diff --git a/.gitignore b/.gitignore index 3550c3a..1ad4a45 100644 --- a/.gitignore +++ b/.gitignore @@ -1,9 +1,9 @@ -*.aux -*.html -*.out -*.pdf -*.gz -*.tex -*.toc -*_files/ -.ipynb_checkpoints/ +*.aux +*.html +*.out +*.pdf +*.gz +*.tex +*.toc +*_files/ +.ipynb_checkpoints/ diff --git a/Designing_Kalman_Filters.ipynb b/Designing_Kalman_Filters.ipynb index 44ebb1e..5bad2c2 100644 --- a/Designing_Kalman_Filters.ipynb +++ b/Designing_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:0eb83ca70e5f2995e7ce5636ce41e9ef64254b9fdb02d4ea13fd4d7c9b49bd2d" + "signature": "sha256:19fd5da8a72ab84659ebb5050018c8255375aa4b43f12f3bca2afe4505bd16c0" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,8 +12,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "

Kalman and Bayesian Filters in Python

\n", - "
Table of Contents
" + "

Designing Kalman Filters

" ] }, { @@ -245,19 +244,12 @@ "output_type": "pyout", "prompt_number": 2, "text": [ - "" + "" ] } ], "prompt_number": 2 }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

Designing Kalman Filters

" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -305,7 +297,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -332,13 +324,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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fjpjg5o8h/8WZXyIiIvJODgdUO3dCs2ED1Bs2QL19O6p27oQUHt5sV7vThW/2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\nB9uIiIi8BWd+yWXkVVXwz89Hy+zZ+H7QCKz+ogJ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NFC7spHdvGx072tI89tq1agYPNjB/vnv3diH9RA1cEF5y584p2LRJzdmzSsxm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\nXY9XYsrgwgUt0tKCMX9+E2bPvnHXhwNLErBxoxH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7d2txOKBFCwujRsWlarc3kflk5ldkGqnhE65IXAhXJC4yT2SkBj8/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KATTsvffcat8+TFMMYzFKESOmzurAuqbMSkWF9Otfp2rChGqdcAJzxS0Rawui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\nP2prpd/8JlVHHRVRQUG1HA6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l0LOniPh4Vx/Lz/dfNq7KIE4fOQKqpkZSW8ewYV62hqAUHZVPmrJvn+tDk5ra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\nwWAA0tJ2o1u3StC0//tHSv+tWLECABA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S+N55B8rGjTE9JzxhAkI33WTSiIhZNjJT6KqrYr5Jjbx9O9LeeANLlyw5+7V/\n/MOL1av1kYrsbA1PPulH27acEqLkYd00X//+ETz4YMBwMetf/uLj3eISiA2wyTwLFsA7f35Mz4kM\nHYq6qVPB5dxE9hW8/faYb1bjWbYMnc4silu5UjG8xbHPBzz2WACdO7P5JXKi4cMjuPtu/cq3SAR4\n5ZV0VFWxN0gENsAmkisqkPbmmzE9R+3bF4Hvfz+2hTQUM2bZyHSyjLr//E9EBg+O6WkXr12L3R9v\nwmuvpRv+/bRpAcMN9InMxrqZPJdfHsKkSSHd10+dit4y+fTpFAzKYdgAm0Q6cgTpr7wS044PWufO\n8D/ySMz7iRKRRXk8CDz8MNQePYSfcizYCr/6kR/BE3W6v7vppiCGDeNycCI3uOuuIPr31/+879sn\n4//+Lx0qPwe3CBtgM0QiSP/NbyCdOCH+nMxM+B99NLopIJmOWTZKmvR0BB55BFqbNuc9NKzKeLbi\nehzyZ0KprATUb2IOl1wSwY036meEiJKFdTO5PB7g4YcD6NBBH3cqL1cwYwYny1qCDbAJfDNnQt6y\nRfwJsozAww9D69TJvEERUcpoeXkI/Nd/nfdGGW/vn4St/jOzxf7TkPftAxDd7uyBB7jXL5HbZGcD\njz4aQLpBImrOHONFsiSG5TTBlPXr4f3ww5ieE7zzTkQGDjRpRGSEWTZKNrV3b9R95ztN/v2qY30w\nt3o4vL5vmmTpUDVa1x3GI48Y7w9KlEysm6nRtauKBx80vofA736XjsOHuSguHmyAE0g6fhxpr76K\nWHarDo8di9CVV5o4KiKyivDYsQhddZXu64eCOfjNrsm6ryuSiieVX6AjDiZjeERkUUOHRnDLLfqd\nIU6dAn7zm3SEwykYlM2xAU4UVUXa//0fpGPHxJ9y0UXRGSFud5Z0zLJRqgTvuKPRFZ+wKuOlym/h\nZCQdbU/uQUZt1dm/+48L5qO/ZzPSf/tb8DccpRrrZmrdcEMIxcX6RXFbt8r44APmgWPFBjhBvHPm\nQFm/Xvh4LTcXgR/+8LyZQCJyGEVB4KGHoHXsCAB478Bl2HayI+6vfRE3BP6OT+pKsfVUFxS3/hrX\ntl8JAJC//hq+999P5aiJKMUkCbjvvgByc/VXmWfP9mLdOuaBY8EGOAHkbdvg++CDGJ4gI/Dgg0Kr\nwskczLJRSmVlIfDww1h7ug+W7e+BXx77T7RVazAj9z8xPHczToYzsKhmMKqCuWef4p07F8qGDSkc\nNLkd62ZzJMShAAAgAElEQVTqZWcD3/9+wPBWAa++moajR3lFWRQb4JYKBpH2+usx7fcbvPFGqIWF\nJg6KiKyupm1PLDvUG788+p8oS78aL7R+HqflLLRS6vDx0P+H8blfYsSK32DhkSFnn5P2+uuA35/C\nURNRqvXtq+Kmm/R54BMnJLz6ahr3BxbEBriFfDNnQt67V/j4SP/+CE3WL3ah5GKWjVJJC9Th4M1P\n4NZdv8RPLvg9Psq4+exagGuyP8KA7F340YXv4s8Df4F71z+CZ7d9GxFNhnT4MNLefTfFoye3Yt20\njuuvD2HAAP3E24YNCubPZ7RSBBvgFpC3bYP3o4+Ej9dat0bdgw+Cm3kSuZdcWQl59JUI7a3G90Z8\njq19rgK80QUsF2dX4pq2C88ee1neOqwY8X0sP9ofV63+GQ7U5cKzYAGjEEQuJ8vAgw/WISdHnwf+\n2998qKpiFOJ82InFqz76EMO1hrpp06C1bWvioEgUs2yUCt7Zs5E16XJ8kHU3nh/0N5z25gAeBZEe\nPdDa68cPus9Eu7zGNSI/7Sg+HvojjGn71dlIBKMQlAqsm9bSpo2GBx/U3zI9GATeeINRiPNhAxyn\nWKMPoeuuQ2TQIBNHRESWVVeHjMceQ8Yzz+D16z/EB/nTGm9/mJWJe6b40dZ70vDpiqQ2ikQ8t/IK\neP7ytyQNnoisauDACEpL9bdI37RJQVkZoxDNYQMch1ijD2q3bgjefLOJI6JYMctGySJXViL7iisg\nHzyIsulLMGffJbpjRowIY+gPh0Ht2xc1NTVNvlbDSMR1P5+AQ4tjuOU6UQuxblrT7bcH0b69Pgrx\n7ruMQjSHDXCswmGkvfGGePRBUVD3wAOAx2PuuIjIcryzZyP78ssRvOMO7Hv5Lfzh7x10x7RurWHK\nlLro9oj33Qf1PHuDN4xEjLuzDxaXid95koicJyMDuO8+RiFixQY4Rt558yDv2SN8fHDyZKjdupk4\nIooHs2xkqgaRh5Pvv4+6734Xf/pzOk4aJBymTq1D69bR/9by89H6e98778ufjUT0n44H70vDCy+k\nx7ITI1FcWDetq39/RiFixQY4BtLRo/DNnCl8vNqtG0LXX2/iiIjIahpGHk4sXozI4MEoL1fwxRf6\nnetHjAhj+PDGnWto0iSoffsKvddleeuwcuj9WLVExY03ZvFyJ5GLNRWFmDHDh2PHWBvOxQY4Br6/\n/lV85TWjD5bGLBuZoWHk4dSbbwKtWyMYBN56K0137NnowzmWLl+OwH33AT6f0HvmK4fw0ZjnUVIS\nxvjxrbF4MWsOmYN109qaikL4/dE8MDXGBliQXFEBz7Jlwscz+kDkIgaRh/pdHubO9aK6Wj/7cvfd\nwbPRh3Np+fkI3n678Nv71pXjyQnL8LvfncKDD2YyEkHkUv37RzB+fFj39SVLPNi8mS1fQ/zXEBEO\nI+3NN4UPZ/TB+phlo0QxijzUq66WMHu2fuZlwIAIRozQ/5ICvjk3Q5MmQe3TR3gcaW+9hTHDT+PT\nT09g1SoPIxGUcKyb9nDbbXXIytJ//c030/jBuAE2wAK88+fHtPCt7p57GH0gcgGjyEND77yThtA5\n61IUBbj77rpG2wAbkuVoLVH02WEj0qFD8M6Zg44dNXzwwUlGIohcKjsbuPVWfRRi1y4ZCxZwQVw9\nNsDnIR0/Dt8HHwgfHx47Fmrv3iaOiBKBWTZqkWYiD/XWrlWwerW+eb3yyhC6dGl667KG56ZaUIDQ\npEnCw/LNmQOpuhqKAjz2WICRCEoo1k37GD8+jJ499fufvf++D8eP88oQwAb4vLyzZokvfGvVKqbc\nHhHZT3ORh3qhkPHCt9xcDTfeGIzp/YI33QStTRuxg0OhRh/Yx4wJMxJB5EKyHN1i8dwrTadPc0Fc\nPTbAzZCqq+FduFD4+OAtt0DLyTFxRJQozLJRPM4Xeai3cKHXsNm8884gMjKafw/duZmZieAddwiP\n0bN0KeTdu88+ZiSCEoV1014uvFDFuHHGC+J27WL7x3+BZvj+/ncgbLxQ5Vxqt24ITZxo8oiIKCUE\nIg/1/H5g1ix9zq6wsOmFb+cTHjVKfEGcpsE3Y0ajLzESQeROt91Wh8zMxl/TNOC99zgLzAa4CfLu\n3TFte1Y3ZYrwYhVKPWbZSJRI5KGhf/7TixMnGjfHkgT8x38Ez7/wDU2cm5KEuqlTo9c1BSjl5ZA3\nb9Z9nZEIagnWTftp3Rr41rf0sau1axVUVLi7BXT3d98M33vvRT8mCQiPHCl85yYisg/RyEO948cl\nfPSRfmalpCSMbt30C1JiEetVprQmahgjEUTuMmFCyPAOce+9lyba5jgSG2AD8qZNUL78UuxgjwfB\nW281d0CUcMyyUbNiiDw0NGuWF4FA4695PMDNN4svfGvu3AzdeCOQpl9cZ0TesgVKebnh3zESQfFg\n3bQnr9e4Bn39tYw1a9x75ZoN8Lk0LTpzIig0YQK0Dh1MHBARJVOskYd61dUSFi7UZ38nTAihQ4fE\nTLNoOTkIXnON8PG+GTMAtemZZ0YiiNyhpCSMggJ9LZgxw9dciXA0NsDnUNavh7x1q9jB6ekITZ5s\n7oDIFMyykZFYIw8NffCBT7dmNi0NmDw5ZPyEJpzv3AxddRW07Gyh15L37IGyalWzxzASQaJYN+1L\nloFbb9XPAu/dK2PJEnf+zLMBPod39mzhY4NXX81tz4icIM7IQ739+yUsXar/JXLNNUHk5CQ4ZNeq\nFUI33CB8uO/DD8+7noGRCCLnGzIkgj599NO9M2f6XPnzzga4Afnrr6FUVAgdq7VujdDVV5s8IjIL\ns2xUL97IQ0Nz5/p0PWZ2toarropt9hcQOzdDpaXQ2rUTej151y4o69YJHctIBDWHddPeJAm4/Xb9\nLZIPHZKwYoX7ZoHZADfgi2H2NzR5Ms67oz0RWVpLIg/1jhwxnv297roQWrVKwCCNeL0I3nyz+OFz\n5ggfy0gEkXP16aNi8GD9dO+cOV7XZYHZAJ8h7d0LZc0aoWO1vDyEJkwweURkJmbZXK5h5GHGjJgj\nDw19/LFXl/3NzIwufouH6LkZHjUK6gUXCB2rbNoEecsW4TE0jERMm8ZIBEWxbjrD9dfrs8B79sj4\n8kt37QjBBvgMXwwzJKFrronuK0JEttMw8lC7aBEiQ4bE/VonTsBw54crrjj/LY9bTJYRuu464cNj\nqXH1xowJY9GiE/j8c0YiiJyib1/VMAs8e7Y+yuVkcTfA+/btw6hRozBgwAAUFxdjwYIFiRxXUknV\n1fAsXy50rJadjdBll5k8IjIbs2zudG7koaWLWOfP9yJ4zmSKzwdcfnl8s79AbOdmeORI4SywUl4O\nec+emMfTsaOGmTMZiSDWTScxmgX++msZmza5Z1407u/U6/Xitddew4YNGzBr1ixMmTIlgcNKLu8/\n/wnR63uhK64Q3oieiCwigZGHen4/8Mkn+ru+TZgQguAuZS3n8USvSAmKJQvcECMRRM4yeHDE8O6U\ns2fra5pTxd0Ad+jQAQMHDgQAFBQUIBgMIhSKf9YjZfx+eD/7TOzY9HSEJk0ydzyUFMyyuUciIw8N\nLVrkxalTjb/m8QBXX92yOhjruRkaNw6a4OI9z8qVkI4fj2dYABiJcDvWTeeQJOD66/W16quvFOzc\n6Y5Z4IR8l/PmzUNxcTG8NszFepYuhe7epU0ITZwIZGWZPCIiSpRERx7qqWo0/nCuUaPCyMtLcogu\nLS16ZUpEOAzPokUtejtGIoicYdiwMPLz9fXKqLY5UYsrV1VVFR599FHMMbi0Nm3aNBQUFAAAcnJy\nMHDgwLMZovpPkil9rGkoLSsDANTU1AAAcnNzDR8fOX4c63JzMezM92aJ8fNx3I/rv2aV8fBxYh8v\nX7QIhX/8IwoqKnByxgx8duoUsGxZwl7/7bfXY9Om3rp6ce216S1+/VGjRsX8/H9nZ2PQqVNon5nZ\naDxG9cy7YAEW5eYCshz3979ixVKMHAkMHz4O99+fiXHjvsatt27F2LHW+P+fj/mYj8UeX311EP/7\nv9FLWfX1Ys6cY+jRYy1KS0ekfHzNPa7/7927dwMA7r33XsRC0rT41/wFAgGUlpbiqaeewqRzogEL\nFy5EUVFRvC+dFPKmTch49lmhY8MTJqAuxn9cIko+ubISmffcA7WgAKd//WtT7tb4v/+bjvLyxlsG\nXXxxBE8+KXY1yQy+d9+Fd+5coWMDjz6KSHFxQt734EEJ992XCU0DXn/9lOGMEhFZU10dMG1aJk6f\nbvz1u+4KxnUjn1QqLy/HhBi2qI07AqFpGqZOnYo77rhD1/zahffM7K8IZn+dpeEnSHIO74cfmhJ5\naKi6WjLcL7O0NDG/LOI9N0OlpcIL+2KpfefDSIR7sG46T1oaMHasvnaVlTn/xhhxN8DLli3DzJkz\n8cYbb2DIkCEYMmQIqqqqEjk2U0nHjsHzxRdCx6p9+0I9E+UgIguq3+Xh2WcTtstDUz791KvbKzMv\nT0NRUWq3RdDatxde4KesWwcpgfWau0QQ2dfEifoGuKpKwsaNzr4xRtwN8KhRoxAMBvHll1+e/ZOf\nn5/IsZnKs2gRdLdvakKotNTk0VCyNcwCk72ZtcuDkVAIWLRIP8M5YUIIcoIWTrfk3IylVnkXLoz7\nfZrCXSKcjXXTmTp31jBggP4Ta1mZsxfDuWOvi3OpqnDx13JyEL70UpMHRETxSEbkoaFVqzw4caJx\nU+fxAOPHi32YNlvk4ouhdeggdKx38WLhSYBYMBJBZD9GEa41axQcOeLcD7GubIDlzZshHTkidGx4\n/PjobzhyFGbZbC6JkYeGPv1UXwsuvTSMnJzELfxq0bkpy+KzwCdPQlm7Nv73agYjEc7EuulcxcUR\n5OY2rmOqCkd/gHVlA+xdtkzsQFlGaPx4cwdDRDFJZuShocOHJVRU6DNxkyZZa6V0aOxYQHBPdo9o\nLYwTIxFE9qAowPjx+lq2dKl+zYNTuK8BDgbhWblS6NDIkCHQ2rUzeUCUCsyy2VOyIw8NLVumnwnp\n3FlD796JXSrd4nMzOxvhESOEDvWsWQPd7ewSjJEI52DddLZx48K6C2lVVRK2b3dmq+jM76oZypdf\nQrfhXRNC48aZOxgiEpOiyEM9TTNugEtKQskchrDQ2LGCB4bgWbXK3MGAkQgiO8jL01BYqP/BXLrU\nmR9aXdcAC8cfsrIQGTzY3MFQyjDLZh+pijw0tHu3jD179OWypCTxi8gScW6qfftCy8sTOtazfHmL\n308UIxH2xrrpfEY1bcUKjxnrZVPOXQ1wDIs+wsOHc/EbUYqlMvLQkNEMSO/eKjp2tGg4TpYRLikR\nOlTZuFF4UXAiMBJBZF2XXhrWLSE4cULChg3O2xPYVQ2w5/PPoxt5Cggx6+RozLJZXIojDw2pKrB8\nub5JGzXKnMVviTo3Q6NHix2oaUmdBQYYibAr1k3ny8wEior0071Lljjvg6q7GmDBxW9a+/ZQe/c2\neTREZMQKkYeGNm1SUFPTuPlWFGDYMGtfE9S6dIHarZvQsclugOsxEkFkPUYxiNWrPfD7UzAYE7mn\nAT55EsqmTUKHhkeNStlsEyUHs2zWZJXIQ0MrV+pnPgYNiqB1a3PeL5HnZlhwxk7euTOpMYiGGImw\nD9ZNdxg8OILMzMZfCwaBdeucFYNwTQPs+eoriF5jC40cafJoiKgRC0UeGtI0oLxcX/TNWPxmhvDI\nkcL/jkp5ucmjaea9GYkgsgyv1/gK15o1zvpw6poGWFm9Wug4tVs3aF26mDwaSjVm2azDapGHhior\nZV38weMBBg82rwFO5Lmp5eYi0q+f0LGeFDbA9RiJsDbWTfcYOlRf47780uOoD6buaIDDYXjWrRM7\ndOhQkwdDRPWsGHloyGj2t1+/CFq1SsFg4hQpLhY6Ttm4EVYI+TESQZR6/ftH4PM1/tqpU8CWLc5p\nG53znTRD2bJF+OYXor8syN6YZUsxi0YezrV6tb75Ki42dwok0edmuKhI7MBQCMpXXyX0vePFSIQ1\nsW66h88XXetwLifFINzRAAvGH7TcXKjdu5s7GCKXs3LkoaEjRyTs2qUvkUZbBFmZlp8PtWtXoWOt\nEINoiJEIotQpLtbXuvJyDzSLbn8eK+c3wJomXNTDxcWWnIWixGOWLTWsHnloyCj+0K2bivbtza3+\nZpybEcFZYOXLL6MbH1tIfSRi5EhGIlKNddNdhgwJ61qiqioJ+/c7o09yfAMs7d8Pqbpa6FjRXxJE\nFCObRB4aSkX8wSxhwWiXVFsLeds2k0cTO0UBHn+ckQiiZGrdOnrHy3M5JQbh+AZYqagQOzA9HZH+\n/c0dDFkGs2zJY5fIQ0PBYPQGGOdKRvzBjHNT7dVLeLZduGamACMRqcW66T5GNW/9emfsB8wG+IzI\nxRdDdwNsImoRO0UeGtq2TdbdNT0nR0OPHtaKBwiTZfEYhIUbYICRCKJkGjJEf6llyxZFVx/tyNkN\nsKYJF/PwwIEmD4ashFk2k9kw8tCQ0exvYWEEchIqplnnZvjii4WOU7ZsAcLWXujHSERqsG66T5cu\nKlq3brzuIRSKThLYnf2/g2ZI+/ZBOnFC6FjGH4gSw46Rh3NVVBjv/2tnquANMRAMQt6+3dzBJAgj\nEUTmkqToh/9zGdVIu3F0Ayw6+6vl5kLLzzd5NGQlzLKZw66Rh4aCQeDrr41ngJPBrHNTy8mBKniX\nS6vHIBpiJCJ5WDfdyaj2GV0lsxs2wAAiffva6vIskeXYPPLQkFH+t00bDZ0723/zy0hhodBxdmqA\nAUYiiMxkdPVr61YFwWAKBpNAzm2AVVW8AWb8wXWYZUscJ0QeGmoq/pCsft7MczMiGINQtm6FHVe5\nMBJhLtZNd7rgAg05Oc7LAdt79M2Q9u+HVFsrdKzorAgRNeaEyMO5jBrgZMUfzCZc64JByDt2mDsY\nkzASQZRYTeWA7R6DcGwDrAgu4tByc6F17GjyaMhqmGVrIQdFHhqKRIBt21LbAJt6brZuLXxbZMWm\nDTDASIRZWDfdyygGsWULG2BLkisrhY6L9OvniF/cRMnitMhDQ/v26fO/2dkaOnWyf/63nmgMQrSG\nWhkjEUSJ0aePfg/0nTtlaDYujY5tgEVnL9QLLzR5JGRFzLLFx4mRh4Z27NCXxB491KR+Rjb73FR7\n9RI6zq4RiHMxEpE4rJvudcEFqu5eYbW1Eg4dsu+HSmc2wJEI5F27xA7t0cPkwRA5QCDgyMjDuSor\n9SWxZ0+b3v2tCZGePYWOk/fvB/x+k0eTHIxEELWMogDdu+troVHNtAv7jrwZ8v79ENqfQ5ahdutm\n/oDIcphlEydXViL7yisdGXk4144d+kxb9+7J7ZTMPje1zp0Bn0/gQE14IsEuGkYiJk9mJCJWrJvu\n1qOHvhZWVto3B+zMBlg0/nDBBUB6usmjIbIvp0ceGopEgF27nD8DDFmGKnjlS3FADvhc9ZGIkhJG\nIohi0aOHvhYaxcbswpE/+aKLN9Tu3c0dCFkWs2znEQgg4yc/gXfBApycMcPRs771mloA165dcld5\nJOPcjHTvDnnLlvMe54SFcEbqIxEjRoRx//2ZuOuuOjz2WACKfSezkoJ1092MJgPqF8LZMRFn39a9\nGaKzFqpgFo7ITdwUeWjICgvgkkW09jllIVxTGIkgEue0hXDOa4A1DfK+fUKHcgGcezHLZsxNkYdz\nWSX+kIxzU3ghXFUVEA6bPJrUYiRCHOumuzW1EG73bnu2kvYcdXNqa4FTp4QOVQsKTB4MkU24ZJeH\n5hw4oC+HXbs6LP97hta5M3RTOUYiEUiHDpk/oBTjLhFEYgoK9DXRqHbagT1H3Qz5wAGh47S8PCAj\nw+TRkFUxy/YNt0YezmVUxDt3Tn4DnJRzU5ahduokdqhgTXUCRiKax7pJ+flsgC1LtFiLFn8iJ3Nz\n5KGhUAg4fFjf7HTs6MwZYEC8BspVVSaPxFoYiSBqWqdO+ppo1w+K7m2AO3c2eSRkZa7PsjHy0MjB\ngxLUc+p6bq6WkotEyTo3Nc4AN4mRCGOur5tk2ABzBtgihCMQ+fkmj4TImhh50DMq4EaX+pxEFayB\nkgsb4HqMRBA11qGDptsu8NgxSXTplaU4rgGWBC/XMQLhbm7NsjHyYMw4/5vc/X/rJevcZAZYDCMR\n33Br3aRveDxA+/b62lhVZb920n4jbo6qCufV2ACTqzDy0Cyj4u34GWDBGijV1AB+v8mjsbb6SMRr\nrzESQWScA7ZfO2m/ETdDOnoUuls5GfF4oLVvb/6AyLLclGVj5OH8jC5tGxX5ZEjauZmdDS07W+hQ\n+fBhkwdjD2PHujsS4aa6SU1zykI4ZzXAx44JHae1bw/IjvrWiQwx8iCmpkZfD4wu8zmN1qGD0HGi\ntdUNGIkgtzOqjUY11Ooc9ZMrHT0qdJyam2vySMjqHJ9lCwSQ8ZOfwLtgAU7OmMFZ32ZoGnD0qH72\nok2b1MwAJ/Pc1HJzge3bz3ucVFOThNHYR30kYvjwMB54IBN33VWHxx4L6BYHOY3j6yYJMaqNx45x\nBjilRBtgzoKRkzHyEBu/HwgGG3/N6wWyslIznmRS27YVOo4zwMbcHokgd2rbVj8DbDSJYHWOaoBl\n0QiEYNEn53Jqlo2Rh9gZzVy0aaOlbI1gMs9N0fNDdHLBjdwUiXBq3aTYGDXAx4/brwF21E+q8Aww\nG2ByGkYe4nb0qH4eoE0b5+d/AfFayBng5rk1EkHuZFQfjx2L3kzITsurbDTU82MDTKKclGVj5KFl\njGaAc3NTtwVaUjPAgrVQ5gywEKdHIpxUNyl+Ph+Qmdn4a6oKnDhhr/PdWQ2w4CyF2qaNySMhSg5G\nHlrOeAEcZ4Ab4gywODdFIsi92ra1/0I4ZzXAx48LHaexAXY922fZeGOLhGkqA5wqSc0AC9ZCZoBj\n49QbZ9i+blLCGNXImhp7/Q5yVgMseDNqzpKRnTHykFinTumLdna2S2aAs7PFPjiFQkA4bP6AHMbp\nkQhyL6Maefq0vc5v5zTAqqrfy6gpGRnmjoUsz65ZNkYeEi8Q0H8tlSUiqeemLAPp6WLHuvx2yPFy\nUiTCrnWTEs+oRtqtRNj3J/Fcov/yPp+9likSAdzlwUR+v37WIj3dHTPAAKBlZEASqJ9SICB862Rq\njLtEkNMY1chAgDPAKSHV1Qkdp3H2l2CvLBsjD+YyKtqpbICTfm6mpYkdJ1hjqWl2j0TYqW6SuTIy\n9DXSbiXCMQ2w8Ayw6OU+Igtg5MF8VotAJJsmWBNFZonp/JwUiSD3MiobRlfTrMwxP3mS0W8xA6LF\nnpzN8lk2Rh6SxmoRiGSfm6JXxURrLJ2fXSMRlq+blDRGNdJuDbBjZoCFizMbYLI4Rh6Sy6h0uKpM\niH6zp0+bOw4XsnskgtzLqGzY7TOyYxpg0QgEM8AEWDfLxshD8rk9AywcgbBbwM8m7BSJsGrdpORz\n9SK4999/H71790afPn3w0UcfJXJM8RHco1ITXfBBlEy8sUXKGO2e6KoyIfrNim4zSTFz6o0zyLmM\nyobdSkRcDXAwGMQTTzyBZcuWYcGCBfjBD36Q6HHFTFL1t+UzxC3QCNbKsjHykDpaExO9qSwTST83\nRYOnTf1jUcJYPRJhpbpJqWVUI+1WIuIq859//jn69++P9u3bo2vXrujatSvWrVuX6LHFRrQB5qwa\nWQgjD6llVDbc9hlZE62JdvvtZlN2ikSQe0mSvh6oqr36q7hK/cGDB9GpUye8/vrr+Pvf/478/Hwc\nOHAg0WOLjWhxZgNMsECWjZEHSzAqG6n+vyHp56bgNyyxAU4aq0YiUl43yTKMyobdSkSLPlred999\nAIB//OMfkAz+NaZNm4aCggIAQE5ODgYOHHj2Ekr9D1KiHq//6iv0rKlBbm4uAKCmpgYAdI9bnxln\not+fj+31eP369Sl9/71PP428igq0WrQIWk5Oyv893Pp42LDo44b1QpKsM76kPJakJutlw8e7N2zA\nRZdfnvrxuujx2LGjsGjRCdx6awiStAtPPNErpeOpZ5V/Hz5O3eM9e7IAlAD4pl6oapukjqf+v3fv\n3g0AuPfeexELSdNi79mXLVuG6dOnY+7cuQCAyy67DK+88gouvvjis8csXLgQRUVFsb503DxLliDt\n1VfPe1y4pAR13/teEkZE1IxIJHqtPdXTjS4XDgN33ZXZ6GuKAvzlL6dSNKLk8/35z/DOn3/e44JT\npiB0pgGm5GK5IKvZtEnGs8823lWrTx8VTz+duhvmlJeXY8KECcLHe+J5k0suuQQbN27EoUOHEAgE\nsHfv3kbNb0qIBvfsNkdPzmT1He9dwgkLOVpM8BvW3BaOthCWC7Iao7Ihy/YqnnFVNJ/Ph+nTp6Ok\npAQTJkzAyy+/nOhxxY4LOSgG517SI3cyKhui62nNkuxzU3gHHXI91k2qp2n64mm3KxRxzQADwC23\n3IJbbrklkWNpEdHZCckKKwmIyBIkKfrn3M/FkYiLZt1Ea6LdfrsRkWmcsIOOzYbbDJ9P7DjBO8aR\ns9WH6VOlrKwMeXl56N27N+KI4VMCGZWOVN7SM+nnpugd3lx1d5DUu/baa5GXl4e8vDy0a9cO/fv3\nxz333INt27albEyprptkHUatlGgbZhWOaYB5O0+yk3nz5iEnJwc1NTX44osvUj0cV8vI0H8Aqatz\nz2ynxNvIW1a/fv0wf/58fPLJJ5g+fTp2796NyZMn48SJE6keGrmcUY1M5S3k4+GYBhiixTmVUztk\nGanOspWVleH2229H27ZtMV9gBT6Zx+izcyovFCU9AyxaE9kAJ11mZiaKi4sxdOhQXHvttfjFL36B\n/fv3Y8WKFSkZT6rrJlmHUdlo1Sr542gJxzTAmuDlOdHZDiKzbNy4EXv37sW4ceNQUlKCefPmpXpI\nrmY0axEIuGcGWLTbF62xZB75TMjy9OnTKR4JuZ3fr6+RaWmcAU4NzgBTDFKZZZs3bx48Hg9GjBiB\n0ca++6cAACAASURBVKNHo6KiAnv37k3ZeNzOKAKRygY42eemaCxMNGZGiaNpGiKRCEKhEHbu3Inp\n06cjJycHY8aMScl4mAGmekY10qiWWpljGmDhDDAbYEqxefPmYdCgQcjKysLo0aMBgDGIFLJaBCLp\nGIGwrDVr1qBDhw7Iz89HcXExKioq8MEHHyAvLy/VQyOXM6qRdvuM7JgGGGlpYtv0hELR2z+Rq6Uq\ny3bkyBGUl5efbXx79+6N/Px8xiBSyCgCkcpFcEnPAAteTucMcPIVFhbi008/xcKFC/HOO++gZ8+e\nuPvuu7Fv376UjIcZYKrHRXBWIsvi2/QwP0UpUlZWBlVVcemllyIQCCAQCGDEiBFYunQp/K6adrQO\no77ONSUiEgGCQbFj2QAnXatWrTBo0CAMHjwYV111Fd59912cPn0av/3tb1M9NHI5owtHdrtIFPeN\nMKxIy8wUijhIJ05Aa906CSMiq0pVlq1+pveOO+7Q/d1nn32GK664ItlDcr3sbP2sxYkT7sgAS8eP\nix2YkeGiO4NYV6tWrdCjRw9s3rw5Je/PDDDVO35cXyOzsjgDnDJamzZCx8lHj5o8EiK9UCiERYsW\nYfz48Zg/f/7ZP3PmzIGiKIxBpEjbtvqifeyYo0pjkyTBWihaW8lcoVAIe/fuRWtO4FCK1dToa6RR\nLbUyZ80At20rdJxo0SfnWrp0adJnM1asWIHa2lrcdNNNKC4ubvR3I0aM4EK4FGnTRn9Pz6NHU5sB\nTta5KVoLVcHaSol18uRJrF69Gqqq4vDhw/jLX/6Cw4cP49vf/nZKxpOKuknWdOyYvkYa1VIrc9Q0\nh2iRlo4dM3kkRHrz5s2DoiiYNGmS7u+uvPJKHDx4EOvXr0/ByNytTRv9rEUqG+BkEq2FnAFOPkmS\nsHnzZlx++eW48sor8cADD6C2thbvvPMOSktLUz08cjG/X58B9nqBrKzUjCdezpoBzskROk6qqTF5\nJGR1qZjFeP755/H8888b/t3999+P+++/P8kjIqCpCIRLMsBsgC1rzpw5qR6CDmd/CTCeIMjJ0YQ2\n4rISR80Aa7m5QscJL/wgIsczaoCPH5eg2utqXlxE10OIxsuIyPmMJgjslv8FnNYAcxEcCeJ+llTP\n59Pfwz4SAWprUzOdkcxzU3gGmA0wgXWToowWCRtFyazOWQ2waAaYEQgiaqBtW/10b02Nza7nxUE6\nckToOC6CI6J6RrXRqIZanTsb4CNHoneEI9dilo0ays3Vz14cPJiaBjhp56amQT54UOxQZoAJrJsU\nVV3NCITlaK1bi92tSFUhCRZ+InK+Tp30sxcHDjiqPOpIx44Z387pXLIMrX178wdERLZgVBuNaqjV\nOavCSxLUTp2EDpUPHDB5MGRlzLJRQ5066WcvqqpSUx6TdW5KgjVQa98+uscRuR7rJgHGDXDnzpwB\nTjk2wEQUq/x8980Ay/v3Cx0nWlOJyPnq6oAjRxpHICQJ6NiRM8ApxwaYRDDLRg0ZXb6rqnJ2Bli0\nBqr5+SaPhOyCdZMOHtS3jXl5Gny+FAymhRzXAGtsgIkoRu3ba7qr/LW1EmprUzOeZJCrqoSOUzt3\nNnkkRGQX+/frJwbsmP8FHNgAi85WSILFn5yJWTZqSJaNL+GlIgaRrHNTdBJA4wwwncG6Scb5XzbA\nliAagZCOH4ejp3eIKCb5+fpFHI7NAQeDkKqrhQ7lDDAR1TPeAcJ+C+AABzbAaNVKeM9KZedOc8dC\nlsUsG53LaBZj167kl8hknJvynj3R292dj8/Hu8DRWaybtHu3viYaLSK2A+c1wADULl2EjpN37DB5\nJERkF92764v4jh1KCkZiPtHap3bpEs2HEJHrBYPA3r36emBUO+3AkZVN7dlT6Di5stLkkZBVMctG\n5+rRQz8junOnDDXJtT0Z56YiWPtEaym5A+umu+3aJesuHOXlacjJYQTCMiI9eggdp3AGmIjO6NhR\nQ6tWjb9WV2e86tnuRGeAI927mzsQIrKNykp9y9ijhz1nfwGHNsCqYAMsHTrEhXAuxSwbnUuSjGeB\nKyuTG4Mw/dwMBiHv3St0KGeAqSHWTXczioQZ1Uy7cGQDrHXoAGRmCh3LhXBEVM9oNmPHDmeVSeEF\ncF4v1K5dzR8QEdmC0Qxwz56cAbYWSRKOQXAhnDsxy0ZGjIp5smeAzT43hRfAde0KeDymjoXshXXT\nvYJBYN8+RiBsQfTSnfL11yaPhIjsoqmFcCITpnahbNsmdBzjD0RUz6gO2nkBHODgBlh4IdzmzUj6\nMm9KOWbZyEjHjpouPVVXFy3+yWL2ualUVAgdxwVwdC7WTffavNko/2vv3smxDbDaq5fYgadOQd69\n29zBEJEtSBLQu7d+unfTJmfsByxVV0M6fFjoWPXCC00eDRHZhVEN7NvX3pfGHNsAa+3bQ2vfXuhY\n0RkRcg5m2agphYX6ol5RkbwG2MxzU7jWZWVxARzpsG66UyRiPANsVCvtxLENMABECguFjmMDTET1\njIr65s2KI3LAwvGHfv14BzgiAhDdCScQaPy1zEygWzdGICxLuAHetIk5YJdhlo2a0r27ioyMxl/z\n+5OXAzbt3NQ08QZYsHaSu7BuulNT8Qe7f0a2+fCbJ1zET5+GvGuXuYMhIluQZaBfv9TGIMwgVVdD\nOnJE6Fg2wERUz6j22T3+ADi8AdbatYveFEOAsnGjyaMhK2GWjZqTygbYrHNTdPZXy86G2qWLKWMg\ne2PddJ9w2Jn5X8DhDTAQQwxi3TqTR0JEdtG/v3EOOBxOwWASRLTGqcz/EtEZ27fLqKtr/LXMTKCg\nwP6xUcdXuZhywKdOmTwasgpm2ag53bqpuv2AA4HkbIdmyrkZDMKzdq3QoYw/UFNYN93nyy/1d4Ps\n18/++V/ADQ1w//6CB0bg4SwwESE6AXrxxfrp3jVr7JkDVioqoJvGaUJYtGYSkeOVl+tr3qBBNr4U\n1oDjG2AtNxeq4B2NlDVrzB0MWQazbHQ+RUX6GMSaNR5oJt/504xzUykvFzpO69AB2gUXJPz9yRlY\nN93l4EEJe/bo20Sj2mhHjm+AASBcXCx0nGftWtg65EdECTNoUBjKOZMfhw8b/0KwNE2DR/DDfbio\nKHo7PCJyvfJyffyhZ08VubkmzwIkic0qeXwiRUViB54+DWXLFnMHQ5bALBudT3Y20KeP0SywuTGI\nRJ+b8q5dkGpqhI6NDB2a0PcmZ2HddBej+ENRkXMmCV3RAKs9ekDLzRU6ljEIIqpXXGwcg7AT4ZrW\nqhUiffqYOxgisoWTJ40X/Q4d6oz4A+CSBhiSJDwL7Fm9GqaH/CjlmGUjEUazHdu3yzh61LyYQKLP\nTc8XXwgdFx40CPDYq7mn5GLddI+vvvLobv+el6c5Yvuzeu5ogHEm2yZAOnQI8tatJo+GiOwgP19D\nly76gr96tT12g5D27hW+yyXjD0RUb9Uqo9nfsKOWCLimAY707w/4fELHepYtM3k0lGrMspEooxXP\nS5d6TXu/RJ6bXtEZO0VB+OKLE/a+5Eysm+5w6pTxAjin7P5QzzUNMHw+RAYPFjrUu2IFd4MgIgDA\niBH6WrB1q4yDBy0+FaKq8Ag2wJF+/YCsLJMHRER2sGqVB6FQ46+1bq0Z3iHTztzTAAMIjRwpduDJ\nk7w1ssMxy0aiunVT0bWrPgaxbJk5edlEnZvyli2QjhwROjYsWhvJ1Vg33cGoto0Yod8W0u5c1QBH\nhgwBWrUSOpYxCCICotvilpToZ4GXLfNaer2sV7SGeb0IX3qpuYMhIls4ckRCRYW+0x01ynlXxV3V\nAMPnQ3jYMKFDPatXA6dPmzwgShVm2SgWI0fqi//+/RIqKxNfQhNyboZC8KxcKXRouKgIyMxs+XuS\n47FuOt/y5fq7Xebna+jVyzm7P9RzVwMMICT6AxwKwbNqlbmDISJbaN9eQ79+RovhrLltmLJ2bXQl\ni4AwmxoiOsMo/jBqVMhRuz/Uc10DrPbtK3xTDO+iRSaPhlKFWTaKlVEMYsUK/V6ZLZWIc9P76adi\nB2ZmCi8OJmLddLbdu2Xs2qVvC41qnxO4rgGGLAvPeMhbt0LeudPc8RCRLQwbFob3nN3Pjh2TDG8X\nmkrSwYPCi3jDI0bw5hdEBAD49FN9LbjwQhX5+RZe7NAC7muAEdslP++CBSaOhFKFWTaKVVYWMGSI\nfrp3/vzE7gnc0nPTu3Ch8N0sQyUlLXovchfWTefy+4F//1tfy0aPDhkc7QyubIDVrl2hdusmdKxn\nyRLhLB0ROdvEifpfBhs2KNi/3yIBuWAQnsWLhQ7VOnSA2ru3ueMhIltYtswDv7/x13w+58YfgDga\n4H379mHUqFEYMGAAiouLscCmM6ShiRPFDgwGxe+mRLbBLBvFo3//iOHlwAULEjcL3JJz0/P555Bq\na4WODU2YAMiunAOhOLFuOpOmGdew0aPDjt4gJubq5/V68dprr2HDhg2YNWsWpkyZYsKwzBcuKQEy\nMoSO9c6fL3xJkYicS5aB0lL9LPBnn3kRCKRgQOfwlpUJHuhFaNw4U8dCRPawdavx4jejK15OEnMD\n3KFDBwwcOBAAUFBQgGAwiNC598yzg4wMhMaMETpU2r8fSkWFyQOiZGKWjeI1ZkwIPl/jr50+Hd0R\nIhHiPTflykrIX38tdGx4+HCgdeu43ofci3XTmcrK9LO/vXur6N7deXv/NtSi61/z5s1DcXExvOcu\njbYJ4RgEAO8nn5g4EiKyi6ws4xtjzJ+f2jvDxVKjQqWlJo6EiOzi+HEJq1bpP7wbXelymmanLF5+\n+WX88Y9/bPS1yZMn49lnn0VVVRUeffRRzJkzp8nnT5s2DQUFBQCAnJwcDBw48OwnyPosUaofT+zf\nH8rGjaipqQEA5J7ZI/jcx8fnz8eGnj1RPHmypcbPx/E9fu211yx5PvKxPR7n5q5ATU3/RvWipgbY\nvDkD/fqpLXr9hjlL0eev+vhjDJozB7lt2pwdT3Sc+nqmdu+Of1dVAQcPWubfk4/t8bj+a1YZDx+3\n/PGCBR4cPNi4XgQC1QiH1wIoSfn4mntc/9+7d+8GANx7772IhaRpsc9ZBAIBlJaW4qmnnsKkSZMM\nj1m4cCGKiopifemkU1auRPorrwgdGx49GnXTppk8IkqGpUuXnv1hIorHU09lYNu2xhfRBg+O4PHH\nWxYGjufc9L35Jrzz5gkdW/fd7yI8fnw8QyOXY910lkAAeOihVqitbbyLzfXXh3DbbcEUjSp+5eXl\nmDBhgvDxMUcgNE3D1KlTcccddzTZ/NpJZOhQaG3bCh3rWb4cUnW1ySOiZGARp5a64gr9JcK1axXD\nxSSxiPncPHFC/K6VrVohPHJk7IMiAuum03z6qVfX/CqK8xe/1Yu5Ui9btgwzZ87EG2+8gSFDhmDI\nkCGoqqoyY2zJ4fGIZ4EjEXg//tjc8RCRLQwfHkaHDv+/vfuOj6pK/wf+uffOnZmEkkJoMUAo0lkw\nIIgEsASEBcEVEbBhF8u6a1vxp7uLiGvFddX1i7oW0FVUQKooIErvRSkxIATZGCKQQp2ZW39/XIow\nk2RmMjXzeb9eeUEmtxzCnTPPPfc5z/F+gDZnTmTnRNi/+gpQ/ButUS+/HHA6w9wiIop1mgYsWODd\nV/XpoyEjIzGqXgUcAOfm5kJRFGzZsuXMV5MmTcLRtohRBw70+0NB/vZbCEeOhLlFFG6/zSEiCoYk\nAUOHegee69bZUFIS/MIYAV2bJ0/6nfoAWYY6ZEhwjSIC+83aZMUKG8rKzu2nBAG4+ur4S30IFqug\nA0Dduv6PAqsq5IULw9seIooL/ftrSE09d7TEMID58+2V7BFa8pIlVg02P2h9+/qd7kVEtZdhAPPm\nefdRPXroyMpKjNFfgAHwGervfw/4Wc5NXrQI8HO1JYpNzGWjULDbgcGDvfPlli+3obw8uFFgv69N\nt9v/m3FRhHL11UG1h+g09pu1w/r1Eg4c8O6fhg9PnNFfgAHwGWZaGrT+/f3b2OWCvYryb0SUOPLy\nVCQnn/uaqgLz54c3F1heuBBCRYVf22q9esGM81Q1Iqo5wwDmzPEe/e3cWUfr1rV74YvzMQD+DWXI\nEGutUz/IX38NobQ0zC2icGEuG4VKcjIwcKD3KPDixTJKSwMfBfbr2jx2DPZ58/w+pjpsWMDtIDof\n+834t369hH37vOOc4cMTo/LDbzEA/g2zSRNriVB/qCrsM2eGt0FEFBcGDfJeHllVgZkzw5MLbJ87\nF3C5/NpW79YNRnZ2WNpBRPFD04BPP3V4vd66tYFOnfQotCi6GACfRx0+3O9tbcuWQfjllzC2hsKF\nuWwUSikpps+6wMuW2VBUFNgocHXXplBa6n/lB4C5vxQy7Dfj23ff+a5QM2qUAiH4wjVxiwHweYzm\nzf0fBTYM2D//PLwNIqK4MGyYgjp1zn3NMIDPP/cecakJ+8yZ1vCyH/QuXWB07BjS8xNR/PF4gFmz\nfOf+dumSeKO/AANgn5SRI60in36wrVsH8aefwtwiCjXmslGo1anjexb1+vUSdu/2v6ut6toUiopg\nW7bM72Mpo0f7vS1Rddhvxq+vvpJ9VqaJxyWPQ4UBsA9mZia0yy7ze3v7xx8DZuLUziMi3666SkV6\nundfMH26PSRdhGP6dGtY2Q9a794wWrWq+UmJKK4dP+677m+vXlrCVX74LQbAlVBGjPC7LrCUnw/b\nmjVhbhGFEnPZKBzsdmDECO8RlZ07JXz/vX9PlSq7NqWtWyFt2uRfQyTJepJFFELsN+PTnDl2nDhx\n7muSBFx/feKO/gIMgCtlpqVBHTzY7+3t//2v37Oyiaj26t9fQ2am93DvtGkOf1N3vSkKHB984Pfm\n2uWXw2zaNMiTEVFtUVws4KuvvAfzKuunEgkD4CooV18Nr1ktlRDKymCfNSvMLaJQYS4bhYs1suLx\nev3AAQFffln9UyVf16Y8fz6EX3/1rwF2O5Rrr/VvW6IAsN+ML6YJfPCBA5p27uuy7PtJVaJhAFyV\nunWhBFBAXl64EEJRURgbRETxoGdPHe3be+fWzZplD3hxDOHQIdjnzPF7e3XQIJhpaQGdg4hqn/Xr\nJWzb5p16NWyY4nOuQqJhAFwNddAgmBkZ/m2s63BMncoJcXGAuWwUToIA3Habx6uYjKIAH31U9eIY\n51+bjg8/tHb0g1m/fkA37USBYL8ZP9xu4MMPvUswNmxoYtiwxFv1zRcGwNWx2+G5+Wa/N5e2b4e0\nbl0YG0RE8aB5cwN5ed4fNGvX2nyOyvgiff89pA0b/D6nMmaM32lbRFR7zZnj+2nTLbd4vFatTFQM\ngP2gX3wx9N/9zu/tHdOmWXVHKGYxl40iYeRIBSkp3k+EfOXlnXbm2nS74Xj/fb/PZVx4IbR+/YJp\nJpFf2G/Gh+JiAfPne8836NZNR/fuibnohS8MgP0hCPCMHQvYbP5tXl5uPbYkooRWpw5www3e6QvF\nxQIWLKh6Qpz900/9n/gmCPDcdhsgsksnSmRVTXwbO9aTkEseV4a9pZ/MzEyoQ4b4vb1t+XJImzeH\nsUVUE8xlo0jp21dDu3beE+JmzrSjqMj70yg3Nxdifj7kr7/2+xxqXh6Mli1r1E6i6rDfjH3ffec7\nxWroUBVNmnB+0m8xAA6Acs01MBs08Ht7x7vvMhWCKMGdnhB3/uCsqgJvveX0XtjN7Ybzrbf8nkxr\n1qvHRS+ICKWlgs+JbxkZps9l2hMdA+BAOJ0BTYgTysqYChGjmMtGkdSihYFBg7wnxP30k+iVq7f/\n2Wf9T33AqYlv9erVuI1E1WG/GbtME3j7bYfP9bhuu80Dh3dcnPAYAAdI79kzoAlxTIUgIgAYNUpB\n06beo7ozZpxNhRDz89E4gKoPxoUXQuvfP2RtJKL49N13Nvzwg3fqQ9++GnJyOPHNFwbAgRIEeO66\nC0hK8nsXx3/+Axw7FsZGUaCYy0aRZrcD99zj9pqEoqrAlClO6Ces1Id0fxexkGW477mHE98oYthv\nxqbKUh/S003ccov3qpRkYc8ZBDMjA54bb/R7e6G8HM533uECGUQJrl07A4MHe6dC7NkjYtHjawJL\nfRg5EuYFF4SyeUQUZ6pKfbjjDg/q1o18m+IFA+AgaVdcAb1LF7+3lzZsgG3x4jC2iALBXDaKFl+p\nEEJZGT5b0hiFJxujrKys2mMYbdoEVJWGKBTYb8aeJUuY+hAsBsDBEgR47r47sFSIjz6CuG9f+NpE\nRDHPKxXC7YG4fz9UU8LkfSPhMqqZrSLLcI8bx9QHogS3f7/I1IcaYA9aA4GmQkBV4fzXv+DzWQVF\nFHPZKJrOpEIYJqTCQpyuhfaLOwMzjt9U5b5MfaBoYb8ZO1wu4F//ckL1zqhi6oOfGADXUKCpEEJJ\niVUfmPnARAlt1CgF2a6dgOvkOa9/V9YVS0u7+dyHqQ9EBFirvRUXey+kc+WVTH3wFwPgmjqdCpGc\n7PcutlWrYFu2LIyNouowl42iLWnLOjwmToZDPHcIR1VUvP2/IShyZ5y7g93Oqg8UVew3Y8Py5TYs\nX27zer1ZM4OpDwFgTxoCZkYG3HfdFdA+jvffZz4wUYISiovhfPttNEs6jLubLfD6uceQMblwJBTj\n7Iec59ZbYWZlRbKZRBRjfvlFwHvveef92u3Agw+6YbdHoVFxigFwiOiXXAJ1wAD/d1AUOF9+GcKR\nI+FrFFWKuWwUNSdOIGnyZOCklfpwefpWXJb+/Zkfy3ZrZbh9rsZ4r2gQAEC79FJol10W8aYS/Rb7\nzehSFOD1153w+Bjkvf12D7KymFoZCAbAIaTcdBOMFi383l4oLYXzn/8ENC2MrSKimGEYcL7xBoTi\n4jMvCQJwd7MFyHSUem3+9eEeWKRfCc8dd8BrBQ0iShimCbz1lgM//+wdtuXmaujXj3FEoBgAh5Ld\nDveDDyKQRbfFggI43n+fk+IijLlsFA326dMhbd3q9XqSpOCRlp9DFnSoym9yggURU7S78ON+Tumm\n6GO/GT3z5slYvdo777dpUxO33+7h/XEQGACHmJmZaY3WBMC2dCkXySCq5WwrVkCeN6/Sn7dKLsFt\nWV+d85qRdQE0RzL++U8nDh/mJxxRItq8WcL06d7JvbJs5f0GsBwB/QYD4DDQ+vaF1q9fQPs4pk2D\ntGNHmFpE52MuG0WS+NNPcLzzTrXbDcrYgKuabgcAmCmpMBs2BAAcPSrg5ZedcLvD2kyiKrHfjLyi\nIgFvvOH0+ZD4rrs8yM42It+oWoIBcJh4brsNRrNm/u+g63C++uo5uYFEFP+Ew4fhfOUV+KxYf/62\nAjCu2Xy0a1jmNZ/g559FvPWWg9lSRAni2DFg8uQkn2tnDR2qom9f5v3WBAPgcHE64X7kEQS0HMvx\n40h67jkI5eXhaxcBYC4bRcixYwG/p4+cPIIH326B9Ebe3fPatTZ88YUcyhYS+Y39ZuToOvDaa06U\nlHinPnXtqmPMGCUKrapdGACHkdm4Mdx//jMgSX7vIxw+DOfzzwMnToSxZUQUdm43kl56KbCnOoKA\nPddcg5SOmXjkETdkH7Hu55/bsXKl92QYIqodTBN47z0Htm/3jh0yM0388Y9urocTAvwVhpneqRM8\nY8cGtI+4fz+ckydbRf8oLJjLRmGlaXC+9hrE3bsD2k0ZORKdT02ibdXKwLhxvld1mjLFgR9+8P/G\nmigU2G9GxowZdixd6n2Tm5wMPPKIC3XqRKFRtRAD4AjQ8vKg5eUFtI+Unw/nG28ABhPcieKKacLx\nzjuQtmwJaDetd2+o11xzzmuXXqph+HDv3GFdB155xYk9e9iFE9UmixfbMGuW96MfUbQqPmRmchJA\nqLD3jARBgGfsWBjt2we0m7RhAxzvvccawWHAXDYKF/v06bAtXx7QPkZ2Njz33AMIgte1ef31Cnr1\n8p7s4vEAL7zgRHExy6NRZLDfDK+1ayW8/77vdQRuuUVB1656hFtUuzEAjhSbDa6HHoKZkRHYbt98\nA/vnn4epUUQUSvL8+ZDnzg1oHzMlBe5HH610AR1RBO67z4OOHb0//I4dE/D880koL2cQTBTPduyQ\n8OabvsudDR+u4qqrqq8iQ4FhABxJ9evD9fjjgVWGACB/8QXkmTPD1KjExFw2CjV54ULY//vfwHZy\nOuH+y19gNmhw5iVf16bdDjz8sBstWninRB06JOCFF5ycN0thx34zPPbtEzF5stNnpcTLLtMwahTn\nA4UDA+AIM7Oy4HrsMesTLQD2GTMgf/FFmFpFRDVhW7QI9mnTAtzJBvfDD8No1cqvzevUAR5/3I2G\nDb2HiH7+WcRLL/muF0pEsauoSMDzzzt9vndzcnTceSeXOQ4XBsBRYLRtC/ef/hRQeTQAsH/2GeTZ\ns8PUqsTCXDYKFdvixXC8/37A+3nuvRd6ly5er1d1baalmRg/3oV69byD4IICES+9xNXiKHzYb4ZW\ncbGAZ59NwpEj3hFu27YGHnzQHWiYQAFgABwlek4OPHfdFfB+9k8/ZToEUYyQv/rKmqgaIOWWW6Bd\nemlQ58zMNPH4426fKcP5+RJeftkJj+/qaUQUI0pKrOC3osI7+M3KMvDoo67KpgVQiDAAjiKtf38o\nY8YEvJ99xgxrYhyrQwSNuWxUU/KCBbBPnRrwfuqwYVAHD6705/5cm61bG5UulLFjhxUEcySYQo39\nZmgUFwt45pkklJV5B78ZGSbGj3ejXr0oNCzBMACOMvXqq6EOGhTwfvKsWbB/+CHrBBNFmmlCnjED\n9o8+CnhXrX9/KKNHh6QZXbro+POf3bD5WBRu+3YJL73kO6+QiKLnl18ETJrkO/ht0MDEU0+50KAB\nB7cigQFwtAkClJtvhtavX8C7ygsXwvHvfwOad41Qqhpz2SgohgHHe+/BHkQakn7xxfDceSeqm9ES\nyLWZk6PjT3/ynSe4c6eEF15IwsmTgbaUyDf2mzVTVGQFv77KFqanW8Fv48YMfiOFAXAsEEV4CVOx\nCAAAGqFJREFU7rkHWp8+Ae9qW70azhdfBId6iMJMUeD8179gW7Ik4F317t3hfvBB+ByuraEePXT8\n8Y++g+CCAhGTJvmeZENEkbN7t4inn072mfOblmbiySddaNKEwW8kMQCOFaIIz733QuvdO+BdpW3b\nkDRpEoQjR8LQsNqJuWwUkBMn4Hz+eUjr1we8q37RRVbVFz+D32CuzV69rJFgX6coLBQxYUISfv2V\nQTDVDPvN4GzZImHSpCQcP+79s/R0E3/9q4tLHEcBA+BYIknw3H9/UEGwuHcvkiZMgHDwYBgaRpS4\nhPJyJE2cCCk/P+B99W7d4P7zn+FztlqIXXyxlRPs61QlJQImTEjCvn3s8okiaflyGyZPdkLxsZZF\ngwZW8Nu0KYPfaGBvGGtOB8FBlEgSSkqQ9Pe/Q9y7NwwNq12Yy0b+EIqKrPfU/v0B76vn5MD98MMB\nL3pTk2uze3cdDz/s9nnKigoBEycmYccOFhal4LDf9J9pAvPmyfi//3NA917FHI0amfjb35j2EE0M\ngGPR6SC4b9+AdxUqKpA0YQJsq1eHoWFEiUPatAnJf/sbhEOHAt5X79ED7oceisjI7/m6ddPx5JMu\n1Knj/TOXC3jhBSfWrmUQTBQuhgF89JEdH3/s++Y3O9vAxIkuNGrE4DeaBNMMTzHZb775Bjk5OeE4\ndOI4NePc9s03Qe2uDh8O5frrAZH3OUR+M03Ic+bA/tlnQdXa1nr3hue++8Iy4S0QRUUCnnvOd7kl\nQQBuuknB4MEql1klCiFFAaZMcWDNGt/v/86ddTz0kBvJyRFuWALYvHkzrrzySr+3Z2QUy0QRnjvu\ngHrttUHtLs+ZA+fkyWAdJCI/eTxwvP467J9+GlTwq151FTwPPBD14BcAsrJMTJzoQlaWd61w0wQ+\n/NCOt95yQFWj0DiiWqi01Mq1ryz47d1bw1/+wuA3VjAAjnWCAGXkSHhuv73a+qG+SJs3I+nvf4dQ\nUhKGxsUv5rLR+YTSUiQ9/TRsa9YEtb8yejSUsWNr/MQllNdmgwZWnmHbtr4XzFm2zIZnnvG9HCvR\n+dhvVm7XLhFPPZWEwkLf7/+rrlLxwAOeaGRFUSUYAMcJbcAAq45oEO8esagIyU89Ben778PQMqL4\nJ+bnI+mppyAWFga+syTBc889UIcPD+omNdzq1QP+3/9zISfHx0wcWPV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HlgEIMXR+AQBeqb7oHd8nmTeyAQg4Or8AAL+qsujtEKMFXYoVP7hvsMcCgAah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\nnFpvuDRJuumu65TYtZNKr7h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"text": [ - "" + "" ] } ], - "prompt_number": 25 + "prompt_number": 18 }, { "cell_type": "markdown", @@ -1173,7 +1165,8 @@ "input": [], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 18 }, { "cell_type": "code", @@ -1181,7 +1174,8 @@ "input": [], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 18 }, { "cell_type": "code", @@ -1189,7 +1183,8 @@ "input": [], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 18 }, { "cell_type": "code", @@ -1197,7 +1192,8 @@ "input": [], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 18 }, { "cell_type": "code", @@ -1205,7 +1201,8 @@ "input": [], "language": "python", "metadata": {}, - "outputs": [] + "outputs": [], + "prompt_number": 18 } ], "metadata": {} diff --git a/Extended_Kalman_Filters.ipynb b/Extended_Kalman_Filters.ipynb index ccaa892..3264be7 100644 --- a/Extended_Kalman_Filters.ipynb +++ b/Extended_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:accc4aa29e12d5a5ed17db77c8d414aad014c9ab74372dff107bdcaaa8e97d40" + "signature": "sha256:e7d1e5240da92450e6d3790326c446f6c2b8d4ef9dd3aa3ae42956412e150699" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,8 +12,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "

Kalman and Bayesian Filters in Python

\n", - "
Table of Contents
" + "# The Extended Kalman Filter" ] }, { @@ -38,6 +37,10 @@ " margin-left: 0% !important;\n", " margin-right: auto;\n", " }\n", + " div.text_cell code {\n", + " background: #F6F6F9;\n", + " color: #0000FF;\n", + " }\n", " h1 {\n", " font-family: 'Open sans',verdana,arial,sans-serif;\n", "\t}\n", @@ -131,7 +134,7 @@ " max-height: 300px;\n", " }\n", " code{\n", - " font-size: 78%;\n", + " font-size: 70%;\n", " }\n", " .rendered_html code{\n", " background-color: transparent;\n", @@ -239,13 +242,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 1, + "prompt_number": 2, "text": [ - "" + "" ] } ], - "prompt_number": 1 + "prompt_number": 2 }, { "cell_type": "markdown", diff --git a/Gaussians.ipynb b/Gaussians.ipynb index 7d3e08b..b35ef84 100644 --- a/Gaussians.ipynb +++ b/Gaussians.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:2d351f8c72f6c3e40db4e6edb6b72d9bad558e859c283e1b4b0f5d677aadc8b5" + "signature": "sha256:a427f15c81a2e5dc1b63cffe28b59aea4fde72a3894132dda51749ce2cdd6035" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,8 +12,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "

Kalman and Bayesian Filters in Python

\n", - "
Table of Contents
" + "#Gaussian Probabilities" ] }, { @@ -22,6 +21,8 @@ "input": [ "#format the book\n", "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", "import book_format\n", "book_format.load_style()" ], @@ -36,6 +37,10 @@ " margin-left: 0% !important;\n", " margin-right: auto;\n", " }\n", + " div.text_cell code {\n", + " background: #F6F6F9;\n", + " color: #0000FF;\n", + " }\n", " h1 {\n", " font-family: 'Open sans',verdana,arial,sans-serif;\n", "\t}\n", @@ -129,554 +134,7 @@ " max-height: 300px;\n", " }\n", " code{\n", - " font-size: 78%;\n", - " }\n", - " .rendered_html code{\n", - " background-color: transparent;\n", - " }\n", - " ul{\n", - " margin: 2em;\n", - " }\n", - " ul li{\n", - " padding-left: 0.5em; \n", - " margin-bottom: 0.5em; \n", - " margin-top: 0.5em; \n", - " }\n", - " ul li li{\n", - " padding-left: 0.2em; \n", - " margin-bottom: 0.2em; \n", - " margin-top: 0.2em; \n", - " }\n", - " ol{\n", - " margin: 2em;\n", - " }\n", - " ol li{\n", - " padding-left: 0.5em; \n", - " margin-bottom: 0.5em; \n", - " margin-top: 0.5em; \n", - " }\n", - " ul li{\n", - " padding-left: 0.5em; \n", - " margin-bottom: 0.5em; \n", - " margin-top: 0.2em; \n", - " }\n", - " a:link{\n", - " font-weight: bold;\n", - " color:#447adb;\n", - " }\n", - " a:visited{\n", - " font-weight: bold;\n", - " color: #1d3b84;\n", - " }\n", - " a:hover{\n", - " font-weight: bold;\n", - " color: #1d3b84;\n", - " }\n", - " a:focus{\n", - " font-weight: bold;\n", - " color:#447adb;\n", - " }\n", - " a:active{\n", - " font-weight: bold;\n", - " color:#447adb;\n", - " }\n", - " .rendered_html :link {\n", - " text-decoration: underline; \n", - " }\n", - " .rendered_html :hover {\n", - " text-decoration: none; \n", - " }\n", - " .rendered_html :visited {\n", - " text-decoration: none;\n", - " }\n", - " .rendered_html :focus {\n", - " text-decoration: none;\n", - " }\n", - " .rendered_html :active {\n", - " text-decoration: none;\n", - " }\n", - " .warning{\n", - " color: rgb( 240, 20, 20 )\n", - " } \n", - " hr {\n", - " color: #f3f3f3;\n", - " background-color: #f3f3f3;\n", - " height: 1px;\n", - " }\n", - " blockquote{\n", - " display:block;\n", - " background: #fcfcfc;\n", - " border-left: 5px solid #c76c0c;\n", - " font-family: 'Open sans',verdana,arial,sans-serif;\n", - " width:680px;\n", - " padding: 10px 10px 10px 10px;\n", - " text-align:justify;\n", - " text-justify:inter-word;\n", - " }\n", - " blockquote p {\n", - " margin-bottom: 0;\n", - " line-height: 125%;\n", - " font-size: 100%;\n", - " }\n", - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 2, - "text": [ - "" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#Gaussian Probabilities\n", - "\n", - "### Introduction\n", - "\n", - "The last chapter ended by discussing some of the drawbacks of the Discrete Bayesian filter. For many tracking and filtering problems our desire is to have a filter that is *unimodal* and *continuous*. That is, we want to model our system using floating point math (continuous) and to have only one belief represented (unimodal). For example, we want to say an aircraft is at (12.34381, -95.54321,2389.5) where that is latitude, longitude, and altidue. We do not want our filter to tell us \"it might be at (1,65,78) or at (34,656,98)\" That doesn't match our physical intuition of how the world works, and as we discussed, it is prohibitively expensive to compute.\n", - "\n", - ">So we desire a unimodal, continuous way to represent probabilities that models how the real world works, and that is very computationally efficient to calculate. As you might guess from the chapter name, Gaussian distributions provide all of these features.\n", - "\n", - "Before we go into the math, lets just look at a graph of the Gaussian distribution to get a sense of what we are talking about." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#ignore this code.\n", - "%matplotlib inline\n", - "from __future__ import division, print_function\n", - "from gaussian_internal import plot_gaussian\n", - "import matplotlib.pylab as pylab\n", - "pylab.rcParams['figure.figsize'] = 10,6\n", - "\n", - "plot_gaussian(mu=100, variance=15*15, xlim=(45,155), xlabel='IQ', ylabel='percent')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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kJUdgoilU6VICxtcmxaK9z4GDtV1Kl0JEMmAzphKc2xePGjJp73Ng+7EmPJxvUboUj/lD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\nYcMGdHR0oLCwEJGRkYiJicGHH36I8PBwREVFob2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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Probably this is immediately recognizable to you as a 'bell curve'. This curve is ubiquitious because under real world conditions most observations are distributed in such a manner. In fact, this is the bell curve for IQ (Intelligence Quotient). You've probably seen this before, and understand it. It tells us that the average IQ is 100, and that the number of people that have IQs higher or lower than that drops off as they get further away from 100. It's hard to see the exact number, but we can see that very few people have an IQ over 150 or under 50, but a lot have an IQ of 90 or 110. \n", - "\n", - "This curve is not unique to IQ distributions - a vast amount of natural phenomena exhibits this sort of distribution, including the sensors that we use in filtering problems. As we will see, it also has all the attributes that we are looking for - it represents a unimodal belief or value as a probabilitiy, it is continuous, and it is computationally efficient. We will soon discover that it also other desirable qualities that we do not yet recognize we need.\n", - "

\n", - "

" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Nomenclature\n", - "\n", - "A bit of nomenclature before we continue - this chart depicts the probability of of a *random variable* having any value between ($-\\infty..\\infty)$. For example, for this chart the probability of the variable being 100 is roughly 2.7%, whereas the probability of it being 80 is around 1%.\n", - "> *Random variable* will be precisely defined later. For now just think of it as a variable that can 'freely' and 'randomly' vary. A dog's position in a hallway, air temperature, and a drone's height above the ground are all random variables. The position of the North Pole is not, nor is a sin wave (a sin wave is anything but 'free').\n", - "\n", - "You may object that human IQs cannot be less than zero, let alone $-\\infty$. This is true, but this is a common limitation of mathematical modelling. \"The map is not the territory\" is a common expression, and it is true for Bayesian filtering and statistics. The Gaussian distribution above very closely models the distribution of IQ test results, but being a model it is necessarily imperfect. The difference between model and reality will come up again and again in these filters. \n", - "\n", - "You will see these distributions called *Gaussian distributions*, *normal distributions*, and *bell curves*. Bell curve is ambiguous because there are other distributions which also look bell shaped but are not Gaussian distributions, so we will not use it further in this book. But *Gaussian* and *normal* both mean the same thing, and are used interchangeably. I will use both throughout this book as different sources will use either term, and so I want you to be used to seeing both. Finally, as in this paragraph, it is typical to shorten the name and just talk about a *Gaussian* or *normal* - these are both typical shortcut names for the *Gaussian distribution*. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Gaussian Distributions\n", - "\n", - "So let us explore how Gaussians work. A Gaussian is a *continuous probability distribution* that is completely described with two parameters, the mean ($\\mu$) and the variance ($\\sigma^2$). It is defined as:\n", - "$$ \n", - "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 }\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

Don't be dissuaded by the equation if you haven't seen it before; you will not need to memorize or manipulate it. The computation of this function is stored in stats.py. \n", - "\n", - "> **Optional:** Let's remind ourselves how to look at a function stored in a file by using the *%load* magic. If you type *%load -s gaussian stats.py* into a code cell and then press CTRL-Enter, the notebook will create a new input cell and load the function into it.\n", - "\n", - " %load -s gaussian stats.py\n", - " \n", - " def gaussian(x, mean, var):\n", - " \"\"\"returns normal distribution for x given a \n", - " gaussian with the specified mean and variance. \n", - " \"\"\"\n", - " return math.exp((-0.5*(x-mean)**2)/var) / \\\n", - " math.sqrt(_two_pi*var)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

We will plot a Gaussian with a mean of 22 $(\\mu=22)$, with a variance of 4 $(\\sigma^2=4)$, and then discuss what this means. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from stats import gaussian\n", - "plot_gaussian(22,4,True,xlabel='$^{\\circ}C$',ylabel=\"Percent\")\n", - "\n", - "print('Probability of 22 is %.2f' % (gaussian(22,22,4)*100))\n", - "print('Probability of 24 is %.2f' % (gaussian(24,22,4)*100))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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YizbYiBFRwJxDI9jb3IcK7qQfUpIk4frSVLx/vFt0KUSkETZiBsW5eSVmoi4YuVTWOLCw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\n++/XYmlxKm4oTVN9TaRl4i/mQoHgeFF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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Probability of 22 is 19.95\n", - "Probability of 24 is 12.10\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So what does this curve *mean*? Assume for a moment that we have a themometer, which reads 22$\\,^{\\circ}C$. No thermometer is perfectly accurate, and so we normally expect that thermometer will read $\\pm$ that temperature by some amount each time we read it. Furthermore, a theorem called **Central Limit Theorem** states that if we make many measurements that the measurements will be normally distributed. If that is true, then this chart can be interpreted as a continuous curve depicting our belief that the temperature is any given temperature. In this curve, we assign a probability of the temperature being exactly $22\\,^{\\circ}C$ is $19.95%$. Looking to the right, we assign the probability that the temperature is $24\\,^{\\circ}C$ is $12.10%$. Because of the curve's symmetry, the probability of $20\\,^{\\circ}C$ is also $12.10%$.\n", - "\n", - "So the mean ($\\mu$) is what it sounds like - the average of all possible probabilities. Because of the symmetric shape of the curve it is also the tallest part of the curve. The thermometer reads $22\\,^{\\circ}C$, so that is what we used for the mean. \n", - "\n", - "> *Important*: I will repeat what I wrote at the top of this section: \"A Gaussian...is completely described with two parameters\"\n", - "\n", - "The standard notation for a normal distribution for a random variable $X$ is $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$. This means I can express the temperature reading of our thermometer as\n", - "\n", - "$$temp = \\mathcal{N}(22,4)$$\n", - "\n", - "This is an **extremely important** result. Gaussians allow me to capture an infinite number of possible values with only two numbers! With the values $\\mu=22$ and $\\sigma^2=4$ I can compute the probability of the temperature being $22\\,^{\\circ}C$, $20\\,^{\\circ}C$, $87.34\\,^{\\circ}C$, or any other arbitrary value.\n", - "\n", - "###### The Variance\n", - "\n", - "Since this is a probability distribution it is required that the area under the curve always equals one. This should be intuitively clear - the area under the curve represents all possible occurances, which must sum to one.\n", - "\n", - "This leads to an important insight. If the variance is small the curve will be narrow. To keep the area equal to 1, the curve must also be tall. On the other hand if the variance is large the curve will be wide, and thus it will also have to be short to make the area equal to 1.\n", - "\n", - "Let's look at that graphically:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "xs = np.arange(15,30,0.1)\n", - "p1, = plt.plot (xs,[gaussian(x, 23, .2) for x in xs],'b')\n", - "p2, = plt.plot (xs,[gaussian(x, 23, 1) for x in xs],'g')\n", - "p3, = plt.plot (xs,[gaussian(x, 23, 5) for x in xs],'r')\n", - "plt.legend([p1,p2,p3], ['var = .2', 'var = 1', 'var = 5'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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m3XyDBw/G5MmTMWjQIACWivbaooqIyN2VlEjo1s1sd1EFAOHhJuj1nGNF7mHSpEl4//33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\ngegcgciK67neFobeFoHeGove1huDLQK9NZxIWwQtrM2QVD1mXF9iSiK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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So what is this telling us? The blue gaussian is very narrow. It is saying that we believe $x=23$, and that we are very sure about that $(90%)$. In contrast, the red gaussian also believes that $x=23$, but we are much less sure about that $(18%)$. Our believe that $x=23$ is lower, and so our belief about the likely possible values for $x$ is spread out - we think it is quite likely that $x=20$ or $x=26$, for example. The blue gaussian has almost completely eliminated $22$ or $24$ as possible value - their probability is almost $0%$, whereas the red curve considers them nearly as likely as $23$.\n", - "\n", - "If we think back to the thermometer, we can consider these three curves as representing the readings from three different thermometers. The blue curve represents a very accurate thermometer, and the red one represents a fairly inaccurate one. Green of course represents one in between the two others. Note the very powerful property the Gaussian distribution affords us - we can entirely represent both the reading and the error of a thermometer with only two numbers - the mean and the variance.\n", - "\n", - "The standard notation for a normal distribution for a random variable $X$ is just $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$ where $\\mu$ is the mean and $\\sigma^2$ is the variance. It may seem odd to use $\\sigma$ squared - why not just $\\sigma$? We will not go into great detail about the math at this point, but in statistics $\\sigma$ is the *standard deviation* of a normal distribution. *Variance* is defined as the square of the standard deviation, hence $\\sigma^2$.\n", - "\n", - "It is worth spending a few words on standard deviation now. The standard deviation is a measure of how much variation from the mean exists. For Gaussian distributions, 68% of all the data falls within one standard deviation($1\\sigma$) of the mean, 95% falls within two standard deviations ($2\\sigma$), and 99.7% within three ($3\\sigma$). This is often called the 68-95-99.7 rule. So if you were told that the average test score in a class was 71 with a standard deviation of 9.4, you could conclude that 95% of the students received a score between 52.2 and 89.8 if the distribution is normal (that is calculated with $71 \\pm (2 * 9.4)$). " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following graph depicts the relationship between the standard deviation and the normal distribution. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from gaussian_internal import display_stddev_plot\n", - "display_stddev_plot()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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\n", - "

**Sidebar**: An equivalent formation for a Gaussian is $\\mathcal{N}(\\mu,1/\\tau)$ where $\\mu$ is the *mean* and $tau$ the *precision*. Here $1/\\tau = \\sigma^2$; it is the reciprocal of the variance. While we do not use this formulation in this book, it underscores that the variance is a measure of how precise our data is. A small variance yields large precision - our measurement is very precise. Conversely, a large variance yields low precision - our belief is spread out across a large area. You should become comfortable with thinking about Gaussians in these equivelant forms. Gaussians reflect our *belief* about a measurement, they express the *precision* of the measurement, and they express how much *variance* there is in the measurements. These are all different ways of stating the same fact.
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Interactive Gaussians\n", - "\n", - "For those that are reading this in IPython Notebook, here is an interactive version of the Gaussian plots. Use the sliders to modify $\\mu$ and $\\sigma^2$. Adjusting $\\mu$ will move the graph to the left and right because you are adjusting the mean, and adjusting $\\sigma^2$ will make the bell curve thicker and thinner." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import math\n", - "from IPython.html.widgets import interact, interactive, fixed\n", - "import IPython.html.widgets as widgets\n", - "\n", - "def plt_g (mu,variance):\n", - " xs = np.arange(2,8,0.1)\n", - " ys = [gaussian (x, mu,variance) for x in xs]\n", - " plt.plot (xs, ys)\n", - " plt.ylim((0,1))\n", - " plt.show()\n", - "\n", - "interact (plt_g, mu=(0,10), variance=widgets.FloatSliderWidget(value=0.6,min=0.2,max=4.5))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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+sLlOcTFR+mwxNzGGWdeek6XYaJdWvV9ndSnAoEUz5QCssZt3Oplv39+uP3+4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\nZ7fqrCFurfxckSblJFtdFgA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AAABJRU5ErkJggg==\n", - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 7, - "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Computational Properties of the Gaussian\n", - "\n", - "Recall how our discrete Bayesian filter worked. We had a vector implemented as a numpy array representing our belief at a certain moment in time. When we performed another measurement using the *sense()* function we had to multiply probabilities together, and when we performed the motion step using the *update()* function we had to shift and add probabilities. I've promised you that the Kalman filter uses essentially the same process, and that it uses Gaussians instead of histograms, so you might reasonable expect that we will be multipling, adding, and shifting Gaussians in the Kalman filter.\n", - "\n", - "A typical textbook would directly launch into a multipage proof of the behavior of Gaussians under these operations, but I don't see the value in that right now. I think the math will be much more intuitive and clear if we just start developing a Kalman filter using Gaussians. I will provide the equations for multiplying and shifting Gaussians at the appropriate time. You will then be able to develop a physical intuition for what these operations do, rather than be forced to digest a lot of fairly abstract math.\n", - "\n", - "The key point, which I will only assert for now, is that all the operations are very simple, and that they preserve the properties of the Gaussian. This is somewhat remarkable, in that the Gaussian is a nonlinear function, and typically if you multiply a nonlinear equation with itself you end up with a different equation. For example, the shape of $sin(x)sin(x)$ is very different from $sin(x)$. But the result of multiplying two Gaussians is yet another Gaussian. This is a fundamental property, and the key reason why Kalman filters are possible." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Summary and Key Points\n", - "\n", - "The following points **must** be understood by you before we continue:\n", - "\n", - "* Normal distributions occur throughout nature\n", - "* They express a continuous probability distribution\n", - "* They are completely described by two parameters: the mean ($\\mu$) and variance ($\\sigma^2$)\n", - "* $\\mu$ is the average of all possible values\n", - "* $\\sigma^2$ represents how much our measurements vary from the mean\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "from IPython.core.display import HTML\n", - "def css_styling():\n", - " styles = open(\"./styles/custom2.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "