From 82717d4830b70c70f1e583bf86cb834c0a895efa Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Thu, 1 May 2014 01:30:47 -0500 Subject: [PATCH] Started progress on the multidimensional kalman filter --- Kalman Filters.ipynb | 301 ++++++++++++++++++-------- Multidimensional Kalman Filters.ipynb | 285 ++++++++++++++++++++++++ gaussian.py | 2 - 3 files changed, 500 insertions(+), 88 deletions(-) create mode 100644 Multidimensional Kalman Filters.ipynb diff --git a/Kalman Filters.ipynb b/Kalman Filters.ipynb index 050b310..0154494 100644 --- a/Kalman Filters.ipynb +++ b/Kalman Filters.ipynb @@ -50,7 +50,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 34 + "prompt_number": 12 }, { "cell_type": "markdown", @@ -74,11 +74,11 @@ "output_type": "stream", "stream": "stdout", "text": [ - "0.0883 1.1333 1.3527 -0.1540 1.0787 1.1940 -0.4908 0.9334 -1.3604 -1.5230 -1.1513 -1.0829 0.5573 0.7816 0.0587 -0.0605 0.0651 -0.4040 0.3429 0.2245\n" + "0.9827 0.4385 1.6524 0.6318 -0.2302 -1.0772 -0.0953 0.1147 1.1092 1.6671 0.1331 0.5139 -0.5076 -0.9376 -0.7724 0.4346 -0.3805 -1.9624 -0.3980 -0.9907\n" ] } ], - "prompt_number": 35 + "prompt_number": 13 }, { "cell_type": "markdown", @@ -117,7 +117,7 @@ "output_type": "display_data", "png": 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"text": [ - "" + "" ] }, { @@ -128,7 +128,7 @@ ] } ], - "prompt_number": 36 + "prompt_number": 14 }, { "cell_type": "markdown", @@ -167,13 +167,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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EvHnwf/8Hb7+tk4cQliKVS4SwgqNH9X9bNFfMe2Im5YLHwYfvQMOGjBsHf/yh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\no9xthQ6K+6qnK1dg1Sr9gZ7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BAmjbtuD6114DDw8120mIB2FxC+6EEMqRI6ocUz6dDvr0UcdHjYLnnoOff1bn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\nxkb+7wohSoC0KCzQlSvQrRv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vXmDMGLrxRUeTu8Yc1dWAl5edLQq1GoiPB959l5RFJnIsCkPXU06OaaEQLQpA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\nGhqoiK5HD+0xW7mebCUUvr40E4MtCoZhHM1VIxQ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fts34H30EHDgAPPEEdw/t3aueXaQvRjG4QwFMnQqkpgJZWeg5IgotLerCWVfH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\n7LQixHh48CY+hYXah1++zH8CAqTNZ/BgHryuq+O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"text": [ - "" + "" ] } ], - "prompt_number": 38 + "prompt_number": 16 }, { "cell_type": "code", @@ -220,13 +220,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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4R4wxLFmyhJycHFauXHnJL3qplCikqk2dCsuWGvr0teHpCbVrw913Q8uWVkcm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\nBklJNX4hP30Ifqay+JnK4mc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Vqxe+vr48+OCDGGNYuHAhGRkZvPfee1f9oldLiUJK27lzMGmi4X/HbJw+7VjP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\n0KABwcHBeHl50bdvX5YtW/a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"text": [ - "" + "" ] } ], - "prompt_number": 39 + "prompt_number": 17 }, { "cell_type": "markdown", @@ -259,11 +259,11 @@ "output_type": "display_data", "png": 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"text": [ - "" + "" ] } ], - "prompt_number": 40 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -281,10 +281,10 @@ "collapsed": false, "input": [ "dog = dog_sensor (23, 0, 5)\n", - "ys = range (100)\n", - "xs = []\n", - "for i in ys:\n", - " xs.append (dog.sense())\n", + "xs = range (100)\n", + "ys = []\n", + "for i in xs:\n", + " ys.append (dog.sense())\n", " \n", "plot (xs,ys)\n", "show()" @@ -295,13 +295,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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7oMATYgNKyY5WzRn09MhEr9XDTKJJR/s6hyM9HE0sz2Dc/1Ao8ISQCcLPqk2Ew0imMzJK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\nfqWUUtu2bcu49iul1OnTp9W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JARL106fTf1fPqe/aRW2GRqJuJ34xEnWzRVL2Xn5l6sypy+EplCr3zaJFJOxm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\noh5lpx6m+CUW087Vm5tpKtJMcuoLFgD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yHYsoOTW+ZYXwISE9ATYGNtB5bovJk4Fdu7jmCSI5DQ1g0yagUyfg7bcFXK+c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\nlxEIBAgICICnpyd+++03WeY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KDFeurMSO2dnsLO7t26KNl+RIc9B/d3+YVzXHpr6bIHnvIwkRK6/w+jW72lZX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\n", "text": [ - "" + "" ] } ], - "prompt_number": 56 + "prompt_number": 21 }, { "cell_type": "markdown", @@ -463,7 +463,8 @@ ], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 22 }, { "cell_type": "markdown", @@ -481,7 +482,8 @@ ], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 23 }, { "cell_type": "markdown", @@ -511,30 +513,30 @@ "output_type": "stream", "stream": "stdout", "text": [ - "time: 0 position = 1.132 variance = 2.500\n", - "time: 1 position = 0.798 variance = 1.667\n", - "time: 2 position = 0.279 variance = 1.250\n", - "time: 3 position = 0.121 variance = 1.000\n", - "time: 4 position = 0.017 variance = 0.833\n", - "time: 5 position = 0.071 variance = 0.714\n", - "time: 6 position = 0.213 variance = 0.625\n", - "time: 7 position = 0.191 variance = 0.556\n", - "time: 8 position = 0.223 variance = 0.500\n", - "time: 9 position = 0.257 variance = 0.455\n", - "time: 10 position = 0.398 variance = 0.417\n", - "time: 11 position = 0.450 variance = 0.385\n", - "time: 12 position = 0.537 variance = 0.357\n", - "time: 13 position = 0.603 variance = 0.333\n", - "time: 14 position = 0.548 variance = 0.312\n", - "time: 15 position = 0.624 variance = 0.294\n", - "time: 16 position = 0.566 variance = 0.278\n", - "time: 17 position = 0.492 variance = 0.263\n", - "time: 18 position = 0.505 variance = 0.250\n", - "time: 19 position = 0.568 variance = 0.238\n" + "time: 0 position = 1.497 variance = 2.500\n", + "time: 1 position = 0.809 variance = 1.667\n", + "time: 2 position = 0.817 variance = 1.250\n", + "time: 3 position = 0.485 variance = 1.000\n", + "time: 4 position = 0.576 variance = 0.833\n", + "time: 5 position = 0.681 variance = 0.714\n", + "time: 6 position = 0.650 variance = 0.625\n", + "time: 7 position = 0.618 variance = 0.556\n", + "time: 8 position = 0.763 variance = 0.500\n", + "time: 9 position = 0.728 variance = 0.455\n", + "time: 10 position = 0.611 variance = 0.417\n", + "time: 11 position = 0.546 variance = 0.385\n", + "time: 12 position = 0.529 variance = 0.357\n", + "time: 13 position = 0.541 variance = 0.333\n", + "time: 14 position = 0.527 variance = 0.312\n", + "time: 15 position = 0.432 variance = 0.294\n", + "time: 16 position = 0.351 variance = 0.278\n", + "time: 17 position = 0.326 variance = 0.263\n", + "time: 18 position = 0.337 variance = 0.250\n", + "time: 19 position = 0.350 variance = 0.238\n" ] } ], - "prompt_number": 55 + "prompt_number": 24 }, { "cell_type": "markdown", @@ -593,7 +595,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 58 + "prompt_number": 25 }, { "cell_type": "markdown", @@ -643,47 +645,47 @@ "stream": "stdout", "text": [ "UPDATE: 1.0000 , 502.0000\n", - "SENSE: 1.9162 , 9.8047\n", + "SENSE: 2.5641 , 9.8047\n", "\n", - "UPDATE: 2.9162 , 11.8047\n", - "SENSE: 3.8256 , 5.4138\n", + "UPDATE: 3.5641 , 11.8047\n", + "SENSE: 0.8489 , 5.4138\n", "\n", - "UPDATE: 4.8256 , 7.4138\n", - "SENSE: -0.0667 , 4.2574\n", + "UPDATE: 1.8489 , 7.4138\n", + "SENSE: 2.1796 , 4.2574\n", "\n", - "UPDATE: 0.9333 , 6.2574\n", - "SENSE: 5.1593 , 3.8490\n", + "UPDATE: 3.1796 , 6.2574\n", + "SENSE: 3.1866 , 3.8490\n", "\n", - "UPDATE: 6.1593 , 5.8490\n", - "SENSE: 4.9393 , 3.6904\n", + "UPDATE: 4.1866 , 5.8490\n", + "SENSE: 3.7578 , 3.6904\n", "\n", - "UPDATE: 5.9393 , 5.6904\n", - "SENSE: 5.9086 , 3.6267\n", + "UPDATE: 4.7578 , 5.6904\n", + "SENSE: 4.2545 , 3.6267\n", "\n", - "UPDATE: 6.9086 , 5.6267\n", - "SENSE: 6.2753 , 3.6007\n", + "UPDATE: 5.2545 , 5.6267\n", + "SENSE: 5.4039 , 3.6007\n", "\n", - "UPDATE: 7.2753 , 5.6007\n", - "SENSE: 8.0741 , 3.5900\n", + "UPDATE: 6.4039 , 5.6007\n", + "SENSE: 7.8103 , 3.5900\n", "\n", - "UPDATE: 9.0741 , 5.5900\n", - "SENSE: 8.0308 , 3.5856\n", + "UPDATE: 8.8103 , 5.5900\n", + "SENSE: 8.9480 , 3.5856\n", "\n", - "UPDATE: 9.0308 , 5.5856\n", - "SENSE: 9.3586 , 3.5838\n", + "UPDATE: 9.9480 , 5.5856\n", + "SENSE: 11.1128 , 3.5838\n", "\n" ] }, { "metadata": {}, "output_type": "display_data", - "png": 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"text": [ - "" + "" ] } ], - "prompt_number": 120 + "prompt_number": 26 }, { "cell_type": "markdown", @@ -766,6 +768,7 @@ "collapsed": false, "input": [ "sensor_error = 30000\n", + "movement_error = 2\n", "pos = (0,500)\n", "\n", "dog = dog_sensor (pos[0], velocity=movement, noise=sensor_error)\n", @@ -773,7 +776,7 @@ "zs = []\n", "ps = []\n", "\n", - "for i in range(100):\n", + "for i in range(1000):\n", " pos = update (pos[0], pos[1], movement, movement_error)\n", " \n", " Z = dog.sense()\n", @@ -794,19 +797,19 @@ { "metadata": {}, "output_type": "display_data", - "png": 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KhYkxOjoapaWliImJQUlJCaIurMhiY2NRUFDQ8dzCwkLE2paOX6DDGERG0qTr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\nose2NAZdArXy1ULo3aTe15eK2iorWcEZg+FqIiOBQ4fo2hP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Iks4ym+H0aQrBiRNVyEoUww8/GGmy9fmVlBTj2qQi8uGHmRgHqBji45mXePdd\nKqg//gDatCE3k7tRo0ePcv8yZdQ1+vjw3mzaBFSsiIseJTF5zGU8dORz1H/lQdTH31i/qzjCip7C\nktpv4C/ch+dTP0aRX+bwXElJiiMqMJCPeiUsitlUDCZMmCgwuCsfdRXuEfZQQUaGoor28zO+x/HY\nu3cr7yUnxaCvyJHkb/nyFLwVKjBE9PvvxuqlLVuoKPTKTt9Z/MorwNNPG0NEZcqwV0DmGPz9N3DP\nPer/NpuRjtvVBLg2bfj4/fdMOi9bpt7r5YVolEPLdr4IwlmU0mKx8EIrDOxyDhMGnsRlFMXSSw/i\nvTkVUTs8GN69MukuMjIYDps0Sd0n8XhE2fn7K14nHx8m2vXK7xpxW9FumzBhogDhLm7vqiLJsbyz\nUSMK2n//JY2DXtg7KpYrV9SMh4wMZxptwTPPqPceOkRh7rgesY5FMegbxY4fZzNYeDgQEKC8CvFC\njh9XYR2LhRZ4hQqkndi+nYns5GR6OFu2kDJb6D70ozVPn2Z/wuHDfExJUd3Tmdh0oRaexGQM9JiL\nL/EFPP83BJUKxQDvvZd5//5QeZTMxDMAJq69vZkoj42lAmvcmNcpHsP48QxZAaxy8vRU5bAFAFMx\nmDDxX0RiInl3HEswASaOn3rKeXtGBsnw/P3VcPvQUCPRHMA6/P37jWym4lkAjLMnJrqeFbFgAUnm\nDh1i2SzABLc+R+CoGMqXZyVRVBTft2EDcwalSrHyStZUpQoFaib7As6coXI4fRqYPVslio8do1KJ\nj2e4TKAP47RtS8G8dStpR3r0yPrXXx73463P2uCvo/6YjccRUfwAkHga8DsPpGlUPIsWMR8hsNmU\nhzNzJu/NoUNqrXK9FgvvbY8eVCR//cX9CxfO/TCjXMAMJZkwcSdj4UIKVk0D1qxRM4WLF6fgXbCA\ngko/a2DsWKOFLuGLJ54AqlenwHSHxETnZjb9bOT0dCX0BcnJXN/o0eQ5evttvpb3XrzI6qKaNZ0V\nA6DmNmRkAOvXK5bTzJJ6pzUA7EOQXMjgwcb1CCmovlFP7kPz5vR+OnZkSe3p00iN6IB/UAuvYSLa\neP+GDhmLsHfqBkRkrFTe0cWL9EguXuR8B73XpO+i7tKFz4WD6dFH1XmvXKFC2reP3sR99zGMlJzs\nTPNxDTAVgwkTBY0ZM9wnKm8kpk9nOGX6dAqS/fvV/06eZMhiwgTFOwTQGi5Zks/1SqBePb4+fpxW\n+dWrDCNTLrATAAAgAElEQVQ5IijImQL6/vuZoAU4Y1nCIIJvvmEi2G7nbOO5cxURno8PBf7Eiaxm\nEsWgp+IGOMJUqLUdO5j9/V13OzuW4ApE6QgtNqAUgzSl+fvj54SWaD6iESpv+gZd8DMuoTg2lOmG\n58+9jaBnOvKc8r60NJaz2mxUCnrFIFxJw4YBb71Fz0wqOFu04OOcOVTa+/ZRccjYz5QU1c9QQDAV\ngwkTBY033zTSMdxMiFA6epSTwfSVRQEB9CT27KFQdgWphpkyhTkFgMeZPJmxfEcBDwDuGleTk6lY\nHJPTklfQNFVZlJpKxdWhAwX6/fezDNbbm+EmHScbNI1rLFuWrx0rriwWCul336U3NGgQP6dvvzXu\nJ/F/wezZOPPzVjxXYj4qH1uLtm2BNyvOwtsYjQefvQsvHB+KOtiLb9ouwCHchS/wPGr5nTKeXwbq\nnD7NPIEk7UUxhIYCdeuy5+R//+M2EfqAkaNJT7Qn3ozN5jokeA0wFYMJEwUNYd28FSDrqFuXVrx0\n5PbvT0GfkEBlkV1FS2goHwMCVHmkzaYa1sQCHz2aVi7guqKpRAlavJGRDO84Cu6qVflot6sJZ2lp\npI3o2NFo6T/0kOpY3r9fWdT6c//yi/EcCxcCL7/MPoBjxzi7ID7eSJgHGLqZE1AcX+1vjCYD6wCd\nO2PRQhueeQaIS/VDIorhBZ8Z2J9eDZ9iMCJm6nIypUoZFd877zDHsXw57//nn3OdFy9SiYoHtnSp\nUmxduqhk9AcfqHWKV2C1KsVQpIhS2gUEUzGYMFHQuFUUg83GcBGgBLxg5kwmjSWWLtQMAD0BIYeT\nDmZNU4JW6BtWr2au4OxZTkm7dIkCUR+eSU2lUC9UiMpJrF9HxVC3LgWoXkHVrk0L3tOTx8jIoEDX\nh+lSUpgAFstfQkkffsj9hZ/pn3/UutzNn46NxXkE4g28g6o4gtV4GBOar8AXX3uhToeK6NwZ+Lzi\nREzBMHTdPwb+SFD3R6qXWrVyvj5RWAkJ9GxOnmQ1lORirlzheoUjLj1dTa87dkw1HB47xkerVXkc\nYWHODYXXCFMxmDCRF2hazs1EsbGKluFmIjFRCXhXBHYjR5K2ATAK5HnzVDWPQD8bQSaRSQL5gw8o\nrDMyKNAklwCQ1O7pp1Xvgghlx3nFwcGk2NB3VteqxZCP3c7wld3O7mKZcAbwnKmppMcGWKHUsiWf\nx8Sw3LRpU8WnBHCNgwYZ1pACH0zpthOdz3+F6tYjOB9wF3YUaYmFeAJP1jtkXOugQc7DjzRNKRs9\nu6pAKrc8PPgnIzol+R0VxXCQUGqkpfFapFdBji0keaI0ChWiJ1TAMBWDCRN5wXffGeO/2SE3sweu\nB/RKS8IOY8cymdysGcMwgrVrKVTatGHlkt3OxPObbypPw8uLIaRKlagASpSgJa+3iPUU02IZV6/O\nx4QEWut6xVC5srGRTI9ff2X+4uGHWY0jFUnx8Sp0ou+qlhCTXOuDD6pr3LqVuYg6dZyTzh99BHz/\nPVLhjbc9xuLu4PNYfaAi2pXYjL1LT2F6xfGolPKvui49evdW1yf48Ucq2qAg3suICGMCfsYMPpYs\nyb4E8S5k3VFRDCPpcwjlygHDhxv3K1aMj0KLcfWqkVOqgGAqBhMm8gJ9yMUd9ENhbhSiooxKy2pl\ntcqbb/J1yZJGgSzC8vPPgRde4OuVK7lNQkyvv84YeFISyyLr1qXVumGDCgvph+PIcz3jarFitN4D\nAzmZ7fBh99PcunWj9wAwXh8Xp4b3APwM1q+nFyFVU1YrK5v27FE5B1FS06YZlMle1EZ/zERN7Ecp\nxGFR4W74fnFRrPnsMJ4+NgohkSsZQhNFNHo0FYzgyBHlgXTvzjyHjw+9iMhIKuDKlUmFATDEFhdH\nBfvzz7xHEgYSTyAujp+PKID69Y3zpEVhzJ3LgT7XGaZiMGEiL6hc2Wh1u8Lw4crVv5FwpIjWD58H\n2D0r1Ufbt6tk8ZIlKiHqOPegVi1aso8/TgG4fj1j4927U9CPGWMcvynCWGLiQ4fSkvb25nrEo8ku\nxg/QUpbQyz//kAJcb7V/8QUT2Js2qfNZrUwcp6erMle7Pev/6enAPDyFcKxFONaiLM7gU7yIY6iM\nv5/9Ag0bApYLunnMX37J9T74ILd9+aU6/8SJKvTm78/E/MmTVIClSiHrhKI4Bw9mKW3ZsmSu1SuG\njAzShSQmsulNN8vGJby9ef+vM0zFYMJEXqBpOdeLOwrkGwXpPRBYrVzvnDlMvDZpQqoIgFVJwkkk\n8wH0TVYicN96S3EQyf6yn54rqUkTCnR9WAlgWCg8nB5Dp07kOwJoRW/dqtYq1UqOSEyk4HQM58ya\nxXNJPsFqVcrGZsNVFII9w46UKzZ8gWfRYnhDTPEbi+4Nj+A4KuFdjEbroH0oiQtMBgP0OAR2O6+3\nVy+1TbqvPTyUVxISQoE+eTJDR5LT0SuG2bPZZf3qq+xQfv55pYCffJLeSb9+7ntfROFERBjnUF8n\nmIrBhIm8QC88s4PF4n7mwPVCoUKq+/XUKVawpKfTOxCeIsG+feq5lJ7a7coSlhj6li0qbCKhJ7kH\nTzxBYR8czIRskSLOikGQnk5CPDnGv/+q+DlAxeBIkbF2La3tdetcM8Ha7coz694dqfDBr2iNtgOC\nUdRyBZVe7YyaNez4Ht3xEj7Glve3oJ/fQhRGZjhQPscSJfh5CWEfQA/pueeMVBwHD6rzSoL96lU1\npOfAAaBzZ3W9+v6DEiX4vShalMq2ZEmGpCT/YrPRA9N7UnY7PYiiRQuU7iI3MLmSTJjICxo3VjX3\n2eGdd27MWhzh48NcAcDk5p9/0tL85BOGdBxRqRJj9+PGUSjrvZwBA/ioV4QZGbTgr16lkKtbl9vv\nvpuPFgsTrzVrGiuT5s1TQ3BEMXz1lZHpVBTS5Mns/j1+HNi8mZ5G4cKkgxDUqkXLXLiDPDywoWh7\nPPnTgyiJM+hx7hdMe+svHPC5B0V2b0aT+YNh9S8BdJkGeNhYXrtvH4/93XdMJk+bphLuAM+9dy8F\nemoqCepkQI5UDr30EhVnp04qHyHKQK8YXnyR15CURCVy5gy9oLZt1fnsdoal+vc33hMJG+mT53v2\nkCo8N0UQ+YTpMZj47+LsWTVfOLcoXlxVhGQHKUnMDnPmqCqVgoSPjypvXLOGVrhwICUlMVkrFNMA\nO4lnz2auYfFiWr2lSlFACd10YqIKP40dS8G1eHH2XlNiIr2BuXPVtu7d6b3oFcPRo8ZjSHJ1+HAS\n+A0cyHCRl5eKx9esmbX7Jx5DMGBhG0ydCvTD1+ja3QPfVxuDfbgbo66ORmh4NTwyoi6azX8RVmiq\nKiojQ824HjJEdXa/+KLxOvQMsN7e9Bwcw4MREdwnKkrlbkQZlCypQnuffMJQ3oEDvNf79rHCSw8J\n5+k9Tbk/b7yhPMH4eCpk4Ya6TjAVg4n/LlaupHWaF5w9axyt6ArTprnvdYiOdh6d6Q75GcLiqsHq\n4kU1+AYwhryOHKFiiYujsJN5yzt2qP1bteK6W7bkc00zcgkBFKilS6v3Sdy8ZUs+L19e0U7oK5NE\nMVitbNZavZoWs6dnloBMf/FlzEZPtD05DdO9XsK9TQphxw6gzjtdsXUL0HpAqDqeeCzCWCqKwWZT\nAlvTnKiy8fDD/Hzj43nfR45U63JF42G1kphQrlNKVD/80OgReHjQU1iwgMlxR9px8X705xDF0Ly5\nUjijR/NRP7PiOsBUDCb+uyhWzPXcAXc4fTrn5rXhw90Lc29v5/9bLEYhrEehQtmTvbnCjh2KmVNg\nt7OiaP16ta1IEeM6xJp3HOsJsFKnWDGGV6KiWJmjaQwd6ZGeruikR4xgUlVw+TJLLfWlpwI9V5Ig\nUzFEn7FghGUiarz/NGY2mokeTU5i+xe7MOjjGpgzB3h5ZCFUrmIx0n/rm/HktYcH+yR27OBc548/\nNiacAYa8hF7CblfUG47WPMByUjm+dJbr2Vj1iIlh42O9egxT1a+v/le9Oum1O3dm/kEgikGvRKQ8\nt4AntjnCVAwm7lwkJBjjxo7ID3WFK8sxr8f19lYllXo4NmHZ7apyx3F6miucOUPhsmWL8/8ee4xK\nQTqFX32VuQH9OhzPDyjunpIlVXgsNZVJ0xUreK12O0tI5RgiQC0WZZEXLqzi51IFpIdQb+jvbUoK\njiQFoVkz4IrVD99MT8OGP73RY1UvFOnWkfvMnas6f/XCcvlyeneybds2TpDr0IF5DFehvqAghuLk\nf97e/A7t28dYv+No0xkzaCiEhHANjRoZ6cv1iI6mUs3IoIcRFsZtvXtTOU2bxrCWvhRVFIN+rdIf\nklOe6xphKgYTdyZOnWKNfXahog0b2LyVV8WQm1LUnBTDL7/QctWjenXWw+uxZ4+yXnv3NlbNuMLV\nq3yPq/Xdd596Xr8+6+kffdS1xwAoem6xwvVcSZIo/uwzPh47xs5fgMfbuNH4/yZNqGD0jVl3322k\n+q5dm5VNmfdtDcLxXNmleOCnoRg6FPjE9zU0fyCNHone47h8mQrv5595bskfLFzIDuOMDF77mjVU\nIgEBbKBzpRjq12eIRgSyhKEOHqQnUKGC8XO123lOCcn9+ac6f3aQe+ztTYXy/vvMW3l7U6nop7C5\nUgwAlUpO57lGmIrBxJ2JLVuAqVOd2TMFcXGsbMkrh/1vvxnj9K6QnGwMCTjizz+dcwyuymC9vSkE\nmjShx5Bd+OCJJ1Sz1/Hj9AIeeMBIIa0vdxSh37ixMfyiVwwSQtGvTxSDhDaEiXTQICqDWbPo4Zw9\ny+3i5dhsvJZy5VTy+8UXnfMgH32Esy+8g374Gr3xHWrW88EfWzwxaBCo6IsWZQxf5iwDVBSRkRT8\ntWoxPyBNaQDpMCIiVGhN8ho9exq7swGGlqpUoSAOCuL5KldWPQTR0XwcPpzvB9jlnJvyZPGI5N7d\ndZe6N2lpVDznz7MYQI/nnzcqgRMnjOHA6wRTMZi4MyFCNru4vd1O111+oLmFUEXkBHdeRevWzsRn\nrhRDWhqTji++SB7/7I555YoqhQQonLduBUaN4ut33qFglsE2Eq6IiaH1/OabrDzSJzRFuIsX06sX\nQ0H33KMSsvrzFy7Mc/j5OZdRZmTwOu6/H5g4EYnFQrDNtwXWXmmM48fpgGzcCAx+xQs157wOvwY1\nsKXde/jfwmaK+2//foZ5vLycuZI8PHjvgoMZltH3D3z9NRPejh3XRYoYp7bNnWts8hOldfQohT+g\njvH00+qzstmo8M6ccU99PW4cczRCXy7UJHY7P2dvb5WA1uPzz40jUitWVE2C1xGmYjBxZyK7+QIC\naY7Ss27mBlLemBPclauWLKlq/y9fJt1Cly7OTUxSC//UUxQINpvi3UlNVcJLhtHrOYsEnp7KShcC\ntjp1+AfwOD160EPQW71i7Q8dylBRsWIMZYWFqbCRICWF91K4kkqUYHJaKpuaNoW2fQf27gU+7LwJ\ntRL/RK/RoRhVcQ5q1OBur7xCeTd/PvDx/CBUequ38RzR0ezAFsXw779M/qan8+/QIb5et87IByWT\nzuT7oE/kyn0qVowltVYrPa7ISOc51nKvAJ7rf//jfbXZ6AGGhmbvncq5qlVjLkbu86xZ9ExkINGt\nQtcOUzGYuFPhKLwcoWm0dI8cydtxg4NpZbvD+PHO5Yh6yGhHgEnS555jQtTREkxPV9QJYsV+9x1p\np1u3VklmX18KPhE4+lCKvpomIoIe0sMPq45eu51J1AUL+NyRh6dKFTbCyTG//95IELhwIV+fPUsB\nKfTTr72W5Y1lXLiEN8Z6oW1bYNeRovjx/g9w6IQ3duyw4Nw56qCdO1mJGREBhm/0ORG5Zx4eVKqR\nkXzDd98p4Z6Robq0r1xR77NYjIrBsbMYUBVC4gVcvco8kCPOnOHjjBnUYLVq8RjR0aw4clcpVLky\n1/7mm+q8vXvzM75wgcp+1SomqG8BmIrBxH8TJ07wB5lb6or0dDW5LCerLqcEtYQ/APU4ZYri2heU\nK6cqeTZsYCWQDK2RR4CC7+pVehUAw0LSoGaxMP8wcyYVQtGi3FdyIFJVJJQYjlxJL71EK1o8K9lf\n4OHBUMjcuRybabfDDiu2fLwDQwt9ig4Pp6LQ7C+xckk6dga3w3dtfkCjLmUYxtq1C8WLA15XE7lO\nfVOcI0QxSJXUP/8w9PXSS3x99aq6l9IM9tJLbIrTNBoKZctSmAvsdoZ2vv6ar8uUYRGAK6V+/jyT\n9QCvV/ohKlZkXmDmTCbFs/s+VavGcJzVagwjdujAJstff3VdxnuTYCoGE3cmRDDq+Xj0ECGaW7K7\ngQMZvy4IrqS+fZVFHBrKXoBt25xLa0NDea5+/ZgAffBB1b2rVwxff02z29eXoa6iRWnFnjzJtRw5\nogbY791r9AokqSzxdcktSFx7/XqGu+R60tPVPevUiUnVihWBevVw8Yo3Fkw5ifDEhXhqbA14xMeh\nQ5sMxKEU/p4ViaCdK1iptG0bldV77/HcYiX37AksW6bWNnWqSnCLYpB+D8mJSOWT3BuAoa/hwyno\nfXxUjmDwYGO83m6nQpFeFi8vvseRYVb2BejV1a7NZHbbtszfaFru6CnkezN5stq2di37QkJCjBQh\ngtOnbwoho6kYTNyZqF+fgiI7iuLg4LyR3YnwbNfOOEHMFV59VVFTuEJEhCKps9spvLy9jUlVwcsv\nc2xliRIU/H/8Qe9BrxgA5VkMGkQlUrgwy3XLl1dT0ADmNoTSo0YNlmKuWuVMoieWuChCef/ly/S0\nunQh1UNICK5+twBdhwSjbAUPTPskA41a+uLAxCWYeM/3eLZXCsdfyn1OTmZi/N13Safds6dxxsXT\nT/Px/HmGrURR9e2rKrkaNGA+JjmZMft69bht+XL+f/FiCu9z55j78PFhSeiIEdwX4DVfuUIeJ70i\niItTVUh6iJe4dCk/W32oUujKFy/O3pvctYvrsdtpYEijmrwfoFLq0sX4vgoV1D24gTAVg4k7E5pG\nYTlokOv/S+xdGDNzglisgYFqrnB2yIkr6fBhRVLXsCE7Yb28XDe96d9jtTK5euSIcQ6y1aoSy2+/\nTaG5bBn/RJja7Xzfrl1KqFWtynUcOMDmLatVlcgKbcSZM/RooqLI7/PXX8DEiUirXAMnMkLw/POs\nprVYLIhBGaxHK7zbbR98/TzJCSX0IZIob9+eZaHC7tq0qVHBxcYysTtqFFlhpZM4IIANaoLChSnY\nbTaWcyYmAo88wvteogS9poceovLQh+4EaWksez171njfz51jQtgRjr0NekRH8xwdO2b/+b37Lr2v\nhAQ+d6UYsmuejI3N/rjXCaZiMHFnwteXVmJ2kB96TIwzX44rSBw+IUHFpLPDRx+590SuXqXQ02PB\nAvd8/LJmqVy6dIkextWrvFZHS1VCTvr1S1J2xQq1Xda5bh2PmZbGeyJx+oQElVRt0war11jQrehS\nlJg6FlWqAEXT4vHGq1cxZ2I0SuCSWudTT/H5nj18FDrqUqWMn4u3NwW0TGwDWKUlDKaiGKpWNZDo\noUwZJm/tdnYN9+3LsM4nn9Cj2b1bla1mMrAa4OnJa3f8LGfOdF155k4xTJtmZJN1BQ8P3os1a1R5\nqkDfKe5KMdyESiVTMZjIHXbuVENIbgf07m2M5TpCnyfIqbQVUKGk+HhafAB/xK6sueyGs+/dq6p2\nHJu7kpMpmN3BYmEoa9IkWql16nDtjvHt9etZoeOoGGRUZGQkH728lNC3WNT+DknQDHhgXdspaPpY\nEJ7+IAz3++zCLu/7kZICTDnUEV0q/AWvwrreAb3iERZZEXiOQnrHDm7Tz0fWh5ZEMfj4GKt+AgNV\nuWiRIiphrJ8Hoe81cFQM8hk4jmrt2NG1tyfCWSrHWrc2/j8kxPk9eqxaxXU+9JBqaNOvBSDR4Ecf\nOR/3Bkxsc4SpGP4L2LAhb2yerjBzZt4pqm82kpJYUeMK5cqphi9XQ2Ac8cMPDIHo3f1vv2WuQg+9\n9afHwYOsrz961KgYbDYVQ9Z39AKs2xdlMW8eyzPff59CUEpe9bz/Bw4AffrQKt28WQn6nj1ZEqtP\n7ALMP0gYRa8YdJfye7F2qITjaLfmJbzU6SQOlG6O/xWZgbuu/A2vU0dVbkRfyePquxYSwl4BX1+j\nUpbPp25dNsA5Qq8YXIXaxJPTLxpgyExGsJYq5UxBIp+BvhnOHfz8qFDFk9Jb/GFhwDPPuH9/UhLD\nZxYLw1Xy/Rg2jOXNAD0pxzDl6dPOVCk3AKZiuFVx/rxrUrP8YMYM4xjF/MCV1XUrIzaWlv3Aga7/\nv2ePSvbmpupjyhQqkk2b1P6uLPzsQkj6GvnPPlPe18WLTAgXKeLcha23op99lgoeUGEiDw8KTEnY\nXr7MMk6ZKSzCunFjNQJTj6lTs6zwJEsx2NMykAEPTMIwNKl3BSV9EtE18SuMwRgkD30LXZuc4cA0\n+V6OHk3BtXOn8bshswI6dFDbqldnQYAk2oUiQry1Bg2ck/qFCqlksStGWoB8V5JfAVRPgl4JenkZ\ny1TlHtpszEc4Kg1X8PDg5/Tmm3yt9xByU8Tw/fdMWsv3QHpBJk1Sazt2jKGwWwCmYrhVUaqUsiSu\nFY5WVX7w5Zc3ZNZsgWH/fv7oskvcnTnDHyKQO8Xg5cWmpj591MD2hg2d99PX/+tRrRqTuKmpRpbO\nKVMYE8+OEuOFF2hpJyVRkZUvz1JXfcPXkSOkzdA0ehlxcdwuVqyb+njtpSGYWuItlLSdRc1e96IM\nYjAckzC25Kf4N70qzqAsBuBrWDS76haXjuZ58xgCe+01hlgSElg2KrxE+uvx9KSXVq0aq6GEx0m6\nlJOTye+kVw79+ql4/w8/qGE4erz4ohrvCfAe//234hyS6i9HNG7Mqqh16/IWIr1wgV7i55+rbblR\nDN260bCQfV2N6oyKYq7pFoA52vNWhnRaXityU3ufG+QmFn+zkJ7O8hhJ6sr17t7NUM2pU0ZBbrfz\nB37qVO4Ug7c3E6D6wTQ1ayohCTDmL9anK29P4uSlS6uJYRMnqvXIkJrwcIYPhCupRw9SQHh4UDg2\namTsnpb5CSKcoqNZEvvqq5wdIXHxcuWUYCpdGtuWxeHlx4sjvfRA7G88DDEtu8M67BU0whZYCrUH\noJvL8NprQIsWPO/u3SqUIpavlxef60s9u3dnCSfAtUtCGshscYbqQ0hIoOU/ejSVuc1mNETWrGHl\nkX6+gyuMHctwj3z+0gfhCC8vVh/9/bcxqZ0TvLx4L/SGVtmy7jvd9e/Vf18ckZvmyRsE02O4VdG0\nqXPMOb84fpyWzrWiIJTL9cKlS0xkfvABY776pOL27WoO8yuvqHnBUs8vuQZ30I+YFJQoQRoIQWQk\nlbmPj2sLcsAACmcvL1qsevTsSWEzZgwV2c8/M5zo5cVGqrvv5v1PTKTgt9mYqLznHlraaWlGriT5\nrIKCFN21ry/QogW02nXwpc9gtO8TgAE+c7H5l3Oo8tUING3hicaFdsEC8P517Mgmtv37qagiIym8\n9fMURKiKoJTzDhyocgb9+tHjdISeYloa8AB6SY5lxocPM4eix/ffO+eQhDpE1pHdd1buVb16eZud\n7EjiB3DanL5xLjuEh9PLyg4yEe4WwK2xChPOKFw4+2lQrhAZ6UzZK9i+nYLmWlCsmJpSVdCIibl2\nS0mSiLt307rWz1TW/5hXrKDg0DTlAZ07l/Pxvb2V8JMwkdVqtDZDQ3mfsitX7d+f+4i1rxeMM2Zw\nnRIiGjKECkIscquVf5s304O4+24ydqan87uSlqbO2bIlvaMhQ4DYWMSes+C334DfazyD/ucmIPTo\nr5hqfxGbfjqPAYXmwnvKOOYv7HalJM+fJ7HeL7/wGiUUNn48lZNA4uby+UmD1rRpDGeFhPCaXVnU\nXl4sYz1zxkiBXbOms7J2leP67jtnZSG5AxGw2X2v8utFu1IMp04pSu68IjVVJdW3bFF5pJsMUzHc\nqujZM29Tmg4eVG67K1yrUB88mKGa6wF3rJSCrVvdX1/RohQCLVqwpl3g4cEfs4R24uNpfb78MoUs\nkDsB8cgjqpTQUdhIyE+qhRzr0S0WVshIrF8Sx3qhtngxFbsIwPPnaa1LWeSsWVRO3bsz/CHsp+np\njLGnp1NZeHtzrU2aANu2YSOao8FDxfFyrzh0mfogAj0S8FOj9xEZH4KaFZOz50ras4dhrl69GOaJ\njlaVQY7XphfYd92lmFuLFAEWLSIv09GjXLtULB0/Ts+tbFn2JOT0GbhSDL6+zuWmesXw+OOKW8kR\nBakYpk2jksoPHnpIzXFu0UJVUt1kmIrhVkWvXsYJVznBXXzyhRdUdYfg0qW8MTnmhT4ir3DXiCbY\nuZNx5uxgtdI61XcoA6Qf2LqVA3YyMhiPFzI0/XsdYbEYcyrdutGC9/d33r9cOQo86UZ2da9++01V\nnAwfTn4haWjz9KSQ3LOH61+7lufu0IGD4GWNpUszrJOUpBLnYWEMoaWlMaF5zz3QMmyYNw+o9vcP\naIGNeO/RHdhbpxfi4oDJex9GgxEPwaplei12u5H2Qj8r2s+PMXrhRypUSD0PCGASuXRppQgSE4GV\nK40GjSjkyEhyN4l3tmgRE7j6pj4h+3MFV4qhUCGGBvWCevt25nmsVn4u2cX+86sYBg9W+SHBtdBl\n//GHIk9s3PiWKQk3FcOdAnfxSVcdlVu20KICaM3lxMfy2mv8Eeqxb5+R4jm/8PZWRGbZ4cgR9z9k\ni0Ulkq1WJZxKlVK0F66qiADn46ak0DLUh/JsNoaoPv9cNbCtWMEQUEAA/2rWZJVLv37GqhXJZUjF\nTdeuXJcIxUKFlMV+5oz6LPTCxs+PFrLwAWWGztKPR2H/urMYec9yfPstMLTo56jbrx4mjrfhg/TB\niCtWBb276mY1FC3K+yBewoULTPaKYpCZxX378px6pSEew9mztP6XL2e4SMpqixcnlYV+ep2+XyMu\nTillkRQAACAASURBVBkj8l3Sdwzv3KlKbx2xbJmavibw9aWy0Svhxx+nEq9WTSksVzhwwNnbyA08\nPdm/osctlBsoKNxZV/NfhjuPwZUFu26dcusnTnQfpgEoJKS5R2CzGTlf8gtPT/feUWwswzi5scoe\neUSVbg4dytcyGnHyZEU2p+9cdfxRX7hAgec433f9euYwypfntbdrx/smbKc//8xz//670VIVS1e8\nmORkrmvlSu534oRKmqan05sQBQAwzq/rmTiJClhja41HsQjee//CfTGLke7hi/nzgYTK92LKx97Y\n+sNJdMAylEw8xrCU3c7Hy5fZv5CWxmsMCOB6Fy9W35FWrbim4cP5+T76KNc1bBjzDHPm8H3ZKXO5\n9kWLVNWRzcbvmyMFhT4pLaG2CROcQzN//MEkrx6SNNZ/fn37MgfUrp36rF2hcOG8eeSC2FjnRHpM\njGsCxNzienni1wBTMdyqGDAgbzXNf/7JUkeAP/Inn1T/q1DBmTFS/2WMiVElj3lBduGlUaPU1LDc\nIDTUGCY6c8ZIbifncCS8++svCik9KlakpVi4sGp8qlKFIYDWrdV9ESpmwLn57/x5RSInEKENMKYs\nwn7ZMoZQLBYl9D7+mI+iND08GD8+d47n0jSGTQBV8jp3LoV3p0587e1NxQHg6OJ/MB3PYdiWLmiK\n31EbkRic+B7aYgUuIAAXEIgpU7j7jBksfilUWPfT/vVXHlvWL/dMrmHkSFryQvu9bZsxCSq5mObN\n+V3y8mI/B8Dae0dvUxTDqVP0AgDG0Vu0cO5F0PdYiICfOtVZ+Pr6GgcEAaraKj89OsKVlFdcvuxs\nIM2Zk/MccHcwFYOJXCMlxT3bpiNkVCRAC1ZvwQwdStc/OyxbBnz6qbHT1hHr1zsLgH/+USyZesye\nnTPRnDu0bQs17BcqTu2YY3jlFeZi9u1jMnPRIgrpsWMZrpGknr7Bz2qlgujRQx1HiNGGDmUJpCiG\nbdvU9ekFq+PMY1mjzBAWyzYwkCGwKVPU1Lc//lAJ0uHDqbRSU3nvhaIhPR3YuRPauvX49FPg/vmv\nYDEehbc1A//DR4hDKRy0V8Nzqx9DAC6iEBw6gpcuVXxIgApTSamkhIssFp575EgqUwk3XbniHOt/\n9FF1D0uVUn0MH3+srHupLBICPJtNzZHWNH6HhGdK8N57qktZPLSzZ5lLyQlSzp2f+L4rvqrcICnJ\ndXNamTJ5P5Z+LbcYTMVwq8JVjbY71Kmj6sYdY57LlzuX0zlaKbGxzuMU9XjnHWcl4FgqKHjxRfdu\nvDskJDgrRP0P+P331fOnn2b11iuvMIzzxhsMV4wZQytORnc61rXLXGIJMYlATExU8wb8/Mj1n2m1\n499/KdR9fZ3zNRERxslmYjHXrEnB+8gjSpikpiqhVK8eFYF8NgMGAF5eyEjJwNx9dVFnSi/MmpGG\nrT0+wcrxe/Bey1/xOH6CDzLvj+NAmb/+Ap5/nv0H+sKCmjXpwelLQuVepKYydyChLIF4BAJ9dY+e\nt0g/F+KJJ/j49998PH+eXeLly7uu8w8L42cgXoN8RqVK5UxtDuTc0V+vXvZd3wWpGB54wNi8lxdM\nnqxoNm4hmIpBj8hI93NbbzT0FSLZ4fvv2Qyn/6Jv3sx2f8GUKQzDnDihcgl6GgGBu3JUV1Uh2Xk0\nrkr63CE9nYokJoZCoUYNxrD37WM1z/Tpat/PP1dKTcpDMzK4LSZGrTEykjX3ffrQQ5D6+mrV2Hy1\nZIkSdiLQRTi2aEFh+s03qjJp/Xo+fvWVMz32e+/xGgoVolUuFqyUU+7axUYzX18e//XXDd5BcvV7\nMA/d0O/Te1F35XgE9O2AL1eEYBJew/bvj6JqyQQmrmW8pkCS6WIQJCRQgcm9EZQsSS9MIKWudjvv\nnZeX8ioEHh6sdvLz4/3S/094i/r04f0R70QE+z//GNfZvTuFpx4PPkgvVW/ECH/SoUO5q+e3WNzT\nxpw4kX2YJr+KYc0aY/5H1pHfcNDQoa55rG4yTMWgR/v2ys2+FZCbL9v8+VQEesvNkdxNLKt//lGx\n23r1VKOWhFLcUUNs2uRMY12hgvPEKcDYN5BbyGD34GCu69tvGb546CE1DS04mFUsMmhGyOTkBx4f\nr0IXMTEU2Jcu8VpF6ZUvT8t2716leOW6v/iCwrd0aUVVIZUr0kAnBHGAIr27/34K0YQEnicpiUJT\nFEPTphTiI0ZwvZlhtsMnvDBoUTj8cRGTMAx16wIfPbIKh1AdG1uNRRusgqVoEV7n1atKSQnFhVRN\n9e9PIjZNU+vUzw1w53nOmUPBJkpRzy1UvjyVXZ06xu9imTJMiH/3HfMmek+kUyfnhkFJzuvx9ttU\nvikpSjHUr8/vWIkSrsM1jvDwYELcFU6c4OeRXbVQcLCR3iS3GD/eeQTr9SzlvkkwFYMeN6rsLDEx\nd922uYEMX3FnAUnJod7q79SJST6ArmyzZq7ff+GC6iJ2LO/LyHAdW23a1LlXwB3S03luWWeLFqzh\nFyEPUGjIZC1pAipZkpUx4jEAylOSsNe+fay6Wb2aDKU7dnD71KlMIhYrxvPK+x1pmCV5KlxJgq1b\nmdOQ/hC5N3/8wceMDKUYbDagVy9oGpB81YIZV7oh0C8Vjd5tixJIwGmUxy7Ux5AhvPTg8DqKU6dI\nEVr7rVrxs6tVS61DvLKyZRmO0n9//fxUXkmqoYoUMSbdrVaVa6lTh8cTQrnkZCqFlBQeZ9w49b71\n61UYzvF+6WnIhQ/J1QS15s1VR76evmPoUBQIxOPILv/g4eF6UltOKFrUeT5CcLDrOdG3Ma5ZCoaG\nhqJOnTqoV68eGma6tvHx8QgPD0f16tURERGBhISErP3Hjx+PatWqoUaNGljjrmHpZuD06ezj5gWJ\n+fNZueMOtWpx2ExO6NGDQjMsTNV5d+1K4Sw4dUoRk7mKyQYHU8C78hh+/lmxdJ44oXofABWfdkS9\nennr4JTQgz4XAFAAiuX7999MNi5dqgRd69b0JvQKTeri9ZZ98+YUbgcOUODJfWrcmEq6ZUulYB15\nc6Sk13H05qxZFJA//UShKvchJgYXLCVx8FIwItNr4Pe/fBGTUQrLFqXj/pnPoPj7ozErpSt+W21D\n3N6zGIfXURpxqlpq4EAKYwkPFSlCL6RxY96b9HR+5r6+XE/RoixDSk42lizrP2sJVVgsvGd16jhX\n1gwezIouYTvNyOC9KFeOylM/1WzYMJVwdpxHof/8ypVjcv39953ZZgHlReTXGNu9Ww0fckROXEkF\niZ9+yr5H5jbFNd81i8WCDRs2YNeuXdieyWw5YcIEhIeH49ChQ2jdujUmZIYC9u/fj/nz52P//v1Y\ntWoVBg0aBHtumC1vJCT+ej2RlpYzU6mvb+7Ivfr0YfXMrl3KSvLyMlpyp05RkGWnGPr0Ifmcq4Rx\nWBjZPAH+yKTjFmCc2JVnEBVFRTRlSu7m1YpgT083/pA//ZQ5kccf57rHj2e4TyAzjy9cUO/LznKT\njl0PDx4XUJ+Bpyc9uBIlmNDWV3AJ2Z0MpAEYPhPvplIlCtmAACS3ewKzPzyPapbDaPnb6+gcORaP\nfdQUdW1/4T28jkGPnkGa5oXf0Rx1/U/CUl7H6T91qqoMSk9nLsRqVQpHuJLS00kwl5yshvR4e6tc\niyiGatUovGvVUgq/d29u9/V1XfVjt9MaLlKEx/HxYc7i9GnjEJ34eJVn6dnTyBf1wAPquydzELKb\nge3hQcWRXxqI3buNuTTHYwM3hq302LGcG0RvMxSIOtUc4mtLlixBn8yqhj59+mDRokUAgMWLF6Nb\nt27w8vJCaGgoqlatmqVMbhncCEX1/vusW3eHZ56hxZUTrFYKtj17VJmkq5hnqVLuh+2kpDgzfgIq\nPDF+PC14vXV+332KskGoEwBSPc+ezRCUm1kAABRTKOCsGOrUodCYP5/7OA5U+fBDllreey89HrFu\nHTn4771Xhav01TeSRLRaGUKxWKiMpR8EUJ24xYsrxZsZ9oq7UhgvDUxD/T+mok7feii/diZmxnfG\niICvcKbpkziiVcW5WCAWwdiCxuj74HFYJETkODhm82aVxE1NpbB/7z2uyWZjTD4qigpcIIrBYqFn\ndc89bAR87TU1sMZqpac3Zgybv6pU4Xe8fHnnz0KUnSPFQ0qKkZ3Xbjd2NOvzB+XKqXxOxYrZN04e\nOECDpWJFFZbKK7y9sy+AsFqppFzNaC5oTJrEnMsdhALxGB566CE0aNAAX2XWL8fGxiIoM34XFBSE\n2Eyr8cyZMwjRTT4KCQlBdH5ZCa8XboTrmZtqiGefzZ4AzBX0YYT77mMiVfDGG2wii41VidurV1X8\nHGAtuSueGjmuPkHpCm3aqModUSa54aMJCVENV5UrUxHs2mUUKHJd4eGq6gZQgl4qasqX56MIRYAV\nTTt3UrjZbExK6wflADzG2bO0/PWjMgH1vG5dwGLBpqJt0X7XO2i+dBjuGt0VHumpeB+v4pth/2JH\nYBtsSG6I1wJm8Hze3kYFvXs3PawGDZQBUrky99FXcS1dynDciBF8Lfv6+xsLC0qXZtXW/PmKjbdG\nDSbOixZVVn1SEgVXWhqVpp7VVY/sFIPjPdE0KuCiRbldP3nO35+KOCd8/TXXpC9SOHAgb8Op0tKy\np7G2Wun93Ijf87VwJd2iuOZBPZs3b0aZMmUQFxeH8PBw1NA3JoGKw+LmpmX3vzFjxmQ9b9GiBVq0\naHGtS80ZrVq5H6SRH5w+zS+oXkDkp0zOHfbsMYZT/PyMVR3yY69bVyUf9+9XjJ+HDin2TEfIl/6F\nF5yZS6OiGNrZvZvHlu5qPb+Oux+mWOPnz9PzKFyYuYRx44CFC9U9098vfQhOQkNyrj//ZPxbJqwB\ntKIrV6a7n5rqmsLj4kUqtr59mXPw8mK46ZlnYPfwgj0DOJVSFqM6pWCDzyKMfi4ZxVfNR4vzCxFS\npSUQegJ4/j5gQmZe47HH2JPQqhXX1qwZE+BffkmhPGgQvYElS1SyVe/J+foaPwu7nUqmcGHjfjKf\nYepUJtkdZwNv3EjFe/fdrMKaPJmlstn9lrJTDI5VRfHxvF/ffktFpO/Qr1fPmbDRFWQIj753JjKS\nuTdXDYSu4K4BtHz5Gxf3v4lcSRs2bMCG60DVfc1XUyazKqVUqVLo3Lkztm/fjqCgIJzNjLnFxMSg\ndGZ5Xbly5XBa96ONiopCuWzCJWPGjMn6uyFKATCWfBYUXAkix9b+a0V4OAWZO64ksfxF2M6ezXI+\ngFVJK1Y4x+c3bqT1/csvtA5LlDAKabtdhRj0M3n372cY6ehR95TaktgNCGBIAWAoxzGhKJU+AJOY\nEupJSKCVKZ6MpjFM16sX/z9yJMMJHTvy9TffqA5xfYll1648rqYBxYtDu3wZmw6URm/PuSje+l4U\nLw7UjV6G2kd+wcFFB/DCqOLo2duKkH/XsstahKa+USkjQwl3+bw1jcqnYUPltchMaqtV5XIcLfpN\nmxTdtaMAioykJ1iyJD0+faxb03h/JJwnv73XXzdWfAHsc7FYqOhnzjR+F3780dib8M8/vCYHI9AJ\nGzdm7wFcucLEtXiZQN5Lxd01tzVuzAl2NwJnz960/qcWLVoYZGVB4ZoUQ3JyMpIyk7VXrlzBmjVr\nULt2bXTs2BGzZs0CAMyaNQudOnUCAHTs2BE//PAD0tLScPz4cRw+fDirkumWwNSpxiSbK9hsxmlT\nOUFqzvVo394YK3aFESOMDJ3Z4X//owAoXFgNVpk1ix2wAuG8d5V7eO01Co4jR5wVw5NP0poX4T5r\nltFj0B9PH+89eVKVi7oj2fPyoqfx5ptc+7BhVAyifA4cYN5E3wCUmqqE2q5dvF79LAGLRVEliPcn\n087q11fVOLqSw4yLiTj/42/4cFQc+uFrNMFmDPiuOeo29MbRY1ZERwPRZe7D69bxKF7Km8eSRH1q\nKu+dzOu1WNgtra/Y8vHh/QkOVslS/QD7xEReR6lStOodmwP37FHXYbUyfLJiBbeNG6cKAp591hgO\ntNvZwyBcR+JtffKJ8zm+/ZbK4amnVN5K4NgXc+yY4sKKjzcWJOgRG5t9r0CjRqqcVeBY+poTcmLk\nvVFYulTd4zsE16QYYmNj0axZM9StWxf3338/2rdvj4iICIwYMQJr165F9erVsW7dOozIjJWGhYWh\na9euCAsLQ5s2bTBt2jS3YaYbjho1cg4lrV6tEq65QfHiztVFnp45ew2pqbmbsTxvHoW3KLQuXSjo\n9T/8Z5+lonClGCZPZjdnaqriuNm0iV6I0DB37cqY/xdfKGscYCmr5Ij0NAl6OgN399PTk4ItJIRK\nYMoUHkcUQ0SEsqgFUoEDKEEicwI2bVLNdZpG4bV7Nz0TPVdSWBguhtTG2xiNhpbt8MdFlMJ5bJ4e\niTrYi2HPJuLAqNl4pf5GlF78FUpYE+GHJJ7Dx4fhH7vdWBywbx8T8DK3ITCQ+7/+OtfRrx+t5IUL\nuX/hwuyDABg+mzPHyJXkeJ8AFTqbNEkRyDnCw4PfiaNHFXeTXPusWRTWrqgkpA/m8mXneQP33pt9\n5dCqVcxhuUJKSvacR3/+yXDSiy+q8aj9+jFnkltUquTcU3Cz4EhSeZvjmnIMlSpVwm4XrIIBAQH4\n1bGCJBOjRo3CqJxq+G9l5GaojB7e3hyxqIdjB7ErfPaZ8/wDVxBB36ABq2wuXXIOOSxYQEGvVwyu\nOjVFyEtpp82mBPHAgbQORZGfOmUctP7mm6oa6I03mPC026ks5s83sr0KVq9W/DqBgYwL6+cl63MF\nAlEcBw6QgygujmGZkBDG8D09abFfvsxY/9ChFDYdOgAALiZ54qf4LpjUqgj80Q5PevyEnhnfIADx\n8CpdGUg4BLw1DDjgDXhmUi60amWk35CcxvHjvO/Fiyth7uvLe1SuHD/3vXvZU/Lrr1x7bCw5jcRb\nAlTIY8QI7u+oGAICeC179nBfd122EybwOzBrlvqs9EUMFy4494sAyutyNbvDx8fYx6CHu/DrgQOu\nSRb1OHTIOJeiVSv3++uRE1dSpUr0Zq638RkebiyjvgNgdj7rsWtXzonhMmXcE3zFxRkFuqenonRw\nh+RkNdAFoHDIKxW2rD0y0jjzeNQo1un7+CjrzpXbLnF+STba7WoOsYysFIESEaG6ZAHuq++GTU/n\n/sePq8E2gsuXVXlfYiKF5UsvUREsX84YvCOFgrc3BUfFilzfr7/SMpYBMKNG0UpOTqYwWr+eCvi3\n31hr37w5IiOBBt2q4oeAgfik5U/YWvtZvFroMwThHLyg6wGw2fhZDB7Me5aayvBYkSK0btPTKWC9\nvFjtNXgwreOaNdl8pudKSkqiQK9WjfmN9euZcNV3qksjY9OmPOb06Sr/A6g1nD7NnIleMZQvr5K9\nH32kSo5PnlThKr3HeuEC1+ooUCVPI8lnx/85bjt4kCWwV6+qXJEjciOQ8ztJDeD3bfhw1//TNIZA\nb0REwqTEuMPRtGnOU51cWVR6JCWpEEFeYLEYu3WB3H3Z5ItfqRJ/2FWqqCY9CQ2JZfX774q6ulIl\n1sZHRyvmSxFUohgktGG3U7Hoq1W8vGgpS6L0ySeVMBMrUmroJam4YgWFW3y86oQtXZqxd0nG1qrF\npLHjtK4iRdjXUKQIQzN//EGBmZGhEn/6uQrx8dDeeguXUQRzFhVFhUdqolEjYOw7Hvh1X1k8nLwI\nlqjTRgUk12a3K2EtQhmgQhPW0UGD+OjhwW3STFa1KudJdOpExRAVRYuyRw9jGO7ECeC55/i8Tx/S\nV//1l+qI1wtLyf1IqE7/vbjrLq6lWzcaBEKOaLOp2Qe7djHkItxSsm499LOSHb/frr7z8+cz8b5t\nW/5nEWgaf2/XohjkHjriRnKemYrhNkdOjJ+5KTvz83NNHCc4ezZnuuwrV5y/uO56BAAKDsemKD2k\n+ezIEZVglQYuV1xJL7zAeQVly1K46/n4RTEkJTGEJMPuZZ0AFUNqquKb0Vt+5cszjPL668YpWe3a\nsTJIlE5QkNEyluN36mTk9AGA2rV538aNY+Jy9WpWvbi6J7/+iisHozAI0+CHy5h1uQu+678RiaF1\n0LNlZrhs7lzmYkJD+TosTDVD6WcFX73quuJk+3YKd7mfV6/ynoiASE+nYrh8mR7N4MFGJfTee4qG\no0QJ/v+++5gvKlTI6NHVqcPyV01T1VeCsDB6sVeu0FuyWim0X3hBfR7+/qp5UJSM4/e8WjXmA44e\npRen/y62a6cmsQmk+umJJ1TVlyMaNHDPIXTkCD2w61HqmR+CvPyidGnXpd63Mf47iuGXX/glPXTI\nNW8LwB+3DA3JDiVL5lxRpEdMjDMD5Jo1zklVR9rjcuWccwyOU8UAVbkUE6PYQsWKkh/cmTP8y67z\nuUQJCkg5//HjtOBff905nPXh/9s7+/ga6/+Pv87ZDbYRuRub29lojNxHKnKXiq8kRYjoW6QU9atv\n36I7ojuKb6VEUm5Kkgq5CylNcm/ldsLcheZ2bDu7fn+8vH0+1znX2YaNwz7Px2OPbWfnXOc61855\nvz+f983rPYrfQ0LsIQndMZQpw1Vwu3a+QmWnT6sdRWamPdE5ebLz+bndTCxfdx0d86JFyqF4NThl\nwYU3l9RH8T9+wTZUw25EYwHaoPm3g+HetIHXQHZ00oOxdCn/HwkJDHsFB6vz8HicHcPevWycGz2a\nx6lUiTpEp04xHm9ZdAxi/OfNUzmYt96i49MNov6/z8iwO5GYGDpLCdF16qQc2uDBNNyi5eRyqZnS\n8hoaN7Y7hjJlfI3xvffy8U4VRuHhvtV1UlTQooX/7uZSpbLvJbhYraTsuJRFLZ9+en65kSuAguMY\nRFzt2LHsS8vySvVUOHrUt9M2Lc23OUdWg0KhQjQsv//O8y1a1Lk8r2NHShD8/LPqZJbVpnzg0tO5\n4/DnGG68kSvoJ57g761a8bmkqUro3Fk1Jq1cSdVP6XLVHcPOnYxlDx2qDKMgzkQcg86qVXYjIcnt\njh256tW7uYWz12wbYvA43kFNbMLsqH74BU0xH20QjRQeU653UJAaVi/PX7EiHdSYMdRJeuEF3q94\ncS4i9ORtcrKSfHC76cBLlOBqv08f5hAiIphEPnVKNX9t28bwncvF67xvn/19qF8Lb5kJQUqCX3rJ\nd1caHKzyOsLw4aygsyw2E77wAhPZ/namJ0+qJHNOhnXIkOx7VAC+d7zlSXTkvZibhrhAZssW31kZ\nVzgFxzHIlvaXX9SEKSec8gd9+yoxuD17fOcMZ4dl8Y2ji/Pdf7+aDCbIG0vCBI8/zg/x3Ln8cpIu\nBpS42m+/ceULqA+1GFmXi6u+7LSSkpKUeJwMbpFwEcAKmrAwu1Fp2VI1OaWmqt3W0KGs7X7nHd9q\nljNnVChJDL3EwkUGXGjblg5t9GiGfX7+GceOAd/jdixAK8xBO/z39tVoVHwzGiMRETiBsRiAH4cu\nRUOsggvgSq5FCxVG1EN24nj0jvHTp5nfSExkeOfxx+k4pHKmcmV7OGbDBmooiWGXRG1KCq+BXsp5\n6hSvodvtW8YrDWRLl/La64Z53z46oPh4u2aRjsvF99grr/jefuQIX9d//5uzY5AcRU6OQQoBsqN+\nfWeZFSE4mGGw3MxeOF9yc355xZAhwIIFl+a5LhEFxzE0aMAtf055BifH8PHHqkMzOdl55Sp4d3LL\n8bzF5Lw/eN7Jq4EDuRJNSqLR97eKBFTFUEYGcw3XXcc3qxi8N99kojgkhLFtecz48Uo7adQo1bgn\nYS29m1nE2uT1lC7tK7q3bZt6LZLErFHDPtbx9GmGhY4dUyWslqUqZ7p3p4OZOJGr48ceAypUgAXg\n2w4fIi42CyPwLJ6/ZiyexQhkpHnw3A0/Yg+iMbzMO2iJxQgK0d7W33/P0JNUzpw86VtCqe9SRBfo\n8GHVcT1zppLvAFQPioS4tmxR/z+9gqdQIXuYRR8k36aNfZUpO9WbblLXUZBrHhbmu1OQsF96Ot+j\nMm8C4DWW6/v550qm25+Aozgu4NKEYvRkeH4c+1I5hssoiZFfXF2vJjuaNvWv3S549xvoSP+CUw24\njvf0KT2hq+O9cpeGKe8P5NKlzEmEh/tvolm3Thmn7dtpkG69lV22hw4pY9Wmjaqd37uXCq733kvn\nc+iQmvImq2p9BkHJkiz/PH2aOZOsLBo6CW+98IK6LrpWUtmydkNctSp3X717q/nNmZmMmxcqRIM8\neDA7i0+ehMcDzJiagXgk4VH8D19MOo2fcDMShy/CetTB6z81Qcftb6HIsBd4XO9+ieBghnVkpoQ4\nOl1o7/RpFVsXx/Dkk4zdr1tHZ6UnF2VojctFRzNwoMqVuN1qTkShQvb3QmiovYpG302JMxFlVR39\nenq/bzZuZPWZ9MboC5Bvv2UYrFkz5opuuomvTR/zqXPyZN7LtWRHcLD/xc7FUrr0+TWiXgy6gOVV\nQsFxDEJ2ZWX+mnWqVVNTs06d4irRH8WK2WcQ6FUqgsSmdfy9uaT7uUcPGt8SJXxzJBER9lryAwdY\nGZSZyZWuk1aSjK4EaIh//plGJyGBNeqZmXwuCbds2qT6FKZPV8ZKktMyrQxg6OLVV2lodI0dy2I4\nIy2NK1MZkRgZSQdyVkbi5JY9GIMB6PpgEURGAm89dxjPYgS2IhY3/3bWmbRpo+r0dRnoGTNUmGbg\nQP5PExJoFOX6yWsQnnqKDWSHDjF8tXmzCrsdPszj645BjHOFCnw/6GEhcY4eDx8jj2vfno7gpZfg\niEyj++03X+e2fz9DmE41/3/+yb9JXkl//0p5sTwmu9X5rl3Mk5QqpYbw5DclS9or3vKS+HjfsFp+\n8fffOZe5X2Hkk7sOYCpVUnFUbx5/3LnxKzhYfbhke+4Pl4srvjVrmFQT3XvdMTRrxh6CjAx+f+UV\n3+3om2/yzSZvuJ9+YugnNZWrW0mA9u7NxqnUVMbiAVZNiXOSstAzZ/x3PsvziMErWpSr+fvvG6ht\nawAAIABJREFU546halUaDVkpS6gpKEgdJyxMleAeP07jCrAb2XsQ/KFDfA5ZvX/+ObZ/sxF7Rv2O\nj6a3xyw8gtswDy2qpOCpZrtQ76lbcc5lZmVxJVitGlVCZ8/mKll2Zg0aqEooPWksPQQSvtE72CXc\nI8l76XDWV7R6k5jbzXBdnTrcgdWpQ8NvWfzfL1vGvITuGHKqWgkOpqNzksTQVWbdblZVeTx0Zv/7\nHx2sLCD0x+rhLSB7xzBnDvMP11xj77cw5MzSpXRE0uNyFVDwHEN4uP8tpj/dFX0GQG4aWdavZ6jC\nsrhCrVPH/oEtUoSGYNcurqxfeYVGVkoQARrktDQ2R61ezbCN7Ar05OGiRb7SEXoZaZ06FEYDGBZZ\nv54ORH8d0sEsu4jx47kLEcO/YwdX/xKKCwpik9knn6iqo7AwJW5XpYqKz0+cSO19nXnzgNdew6n5\ny/FF3Xcw1fUDloW2QjWMxe1l0pGMKiiNQ8AoKAeoXzuRapaQi8fDWn/ArpUEqA+thOHcbv5P5Peo\nKCUFIivMQYOUvpI4Bn3HUKOGciIPP8zfv/mG97/vPn5v2pRhPTm2CPv5Qw/feTuGRo24sr7rLh77\nqad4bP1/KI5BN/4jRjBMKCXGIrfhtPjxLpe+VHTtyg5qfabDlcb27Rc2PzqAKTihpIwMfkhbt2ZM\n1ruMMrfoDVv+8I4D9+5tzw/Mm0eDFx6uDE50tKoqArhjOHaMhichwZ6o81dVoks6yAq3Tx8acL2U\n0Tt5LuebmMi+gNhYtTqV1aaIr8n9+/a1JzFbt1aKrq+/zg9KZCQsAH9PWQCsXIk9W9MwYQLQPek5\nFG7XHGVHPonPtzdGT3yKPVOXY0ODBzFy0EE6BcE7bCaGPzFRxfWPHqXRBFTZJkDn2rmz3bF7NxLq\nOwFxbDfeyLGltWsrI6rvMNxuFYv/4AOWn4rBlfBN27ZKFfbuu3M2fJUr83/u5BgApY4bFua8OJFd\nsB6qkv+3qLYC/hc2OTVY5hebNuWPZPXRo2p+dX5Ttar/KMQVSsFxDJs3cxUfEsLQi/cKLisr+zJW\noUaN7Mvrdu606/IDjHVrk+tsz6mPNaxVSyUP//mHIZnoaBoYt1s5Bn8hATmvrVtp/AsX5uq9Xz+7\n9pL3ZDEx/vqKVyaj6eihiWeeUeGi7dvh+flXbCzcAEuXAh9MDsPd/4xH4yNzUBKHUeb+1ohuXB6x\nNUOwaBHQ5InGWP/sVPyO+lhQsS/uxxSUfPM/7GOQecyyAxBuuYXfpdR1yhSG62Sl1qMHeyv00tGU\nFJVUF8LCVEhs0CC7/LXuWLt2pYMIDma4yJ+CqNz/r7/sjkGuZ2ysUlTNjmuuYd4kJUWN+PTmxx95\nXfT/XWwsnU5MDAX/9Pe15D5cLuU4/ZUrX64dw8VoJWVHZqazCKMhV1xdjsHj8R3KnZVF4/Djj6ok\nMDVVNbwJZ844zzwGuGqVZh4nLRmdw4dVwtZ7deZy2ZvdvD8UBw74Gv3atVkFdPSoio+L3pEcUwgP\nZ2hEVmAtW/IcZDbAV19RQqJpU8aTJ03i60pI4P11rSQ9aSmcOUNdnlGjgJAQ/I1S+N+/12Fowkxc\n370mOnak1M93CwqjafBKPFbuK/yGhjiNQpiPNvinXit8Puh3PPpKJOJe7o44bKUkOACsWKHOYeJE\n316RYsWYMwgKovOYOZM/r1rFv+/apYyfvA7vfg6ATvHRR/mz96QyXStJKF/et0vdm9RU7rTEMWze\nzPxHTu8VJ1q18q+1Jbsb/X1Vrx5nZIwYwRCgPsWtc2dVaSfCj/6M8OXaMaSl5U9Fzz//5Dxv3OCX\nq8sxvPcet9w6EydyK62/+Zo1sw9/AbJfubz/PmPmlsUa865d/Z+DLurmtLL3ePhh2LOHRkpWwgAN\n//TpvhUOZ85wF7J7N0soZ85UMWV5XTt30jAtX65yFZUqKXkFEUlr1YqSCcOGUSiuUiUmMCW/Yllq\n+ljRoj614Is7jMYbG27DQ8sfQD2sxperKsOTdgYj8Qy2bqUP/e4bDwa/XhbdJ9yKmGF9UAjpiMcf\nKJy4lL0k+pwJ73i3201DJ5PWAFYtieZQ79487z17mNiWax0UpFbDsmrWV+5JSb6lmJUqqR1Ho0aq\nUEAfN1m2rHJeOnPnqgS/hAMjIuxVaBfiGEJCOBc6O7x3DJUqMWx27Jj9Paw/v1RZ+TPC+pyLS8mO\nHfnTy5BTV7YhW64ux+A0FEZ2EPKB2L+fxtNbfE2UHiVRpyNzBaZMYaWRqJbmhMfDsI7EfevVowFe\ntYohmzJleEydxx5jF2VYGBPTgEoi9u5NRwcogyiPz8zkcStUUEPk3W7eLyODH5SMDL5ub6dYuDCl\nC8SQnDzJyqZPPz2nv/QjmqMjvkbve0/ir+0ZKFf0OGajA5Z8uBWv4gXcjrm8xF26sOnq0UdZiSPG\nVti/376r0yXJ+/WzaxQJM2YwTBQbS+Mu8f6NG1Wfha5vBHBXIeWwbjd3IOKQPv2Ujxs4kAZ+0SIl\nLdKpk+9gJSeGDVPFAJIET0jg+ywuzt7kl9e0a6c0iPr25UJF10oSnByDP7p0YS7qcpAfyqRXWV/B\npSbwHYN09OaGMmV8xwVK/4GspNLSuBLWR18C6gPktNKYOpWlmCtX2m/ftcu36Uze5FlZNDAHD6rQ\nT3o6P8AnT/qukvQEnAzICQ+nUZS/Va/um2do0oS7pAULaCiDgpSh2rhRJW9ffpkliU6jS8uW5eOf\nfJIhq7NaQcfTgjEJPdEbE9AOc1EmtjjWu+ti7CupeHllO9QN2eRr+HfuZOz/8GH/Q931lXvLlurn\nDRvUa3W7uTOS+RfR0fxd/iaIsfv9d7vhe+wx1UB37bV2McB+/exaVY0a8VwffZSOIac6/v37eV11\npVmAO40tWxhaWrGCz5EfKp/vv8/ku46TVtKAASpno2tEOaErr15qnPJvhstK4DsGIPcrCj0cNHgw\nt9aVK9sHv8yaxaSunvSVxwK+Blv0ezIzlS6QlG1Kx7DTueoOYvVq5h0yMvjha9dOGYzISDorSeTK\nY559lgZ01Ci7RLe3Y3C51KwFMRZiHJYsYRmlqH0eOsT6eyd+/BE4dAinS5bHikmbMTBrFGoPuAmj\n8QSuwVFsf2gkPrxhAq4JOaVW80OH2lU3u3dnZU+/ftQbGj3aWUTtzBle/9GjaRTEoC9frjqQ3W7m\nDPr3Z4hm82Z1zXQHkJTEiqgjR3xXxCEh3LVUrcoSZen6ltWzOAB9sM7+/WrGsnDsmN2ROGlRicCd\nnrTfvp07C5E/z0/++ou7UZnF7E1IiJr1EEgUK5Y/3c9ly17aLu6rjMB2DGJcczskXBzDxo0MhZw6\nxZK1r77iyrZbN19VU8FfE5Aojno8DOUASl/Ie7UMqHJWcTSWxRDG7NlKJVTnxAl73T1AR/LMM8pQ\nHTnCOHJoqDq/Dh3UTkq0kg4donBZhQqq2SY8nGWQHg9LV6+5Rjmz0aOBb79FVhYw59+zUGHSKyiC\n0+j71nW4xkrFxx+7sAb1MBpPIuraNJ6jPnnM29Bs2MB6e33VL9o90tcA8LX07Mn/h1QZtWvH//Pw\n4dyxfP018znPP68qh0Raw+1mCSjAa9uwIXMXN9/MhKtQpoyaIdyjBx2LJOODgljFA9jfX051/g88\nYJdjl/eKvnOpUkXlFURvKDSUeSER4MsP/viDO1JpQsxuumAgor+f8pLQULMTuQgC2zGIjENu44U3\n38wEtFTZSDgnOprzgfW6+xYt7EqVxYoxd+DvTVq9Oo81caIyCNdeyxW/TpkyaiymnAPAevdevVSy\nU15TcDANv6xm9ccAXEF/9x0fW6KESnSuXKkcw759fG179rCJye1mKKVTJzVJDWB1U1oasHgxTu/c\njw+fTEK7DsGoHJWOJ/56Ah/gERxFMWz6aAVexhDc2sJSMtt//01Z6n37GKKQ/0uZMpxpMG8er8c/\n/yjne+oUz2P2bN+Kr9Gj7TMDunShE4+KYm7lscfsgnA6jzyilGA/+IC7uuho/v9E5hpw3mnqq/2g\nIF4vQDX5ec9COHWKu0y9wU3fKQh//skQpdvN8GXjxnxMfpVjComJzDMNGnTppCzyEm/F3ryiaFHf\nsLIh1wS2Y8gpYeaNVNHIKt/JMMhtS5b4zqrNbrC5VIp4PDTClsX763HZe+7hKvfYMbXq1ENLgwcr\nBdOoKN7v6FHfFWV4OO+vi8+9+CJlFzp1UtPNvD9Qp0/z/Dds4M6hRQtVepqVhaUri6ATvsKND8ah\nXkI6xqMv7sV0PFd4FNZnXIc7MAfFcFyd87JldEhyvSS5/9dfytj9/Tdr79u2te+GundXP0vs20lP\nRoTkypalEdZ7ELx3d+JUY2KUowkNpfF1SvL6C0FOmMD31c6dfJ7du1Ul05AhSklXzh1w1kpyGpyk\n7zwvhWPYvj3niYGBzJ49vkOA8oJy5VR+xXDeBLZjsCy7CqY/vvqK4Ze9exljFaPsZCx04+UtgXHH\nHQxj6EgVkF7jLuMVS5dWlS8AE8U//MCdxaZNakD8Pffw78uW8YMcH89VtDgmvXwT4Op5/Hh7yeaW\nLYyXJyYqZySqpFJlJJo/zz/PTtfgYHh27sazXzVE+W/eQ4+nyqIkDmPIyWfwTo0PsBzN0AuT8Eja\nKBSGV/L7lVfoFIoUUQNehgxh5UpsrN3YyRQ1ubbXXWc36mJcCxdm6ENPyD78sOonSEqyJ+FTUlTV\nVadOdu2jyEgmrosUsYvo6fjrUu/dWymjzpjB17JjB3dugP0c/GklFS3qHLbJyGAiXHpH8tsxfPZZ\n9qKOBsMFENiOoVAh3+oLJzp3poE5cYKxacGymG8Q4w7YV/jeH9jSpX2NSa9ePI4+ZB3wX4YYFcVh\nQAkJXJFGRjKMJY/NyOCx9NiqSDFIhZMeirrnHq5Mz5yh4QTU0B+Ph69PX+ECyEo7gx0HI/D4gjtR\n5vsJ+HlZJn5aWww7f9qNj/BvtMV8tC7+G0Jx1mDrarAAZZnLl1cOtl49lsKOGMFzmzlThesAZTSl\nucpbNE93EjVq2MNmgqzuQ0MZlrrlFiqxvv762RflYGDFuGdmsjrL+3hPP81jZSd/oh/3wAH+//UZ\nxk5aSUWL+jZSCuXKccHRqxcfM2vWVafVb7j6Cfx37FNP+Z9apVO5skpkyuq+RAmuymfPpgHYtUvF\npoHzC1MB3JWI7IRTmKJZMxpH7won0WxJS+NtK1fSYGzZQkM0dy5zGFLtJElYgGWU5crZtZKOHlXH\nP/taT6EIhuE53Ilv0XDVe4h962EcLxaN9RXb46dpexETA7iDtJi4v5BZ//78XqiQfVQnoCqgMjOZ\n7BXEMcjMA29doMWLqQOlO9Pdu5lgF7Ky6JCaNmVYSu67bh2dabdu9oqqBQsYEoqIUIl1bzIzGSLK\nblxr2bL2nEG9eqr6DFDOUR9xKppFTsjuZ/BgFfq6yuYBG65+At8xzJiRs9R1795clYvREtngokVp\nfGfNYlK0UiX7yk8PD6Snq0SkP8aNY9gKoMFJTFQrWkCNehSjLiEUmYsMKIM8cyYNVkgIq2NKlaIT\n/PhjrtbPNpaheHGep96Qd+wYq4vOxvy/wx2oh9X4Mag1bsViDC82EsetCEycCERl7GTo6rffWE0l\nyrJOoZczZ1SDX6FCynE++CDlM3RRPf3xLhcNvwzt0cUAAYZWmjdX1VwAQ0STJ6vf33uPfRYvvsjf\n9RCix8Odk+5w3n6b13rSJBVjX7xYXXtAOVB/C4C+fRkO0quMvKUh3G6+Pn9lvt7oMhsScsqP0ZVC\n7dr+VYENhgsk8B2D7AJ0jh61r9jlw/jDD1yJhoSoGmYJY+gjFgGGePQP7IoVrId3Yts2/t3jUaGq\nRYtovEWrR55jwAClleS0Kl+/nuckpY0AncLy5Qx5XH+93ZCVL+8j+Hdm32HMaTgU3y0sjMF/P4t+\neB8v4kXMbfACBoWNQ9siyxCGNNbPHzrEHUejRlyhjxvH3oIyZegsunRRB5bGOoBVWm43QzQiEHf6\ntJrPLM66b1+u6ps35+81atiVSAElCqcb7aFD7f0ZkpSX2yScBfiGYqZM4TUOCuJziQTIiy8y/CQ4\naSXpSHeyPsPZSUzu1Vdz30vj7RjyW5iuWTOVwzIY8ojAdwxOc2ErVrTvIt58kwZOYu99+/pWwOjG\n4c47WQ2j36d1a+eQw9tvU5OnaVN7ohlQBl6Mhrckh55UFuM1fjx3BmvXchfToAHPrXZtJmWXLrVX\nKZ3VLspEEPYgCq9FjUV57MWwTR3x/vvAjoxorEY93Hd8PEKKFeFOROQSZs1SwnNCZCQN6IwZfO6q\nVWmww8PVdbYsGt4jR4Bff2VHtFwrMfricNu3t+dGBg60K5bqoyz9qYYCaicn/6dTp1Rex+3mTkp2\nUaKa+e679mN47wx0rSQnYmIY7ildmjsHl4tltN5aRc8953uMr79WOxKdS+0YKldW3f0GQx4R2IN6\n0tMZCvLeMXh/4KTksVgxGhgnfXf5sJ44oZqV/vhDhSzEuA8YQMNdqZKKFcuMXDFMDRpwJZ2erqZp\nOXVvStfzkiX2c5JkeHAwh+MsWqTi+IMGqWSpx4PjJ91Y9EccXsZK7Ampgtqls/Bzyo2oMXUccEsV\nYGtloH1JxrynT+f3+HhWCpUvTwfwzz+cxjZgAJ1XZCSva1wcHUPhwtypWBYruzIzGVKSBqGjR+0h\nOEAZyg4duMqXENvzzzMn9NBDDKE5GU/9/yF06EDHqDuG6Gg1MGfCBIaSKlZUzz1njv0Y11/Paw3w\n/hL+8bdj0CU7unbl+8ffXG1vnnmG7yPv3VFkpBqMdCkcg9ktGPKBwN4xSOWH945BjwPrq/7QUM7L\nLVeO8eu4OHuJI6AeV7myc5w9KYmrR10WQQzQ8eM0rN2703DKqlmOo4cxDh5kZc3u3TRWspsBlEyE\nvI59++x/f+EFLMKt6NDRhdpVj+PNn5tgYP2fcWCfhYXDElEDm9U1iY1lc5Uks/VxkhERdGI//khn\nI9VCt95KRwHQgPfowVBWSAib2EQGRHIGlsVjduqkHKhelaMbeZFk+Osv5l9y27zkdtMpyQzgZs3U\nRDmRABcjqxt6PcTz5ptql9anj9JKyo00wrBhuXcKAB2WU3ipcmXusABes/yaaWww5COB7RjEqOit\n7WlpDHGIkQgLU81qUnqYlUWjsHUrV5mVKyvjJR/aMmXsqzldg6h+fRp279Xu9ddzxzFnDlet4hjk\nsR9+qO6rN7Zt2cIdQ0wMnYcMBCpZ0pY/OIkwjMEAdMUUdAydg86dXZho9cZPNz+PB7qmw1XyWvt5\nZmWp3+fNU87MO4TiducuRv766yxJnTqVu4+FC9VrkHnR8nx6glkM9cqVFJAD6Ix27KAarRNxcdyZ\nCUFBajgRwJ1B/fqqcmn5ctWdrId19DxFUJBvh/INN9hDWzqzZyttpvzA5eIO8Ndf8+85DIZ8IPAd\nQ9WqKlQEKJ0fMerh4cC0aUz8imP44QfG8AHuGJYsocEoVUqFcVauVEauY0d1/MxMrrSHDuWcAp2n\nnmLYR0IQYtSjoxl6OnRIrTp1SYzNm3mfJ59UUtoAEBaGjMJF8WdwLYzBAMRgO+bhNrTCQiRtK4Se\nPYHmp+fBlZGuqonknB99lCGu999Xz7N9O3cDJUqoQTHAuc5nHDzIn2vXpsT0Wa2kc0gVVWgoczZ6\n97Y4BnGG+qpdkvhHjyoFWjnWbbcxpKM/D8DQTc+e6vdevZiYF2ckz6HLckv1kdut8gDZKYLGxqoB\nQE6MH5993iMv2LnTt4HRYAhwAjvH4CSJIbF6WQFLfN+yGOq47TZWrYhhcrtptCtV4opUn8Ylxlsq\nlt5/n44jPJzNTt55A4/HXpNerRpDS6mpaqV8zz00OLpjkOTy2clhxxGBz3E/1k1siE9W34sI6xja\n41t8hu5ohbOibxU+5veTJ9nnIJLT4ni2b6dYnuQjPv5YDaCfMYMhHdFx8t4x3HQTG9T69uXgngoV\naERlpyETzgAa5uRkOqEWLVh6KscE+LhvvmEH7qlTSrTugQdYSjp/PsNze/faJb9lZoTg3RTnzcKF\nDIsBVF2tXZvP609g8eBB5/kcOtJkmJXFcFx8fPb39yY3u7D87nw2GPKBK9cx/Pe/TDBmZXFl37Qp\nO11LlOAOQnYBeoxbJA8E74EsCQlqx5Ca6mt0JOY+aRINYmgowxTiFADW4586ZR/DeLaTOXnCj1i4\nvDDG4GeUxGG0X/IR1oYvQezJtXDDy8h89pl9khjA1efGjSxD7dWLYRd9fOGxY3RoXbvyvjJ9TXYM\nYviXL1creI+HOQZdYPDpp9XPjz3Ga1K4ML88HoaBJOSzbZtKbut9CTLnuHt3Guny5bMPqchAoYgI\n57/rcxuio5X8hr8dQ27yBdu3M1eSlsZrnV2HtBO5yV0Yx2C4Agnsd2xoqO+kNelclhi3t6xEz572\nlb6eRzhyxK6VJIZ30CB+r1WLRj88nGERaT4D7HIZvXoxjPTFF0yyxsXZ49iFCzOstHUr0KgR1t43\nAo9v6IuGj9+A75eG48HwL7BgeRgGYRSqn1wD98yv6FBatVJyDD162PsqUlOZFJ8yhav3uDiu3l9/\nXcXZN25U99fDYEFB9jLKdetUSGrXLhp3fwq2YWF8bSdO8Fq43fYeDEDtIurXV6t0MbL6gJzsmDZN\ndV0LJ05wJ+REeDjPIbeS7E5s2MDcjNvN94+TyJ8/ihb1lVB3wjgGwxVIYL9jq1VTK09BupMjI2l8\nvB3H1Kn2uPKBA+oYO3f6DgifP5+9CgANYK1aXN3efTcdzLPP0qHo8XCAq3NxOl9+ea6W3AKw7u1F\neKDMHFSuWxx3PloJrWf1h2UBvz/zJWZVfxZPnByG4JJamWNEBBvDKla0N+IFBTEXEBqqwhZiZHTn\n59RI592j8cknduMvj9m+nTFwl8u3JFXn5EnmJIKCGFrSd1uyq4uP5/W9917/x/GHNJvpHD1K4T4n\nsrJ4XXKSNZk503/J6FtvsUdBnvd8dgz79uWuo1kmuRkMVxCB7RgAfni9E4TXXUehultuUTsHKQEN\nDmb4IiKCSev16ymVADiXTkpvgqY7hDFjuFqVqqQSJVgKuWSJvQnu7Go4LbY2Zj72I8ZcOxQN8Rua\nPNcc1+Ao5t34Ku64A5jxv4MYE/EcKhU5yHxBmzbKGdWty+dp0UKtjufOpeMLCmLJpi5PIUZMN4hu\nNxvNdHRjFBzMKizdMXhfC6mgmT7d9xoBKhQlz6vLfHgb9GnTWDIsnD7tmwRet86eWHZaWZ8547/c\n0+2m88tuVkdWFh28v1zAoEHMbTjNV8iJ8PDc318XHDQYrgAC3zEsXMhegOPH1apSVpEHDjD0UqqU\navQJCmIMeulSJlUPH2ZSOTWVtf7eK0wRQ9PVSzMzmSiVDlthyBDgjz/wFypiLB7F05/WQpUKGbj2\nWuCtj4phSXoTPIHR2F/vDrwbNAg1wnahXz/glu4VGFoSY713LxPUZcrQKbzyiv15bruNK1KZ36zr\nOIkRe/VVpWYqBltPtuqls0KJEmry2eHDLOXVZSfCwuwSGTpy7Z20kpxW7bqR37jRtxFr2jSG7YQv\nv2T5qM7FVvPIriinUI7TRLa8IizMN5dlMAQ4ge8YpHKkfHk6h6wsJYeRns7VtIRCJk1iOCAlhfeR\nZCmghMbkdxkOEhnJ1foPPyij6fHwuN4hGo8H476LQnVsxlLcgv2IxKev7MKePZwN/9UMoDs+R7Ff\n5/PxUhkFqNAHoMZHjhjBnY2/cEhQEA1LmzbMAwDKeDVpohyB280dyB132B8vpaOCy2XfEWzYoJys\nv0TqXXfROS9cSGeVkMBZD3IdGza07w6ElBR+r1uX95HfhTFjWAkkrFnjq6Kbmxh+dshOIaeVfX46\nhkvR/Www5DGB7xhERC84WE0Ckz6CM2dobMeMYTJYehxuu40CcXrFiqyuAYaawsLoPFq0oITz3Xcr\nQyWOweMBJk9G+uLlmPZkInqs6I9RX0Thd9THl+iCyeiJm2oeQcniZ41k27bKCJ06xeohmYuclcXQ\nl5x3ejqnV8XHqxnGa9faQ1jVq9OBZGaq16LLS4vhdLmYmL72Wpaiyn03b/a9nmL8GjbksYOCeEzR\ncvJm1iwO6pHVe1gYw3biNB980L9WzwsvqHGTTrMUdJwcU7lyuRevcyIkJHdhHJeLDvp8Qkm5xTgG\nwxVI4DqGxYu5Q9ixg0ZIxm6++aYqO5UdQ9GiNFhZWSzRLFKEDV6icgrYk7GffcZE9KJFNAYPPKAM\n0D33AJmZyAoOxf5jYfix5wS0eqgy3ptaHNWsLfhlwp+o+ct4dawmTewjOL2Ny6JFDOtkZamqJqnU\ncbs5hlTkIE6dYoJXavynTWOYLCODr2/dOqXDA1DZ9Y8/VAPgq6/yNcvxnUo55fzke/nyOYuwicy3\noA8ZeuQRZ0nqpk2505EpdCKI548+feySInmB252zlLrQu3f2zXIXcw7GMRiuMALXMYwdS8O3YYPa\nMWRlKbE5Yds2FbvPymJFTEgIv+64Q9XFSznr6NH83rixMm5na/gPoAxeXnoL7sdnKP9Ie9ScNQzd\nMAWtdnyIJe3fxlC8zI1H48ZqCllICA3grl006GJwk5KAl19mnuLXX+3JVYnjy+1BQXRcKSlM0n7w\nAf/+9NM0+vv20YDXru17nWrUUBVKxYrRgUh1UXZVRsLttytHdOaMXbNJsCyGraR8Nioq52N7Cwv6\nG2wjeM9BuNS8+27+5AJ27PAV2jMYApzAdQxff82EsdtNaeT9+7ly1stX16yh49i6lat2Mb4eD2Pu\n69YprR7ZMYjeTmSkbSW3CvXREovwlycK9RqF4KdCrXHosZewD+UxBK/AHezmTqRECT5HXBxXmEWL\nMgl+992sIBLHYFkq1JWSwrBI4cLsNp44kaGc777jKvnkSZ7ro4/aQyeyw9i923kYiy6mnpx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CRspBv7TZvYYVykCLBoke9j9PuOGwe8957/49evz6+cEEVWb7ZsYX+EUKyYXVsJYChq50410tNg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\nAElFTkSuQmCC\n", "text": [ - "" + "" ] } ], - "prompt_number": 121 + "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "In this example the noise is extreme Yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter.\n", + "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter.\n", "\n", "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" ] @@ -816,6 +819,7 @@ "collapsed": false, "input": [ "sensor_error = 30\n", + "movement_error = 2\n", "pos = (1000,500)\n", "\n", "dog = dog_sensor (0, velocity=movement, noise=sensor_error)\n", @@ -844,13 +848,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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48MEHeeWVV3I05RgMBgx5/MObmmnVZX9/f/z9/c0pjhDWU6oUrF2bo8388mWd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\nsuohISG8/vrr7Nixg6pVqxq3h4eHM2j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Ak5MTISEhAOzYsYOmTZvSu3dv/P39AfD396dv376GnEaIEuX6dTXyZvny1IAP\nUKcOVKkCHDqkFkSxsoIzZ1RBNUMdOKAWMpfZuBbP4Cqbx44d47XXXiM+Ph4XFxe+++47kpKS8PHx\n4dKlSzg7O/PTTz9RpUqV9CeWnr4oLjZuhKQkMKTzsmED1KtHUrOW9O+v1qedPz+bfZOS1I1da2t4\n6y2Vjhk/vuDnBoiMVAE/OVnKHRdzUlpZiMK2YQPMmwf79hXo7XfuwJaP9rP560i2lutHS9swtvxd\nhdJ10qx6tXMnrF2r6imktWKFKoT/449q2auffsq8+HleRUen/2ohiiUprSxEYbl/X42f7NlTTW46\nezZv75s9Wz/Ddts21VFfcaYTHQc58691J3Zca0np6pXSv6dGDVUIP6OOHVVq5tEj2L8/l3oLuZCA\nL5CgL0T2Vq1S6RUbG3j1VdXrzk14OCxcyJ3y9rz5Jrzxhnrb1q0wZnk76i2cCM89l/nGrKureu+j\nR5m337wJ//yjyjVkKpYvRP5I0BciO3v3qhXGAYYPh++/V/n2nPz3vxx7bhqtutqSlAQnToCnZ5rX\nX3lFjb3MqEwZNbom47cJKyv1DeDmTVlkXBiFBH0hsrNvHzz5pPq5WTOoXZu7AXuz3//2bdZ+E8cz\nmycyezYsXQqVKmW/eyaVK6t8UEYtWqgbsVmukCJE/kjQFyIr0dEQGwtNmhAbq9b47qz7myovdOP1\n1+HWrfS7x8fDlH5nmYIvf/xZikGDCnDOzp3VsMqsPC6pLIShTBr0k5NNeXYhcrBvH3TqxOq1VjRo\noDIs/zfDhqtXddjYqI7/pk1qtuyECWqM/akjj/jnl4iCz31asAD++9+sX5s2Td1fEMJAJh2yef26\nJus5CPO0bBlB5yrSY9nL7NypqiCntWsXvPYaJCbCsGEq5d/AKUHd9BWiEBXrcfqnT2u4uZni7MJi\naVqeJiddu6ZWppo/H158Met9Ur6pStViUZQMDfomHf917RoS9IXhdu5UxWxu3ABbW1WzJoOkJFg5\n4V/cLwXQfsOHOR4uMRFeflmVvcku4IMEe1E8mfR/2+vXTXl2USJcvw4+Pqr33qRJ6hDLNIKD1SCc\nJXvc6LP1LaZNyzwcHtQytQEBqtpC2bJqOdksBQdnfQAhigGT9/SFyNYTT8DmzTnPJPXzU93yWbP0\nm27ehMuX1WPPHjXy5uOP4Y1hNlyr2ow3T4TSrl0pPvhAFbO8dk3Ni1q/HlxcVA9/xAgoVSqbc44c\nqcoyPPU0FBSjAAAafklEQVSUUT+uEEVBgr4wT1evqtIHjxfjyZKmQUyMCsCo/59efx3+/FNNXq1d\nWwXxwxNXUrepM5Trir2bHb99eJhV59rz669QrZpaWLxFC5g6NY9D4bt2hb/+Sg36+/apCmoFrYkj\nRBGSoC/MU1CQWkM2p5uuOh2sXAmoOU0jR6pqCT/9BKVLP94nIQHqvg/9d6rnrVujO3qEV99sz6uv\nZjhefDz0HwiffZbzmPhu3eCLL1KfjxkDS5ZI0BfFgkmDvuT0RbYOH1bpnVwkJ8OUKbB6tYr/3bun\neTE2Fn79Va032KSJ2ta6tapRn5VJk9Qd33r1cj7pk0+qHFBCAsTFqdxQHtoqhDmQnr4wT0FB8NJL\nOe7y6BEMHaoyPMeOZVGA8pNP4NNP4bvvUreNHp11sv7779XXhX/+yX1Yjp2dygMFBakZtF27SiE0\nUWyYdPSOBH2RrePHVXoH1M3cpUvTvXzrFjz7rOrpBwRkU3H43XdVDfq04y6trTOnjG7ehIkT1beC\nypXz1r5Ro1Q6aNcuePrpPH8sIUzNpJOzHB01IiJMcXZh9h49UrNbrazU8oGDBkFICMydy/FWQxny\nYT26doVFi3IYZZNXixerOgtr1+b/vW5uKrfUurWBjRAib4r95Kw8TpAUliZtvfl27cDWlludezLj\n0ih+THRi9hw1Usco/++0bZvl+P5cJSWpFFTLlkZohBBFw6Q9/fLlNWJioGJFU7RAFBeJibBi9EE+\nWuVKLx9bfD+1pkaN3N8nRElUrJdLrFFD8voie8nJamnYJk3gx9AO/LbLjqUrjBDwk5LUiBshLJBJ\n0zspQV/KhJcAd+6owfEdO6r8eL5WD8ksIQG8vODhQ/j66wyrTxkqNhZatVI3cCW3KCyMSYN+9erS\n0y8xZs5Uk5Nq1oTt23OuVJaTR4/gzh3+s6g65cqpwTFGj8s1aqjCbGFhshqVsDgmT+/IBK0S4vhx\nVXS+d2/YuLHgx/n7b/Z2/4ilS9Xw+kLriLdurb6RCGFhjBL0k5KSaN26Nb179wYgNjYWLy8vXF1d\n8fb2Ji4uLsv3SU6/BDlxIjXob9mS+wLi2bi17yRDLn7MkiU511kzWN26qm7DgweFeBIhzI9Rgv6i\nRYtwd3dH97hb5ufnh5eXFyEhIXh6euKXRX1zkKBfYly9qtIyjo6qhEGtWnDwYL4Pk5wMby9tTY82\n13ncfyg8ffrAwIFQrlwhn0gI82Jw0I+MjGTLli289tpr+mFEGzZsYNiwYQAMGzaM33//Pcv3Sk6/\nhEjp5afkYvr0UROq8iA5GQ4cUJNn69WDCzEV+MwvoRAb+5i3t5pUJYSFMfhG7jvvvMOnn37K7du3\n9dtiYmKwf1wS197enpiYmCzfKz39YiI0VN3wzC7BfuMGdOmS+vw//wErKzRNfQm4dAmiotRgmbg4\n9d/QUFX37OxZlWnx8YGAlddo+tyT8MStovlcQlggg4L+pk2bqFmzJq1btyYwMDDLfXQ6nT7tk9GG\nDTM5ckQN/PDw8MDDw8OQ5ojCoGnqpufKlfDCC1nv4+OjHsDt27BunRXff68yPLa2KqjXqaPq41Sp\noh49esCECdC4cZpyN38chWnTpHiZEGkEBgZmG18LwqAZudOmTWPlypVYW1vz8OFDbt++Tf/+/fnn\nn38IDAzEwcGBK1eu8PTTT3MmQzlbnU5HSIhGz55w/rzBn0MUlpgYdUf1iSdUBcps/oBrGowbBz/8\noOqPDRumxtlXqFDE7RWihDPpjNy5c+cSERFBWFgYa9asoXv37qxcuZI+ffrg7+8PgL+/P3379s3y\n/ZLeKSY+/1zNktq2Ldtd/vc/lcY/dw5++02tMysBXwjzY9Rx+ilpnClTpvDHH3/g6urKzp07mTJl\nSpb7V64M9+/LGtNF5tEjuHgxf++xt1d5mAULsh3pcu4cfPSRygBlWSLBzw82bEitsAdw8mT+2iGE\nMAqTFlzTNI1ateDff1XOVxSyGTPUTVYj/soTE9XqgQMHwvjx2ey0fTtMn67yeAkJatZucrJaHcvO\nzmhtEcISFOvSypA6K1eCfhG4cUOt/2pEn06OoVypKowdWyb7nby91QPU8J1Ll1QVNRsbo7ZFCJE7\nswj6ktcvIgcPqi65ATRNrWXy99+wbx+sX1mWwwu2Y2WVx9lUKcN3hBAmYdLaOyATtIrMw4dw6lTq\nEoT5lJwMP/8MzZqpTvsfAUm0bqWx36E/dZ92MXJjhRCFRXr6luLoUTUovnz5vL8nLg4WLSKgwwym\nTFHZmM8+U2PsdTNmwZ8n4Np+aNSo8NothDAqk/f0pdJmEalRQ93IzY+zZ9n2wzVGjoRZs9SQzGef\nfTxU///+T826at9ecvNCFCNmEfSlp18EXFzU4HlNg7/+yjyCZ9s2tehsGmH7oxkaMZu1a9Vk3HTz\nssqUUauSG3GmoBCi8EnQtzQ6HbzyilpA5DFNg9XBLVj7qw2JiWrb/fvQb14H/u+pvXTtaqK2CiGM\nzuQ5fbmRawJt2kBQEDRoQEwMvPYaREY6UOnOq3xQP5GJk6z55x9oVi6UcQMl9yZESSI9fQuyb59K\n00yMmcr/ltqwdKlaKrZFCzh4UMfu5z7lpzf+ZP9+tW74khofomvU0NTNFkIYkcl7+nIjt2hER6tC\nmO+/DwnHbAn64yZXrOHn7+/TJfR7KP0WdOlC+/CNrF3bQ71p7VtqjKYQosQweRmGxERV0uXRI7Ay\n+feOkilx0gd47ZlOt54VmTULiIxUKZ6YGLWe7RdfwI4dasbVpEmwf7+pmyyEyIZJq2wag7W1qrke\nG2vqlpRQmsaM/9ljXdaGjz56vK1OHejVS60PGxCgBt4DdOigRvYIIUosk6d3IDWvX726qVtSsiQk\nwOpFV/k+fiCHfy5DqVKPX9DpYMUKNWwnIADWr1fbS5UidSchRElkNkFf8vqGu3dPVU4+fVpVMt60\nCRralWJd14XUrJnF4vTnz6u8muTthbAYZhH069RRw8ZlPHg+hIbC339zKugRn21rxqaIFtxJLEe9\nejpcXKBnT5gzBxz/M01NzMpKSmonu7VvhRAljslz+gCenir+WJyYGPSzofJp75zdPPe+O89864NL\n/SSCavfm/nszOHNaY/NmGDsWHO+egZ074dVXsz7IU0/BxIlZv/bBB7KOpRAlkMlH74AaTNKypYqB\nFrMmtqapxWRff13NkN2/Xw2aT7s6VWCgurE6fbq+Nx4SouLxkSOq/M2QIVC2LHD1KixdClOnpu+5\nP3z4eId8uHxZfTsICQEnJ4M/qhDCeIr96B0AR0dVu8uiRgpu3KhuZLz8snr+0UcqCZ8iKQnefhuW\nLyd5/EQOHtAYOxY6d4aOHeHMGfX3Qh/Pa9aEadMyp2ryG/AB3nlH/bGQlW2EKHHMIugDPPccbN5s\n6lYUkYQENUvq009Tv9q88gqsWpW6T2IiRwbMZnjnEGp9PYORz0VjW1EjOFj19AsSy/Osdm31X5k4\nIUSJYzb/qi0q6K9dqwLrs8+mbuvfH3btgthY4uNhpm8Znv2mHy3blebAv9acavISvgOPUbNmEbTv\nww/hl1+K4ERCiKJmFjl9UNkMBwe1SHq9eqZoUREaP159yEmT0m3WXnyJfxsP5o0t/ahdG779NrXT\nTXKy9LyFEAbn9M0m6AMMHary1WPGmKJFRSgwEGrVUitZof7QrVsHv668S3zsXWYsdmDECBlJKYTI\nrETcyE1hMSkeDw99wF+1Cvr0UYtPrf21NOGf/crIEZoEfCFEoTCopx8REcHQoUO5evUqOp2ON954\ng/HjxxMbG8vLL7/MxYsXcXZ25qeffqJKlSrpT5zFX6u4ODWKJzo6f0u5FleHD6u0/s6d0Ly5qVsj\nhCgOTNrTt7GxYeHChZw6dYoDBw7w1Vdfcfr0afz8/PDy8iIkJARPT0/8/LIoAZCFKlVU8cdduwxp\nlZkID4clS9IPw0zj6lV17/brryXgCyGKjkFB38HBgVatWgFQsWJFmjRpQlRUFBs2bGDYsGEADBs2\njN9//z3Px3zuOcjH7uZr0CDYsgW2b8/0UkICvPSSmlg1YIAJ2iaEsFhGy+mHh4dz5MgROnToQExM\nDPb29gDY29sTExOT5+O8+qoaLXj5srFaZgKaBsHBauLViROZXnrrLVVOetYsE7VPCGGxjFL04O7d\nuwwYMIBFixZha2ub7jWdTocum7uSM2fO1P/s4eGBh4cHtWrBiBHg56fW9iiWIiNVOQUPDxg3TkV6\nnQ5Ng8md9xF8rxV//F1BqhgLIXIVGBhIYGCg8Q6oGSg+Pl7z9vbWFi5cqN/WuHFj7cqVK5qmadrl\ny5e1xo0bZ3pfTqeOjtY0OztNi4gwtHUmsnWrtqv1O1rbtsnaJ+VnaHFn1LWYO1fTmpU+q93YG2zi\nBgohiitDw7ZB6R1N0xg1ahTu7u5MTFOtsU+fPvj7+wPg7+9P375983Vce3t47TWYO9eQ1hXAw4eq\nVw5w9Ki6y1oAQduu4XNmFm++qeOo7ZPUb1uNAQNg6bca2/GmatsGRmy0EELknUFDNvfu3Uu3bt1o\n0aKFPoXj6+tL+/bt8fHx4dKlS/kaspnWtWvg5qaqSdatW9AW5kNysrqr2qsX2muvs/N/Z2nx1ZvU\nOBWYadeEBLh0CS5cgIgIaN8+dR2SkBDwaHeXr147Qr/PusLRo0TgxKqAavi0PkeDcc+pnYQQogBK\n1IzcjKZOVWvnfvNNETRo504YP55H+4MYM7E0f+7QuH3pJsPetuW9qTZUqaJGFa1apXatVQsaNFBl\nEnbvhkqV1IicFStU6ZpRo7I4xy+/wPffpy5PKIQQ+WRo0Dfr6vXvvQctWkC7dtC7t3q0alVI5Qn2\n7SO6mw8Dni2NvT2cPKXjVpdX+ez6Upo3r01yMnTpAq/2v8+6J76gwrtvgp0doL4k7N+v6qhNnZpN\nwAe1jmGTJoXQeCGEyBuz7umDSqXs3avKz//6q1pl69tvDag9tmULHD8OU6ak27yv4yQGhX7MyLfL\n89FHj48/ejQ0aULsq+NJTn68cPt336nVSwDmz1fj8fP6V+jiRXXPwNm5gI0XQli6Ep3eyejePejV\nSy3qtHRp/gP/1avwn9GX6XDkG14KnkXZshAfD7Nmaizzu8qSFWXoMzTNvYdly1RxtJUrU7dt26YK\n5ZQvD2++qe46r1sHlSvnrzFCCFEAFhX0oeCBf9+eZAb2uUefl8pyftlujlT1ZMhQnSp4WS2eZbYT\nsf9lcfo3RUercgodO2Z90IQE+PlnlXeqWDHfn0UIIfLL4oI+pAb+KlXUKoNPPJH6WlCQmtT14H4y\nbZ6wok0bNSl23pxElpUezfNXvoWOHQkdv4hlJzvQoIHKwRvtPsGePeDqqr4BpFi2TN2RnjzZSCcR\nQliqElVaOa8qVFCp+c6dVdGyLl3gv/+F7t1VmWL3xOP0jvqGmBiYPVvdDzgwbhXPP/f4QnXpgkv4\nn8ydq+YDGPXG8LvvqrGcaVWqBPv2GfEkQghRMMWyp59WYiJs2KDS6s89Bz4+UPp+nBpPeeqUGlsJ\nagx+v36pxX2++y7bCpgFlpysAnxkpPoakuLMGdW40FDjnk8IYXEsMr2TJ6NHqxTLzJkqGNesqWbZ\nOjrC/fsqR1SjhnHPGRYGXbuqoJ9WYqK6+fv996q0phBCFJBFpnfyZNw4NasrPl71+O3sVMAHNfIm\nvwF/xgz1lSIn8+Y9HteZgfXj6RDlyuXvnEIIYWRmPTnLIO7u0LSpyvt066bG1Gdl82ZwclKzwLLT\npQucP6+m4ubk/Hn9MoiZ3LsnQV8IYXLFp6d/8qQaM5+TU6dU/jzF+++rVI6TE7zwQtbvWbAAoqJy\nPq6NjcrVu7vnvN8ff8Dq1Vm/Vr68rHQuhDC54tPT//ZblaP38Mh+Hz8/NaTHzU099/bO+ZiJifDP\nP9mPw0/RpYu6L5Bb0NbpJLALIcxa8biRq2lqNM7GjWqy1P79MGdO+n0SEsDBQZVYqFMnb8fdv1/d\nWD1/Puf9EhPVf62Lz99IIUTJZBk3ck+eVD3opk2hYUM1Cibjh96zR03TzWvAB/Wt4M6d3PeztpaA\nL4QoEYpHJNuwQc260unUjdJy5VSh/TZtUvf5/ffs8/bZWb0aqlUzbluFEMKMFY+efkrQBxX4+/RJ\nP3zyzh1VgjO/QX/gQPDyMl47hRDCzJlf0P/jD3j5Zbh9O3XbpElq0lOKjEG/bFm1tmLK8lVCCCGy\nZH43cr28VM+9bVv48sus35yYqNZQPH4868lQQghRQpWsMgznzqnhkRER6kZt2bLZHyA+HkqXLtxG\nCiGEmSlZyyV+8w2MGAFlyuS+rwR8IYTIN/MK+jVqwIsvmroVQghRYplXekcIIUSOLGNylhBCCKMo\ntKAfEBCAm5sbjRo1Yt68eYV1GiGEEPlQKOmdpKQkGjduzI4dO6hTpw7t2rVj9erVNGnSJPXEkt4R\nQoh8M8v0zqFDh2jYsCHOzs7Y2NgwcOBA1q9fn/XODx5krqMjhBCiUBRK0I+KisLJyUn/3NHRkajs\nata/+y588UVhNEMIIUQGhTJkU5fHmvIzJ06EFStg3Dg8AgPxyKlWvhBCWKDAwEACc1tAKh8KJejX\nqVOHiIgI/fOIiAgcU9anTWPmnTvw3nvw8ceF0QwhhCj2PDw80nWIZ82aZdDxCuVGbmJiIo0bN+bP\nP/+kdu3atG/fPusbudWrQ0iIWrRcCCFErsyyDIO1tTVffvklPXr0ICkpiVGjRqUL+Hrjx0vAF0KI\nImTaGbm3bqkFx4UQQuRJyaqyKYQQIkdmOU5fCCGEeZKgL4QQFkSCvhBCWBAJ+kIIYUEk6AshhAWR\noC+EEBZEgr4QQlgQCfpCCGFBJOgLIYQFkaAvhBAWRIK+EEJYEAn6QghhQSToCyGEBZGgL4QQFkSC\nvhBCWBAJ+kIIYUEk6AshhAWRoC+EEBZEgr4QQlgQCfpCCGFBJOgLIYQFKXDQnzx5Mk2aNKFly5b0\n79+fW7du6V/z9fWlUaNGuLm5sX37dqM0VAghhOEKHPS9vb05deoUx44dw9XVFV9fXwCCg4NZu3Yt\nwcHBBAQEMGbMGJKTk43W4JIoMDDQ1E0wG3ItUsm1SCXXwngKHPS9vLywslJv79ChA5GRkQCsX7+e\nQYMGYWNjg7OzMw0bNuTQoUPGaW0JJf9Dp5JrkUquRSq5FsZjlJz+8uXL6dWrFwCXL1/G0dFR/5qj\noyNRUVHGOI0QQggDWef0opeXF9HR0Zm2z507l969ewMwZ84cSpcuzeDBg7M9jk6nM7CZQgghjEIz\nwHfffad17txZe/DggX6br6+v5uvrq3/eo0cP7cCBA5ne6+LiogHykIc85CGPfDxcXFwMCduaTtM0\njQIICAhg0qRJ7N69m+rVq+u3BwcHM3jwYA4dOkRUVBTPPPMM58+fl96+EEKYgRzTOzkZN24c8fHx\neHl5AdCpUycWL16Mu7s7Pj4+uLu7Y21tzeLFiyXgCyGEmShwT18IIUTxY5IZuQEBAbi5udGoUSPm\nzZtniiaYTEREBE8//TRNmzalWbNmfPHFFwDExsbi5eWFq6sr3t7exMXFmbilRScpKYnWrVvrBwdY\n6rWIi4vjxRdfpEmTJri7u3Pw4EGLvRa+vr40bdqU5s2bM3jwYB49emQx12LkyJHY29vTvHlz/bac\nPnt+J8MWedBPSkpi7NixBAQEEBwczOrVqzl9+nRRN8NkbGxsWLhwIadOneLAgQN89dVXnD59Gj8/\nP7y8vAgJCcHT0xM/Pz9TN7XILFq0CHd3d30a0FKvxYQJE+jVqxenT5/m+PHjuLm5WeS1CA8P59tv\nvyUoKIgTJ06QlJTEmjVrLOZajBgxgoCAgHTbsvvsBZoMa9Bt4AL4+++/tR49euifZxztY2leeOEF\n7Y8//tAaN26sRUdHa5qmaVeuXNEaN25s4pYVjYiICM3T01PbuXOn9vzzz2uaplnktYiLi9Pq16+f\nabslXosbN25orq6uWmxsrJaQkKA9//zz2vbt2y3qWoSFhWnNmjXTP8/us8+dO1fz8/PT79ejRw9t\n//79OR67yHv6UVFRODk56Z9b8uSt8PBwjhw5QocOHYiJicHe3h4Ae3t7YmJiTNy6ovHOO+/w6aef\n6md3AxZ5LcLCwqhRowYjRoygTZs2vP7669y7d88ir0XVqlWZNGkSdevWpXbt2lSpUgUvLy+LvBYp\nsvvsBZkMW+RBX0byKHfv3mXAgAEsWrQIW1vbdK/pdDqLuE6bNm2iZs2atG7dGi2b8QSWci0SExMJ\nCgpizJgxBAUFUaFChUzpC0u5FqGhoXz++eeEh4dz+fJl7t69yw8//JBuH0u5FlnJ7bPndl2KPOjX\nqVOHiIgI/fOIiIh0f6ksQUJCAgMGDGDIkCH07dsXUH+9U2Y/X7lyhZo1a5qyiUXi77//ZsOGDdSv\nX59Bgwaxc+dOhgwZYpHXwtHREUdHR9q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"text": [ - "" + "" ] } ], - "prompt_number": 133 + "prompt_number": 28 }, { "cell_type": "markdown", @@ -866,6 +870,7 @@ "collapsed": false, "input": [ "sensor_error = 30000\n", + "movement_error = 2\n", "pos = (1000,500)\n", "\n", "dog = dog_sensor (0, velocity=movement, noise=sensor_error)\n", @@ -894,27 +899,151 @@ { "metadata": {}, "output_type": "display_data", - "png": 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WGQmSLpqSwglt+/fzefnyJAP9vXnpJZIpQGJ47DGuXQR5njw4VKcLxjVchXZY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\nR7KLPM3OqFiRRYj6dFU99IFufUzBHex2VdMwf77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9g2rUoPBt0oRuGWmpIQLbuY5BjqVv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\n7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QbQmyYiwMlc95jRMnCnoEKlQUEmg02eualhnklMnM0K+fZfeTnx/QqJH155Np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"text": [ - "" + "" ] } ], - "prompt_number": 136 + "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. " + "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", + "\n", + "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = None\n", + "\n", + "dog = dog_sensor (0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " if pos == None:\n", + " pos = (Z, 500)\n", + " \n", + " pos = sense (pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + " pos = update (pos[0], pos[1], movement, movement_error)\n", + "\n", + "p1, = plot (zs,c='r', linestyle='dashed')\n", + "p2, = plot (ps, c='b')\n", + "legend ([p1,p2], ['measurement', 'filter'], 2)\n", + "show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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aUUOaMQTDSnrIEKF4xo6lCqfVq8l6r1fPiqL73gcj8N6uLvC6cASe65dhzBx/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+ "text": [ + "" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", + "\n", + "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "#Explaining the Results" + "####Explaining the Results\n", + "\n", + "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. In these example we do not have 1 sensor but 2. The first sensor is the RFID sensor that outputs the position measurement, and the second sensor measures our dog's movement using an intertial tracker. How does our filter perform if that tracker is also noisy? Let's see:\n", + "\n" ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_sensor = 30000\n", + "pos = (0,500)\n", + "\n", + "dog = dog_sensor (0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = sense (pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + " pos = update (pos[0], pos[1], movement, movement_error)\n", + "\n", + "p1, = plot (zs,c='r', linestyle='dashed')\n", + "p2, = plot (ps, c='b')\n", + "legend ([p1,p2], ['measurement', 'filter'], 2)\n", + "show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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BuwYuQe1v1wBONYDmzeX1uHdPUmIokZlJfaiLCVrlswYNTxqGDJHpl48bWVnk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sNwJIwYjzlzfRDx5VEEIh4BD3WiYtH3J3QK1sSp1Xt56SUeMyiIOYzp05k0Bcwxc10AWROxr7/O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\njqZVX7o0P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+ "text": [ + "" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distintly jagged. But, it still mostly tracks the dog. What is happening here?\n", + "\n", + "This illustrates the effects of *multi-sensor fusion*. Suppose the dog is actually at 10.0, and we get subsequent measurement readings of -289.78 and 301.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -289 to 301 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose with the readings of -289.78 to 301.43 we get a velocity reading of 590. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well. Finally, suppose the velocity reading was -678.8. This completely contradicts the RFID reading - we may not be sure from these few values which sensor is most inaccurate, but perhaps by now you will trust that the gaussians expressing our beliefs will correctly handle these cases. It's a bit hard to talk about while working with 1D problems, so we will take this topic up in great detail in the next chapter where we develop multidimensional Kalman filters. Remark\n", + "\n", + "Besides that issue, we are modelling the noise in our sensors using gaussians which model their real world performance. We are multiplying the gaussians (probabilities) when we get a new position measurement, adding the gaussians when we get a movement update. This is algorithmically correct (this is how the histogram filter works) and mathematically correct - why wouldn't it work? \n", + "\n", + "#### Summary\n", + "This takes some time to assimulate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", + "\n", + "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter until you do understand it. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work.\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 31 } ], "metadata": {} diff --git a/Multidimensional Kalman Filters.ipynb b/Multidimensional Kalman Filters.ipynb new file mode 100644 index 0000000..eebcd82 --- /dev/null +++ b/Multidimensional Kalman Filters.ipynb @@ -0,0 +1,285 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Multidimensional Kalman Filters\n", + "\n", + "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n", + "\n", + "\n", + "## Multivariate Normal Distributions\n", + "\n", + "What might a multivariate (meaning multidimensional) normal distribution look like? Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that x = 2 and y = 7. Therefore we can see that for N dimensions, we need N means, like so:\n", + "$$ \\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix} \n", + "$$\n", + "\n", + "Therefore for this example we would have\n", + "$$\n", + "\\mu = \\begin{bmatrix}2\\\\7\\end{bmatrix} \n", + "$$\n", + "\n", + "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 8. While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use a matrix to denote this:\n", + "\n", + "$$\n", + "\\Sigma = \\begin{pmatrix}\n", + " {\\sigma}_{1,1} & {\\sigma}_{1,2} & \\cdots & {\\sigma}_{1,n} \\\\\n", + " {\\sigma}_{2,1} &{\\sigma}_{2,2} & \\cdots & {\\sigma}_{2,n} \\\\\n", + " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + " {\\sigma}_{n,1} & {\\sigma}_{n,2} & \\cdots & {\\sigma}_{n,n}\n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "This is called the covariance matrix, and is probably a bit confusing at the moment. Rather than explain the math in detail at the moment, we will take our usual tactic of building our intuition first with various physical models. \n", + "\n", + "So here is the full equation for the multivarate normal distribution.\n", + "\n", + "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n", + "\n", + "I urge you to not try to remember this function. We will program it once in a function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the univarate normal distribution except it uses matrices instead of scalar values. If you are reasonably well-versed in linear algebra this equation should look quite managable; if not, don't worry, the python is coming up next!\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import math\n", + "def multivariate_gaussian (x, mu, cov):\n", + " n = len(x)\n", + " det = np.sqrt(np.prod(np.diag(cov)))\n", + " frac = (2*math.pi)**(-n/2.) * (1./det)\n", + " fprime = (x - mu)**2\n", + " return frac * np.exp(-0.5*np.dot(fprime, 1./np.diag(cov)))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 57 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n", + "\n", + "First, let's find the probability for our dog being at 2.5, 7.3 if we believe he is at (2,7) with a variance of 4 for x and a variance of 5 for y. This function requires us to pass everything in as numpy arrays (we will soon provide a more robust version that works with numpy matrices, numpy arrays, and/or scalars in any combinations. That code contains a lot of boilerplate which obscures the algorithm).\n", + "\n", + "So we set x to (2.5,7.3)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.array([2.5, 7.3])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 83 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we set the mean of our belief:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mu = np.array([2,7])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 84 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between x and y, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the x direction or y direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cov = np.array([[4,0],[0,5]])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 92 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now just call the function" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print multivariate_gaussian (x,mu,cov)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0341841496392\n" + ] + } + ], + "prompt_number": 93 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check the probability for the dog being at exactly (2,7)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.array([2,7])\n", + "print multivariate_gaussian (x,mu,cov)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0355881271709\n" + ] + } + ], + "prompt_number": 94 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These numbers are not easy to interpret. Let's plot this in 3D, with the z coordinate being the probability." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from mpl_toolkits.mplot3d import Axes3D\n", + "xs, ys = arange (-8, 13, .1), arange (-8, 20, .1)\n", + "xv, yv = meshgrid (xs, ys)\n", + "\n", + "zs = np.array([multivariate_gaussian(np.array([x,y]),mu,cov) for x,y in zip(np.ravel(xv), np.ravel(yv))])\n", + "zv = zs.reshape(xv.shape)\n", + "\n", + "ax = plt.figure().add_subplot(111, projection='3d')\n", + "ax.plot_surface (xv, yv, zv)\n", + "show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Wrcr8NVx5dQeCSJ34ErACmIbIapCYAuwEWipincvzyGcVV7prryT0aoA6UUk4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+ "text": [ + "" + ] + } + ], + "prompt_number": 104 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability quickly drops away in all directions.\n", + "\n", + "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if x and y both have the same variance or not. So for most of the rest of this book we will display multidimensional gaussian using contour plots.\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy.linalg as linalg\n", + "def plot_sigma_ellipse(x, y, cov):\n", + " # Get the sigma ellipse by transforming a circle by the cholesky decomposition\n", + "\n", + " L = linalg.cholesky(cov)\n", + " t = linspace(0,2*pi,100)\n", + " unit_circle = np.array([cos(t), sin(t)])\n", + "\n", + " E1 = L.dot(unit_circle)\n", + " axis('equal')\n", + " plot(E1[0]+x, E1[1]+y)\n", + " scatter(x,y,marker='+') # mark the center\n", + " show()\n", + " \n", + "cov = array ([[2,0],[0,2]])\n", + "plot_sigma_ellipse (2,7,cov)\n", + "\n", + "cov = array ([[2,0],[0,12]])\n", + "plot_sigma_ellipse (2,7,cov)\n", + "\n", + "cov = array ([[2,3],[1,2.5]])\n", + "plot_sigma_ellipse (2,7,cov)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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C5XKd0+/xeIx8wYIFzJw5k6VLl9Z4btu2bVm3bh3Nmzc/+UYaI69VjzwCjRrBU0/ZTiLB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\n/9FVuJyd/lqIzzg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IyDA32KR6vfkm9OoFDz0EL7+sHQyl6qlH7sdee80sNvn4Y9tJaoa8PHOu5sqV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\nRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 155 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/gaussian.py b/gaussian.py index 5ac2999..2225c20 100644 --- a/gaussian.py +++ b/gaussian.py @@ -70,7 +70,6 @@ def norm_plot (mean, var): xs = np.arange (min_x, max_x, 0.1) ys = [gaussian (x,23,5) for x in xs] plt.plot (xs,ys) - plt.show() if __name__ == '__main__': from scipy.stats import norm @@ -88,4 +87,3 @@ if __name__ == '__main__': assert rv.pdf(1.2) == x2 assert abs(x2- x3) < 0.00000001 print "all tests passed" -