2jiE5AAAAF1SYAADHNGQHtGUEJgCA\nJIIScDQMyQEAALggMAEAALggMAEAALggMAEAALggMAEAALggMAEAALggMAEAALggMAEAALggMAEA\nALggMAHAKWDG4zLj8WN+HkDzQmACgEZmxuPKKS1VTmnpAeHoSM8DaH4ITADQCKqq/Kqq8h/z8UYi\nQWgCmjE23wWAk2z58gwVFWVJkmbNqtGgQWHtKSmRdOAGt7bPpz0lJTISCWWXlUmS9pSUsAku0AxR\nYQKAk6iqyq+ioixVVpqqrDRVVJSlqiq/bJ/vsEHI9vnkePndFWju+FsKAI2svt6jbduCCgYthUKx\nQ15vqDQ1/Ayg+SEwAcBJFArFNGtWTWpIbsaMsFau9Gr16uQ/tyNGeHXuuXWHvO9IQamhr4kgBTQt\nAhMAnGSDBoW1cGFckTpDC15KU1aWVF4ekCT17GnrtNP8atfu0ErTwRpm0Un0NgFNjR4mAGgEHbLC\nar/yDeXlOZo6NZjqaZo6NaidO70yLSt1rCcSkScSkRmPp/48nKOt2fRVZ+UB+GqoMAFAI8n/ZJl6\nD7lQUnrquXbtbFVVmVoTy9bAXrukWExZM2ZIkqJXXSVz61aZe/aodswYOV5vahbd0WbSHW5WHoCT\niwoTADQC2+dT9e236+xz4po5M6y8PFt9+yb0i19EdMcdmfre97O0aHlHed9/X1b37pIko7ZW3pUr\nZbdvr8z585MLWkajyi4rU/ajj8rOzz/ke440Kw/AyUWFCQAaSUMV6OKLa1RebmvPHkNFRZmqrEz+\nrjp+fIb++teR6jtop/wffihz61YlzjlH5o4d8mzdKqtbNwU++khGNCo5jqyCAtWOGSPb59Pmzcmq\nVfv2iSa7PqAtocIEAKfAGWeElZ3tHPL8rl2m3ljdSdq5U1bv3vKuWpUMS6edJuvMM1MVKKt7d9m2\nrU92hPTmm1kaPTpbo0dn6/33A/rv/96jvDxbeXm2nvzNJnXIPnQWHoATQ2ACgEa0f6N2RoatiRMj\nqXAzcWJEkyal68svTW0ccI28q1fL7tIlGZZ69VJ0wADZeXmK9+mjz8aM01s5I/X55x498MC+JvKS\nkgwFg4ZeeekLLX3wRQ3/6EnJOTSYATgxDMkBQCPZf1mAmnHj1HdpuSp6/1APPlintWs9mjw5qKoq\nU/fdl67y8hp9efUYdXjkd5JtS5altOpqJXJy9GHXy7X7U1MlJenavdvUxIkRTZ5sqqpq3++87TtY\nMq88R9U6h+UHgEZAhQkATgEjkZBvwwYN/7xcZ55pqbw8cEDgef55v954p53qf/YzGZYleTxKXHqp\nFtrf1HXXZevWWzM1dmxMsZg0dWpQN98cVV6erUceCaugW40kHXH7FQAn7oQCUyQSUVFRkXJzc9W+\nfXvdeeedJ+u8AKBVqC4uTi4DEAgofv75cvLzdXavapWVhVNDcxMm1GvOnIBKSjK0cmO2Ivffr1VD\ni7RqeyeNH5+RGn6bNi1No0cnF7w8+2xLf/1rtb715X8rZ9q0I67PBODkOKEhuZKSEn3yySdau3at\nOnXqpLVr156s8wKAFu3gVbodr1feNWtkvPeevCtXaujNN6u83Nbzz/s1ZUqaJKmwMKrevW29+nY7\nFRdnqLAwesjnZmY6mjgxoi5dLJ1xWo08y6oPu9wAgJPruANTJBLRnDlz9N5776lz586SpH79+p20\nEwOA1iywbJnyzhmhiy5KaMECn4qKohozJqZ160wVFyerSnPmBPTAAxFNnRqUJE2ZEtZpp1nq3CGm\n9tn1MmJxmRUVTXwlQNtw3IFpw4YNMgxDzz33nGbMmKHc3Fz95je/0bXXXnsyzw8AWiTb59OekpLU\nz5JUc+edSlu5UrIseTZuVOdEQmf0+ZbKy2sUCkkbNpjavNmT+oyqKlOzZgX0xBO1at/ekc9nq298\nldKe+KvsHj1k5+bKiEblBAJNco1AW3Lcgam6ulqxWEybNm3Sli1b9Oabb+rqq6/WRx99pLy8vNRx\nubm5J+VEmxvf3n8AW+v1tXbcv5arpd47q65O5u9/L6tLF9m5uUoMGCBPRYV6hXbrk6p2Wr3ao61b\nTVVUGJo4cV9VqagoqmDQUV6erY671itt7lzJ45HdoYPMqipZvXvLuekmtQ+FUt8jSZ709COeS1Nq\nqfcPSW35/h13YEpPT5dlWZowYYL8fr+GDRumM888U2+99dYBVabJkyenfr700ks1dOjQEztjAGjm\njhZazIoKxUeNUuDxx1U/frw+2NJedXWm7rknuWRAaWmtqqvNVP9Sr16WvnZWtdIefliy7eRK4Dt3\nyty1S873viczLU3evd9j1dXJ3PtvrvXAA802NAHNxeuvv64lS5akHg8fPvyIxx53YOrVq5cMw3A9\nbty4cQc83rVr1/F+ZbPSkK5by/W0Ndy/lqu537v9m72/3G+TXDMel+eHP5SvokLGO+9o590TtHp9\njl5+2acFC3waOzamKVPSVFKSqd/+NqxRo2KSHHXs6OiVt9rpijFjlDZvnsxdu2RWVMju0UO1sZhs\nx5EikX3fbduSkqMA9t7nm5Pmfv9wdK3t/vXv31/9+/dPPV63bt0Rjz3uZQXat2+voUOHavr06Uok\nElq6dKk2bNigiy+++Hg/EgBaJTMeV9bcucqcOVOelSu14Yxv6+332um22zJVXh7Q2LExzZ7tTy0Z\n0KmTo44dbT33nE/9+7fX3Xdn6H37XNUXFkqOI7t7d9VdddUh39PQN7Vnv6AG4OQ4oWUF/vSnP+mW\nW25Ru3bt1K1bNz3zzDMH9C8BQFtzuGZvSbJzc2W1b6/FnW9U/adGan0lSZo2LS01BFdWFlb//pYu\nvDAn9bqU3O3k04x+6rvtfyRJacuWybtq1QHhqGEtJsIScPKdUGA67bTTtHjx4pN0KgDQOhwusEQu\nu0zvrs/VopcPH2aGDYsrI8PRBX2q9eYH2XrooTrdd1+yB2nixIjuvDNDv/pVRKf9+MfyvvaaZFky\nolEZiYTk8x2y7hOhCTi52BoFABqRGY8rc+5cvfdhSC/vDUsLFvg0YUJ9aqXvsrKwuna1dEHnLfL+\n4x/6etdN6tEjoT//uUaFhVFNnhzU+vVejR+foQ8qOimRmyurVy/FLrtMjpctQYFTgcAEAI3JNLW0\n34/00kt+LVjgU69etoqKopo926/CwqieeqpWfU+PqO9Lj8v79tuSpOCsWereqU6GodSec6GQnRq2\n+7jn5fK//LJ8b7yR/Iq9Q3H0LwGNh8AEAI3os8pMvfxKIDUT7vHHA9qxw9CMGWF95zsxDRxYq87+\nnbLPOEPeVask01T0O99R3opXJMfW9Olh9e2b0AMPRFReHlBhYZY+/dSrnd+6UVJyU9+suXOVNXeu\nJPqXgMZCLRcAGllDWJo926+RI+O69NKEQiFb+fkReSIRZf7xj1I8rviwYfJ88om8K1bI7tpVX9/6\nB334zTv0yCNh3XJLVqoJ/O67M/TUU2fo3AkTZMRi8mzaJEmpfiYAJx8VJgBoRF27RvSrX0VSYenK\nK+MaOLBW+fmRZH/T/PlSIiE5joyqKkmSYdsyKyoUGTVKPdp/qcO1Kb30kk8rVufI8fvlBALJ/9HP\nBDQa/nYBQCP7xjdqNGdOQlIyQB3M7tJFMk3J61Xtd78rMx6XY5pyPB7lPPywzh85UjNmXKbx4zMk\nSRMm1Gv2bL8kKSMjS2fec09yfSaqS0CjocIEAKdA166RQ8KS7fOpdswYmV98IfPzz1U3bJisYFDx\n7GwlMjNTx/nXrNF5A2r01FO1KixMNoyPHRvTggU+RSKGdu0OEJaARkZgAoAmZAWDqdltVjB4yGs1\n48fL3LZN3Z6cpqwsS4MHJzRyZFyzZ/tVVBTVihUe1dUzWAA0NgITADQx2+c7YoXI9vlk2LaMujqd\n3nWPAgFHkjRyZFyZmbZCISkj0zmVpwu0SfxaAgDNmBUMqnrvViuW36+vfa1W7dql68svTa1c6dHX\nvhZXu3axJj5LoPUjMAFAM7P/nnBmPK6sxx+XtG/LkzPOqFNVlV+nny6FQsmwVFWVbAJveAzg5GJI\nDgCakYY94XJKS1PB6XBCoVgqHC1fnqERI0IaMSKk5cszTtWpAm0KFSYAaMZsn0979g7JHa7PqarK\nr6KifYtaFhVlaeHCOJUm4CQjMAFAM3K4gHS0JQMM2zol5wW0dQzJAUAzc7RZc/sz43EV/M8jevI3\nm5SXZysvz9asWTVUl4BGQIUJAFowIxLR8I+e1Csv/ViO6SEsAY2EwAQALdT+w3ftfZYkhueAxkJg\nAoAWjC1RgFODHiYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAX\nBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYAAAAXBCYA+IrMeFxmPN7UpwHgFCIwAcBX\nYMbjyiktVU5pKaEJaEMITAAAAC68TX0CANBUNm9OlyQVdKuRbFu2z+f6Htvn056SktTPANoGKkwA\n2qQlS7I0enS2Ro/O1uL/a6fMuXOPeYjN9vkOG5aqqvyqqvKf7FMF0AwQmAC0OZs3p6ukJEOVlaYq\nK02V3JOh9y8cK5nmAQ3dX6W5e/nyDI0YEdKIESEtX57RmKcPoAkQmAC0PY5zyFM7d/u0an22Mp5/\nXjmlpfJEIsfc3L1tW1CLFvkVi0mVlaaKirKoNAGtDIEJQJthxuPyRCIa8H//qdLpYeXl2crLszVx\nYkSTJqVrzRqvXut5q6z8fNfPaQhRb7+dqWuuyVF5eUCTJtUrFLJPxaUAOMVo+gbQJjQsByBJdn6+\nrvrsD+r61x/p2WcDmjw5qKoqU1OnmiosjCrjO0U6OxhWzbhxyeP361dq+BwrP1/vXvQjLVniUywm\nVVWZmjYtTTffHNXw4TGFQrEmuU4AjYPABKDNqR0zRo7Xq/Y1CZWXZ6uqylQoZKuwMKqzz7YUDhva\nU+VVwcxSWd26qW7MGDlmsiDveDxKFBTopa63qbgw2as0aVK9pkxJkyT9+7/Xq2vXSJNdG4DGwZAc\ngDbB9vlUXVysmnHj5Hi9sn0+hUIxzZwZVt++CT3wQETl5QFNn54mw5C+rPYrMnKkPFu3KvOxx+Tf\nskVZjz6qwLJlWnnBzXrjDa+uuiqmWEypytLjj9cSloBWigoTgDbBjMeVOX++FI9LPl+qynTxxTX6\n4x8t3XBDtmIx6cEHw8rMlOrrDa1qf6kGtXtLRm2tPBs3qv4HP9D6xBmq3WNqwQKfdu82NWlSvWbP\n9uu666I6/fS6pr5MAI2EChOANsFIJGQVFMjz2WfybNqk9MWLUzPg/L7krLmf/zwsyzJ1331Bbdzo\nUTxuaufYYiUGDlRi2DC98mlfjR6drVtvzdTYsfuqS9On1ym/YsUBs+nYbw5oXQhMAFo9Mx5XdlmZ\nfG+8IaugQI7HIycjQ4kBA2QkEiroWKVHHw3rnHNsPfJIQD/+cb3WrvXoxRf9emdlphKXX65/fdpF\nd9+9b+2madPSNHp0srE7I2gp7/MPDvg+9psDWhcCE4A2pe7qq2Xn58u3dKnMykpll5VJlqUrOiyX\nx+Pojjuiqqz0qLw8oPLygDp0sLQ13F6Soz/8oVbnn79v9ltmpqOysrAGVC9V+KqrJImABLRS9DAB\naPUa9n8zEgllzp8vc/v25OKVe/9n1NfLu2GDOlxyrizL1r33JitJw4ZF1auX9MYbXpWUJGfETZ8e\n1lNPORo7NqZQyNYg+y0Fn/+n4n37JsOXpD0lJew3B7QyBCYAbYLt88mUZFZUKH7ppTKqquTk5MjO\ny1PmH/8oOy9PedFPVZNeIEkKhWzNmVOnTZvM1DYqknTPPRkqL69RIGCrT2KN/IvfUfTb35ZxUGWJ\noAS0LgQmAG1GQ6VJksxoVEYiofTnnlNiwACZO3cq7amndMZPf6qyMo8uuiiht97y6s03D/1n0jAc\n9cndKc+KCtkdOyrw978rYBiKXnWVomeccaovC8ApQA8TgDbF9vlkJBIKLl2qtGXLZJ1+urwffCDP\n1q2yu3SR5803ddFFCa1Z49Hdd2dozpyAJkyoT22jUloa1oCCGqWVlclJTz/gs42aGgWXLqXZG2iF\nCEwA2pTUjLl33pFZWSk7N1cyDDkej6yCAlmDBunjj0299FJySK2qytSUKWkqLIxq7twaDRmSkKqq\nZMTjskMhOTk5itx8s+Lnnivf0qVNfHUAGguBCUCb5Hg8svPyFM/LU/ySS2Tn5ckKBvXqik7629/8\nWrDAl6os+f3SwIGWgkFbF16Yo49jPVV/ySXyv/66JMmoq5O5c6fsHj1UN2zYvmE/qkxAq0EPE4A2\npWGLlPTFi5N9S8uWyfziCxm7d+vj/KEqviZDsZj0i19E9Ic/BFRYGNXgwQkFg7befDP5O+bOnaba\nfe1b6r70Psmy5Nm0STJNmdu3y/Em/1lt2Oh3T0kJDeBAK0CFCUCb5Fu+XJ5PP5WTlSU7N1e77hqv\n6mpDUnIY7le/CurGG6MaOTKm7t0T8vtt/fa3WfrZzyK65550bd9uKnLttaklCuyOHWXn58tIJGQk\nEk18dQBONipMANocx+uVEwgk12EyDCX69tUnm7P16qs+3XdfRA89FJQktWuX3FOuTx9p9Wqfrr8+\nql//Oii/X0okpPXZF6nvjUElcnOV/sILkmEk13mqqFB1cXFqk18ALR+BCUCb1BBoDEmrP26nREJ6\n7jm/xo2L6gc/qFfv3rZOO83SoNN2qCoRUk6Oo3nzAvL7pdLSsJ5+2q9/+7e4vB+uUNonn8ju2FGe\nbdsUv+ACmRUVhCWglWFIDkCb0rDPW3ZZmWQY+uizHH3yiUd//GNAv/hFRI8/HlA0aqhbN1uD+lbL\n8+67Cn2+XmefndDcuTX67/+u0T//6dWAAY5KStL1r34/SC4v4PEkK1c5ObLz85v6MgGcZFSYALRJ\nTjCod1Zkq3KHV7Nn+3XnnVHNm+fTI4+ElZYmdelYK//TT8v8/HP543F1vekmbY8O1D/+4Zffb2jK\nlGS1KVJvasv3SxTy7lbG88/L/9prsgoKmvryAJxkBCYAbUrDat+79qTpR9/MVkaGrV/9KqKysoDG\njo3Jtg3FY5a6/eUPcoJByUwW4v1Llqjvtd20Z0gHFRdnyO+XJkyo109/mq5Zsxy1Oy0tORQXCKh2\nzBiG44BWhsAEoM2xfT45pkeStHGjV7/4RVD33x9Rz562TNNW3961qul1q6Rkg7gZjcrxeOQ3HOXn\nJ1RYGFVtraEpU9Lk9yd7x6tq0yU23AVaLXqYALRJoVBMs2bVKC/PVjhsql07R3l5cZ15ZkS2xyMr\nGJQVDMr2+ZTIzJTj9Sr70UfVb/1zuuiihF580Z9qAH/00YDCYY9sn4+wBLRSVJgAtFmDBoW1cGFy\nNe5QKHZM7/F/8IHOv/0q/fnPthxHmjo1TevX+xQM1jbmqQJoYgQmAG3asQalht4nScr0JRSNBlRU\nlCVJmjWr5pg/B0DLRGACgGO0/3Db8VSnALRcBCYAOE4EJaDtoOkbAADABYEJAADABYEJAADABYEJ\nAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADA\nBYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJ\nAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADABYEJAADA\nBYEJAADABYEJAADABYEJAADABYEJAADAxQkHpqVLl8o0Tc2ePftknA8AAECzc0KBKZFI6N5779VZ\nZ50lwzBO1jkBAAA0KycUmMrKynTVVVepU6dOJ+t8AAAAmp3jDkyVlZX685//rHvuuedkng8AAECz\n4z3eN/7kJz/R/fffr0AgcNTjcnNzj/crmjWfzyep9V5fa8f9a7m4dy0b969la8v377gC0xtvvKFN\nmzbphhtuSD3nOM5hj508eXLq50svvVRDhw49nq8EAAA4qV5//XUtWbIk9Xj48OFHPPa4AtPy5cu1\nbNkymea+Eb3XX39da9as0fTp0w84dty4cQc83rVr1/F8ZbPTkK5by/W0Ndy/lot717Jx/1q21nb/\n+vfvr/79+6cer1u37ojHHlcP0/jx42Xbdup/Q4cO1ZNPPnlIWAIAAGgNWLgSAADAxXE3fe9v0aJF\nJ+NjAAAAmiUqTAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4I\nTAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAA\nAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4I\nTAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAA\nAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4I\nTAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAA\nAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4I\nTAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAC4ITAAAAP+/vfsLrbr+4zj+Xnnc/DdtK1Nnk4hE\nTBTtD6VYZhdCWShUWoKGlkJ4IV2FUCReFEiWKEpGsrqw7CpIsB9FoASKSVFWk6GFK03nn9bUbR49\n83chKtav32f/2tfjHg8QPGdn+sLvGd+n5+ycJQgmAIAEwQQAkCCYAAASBBMAQIJgAgBIEEwAAAmC\nCQAgQTABACQIJgCABMEEAJAgmAAAEgQTAECCYAIASBBMAAAJggkAIEEwAQAkCCYAgATBBACQIJgA\nABIEEwBAgmACAEgQTAAACYIJACBBMAEAJAgmAIAEwQQAkCCYAAASBBMAQIJgAgBI6JP1gGJVKBSy\nngAAPao3n/sEUwfV15fFN9/kYuvWi/90M2cOikmTzkV1dWvGywDg3+Hc14VgOn/+fCxcuDC++OKL\naG5ujkmTJsW6deti7Nix3bnvmvLdd/1j7tzyaGq68kzmtm19o7y8LT76qCkmTGjOcB0AdD/nvos6\n/T1MhUIh7rzzztizZ080NjbGE088EbNmzerObdeU+vqyv91hLmlquiHmzi2P+vqyDJYBwL/Due+K\nTgdTaWlpvPLKKzFixIiIiHjuuedi//79ceLEiW4bdy355pvc/7zDXNLUdEN8+22uBxcBwL/Lue+K\nbvsepp07d0ZVVVVUVlZedf1fLxejQqFw+Xnb/+fTT0tjwYIb48Ybb+yBVXRFLnfxC/x6uH/2No5d\ncXP8iodz39W6JZj+/PPPWLZsWaxevfpvH1u5cuXl3z/44IPx0EMPdcdfCQDQJdu3b48dO3Zcvvzw\nww//4227HExnz56N2bNnx9y5c+Opp57628dffPHFqy4X61N2M2cOim3b+v7f2zz++NlobDzVQ4vo\nikv/uy3W+2Nv5tgVN8evuFzv575x48bFuHHjLl+ura39x9t26Y0rC4VCPPPMMzF69OhYsWJFV/6o\na96kSeeivLztHz9eXt4WEyee68FFAPDvcu67okvBtGTJkrjhhhti/fr13bXnmlVd3RoffdT0P+84\nl15a2ZvejwKA659z3xWdfkru4MGDsWnTpujfv38MHjz48vWfffZZTJkypVvGXWsmTGiO//ynLb79\nNheffloaERcfipw4sXe9eRcAvYdz30WdDqZRo0ZFW9s/P0x3vaqubo3q6tZYsODiqwGK9XlbAGgv\n5z4/GqXTrveXTwLAX/Xmc1+XvocJAKA3EEwAAAmCCQAgQTABACQIJgCABMEEAJAgmAAAEgQTAECC\nYAIASBBMAAAJggkAIEEwAQAkCCYAgATBBACQIJgAABIEEwBAgmACAEgQTAAACYIJACBBMAEAJAgm\nAIAEwQQAkCCYAAASBBMAQIJgAgBIEEwAAAmCCQAgQTABACQIJgCABMEEAJAgmAAAEgQTAECCYAIA\nSMh8XUAAAAcySURBVBBMAAAJggkAIEEwAQAkCCYAgATBBACQIJgAABIEEwBAgmACAEgQTAAACYIJ\nACBBMAEAJAgmAIAEwQQAkCCYAAASBBMAQIJgAgBIEEwAAAmCCQAgQTABACQIJgCABMEEAJAgmAAA\nEgQTAECCYAIASBBMAAAJggkAIEEwAQAkCCYAgATBBACQIJgAABIEEwBAgmACAEgQTAAACYIJACBB\nMAEAJAgmAIAEwQQAkCCYAAASBBMAQIJgAgBIEEwAAAmCCQAgQTABACQIJgCABMEEAJAgmAAAEgQT\nAECCYAIASBBMAAAJggkAIEEwAQAkCCYAgATBBACQIJgAABIEEwBAgmACAEgQTAAACYIJACBBMAEA\nJAgmAIAEwQQAkCCYAAASBBMAQIJgAgBIEEwAAAmCCQAgQTABACR0KZh+++23mDZtWgwYMCDuvvvu\n+PHHH7trFwDANaNLwbR48eIYP358nDx5MubMmRNz5szprl1Foba2NusJdIHjV7wcu+Lm+BW33nr8\nOh1MTU1N8fnnn8fLL78cpaWlsWzZsjh48GD88MMP3bnvmtZb7zTXC8eveDl2xc3xK2699fh1Opj2\n798fZWVlMWDAgJg6dWr88ssvcccdd8S+ffu6cx8AQOb6dPYTz5w5EwMHDoxTp05FbW1t/PHHHzFo\n0KA4c+bMVberrKzs8shrUS6Xi+nTp8eQIUOynkInOH7Fy7Erbo5fcevNx6/TwTRgwIA4ffp0jBw5\nMo4fPx4REadOnYqBAwdedbuvvvqqawsBADJWcuHChQud+cSmpqaoqKiIgwcPRlVVVeTz+aisrIyd\nO3fGuHHjunsnAEBmOv09TOXl5TFjxox44403orW1Nd56660YNWqUWAIArjtdeluBd955J/bu3RsV\nFRXx8ccfx5YtW7prFwDANaPTT8kBAPQWfjQKAECCYAIASBBMAAAJnX4fpt7sxIkTsXbt2jhw4ECM\nGDEili5dGrfddlvWs2iHQqEQGzZsiL1798bZs2fj9ttvj0WLFsXIkSOznkYH1NbWxmuvvRZLliyJ\n6dOnZz2Hdsrn81FTUxO7du2KCxcuxJQpU+L555/PehbtVF9fH++++27U19fHTTfdFM8++2zcd999\nWc/qMR5h6oSNGzdGdXV1bNq0KSZPnhxvv/121pNop7a2thg2bFi8/vrrUVNTE/fcc0+sWrUq61l0\nQKFQiM2bN0dVVVXWU+igmpqaOHr0aKxevTo2bdoUM2bMyHoSHbB27dqYOHFivP/++7Fw4cJYu3Zt\nnD59OutZPUYwdVBzc3N8//33MWvWrMjlcvHYY4/FsWPHor6+PutptEMul4snn3wyKioqIiJi2rRp\nceTIkTh16lTGy2ivbdu2xaRJk2Lw4MFZT6ED8vl87NixIxYuXBhDhgyJkpISj8wXmcOHD8f9998f\nERHjx4+Pvn37RkNDQ8areo5g6qAjR45ELpeLsrKyePXVV6OhoSFuvfXWOHz4cNbT6IS6urqoqKiI\nQYMGZT2FdmhsbIzt27fHzJkzs55CBx0+fDhKSkpi9+7d8cILL8RLL70Uu3fvznoWHTBhwoTYtWtX\ntLW1xXfffRf9+vXrVdErmDro7NmzUVZWFi0tLXHo0KE4ffp09OvXL1pbW7OeRgc1NzdHTU1NzJ8/\nP+sptNMHH3wQs2fPjlwul/UUOqilpSXOnz8fDQ0NsWHDhli0aFGsW7cuGhsbs55GO82fPz++/PLL\nmDdvXrz55puxePHiXvW1KJg6qLS0NFpbW6OysjLee++9GD16dLS0tERZWVnW0+iAc+fOxapVq2LK\nlCnxwAMPZD2Hdti3b18cO3YsJk+enPUUOqG0tDTa2tri8ccfjz59+sRdd90Vw4cPj7q6uqyn0Q75\nfD5WrlwZ8+fPj82bN8fy5ctjzZo1cfz48ayn9RivkuugYcOGRT6fj5MnT0ZFRUWcP38+jh49GiNG\njMh6Gu3U1tYWa9asieHDh8fTTz+d9Rza6eeff466urqYM2fO5et++umn+PXXX2PBggUZLqM9hg4d\nmvUEuqC+vj5aWlouvypuzJgxMXTo0Kirq4ubb74543U9wyNMHdS/f/+YMGFCfPLJJ5HP52Pr1q1x\nyy23RHV1ddbTaKeNGzdGSUmJlzMXmUcffTS2bNly+dfYsWNjyZIlYqlIDBw4MMaOHRtbt26NQqEQ\ntbW18fvvv8fo0aOznkY7DB06NPL5fHz99ddx4cKFOHDgQBw6dKhXvVrVz5LrhEvvw7R///6oqqry\nPkxF5NixY7F06dLo27dvlJSUXL5++fLlMWbMmAyX0VErVqyIqVOneh+mItLQ0BDr16+PAwcORGVl\nZcybNy/uvfferGfRTnv27IkPP/wwjh8/HuXl5TFr1qx45JFHsp7VYwQTAECCp+QAABIEEwBAgmAC\nAEgQTAAACYIJACBBMAEAJAgmAIAEwQQAkPBfdetTJhGfA1UAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade433d8d0>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I placed the sensors nearly orthogonal to the target's initial position so we get theese lovely 'x' shape intersections. I then computed the (x, y) coordinate corresponding to the two noisy bearing measurements and plotted them with red dots to show the distribution of the noisy measurements in x and y. We can see how the errors in x and y change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the y coordinate of sensor B the shape becomes strongly elliptical.\n",
      "\n",
      "Next I will alter the starting positions and rerun the simulation. Here the shape of the errors in x and y changes radically as the target position changes relative to the two sensors. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sa = [3, 4]\n",
      "sb = [3, 9]\n",
      "pos= [4, 4]\n",
      "\n",
      "plt.scatter(*sa, s=100)\n",
      "plt.scatter(*sb, s=100)\n",
      "plot_iscts(N=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ccAGvvvoqb7/9NsOHD/9sIxYRkX/aPp2291s+cIJBsKzktnzDtnF9PlJeeAG7\nqIjA6tVgGLh+P7t3WfzgBxlEo3DRRVEyMlwKC20MI3GsaBTKyhKduidOnMXkqR9jvfoq/tWryXjj\nDRrbwtBtt2EPGkR81Ch8GzcmGk3adnJMzTNm4Pp8qlWSXuWwIalfv34sX76c6667jm9/+9sMGDCA\niooKRo8e3RXjExGRg3D8/mQn7vbhw/H7aZg/HysUImPpUjLffpumOXPwvfYaTmFhYjdaPI5/xw7i\nxgAA6utNfve7FPLyHL761SimCbfeGuLnP0/MLjU3G5SVpfNf/5XLmEGD8EMyCLmWhV1YiLV1K+ZH\nH9F0xRWJ1gT9+xObOJHWMWP+6ZvjinSnDrUAOP/889m4cSONjY1UV1fz3e9+t7PHJSIih9H+5rFW\nOIwVDu+zBT/tyScxotHk14bjgOvSOmMG8dGjeSd4Mjt2mCxcGE62BVi4MExWlsPu3SZ33x0kFDL3\nua1JQ4PJCztP4uNZc4kPH44TDGKnphK6+GLclBTapqCc/Hysbdvw/9//kbp27QFjE+kNdO82EZFe\nzsnPJ6uykuzbbiNz+XLMWCzRdbumBruwMNEl27KITpqEuX07qf/1XziFhcRtg5YWk6VLg0ybFmXa\ntChLlwaJRg2Kix1uuCHMPfc0s2xZgEAAFixo5ZZbUrAsgw8i+bw1YVZyBiuekUFjWRlOfj6ZS5YQ\nmj49MWNlGJg7d5K2enVybCK9he7dJiLSS3n1SWrj+nzYRUU4ubmJwmrAzczEcF0Aoscfj3+Xy8CB\nNj/+cZirr07scrvzzhAj6p8nsPpN+lx6KW9szWHq1BjNzQb33BNg7twI3/lO4t5ulZUhLCuVgoJw\n8jPN2trEY8ui8corgURNVNaee88Z8XhiV5xIL6CQJCLSizl+P7QLS+2Lo5tnzCCrspKsjRtx9uwu\na7riCgI1NXzwUTbbPrJ49VUfI0faPPRQI9u2WRQXxzHrDOInn0zKHXcwprSUTycOTRZvt93bDdoX\ndPs4Y8Juz9DWUF6O6/Mlu3If6ka4Ij2NflpFRI4CbWGpvQNuRJufT8ZvfwuxGPFvn8GOHRb3358C\nwMKFYT7+2OD4ojjRoUPJuOce4qNHE/jzn5l8wgncd985bNt2YIWGbcMLL/gY0D+TLxQ3JYrJPcZ2\nsJ14Ij2ZapJERI5Sjt+frBMCCE2fDoaBPXQo4bCZnBWqq0s8PvvsGKNeuY/MJUuIjx4NPh9Ov34E\nqqsZ+8VhQsofAAAgAElEQVSdnHr8x1RW7r33249+FOaEExyqqoJcMjOL51/sQ2NjwPOGvIe795xI\nT6SZJBGRo1j7OiEnGKShvJya2iyeeezAwJKd7eJ7771EB+2GBkLTpyebQ+I45BX7yDt+N/ffn9j9\n9re/Wdx3X0py+W3evHTuucfF7/dx8sktXXaOIp1FIUlE5CjmtdRlGGCacNNNLfz4x4lbhFRWhhgx\nIoD9k5/Q0tSEEwwmZ6IyVqwgq7IycRzHYfTwRj7YkUG/fg733Zeyz+etXp34jMGD4+TkRJO72TSL\nJL2RQpKIyFFu/4BSV5eYAerTx+Guu0JkZTkUF8ewrEysnBzie3bAwb4zUe0LsofOn8+m6kzuuivE\nvHmJnXELFrSybFmAqVNjbNsWwMJmyB8rMcLhfZbeRHoLhSQRkWNIfX2AH/wgI1mLNG9eOg891EhG\nRtTz9e1novbhupx4YpimpgD33efy9NN+li0LUFoawbJg/vw0pk71c86o73LWP37XyWcl0jkUkkRE\njnEDciOH/H77GaD9l+4yM6OMHh0lKyuNk06yeestiz/8IUggkLiVyXd/XMRfnr6Kvn7b89giPZl2\nt4mIHENycqIsXdqU3KH2m3sa6duv4wHmYLvUhg5tITvb5b//O5jszt12KxPXtD638Yt0Jc0kiYgc\nY8aPD7FqVaKgOifHe5ntn3HGGU088UScnTtNrroqnUAAli5t+lw/Q6QrKSSJiByDOiu45OeHyc+H\nhx/+/EOYSFdTSBIRkc+dwpEcDVSTJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCIiIuJBIUlERETEg0KSiIiIiAeFJBEREREPCkkiIiIiHhSS\nRERERDwoJImIiIh4UEgSERER8aCQJCJyCGYshhmLdfcwRKQbKCSJiByEGYuRXVFBdkWFgpLIMUgh\nSURERMSDr7sHICLS09TXBwDIyYGG8nIAHL//sO9rm23qyGtFpOfTTJKISDsbNqQzZUoOU6bksGFD\nOo7f7xl69q9V0tKcyNFHIUlEZI/6+gClpZnU1ZnU1ZmUlmYmZ5Xa2z8QmbEYRjze4c/wOqaI9Dxa\nbhMR6YC9S3DRfZ43IxHSV67ErK2lsawM1+c76HLbqxvSubw0E4ClS5sYPz7UuYMWkc9EM0kiInvk\n5ERZurSJvDyHvDyHpUubyMmJsmFDOhdf3Idly9L5+98TS3AN5eU0zZlD5pIlWDU1OPn5wMHrkXZ9\n6uPyDsxSiUjPoZAkItLO+PEhVq2qZ9WqesaPD1FfH2DhwnRmz45SVRVk1qxMXnwxE0yT9JUrMSIR\n3EAAJzeXrMpKfM3N+JqbscLh5FKcadvUNwS44YYWysrC5OQ4ADQ1aTJfpCfTf6EiIvtpv6TW1ORj\n6tQYt9+eQl2dybhxUYJBh801WQwouZhC6xHcPn0w6+qIDx9Oymuv4V+3DqegAPv447Edh/UZU/n4\nY4uf/jQNgJ/9LExurk0g4HbXKYpIB2gmSUTkEAIBl9NPTxRljxsX5dprW6mu9nHJJZmc9bUhPHv8\n93BjMZy8POxhw7Cqq3Hy8rC2bsXYvp13h5xLRgb07euQnx+nrs7k5ptTKShwGDgw3M1nJyKHopkk\nEZGDMGMxBmW38GEwl5tvbqFvX4c1a/xUVQWpqzPJyXFYvdpPzkUzOXFoEzQ1kbJjB7GTT8b86CM+\n/NdZfPC6j/LydADuuCPEbbdBba2P9PQDZ5HUZ0mkZ1FIEhHx0LbN34hEmDRiBO+OuYgWNz35/Zwc\nh5/9LMyOHQbvvOMjEsnilC9C9KyzMHbtovVHP+LD9328/LKPaBTq603mz0/n179uxrYN8vPD+3yW\nEY+TVVkJJBpYKiiJdL/DhqStW7cyYsSIfZ4LhUKsWLGCr33ta502MBGRnsJsaWFwXohddgpnnBFj\nyBCHjz82ALj//hT69HH4+c/D/HVTFiedfjoZLS08s74PV12VCFXXXtvKLbekAJCT4zJ6x/8QbT4F\nJxgEILuiIrk7TkR6jsOGpMGDB9PU1JT8urq6mnHjxjF16tROHZiISHdq2+bf1iQybfVqAvn5pI05\nidzcbMDg3/4tk2gUZs+OMm9eIhA995zD9t0ZvPSSj2nTojzySIDbb09h1qwIEybEGeX+jeALL+Df\ntg2ztpamOXP2fqaCkkiPcsSF2/feey8XXXQRqampnTEeEZEew/H7sff8rjM/+oiUxx6j3123MSav\nDsNI1BRddFE0ufPt1FOj1NVBS4vJSSfZbNxocu21rfTp4zB9epRRo+KYTU3ETz4Zc8cOiMUI/uMf\nNF9+Oc0zZmDW1mLW1nbnKYtIO0dUk+Q4Dg8++CD3339/Z41HRKRHscJhDNsGnw8MA0wT35o1jB45\nkrvvHs3atXt/jf7sZ2E2b95bqH3rrSHuvjvIHXe0EI26DFr/JwzHwayvJ3bGGbgpKQSfeIIg0Dh/\nPo1lZYAKt0V6iiMKSc888wyGYXD22Wcf8L3c3NzPbVByaP49v0B1zbuOrnnX6wnXPFZfj++223BN\nk+j8+di+xK9MY9UqUh98kLPOP5+B3/gyEyfGmTAhTnW1SXl5OnV1iUn6H/0onRtuaCE722F4/E38\nf/sbsZIS4gUF+N54g/jYscnPCloWwbvvBsC5/nqstLQuP9+ecM2PNbrmXc9/BH+EHFFIuu+++/jW\nt77l+b0bb7wx+bikpIRJkyYdyaFFRHok1zQxbBvfihU4/ftj7txJdNo0zE8+IeV//5cTL/BTOOFU\ntm+H1lbjgPcXFdkMGuQCRcRHjyawejWuYeAUFOAefzzhq67C9Pvx5+R0+bmJHCvWrFnD888/D4Bl\nWZSUlHTofYbruh1q+bpr1y7y8/N5/fXXOfHEE/f53rPPPsvw4cOPcMjyz2r7i2Pnzp3dPJJjh655\n1+sp19zX3Ezq2rWYO3dCLIbTrx++TZvAtomPGkV8xAg2OiNwXZPaWgPbNrj66sRy2513hhg3Lk5J\nSTaVlSFGjYxSsOIerA8/xCksxC4qIvB//4ebkkJDeXnyM7trua2nXPNjia5518vNzWXdunVMnjz5\nsK/t8EzSQw89xKhRow4ISCIiRzPXsvBt3AhAfNQozLo6jGgUNxAgPmgQG50RNDVZ/OUvfp56ys8v\nfhHipptC2LZBcXGcmTPTiUbhhRd89O3r0HTeHI6vfhrTMLCqq3HNvftnvMKRGkyKdJ8O7277/e9/\nz6xZszpzLCIiPYoZi5GxYgVGJAJA+CtfwfzkE1pnzCB+wgm84vsyH33k47vfzaCqKsjs2VF+8pN0\nbNugTx+Xjz+GDz7wce21rTz1lJ8nnwzwyScWH5x4HnZ2Ns5xx9E8d+5Bm0e2NbTMrqhIhiUR6Tod\nDkmvvPIKc+fO7cyxiIj0OGZtLXZREY1lZcQzMmgsK8PasoXtX7kI0zRYvz7RUbuuzuT221OYOjXG\nCSfYnHZanFDIx6xZEZYtCzB7dpSqqiDf+U4G1dU+XuY07ECAtCefxIjHFYJEeiDdlkRE5CDaGkq2\nPQZwfT4cw+Dv/8ikrOzAjtpTpsQYM6wRNm/mpJPGkZvrACR7KQGUlaXzu981884XzueLQzce9HYk\nXp8vIl3niJtJiogcS9rCSfvaoDdPuIiyssRW/7YZpFmzIlRWhjj9hI9IvekmDNflOHYw+guNnHvu\ngbNEf/mLn40b/Tz78Vhih6j1dPx+BSSRbqKQJCJyCGYsRuby5WQuX45p2/z1rxnE4wdu9Z82Lcq4\nMc1Yr75KbOxYgo8+Subdd0MoxCkjG6isDJGX55CX57BgQaJGKRpNzCq9MORSGhYsUBgS6WEUkkRE\nDsGMRCAWw2hs5J33MgFYvDjIHXfsDT2VlSFychyOe/DXBNaswdy9O3EfNtcF28YIhZh8wvvce28z\nM2cmapSuuy5MRUViie6ZZ/y8tyUT07a781RFZD+qSRIROQgzFiNzyRKwLJ6beA1/eSwIwDnnxPnN\nbwIsXtyMZUFBvk3RP1ZhNjQkglEsRnzsWFouvJDMxYuxCwvB5+O0L32JzIvGMm1alB//OJVQyGTB\nglaWLQsA8OXTDb5yeiOOZXXnaYvIHppJEhE5jNrRk/nH1jSqqoJUVQWJRAxOP91m7twMjHArQ3J2\nEjnlFJquuILYqacmOnPX1eEGEuHH2r6dlvPPJ7B+Pac8egNmrJWf/KQ1Oas0e3aUBx4IcuW8TN7Y\nlNXNZysibTSTJCJyEG27y+o/ymDRhanJ3WmLFqXy618387XpuxiU10rcl4YZi5FVWUl81KhER27D\ngK98hcbyclzLwvX5MD/5BGIxTn23iu1nf4M+F6UCcMstKdTXm+TlOTz1VICCghg5OdHuPHURQSFJ\nROSQHL+f1LQD796UkeFQUBjBwYcZi2HE4wCJ25cYBkYkQvrDD4PfT9MllyQDlxGP4/p8ZPldsnJb\n+PKXLaqqgsmC7sTMUlefpYh4UUgSETmMnJwoS5c2UVqaKNz+9a+bOemkFmBvV2yAxrIyXJ8PIx4n\nY8UKrJoa7KKi5HEcvx/228E2cWITv/99YgZp2bIAixaFNIsk0kMoJImIdMD48SFWrUr0OzpYiHF9\nvmQQarrkkuSs0eG29o8aFaKgIMbs2Qc/toh0PYUkEZEO8gowB+uK7TVrdKTHFpHupZAkIvIZqQmk\nyNFJLQBEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHx4OvuAYiIeLFbWrp7CCJyjFNIEpEex4zFMG+7LfF43jwc\nv7+bRyQixyItt4mIiIh40EySiPQ4jt9P/OqrE19Eo1jhMK7Ph+P3Y8ZiB7xWRKQzKCSJSI9jhcNY\nixfjFBSQvX07RiSCXVREaPp0MpcsASA+ahTmzp00XXKJgpKIdAqFJBHpUcxYjIwVKzBaW3H69gXb\nxvrgAwBS165NBibfa69hOA5GPA57QlJ9fQCAnJxodw1fRI4iqkkSkW5nxmIHLKNFJ0/G9/rrYNs0\nlZXRPGNG4vmzz6blggtwhgzBDQZx/X7q6wP8/e/pXHxxH6ZMyWHDhvTuOA0ROcooJIlIt6itTeX9\n99PYsT2VtGefJXP5cqxwGCMex9yxA//atcRHj8bato2MpUsxIxHMjz7C2ryZjHvuwaytpfGqq9j8\nQRbV1QFeeMHHnDkRolEoLc1MziqJiPyzFJJEpMutW5fJ+edn873vZfDxJxavD7uI6Eknkfraa6S+\n9hrEYjgDBmAXF+NaFtg2aY89Bq6Lffzx4LpExo/n7Q/6EIsZvPGGxfLlQUzT5VvfinT36YnIUUIh\nSUS61I4dqcybl040CpdfHuGHP0xj5cogL/tKsMeMwb96NfExYzA//JDgY48RHz2a6HnngetibduG\nf/16Wr//ff5WeD67d5ssWpRCdjaUlbWyeHEKI0faLF3apLokEfnMVLgtIt3im9+M8JvfBPnBDyL8\n+tfBxJPn5TFh7lwCjz8Oroth29jFxQQffZT4mDFER47kvfyvUPOWjyuvTNQd3XFHiPvuCzBihMPU\nqTHGjo2Rnx/uxjMTkaOFZpJEpEsNymvmVxWNjBplc8kliYB0+eURqqqC/L//l8FzmwqJXnopTn4+\ndkEB5s6duBkZ7D73X3gzexJNTSa33x6krs6krs5k/vx05sxJLLF99exGCgc0dfMZisjRokMhKRwO\nU1paSm5uLn379uWKK67o7HGJyFEmuYPNcZi6u4pRo2J85StxLrwwyq23piZDz9y56bzydhbRWbMA\nsEeN4o3p1/LW29l8//vpXHppJnPnRhg2LJ48dna2y+QzWzn99aXgut11iiJylOlQSCovL+f9999n\n06ZN1NfXM2fOnM4el4gcRcxYjOyKCrIrKpJ9jYZvfgK/32XSpPgBrw8EYNPWTOovu5xnNw3ioouy\n+M53Mpg9O0o0Cldfnc7Cha3k5TncdVeIfjkRJgz/hNDMmWosKSKfm8OGpHA4zAMPPEBlZSXHHXcc\nhmEwYsSIrhibiByFDNvGt3Ejvro6hhfWEwg4LFwYJi/PIS8v8Tg93SEry2Xz5iAvvOAjGoW6OpPb\nb0/hoosSBdn9+zvcd18zp5/eyHFpDWRWVJBVUYEVVj2SiHw+DhuSNm/ejGEYPProo+Tl5TFixAhW\nrlzZFWMTkaOE4/fTWFaGk59P6tq1NH//+7RMm0baQw8xrnkNxcU2M2dGmDkzwowZUUIheOcdH9/6\nViZVVUGuvbaVnBwHgIwMl7vuClFYaDOhYAuBaGuiNUBhYTefpYgcbQ67u62xsZFoNEpNTQ1bt25l\n/fr1nH/++fzjH/8gLy8v+brc3NxOHajs5d+znKBr3nV0zT87u6UFu39//C+/jH/DBsLz5gGQ8vTT\nnD2smrHzv0NdHdTUmLguyeJsgNtvT2HWrAijR9sMGmQzdGiMXLMR3+pX8BkG5qefgt9P9Jpr6NPu\n95IcGf2cdz1d867nP4Il+cOGpLS0NGzbZsGCBQQCAc4880y+8IUv8NJLLzF9+vTk62688cbk45KS\nEiZNmnSEwxaRo5mVlkb87LPhr38FwJ+dTewb38CNRKBPH/72N5OGBpOrr05s7f/lL0N8+qnJe+8l\nfk1dcEEUw3AYk7sd37Pr8W3ahBGJED3zTKz33wfADajLtogcaM2aNTz//PMAWJZFSUlJh9532JBU\nXFyMYRiHPdD+xdw7d+7s0ADkyLX9xaFr3HV0zT87MxbDiMdpLS/HtSzcaJTg66+zeei5RHaZ2LbB\n1VenJ2ePrr46nRtuaOGnP02jsjJEv34Opglk9cHJz4eNG8EwMBobE125fT6ao1Ec/X/0T9PPedfT\nNe8aI0eOZOTIkUDimq9bt65D7ztsTVLfvn2ZNGkSd9xxB/F4nLVr17J582ZOO+20zzZiETlmJHe3\n3XYb6StX4vr9hKKprAn+Cy++GOCSSzJZs+bAKfAvftHmT39qZOTIOOeem83vfpfCsy/3wRk6FKeg\ngNYZMzB378YZPDhR86SdbSLyOepQx+17772Xf//3f6dPnz4UFhbyhz/8YZ96JBGRjrL79ePt9zJp\nbbVYs8ZPVVWi9uiBB4Jcf32YRYtSAaioCJGf77B8uY/Fi9NZsKCVW25JoaoqyL33DuG0CROI5+fT\nesIJAApIIvK561BIGjp0KKtXr+7koYjI0crx+2koL8cwTTZ/kIkbM3jmmX1DTX29ydKlQZYvb8Iw\nXEYW7uLld/ty+ukOn34a4ZZbUgCYOTPC9u0mrxadwuiUXQpHItJpdFsSEekSjt/P6vV9+MY3snji\niQBPPeWnuHjfHkm/+EWY1FSHkb63CTz0EBOOqyE93WHixDgDBjhcf32YqqogP/1pGtu2WfxjR5/u\nPi0ROYopJIlIl6iuTueqq9KTS2tz5kRYsiTIxx8b3H9/Ew891EjJ2E8Ymv4h1tatxEePJuW3v+UL\nO1+kqCjO4sUhFi3ae/uS665Lo7nZ4IUXMrv71ETkKNWh5TYRkc+ivj5A+0bY9fUmS5YEWbq0GTA4\nLmUXA99dS2vBBNxgEOuDDyAWI1ZSQry4mIFZYZqb0zyOa9DcbLBlSxpDhrR02fmIyLFBIUlEusRv\nfhPkzjtDXHVVog/S9deHwbY5ueYxyMzE//LLWNu24Rx3HBgGBAK4p55KLDVRyH1icROLF1vMnZt4\n/x13hNi92+SGGxLhaelSg/HjQ91zciJyVFJIEpFOl5MT5bLLItx/f5AHH2wiEHAZuPPvDHxzA6Fp\n0zBsG2vzZqytWzFra4lNmkTguecwFy8mfNVVOH4/ruMw5ZM/8vDDM2lqMlm71sd996Uk+yqVlmay\nalWMnJxoN5+tiBwtFJJEpEuMHx9i2NBWgi+/TF5LDVZNDQCuz4fr82F/4QuYH34IQGTUKPzr1ycb\n2ZqxGAAt//IvnODsYuN7fQmHD9/kVkTks1BIEpEu07efjXnuGJoZk3zO8fsxYzH8L7yAk5+Pc9xx\n2Kmp2D/6EQBGSwsZK1Zg1tbSUF6OHQxy0kkttLYaDBniJPsqLV3apFkkEflcKSSJSJc6VF8j8+OP\nab7kEgB8v/wlruuSMXAgVk0NdlERRjyOFY/j+nyMGxeiuDjAxIlRUlNtBSQR+dwpJIlIt2trNtn2\n2IzFcF0XXBcANxgkNH06GStWYNXU4AaDNJSX06cP9FGrJBHpJApJItIjxUePBqClpATXp19VItL1\n9JtHRLpd2w1wgcTtS+Jx/H/9a+KbJSXJJbqmSy7B2LPcptuRiEhnU0gSkR7H9flwU1KSj9s4fj8o\nHIlIF1FIEpFut39NEoD7058mvm7fqltEpAspJIlIj7D/8pmVtuc2JApJItJNdINbEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIRERHxoJAkIiIi4kEhSURERMSDQpKIiIiIB4UkEREREQ8KSSIi\nIiIeFJJEREREPCgkiYiIiHhQSBIREZH/3969B0dZ33sc/+yz++wSciEkEMJFAgzjIE1F1KEiIzCo\nlHFAj5YCXpowYI0wcCBoTY2tdYShFRDEIIgVyzCnCOONHnUcawEDCFZzcLgoDBaQACFyaxJgk709\ne/6ICVJ+QhCySzbv14wzEnfXLz8B3/k9v30WBkQSAACAAZEEAABgQCQBAAAYEEkAAAAGRBIAAIAB\nkQQAAGBAJAEAABgQSQAAAAZEEgAAgAGRBAAAYEAkAQAAGBBJAAAABkQSAACAAZEEAABgQCQBAAAY\nEEkAAAAGRBIAAIABkQQAAGBAJAEAABgQSQAAAAZEEgAAgAGRBAAAYEAkAQAAGBBJAAAABkQSAACA\nAZEEAABgQCQBAAAYEEkAmsQKhWSFQvEeAwBihkgCcFFWKKR2Cxao3YIFhBKAVoNIAgAAMPDEewAA\nVz/HtlVdWNj49wDQGhBJQCvWcOnsP8PH9HXiCEBrw+U2oJVy19YqdfVqtVuwQO7a2sYwskIhpa5e\nrdTVqzl/BKBVYycJaIWsUEhtP/5YTnq6nMxMpbz1lqyKClUXFsoVDsu9f3/94wIBSefvIp086ZUk\nZWQEYzs4AMQQO0lAK2QFArI//1z21q2KpqVJksI//WljFEV9PkV9PiVt3HjejlJZWbLuvDNDd96Z\nobKy5LjMDwCxQCQBCc4KheSurW28pGaFQnI5juRySS6XXDU18o8cKc/WrUpbsKB+h6lLF51+9FHZ\nZWVy1dTo4JFkHT6cpKoqrwoKUlVZaamy0lJBQWrjrhIAJBoutwEJ5vuXwhrub6RQSE6XLpJty6qo\nkEIhBe66S9GkJIW6dVPbv/1NTufO9eEkyaqokOPzadfd03XSm621/2vrnXe8evbZWqWnO6qs5Psr\nAImPSAISyM6dSTpwoP78UI/ubv30uvA5/9zJzJR1+LDkdkuS3Hv3yv3NN4r06CF7wwaFe/fWzr73\nSX3vU8VWj6ZMqb+cVlRUq8mTA3r66SS98MIZjR+fKklauvQU55IAJCwiCUgQ1dVeHT3q0dNPt5Uk\nlZSc0ZlAG6mwUO7Tp6VIRCmvvCKna1eFc3NlHTkiz7Ztksulunvv1d7xf9C/vknSf9+XrHHjAlq1\nyte4Y/Tcc0kaNy6gESNCysx09NFHJyVxcBtAYiOSgARx/LhHv/lNcmPYTJ2arNdei+rm3IDavvOO\nnI4dJbdbkZ49ZVVUyKqo0N68J3XGlaJg0CUrKD39dJIqKy2dPu0y/juG3xFQt06n5Xy3EwUAiaxJ\nBwuGDh2qpKQkpaamKjU1Vfn5+c09F4BL5DJ0zd//butfh1IV7N9fnm3bVJeXp31dBmp77lht+3mh\nDpxI05YtXo0Zk6bRo9M0ZUqdMjIcvf22V0VFtcrOdpSd7Wj2bL+GDa7VbV++IjlO7H9yABAHTdpJ\ncjtxtk4AABDgSURBVLlceumllzRhwoTmngfAj9Q755RKStyaOrX+HNFjj9Vp2TKvhg8P6fT1t+pf\nWbeq+t+WDh50q7i4/pLc7Nl+LV169rLarFltlZdXf6nN54sqP79OQ4eGlZMTVPtkv07fOJY7bwNo\nNZp8uS0ajTbnHAAuQ8O72HIe/INefvm0Pv7Y1ptvevT++6d0+LBLBw64tH+/W1u3es45a1Rc3Fbj\nxgW0e/fZPwpGjQpqxIigUlMd/exnUnZ2rSTJ4eo8gFamye/jffLJJ9WxY0cNHz5cu3fvbs6ZAFyC\nhvsgKRRS72NblJsb0S9/Wad58/w6dMilffvcWr/e1hNPJBvPGg0cGG68rLZw4RllZDjq1MlRjx61\njYEEAK1Rk741nDdvnnJzcxWJRDRz5kzdfffd+uqrr+TxnH16ZmZmsw2Jc9nfXe5gzWPnalrziN8v\nSXK3bauI36/oypWKtG2rvY/O0hm/VHfI0smTLhUXt1VVlaXi4lr16RNRTk5Yb7/t1ZNP1un559tI\nkn73O786dozozTdr5HJJ19X+n9zte8uXnS2pbRx/llfXmrcWrHnsseaxZ1/CkQFX9BKvo0WjUbVr\n106bN29Wbm6uJGnt2rVav35942MGDx6sIUOGXMrL4hI0/AcO8eGjMXO1rHnE75c1c6YkKfz73+vA\nIem0X7Is6eBBt8rL3XruuSRJ0hNP1GrWrCR5vdK4cQENHx7ShAkpSk93NH++X6mpjmw7qk4pNeq4\nepmcbt1kHTsm+XxyTZwod9urI5LiveatCWsee6x5bJSWlmrDhg2SJLfbrcGDB+v222+/6PN+1CED\nl8t13hmlyZMnn/PjEydO/JiXRhM0fMfBGsdOvNa84TPTGg5LW6GQknNytPOmhxTa4VIkIu3b51aX\nLlFt3Gifc95ozpwk3XdfUO+9V38Hbq83qrfeqpEkud1RXdv+mLxvvCHZts489JAkKXnNGlmHDqm6\npkZObXwvtfHrPPZY89hjzWMjNze3cWMnMzNTmzZtatLzLhpJ1dXV2rx5s4YNGyZJ+uMf/6hOnTqp\nb9++lzEugItpOIwdTUrS/vunS26v/P4k7cueoOm/PHsn7J49Izp0yHy8MCUlquLiWnXtGlF2tiPL\nkvzf7Ty1efFFuSIRRXr2lOPzybFtnRo7VpJ4BxsAqAmRFAqF9NRTT+nrr7+WbdsaMGCA3n33Xbm5\nmRzQ7MI9e2rr9XkKfutSTY0lt1uaPj35nDthP/usX8uWeTV9ep1ycpzGy20vvXRGXbuG5Tj1YXTH\nHe00b94ZSVFlZ0cVuOUW+bZskfO9sxDEEQCcddFI6tChg7Zu3RqLWQDo+x9QK73faYIKHzi7a9Sj\nR+S8x+/da6mgIKgXXmijSZMCev31U0pOjqp36CvJ49MnR3rryBG3Zs8+I9uOatq0FEnSokX36OfX\nnpBnxw7pjjti9xMEgBaCG58AV5GysmQVFNR/eOyqVadUWHjurtEjj9RqwYIzKiw8G069ekXUqVNE\n8+aF5fOEdd3Hr8pz4IBCN9wgz7ZtGvT44/qnp4MOHrQ0bdrZ15syJVn/+HCcMv+rjh0kADAgkoCr\nxMmTXhUUpDZGzL//ff49jWpqLL32mkerVtXIsuoPY197cK28H+89+3EhlqXQTTep7pZb5EtPl3fl\nSnW6a5Is6/zf7lHLTSABwA8gkoCr1OLFvnN2jRYuPKNrrgkrHHapU4c6tbeqlfrCC1I0qlD//pKk\naPv2qrvhBjk+nyTJfeCA3IcPq/fG/9HBnuM1e7a/8SNJli49pYyMYHx+cgDQAhBJwFUiIyOopUtP\nNV5umzbukG4a5NXbb9efQ8rJ8Te+480VCCg4bJgiPXpI392Owzp2TNb27bI3b1Z1YWHju9Vc4bCi\nHo8GWDX65lCK3nijRunpYQIJAC6CSAKuIjfffEb/+LBOvn/+U12+3qKa2x9VTo7/vMdFLUvuPXvk\nZGerbtAgRS1LLsdRyssvn/M4x7al711O657Dx4wAQFMRScBVpn2HiKzh/VSjfuedF3JsW9WFhbIC\nASWvWSO7rEyeHTsad46qCwsbHwcAuDxN/oBbALHj2PZ5oWOFQrJCITm2rXBKik7/4heKfnf26ELP\nAwD8OOwkAS1Aw1kkSY27RlGPRzVTpyrq8RBGANAM2EkCWqCGaEorKYn3KACQsNhJAlqA7583kiRX\nOBzHaQCgdSCSgBbCse1zLrtxqQ0AmheX24AWikACgObFThLQgvA2fwCIHSIJaGGIIwCIDS63AQAA\nGBBJAAAABkQSAACAAZEEAABgQCQBAAAYEEkAAAAGRBIAAIABkQQAAGBAJAEAABgQSQAAAAZEEgAA\ngAGRBAAAYEAkAQAAGBBJAAAABkQSAACAAZEEAAB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       "text": [
        "<matplotlib.figure.Figure at 0x7fade41587f0>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Implementation (Optional)\n",
      "\n",
      "Implementing the UKF is quite straightforward. First, let's write the code to compute the mean and covariance given the sigma points. \n",
      "\n",
      "We will store the sigma points and weights in matrices, like so:\n",
      "\n",
      "$$ \n",
      "\\begin{aligned}\n",
      "weights &= \n",
      "\\begin{bmatrix}\n",
      "w_1&w_2& \\dots & w_{2n+1}\n",
      "\\end{bmatrix} \n",
      "\\\\\n",
      "sigmas &= \n",
      "\\begin{bmatrix}\n",
      "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} &  \\mathcal{X}_{0,2} \\\\\n",
      "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} &  \\mathcal{X}_{1,2} \\\\\n",
      "\\vdots & \\vdots & \\vdots \\\\\n",
      "\\mathcal{X}_{2n+1,0} & \\mathcal{X}_{2n+1,1} & \\mathcal{X}_{2n+1,2}\n",
      "\\end{bmatrix} \\\\\n",
      "sigmas &= \n",
      "\\begin{bmatrix}\n",
      "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} &  \\mathcal{X}_{0,2n+1} \\\\\n",
      "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} &  \\mathcal{X}_{1,2n+1} \\\\\n",
      "\\vdots & \\vdots & \\vdots \\\\\n",
      "\\mathcal{X}_{D-1,0} & \\mathcal{X}_{D-1,1} & \\mathcal{X}_{D-1,2n+1}\n",
      "\\end{bmatrix}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "In other words, each column contains the $2n+1$ sigma points for one dimension in our problem. The $0th$ sigma point is always the mean, so first row of sigma's contains the mean of each of our dimensions. The second through nth row contains the $\\mu+\\sqrt{(n+\\lambda)\\Sigma}$ terms, and the $n+1$ to $2n$ rows contains the $\\mu-\\sqrt{(n+\\lambda)\\Sigma}$ terms. the choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code a bit easier to code as I can refer to the ith sigma point for all dimensions as `sigmas[i]`."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Weights\n",
      "\n",
      "Computing the weights in numpy is extremely simple. Recall that for the Julier implementation\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "W_0 &= \\frac{\\kappa}{n+\\kappa} \\\\\n",
      "W_i &= \\frac{1}{2(n+\\kappa)}\\,\\,\\,\\text{for i=1,2..2n}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "These two lines of code implement these equations with the `np.full()` method, which creates and fills an array with the same value. Then the value for the mean($W_0$) is computed and overwrites the filled in value. \n",
      "\n",
      "    W = np.full((2*n+1,1), .5 / (n+kappa))\n",
      "    W[0] = kappa / (n+kappa)\n",
      "    \n",
      "Our final function will look something like this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def weights(n, kappa):\n",
      "    \"\"\" Computes the weights for an unscented Kalman filter. \"\"\"\n",
      "\n",
      "    k = .5 / (n+kappa)\n",
      "    W = np.full(2*n+1, k)\n",
      "    W[0] = kappa / (n+kappa)\n",
      "    return W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Sigma Points\n",
      "The equations for the sigma points are:\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathcal{X}_0 &= \\mu \\\\\n",
      "\\mathcal{X}_i &= \\mu +  \\bigg[\\sqrt{(n+\\kappa)\\Sigma}  \\bigg]_i\\,\\,\\,\\, &\\text{for}\\text{ i=1 .. n} \\\\\n",
      "\\mathcal{X}_i &= \\mu - \\bigg[\\sqrt{(n+\\kappa)\\Sigma}\\bigg]_{i-n}\\,\\,\\,\\,\\, &\\text{for}\\text{ i=(n+1) .. 2n}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "\n",
      "The Python for this is not much more difficult once we wrap our heads around the $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ term.\n",
      "\n",
      "The term $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ has to be a matrix because $\\Sigma$ is a matrix. The subscript $i$ is choosing the column vector of the matrix. What is the 'square root of a matrix'? The usual definition is that the square root of a matrix $\\Sigma$ is just the matrix $S$ that, when multiplied by itself, yields $\\Sigma$.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\text{if }\\Sigma = SS \\\\\n",
      "\\\\\n",
      "\\text{then }S = \\sqrt{\\Sigma}\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "However there is an alternative definition, and we will chose that because it has numerical properties that makes it much easier for us to compute its value. We can alternatively define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n",
      "\n",
      "$$\n",
      "\\Sigma = SS^\\mathsf{T} \\\\\n",
      "$$\n",
      "\n",
      "This latter method is typically chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition* [3]. \n",
      "Numpy provides this with the `numpy.linalg.cholesky()` method. If your language of choice is Fortran, C, C++, or the like standard libraries such as LAPACK also provide this routine. And, of course, matlab provides `chol()`, which does the same thing.\n",
      "\n",
      "This method returns a lower triangular matrix, so we will take the transpose of it so that in our for loop we can access it row-wise as `U[i]`, rather than the more cumbersome column-wise notation `U[i,:]`.\n",
      "\n",
      "    Sigmas = np.zeros((2*n+1, n))\n",
      "    U = linalg.cholesky((n+kappa)*P).T\n",
      "\n",
      "    for k in range (n):\n",
      "        Sigmas[k+1]   = X + U[k]\n",
      "        Sigmas[n+k+1] = X - U[k]\n",
      "\n",
      "    Sigmas[0] = X"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's implement the unscented transform. Recall the equations\n",
      "$$\\begin{aligned}\n",
      "\\mu &= \\sum_i w_i\\mathcal{X}_i\\;\\;\\;&(2) \\\\\n",
      "\\Sigma &= \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\\;\\;\\;&(3)\n",
      "\\end{aligned}\n",
      "$$\n",
      "\n",
      "The scaled UKF uses different weights for the means and covariance, so we will use the variable `Wm` for the mean weights and `Wc` for the covariance weights.\n",
      "\n",
      "We implement the sum of the means with\n",
      "\n",
      "    X = np.dot (Wm, Sigmas)\n",
      "\n",
      "If you are not a heavy user of numpy this may look foreign to you. Numpy is not just a library that make linear algebra possible; under the hood it is written in C to achieve much faster speeds than Python can reach. A typical speedup is 100x. To get that speedup we must avoid using for loops, and instead use numpy's built in functions to perform calculations. So, instead of writing a for loop to compute the sum, we call the built in `numpy.dot(x,y)` method. If passed a 1D array and a 2D array it will compute sum of inner products:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([10, 100])\n",
      "b = np.array([[1, 2, 3],\n",
      "              [4, 5, 6]])\n",
      "\n",
      "np.dot(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([410, 520, 630])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All that is left is to compute $\\mathbf{P} = \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}} + \\mathbf{Q}$\n",
      "\n",
      "    kmax, n = Sigmas.shape\n",
      "    P = zeros((n, n))\n",
      "    for k in range(kmax):\n",
      "        y = Sigmas[k] - x\n",
      "        P += Wc[k] * np.outer(y, y) \n",
      "    P += Q\n",
      "\n",
      "This introduces another feature of numpy. The state variable $X$ is one dimensional, as is $Xi[k]$, so the difference $Xi[k]-X$ is also one dimensional. numpy will not compute the transpose of a 1-D array; it considers the transpose of `[1,2,3]` to be `[1,2,3]`. So we call the function `np.outer(y,y)` which computes the value of $yy^\\mathsf{T}$ for a 1D array $y$.\n",
      "\n",
      "Our `sigma_points` function can be implemented as below"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sigma_points(x, P, kappa):\n",
      "    \"\"\" Computes the sigma pointsfor an unscented Kalman filter\n",
      "    given the mean (x) and covariance(P) of the filter.\n",
      "    kappa is an arbitrary constant. Returns tuple of the sigma points\n",
      "    and weights.\n",
      "\n",
      "    Works with both scalar and array inputs:\n",
      "    sigma_points (5, 9, 2) # mean 5, covariance 9\n",
      "    sigma_points ([5, 2], 9*eye(2), 2) # means 5 and 2, covariance 9I\n",
      "\n",
      "    **Parameters**\n",
      "\n",
      "    X An array-like object of the means of length n\n",
      "        Can be a scalar if 1D.\n",
      "        examples: 1, [1,2], np.array([1,2])\n",
      "\n",
      "    P : scalar, or np.array\n",
      "       Covariance of the filter. If scalar, is treated as eye(n)*P.\n",
      "\n",
      "    kappa : float\n",
      "        Scaling factor.\n",
      "\n",
      "    **Returns**\n",
      "\n",
      "    sigmas : np.array, of size (n, 2n+1)\n",
      "        2D array of sigma points. Each column contains all of\n",
      "        the sigmas for one dimension in the problem space. They\n",
      "        are ordered as:\n",
      "\n",
      "        .. math::\n",
      "            sigmas[0]    = x \\n\n",
      "            sigmas[1..n] = x + [\\sqrt{(n+\\kappa)P}]_k \\n\n",
      "            sigmas[n+1..2n] = x - [\\sqrt{(n+\\kappa)P}]_k\n",
      "    \"\"\"\n",
      "\n",
      "    if np.isscalar(x):\n",
      "        x = asarray([x])\n",
      "    n = np.size(x)  # dimension of problem\n",
      "\n",
      "    if  np.isscalar(P):\n",
      "        P = eye(n)*P\n",
      "\n",
      "    Sigmas = zeros((2*n+1, n))\n",
      "\n",
      "    # implements U'*U = (n+kappa)*P. Returns lower triangular matrix.\n",
      "    # Take transpose so we can access with U[i]\n",
      "    U = cholesky((n+kappa)*P).T\n",
      "    #U = sqrtm((n+kappa)*P).T\n",
      "\n",
      "    for k in range(n):\n",
      "        Sigmas[k+1]   = x + U[k]\n",
      "        Sigmas[n+k+1] = x - U[k]\n",
      "\n",
      "    # handle value for the mean separately as special case\n",
      "    Sigmas[0] = x\n",
      "\n",
      "    return Sigmas"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Predict Step\n",
      "\n",
      "For the predict step, we will generate the weights and sigma points as specified above. We pass each sigma point through the function f.\n",
      "\n",
      "$$\\mathcal{X_f} = f(\\mathcal{X})$$\n",
      "\n",
      "Then we compute the predicted mean and covariance using the unscented transform. In the code below you can see that I am assuming that this is a method in a class that stores the various matrices and vectors needed by the filter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def predict(self):\n",
      "    \"\"\" Performs the predict step of the UKF. On return, self.xp and\n",
      "    self.Pp contain the predicted state (xp) and covariance (Pp). 'p'\n",
      "    stands for prediction.\n",
      "\n",
      "    Important: this MUST be called before update() is called for the first\n",
      "    time.\n",
      "    \"\"\"\n",
      "\n",
      "    # calculate sigma points for given mean and covariance\n",
      "    sigmas = self.sigma_points(self.x, self.P, self.kappa)\n",
      "\n",
      "    for i in range(self._num_sigmas):\n",
      "        self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n",
      "\n",
      "    self.xp, self.Pp = unscented_transform(\n",
      "                       self.sigmas_f, self.W, self.W, self.Q)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Update Step\n",
      "\n",
      "The update step converts the sigmas into measurement space via the `h(x)` function.\n",
      "\n",
      "\n",
      "$$\\mathcal{X_z} = h(\\mathcal{X_f})$$\n",
      "\n",
      "The mean an covariance of those points is computed with the  unscented transform. The residual and Kalman gain is then computed. The cross variance is computed as:\n",
      "\n",
      "\n",
      "$$\\mathbf{P}_{xz} =\\sum W(\\mathcal{X}-x)(\\mathcal{X_z}-\\mathbf{x}_z)^\\mathsf{T}$$\n",
      "\n",
      "\n",
      "Finally, we compute the new state estimate using the residual and Kalman gain:\n",
      "\n",
      "$$\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n",
      "\n",
      "and the new covariance is computed as:\n",
      "\n",
      "$$ \\mathbf{P} = \\mathbf{P}^- - \\mathbf{PKP}_z\\mathbf{K}^\\mathsf{T}$$\n",
      "\n",
      "This function can be implemented as follows, assuming it is a method of a class that stores the necessary matrices and data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def update(self, z):\n",
      "    \"\"\" Update the UKF with the given measurements. On return,\n",
      "    self.x and self.P contain the new mean and covariance of the filter.\n",
      "\n",
      "    **Parameters**\n",
      "\n",
      "    z : numpy.array of shape (dim_z)\n",
      "        measurement vector\n",
      "    \"\"\"\n",
      "\n",
      "    # rename for readability\n",
      "    sigmas_f = self.sigmas_f\n",
      "    sigmas_h = self.sigmas_h\n",
      "\n",
      "    # transform sigma points into measurement space\n",
      "    for i in range(self._num_sigmas):\n",
      "        sigmas_h[i] = self.hx(sigmas_f[i])\n",
      "\n",
      "    # mean and covariance of prediction passed through inscented transform\n",
      "    zp, Pz = unscented_transform(sigmas_h, self.W, self.W, self.R)\n",
      "\n",
      "    # compute cross variance of the state and the measurements\n",
      "    Pxz = zeros((self._dim_x, self._dim_z))\n",
      "    for i in range(self._num_sigmas):\n",
      "        Pxz += self.W[i] * np.outer(sigmas_f[i] - self.xp,\n",
      "                                    sigmas_h[i] - zp)\n",
      "\n",
      "    K = dot(Pxz, inv(Pz)) # Kalman gain\n",
      "\n",
      "    self.x = self.xp + dot(K, z-zp)\n",
      "    self.P = self.Pp - dot3(K, Pz, K.T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Full Source from FilterPy\n",
      "\n",
      "Without further explanation, here is the full source from FilterPy.\n",
      "\n",
      "** author's note ** this is somewhat dated, but I am not going to update this section every time I make a minor change to the filterpy code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import (absolute_import, division, print_function,\n",
      "                        unicode_literals)\n",
      "\n",
      "from numpy.linalg import inv, cholesky\n",
      "import numpy as np\n",
      "from numpy import asarray, eye, zeros, dot\n",
      "from filterpy.common import dot3\n",
      "\n",
      "\n",
      "class UnscentedKalmanFilter(object):\n",
      "    \"\"\" Implements the Unscented Kalman filter (UKF) as defined by Simon J.\n",
      "    Julier and Jeffery K. Uhlmann [1]. Succintly, the UKF selects a set of\n",
      "    sigma points and weights inside the covariance matrix of the filter's\n",
      "    state. These points are transformed through the nonlinear process being\n",
      "    filtered, and are rebuilt into a mean and covariance by computed the\n",
      "    weighted mean and expected value of the transformed points. Read the paper;\n",
      "    it is excellent. My book \"Kalman and Bayesian Filters in Python\" [2]\n",
      "    explains the algorithm, develops this code, and provides examples of the\n",
      "    filter in use.\n",
      "\n",
      "\n",
      "    You will have to set the following attributes after constructing this\n",
      "    object for the filter to perform properly.\n",
      "\n",
      "    **Attributes**\n",
      "\n",
      "    x : numpy.array(dim_x)\n",
      "        state estimate vector\n",
      "\n",
      "    P : numpy.array(dim_x, dim_x)\n",
      "        covariance estimate matrix\n",
      "\n",
      "    R : numpy.array(dim_z, dim_z)\n",
      "        measurement noise matrix\n",
      "\n",
      "    Q : numpy.array(dim_x, dim_x)\n",
      "        process noise matrix\n",
      "\n",
      "\n",
      "    You may read the following attributes.\n",
      "\n",
      "    **Readable Attributes**\n",
      "\n",
      "    xp : numpy.array(dim_x)\n",
      "        predicted state (result of predict())\n",
      "\n",
      "    Pp : numpy.array(dim_x, dim_x)\n",
      "        predicted covariance matrix (result of predict())\n",
      "\n",
      "\n",
      "    **References**\n",
      "\n",
      "    .. [1] Julier, Simon J. \"A New Extension of the Kalman Filter to Nonlinear\n",
      "        Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and\n",
      "        Target Recognition VI, 182 (July 28, 1997)\n",
      "\n",
      "    .. [2] Labbe, Roger R. \"Kalman and Bayesian Filters in Python\"\n",
      "\n",
      "        https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python\n",
      "    \"\"\"\n",
      "\n",
      "    def __init__(self, dim_x, dim_z, dt, hx, fx, kappa=0.):\n",
      "        \"\"\" Create a Kalman filter. You are responsible for setting the\n",
      "        various state variables to reasonable values; the defaults below will\n",
      "        not give you a functional filter.\n",
      "\n",
      "        **Parameters**\n",
      "\n",
      "        dim_x : int\n",
      "            Number of state variables for the filter. For example, if\n",
      "            you are tracking the position and velocity of an object in two\n",
      "            dimensions, dim_x would be 4.\n",
      "\n",
      "\n",
      "        dim_z : int\n",
      "            Number of of measurement inputs. For example, if the sensor\n",
      "            provides you with position in (x,y), dim_z would be 2.\n",
      "\n",
      "        dt : float\n",
      "            Time between steps in seconds.\n",
      "\n",
      "        hx : function(x)\n",
      "            Measurement function. Converts state vector x into a measurement\n",
      "            vector of shape (dim_z).\n",
      "\n",
      "        fx : function(x,dt)\n",
      "            function that returns the state x transformed by the\n",
      "            state transistion function. dt is the time step in seconds.\n",
      "\n",
      "        kappa : float, default=0.\n",
      "            Scaling factor that can reduce high order errors. kappa=0 gives\n",
      "            the standard unscented filter. According to [1], if you set\n",
      "            kappa to 3-dim_x for a Gaussian x you will minimize the fourth\n",
      "            order errors in x and P.\n",
      "\n",
      "        **References**\n",
      "\n",
      "        [1] S. Julier, J. Uhlmann, and H. Durrant-Whyte. \"A new method for\n",
      "            the nonlinear transformation of means and covariances in filters\n",
      "            and estimators,\" IEEE Transactions on Automatic Control, 45(3),\n",
      "            pp. 477-482 (March 2000).\n",
      "        \"\"\"\n",
      "\n",
      "        self.Q = eye(dim_x)\n",
      "        self.R = eye(dim_z)\n",
      "        self.x = zeros(dim_x)\n",
      "        self.P = eye(dim_x)\n",
      "        self.xp = None\n",
      "        self.Pp = None\n",
      "        self._dim_x = dim_x\n",
      "        self._dim_z = dim_z\n",
      "        self._dt = dt\n",
      "        self._num_sigmas = 2*dim_x + 1\n",
      "        self.kappa = kappa\n",
      "        self.hx = hx\n",
      "        self.fx = fx\n",
      "\n",
      "        # weights for the sigma points\n",
      "        self.W = self.weights(dim_x, kappa)\n",
      "\n",
      "        # sigma points transformed through f(x) and h(x)\n",
      "        # variables for efficiency so we don't recreate every update\n",
      "        self.sigmas_f = zeros((2*self._dim_x+1, self._dim_x))\n",
      "        self.sigmas_h = zeros((self._num_sigmas, self._dim_z))\n",
      "\n",
      "\n",
      "    def update(self, z, residual=np.subtract, UT=None):\n",
      "        \"\"\" Update the UKF with the given measurements. On return,\n",
      "        self.x and self.P contain the new mean and covariance of the filter.\n",
      "\n",
      "        **Parameters**\n",
      "\n",
      "        z : numpy.array of shape (dim_z)\n",
      "            measurement vector\n",
      "\n",
      "        residual : function (z, z2), optional\n",
      "            Optional function that computes the residual (difference) between\n",
      "            the two measurement vectors. If you do not provide this, then the\n",
      "            built in minus operator will be used. You will normally want to use\n",
      "            the built in unless your residual computation is nonlinear (for\n",
      "            example, if they are angles)\n",
      "\n",
      "        UT : function(sigmas, Wm, Wc, noise_cov), optional\n",
      "            Optional function to compute the unscented transform for the sigma\n",
      "            points passed through hx. Typically the default function will\n",
      "            work, but if for example you are using angles the default method\n",
      "            of computing means and residuals will not work, and you will have\n",
      "            to define how to compute it.\n",
      "        \"\"\"\n",
      "\n",
      "        # rename for readability\n",
      "        sigmas_f = self.sigmas_f\n",
      "        sigmas_h = self.sigmas_h\n",
      "        W = self.W\n",
      "\n",
      "        if UT is None:\n",
      "            UT = unscented_transform\n",
      "\n",
      "        # transform sigma points into measurement space\n",
      "        for i in range(self._num_sigmas):\n",
      "            sigmas_h[i] = self.hx(sigmas_f[i])\n",
      "\n",
      "        # mean and covariance of prediction passed through inscented transform\n",
      "        zp, Pz = UT(sigmas_h, self.W, self.W, self.R)\n",
      "\n",
      "        # compute cross variance of the state and the measurements\n",
      "        Pxz = zeros((self._dim_x, self._dim_z))\n",
      "        for i in range(self._num_sigmas):\n",
      "            Pxz += self.W[i] * np.outer(sigmas_f[i] - self.xp,\n",
      "                                        residual(sigmas_h[i], zp))\n",
      "\n",
      "        K = dot(Pxz, inv(Pz)) # Kalman gain\n",
      "\n",
      "        y = residual(z, zp)\n",
      "\n",
      "        self.x = self.xp + dot(K, y)\n",
      "        self.P = self.Pp - dot3(K, Pz, K.T)\n",
      "\n",
      "\n",
      "    def predict(self):\n",
      "        \"\"\" Performs the predict step of the UKF. On return, self.xp and\n",
      "        self.Pp contain the predicted state (xp) and covariance (Pp). 'p'\n",
      "        stands for prediction.\n",
      "\n",
      "        Important: this MUST be called before update() is called for the first\n",
      "        time.\n",
      "        \"\"\"\n",
      "\n",
      "        # calculate sigma points for given mean and covariance\n",
      "        sigmas = self.sigma_points(self.x, self.P, self.kappa)\n",
      "\n",
      "        for i in range(self._num_sigmas):\n",
      "            self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n",
      "\n",
      "        self.xp, self.Pp = unscented_transform(\n",
      "                           self.sigmas_f, self.W, self.W, self.Q)\n",
      "\n",
      "\n",
      "\n",
      "    @staticmethod\n",
      "    def weights(n, kappa):\n",
      "        \"\"\" Computes the weights for an unscented Kalman filter.  See\n",
      "        __init__() for meaning of parameters.\n",
      "        \"\"\"\n",
      "\n",
      "        k = .5 / (n+kappa)\n",
      "        W = np.full(2*n+1, k)\n",
      "        W[0] = kappa / (n+kappa)\n",
      "        return W\n",
      "\n",
      "\n",
      "    @staticmethod\n",
      "    def sigma_points(x, P, kappa):\n",
      "        \"\"\" Computes the sigma pointsfor an unscented Kalman filter\n",
      "        given the mean (x) and covariance(P) of the filter.\n",
      "        kappa is an arbitrary constant. Returns tuple of the sigma points\n",
      "        and weights.\n",
      "\n",
      "        Works with both scalar and array inputs:\n",
      "        sigma_points (5, 9, 2) # mean 5, covariance 9\n",
      "        sigma_points ([5, 2], 9*eye(2), 2) # means 5 and 2, covariance 9I\n",
      "\n",
      "        **Parameters**\n",
      "\n",
      "        X An array-like object of the means of length n\n",
      "            Can be a scalar if 1D.\n",
      "            examples: 1, [1,2], np.array([1,2])\n",
      "\n",
      "        P : scalar, or np.array\n",
      "           Covariance of the filter. If scalar, is treated as eye(n)*P.\n",
      "\n",
      "        kappa : float\n",
      "            Scaling factor.\n",
      "\n",
      "        **Returns**\n",
      "\n",
      "        sigmas : np.array, of size (n, 2n+1)\n",
      "            2D array of sigma points. Each column contains all of\n",
      "            the sigmas for one dimension in the problem space. They\n",
      "            are ordered as:\n",
      "\n",
      "            .. math::\n",
      "                sigmas[0]    = x \\n\n",
      "                sigmas[1..n] = x + [\\sqrt{(n+\\kappa)P}]_k \\n\n",
      "                sigmas[n+1..2n] = x - [\\sqrt{(n+\\kappa)P}]_k\n",
      "        \"\"\"\n",
      "\n",
      "        if np.isscalar(x):\n",
      "            x = asarray([x])\n",
      "        n = np.size(x)  # dimension of problem\n",
      "\n",
      "        if  np.isscalar(P):\n",
      "            P = eye(n)*P\n",
      "\n",
      "        Sigmas = zeros((2*n+1, n))\n",
      "\n",
      "        # implements U'*U = (n+kappa)*P. Returns lower triangular matrix.\n",
      "        # Take transpose so we can access with U[i]\n",
      "        U = cholesky((n+kappa)*P).T\n",
      "\n",
      "        for k in range(n):\n",
      "            Sigmas[k+1]   = x + U[k]\n",
      "            Sigmas[n+k+1] = x - U[k]\n",
      "\n",
      "        # handle value for the mean separately as special case\n",
      "        Sigmas[0] = x\n",
      "\n",
      "        return Sigmas\n",
      "\n",
      "\n",
      "def unscented_transform(Sigmas, Wm, Wc, noise_cov):\n",
      "    \"\"\" Computes unscented transform of a set of sigma points and weights.\n",
      "    returns the mean and covariance in a tuple.\n",
      "    \"\"\"\n",
      "\n",
      "    kmax, n = Sigmas.shape\n",
      "\n",
      "    # new mean is just the sum of the sigmas * weight\n",
      "    x = dot(Wm, Sigmas)    # \\Sigma^n_1 (W[k]*Xi[k])\n",
      "\n",
      "    # new covariance is the sum of the outer product of the residuals\n",
      "    # times the weights\n",
      "    P = zeros((n, n))\n",
      "    for k in range(kmax):\n",
      "        y = Sigmas[k] - x\n",
      "        P += Wc[k] * np.outer(y, y)\n",
      "\n",
      "    return (x, P + noise_cov)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Radar Tracking\n",
      "\n",
      "So far the performance of the filter hasn't looked very good. However, that is not the fault of the filter, but because I chose problems that were very easy to formulate due to a paucity of sensor information. Let's now solve a more realistic problem.\n",
      "\n",
      "We will use the radar tracking problem that we developed in the EKF chapter. We simulated tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
      "\n",
      "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ekf_internal\n",
      "ekf_internal.show_radar_chart()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AwhN4AIDCE3gAgMITeACAwhN4AIDCE3gAgMITeACAwhN4AIDCE3gAgMITeACAwhN4AIDC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\nzkoyqW11AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fadd85686d8>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As in the EKF chapter  we need 3 state variables - horizontal distance, velocity, and altitude.\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude\\end{bmatrix}=  \\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our state transtion function is linear \n",
      "\n",
      "$$\\dot{\\mathbf{x}} = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n",
      "\\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix} \n",
      "$$\n",
      "\n",
      "but as discussed earlier we will need to provide a Python function to compute the transition. We could code this as\n",
      "\n",
      "    def fx(x, dt):\n",
      "        A = np.eye(3) + dt * np.array ([[0, 1, 0],\n",
      "                                        [0, 0, 0],\n",
      "                                        [0, 0, 0]])\n",
      "        return A.dot(x)\n",
      "        \n",
      "The measurement function is nonlinear. For the EKF we had to compute the Jacobian so that the EKF could linearize the nonlinear function. Here we merely provide the nonlinear function and the UKF passes the sigma points through the function and uses the unscented transform to compute the new mean and covariance. We can write this function as\n",
      "\n",
      "    def hx(x):\n",
      "        return np.sqrt(x[0]**2 + x[2]**2)\n",
      "        \n",
      "And that is the majority of the work. As with any Kalman filter we need to design R, Q, and P, but we have discussed this topic in detail in the *Multivariate Kalman Filter* chaper, so I will not spend a lot of time on it here. I will assume 'reasonable' values for each of these matrices, and just present the result.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "\n",
      "class RadarSim(object):\n",
      "    def __init__(self, dt):\n",
      "        self.x = 0\n",
      "        self.dt = dt\n",
      "\n",
      "    def get_range(self):\n",
      "        vel = 100  + 5*randn()\n",
      "        alt = 1000 + 10*randn()\n",
      "        self.x += vel*self.dt\n",
      "\n",
      "        v = self.x * 0.05*randn()\n",
      "        rng = (self.x**2 + alt**2)**.5 + v\n",
      "        return rng\n",
      "    \n",
      "def fx(x, dt):\n",
      "    A = np.eye(3) + dt * np.array ([[0, 1, 0],\n",
      "                                    [0, 0, 0],\n",
      "                                    [0, 0, 0]])\n",
      "    return A.dot(x)\n",
      "\n",
      "def hx(x):\n",
      "    return np.sqrt (x[0]**2 + x[2]**2)\n",
      "\n",
      "dt = 0.05\n",
      "\n",
      "kf = UKF(3, 1, dt, fx=fx, hx=hx, kappa=0.)\n",
      "\n",
      "kf.Q *= 0.01\n",
      "kf.R = 10\n",
      "kf.x = np.array([0., 90., 1100.])\n",
      "kf.P *= 100.\n",
      "radar = RadarSim(dt)\n",
      "random.seed(200)\n",
      "\n",
      "t = np.arange(0,20+dt, dt)\n",
      "n = len(t)\n",
      "\n",
      "xs = []\n",
      "for i in range(len(t)):\n",
      "    r = radar.get_range()\n",
      "    kf.predict()\n",
      "    kf.update([r])\n",
      "    \n",
      "    xs.append(kf.x)\n",
      "\n",
      "xs = np.asarray(xs)\n",
      "plt.figure()\n",
      "plt.subplot(311)\n",
      "plt.plot(t, xs[:,0])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('position')\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.plot(t, xs[:,1])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('velocity')\n",
      "\n",
      "plt.subplot(313)\n",
      "plt.plot(t, xs[:,2])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('altitude')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TqKurc5hXVFRERkYGnp7nhqipq6u76C/OsmXL7J+Tk5PtVw1FRL6LxWLFYDBQ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\nQvQA/x+rw8NUYOPoEwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fade42e3278>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The estimates are not perfect, but this is still a very difficult filtering problem. As the aircraft goes further downrange a very small measurement error can translate into a very large error in velocity and altitude. We are simulating a velocity of 100 and an altitude of 1000. The filter does not produce exactly these numbers, but it does quite well considering that the only measurement we are receiving is range to the aircraft. This is a classical problem that is presented while learning Kalman filters, and so I have presented it here. However, recognize that this is a very difficult problem for the filter because it is easy for us. If we ran this simulation for 50-100 seconds the filter would begin to diverge because the information in the measurement would be swamped by the noise in the signal."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Tracking a Circle\n",
      "\n",
      "Let's see how easy it is to deal with state equations which differ markedly, and nonlinearly, from the measurements. Let's assume that we are tracking an object travelling in a circle; perhaps a race car on a track. Our measurements give us coordinates in x,y, and we want to filter the car's position, heading, and speed on the race course. \n",
      "\n",
      "With a linear Kalman filter we don't have a lot of choice but to implement it as a constant acceleration model. $\\mathbf{H}$, the measurement matrix, must "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Batch Processing\n",
      "\n",
      "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in `KalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays. It may seem a bit trivial, but you will almost always want to do this if you can for several reasons. First, it will execute a bit quicker than if you implement the loop yourself. Second, the logic in your code will be a bit cleaner, and you will have a reduced chance of bugs. Third, and most importantly, it you batch process your data you can then use an extremely powerful techique to generate far smoother results than you have seen so far. We will present that technique in the next section; here I will show you how to use `KalmanFilter.batch_filter()`.\n",
      "\n",
      "All you have to do is collect your measurements into an array or list. Maybe it is in a CSV file, for example.\n",
      "\n",
      "    zs = read_altitude_from_csv()\n",
      "\n",
      "Or maybe you will generate it using a generator:\n",
      "\n",
      "    zs = [some_func(i) for i in range(1000)]\n",
      "    \n",
      "Just do whatever it takes to get your measurements in an array.\n",
      "\n",
      "Now we will just call the `batch_filter()` method.\n",
      "\n",
      "    Xs, Ps, Xs_pred, Ps_pred = kfilter.batch_filter(zs)\n",
      "    \n",
      "The funtion takes the list/array of measurements, filters it, and returns a list of state estimates (Xs), covariance matrices (Ps), and the predictions for the same (Xs_pred, Ps_pred).\n",
      "\n",
      "Here is a complete example drawing from the radar tracking problem above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy.random as random\n",
      "\n",
      "dt = 0.05\n",
      "kf = UKF(3, 1, dt, fx=fx, hx=hx, kappa=0.)\n",
      "\n",
      "kf.Q *= 0.01\n",
      "kf.R = 10\n",
      "kf.x = np.array([0., 90., 1100.])\n",
      "kf.P *= 100.\n",
      "radar = RadarSim(dt)\n",
      "\n",
      "t = np.arange(0,20+dt, dt)\n",
      "n = len(t)\n",
      "\n",
      "random.seed(200)\n",
      "rs = [radar.get_range() for i in range(n)]\n",
      "xs, covs = kf.batch_filter(rs)\n",
      "\n",
      "plt.figure()\n",
      "plt.subplot(311)\n",
      "plt.plot(t, xs[:,0])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('position')\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.plot(t, xs[:,1])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('velocity')\n",
      "\n",
      "plt.subplot(313)\n",
      "plt.plot(t, xs[:,2])\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('altitude')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TqKurc5hXVFRERkYGnp7nhqipq6u76C/OsmXL7J+Tk5PtVw1FRL6LxWLFYDBQ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\nr7MyNDWKX04ZzHUj+hMVGigf0mdxuDzUWhyd+j/bk0lQJzpKg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       "text": [
        "<matplotlib.figure.Figure at 0x7fadd857e3c8>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Smoothing the Results\n",
      "\n",
      "I have an entire chapter on using the Kalman filter to smooth data; I will not repeat the chapter's information here. However, it is so easy to use, and offers such a profoundly improved output that I will tease you will a few examples. The smoothing chapter is not especially difficult; you are sufficiently prepared to read it now.\n",
      "\n",
      "Briefly, the recursive form of Kalman filtering that we have been using up to now use information from the past to generate the current estimate. Recall the last section, where we used batch processing to filter a collection of measurements. This implies that we know now only the past, but the future! This is a key insight.\n",
      "\n",
      "Let's assume that  we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n",
      "\n",
      "However, if we have measurements from the future we can often figure out if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a true indication that a turn was initiated. On the other hand, if the subsequent measurements continued on in a straight line we would know that the measurement was noisy and should be mostly ignored.\n",
      "\n",
      "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `filterpy`. The algorithm that we have implemented is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n",
      "\n",
      "The routine is `UnscentedKalmanFilter.rts_smoother()`. Using it is trivial; we pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ms,_,_ = kf.rts_smoother(xs, covs)\n",
      "plt.figure()\n",
      "plt.subplot(311)\n",
      "plt.plot(t[0:100], xs[0:100,0])\n",
      "plt.plot(t[0:100], Ms[0:100,0],c='k')\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('position')\n",
      "\n",
      "plt.subplot(312)\n",
      "plt.plot(t[0:100], xs[0:100,1])\n",
      "plt.plot(t[0:100], Ms[0:100,1],c='k')\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('velocity')\n",
      "\n",
      "plt.subplot(313)\n",
      "plt.plot(t[0:100], xs[0:100,2])\n",
      "plt.plot(t[0:100], Ms[0:100,2],c='k')\n",
      "plt.xlabel('time(sec)')\n",
      "plt.ylabel('altitude')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7KpVKwsLCiImJITY2ltDQUAnYhLjJ9TuAs7e3P+9+GxsbHn/88f5mL4QQQ4LB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\npaKiot3pum2Ac7lcGAwGmpubqaiooKmpCaPRiNPpjHfRhDhnO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       "text": [
        "<matplotlib.figure.Figure at 0x7fadd6ac9710>"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It was difficult to see the improvement in the position if I plotted all the data, so I have only displayed the first 5 seconds of output. From these charts we can see that the improvement in the position is decent, but the improvement in the velocity and altitude is truly spectacular."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### The Scaled Unscented Transform\n",
      "\n",
      "todo"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Nonlinear State Variables\n",
      "\n",
      "todo"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## References\n",
      "\n",
      "- [1] Simon, Dan. *Optimal State Estimation*, John Wiley & Sons, 2006.\n",
      "\n",
      "- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman  Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n",
      "\n",
      "- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}