From 1633d9cda9eadd3725a545d6720ee22229afe314 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sat, 13 Jun 2015 20:05:10 -0700 Subject: [PATCH] Added fixed lag section. --- 12_Smoothing.ipynb | 281 +++++++++++++++++++++++++++++-------- code/smoothing_internal.py | 57 ++++++++ 2 files changed, 279 insertions(+), 59 deletions(-) create mode 100644 code/smoothing_internal.py diff --git a/12_Smoothing.ipynb b/12_Smoothing.ipynb index e0b03ef..54c9752 100644 --- a/12_Smoothing.ipynb +++ b/12_Smoothing.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -30,7 +30,7 @@ "@import url('http://fonts.googleapis.com/css?family=Arimo');\n", "\n", " div.cell{\n", - " width: 850px;\n", + " width: 900px;\n", " margin-left: 0% !important;\n", " margin-right: auto;\n", " }\n", @@ -109,7 +109,7 @@ " color: #1d3b84;\n", " font-size: 16pt;\n", " margin-bottom: 0em;\n", - " margin-top: 1.5em;\n", + " margin-top: 0.5em;\n", " display: block;\n", " white-space: nowrap;\n", " }\n", @@ -117,9 +117,6 @@ " font-family: 'Arimo',verdana,arial,sans-serif;\n", " line-height: 125%;\n", " font-size: 120%;\n", - " width:740px;\n", - " margin-left:auto;\n", - " margin-right:auto;\n", " text-align:justify;\n", " text-justify:inter-word;\n", " }\n", @@ -133,6 +130,11 @@ " overflow-y: scroll;\n", " max-height: 50000px;\n", " }\n", + " div.output_wrapper{\n", + " margin-top:0.2em;\n", + " margin-bottom:0.2em;\n", + "}\n", + "\n", " code{\n", " font-size: 70%;\n", " }\n", @@ -235,7 +237,10 @@ " },\n", " displayAlign: 'center', // Change this to 'center' to center equations.\n", " \"HTML-CSS\": {\n", - " scale:85,\n", + " scale:100,\n", + " availableFonts: [\"Neo-Euler\"],\n", + " preferredFont: \"Neo-Euler\",\n", + " webFont: \"Neo-Euler\",\n", " styles: {'.MathJax_Display': {\"margin\": 4}}\n", " }\n", " });\n", @@ -245,7 +250,7 @@ "" ] }, - "execution_count": 1, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -253,6 +258,8 @@ "source": [ "#format the book\n", "%matplotlib inline\n", + "%load_ext autoreload\n", + "%autoreload 2\n", "from __future__ import division, print_function\n", "import book_format\n", "book_format.load_style()" @@ -269,23 +276,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "It has probably struck you by now that the performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement is far from the current track, like so (I'll only consider 1 dimension for simplicity):\n", - "\n", - " 10.1 10.2 9.8 10.1 10.2 10.3 10.1 9.9 10.2 10.0 9.9 12.4" + "It has probably struck you by now that the performance of the Kalman filter is not optimal when you consider future data. For example, suppose we are tracking an aircraft, and the latest measurement deviates far from the current track, like so (I'll only consider 1 dimension for simplicity):" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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mDhw4YLiGUqmEUqk0bI+OjmL37t1IT0/H+vXrcfr0aRw5cgR33XWXhV4iEREREc3UZF1a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\nAerFpb478w7FAAAAAElFTkSuQmCC\n", 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aNWuwbt06bNy4EZmZmZBIJJg7dy4aGhq6eUTg6NGjSElJwZNPPonc3Fzs2rULFy5cwOOP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\nIiIT8b8xfRo2r76mgAAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -295,7 +300,7 @@ "source": [ "import matplotlib.pyplot as plt\n", "\n", - "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, 10.1, 9.9, 10.2, 10.0, 9.9, 12.4]\n", + "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, 10.1, 9.9, 10.2, 10.0, 9.9, 11.4]\n", "plt.plot(data)\n", "plt.show()" ] @@ -321,16 +326,16 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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dhqRbHoSHi3cnj0DEoE1ERESkV99Yg+0/fYX9J7ZDJ2g7PWdkxDjMnvgw/D2DzVwdWRsG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\nDqG1tRWDBw82xsMTEREREVkdo66jrVa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SbQ/BTelp4B6IGLSJiIiIdBqb67Dnhy/w/U97oNGqDe4zPmwK7p7+MHzdA83cHVkbBm0i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\n1iy+DvRT1wXf+DrQM7VajSVLluCVV15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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -347,28 +352,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - " \n", "Given these future measurements we can infer that yes, the aircraft initiated a turn. \n", "\n", - "On the other hand, suppose these are the following measurements.\n", - "\n", - " 9.8 10.2 9.9 10.1 10.0 10.3 9.9 10.1\n", - " \n", - "In this case we are led to conclude that the aircraft did not turn and that the outlying measurement was merely very noisy. " + "On the other hand, suppose these are the following measurements." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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twZOQgH64eD1bsy0vv44xUZMs2CMioo4ZDM4zMjKQmJgIoC2PPCUlBSkpKVi6\ndCk++eQT/Pa3v0VDQwNefPFFVFZWYsKECdizZw/69OmjuUZhYaEgB72lpQUrVqxAUVERPDw8MGLE\nCOzcuROzZs0y0UskIqKuUmjVAZf4hcHJySTTk8xGu9Y5R86JyJoZ/MSdOnUqVCqVwQu0B+wdOXjw\noGB7xYoVWLFiRTe6SERE5iIrt4/Fh+4UGsByikRkO7jyDxERadhbvjkASPzDBdslVTK0Klss1Bsi\nIsMYnBMRkYb28vahgf0t1BPj8XTzgq9XgGZbpVKitEph4AwiIsthcE5ERAAAtVqtE5xLA2w/OAeA\nEK3Rc0XF9Q6OJCKyLAbnREQEAKipq0R9003NtquLO/x8bHcBojuF+gvTc5h3TkTWisE5EREBAGTl\nWvnm/hEQi+zjayJEK3dezpFzIrJS9vGpS0REvSbXDs7tYDJoO+1yisUVRRbqCRGRYQzOiYgIACAv\ns7/JoO1CArQqtlTKoFS2Wqg3REQdY3BOREQAdNNa7GUyKHCrYksff822UtWKkiq5BXtERKSfbS/7\nRmRBKpUS8vLryJNdQJ7sAnKvn4eLsxsqcR0Jd82Eh1ufzi9CZCVUKqXOypn2lNYCACEBEaiuq9Bs\nKyoKdRYoIrIFVTfL8eOxz5Enu4CRg8dj9oTH4OLsaulukZEwOCfqoqbmBlxTXEae/CLyZRdwTXEZ\njc31Osd9f/S/2JPxDRLumol7Rj+AvnfUVyayVuU1JWhpbdZs9/HwgbdnXwv2yPhC/CNw6foZzbai\n/DoQdbcFe0TUfacuH8HXB9ZrKivtz9qG68VX8cz9K+Hh5mnh3pExMDgn6kDVzXLkyS4gX34RebIL\nuFGaD5Va1aVzm5obsD9rG9JO/4CxQ+9BYtw8nQlpRNZE32RQkUhkod6YhvaTAO0nBUTWrL7xJr5J\n+xeyLqXr7MstOosPUv+I5+f+H7w9fS3QOzImBudEaE9RKUSe/ALyZReRJ7+AipqSXl9XqWrFiZz9\nOJGzHyMGjsP0uAUYKB1qhB4TGZesTDvf3L5SWgAgRLvWOYNzshGXrp/B5r3/RPXN8g6PKSy5irXf\n/h4vzn8Tft72sT6Bo2JwTg6pqaURBYpc5Msv4KrsAq7JL+lNUelMH3dvREqHYWDoUDRWq1FSU4gr\npadxs6Fa59hzeT/hXN5PGBg6DEnx8xETGW83NaTJ9mmvDBpqR5NB23VUscXJiV+FZJ2aW5vw/dFN\nOJT9g87MALZ7AAAgAElEQVQ+JydnBPhIUFJ5Q9NWUnkDa75eieXz34REa1Vcsh38RCKHUF1XgTzZ\nReTJcpAvu4ii0rwup6jcKbivVBOMD5QOQ7BfmObRf2ZmJkJ8+2PRAy/gp5yDOHBqG8qqFTrXyJNf\nQN73FyDxD0dS7HzED50CZyeXXr9Got5whOC8vWJL+6RQpaoVpdVyppyRVSosuYr/7v6H3pr8YYED\nsHjmqwjwkeDjH/6My4U/a/ZV3izDmm9/jxfm/h/6SQabs8tkJAzOye6o1Cooyq+3BeO30lTKa4q7\nfR0nsTMiJIMwMHQYBkqHIjJ0aJcmyLk6uyFh5CzcPeJenLl6AvsyU1FYclXnuOKKInyx7338eOIL\nTB39AO4eMYOTecgiWlpbBKNvAOy2ikmIv7Bii7y8kME5WRWlSol9manYdXILVCqlYJ8IIiTFzUfy\nhIVwcW4b1Hluzh/x393v4cyV45rj6hpq8P53b2DZA39AdMRdZu0/9R6Dc7J5zS1NKCi+jDxZWxWV\nfMUlNDTVdfs6nu7eiAwdcisYH4Z+ksG9Kk0lFjthTNQkjB58N3KLzmJf1lZcLDitc1z1zXJsP/IZ\n9vz0NSaNTMbU0ffDp49fj+9L1F0llTcET5L8vALtthRoSEAELhXeUbGFeedkRUqr5Ni0Zw2uyS/p\n7PP3CcbiGa9gUFiMoN3F2QVPJv8GXx1Yj+Pn92ram1oasX77n7A0+dcYOWiCyftOxsPgXA/tkddr\n8ktobm3CtDFzkRg71+4qGNiamrrKttrit0oaFpbm6YwudEWQbygipUMxUDocA6VDEewXZpIccJFI\nhOiIkYiOGImi0jzsz9qG05eP6KTVNDTXY1/mdzh4ejvGD5uGxNh5CPYLM3p/HE1x5Q1sTf8EhcVX\nMDh8BJLi5vNRrxZ9lVrslfYouUIrncfSlMpW7DzxJTIupiE8eBDmTFrMkX0HoFarcezcHmw9/Cma\nWxp19k+ImY4FU56Gu6uH3vPFYic8mrQcfdy9sS8rVdPeqmzBf378Gx6b/iLGD08yWf/JuBico+sj\nr9uPfIayagUemroMYrGTBXrqeFRqFYorijQlDa/KclBe3bMUlfDggbdyxYcjMnQofPqYv4ZzeNBA\nPDHrV7j/7sdx8NQOHD+/V1BbGmj7cj52bi+On9uHkYPGIyl+AQaERJu9r7ZOrVbj8M87sf3IRs3/\nx6dzj+J07lFEh9+FpPgFGNpvNH9sQ0++eaD95Zu3s+Zyis0tTfhk59+Qcy0LQFs510sF2ZiTsAST\nR83mBHI7VVNXiS/3rcP5a5k6+7w8fPFo0nKMHDS+0+uIRCLMSVgCT3cv7Dj6X027Wq3C53vfR13j\nTSTGzjVq38k0HDI4783I69Gz/0ND000smvEKJ/GZQHNrE64XX2kLxmUXkS+/qFlooTs83Pog8tak\nzfYUFVdnNxP0uGcCfCR4cOoyzBr/CA6f2Yn0Mz+irrFWcIwaapy5egJnrp7A4LAYJMXNx/ABcQwm\nu6D6ZgU+3/tPXLyerXf/5aKzuFx0FmGBA5AUNx9johPg5MA/uGUOPHJuLRVb6ptu4l873kae7IKg\nvUXZjO8O/Rvn8jLw2L0vwc870EI9JFM4c+U4tuz/UOfzHwBGDByHhUnLu70Y2PT4Bejj7o0tBz6C\n+o4ntNsOf4r6xlrcN/Fxfo9YObsPzo018nqnU5ePoL6pDk/f9zrcXNyN1FPHVFtf1fbE4lZJw6KS\nPChVrd2+ToCvRJMrPlA6DBL/cJsYZfLy8EHyhEeRFDcfJ3L248CpbXrrq1+5cR5XbpxHaEA/JMXN\nR1z0ZIsHE9ZKe/U8Q26UXcN/d/8DPxzbjGmxczEhZrpD/k07QqWWdp7uXvDp44eaukoAbRVbyqoV\nFi07V1NXiQ+3vQVZ2bUOj7lUeAZ/+fwVPDztecQNmWy+zpFJNDTV4btD/8ZPFw7q7HNzcceCKU9j\nQsz0HgfRE0fcC093L3z2v79Dqbz9nbon41vUNdTioWnPMgPAionUarXa0p3oSHX17VrRvr5dW/Hq\nzpHXvFv1q3sy8urp5oXI0KGIlA6FxC8M36Z9LJjhDwADQofguTlvoI+7d7ev74jUajWKK4sEJQ1L\nq+Xdvo5Y7ISIoIGCkobWMIEyM7PtkWR8fHyPr6FUKZGdewz7slJxozS/w+P8vAIxNXYO7o65F24d\n5CA6mvqmm/j24MfIvHRIZ5+bqwfujVuAi4VncKXoXIfX6OPujcmjZmPKqPvg5eFjyu5aXPv7dcTI\nGPz2o4WadpFIjNXLt/RqMrS1W5eaIpgU+tTs32J01N0W6Ut5dTHWbU3RKbsa7BeGmrpKvesvxEZP\nxsPTnoOnu5e5umkVjPEZaw1yi87h8z1rUVFbqrNvYOgwLJr5CgJ9Q4xyr0vXz+DjH/6sk8c+JmoS\nFs98lRkAJtSTGLadzQfn7SOvebIc5Mkv9njkNdA3BAOlw26lQgyHxF84ObC8phgfbn0LpVUywXmh\nAf2wfP6b8O3j3+172ruW1ubbP5TkF5Avv4R6PY/uOuPh6nnrh1JbScP+kmi4ulhPiko7Y35xqNVq\nXLp+BvuztgqCCG2ebl5IGJmMe0bf1+1Hn/bk0vUz+HzvP1GlZ/W8QWExWDTjZQT4SAAABYrL2Je1\nFT9fOQE19H/8uTi7YsLw6UiMnYsAX4lJ+24p7e/XwHAfvPfVbzXtwX5heGPJOkt1yyy+O/RvwaIu\nyRMWInn8I2bvh6ysAB9ue1Mzit9uoHQYnp3zBzQ2NWDz3rV6f1D6egXg8ekvYWj/0ebqrsXZenDe\n0tqCH49/joOntut89jiJnTF7wkIkxc0z+oh2geIy1m//fzqpM0P7jcbT9//OIZ8WmoPDBOcqtQol\nlTc0o+LmHnmtqavCR9vf0hnRDPCRYPn8NxHUN7TbfbEntfXVyJdf1ATjhSVXBY/TuirAR9JWReVW\nffGQgH42kaJiqi+O68VXcODUNpzOPSbIH7yTi5Mrxg1PRGLsXId6H3a2et79Exdh2pgH9H7ZlVTK\ncODUNvx04SBalS16ry8SiTEmahKS4uYjInig0ftvSe3v12b3SmzZfzsYHzV4Ip6+73VLdcssjp7d\nja8OfKTZjo1OwNLk35i1D/nyi9iwfZXOk92YAfF4cvYKzQCESq3CodM/4Ptjm/S+T6eMug9zJi2x\nygELY7Pl4PxG6TVs2v0PnfkdQNsg3+KZryI8yHSfMYqKQqzb+iaqtQYwBoQMwXNzmQFgCg4RnG85\n9L6RRl6Hob8kqscfZA1NdfjXjrdxVZYjaPfx9MML81IQFjSgR9e1NWq1GiVVsjt+KF1AidZTha4Q\ni8QIDxp4q6ThMAwMHQZfL9t8CmHqL47SKjkOnt6Bk+f3o0XZrPcYkUiMUYMnYHrcArsvF2ho9Txp\n4AAsnvFql/4ea+oqcSj7Bxz5eRca9KQQtBvSbxSmxy1AdMRIu5hM1f5+LajLFvy4mTX+EcyesLCj\n0+zC1Rs5WPvt7zXboQH9sHLRP812/wsFp/GfH/6C5tYmQXvckClYdO/LeueTyMoKsGn3P3BDT166\nxC8ci2e+avd/87YYnKtUShw4tR0/Hv9C56m+CCJMHfMA7r97kVnSyCpqSvDh1jd1vqtDA/ph+bw3\nbfa711o5RHD+x8+e6PJ5wpHXYQgJiDDqyGtzaxM+3fkuzucLyx55uHriubl/xEDpMKPdyxpl5x7D\ntiOf6Z242Bl3V08MCB2ieWLRPyTabh6pmeuLo7a+GulnfsThMzsNzqew13KBna2elxg3D7MnPKZZ\nPa+rGpsbcOzcHhw8vUNndOlOEcGDkBQ3H6MGT7TpCi/t79cT13cIlv62ZP61udQ33sTvNizSbDuJ\nnbH6xa/M8t/z1OUj2LR7jU6gNmXUbCy45xmD31WtyhbsOrEF+7K26jxFE4udMGvcw7h37IM2/b7U\n1p7id+D0dlyTXYarszuGR47WrE8R1FdqtZ9v5dXF2Lxnrc5gHtA2b+jxGa+YffXO2voqfLTtTygq\nzRO0+/sE48X5b9nsk1elshWnco+guKII99+9qPMTzMChg3NLjbwqla34fN/7yLwonHzm4uyKp+97\nHcMHxJm8D+bW0FSHb9M+RsbFtC6f4+8ddEf60HCEBkTY7Qxxc4/qNDU34Pj5fTh4egcq9UwsamdP\n5QI7Wz1v0YxXMFhr9bzualW2IOvSYezP2mqwBnaArwSJY+ZifEySVZXp7Kr29+vWU++jtuH2Z+0f\nlqyDxAEWv3rj308Kcr3/sPgDk1dsOXp2N74+sF4n3zh5/KOYNf6RLgeZebIL2LRnjd7KY/1DorF4\nxqsI9pMapc+W0jY5/ij2ZW01ODney8O3bWXnW8F6eNCgbv8wNza1Wo2TOQfw3aGP0aRnQaFxw6bh\nF/c8Y7FVeBua6vCv79/B1RvnBe3enn2xfF4KwoIiLdKvntD+HhSJxHhjyTqr+JHhUMG5cOR1OPqH\nRFls5FWlVmFr+ic6+a5isRMWz3gFcUOmWKRfppBbdBab9/zTYBAoEokRFjRAUNKwr1eAGXtpWZZ6\n5No+YrA/c6vefMZ2/t5BNlsusLPV88YPT8KCKU/Dw83TaPdUqVXIyc/C/qyteke+2nl5+GLKqNmY\nPGq2TeVtZmZmoqG5Dt9k/EPT5uzkgneXb7H5H3Fd8UHq/wmeGDx93+sYNXiiSe6lVquxN+Nb/HD8\nc519v7jnGdwz+v5uX7OxuQFb0z8RLNfeztXZDfMmP4lJd8202lHljjS3NOFEzj4cOLW9R09nnZ1c\n0E8yuC1Yv1VxzZx/l7X1Vdiy/0OczftJZ5+nuzceSXwBY6zgyVRzaxM+2/V3nNPqp4erJ56d8wYG\nhQ23UM+6pra+Culndup9gpxw1yw8nPi8hXp2m0ME5z8XHMPA0GFWN/KqVqux+6evsfPEl4J2EUR4\ncOoyTB4120I9M46W1mb8cGwz0k5/r3d2+eDwGM2H4ICQaIcu62fpfEi1Wo0LBaexLyvVrsoFGlo9\nr4+HDxYmLcfIQRNM2od8+UXsz9qKs1d/6rDCi6uLOybGTMe0MXPg7xNs0v4YQ2ZmJhRV17Dn/GZN\nW1hQJF5/7B8GzrIf2hVbZk9YiFkmqNiiUquw/fBnOHh6h6BdLBLj8RmvYOzQe3p1/bN5P2HLvnWC\npx/thvePxcJ7f2kT1cRuNtR0uCBbb0n8wwWDRoG+ISb50WJr/y2UKiW+3PeBTq11F2dXPDX7t4iJ\ntL7c/tIqOQ6e2o6TOQc6nHvl6uKOVc98CncLxyMmC87T09OxevVqnDp1CjKZDJ9++imeeEKYXvLm\nm2/i448/RmVlJcaPH49169Zh+HDDv7gOHTqEX/3qV8jJyYFUKsVvf/tbPPfcc0Z9YeaWfmYnvkv7\nWOeLe/aEhZg57mGbG70AgKLSPGzavUZngRLAPLPLbY2lg/M72Uu5QEOr58VExmNh0i/h08d8JSSL\nK4qw/9Q2ZFxM67ASkVgkRuyQyUiKnW/VE8QzMzNxQZaBjPzdmraxQ6di8cxXLdgr8zFHxRalSokt\n+9bh5IUDgnYXJ1c8dZ/xgp/a+ip8uf9DnVFQoO3H+COJL1jtPILymmIcPLUDJ87v05kg204EEUYO\nGo8Qz2goVa1w8VIhT962jom+tJHOeHv4akrzDpQOR3hQZK/qfdvyUwyVWoVt6Z8iLft7QbtY7IRF\n976M+F7+eDSW68VXsD9rK7KvHO+wapmzkwvGD0+ymqplJgvOd+3ahaNHj2LMmDFYsmQJPvroIyxZ\nskSz/69//SvefvttbNy4EdHR0fjTn/6EI0eO4NKlS/Dy0r84Qn5+PkaMGIFnnnkGy5cvx+HDh7F8\n+XJs2bIFCxYsMNoLs4SsS+nYtGetziS1e0bfj/lTnrKJcoBA2+zy/VnbsPPEl3pnl0+LnYP7Jj5u\n14uU9IQ1BeftbLVcoKHV81xvrZ43sRer5/VW9c2KtgovZ/+nd5GYdsP7xyIpfj4Gh42wui/mzMxM\nHL/yI3KLT2va5kxagunxCwycZT+0K7ZIA/rjd4vWGu36La3N+GzXap30BndXTzw35w8Y1Mu5EdrU\najVO5OxH6qF/6w1Yxw6digenLrNYnrO2otI87M/ahtOXj0DVQbDl5OSM8cOmITF2HoL9wnQ+Y5Uq\nJWRlBciXX2hbaVp2AZU3y7rdFxcnV/QLidIUKogMHdrlBZ7sIf9frVZjT8Y3+PH4F4J2EUT4xdRl\nmGKhDID2ycD7slIFKWjaPN28MHlUMiaPvM+sgzWdMUtai7e3N9atW6cJztVqNaRSKV5++WWsXLkS\nANDY2Ijg4GCsXr0azz77rN7rvP7669i2bRsuXbo9oWvZsmU4f/48jh07ZrQXZinn8zPxyc6/oaVV\n+Lhl7NCpeGz6L61+yfWyagU2716LPPkFnX1+3kFYNONlRIWbd3a5rbDG4LxdTV1lW4WXn3ehoamu\nw+OsoVygodXzIkOHYtGMV6xiVARo+xHRXuFFeyGZO/WXRCEpbj5GDhpvNWl5mZmZ2PXzZyitvV2K\n8rk5b1jlo2xTqGusxcoNizXbTk7OWL3cOBVbGprq8fEP7+ikl3l7+OKF+SkmfeJYVq3A5j1rkSez\nvs9wtVqN3KKz2JeZiovXszs8zsPV89biavcL1iDpymdsRU2pJljPk1+ArKygw5FWQ0ID+t1alLAt\nFSbARyL4TLTHyjmHf96Fbw/+S3fC8oSFmGXGDICuTga29pWyLRKc5+XlYfDgwcjIyEBc3O3KJPff\nfz8CAwPx2Wef6b3OlClTMGrUKLz//vuatm+++QaPP/44Ghoa4OR0+41si8E50DYi868dq3RqJo+I\nHIuls39jlZUd1Go1Tpzfh9T0/1jl7HJbYM3BeTtrLhdoaPU8sdgJsycsxPS4+VYT3N6ppbUFmZcO\n4UDWNhRX6tZdbxfUV4rE2LkYN2yaxZ88ZWRkYMvJdwV5m2899TH8vIMs2CvzeuPjJ1FTf0fFFiNU\nqqmtr8b67X9CYclVQbu/dxCWz3/LLKOoKpUS+09tx04rqK3d3p8zV09gf+ZWXC+50uFxvl4BmDbm\nAUyMmaF3cndPPmMbmupxTXEJ+beC9WuKy3onlXfGx9NPU6I52E+KH45/rjdwtPWa81mXDmPTnjUW\nyQDo6mTg0IB+SIqbj7joyVY94NmbGLbHr0qhUAAAJBJhrmpwcDBkso4XoykuLtY5RyKRoLW1FWVl\nZTr7bNGgsOF4+cF38OG2N1FbX6VpP5efgY+2/QnPPvB7qwpya+qqsGX/OpzLz9DZZ+35itQ97q4e\nSIydiymjZhssF1hYchWf7VpttnKBhlbPC/GPwOKZr1lNyo0+Ls4umBgzHeOHJ+JcXgb2ZaXqLfdY\nWiXDVwc+wo4jGzWjcpG9XBitp+qaqgWBuburJ/p6BZq1D5YWEhAhCM4V5dd7FZxX1JTiw21voqTy\nhqA9NKAfXpiXYrbqVWKxE+6NX4Bh/UfrzBtSQ42Dp3fg4vVsk88bam5twk85B3Hg1DaUVSs6PE7i\nH47pcfMRN2RKr3K/9fFw88Sw/mMwrP8YAG2jsjdK82+vZi27gOq6ik6vU1NfiTNXjuPMleMdHnPP\n6PvxwKTFVjkA11VxQybDw60P/vPjXwQZAIeyf0BdYy0en/6S0QPirk4GHhwWg6S4+Rg+IM7q0gSN\nrccj58eOHUNCQgKuX7+O8PDbtWGfeuopyOVy7Nq1S+91hgwZgsWLF+ONN97QtKWnp2Pq1KmQy+WC\n4PzOXx25ubnde2VWoLahAnvPf4GbTVWCdv8+IUgavhAerpYP0K+XX8KJqz+isUU3bzbMbzAmDr4P\nnq62Ux6OuketVuNG5RWcu3EMJTUd1/R2d/HE0NCxGBISDzcX4z0+VKlVyLlxEtnX06BSK3X2D5OO\nR2z/aXASW+/oSEeKa67jfNFxFFV2/tklEokR0CcEQT4RCPaJQLB3ODxcu5bz2lNFFbk4cOErzXaQ\ndziSRy416T2tzU95u3FRfntQYnS/ezAyYnKPrlVdX4a95z9HfbMwuAj0CkPS8EeN+nfTHUpVK04X\npCFHdkJnn1gkxuh+UzE8bIJRR0SbWhpwSZGFi/IMNLZ0nEYX5B2OEeF3I9wvymLBllqtRl1TNUpq\nClFSW4TSmkJU1nevhKOnqzfujnoA0r7WO4DQXSU1hTiQ8xWalcKnDOF+UZgyZIFRfkTdbKxCjuwk\nrhRno1Wlf04UAPQLGIqYsIkI8rat9ReioqI0/9tsI+chISEA2kbC7wzOi4uLNfs6Oq991P3Oc5yd\nnREYaF+jNt4e/ph11xPYl/MFqupv589W1Cnwv7MbcW/MY/Byt8zkhZbWJmTk78WVEt28P2exC+Ij\npyNKEmv3v04dnUgkQrh/FML9o1BaU4RzN46jsEJ3xLexpR7Z1w/hXNExREnGYJh0XK/fuzcbq3Ak\nd7veHwWerj6YFPUAQvvazmIY2iQ+/SA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BqCvP6+nqAwc7x3Y9571Si9ppLsxDJyLrxQCdiIj0Rt8VXGrpVHJhHjoRWTEG6EREpDeK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\nOSfR2PRiM58VtS2Wt/Sg2XMAsGgxQC+tfASptKmVsxVLSv8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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -385,34 +385,43 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Since this type of smoothing requires knowing data from \"the future\", there are some applications for the Kalman filter where these observations are not helpful. For example, if we are using a Kalman filter as our navigation filter for an aircraft we have little interest in where we have been. While we could use a smoother to create a smooth history for the plane, we probably are not interested in it. However if we can afford a bit of latency some smoothers only require a few measurements into the future produce better results. And, of course any problem where we can batch collect the data and then run the Kalman filter on the data will be able to take maximum advantage of this type of algorithm." + "In this case we are led to conclude that the aircraft did not turn and that the outlying measurement was merely very noisy. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Types of Smoothers" + "## An Overview of How They Work\n", + "\n", + "The Kalman filter is a **recursive** filter - it's estimate at step `k` is partially based on its estimate from step `k-1`. But this means that the estimate from step `k-1` is partially based on step `k-2`, and so on back to the first measurement. Hence, the estimate at step `k` depends on *all* of the previous measurements, though to varying degrees. `k-1` has the most influence, `k-2` has the next most, and so on. \n", + "\n", + "Smoothing filters incorporate future measurements into the estimate for step `k`. The measurement from `k+1` will have the most effect, `k+2` will have less effect, `k+3` less yet, and so on. \n", + "\n", + "This topic is called **smoothing**, but I think that is a misleading name. I could smooth the data above just by passing it through a low pass filter. The result would be smooth, but not necessarily accurate because a low pass filter will remove real variations just as much as it removes noise. In contrast, Kalman smoothers are *optimal* - they incorporate all available information to make the best estimate that is mathematically achievable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Types of Smoothers\n", + "\n", "There are three broad classes of Kalman smoothers that produce better tracking in these situations.\n", "\n", - "* Fixed Point Smoothing\n", - "\n", - "Fixed point smoothers start out as a normal Kalman filter. But once they get to measurement 4 (say) it then looks backwards and revises the filter output for the previous measurement(s). So, at step 5 the filter will produce a result for 5, and update the result for measurement 4 taking measurement 5 into account. When measurement 6 comes in the filter produces the result for 6, and then goes back and revises 4 using the measurements from 5 and 6. It will revise the output for measurement 5 as well. This process continues, with all previous outputs being revised each time a new input comes in.\n", - "\n", - "* Fixed Lag Smoothing\n", - "\n", - "Fixed lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will ingest the first 3 measurements but not output a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurements 1 through 4 into account. When the 5th measurement comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account.\n", - "\n", - "\n", "* Fixed Interval Smoothing\n", "\n", - "This is a batch processing based filter. It requires all measurements for the track before it attempts to filter the data. Having the full history and future of the data allows it to find the optimal answer, at the cost of not being able to run in real time. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n", + "This is a batch processing based filter. This filter waits for all of the data to be collected before making any estimates. For example, you may be a scientist collecting data for an experiment, and don't need to know the result until the experiment is complete. A fixed interval smoother will collect all the data than estimate the state at each measurement using all available previous and future measurements. If it is possible for you to run your Kalman filter in batch mode it is always recommended to use one of these filters a it will provide much better results than the recursive forms of the filter from the previous chapters.\n", + "\n", + "\n", + "* Fixed Lag Smoothing\n", + "\n", + "Fixed lag smoothers introduce latency into the output. Suppose we choose a lag of 4 steps. The filter will ingest the first 3 measurements but not output a filtered result. Then, when the 4th measurement comes in the filter will produce the output for measurement 1, taking measurements 1 through 4 into account. When the 5th measurement comes in, the filter will produce the result for measurement 2, taking measurements 2 through 5 into account. This is useful when you need recent data but can afford a bit of lag. For example, perhaps you are using machine vision to monitor a manufacturing process. If you can afford a few seconds delay in the estimate a fixed lag smoother will allow you to produce very accurate and smooth results.\n", + "\n", + "\n", + "* Fixed Point Smoothing\n", + "\n", + "Fixed point smoothers start out as a normal Kalman filter. But once they get to measurement 4 (say) it then looks backwards and revises the filter output for the previous measurement(s). So, at step 5 the filter will produce a result for 5, and update the result for measurement 4 taking measurement 5 into account. When measurement 6 comes in the filter produces the result for 6, and then goes back and revises 4 using the measurements from 5 and 6. It will revise the output for measurement 5 as well. This process continues, with all previous outputs being revised each time a new input comes in. This filter can be used to fill in gaps. For example, suppose you did not get a sensor reading at step `k`. Instead of just using the prediction from step `k-1` you can continue using data collected at steps `k+1`, `k+2`, and so on to refine the estimate. \n", "\n", "\n", "The choice of these filters depends on your needs and how much memory and processing time you can spare. Fixed point smoothing requires storage of all measurements, and is very costly to compute because the output is for every time step is recomputed for every measurement. On the other hand, the filter does produce a decent output for the current measurement, so this filter can be used for real time applications.\n", @@ -436,20 +445,6 @@ "not done" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Fixed Lag Smoothing" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "not done" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -467,7 +462,7 @@ "\n", "The RTS smoother works by first running the Kalman filter in a batch mode, computing the filter output for each step. Given the filter output for each measurement along with the covariance matrix corresponding to each output the RTS runs over the data backwards, incorporating it's knowledge of the future into the past measurements. When it reaches the first measurement it is done, and the filtered output incorporates all of the information in a maximally optimal form.\n", "\n", - "The equations for the RTS smoother are very straightforward and easy to implement. This derivation is for the linear Kalman filter. Similar derivations exist for the EKF and UKF. These steps are performed on the output of the batch processing, going backwards from the most recent in time back to the first estimate. Each iteration incorporates the knowledge of the future into the state estimate. Since the state estimate already incorporates all of the past measurements the result will be that each estimate will contain knowledge of all measurements in the past and future.\n", + "The equations for the RTS smoother are very straightforward and easy to implement. This derivation is for the linear Kalman filter. Similar derivations exist for the EKF and UKF. These steps are performed on the output of the batch processing, going backwards from the most recent in time back to the first estimate. Each iteration incorporates the knowledge of the future into the state estimate. Since the state estimate already incorporates all of the past measurements the result will be that each estimate will contain knowledge of all measurements in the past and future. Here is it very important to distinguish between past, present, and future so I have used subscripts to denote whether the data is from the future or not.\n", "\n", " Predict Step\n", " \n", @@ -507,16 +502,16 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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NOtPp1GlXX37Z6JSYWq2Wr7/+mvfff9/gycHWrVuJjo4mLCzM4HhXV1dcXV1N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\n+RjWavc6y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kMiwtLbGwsGDz5s38+c9/7lPQVKkkzlzoKUlJyYGThXDV4pV9Ym8D4YHqcpSI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -530,7 +525,7 @@ "from filterpy.kalman import KalmanFilter\n", "import book_plots as bp\n", "\n", - "def plot_rts(noise):\n", + "def plot_rts(noise, Q=0.001):\n", " random.seed(123)\n", " fk = KalmanFilter(dim_x=2, dim_z=1)\n", "\n", @@ -542,7 +537,7 @@ " fk.H = np.array([[1., 0.]]) # Measurement function\n", " fk.P = 10. # covariance matrix\n", " fk.R = noise # state uncertainty\n", - " fk.Q = 0.001 # process uncertainty\n", + " fk.Q = Q # process uncertainty\n", "\n", " # create noisy data\n", " zs = np.asarray([t + random.randn()*noise for t in range (40)])\n", @@ -593,6 +588,172 @@ "plot_rts(noise=1.)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "However, we must understand that this smoothing is predicated on the system model. We have told the filter that that what we are tracking follows a constant velocity model with very low process error. When the filter *looks ahead* it sees that the future behavior closely matches a constant velocity so it is able to reject most of the noise in the signal. Suppose instead our system has a lot of process noise. For example, if we are tracking a light aircraft in gusty winds its velocity will change often, and the filter will be less able to distinguish between noise and erratic movement due to the wind. We can see this in the next graph. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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Np+ZUjxP/d5WOx6s+iqPUZ0JoNBq0Wi21a9fGxcUFf39/vLy8AN0/+AcOHGDu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\nH37I22+/Tfv27Qt1T7RaidR0LWmZCtI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CL5fWpKQnyb9bWlrKFU9u8/nnn5OUlPTPQx+K\ngqJ8Dp+LIbjdAHns/PnzDBs2TBblt/n222+5ePGiTs8vaLzoTJjv3r2bSZMmsX//fqKjozE0NCQi\nIoIbN27INnPnzmXevHksXLiQ+Ph4HB0d6du3r0aURSAQ1Jy40zux+V+OpYHSAA9n/ee21jVl5aVk\n5abh0tSd0jKJhb9L+IyEjxZDfgHY3lygYV9u2pnnnh3LiV9hzw8KxvVXYFYPU1bqE5mZmfz3v//l\npZdewsvLCy8vL15++WXWrFlDVlYWrq6ujB8/nhUrVnDlyhVOnz7NwoULGTZsmEb+rFczfy5cPV2H\nr6QCXabGaCOvMIc9Z9Zr7ZKpT3zcAjh/tXIgTBunLx0h79b1+xs2EJo7+ZCek0ppeQlwp4SilZWV\nbFNaWsqUKVMoLi6uapkaY25qxdujvsDa4s77/I8//pA3Bd/GysqKH374gRYtWujs3ILGjc6ee23d\nulXj919//RUbGxv27dvHoEGDkCSJ+fPnM23aNJ544gmgoi2to6Mjq1at4uWXX9aVKwLBI0VOfgY3\nbmXj1cyvrl2pVZRKA94Y/jlrooz4aDFcTL9rUiqh3MAVCQMUVEQv//vL+wT10K8wa+jcunWLPXv2\nyHnix48f15i3tbUlNDRUzhNv1apVtXJ3Xe09MDO1qHa1oCtZyTjYNsPEyPSBX0tdkHo9CfemrbVu\nBNQnIe0GaHRCrQqVWsVvOxYw6clPsOHhyk/WF4wNTXBp6s7ljPN4u1bk/Lu5uTFr1iymTJki22Vk\nZHD+/HkCAgJ0cl6FQoGTnavG2Ntvv01CQgIJCQkA+Pr6ClEuqDF6S0jLz89HrVZjZ1fR9CIlJYWM\njAz69esn25iamtKrVy/27dsnhLlA8ICcuBBHgGcgBnqOBtYnJEni7/1KPvzRkxPanuArTJA8vmT8\noEncSvmeG9ezCeoRWOt+1ndKS0s5ePCgLMQPHjxIeXm5PG9qakpwcLAsxDt27IiBQc3fZ0qlAW+P\nnFtt+yWbPue1xz/CqYlbjc9VV9y4mc3ptDjC/UfX+rkd/yEQqyLp0hGaWDni3KS5nj2qXZ4b+C5W\n5poNtoYOHcquXbvkyjlff/01Li767YxrZGTEwoULGTx4ML169WLWrFmYmZnp9ZyCxofehPmUKVPo\n2LGjXErq2rVrADg5OWnYOTo6kpaWpi83BIJGz/ELBwjt9Hhdu1Fr7D0q8cGPEHtc+7y5Kbw1CqaO\nARvLFsCXqFS1l/Nbn1Gr1Rw/fpyVK1cSFxfH8ePHKSgokOdvd78MDw8nPDycnj17Ympau1Hr6/lZ\nlJaVVFts1gfUahW/bp+Pn0sgTS2d69qdKjmQGEU3/7C6dkPnNLF21Do+c+ZM2rdvz9ixY7XeUL72\n2mu4ubnRrl07AgIC8PDwqHb1lOLiYq3/N5ycnNi8eTMODg4NprSpoH6hF2H+9ttvs2/fPmJiYqr1\nxryXze1HQgLdIa6pfqiL61pWXsLljBQKslQkXK98/nJVGYYGRrXul65JSEjg7FUzftjkSmyijVYb\nQwM1T/TM5rl+6dhbl3NOt3u9GiSSJHH16lXi4uKIj48nISGB3NxcDRtPT0+6du1KYGAgnTp10sjN\nPXnyZG27THLmCZqYu3Do0CG9nSPnVjq25g4YKHXzFXgh8xg38/PpHjAUqJ+fscVlhSSmHMavaVC9\n9K86PIjfbdq04ciRys0Lbty4USkF18zMDB8fH6ZPn16lQFer1WzcuJHIyEjmzJmDtbX2WvCpqak1\n9rWuaKjvh/pKy5YtH+p4nQvzt956i7Vr17Jz506NvCpn54ooQkZGBm5udx5PZmRkyHMCgaBmGBma\nMCLwDa0CI+3GBU5e3U+/AP1WodA3V7KN+XFLM7YfboIkVb6JVygkHut0nVcGpuFqX1oHHtYvcnJy\nSEhIID4+nri4ONLT0zXmnZycCAwMlH/02XzlQcjMv4yTtbtez3Hgwt90aRGOk03NmvJUhadDW9zs\nWtV6bnlNSMk6iVuTlhgbNqy8fX2RnJxcaayoqIjc3FytorywsJCYmBg2bdlI+tVMABYsWMC0adMe\nKL1LIKgKnQrzKVOmsG7dOnbu3Fmp45mnpyfOzs5s376dzp07AxWPgmJiYvjqq6+qXLNLly66dPGR\n5vZdsbimuqW+XteiEn/2/Lyedu3bYmx0/w139Y1rORJvfJHJ+n0OqNTan6oN6gmzXlbQvqU9YM+l\nS5fw8NCN2Goo5Ofns2fPHqKiooiMjKwU5W7SpInGhk0fHx85Gl3f3rMA204v4/HuY2nu6KW3c1wu\nPI6hqVrnr78+fBZIkqT1KXSLPDfUalWDShG6jT6ua2xsrNbxrl27aj1PbGwsixcv1hg7duwYsbGx\nvP322zrzqzapD+/XxkheXt5DHa8zYT5x4kRWrlzJhg0bsLGxkXPKrayssLCwQKFQ8OabbzJ79mx8\nfX1p2bIls2bNwsrKijFjxujKDYFA8D/MTMxp7uDF+aun8G/Rqa7dqTZ5tyS+XAXz10Bhsfbc0XY+\nuYwIjWH6hCHyWFxcHKNGjaJ///688cYb+Pk1zio1JSUlHDhwQBbicXFxGjn0ZmZmhISEyHniHTp0\nqDcRvazcdHJv5dDSTXtlDJVahadza1xr2F6+pni7+hNzYptez1EX/LDhEwb1GKO1Q6y9TeN/Ml3d\nqj8AI0eOxNvbm5MnT3Ly5ElOnDhBfn5+lVVbTpw4UWnM1tZWDjQKBLpCZ8L8hx9+QKFQEB4erjH+\n8ccf89FHHwHw3nvvUVRUxMSJE7lx4wbdu3dn+/btWFhY6MoNgUBwF74eHUhKPdoghHlxicQP62H2\nCsipIuDQ1htmvwqFJb/T1EZTtC9YUFG3fOvWrWzdupW3336byZMn69ttvaNWqzl69KgsxPfu3UtR\nUZE8b2BgQI8ePWQh3qNHD0xM6ucTkswbV4k+vLFKYW6gNGBMX/3/m3k182fl9gWo1Sq91zavTZpa\nO3L+6kmtwryxczXrIiu2zWPa2AX3NwZcXFwYPHgwgwcPBiqeNKSmpmJpaanV/vARzTzstm3bsmjR\nIo3UXIFAF+hMmP+z01ZVzJgxgxkzZujqtAKB4B74undgVeTCunbjnqhUEiu3wYwlkJqh3cazGXzy\nIjwdAQYGCuavTaZDy+7yfFxcXKVH0926ddOn23pDkiTOnz8vt7qPjo7m+nXNhjABAQGyEO/du3eV\nG9DqG57NfEn9+6s635RsaWaNjWUTrmZf1OgcW11yb+WgVCixtrC7v3Et4uMWQHzSLsI6DatrV2od\n5yZu5ORnUlhyC3MT7eL6XigUinumwZk0gVZtvFCXKImIiODNN9+stzfAgoaN3solCgQC/aFSlZOU\nepQ2nvfODWzu6I2psTklZcX1rlmLJElsioUPf4STlfdhAdDEsoznHkvns8nuGBtV5M2q1SquZqfg\n6uAp292Olt8mKCiIrl276s13XXPt2jVZiEdGRnL58mWNeXd3dyIiIggPDycsLKzBbpg3N7HE3saZ\ny5nJeLq0rlNfgtv2R6WueRlNtVrF8r+/pp13d0I7DdWDZw+Oj2sb1kT/0OieBFQHAwND3B29uXTt\nHH4eHXW6dnFpERYtSlg7fR02Fo2jMZOg/iKEuUDQADl/9RRbD665rzBXKg14a+TnteRV9Yk9LvGv\nH6quRW5pVlGHvHerk1iYqjE2uhPJysxNw8rcVo6KaYuWv/HGG3rzXRfk5eWxe/duWYyfOqXZTr1p\n06aEhYXJUXFvb+9GUxPZ29Wf5LTEOhfmvTsMfqDjdiT8gVJpQO+OD3a8PrG2sMPa3E7jSUDmjas4\n2DZrNO+fe+Hp4ktKWpLOhbmpsRkfjF1Q756QCBonQpgLBA2Q4xcO0s67+/0N6xknkyU+/A/8pb0g\nAkaG8NoT8OGz4GCnICGhcopcxvUrGukH3t7evPLKK6xYsYKioiJ69uxZ76LlJSUl7Nu3Txbi8fHx\nGhs2zc3N6dWrlyzE27dvX+1GJw0Nr2b+JCTtJrzzE3XtSo1JST/DnqObmTr663pbGrGlWwBXsyqE\nee6tHL5e8x6fvvBLg6zMVFM8XXzZfXSTXtYWolxQWwhhLhA0MNSSmuPJB5n0xMy6dqXaXLom8fES\nWLEVJKnyvEIBYx+DmS9CC5d7R/ba+/QgwOuO8G7atCn/+te/eOmll1i8eHGlDeh1gUql4siRI7IQ\nj4mJqbRhMygoSBbi3bt3x9jYuA49rj1augVQVFJQaTwhaTdNbZzrPJJeFUUlhazYNo+RYa9hZ2Vf\n1+5UyYg+L8lpLHGnd9KxZc9HQpQDeLq0ZuvBNVWWjBQIGgJCmAsEDYzLGRcwNTLDqUn9rwaQnSsx\newUs+hNKy7TbDOoJn70C7Xyq/0VqoCV/9rZArwskSeLs2bOyEN+5cyc3btzQsGnbtq2cJ96rVy+N\nDpuPElbmtgS1fazS+N7jfzOw++g68Kh6nEk9iq97R9r71O8nVbdFuSRJHEyMZmy/+p3WpUsszKyZ\nOrrqvigCQUNACHOBoIFx/MIB2nrX74ojBUUS36yBr1ZBfuXgKADd28Dnr0OvDg0zspWWliYL8aio\nKK5cuaIx36JFC40Nm46O2muyCyrqT1/NvkiLehotB+jQsiftfXrUtRvVJiU9CYVCQQvn+ntNBQJB\nZYQwFwgaGJ4uvjjYutTomMLiW5xIPkg3f/2meRSVSPy0ET7/FTKua7fxa1ERIX88hAb1uDk3N5dd\nu3bJQvz06dMa8/b29oSFhcli3MtLf50rGxuXrp3Fpal7rVcOKi4tIjLhTwb3fKZa9g3p/XogMYru\n/uENyuf6hCRJbDmwioguw+tdRStB40YIc4GggRHgFVjjYwyUBvy+azEdWgbp5UumpFRiyV8wZwWk\nZWu3cXOEj1+A8f3B0PDhxEJiYiL5+fl0766/tILi4mJiY2NlIZ6QkKDRr8HCwoJevXrJQrxt27aN\ndsOmvjl/NREfV/9aP6+xkQkxx/8mpP2ARlcGr7mDF+3qedpNfSbx4iFOJsczsLvoTC6oXYQwFwge\nAUyMzWju6M2Fq6fwb6G7FtKlZRLLtsBny+FyFc2B7Kxg2niYOBzMTB5OkN+4mY2FmRVz5swhJiaG\nrl278uabb9K9e/eHjgyqVCoOHz5MZGQkUVFRxMbGUlxcLM8bGhrSs2dPWYh37dr1kdmwqW8uXD1F\nnw5Dav28SoUSz2a+XLiaSKdWwbV+fn0S0n5gXbvQoIlM+JOILk+KJw6CWkcI80cItaQm6+YV4N61\nrwWNE1/3DiRdOqoTYV5WLvHrVpi1DC6ma7cxN4U3noL3ngFbK918ua2O+h4HA29iYmKAihrmY8aM\nYePGjbRr165Ga0mSxJkzZ2QhvmvXLnJzczVs2rdvLwvxkJCQKtt1C2rOnmNbsLOyp61XVwZ0G4Wr\nQ92k/ng3q6ir/k9hnpKeRFl5Ka2a1+x9Jah70nNSMVAa4Gjn+kDHp6QnkXsrhw4tg3TsmUBwf4Qw\nf4RIzUliz5k/GRT2ZF278tCUq8pQS2qMDR+NMmC6wNejIyu3f/tQa5SXS6zaAZ8uhQtXtduYGsPr\nwysEuaOd7qJNkiRxJTOZmN1JGuPdunWrtii/cuWKxobNtLQ0jXkvLy/Cw8OJiIggNDQUBwcHnfkv\n0ESS1JxKiaetV1e8XdvUmR/erv6sjf6PxlhRSQHLt85jeO8X68grwcNw/MJBikoKGBYy4YGOj0z4\nk9BOj2ut/iQQ6BshzB8h8gorkn9LSoswMTarY28ejlMpCew/Fcmrj/+7rl1pMLg5eHKzMJcbN7Nr\nXIdZpZJYGw2f/AJnUrXbmBjDK4/D+2PBxV73j39zb+WQfTWf/fuOaoy/+eabVR5z48YNdu7cKQvx\nM2fOaMw7OjpqbNhs0aKFzv0WaMermT8xx7fWtRs0d/QmK+8aRSUFmJlYIEkSa6P/g79HJ9p61a9G\nVYLq4eniy+b9vz3QsTcLc7mSmcyz/d/RsVcCQfUQwvwRIvPmFbwd26Gopx3rasKplAT8PDqSePEw\nVzIv0K/rU3Xtkt75edPnhHV+4oEbsCiVBozpOxkjw+rnRavVEn/sgpk/Q+JF7TZGhvDS0Io8clcH\n/eVjXs68wOUTeRpj3bp109gAWlRURGxsrJyecvjwYY0Nm5aWlvTu3VuOigcEBIgc0jrC1d6D/ILr\n3CzMw8rcps78MDQw4sVB/5Lrf8cn7eJKdgrvPv11nfkkeDg8nHy4mpVCWXkZRoZGNTrWytyW6c8u\nqtHnpECgS4Qwf4QwMjCmc4vwBt8FTi2pOXXxEH0DR1BcWkhc0q5GL8wLS26RdPkYY/tNeah1qhsB\nlCSJjXvh45/h+HntNoYG8Nxg+HA8uDvrX9xeyUzmxUnjyDlfxk8//UROTg6TJk3i4MGDshDft28f\nJSUl8jFGRkYEBwfLQjwwMBAjo5p9UQv0g1JpQAsXX5LTTtd50x5fjw4AZOddY/3epUx6YmaD/5x8\nlDExNsOxiStXsi7g6eJb4+OFKBfUJUKYP0L08R1R1y7ohMsZFzA3scTB1gW1pKag+CbX8zNpYt14\nG7gkphzCx7WN3lOQJEli874KQX74jHYbAwMYPwCmPwuezWov2qxUKvH1bIfC2YybN2+yZs0aBg0a\nRH5+vmyjUCjo2LGj3Oo+JCQECwuLWvNRUDO8m/lxIS2xzoX5bW4W5jK05zhcHTzr2hXBQ+Lp7EtK\netIDCXOBoC4RwlzQ4DiVkkAbz4rKMkqFEt/m7UlKPUbPgL517Jn+OH7hIO289Sdeysslft8Fc3+F\nY1VEyJVKeKYfTJ8ALZvXniC/du0ay5YtIzIykujoaNLTNcvA+Pj4yEI8NDQUe/ua5c8L6o7OrXuR\nk59Z127IeLr4CiHXSOjQsieFxTfr2g2BoMYIYS5ocJSry2l3V0t6X48OnLp4qNEK87LyUpJSj/JU\n6Cs6X7u4pKIO+VerIDlNu41CAaPC4aPnwddD/4L8+vXr8obNzZs3k5qqudvUyclJFuLh4eF4eHjo\n3SeBfmhq40RTG6e6dkOgZyRJorS0FEmSHuj42//H7+4rcD+a2/vU+JhHjQe5ro86CoUCY2Njve5N\nEsJc0OAYGjRO4/fW7h3YELMctaRG2Qg2tv6T9JxUPF18H3iDXFpaGvn5+bRu3Vr+MMm7JfHDevh2\nLWRcr/rYEaEVgjzAS38fQoWFhcTExBAVFUVkZCRHjhzR+AK3sLAgLCxMzhP39/cXGzYFggaCWq2m\npKQEY2NjDAwerPygqanuuxULxHV9EFQqFcXFxZiYmOit07MQ5o8YkiTx0/99xvOD3sPQoHFsgrO1\nbMr0cQsbpSgHcHfyuW9ZyO3bt9O7d29MTCpvWFu1ahXff/89zZs3p2dwBJnqCFYfCKCkzErrWgpF\nhSCfNg46tNK9AC4vLyc+Pl4W4vv376e0tFSeNzY2pmfPnoSHh9OsWTPi4uIYPHgwAwcOFC3vBYIG\nRmlpKaampuJmWtAoMDAwwNTUlJKSEr3d2Ahh/ghwOTOZkrIioOIxTPr1VK7nZz5wV7T6iIWZdV27\noFfu9aW2b98+XnnlFby9vZk9ezZdu2pWXomMjATg8uXLrFm9FFiKg8KGHLuvKDINl+2MDCs2db47\nBlq567Yx0KlTp2Qhvnv3bm7evJP7qVAo6Ny5s5yaEhwcjLm5OQCrV69m27ZtbNu2jQULFvDGG28w\naNAg8SUvEDQgxP9XQWNC3+9nIcwfAeKTdmFpakUTZUWlAXsbZ7LzrjUqYf6oUlJSwocffgjAhQsX\nGDVqFFOnTmXixIkAbN+TWqmpDoCBlEeZYcX7wdIMXhkGb47SXR3yS5cuaXTYzMjI0Jhv1aqVxobN\nJk2aaF1n3bp18t/PnTvH8uXLGTRokE58FAgEAoGgviGE+SNAStpphgY/S961ig0eDjYuZOWm3+co\nQUNg4cKFXLx4Uf5doVDQvXt39hyVmPsrRO4twNakD2Yl+1BwJ12kzNALY0sHZoyH158AO+sKQS5J\nEi+//DJ+fn44ODhgbW2NtbU1bm5utGzZsko/srOz5Q2bkZGRXLhwQWPe2dlZ7q4ZHh5O8+bN7/va\njh49ypEjRzTG3nzzTRF9EwgEAkGjRQjzRk5peQnpOal4OLXk+LUTANjbVkTMGxoHE6No7uhNM/sW\nde1KveDcuXP8+OOPGmNBYWOYsrgT+078b8DIl6ymv6BQF2Bashfz4kgsS6PpERxBi8B3eO2Jz7C7\nq/776dOniYyMlNNfbvP4448zf/58+feCggL27t3L0qVL2bZtG3l5mh05zc3N6du3ryzE/fz8UCgU\nxMXF8ccff1BeXo5arZb/7NmzJ2FhYRprLFu2jNatW8sR/y5dutCzZ8+HvWwCgUAgENRbhDBv5KRm\nnMe5qbtGFzt7GxfOXTlZh17VHEmS2HpwLS8NmValTbmqjBs3s3GwdalFz/RHVm46Wblp+LforHV+\nw4YNlJWVyb8rjB1YdepdJC37IyWlBV7+/Xl/XH+G9y6nvKyY9bFLuJRxXqMx044dO7Sey9zcipk0\nHAAAIABJREFUnNjYWDk1Zf/+/Rrnhood/qamppiZmfHMM8/w5ZdfVlonISGBb7/9ttK4sbGxhjC/\nnaIzf/58WZhPmTJFRMsFAoFA0KgRJQ4aOclpp/H6R8MMH9c2DOk5rooj6ifXrl9BLalxaVp1zepr\n1y/z48ZPa9Er/ZKQtJuk1GNVzr/zzjs8+/oCFEYVDXUyLWYgKStvgu0RABvnwrEVMPYxBWamRlhZ\nWTG23xt0bKkZgb4dKb9ddzgvL4+MjAy+/vprgoODmTFjBnv27KG8vJwuXbrQr18/nJyccHd3x9nZ\nGVtbW0xMTLC1tdXqc1VVVcrLyzV+NzExwcHBQbZv7e9DUFBQlddCIBAIapNly5ahVCpRKpXExMRo\ntfHx8UGpVBIaGlrL3gnuZt++fcycObPSk936ihDmjRxPl9YE+vXRGDM3taSZfcNqynIqJZ42nl3u\nGTFtZt+CopICcvIzqrRpSBy/cID2dzVSuo0kSfwVI9H1RQWfbBhMatMdXLf5mELTARp2A3vA7u8h\n5j8wJFiBUql57ZRKzZrCKSkphIaG4uLiQnZ2Nmlpady4cYOioiJKS0tp3bo1EydO5M8//yQnJ4f4\n+HjCw8MxMzOrJLitrbVXyTE01P6QTq1Wax1XKpUYGhnw3r+mimi5QCCod5iZmbFq1apK4wcOHCA5\nOVmUiqwHNDRhLlJZGjkt3drWtQs64dTFQ/Tt8uQ9bZQKJa3dO3Am9Rg9A/rVkmf6IScvg7yCGxrt\nwSVJYst+mPkzJCTdsVUrbbhpMR6oqEH+VChMGw/tW977yyArK4vo6Gg5PSU5OVljvlmzZnJTn7Cw\nMNzc3CqtMWHCBPr27Ut+fr7Gzz9LNt6mU6dOTJkypUJwGxrKfwYEBGi1DwwMxKYF9O4ZrnVeIBAI\n6pIBAwawbt06FixYoBF4WLVqFb6+vg/cVKm+UFBQgIWFRV27oRMetPNsrSPVQ3Jzc+Ufge6Ij4+X\n4uPj69qNGnOrKF+auuhpqaSs+L62BxOjpZ83za0Fr+6gj+safWij9Nv2BZIkSZJarZa27FNL3V5U\nS4qeVf+MnK6WTlxQV7nmzZs3pc2bN0tvv/221L59ewnQ+LGxsZGGDRsmLVy4UDp9+rSkVle9Vm3R\nUN+z9R1xXfWDuK6VKSoqqmsX9MLSpUslhUIh/f7775JSqZQ2bdokz5WXl0tOTk7SrFmzpICAACk0\nNFSeU6vV0oIFC6SAgADJ1NRUcnR0lF544QUpOztbY/2NGzdKgwcPltzc3CQTExPJw8NDevfdd6Xi\nYs3vwWvXrkkvvPCCbOfk5CQNGDBAOnXqlGyjUCikjz/+uNJr8PDwkCZMmFDpNUVHR0uTJ0+WHB0d\nJYVCIc/HxcVJAwYMkGxsbCQzMzMpODhY2rlzp8aaM2bMkBQKhXT69GnpmWeekWxsbCR7e3vpgw8+\nkCRJklJTU6WhQ4dK1tbWkpOTk/Tll19W8qu4uFj6+OOPJR8fH8nExERydXWV3nrrLamwsFDDTqFQ\nSK+++qq0fv16qU2bNpKJiYnUpk0baevWrZX8+efP7t27JUmSpEOHDkkDBgyQHBwcJFNTU8nDw0Ma\nN27cfd+395p/WA0rIuaCeo+xoSkTn5iJsWHlrpb/pLV7e/7c8wtqtapSqkZD4njyQcI6DmPrAYmZ\nP8PBRFCoCzFU51BuqFlqcHgf+Oh5aOutGSEvLS3l4MGDckT8wIEDGrncpqamBAUFyWUMO3Xq1OCj\nOwKBQFCbuLm5ERISwqpVq+QeC5GRkWRmZjJ69GhWr16tYf/aa6/xyy+/MGHCBN544w1SU1P57rvv\niIuLIz4+Xu7evGzZMszMzJgyZQo2Njbs37+fb775hsuXL2usOWLECE6ePMnkyZPx9PQkMzOTPXv2\ncO7cOfz9/WU7bek0CoVC6/jkyZNp0qQJ//73v+X0j927d/PYY4/RqVMnZsyYgaGhIb/++iv9+vVj\nx44d9O7dW2ON0aNH4+fnx9y5c9m8eTNz5szBxsaGJUuWEBERwRdffMHKlSt577336Ny5s5yHL0kS\nTzzxBHv27OHll1/G39+fxMREFi1axKlTp9i2bZvGefbv389ff/3F66+/jqWlJQsWLGD48OGkpqbS\npEkThg8fzrlz51i9ejXz58/H3r5iT5afnx9ZWVn07dsXR0dH3n//fezs7EhNTeWvv/6isLBQb509\n78sDyXk9IyLm+uFRieasjf5Ryi+ovfeOrq+rWq2WflifKHV/sVwjIm7X5jPJ3dNXsmm7SFL0KJGG\nT1NLR8/eiWqrVCrp6NGj0ldffSUNGDBAsrCw0IiIK5VKqWvXrtIHH3wgRUVFyXf856+clIpLCqty\np055VN6ztY24rvpBXNfKNPaI+cGDB6Uff/xRsrCwkCO648aNk3r06CFJkiS1adNGjpjHxsZKCoVC\nWrlypcZaMTExkkKhkH766Sd57J/RYUmSpNmzZ0tKpVK6fPmyJEmSdOPGDUmhUEhff/31PX1VKBTS\nzJkzK423aNFCeu655yq9pu7du0sqlUoeV6vVUuvWraW+fftqHF9aWiq1adNG6tmzpzx2O0L94osv\nymMqlUpq3ry5pFAopNmzZ8vjubm5krm5uTR27Fh57LfffpOUSqW0Z88ejXP99ttvkkKhkLZv367x\nukxMTKQLFy7IY8ePH5cUCoW0cOFCeezLL7+UFAqFdOnSJY01N2zYICkUCunQoUNartq90WfEXGz+\nfEQ5e/k463b+VNdu6IWnQl/Gytymrt2oMZIksSNOIuQ1eP1LXw4m3vnvaVR2CuuCX1BKxdjd/ILe\npo/z9SupWBmk8NNPPzFq1CicnJzo0KEDU6dO5e+//6agoAA/Pz8mTZrEhg0byMnJ4eDBg3z22WeE\nhYXJ0YC/D67h7JUTVblVJ5SWlaCWtG8IFQgEgvrEU089RVlZGRs2bKCoqIgNGzbwzDPPVLJbu3Yt\nlpaW9OvXj+zsbPmndevWODo6snPnTtnWzMwMqNgYn5eXR3Z2NkFBQUiSJDdeMzMzw9jYmJ07d3Lj\nxg2dvZ6XXnpJY0P/sWPHOHv2LKNHj9bwOy8vj4iICA4ePEhxcbHGGi+++KL8d6VSSefOnVEoFLzw\nwgvyuI2NDa1btyYlJUXjGrVq1Qp/f3+Nc/Xq1QuFQqFxjQBCQ0Px8vKSf2/bti3W1tYaa1bF7eph\nf/31V6XKYHWJSGVppNwqymdt9H94ftB7WudNjMxISU/SOieoXSRJIjIePl0KMce1GahomvsBClSo\nVCqKiopIPHWY3r17c+nSJQ1TNzc3jQ2bzZo1u+/5fd07kHTpKG29tG/YrA0kSeLa9cucvnSY05eO\ncDH9DO+Onldn/ggEgrphy4HVbD24ptJ4/26jGNh99EPb6wM7Ozsee+wxVq5ciVKppKioiFGjRlWy\nO3v2LLdu3cLJyUnrOllZWfLfT548yXvvvcfu3bspKirSsLudXmJiYsLcuXOZOnUqTk5OdOvWjYED\nBzJu3Ditm/Wri7e3dyW/AQ1RfTcKhYKcnBxcXV3lMXd3dw0bGxsbjIyMcHR01Bi3trbWeN1nz57l\nzJkzODg4aD3P3bbazgMV/x7VuVHp3bs3I0aMYObMmcybN4/evXszdOhQxowZg7m5+X2P1xdCmDdS\nUtKTKCotqHLewdaFrLx0JEkSpZzqCLVa4v9iYM4KiD+t3UZS3cRX8W/SMnaTXVRUqamPnZ0doaGh\nshhv2bJljf89fT06sHTLVw/6Mh6aqEMb2H30L5QKJX4enQhpN4DnB76PmYk5qaTVmV8CgaD2Gdh9\ndI0EdU3t9cWYMWMYP348+fn59O3bV85lvhu1Wk3Tpk1Zs6byjQRUfJ5DhfAODQ3FysqK2bNn4+Pj\ng5mZGVeuXGHChAka5WWnTJnC448/zsaNG9mxYweffvops2fPZtOmTZXyvv9JVVHi29H6u/0GmDt3\nLp07a29498/Xq22/UlXfTdJd1VLUajVt2rTR2ogOqBRsqmpflFTNCixr164lPj6eTZs2sWPHDl5+\n+WXmzJnDgQMHtN4c1AZCmDdSKhoL+VU5b25qiYHCgFtF+fU67aO4tAhTY7P7GzYgyssl1kTB57/C\nqX88bZPUpXDzAORFYqeOJj8zjqS7PjwVCgWurq5MmjSJiIgIOnTo8NAbNpvZt6C4pICcvAya2miP\n5OgTH1d/Ajy74GjnKm4SBQJBg+Txxx/HxMSEffv2sXz5cq023t7eREZG0q1bt3uWINy5cyc5OTn8\n+eefhISEyONVdWZu0aIFU6ZMYcqUKVy9epUOHTrw2WefycLczs6O3NxcjWNKS0tJT0+v1mu7HUG3\ntLTU6NCsD3x8fDh06JBOz3O/75XAwEACAwOZOXMmW7duZeDAgSxevJgPPvhAZz7UBJ3mmO/Zs4eh\nQ4fi5uaGUqnU+ub8+OOPcXV1xdzcnNDQUBITE3XpguB/pKQnadTA1oa9rQvZedX7j1kX5ORn8NmK\niQ2n9uh9KCmV+GmjhO9oGPdJhSiXJDXSrSNIV79EShwAcU3gVB+4MosbaftAkujYsSNt2rTByckJ\nf39/EhISeP/99+ncubNOqqjcrv+elHr04V/kP8gvyCXu9E5WbP2Gvw/8V6uNh3MrnJq4CVEuEAga\nLGZmZvzwww/MmDGDYcOGabV5+umnUavVfPLJJ5XmVCqVLJ5vf67fHRlXq9XMm6eZ3ldUVFQpzcXV\n1RUHBweNZjre3t7s3r1bw+6nn36qsrHbP+nSpQs+Pj7MmzePW7duVZr/Z3pJVVTnM37UqFFkZGTw\nww8/VJorKSnRev77cfsm6Pr16xrjubm5lfRFx44dAeq0GZFOI+YFBQW0a9eOZ599lvHjx1f6R5g7\ndy7z5s1j+fLltGrVik8++YS+ffty5swZLC0tdenKI01ZeRlXslJo4dL6nnb2Ns5k5127r4CvK06l\nHKK1e/sHEmxFJYVsi1vDsJDn9OBZzSgokvhxI8xbDVezJCi+AHlR//vZCeU5GvZ+/n70jehLeHg4\nvXv3xsbGBkmS+OOPP1AoFFXmJz4M3dtEUK4qu79hNTmVksDfB/5LVm4aLZu3w8+jI34enXS2vkAg\nENQ3xo4dq3X8tvgLCQlh4sSJfPnllxw/fpx+/fphYmLC+fPn+eOPP/j0008ZP348wcHBNG3alGef\nfZbJkydjaGjI77//TkGBZnrqmTNnCAsLY+TIkfj7+2NiYsKWLVtISkri66+/lu1efPFFXn31VUaM\nGEFERATHjh1j+/bt2NvbVyvwpVAo+Pnnn+nfvz/+/v48//zzuLq6kpaWJgv+6Ojo+65T1bnuHh87\ndiy///47EydOZPfu3fKG1zNnzrBu3Tp+//13evXqVaPzBAYGAjBt2jRGjx6NsbEx4eHh/Pbbb3z/\n/fc8+eSTeHl5UVRUxNKlSzE0NGTEiBH3fT36QqfCfMCAAQwYUNEWfMKECRpzkiQxf/58pk2bxhNP\nPAHA8uXLcXR0ZNWqVbz88su6dOWR5krWBRxsXe6bAjK89wuY1OM0kVMpCXRv82AdH02MTYlP2k1I\nu4F1kp4BcCNfYuEfMH/lNa5fjoa8SMiNhtJUDTsLG3f69g2jZ3BLbplcYeariyqtpVAo9PpB0aq5\n7jrE3izM4699KxnUYwz+Hp0wMBAZcwKBoPFRnaDRP2uFf/fdd3Tq1In//Oc/TJ8+HUNDQzw8PBg1\napScvmFnZ8fmzZt55513mDFjBlZWVgwfPpxXX32Vdu3ayWu5u7szduxYoqKiWLVqFQqFgtatW8t1\n0m/z0ksvkZKSws8//8zWrVvp1asXO3bsIDw8vNJrqOo1hYSEcODAAT799FMWLVpEfn4+Li4uBAYG\nalRgqao2enXHFQoFf/75J/Pnz2f58uVs3LgRMzMzvL29mThxIm3b3v+76p/n6dy5M3PmzGHRokU8\n//zzSJLEzp076dOnDwkJCaxdu5Zr165hbW1Np06d+P7772UxXxcoJD3lCVhZWfH9998zfnxFq/Dk\n5GR8fHyIj4/X2DwwePBg7O3tWbZsmTx29yMEG5v6m/9cX1GpyskvvIGdlebGhYSEBKDisVR9p6Ss\nmOlLnuOT55dgZvJg7YBXbPsG72b+BLV9TMfeafLP63r+Yh7/mrubvzZHUZodBUWnNA8wbILSNoye\nIWF8/FYEYcE+KBQK1u78ETtLe/oGDterv7WBrjYVN6T3bENCXFf9IK5rZYqLi+uuUYtAoCfu9b5+\nWA1ba6Gsa9euAVR6DO/o6Ehamqi8oEsMDAwrifKGxtnLx/Fw9HlgUQ4VZQBPJMfpXZiXlpZy4sQJ\nVvy2gbXro8i4FA+o7hgozcE6BGzCMHUM59UxHZj6jBJXhzvCNePGVY6ci+WdUV+Qn5+PtbW1Xn3W\nNyJfXCAQCASCmlMvnjHf60v8dgRCoDsawjU9n3GcpibuD+VrcSmcvniEuPg4lArd7XNWqVScPXuW\n+Ph44uPjOXzkKKUldzdXMACrnmATBjbhYNUdKwsDRoZk8XTvDGwtj5B+CdL/V4K8XFXG38eXEuAS\nxPnTF3n//fdxcnLihRdeoGnTpjrzW9eUlZdwIesErZ07612IN4T3bENEXFf9IK7rHTw8PETEXNDo\nuHnzJidPntQ617Jly4dau9aEubOzMwAZGRkahe8zMjLkOYHgNj5OHR56DXNjK8yNrcm5lYaD1YM3\nW5AkidTUVFmIJyQkkJ+f/4+Ttb0jxK17oTCsiHjbWZYxpk8Gw0OysDTVvgNeQqKlcydaOXdi48aN\npKamkpqayokTJxgzZgz9+/evVxFoSZJIvX6G+ORtuNh6oZZUGCjqxT2+QCAQCAQNmlr7NvX09MTZ\n2Znt27fLOebFxcXExMTw1VdVNzcRuXq6o6r8x8bcZKhZCweaWDvWuBZ6eno6UVFRREVFERkZyZUr\nVzTmDc09KLcMrxDiNmEojDVTtJo7wbtj4PnBRpibNgea3/N8PehJamoqf/zxhzxWXFzM9evXa3UT\nStShDTSz98DPo6PW+ev5mazb9RPZudd4Ycj7tHQL0Ks/ImdXP4jrqh/Eda3MP1u1CwSNASsrqyr/\nnz9sqUWdl0s8d+4cUFFz89KlSxw9epSmTZvSvHlz3nzzTWbPno2vry8tW7Zk1qxZWFlZMWbMGF26\n8UhTUlaMiVH1Hxuu3P4tAZ6BdGjZU49e1R3N7D2qZZeXl8euXbtkMf7P+vp2dvbYuoVxtTSMUotw\nyk28tN7MtGoO74+DZ/qBsVH1b3YkSWL69OkaX2K2trZMnz692mvoAoUCjl84qFWYp6Sf4af/m0Wf\njkN4fuD7GBka1apvAoFAIBA0dnQqzOPj4+VyPwqFghkzZjBjxgwmTJjAL7/8wnvvvUdRURETJ07k\nxo0bdO/ene3bt9+zA5agZsxb8x5j+71Jc0evatlbmFqRlXdNz17VP4qLi9m3b58sxOPj4zWaLZib\nm9OrV2/sPcJIvB7O4SvtyP1fnro2ud3O8xYfPGfJ8D5gYFDzpw9bt25l7969GmMffPBBreeY+7p3\nYO/xOVrnmjt68faoL3CwdalVnwQCgUAgeFTQqTDv06fPfTtJ3RbrAt1TWHKL6/mZNGvqXu1j7G1d\nuJqVrEev6gcqlYrDhw/LQjwmJkYjOm1oaEjPnj0JDw+nY2AYh9O68fMmY9JOVMxry/QxMYbRfSHM\nLxHf5kU1enytUqswUN7p2hkaGsrrr7/OTz/9RHl5Od27d6+TBgcuTT0oKyslKze9kgA3NDASolwg\nEAgEAj0idmw1Ii6mn6W5k0+NGrrY2zhz9Nw+PXpVM86kHkMtqavMca4ukiRx9uxZIiMjiYqKYufO\nnXK749u0a9eOiIgIwsPDCQkJITHVkoW/w5wvoKy86rWbO8FrT8CLQ8DeVkFCQlHVxlo4fDaGw2f3\n8uLgafKYqakp7777LkOHDmXmzJl8+umndZL3r1AoaO3enoOJ0Qzu+Uytn18gEAgEgkcZIcwbESnp\np/Fy8a3RMQ62LmTXo1SWmBNbCfC8/2bH3bt3884771BQUMAbb7zBa6+9xtWrV+WIeFRUFFevXtU4\nxtPTUxbioaGhODo6UlIqsSYKIt6C+NP3PmdYZ5g4HIYEgaHhg4nm3bFRTP/kfcaNel7rfOvWrVm1\natUDra0r2vv0YHvcOiHMBQKBQCCoZYQwb0QkpyUR1unxGh1jZ+XAraI8ylVlGBrU7Wa+clUZZ1OP\nMTL0lXvaXbt2jYkTJ5Kfn09xcTGbNm1iwYIFJCUladg5ODgQFhZGeHg4J29EMf3lb3CwdUGSJBKS\n4NOVEv+NhJx7bKA2N4Vx/WHScGjj9WBiXJIkDh48yMKFC4mNjQVgzW9/8MKzr2BgYHCfo2ufdt7d\naOfdra7dEAgEAoHgkaPRCnOVWkXsia0EBTxWo9SOhookSZSWl+BZw4i5gdKAua/+VueiHODC1UQc\nm7hhZW6rdb6oqIjY2FimTZvGuXPnKC0tBWDLli0AWFpa0qtXLzkqvm7dOoyMjAgICMDoxk32HD3D\n2VRnft0KSZfu7YuPG7z+JEwYCLZWD55SkpWVxauvvsrhw4c1xpOTk9m2bRsDBw584LUFAoFAIBA0\nLhqtYi0pK+L3XYu5cDWRZ/u/jVJZ/yKTukShUPDOqC8e6Nj6IMoBTqUkEOB5ZwOlSqXi0KFDcp54\nbGwsJSUlGseYmJgwfPhwXn/9dbp27YqRUcVrKSoq4vfff6e4uJilS5eiMLTmltFlCk0LKDSNAIWx\nVh8GdIdJI+CxbqBUPnyOd9OmTSs3I/ofUVFRQpgLBAKBQCCQ0V2f8nqGuYklX09cS0HxTVZHLUIt\n3btazKPEmTNn+Pnnn+vaDQ0kSeJEchxGpbZ89913DBs2jKZNm9KtWzc+/PBDoqOjKSkpwcrKCmtr\naxwdHXF3d6dHjx6sWLGCoKAgWZSrVBLfL9OsuiKV52NRtIGmue8Dksa57axgykg4uwY2f61gQA+F\nTkQ5gFKp5LXXXtMY69q1K8uWLbtnYy2BQCAQ1F+WLVuGUqmUf4yMjHBzc2P8+PFcunSJCRMmaMxX\n9RMaGiqv+ffffxMWFoaLiwvm5ua0aNGCYcOGsXr16jp8pYLaptFGzAGMDI15acgHLFr/MX/u/pnh\nvV9stB0uq0N6ejpr164lNjYWSZLo0aMH/v7+derTlStX5O6a27dv4+PMnzTmvb29CQ8PJyIigqCg\nIP744w8WLVoki+4vv/xSztM+lSzx6zb4bRsUnYvCSsv5ikx6gcIEQwMY1LMif3xQT1i9ajlzZuzF\nxMQEU1NTTExMMDExYciQIXKn2rs5fvw46enpmJqacv78ec6fP8/Zs2e1NssaMmQI33zzDa1ateK1\n114TXQEFAoGgkTBz5ky8vb0pLi5m//79LFu2jD179rB69Wr69esn2yUmJjJ79mwmTZpE9+7d5XEn\np4qu0fPmzWPq1KkEBwfz3nvvYWVlRXJyMnv27GHJkiWMHj261l+boG5o1MIcwMTIlFcen87CPz/i\nTOoxfD061LVLdca3337LhQsX5N/nzZvHkiVLatWH69evs2vXLjk95ezZsxrzjo6OshAPDw/Hw0Oz\nc+fkyZN54okn+OyzzzA3N8fDuzML1kn8+jccOnPHTmE9nSKT3pgXR2JWHI2BVFEqsUnzYD56GUaF\ng4PdnZu0xMREoqOjK/nr5+enVZj/9ttvrF27VmNsx44dPPnkk5iaanZeNTIyYvPmzVhbW1fvIgkE\nAoGgQfDYY4/RtWtXAJ5//nns7e2ZO3cuKSkpGoGaXbt2MXv2bIKDgxk5cqTGGuXl5XzyySeEhoYS\nFRVV6RxZWVn6fRGCekWjF+ZQkdby5lNzMDY0qWtX6pSnnnqKzz//XP49KiqKI0eO0LFjR4pKCjEz\nMdf5OQsLC4mNjZWF+OHDh5GkO6kkVlZW9O7dWxbjbdq0ue9TDSdnVx4bvYhf/q8M18ehXFXZRlJa\nUGTWnyKz/rg5lBPufwirsh3M+HAgtraV1/9n7vptTEy0v2e02efk5LB27VrGjx9faU6IcoFAIGj8\nBAcHM3fuXC5fvlztY7Kzs8nPzyc4OFjrvIODg67cEzQAHglhDjRqUZ6ecxlJUtHMvkWluVmzZuHn\n58eQIUPo1KkTrVq10ohSz5s3j5+XLuHDxc/y1ev/fehNsuXl5SQkJMhCfN++fXL1FKiIHt/usBkR\nEUGXLl3k3PD7ceaSxM+b4NetkHEdoOrjLMxgeG8YNwD6dDTEwKA70L1Ke10Ic4Bff/2VcePGcf1m\nJuWqcpzsXKs8p0AgEAgaFxcvXgTA2dm52sc4OjpiZmbGX3/9xZQpU2jSpImevBM0BBqlMN+yfzUd\nWvakmb3H/Y0bAbEn/sbOyqGSMD9//ry8yfOLL74gIiKCkSNHMmvWLNnm0KFDZGVkY2FmTe6tHJpY\nO9bo3JIkkZiYKOeJ7969W6MKiUKhoFOnToSHhxMeHk5wcDAWFhbVXr+gSGJdNPyyCWKO39tWoYDw\nzhVi/IleYGle/f0EkyZNYsSIERQXF1NSUiL/VJWD3759e1QqFSUlJWRnZ6NQKOjbty9jx45FpS5n\n6Zav6NK6lxDmAoFAUAOUQdL9jR4Cdaxu95nl5uaSnZ1NcXExBw8eZObMmTg7O/Pkk09Wew2lUsn7\n77/Pxx9/jLu7O0FBQQQHB2ukyQgeHRqdMFdLavYe30KPgL73tS0rL8PIsH6UCnwYktOTGNGqV6Xx\nu/PHMzMziYuLY9iwYfTo0YNDhw4xduxYXn31VRwcHLC3cSY771q1hHlqaqosxKOjo7l2TbNzaMuW\nLeWIeJ8+fWjatOk91ystK8HY6E5kWpIk4k/Dkr9g/frNFJYaUmTar0J5a8GvBYwfAM/0AzfHB/vQ\nDQgIICAgoNr2r776qvz3hIQEAHlT55+7f8bawo7eHQY/kC8CgUAgaBj0799f4/cOHTqCt4EZAAAg\nAElEQVSwbt06rKy0lR+omo8++ggvLy8WLVpEdHQ0O3bsYMaMGbRs2ZIVK1bQrZto+vao0OiEecb1\nK5iamGNnZX9PO7Wk5tt103is20jaejXcO9KS0iIyr1+luaOXxnhWVhbr16/XGBsyZAgKhYJPP/0U\nc3NzXFxc5DkHG2eyctNp1bxdpXPk5OSwc+dOWYyfP39eY97Z2VmOiIeHh+Pu7l5t/9VqFTOXvsz7\nz8yntMyWldsqouMnk0GpzqVZ1kdYqm9QZBLCdZsZlBtWvE5rC3g6Al4YAl18qTfVdo5fOMjxCwd4\nd8y8euOTQCAQCPTDd999h5+fH3l5eSxdupRNmzaxf/9+vL29a7zW2LFjGTt2LIWFhSQkJLB69WoW\nL17MoEGDSEpKwt7+3rpG0DhodML8/JWT+LjeP/KpVCh5KvQVfvy/WRj3N6G1e/ta8E73XLx2FlcH\nT4wMNRvmrFy5UiO329XVVb7j1vaBcTtiDlBQUEBMTIwsxI8ePaqxYdPa2po+ffrIUXE/P78HFqEp\n6ee4ltONlz63ZeNeKC27M2eT/w0G6hsAmJXsxTnrSVr0jeXFYRaMCAVz0wc75+GzMXi6+N735q2m\nXM/PZE3UIl4c8gEWpjWLlggEAoGg4REYGCinmzz++OP07t2bSZMmMWDAgPs+La4Kc3NzevXqRa9e\nvXB0dOTTTz/l77//Zty4cbp0XVBPaXTC/EJaIn4eHatl6+HckucHvcfPm+fy0uBpeDXz07N3uicl\nPQmvZr4aY5IkERsbqzH2/PPPy/W+/0lZWRlpKdf5e9tmvpm+lH379lFWdkchGxsbExQUJEfEu3Tp\ngqHhw711Ll2TWLoZfvjTjazc1yrNG5UlYlX4m8bYiy++xEcfWD7UeQESLx6isPgWwe3639+4BlzJ\nSqFf16fwdGmt03UFAoHgUUHXOeC1iVKp5PPPPyckJISvv/6a2bNnP/SagYGBQEUfEsGjQaMS5pIk\ncf7KKYb0rP5dpY9rG8Y/9hZLNn3Oa8M+orljRTQ5OzubNWvWsH//fvz8/Hj33XcxNtbexr0ucWnq\njo2l5l25QqFgzZo1REVFsXjxYs6cOcPIkSNJSkoCKq7TyZMniYqKIioqit27d3Pz5k2N47t06SIL\n8aCgIMzNH76UYnauxO87YU0U7DkKFUF4LRtBJYmmeTNQcKdbq4eHB++/89JD+wDQ2r0Dx87v17kw\nb+ctcgAFAoHgUSYoKIgePXrwn//8hw8//LBaxQ6Kioo4fPgwQUFBlea2bNkCgK+vb6U5QeOkUQlz\ngNeGfVTjyiJ+Hh0ZFfYayWmnae7oTXl5OQMHDpSL+sfGxlJaWsrMmTP14fJD0d6nh9ZxAwMD+vXr\nR79+/cjIyCA7O5uNGzcSHx/PkSNHyMzM1LD38PDA0NCQkSNHMnXqVJ2Va8q7JbFhT4UY3xEPKi01\nx++mZXMY1SuTnf/N5spdZWA/+uijKksX1pTWzdvz+66fUKlVGDxkeUiBQCAQCO5m6tSpDB8+nCVL\nljBlypT72hcUFBASEkJgYCADBgzA3d2dmzdvEhkZyebNm+nevTuDB4tiAo8KjUqYKxQKXB08H+jY\n9j53alwbGhoybNgwFi9eLI+tXLmSkSNH0qZNm4f2szbIzs4mOjpazhNPTk7WmG/WrBnh4eG0bduW\nAwcOcPjwYVQqFQcOHHjoZjiFxRKbYuG/kbBlv2beuDbMTOCpUHh+CIS0B4XCmZIXtvHzzz+zcOFC\nevToQVhY2EP5dDfWFrY0sXbk0rVzldKAqosQ9QKBQPBoU9XeqmHDhuHj48P8+fOZPHkySqXynvZ2\ndnYsWbKEzZs3s2LFCq5du4ZCocDHx4cZM2bw7rvvymsIGj8K6e5dffWEvLw8+e82NjZ6O09WVhbZ\n2dn4+VXOLb98+TK9emmWIOzUqRPr1q2rl/9Bbt26xd69e+X0lKNHj2rM29jY0LFjRwIDA3nuuefw\n9fVFoVCQnJxMv379UN0Vyv7yyy8ZMWJEjc5fUiqx7WBFZPz/YqCg6P7HdPWH5wZVVFexsdT+gZWW\nloYkSbi66rYe+MaY5RgZGjOw++gaH3v28nHW7fyJMX0n4+nSulK5RIHuENdWP4jrqh/Eda1McXEx\npqamde2GQKBT7vW+flgN26gi5tXl2LFjLFu2jC1btuDn58eGDRsq2TRv3hwPDw8uXbokj6WkpHDp\n0iU8PR8sKq9LysrKOHjwoCzEDxw4oLFh08TEhODgYDlPvFOnTrJYv/tGxMvLi+HDh7N27Vp57Ntv\nv2Xo0KH3zakvL5fYeRj+GwXrd0PuzXuaAxDgBaMi4Olw8Ha7/yafZs2a3X/RB6C7fzgFxbdqdExe\nwXU27F1Gctpphvd+kRbOrfTim0AgEAgEgkeTR0aYl5eXs2nTJpYvX64RTT527BhHjhyhY8fKlVzW\nrl/FtHenszN6F2PGjGHq1KnY2trWptsyarWaEydOyEJ8z5493Lp1R1gqlUrc3Nxo06YNr7/+On37\n9sXMzKxaa0+ePJn169fLwv7KlSusW7eOZ555ppKtSiWx/ySsjoTfoyEr9/7re7tWRMVHRUCAV/3Y\nce/UxK3atiq1ipjjf7M1bi092vTlg3GvY2IkIkACgUAgEAh0S6MR5vfr4qlQKPjqq6+4evVqpbnl\ny5drFeaHz+7FtbMp6yaupXPH2n80mZKSQmRkJFFRUURHR8ubUW/j6u7ME0NHEB4eTuvWrRkyZAhn\nzpxh2rRpHDlyhHfffbda1VTc3Nx4+umn+fXXXwFo0qSJXA6xqKSiC2fMMYg9DvtOQl41As2uDnci\n452r0QAoKSkJd3d3nVR/0TUqVTmXMs4xZcRnODdpXtfuCAQCgUAgaKQ0GmG+btePeDq3pkdAX63z\nBgYGjBs3js8//1xjvEWLFlXmAz7WdSTnr5wE82okTOuAzMxMecNmVFQUKSkpGvOurq5EREQQHh6O\nUwtrkq8f59XH/w3AZ599JueJFxYWsnfvXv79739X+9wTJ05ky5bNtGjvwainl5NwzpIFr0gkJEFZ\nefXWcLCFEWEVYjyoHSiV1YuOFxUV8cILLwDwwQcfMHDgwHrVNdPYyITxj71V124IBAKBQCBo5DQa\nYX7hyin6dLh3OaFRo0Yxf/58iouL6d27NxMmTKBXr15Vbub8//buPK6pK+0D+O8mEBJEdtmRfVEQ\nFxAFFQXEXbuodasVaEXbupTW145tR3AZcZmxrVX74lLRtxYto+87HXXqVhWoqOMCKovIooKyCoIg\nCCT3/SNjNLIlISEJfb6fD5+PnHvuzZPjUR5uzn0OwzDw9RyN9Lu/w9djlNJjfvr0KZKTkyWJ+M2b\nN6WOGxsbIyQkRLJO3N3dXZKw/m/yD3Cy9pRc5/Dhw1Lnvv/++50+pMqyLO6XAqk3gdQMCzxzTcXR\nHD6Oxsr+HowMgLdGi5PxEF9AR6fzhLqmvgq3C/6NEQPGAwB27tyJR48eAQCWLFmCoKAg7Nu3TyMf\nsiWEEEIIUZUekZjX1FWh/nkdrMz6dtjP2NgYW7ZsQf/+/eHs7CzTtX1chuF/k3/A86YG6PFertkW\nCoW4d+9em9vbt6epqQmXLl2SJOKXL19GS8vL29F8Ph+jRo2SJOKDBw9ud7fOgpIcTBsh3kjp8OHD\nUhsEmZmZ4e233251jlAE5JcIcPk+i99vihPyYqly5rKtmzY1BMb5i5eqTBgG6PHku7t950EG7jzI\nwIgB43Hv3j3s2rVL6ri7u7takvLiigKcuXoUc8OWgqejnJrphBBCCCGy6hGJed7DTLjY9AOH4SA/\nPx+rV6/GggULEBoa2iqxlbdIfy9+bzhaeyDz3jUMcR8JALh+/TpiYmJQUlKCs2fPtlsORyQS4ebN\nm5J14snJyXj27JnkOIfDwbBhwyTLUwICAmQqK9XU8hwllffhYCmuCpKRkSF1fP78+ZLNeB6Usjj9\nb+D0FeDXSwNR+0z+v3JHa3F98RE+wEgfwNNB9mUqbblbdAtudt4AgHXr1qGpqUlyrE+fPli2bJnC\n15bXySs/Q4fLw5O6Sly/k4LJgfOgw23/WQVCCCGEEFXpEYl5/sNMuNqKE72EhARcvHgRFy9ehL29\nPVauXNnlHbOmB72PXgLxpjurV6+WPCQJAFu3bpXsCMqyLAoKCiSJ+Llz51BZWSl1rf79+0sS8dGj\nRytU47KoLA9Wpvbg6YqT7++++w6RkZHYvXs3zp+/AAv3eVj2NYvTV4A7D149s/O/boZh4dH3OUL9\n+BjpAwR4i9BQkwcPDw+542zP3eJbCPV7CxkZGfjtt9+kjq1atQq9e/dW2mt1xszQEgdOfo3hXmOx\nav53MBB0bXMlQgghhBBF9YjEvK6hFgHeYaitrcXRo0cl7UVFRRCJRF2+/qul9czNzaWOJSQkwMDA\nADk5OTh79qxU3XNAXA89NDQUY8eORUhICKytrbscj425I+aGLQUgLl94Ixc4dXMQsjk7UGBWg3nr\nZU/29XjAsP7AyIH4TyLOwMhAAJZlcfr0aUSFb0VxcTGSk5Nhamra5dgf15ShRdgCSxM7WJnaIyEh\nAWvWrEFhYSH8/Pzw5ptvdvk15DHYfSTsLVzkKp9ICCGEEKIKPSIxj5y8EgCwZ88eqaUilpaWmDhx\nolJfa86cOdi1axcePHiAxsZGNDc3Y+XKlZLjpqamCA4OltwVd3V1VXqFkcon+jh1pS9OX2Fx5ipQ\nVfvq0Y6T8t6CFowZooMRA8XLU4a4t71GPDIyEufPn5d8Hx8fj1WrVnU59tziW3C185aMyejRo/Hr\nr7/ihx9+QFBQULdXY+FyuJSUE0IIIUQj9IjEHBA/jHngwAGptnnz5kFXt2vrhZ8/f45Lly5Jlqdc\nuXJFavt6hmGgp6eHefPm4aOPPsKgQYOU/uBidS2L1JvAmaviteI59zs/5wUuFwjwAsL8Afve2ejX\n9xmG+Xdekz0wMFAqMT9w4ADef/99WFhYKPAOXnK26Qe7PtI7p/J4PCxevLhL1yWEEEII0XY9JjG/\nf/++1N1yHo+HuXPnyn0dkUiE9PR0SSKekpKChoaXdcy5XC4CAgLQ0NCA0tJSWFlZYdWqVZgxY4bS\nEvKSShYpGUByurhyyq18gGVlP9/NHggbKq6cMmYIYNhLfBf66tVnnZz50vz587Fnzx6Ul4vLtjQ2\nNmLHjh2S9fSKEAqFyLxxB0OGDFH4GoQQQgghPVWPScydnZ3x+++/49ixY0hISICnpyfMzMw6PY9l\nWeTl5eHs2bM4c+YMzp07h6qqKqk+3t7eCA0NRXBwMPyGDYGtlT2KioqwZ88eREdHw9jYWOG4WZZF\nwUOIE/EM8Q6becWdn2dcuwkM24LaXuHobWKLUF/xXfGwoYCTTdeXg/D5fCxZsgSrV6+WtCUmJiIq\nKgq2trZyXau4uBhJSUlISkpCSUkJVq9ejYiIiC7HSAghhBDSk/SoHVz09PQwffp0/PLLL1i3bl27\n/UpKSnDw4EFERETAwcEB7u7u+PDDD3HkyBFUVVXBwcEBkZGR+Omnn1BaWopbt27hm2++gbkzH2fS\nkwCIH+pcs2aN3Em5SMTiVj6LnUdZzFnNwv5NwG0WELkBSDguW1Kui2oYP9sPw/q96Fs5BnNdlyH+\ns2pEvcEoJSm/X5qL+sanmDVrliQJt7OzQ1xcHCwtLWW+TkZGBhYsWICgoCBs27YNJSUlAMR111l5\nPgIghBBCNExCQgI4HA6uXLki1V5XV4dRo0aBx+NJClLExsaCw+G0+bV169ZujbuhoQGxsbG4cOFC\nt7xeVlYWYmNjWxXHIG3T6jvmZVXFaGppgr2F9GZBDMNI1QOvqanBhQsXJHfFs7KypPqbmZlJdtgc\nO3YsnJ2d23wIcYDzMPySuh/NLU3Q1eHJFGN9A4tb+eIlKSn/WZpS/bTz86TfDzDARVw15WnDXjgz\n5UjY0wgAEImEuH79mlJLDJ64dAgjfSZggLM/vvjiC1RXV2PmzJng8WR7zy80NzcjOTm5VfudO3eQ\nnp6OwYMHKytkQgghRO3q6+sxadIkXLlyBYcOHWq12d+OHTtalUn29fXtzhBRX1+PtWvXgsPhYPTo\n0Sp/vaysLKxduxYhISFwcHBQ+etpO61OzNMyz4DPE7RKzBsbG5GWliZJxK9evSr1wKa+vj6CgoIk\nibiPj49M68MNexnDto8Tch6kY4Czv9QxkYhF4SPgZj6QfleIzAIubuYD+Q/lWx8OADpcwM9TXMIw\naBAwYgBgYsigrqEWq/ecxj/350v1Dw8P7/JDrq8yN7JCZU0pAGDSpEmd9m9ubm7z9X19feHq6oq8\nvDxJm0AgwJQpU2BoSPXCCSGE9BwvkvLLly8jMTGxzR24p0+f3uUiCsrS3Z9c0yflslHLUpadO3fC\nyckJAoEAfn5+SE1NVeg6+Q8z4WLrBaFQiKtXr2LTpk0YN24cTExMEBISgr/85S+4fPkyGIbBiBEj\nsHr1aly4cAHV1dX417/+hRUrVshdRWWQ2wik3rqKlHQWO46wWLSZRWAUC6NxgNs7QixYfgB7N43H\n/56rRV6xbEm5QA8I8QVWRwKnvwWqTwIXdzHY/DGDKSMYmBiK794XluTgWTEXjx8/lpxrYGCA2bNn\nyz12HTE3tsLj/yTmHcnOzkZMTAz8/f1RXNx6DQ7DMJg1axYAwLOfB8JmDMfly5exefNmuLi4KDVm\nQgghRF2ePXuGyZMn49KlS+0m5V1x5MgR+Pn5QV9fH+bm5pg7dy6Kioqk+owZMwbBwcGtzg0PD4eT\nk7ga2r179yS/GKxZs0aynCYyMhLAyyU32dnZmDt3LoyNjWFqaorFixejvr5e6rocDqfNghCOjo6S\n58gSEhLwzjvvAACCg4Mlr/d6FT3yUrffMT98+DA++eQTfP/99xg5ciR27NiBiRMnIisrC/b29jJd\ng2VZ3Lp9EyeOnsW3Kw+jqqqq1YTx8fFBaGgoQkNDERQUpNBSj5YWFrlF4rvgN/PE1VEy8sahuJzb\nqq9e0zVYP4kBr0W8TMb46deoNopp87pGBuJlKaMGAUEDgSEeAE+387XhhY9y0FLPBcMwkt88Z82a\npfS7z+ZGVsi5n97mMaFQiKSkJCQmJuLmzZuS9qSkJERHR7fqP2PGDAQEBKCq5T4elOV1666ehBBC\ntMuLBPJ1hYWFSumvCvX19Zg8eTLS0tI6TcofP34sdTOQw+F0unnfjz/+iPfeew9+fn7YuHEjysvL\nsW3bNqSmpuLGjRuSQhcMw7S7F8iLdgsLC3z//ff48MMP8fbbb0tiff1m2ezZsyXPlt24cQO7du1C\nUVERjh8/3uZ1X297da+SZcuWYdu2bfjyyy/Rr18/AOKSzKRt3Z6Yb926FREREXj//fcBANu2bcOv\nv/6K77//Hhs2bGj3vEePHuHs2bOS5SkPHz6UOs7j8eDr64tly5YhJCRE7o+KGp+zuFUA3MgVf6Xn\nihPyhuev92ydlAMA/3mqJCkHgN71/4M6/XfQwusHVztgkJt4Q59RAwFvZ4DLlf8hzcKSHKz4r8/w\n5WdrsW/fPvzf//0fwsPD5b5OZ8yNrCVLWV7H5XLh7++Pv/71r1LtSUlJWLZsGbhc6fExNjaGsbEx\nfjh+HN7OQ5UeKyGEEKJOERERePToUZtryl/n5eUl9b25ubmkLHFbmpubsWLFCvTv3x8pKSnQ09MD\nAISFhSE4OBgbN27Eli1bAIhvWraXmL+4maevr4/p06fjww8/hI+PT7tlpe3s7KSScGtra6xbtw5n\nz55FaGhoh+/xVU5OThg5ciS2bduGsLAwBAUFyXzuH1W3JuZNTU24fv261E6ZADBu3DhcvHixzXOW\nLl2KM2fOICcnR6rdyLg39Ph8CJtF4PP50NXVRXBwsEzLOmrqWKTffZmA37gLZN0DXlmGLrdag0Uw\nbDwKTrP4oyUGIgT3WY2/J/0MA/2urxgSsSJUPa2Ag5U7BHr6WLt2LVatWgWBQNDla7/O3MgSfS1c\nWv0jb25uxpEjR/Ddd99JLacBxBsx3bt3r80lKiJWhLsPb+OtICqRSAghpGcpLy8Hn89H3759O+2b\nlJQEExMTyfedFVW4evUqysvL8ec//1mSlAPiO9G+vr44fvy4JDFXpiVLlkh9v2zZMqxbtw7Hjh2T\nKzEn8uvWxLyyshJCobBVyT0LCwuUlrZ9h3b79u0AxA8NDhkyBEOHDsXQoUNRWnMP323eDbwsvgI/\nPz9cvXpV+jVrdZBbrI87xfq481AfucUCFFfy0RVcDgtHy0a42jyDq3UDXG0a4GrbgKK8edi0aaOk\n352sa4j//mulPfU8ZUAUMm9ldd6xE6+PUVu8+ozGtWvXpNoyMzMRGxsr1ebj44OxY8fCz88P1dXV\nbV67ur4cHJaL/Dv3AfTcckmyjCtRDI2tatC4qgaN60sODg5SVdJ6ovj4eKxYsQITJ07EhQsX0L9/\n/3b7jho1Sq5P9F+UGPTw8Gh1zNPTE0eOHJE/YBm4ublJfW9mZgYTExMqefgfT58+xe3bt9s89vrY\nyUvjq7JERUVh6NCh8PLykqr8cfK7k1L9fHx8YG1jj8z7+kjPN0B6gQEy7/dCZa18Jf5eZ2rQDDfb\nBrjZPhMn4DYNcLRsBE+n9VOdln6+8PX1lSS07u7uMv0GLav2PqLqLl5eXoiOjkZaWhrs7OwwZswY\nmeqaP657BEsjKpFECCGkY/KuDe/OteTt8fDwwMmTJxEcHIxx48YhJSWl3bXvyvZqXtBejiDsynKA\nV8haVaWlpUUpr/dH1a2Jubm5ObhcLsrKyqTay8rKYG1t3eY58fHxrdpaWlpQUVEh1VbOX4qxX/ji\nWaPi8TlaA4PdgMEewGB38Z+tzXXBMDwARp2eD4jX0M+ZMwfR0dF4++235ar40haWZVFZWYlnz551\nuf7ni7s4fn5+Cl/Dz88Py5Ytk+8c+EEobAGXq/G/BypEGeNK2kZjqxo0rqpB49paY2MXfihrkUGD\nBuHYsWMYN24cwsLCkJKS0m5eI48XP/dzcnIwduxYqWM5OTlwdHSUfG9iYtLmLyr379+XKYF/VW5u\nLlxdXSXfV1ZW4smTJ61e78mTJ1LnNTU1STYTlOf1tE3v3r3b/XdeU1PTpWt3a7nEFw9onjp1Sqr9\n9OnTMj2hW1bF4sg5Fv+1g4tyy3+iwjwBz/TGoJnriMtFwTIn5RwO0N8ReHc88NelwNltwON/AQV/\nZ3AkjsFX4QwmBzKw6dP+E87t6du3Ly5cuIAZM2YonJTX19cjIiICY8eORb9+/eDvL97op72PTbRB\nT03KCSGEEAAYMWIEjhw5gqKiIowbNw5VVVVdvubQoUNhaWmJ+Ph4PH/+shpFSkoKrl27hilTpkja\nXF1dkZOTg8rKSklbRkYGfv/9d6lr6uvrA0CH8b1YRvzCtm3bAACTJ0+WtLm4uLTaPXTXrl0QiURS\nbb169er09chL3Z4tffrpp5g/fz78/f0RGBiI//7v/0ZpaSkWL17cZv99x1mk3gRSM4C7UiU7OQAv\nCM/MgsCIngFM20mwHg/wcQEG/ecO+GB38S6a+vyu/wZ36koSHK094W4/QKpdR0d6WFmWxd27d1FU\nVISioiIUFxejqKgIpaWlOHr0aKtKJvr6+khLS5P6R3jx4kVMnToVw4cPx5YtW2BnZ9fl+AkhhBCi\nPBMmTMCPP/6IOXPmYOLEiTh79iwMDAwUvp6Ojg62bNmC9957D6NGjcK8efNQUVGBbdu2wc7ODp9/\n/rmkb2RkJLZu3Yrx48cjMjIS5eXliI+Ph7e3N2prayX9BAIBvLy8cOjQIbi7u8PU1BTOzs7w93+5\nceKjR48wadIkTJ48GRkZGdizZw/Gjx8v9eDnBx98gMWLF2PGjBkYO3YsMjIycOrUKZibm0stexky\nZAi4XC7i4uJQXV0NgUCA4cOHS919Jy91e2L+zjvv4PHjx1i/fj1KSkowYMAAnDhxot0a5u+3X0FR\nguXoS/5sbSYuSTjCR7xzprczoKujmo9RdHR0ce1OcqvE/HUMw2DGjBl4+vRpq2NlZWWwsbFp1d/O\nzg75+fmt+t+/f19Ss1SVGpsakFn4b/h6UGkjQgghpC1tfao+c+ZM1NbWYuHChXjjjTdw4sSJdvvK\n4t1334W+vj7i4uLwpz/9Cb169cKUKVOwadMmqRronp6eOHDgAFavXo3PPvsMXl5e+PHHH3Hw4MFW\nd7b37t2LZcuW4bPPPsPz588RHh4ulZgnJiZi/fr1+PLLL8HhcLBw4UL87W9/k7rGwoULUVhYiL17\n9+LXX39FUFAQTp8+jdDQUKn3amFhgd27d2PDhg2IioqCSCTCvn37KDFvB8Nq4B6pr67PMZnU8eY5\nHn3FSfiogeJNe5xtu289U1VtObYcWoH17//Q6VKNSZMmITs7u1X7oUOHMGzYsFbtEREROH/+PADx\n7p729vbw9PTEhx9+qPATv/Ksf2x4/gx/3huJLR8m9sj1YcpE60pVh8ZWNWhcVYPGtbXGxsYeX5Wl\nJ4mNjcXatWtRWloq934wfyQdzetXc1gjI9meT3yVVi385XIBF9squNk/QuRkb4zwASxM1Jc0mhpa\nwNzQEneLb8PTYVCHfe3t7dtMzIuLi9tMzFesWAHvkX1hY2eD2eOiuj05FujpQ1eHh6fPnsCwl0nn\nJ7RBJBLiQXk+HK3clRwdIYQQQkjPo/GJeajfyzvi5/6xFvcfZ+CDmYswemjHy0e6yyC3QKTnXew0\nMR84cCCePn0Ke3t72NnZwd7eHvb29u3e/bayN0dFagEWB32mtjvWff6zA6iiiXlReQESz2zHqne3\nKTkyQgghhJCeR+MT89PfipPSkpISLEr8HwiFQlw5uwzTpk1DTExMlx6qUIZBroH49u9fdLgVLgB8\n9NFH+Oijj2S+7skrSRjlMwG9BB0v5VElcyMrVDwpgbNNP4XOv1t8C2523kqOip7BnxEAABN/SURB\nVBBCCCGqwDDyV6MjytWt5RK74scff5QUyW9qakJ6erqkBI86mRlZ4ov525U6kYXCFlTVlCF48BtK\nu6YizI2sUFnT9o6ssrhbfBtudprxyQYhhBBCOhYTEwOhUEjry9VIKxLzxsZGJCYmSrWFh4drzG91\nfJ5AqdfjcnWwZPo66PPV+2mAR9+BsDF3VOhcobAFBSXZcLX1Um5QhBBCCCE9lMYvZQGAf/zjH6iu\nrpZ8b2hoiLfeekuNEf0xuNj2V/jcB+V5MDe0VOtSHEIIIYQQbaIVd8zT09Olvp89e7Zk5yqiuUYN\nnKTuEAghhBBCtIZWJOZxcXE4duwYZsyYAYFAgPnz56s7JNIJJ2tPBHqPU3cYhBBCCCFaQysScwDw\n8vLCli1bcOXKFY3cjp5lWdwquAIRK1L4Gs0tzUqMiBBCCCGEaBOtScxfUHd5xPYwDIPjaT+h8FHr\nTYRk8ajyHrYkfgoN3IiVEEIIIYR0A61IzFmWxfPmRnWH0anBboG4cfeiQuf+6/JhDPcK1ZhKMy/k\nP8xC9v0b6g6DEEIIIaTH04rEvKy6GJsPRqs7jE4Ncg1ERl6a3MtZiisKUFiSg5EDJqooMsWVVhXh\nem6qusMghBBCyCtiY2PB4XBQXl6u7lCIEml8Yl5QUID8h1lwsvFUdyidsjS1gz7fAPdK7sh13olL\nhxDmNx08XT0VRaY4eTcZam5pQtK5XbQkhxBCSI928eJFrFmzBjU1NeoOhfQgGp+Yh4aGInZVHPgi\nU3WHIpNBroFIl2M5y4OyPBSV52tsBZM+xtZyJeaFJXfwoDxP45bkEEIIIcpEiTlRBY1PzAEgP/sB\n+jkPVHcYMvHvFww3e9m3oedyuHgneBF0dXgqjEpxxgZmqG+oRVPLc5n63y2+BTc72d8/IYQQos1k\n+YS4oaGhGyIhPYFWJOZ9Pfugv5t2JHtmRpYY4Owvc3/bPk5y9e9uHA4Xpr374HFNmUz9xYm5t4qj\nIoQQQtQnNjYWK1euBAA4OTmBw+GAw+HgwoULcHR0xMSJE3H27FkMGzYMAoEAmzdvBgD88ssvmDp1\nKuzt7cHn8+Ho6IiVK1fi+fPWN79yc3MxZ84cWFhYQCAQwN3dHdHRHT9v9+jRI/Tv3x/u7u4oLi5W\n/hsnKqej7gBkMfXtCbQ0Qo0mDp8NgV6vTvs1NT9HcUUhnG36dUNUhBBCiHpMnz4dd+/eRWJiIr75\n5huYm5sDAPr16weGYZCXl4eZM2ciKioKCxcuRN++fQEACQkJEAgEWL58OYyMjJCWloavv/4aRUVF\nSExMlFw/MzMTI0aMgI6ODqKiouDs7IzCwkL8/PPP+Prrr9uM6f79+wgNDQWfz0dKSgosLS1VPxBE\n6TQ+Mffx8cGnkbHqDuMPzdcjSKZ+BY+yYWfuBD1dvoojIoQQQtRnwIABGDx4MBITE/Hmm29KEm9A\nvLQlPz8fv/zyC6ZMmSJ13sGDByEQCCTfL1y4EG5ubvjqq6+wZcsWyQaKH3/8MUQiEa5duwYHBwdJ\n/7/85S9txpOXl4fQ0FCYmZnh9OnTMDMzU+bbJd1I45eyRERE0N1yLdHX0hXvhCxWdxiEEEK0FMMw\nKv3qLvb29q2ScgCSpFwkEqGmpgaVlZUYMWIEWJbFjRviPUMqKiqQnJyM8PBwqaS8PVlZWQgKCoK1\ntTXOnTtHSbmW0/jEfPLkyeoOQWHt1TMvq36I2vrqbo5G9fT5BrAx7/w/EUIIIaQnc3Z2brP99u3b\nmDRpEnr37g0TExNYWFhgzJgxACCp7lJQUAAA8PaW7XmtadOmQV9fH2fOnIGRkVHXgydqpfGJua6u\nrrpDUEj10wpsOvhJq6e1WZbFobM7aTdNQggh5DUsy6r0q7u8ulzlhZqaGgQHByMnJwcbNmzAP//5\nT5w5cwYJCQkAxHfRFTFz5kwUFBRIrkO0m8avMddWxgbmaBG2oKg8H30tXSXtuUU3UVtfDT/P0WqM\njhBCCCFdIe/SmHPnzuHx48c4evQoRo0aJWk/ffq0VD8XFxcAwK1bt2S6blxcHPh8PpYvXw4DAwOE\nh4fLFRfRLBp/x7y5pVndISiEYRgMcg2Q2myIZVmcuJSICcNmgcvhqjE6+R27eBDVTyvVHQYhhBCi\nEXr1Elcrq6qqkqk/lyv+uf/qnXGRSIStW7dK9TM3N8fo0aORkJCAe/fuSR1r767/jh07MH/+fCxc\nuBBJSUmyvgWigTT+jjmXo/G/O7RrkNsI/HBiE6aOmA+GYZDzIB3PGuvg6z5S3aHJrbAkBy62/WHS\n27zN40KRUOt+2SCEEEIUNXToUADAqlWrMGfOHPB4PISEhLTbf+TIkTAzM8OCBQuwdOlS6Ojo4O9/\n/zvq6+tb9f3uu+8wcuRI+Pr6YtGiRXBycsKDBw9w+PBh5Obmtnn9H374AXV1dXj33XfRq1cvTJo0\nSTlvlHQrjc96OVqc7Nn1cQIAFFcUAgD+dfkQJg6frZXvydzICpU1pW0ea3hej9V734dIJOzmqAgh\nhBD18PX1RVxcHLKyshAZGYl58+YhOzu73SUuJiYmOH78OOzt7RETE4ONGzdi4MCBOHDgQKu+3t7e\nuHTpEkJCQhAfH4/ly5cjKSkJ06ZNk/R5vdIMh8NBYmIiQkNDMXPmTJw/f17p75monsbfMddmDMPA\nv18ISquKYG/hjHljl6KPiY26w1KIubE1HreTmOc9zIS1WV+t/IWDEEIIUdTnn3+Ozz//XKqtsLCw\n3f7+/v5ISUlp1d7Wg5+enp4dLkuJiYlBTEyMVJuuri5OnDjRWdhEg1FirmITh82S/NnS1E6NkXSN\nuZEV7pXktHnsbvFtuNkN6OaICCGEEEJ6Fo1fykI0Q0dLWe4W36LEnBBCCCGkiygxJzKxNLHF1MD5\nrdrrG5+isqYUDq+UhCSEEEIIIfKjxJzIhKerB2/noa3ay6sfop/DYHC5tCqKEEIIIaQrKJsiXeJk\n7Qkna091h0EIIYQQovXojjkhhBBCCCEagBJzQgghhBBCNAAl5oQQQghRmfa2kSdEG6l6PistMd+1\naxeCg4NhbGwMDoeDBw8etOpTXV2N+fPnw9jYGMbGxnjvvfdQU1OjrBCIilXWlOLQ2R3qDoMQQoiW\n4PF4aGxshFBIO0MT7ScUCtHY2Agej6ey11Daw58NDQ2YMGEC3nzzTURHR7fZZ+7cuSguLsbJkyfB\nsiw++OADzJ8/H7/88ouywiAqpKcrQPrdNMwO/RgAkJF3CV5OvtDh6qo5MkIIIZqIw+GAz+ejqakJ\nzc3NCl3j6dOnAIDevXsrM7Q/PBpX+TEMAz6fD4ZhVPYaSkvMly9fDgC4evVqm8ezs7Nx8uRJ/P77\n7xg2bBgAID4+HqNGjUJubi7c3d2VFQpREQOBIYSsEM8a69AsbELime3YELVf3WERQgjRYAzDQE9P\nT+Hzb9++DQDw8/NTVkgENK6aqtvWmKelpcHAwAABAQGStsDAQPTq1QtpaWndFQbpAoZh0MfIGpU1\npcgrvg0X2/7gcLjqDosQQgghpEfotjrmpaWl6NOnj1QbwzCwsLBAaWnbW70D7d+BJ4rryphyRXq4\nfP13lNbcg7F+H/r7eQWNherQ2KoGjatq0LiqBo2ratC4Kpebm1uXzu/wjvlXX30FDofT4VdycnKX\nAiDaxYBvgqeN1Situ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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_rts(noise=7., Q=.1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This underscores the fact that these filters are not *smoothing* the data in colloquial sense of the term. The filter is making an optimal estimate based on previous measurements, future measurements, and what you tell it about the behavior of the system and the noise in the system and measurements." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Fixed Lag Smoothing\n", + "\n", + "The RTS smoother presented above should always be your choice of algorithm if you can run in batch mode because it incorporates all available data into each estimate. Not all problems allow you to do that, but you may still be interested in receiving smoothed values for previous estimates. The number line below illustrates this concept." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from smoothing_internal import *\n", + "with book_format.figsize(y=3.):\n", + " show_fixed_lag_numberline()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At step $k$ we can estimate $x_k$ using the normal Kalman filter equations. However, we can make a better estimate for $x_{k-1}$ by using the measurement received for $x_k$. Likewise, we can make a better estimate for $x_{k-2}$ by using the measurements recevied for $x_{k-1}$ and $x_{k}$. We can extend this computation back for an arbitrary $N$ steps.\n", + "\n", + "Derivation for this math is beyond the scope of this book; Dan Simon's *Optimal State Estimation* [2] has a very good exposition if you are interested. The essense of the idea is that instead of having a state vector $\\mathbf{x}$ we make an augmented state containing\n", + "\n", + "$$\\mathbf{x} = \\begin{bmatrix}\\mathbf{x}_k \\\\ \\mathbf{x}_{k-1} \\\\ \\vdots\\\\ \\mathbf{x}_{k-N+1}\\end{bmatrix}$$\n", + "\n", + "This yields a very large covariance matrix that contains the covariance between states at different steps. FilterPy's class `FixedLagSmoother` takes care of all of this computation for you, including creation of the augmented matrices. All you need to do is compose it just as if you are using the `KalmanFilter` class and then call `smooth()`, which implements the predict and update steps of the algorithm. \n", + "\n", + "Each call of `smooth` computes the estimate for the current measurement, but it also goes back and adjusts the previous `N-1` points as well. The smoothed values are contained in the list `FixedLagSmoother.xSmooth`. If you use `FixedLagSmoother.x` you will get the most recent estimate, but it is not smoothed and is no different from a standard Kalman filter output." + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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AXi85OZldu3YRGxvb6H0Za1X+vR7+vAwOHGm437C+8OyvYfZ4cHNrP4EcLlRD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\nIjID/w9l7ekaxOgMEAAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "standard deviation fixed lag: 0.682200657746\n", + "standard deviation kalman: 0.915729357528\n" + ] + } + ], + "source": [ + "from filterpy.kalman import FixedLagSmoother, KalmanFilter\n", + "import numpy.random as random\n", + "\n", + "fls = FixedLagSmoother(dim_x=2, dim_z=1, N=8)\n", + "\n", + "fls.x = np.array([0., .5])\n", + "fls.F = np.array([[1.,1.],\n", + " [0.,1.]])\n", + "\n", + "fls.H = np.array([[1.,0.]])\n", + "fls.P *= 200\n", + "fls.R *= 5.\n", + "fls.Q *= 0.001\n", + "\n", + "kf = KalmanFilter(dim_x=2, dim_z=1)\n", + "kf.x = np.array([0., .5])\n", + "kf.F = np.array([[1.,1.],\n", + " [0.,1.]])\n", + "kf.H = np.array([[1.,0.]])\n", + "kf.P *= 200\n", + "kf.R *= 5.\n", + "kf.Q *= 0.001\n", + "\n", + "N = 4 # size of lag\n", + "\n", + "nom = np.array([t/2. for t in range (0, 40)])\n", + "zs = np.array([t + random.randn()*5.1 for t in nom])\n", + "\n", + "for z in zs:\n", + " fls.smooth(z)\n", + " \n", + "kf_x, _, _, _ = kf.batch_filter(zs)\n", + "x_smooth = np.array(fls.xSmooth)[:, 0]\n", + "\n", + "\n", + "fls_res = abs(x_smooth - nom)\n", + "kf_res = abs(kf_x[:, 0] - nom)\n", + "\n", + "plt.plot(zs,'o', alpha=0.5, marker='o', label='zs')\n", + "plt.plot(x_smooth, label='FLS')\n", + "plt.plot(kf_x[:, 0], label='KF', ls='--')\n", + "plt.legend(loc=4)\n", + "plt.show()\n", + "\n", + "print('standard deviation fixed lag:', np.mean(fls_res))\n", + "print('standard deviation kalman:', np.mean(kf_res))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here I have set `N=8` which means that we will incorporate 8 future measurements into our estimates. This provides us with a very smooth estimate once the filter converges, at the cost of roughly 8x the amount of computation of the standard Kalman filter. Feel free to experiment with larger and smaller values of `N`. I chose 8 somewhat at random, not due to any theoretical concerns." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -606,6 +767,8 @@ "source": [ "[1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965).\n", "\n", + "[2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006.\n", + "\n", "http://arc.aiaa.org/doi/abs/10.2514/3.3166" ] } diff --git a/code/smoothing_internal.py b/code/smoothing_internal.py new file mode 100644 index 0000000..aad18b3 --- /dev/null +++ b/code/smoothing_internal.py @@ -0,0 +1,57 @@ +# -*- coding: utf-8 -*- +""" +Created on Tue May 27 21:21:19 2014 + +@author: rlabbe +""" +from filterpy.kalman import UnscentedKalmanFilter as UKF +from filterpy.kalman import MerweScaledSigmaPoints +import matplotlib.pyplot as plt +from matplotlib.patches import Ellipse,Arrow +import math +import numpy as np +import stats +from stats import plot_covariance_ellipse + + +def show_fixed_lag_numberline(): + fig = plt.figure() + ax = fig.add_subplot(111) + ax.set_xlim(0,10) + ax.set_ylim(0,10) + + # draw lines + xmin = 1 + xmax = 9 + y = 5 + height = 1 + + plt.hlines(y, xmin, xmax) + plt.vlines(xmin, y - height / 2., y + height / 2.) + plt.vlines(4.5, y - height / 2., y + height / 2.) + plt.vlines(6, y - height / 2., y + height / 2.) + plt.vlines(xmax, y - height / 2., y + height / 2.) + plt.vlines(xmax-1, y - height / 2., y + height / 2.) + + # add numbers + plt.text(xmin, y-1.1, '$x_0$', fontsize=20, horizontalalignment='center') + plt.text(xmax, y-1.1, '$x_k$', fontsize=20, horizontalalignment='center') + plt.text(xmax-1, y-1.1, '$x_{k-1}$', fontsize=20, horizontalalignment='center') + plt.text(4.5, y-1.1, '$x_{k-N+1}$', fontsize=20, horizontalalignment='center') + plt.text(6, y-1.1, '$x_{k-N+2}$', fontsize=20, horizontalalignment='center') + plt.text(2.7, y-1.1, '.....', fontsize=20, horizontalalignment='center') + plt.text(7.2, y-1.1, '.....', fontsize=20, horizontalalignment='center') + + plt.axis('off') + plt.show() + +if __name__ == '__main__': + + #show_2d_transform() + #show_sigma_selections() + + show_sigma_transform(True) + #show_four_gps() + #show_sigma_transform() + #show_sigma_selections() +