From 43070a4439c021182d2207d2f987e0cda5d864f9 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sat, 18 Jul 2015 17:21:27 -0700 Subject: [PATCH] Copy edit of UKF chapter. Also found a mistake in the text about computing the residual of angles that was duplicated in the EKF chapter, so I fixed the error in that chapter as well. I pulled out the 'track in a circle' example as it is the usual sort of textbook nonsense problem that no one cares about. I created an 'old-content' Notebook in case anyone still wants to see it; I may put more content there as I continue to edit. --- 10-Unscented-Kalman-Filter.ipynb | 780 +++++++++---------------------- 11-Extended-Kalman-Filters.ipynb | 4 +- code/ekf_internal.py | 2 +- code/ukf_internal.py | 3 +- old-content.ipynb | 275 +++++++++++ 5 files changed, 492 insertions(+), 572 deletions(-) create mode 100644 old-content.ipynb diff --git a/10-Unscented-Kalman-Filter.ipynb b/10-Unscented-Kalman-Filter.ipynb index bef1ee1..fb3aaee 100644 --- a/10-Unscented-Kalman-Filter.ipynb +++ b/10-Unscented-Kalman-Filter.ipynb @@ -294,9 +294,9 @@ "outputs": [ { "data": { - "image/png": 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RUctxSL0WKqsswbJNCxotqDt7BGDGXf/F/cNnsqAmAuDt7os59y9GeJdBeper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\nbYo9IiJnZveiWhRFxMbGQiaTYdeuXfbunoio3ebOnYu0tDT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21Q8hpyQdhy//gCpFudayNnIf+LkHw9ulC8xkfAOA6EGUVOTj3K1o3My9DBH1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\nYlJNREREROQkJtVERERERE76f+qZr2IL3n+nAAAAAElFTkSuQmCC\n", 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wWq243e7YfaJtyKJMJhMOhwO/38/48eMpLi5m3rx5TJ06VUpsblA4HGbTrk1k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\n7ASG6V2Wzt4G/p5HK+FPB8W6QmJrB0X9w2m4aOmgqCgKmqY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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -403,14 +403,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "Difference in mean x=0.153, y=42.145\n" + "Difference in mean x=-0.168, y=42.935\n" ] }, { "data": { - "image/png": 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SL9mnPEf+yP5DoRA8Hg+SySQaGhpQVlaGyspKm7pJEiozz3XXPMfntUml0Ofz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\nLS20dOlS8vf3J39/f8rOzqbW1lanYhcWFlrE6/m+Z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PBoMIBAIq65vZ5SRgJIIcN4lnPB5HQ0ODze1OIhsMBpWLXo5JT/KR91ZPQtLb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\ns7Oz6nQ6arfboVWXk9DZ2dmQS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ZBsaD/Hj7iofaB+zz+fj000955513+OSTT0ilUqTTaRKJbMCy2WwYhkF5eTkv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\nbVte2hnuxEQwylR8CqdDwW4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oHpokFBqlo+8kj1Q8gXYftxvMBoqiUFJSQklJfvaVWpaJ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\ny8zf/PGDOT0SKh6Ps3//fr7//e/zzz/4IdFYlFQ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F1GyCnsp1bG73aayZyE1S+BWRyxx2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\nDIVfERERESkYCr8iIiIiUjD+P+YRYgeIfMgRAAAAAElFTkSuQmCC\n", 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jxsr4hSgsVgIAjA2bYcrgt9Fcbi5yMmroPJ07YFSvqUI7/UwKdqVtFDERETUG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\nAElFTkSuQmCC\n", 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iizg3Z+HlqvkeRBeXkizHWhhNl9T5im0z6/Ktpum8MZ9gaQkGfSHZHCq2xW61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\nr7c7Ey57QYLfTbGrZ/vKsu2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A93g8nDlzhlOnTmEYhmzePETSpQKhARgd8HXtTvVyrUG9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\nzO3bd/jVr35FIvH8BJlqp81prYLTMyKTgXTSxW4uzrJcVmE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ZBsaD/Hj7iofaB+zz+fj000955513+OSTT0ilUqTTaRKJbMCy2WwYhkF5eTkv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\nbVte2hnuxEQwylR8CqdDwW4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oHpokFBqlo+8kj1Q8gXYftxvMBoqiUFJSQklJfvaVWpaJ\n33/puu0MXuD67QwuTDNFaWk77e2v09b2MqWlC3KtGNe3Y0SjI0Qig0QiI8Ri48Tj4ySTU3y7IpwN\ny98MbaXTEUhHSMagZ7KPnosnAdA0DVXNtkuYpolpmjdUXxVFQVXVXMCcaSm4lVgsllvVpWkahmHk\nVnV5PB4qKyupqamhqamJ5uZmmpubcyF2JtDW1NTgcDycKmwkniSRieM0iq/fXdy9cDRNpS7DbmJu\nKK5HeSHukqIo/PGzaxia+D3hcJArgTMsK3t0TvU63o07rSInk1MMDn5CT89bDAx8nLvkIlu5VbDb\nS8huZ9jCwoVv0NKyG5frxmqTrpdQWjr/O8+TTken2y0GGB8/xtDQ53i9J0kkfDMn/s6Xz2RuDMm3\nen9v9/cz77NlWbk2hpKSEioqKqirq6O1tZX58+fT2tp6U4W5tLT0vnyOxePxXF/v3YrEU8TTCQxD\nwo6ASDRDa6Wbco+0wIjiJ+FXzHkuh53/+pUNhKKHOX5ihN5wR1EOwN2r7+sfjsWGrrts4swNl01k\nN0MYaFoZ8+a9woIF+2ho2H7TWjTLMkkkJonFxqefxojFxolGRwiH+4lEhm4YvrOsNJrmQFGmV3WZ\n6dzg3Z3QNC3XpqDr+g2tCzO9uIlEgmQyic1my21RyP57ZP8uu+nCIh6PE4/H8Xq9dHZ2Aje2NgC5\nYTXTNCkpKckNn9XX1+cqwt9uw6ipqaGioiJXob7eBx98wE9+8hMaGxtZvnw5GzduZOXKlaxYsYJF\nixbd9jKPRDJNNJkAJYPdJpXfuS6eyIBpp8ThwuOUFhhR/KTnV4hpl/sn+A9vfcWpUyZNttU0uIpj\n6ON+9Pze+qpkE+gFTmMYl0inJwHlpssmSkrm0dr6AjU167HbS4nHs8E2Ehm4bkDOSyIxSTodRlXt\nqKqe2zf8/WvXVGy2mQCs5PYTK4oyvZ+4ClXVSacjRCLDQHaH8UyrxMyVx9u2beOnP/0pL7zwAtXV\nN15+Ypomk5OTTExM4PV6b3gaHBy8aX9uKBRCVdXcUBtkh+ISiQTp9O37lmde5vrBtmQySSqVwuVy\n5cJybW0tTU1NjI6O8sUXXxCPx3Mv73Zn+9ZjsRi1tbUsW7aMDRs2sGrVKpYvX86SJUuIpeDgqUv0\nRzpZvvD+XmssCs/oRIJYwMOTix5h3eKGfB9HiHsmA29C3IXD5/v563fPcvaswhL3Y1QYNfk+0j25\nX9seQqEQ7733HpFImGxV9W+Bk2Q3MKSYqbQqSnY4zWZzoSja9JBaKledBSW34uy7hte+vUPYNJPT\nF264MYxyHI4aXK7s/mCPpxWns3b6qS73+5n9wdezLAuf7wwXu/6W3t63yMQn0e0asVgs92+TTCZZ\nvnw5P/vZz9izZw8LFy6843/v69/O1NTUTUHZ6/UyPDycC8ter5fJyUmmpqZy68m+XSW+3UqzuzET\nihVFIRqNUl5RQWV9E41Lmli7YTEt7S00L2jOXQ0s5pbO3gjV9nnsWr2c5prSfB9HiHsm4VeIu/TO\n7zt467NuOi7YWV2+GZctP4Ni9+rW1dpv7NqV3fOb/bF/cnqwbOyGdoNIZJhwuI9AoI9AoB+IADMX\nT9xZa0GWct0NcgqmmcE0sy0DM7fHOZ11uN2NeDytuFyNNwXa+3nVsmVZXAh8hbPsEk16F1dO/IYz\nZ85gGAahULZC7nBkbyGrrq7mJz/5Cfv27WPDhg23bD+4H6LR6C3D8ujoKAMDA4yMjOTCcjAYJJlM\nYhhGLrj/IAo4nA5UVSURS+AuddM0v4mFKxcyf8l8Wha20NLegsvjun/vqJhVTNPi9KUQj9StZffG\nxRi6dEOKwifhV4i7ZFkW/+WDU3x0aJhr3S7WVDyJrhXe0vcbq7UA14DzgB/w8/+3d+fxcdf3ncdf\ncx+aQ6MZSaP7liXLl3zbgG3AYMDGgRAKpIHsJk3S5ug22za723Z36eOxTTYt5Nhe2yZps4QckDhA\nzBFuDATft3zItizrPkaa0dz3/PYPB4ODb0sajebzfDz80GBrPB/xGM+8f9/5fD9flSqE0ZgkkfCf\nO8b4g9aBs+E0k7ncqqOGs1sHVKjV/HasmBG9vhCj0fWh1dmq3x6HfH6g1emsWdtcGEkFOeh/m2XL\nFP7Hp2/EboSXXnqJn/zkJ7z++uvodDpCoRCZTAatVovJZEKtVrN582YeeOABbr311mmbzHAh8Xic\njRs3XvTi5nqp1CqUzNm3B4vdQnlNOY3zGqlvrWfl+pXYHLJCOBv4g0kGBtSsqm1nzcLZ0eolhIRf\nIa5BMpXm8ae389YOH96hQuYXrkKbYyPQhoYG2bp164d+5y3gaS5+sMT5q7Nnx4UlUJQ0Op2VZFKP\nolgAO1D02682wIrJVMqGDffjdNb+9jCL3HA6eJSUtYs71xXx5w+uPhfEE4kE27Zt4+mnn+aZZ54h\nHqUfA34AACAASURBVI+fa0F4f3RcPB5nzZo1F+0Tng5/9md/xjvvvHPV9wtG4gRjYQwGrvq4Z51B\nxxf/5xepbqq+6scVM0/vYBRtopi1rfNpqZ7+57AQU0HCrxDXKBCO882fvsuOvREiY07mOVagVmmy\nXdYV+2j43Qv8gLPtClrAjNVahs1W+aHe2dLz+mZNplL0+rP//q+0hSKXpDIp9oy/QduCOF+5fxGr\n2qo+8j2KonDgwAG2bNnCT3/6UwYHB1GpVBftE77nnntoaMjuEcqX88ruLnb07qFtjhG9TqY95LPD\nnUHqbC3c3t6C0y7tLWJ2kPArxHUY80f425/9hl17YyQnSplbuBS1KjfCQjAYZOvWX53b6Ha2VzcC\nWAEdFouFzZs3Y7FcWU/zVByVPBOMRPsYUg6w7kYj/+uzt6DTXvoCp7e3l+eee44nn3wy633C1+r5\n7SfY1b+bJfOsV73yK2aPeCLD0RNRllUu4Y7ljTl38SrExUj4FeI6DY0H+bufvcfufQlUoXJa7Itz\n4k3iaja8Xc3fmc2jkqeCoijs975DTbOfP7yvjfVL6q/4vhMTE5fsEzYajWg0mhnTJwxnW3pe2NHJ\ngZF9LJknr+35zONNEBg3c2PTQpbOKc92OUJMGgm/QkyCnuEJHn96B3v2JTHEq2myLsiJwDdbV2sn\n23h8hDPJXay70cDffPaWa9rx/n6f8FNPPcWzzz57wT7hRCJxXp+w0+mcgp/m0sLRBC/uPk6nr4OF\nLbk5yURMjpNnwhRpqrllfhvVpfI+L2YPCb9CTJJTA16+9fQO9u5PY03VU2+ZmxMBeDau1k42RVE4\n6PsNFQ0+vvDxVjYsv/rZvr/7983UPmFfMMqv98oBF/kunVY4cCxIu3sxG5Y1YZQRZ2IWkfArxCQ6\n0j3Kd7fsZv+BDEVKM7WWOdkuSUwSb3yU7sRO1t1k4Ot/cCt63eRtbuzp6eG5557jxz/+cdb7hIe9\nIV49cITRRDfNdQVT8hhi5hvzJfB5DKysW8jqeR/d6ClELrtchp1ZuzCEmOHa6kr4w82LWThfxTgn\nOBM6zkWuH0WOceiLUScL6e6N8+7h3kn9u2tqavjjP/5jdu7cycjICP/yL//Cpk2bMJlM6PV6YrEY\nfX19fOc732H9+vUUFRXxyCOP8MILL5w7uniyJJJpkukUWq2s/Ocz70SSIlMR5S5pfRH5R8KvEFdp\ncXMZX/hYO4sWqvCqTnI6dFQC8CygUqmoLmiirw9e2dNFKn2xecjXp7CwkIceeoitW7cyMTHBL37x\nCz7zmc/gdDoxGo3E43H8fj9PPvkkn/zkJ3E4HGzYsIEnnniC8fHx6378RCpNKpNCJ+E3b6XSCsFw\nBofJQVmRtL6I/CPhV4hrsKylgi/du4T2hWqCmtOcCh6WADwLFOlLycSsdPdHOXhqeMofT6/Xc9tt\nt/H9738fj8fD22+/zde+9jXq6+sxGAwkk0lisRivvPIKX/rSlygvL6e9vZ3HH3+crq6ua3rMRPJs\n+NVq5eU/X/n8SWwGO6UOqxxnLPKS9PwKcR06ukf5x2f2cOBgGkO8imbbQtlIluMGI2fwGw9z7+0u\nvnr/qqzVcSV9wsXFxTzwwAPcd999V9wnfPj0CNs6D2K0BSh15d6x3eL6HesK4TbWcfO8VqpK5P1d\nzD7S8yvEFJpXV8J/+sRylrRrSZj6OO7fR0aZmo/LxfQoMVYwMa7hcNcYo75w1uq4UJ/wxo0bz+sT\n7u3t5dvf/vZ5fcIvvvjiJfuEFeXsL7lGy0/xRIZoVEWRyUGZU/p9RX6S8CvEdWqpdvHV+1ewtF1H\nxjLIMf9eCcA5TKvW4dSXMzIC7xzqyXY5wAd9ws8///xl+4Qfeuihy/YJKyjyCUWeGp9InN3o5rSh\n1UgEEPlJ2h6EmCQ9wxN8+xc72XcwQdLvYq59KVq1LttliWsQSPg4EXuXtTfp+dsv3DZjQ8K1zBMO\nKQVs6zyApShMcZEccpJvDncGqbPN4daFLZQ4ZNSdmJ1kzq8Q06jfE+C7W3ay/1CMiVEb8wqXY9CY\nsl2WuEpnjzx+m/rWAH/+qSU5c/TrlfQJ2x1FzF25ilV3LmbZDXOnbJ6wmHmC4RRnetMsrWjntqX1\nsvovZi0Jv0JMs3F/hL9/Zhd7DgXp7zHSZl+BRWfLdlniKg1GzhAwHuYTd5bwlY+vyHY5V21iYoKX\nXnqJH//4x7zxxhvodDqCwSCKoqDWaNAbdGg0Gpbfspyb7rqJBSsXoDfISvBsdqonglVVzk1zWplT\n7cp2OUJMGQm/QmRBJJbkn3+1m/f2j3PqhJY51qU4DMXZLktchUQ6zp6JV1lzo5pvffH2nB4JlUgk\n2LZtG0899RQ//8UWYvEY6VSSdCqNSqXCaDaSSqZoW9bGurvXsXTtUmwOuWCbTRLJDB2dEdrL2rl9\naaMcZyxmtctlWM2jjz766IXuGI/Hz902Go2TX5kQs5hOq2F5SwXhRIRQ0k/n4CBaTFh0ciGZKzRq\nLeOxUfQFEVrrHLhz+DAAjUZDQ0MDmzdv5rZ7HsZcW0FRqZHAuI94LI6SUUgmkgz3DXPgvQP88ge/\nZPur24lFY9iddqx2mQqQ64Y8cYw4mFtRRXWpvA6J2e1yGVbCrxBTRK1W0d7kRqPN4IuNc2pomFQK\n7Dqn9NrliEQ6TlgZo8ytY0FDabbLmRRD4yF8JFiybi6/97l7uHnzzbjKXAQnggR8ATRaDYlYAt+Y\njyN7jvDST1/i5adfxuvxUmAtwFHskOdvjslkFE73x6ix17GkqRKTQTbiitntchlW2h6EmAbbDpzh\nRy93cKhDwZSspNm2ALVKk+2yxGWEkn6OR99m/Toj//vz62dF6Nt/cohtnQcodEVwOs7v8Q0FQux9\ney/bnt/GoR2H0Gg0xCIxFEVBo9Wg00ufcC4a9yXwjOpYXr2AtYtqs12OEFPuchlWmn6EmAZrF9Xi\nsJr4V8M+Dh/p56AvxFz7Mgwa+VRlJivQ2kjHTQx5ovR7ArPiNCytRo1GrSGV/ui6h8VmYe2mtazd\ntJZkIknH7g7efeldtr+6nVQyRSqRIpaK8dav3mLH6ztIJaRPOBeMjCcot1RSV+bIdilCzAiy8ivE\nNOr3BPjn53azvyPCYJ+RVtsSbPqibJeVNdGoh9/85st4vYeJxcYoLV1Ne/tfUlKy7AruO8qvf303\nmza9gU43dfNKTwYOYS7r4csPtnLH8sYpe5zpcrx3jDePHkRt9lJeemUXX4qicProad575T3eefEd\nxkfHUaEiEU8AnNswV91YzbrN61hx6wrKqsum8scQVygUSdHVnWRp5WJuW1KPZobOrBZiMsmGNyFm\nEFuBgRWtlUzE/ETSAY4NDqDFgEVrnxUfqV+NTCbFc8+tZPHiv2LVqsfx+0/R1fVTTpz4IRUVt2Gx\nVF70vslkiJdeupP29r/E6Zw/pXWmMgkCmWFqKvUsac6Neb+X4g/FOOMZI6UOYbdeWe+nSqWiqKSI\nhasWcvcjd0ufcA7pH45RqHUzv6aK0hzetCnE1ZANb0LMMHqdhhWtlaBKEkz6OD06QigWxWEoRqXK\nn1WZdDpBQUEFNTWbACgrW8fx498jmQwTCJxgzpz/eMH7ZTJJXnnlXpqbP01j44PTUutQtAe3W+Hm\n9rppebypFIomODPqIU4Ah+3aNj4V2AqYs3AOG35vAxs/tZHK+kqSiSRjQ2PngnA4GObk4ZNs27qN\nZ37wDH1dfej0OlxlLjRa6XefDvFEhr7BBA1F9SxprkAn/99FnpDwK8QMpFKpmFdXQrmrgLGoh9HA\nBH2+URyG4rw5Elmt1uJwzD333xqNgUQiyPDwO4RCvdTUfAyz2X3efRRF4a23/gOlpatoa/vStNSp\nVes54++iqDjBhmUNOf+xcSSepHtknEjaT1Hh9T/X9AY9tc21rN20lns/ey/NC5vR6rSMDoyiUqlI\nJVLEY3F6TvSw681d/Pz//pyje4+CAs5SJwaTYRJ+KnEhfUNRbJpi5lVVy3gzkVck/Aoxg1UW21jY\nWMpoyEMoEeLE8AAmjQWzNj8/nnQ45tLR8X9QlAxqtY7q6jvP+/OdO/8LOp2FpUsfnbaaVCoVntgQ\ntqI4y+e6KbTk9uthLJHi9PA4gaQXl2NyJzVoNBrKqstYccsKPv4HH2fJTUuw2C14R73nzxPu/eg8\n4UJXIRZ7fj7vp0I8kaF3IEGjs5FlcyrR62TVV+QPCb9CzHC2AgMrWysJJUPElAAnhweJJhIU6l15\n1QYBoNNZGB3djd9/gnC4l/nz//O5XtHDh79LMHiaG2/8x2mvK5D0ojEFmdfoyPkVtGQqQ9fQOL74\nGCXOqRtTdrV9wi/+5MUL9glvfWIrz/zbM1gLrRSXF6NW59e/iWv14VXfmtLCbJcjxLSSOb9C5AhF\nUXh9XzdPv3mMzs4MYZ+NVvtizNr8Ol2rq+tpXn/9bC/vpk1vUl6+lq6up+jq+hm33bYlKxcEveGT\npB3H+cInGrhv7dzL32EGC0cTvLj7OJ2+Dha2ZOe5dd484e2H0GgvPk/4yJ4jjA6MYiowodFqWP/x\n9ay/bz3VjdVZqT0XxBMZjpyIsNC9kPWLG7GYZBazyC8y7UGIHKFSqagvd7CwoRRvdJxoOsjxoT60\n6PNqGoTVWsOhQ4+hKBn0+kI0GgMdHd/h9tufQZ2lfuhIKkRMO8L8ZlvOn/SmVqvoGvAxEBi84lFn\nk+0jfcILmtHoNIwOfrRPOB6Nk8lkSCVTJOIJTnWc4pWfv8Ibz71BJp3BXe3GaJL3qA+TVV+R76Tt\nQYgcY7cYWd1WRZo4UWWC7rERJiJBCvUuNHlwKpxGo2dk5D0CgS6CwTP4fIe5/fbnpnSW7+VEU2Ei\n6iHamiwsbs7t+bVqtYrekQCDgRGKCjVoNdm9qDrXJ3zr+X3C4yPjxONxUonUed+fyWRIp9MEJ4Ic\n2XOEZ//9WQ5tP4TRZMRd5c77SRLv9/o2OBuk11fkLQm/QuQgrUbNokY3lSUWvLExJqJ+TnsGKdDa\nMWrM2S5vyiUSAfr6XiSVCrNmzb+eNxUiG2KZKEEGaGk0s7y1Iqu1TIYRX5jBgAdzQQaDfub00H64\nT3jzI5vZ/+5+PEOei35/OpUmk84wOjDKvnf2seV7WxjoHsDutONyu/Lm05IPk1VfIS6fYeV4YyFm\nsGUtFdSVOfjBi/vYe8RH58n3cMZqqbW0olXP3n++5eU3n7s9NPQ2lZW3Z7Ea0Kq0pNNnJyXMBmaj\nDqPGQDwRznYpF6UoCulUGo1Wg8FoIBaJkclkLvr90XAUgG1bt7H91e0YzUY23L+BW+69JW9Om4sn\nMvgmMixwu2mqdGa7HCFmLFn5FWKGMxt1rJpbSUGBmlDahzfio3tsALPWikmbvVaAqZJOJ9i27TMo\nSopEYoJEwsfcuX+U1ZpSmSSeVA+NdXrWLKzJai2TIRRN0Ds2TkK58lPepptKpeL2+29n8yObaV7Q\njM1hI+QPEQlFMJlNpFNpLrRfW1EUUskUsUiMzkOd/Pqnv+adl95BrVbjrnajN8zezV/d/RGK9G7a\nKqtk1VfkNZn2IMQs0u8J8MTLBznQOcHJE1CorqbeMnfWHIyhKBlef/1BamvvIRodZfv2s6POHnjg\nJDZbfdbqmkiM0ZvZzic2OvnT31udtTomy+BYkFcPHmE8fYammty6gIqEIhzde5QDvznAnrf3MNI/\ngsFoIBqJomQu+HYGgMFkIJPOsGDlAu566C7ab2xHq5s9n54EQim6e5K0ly/i1sX1GPWz52cT4mrJ\ntAchZhFbgYEb5lVjt2oIZXx4IxN0efoxaQtmxcEY7777RZzOBbS2fgGz2U1Hx3cBMJvduN03Zq2u\nQNJHXD/E8vkOljSXZ62OyZLJKJwZ8eEJeyh15dYJazq9jvLachbftJhNn9rE3Q/fTdP8JmyFZ1eG\no5EoBrOBdCoNH8rC7/cHD/UMsfut3fzy+79kdHCUouKiczOFc5WiKJzqiVBlq2VRXSWljtx/LRDi\nesjKrxCz1LA3xBMvH2TfMS8nToJVqaDe0oZek1th5n27d/93Uqkwq1Z969zvPfPMcjyePTgcbdx/\n/+Gs1dYfPk3cfoTP3VfHA7fMy1odkyWVzvD89k72D+9l6fzZ9foeCoQ4tvcY+3+zn73v7MUz6EFv\n0F9wZVitVqMz6LAWWrnzwTu5+WM343K7slT5tRsZi+Mb17G4Yj43t9ehVudukBdiMsjKrxCzlMWk\nZ1VbFc5CPcH0OP6Yn5OjvahV6pybC9zR8fd4vQdZs+Z75/1+Oh2lr+/XxGIeqqs3UlCQnVXXsfgQ\nepuPtUvKaKwoykoNk+n9cWdDwVEcM2Dc2WTSG/RU1FWwZM0S7n74bjZ+aiONbY1Y7VZC/hCxSAyj\n2UgqmTq3qS4SinBs/zGe/9Hz7HpjFzq9DneVG51+5rcTJVMZunqjNDqaWDanCqs5Ny9+hZhMMupM\niFlMpVJRV+ZgeUs5ScKktUEG/R4G/MOYtZacGIt26tRP6Op6ittu+wWq35ljbLM10dHxXRQlTTod\npa7u3qzUOBztxeIKcuuySqpKZsdK6XggynDAi0afwGycvbNg3w/DS9cuPRuGf38jDfMasNgtBCeC\nxKJnw3AiliCdTuMd9XLgvQNs+f4WTh87jdU+s49V7huKYVY5aS2voaU691athZgKEn6FyAMFRj3L\nWyporCwkkpkgqQpxarSfQCyEVeeYsRvi+vp+zYEDX+eOO15EqzV95M+1WhPBYDfj4wfw+4/T3Pxp\n9Hr7b+/7MjqdFZ1uavsbFUWhK9RBbX2aT6xrmTUra+FYkgGvj3hm5k58mAp6o57KusqzYfiRu7nr\nk3fR0NaAxWYh6A8Sj8bR6DTEY3H6u/rZ/up2nvv35/CN+XC5XdidM+fiJxJN0z+UosnZxIrWSgyz\naAOfENdDen6FyDPJVJpX95zmhR0n6TqdZnBAQ4WxicqCetQz6IS4kZEdvP32Z9m48TXM5ovPYQ2F\netmypZ143Ed19SY2bHgWn+8IL798D/fddwC93jqldYaSAY5Ht3HbzSa+8blbc6qd5FI8E2Fe2X+M\n/shJ5jbKBqn3vX9y3P7f7GffO/sYHxkHBVKpszOey2rKuPOhO1m7aS0OlyOrtR7rCuHUVbGysZm2\nupKs1iLETHK5DCvhV4hZyheM8ottR3n30CCnuyA0Yaa2oIViY/mMCHDPPruKdet+SGHhnMt+r99/\nir17/5rBwTfQ6SwUFrawYsXfUVjYPOV19oe7iFmP8ul7qnlkw8Ipf7zpkkyleWHHCQ6M7KN9rlU2\nSV1EwBc4G4bf3c++d/cxOjAKnG05mrtkLht/fyPLb1k+7fODPd4EoyNqFpXP49bF9ejy/FhnIT5M\nwq8Qea6zd4yfvdnBsa4g3WcgHbFRa5lDkb50RoTgme6QbzsVjWP8108vYemc3B9z9mHbDpxh+5n9\nVFeDtUA+Mr8SAV+Ajt0d7P/Nfva/u5/RgVGMZiMr169k06c20bxg6i/I4okMR0+GaXG1cUNrHRXF\ntil/TCFyyeUyrLzaCTHLzal28d8fXsuOo/1s3d7JyTMBzpzZTV/YQa2lhUK9bJK5mHAqSEQZo6RY\nQ+ss3EzktJuxGqwEQz4Jv1fI5rCx+vbVrL797GEnAV+Ajl0d7H9vP4d3Hp6W8NvdH8FdUEF9abEE\nXyGugbzaCZEH1GoVq+dVsby1grcP9vDizpN0nfFxsnc7xnAxtZYWrDo5DvV39YZOUFkJaxdWU2Ca\nfcfiOm0mbAYrw+ExZtea9vSxOWys3rCa1Rum5+S/kbE4mYSJ2vJKFtSXTstjCjHbSPgVIo9oNWpu\nWVzHDfOqeH1fNy/v7qK7x8PRPg8W3FSZG7Dpc3+O7WQIp4L4M4O0VWnYsLwx2+VMCafNjFVvpcuX\nJp1R0Ejf74wWi6cZHEnQ6mpmQUMpep30+QpxLST8CpGHDHotd61sYu3CGl7Z08Vre7vp6x+ms38Y\nfaiIyoKGvO4JVhSFntBxKith3aJqCi2zc9yjXqfBaSugwGshEEzhsOfGyLPdb+3m5adfZqR/hOKy\nYm6880Zu/tjNl32+plNpvvGVb4AKHvijB2ia3zRNFV8/RVE43Rel3FJJY1kx7iKZ0CHEtZLwK0Qe\nKzDpufemVm5dXM+b+7t588AZege89PZ76R63UFnQQImxYkaNSJsOI7F+opphFtTM3lXf95U7rRSN\nOPH6B2Z8+PV7/Tz2p49xaMehc7/Xe7KXvW/v5Z0X3+Ev/uEvLnkqW8fuDna/tRuAQzsO8fjPH6eq\noWrK654MI2MJVGkzNaUVzJOxZkJcFznkQgiBQa+lpdrFzYtqKSs2ouiDqA0RhoMjdPv6UFAway1o\n8iAEh5J+OoN7mDdf4bObFtJU6cx2SVPKqNcy4InQ4xuk1KVHPYNX+7/x5W/g9Xh57KnH2PTIJiw2\nC50HO8mkMwz1DhGLxlh84+KL3r9jVwe73tgFnF0FjkVirFy/crrKv2aRWJoz/XGai5pZ0VKNrWB2\nHLQixFSRE96EEFdMq1FTV+bg5kW11JZbURsiaExhxmNjdI2fIZwMolXrMKhNs7IlIp6OcnhiO43N\nSe5cXcWm1ZefQZzrdFoNYxNRRgNedPo0phl81PH8FfO573P3YbFbsNgszF8+n8Z5jbz9wtugwIlD\nJ1h0wyJc7gtP5qifW8/6+9YTDUc5ffQ06XSaux66a5p/iquTTit0doeptNQyr6qShgrpyRficiT8\nCiGumlqtoqLYxk0LqmmtKcJgTqA1h0mpA/T5+xkIDpBWUhg1BWjVs6N7KpicoGNiJ5W1MdYsdfK5\nTUvy5uCHVCrDyEQYf3yCohnc+mC2mD9y0VVWU0ZwIsiJQycAiEVi3LDhhov+HQXWApbfspwD7x0g\nmUjO+PDb1RfBjJOW0lqWzinPm+ekENfjchl2drxrCSGmhEqlYm5tMXNrixn3R3jvSB/vHemjZyDM\n8PBx9nk6sWlLcZuqcOhLUKvU2S75moxGBzgdOUjTnDQrFzr5w7uXotXk5s9yLcqcVhwmB32jPTk5\n9eHhrz7MG8++QSQUYcdrOwj5Q1jsl94QNnfJXHpP9k5ThddmyBMnGTXQ4j4bfDV59JwUYipJ+BVC\nXBGn3czdq+ewcWUzx3o8vHu4l30nRxgeHqZ/dJjOMS1F+lKcBjdF+hI0ObAinMqk6A2fYCzTxfyF\ncMfKGh68ZV5eBV8As1FHsc2Sc1Mf3mc0G1m9YTWvbXmNVDJFx+6Oy/byeke9tLS3TFOFVy8QSjE8\nmqatuIUlTeWzcs60ENky89+dhBAzilqtoq2uhLa6EgLhONuP9LG7c5CuAT/jYwOMjA9wclyDXVeM\ny+CmyFCKTj2z3rgzSobhaA+94ZM4XHGWNKr41O3zWLuwZlb2Ml+JcqcV54iLUW9fzoVfgDUb1/Da\nltcAOLbv2CXDbzqd5uB7B7nvD+6brvKuSjyRoasvSoOjibYaN6Uy1kyISSXhVwhxzWwFBjYsb2TD\n8kbG/BH2nxxi/8lhOnu9eL3DjI0N0+VVUaB2YNe7KNS7sOkKszY6LZ1JMRYfoid8ggJ7hPmLYH6T\ng0+smZv3G4mqSuyU9LroH+wjEktjnsEb3y6kZVELao2aTDrD6WOnL/m9O1/fid1lp7qpepqqu3KZ\njEJXb4RSUzkNpWXMqZrd00aEyAYJv0KISeGym7ltaQO3LW1gIhTj4Klh9p8a5ljPGL4JL/4JL2cm\nThCe0GDR2rHpirDpHVi0hejVhilbcU1lknjjo4zFB5lIerAXppnTBi31Vu65sYWFDfl7mMeH6XUa\nakoLGQiUMjI2Sl2lOdslXRWDyUBNcw3dx7oZ7hu+5Pdu+d4WNn5y4zRVdnV6BqPoFBuNrmoWN5XJ\nc1OIKSDhVwgx6QotRtYuqmXtolqi8SQn+70c7x2js2+MnuEAwaCXQMDLYADCfsikdJi1FkwaC2at\n5dxtvdqIRqW54gCQzCSIpIKEU8FzX8NpH3ZHBlcZNBdBS00Rq9uqWNVWJTvnf0d9mYNTQyUcGh6m\nsjSDTpdbvc8VtRV0H+tmfGQcRVEu+LzZ9cYuPEMe1m1eN/0FXsbgaIxwUEtbST1L55TL8cVCTBEJ\nv0KIKWUy6FjQUMqChlIAwtEEp4d8dA366Br0MuAJMhFKEI34iER8RCIwHIVIGJJJSKdVaFU6tGrd\nua8qVKSVFGklTUZJk1bSpJUUqJOYC6CgAMwF4DKDzaaipcbJ4qYy2pvKZu1RxZOhwKSnyuWg3+9k\nZNxPpTu3/l+5q9wAZNIZouEoZsv5q9fpVJoffftH3P/5+9EbZlYfusebwONRmFsyh6XNldjleSrE\nlJHwK4SYVgUmPfPrS5lffzYMK4pCKJpg2BtiaDzEsPfsrxFfiFA0QTSeIpVK/PYXpFKgABo1qDWg\n0Xxw22LSUua0UO60UlFso6zIQnWpHatZTsS6UvVlDrpH3Bwb91BWYsipsWeOYse52xcKvy/85AWS\niSR3PHjHdJd2Sb5Akv6hFK2uVhY3VlLusma7JCFmNQm/QoisUqlUWM0GrGbDBY8STqczRBMpIrEk\nkXiSSCxJRlHQazUYdBr0Og0GnRaDToPZqJMeyetUZDNR5iikL1DImDdKqSt3Lhw+PNs3Fomd92e9\nJ3t58jtP8hf/8Bfo9DNnmkUwnOJMX5ymojksqC2n1l2Y7ZKEmPUk/AohZjSNRo3FpMcic06nTUO5\ng/7xck54juF06NFqcuOCosBScO52NBw9dzsejfPNr36TFbesYNHqRdko7YIisTSnzkSpL2yiraqC\nOdUXPpZZCDG5cms3gxBCiClX5rRS7XJRqHcyOBK7/B1mCK3ug/WceOyD403/6dF/wj/u57P/7bPZ\nKOuC4okMJ89EqLbV0lJRwfz6kmyXJETekPArhBDiI+bVlVBlr2TcmyESS2e7nCvy4fCrKApwF9Ec\nUgAACCtJREFUdqzZtq3b+OrffpVC58xoKUgkM3R2h3GbKml2V9He6JZ2HSGmkYRfIYQQH2ErMNBY\n5qLcVkHvYPTyd5hpFHj9l6/zxLee4IEvPsCSm5ZkuyIAYvE0x7pCFBsqaC6tYVlLOZo8O05biGyT\nnl8hhBAX1FLtYmAsgGdwlPGJBM7C3Oi7VhSFXW/uYuuPtrJkzRIe+vJD2S4JONvje6I7QkVBDc3u\nala0VqDTyixfIaabXG4KIYS4IJ1WQ2t1MTWFtfQNxUhnlGyXdEmpVOrc7ed++BwNbQ187dtfy2JF\nHwhFUnSejlBlraO1vIZVcysl+AqRJRJ+hRBCXFR1qZ2qIhd2nZMz/TO7/SESjJy7Xd1UzaP/+ihG\nc/YPiwiEUpzsjlJnb6StopoVrZXS6iBEFsm/PiGEEBelUqlY1OimvqiOaFjL6Hj88neaAs/82zO8\nuuXVi/55Kplix2s7AKhqrOJv/t/fnDf3N1t8gSRdPTEaHM3Mq6pi6ZxyOVZbiCyTnl8hhBCXZDUb\naG8sI5qMc2z4CAVmLQWm6f3I/sWfvIi10Mot99yCRnP+Y3uGPDz2p49xfP9x6lrr+Ovv/zU2h21a\n67sQjzdB/1CSpqI5zKuuOHeqoRAiu2TlVwghxGVVFNtoqSylxl7HqZ4wqfT09v8m40m6jnTxzT/5\nJp4hDwCJeIJfPfErvnL3Vzi+/zjzls3j6098HXuRfVpr+12ZjMKZgSjDIwqtrrm011dL8BViBpGV\nXyGEEFekrbaEiVCMUCLI6d5xmusKLn+nSdJ+UztvPPMGO1/byc7XduJwOQgFQyTjSVQqFXc8eAef\n/8vPo8nyJrJkKsOpngjatJX5pY20N5ZTWZz9VWghxAck/AohhLgiarWKpXPKCccSHBwK0zsYpbrc\nNC2P/fCfPMzuN3cTnAgC4BvzAWC2mPn8X32emz9287TUcSmhcIquvihOQymNJbUsa6mg0JL9DXdC\niPOplPePwfkdfr//3G27PbsfIQkhhJg5PBNh3jvSyzHPcaz25LQF4P7T/fzwsR/SsasDjVbDDRtu\n4IEvPoCz1Dktj38pw544Q6Mp6grrqS92s2ROOUa9rC8JkQ2Xy7ASfoUQQly1YW+Incf6pj0AzzTJ\nZIYzA1ESUQONRY3MrXbTWuOS44qFyKLLZVi5LBVCCHHV3EUWVrRWAXD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HliFircpEImFutyOIToRRzkFtL0mh7JMEkWul240VjUYRiUSQSCQs/TiRVuBQ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\nOHLp4OBwIIIyNxwOo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Ti/lDXakUV1bIJrAci3AYSJItxCRs7+612uiwZq2RSUecnMvJhBRxRZmUwSgc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\nWS2WOdcsHvf5i7NCkuwpSMb140qHNO6J2zcYeWzt27TMFq1imQutkgR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AcAs9/Z0q/TCYl9WfU//g1FvdeXh4Kjk6U4mWjCvBPDxBloh4BfgGubBjYHYR1AEAwJxx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\nEgR1aMw+qlMlb+uPp19VW0/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zs1OrV6/Wvn37lJOTM11tAMBfbHBoQMVVhTpW8o4uXrowbk1cZLJW53xWK7Nv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\nRjkcIzpeeliHTvxaHT0t15z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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1144,7 +1144,7 @@ "source": [ "This gave me a standard deviation 0f 0.013 which is quite small. \n", "\n", - "You can see that there is not much difference in the implementation of the UKF vs linear Kalman filter. We merely replace $\\mathbf{F}$ with the function *f(x)*, and the matrix $\\mathbf{H}$ with the function *h(x)*. The rest of the theory and implementation remains the same. Well, of course under the hood the `FilterPy` implementation is quite different than the Kalman filter code, but from a designer's point of view the problem formulation and filter design is very similar." + "So far implementation of the UKF is not *that* different from the linear Kalman filter. Instead of implementing the state function and measurement function as the matrices $\\mathbf{F}$ and $\\mathbf{H}$ you supply functions `f(x)` and `h(x)`. The rest of the theory and implementation remains the same. Of course the `FilterPy` code for the UKF is quite different than the Kalman filter code, but from a designer's point of view the problem formulation and filter design is very similar." ] }, { @@ -1154,20 +1154,13 @@ "## Tracking a Flying Airplane" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### First Attempt" - ] - }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's tackle our first nonlinear problem. To minimize the number of things that change I will keep the problem formulation very similar to the linear tracking problem above. For this problem we will write a filter to track a flying airplane using a stationary radar as the sensor. To keep the problem as close to the previous one as possible we will track in two dimensions, not three. We will track one dimension on the ground and the altitude of the aircraft. The second dimension on the ground adds no difficulty or different information, so we can do this with no loss of generality.\n", "\n", - " Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. True integration of sensors for applications like military radar and aircraft navigation systems have to take many factors into account which I am not currently interested in trying to cover in this book. So if any practitioners in the the field are reading this they will be rightfully scoffing at my exposition. My only defense is to argue that I am not trying to teach you how to design a military grade radar tracking system, but instead trying to familiarize you with the implementation of the UKF. \n", + " Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the **slant distance** - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. True integration of sensors for applications like military radar and aircraft navigation systems have to take many factors into account which I am not currently interested in trying to cover in this book. So if any practitioners in the the field are reading this they will be rightfully scoffing at my exposition. My only defense is to argue that I am not trying to teach you how to design a military grade radar tracking system, but instead trying to familiarize you with the implementation of the UKF. \n", " \n", "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below." ] @@ -1182,9 +1175,9 @@ "outputs": [ { "data": { - "image/png": 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V7tdMn25ef+01M3rrckkNGkiffirVqiX99JM0fLhUo4Y0ZIgJuA0bSsOGmSkPkuTrK11/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\nSUVORK5CYII=\n", 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RkaHo6GgFBQUpPDxcL774oh577LHsc/72t7+pVatWevXVV7OPLVy4UNWqVdOG\nDRvUtm3bQj0TKAzCLwDPOXvWjOz+9JMZ6W3YUOrZU2rUyNuVAWXab7/9psmTJys+Pl5//PGHXC6X\nXC6X9u/fnyv8FrXt27frxhtvVFBQUPaxDh06uJ3z888/KzY2VhUrVnQ77nA4tHfvXsIvihThF8DV\nsyzp11/NJhNJSVJQEI1qgBf07t1bDRo00Pz581W3bl2VK1dO4eHhSk9Pv6b7Xjr9wOk0rUIXN8tl\nZGTkui6f/bPcXu/du7dmzZqV67XCjjQDhUX4BVA4SUlmVYZffzVzdVu0MI1q//1RKoDilZSUpJ07\nd2revHnq0qWLJGnjxo3KzMzM8/wLc3yzsrIue18/P79c96jx350TDx8+rNatW0uSfvnlF7dzwsPD\ntXDhQp07dy579DcuLs7tnMjISC1evFgNGjTINScZKGqs9gDg8jIypDVrclZh+PBDqXlzacYM8+vh\nhwm+gBdVqVJF1atX1/z587Vnzx6tXr1aTz75ZL6hMiQkRIGBgVqyZImOHj3qthXsxUJDQ7V161bt\n2rVLx48fV2ZmpgIDA9WhQwe99tpr2rZtm9atW6fnnnvO7boBAwbIx8dHQ4YM0bZt27Rs2TK98sor\nbuc8/fTTSk5O1kMPPaT4+Hjt3btXy5cv1/Dhw5WSkuKZDwbIB+EXQG4JCdK775qwO2OGdOaMNHas\n+XrsWCkighUagBLC6XRq0aJF2rJliyIiIjRq1CjNmDFD/v7+eZ7v4+OjuXPn6r333lPdunV13333\nSTJTHC6e5jBs2DDdcMMNatOmjWrWrKl169ZJMs10klkq7amnnsoVbMuXL69vv/1Wu3fvVmRkpP78\n5z9r5syZbveuXbu21q5dK6fTqTvuuEMtWrTQyJEjFRAQkG/dgKc4rHwm5lz8L8Hg4OBiKwiAF5w9\nK61aJcXHS1lZOY1qDRt6uzKgzFq82MwaCg/3diVA2XKlDMtEG8COLEvassU0qp04YZYeu/VWs9kE\n8+8AAGUYf8sBdvHHH6ZR7T//MVMWIiKkwYOlatW8XRkAAMWG8AuUVRkZUlycWXf3/HnTlNajh9S/\nP/N1AQC2RfgFypLffzc7qh08aKYvdOggPfusWX8XAAAQfoFSLSUlp1HN5TI7qd11l9SggbcrAwCg\nRCL8AqWJZUmbN5tGtVOnchrVXnqJRjUAAAqAvy2Bku7YMdOotm2bmat7443SkCFS1arergwAgFKH\n8AuUNBn9W5nrAAANm0lEQVQZ0rp1UmyslJoq1ahhGtUGDKBRDQCAa0T4BUqC334zjWqHDkm+vtJN\nN0nPPScFBnq7MgAAyhTCL+ANKSnSypXS+vVmR7WwMOnuu6X69b1dGQAAZRrhFygOLpdpVFuxIqdR\nrWtXacoUqVw5b1cHAIBtEH6BonLsmBQTI23fbubqtmolPf64VKWKtysDAMC2CL+Ap6Snm0a1f//b\nNKqFhJhGtUceoVENAIASgvALXIs9e8zo7oVGtY4daVQDAKAEI/wChXHmTE6jmsslXXed1KePVK+e\ntysDAAAFQPgFLsflkn75xTSqJSdLFSqYRrWpU2lUAwCgFCL8Apc6etRMZdixQ3I6TaPasGFS5cre\nrgwAAFwjwi+Qni6tXWsa1dLSTKPa7bdLjz5KoxoAAGUM4Rf2Y1k5jWqHD0t+fqZR7c9/lgICvF0d\nAAAoQoRf2MPp09IPP0g//2zm8TZuLN17r1S3rrcrAwAAxYjwi7LJ5ZI2bZKWLzfBt2JFqVs3s4Uw\njWoAANgW4Rdlx5EjZirDzp2mUe1Pf5KGD6dRDQAAZCP8ovRKSzONamvWmK9r1ZJ69pQee4xGNQAA\nkCfCL0oPy5J27zaju4mJplHt5ptpVAMAAAVG+EXJlpyc06hmWVKTJlLfvlKdOt6uDAAAlEKEX5Qs\nLpcJuj/8YBrVKlUyjWp9+tCoBgAArhnhF96XmCgtXSrt2mUCbmSk9OSTUnCwtysDAABlDOEXxS8t\nzTSprVljdlerXds0qg0aRKMaAAAoUoRfFD3LMqO6MTFmOTI/P+mWW6QJEyR/f29XBwAAbITwi6KR\nnCytWCFt3GjCb9Om0gMPmFFeAAAALyH8wjOysnIa1c6cMY1qt91mthB2Or1dHQAAgCTCL67F4cOm\nUW33btOo1rq1NGKECb4AAAAlEOEXBZeamtOolpFh1trt2VMaPJhGNQAAUCoQfpE/y5J27jSNaseO\nmea0W26RJk6kUQ0AAJRKhF+4O3XKNKpt2mTCb7NmUr9+Uq1a3q4MAADgmhF+7S4rS9qwwTSqpaSY\njSVuu0267z4a1QAAQJlD+LWjQ4dMo9qePaZRrU0b6emnaVQDAABlHuHXDlJTpdhYad0606hWt65p\nVBsyxNuVAQAAFCvCb1lkWdKOHWZ099gxKSBA6txZmjTJ7K52lY4elebMkUJDpYoVpcREM2ti9GjJ\n19eD9QMAABQRwm9ZcfKkaVT75RcTfq+/XurfX6pZ0yO3379f6t1b+uc/pebNc44vXGiOf/ed5MP/\nmgAAQAlHXCmtsrKk9eullStNo1rlyqZRrW/fImlUGz5ceugh9+ArSYMGSe++K82eLT3/vMcfCwAA\n4FEOy7KsvF5ITk7O/jo4OLjYCsJlHDxopjLs3WsCbtu2UteuZg5CEUpMNNOEP/vMfN+3b85r8+eb\nshYvNjMtAAAFs3ix1KKFFB7u7UqAsuVKGZaR35Ls/PmcRrXMTJNAb79devzxYi1j3z7ze+3aUo8e\n7o9v3FgaOjTnHAAAgJKM8FuSWJa0bZu0bJlpVAsMNI1qL7xwTY1q16p+ffO7r6+ZYXGpKVOkhg2L\ntyYAAICrQfj1thMnpOXLpc2bTfgND/doo5on1K1rRnyXLTNLAl9qxQopKqr46wIAACgswm9xy8x0\nb1SrUkXq3l164IESvaPae+9Jd91lymzSJOf4Bx+YldSee85rpQEAABQY4bc4HDhgGtV+/93sqNa2\nrfTMM1KFCt6urMDq1zc7IL/1llSnjtkMLjHRDFYvXWreFgAAQElH+C0K589Lq1dLP/5oRnrr1TON\namFh3q7smtSoIb38srerAAAAuHqEX0+wLOk//zGTYo8fz2lUe/FFtj4DAAAoQQi/VyspyTSqbdli\nvm/eXHr0UTM8CgAAgBKJ8FtQmZlSfLxpVDt7Vqpa1SyB0K+f5HB4uzoAAAAUAOH3cvbvN91cCQmm\no6tdO2n06FLVqAYAAIAchN+LnTtnGtXi4sxIb/36plEtNNTblQEAAMAD7B1+LUvautU0qiUlmUa1\nLl1oVAMAACij7Bd+k5JM2P31V/N9ixbSY4/RqAYAAGADpT78ulwuHTiQIUmqX99Xzkt3ScvMNNMY\nVq0y0xqqVzc7qj30EI1qAIAit2GDtGiRNHCgFBHh7WoAlOrw63K5FBOTpqgof0lSdHSaevb0l/PC\njmoJCZKPj9S+vTR2rFS+vHcLBgDYTps2UsuW0kcfSR9+SAgGvM1hWZaV1wvJycnZXwcHBxdbQYWx\nb1+aOnTw1ZEjZrS3alWXFryXrtqblkuRkWYfXgAASoiMDOn7783YTJMm0oMPSuHh3q4KKFuulGFL\n9cjvpSxLOplcTr4depsDx71bDwAAF7MsM+MuJUW67jqpcWNvVwTYT6ke+b102kPbtiN05sxOrVy5\n0suVAQCQw7Kkr76SYmOlPn2kW2/1dkVA2XWlDOvMdaQYDB48WE6nU06nU76+vqpXr54GDRqkxMTE\nQt3H6XSqZ09/xcVlKC4uQ/Xrl5ODJjbA4yzLUufOndWnTx+34+fOnVOzZs00YsQIL1UGlHybNknj\nxkmVK0tvvEHwBbzNK+HX4XCoR48eOnLkiPbt26fo6GitXLlSAwcOLPS9nE6nGjb0V8OG/nI4HMpn\nILvAMjMzr+l6oCxyOBxauHChVq5cqejo6Ozjzz//vCzL0uzZs71YHVCytWxJ6AVKEq+EX8uy5O/v\nr5CQENWpU0c9evTQgw8+qLi4OElmOsPjjz+usLAwBQUFqWnTpnr99dfdgm1WVpaee+45Va1aVVWr\nVtXYsWOVlZXl9pwlS5aoU6dOqlq1qqpVq6Y77rhDO3bsyH49ISFBTqdT//rXv9StWzcFBQVp/vz5\nxfMhAKVMaGioZs2apbFjx2r//v1asWKF5s2bpw8++ECBgYHeLg8oscqV83YFAC7mlfAryS3I7t27\nV0uWLFHbtm0lmfBbr149ffrpp9qxY4deeeUV/eUvf3EbcZo9e7bee+89zZ8/X3FxccrKytInn3zi\nNu3h3LlzevbZZ7V+/XqtXr1awcHBuvvuu5WRkeFWy8SJEzVy5Eht375d99xzTxG/c6D0Gj58uDp0\n6KBHH31UQ4YM0bhx49SxY0dvlwUAQIF5peFt8ODB+vjjjxUQEKCsrCylpqaqV69eWrhwoapWrZrn\nNRMmTNDPP/+sZcuWSZLq1KmjUaNGaeLEiZJMmL7++utVt25d/fDDD3ne4+zZswoODlZsbKw6duyo\nhIQEhYWFafbs2Ro7dqxH3yNQVl34/02TJk20detW+bIVOACgBCmRDW+S1KVLF23evFnx8fEaNWqU\nVq9eraNHj2a/Pm/ePLVp00YhISGqWLGi3nzzTR04cECSeVNHjhzRTTfdlH2+w+FQ+/bt3UaUf/vt\nNw0YMECNGzdWcHCwatWqJZfLpf3797vV0qZNmyJ+t0DZ8f777ysoKEgHDx7U3r17vV0OAACF4rXw\nGxgYqLCwMLVo0UJz5sxRmzZtNHr0aEnSokWLNHbsWA0ZMkQxMTHavHmzRowYobS0tMve89JB7N69\neyspKUnz589XfHy8Nm3aJB8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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1202,7 +1195,7 @@ "source": [ "We will assume that the aircraft is flying at a constant altitude, so a three variable state vector will work.\n", "\n", - "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude\\end{bmatrix}= \\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix}$$" + "$$\\mathbf{x} = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}= \\begin{bmatrix}x_\\mathtt{pos} \\\\x_\\mathtt{vel}\\\\ y_\\mathtt{alt}\\end{bmatrix}= \\begin{bmatrix}x \\\\ \\dot{x}\\\\ y\\end{bmatrix}$$" ] }, { @@ -1212,10 +1205,10 @@ "Our state transition function is linear \n", "\n", "$$\\mathbf{x}^- = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n", - "\\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix} \n", + "\\begin{bmatrix}x \\\\ \\dot{x}\\\\ y\\end{bmatrix}\n", "$$\n", "\n", - "and we can implement that very much like we did for the previous problem." + "which we can implement very much like the previous problem." ] }, { @@ -1245,11 +1238,11 @@ "\n", "If we represent the position of the radar station with an (x,y) coordinate computation of the range and bearing is straightforward. To compute the range we use the Pythagorean theorem:\n", "\n", - "$$range = \\sqrt{(x_{ac} - x_{radar})^2 + (z_{ac} - z_{radar})^2}$$\n", + "$$\\mathtt{range} = \\sqrt{(x_\\mathtt{ac} - x_\\mathtt{radar})^2 + (z_\\mathtt{ac} - z_\\mathtt{radar})^2}$$\n", "\n", "To compute the bearing we need to use the arctangent function.\n", "\n", - "$$bearing = \\tan^{-1}{\\frac{z_{ac} - z_{radar}}{x_{ac} - x_{radar}}}$$\n", + "$$\\mathtt{bearing} = \\tan^{-1}{\\frac{z_\\mathtt{ac} - z_\\mathtt{radar}}{x_\\mathtt{ac} - x_\\mathtt{radar}}}$$\n", "\n", "As with the state transition function we need to define a Python function to compute this for the filter. I'll take advantage of the fact that a function can own a variable to store the radar's position." ] @@ -1277,7 +1270,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "**Important Note**: There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem.\n", + "There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem.\n", "\n", "We need to simulate the Radar station and the movement of the aircraft. By now this should be second nature for you, so I will present the code without much discussion." ] @@ -1323,8 +1316,7 @@ " return rng, brg\n", " \n", " \n", - "class ACSim(object):\n", - " \n", + "class ACSim(object): \n", " def __init__(self, pos, vel, vel_std):\n", " self.pos = np.asarray(pos, dtype=float)\n", " self.vel = np.asarray(vel, dtype=float)\n", @@ -1347,12 +1339,12 @@ "source": [ "Now let's put it all together. A military grade radar system can achieve 1 meter RMS range accuracy, and 1 mrad RMS for bearing [1]. We will assume a more modest 5 meter range accuracy, and 0.5$^\\circ$ angular accuracy as this provides a more challenging data set for the filter.\n", "\n", - "I'll start with the aircraft positioned directly over the radar station, flying away from it at 100 m/s. A typical radar might update only once every 12 seconds and so we will use that for our update period. " + "I'll start with the aircraft positioned directly over the radar station flying at 100 m/s. A typical radar might update only once every 12 seconds and so we will use that for our update period. " ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 53, "metadata": { "collapsed": false, "scrolled": false @@ -1362,7 +1354,7 @@ "data": { "image/png": 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2WXwWvaeHN9ITs6FW5kIRk8blUkREDmZzuH/zzTfx7//+7wgPD8f8+fMxb968\nUTX8NSsR0dRyvfcaKprPoKatDAcKLo45i35u/F1QKzVIiVPDfYaHEzolIiJgHOH+5z//OZYsWYLP\nP/8c7u7cCkhENFX19fegtPo09CYtLtQVw2IVmUUvdUNyTDpUSg3mJSyAt6ePEzolIqJvsjncm81m\nPPbYYwz2RERT0MDgAM7XGWAwaXGuuhD9g32jaiSQIDEqBWplLtKTFnIWPRGRC7I53C9YsABGo/g1\nlkRENPlYrBZU1JdCb9LibOVJ9PSLbxYP8otEfHAqVt73j5jpx10mRESuzOZw/84772D58uVQqVR4\n6qmnJuTJd+zYgU8++QQmkwmenp7Izs7Gjh07kJqaOqJuy5Yt2Lt3L8xmMxYsWIDdu3cjJSVlQnog\nIppOrIIVtU1G6I1aFFecQFdPh2hdRNBsqBQaqBQ5qKtsAAAGeyKiScDmcP/II4+gv78fzzzzDJ5/\n/nlERUXBze3vUxBuTMspLy+3+cm/+uorrF+/HnfddResVis2bdqE+++/H+Xl5QgMDAQAvPHGG9i1\naxf2798PhUKBrVu3Ii8vD0ajEX5+fuP4qxIRTU+CIKCxrRZFxnwYTDqYu1pF64ICwqBWDgX6yOC4\n4dvr0OCgTomI6E7ZHO7DwsIQHh4OhUIxZs14p+UcOXJkxMcHDhyATCZDQUEBHnroIQiCgLfeegsb\nNmzAqlWrAAD79+9HaGgoPvzwQ6xdu3Zcz0dENJ20dTRDb9RCb8xH85V60ZoA30BkyhdDrcxFbJic\nU8+IiCY5m8P9X/7yFzu2MaSzsxNWq3X4Vfuamhq0tLRg6dKlwzVeXl7Izc1FQUEBwz0R0Td0dl/F\nmQrdTWfR+3j6IUO+ECpFLpKiUiDlLHoioilDItzYROUCHn/8cVRVVaGoqAgSiQQFBQXIycnBxYsX\nER0dPVz3ve99D42NjcOv/Hd0/P2a0YqKCof3TUTkTP2Dfai/cgHVrWVovloDAaO/rc+QuiNmlgLx\nIXMRMTOBy6WIiFyAXC4f/rNMJpuQxxzXhtr+/n7s3bsXn332Gerq6gAAcXFxWLFiBZ599tk7GpP5\nyiuvoKCgADqdzqZfC/NXx0Q0nVmsg2gwV6KmtQz1V0ywCpZRNRKJFFEzExEfkoroWQq4u3G5FBHR\nVDeuOfdLlixBSUkJwsLCkJSUBADQ6/X4/PPPsXfvXnzxxRfDl9SMx8svv4yDBw/i+PHjiIuLG749\nPDwcANDdisrYAAAgAElEQVTS0jLilfuWlpbh+74pKytr3M9P4oqKigDwTO2BZ2sfU/1crVYLKi6d\ng96Yj5KbjK5MjEpFljIXGUkL4TsBs+in+rk6C8/VPniu9sFztY+vX30yUWwO9xs2bEBZWRn27duH\np59+GlKpFABgtVrx29/+Fs8++yw2bNiAX/7yl+Nq4MUXX8ShQ4dw/PjxUW/WjY+PR3h4OI4ePQq1\nWg0A6O3thU6nw86dO8f1PEREk5EgCLjYUgn93ybddF43i9ZFhcQjS5kLlSIHgf4hDu6SiIhchc3h\n/tNPP8W6deuwevXqEbdLpVI8/fTTOHPmDH73u9+NK9yvW7cOH3zwAQ4fPgyZTIbm5mYAgL+/P3x9\nfSGRSPDSSy9h+/btSE5Ohlwux7Zt2+Dv748nn3zS5uchIppsWq5cGp5009rRJFoTJAv7W6DPRURQ\njIM7JCIiV2RzuL969erwpThiEhISYDaLv6I0lj179kAikeC+++4bcfuWLVuwadMmAMCrr76Knp4e\nrFu3DmazGdnZ2Th69Ch8fX3H9VxERK6uvaMFBpMOBpMWDW21ojX+3jKolBqOriQiIlE2h/vExEQc\nPnwYL7zwwqgfJoIg4NNPP71p+BdjtVptqtu8eTM2b948rscmIpoMOq5dgaFChzOmE2OOrvT08EZG\n4kKolbmQx8zjpBsiIhqTzeF+/fr1eOGFF/DAAw/gxRdfhFKpBABcuHABb7/9Nr744gvs2bPHbo0S\nEU0V13o6UVJ5EnpjPqoaysVHV7q5IzVODbUyFynxanjM8HRCp0RENNnYHO6ff/55tLW14bXXXsOx\nY8dG3Ofh4YHXXnsNzz333IQ3SEQ0FfT0deNs1V9hMOlgvFgMqzD6N5dSqRuSZ2dArdRgbvx8eHv6\nOKFTIiKazMY1537jxo147rnncOzYseE597GxsVi6dCmCgoLs0iAR0WTVN9CLspoiGExalNXqYbEM\njqqRSKSQR6VCpdQgPTF7QkZXEhHR9DWucA8AISEh+M53vmOPXoiIJr2BwQGcrzPAYNLhXPVp9A/2\nidbFRyRDpchBpnwxAnzHvx+EiIhIzLjDPRERjWSxDMJ0qRQGoxZnq06NuVwqOjQBaoUGmfLFmBUQ\n6uAuiYhoOhgz3EulUkgkEvT09MDDw2P4Y0EY/cavGyQSCSyW0SvQiYimGqtgRU3jeeiNWpypLEB3\nT6doXdisaKgVGqgUOQgNjHJwl0RENN2MGe43bdoEiUQCNze34Y+JiKYzQRBQf7kKBpMWBpMOV6+1\ni9YFycKGA31EUCxn0RMRkcOMGe63bNly04+JiKaLpvb6oUBv1I65LVbmF4RM+WKoFRrMDktioCci\nIqew+Zr7rVu34tvf/jbmzp0ren9ZWRl+//vf8xV+IpoSbmyL1Zu0aBxjW6yvlz8y5IuhVmqQEDkH\nUonUsU0SERF9g83hfsuWLUhKShoz3JeWluKnP/0pwz0RTVod3VdQXFEAvVF7022x6YnZUCk0UMak\nwc2NcwmIiMh1TNhPpa6uLsyYwR9yRDS5dPd2oaTyFAzGfFQ0lEEQWS7l7uaB1PgsqJUazIlTcVss\nERG5rJum8ZKSEpSUlAxPyNFqtRgcHL2E5cqVK9izZw+Sk5Pt0yUR0QTq6+9BafVp6E1aXKgrhsU6\n+vva17fFzktYAC8Pbyd0SkREND43Dfd/+MMfsHXr1uGP33vvPbz33nuitYGBgThw4MDEdkdENEEG\nBvtRXmuAwaTFuZpCDAz2j6qRQILE6FSoFRpkJC3ktlgiIpp0bhru165dixUrVgAA5s+fj61bt+LB\nBx8cUSORSODr64vExES4u7vbr1MionGyWC0w1Z+FwahFSdUp9I6xXCo2XAGVIgcqeQ5kfrMc3CUR\nEdHEuWm4j4yMRGRkJADgyy+/REpKCkJDuVWRiFyXIAioaiiD3qRDcUUBrvV0iNZFBM0emkWv1CBY\nFu7gLomIiOzD5nfA3nPPPXZsg4jo9t1YLlVUcwy1bWW43t8lWhcsC4dKoYFaqUFE0GwHd0lERGR/\nY4b77373u5BIJNi7dy/c3NyGP76VX/3qVxPaIBHRWJqv1ENvHNoW23q1UbRG5jsLmYocLpciIqJp\nYcxwf/z4cUgkElitVri5uQ1/PBZBEPhDk4jsrr2zBQajDgaTFg23WC6lUuQgMSqFy6WIiGjaGDPc\n19bW3vRjIiJH6ew240zFiVsul4qSJSE+JBUrljzK5VJERDQtOfWnX35+Pnbu3AmDwYDGxkbs27cP\nq1evHr5/zZo1+M1vfjPic7Kzs1FQUODoVonIwa73XkNJ5UnoTVpUXDpn03Kps8WlAMBgT0RE05bN\nPwGbm5vR1NSEzMzM4dvOnz+P//7v/0ZHRweeeOIJfPvb3x7Xk3d3dyMtLQ2rV6/GM888M+qyHolE\ngry8vBHz8z08PMb1HEQ0efQP9OFcTSGKjPk4X2u45XKpufHz4e3p44ROiYiIXJPN4X79+vW4fPky\n8vPzAQxtpb377rtx9epVeHl54eOPP8bhw4fxD//wDzY/+bJly7Bs2TIAQ6/Sf5MgCPDw8OD4TaIp\nbNAyAOPFEhQZ81FafRr9A72jar6+XCo9aSH8uFyKiIhIlM3h/uTJk3jhhReGP/7ggw9gNpthMBiQ\nnJyM++67Dzt37hxXuL8ViUQCnU6HsLAwzJw5E3fffTdef/11hISETNhzEJHjWQXr0Cx6oxbFlSdx\nvVd8dOXsMDnUCg0yFYsx0y/IwV0SERFNPhJBEARbCr28vLBnzx5897vfBQDk5eXBYrHgyy+/BADs\n3r0bmzZtQnt7+2014u/vj927d+OZZ54Zvu2jjz6Cr68v4uPjUVNTg40bN8JisUCv14+4PKej4+9L\naioqKm7r+YnIvgRBwJXuZtS0nkNtW/mYs+hl3kGID5mLuOBUBHhzWywREU1dcrl8+M8ymWxCHtPm\nV+5nzZqFpqYmAMD169dx4sQJbNq0afh+iUSC3t7Rv06/E0888cTwn1NTU6FWqxEbG4vPPvsMq1at\nmtDnIiL76Ljehpq2MtS0lqGr94poja9nAOKCUxEfnIpA3zCO1SUiIrpNNof7nJwcvPvuu0hOTsaR\nI0fQ29uLlStXDt9vMpkQFRVllyZviIiIQHR0NCorK8esycrKsmsP00lRUREAnqk9TPWzNXe1wmDS\nQW/U4lJrtWiNr3cAMuWLoVZoEB+ZPCGz6Kf6uToLz9U+eK72wXO1D56rfXz96pOJYnO43759Ox54\n4AE8+uijAIBXXnkFKSkpAIDBwUEcOnQIy5cvn/AGv661tRUNDQ2IiIiw6/MQ0fh1Xe9AcWUBDEYt\nqhrLRWs8PbyRnpgNlUIDZUwaR1YSERFNMJt/siYlJeHChQsoLy9HQEAA4uPjh+/r6enB7t27kZGR\nMa4n7+7uHr5G3mq1oq6uDsXFxQgKCsKsWbOwefNmPProowgPD0dtbS02bNiAsLAwXpJD5CJ6+q7j\nbNUp6E1amC6WwCoyi36GmztS49RQKXORGq+GxwxPJ3RKREQ0PYzrZTN3d3ekp6ePut3f3x8PP/zw\nuJ+8sLAQS5YsATB0zf7mzZuxefNmrFmzBu+++y7OnTuHAwcO4OrVq4iIiMCSJUvw8ccfw9fXd9zP\nRUQTo3+wD2U1ehiM+Sir1WPQMjCqRiqRQhGTBrUyF2mJC+Dtyf9niYiIHGFc4b6/vx979+7FZ599\nhrq6OgBAXFwcVqxYgWeffRbu7u7jevJ77rkHVuvoV/puOHLkyLgej4jsw2IZxIWLxTCYdDhb/Vf0\n9feI1iVEzIFKqUFG0iIE+M50cJdERERkc7g3m81YsmQJSkpKEBYWhqSkJACAXq/H559/jr179+KL\nL75AYGCg3ZolIscZmkVfDoNRi+LKAnSPMYs+KiQeaoUGKkUOZgVw4RwREZEz2RzuN2zYgLKyMuzb\ntw9PP/00pNKhyRZWqxW//e1v8eyzz2LDhg345S9/abdmici+BEFA/eUq6I35MFScQMc18b0VoTMj\noVJqoFZoEDYr2sFdEhER0VhsDveffvop1q1bh9WrV4+4XSqV4umnn8aZM2fwu9/9juGeaBJqaq+H\nwZQPg1GH1o4m0ZqZfkFQKTRQKzWIDkngLHoiIiIXZHO4v3r16vClOGISEhJgNpsnpCkisr/2zhYY\njDroTVo0ttWK1vh5y5AhXwS1IgfxkXMmZBY9ERER2Y/N4T4xMRGHDx/GCy+8MOoVO0EQ8Omnn940\n/BOR83V2m3Gm4gT0Ri1qm42iNV4ePkhLXAC1MheKmDS4Sd0c3CURERHdLpvD/fr16/HCCy/ggQce\nwIsvvgilUgkAuHDhAt5++2188cUX2LNnj90aJaLbc733GoorT8JgzEdFQxkEkVn07m4eSI3Pglqp\nQUqcGu4zPJzQKREREd0pm8P9888/j7a2Nrz22ms4duzYiPs8PDzw2muv4bnnnpvwBolo/Pr6e1Ba\nfRp6kxYX6ophsQ6OqpFK3ZA8OwNqpQbzEhbAy8PbCZ0SERHRRBrXnPuNGzfiueeew7Fjx3Dx4kUA\nQGxsLPLy8hAUFGSXBonINgODAzhfp4feqMW5mkIMDPaPqpFAgsToVKgVGmQkLYSvd4ATOiUiIiJ7\nGVe4B4CzZ8/i9OnTqK2thUQiQUtLC0JCQnDffffZoz8iugmL1QJT/dmh5VKVJ9HTf120LjZMDpVS\nA5U8BzK/WQ7ukoiIiBzF5nDf3d2Nxx9/HJ9//jkAIDAwEIIg4OrVq3jrrbfwwAMP4NChQ/Dz87Nb\ns0Q0tFyqpvECDCYdiitOoKunQ7QuImj20HIppQbBsnAHd0lERETOYHO4/9GPfoTPP/8cP/nJT/DD\nH/5w+DKctrY2vP3229i2bRt+9KMf4b333rNbs0TTlSAIuNRaDYNJC4NRB/O1NtG6IFkY1IpcqBQ5\niAyOdXCXRERE5Gw2h/uDBw/i2WefxU9/+tMRtwcHB2Pr1q1obm7GoUOHGO6JJtBlcwP0Ri30Ji0u\nmxtEawJ8A6GS50Ct1GB2mJzLpYiIiKYxm8O91WpFZmbmmPenp6fj4MGDE9IU0XRm7mqDwaSD3pSP\nS5erRWt8vPyRkbQQaqUGiZEpkHIWPREREWEc4X758uX44x//iH/5l38Rvf+zzz7DQw89NGGNEU0n\n13o6UVxRAL1Ji+qGcggQRtV4unthXuICqBUaJM/OgJvbuN8PT0RERFOczengJz/5Cf7xH/8RDz30\nENavXw+5XA4AMJlMeOedd9DY2Ij/+q//wuXLl0d8Xmho6MR2TDRFDAz24fT54zAYtbhQXwKr1TKq\nxs1tBlLj1FArc5EalwUPd08ndEpERESThc3hPjU1FQBQWlo6PDFnrJobJBIJLJbRgYVouhoY7Ed5\nrQFfXfgUl8wVosulJBIpFDHzoFbkIi1pAXw8OYGKiIiIbGNzuN+0adO4H5xv7CMamkVfUV8KvUl7\n01n0cRFKqBUaZMpzEOA708FdEhER0VRgc7jfsmWLHdsgmloEQUBtsxF6Yz7OmMaeRR8ZFAuVUgO1\nQoMgWZiDuyQiIqKpxqnvyMvPz8fOnTthMBjQ2NiIffv2YfXq1SNqtmzZgr1798JsNmPBggXYvXs3\nUlJSnNQx0dgEQUBjWy30Ri0MJi2udLWK1gUFhCEyIAnxIXNxf+4yB3dJREREU5lTw313dzfS0tKw\nevVqPPPMM6Mu43njjTewa9cu7N+/HwqFAlu3bkVeXh6MRiM34ZLLuGxuhME0NIu+5col0ZoAn0Bk\nKhZDrcxFbJgcer3ewV0SERHRdODUcL9s2TIsWzb0yuWaNWtG3CcIAt566y1s2LABq1atAgDs378f\noaGh+PDDD7F27VpHt0s0zNzVhjMVOuiNWtRfrhKt8fb0RXrSQmQpc5EUlcpZ9ERERGR3Ljsou6am\nBi0tLVi6dOnwbV5eXsjNzUVBQQHDPTmcLbPoPWZ4Yl7CfKiUGiTPzoT7DHcndEpERETTlcuG++bm\nZgBAWNjINxmGhoaisbHRGS3RNNTTdx2l1X+F3qiF8WIxrIJ1VI2bdAbmxKmgVmgwN+EueLp7OaFT\nIiIiIhcO9zdzsxGbRUVFDuxkephuZzpoGUCDuRI1bWVoMFeKz6KHBOGyOMSFpGJ2kBKeM7whdAGl\nJefG9VzT7WwdhedqHzxX++C52gfP1T54rhPrxlLYieSy4T48PBwA0NLSgujo6OHbW1pahu8jmihW\nqwVNHTWoaS1D/RUjBiz9onUh/tGIC05FXPAceHvwTd1ERETkWlw23MfHxyM8PBxHjx6FWq0GAPT2\n9kKn02Hnzp1jfl5WVpajWpzybvzrfKqeqdVqQVXjeRiMWhRXFqC7t0u0Lio4DiplLlSKxQgKmJhZ\n9FP9bJ2F52ofPFf74LnaB8/VPniu9tHRIb4H5044fRRmRUUFAMBqtaKurg7FxcUICgpCTEwMXnrp\nJWzfvh3JycmQy+XYtm0b/P398eSTTzqzbZrEBEFAXUsFDEYtzlScQEf3FdG6EFnE0HIppQbhs2Ic\n3CURERHR7XFquC8sLMSSJUsADF1Hv3nzZmzevBlr1qzBr371K7z66qvo6enBunXrYDabkZ2djaNH\nj8LX19eZbdMkM7Rcqg4GkxYGkw7tnS2idTK/IKgVOVApNIgJTbzpezuIiIiIXJFTw/0999wDq3X0\n9JGvuxH4icbrsrkBepMOhpssl/LzliFDvghqRQ7iI+dAKpE6uEsiIiKiieOy19wT3Y4rna1Dy6VM\nWly6XC1a4+3hg7SkhVApcqCISYMbl0sRERHRFMFwT5NeZ/dVFFeegMGoQ3XTedEaLpciIiKi6YDh\nnial673XUFJ5EgaTDqZLpRDElku5zUBqnBoqhQap8VlcLkVERERTHsM9TRp9/T0orT4NvUmLC3XF\nosulpBIpFLPToVbkIC0xG96efPM1ERERTR8M9+TS+gf7cL7WAL1Ji7KaIgwMjl4uJYEECVEpUCs0\nSE9aCH8fmRM6JSIiInI+hntyORbLIIz1JTCYdCipOoW+/h7RutgwOVQKDTLkixDoH+zgLomIiIhc\nD8M9uYShbbHl0Bu1KKk8Oea22MigWKgUOchU5CBkZoSDuyQiIiJybQz35DSCIKC22QSDaWhbbGe3\nWbRuaFvs0HKpiKDZDu6SiIiIaPJguCeHGtoWWzu8XOpK52XRupl+QVApNFApcrgtloiIiMhGDPfk\nEMPbYo1atJjFt8X6e8uQIV8MlSIH8ZHJ3BZLRERENE4M92Q35q5WGEw66I1aXGodY1uspy/SE7Oh\nUmggj5nHbbFEREREd4DhniZU1/UOFFecgN6kRXUjt8USERERORLDPd2xnr7rKK3+K/RGLYwXi2EV\n2RY7w80dKXFqqBQ53BZLREREZCcM93RbBgb7UVZTBL1Ji/IaPQYso5dLSSVSKGLSoFZquC2WiIiI\nyAEY7slmFqsFpvqz0Bvzb7pcKiFiDlRKDTLli+DvM9PBXRIRERFNXwz3dFOCIKCqoRx6kxbFFQW4\n1tMhWhcVHAeVMhdqRQ5mBYQ6uEsiIiIiAhjuSYQgCGhoq4G+9gvUtpWhu6BTtG5ouZQGaqUG4bNi\nHNwlEREREX0Twz0Nu2xuhN6kveksepnvLGQqcqBWaDA7LInLpYiIiIhcCMP9NGfuasOZiqFZ9PWX\nq0RrfLz8kZG0EGqlBomRKZByFj0RERGRS3L5cL9lyxZs3bp1xG3h4eFobGx0UkeT37WeThRXFAzN\nom8ohwBhVI2HuxeiZImID5mLFfc9ihlunEVPRERE5OpcPtwDQHJyMv7yl78Mf+zmxleOx6u3v2d4\nFv2Fi8WwWi2jatzcZiAlVgW1Mhep8VkoLTkHAAz2RERERJPEpAj3bm5uCA3lBJbxGhjsR3mtAXpT\nPsqqi0Rn0UskUiii50Gl1CA9MRs+Xn5O6JSIiIiIJsKkCPfV1dWIioqCp6cnFixYgO3btyM+Pt7Z\nbbmkG7PoDUYtSqpOobf/umhdXLgSaqUGmfLFCPANdHCXRERERGQPLh/us7OzsX//fiQnJ6OlpQXb\ntm3DokWLUFZWhlmzZjm7PZdgFayobTJCb9SiuOIEusaYRR8ZFDs0ulKhQZAszMFdEhEREZG9SQRB\nGP1uShd2/fp1xMfH48c//jFefvllAEBHx9/DbEVFhbNacyhBEGDubkFNW9nQLPo+8Vn0fl4zER+c\niviQuZjpE+LgLomIiIhoLHK5fPjPMplsQh7T5V+5/yYfHx+kpqaisrLS2a04Rcf1dtT+LdB39LSL\n1ni7+yEuOAXxIakI8ovkLHoiIiKiaWLShfve3l6cP38eS5YsEb0/KyvLwR3Z35XOyzCYdDCYdLjU\nWi1a4+Pphwz5QqgUuUiKmphZ9EVFRQCm5pk6G8/WPniu9sFztQ+eq33wXO2D52ofX7/6ZKK4fLj/\n13/9V6xcuRIxMTG4fPkyXnvtNfT09GD16tXObs2uOrvNOFNxAgaTDjVNF0RrPNy9MC9hPtQKDZJj\nMziykoiIiGiac/lw39DQgO985ztoa2tDSEgIFi5ciFOnTiEmJsbZrU24673XUFx5EgaTFhWXzkEQ\nrKNqZri5IyVODbVSg9S4LHi4ezqhUyIiIiJyRS4f7n/3u985uwW76uvvQWn1aehNWlyoK4bFOjiq\nRiqRQjk7AypFDtISF8Db09cJnRIRERGRq3P5cD8V3VguZTBpca6mEAODIsulIEFiVApUCg3SkxbC\n32di3kFNRERERFMXw72DWCyDMF0qhd6Yj7NVfx1zudTsMDnUCg0y5IsQ6B/s4C6JiIiIaDJjuLcj\nq2BFTeN56I1anKksQHeP+Cz6iKDZUCk0UClyEDIzwsFdEhEREdFUwXA/wQRBwKXWGhhM+TAYdTBf\naxOtC5KFQa3IhUqRg8jgWAd3SURERERTEcP9BLlsboDeqIXepMVlc4Nojcx3FjIVOVArNJgdlsTl\nUkREREQ0oRju74C5qxUG0wnoTfm4dHmM5VJe/shIWgi1UoPEyIlZLkVEREREJIbhfpyu9XQOLZcy\nalHVWC5a4+HuhbSEBVArNVDOTudyKSIiIiJyCIZ7G/T29+Bs1SkYjFpcuFgMq8hyKTe3GUiNU0Ol\n0GBu/F1cLkVEREREDsdwP4ahWfR66I1alNUUYcAiMoteIoUieh5USg3Sk7Lh4+nnhE6JiIiIiIYw\n3H+NxTIIY/1ZGEzam86ij4tQQq3QIFO+GAG+gQ7ukoiIiIhI3LQP91bBiqqGchhMOhTfZBZ9ZHAc\n1AoNVMocBAWEObhLIiIiIqJbm5bhXhAEXGypgN6kwxmTDh3dV0TrbsyiVys1iAia7eAuiYiIiIjG\nZ9qEe0EQ0NReB71RC4NJh/bOFtE6mV8QVPLFUHEWPRERERFNMlM+3F82N8JgGgr0zVfqRWt8vQOQ\nmbQIaqUG8ZFzIJVIHdwlEREREdGdm5Lh/kpn69AsepMW9ZerRGu8PXyQlrQQKkUOFDFpcONyKSIi\nIiKa5KZcuH/r4AZUN50Xvc9jhifmJsyHSpGDObEquM/gcikiIiIimjqmXLj/ZrB3c5uBlFjV0HKp\nhLvg6e7lpM6IiIiIiOxryoV7AJBKpFDEpEGl0CAtaQGXSxERERHRtDDlwv1j96xFhnwR/H1mOrsV\nIiIiIiKHmhRjYd59913Ex8fD29sbWVlZ0Ol0Y9Zq0pcz2BMRERHRtOTy4f6jjz7CSy+9hI0bN6K4\nuBiLFi3CsmXLUF8vPtaSiIiIiGi6cvlwv2vXLnz3u9/FP//zP0OpVOLtt99GREQE9uzZ4+zWiIiI\niIhcikuH+/7+fhgMBixdunTE7UuXLkVBQYGTuiIiIiIick0uHe7b2tpgsVgQFhY24vbQ0FA0Nzc7\nqSsiIiIiItc05abldHR0OLuFKUMulwPgmdoDz9Y+eK72wXO1D56rffBc7YPnOnm49Cv3wcHBcHNz\nQ0tLy4jbW1paEBER4aSuiIiIiIhck0uHew8PD6jVahw9enTE7X/+85+xaNEiJ3VFREREROSaXP6y\nnFdeeQVPP/005s+fj0WLFuGXv/wlmpub8fzzzw/XyGQyJ3ZIREREROQaXD7cP/7442hvb8e2bdvQ\n1NSEefPm4U9/+hNiYmKc3RoRERERkUuRCIIgOLsJIiIiIiK6cy59zb2t3n33XcTHx8Pb2xtZWVnQ\n6XTObmlS2bJlC6RS6Yj/IiMjR9VERUXBx8cH9957L8rLy53UrevKz8/HypUrER0dDalUiv3794+q\nudU59vX14Qc/+AFCQkLg5+eHb33rW2hoaHDUX8El3epc16xZM+rr95vvyeG5jrZjxw7cddddkMlk\nCA0NxcqVK1FWVjaqjl+z42PLufJrdvx2796N9PR0yGQyyGQyLFq0CH/6059G1PBrdfxuda78Wp0Y\nO3bsgFQqxQ9+8IMRt9vra3bSh/uPPvoIL730EjZu3Iji4mIsWrQIy5YtQ319vbNbm1SSk5PR3Nw8\n/F9paenwfW+88QZ27dqFd955B4WFhQgNDUVeXh6uXbvmxI5dT3d3N9LS0vDzn/8c3t7ekEgkI+63\n5RxfeuklfPLJJ/jf//1faLVadHZ2YsWKFbBarY7+67iMW52rRCJBXl7eiK/fb/7Q57mO9tVXX2H9\n+vU4efIkvvzyS8yYMQP3338/zGbzcA2/ZsfPlnPl1+z4xcTE4Gc/+xnOnDkDvV6PJUuW4OGHH0ZJ\nSQkAfq3erludK79W79ypU6ewd+9epKWljfj5ZdevWWGSmz9/vrB27doRt8nlcmHDhg1O6mjy2bx5\nszB37lzR+6xWqxAeHi5s3759+Laenh7B399feO+99xzV4qTj5+cn7N+/f/hjW87x6tWrgsf/b+/u\nY6Ku4ziAv3+HHHCKiiKIQAj4jC4ZaOADICnZcAbzEc1KSytNXbr5lBGQQ63pzCU5e9r9EfnAcLVq\nCYxNRd0AAA1sSURBVCXyMG0zUcSHJOJKtCRBpW55hNynPxg/O+DgRPQOfL82Nu5339/9vvfeZ9yH\nH9/fD61WMjMz1TGVlZWi0WjkyJEjD2/yDqx5riIizz//vMyYMcPqPszVNkajUZycnOSrr74SEdZs\nZ2meqwhrtrP069dP9u3bx1rtZE25irBW79etW7ckODhYjh07JjExMbJy5UoRefA/X7v0mft///0X\nxcXFiIuLs9geFxeH48eP22lWXVNFRQV8fX0RFBSEpKQkGAwGAIDBYEBVVZVFxq6uroiKimLG98CW\nHE+dOoX6+nqLMX5+fhg5ciSzboOiKCgqKoK3tzeGDx+OZcuW4fr16+rzzNU2f/31F8xmMzw8PACw\nZjtL81wB1uz9amhowP79+2EymRAVFcVa7STNcwVYq/dr2bJlmDNnDqKjoyH/u8T1Qdesw98tpy3V\n1dVoaGiAt7e3xXYvLy9cu3bNTrPqeiIiIqDX6zFixAhUVVVhy5YtmDBhAs6fP6/m2FrGv//+uz2m\n2yXZkuO1a9fg5OSE/v37W4zx9vZu8Y/c6K7p06dj1qxZCAwMhMFgwObNmxEbG4tTp05Bq9UyVxut\nXr0aoaGhiIyMBMCa7SzNcwVYsx1VWlqKyMhI1NXVwc3NDQcPHsTw4cPVRoe12jHWcgVYq/fjww8/\nREVFBTIzMwHAYknOg/752qWbe+oc06dPV78fPXo0IiMjERgYCL1ejyeeeMLqfs3XPlPHMMf7M2/e\nPPX7kJAQhIWFISAgAF9//TUSExPtOLOuY82aNTh+/DiKiopsqkfWrG2s5cqa7ZgRI0bg7NmzqK2t\nxaFDhzB//nzk5eW1uQ9rtX3Wcg0PD2etdtClS5fwxhtvoKioCE5OTgAAEbE4e29NZ9Rsl16W4+np\nCScnpxa/wVRVVcHHx8dOs+r6dDodQkJCUF5erubYWsYDBw60x/S6pKas2spx4MCBaGhoQE1NjcWY\na9euMet74OPjAz8/P5SXlwNgru15/fXXceDAARw9ehSDBw9Wt7Nm74+1XFvDmrWNs7MzgoKCEBoa\nivT0dERERGDPnj02fU4xU+us5doa1qptTpw4gerqaoSEhMDZ2RnOzs4oKChARkYGtFotPD09ATy4\nmu3Szb1Wq0VYWBhycnIstufm5ra4VRPZzmQy4eLFi/Dx8UFgYCAGDhxokbHJZEJRUREzvge25BgW\nFgZnZ2eLMVeuXMFPP/3ErO/B9evXcfXqVfUDn7lat3r1arUBHTZsmMVzrNmOayvX1rBmO6ahoQFm\ns5m12smacm0Na9U2iYmJOHfuHEpKSlBSUoIzZ84gPDwcSUlJOHPmDIYOHfpga7azrwx+2A4cOCBa\nrVY++ugjuXDhgqxatUrc3d3l8uXL9p5al7F27VrJz8+XiooK+eGHHyQ+Pl769OmjZrh9+3bp06eP\nZGdnS2lpqcybN098fX3FaDTaeeaOxWg0yunTp+X06dOi0+kkLS1NTp8+fU85vvrqq+Ln5yffffed\nFBcXS0xMjISGhorZbLbX27K7tnI1Go2ydu1aOXHihBgMBsnLy5OIiAjx9/dnru1Yvny59O7dW44e\nPSp//PGH+vX/3Fiz9669XFmzHbN+/XopLCwUg8EgZ8+elQ0bNohGo5GcnBwRYa12VFu5slY7V3R0\ntLz22mvq4wdZs12+uRcRycjIkMGDB4uLi4uEh4dLYWGhvafUpcyfP18GDRokWq1WfH19Zfbs2XLx\n4kWLMSkpKeLj4yOurq4SExMj58+ft9NsHVdeXp4oiiKKoohGo1G/X7x4sTqmvRzr6upk5cqV0r9/\nf9HpdDJz5ky5cuXKw34rDqWtXG/fvi1PPfWUeHl5iVarlYCAAFm8eHGLzJhrS83zbPpKTU21GMea\nvTft5cqa7ZgXXnhBAgICxMXFRby8vGTatGlqY9+EtXrv2sqVtdq5/n8rzCYPqmYVERtW9xMRERER\nkcPr0mvuiYiIiIjoLjb3RERERETdBJt7IiIiIqJugs09EREREVE3weaeiIiIiKibYHNPRERERNRN\nsLknIiIiIuom2NwTEXUBMTExmDJlil3nsGPHDgQHB1v91/QPw7hx47B+/Xq7HZ+IyNGxuSciciDH\njx9HamoqamtrLbYrigJFUew0K+Dvv//G1q1bsW7dOmg09vvo2LRpE/bs2YOqqiq7zYGIyJGxuSci\nciDWmvvc3Fzk5OTYaVbAJ598ApPJhOeee85ucwCAhIQE9O7dG3v27LHrPIiIHBWbeyIiByQiFo97\n9OiBHj162Gk2jc19fHw83Nzc7DYHoPEvGLNnz4Zer2+RERERsbknInIYKSkpWLduHQAgMDAQGo0G\nGo0G+fn5Ldbc//rrr9BoNNi+fTsyMjIQFBSEnj1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dgl+urn5fZV/Pljxx3z/1PrD3XgX7duLpMfNYsOYdSsqKKCot4IsVb/DEyDm3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\nPadmzZrJZrNp0qRJLivs4sWLKigokJ+fn9Nxf39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KUVyRi6LOFoHyPCiri3Qa2C0e39wKHi6+4lP/zt9ujp6wt3HUy7+1IAi4lX8F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\nHD16VFy/fl1+PRo35uyTaymuzNm2e+edd0RGRoYoKCgQ58+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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1395,10 +1387,8 @@ "import math\n", "\n", "dt = 12. # 12 seconds between readings\n", - "\n", "range_std = 5 # meters\n", "bearing_std = math.radians(0.5)\n", - "\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", @@ -1414,23 +1404,19 @@ "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", - "\n", + "random.seed(200)\n", "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", - "random.seed(200)\n", - "\n", - "t = np.arange(0, 360 + dt, dt)\n", - "n = len(t)\n", - "\n", + "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", - "for i in range(len(t)):\n", + "for _ in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x) \n", - "ukf_internal.plot_radar(xs, t)" + "ukf_internal.plot_radar(xs, time)" ] }, { @@ -1451,12 +1437,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The previous example produced extremely good results, but it also relied on an assumption of an aircraft flying at a constant speed with no change in altitude. I will relax that assumption by allowing the aircraft to change altitude. First, let's see the performance of the previous code if the aircraft starts climbing after one minute." + "The previous example produced extremely good results, but it also relied on an assumption of an aircraft flying at a constant speed with no change in altitude. I will relax that assumption by allowing the aircraft to change altitude. Here are the results if the aircraft starts climbing after one minute." ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 54, "metadata": { "collapsed": false, "scrolled": false @@ -1466,7 +1452,7 @@ "data": { "image/png": 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oqCjNONHR0bCysoJcLmc4ICLqQ3FFPg6deQ/FFXlax50krlgx81kE+05/oP8+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\nIQQAwMvLCwYGBlCpVNL2oqIinD17Fn5+fm03ASI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1488,13 +1474,10 @@ "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "random.seed(200)\n", - "\n", - "t = np.arange(0, 360 + dt, dt)\n", - "n = len(t)\n", - "\n", + "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", - "for i in t:\n", - " if i >= 60:\n", + "for t in time:\n", + " if t >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", @@ -1502,7 +1485,7 @@ " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", - "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=False, plot_alt=True)\n", + "ukf_internal.plot_radar(xs, time, plot_x=False, plot_vel=False, plot_alt=True)\n", "print('Actual altitude: {:.1f}'.format(ac.pos[1]))\n", "print('UKF altitude : {:.1f}'.format(xs[-1][2]))" ] @@ -1516,12 +1499,12 @@ "I hope you answered add climb rate to the state, like so:\n", "\n", "\n", - "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude \\\\ climb rate\\end{bmatrix}= \\begin{bmatrix}x \\\\\\dot{x}\\\\ z \\\\ \\dot{z}\\end{bmatrix}$$\n", + "$$\\mathbf{x} = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude} \\\\ \\mathtt{climb\\, rate}\\end{bmatrix}= \\begin{bmatrix}x \\\\\\dot{x}\\\\ y \\\\ \\dot{y}\\end{bmatrix}$$\n", "\n", "This requires the following change to the state transition function, which is still linear.\n", "\n", "$$\\mathbf{x}^- = \\begin{bmatrix} 1 & \\Delta t & 0 &0 \\\\ 0& 1& 0 &0\\\\ 0&0&1&dt \\\\ 0&0&0&1\\end{bmatrix}\n", - "\\begin{bmatrix}x \\\\\\dot{x}\\\\ z\\\\ \\dot{z}\\end{bmatrix} \n", + "\\begin{bmatrix}x \\\\\\dot{x}\\\\ y\\\\ \\dot{y}\\end{bmatrix} \n", "$$\n", "\n", "The measurement function stays the same, but we will have to alter Q to account for the state dimensionality change." @@ -1529,7 +1512,36 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 76, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def cv_UKF(fx, hx, R_std):\n", + " def f_cv_radar(x, dt):\n", + " \"\"\" state transition function for a constant velocity aircraft\"\"\"\n", + " F = np.array([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]], dtype=float)\n", + " return np.dot(F, x)\n", + "\n", + " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", + " kf = UKF(4, len(R_std), dt, fx=fx, hx=hx, points=points)\n", + "\n", + " kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", + " kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", + " kf.R = np.diag(R_std)\n", + " kf.R = np.dot(kf.R, kf.R) # square to get rariance\n", + " kf.x = np.array([0., 90., 1100., 0.])\n", + " kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", + " return kf" + ] + }, + { + "cell_type": "code", + "execution_count": 77, "metadata": { "collapsed": false, "scrolled": false @@ -1537,9 +1549,9 @@ "outputs": [ { "data": { - "image/png": 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Ef39/4uPjOXbsmFObgoICEhISCAwMJDAwkNGjR1NYeOl6zyIiIjeagpITfLRq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\nRVpaGmJjY6W4oKAgaVx3j4mIqFcTRET01PnLX/4iZDKZuHTpklZ7RES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07BHe+PMXQkBQQIhuPSqdgsKBiIiIdEg1tdVs3/8m2WezKCkv4FJN+U3vy2TyIaxHBL16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\nGNOnT7f4HTZsNStIzJo1S6xbt85ibNKkSWLLli1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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1550,40 +1562,19 @@ "output_type": "stream", "text": [ "Actual altitude: 2561.9\n", - "UKF altitude : 2432.9\n" + "UKF altitude : 1712.1\n" ] } ], "source": [ - "def f_cv_radar(x, dt):\n", - " \"\"\" state transition function for a constant velocity aircraft\"\"\"\n", - " \n", - " F = np.array([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]], dtype=float)\n", - " return np.dot(F, x)\n", - "\n", + "random.seed(200)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", - "points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", - "kf = UKF(4, 2, dt, fx=f_cv_radar, hx=h_radar, points=points)\n", - "\n", - "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", - "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", - "\n", - "kf.R = np.diag([range_std**2, bearing_std**2])\n", - "kf.x = np.array([0., 90., 1100., 0.])\n", - "kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", - "\n", - "random.seed(200)\n", - "\n", - "t = np.arange(0, 360 + dt, dt)\n", - "n = len(t)\n", - "\n", + "kf = cv_UKF(f_cv_radar, h_radar, R_std=[range_std, bearing_std])\n", + "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", - "for i in t:\n", - " if i >= 60:\n", + "for t in time:\n", + " if t >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", @@ -1591,7 +1582,7 @@ " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", - "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=False, plot_alt=True)\n", + "ukf_internal.plot_radar(xs, time, plot_x=False, plot_vel=False, plot_alt=True)\n", "print('Actual altitude: {:.1f}'.format(ac.pos[1]))\n", "print('UKF altitude : {:.1f}'.format(xs[-1][2]))" ] @@ -1614,14 +1605,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's consider a simple example of sensor fusion. Suppose we have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system, where you have to account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", + "Now let's consider an example of sensor fusion. We have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system, where you have to account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", "\n", "The accuracy of the radar system in the last examples allowed us to estimate velocities to within a m/s or so, so we have to degrade that accuracy to be able to easily see the effect of the sensor fusion. Let's change the range error to 500 meters and then compute the standard deviation of the computed velocity. I'll skip the first several measurements because the filter is converging during that time, causing artificially large deviations." ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 78, "metadata": { "collapsed": false, "scrolled": false @@ -1631,7 +1622,7 @@ "data": { "image/png": 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29OkyxKjn/60RfSZjY20LwKWSbLILM0x6PSFEy2OjdgCNdb2m/6uvvuLw4cMkJycDKLMj\nd5oluf58YVxyX01D7qtpyH01DVPc183HVio/B7ftzunjZ4AzyjEfuy54ugaQX3wenV7HJz/9HxPC\nn8XB1sko1997er3yc2DrLqQeSTfKeW+no1cvjucY7uXhczvxS+og69lMQN4HTEPuq3GFhIQY/ZwW\nOfPv4+MDQF5eXr3jeXl5ymNbt24lNTUVFxcXbG1tsbMz1Ek+8sgjREVFmTdgIYQQRne5JJfswtPK\nuHvAfTc8R6OxZkiXydjZGDrllFVdJeHkz0Ypl6nRVpOZX9tJqJN3+D2fsyG6+w9EY2VoYpFffJ7c\nojNmua4QomWwyJn/4OBgfHx8iIuLo0+fPgBUVFSwc+dO3nnnHQDeeustXn31VeU1er2eHj168M47\n7zBp0qRbnrtv376mDb6Fuf4JX+6rccl9NQ25r6Zhqvv6+bq3lZ/DQwYyfMitSzw9fF359OcFAJwv\nOEmJdQ7RETG3fH5DJKVvp1pbCYCnuy/jh08x2wx8buUJdh/ZAEBGYQoTRz5kluu2BPI+YBpyX02j\nqMj4ncxUS/5LS0s5efIkADqdjqysLFJSUvDw8CAwMJDZs2ezYMECQkNDCQkJYf78+bi5ufHYY48B\n4Ofnh5+f3w3nDQwMJCgoyJy/ihBCCCO7WJBNyqk9ynhU3wdv+/weHfozrHcM2w+uBWDt7i/p4BdK\ne5/Odx1D3YW+A7qNMGvpzai+U0g4Goder+P0hWOcPH+UkIDuZru+EKL5Uq3sJykpiYiICCIiIqio\nqCA2NpaIiAhiY2MBmDNnDi+99BKzZs2iX79+5OXlERcXh7Ozs1ohCyGEMJMt+9egv9a6M6x9BIFe\nHe74mphB02jnbaiP1epq+Hz9Isoqb9wbpiHyC3M4deEYABorDQPCht/Vee5WGzcvOnr1VMYb931r\n1usLIZov1ZL/YcOGodPp0Ol0aLVa5efPPvtMeU5sbCzZ2dmUl5ezbds2unbtettz6nQ6pkyZctvn\nCCGEsGwFxZdITNumjEf1m9qg19lY2/LU2D/jaGdY7Hvl6kVWblp6V/X/e49tVn7uGtQHd5c2jT7H\nveoRMAgrDN82nDh/xOidjIQQLZNFLvgVQgjRcm07uBatrgaAYN9QOvrdfuKnLg93bx4b9aIyPnR6\nLzsPr2vU9bU6LfvStipjU/b2vx1Xh9Z08OqhjDckfqdKHEKI5kWSfyGEEBajtPwqCUfjlPHofg82\nuta+V6f7iOo1Thmv2fk55y6evs0r6ks9s5+rpQUAuDq1oltQn0Zd35h6BAzGysrwT3V61kHO5J5Q\nLRYhRPMgyb8QQgiLsePQr1RVVwDg1zaIrneZeE8aPIMAT8M6Aa22hs/XvU15ZVmDXlu35GdA2HCs\nrdVrjOfm2IY+nWs3Ftsgtf9CiHskyb8QQgiLUFFVTnzKr8p4VN+7b61pa2PHU+Nexd7OEYBLRbl8\nu/XDO9b/Xy0t4Fhm7SZFkd1G3NX1jWl0/weV2v/UM/vJvpSlckRCiKZMkn8hhBAWIeHoRqU7j4e7\nN+Ehg+7pfJ6tfPnd8BeU8YETu+qVFN1MYto2dNe6DHX064pXa/97isEYfNoE0rNTpDLeduAnFaMR\nQjR1kvwLIYRQXXVNNdsOrFXGI/tMwVpjfc/n7dNlCAO7j1bGq3b8hwv5Z276XL1eX6/kR62Fvjcz\nPKJ288rk4/EUlV5RMRohRFMmyb8QQgjVJaVvUxJaN+fW9DdiX/0pQ5/Bz6M9ADXaaj5f/zaVVeU3\nPC8jO5WLhdkAONg5ER4y0Ggx3Ktg31CCfLsAhj0Mdh5qXAcjIYS4TpJ/IYQQqtLqtGxOXq2Mo3tP\nwtbG1mjnt7Ox56lxr2Jn6wDAxYILfLvt3zfU/++pM+vfp/MQ7K8931IM7107+7/r8AYqry2MFkKI\nxpDkXwghhKpSTiZwqSgXACd7Fwb1GGP0a3i3CeDh6OeUcXL6Dval1vbyL68s5eDJ3crYkkp+ruvZ\ncQAe7t4AlFWW1ItfCCEaSpJ/IYQQqtHr9WxOXqWMo3qNx+Fahx5j6x8WzYCutd17vt/+MTmXzwKG\nxcDVNVUA+Hm0p513J5PEcC80GmuGhU9UxtsPrkWn06oYkRCiKZLkXwghhGpSz+znwqUzgKE8Z2j4\neJNe78Fhv8enTSAA1TVVfL7ubaqqK+uV/NzXfdRdtxg1tciuI3CydwEM7UuPZCSqHJEQoqmR5F8I\nIYRqNtWZ9R/YfTTOjm4mvZ69rQNPjXsVWxs7AHKvnOOTn9/ibN5JAKytbejbJcqkMdwLezvHemVR\nW6XtpxCikST5F0IIoYrTF46RkZ0GgLXGhug67SxNydejHQ8Om6mMT5w7rPzcq2OkyT+A3KuoXuOx\n1hh2Hc7MSScz57jKEQkhmhJJ/oUQQqhiU1LtrH+/0KG0dm1rtmtHdh1B3y5Db3Lc8hb6/pa7Sxv6\ndBmijGXTLyFEY0jyL4QQwuzO52eQmnUAACusGNl3ilmvb2VlxcPDn8erlZ9yrI2rJ53b9TRrHHcr\nuk7bz0On9yrdkoQQ4k4k+RdCCGF2dfv69wq5D6/W/maPwcHOkafGvYqzgysAYyN/h8aqafyz6O8Z\nRGi7cAD0eh3bD/6sckRCiKZC1Xe5+Ph4YmJiCAgIQKPRsGzZshueM2/ePPz9/XFyciI6OprU1FTl\nsYKCAl588UXCwsJwcnKiXbt2vPDCC1y5ItueCyGEpcovzOHgyQRlPKrvg6rF4u8ZzF+mf0DsjI/r\ntQFtCuqukdibuoWyihIVoxFCNBWqJv+lpaX07NmTd999F0dHxxtaqy1cuJDFixezdOlSkpKS8PLy\nYtSoUZSUGN7gsrOzyc7O5u233+bo0aMsX76c+Ph4Hn30UTV+HSGEEA2wZf9q9HodAKHtexPo1UHV\neJwd3ZTNs5qS0Hbh+Hm0B6CquoLdRzaqHJEQoilQNfkfO3Ys8+fPZ+rUqWg09UPR6/UsWbKEuXPn\nMnnyZLp168ayZcsoLi5mxYoVAHTr1o1Vq1YxYcIEOnToQFRUFG+//TabN29WPiAIIYSwHIUll9mX\nuk0Zj+6n3qx/U2dlZUV0RIwyjj/0KzXaahUjEkI0BRZb3JiZmUleXh6jR49Wjjk4OBAVFUVCQsIt\nX1dUVIS9vT1OTk7mCFMIIUQjbDvwE1pdDQDBvqF09OuqckRNW0TnKNycWgNQVHqFAyd2qRyREMLS\n2agdwK3k5ho6F3h71/8q1svLi+zs7Ju+prCwkL/+9a/MnDnzhm8SrktOTjZuoAKQ+2oqcl9NQ+6r\nadzpvlZUl7Hz0HplHNyqF/v37zd1WE3ene5rx7a9OHh2OwC/7lqJVYmLxe5QbEnkfcA05L4aV0hI\niNHPabEz/7dzsze1kpISJk6cSGBgIP/85z9ViEoIIcTtHM9JpkZnKEtp5eSFf+tOKkfUPHT26YON\nxhaAgrKL5BRlqhyR8dRoq8m7elb5tkgIce8sdubfx8cHgLy8PAICApTjeXl5ymPXlZSUMG7cODQa\nDb/88gt2dna3PG/fvn1NE3ALdf0TvtxX45L7ahpyX02jIfe1sqqcH/a/q4wnRT1Bny79TB5bU9aY\nv9ecyjTiD60D4HxJGjEjHzZpbOag1+v5YPX/cuL8EXw92vHHB99S2rLeC3kfMA25r6ZRVFRk9HNa\n7Mx/cHAwPj4+xMXFKccqKirYtWsXAwcOVI4VFxdz//33o9frWbdundT6CyGEBdp9NI6yimIAPNy9\nCQ8ZpHJEzcvQ8IlYYfhWPD3rINmXslSO6N4dPr2PE+ePAJBz+Sz//eUfsqBZCCNQvdVnSkoKKSkp\n6HQ6srKySElJ4dy5c1hZWTF79mwWLlzImjVrOHr0KDNmzMDV1ZXHHnsMMCT+o0ePprCwkM8//5zi\n4mJyc3PJzc2lulreIIQQwhJU11Sz7cBPynhknylYa6xVjKj58WzlS8+OA5TxtoNrVYzm3un0Otbv\n+6besVMXjvHNlg/R6/UqRSVE86Bq8p+UlERERAQRERFUVFQQGxtLREQEsbGxAMyZM4eXXnqJWbNm\n0a9fP/Ly8oiLi8PZ2RmA/fv3s2/fPtLS0ujcuTN+fn74+fnh7+/Pnj171PzVhBBCXJOUvp2iUsPm\ni25OrekfFq1yRM1TdMQDys/Jx3co97wpOnxqL9mXzgAo32gAJKZtY2PidypFJUTzoGrN/7Bhw9Dp\ndLd9TmxsrPJh4G5eL4QQQj06nZYtyauVcXTEJGxtbr0uS9y9Dn6hBPl04UzucbTaGnYeWseEgU+o\nHVaj/XbWf3ifSZRVlLLn2CYA1u1diYe7D/1Ch6oVohBNmsXW/AshhGj6Uk7tIb8oBwAnexcG9Rij\nckTN2/CIScrPuw5voLK6QsVo7s6hU3vIuXwWADtbB4ZHTObh6OfoEthLec6Kze9z+sIxtUIUokmT\n5F8IIYRJ6PV6NiX9oIyH9BqHg52jihE1fz07DsDD3bA/TlllCftSt6ocUePo9Do27PtWGUf1HIer\nkzvW1jY8PX4OPm0CAdBqa/j0l39wseDm+/4IIW5Nkn8hhBAmkZZ1gAvX6rbtbOwZGj5B3YBaAI3G\nmmHhE5Xx9oNr0em0KkbUOCknE5RZf3tbB4b3qV3H4GjvzHOT/oKrUysAyiqK+finv1NaflWVWIVo\nqiT5F0IIYXRanZa1u79SxgO7j8bF0U3FiFqOyK4jcLQ3NMa4VJTLkYwklSNqGJ1OW6/Wf2j4hBv+\nZjzcvJk58Q1l3Uh+UQ6f/vJ/VNdIhz8hGqrByX9kZCQfffQRV6403e4BQgghzCP+0K9KtxY7G3ui\n69SiC9Oyt3NkUI/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ntjP/txvfq6SkJIYPHw4YvjGIjY0lNjaWGTNm8NlnnzFnzhzKy8uZ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1648,26 +1639,14 @@ "source": [ "range_std = 500.\n", "bearing_std = math.degrees(0.5)\n", + "random.seed(200)\n", "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", - "points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", - "kf = UKF(4, 2, dt, fx=f_cv_radar, hx=h_radar, points=points)\n", - "\n", - "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", - "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", - "\n", - "kf.R = np.diag([range_std**2, bearing_std**2])\n", - "kf.x = np.array([0., 90., 1100., 0.])\n", - "kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", - "\n", - "random.seed(200)\n", - "\n", - "t = np.arange(0, 360 + dt, dt)\n", - "n = len(t)\n", - "\n", + "kf = cv_UKF(f_cv_radar, h_radar, R_std=[range_std, bearing_std])\n", + "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", - "for i in t:\n", + "for _ in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", @@ -1675,13 +1654,13 @@ " xs.append(kf.x)\n", "\n", "xs = np.asarray(xs)\n", - "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=True, plot_alt=False)\n", + "ukf_internal.plot_radar(xs, time, plot_x=False, plot_vel=True, plot_alt=False)\n", "print('Velocity standard deviation {:.1f} m/s'.format(np.std(xs[10:, 1])))" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 79, "metadata": { "collapsed": false, "scrolled": false @@ -1689,9 +1668,9 @@ "outputs": [ { "data": { - "image/png": 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b7ij4NwHVTWUa7RrRbYh7ukb59PRjCmU+h4oLp9V+iSb+qP/8mUtga21nxN5M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\n", 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0fDMdBf9GoKa5XK1dK7wNUW/3GJ+eeYyhzOdw8WG02i9Rxx/1nx+1BNaWNgbs\nzdQkzU7lKq1UNZWhpbPRwD0i2lbZWIa9h55BHm9BpVphOd79YrfeUr3KavNwu6EYgLIK1bpF2zTa\nL5Bf7rOVRv51jR/8uzl76fRc9jaOmM1bDJFSf3SLgn8jMLxiDAsWZbW5BuqNcRmQ9XOLEDFg4O8Z\nbOAeKcWGqI9SdPS0GrhHxJAGZQPIKb/ItVOMsMqPJpzsXRDLe6rFX6yMmDaFQo6M64fx9pHnuQIK\nfLUtt7H/2B+4VXZ11g9Wga8v/4trL4pbAy/XWRrtyx/8aWqrxaBsUOv9IyodIt1X+uHjp/4UUPCv\nUxT8G4GaUcpFlhhp6k9xVTaulfygt/r2TW013IQwL9dZXK69odnZ2COKN0pRSKP/M1pRVTak/RIA\ngIezj1oJTVOzIDqN286iuv9moVvcgXeP7caJK//mvp92Ng54fN1O/GTVL7jP1bdUYv8Xf4BEh6Ve\n88ovcyk7VpbWuGfBjzTe197WER4uPgAAuUKG5g6ab6VLaqv7Ouk++I8PWwA7GwckRS1D2vwNOj/f\nTGbYsikEcrls1NzF0ppcKBTyURc7MZSbtfl476s9AJS/FNYtfFDn56w3ksW9RpMQfhdKa5Q3aQUV\n17B83noD94gYCj/lJyUmbcxyhaYgLjQF9jaO6O0Xo0PUioqGYkQGxBu6W2SKiquy8cnpt9UC+tBZ\n0Xjsnme5PG4GDD794V2wYNHQWoX9X/wBO+57GY52zlrti1wuwzdXDnHt5fM2wMXRfVLHCPQKR3u3\nMh+8rqVSbR4A0S595vwDyiePrz75MSyMKO4xVzTyb2ANbdUYlA8AANwcPbnSgL19ItQIjWsJc34K\nwLncr/UyQYx/Y+RvJPn+d8wJSwEDZZBX0VCs09EyYrxEvV0oqVE9qUvhjZybIitLKyTy1ie4XnrO\ncJ0hUzYoG8QXmQfw3ld7uN9NDBjcveAB/Or+P6kFc4vmrMG2Nf+P+33W0FaN/Udf0vrcs6slP6C1\nSzmPxM7GAauTtkz6GPxBIFrsS7f0HfwDoMBfTwwa/GdmZmLjxo0ICAiAQCDAwYMHR3xm9+7d8Pf3\nh729PVasWIGSkhK1999//32sWLECrq6uEAgEqK01rceANULVZN/gWVGI4dW6NaaqP3KFHEWVWVy7\nb6AXF/O/0/l569uMY2Xf0bg4uCN4VhQAZR5rUVW2gXtEDCHn1kUuDS5sVozG+cvGjF/1J6/8EvoH\n+wzYGzIflyFLAAAgAElEQVRZLZ2N+L/Dv8O53K+411wc3LHjvpdx76KHRg2w7opdhYfW/oq7AWhs\nr8H+L16CqLdLK30akPXj5LXPuPbqpPtgb+s46eOoV/yh4F9XZPJBdN+p8Q8Gbk6eBu4R0SaDBv8S\niQQJCQnYt28f7OzsRjwq37t3L958803s378fWVlZ8Pb2xpo1ayAWq0acpVIp7rnnHvzxj3/Ud/e1\ngp/vH+IbpTbZrqT6hiG6NKqKhpIRI/1n876GTK67CVcKhRyNbdVc29iCfwBI4FX9obz/men6sJQf\ncxDsEwlvN38AQP9gn1GVs+0bkOJWXQEGBmmF19FcLz2L1/7zrNpT07jQZPzuobcQFTh++taCmBV4\n+O5fg2GUoUFTey3eOfoSeiTTvwG4kP8tuiXKYNLZwW3KaZL8Sb8NbdWQy2XT7hsZiV/j38VRtzX+\nif4ZNPhPT0/Hnj17sHXrVggE6l1hWRZvvfUWnnvuOWzZsgVxcXE4ePAgRCIRDh1S5Qz++te/xu9+\n9zssWbJE393XCn6Zz2CfKMwOSoBg6BdvbcttrY26TNdoga1E2oNyoe6qEgk7GzEoU6ZEuTi4w8ne\nVWfnmir+ar+lNbkUkMwwTe21XOqBpYUV5kea5u+h4RiGMcqa/wqFHH87/kfs/+IP2HfkeZ0OPpia\nvgEpPj71f/gkYx/3pMbCwhL3pf4MT254QeP8/ZToNDyyVnUD0NxRh3eOvsgF7lPR2y/G6ayjXPue\nBT+GtdXUSuE62bvAzVE5Ci2TD6K5o37K/SJjM0TKD9Efo835r6qqglAoxNq1a7nXbG1tkZqaisuX\nL4+zp+no7RdD2Kn8xSVgBAj0Doe9jSNCZ0VznymtMXzJT5Zl1VZiTAhfyG0XN1yBXEeVfxqMsL7/\ncN5u/vB1DwSgLPdIJVpnlixePvycsJQppTEYq5To5VwKyK3aAnSK2gzcI6Cw8jqqmsoAKPO9z9w4\nbuAeGYda4W28duhZZJed517zcvXDsz/ai7T5GyY9AT05ejkeu+dZbiBK2FmPd46+xKWBTNaZG8e5\nJ8eeLr5YFLd6Sse5I9CHl/pD9f51goJ/82a01X6am5UrZfr4+Ki97u3tjcbGqS88k51tPHnZjV2q\n4NbV3hsF+YUAAGcrHwDKuQ0Xc05DIHEyRPc47eJmri60lYUNYj2X4VZtIfoGJegdEKGqtRAW2dqf\npJNdpVriWyCzMarvHZ+XfRCaO+oAAGevf4uBTu39szLWr9nUaeO6KlgFLhee5truloFm9/3ycQlG\nc3c1WLA4/sO/ER8w/pMNXX79LMviu4J/qb323bXPYDXgCidbN52d1xiMdV1ZlkVp43Xk1PygVpI1\n3DsBC8LugbC2E8LaqX5PbLE0ajMu3DwGFixaOhvwl3//FnfPeRj2NppXAeodEOHMjS+5dozPIuTm\n5k2xT0qCQVtuO7voCix6XaZ0HHP796pNRTX53Ha/WD6pa0XXVbsiIyO1fkyNR/4XLlyIv/3tb+jo\nmPqjP20x5TJ6fG2iBm7b08mP2/Z3i+C2G7sqDV5nu669jNsOcI+EtaUNYv1U6S5F9Zd10scOSTO3\n7e7gq/Xja0ug+2xuu66j3ODfL6Ifzd3V6B1QLohka2UPP1fjfDo1HeHeqrUsKlsKwbKswfoi7KlF\nm1h94EeukOFaxUmD9stQ+gYlOFP6GbKrT3O/cywF1lgauQlLIjfCysJ62ucI8YxF6uz7uBQgUV8H\nThX9C5J+zSubFdZdhEyhTM9yc/BBiGfstPvl7qCaVN8hbh7nk2SqJP2qlGNH26ndXBHjpfEQ5cDA\nAHbs2IFnnnkG6enpeOSRR7BhwwZYWelmEoivrzLYEwqFCAgI4F4XCoXce1ORnJw87b5pS07jKW47\nec4SJMcp+8ayLC6UH0W3pAMDsj54+jsjzC96rMPo3PdlqtG2tJR1mB+ZjLj4WJR+eA3Sfgl6+jpg\n5Tqo1XxnlmVx9MY+rr180Rp4uhjnDYCCVeBS5ZfoFrdjQCaFq6/dhBPrJnJn5MSYfl7NgTav68en\nLnDbd8WtxIIFd43zadMUPxCHrOoMDAz2oVvaBu9AVwT7jhyF0sfP69+Pf8tth/vHobKhBCxYNHZV\nwNJ1wGzmW/CNdV1v1RXg+Km/okfSyb0W5B2Bx9J/o/VqU8lIRkREJD787jUoFHKI+jpxvvxz/HLr\nK3Bz8hp337buZnxyRTXK/+PVT6oVtZiqKEk4zpR+CgDolrYiMXH+pNbEod+vE7tYpZqjkRi/ALOD\n5k64D11X3eju1m7JXWASI/85OTkoLi7Gs88+i9zcXNx///3w9fXFU089pZMc/NDQUPj6+iIjI4N7\nra+vDxcvXsTixYu1fj59Y1lWrdJPsG8Ut80wDGJCeCU/awxX9ae1qwmN7TUAlBMaY4PnA1CucJs6\ndx33uYysI1odfesSt3HLzNta2xt1zqGAEVDVnxmmb0Cqtvw8f3KsObGxtsO8iEVc21ATfxtaq7m1\nFBgweHDVDixNSOfeP3r+H5D29xqkb/okl8tw4vIn+OsXu9QC/5WJm/D0j/5XZ2Vm50YsxOPrdsJC\noBwvbOtuxttHXlTLCx/Nt1f+w5XBDfePUytlPR3ODm7cmjgDsn4IO6eeCkxGRzn/5m1SE35jYmLw\n6quvoqqqCufOncPWrVvx+eefY+nSpYiIiMDu3btx+7bmC1NJJBLk5eUhLy8PCoUCNTU1yMvLQ11d\nHRiGwdNPP429e/fi2LFjKCoqwvbt2+Hk5IRt27Zxx2hubkZeXh5u3VIG0sXFxcjLy0NnZ+dYpzUK\nHaIWiKTKuzlba3v4uPurvR/L+yVZYsB6/4WV17nt2UFzYWNtx7WXz9sAS4HyyU9DaxW32q028Ff2\n9fcK5SaeGSt+1Z+CimszMg1hJsm/fQUDMmVlp1keQUY7IV0bFsSs5LZv3LpgkAo7P9w4xm3PjVgE\nbzc/rF/8EJztlQFgj6QT3149NNbuZqGjpxX7jr6gHGgZKsHoaOeCpza9hM3LfqrzUowJ4Xfh8Xt3\nwsJCeQPQ3iPE20dfRHuPcNTPN7RW4cbNTK69YfEjWk3ZVav3T5N+tYpq/Ju/KUVUDMMgNTUV77//\nPqqqqvDAAw+gsrISL7/8MqKiorB06VIcO3ZswuNkZWUhMTERiYmJ6Ovrw65du5CYmIhdu3YBAHbu\n3IlnnnkGO3bsQEpKCoRCITIyMuDg4MAd4+9//zsSExPx8MMPg2EY3HvvvUhKSsLXX389lS9Nb/gl\nPoN8IkYEt7OD5nKPMetaKtRGefSpkF/lJ0w9rcHRzhmRPvO5dkbWEa2dl1+j2hjr+w8X4R8HOxvl\nz2WnqBX1vEpFxPxk8Wv7R6eZzTyk0UQExHHpHb19IhRX6fdJZHuPEDm3VClWq4ZWhbWzccCW1Me5\n1zPzv0Wtka2Kri2DsgH89dguVDfd5F6bHTgXv3vo/7SSRqOp+LAF+K97f8/dAHT0tODtIy+ivXvk\nDcCJy//mblLmhC3QeupqoJcq+K9rod+32kQ1/s3flIJ/lmVx5swZPP744wgKCsLhw4cxd+5cvPnm\nm3jnnXcgkUiwdetWPPfcc+MeJy0tDQqFAgqFAnK5nNs+cOAA95ldu3ahsbERUqkUZ8+eRWys+mSh\n3bt3jziGXC7Ho48+OpUvTW+qhy3uNZydjQPCDFzyU9TbhcqhsnoMGMwJSxnxmVj/hdyNS2VjKSoa\nirVy7gYjXtl3NBYWlogLVeU58kujEvPS0dOK8voiAADDCJASnWbYDumYYNjXmFWm39SfszlfcRNa\nIwPi1eYcJEYt5XKRWVaBz8/8nUszMSfn806gtUuZ2iIQWGDDkkfx31t2wcXBXe99iQtNxhPrn+MC\nwk5RK94+8gLaulUTbysaSlBcrcz/ZsBg/aKHtN6PAG/V07Y6WulXqyjlx/xNKvgvLCzE7373OwQF\nBWH16tX47rvv8MQTTyA/Px+5ubl4+umnsWPHDuTm5uLJJ5/E+++/r6t+m7yx8v35YngjOtpMqdFU\nUVU22KE/uqF+0aMusuVg44wwXkUQ/kIu06E+8m8aKRVqef8U/Jut7JvnuVGx2YEJcHHUfwCmbwt4\nKxcXV92AWKp5tZfpEEt7cKVYVU51dfJ9au8zDIMH0n7OBaK1LbdxsfAUzIl0QIxTWYe59pZlP8Wa\n5PsMmgoZG5KEJzY8z1UU6hS34e0jL6C1qwksy+LrS6oiEcnRy+HnGaz1Pqin/Ri+Kp45oeDf/Gn8\n22Pu3LmYO3cu3nnnHSxZsgTffPMNGhoa8PrrryM+fmRlk+XLlxt93r2hyOUyteA22Gf0Gq78vP/S\nmlydLaY1loIK1YRGfk77cHP8F3Ol4Epqcqb9CFbSJ0LH0LoCFhaW8HEPmGAP4xATPJ8LQhrba9Da\n1WTgHhFtY1lWbWGvFDOd6Duct5s/QnyVJW3lCplaLrcuZeZ/w63y7e8ViuigeaP0zQ9rUu7n2icu\nfzKt1WiNTV7tefQPSAEAPu4BWBp/j4F7pBQTPF/tBqBL3I63j76I83knUNlUCgCwEFhi3cIHdXJ+\nV0cPONopS1D2D0jR1kUlP7WlQ6QK/j0o+DdLGgf/jo6OeO+999DU1IRPP/0U6enpEAjG3n3Tpk2o\nrKQ8vNE0ttdgUK78g+bm5MVVLRjOzzMYLo4eAABpv0TtaYGu9Q9IcbNWtchHfNjYwb+znbtamb3T\n2dPL/W9orea2Z7kHmUy+oY21nVpwQlV/zE+t8Da3KreNle24N8Xmhl/RiH8DpCv9g33IzFeV91yd\ntGXMuRWrk+6Dt6tyrZS+gV4cy/xQ5/3Thw6JELeFqlKZW5b9lMu3NwbRwfPw5MYXYGWpvAHoFrfj\ni8x/cu8vib8bHi4+Y+0+LQzDUOqPjrTzR/6dKPg3RxoH/4cOHcJDDz0EF5fRF3vo7e1FbW0t17a3\nt0dISMi0O2iOqtVSfsZeuY1hGINV/SmtyeWqevh5BE9YQm4N73F8fvkVCDsbxvn0+PiTZU0h358v\nfljVH2Je+Pnu8yIWw8bKdpxPm5fEqKVc4FnbchtN7XU6Pd/V4u/RO1Tu18PZB/PGqeNvZWmFH618\nimvn3LpgkHlS2sSyLLKrTnMpZjHBiXqd3Kup2UFz8fONL8Ha0kbtdWsrW6xNeUCn5w6iij86QWk/\n5k/j4D80NBTHjx8f8/2vvvoKoaGmFagZSs0Ek335YkP4wb/+qmwU8Eat4zUY3fT3CkVcyNAiZWDx\nffYXUz63WvDvbRr5/nfMCU3hUqCqGssg6u2aYA9iKmTyQdy4qao6M1NSfu6wt3VEfOgCrn299IzO\nziWXy3Am50uuvSJxEywmWMQpKjABydHLufbhs+9x5VhNUVFVFpq7qwEoJ11vXvZTw3ZoHFGB8fj5\nJvUbgBXzN8LZYeQ8MW3izwejij/aQ8G/+dPajCGZTKatQ5k9fpnPYJ/xg/+oQFXJz/rWSr2U/JTL\nZSiuyubamqY28PNus8rOoaOndUrnb+DX+Pc0rRtKJ3sXrkoTCxaFlVkG7hHRlpLqHG7hOTdHT0QE\nxBm4R/rHT/3JLjuvs8o6OeWX0Dk078fBzhkLY1dptN/mpT/lSu62dTdrrQCBvsnkgzjOS11aEn8P\nZnkEGrBHE4sMmINfbNmNQO9wzA1fOGJyti6oTfptqaT1VbSAavzPDFoJ/ru6unDy5El4e9Md4kR6\n+8VczrCAEaj98hqNnY09wvxiuLY+qv7cbiiGtF8CQBnkaFptJ8wvGhH+yoBIoZDjTM7YT4rGMiDr\nh7BDeX0YMPA3sbQfAEgIX8htU9Uf86FW2z8mzegXntOFmOD5cBqaZNkt6cDNugKtn4NlWbVFvZbP\nvRfWVjbj7KHi7OCKjUtUZZ6/z/6C+31iSi7kf4fWbmXBACsLG6Qv/ImBe6SZML8Y/M+Db+Bn63+v\nl5Q4d2dv2Ns4AlD+bZ1oxWEyMarxPzOM+9frj3/8IwQCASwslCPPDz/8MAQCwYj/3N3dcejQITz4\noG5m9ZuT2mbVIjR+niEa/VHj5/0X6yH1p3BYys9kFjDij/5fKT496bSXprZarmSbp+ss2PJWFDYV\n8eGq1IibdfnoG6rUQUyXpE+EIt7TMHOv7T8WCwtLJM1O5drXS7Vf87+0JgeNbdUAAGtLGyxLSJ/U\n/ovmrFGrTPT52fdMakRYLO3ByWufcu25galwtHM2YI+MF0361T5K+ZkZxi0bkJKSgl/84hcAgHff\nfRdr1qxBZKT6BFWGYeDg4ICUlBTcd5/uH/OZuhohP+Vn7Mm+fLEhSfjq0scAgJu1+ZAr5BPmv04V\ny7JqE1UnW80kOmgeAr3DUddSgUHZAM7nncD6xQ9rvL8pT/a9w9PFF36eIWhsq4ZMPojSmhy1akjE\n9OTcugi5QpnaGOwTaTLlZ3VhQewKnMtTrqBeUHEV0v5erR6fP19o0Zw1cJhk4CtgBPjxyqfw2n9+\nAwWrQHl9IbJvnjeZG7bvrn4K6YDymjrZumP2rOQJ9pjZAr3DcGvoCVRdSwXmRS42cI9MGwX/M8O4\nwf+6deuwbt06AIBYLMZTTz2FhQsXjrcLmYAmi3sNN8sjCK6OHugSt0PaL0F1002E+8dOvOMU1LVU\noEvcDgCwt3FEuP/k8poZhsHalPvxz2/2AgAy87/FqqQtXB7uRNTy/U00+AeUN013Ri8LKq5R8G/i\nZmJt/7EEeIVxN7eDsgHk3b4MK2hnYmd18y3cHlolXCCwwIr5m6Z0HH+vUCyftx5nc78CABzL/BBx\nIcmwt3XUSj91pam9DpcKT3Lt5JDVOhvoMReB3hHcdl0rTfqdLqrxPzNonLT60UcfUeA/TSzLTin4\nZxhGb1V/+KP+c8JSpvSHJz78Lvi4KUdG+wZ6caHgO433recF/6aysu9o+E9MSqqyubKpxPS0dDag\nuvkmAOWiRYlRSw3cI8PjT/zVZuoPf9Q/KWoZ3J29pnys9IUPwnVonRSxtFtt1VljdfzCh1zaY1RA\nPALcNXs6PJOpV/ypMKkUL2PEL9RBNf7N15jBf2ZmJjIzM7l/SHfaE/1HxtYhaoFI2g0AsLW2h4+7\nv8b78us7l+hw0q9avv84C3uNR8AI1Co9nMv9GgODE5fcUyjk3Gg5YNrBv79nKNydlIGLdKAX5fVF\nBu4RmaqssnPcdlxoEuVfA0iencpNeK5oKIaob/pVyISdDWoT5FclbZnW8Wyt7bB1+RNc+1LRKVQ1\nlU3rmLpUUn2DK+jAMAJsSf3ZpOZbzVSerr6wtbYHAEikPegStxm4R6aN0n5mhjHTftLS0sAwDKRS\nKaytrZGWljbhwRiGgVyum9Jv5oBf4jPIJ2JS1UKiAufCQmAJuUKGhtYqdIs74OLortX+tXQ2oqld\nuVCblYU1ooPnTbDH2JJnp+Lbq/9Bp6gVYmk3rhSfxvJ568fdp7WriavL7WzvpvMa0brEMAziw+/C\n+bwTAJRVf2KC5xu4V2SyFKxCPeUneman/Nzh7OCG6OD53FPIypZCzA1KnWCv8f1w4xhXZSQuJBl+\nnsHT7mdC+F2IC03mShd/dubv+J8H3zC6VBq5XIZjF1SlPRfFrYK/VwiaaiiQnYiAESDAK5RLF6tr\nqYSb09SfGM10FPzPDGMG/2fOKBdwsbKyUmuTqauexOJew9la2yHcLwa36gsBKEf/F8Wt1mr/Ciuv\nc9uzg+dNq1SbhYUlViVtwZFz7wMAztw4jiXxd49bNswcJvvyJYQvVAX/lddx/4onZ2R5SF1iWRZH\nz3+AK0XfI9AnHHfFrMS8yCWws7HXyvErGkrQMVRv3t7WyShXWDWUBTErVMF/ayESApdN+Vjd4g61\nJyyrk6c36n8HwzC4P+0J3KorwKBsAI1t1TifdwIrE6c2l0BXLhWd4kqS2ljbYd3ChwzcI9MS4B3O\nC/4rJl2ogijJ5IPokqhq/Ls6Uo1/czXuyP94bTJ5tWoj/5PP5YwJSeKC/9JqHQT//Co/U0z54VsY\ntwqnrn0GkbQbneI2ZJdlYmHc2Iv1mPLKvqMJ84uBg60TJH0idEs6UCu8PembPjK+rLJzyMz/FgBQ\n2ViKysZSHD3/D8yNWIS7YlciImDOtG64+LX9E6OWwsqSal7fER+2AHbW9pAO9ELU14lWUT2AlCkd\n61zeV5DLldWUQmbNRpif9goaeDj7IP2un3AV0769+h/Mj1xsNKPDvX1ifHtVVdpzbcoDJv3U0xCG\nL/ZFpqZL3A52aM6Js6M7/b4zYxr/VRSLxaitrR3z/draWkgkEq10yhzJ5TK1GsRTCQL5k35v1uZx\nfyy1oUfSxeXDMowAc8Km9kecz9rSBmm8Ebbvb3wx7oqg9WZS6ecOC4EF5oSqrmMBLfilVd2SDhw9\n/48Rrw/I+pFVdg77v/gDXv7w5/j2yn/Q1t086eMPDPYj9/Zlrn3XDK/yM5yVpTXm8yY/V7RMbcGv\n3n4xLhae4tqrk+7Teq77ivkbMcsjCAAwMNiHo+f/qdXjT8fJa5+hd2jlaA9nH6RNkB5JRgrk1/pv\npVr/U8VP+fGgyb5mTePg/9lnn8WmTWM/Kt28eTN++9vfaqVT5qixvQaD8gEAgJuTF5wd3CZ9DF/3\nQG60SjrQi6qhCiTaUFR1ncu3DfeL0dqkxqXx98BuaDJWS2cD8scIgFmWNZtKP3wJEbTary6wLIvP\nfvgbtxK1u7M3Ni/7Kfw81PPEO0StOHn9M7z80VPYd+QF3Bbmc/8OJ1JYeQ39Qwu0ebv5T+lpnblb\nELOS265uK+Hm7EzGpYJT3HX2cQvQysDDcBYWlvjRiqe4dkHFVbU0R0MRdjYgs+Bbrr1x6WOwsrQ2\nYI9Mk7erH6yH0lR7JJ3oHkpdIZPTTvn+M4bGwf/p06exefPmMd/fsmULMjIytNIpc1StVuJzakEE\nwzBqq/2WVGuv6g9/VDpei/mSdjb2WDb3Xq59OuvIqKXYusTtkEh7AChzXj1cfLTWB0OaHTQX1pbK\nVZyFnfVcXi+ZnuybmSiqyuLa21b/EisTN+F3D72F/3nwDaTOvRf2tk5q+1Q0FOPy7a9x+Pr/4ZOM\nfSivL+LKKo7mOm+i74LoNKq8MorQWbPh5TILADAo70dRZdYEe6gblA1wC4YBwMqkzTqbFxPuH4uF\nvFTJI+c+QP9gn07OpakvL3zEPQ0N94vFvIhFBu2PqRIILBDgqXpaTKk/U0OTfWcOjX/LNjU1wd9/\n7NKUPj4+aGho0EqnzFHNNCb78sXwUn9KtVTvv29Aipt1+VxbG/n+fMvnredGs+pbK1FakzviM/x8\nf3/PELOZGGttaYNoXpUfSv2Zvm5JB46e+4BrL01IR1RgPADlDXKgdzjuT3sCr/zsAB5ftxNxoclq\nP08yxSCul57FO0dfxCsf/Te+u/op2nuE6ucQd6CsNo9rJ5vI6rD6xjAMUmLSuPb1kskVhsgqOwdR\nbxcAwMXBHcmzl2uzeyNsWvIoHIZuCjtFrTh57TOdnm88N2vzuRtYBgy2pD5ON5jTwJ8nxk+xJZqj\n4H/m0DjC8vT0RHFx8Zjvl5aWwtVV80lKmZmZ2LhxIwICAiAQCHDw4MERn9m9ezf8/f1hb2+PFStW\noKSkRO39/v5+/PKXv4SXlxccHR2xadMmo70B4Zf5DPaZevA/OzABFgLlPO2GtmpuNd7pKK3J4eYP\n+HuGaH3U3cneBYvnrOXap7OOjPhMgxmm/NzBrzxRUEnB/3SwLIvPzvwdvf1iAMo/UJuWPDrqZ60s\nrTAvcjF+vvFFvPyzf2LT0u1wsVOvXtHeI8R31z7FHz/8Od45+hKul55F/2Afsm9mchPfIgPip7XY\nlLnjB/+ltXkap1woFHL8cOM4106bv1HnEwwd7Jyxedl2rn029yu1tUX0Ra6Q44tM1byDBTErEOQT\nMc4eZCKBFPxPm1rOPwX/Zk3j4P/ee+/F+++/j6yskY91r1+/jvfeew/r1q3T+MQSiQQJCQnYt28f\n7OzsRox47N27F2+++Sb279+PrKwseHt7Y82aNRCLxdxnnn76aXzxxRf49NNPceHCBfT09GD9+vVQ\nKMZ+lG8I0n4JhJ3KdA8BI1CrTDBZNtZ2CPdXVcIo1ULqj65SfvhWJm7ibloqGktQ0aB+I2mO+f53\n8Eeea5pvaeWGbaa6cTMTRbxc7W2r/x9srO0m3M/ZwQ2rkjZj4/yfY13C41iakA47Gwe1z5TXF+KT\njH148YPt+D77KPf6Al5wS0bycPaBj7NyMi3LKnDjpmaLPRZUXENrVyMAwM7aXm2AQJcWxKxEuH8c\nAOUNyOdn3hs3/UsXrhZ/z62pYm1li/WLH9br+c0RVfyZPhr5nzk0Dv53794Nd3d3LF68GBs3bsTz\nzz+P559/Hhs2bMDixYvh7u6OV155ReMTp6enY8+ePdi6dSsEAvVusCyLt956C8899xy2bNmCuLg4\nHDx4ECKRCIcOHQIAdHd348CBA3j99dexatUqzJ8/H//6179QUFCA77//XuN+6EOt8Da3PcszGNZW\nNtM6Hr/qz3RX+5XJB1EytAAOAJ3VR3Zz8lIbITyddVTtffUyn6Zf6YfPwdYJEUPBBgCjmGhoinok\nnTjCq+6zJP4eRAUmTOoYDMPA08kPP1rxc+z5rw+xPf23iA1OBMNLC+of7INkqPqKlaU15kYs1s4X\nYMbCvVXfh+slZ0ed18PHsiy+v3GMaytvxrSzNsNEGIbBj1Y8BcHQQl+VTaW4VvyDXs4NKAeDvrly\niGuvSb5P6ws2zkQ+7oGwslCml3aK2yDq7TZwj0wL1fifWTQO/mfNmoWsrCw89NBDOH/+PP785z/j\nz3/+My5cuIBHHnkE2dnZ484JmIyqqioIhUKsXasaCbK1tUVqaiouX1aW3rtx4wYGBwfVPhMQEICY\nmBjuM8ZCbXGvaaT83MFfaOhmbf60Sn6W1xdBOtALQHmn7++pu8BbWcJP+SNXUpPDBfy9/WJuxMFC\nYKHbYikAACAASURBVAlf90Cd9cFQ+E9UqOrP5LEsi8/P/p0riejm5IVNSx+b1jGtLK2RGLUUT23+\nA15+/B/YsORR+LgFqH1mfuQS2GrwZGGmC/aI4Z7sNbbXqD3JG015fRFqhcpUSEsLKyyft0HnfeSb\n5RGIVYmqAhZfXvpYb8FiRtZhiKXKc7k5emKFkS04ZqosBBZqq0LzB5TIxKjG/8wy5iJfo/H19cVH\nH32EAwcOoLVVueqll5fXiJH76WpuVtbk9vFRzz339vZGY2Mj9xkLCwt4eHiofcbHxwdCofrkPb7s\n7Owx39OV/DLVSC/bZzXtPrAsCwcbF0j6u9E30Ivvzn0JX5fgiXccxdWK77htH4cQ3LgxtUnEmn5N\nwR7RqG5Tzt347NQ/sDz6PjR3V3PvO9t5IC83f4y9TVi/KoC8WVeAy1cvwtpy4hWUDfHzaoyqWovV\n0tOSgtagqGDsOUgTGe26uiEIa2MeQ5u4EdWtxVCwCoQ5J9H3QANWljYI8ohGVWsRAODEuU+REjZ2\nGs/3xaqR7zDPeNwqvT3mZ3XFyzICjjYuEPd3o7dPhANfvoElkRt1ek6RtANnc1XVjeb4LUVBXuGE\n+9HPoGZsGFWJ6qu5mZC0jr2uDEDXla+pS3XDbs3YTeva0HXVrshI7ZeZnlLUzjAMBAIBBAKB3qsT\nmFo1BJZl0SZu5NqeTtN/OsIwDPzdVPmNDZ1T+8PJsizqOlRPJQI9Zk+7bxOZ469KoahpL0GPtB0d\nYtXNmruDr877YAgONi7wcFCWRGRZBeqn+D2biaQDYlyvPMm1o3wS4eeqm3khDMPAy8kfKWFrcVf4\nPRrdoBElfupPVVvRmAv6dYib0dilGpWN9V846ud0zdLCCgvC0rl2RUsBShqvQa7Q3uKJw92oOQMF\nq7wunk7+CPGMm2APMhkevL8fHeLJL+w3k4n7VU++HG1phWlzN6mR//Lycjz//PM4efIkt5qvo6Mj\n0tPT8ac//QkREdqpVuDrq/wHLBQKERCgegwvFAq593x9fSGXy9He3q42+t/c3IzU1NQxj52cnKyV\nPmqqvUeIvsvKa2VrbY+Vy+7WShlLG3cFbn2tzPfv7Guc0tdV03wL0svKNAoHWyekr9gMi6E8WE3d\nucOfzPkru3NRMlSmtLnvFgR2qsl282JSkDxPv98jfWlXVHK5vmK2ZdxrNpXrao5YlsWBb/aiX6Zc\nBMrNyQs/2/LbKeeH03XVjezsbPi6hMDF0QPd4nb0DfbCzpNBfNjI63zwuze47XkRi7FymX4m+o4m\nGcnoGKxF3tBKztlVp3FTmIUV8zdiSfw9Wp2HUF5fhNpLZVz7kfRfIXTW+AMu9PM6OT4tbrhS8Q0A\nQDzYMeZ1o+s6kvCKaiAwMiRmSteGrqtudHdrPyVR4yi0uLgYKSkp+Oqrr3DPPffghRdewAsvvIC7\n774bx48fR0pKyrilQCcjNDQUvr6+aouG9fX14eLFi1i8WDlynJSUBCsrK7XP1NfXo6ysjPuMMeCX\n+AzyidBa/fqowARYWKhybDtFbZM+Bj+NYk5oyqQD/6lam3I/t3297Bxu1hVw7QAv85rsy5cQrhrh\nLK3OwaBMs5VmZ7Lc8kvIr7jKtR9ctUNvE0PJ5AgYAVJ4dfqzeIuk3dHeLURO+SWuvTr5Pn10bVxb\nl/+XWnljUW8Xvrr0MXZ/+AS+ufJvrcwFUCjkOJZ5gGsnzU6dMPAnkzfLI4ibe9LeI0Rvn3iCPcgd\nVOlnZtE4Ev39738POzs7FBcX4/Dhw3jllVfwyiuv4PDhwygpKYGtrS1+//vfa3xiiUSCvLw85OXl\nQaFQoKamBnl5eairqwPDMHj66aexd+9eHDt2DEVFRdi+fTucnJywbds2AICLiwt+9rOfYefOnfjh\nhx+Qm5uLRx55BHPnzsXq1asnOLv+8Bf3CvbRXt6WjZUtIvxUj4xLp1D1h19zXlclPkcT5hejVmqv\nm1f60k+HE44Nzdc9kFsNtX+wD7d4Nz1kJFFvFw6ffY9rL56zBtHB8wzYIzKRBbEruO3Cqutc1aQ7\nzuR8yU0qjAqIN4ra9i6O7vj9Q/uwJfVxuDiqniJL+yU4df0wdn/4BI6e/wc6Ra1TPsf10nPcBFQr\nS2tsXPLItPtNRrK0sMIszyCuTfX+NUc1/mcWjYP/CxcuYMeOHaOm9oSHh2PHjh3IzNSsvjMAZGVl\nITExEYmJiejr68OuXbuQmJiIXbt2AQB27tyJZ555Bjt27EBKSgqEQiEyMjLg4KCqzf3WW29hy5Yt\n+PGPf4ylS5fC2dkZX3/9tVHNC1Bb3GsaK/uOhl/1p2SS9f6FnQ0QdijXHlCuQqvfoIo/+n+Hp4uv\nWY/qMgyjdpNFq/2O7/DZ97ng0c3RE5uW/tTAPSIT8XUPRNDQIIdcLkPOrYvce6LeblwtUZVhXmUE\no/532FjZYsX8jfjDY3/Hg6t2wMvVj3tvUDaA83kn8PJH/41/n34Hws7JLSTZNyDFicufcO2ViZvh\n5kSLxulKEL/eP1X80RiN/M8sGgf/MpkMdnZjl7yzs7ODTKb5RKm0tDQoFAooFArI5XJu+8AB1aPR\nXbt2obGxEVKpFGfPnkVsbKzaMaytrfH222+jra0NEokEX375pdbKjWqDXC5TG3kI0Xrwr6r3f7Mu\nHzL5oMb78gPP6OD5sLac3toDkxUdNE9tOXbA/Bb3Gg1/HYWiyutjToqc6XLLL3F52ADwk9WU7mMq\n+Iui8VN/MvO/4VLdArzCEB1kfE9xrCytsGjOGrzwyDvYnv5b+PPSEOUKGa6V/IBXP/5/OPDNXzQe\nVf4++yh6ejsBAC4O7lidtEUnfSdKAV6q4L+OFvvSCNX4n3k0Dv6TkpLwwQcfoLOzc8R7nZ2d+OCD\nD2iSxzCN7TUYlCv/2Lk5ecHZwU2rx/d28+fu0PsHpKhsLJtgDxV+rXldLew1HoZhsDZZffTfnPP9\n7wjxjYKTvbKSgkjajaqmmwbu0egGZQOoairD2dyvcCbnS0j7e/V2blFvNz7npfssiluDmOD5ejs/\nmZ6kqGVc3nV1800IOxvQPyDFhfxvuc+sStpiVE9ohxMILJAYtRQ7H3wTT216CeF+qoEnFizybl/G\na//5Dd49/keU1xeNuahZR08LzuR8ybXXL35YoxWpydQF8gaVKO1HM1Tjf+bRuNrPyy+/jNWrV2P2\n7Nl47LHHMHu2crJSWVkZPv74Y3R1deG9996b4CgzC39xr2Bf7ddpZRgGsSFJuFigrNVfWnMDUYHx\nE+7XLelAdbMy6BQwAsTx0of0KSFiIbzd/NEy9Bg90Ajyf3VNILBAfFgKLhedBgAUVl5DuH/sBHvp\nFsuyaO8RorrpJqqbb6G6+RYaWqvUSh6ez/0aP171C7WnTbpy5Nz7kEh7AACujh7YvGy7zs9JtMfB\nzhlxockoGJqonVV6Fo52LujtV06+9HD2wbxI4ynKMJ47v2NjQ5JQ0VCC09lHuUplAFBWk4uymlyE\nzJqNtcn3Iy40We2m5qtLH3NPZAO9w9VWOSe64ecZAgEjgIJVoLWrEdL+XnpqOAG1fH8nSvmZCTQO\n/pcvX46MjAz85je/wRtvvKH2XmJiIj7//HMsX758jL1nJv5kX22n/NwRG5zIBf8l1TnYtHT7hPsU\nVWZx2+H+cXCwcx7n07ojYAR4aM2v8NkP7yLAOwyzg+YapB/6Fh92Fxf8592+grkRi+Dq6AkXBzcI\n9FBxSdrfi1ph+f9v787joqr3/4G/ZliHRWTfBQZQEFwQXElExC29LqkpmZlm3u+tTG/dSquby1Wz\n7Jb1S+3mvfcbLuUWZVbfwBVEpRJwNwVBARFERBZlnTm/P5AjIzvMMIPzej4ePB5zzpw55z2f+7n5\nnnM+n/cH1/Ku4PqDZL9uxdGmFJXdxhf7VmGwfwSmhs2HmamFRmJLTTuB1HrVYGaNehkyE/NmPkG6\naJB/eL3k/yhQLyGOGDC50yqLqZO3a294u/ZGTkEGDp6KQWraCfFu6bWbl/Hl/jVwsfXA6IHT0N83\nFNfz0lTmPDwV9oLaqr1R04wMjeFk2wO5t68BAG7czoSPK9dTaE4hx/vrnTbV+R85ciRSUlJw8+ZN\nXL9+HQDg4eEBZ2dnjQTX1V3PrzfZV42Vfurzde8DAwNDKBQ1uFmYhaLSghYnk53V8pCf+ryce2Hp\ns59qNYbO1tO9H0yMTFFZXYE7Jbfwye7aKllSqQGszG1gbWkHZZUU5ibdcN/oFqwt7Wr/LOxgZmrZ\npuESSqUCeXdyxCT/Wt5l5BVmQ0DjwxTqc+juAndHH/yRdVq8E//rpcO4lJWKmRF/QR/5oPY1QBNK\n7xerVPcZ0ntUpzxpIPXr7RkMc1NL3KsoRVHZwzLEFjIrDA4YpcXIOs7NXo7nx/8NTw7JxaHk7/Db\npSPiU7LcwuuI/uVj/Hhyhzj0CQD6+w7T+hM+feJuLxeT/+z8q0z+W8DJvvqnTcl/HWdnZyb8LSiv\nvIdbd2qHs0glUrg7aGZIi4mRKXxdA/FH1mkAtXf/Q/uMbSau+yolJvvItZv86yMjQyP08xmK3y4d\nUdmvVCpQVFqgUlLwwo2TKscYG5qg+4MfAtaWdvVe28Pa0g4mxjLk3MoQE/3r+WmorCpvMSaZiTk8\nnHrC88Gfh6Ov+ESo9H4xvo3fIt7FLLlXhC371yK453BMC38RFmp6cvRt/BbxCYSVhS2mhLG6T1dl\naGCE4F5hSDjzk8r+sH5PdnpxAU1xsHZBVOTLGDd4Jo6k/oAT52JRVVMJoHY9gzqGBkaYHDpXW2Hq\nJXdHb/x66TAAILuA4/5bwuRf/zSZ/LelbGd9za2uq0+y8tPFu6vOdh4wNtLcP3j+ngPE5P/S9eaT\n/4vXksW7VG4Octh0Y8k5bZgaNh/dLexws/A6ispu425pYYtDbwCgqqYSt4puiPMk2kMikcLFtgc8\nnXrB07knPJ16wd7apckhCZZmVnh+/N8Q5PsEdh/5AqX37wIAkq8cw+Xss5gxciGCfEPbHQ8AnE47\noTJEImrUSzAz0czQIuocg/xHqiT/xkamGN7vSS1GpBnWlnZ4Kmw+xg6cjvgzPyHh9E/i/AYACA+a\npLKIGGle/Yo/Oaz40yLW+Nc/TSb/4eHhbT6ZRCKBQsHShYDqZF9PR82M968T4Bksrh55Oau25Keh\nQeOz9c/VW9irL+/6a425qSUmDputsq+qphJ3SwtRVFqA1HOncL+qBDJL4wc/Dm6jqLQAldUVbb5W\nNzNreDr3hIdTL3g69UQPB+92VRzp5zMEPm4B+C7hv+JTi7LyYvzvz+uR4pOIGeEL21XRqqy8RGW4\nz+Deo1TWsKCuyd3BG0427si7kw0AGBYwGuamllqOSnPMZd3w5JAoRAyYghPnY5FyORF23Z0xdtAM\nbYemd1ztPSGRSCEIytpqU9UVMDEy1XZYOot3/vVPk8n/4cOHOzOOx47Kyr4amuxbx767C2ytHFFY\nnI/K6gpk5F5CT/e+DY6rrqnGhXqVKrQ93p9UGRuawMHaBQ7WLii9VVshpH75XEEQUF5178EPgbq/\ngno/Dm7jfkUpHG3da+/qPxjCY21pr7ayiuamlnh2zGIE+YZi1+HNuPtgdeYz6SeRlnMe00a8gJBe\nI9p0vW+PbkFp3XAfcxtM5XCfx4JEIsHkJ+Ziy/61sLNyQqQOLeqlSabGMkQMmIKIAVO0HYreMjEy\nhaO1K/LuZEMQlLhRcA1yFz9th6WTFIoa1vjXQ2q980+1BEHo1ORfIpGgt0cwjp2traN98VpKo8l/\nWs45cfy3rZUjnG09NBoXqZdEIoGZiQXMTCzgYuep1VgCvEKw7NnPsC/xK7Fy0f2KUmyL3YCUK4mY\nGfEXdLewbfE8Z9KTkHzlmLg9i8N9HisBXiFY/9JOSCSSJp9GEmmCm4NcfOqUU3CVyX8TWONfP7Wr\n7lhaWhqOHz+Ou3fvqjuex0JRaYF4J9PEWAZHG82vOly/Kkr9OtT1qSzsJR+s04vskO6TmZhj1qiX\n8fLUlSqPii9knsLabYtw8vyBJhc/AoB75SXYfeQLcXuQ/0gEeHGhwMeNkaExE3/qdO71V/rN1+yk\nX0EQcOl6apdcVEylzGcLlQLp8dGm5H/Hjh1wd3dHr169EBYWhpSUFABAQUEBfH19sWvXLo0E2dWo\nLO7l4NMptZ193fqI/8Dm3cnGnZIClfeVghLnMn4Ttznkh9SlV49+WDb7U4TVm8xZUXUf3xzaiE3f\nr1AZT1rft/H/EScPW5nb4KmwFzolXiJ6/Lk71kv+CzQ76Xdf4lfY/P1KrP/mdeyI+6xTV0TvKI73\n10+tzkq//fZbzJkzB71798ZHH32kckfP3t4e/v7+2LZtm0aC7Go6c8hPHWMjE/i4BYrbl66nPBJT\nGkruFwGorbXt5cxHoKQ+JsYyTA9fiMXT18De6mEZ4MtZZ/D+9ldx7MzPUD54tAzUrjVx6nK8uD1r\n1EsaWziMiPSPq52X+DqvMAvVNVUauc6l66k4nLJP3P710mF88PUSXL1xQSPXUzdW+tFPrU7+16xZ\ng1GjRiE2NhbPPfdcg/cHDx6MM2fOqDW4rup6Xr3FvTop+Qdqq/7UufDI0J+61TYBIFA+sFNWkiX9\n4+0agLdmb0DEgMmQPHjiVVldgT1Hv8Tn3/4dBXdv4l5FKXYd3ix+hsN9iEjdZCZmsO/uAqD2yXfd\nol/qdK+8BDsOfNZg/52SW/hs77v44fg21Ciq1X5ddbpTyjv/+qjVyf+lS5fw1FNNV2twcHDArVuN\nP97XJwpFjcq4P89OTP79PR6O+7+SfRbVNbX/0REEQXVVX5b4JA0yNjLBlOHzsGTG+3C0cRP3p9+4\ngHU7FmPzdyvF4T7dzK053IeINMLdod7QHzXX+xcEATsPb0bJvdon6pYyK8yM+AtkJua170PAwVPf\n4p+73sTNwiy1XludVMf8M/nXF61O/s3NzVFWVtbk+xkZGbCzY4mo3MLrqFbUPl60trRvV93z9nKw\ndoGdlRMAoKq6Ahm5FwEA+UU5KLibC6B2oZ2ePRpWAiJSNy/nXngz6hOMGThdnPdSXVOFrFvp4jEz\nI/7C4T5EpBHuDnLxtbon4/526QjOpD9cgT0q8hWE9hmLpbM/Vam2d6MgE+u/eR1HUn9QGfqoKzjm\nXz+1OvmPiIjAV199hcrKygbv5ebmYsuWLRg7tumVZfWF6pAf306/fv3Fkeqq/tS/6+/vEQRjQ82t\nNkxUn5GhESYOexavz1rfoDxpiN8I9JEP0k5gRPTYU7nzX6C+5L+wOB9747eI26GBYxEoHwigdsXn\nl6auwFNhL4hFOGoU1fgu4b/Y9N0KFJXeVlscHaVQ1IhrtQC1NyxJP7Q6+V+9ejVyc3MREhKCTZs2\nAQB+/vlnvPXWWwgMDIREIsHy5cs1FmhXoTLZV8Mr+zZGpeTng0m/KiU+WeWHtMDdwRt/m7Ue44dE\nwdKsO3zcAjFtxAJth0VEjzE3+4d3/m/ezlLL+HulUoFtsRvENXPsu7tgyiMLE0olUoQH/QlvRH0M\nV/uHE4+vZJ/Fuh2LkXz5GHRB/Rr/Vuas8a9PWp389+zZEydOnICzszNWrlwJAPj444+xfv16BAUF\n4fjx4/Dw4KJR1/IfJv+eWrjz7+MWCCMDYwBA/p0cZOT+gev5tU8jpFIDBHhyYiVph6GBEcYPnok1\nL36FRU/9A+amltoOiYgeY2amFrDt5ggAUChr1DL2/mDyd8i4eQlAbZL/3NglMDEybfRYZ1t3vD7z\nQ4wOmQYJatfVKa+8h+hf/onoXz7G/Yqmh1J3hkIO+dFbrU7+ExIS4O/vj7i4OBQUFCApKQknTpxA\nXl4eDh06hJ49O/8ut64pr7yHW3duAKj9j4K7g0+nx2BsaALfeiU/9xz9l/ja1zWQ46tJJ3CBOSLq\nDOqc9JuVn46fk74Rt8cNntliRT9DAyP8KXQOXp2+RiXBTr6cgHU7FuNK9tkOxdQRHO+vv1qd/IeH\nh8Pd3R2vvfYa0tPTMWjQIAwZMgQODprtMKWlpViyZAk8PT1hZmaG0NBQnDp1Snw/Pz8fzz//PFxd\nXWFubo7x48cjPT29mTNqTlZ+OgTUrn/gbOcBYyPtjK33rzf050ZBpvi6D4f8EBGRHnGrN+k3pwOT\nfquqK7EtdgOUSgUAwNOpF0YPnN7qz3u79sZbz2zA4N6jxH13ywrxecx7iEn4r8bWIWgOa/zrr1Yn\n/1u3bkX//v2xceNGDBkyBN7e3nj77bdx9qxmf7UuWLAABw4cwNatW3H+/HmMGTMGkZGRyM3NhSAI\nmDJlCq5evYp9+/YhNTUVHh4eiIyMxP37nb/CXv2VfT21MN6/Tv1Jv/X1eTAhiYiISB+o3vlvf/K/\nLzEa+UU5AGqr5s0ZuwQGbVwvR2ZihtmjF+GFCW+pDHs8mvoDPtr5N5WbdZ2BNf71V6uT/2effRb7\n9+9Hfn4+/vOf/8DHxwcfffQR+vfvj4CAAKxatQpXrlxp+URtUF5ejpiYGKxbtw5hYWGQy+VYvnw5\nfHx8sHnzZqSlpeHXX3/Fpk2bEBISgp49e2Lz5s0oLy/HN9980/IF1KxubD3QuYt7Pcq+u7O4uEmd\nHg4+nMlPRER6pf6k3xu3r0GhqGnzOS5eS8axsz+L29PCXoB9d+dmPtG8fj5DsezZz9C73to8Nwuz\n8NHON3DwVIz4dEHTWONff7U6+a/TvXt3zJs3D7GxscjNzcXmzZvh6OiIVatWwd/fX63B1dTUQKFQ\nwMREdfiMqakpEhMTUVVV+5is/vsSiQTGxsY4fvy4WmNpiSAIqpV+tJj8A6pVfwAO+SEiIv1jaWYF\na4vaNYhqFNXi3fvWKisvwdcHPhe3+3oPxpCAyA7H1c3cGn+e/Hc8PfJ/YGRYW6RDoazBD8e34v/F\nvIfCkvwOX6MlHPOvvww78uHu3bvDxcUFLi4uMDExQXl5ubriAgBYWlpi6NChWL16NQIDA+Ho6Ihv\nvvkGSUlJ8PX1hZ+fH3r06IG3334bW7Zsgbm5OT755BPcuHEDN2/ebPSc9ecLqFNZxV1x1VIjA2Nk\nZ9zEjUzN/5+3KYZVqpVUDCosNPbdAc21q75ju2oG21Uz2K6awXbtGAtjGxShtr5+wq+H4OPYD0DL\n7SoIAo7+sRcl92tX8TU1Moef7TAkJyerLTZT2GFC3xdw7Mo+FJbVLsZ59cYFrN26CIPk4yC376OR\nAglKpQJ36605kJmWhSxprlrOzf6qXr6+6q8c2eY7/wqFArGxsZg3bx7s7e0xefJkHDp0CPPnz8ex\nY+qvXbtt2zZIpVK4ubnB1NQUn3/+OaKioiCRSGBoaIiYmBhcvXoVtra2MDc3R3x8PMaPHw+ptM1f\nrUNulz38P42thYu4oqm2OHbrAZlRbWUfG3MnWMm4+jIREekfW4uHQ3Tu3Mtr9efSb51B9p3L4nao\n759gamSu1tgAoJvMFuP7zEVf9+FiSdBqRRWOp/2ApKs/QxAEtV/zXlWJWKBEZmwJA2mH7gVTF9Pq\n/7UPHz6MXbt2ISYmBoWFhbC2tsb06dMxa9YshIeHw8CgbRNfWksul+Po0aMoLy9HSUkJHB0dMXPm\nTHh7107iGTBgAFJTU1FaWoqqqirY2tpi8ODBGDSo8ZVDQ0I0U+c+O+HhxOc+vsEau05bePq64eK1\nFAT5DtPYeP+6X/i68H0fJ2xXzWC7agbbVTPYruohswVOZ8UDAKrwsLZ+c+1acPcmdv32kbj9RN/x\nmDxyluaCBDBo0GBk3pyI7bEbUFBcO3ohLT8Vw4NHo7/vMLVe60r2OeDBAwwnW1e19DH2V80oLi5W\n+zlbnfxHRkbC0tISkyZNwqxZszB27FgYGnbeL0WZTAaZTIaioiLExcVh/fr1Ku9bWtYOc0lLS0Ny\ncjLWrFnTabEBwPU83ZjsW5+TjTucbNy1HQYREZHWqJT7LMiA0kvZ7NN5hVKBbXEbUFldAQBwsHbF\nlCee13SYAAAv515485mPsT3uU5y5mgQA2Ht0C3r26AszE/Wt08Px/vqt1dn77t27MXHiRJiaNr6S\nnabExcVBoVDAz88P6enpeOONN+Dv749582qX096zZw/s7Ozg4eGBc+fOYfHixZg6dSoiIzs+Iae1\nFIoaZBc8LCHmqSPJPxERkb6zMrdBN3NrlNwrQlVNJUrK76C7WdNDYQ+e+hbXbtYO95FKDfDc2L92\n6ro9JsYyRI1+BZl5l1Fyrwgl94vwQ+JWzBr1ktquwRr/+q3VA9OnT5/e6Yk/UPu4Y9GiRfD398fc\nuXMRFhaG2NhYcZhRXl4e5s6dC39/fyxevBhz587t9DKfuYVZ4gId1pb26GZu3anXJyIioqa52z+s\n93+nrPGCIEDtU/z/S9opbj85eBZ6OPpoNLbGmJlYYPqIF8XtE+fjkH7jgtrOzxr/+k27s1JbYcaM\nGUhPT0dFRQVyc3Px2WefiUN8AGDRokXIyspCZWUlrl27hpUrV3bqcCQAqiU+HdU/K5uIiIjar/5i\nX4VNTPqtrK7AtthPoBSUAAC5sz8iQ57qlPga089nKPrIH85f3Hlwo9pWAmaNf/2m88l/V6BL9f2J\niIhIVf1x/03d+f/+2Fe4dbe2cp+JsQxzxi6BtI2r+KqTRCLBjJF/homxDABw624u4n7fo5Zzc8y/\nfmPyrwbX8h8m/55OvPNPRESkS9zrJ//38hqUz7yQeQrHz/0ibk8f8SJsrRw7Lb6mdLewxaRhc8Tt\nA6dikHv7eofOqVDU4G5ZobitqWqApLuY/HdQeeU93LpzAwAglUjh7tD5YwOJiIioad0t7GAhswJQ\nW0O/tKJIfK/0/l18feD/idv9fIZikP/ITo+xKaF9x8HL2Q9A7eJcOw9tglKpaPf57pYVQngwtMnK\n3AZGhkZqiZO6Dib/HZSVny4ulOFs59GpFQGIiIioZRKJRGXoT+GDoT+CIOCbQ5tQWl5bS72bhs+Q\nUgAAH0pJREFUuTVmRfxFI6vqtpdUIsWsUS+LC3Fdy7uMxHpPKdqqkEN+9B6T/w6qP97f05Hj/YmI\niHSRu73q0B8AOHnhAM5n/Cbunz36VZjLunV6bC1xtnXH6IHTxO39x7ehqLSgXefieH9i8t9B1/If\nLu7Vg+P9iYiIdJJKxZ+ym7hVlIuY+P+I+0b0nwh/jyBthNYqo0Omw9HGDUBtZaI9R75sMHehNVjj\nn5j8d4AgCKp3/lnph4iISCfVT/7v3MvDtrgNqKqpBAA42bjjT6FzmvqoTjAyNMKsiIcLfZ3P/B2n\n00+0+Tys8U9M/jugqLQApffvAqgtC+Zo7arliIiIiKgxNt0cYGZiAQCoqqkQb94ZSA0xZ+xfYWyo\n+3P2vF17I7TPOHF779EtuF9R1qZz1L/zz0o/+onJfwdcq1/f38FHq/WAiYiIqGmPTvqt8+TQZ1RK\ngeq6SaFzYGVuA6C2UtH3iV+16fMc9kNM/juAi3sRERF1HY8m+d6uARg1YLKWomkfmYk5ZoxcKG4n\nXTiItJxzrfqsQqlgjX9i8t8R1+tN9mXyT0REpNvqr8VjamyGOWMWd8mn9n29h6Cf9xBxe+ehzeL8\nhebcLbsN5YMa/93MrWFkaKyxGEl3MflvJ4WiBtm3rorbHqz0Q0REpNP6eg+Gk5UnTI3MMXfca116\nwuv08IWQGZsBAAru5iLutz0tfoZlPglg8t9uuYVZqK6pAgBYW9iJ4++IiIhINxkaGGFM4LOYMXAJ\nArxCtB1Oh1hZ2GDSE3PF7YPJ3+FGwbVmP6My3t+Syb++YvLfThzvT0RE1DXp0gq+HTE0cDS8XXoD\nAJRKBXYe2gilUtHk8VzdlwAm/+3G5J+IiIi0SSqRYtaol2BgYAigdi7isbP/1+TxHPZDAJP/druW\nX39xL473JyIios7naOOGMQNniNv7T2xXSfLrY/JPAJP/dimvvIdbd24AqP3VXb96ABEREVFnGh3y\nFJxtewAAqqorsPvIvyAIQoPjWOOfACb/7ZKVnw4Btf+ncrbzgLGR7q8KSERERI8nQwMjzBr1EiSo\nnctw8VoyUq4kqhzDGv9UR6eT/9LSUixZsgSenp4wMzNDaGgoTp06Jb5fUlKCl156Ce7u7jAzM4Of\nnx82bNig8bhOXU4QX3s69dL49YiIiIia4+Xshyf6jhe3Y+L/jXsVpeI2a/xTHZ1O/hcsWIADBw5g\n69atOH/+PMaMGYPIyEjk5uYCAJYsWYLY2Fhs374df/zxB9555x0sXboU27dv11hMJfeKcOpyvLg9\nyD9cY9ciIiIiaq2Jw56FlYUtAKC0vBjfH/tKfI/j/amOzib/5eXliImJwbp16xAWFga5XI7ly5fD\nx8cHmzdvBgD8/vvveO655zBixAj06NEDc+bMwZAhQ/Dbb79pLK6EMz9DoagBAHg694KXs5/GrkVE\nRETUWjITMzw98s/i9q8XD+FK9lkArPFPD+ls8l9TUwOFQgETE9Xx9Kampjh+/DgAYPz48fjhhx+Q\nk5MDADhx4gROnz6NcePGaSSmyuoKJJ77RdyOCJqskesQERERtUcf+SD09xkmbu88tAlVNZWs8U8i\nnU3+LS0tMXToUKxevRq5ublQKBTYvn07kpKScPPmTQDABx98gN69e6NHjx4wNjZGeHg4PvzwQzz5\n5JMaiem3i4dx/8H4OdtujujrPVgj1yEiIiJqr2nhCyAzNgMA3C7Owy+/7uawHxJJhMZqQemIjIwM\nzJ8/HwkJCTAwMEBwcDB8fX2RkpKCCxcu4PXXX8f+/fvxySefwMPDA/Hx8Vi6dCn27t2LsWPHiucp\nLi4WX6elpbUrFqWgxL6UzSitKAIADPQaA3+XQR37gkREREQakJaXipNXfwIASCCBmYkl7lWWAAAi\ne0fBxdpbm+FRK/n6PlxLysrKSi3nNFTLWTRELpfj6NGjKC8vR0lJCRwdHTFz5kzI5XLcv38fGzZs\nwPfff48JEyYAAAIDA3H69Gl89NFHKsm/OuTcSRMTf2MDU/g49lfr+YmIiIjUxcexPzIKziG/JAsC\nBDHxBwAL0+5ajIy0TaeT/zoymQwymQxFRUWIi4vD+vXroVTWlquSSlVHLkml0kYXtqgTEhLSrhiO\n74kRX4f1fxJDBw9r5mj9UVd6tb3tSo1ju2oG21Uz2K6awXbVDH1qVw8fF6zbsQQ1imqV/cOHjlR7\nqU99atfOVH/0irrodPIfFxcHhUIBPz8/pKen44033oC/vz/mzZsHAwMDjBo1CkuXLoWFhQV69OiB\n+Ph4bNu2DevXr1drHNfz0nA19yIAQCo1QFj/CWo9PxEREZG6OVi7Yuygp/HTyR3iPtb4J52d8AvU\n/tpZtGgR/P39MXfuXISFhSE2NhYGBgYAgB07dmDw4MF49tlnERAQgA8//BCrV6/Gyy+/rNY4jqTu\nE18H9xyO7g9q6BIRERHpslHBU+Bs20Pc5mRf0uk7/zNmzMCMGTOafN/e3h7//ve/NRrDnZJbOJ12\nQtweOWCSRq9HREREpC6GBkaIinwFn+59GwpFDXq69dF2SKRlOp3864Kjp38Ul8Pu6dYHbvZyLUdE\nRERE1HqeTj3xt5nrcbs4D4FyVirUd0z+m1FeeQ8nLxwQt0cO4KJeRERE1PW42nvB1d5L22GQDtDp\nMf/advLCAVRWlQMAHG3c4O85QMsRERERERG1H5P/JigUNYhP/VHcHhk0GVIJm4uIiIiIui5ms004\nnX4CRWW3AQAWMisM9Buh5YiIiIiIiDqGyX8jBEHA4ZSH5T2H9x3PmrhERERE1OUx+W9E+o0LyL51\nFQBgZGCMJ/qO13JEREREREQdx+S/EUfq3fUf6B8OSzMrLUZDRERERKQeTP4fcavoBs5n/i5ujwzi\nol5ERERE9Hhg8v+II6n7xdcBXiFwtHHTYjREREREROrD5L+esvIS/HbxsLgdwUW9iIiIiOgxwuS/\nnsSz/4dqRRUAwM1eDh/XQC1HRERERESkPkz+H6iuqcKxMz+L2yMHTIZEItFiRERERERE6sXk/4FT\nf8SjtLwYANDdwhYDfEO1HBERERERkXox+Uftol5HUn8Qt0f0nwgDA0MtRkREREREpH5M/gFcup6K\nvDvZAAATI1MMDRyt5YiIiIiIiNSPyT9UF/UaEhAJMxMLLUZDRERERKQZep/83yjIxOXsMwAAiUSK\n8P5/0nJERERERESaoffJf/2x/v18hsDWylGL0RARERERaY7OJ/+lpaVYsmQJPD09YWZmhtDQUJw6\ndUp8XyqVNvr3yiuvtHju4rI7SL58TNyOGDBFI9+BiIiIiEgX6Hzyv2DBAhw4cABbt27F+fPnMWbM\nGERGRiI3NxcAkJeXp/K3f/9+AMDMmTNbPHf8mZ+gUNYAAOTO/vB06qm5L0JEREREpGU6nfyXl5cj\nJiYG69atQ1hYGORyOZYvXw4fHx9s3rwZAODg4KDy9/3336NXr14YPnx4s+eurCrH8XO/iNsjB0zW\n6HchIiIiItI2nU7+a2pqoFAoYGJiorLf1NQUiYmJDY4vKyvDzp078eKLL7Z47l8vHUZ55T0AgJ2V\nE/rIB6onaCIiIiIiHaXTyb+lpSWGDh2K1atXIzc3FwqFAtu3b0dSUhLy8vIaHP/111+juroac+fO\nbfa8SqVCZaJveNCfIJUaqD1+IiIiIiJdIhEEQdB2EM3JyMjA/PnzkZCQAAMDAwQHB8PX1xfJycm4\nePGiyrEDBw6Et7c3du7cqbK/uLhYfJ2WlobrhX8g/o+9AABjQ1NMC3kVRgbGmv8yRERERESt5Ovr\nK762srJSyzl1+s4/AMjlchw9ehT37t1DTk4OkpKSUFVVBW9vb5XjTp8+jeTk5FYN+bl4I0l83dNp\nABN/IiIiItILhtoOoLVkMhlkMhmKiooQFxeH9evXq7z/5ZdfQi6XY9SoUc2ex9bVEgXHcwAABlJD\nzBy7AFYWNhqL+3FXV3Y1JCREy5E8XtiumsF21Qy2q2awXTWD7aoZbFfNqD96RV10PvmPi4uDQqGA\nn58f0tPT8cYbb8Df3x/z5s0Tj7l//z527NiBpUuXtni+I6n7xNfBvYYz8SciIiIivaHzyX9xcTGW\nLVuGnJwc2NjYYPr06VizZg0MDB5O0N21axfKy8tVfhA05Uz6wyE/I4MmaSRmIiIiIiJdpPPJ/4wZ\nMzBjxoxmj5k3b16rEn8AEAQlAKCXez+42nt1OD4iIiIioq5C5yf8agoX9SIiIiIifaOXyb+zbQ/4\newRpOwwiIiIiok6ll8l/eNAkSCQSbYdBRERERNSp9C75t5RZIaRXmLbDICIiIiLqdHqX/A/v9ySM\nDLmoFxERERHpH71L/p/oO17bIRARERERaYXeJf8Wsm7aDoGIiIiISCv0LvknIiIiItJXTP6JiIiI\niPQEk38iIiIiIj3B5J+IiIiISE8w+SciIiIi0hNM/omIiIiI9ASTfyIiIiIiPcHkn4iIiIhITzD5\nJyIiIiLSE0z+iYiIiIj0BJN/IiIiIiI9weSfiIiIiEhP6HTyX1paiiVLlsDT0xNmZmYIDQ3FqVOn\nVI65cuUKnnrqKVhbW8Pc3BzBwcH4448/tBQxEREREZHu0unkf8GCBThw4AC2bt2K8+fPY8yYMYiM\njERubi4AIDMzE6GhofD29saRI0dw4cIFrFmzBhYWFlqOnIiIiIhI9xhqO4CmlJeXIyYmBjExMQgL\nCwMALF++HPv378fmzZvxj3/8A++88w7GjRuH9evXi5/z9PTUUsRERERERLpNZ+/819TUQKFQwMTE\nRGW/qakpjh8/DkEQ8OOPP8Lf3x/jxo2Dg4MDBg0ahN27d2spYiIiIiIi3aazyb+lpSWGDh2K1atX\nIzc3FwqFAtu3b0dSUhJu3ryJW7duoaysDGvXrsW4ceNw8OBBREVFYfbs2fj555+1HT4RERERkc6R\nCIIgaDuIpmRkZGD+/PlISEiAgYEBgoOD4evri5SUFBw8eBCurq545plnsH37dvEzs2fPRlFRkcoP\ngOLiYm2ET0RERESkFlZWVmo5j87e+QcAuVyOo0eP4t69e8jJyUFSUhKqqqogl8thZ2cHQ0ND9O7d\nW+Uzfn5+yMrK0lLERERERES6S6eT/zoymQyOjo4oKipCXFwcJk+eDCMjIwwcOLBBWc8rV65w0i8R\nERERUSN0ttoPAMTFxUGhUMDPzw/p6el444034O/vj3nz5gEA3nzzTTz99NMYPnw4Ro4ciSNHjmDX\nrl3Yt2+fynnU9ZiEiIiIiKgr0+kx/3v27MGyZcuQk5MDGxsbTJ8+HWvWrIGlpaV4THR0NNauXYvs\n7Gz07NkTy5Ytw8yZM7UYNRERERGRbtLp5J+IiIiIiNSnS4z576hNmzbBy8sLMpkMISEhSExM1HZI\nXcqKFSsglUpV/lxcXBoc4+rqCjMzM4wcORIXL17UUrS6KyEhAZMmTYKbmxukUimio6MbHNNSO1ZW\nVmLRokWwt7eHhYUFJk+ejBs3bnTWV9BJLbXr888/36D/Dhs2TOUYtmtD77//PgYOHAgrKys4ODhg\n0qRJuHDhQoPj2GfbpjXtyj7bdhs3bkS/fv1gZWUFKysrDBs2rEHZb/bVtmupXdlX1eP999+HVCrF\nokWLVPZrqs8+9sn/rl27sGTJErz77rs4ffo0hg0bhvHjxyM7O1vboXUpfn5+yMvLE//OnTsnvvfB\nBx/g448/xueff47ff/8dDg4OGD16NMrKyrQYse65d+8e+vbti08//RQymQwSiUTl/da045IlSxAT\nE4OdO3fi2LFjKCkpwcSJE6FUKjv76+iMltpVIpFg9OjRKv330aSA7dpQfHw8XnnlFZw8eRKHDx+G\noaEhIiMjUVRUJB7DPtt2rWlX9tm2c3d3x4cffojU1FQkJycjIiICU6ZMwZkzZwCwr7ZXS+3Kvtpx\nSUlJ2LJlC/r27avy75dG+6zwmBs0aJCwcOFClX2+vr7CsmXLtBRR17N8+XIhMDCw0feUSqXg5OQk\nrF27VtxXXl4uWFpaCv/61786K8Qux8LCQoiOjha3W9OOd+/eFYyNjYWvv/5aPCY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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1717,27 +1696,18 @@ "\n", "range_std = 500.\n", "bearing_std = math.degrees(0.5)\n", - "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "vel_std = 2.\n", "\n", - "ac = ACSim(ac_pos, (100, 0), 0.02)\n", - "points = MerweScaledSigmaPoints(n=4, alpha=.2, beta=2., kappa=-1.)\n", - "kf = UKF(4, 4, dt, fx=f_cv_radar, hx=h_vel, points=points)\n", - "\n", - "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", - "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", - "\n", - "kf.R = np.diag([range_std**2, bearing_std**2, vel_std**2, vel_std**2])\n", - "kf.x = np.array([0., 90., 1100., 0.])\n", - "kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", - "\n", "random.seed(200)\n", + "ac = ACSim(ac_pos, (100, 0), 0.02)\n", + "radar = RadarStation((0, 0), range_std, bearing_std)\n", "\n", - "t = np.arange(0, 360 + dt, dt)\n", - "n = len(t)\n", + "kf = cv_UKF(f_cv_radar, h_vel, \n", + " R_std=[range_std, bearing_std, vel_std, vel_std])\n", "\n", + "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", - "for i in t:\n", + "for t in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " vx = ac.vel[0] + randn()*vel_std\n", @@ -1746,7 +1716,7 @@ " kf.update([r[0], r[1], vx, vz]) \n", " xs.append(kf.x)\n", "xs = np.asarray(xs)\n", - "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=True, plot_alt=False)\n", + "ukf_internal.plot_radar(xs, time, plot_x=False, plot_vel=True, plot_alt=False)\n", "print('Velocity standard deviation {:.1f} m/s'.format(np.std(xs[10:,1])))" ] }, @@ -1756,7 +1726,7 @@ "source": [ "By incorporating the velocity sensor we were able to reduce the standard deviation from 3.5 m/s to 1.3 m/s. \n", "\n", - "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to something called the *Complementary filter*, which uses the high update rate of the inertial sensor with the position accurate but slow estimates of the GPS to produce very high rate yet very accurate position and velocity estimates. This will be the topic of a future chapter. " + "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to something called the **Complementary filter**, which uses the high update rate of the inertial sensor with the position accurate but slow estimates of the GPS to produce very high rate yet very accurate position and velocity estimates." ] }, { @@ -1770,7 +1740,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The last sensor fusion problem was somewhat a toy example due to the existence of techniques like the *Complementary filter*. Let's tackle a problem that is not so toy-like. Before the advent of GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill the basics if you are interested. In general these systems are beacons that allow you to extract either the range, bearing, or range and bearing to the beacon. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the \"radial\" - the direction from the VOR station on the ground to the aircraft. Using a chart they can extend these two radials - the intersection point is the position of the aircraft.\n", + "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill the basics if you are interested. In general these systems are beacons that allow you to extract the range and/or bearing to the beacon. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the \"radial\" - the direction from the VOR station on the ground to the aircraft. Using a chart they can extend these two radials - the intersection point is the position of the aircraft.\n", "\n", "That is a very manual and low accuracy approach. We can use a Kalman filter to filter the data and produce far more accurate position estimates. Let's work through that." ] @@ -1779,7 +1749,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. In the chart the width of the circle is intended to denote a different amount of sensor noise." + "The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. The width of the circle is proportional to the amount of sensor noise." ] }, { @@ -1792,9 +1762,9 @@ "outputs": [ { "data": { - "image/png": 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lBtVE31JVFW98uU+z+pn2QZfiK91jdNpY/OiuFzEuYzI6vl7d7fz4GBNMWTmo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\nYII=\n", 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YVBN9S1VVvPHlTs36Z9oHXUigdI+Z43Kw4+X7sXByLtq/Wdbl/olxZphz81Fp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\njs9KT+JwrS2k80iyGvDAlaOQkSxgA5miwLJjA0z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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1815,15 +1785,13 @@ "def bearing(sensor, target):\n", " return math.atan2(target[1] - sensor[1], target[0] - sensor[0])```\n", "\n", - "So our filter will need to receive a vector of 2 measurements during each update, one for each sensor. We can implement that as:\n", + "The filter receives a vector of 2 measurements during each update, one for each sensor. We can implement that as:\n", "\n", "```python\n", "def measurement(A_pos, B_pos, pos):\n", " angle_a = bearing(A_pos, pos)\n", " angle_b = bearing(B_pos, pos)\n", - " return [angle_a, angle_b]```\n", - "\n", - "The design of the measurement function and state transition function can remain the same as nothing has changed that would affect them. " + " return [angle_a, angle_b]```" ] }, { @@ -1838,7 +1806,7 @@ "data": { "image/png": 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HBi2Xej8pB4iPruR/PDyURdlgi9KHO0VEBisFdBGRm5BhGOw9Chu2wqYdUH0R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\nqm4EJ8tmUHzuTto6Qj1ec/Qw1/SVtOg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oFAoYjUbIZDL4+fnZPE6tVsNkMg316YmIiIiI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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1865,13 +1833,11 @@ " x[2] += x[3]\n", " return x\n", "\n", - "\n", "def hx_VOR(x):\n", " # measurement to A\n", " pos = (x[0], x[2])\n", " return measurement(sa_pos, sb_pos, pos)\n", "\n", - "\n", "def moving_target_filter(target_pos, std_noise, Q, dt=0.1, kappa=0.0):\n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n", " f = UKF(dim_x=4, dim_z=2, dt=dt, hx=hx_VOR, fx=fx_VOR, points=points)\n", @@ -1880,13 +1846,10 @@ " q = Q_discrete_white_noise(2, dt, Q)\n", " f.Q[0:2, 0:2] = q\n", " f.Q[2:4, 2:4] = q\n", - "\n", " f.R *= std_noise**2\n", - " f.P *= 1000\n", - " \n", + " f.P *= 1000 \n", " return f\n", "\n", - "\n", "def plot_straight_line_target(f, std_noise):\n", " xs = []\n", " txs = []\n", @@ -1940,7 +1903,7 @@ "data": { "image/png": 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X7xcuXIjVaiU2Npbbb78dAMMw8PDwwGazXXAfmZmZzJs3j/nz59O/f3/nfsLCwli9ejUD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\n1klsbKzExsZKeXm5DA0N6bbV3d0tJSUlYrFYJD4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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1959,312 +1922,14 @@ "source": [ "This is untenable behavior for a real world filter. `FilterPy`'s UKF code allows you to provide it a function to compute the residuals in cases of nonlinear behavior like this, but this requires more knowledge about `FilterPy`'s implementation than we yet process.\n", "\n", - "Finally, let's discuss the sensor fusion method that we used. We used the measurement from each bearing and had the Kalman filter's equations compute the world position from the measurements. This is equivalent to doing a weighted least squares solution. In the *Kalman Filter Math* chapter we discussed the limited accuracy of such a scheme and introduced an *Iterative Least Squares* (ILS) algorithm to produce greater accuracy. If you wanted to use that scheme you would write an ILS algorithm to solve the geometry of your problem, and pass the result of that calculation into the `update()` method as the measurement to be filtered. This imposes on you the need to compute the correct noise matrix for this computed positions, which may not be trivial. Perhaps in a later release of this book I will develop an example, but regardless it will take you a significant amount of research and experiment to design the best method for your application. For example, the ILS is probably the most common algorithm used to turn GPS pseudoranges into a position, but the literature discusses a number of alternatives. Sometimes there are faster methods, sometimes the iterative method does not converge, or does not converge fast enough, or requires too much computation for an embedded system. " + "Finally, let's discuss the sensor fusion method that we used. We used the measurement from each bearing and had the Kalman filter's equations compute the world position from the measurements. This is equivalent to doing a weighted least squares solution. In the *Kalman Filter Math* chapter we discussed the limited accuracy of such a scheme and introduced an *Iterative Least Squares* (ILS) algorithm to produce greater accuracy. If you wanted to use that scheme you would write an ILS algorithm to solve the geometry of your problem, and pass the result of that calculation into the `update()` method as the measurement to be filtered. This imposes on you the need to compute the correct noise matrix for this computed positions, which may not be trivial. For example, the ILS is probably the most common algorithm used to turn GPS pseudoranges into a position, but the literature discusses a number of alternatives. Sometimes there are faster methods, sometimes the iterative method does not converge, or does not converge fast enough, or requires too much computation for an embedded system. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Exercise: Track a target moving in a circle" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Change the simulated target movement to move in a circle. Avoid angular nonlinearities by putting the sensors well outside the movement range of the target, and avoid the angles $0^\\circ$ and $180^\\circ$." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [], - "source": [ - "# your solution here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have a few choices here. First, if we know the movement of the target we can design our filter's state transition function so that it correctly predicts the circular movement. For example, suppose we were tracking a boat race optically - we would want to take track shape into account with our filter. However, in this chapter we have not been talking about such constrained behavior, so I will not build knowledge of the movement into the filter. So my implementation looks like this." - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [], - "source": [ - "def plot_circular_target(kf, std_noise, target_pos):\n", - " xs = []\n", - " txs = []\n", - " radius = 100\n", - " for i in range(300):\n", - " target_pos[0] = math.cos(i/10)*radius + randn()*0.0001\n", - " target_pos[1] = math.sin(i/10)*radius + randn()*0.0001\n", - " txs.append((target_pos[0], target_pos[1]))\n", - "\n", - " z = measurement(sa_pos, sb_pos, target_pos)\n", - " z[0] += randn() * std_noise\n", - " z[1] += randn() * std_noise\n", - "\n", - " kf.predict()\n", - " kf.update(z)\n", - " xs.append(kf.x)\n", - "\n", - " xs = np.asarray(xs)\n", - " txs = np.asarray(txs)\n", - "\n", - " plt.plot(xs[:, 0], xs[:, 2])\n", - " plt.plot(txs[: ,0], txs[:, 1], linestyle='-.')\n", - " plt.axis('equal')\n", - " plt.show()\n", - "\n", - "sa_pos = [-240, 200]\n", - "sb_pos = [240, 200]" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false, - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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InZaZfY7v1s0vtc/EgTMYdNG0hPJKzzDoe2F++bdrYMt+SP4RZlyjYF4feLib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\ntm3btDFCCFhaWuKbb77B6NGjtdsvXbp00ydHRERERGSq7O3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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "np.random.seed(12283)\n", - "std_noise = math.radians(0.5)\n", - "target_pos = [0, 0]\n", - "f = moving_target_filter(target_pos, std_noise, Q=1.1)\n", - "plot_circular_target(f, std_noise, target_pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Discussion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The filter tracks the movement of the target, but never really converges on the track. This is because the filter is modeling a constant velocity target, but the target is anything but constant velocity. As mentioned above we could model the circular behavior by defining the `fx()` function, but then we would have problems when the target is not moving in a circle. Instead, lets tell the filter we are are less sure about our process model by making $\\mathbf{Q}$ larger. Here I have increased the variance from 0.1 to 1.0" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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8q/nBRO+ONa+Ln55h+UCi3cc3lEBmIlJWqDgXkTIhM/sChmG5DKIJEwGVClaA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\npBFszomIiIiINILNORERERGRRrA5JyIiIiLSCDb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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "np.random.seed(12283)\n", - "std_noise = math.radians(0.5)\n", - "cf = moving_target_filter(target_pos, std_noise, Q=10.)\n", - "target_pos = [0, 0]\n", - "plot_circular_target(cf, std_noise, target_pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The convergence is not perfect, but it is far better. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise: Sensor Position Effects" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Is the behavior of the filter invariant for any sensor position? Find a sensor position that produces bad filter behavior." - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [], - "source": [ - "# your answer here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have already discussed the problem of angles being modal, so causing that problem by putting the sensors at `y=0` would be a trivial solution. However, let's be more subtle than that. We want to create a situation where there are an infinite number of solutions for the sensor readings. We can achieve that whenever the target lies on the straight line between the two sensors. In that case there is no triangulation possible and there is no unique solution. My solution is as follows." - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "std_noise = math.radians(0.5)\n", - "sa_pos = [-200, 200]\n", - "sb_pos = [200, -200]\n", - "plt.scatter(*sa_pos, s=200)\n", - "plt.scatter(*sb_pos, s=200)\n", - "target_pos = [0, 0]\n", - "cf = moving_target_filter(target_pos, std_noise, Q=10.)\n", - "plot_circular_target(cf, std_noise, target_pos)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I put the sensors at the upper left hand side and lower right hand side of the target's movement. We can see how the filter diverges when the target enters the region directly between the two sensors. The state transition always predicts that the target is moving in a straight line. When the target is between the two sensors this straight line movement is well described the bearing measurements from the two sensors so the filter estimate starts to approximate a straight line. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise: Compute Position Errors" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The position errors of the filter vary depending on how far away the target is from a sensor. Write a function that computes the distance error due to a bearing error. " - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [], - "source": [ - "# your solution here" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Basic trigonometry gives us this answer." - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "\n", - "Error of 1 degree at 100km is 1.75km\n" - ] - } - ], - "source": [ - "def distance_error(target_distance, angle_error):\n", - " x = 1 - math.cos(angle_error)\n", - " y = math.sin(angle_error)\n", - " return target_distance*(x**2 + y**2)**.5\n", - "\n", - "d = distance_error(100, math.radians(1.))\n", - "print('\\n\\nError of 1 degree at 100km is {:.3}km'.format(d))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Discussion" + "## Effects of Sensor Error and Geometry" ] }, { @@ -2276,7 +1941,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 26, "metadata": { "collapsed": false, "scrolled": false @@ -2284,9 +1949,9 @@ "outputs": [ { "data": { - "image/png": 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HU5NBTU2MXbscLc5du9bF5ZenSKUcXHut/f/Z3LkxwuEUOTkNnHGGRZ8+XTCM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\nfvk3HpiIiHROsVgM+ASPB3w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t3rUryY03+qivN6ivN7j9dj///u8efv3rBKlUqg1GLHJy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\n5JFH/BVPtaR6xb8npqb1t+3/2VQ6i4iIoLlz59L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HbNrktpe0b2+zZYvJxIluRfzOO6MkEnFyc2PE4wb9+mlhpYjI8URhW0TkG+Tm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\nr35lMWuW+7ptw1VXJbjkkn2TTMrLLXr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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2329,7 +1994,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 85, "metadata": { "collapsed": false, "scrolled": false @@ -2337,9 +2002,9 @@ "outputs": [ { "data": { - "image/png": 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lS8qCDyLOmeNRmzYBrVpl17hxCXrttUrt319aY93prTs3qKj4gKSqdaMvvaBP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\nU6dq9uzZysvLU//+/TV8+HD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DQOyzBAKBQDgX6Nevn+Li4vTcc8+pXbt2WrhwoUaMGKFOnTrp008/lSSVlpYGX79t27bw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\nlVS1bvTlXS5v8No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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2354,9 +2019,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can see that each individual measurement has a very large position error. However, when we plot successive measurements we suddenly have a clear trend - the target is obviously moving towards the upper right. When the Kalman filter (whether a linear KF, an EKF, or UKF) computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately $45^\\circ$ degree line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this sort of noise distribution. Of course, this graph makes it look easy because we have computed 100 possible measurements for each position update and plotted them all. This makes it easy for us to see where the target is moving. In contrast, the Kalman filter only gets 1 measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", + "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately $45^\\circ$ degree line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this sort of noise distribution. This graph makes it look easy because we have computed 100 possible measurements for each position update and plotted them all. This makes it easy for us to see where the target is moving. In contrast, the Kalman filter only gets 1 measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", "\n", - "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose in the example above we told the filter that the initial position of the target was 1000km away from the sensor (vs the actual distance of 7.07 km), and that we were highly confident in that guess by setting $\\mathbf{P}$ very small. At that distance a $1^\\circ$ error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." + "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose we set the intial position to be 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf{P}$ very small. At that distance a $1^\\circ$ error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." ] }, { @@ -2368,7 +2033,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 84, "metadata": { "collapsed": false, "scrolled": false @@ -2376,9 +2041,9 @@ "outputs": [ { "data": { - "image/png": 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Rj3/+00VJicmWq4finT073qVLDVVpD/HLL79k4MCBHDp0iCZNmtC9e3dyc3NJ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\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2400,7 +2065,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 83, "metadata": { "collapsed": false, "scrolled": false @@ -2408,9 +2073,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2565,7 +2230,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 30, "metadata": { "collapsed": false, "scrolled": false @@ -2577,7 +2242,7 @@ "array([410, 520, 630])" ] }, - "execution_count": 38, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -2632,7 +2297,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 31, "metadata": { "collapsed": true }, @@ -2690,7 +2355,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 32, "metadata": { "collapsed": false, "scrolled": false @@ -2729,7 +2394,7 @@ "\n", "FilterPy has generalized the code somewhat. You can specify different sigma point algorithms, specify how to compute the residual of the state variables (you can not subtract angles because they are modular), provide a matrix square root function, and more. See the help for details.\n", "\n", - "https://filterpy.readthedocs.org/en/latest/#filterpy-kalman" + "https://filterpy.readthedocs.org/#unscented-kalman-filter" ] }, { @@ -2743,19 +2408,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in FilterPy's `UnscentedKalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays. It may seem a bit trivial, but you will almost always want to do this if you can for several reasons. First, it will execute a bit quicker than if you implement the loop yourself. Second, the logic in your code will be a bit cleaner, and you will have a reduced chance of bugs. Third, and most importantly, it you batch process your data you can then use an extremely powerful technique to generate far smoother results than you have seen so far. We will present that technique in the next section; here I will show you how to use `UnscentedKalmanFilter.batch_filter()`.\n", + "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once.\n", "\n", - "Collect your measurements into an array or list. Maybe it is in a CSV file, for example.\n", + "Collect your measurements into an array or list.\n", "\n", "```python\n", "zs = read_altitude_from_csv()```\n", "\n", - "Or maybe you will generate it using a generator:\n", - "\n", - "```python\n", - "zs = [some_func(i) for i in range(1000)]```\n", - "\n", - "Now we call the `batch_filter()` method.\n", + "Then call the `batch_filter()` method.\n", "\n", "```python\n", "Xs, Ps = ukf.batch_filter(zs)```\n", @@ -2767,7 +2427,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 33, "metadata": { "collapsed": false, "scrolled": false @@ -2777,7 +2437,7 @@ "data": { "image/png": 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2WXwWvaeHN9ITs6FW5kIRk8blUkREDmZzuH/zzTfx7//+7wgPD8f8+fMxb968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\nGo0G+fn5Ldbc//rrr9BoNNi+fTsyMjIQFBSEnj1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dgl+urn5fZV/Pljxx3z/1PrD3XgX7duLpMfNYsOYdSsqKKCot4IsVb/DEyDm3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\nPadmzZrJZrNp0qRJLivs4sWLKigokJ+fn9Nxf39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KUVyRi6LOFoHyPCiri3Qa2C0e39wKHi6+4lP/zt9ujp6wt3HUy7+1IAi4lX8F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\nCwQKAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2843,44 +2503,6 @@ "ukf_internal.plot_radar(xs, t)" ] }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[ 543.42853628, 87.77491996, -5.26709207],\n", - " [ 87.77491996, 14.51416192, 0.01521311],\n", - " [ -5.26709207, 0.01521311, 195.7945557 ]])" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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nOjVh84dDn8gcWKWOxe27Gbw4fxtHL0YD0K2lB0sm98G7Xs1KzVHVVNffjXZt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\nAyn48UAKgPrZKoYGemJoDy8M7uEJB1terr45yr9aiT0nMrA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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import filterpy.stats as stats\n", - "P = np.array([[kf.P[0,0], kf.P[0, 2]], [kf.P[0,2], kf.P[2,2]]])\n", - "stats.plot_covariance_ellipse((0, 0), P, variance=[1, 4, 9])\n", - "kf.P" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -2892,20 +2514,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Briefly, the recursive form of Kalman filtering that we have been using up to now use information from the past to generate the current estimate. Recall the last section, where we used batch processing to filter a collection of measurements. This implies that we know now only the past, but the future! This is a key insight.\n", - "\n", "Let's assume that we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n", "\n", - "However, if we have measurements from the future we can often figure out if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a true indication that a turn was initiated. On the other hand, if the subsequent measurements continued on in a straight line we would know that the measurement was noisy and should be mostly ignored.\n", "\n", - "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `FilterPy`. The algorithm that we have implemented is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n", + "However, if we are collecting data and post-processing it we have measurements after the questionable one that informs us if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a true indication that a turn was initiated.\n", + "\n", + "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `FilterPy`. The algorithm that we have implemented is called an **RTS smoother**, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n", "\n", "The routine is `UnscentedKalmanFilter.rts_smoother()`. Using it is trivial; we pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain." ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 34, "metadata": { "collapsed": false, "scrolled": false @@ -2922,7 +2543,7 @@ "data": { "image/png": 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55ZVXcDqdtccLCgr41a9+xa9+9atrFv+beQ2Hw1F7195qtZKXl8fYsWNrz/H0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\nUV1drbc1EBEZMjb3REQGpKPmPiMjA+np6XpaFfD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8PAN5fvj795QZqrzmr/2Uk5eV6N7HLYCXRn3K7mMSHy+G7WF3fu2Tg2DOK0rF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\n9oX+7r9kBhA1U3drNsPCwjSOu3Xrhl27dsHW1vbJ4lqyBF5eXli3bh1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PmAZba3vIBDnkcs2bfnUiPLQf5A2W/j6v7R1tuJp/HuezT+PStZ/7HJHLwswS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\ndYWDgwOysrIwZ84cnD17Frt379bJdRERERER6SOJ0PNp7S5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Lf2ho6EPbent7A6h5a1GP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\nQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2958,7 +2579,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "From these charts we can see that the improvement in the position is small, but the improvement in the velocity is good, and spectacular for the altitude. The difference in the position are very small, so I printed the difference between the UKF and the smoothed results for the last 5 points." + "From these charts we can see that the improvement in the position is small, but the improvement in the velocity is good, and spectacular for the altitude. The difference in the position are very small, so I printed the difference between the UKF and the smoothed results for the last 5 points. I recommend always usng the RTS smoother if you can post-process your data." ] }, { @@ -2979,7 +2600,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 35, "metadata": { "collapsed": false, "scrolled": false @@ -3026,7 +2647,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 36, "metadata": { "collapsed": false, "scrolled": true @@ -3070,7 +2691,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -3100,7 +2721,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -3123,7 +2744,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 39, "metadata": { "collapsed": false }, @@ -3146,7 +2767,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 40, "metadata": { "collapsed": false }, @@ -3180,25 +2801,28 @@ "source": [ "It is time to try a real problem. I warn you that this is far from a simple problem. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world solution. \n", "\n", - "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. Or, it might be one of those small robots that vacuum your house. It could be a search and rescue device meant to go into dangerous areas to search for survivors. It doesn't matter too much. \n", + "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house. It could be a search and rescue device meant to go into dangerous areas to search for survivors, or a robot in a warehouse. It doesn't matter too much. \n", "\n", - "Our robot is wheeled, which means that it manuevers by turning it's wheels. When it does so, the robot pivots around the rear axle while moving forward. This is nonlinear behavior which we will have to account for. The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", + "Our robot is wheeled and manuevers by pivoting the front wheels. When it does so, the robot pivots around the rear axle while moving forward. This is nonlinear behavior which we will have to account for. \n", + "\n", + "The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", "\n", "### Robot Motion Model" ] }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 41, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3213,9 +2837,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "At a first approximation n automobile steers by turning the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modelling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. \n", + "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler **bicycle model** has been found to perform well. \n", "\n", - "I have depicted this model above. Here we see the front tire is pointing in direction $\\alpha$. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. If you google bicycle model you will find that we can compute the turn angle $\\beta$ with\n", + "I have depicted this model above. Here we see the front tire is pointing in direction $\\alpha$ relative to the wheelbase. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. We can compute the turn angle $\\beta$ with\n", "\n", "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n", "\n", @@ -3282,7 +2906,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 42, "metadata": { "collapsed": true }, @@ -3295,7 +2919,7 @@ " vel = u[0]\n", " steering_angle = u[1]\n", "\n", - " dist = vel*dt\n", + " dist = vel * dt\n", " if abs(steering_angle) > 0.001:\n", " beta = dist / wheelbase * tan(steering_angle)\n", " r = wheelbase / tan(steering_angle) # radius\n", @@ -3312,12 +2936,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we can use this function to implement the function `f(x)` which implements the system model." + "We can use this function to implement the function state transition model `f(x)`." ] }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 43, "metadata": { "collapsed": true }, @@ -3333,7 +2957,7 @@ "source": [ "### Design the Measurement Model\n", "\n", - "Now we need to design our measurement model. For this problem we are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. Using $p$ be the position of a landmark, the range $r$ is\n", + "Now we need to design our measurement model. For this problem we are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. If $p$ is the position of a landmark, the range $r$ is\n", "\n", "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n", "\n", @@ -3341,7 +2965,7 @@ "\n", "$$\\phi = \\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$$\n", "\n", - "Thus our function is\n", + "Thus our measurement function is\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{x}& = h(x,p) &+ \\mathcal{N}(0, R)\\\\\n", @@ -3376,14 +3000,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Before we begin coding the main loop we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a bearing difference of $-358^\\circ$. this will throw off the computation of the Kalman gain because the correct angle difference in this case is $-2^\\circ$. So we will have to write code to correctly compute the bearing residual." + "Before we begin coding the main loop we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Subtracting them gives $-358^\\circ$. this will throw off the computation of the Kalman gain because the correct angle difference in this case is $2^\\circ$. So we will have to write code to correctly compute the bearing residual." ] }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 113, "metadata": { - "collapsed": true + "collapsed": false }, "outputs": [], "source": [ @@ -3394,16 +3018,35 @@ " return x" ] }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.0\n" + ] + } + ], + "source": [ + "print(np.rad2deg(normalize_angle(np.deg2rad(1-359))))" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The state vector has the bearing at position 2, but the measurement vector has it at position 1, so we need to write functions to handle each. Furthermore, the function for the residual in the measurement will be passed an array of several measurements, one per landmark. These will be passed into the `UnscentedKalmanFilter.__init__()` function." + "The state vector has the bearing at position 2, but the measurement vector has it at position 1, so we need to write functions to handle each. Furthermore, the function for the residual in the measurement will be passed an array of several measurements, one per landmark. These will be passed into the `UnscentedKalmanFilter.__init__()` method." ] }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 45, "metadata": { "collapsed": true }, @@ -3440,7 +3083,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 46, "metadata": { "collapsed": true }, @@ -3474,7 +3117,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 47, "metadata": { "collapsed": true }, @@ -3508,7 +3151,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "These functions take advantage of the fact that NumPy's trigometric functions operate on arrays, and `dot` performs element-wise multiplication. NumPy is implemented in C and Fortran, so `sum(dot(sin(x), w))` is much faster than writing the equivalent loop in Python. Once you are used to seeing it, I think it is as readable as the loop form.\n", + "These functions take advantage of the fact that NumPy's trigometric functions operate on arrays, and `dot` performs element-wise multiplication. NumPy is implemented in C and Fortran, so `sum(dot(sin(x), w))` is much faster than writing the equivalent loop in Python.\n", "\n", "With that done we are now ready to implement the UKF. You've seen this sort of code many times, so I will not describe it in detail. There is one new thing here that is important to discuss. When we construct the sigma points and filter we have to provide it the functions that we have written to compute the residuals and means.\n", "\n", @@ -3525,7 +3168,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 115, "metadata": { "collapsed": false }, @@ -3539,7 +3182,8 @@ "def run_localization(cmds, landmarks, sigma_vel, sigma_steer, sigma_range, \n", " sigma_bearing, ellipse_step=1, step=10):\n", "\n", - " points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, subtract=residual_x)\n", + " points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", + " subtract=residual_x)\n", " ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=fx, hx=Hx, dt=dt,\n", " points=points, x_mean_fn=state_mean, z_mean_fn=z_mean,\n", " residual_x=residual_x, residual_z=residual_h)\n", @@ -3588,7 +3232,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 116, "metadata": { "collapsed": false, "scrolled": true @@ -3596,9 +3240,9 @@ "outputs": [ { "data": { - "image/png": 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vJvDfAKFQmFMK0iLa+3w+fvXz23jjmSUAjJ09i6t/fgl6vY7RYyE+HmbP7jkb\nTidUuerYsb+Obxbm9Tu2KaMzyUyMYfV2J2VNDTR1NuK0GsmKS2dEZsIQPBtCiC9CAmkhhBCDoqwM\n5s7tO1BescLL6NHHcEBfgF6nEggH8Qf9mPWfzTjr9Qojhpkoq/Szs7YYw2YdMTYTw9K7tjKsqanh\n0ksvZcOGDZjNZhb++C78GWkcrHBRkGcBumaiPy8j1ciePTXsPJjJmWMzjzi2jKQYrj53PFWN7ZTX\nudCpCmNykzDJjLQQx538FgohhPjaM+h1xNqMGFQTXl90Ro2cTCPBoJeS+t28tcHAVeeO48CenVxy\nySVUV1eTmZnJa6+9Rmp2Ac998AkfV+2gxhYgLdkQtd13jEOHauikwdVGZcPRZd5QFIXMpBgyk2IG\n43KFEINE0t8JIYT42jPoVZLjzRgVC+7O3vM852WbUC0d7Kzexy9/9yDTp0+nurqaadOmsWXLFiZN\nmkRGUgznTurKBX2oLESrq/dc1HFOPS5fK2W1bQRD/e8gLIQ4cUkgLYQQ4mvPoNeRkWQn1uygwx0m\nGIyelVZVhRF5Blb/+3GefPAufD4f3//+9/nggw9ISUnpqXfq8FSmjculIH4Eu/Z58XijA+UYu4on\n5KauuZOABNJCnLQkkBZCCPGVFQqFj3rGN8ZqIjPFgUMfR0NT9Ezyzu0d/ONXD7N3zVoUVeWi797O\n/7v7DxiNxoh6iqIwY2Iuk/KzybTl80mJJ2qW22JR8YU8tHb4CYZkq28hTlayRloIIcRXjqZpVDa0\nsausCV8gSEaig7w0J7E2c5/5l01GPeOHJVJcnkJVfQtpKYaespoDVbz427/haW3EHudg1g+ux5ky\njpXbDrLgvIkoSmSfOp3KvDMK8PlDfHxAx85d+xmeZyAhvutjNxzW0OsM6BS1Kze0EOKkJIG0EEKI\nr5yKhjZe/KCYsuZqguEAMaZYkh3xnD0xk8KCNIwGXa/tRmQmkBmfSEWZGVdbiNgYHe+8tJUPljxN\nKODDmpjNJb+4hfGT4ti0o4l9tbV8ciCNifkpUX1ZTAYunjYSk0nPx3tN7D9QSmOzj6QEHa72MBa9\nBbPB8GkeawmmhTgZSSAthBBiUOTkdKW466/8WNlYXMnehv1gbiYmRk9Dax2VNSZaO9upaWznvNPy\nsVmMUe2sZgPj8xPZ15BCedUhKpe9x/v/XAFA2tgpjJl7Laec3tUuL8vEwcpDbNqVxIRhyVGz0gBW\ni5ELzhzbdyuoAAAgAElEQVRBitPG2h02GtwN1FQ0o6oqebE5DEuPJ9DR2mtbIcSJTwJpIYQQg2L0\naPMJkSc6FApT2+ymxdvM5NEmTEaVzDQDjU1B9h0qobPEQ7snwKXTR0UF04qiMDE/hbVbzLx0/xPU\nle5GURXOuPRS/HHn8sEqBZ2hKzf0sGF6yqrcVDY3sL+qmeF9bJBiNOg4Y2wmeWlOdh5o5mC1C52q\nY3h6AtkpMRzqlCBaiJOVBNJCCCG+Ujq9ATr9XlADmIyWnuOJCXqsFpXivfvZdhAcFgPnnzUCgz5y\nmcf+PcX87a6bqKupwmSzsfDumxg5uesbQkJC5C6FqUkGqppr2bavts9AGro2fElPdBBjMzF5VDJe\nX9e25GYTmPtYZiKEOPFJ1g4hhBBfKVazAb1OTygcvfbYalUZO8JCVedBNu2t4L9F5YQ+l9VjyZIl\nTJ06lbqaKnJHjOX82xdjTh3WU374LoVpyQaaPU0cqG2ipd3T77gURcFhNREfYyHBaSTBacDpMGPQ\ny0exECcr+e0VQgjxlaLTqTjMRoyqCY83FFVutaqMzDey37WHNTvKKDpQh8fj4cYbb+Smm27C7/dz\nyy238Nbb73HqiNOorA7S1tGVDu/wXQqNBh3x8Sq1HXXsLm86qvEpioLZqMdiMqDXycewECezfn+D\n165dy4UXXkhmZiaqqrJ06dI+6958882oqsqDDz446IMUQgghvojkOBs2o4229uhAGiDOqSMnS6W0\neQ+vvPsRZ541lSeffBKz2czTTz/N3/72N8bkpTGpIJPhCcMp2evB5+89H3V8rJ5Wj4uqxrahvCQh\nxAmo30Da7XYzYcIEHnroISwWS593Fb/88sts3ryZ9PR0ufNYCCHEcZeT4iTJnkB9LxurdEtLMdBw\naBsP3PEddmzfRl5eHhs2bGDhwoU9dWZNGsYpObmkWjPZuaczYhlIt5gYHW2+Nupb3JLGToivmX4D\n6blz53Lvvfdy6aWXoqq9Vy0rK+O2227jhRdewGAw9FpHCCGEOJZG5ySS6kiivR08vuhZ6dK9Yd57\n5i3ef+QJvO4OCiacwatvfcApp5wSUU+nU7lo6kgmZAzHQjwl+zyEwpHBtEGnoNdruP0eOjz+Ib0u\nIcSJ5UstzgoGg1x11VXceeedjBw5crDGJIQQQkTQNI1Ob4C65g7qWjrwB3pfstHNYjJQkJFIoi2R\nmvpARFlnm5sX7v0bbz/1BgCnf2su37jhh5RUd/bar9Vs5JKzR3NKxmgUn4Oduzvx+j+b6Q5rGooK\niqIRll0Khfha+VLp7xYvXkxycjI333zzYI1HCCGEiFLZ0Ma7mw99ug5ZIyXOzqjseKaMzsBs6v2v\noROGJbP1QAo7G+rJSTei06n8950DrPjr3/G2NaM3Wznv5u8y/fyxfLyjkdLKZupbOshMjo3qKyHW\nymXTx2BYp+OTmj3sKK4lN9tArEOHLxgmHAKr0YLDahriZ0IIcSIZcCC9evVqli5dyvbt2yOOH836\nsC1btgyoTIiBkNeUGAryujp2vP4g72yrpaSugjatnrAGBs1C0o5k3l+fwNTRSSQ6zFHtNE2Djk58\nLSE2byunbutmPnxxJVo4DNZcxn3rSqypNmprKwkFYeeBnbz+npvJBQno1N7v9xkZH6Cx3o7XF0PR\njhpCihdVBac+Ca+rga1bPx7wdcprSgwFeV19eQUFBX2WDTiQXrNmDTU1NaSlpfUcC4VC3HHHHTz0\n0EOUl5cPtGshhBCiR4vbT01rO23UM2o46FTocHuoqD1EW20bbm+As8ekkJVoi2inKAqnDounvDaG\nN554ksa9ewE4dfbpeOIvZcbsdsAHQLwTKttbOFiXwvjcWKx9zHLbzQbOnZDOniobB+oSae7sQEMj\n2R7LxNy4IX0ehBAnngEH0j/4wQ+4/PLLe/5f0zRmz57N1VdfzU033dRv28mTJ0cd6/7G1FuZEAMh\nrykxFOR1deytL67AltBEvimJvNzPZp5HjtDYc8BLQ3sb5e4czpoyipQ4e0TbzZs38+YT99JYU4XB\nYuaa/3cd488+lX37ICvL2VNP0zQ8fg8Gi4OE9HzG5iX3O6Ypn7apb3GjAYmx1gHnhJbXlBgK8roa\nPC6Xq8+yfgNpt9tNaWkpAOFwmLKyMrZv305CQgJZWVkkJSVF1DcYDKSmpvY7BS6EEEJ8EcFgmGA4\ngNEQudxCp1MYPdxMSWkHRVV7sa4zcNU3x2K3mtA0jYcffphFixYRCATIyh/NxCuvxDm8a9b48I1V\nFEUhzqmnvd1FdaObEVmhqK3DD6coCinx9n7rCCG+2vr9+rx582YKCwspLCzE6/WyePFiCgsLWbx4\n8bEanxBCiK85i0mPUWfAF4jO4awoCqPyLXjVRj6pOMDyDXtpamrmsssu4yc/+QmBQIBbb72VN956\nlzNGn01FZYjGlkAvZwG7VcUb8tDo8hII9r75ihBCfF6/M9IzZswgHD76N5ODBw9+6QEJIYQQn+e0\nmbEYLDR7e7+ZXadTGDvSwrad5by7poafX/8gVRVlxMTE8OSTT3LZZZcB0OEP4wv6KNlfgnm0gt0W\n+RFoMikENT8dnYGoXNFCCNGbL5X+TgghhBhqKfE2Yi129jRpBIMaen10Rg2jQaG1eAP/fvo1wqEg\nE085hX+//DL5+fk9daaOy6Kl3YM35Kdo9z7GjDAT6/jsY1DTQAHCYckHLYQ4OhJICyGEOOb8gRDB\nUBhVVTDqdah9pJsDiLGZyUlxsrveSUOzm7RkY0R50bZ2Ni1bSsmGIgDGT5/NPfc+GBFEQ9cykLlT\nCvD6g+gO6CnetZeszBDpKUZ0OoW29hBWvZ34GMvgX7AQ4itJAmkhhBDHVJvbR6c3hNcXRq9TMBoV\nTAYVh9XUZ0A9MiuBbQeTqG1sjQik9368i+fu/AeBThcWu5WLfnItQedYdlW0cpbLTWJsZEo8vU7l\n0umjcdrN2HZbKa07QGW1C7tNxetVGRmbSmZSzIAzcAghvl4kkBZCCHHMeHwB2joCbNxZx6G6FjRN\nI9ZmJiPJzqRRicQ5LJiM0R9No7ISSXEksL9sP15vGINe44UH32DbincADWfWcM7/0Xc5dUo8u0s9\nVLfVs6uskbMn2KL6UlWVWZPzyUmJZX1xHOV1bXT43NhibIzNSSM/Mwajof+MHUIIARJICyGEOIb8\ngRBrd1RSVH6I8o4DhLUwNoOd2LoESivTOff0bPLTnVgO2xDFYjYwKjuRg01p7NhaxMZn/0n5rkOg\nKJB6PpOvnocjoSv4TU4ycOhAA3sqmjljTGafaexGZCWSmxpHo8tNU5sXs8GI02HEatIfMfWdEEKA\nBNJCCCGOIY8vwMGaFg62lzJyuB6rxUC7u5PKahctdU241nRy3ml5FBakRs1MnzU2k+dfeJ5XHn+A\noM+HMzmOa35zIx8VD2fu3M/qOWN0+DU3lY0uqpvayUlx0hejQUd6Ygyp8Q5C4TA6Ve13vbYQQnye\nBNJCCCGOmbL6Npo9zdhsGrExXbO+8U49cbE6yis72NuwE2UL2EwGxuQl9axV7ujo4Kc/vpXnnn4a\ngKyJE7jxnoXYY+2ErZHnUFWFxAQ9DR2N7K9qITs5FkXpPzhWVQVVlVloIcQXI4G0EEKIY8bjC+AJ\nubE7IgNbRVHIyTKiqH721e/h7U0G7FYjualOtm3bylVXXUVpaSkWi4VvXf9T1OF51LV0Yo+N3qUQ\nINauo97V2bO5iqx5FkIMBQmkhRBCHDMGnYpeVQmFes/TnJVuwOv1sLexlDf/q9JQ/DZ/vO9eAoEA\n48eP58UXX8Qan8ayVSVsrf4Ei9lPeqoxqh+zWcEf9tLW4f90cxUJpIUQg08CaSGEEMeMw2bCqDfS\n6us9kFYUhfxcIx+tL+WPD/+B6n0lAPzoRz/igQcewGw2A3Deafl41/spKv8EszlIvDPy40ynKoS1\nMF5/iJBsriKEGCISSAshhDhmkp1WYi12yuqDaJoWtXZZ0zS2vreRNx96EZ/Hiz02nof/9hjXXX15\nRL2J+Sm0tHvwBQPs3beb3GyN1OTPMn10esJY9DbsFiOaJoG0EGJoSCAthBDiS9E0jeY2DyaDDpOx\n/9RxqfEOUp2xlNRbcLUHccZ8Fvy6XR08+qvnqCnZCsCwyROZ9q1bMKeMxeMLRKTEUxSF6RNyCATD\n6Hca2Fexl6ZWL6lJeswmlZr6IPHGOJKdNtQj3GgohBADJYG0EEKIAatv7uDtzfupaHBhUA3Ex5jJ\nSY1hyugMYmzmXtsUZMTzSWUC9U21PYH07k3FvPTHpbQ1uTBZzVx867eZ+M0z2F7sZXd5A2e2pJOT\nGpnGTqdTmVmYR5LTyuqtNg42VVFT3kpQ8+M0p5ERk8GonATZpVAIMWQkkBZCCDEgHl+AF1fv5JOq\nPTR5G1FRMdVaSKlMY29FC+dOzqUgIyEqL/PIrERSSpLYXldJZrKXt5e8yrpXV3cV2vJJ/sYNeKyJ\nmEyQEKfS3NlEaWUL6YmOqNlunU7llOGppCc4KDqQxMHqdtyeILE2M5NGphEXY5CMHUKIISOBtBBC\niAHZXd5IVWsdHqWJsybZAehwhzlUcZBNZY20dniYfXo+pwxPjZgVTkt0kJecyKYdbfzvg4/TUl2H\nTq9j9vUXsqvlPH70o8/qJsTpKW9tZl9VK2eMzeh12YiiKKTE23HazZw+OkQgGCKsgUGvYrcYj5hD\nWgghBkoCaSGEEAOyu7yRencDaakGdLquYDU2Rsf40RbKqzrZWbcTPlKwGPWMzknqmZkOBoNs++Bf\nvPW/9xEOhUjKTuXaO79LZkE2+jWR54iNUfFp7dQ0tdHY2ondEp3qrpvJqMdk1PfcXCgBtBBiqEkg\nLYQQYkA6PAHc/g6GxUQGt6qqkJtlAvzsadzNfzbqsVmM5KTEsnv3bhYuXMjmzZsBGH/OeRReNpPM\ngq71z9/4BlF9OWP1tPldVDV2kJkcc8Q1zxJACyGOFQmkhRBCDIiqdAW64T7yNOdkGvD5OtnVsJfl\n/1Vp3vU+9/3PPfh8PrKysnjokUc56HOyuXI75dVestN7vznRbFYIeP20uf0EQ2G5eVAIccKQQFoI\nIcSA2C1GDDojfn8QrNHliqJQMMzEf1fv4b6H7qPmwG4Avvvd7/Lggw8SGxvLrrIGvAEf2z7dpTAp\nPnrphl6n4CeEzx/uM2gXQojj4Yhf69euXcuFF15IZmYmqqqydOnSnrJgMMgdd9zBxIkTsdvtpKen\nc80111BRUTGkgxZCCDE0QqEwwVD4qOrGOSw4jDZc7aFey8PhMP99ZSVv/fEBag7sxuFM5B//XMYT\nT/yd2NhYAEbnJPGN8cMZmzyK0gN+ml2BqH4CAQ2dokNRFNlcRQhxQjliIO12u5kwYQIPPfQQFosl\nYu2Z2+1m27Zt/OY3v2Hbtm28/vrrVFRUMGfOHEKh3t9YhRBCnHhCoTCtHV6a2rw0tnppcnXi6vD2\nG1Tnp8eRZEvE1RYmdFi9puoG/vf7/8vrjywj6Asw4qzTueLX92NLm0CnLzJYPmtcFqcX5DMqcRS7\n9wYoq/L2BMyaptHYHMRpSiA7OQadLOsQQpxAjri0Y+7cucydOxeA6667LqIsNjaWd999N+LY448/\nztixY9m9ezdjx44dvJEKIYQYMu0eP662MG3tQcrqWwGNhFgz6clmEmMt2HrJlpGdEkuyI5FdDQpu\nb4gYm0o4HGbDG2t587FX8Ht9WGJiuPIX1zB88gSKijvYW9HEtAnpWIz6nqBYURTmnD4cm9mAtcTC\n7vr9VNW4cDr0hMIKFsVJnCWG9CQrBgmkhRAnkEFfI+1yuQCIi4sb7K6FEEIMAX8ghMcb5kBVGzsO\nVFHbUUtIC2HAjMVg49SCFM4Yk0ZCrDXir5IGvY789HiK6xJoaGom2N7GsvufoXRr11po4k4j+ewr\nMafaMZvBZtdw+V2UVrThsJkiUtmpqsI3TsklKzmGlVtjqWluw+XtIAykxiVz9sRMLCa9zEgLIU4o\nivYFFpw5HA7++te/smDBgl7L/X4/55xzDklJSbz22msRZd0BNkBpaekAhyuEEGKwdfqCNLWGWLWz\njgOde9GbOzEaNLw+BZ9XT7wulWxnEmeNjicjwRbRtrbVw4qtB3h/5fMcWL2KoC+AxWFl4gUXUNFx\nFlVVZqZMcZGV5cNi8+FuSmBc4nCmT4gn1tp7TmhN02hu99PQ5sUXCJEeb8Vq0mM16SS1nRDimCso\nKOj57+77O7oN2ox0MBjk2muvpa2tjTfffHOwuhVCCDHEwmGNmhYv7QEXqrGTvKzu+RWNTk+AypoK\ndjW1E9gZ5JsTUkmNs/S09bbW8Z+//5FD+3YBMPy0UXxz4VyssTYyK9uoqPBx5pltAAQCUFfvoqnd\nh9cHVmMYgz56hllRFBJiTCTEmNA0TYJnIcQJa1AC6WAwyFVXXUVxcTGrV68+4rKOyZMnRx3bsmVL\nn2VCDIS8psRQ+Cq+rtrcPg62laJvrWJMWirJiZEfDQXDNfbs99Lq7qSsw8KU00bjtBl54IEHuPvu\nu/H7/Tic8Yy/+CJmXFxIgrNrpjkrC5KSICvrsxmcVreHJHsSWbmjycuw4rCajum1noi+iq8pcfzJ\n62rwfH5VxeG+dCAdCAS48sorKSkpYfXq1SQnJ3/ZLoUQQhxDqqoQDIXxh/xYzNGzv6qqMDLfTPGe\nVj6p3Evt0j28/uT9FBV9AnTlhf7W9T9h/b5y9hzYzcTRKlZL18fL8OGRfRkNCmElSEdnAH9AsjsJ\nIU5uRwyk3W53z5rmcDhMWVkZ27dvJyEhgfT0dC6//HK2bNnC8uXL0TSN2tpaAJxOJ2Zz77tUCSGE\nGBrhsEanL9CTts6gUzEadBj0uj7bqIqCXq8ACuE+st2pqsLwbJXn/ryE3SvXoIXD5OXl8fe//52Z\nM2cSDmt4gjo6/T6K9hykcKwNg6G3ZRtd/2phCIW7xquqsnRDCHFyOuLtz5s3b6awsJDCwkK8Xi+L\nFy+msLCQxYsXU1lZyRtvvEFNTQ2TJk0iPT2957Fs2bJjMX4hhBCfCoc1Wju8NLcGaWoO09wSpqk1\nSHObj/ZOX5+7Ahr0KjE2A3rFgM/fe5392/fyfzffy673V6FpGlPnXsGb769l5syZQFegff6ZI5iY\nPYwEQxo7dnXi9UVG5aGQhrtTw6q34bCYCIUg1FfkLoQQJ4EjzkjPmDGDcD9vdP2VCSGEOHY6PH7a\nOzTCQR16RaGisRVVVbEY9MQ7DQTsYWJsJvSHpZAz6HWkxFmxGxw0t7ZErJH2uj28+fgrbHhjLQCp\nuemcvfBKHPET2ba/mdF5GT03A5qMer41bTSBQIhPKo1sKyonN8tEvFOH0ahQXRsg1hBPZoITh9WM\npoWQjQqFECezQc8jLYQQ4tjTNI1AMEQgADVNrWwpraTB3YBO0WHWWbAaLEwYnsLEgnicDnNUMF2Q\nGU+iLZEdDYcIhTRUFYrWbuPVh1+irbEVRdUxa8FcZl4zF0XVsWl7I6U1DeyvbmF4RnxPPw6biatn\njiduk4Xt++Ooqq2gqspNUAtg1dspiMtjeEYioXAYnQ5Z1iGEOKlJIC2EEF8BwVAYfwCaWjv5sGQ/\nu5qKMFt9AHR2aBix0+jOpbw+hfNOzyYtwRERxCbEWslKimFvk4OyfTWsevpflGwoAiAmLZe2uAWQ\nlsGhsq4bCNNTDNS01rGnoikikAawWoxcOHUkwzPi+Xh3Mk0uL8FwkDi7jVPzM8hNjqPN48WgV6IC\neiGEOJlIIC2EEF8Bmtb1OFjXTK27iviEADlZ5k/LNBqbfRysLKatrBWPP8ClMwpIdtp6lmXodSq5\nKXbKn1zH+uXPE/T7MdvMnHbxJZgzp/Pe+5EBb1KCgR3VTRysbiEQCGEwRN7MaNDrGJeXTE6qk05P\nmObWACa9Ab1OR7vHh80GJkPfN0AKIcTJQAJpIYT4ClAUCIZCHKprodFTx7g8/efKFJIS9MQ4VHaV\nVlJSo2Far/Kt6SOIc3RtrrJx40Zu/d732FnUNQs9Zmohl//sSmISunJAt7TC7Nmfnc9qUTGYg9S6\nWjlU20pBVkLUmHQ6FafdjFEfwGxSCAQ1QqEQej2YjTpslt53NhRCiJOFBNJCCPEVoCoKwVCIzoAX\nVRfCbIoOUk1GldEFJnburqKowoB9s55zxqfw28V38dhjj6FpGmkZWUy99EZ0eXbscZ9tB37aadHn\nTIzT0+xqoaze1Wsg3c1qNmA1GwiFwoTCGjpVQSdLOoQQXwHyTiaEECegYChMh8ePq8NLe6cPrz/Y\nZ/o66LppT6frWsah0Xc9k1FlTIGJms4DvPDSPxkzZgyPPvooOp2OO+64g13FxcydfQEWJY6D5b6e\ndodvrAJgtejwhnx0ePxHdU26T3NaSxAthPiqkBlpIYQ4wfj8Qdo6/XR2gj8QJhAMEmM3YDEr2CxG\nzMbot25FUXBYTZgNBnz+/tOSdrY2s+Wfz3FgWwkAp085gyV/f4Lx48cDMHNSHo1tbrZVFWEy+shM\n730bb70OQuEQ/kBINlYRQnwtSSAthBAnkHBYo73Tj8ulUVrZzL7qRlydHgw6PVazgTF5cRQWpOB0\nmHtuFOxmNRuItZswNJjpcIew2yJv5tu9K0D5pnf44Lm3CfoDGK0Wzrr4Oyz60c8YP35kT72cFCdz\nTy8gsD7EjqoiDMYAKYmGqLEGgqBTdYCCpmmABNJCiK8XCaSFEOIE4gsE8fpgW2kNO6vKOdhail/z\ngKbDpFooa0pjT3kz552Ww/DMyHXJJoOOvLQYiqriaWppjAikSzYU8fwfX8TT2gjAqeeeznk3XMq+\nShMlZY1MHZeN89MbDwHGD0vB7fHj3xKk5GAJXq+frHRDxKxzU3OQOGM8GYmOIX5WhBDixCSBtBBC\nnEB8gRBtHQEO1jVT2lLCsDyVeKeVYFCjvSNAWdU+msoacHncXHDmCMblpfS0VRSF/PR4Em3xHGyu\nISfTSFNNI8/94SXKdnwCgCEmnXk3X8X0+SMAaOjwUNvewN7KZk4fnRExliljMgmEwhh2GCht2E9j\ns4uUpK4lJp2dYdxulWEJCeSnx8m6ZyHE15IE0kIIcQLRNI09FU00dNbhiNGId3a9Tev1CnFOHbEx\nZg6Wt1FUU4xhkw67xUhualxP+7w0JymxTnbXabzxxOuse/k9gv4ABrMZx8gLaNadg0evY9++rhsI\nE+N11FY2caAmOpBWFIVp47NJjbezcqud/bV1dDS10RryYNAZKIjN5NSCVOxWSWMnhPh6kkBaCCFO\nIJoGja5OWrxNpGZHb1iiqgr5uWb2aV4+qSnBuE7HVTPHkeTsSlVnMurpqCzig/+9H1djHQCF557O\nBbdcRn1LLPv3R+aDTnAaKD3gorzORYfHj/2w3M6KolCQmUB6goOSshRqGj20tPlAgTG5iQzPjMFm\njl4/LYQQXwcSSAshxAlEUboyYYS0IAZ93zfv5eeaKN7bQVH1XmI/MvGdWRM5dOggt912G8uXLwcg\nNjWd+T+4nEnTxwAQ00uqZ71ewWFXaPG4qGxoY1R2Yq/ns1mMTBqRjn9YiEAwhKZ17YZoMemjbnoU\nQoivCwmkhRDiBKJTVfQ6ha5MGH3XUxSF0cMtbP6knuJDB7nlJ/9k6d8fwefz4XA4uPFHt2POn0Rp\n2x58/jAmY9ca5t7yQVssKl7/kfNBq6qC2ajvNf2eEEJ8Hcm7oRBCDKFwWMPjC+DxBVAVBZNRj9Gg\nw6CPXrYBYNCr2Kx6dIoRj9dHTD8JMVQV/BXF/PWp/6GztQWAa6+9lvvvv5/U1FReXLmT9lI3Rbur\nOHWsDZ2u95ljnaoQCocIBPvPPy2EECKSBNJCCDFEgqEwdc0drC+qYV91M+GwhsNqJCHWzKQRqYzI\nSojaxMSo15GZbMexLxZXWyspSZFv0/v2df1rCpXx+iPLOFjUdSApK5d77n2A7y+4rKfuRVNH0ukL\nsOlggJ17Ghg/ytrrpinBkIZBUWVDFSGE+IIkkBZCiCHS0OrmxQ92c6i5nAZvDSEthE4xYNXZ2Vud\nxcS8NM6bPAy79bOdA3U6lezkGGKMsdS4goTDxogAt2SHi31rXqe6aD2apmF3/n/27jxKrru+8/77\nrnVr6+rqfVW3utXaF2zLO5aXAEZmSZwcIBMywcnh4TkZwiTkmZOTOBxgCGEbBjLhZGGYCZjnCeOZ\nTAKTBJsAwca7LVmybFmW1OpWL+p9rb3u/vxRUkstdcuSuiVL9vd10FG7btW9V0111ad+/b3fb5K3\n/+p7SPfsIt7Us+j4McvkV+7YhOP47BlyOXBonk09Flbk9Gp4EIRMz/pc31hLR2PV5f+mCCHEm4gE\naSGEuAxsx2Pf0QkG50bIq6Ns32JimiaOEzIzl+PQyAHmirPMZIr86i9sJXlGmK5NxWhKV9GXiZPN\n+VSnNI685vLD7/yMkT2PQFBGUVV2vPMdfODfvwcjFuG5FwuMzp7beaM6GeX+XZvgCXht4jj7Xj5B\nS5NOdUrHMlWGR20SWoo19WmaamSwihBCXAwJ0kIIcRnMZku83DfFZGmEzRtNLKtysZ9lKbQ2m9TW\n6Lx6dJj9wz6RJ3V+9Z6tmEZlpThq6mzoqObIRCPDo8c58cpR/vEv/zczo1MA1K3bxkc/8wHq208P\nY0klVWaLc/SPzrG9u3HRuTTVJPjIu3fwoxcSvDpUx4nMKH2TRZygTCqSZnPT2nN6SAshhHh95x1F\n9cQTT/D+97+ftrY2VFXloYceOuc+n/3sZ2ltbSUWi3H33Xdz6NChy3ayQghxrZiYyzNTmCWe8EnE\nz32ptSIq2zfGmHVGODB0nH9+9gjhyTYdmqayo7sRPVfg0a/9Nd/+1F8xMzpFY2cz7/3k7/KBP/yd\nRSEaIF2tM1vKMDyZWfJ8YpbJL+/axIfvuY5fvOEmdm+7hbvW3cK7tt3Av7lnOxuWaXsnhBBieedd\nkYbDJAEAACAASURBVC4UCmzfvp2PfOQj/MZv/MY5vUK//OUv87WvfY2HHnqI9evX87nPfY53vvOd\nHDlyhEQicVlPXAixMq+9VmZwcPntHR2waZN15U7oTSZfcrB9m2hi+fUKw1DYujHKgVf7ifZbtDek\nuHFjKxMTE3zmM5/hW9/6FkEQYMZi7P6t93H7L92Jtky3DyuiMOM5FG33vOfV1ZKmqyV93vsIIYS4\nMOcN0rt372b37t0APPDAA4u2hWHIn/3Zn/FHf/RH3H///QA89NBDNDQ08L3vfY+Pfexjl+eMhRCr\nYnAQdu9ePig/+miZTZuu4Am9yQRhSBAGaOf9vR/Eoho9XRGO9ffz5P4o//zwf+Nr//mr5PN5NE3j\n7vd8iJbb78Sqd1HU5XemKQphGOAH52k+LYQQYlW9zkv88o4fP87ExATvete7Fm6zLItdu3bxzDPP\nrMrJCSHE1cT3A8qOT6HsUSg52I63UI5xNtPQMTQdx3n9YFuT0hh66Qk+/e9+mc/9x8+Sz+d53/ve\nxyuvvMJDf/NNbui6ATef4PjQ8gNTHC9EUzXMZVashRBCrL5LvthwfHwcgMbGxXV6DQ0NjI6Onvex\ne/fuvaRtQlwKeU4tLZfrAJZfkc7lcuzde/DKndBVruz6FMseE7MuRdvnxOSzJOM6MUshampEjMUB\ndmquSH4mx7A7xRlNNBbs25fg+uvzDLzcx1MP/yvTw5MANLZ38ek//A/cdNONFAoF8vmjrEkW6RuI\n09c7wdTUJM0NlWEsZzo2GFIVtDM3OczevYXL9W0Ql5G8VonLQZ5XK9fT07PstsvStePsWmohhLiW\nOZ7P4ESB/X1Z5ksFXBwMTHTVpLEqyva1SWpTJvGIvvD6l46bJK0oflHHcT1MY/E+D++bZeAnf8fQ\nweMAJGur6Lzzbm68/v20dncv3E9RFNrq4ty2qQ7/YMhoZoTewjxN9RCLga5BJgfFgkF3TZp1TdLC\nTgghrpRLDtJNTU0ATExM0NbWtnD7xMTEwrbl7Ny585zbTn1iWmqbEJdCnlPnNz1dPu/2ZDIp37uT\njo/N8bOjh5g15hnL92NFoKqqloKtYGjNHJ6u5bbmNtavryeVqKzy+37AiVKS+VfyJJIFGusrSfpH\n/zjHs//wf8gPPAeE6FaUdz+wm7fffw8DYx5GqYralk52butYdA43+AE33zDPj/cM0jcxxlR5jOnZ\nEn7oYKpxbu5ay107urnzxu6zT19c5eS1SlwO8rxaPZnM0t2QYAVBeu3atTQ1NfHjH/+YG264AYBy\nucxTTz3FV7/61UvdrRBCXFXKtsvPXxpmKDOAVZVjQzpEUaC9PYrjhAyNjHN4bpbSvhKqAjs3NhKP\nmmiayrq2avb3N3Ji7AhJy+Xx//ljnvi7n+LaLigau37lLt7xb+8jnqp0OaqugtG5LCNTuXPOQ9dU\nulrS/No7Yhzoq+XIYCuZgk3RdqiOW+zc2MiNm1qu9LdHCCHe0l63/V1vby8AQRAwODjISy+9RG1t\nLe3t7fze7/0eX/jCF9i4cSM9PT18/vOfJ5lM8mu/9mtX5OSFEOJyOz42z7HxCTLeJDe0xxgbO73N\nNBXWrY0wMeUycOIIjx8wSCVMNnXUEjF1Nq2ppzGR5Cf/+CT/8Pi/UM5Xapd33HUDdTvu57776xcd\nqyqu0evmmc6U8P0A7ayWH4qikEpY3LqllRvWN+H6AbbrETV1YpaJ/notQoQQQqyq8wbpPXv2cM89\n9wCVF/DPfOYzfOYzn+GBBx7gb/7mb/iDP/gDSqUSH//4x5mbm+OWW27hxz/+MfF4/IqcvBDi0nV0\nVFrcnW+7gPHZPLOlWRrrdXR96es/GusNbNuhf/oo//KCSXXCpKU2wd/+v9/hS5/+DFMTlYuz127v\n4b3/9/10blm6/ELTFBQlxPNDvCWC9CmGrmFIdw4hhHjDnTdI33XXXQRBcN4dnArXQohry6ZNlvSJ\nvgCZQpmyV6Qhdv6LqNtbDUrlIgOz/XztL57m0f/5Vxw7dgyANd0b2fKuX6RxexNrNkSX3Yfnh2iK\njnaeftFCCCGuHpela4cQQlytwjCkZHs4nk8QVOqddU3F1DUi5rkviY4X4AUemvr63YicyV5+8Bdf\nYX7kBADr1q3j85//PLfdfS9///gxXh4/SN9AjnVrzSW7G+XzAZYWJW4t0S9PCCHEVUeCtBDiLSMI\nQrJFm3zB5/hojvHZPKahkU5GaKqN0lgTJRmLoJ4RmmMRHVM3KDtLl8H8/OfQUdfHI//1B/QdOApA\nPJXm1z/6Sf7Tf/wPJONRfD/gvbd1UX7c5bXpVznaX6JrjYlhnD5OGIacGHNpjnXR3ZpedA5CCCGu\nThKkhRBvGbmiTd+JHE+/coLp/CxZZw4VDUOziKoJNq6p544dLTSk4ws1yPXVcRJmnELx3PZHY/0j\n/PSb/4fi6AEAoskYuz54L4met9PVfjv+yco4TVPpaEpx3y1dKM8pDGUHOXBonIY6jVhURdcUJqY8\nzCBFS3UDG9trpLxDCCGuARKkhRBvCSXbZSZj89i+AXrnDlMMZ6mr0fADyJcDhjIwc7SV0ekc776l\nk41r6lBVhbrqGIlInNnC6etFZkem+V9f/hGjB18EQhTNZN1tv8BH/uBdRJMxXny5SLZUZC5XpjpZ\nqYk2dI2e9hoSsQg/2xtnaLqB+ewMs/NlHN8hbbXQWNPMzZtbiEUNWZEWQohrgARpIcRbQtnxeGzf\nEEPZQXxjjh091qKwWrYD+gdGeHk8g/+sTzJm0t6QorkmSXW0itemQoaPjfLof/8+R557FULQDJ14\nx9v55Jfvo6o2tbCveFSl7BWZzpboaKpeOE40YtBWn+T+O7s5NtzA8ESOYtml5HjUVsXY1FFLU71J\ndIlabSGEEFcfebUWQrzpBUHIyFSOvolJZpwRtm2yzlnxtSIqm9ZHONKX5+hUH48+H+FDd28ilbBI\nBAVe+bt/4Pt7niEMQ1RN5Zb33sE9H343L79WQ1Xt4uPFYiqluSLT82U8P8BUT7eqq9RkR9m0VqOr\nLYnnge+DpkHEVEjGzGXb3gkhhLi6SJAWQrzp+UHA0ESOjF0p5zDNpcsmFEWhZ22EA4emODQyyMOP\nzPD8j77Hd7/7XXzfR1FVNu/awS2/9Ha2XLcNgDsbzt2Ppio4SoDnBfhBACzu+ayqClXxCGEY4noB\nQRiiKgqmIb2hhRDiWiJBWgjxphcEIbO5MkW/QEvi/Ku9mqbQnCry93/xFb6x9wUC30fTNO7efT9N\nt9xBTpsmWXv+fbheiK4YREx9yTZ3pygSnoUQ4pomQVoIcU1zXJ/5fJlE1CQaWTq4KoqC7bo4vo1p\nLB9s5yZn+dn3fsTz//wUvuejKAr37P5F/vq//CfqGtv42399mUf2/YzRiQJr1ix/Trl8QIMeI520\nUM8TpIUQQlzbJEgLIa5JE7N5Xjg8Qv9ohmypQEQ3qU5YNNUkuG1rG3Wp+MJ9VVUhGtHRFQPXO7cf\n9MzoFH/7n3/EiQPPLgTo7XfdSMuN97L75vfRvmYtVkTnvbeu50hfP6/N9jI8YtPWcu5glZk5D9+x\nqK5O01QbQ5d6ZyGEeNOSIC2EuOYMT2b43z9/jaOTA0wVJ1B1D89T0BWTulgdR05Mc8fWNdy8uQ1F\nUdDUykV8hhrBcUoL+5kYHOdf//ZR9v/0BYIgQFEU3nb3Tt75kffQ1NnC3pcLTGezTMzl6WiqprMp\nzc3rGvCOBEyO55nPluloM4nHVDRNIZvzGRhy6Yz3cMOGZpIxU9rYCSHEm5gEaSHENWU2W+Sfnunl\n5dHDqLF5rl9nYVlRgiCkbIcMj07wwvAUuXKeTMHm3pvWoSgKiahBRDMplgNG+07w0//vEV5+fB9h\nGIKiQu2ttN74btbc2kRTZ+VYVkSh7NnkSvbC8Te2pTB0lQk7zrHJEY4encALy6haiKFYtMXX05Zu\nYPu6WuKW8cZ8k4QQQlwREqSFeIMFQVhpqaYq570wTVTGaP/0xeMcHOkjMOfZsi66sOKrqgqxqMKG\n7ijTaZdDfa+hqwYtdUm2dTWypiFFeXySH/31Nxk9+CpQ6QN907tv4+5fu5eH/6GOj3988fGsiIpd\nsskXnUW3dzcleffGrTz7ag39ox3M5xxs1yFhxehpq2HnpgYSMWNhOqIQQog3JwnSQlwBQRDiej6O\n5+MH4UJ4DoEggDAEVa20TdNUBV1T0TQV/eQfUTGfK9M3OsdEcZSbrostWzZRV2PgOCGvnThC1b4o\ng0df4b987Sv89Cc/AUA3DW593x3c9aF3Ud2QBmDr1nP3Yxoqdt6lYLvnbEslLN65s4uS4+G4Htmi\nQyxioGsqMcvAkqEqQgjxpiev9EJcJmEYYrs+tuPheAGOA65bGb5xKjwDKCgoysn/VkJ0PURVA3Qd\ndB1MQyFi6Fim/pavtz0+Mc9McZbqagXjPN03AJobDQ4+u4+v/PWfM3bsMADRWJytd7yb9ju3c+st\njYu+n3feee4+HDfEUE1ikaVLNDRNJRE1IWpSnYiiKMhvFYQQ4i1EgrQQl0HJdimWXWwHbBs8DwxN\nQ9c0ohEVRVGWDMVBEOIHAZ4f4NohpaKPooZEIi5WxCVialim/qYrGfD9ylASAF1Tlw2jE7N5cuU8\nqfrlX7p8z+elx/by2MM/ZqzvBABWLMHv/M7v8Duf+Pf8cO8IewYO0j+UY11n5Lznlc36rInFqUvF\nXvff8Fb/kCOEEG9FEqSFWEWeH5AvOZTKAYUCaIqGaWgkrQv7UVNVBVXVFgVl16usas+VfAzDJxr1\nMQ2FRNS85gO17XgUbRfXC5nP2fhBQG1VhIhZWYGPLFEeEYQh2hKh1S7ZPPLdp3n1Zz9lbmIGgGRN\nFRvv3sUNb/8gv/gLd9LR1sxu1SJXdHhp7ADjMZemhqVXm2fnPXzXpC5RTXNNcnX/4UIIId4UJEgL\nsQrCMKRYdinZHvkCeK5C3FqdoGvolWAdhiFlxyOX9dD0ENeziUY04ta12WItV7SZyzq81DvNsROz\nZEp5gsDHMqKkEhG6Wqu4cWMzdanYwgq1rmmoioYfhAv7yc/nefr7j/HU9x+jmC0AUN/eyF0fehc7\n33Uz83k4MWAzOJ7h9q0hnc3V3HN9B4VnyxwdOkTZdmhvMdC009/Dsh3QP+DSkdzEdT0NRMxr+wOL\nEEKIy0OCtBArFAQhmUKZQjGkXAZTN6hOrH7bM0VRiEYMohGDku2SybjYlo/rVab6XUujpvMlh7ms\nww+fOc7x2WEmiqO4YQFNV7CzIeZslKMTDRwZmuWdN3ayuaMeVVUwdBVNVfH8kNmxaX7+dz/l+R8+\nhXvqYsD4Wnbcey+3vHsH69dXLtKMRwPcwCFXdHFcn4ip87Z1TZRsD+OAweDsAPtnZqhKakQtBdeD\nmbmAxkgHm9tbuX590zW/8i+EEOLyWHGQ9jyPT3/60zz88MOMjY3R3NzMhz/8YT772c+iafLmI97c\nToXobC7Ec1WSlol2BbpsRCMGEUOnUHaYd3083yZm6ZUL365ytuORyTs88uxx+mYGGLeP073WpCoZ\nRVEUgiCkUAwYPDHEiyNT5EpFnFvXc/36FqrjEQrjkzz10HcYePElgiAAYM3WrTTsuJe9r/XQuEFB\nPeP/AlWDkADbCRZWsg1d49YtbTTVJHjipSoGJmYouUUcu4yqqKxL1LCuuZ537FxDMnb+OmohhBBv\nXSsO0l/4whf45je/yXe/+122bdvGgQMHeOCBB4hEInzqU59ajXMU4qp0Zoj2XZWqWOSKdmxQVYVk\nLELZ8chkHFzXw/cDquJX9jwuVtnxeO7gGH3Tw4yXj7N5QwQrcjr5qqpCMqGxZYPFiVGH18Zew3rR\n4NUXn+a/ffMveeLnj5+8n8oN77yZu371XbR0t1Ue/D/g3nsXH09TFQICXC+oDF85ydA11rXW0Fyb\n4MRUjpmMzXzORlFgbUuKlro4yei1WTYjhBDiylhxkN6zZw/vf//7ec973gPAmjVreO9738sLL7yw\n4pMT4mp1dohOXuEQfSbL1DE0lXzJJgwDwL7iYToIQoKw0hv7fF03fD8gX3I5dmKOscIQ69ebi0L0\nmRRFobEW9v7oMR79yp+QmRwDIGJF6bl5Fzvvv41tb2ta9Jgbbzx3P44boqsGpq4SnrXt1IeRDe0m\nbrOP51fGhOuaek2VygghhHhjrDhI7969my9/+cscOXKEDRs2cOjQIR577DEefPDB1Tg/Ia46YXj1\nhOhTNE0lGbXIFstAQIhN6gqE6bLjUXY8XC/A90+dC+iagnWy88aZ5+B4PoPjOWbLs5hRl0TcWnK/\nmel5nv7+Yzz7T08uXECYTNfx6w/8X3zkgd/kkb2j9GZfIZvzqUqeDrzr1i2xr6xPlZmmLhVf9t+h\nqgoRU0eKOIQQQlwMJTzzd52X6MEHH+RLX/oSuq7jeR6f+tSn+NznPrfoPplMZuHr3t7elR5SiDdM\nyfHIFUIcWyce0d/wEH2mIAwplF0M0yceg4R1ec4vDEMKZY+yE1IowomZErM5m4LtYugq8YhGKqHR\n3RIjHY9g6JVV55Lj8cyhWfae6MNMT9JQu3i/kwNj7PvR8xx97hCBX6l/buxqYdNdN6PXX8dNbVt4\nx44m9vVmeXlkjEl/gHWdleE1S34/Ajg2oNCgdnN7Txsb2uNEZeKgEEKIi9DT07PwdSqVWrRtxe8o\nf/7nf863v/1tHn74YbZs2cL+/fv53d/9XTo7O/mt3/qtle5eiKuK5weUnYByWbvqQjSAqijELYOi\nrVAoeoC36mE6DEPyZY9CEUamHY6MzjPvzpNxZyn7ZXTVQMfEnLA4PJJmc3sV2zqqiVk6YVgJ+wE+\npxphBEHA8f297Hv0eUaODAGVso6eGzdx3btvormnDVA42GsznSuQL3tsW5tkOutgZ0ocHx6nvSXE\nipx9njA0qhALa6m1qmmuiaKrMm5dCCHE6llxkP7TP/1TPvWpT/HBD34QgC1btjA4OMgXv/jFZYP0\nzp07z7lt7969y24T4lJcjufUfL7MfCZAxVh2bPTVIAxDskWbiBWQSmqr2nkiX3LI5DwGRwscmR1g\n3uqDqgLr6yzi8RiuG1K2Q+YzDjPzkwwUEsRzUe5/2wY0TWWsfJxBJ0Mk4dH/3As8/f3HmRmdAiAS\ns6juvp2PPngPNc11i45bcktE3Ti1zZ1c19NMd0+BHz5znJHsKEO5fmoNhWRCJWop2E7IxKRHbaKK\n7V07ePvWTjpaI9RURVf8oUJeq8Rqk+eUuBzkebV6zqyqONuKg3QYhqhnrfKoqsoqVIwIcVUp2S6l\ncoDnKpelT/RqUhSFZDRCtlhG130M3cM6T0mD7wc4no8fVC4YVBUFTVMxdW1R1wrfDyjbHiOTRZ5/\nbZDXZg4SS5Xo6jij1jkKKaCxXieT9Tnaf4Ty8SLRiMa9N3Yz2H+EJ/7Hf+fY3qdwbQeAmqZaNt55\nD1br7fzs51H2vAzdhcU1z/GYSmG6TL7kEo0Y1FVbvOfWdbzwWoL0ZA2TpXHm80VGvSKmFqE+WkdT\ndRM3bWinobYyLfFq+w2CEEKIa9uKg/Qv/dIv8aUvfYm1a9eyefNm9u/fz9e//nU+8pGPrMb5CXFV\nCILK5MJCAeLW1d+rGSoX0MUiJvm8ja45GJp6To9r/+RIc9sNcBzw/UpJhKKAroNpgqmrxCwDQ9co\nOR7FEhwamORY5hhGPM/aNct/P1JVGts3RXnxwAAP/6/9fP7/+QkHX9qzsL3nhk28/f672HzrdvqP\nq/T1necfpCic2XYjGYsQAnfsaKV7sobpbCvFsku2aGOZOs3pJM21VViWQjxWKXkRQgghVtOKg/TX\nv/51qqqq+PjHP87ExATNzc187GMf49Of/vRqnJ8QV4WS7VIsga5q19SUO9PQcH2dfMFD1x2qE6dX\njm3HI19ymJ71GBjPkis6eL6/MOylLhUjFbcwjADbrQx8cVyfmXmb0bl5ZsuTXNdz/s4g2ZkMz//w\nKZ7+wc/JzVZ+NRaNxdly8ztpunUjd72zc+Hx69ZV/szOntsLGuDUUcKTaVpVFVLxCKriYBhR6tNR\nPA9UpfJhIQgDLAviMeWK9/gWQgjx1rDiIB2Px/nqV7/KV7/61dU4HyGuSrbrY9uQuMyrmkEQ4vkB\nISHKyeioqcqKpiXGLZNMIaBQDNA1h0TUxHF95nM2T788ztET02TcWQpuHtd3Kj2XtQi10Tpa0zVs\n7mik2rUo2w6263BiKkfGniVdraDr54bTMAwZPNTPU99/nJcffxHfq/TFS7c0sv7Wd/DhD34UL0jy\n0uQ+MlmP6tTiDyZL9YKGSj9oTa30zD5FURSq4hEihodlenh+ZfCKooCuVT5IxC0ZqiKEEOLykD5Q\nQrwO2/Eo2yEqKvplGP/t+wElx8PzfTw/xPNOl1cAqCoYuoKhqxi6RsS4+B/bhGWSLZYxDA9DU5nL\nlfinp4/TNznKcL6fWMIjVa2RMBRcr3Kx4MGZAYaytYzMrWVDSzMb2+opugEj01kyTobq9OIAbBfL\n7P/ZHp79xyc4cfRk9w1VYevb38bt99/F2u0beOGlItMFn01tMcZyrRwf6mX7ZgtNOx10l+oFHYYh\ns/M+HVaalrqqc7ZHTJ2IqROG4cIYcE1VZBVaCCHEZSVBWojXYbs+jlMJa6spCEKKtkPJrqx2Ow6E\noYKuViYDniph8E+uUBuGj2n6REz3nGEnvh9gez7eqQsGT65oq+rJKX26hmUYFIsunl/kiZdGODQ2\nwJRznPU9JsnEuYNR1rSGjE1meGX8RYruRvwgoK0mje0EOJ7Lqc8UJ3qHeO4fn2TfT5/HLtkAWIk4\nt73/Dm59/y5qmk43i66p1sg4GRLxdjpqWihMZOkfnKKn6/xdReYyPoobpakxTWtdctn7VaYSSngW\nQghxZUiQFuI8giDEcX1cF+Lx1auN9vyAXNGmUAyxbTB1nYSloy3T57hS8uFTLnkUiwHRqEvU8ohb\nJrbrMTlfYHgix9R8EccNAIWqmEVdKkZzbQIrohIxFcqOx8DQJPv7hhkvHWfrpghRa+ljappCW7NB\ndZXG4d4jKMMadtnHc1TKhTJ7/uVJDj/+LMNHBhce07m1m0TnLho33cB97zm3DCad0pgey5Ir2dxz\nQwfZJ8ocns8xeMKmvcVYsgQjX/DpH/Bpj3expavuklbkhRBCiMtB3pGEOA/H87EdMDRt1coEHNcn\nV7IpFCDwVaqikdet4VVVBVPVMQ0d1/cplVxKZY8hZ4pX+iYYnp4n781TCvKEoY+qaFh6jIReRcpK\n01GfZn1bHaHi8szLo/TN99LTYywbos+UiKv0dOkc6X2Vod5eXnnyx7yy51E8uwxANBFj57230LL9\nDvpGW9i7Fw6OQSZbqXc+s1TDNFW8wEdTFZpqLW7d0o5/0Gdwvo+D2TnaWgziMZWIqeL7ITNzPkMj\nHp2JDWxuXcN1PQ2YxrVzsacQQog3NwnSQpyH61VWoy+kU0e2UGZyPs98oYyigELlIsH6VJz6VBxD\n1yrt5so22Sxoik4yevGt9AxNQ7NUjozM89hLvYyVBykpU9TV6FTFNXS9Mhq7WJpjODfEUMFiprSG\nsdkW6lNxTkzNU1RzVCXPrTVeil2yOfzkHp78wROM9Z5efW7o7mTXL+9i5ztuxIhU/h03ATU1le1L\ndt5QKvXOYQiJqMnW7jRR0+C5Q1EmCpOMD49R9IoElCFUSZrVdCda6W5s5h03rrlmWg8KIYR4a5Ag\nLcR5eH6A70NUX3rltux4HB6epHdkmrlinpyToeQWCKm0a9NUg4SZpMpMUleVoCGdoDZWja5EVhQK\nx+czPHnwOAOFoyiRDN0dBomYiqmf/pGuTVf+zuV9hkePMjszhTJcy3huhli9Qq7koC/RWxoqYXf4\n8AAvPPIM+3/2AuVCZfXZiFqs3XE3PdfvRmt32LbDXAjRp3R3L3/elVbQIUEYYugaVfEI69ZAXfV6\nXj1ew3RmDfmyTdG20VSN6niMzqYUW7rSVMXNVa9TF0IIIVZC3pWEWEYYhgRBSBCwZNg8emKKF3tH\nOJE5wWhhBF8pUZXQiKVUVKXSecPzQobyAaVZsCbiJNRGaowm3tbVxob2hoUuIK7vMzGXZSqbJ1Mo\nAaAqCsmYRX1VgoZUEvNkbXDZcXn20CBDuX6sZIE1rVFcz8d2QsDF1BfXJicTGht7LEbHsxwcmaVQ\ndmiv8cgXDAzNIREzF2qzc7NZ9v74Ofb86BkmBsYW9tGxpYtb37eL9h076D1moRfb8INhZucdIqa/\naMV+qa4bp5TKIaYWWahzNg2N6oSFrjncFGvAccDzoFh2MXSVqKURi0LMMojJQBUhhBBXGQnSQizD\nD0LcMwZ8nGnv0RPsOdbPsfnDmNEy69YZJBOxZffleQHjUyWGBoYZc6fJOhkGJue4aX0b07kCh4fH\nmSpOkXczFLw8UDluVIuRMFKkImk6G+rY1N7E8NQsA9NjlJRJNrXEKm3edAXH8VAIURUfXVtciqIq\nCm3NJoPDNqPZGWJFlXRWw9RVFGwG9x9mz4+e5bVnXyEIAgCsZJKbd9/Mje++jeauVqBy0ePASBHF\n84kqDQyPDFCbvvAhNTNzHtWRalrrT3fe0DSVVMIiGvErpTR+QDo0URQFQ1OxTH1FfbSFEEKIy0WC\ntBDL8E+WdZzZSSMMQ559bYj9x49zZO4gHWtU6mvPbR13tjBUSMYM1neZeG7I4Mgxpkdm2NN7HC1S\nxtYnMSyHqqRGY0xFUU62xyvlGC+McnxaZSTfxNHRVuZzDlPlMZqazIX+y6qqous6juOhaj6qqiz5\nAaChzmBoRmW2ME3va9Mc7O2l9+l9FDK5hf1suX0HRtNt1HVvY/d9ZwVyVaGmRsPxAxJaPYFfpH9w\nim0bX79MpVgMyOdUNjTX09Nac85209DkQkIhhBDXFAnSQizD8wM8rzLY45SjJ6Z5aeA4R+ZfUJWk\nnQAAHfBJREFUobtLJ526sODneSGuraPrClZEYX13hOf2TXBi5jBGtMTGriQbu2o5PQi7ojoFYGA7\nAeOT4xyYHGNmLEnRGKa9a3EY1VUVX1GxnQBV8bHMc4N04JUoHT3AxME9HB2bXri9fk0TN+6+jfr1\nt/Dq0RR79wIDMJ85t/NGPKriW2W662qJzekM5YsMjTi0txjLdjYp2wGHj9m0xteyqaOWZOz8faOF\nEEKIa4EEaSGW4Z+sjzZPXmiYLznsOTrEsfmjrF2jXXCIDoIQP4AwVBeGhYxO2Ph6FqN6HCWSZ65c\nT98YdDXVLhlGI6ZKR5sJ2PQOncBTZ+gb9+luqSdmnl4NNg0N2wlwvRBdq5R4eK7HsRcPcuCx5zny\n/Mv4ngeAGjFo3L6Zt7/nTtbtWEc8phKNGGy/4fydNyIRFRSfeFxha1UL6pjD+Ewfr+ULdLSbxGOL\nA3y+ENDbb1NvdrC5uZPbtrZdcCmIEEIIcTWTIC3EMk61aTsVbPccHWYwM0g0YVNbc+ErqkEAvqeg\nnFxtzhU8xqZLzDmTtKyxCRWFqekJmKvcv7v53JXpUzRNIVUNs36RiWIZRkO6WxoWwrSCcrLEw2W8\nt5cjT+/j4JN7KeUKlR0oCunObqKb19J8Ux2EKbT6OsKgMhrc0AN0TT1v5w1DVwhwCcOAzuYk8XgH\nQ5NVjORGOHxkGFW3iUQUTEOhWArwbJOmeBddte3svmUt1UtMURRCCCGuRRKkhbgAhbLDwMQM44UT\n7Nh6cWUJQQCBr3Cq1Hpi2iXjTpNMlzEjAaBSXwdTMxOo8xpxy6QpvXSP5yCotJCrTmmEeoGJ4gTq\nuMqG1kZ0TWN2bIJXn3yeV594nszk6dKNxs5Wtt99M9vuvIn+8Qj9U6MY5gzZQo7pbIH2hhSep+J5\nPrqmnrfzhuOGGJpJKmERj2pUp5P0tNXQe6Ka/vFmyl4Z2y9j+zb10SiJqiSdTWlu3tpAbcpa6FQi\nhBBCXOskSAuxjJBKCzuA/rFZpouTpFIKpnlxEw7DMCQMKhcQel7IfNal6OVoSbkL94mYKrXpSpg2\np0wSlkkieu7KraJUTiwMFWrTOlMzBcanRxh57kXGD7zKWO/xhfvG0ynWvG0nd/3ybTStbVu4vdF3\nmc6mmJvPY8TKlL0yRdtF0yL4QUgYhued4pgvBMSNBHVVMeJRk1hcwTINqqua2LK2gWzBoWR7FMoO\n8ahBW0OcZFwlHjWIRqSFnRBCiDcPCdJCvA4F6B+fYao0SeuaS/+RUVCYz3kUvTxm1EXTw0Xbo5ZK\nPOEzVZzAGtfZvKYR7aw2dhFTwVBNCnmPscE+xvYeZ/rQCASVfZlWhPU3X8+WXTfT0LOWF/eplFgc\nXhvrNUYn4mRnEjglGztqUyg7VMUsPD/ED8KFWu6zhWHI7LzP5upaGqoT6DokYxGSsQhlxyMe80hX\nWwsr55paqduORQxpYSeEEOJNR4K0EK/Ddj1mswWKXo5U1cXX94ZAiAIKlMo+tl/GivtL3rc6pTHh\nlJguzDE6G6W9Pr2wzSk7DL90gCOPvMB0/6uE3sl9qArJdW1033gTu+7dRTQWZWgIXnjB5fnnQ04M\nBfyCotHZWbm7pqp0thkUiw0Mzbtk7CKFehdNUwl8nyAIYZlrAccmPCyqqE+mSEQtNMPD0DVUVVkY\nmnJqkI2iKKjqxa3eCyGEENcSCdJCvI75fImCVyAaXXkwtJ0QL3SIGcGS2xWgplpncnKO8bkkNfEI\nwy8f5blH9zLy6ss4ZXvhvlVrG2m5qZPG6zrJujoxapkrO0RjUdasAT9QOTHiMzQUcPx4JRmfCtN1\nNQbr1oaUD7dwfHqEmRkPtQ18IAgDlkrSubzP6FjI1roN3NDThhd4JCywzhrbrSjKQn9rIYQQ4s1M\ngrQQryNbsrH9ElHr0sKhooCqBoRBiO+HBGGAqoXL3n9+LqQ8dIIX9r3AvxwewC2dDs8t69fSsPFt\nhC0dmC0l0nWVbSknYGZ2nulsiqbqJKqq0tmh4gU+E50hd9997nGaGgwKxYDp6WZmpzx6B2wa6itj\nuc8UhiGT0z7DIz7dqY1c37WGdCKKEQmwIrqsOgshhHjLWpUgPTY2xh/+4R/y6KOPksvl6Orq4q/+\n6q/YtWvXauxeiDeEpipoGhTLLo7vYkQuLTCqioKigB+AqlZqpcOzcnTgBcwcGWd073FO7BkiOGPl\nOd7QTsHYyc27d7Jxey1VKZ+XD5WZyQ5QlXbQtBDTVNE0l6JbJFMskU7EURSF1jaodMYLObulnqoo\nNDcYNNYpJIIWIuWAvr5xJmdsUvEAw1Bw3ZBcPsAkyeZ0D9s62ljfWoeqByTiCjG5eFAIIcRb2IqD\n9Pz8PLfffju7du3ikUceob6+nv7+fhoaGlbj/IR4w2iqiqpW6pAVRalk0UugqqBqAZ5TGbGtKCph\noOA7HlOvjjK2b5CJA8O4RWfhMWZdNanNa+i66W001W0jM1W1sKpcLKlUJyMUsymyc87CqnQsplIo\n5JnLF0kn4pVjo9DeHhKEIeoSnTgcN6SlNsn2hg5qUzF6R5rw1RyGD77vEVcN2qoTNFSl2bymkcZ0\nAlUPSCYqFxnKarQQQoi3shUH6a985Su0trbyne98Z+G2jo6Ole5WiDfcqRVpqATSYAVBWtNPtsFz\ny8wdOsKxvpeYOzKEb3sL90u0VNN8fQdOXSfb356mWArIZQyODZa4acvpvtK6Bq3NGtlCLVPZHPGk\nixkJiEU1MpkCuVJ5oYWdolRa+C1T9kwuH5AyU7TXp9nWXcf2njoK5TKEGoWyi2XoVCeiVCcsDEMh\nEgmJRVWSUVO6cAghhHjLW3GQ/sEPfsDu3bv50Ic+xOOPP05LSwsf/ehH+fjHP74a5yfEG0bTVDQN\nQkIURa10s7gExWyB/T9/iVd+foD+A4cIvNPhOdVZS/P1HTRdt4ZkczUA0zOVbYW8yuBImYkjRdKW\nCxh0doJuKCSSIXXpCO5sAzPjHvUtRXQjRNNDHN+h5LqLRocvxQ9C5jI+G5L1tNaliRg6iYRGZzxK\nxNDx/MqIdKiEd01TsUz9nIsLhRBCiLeqFb8j9vf385d/+Zf8/u//Pg8++CD79+/nE5/4BICEaXFN\nO7UibZk6lmYxbV9ckO47cJSfPPRD+l46SnAqkSoK6Y4uYj0tbHhHE/G6xDmPq6ut/F1fD4qmYAUl\n3naDTX11pR5ZVRR0PaS1WaVcThEUA6bGxqlvLmIaCk7gUCo7i4P0EhUYYxMuKb2O5lTNyR7SPglT\nIxWvDE451cYOkNVnIYQQYglKGJ592dPFMU2Tm266iaeeemrhtj/+4z/m+9//PocOHVq4LZPJLHzd\n29u7kkMKccVkig6T0yFP945xtPAym3tCzjP0b5HhV4/z91/6W1RNJdHSzY47e2jq2cZMMcFYaZSq\nxilMyzvvPgpFmJ+sZktbLS3p+MLtYQi2A6W8wdiUQsbJUlSn0KN5jDBOR3UDNYkojudjGAGWqaIq\np8NwrgBj4zpd0c3s7GgjHlFRDZf6WkjFDTSpfRZCCCEA6OnpWfg6lUot2rbiFemWlhY2b9686LaN\nGzcyNDS00l0L8YbTFIWYpRDVTTRMHNcmcv6KiQWtGzu48YO/QpDYxosHminG58nbAYmYR9SJUypk\nXzdIGzpY8RK2u/h+igKGAWHMo7HeRJ2uQnN0pmenMfQQN1H5fHzqY7Jyckk6DGE2AzMzOu2RdfTU\n11EdsyjYJeLRAFPXJEQLIYQQF2jFQfr222/n8OHDi247evQonacmPyxh586d59y2d+/eZbcJcSlW\n4zlVLLvMzLvMM0huIEtVKktD3YX/2HT8u8qFt7X/Au94R4piKWR+Vsc9nmCsXCYZN88ZFX6mysqz\nhxVP0tLSwtk1Go4bYtshzQ0GsxmPvqFasqUS2ZxGwophmAGWpWCaOsVSSCbnYykpbl27juvWdrGt\nowXb9pgtZWhrVVnTWIVpLDPWUADyWiVWnzynxOUgz6vVc2ZVxdlWHKQ/+clPctttt/GFL3yBD37w\ng+zfv59vfOMbfPGLX1zproV4w5mGhmm6NKWT1E7UMzE7e1FB+pTubtA0BUMPicdDUnGTrFtNZs6l\npt5e9nGVrnsBQbh0CzvTONWWw6VWNbHLceanmmmO1RMNPbKFeUq2h2/oWFqMhkQ1jclatnW20lZX\nubixYNtEzJCopUmIFkIIIS7CioP0zp07+cEPfsCDDz7In/zJn9DR0cHnP/95fvu3f3s1zk+IN5Su\nqRi6Qlt9FTXHa+ifV3CcENO8uPKHdesqf5umgh/4NNYbZPK1jGezJKoq7euWowCcp4WdaapAgKI6\n+GFIW00Nd2/ahqpAzs1hRVQMXSMZjVBXlaA2WRnWEgQhBdtG0X2smEIyeoE1K0IIIYQAVmmy4X33\n3cd99923GrsS4qpjGhrJeEhTTYp0po7p2Vlami5top+qKpgGVKd9auYilGYbmB73aGovoi7TGOPU\nqnR4nokwpqmiqAFOWCJuRYgYGpap05GOUVcVRz1j534Q4LgejucRiYREdEgmIuiarEYLIYQQF0Ma\nwgrxOiKGRiTi0V6fonmyhcMTkzQ16Jc81c8wFHw/pLNdpVBIYReLzE4G1DWVl7x/5YJBZakOdosU\nSyEJo4q2umpqa3WCwAMVsqXywuMrPbErFyomk2CZGmGoYhoBurS4E0IIIS6KBGkhXoeha5iGQmt9\nkpZ0HSfyNYxPZi95VRogElEIw5DutTrlIw1MFxxmp8Jz6qUrbZxVdE1De50V48kpl7poG2sbaklY\nBtG4QtwyK/XVQUgYVla3dU1B1yor1rqmMp8voetItw4hhBDiIkmQFuICRAydSMRl85oGxufXcnD8\nReprdQzj0sKnoihYFqTTIT1dJmF/KzPZEWZCqKm3F3pVu26ArhpY5vlD++y8h1OyaKptoam2iqoq\nhap4fGEKYRieDtLKGRcshicvYtRUGboihBBCXCx55xTiAlimTtSCulScroYGGq02+gZsVjLPSFEU\nIhGFhgaFjetMas1WvFw148MxXKfyo2nbIREtQuw8QTqX9xke8ViT6GF9ayM1KYOYpS0a5a0oCqqq\nLArRUBkTrusSooUQQohLIe+eQlwAVVUqYToKO7qbWVfbjVdKMDZx/oEqF7LfqKXQ2KCybZNBU7wV\ny2tibCjG3LRJNhcSMxKkEtFzHhuGIZPTLn0DHmuim1hb18ymzjSJmEbcurAOHJ4foKpIfbQQQghx\nCaS0Q4gLFLMMyo5Huaxxy6YOcuUiB8f2k4j7VCUvvePFqZXp+jqFeDygf6CasckYc9NzTGezRGpi\nFNMa+B4K4AdQKAbMZVzMMEVHtIMtbe3cuqWVRMy44BAN4Ho+piVBWgghhLgUEqSFuECKohCNGJQs\nl1olxvXdayh7JY72vcqGdZBMrKx9nK4rJBMqmzeYtDZr7NmvEDHbaTRSlGchE5Qq54FCVE/QHknR\nlKrlup4mulvSxCLmRQ1UCcMQL/BJmpXOJGJ5r71WZnCw8nUuV5lWOT19ustKRwds2mS9EacmhBDi\nDSRBWoiLEI3oRC2Xctln+9pmCmWHcDDkyLFDrO9mRSvTUAnrpgmqGtJYE2Nj9zauX9dKpuBQKDsE\nASgq1KViNKUTNNckiRjGJU0kdDwfw6j0yT67dlosNjgIu3efCsrnBuZHHy2zadOVPSchhBBvPAnS\nQlyEU6vS5ahLseRyx9a1qIqCMqhwtO8Q7a0hjfUr+7Eq2wEDwx49tZu4e/s6NrY3nGxfd3oki3ry\n4sGVsB0PKyar0UIIIcSlkiAtxEWKRnTsqIfrBhRtl9u3dKKqKsaAybHRI8xnSnR1mJfUGq9YCjjc\na9Ma66KnsZUNbfUAJ0Pz6q0ae35AQIAVUYiY8jIghBBCXAp5BxXiIimKQjIWwffLzGc8PF/jts0d\nNKWTVB1O0D/bx4FXR2hp0mms19G0CwvA0zMeAyc8OhLr2drSxd071l22kouy4xGJyGq0EEIIsRIS\npIW4BLqmEo8aeL5LPudQFbPoaq6hoTrBM4fi9E80MjIzxL7xaWrTGqmkSjKhYZqLh6GUyiHZnM/k\ntAdunPWpTWxqaeeu7V2Xrbez5wd4gUfCgmjk0qczCiGEEG91EqSFuETRiIHrBbiuT6HskIxFSERN\n3nXDekZnmnjleAND0zPMlKaYzmXpdzKomoeiKiiA54foWCTNNO1WPS2NjVzX3UJ3S+1lvfivUHaI\nxSrt/FZaZy2EEEK8lUmQFmIFkjETzy8z7/oUbZfYyRXeltoqWmqrmMuVGJ6eZ3I+z9R8gbxdpHLJ\nYIiqaFTH4jRUJ2ipqWJtU81lnzBYsl1ULSBqKcQsWY0WQgghVkKCtBArUKmXNgkCm0zWpVAOFw1E\nSSejpJOVqYRhGFIou0BIGFYuILyY4SkrFQQhZdcllYJE9Mod982go6PS4g4gl8sBkEwmF20XQgjx\n1iNBWogVMnSNqngEsMnmPApllgzIiqK8oQG2UHawLIhZOoYuFxlejE2brIU+0Xv3HgRg586db+AZ\nCSGEuBrIXGAhVoFpVMJ0VRL80CNfct7oU1okX7JB9YnHFOJS0iGEEEKsCgnSQqwS09BIJSphOuDq\nCdP5kk2o+KSqFKriEZliKIQQQqwSCdJCrCJDr4TpVBWEike2UCYIwtd/4GVydojWL/PFjEIIIcRb\nyaq+q37xi19EVVU+8YlPrOZuhbimVMK0RXVKwbQCssUytutd0XMIw1BCtBBCCHGZrdrFhs899xzf\n+ta32L59u/zqWLzl6ZpKdcJC1xwMwyefd3Bcn1jEuOwt7hzXp+Q4aHpIVQIJ0UIIIcRlsirvrplM\nhl//9V/n29/+Nul0ejV2KcQ179Qo8eqESbpawYj4ZEtlCmUH3w9W/XhBEJIr2pRcm3giJJ06FeYl\nRAshhBCXw6qsSH/sYx/jAx/4AHfeeSdh+MbVgwpxNYqYOqahYRoupulRLntkSx6aohIxdSLGyn4M\nK/2hPWzXxbIgHqsMW7FM6W4phBBCXE4rfqf91re+RX9/P9/73vcApKxDiCWc6iEdNXXKlkfZ8bCd\nANt2KNkuhq5haBqaqlxQ6YfvB7h+gON6+GGAaUIqBdGIRtwyZfS3EEIIcQUo4QqWkI8cOcIdd9zB\nU089xfr16wG466672LZtG9/4xjcW3TeTySx83dvbe6mHFOJNIQxDHC/A8QJcL8RxFHwfgkAhDBRU\nVUVVTn8wDcIQKv8jCEMUJUDXQ3QdDCPE1FVMXZUyDiGEEGKV9fT0LHydSqUWbVvRivSzzz7L9PQ0\nW7ZsWbjN932efPJJvvnNb1IoFDAMGf4gxNkURSFiaEQMDc8P8CIhflD5E4QBvu/j+wphCIoCugKK\nEqIooKqVP4amomsKhqbKb4KEEEKIN8CKVqQzmQwjIyML/x2GIb/5m7/J+vXrefDBB9m8efOi+55y\ndpoH2Lt3LyBjd8XquZafU54f4PsBIaBQCd6qqiz6WrwxruXnlbg6yXNKXA7yvFo958uwK1qRTqVS\n5+wwFouRTqcXhWghxMXRNSnTEEIIIa52q/5OrSiK/JpZCCGEEEK86a16f6zHHntstXcphBBCCCHE\nVUd+dyyEEEIIIcQlkCAthBBCCCHEJZAgLYQQQgghxCWQIC2EEEIIIcQlkCAthBBCCCHEJZAgLYQQ\nQgghxCWQIC2EEEIIIcQlkCAthBBCCCHEJZAgLYQQQgghxCWQIC2EEEIIIcQlkCAthBBCCCHEJZAg\nLYQQQggh/v/27iYkqreN4/jvjKZOpcfeJi3jr0VaiwrphXQRGRlFIC0jMmpTCwXTVYHUBJHVIgpS\nSIiwIlIpWkSUgaINDmWZFUpBECXETAWijGjFzP2skmfq//Qyjs7Y8/3AIOea23uuxY/h4nDmHESA\nQRoAAACIAIM0AAAAEAEGaQAAACACDNIAAABABBikAQAAgAgwSAMAAAARYJAGAAAAIjDuQbqmpkZr\n166VbdtyuVwqKSlRb29vNHoDAAAA4ta4B+n29naVl5fL6/WqtbVViYmJ2rx5swYGBqLRHwAAABCX\nEse7wd27d8OOr1y5Itu21dnZqe3bt493ewAAACAuRf0a6aGhIYVCIc2aNSvaWwMAAABxI+qDdEVF\nhfLz81VQUBDtrQEAAIC4YRljTLQ2q6qqUlNTkzwej7Kzs8PeGxwcjNbHAAAAAJPOtu2w43FfI/1N\nZWWlmpqa1NbW9sMQDQAAAPxtojJIV1RUqLm5WW1tbcrNzY3GlgAAAEBcG/elHWVlZbp69apu3bql\n5cuXj9VTU1M1Y8aMcTcIAAAAxKNxD9IOh0OWZen7bdxut44cOTKu5gAAAIB4FdUfGwIAAAD/L6J+\n+7s/VV9fr6KiIqWnp8vhcOjdu3c/rBkYGFBpaanS09OVnp6uPXv2cBcQ/FJdXZ1ycnLkdDq1Zs0a\neTyeWLeEKaKjo0MlJSXKysqSw+FQQ0PDD2vcbrcWLlyo6dOnq6ioSH19fTHoFFNFTU2N1q5dK9u2\n5XK5VFJSot7e3h/WkSv8idraWq1atUq2bcu2bRUWFurOnTtha8jUxIr5ID0yMqKtW7fq2LFj/3PN\nrl271NPTo3v37unu3bvq7u5WaWnpJHaJqaaxsVEHDx5UdXW1enp6VFhYqG3btqm/vz/WrWEKGB4e\n1sqVK3Xu3Dk5nU5ZlhX2/qlTp3TmzBmdP39eXV1dcrlcKi4uViAQiFHHiHft7e0qLy+X1+tVa2ur\nEhMTtXnzZg0MDIytIVf4U4sWLdLp06f19OlTPXnyRJs2bdKOHTv07NkzSWRqUpg40dXVZSzLMm/f\nvg2r9/X1GcuyTGdn51jN4/EYy7LMq1evJrtNTBHr1q0z+/fvD6stXbrUHD58OEYdYaqaOXOmaWho\nGDsOhUImIyPDnDhxYqw2MjJiUlNTzYULF2LRIqagQCBgEhISzO3bt40x5ArRM3v2bFNfX0+mJknM\nz0j/itfr1cyZM8OelFhYWKgZM2bI6/XGsDPEqy9fvqi7u1tbtmwJq2/ZskWdnZ0x6gp/izdv3sjv\n94flKyUlRRs2bCBf+G1DQ0MKhUKaNWuWJHKF8QsGg7p+/bpGR0e1YcMGMjVJovZAloni8/k0b968\nsJplWXK5XPL5fDHqCvHs06dPCgaDmj9/flidzCAavmXo3/L1/v37WLSEKaiiokL5+fljJ4nIFSL1\n4sULFRQU6PPnz3I6nWpqalJeXt7YsEymJtaEnJGurq6Ww+H46aujo2MiPhoAYub7a6mBf1NVVaXO\nzk7duHHjtzJDrvAzy5Yt0/Pnz/Xo0SOVl5dr586devz48U//h0xFz4Scka6srNSePXt+umbRokW/\ntVdGRoY+fvwYVjPG6MOHD8rIyIi4R/y95s6dq4SEBPn9/rC63+9XZmZmjLrC3+Lb947f71dWVtZY\n3e/3852EX6qsrFRTU5Pa2tqUnZ09VidXiNS0adO0ePFiSVJ+fr66urpUW1s79iwPMjWxJuSM9Jw5\nc5Sbm/vTl9Pp/K29CgoKFAgEwq6H9nq9Gh4eVmFh4US0jykuKSlJq1evVktLS1j9/v37ZAbjlpOT\no4yMjLB8jY6OyuPxkC/8VEVFhRobG9Xa2qrc3Nyw98gVoiUYDCoUCpGpSZLgdrvdsWzA5/Pp9evX\nevnypW7evKni4mINDw8rOTlZTqdT8+bN08OHD3Xt2jXl5+erv79fBw4c0Pr161VWVhbL1hHH0tLS\ndPToUS1YsEBOp1PHjx+Xx+PRpUuXZNt2rNtDnBseHlZfX598Pp8uXryoFStWyLZtff36VbZtKxgM\n6uTJk8rLy1MwGFRVVZX8fr/q6+uVlJQU6/YRh8rKynT58mU1NzcrKytLgUBAgUBAlmUpKSlJlmWR\nK/yxQ4cOKSUlRaFQSP39/Tp79qyuXbum06dPa8mSJWRqMsT6tiFHjx41lmUZy7KMw+EY+/vft5sa\nGBgwu3fvNmlpaSYtLc2UlpaawcHBGHaNqaCurs5kZ2eb5ORks2bNGvPgwYNYt4Qpoq2t7YfvJcuy\nzL59+8bWuN1uk5mZaVJSUszGjRtNb29vDDtGvPs+S99ex44dC1tHrvAn9u7da/755x+TnJxsXC6X\nKS4uNi0tLWFryNTE4hHhAAAAQATi/j7SAAAAQDxikAYAAAAiwCANAAAARIBBGgAAAIgAgzQAAAAQ\nAQZpAAAAIAIM0gAAAEAEGKQBAACACDBIAwAAABH4DwbBWroO/WZ2AAAAAElFTkSuQmCC\n", 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qcaBTFUxG+dMtxEAhv41CCCHOaXqdSrC/GZPOgr25jtBj/jRGRxpxuto4UJaB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\n1jNv2ij8fUwedaaPTaaspp7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jZGVBSkr7f/v76ajJ/pa/vv0QTfW16PV67rvvPh566CGs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\njdNQHSeViGAaLpYJqaoUjlO5VgBVBdOEiKUQjxhYEqKFEEK8BcirmRD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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3608,13 +3252,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "[ 0.0092 0.0187 0.0007]\n" + "[ 0.0099 0.0183 0.0007]\n" ] } ], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15]])\n", - "cmds = [np.array([1.1, .01])]*200\n", + "cmds = [np.array([1.1, .01])] * 200\n", "ukf = run_localization(cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1)\n", "print(ukf.P.diagonal())" @@ -3624,7 +3268,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the EKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." + "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." ] }, { @@ -3633,12 +3277,12 @@ "source": [ "### Steering the Robot\n", "\n", - "While the robot was turning in the example above, we really can't say it was being driven realistically. The velocity and steering angles never changed, which doesn't pose much of a problem for the Kalman filter. We could implement a complicated PID controlled robot simulation, but I will just generate varying steering commands using NumPy's `linspace` method. I'll also add more landmarks as the robot will be travelling much further than in the first example." + "While we turned the robot in the example above, we really can't say it was being driven realistically. The velocity and steering angles never changed, which doesn't pose much of a problem for the Kalman filter. We could implement a complicated PID controlled robot simulation, but I will just generate varying steering commands using NumPy's `linspace` method. I'll also add more landmarks as the robot will be travelling much further than in the first example." ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 50, "metadata": { "collapsed": true }, @@ -3673,7 +3317,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 51, "metadata": { "collapsed": false, "scrolled": true @@ -3683,7 +3327,7 @@ "data": { "image/png": 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px47IxWRnZuPoXQMqv43hP5q4cx1UaN8BKyszVQM9eKyaHyVd/2/Yn4eHB4MG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\ngg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3708,12 +3352,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "You can see that the uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can force some error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further from the landmarks." + "You can see that the uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can incorporate error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further away." ] }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 52, "metadata": { "collapsed": false }, @@ -3722,7 +3366,7 @@ "data": { "image/png": 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3ITBQR3l1FXZOTngHRRLmd/a5lpEjRzJnzhzg7CeCn3/xFZ+uWEn6yWOcjkvh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\njblz52IwGPjyyy/p3bs3zz7+Jyrz8xv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PBbDbFDLTLFR6KzlwrJawvIMmzhNnDNNr1qxh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\n1ddy7LMtFKz/BH9LMwDjxo3joYceYv78+WjaqUOyoigSooUQQgjRIRK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2eaQ3bdoFyNgt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\nOtZWkKUAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3749,7 +3393,7 @@ "source": [ "## Discussion\n", "\n", - "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working. On the other hand, if you have implemented an EKF or linearized Kalman filter you are perhaps bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. As you will see in the next chapter the EKF for the same problems requires some fairly difficult mathematics. In fact, for many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", + "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working because of the need to handle the modular math of angles. On the other hand, if you have implemented an EKF or linearized Kalman filter you are perhaps bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. As you will see in the next chapter the EKF for the same problems requires some fairly difficult mathematics. In fact, for many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", "\n", "However, the advantage of the UKF over the EKF is not only the relative ease of implementation. It is somewhat premature to discuss this because you haven't learned the EKF yet, but the EKF linearizes the problem at one point and passes that point through a linear Kalman filter. In contrast, the UKF takes $2n+1$ samples. Therefore the UKF is almost always more accurate than the EKF, especially when the problem is highly nonlinear. While it is not true that the UKF is guaranteed to always outperform the EKF, in practice it has been shown to perform at least as well, and usually much better than the EKF. \n", "\n", diff --git a/11-Extended-Kalman-Filters.ipynb b/11-Extended-Kalman-Filters.ipynb index b642c91..9bfc970 100644 --- a/11-Extended-Kalman-Filters.ipynb +++ b/11-Extended-Kalman-Filters.ipynb @@ -1536,7 +1536,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a bearing difference of $-358^\\circ$, which will throw off the computation of the Kalman gain. The correct angle difference in this case is $-2^\\circ$. So we will have to write code to correctly compute the bearing residual." + "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a bearing difference of $-358^\\circ$, which will throw off the computation of the Kalman gain. The correct angle difference in this case is $2^\\circ$. So we will have to write code to correctly compute the bearing residual." ] }, { @@ -1547,7 +1547,7 @@ }, "outputs": [], "source": [ - "def residual(a,b):\n", + "def residual(a, b):\n", " \"\"\" compute residual (a-b) between two measurement containing \n", " [range, bearing]. Bearing is normalized to [-pi, pi)\"\"\"\n", " y = a - b\n", diff --git a/code/ekf_internal.py b/code/ekf_internal.py index 6833ea6..147a2d5 100644 --- a/code/ekf_internal.py +++ b/code/ekf_internal.py @@ -204,7 +204,7 @@ def show_radar_chart(): - ax.annotate('$\Theta$ (', xy=(1.2, 1.1), color='b') + ax.annotate('$\Theta$', xy=(1.2, 1.1), color='b') ax.annotate('Aircraft', xy=(2.04,2.), color='b') ax.annotate('altitude', xy=(2.04,1.5), color='k') ax.annotate('X', xy=(1.5, .9)) diff --git a/code/ukf_internal.py b/code/ukf_internal.py index a699363..77d0bfd 100644 --- a/code/ukf_internal.py +++ b/code/ukf_internal.py @@ -381,7 +381,7 @@ def _plot_iscts(pos, sa, sb, N=4): plt.scatter(xs_a, ys_a) plt.scatter(xs_b, ys_b) plt.gca().set_aspect('equal') - plt.show() + def plot_iscts_two_sensors(): pos = np.array([4., 4,]) @@ -401,6 +401,7 @@ def plot_iscts_two_sensors_changed_sensors(): plt.scatter(*sa, s=100) plt.scatter(*sb, s=100) _plot_iscts(pos, sa, sb, N=5) + plt.ylim(3.8, 8.5) if __name__ == '__main__': diff --git a/old-content.ipynb b/old-content.ipynb new file mode 100644 index 0000000..ee913f9 --- /dev/null +++ b/old-content.ipynb @@ -0,0 +1,275 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This contains text and code that I've removed from the book because it is redundant or replaced with what I think of as better material. Maybe you liked it, so I'll save it here for now." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise: Track a target moving in a circle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Change the simulated target movement to move in a circle. Avoid angular nonlinearities by putting the sensors well outside the movement range of the target, and avoid the angles $0^\\circ$ and $180^\\circ$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# your solution here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution\n", + "We have a few choices here. First, if we know the movement of the target we can design our filter's state transition function so that it correctly predicts the circular movement. For example, suppose we were tracking a boat race optically - we would want to take track shape into account with our filter. However, in this chapter we have not been talking about such constrained behavior, so I will not build knowledge of the movement into the filter. So my implementation looks like this." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_circular_target(kf, std_noise, target_pos):\n", + " xs = []\n", + " txs = []\n", + " radius = 100\n", + " for i in range(300):\n", + " target_pos[0] = math.cos(i/10)*radius + randn()*0.0001\n", + " target_pos[1] = math.sin(i/10)*radius + randn()*0.0001\n", + " txs.append((target_pos[0], target_pos[1]))\n", + "\n", + " z = measurement(sa_pos, sb_pos, target_pos)\n", + " z[0] += randn() * std_noise\n", + " z[1] += randn() * std_noise\n", + "\n", + " kf.predict()\n", + " kf.update(z)\n", + " xs.append(kf.x)\n", + "\n", + " xs = np.asarray(xs)\n", + " txs = np.asarray(txs)\n", + "\n", + " plt.plot(xs[:, 0], xs[:, 2])\n", + " plt.plot(txs[: ,0], txs[:, 1], linestyle='-.')\n", + " plt.axis('equal')\n", + " plt.show()\n", + "\n", + "sa_pos = [-240, 200]\n", + "sb_pos = [240, 200]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "np.random.seed(12283)\n", + "std_noise = math.radians(0.5)\n", + "target_pos = [0, 0]\n", + "f = moving_target_filter(target_pos, std_noise, Q=1.1)\n", + "plot_circular_target(f, std_noise, target_pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Discussion\n", + "\n", + "The filter tracks the movement of the target, but never really converges on the track. This is because the filter is modeling a constant velocity target, but the target is anything but constant velocity. As mentioned above we could model the circular behavior by defining the `fx()` function, but then we would have problems when the target is not moving in a circle. Instead, lets tell the filter we are are less sure about our process model by making $\\mathbf{Q}$ larger. Here I have increased the variance from 0.1 to 1.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "np.random.seed(12283)\n", + "std_noise = math.radians(0.5)\n", + "cf = moving_target_filter(target_pos, std_noise, Q=10.)\n", + "target_pos = [0, 0]\n", + "plot_circular_target(cf, std_noise, target_pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The convergence is not perfect, but it is far better. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise: Sensor Position Effects\n", + "\n", + "Is the behavior of the filter invariant for any sensor position? Find a sensor position that produces bad filter behavior." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# your answer here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution\n", + "\n", + "We have already discussed the problem of angles being modal, so causing that problem by putting the sensors at `y=0` would be a trivial solution. However, let's be more subtle than that. We want to create a situation where there are an infinite number of solutions for the sensor readings. We can achieve that whenever the target lies on the straight line between the two sensors. In that case there is no triangulation possible and there is no unique solution. My solution is as follows." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "std_noise = math.radians(0.5)\n", + "sa_pos = [-200, 200]\n", + "sb_pos = [200, -200]\n", + "plt.scatter(*sa_pos, s=200)\n", + "plt.scatter(*sb_pos, s=200)\n", + "target_pos = [0, 0]\n", + "cf = moving_target_filter(target_pos, std_noise, Q=10.)\n", + "plot_circular_target(cf, std_noise, target_pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I put the sensors at the upper left hand side and lower right hand side of the target's movement. We can see how the filter diverges when the target enters the region directly between the two sensors. The state transition always predicts that the target is moving in a straight line. When the target is between the two sensors this straight line movement is well described the bearing measurements from the two sensors so the filter estimate starts to approximate a straight line. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise: Compute Position Errors\n", + "\n", + "The position errors of the filter vary depending on how far away the target is from a sensor. Write a function that computes the distance error due to a bearing error. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# your solution here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Solution\n", + "\n", + "Basic trigonometry gives us this answer." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def distance_error(target_distance, angle_error):\n", + " x = 1 - math.cos(angle_error)\n", + " y = math.sin(angle_error)\n", + " return target_distance*(x**2 + y**2)**.5\n", + "\n", + "d = distance_error(100, math.radians(1.))\n", + "print('\\n\\nError of 1 degree at 100km is {:.3}km'.format(d))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.4.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}