From e1ce21b25c68fb5c2c8c5bbcacf96914a9988ce3 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Tue, 3 Jun 2014 11:19:46 -0700 Subject: [PATCH] Added section numbering to each chapter. --- Designing_Kalman_Filters.ipynb | 428 +-- Extended_Kalman_Filters.ipynb | 300 +- Gaussians.ipynb | 298 +- Kalman_Filter_Math.ipynb | 298 +- Kalman_Filters.ipynb | 4230 ++++++++++++------------- Multidimensional_Kalman_Filters.ipynb | 298 +- Preface.ipynb | 117 +- Signals_and_Noise.ipynb | 298 +- Unscented_Kalman_Filter.ipynb | 298 +- Untitled0.ipynb | 593 +--- discrete_bayes.ipynb | 298 +- g-h_filter.ipynb | 298 +- 12 files changed, 3182 insertions(+), 4572 deletions(-) diff --git a/Designing_Kalman_Filters.ipynb b/Designing_Kalman_Filters.ipynb index 8e6b950..5e28291 100644 --- a/Designing_Kalman_Filters.ipynb +++ b/Designing_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:6790e915a872d1db0a6db2a07a08d735d2be341faf2b0c3720abe5b9628ae04e" + "signature": "sha256:63ae152874a0161848cb3170c24f73b9279fc0e24f7cb997ec958a1870ce9c18" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,102 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 @@ -336,9 +211,9 @@ { "metadata": {}, "output_type": 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ef58fTQCA2ONfG4RUVlYW7xIQIdOy8/ulpiarZ93V1f2fXZmWH44jO7ORnz3R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\nPTWCHWEAAADYEo0wQmJWylx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2RCOMiJiVMpcp2S1a5NXMmT6Vlgb15JMttp8NPsqU/HAisjMb+dkT5wgDSIox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\n6hy67bY8SZ3nCt95Z546OpJ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r4RUivkbFr/gcza2JWSk32x7rrl0EPfIIEf37E/jSS2A0XDr/h+1FPPzddu4c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\nD1dyXN/vITwVFTr3z536+uSFWjWvQLmpcRcdAwA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Eziq9yIR/brmAz35LwxMhNvwrbTfaz3kK+m7doB8wALi2ehMAGLw0+M+4KGxLLsa7mmi8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\njzR36JASmXSIBwAAgEPQ/D7Ab86N6tkt65XnnT+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m/5RNlCjhomrV1Benaalf34mXl8qyZaak7ZddLujf35s33rBRvHjqs8heRQqm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\n7MkFX5DrhfBOxoXIDI8Vfvv3759Z5yGEEJnm+HENb7xhwc9P5auvYql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NM3PqlJZFi2Iw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Ynjhz2c/H7X/xLe3XhPOIi9oj5xTRtStXd3Gjw5il5D6vF4rx9punsWg/7agXtnVcNqNXjvvTDu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\nWjUlvyIiI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Cs2dVREQo8PaGefPiaNvW4nLy+9Brr3nRqpWFfv2S75RmMEDdun4oFLBl0nou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Ps0tAlKirrGRnu7VunVNvvVVYJ18PkYm1BTV1rKx8+qlDSUkhtW3Lq0uw7tpC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\n6ZRWrizSU0+Vqn17nkEBQE0wYwxEKa9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Nl4hsomvX2Adas5u6Llrkw/z58UWsqGlsgFMg8OabUDZtius56oQJiNxyi0Uj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\nUiT95S9BVWEBAM+4cfCMHw+ItetWQ3ltZmVZeYbt2vleMGfZMhl//av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zdeuq/Yptm66ZI7sa1emtSdRmZxHkZx2s/AIAgiq7wK25X2bpk01eXZbeRjOv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\nk6J8uebPV8LNNyu5QwfFvvx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VKmnd+sRK77o0VnoBBAU6vwAAnwjfuFGOTz+V6/bb5UlIoNMLoEHQ+QUABERx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\n22/Lvm2bXNdco4KZM+v0PnR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"text": [ - "" + "" ] } ], @@ -1291,7 +1166,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 27 + "prompt_number": 19 }, { "cell_type": "markdown", @@ -1325,11 +1200,11 @@ "output_type": "display_data", "png": 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DcyWWqcUijqgXyqxIzP+rryyuuiqNa65J4+KL05k/PzaXiiMx+3ii/M0KR/5f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\nfv36Yds2a9asoaCggKysLPLy8sjNzWX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"text": [ - "" + "" ] } ], - "prompt_number": 28 + "prompt_number": 20 }, { "cell_type": "markdown", @@ -1410,7 +1285,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 29 + "prompt_number": 21 }, { "cell_type": "code", @@ -1436,13 +1311,14 @@ "\n", " p1, = plt.plot (xs, ys, 'r--')\n", " p2, = plt.plot (pxs, pys)\n", + " plt.axis('equal')\n", " plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", " plt.show()" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 41 + "prompt_number": 22 }, { "cell_type": "code", @@ -1451,7 +1327,7 @@ "dt = 0.1\n", "f1 = ball_filter(dt,R=0.1, Q=0.1)\n", "\n", - "traj = BallTrajectory2D (20., angle_degrees=45., noise_scale=0.0)\n", + "traj = BallTrajectory2D (20., angle_degrees=60., noise_scale=0.0)\n", "zs = [traj.update(t) for t in np.arange(dt,100,dt)]\n", "\n", "plot_ball_filter (zs)" @@ -1462,13 +1338,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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plJJryvvhh9t/yc+HIj4eythYKGJiHjnuAVGEkJ0N0dn5ycOoILPZp8wcc5KOWUnDnEzn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\nP3WGrtHKhk42dLKjlQ2d7OK51cTx31DBwDStKf/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UR0SWgDO/ZHVsV6+G3axZKFmyBNpu3XDgSj4+OpSC3pEeGNTIh8snEZm5tIIy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\nKiSp5cCBAxUfPD065ikOsxSLeYrFPMU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qo2O4r1OvLWRnQ/TxAXTO6z8mIs/Etgeiu7FYoF6+HF5LlqDspZdg/Mc/AOWt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\n2r/+5P6/Tqdq/vQnRa9fL0dlpXXhcEXs/AIAAHR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U+vbtixMnTkjG/nfvv/8+8vLy0KlTJzRp0gSvv/46LBbLTefe7v7z58/HrFmz0LJlSyyU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\nPX5XKCxWEf85ll21E27zABuRo7DQdbI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cS9E5IlR0LCLSEa5bmBjuRj2YSq3BR4dTcSSnCqsmdIPf4F46fwx2Lxb7F8uY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\noN8rGTdENce+0pcfHTZdStSJqCb5ktevf//sop6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jN9pjs39x2L183XFAHjlyJNavX19zW6PR4O2338Y333yDTZs2YcWKFXf8OFFj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\nwZ/rt/WWAAAAAElFTkSuQmCC\n", "text": [ - "" + "" ] } ], - "prompt_number": 43 + "prompt_number": 24 }, { "cell_type": "markdown", @@ -1539,7 +1415,7 @@ "dt = 0.1\n", "f1 = ball_filter(dt, R=.16, Q=0.0)\n", "\n", - "traj = BallTrajectory2D (40., angle_degrees=45., noise_scale=0.4)\n", + "traj = BallTrajectory2D (40., angle_degrees=60., noise_scale=0.4)\n", "zs = [traj.update(t) for t in np.arange(dt,100,dt)]\n", "plot_ball_filter (zs)" ], @@ -1549,13 +1425,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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O9dcPYsTBX7midW3uOa8eIQF2Xli5D8Pw3A9TfTEnX6WszFFOnqcGWcTNbPv3\nEzJhAmGXX07JwIHkrVhBSf/+lLkMluw4zBs/H+Dq9vFWlylSfdjtlPTrR/6CBRQ99xyuWrUAcNht\nTDq/PluyCvl0Y7bFRYqIL9EMsoibBT73HLajRzl+221Qowal/22MP1yTSa1gP0a0i6NDHX0oT8RX\nZOQ7uf3zbUzsWY9OdfVvU6QqqegMsj6ZIOJmzltvBaCkzMWiLYeYuTaT2mEB3N69Lq3jwzR3LOJj\n4sIDua9nHR76Zg9PDUghqVaQ1SWJiMU0YuGjNF9knmVZGcaJX39QXOri803ZjJ69ieVpR7jnvHr8\na0AKbRLCLW2OdUyZp6zMqUo5dfjkHSb8NIf7528l73ipW5+7KuXkacrKHOXkeWqQRSrAsW4dYZde\nit/ixeW3HS91MWdDFtfM2sRPe/OY2juZf/ZvRMu4MAsrFREznOPH069uCOcv+4zpH/xAqVa2EKnW\nNIMsciby8giePp2Azz7j2KRJFI8cyTHDxhebD/Hx+iyaxYZyVbs4UqJDrK5URCpi/Xoe/HgttQ0n\nN93QDxITra5IRM6C1kEW8STDwP+TT4jo2hWb00neypXkXnU1H244xDX/2cS27CIe7deIBy5qoOZY\npDJr1Yq77xrKmvgU5r09z+pqRMQiapB9lOaLzPNKVsXFBMyZw5HXXue7ux/h+S2FXDtrE3tyj/Pk\ngBSmXpBMg6hgz9dxFnRMmaeszKmqOYWGBfPgVV14u945rN6Xd9bPV1Vz8gRlZY5y8jytYiFyGsdL\nXaw+eIzvxk7jxx1Hic86QLd6ETw7uDEJNQKtLk9EPCC+RiBTeyfzyOI0nh6YQt2aWtlCpDrRDLLI\nXyhwlvJDeh4r9xzhl/35NI4J4dx6NelaL4LYsACryxMRL5m/5RCz1mXx3MWNCQ/0w751KzgcuBo1\nsro0ETFB6yCLuEHOnoO8OGc1v9SsS5uEcM6tH8Ht3ZOoEaR/KiLVUf+m0ew+cpxpi3czvV9Dgjdu\nJOSeezh+8804J0wAf3+rSxQRD9AMso/SfJF57spqzcx53DxnM03L8vhwSEMe6tOAPo2jqkxzrGPK\nPGVlTnXJ6YbOiTjs8OQ3e9jcsx9HFy/Gf/lywi+8EMeaNafdv7rk5A7Kyhzl5HlV439+kbNQVlrG\nf174mC+JZkqnKFqd29vqkkTEhzjsNqb2Tuad1Qd5dOlu8p1ltJ/wJJ0PbKH7deOIuHIIx++5x+oy\nRcSNNIN3X347AAAgAElEQVQs1Vpu/jGeeGUhlJRw76ge1KxT2+qSRMTHZeYX88v+PH7Zn88v+/KI\ntJXQvnEcnerUoH1iOHZdTl7EZ2gGWeQMrT2Qz2PL9jAgPpzhl52LI0grUojI6dUOD6B/02j6N42m\nzGWwI6eI1fvyeXXVfqJDA7irZxK1QjSbLFKZaQbZR2m+yLwzzcplGHy4JoN/Lt3NxJ5JjBzZu1o0\nxzqmzFNW5iinE+MXTWJOXEHzxUub0igqmJs+3cLPv1s/WTmZp6zMUU6epzPIUq0cPV7K48t2c6zE\nxfOXNCEmVEu2iYh7+NltjO6UQLvEcP41bzO9SjIZNba/1WWJSAVoBlmqjY0HjvLokt30ahzNtR0T\n8LNrTlBEPCN/VzrPvrecg6G1mDSoJXUbJ1ldkki1VNEZZI1YSJVnGAYf/7SHh+esY+LGBYztnKjm\nWEQ8KrxBElOnXMlg/6NMXJDGwllLMAyvno8SkbOgBtlHab7IvL/Lylnq4vEvNvDN178y4+BS2j8y\n0YuV+RYdU+YpK3OU09+z+fnR99bh3BCyl093FfDojEXkO0utLsun6ZgyRzl5nhpkqbKyC4uZOPMX\n/Jcu49m4o9Scdj/4aexeRLwrqGl9/n1jTyIb1OWmOVtYn1FgdUkichqaQZYqaWNmAdMW7mD4wve4\ndOxgys7raXVJIiKsSj/KM8vT6d80mpHt4nBo3EvEozSDLPJfC7bm8OCiNO44P5mL/z1ZzbGI+Iwu\nSRG8eGlTtmQVMvGL7WTkO60uSUT+ghpkH6X5IvN+y6rMZfDy9/uYtS6Tpwam0LluBEZUlMXV+Q4d\nU+YpK3OUkzl/zCkqxJ/p/RrSPbkmt77/C0+/uog56zNZn1FAUXGZRVX6Bh1T5ignz6vQQGZubi5j\nx46ltLQUwzAYN24cqampzJs3j2effRaASZMm0atXL7cWK3IqecdLmb5kNw47PDe4MWGBmjUWEd9l\nt9m4rFUs3Vy5bH5lHlt372Jpm66kFRlEh/jTKCqYhtHBNIoKoVFUMDWDdWU+EW+q0AxyaWkpJSUl\nBAcHk5ubS2pqKt9++y39+vVj9uzZOJ1ORo0axaJFi/60r2aQxd125x7jwQU7OLeGizH9W2umT0Qq\nl7IyAmfMIOiZZyiYOJGdl49ix+Hj7MgpYmfOMXbkHCPYz861HePp01g/FRM5ExWdQa7QaTY/Pz/8\n/rsaQH5+PgEBAaxdu5aUlBQiIyMBiIuLY8uWLTRt2rQiLyFiyvd7jvLMsjRu/ep1LujSCKe9jdUl\niYicGYcD5/jxlPTtS8gtt9AEqD9uHBemnPj/1DAMNmcV8cCiXXStF0G4fkIm4nEVnkEuLCxk0KBB\nDBo0iPvuu49Dhw4RExPDzJkzmT9/PjExMWRlZbmz1mpF80Wnt2h7Ds8t28njr95L7z4dcN52m9Ul\n+TQdU+YpK3OUkzlmc3I1bEjBF1/gHD36pNttNhvNa4fSrV4E/1mb6YkSfYaOKXOUk+dVuEEODQ1l\n7ty5fPLJJzzxxBM4nSc+iTts2DD69z9x7XmbTT/qFs9YnnaE15en8eLLEykZ2o/ia6+1uiQRkbNn\nt0Ng4F/eNap9PPO35pBVUOzlokSqn7P+OU3Dhg1JSEggMTGR+fPnl9+enZ1NTEzMX+4zfvx4kpJO\nXJc+IiKCVq1a0b17d+B/74q0re1TbW8vcDA/K5jn3rmf/TeO4mhKCo3BZ+rz1e3u3bv7VD3arvzb\nv93mK/VU6e2CAjavWUObMH/eWX2Qu86r51v1uXH7N75Sjy9u6/v53x8/K1asID09HYCxY8dSERX6\nkF5mZiYBAQHUqlWL7Oxshg4dypw5c7jiiivKP6R3zTXXsHDhwj/tqw/pydlYdzCfRxbv5qGLGtA8\n1ICwMKtLEhHxLMMgbOBASnv3Jufm2xg9ezOPpzYiOTLY6spEfJ5XLxRy8OBBRo0axaBBgxgzZgyT\nJk0iKiqKiRMnMnz4cK699lqmTJlSkaeW//rjO2mBLVmFPLJ4N1N616d57dDy5lhZmaOczFNW5ign\nc846J5uNwtdew3/ePGJuv4XhLaN4/acD7inOx+iYMkc5eZ5fRXZq27Ytc+fO/dPtqamppKamnnVR\nIn+0K+cY9y/cxcSeSbRLCLe6HBERrzLi48mfO5fQceO48r4bmXPVdNYeyKeNvh+KeESFRizOhkYs\n5EztO5TP3V/u4Mbu9Tm/YS2ryxERsY7LRdD06SzbcID3r7yF5y5tpg/Ei/wNr45YiHhLZvZRJn+4\nmut3fKPmWETEbuf4P/5B16k34bLb+TbtiNUViVRJapB9lOaLICfzMJPf/5Fh2Rvo/cDNp3ycsjJH\nOZmnrMxRTuZ4IiejdWvGdkrkzZ8PUFLmcvvzW0XHlDnKyfPUIItPytufydR3f6D/8f0MeHA8+FVo\nXF5EpMpqlxhOQo1A5m3JsboUkSpHM8jicwqLnEx+bgHtg0u45pYh2Ox6Hyci8ld25hQxZcFO3ri8\nOeG7tuNKTIRwfXBP5DeaQZYq4VhJGf9YvIcmrRpwza1D1RyLiPyNhlEhdEgM56P1WQTOnEn4pZdi\nO6K5ZJGzpe7DR1XH+aLiMhcPfZ1GfI1AbkptafqT2dUxq4pQTuYpK3OUkzmezumaDgl8vimbfXdP\nofSccwgbPBhbdrZHX9NTdEyZo5w8Tw2y+IRSl8GjS3YT4u/gzh5J2LVskYiIKbXDAxjcPIZ/Lt1D\n3oMPUdK/P+EDB2Lbv9/q0kQqLc0gi7UMA9euNP65x0ZRsYsHL0rG36H3bSIiZ8JlGDzydRrBAQ7u\n7plE0PPPE/j22+StWAHBuiS1VF+aQZbKp7gYxx0Tefj9Hzhe4uL+C9Uci4hUhN1m495e9UnPPc77\nazJx3norBe+/r+ZYpILUjfioqj5fZMvKwj70cu6qcz6B53TigYsaEOhXscOxqmflLsrJPGVljnIy\nx1s5BfnZeahPAxZsPcSSHYdxNW3qldd1Jx1T5ignz1ODLF7nWLsW18CLuTn1dhK6tOWeCxvhZ9fM\nsYjI2YoK8eeRPg15+Yf9bMgosLockUpLM8jiXfn5lFzYnwnjnqJzizpc1ynB9GoVIiJizs/78vjX\nN3t4emBjEiMC/3fHsWMau5BqRTPIUikcJIDr73iFXu3qqTkWEfGQjnVqcHX7eP6xcCd5x0tP3Oh0\nUqNnT/wWLbK2OJFKQA2yj6qK80XpuceZ+MV2Lm1Vm+Ft49zWHFfFrDxBOZmnrMxRTuZYldPAZtGc\nkxTBw1+nUVLmgsBACl98kdAJE/D//HNLajodHVPmKCfPU4MsXrH9UBH3zNvO6I7xXNwixupyRESq\nhes6JRAW6OCZFXsxDIOyzp0p+OgjQu69l4APPrC6PBGfpRlk8Ri/777DlpXFL10v4uGv07ite126\n169pdVkiItXKsZIy7vpyO13r1WRkuzgA7Nu2EXbZZTjHj8c5bpzFFYp4jmaQxacEvP02IWPG8Km9\nNg9/ncak8+upORYRsUCwv4OH+zQsX/4NwNW4Mfnz5uFKTLS4OhHfpAbZR1Xa+aLSUoInT+b4a29x\nx2Mf8aUrkqcHptChTg2PvWSlzcrLlJN5ysoc5WSOL+T0V8u/GXXqUDJokMWVncwXsqoMlJPnqUEW\nt7EdPUrYsGH8esjJyHHPUichkmcHN6ZuzSCrSxMRqfaSI4O557x6PPx1Got3HMZleHXCUqRS0Qyy\nuE3Zxk2889V6FsU1567z6tE+0XNnjUVEpGLWZxTwf6v24zIMru+cSNuEcKtLEvEYzSCLpfYdPc6t\n2+3sbtmJl4c0U3MsIuKjWsWF8ezgxlzWqjZPL0/nH1/tZE/uMeDEh/dChw+HvDyLqxSxlhpkH1VZ\n5osMw2DB1hzumLudfo2jePCiZCKC/LxaQ2XJymrKyTxlZY5yMscXc7LbbPRqWIvXLmtG24Rw7vpy\nB88sTyc7PgkjIYHwSy/FlpPj9bp8MStfpJw8Tw2yVIzLRb6zlOlLdvPpxiyeHNCIQc1jdGU8EZFK\nJMBhZ2irWN64vBmhAQ5u+HQbr1w1kaO9LiB8wABs+/dbXaKIJTSDLGeuqIgdt9/HQ12vomvTOMZ2\nSiDAT++1REQqu4x8J2/+fJC1B/MZnbuZS197jOMff4SrQQOrSxOpkIrOIHv3Z+FS6ZUdOcqsaa/z\nebuh3H5+A7okR1pdkoiIuElceCCTe9VnW3YRr/4YxEcTXuSWtbtorQZZqhmd9vNRvjhflLE3k7tf\nXsKGOk148eqOPtMc+2JWvkg5maeszFFO5lTGnBrHhPBEaiOu69OcaYW1+XHvUa+8bmXMygrKyfPU\nIIspS1encdunWznPv4BHbu1PZFig1SWJiIgH2Ww2zkmK4KE+DfjXN+msO5hvdUkiXqMZZPlbRcVl\nvPD9PrbuP8L9R3+l3rhrQB/EExGpVn49kM+jS3bzSJ8GNI0NtbocEdM0gyxutyWrkMeW7aZNfDgv\nXN6SYP82VpckIiIWaJcQzp09knhg0S7+FZdP/XqxuBo1srosEY/RiIWPsnK+qMxl8OGaDP6xcBdj\nOiVwR48kgv0dltVzOprFMkc5maeszFFO5lSVnLrWi2DcOXWYlOZH7jU3YN+xw+2vUVWy8jTl5Hk6\ngywnKS5zcd9XOylzwYuXNCE2LMDqkkRExEf0aliL4yUNuJl/8uqI0YS89waulBSryxJxO80gy0m+\n3HKI5b+k8eSRnygdP97qckRExAd9siGLL1ftYsYrdxDwwTtqksVnVXQGWSMWUq7UZfCf73dz0/89\nBK1bW12OiIj4qCEtY+nVrh43j3uasqtHg9NpdUkibqUG2UdZMV+07D+LqLNrMw2efJDS7t29/voV\npVksc5STecrKHOVkTlXNaUS7ONq3TOK2u16hyOaeic2qmpW7KSfPU4MsANhn/ocP9pVxVf+2lHXs\naHU5IiLi42w2G9d3TiC5dg0eWLQLZ6nL6pJE3EYzyAJOJysn/IOP+4zgqSu0lJuIiJhX5jJ44ps9\nFBWXcf+Fyfg7dO5NfIdmkKXCyvwDeL3vtVzVLdnqUkREpJJx2G3cfV49AJ5dsRfDMMDw6rk3EbdT\ng+yjvDlftGL3EcICHbRPDPfaa7qTZrHMUU7mKStzlJM51SEnP7uNKb3rszv3OB9+vZGwAQMgL++M\nn6c6ZOUOysnz1CBXcy7D4INfMxjRLg6bLiEtIiIVFOzv4OE+DZifY2Nel1TCRoyAY8esLkukQjSD\nXB0VFEBYGHDi7PGHazJ44eImapBFROSs7ck9xt1f7uDhXz+iw4FtFL7zDvj7W12WVFOaQRZTbEeO\nEN6vH37ffIOhs8ciIuJm9WoFM6V3fe5vN5S0kEhCJkwAl1a4kMpFDbKP8sh8UVERYcOHU9qjB6U9\ne/Lj3jxchkHXpAj3v5YXaRbLHOVknrIyRzmZUx1zapsQzg1d6jDxwpvILSzGsXmzqf2qY1YVoZw8\nzz0re4vvKykhdMwYyurV49j06RjAe79mcFVbnT0WERH3uzAlkox8JxODJ/GvxikEW12QyBnQDHJ1\n4HIRMn48tiNHKHz3XfD35+d9ecz4YT8zhjbFrgZZREQ8wDAMnvo2nXzniTWSHXb9fyPepRlkOSVb\nbi44HBS+8Qb4+2MYBu//msHwtrXVHIuIiMfYbDZu616X46VlvPLD/hNrJItUAmqQfZQ754uMqCiK\nXnwRQkIAWHuwgKPHSzmvQS23vYaVNItljnIyT1mZo5zMqe45+Tvs/OOCZNYczGfOxmwAbFlZf/nY\n6p6VWcrJ8yrUIGdmZjJ8+HAGDhzIkCFDWLlyJQDz5s2jb9++9O3bl6VLl7q1UHGPg/lOXv/pAMPa\n1NaPukRExCvCAv2Y1qchH63LYsXWTGpccAH+c+daXZbIKVVoBjknJ4dDhw7RpEkTDhw4wLBhw1i8\neDH9+vVj9uzZOJ1ORo0axaJFi/60r2aQvc8wDDZlFvLxhmzWHcynf9Noru0QrwZZRES8avuhIqYs\n2Mm05DI6j7mSwhdeoPSii6wuS6owr84gR0VF0aRJEwASEhIoKSlhzZo1pKSkEBkZSXx8PHFxcWzZ\nsqUiTy9nwXbwIIHPPQeGQanLYOnOXG79fBv/+nYPbeLDeHdYC67rlKDmWEREvC4lOoS7eiYxdZed\n155+n8BbbsVv2TKryxL5k7OeQV6+fDktWrQgJyeHmJgYZs6cyfz584mJiSHrFDNGcnoVmS9yrFpF\njQsvpKAUZq3L4pr/bOSLzYcY3rY2r1/WnItbxBDs7/BAtdbSLJY5ysk8ZWWOcjJHOZ2sS1IEz13c\nhF8dNRkx9T22PfQUft9/Dygrs5ST553VOsjZ2dk88cQTvPTSS2zcuBGAYcOGAbBo0aJTrq87fvx4\nkpKSAIiIiKBVq1Z0794d+N8Xvbpv/8bs43vv3EnOi6/xyITH+CEokW6Hj/HARQ3I2vILrr2ZOOr5\n1t/Pndvr16/3qXq0Xfm3f+Mr9fjq9vr1632qHl/d/o2v1OML2wk1AukfmsFml4P7Rj1Ip31ltFi2\ngp2b9f1c22f/723FihWkp6cDMHbsWCqiwusgO51ORo8ezfjx4+nevTurV6/m1Vdf5ZVXXgHg6quv\nZurUqTRt2vSk/TSD7F6G08mOR55hFrH82qg9/VvEcnHzaKJDA6wuTURE5LQKi8t4Z/VBlu7MZUyn\nBPo0jtQSpOI2FZ1B9qvIixmGweTJkxk4cGB5596qVSu2b9/O4cOHcTqdZGZm/qk5FvcpdRksT8vl\n4zUZFCV245IuydzZKqFKjlCIiEjVFRrg4KaudbgoJZJnv9vLwm053HJuXZIjde09sU6FZpBXr17N\nwoULmTVrFpdccgmXXnopR44cYeLEiQwfPpxrr72WKVOmuLvWauWPP5r7vcNFJdz62Va+2JzDiI6J\nvDauB4Pb1622zfHfZSX/o5zMU1bmKCdzlJM5jaJDuDwym96NIrln3g7e/PmALixyCjqmPK9CZ5A7\nduzIhg0b/nR7amoqqampZ12UnNr+o06mLNjBRY2jGNG29innvEVERCobuw0GNovmvO0/MXmnQai/\ngyva1La6LKmGKjyDXFGaQa64bRl53L94D1d3iGdA02iryxEREfGIgDff5Ojr7zL6xmeYeH4ynerW\nsLokqaS8ug6yeN8v2zO47+O13JG3Qc2xiIhUacWjR1Pzqst4dNZj/GtZGvuPOq0uSaoZNcg+6vfz\nRcu2ZvHYwh1MO/gdXW64wsKqfJNmscxRTuYpK3OUkznKybzfZ+UcP57mnZtz/cqPeHDhDoqKyyys\nzLfomPI8Ncg+7tMNmbz69Vae3fAJjR+6GxzV84N4IiJS/Ry/7z4Gu7JovX0NT3yzB5c+tCdeohlk\nH2UYBm/9fJAVP+/g34tfIfzd1yFYS96IiEg1U1xM6fYd3LXTj451whnZPt7qiqQS0QxyFVLmMnhm\n+V5+2ZfHi3u/psZrL6k5FhGR6ikgAL8WzfnHhcnM25rDyj1HrK5IqgE1yD7GWeri4a/T2LY/kycG\nphD06MMYNWtaXZZP0yyWOcrJPGVljnIyRzmZ93dZRYX4c/8FyTyzfC97co95sSrfo2PK89Qg+5B8\nZymT5+8g2N/O8DrOanvhDxERkb/SNDaU6zsn8OCiNAqcpVaXI1WYZpB9xKHCYiYv2EmHxHBu6JKo\n69CLiIicwoy3l5AeFs3Dl7bCYdf/l3JqmkGuxNKPHOeOudvpU9ufG1tHqjkWERH5Gzf5ZeBav4G3\nv91hdSlSRalBtlhxmYupC3YysnE4100cQcD8+YDmi86EsjJHOZmnrMxRTuYoJ/PMZuUacRUPhGay\nbE06yzYd9HBVvkfHlOepQbbYgq05JNXw57IpN1DSrx8lQ4daXZKIiIjPC7rrdv55YDkvLdvFzqx8\nq8uRKkYzyBZylrq4dtZGnvj2TZoYhRS9/DLY9Z5FRETElJISfrjjYV5u0ZfnRp9DRJCf1RWJj9EM\nciU0d1M2LTJ20SxrN0XPP6/mWERE5Ez4+3POP++hZ4OaTFucRplLV9oT91BHZpFjJWXMXpfFaGca\nBW+/DQEBJ92v+SLzlJU5ysk8ZWWOcjJHOZlXoazCw7n2ohb4O2z834/73V+UD9Ix5XlqkC3y6cZs\n2iaGkzj5dggPt7ocERGRSsthtzG5V31W7j7Kj3uPWl2OVAGaQbZAgbOU0bM388ygFOpEBFldjoiI\nSJWw7mA+jy7dzcuXNqVWsL/V5YgP0AxyJfLJhmzOSaqh5lhERMSNWseHc2HDSJ796CeMkhKry5FK\nTA2ylx0tKubzTdmMaBf3t4/TfJF5ysoc5WSesjJHOZmjnMxzR1aj2sWSnXWUxU++dfYF+SgdU56n\nBtmLHKtX8+nDM+iZXJO48ECryxEREalyAgL8ufey9vxfWBOy3pttdTlSSWkG2UtsR45QnDqY4dc9\nzSvDWhMdGnD6nURERKRCPluygWUrNvF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pumYeT7y7goKTuWaXIyIuRP+6uzjNKhnntCwLCvAZPx6/wYMrfpRbXM6YBXuJ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\nrCz+v7ups//fDQ0N5OqGlv0oODiYn6FuaLsftTyFmDxd09F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"text": [ - "" + "" ] } ], - "prompt_number": 44 + "prompt_number": 25 }, { "cell_type": "markdown", @@ -1583,8 +1459,7 @@ "\n", "x,y = baseball.compute_trajectory(v_0_mph = 90., theta=65., dt=dt)\n", "zs = zip (x,y)\n", - "plot_ball_filter (zs)\n", - "\n" + "plot_ball_filter (zs)" ], "language": "python", "metadata": {}, @@ -1592,13 +1467,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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s3nWc8Qv20K1RLEPb1T7nzUFExBhe6zGWwKBeJ+NUptwfzivlycV7eWF5Ote2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\nH3s8Hrnd7u+97pH5Tyor65tbiSQnJysnJ+fwjxoOfYA4bpv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cmY15Sc3RxN8gQ1VUV0o+93y9dHjutjgs3JWNnDJznfbx+v57+E2f7trCJKLk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\n/uQk/cMdy51/LfKkqLNfsAOc4PkGmFka226X3zf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"text": [ - "" + "" ] } ], - "prompt_number": 61 + "prompt_number": 26 }, { "cell_type": "code", @@ -1627,9 +1502,10 @@ " f1.R = np.mat(np.eye(6)) * R \n", " \n", " f1.Q = np.zeros((6,6))\n", - " f1.Q[4,4] = Q\n", + " f1.Q[2,2] = Q \n", + " f1.Q[5,5] = Q\n", " f1.x = np.mat([0, 0 , 0, 0, 0, 0]).T\n", - " f1.P = np.eye(6) * 5.\n", + " f1.P = np.eye(6) * 50.\n", " f1.B = 0.\n", " f1.u = 0\n", " \n", @@ -1638,7 +1514,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 67 + "prompt_number": 31 }, { "cell_type": "code", @@ -1664,28 +1540,26 @@ "\n", " p1, = plt.plot (xs, ys, 'r--')\n", " p2, = plt.plot (pxs, pys)\n", + " plt.axis('equal')\n", " plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", " plt.show()" ], "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 85 + "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "dt = 0.1\n", - "noise = 0.3\n", + "noise = 0.2\n", "f1 = ball_filter6(dt, R=.16, Q=0.1)\n", "\n", "x,y = baseball.compute_trajectory(v_0_mph = 90., theta=65., dt=dt)\n", - "zs = zip (x,y)\n", - "znoise = [(i+randn()*noise,j+randn()*noise) for (i,j) in zs]\n", - "plot_ball_filter6 (znoise)\n", - "print (zs[0:5])\n", - "print (znoise[0:5])" + "znoise = [(i+randn()*noise,j+randn()*noise) for (i,j) in zip(x,y)]\n", + "plot_ball_filter6 (znoise)" ], "language": "python", "metadata": {}, @@ -1693,21 +1567,53 @@ { "metadata": {}, "output_type": "display_data", - "png": 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eEQelS0KLNDSGgfPPP7Mvrj1zN6ezNa2QIe1CGNgqRA2xiA1yOnToxJFk95NH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\nIXuzyD+4dKoxvuKKK5SUlNThWElJibKzs5WcnKz09HQ5nU6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EJBPVN8CcpREb8xOHWa/H3Hkr0avyFJI6BjA7wTlKfu7OWtzfJwwf+nSF2wsv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\nLtqZjX6FsagBuKGhQU6nc87a27dvVVdXJ5fLper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"text": [ - "" + "" ] - }, + } + ], + "prompt_number": 33 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "look at P" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print (f1.P)" + ], + "language": "python", + "metadata": {}, + "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ - "[(0.0, 0.0), (1.700193266982834, 3.646076227248443), (3.363396716383785, 7.114827534704153), (4.989282707845675, 10.407750130907692), (6.577522827472383, 13.526428179417952)]\n", - "[(0.0077428794280200615, -0.24993790836595048), (1.6319949358597867, 3.906624591863025), (2.927767750429539, 7.282837525906626), (4.889897158515106, 10.321582956313172), (6.55031695691016, 13.756792084374545)]\n" + "[[ 0.02143298 0.01351531 0.00364892 0. 0. 0. ]\n", + " [ 0.01351531 0.01153516 0.00352809 0. 0. 0. ]\n", + " [ 0.00364892 0.00352809 0.00115592 0. 0. 0. ]\n", + " [ 0. 0. 0. 0.05456716 0.11122734 0.01865339]\n", + " [ 0. 0. 0. 0.11122734 0.5379301 0.07344247]\n", + " [ 0. 0. 0. 0.01865339 0.07344247 0.18002138]]\n" ] } ], - "prompt_number": 88 + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 30 } ], "metadata": {} diff --git a/Extended_Kalman_Filters.ipynb b/Extended_Kalman_Filters.ipynb index 4eba802..8c4887e 100644 --- a/Extended_Kalman_Filters.ipynb +++ b/Extended_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:33c57875ece7c340a1489961be89bf26faefec05e914f558690242db4a4be9a8" + "signature": "sha256:cd6116a16a3f1c69eb33c20e75304e2535541d84c9849c2e98cdfccb2c84b043" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 @@ -544,4 +418,4 @@ "metadata": {} } ] -} +} \ No newline at end of file diff --git a/Gaussians.ipynb b/Gaussians.ipynb index e2dfd1d..fa1e7be 100644 --- a/Gaussians.ipynb +++ b/Gaussians.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:0ed2a79c9b9a5af478fd7349a380e31cad560037d74dc59e4deeb96893227198" + "signature": "sha256:d156d193bfb418b2b1abcbaa1a819c9a4e429e43842b4ecfaccb12444ce39e88" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 diff --git a/Kalman_Filter_Math.ipynb b/Kalman_Filter_Math.ipynb index a1bc7ab..b910357 100644 --- a/Kalman_Filter_Math.ipynb +++ b/Kalman_Filter_Math.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:f158f09893aa87588564de2be08ea1c524a480e55505bd5055afe9cb4993d21b" + "signature": "sha256:c8c5ef2a9d75930ce887514f19e5ab0d95859f408b5bcf5d2547bb57b8d0ef6d" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 diff --git a/Kalman_Filters.ipynb b/Kalman_Filters.ipynb index 42a5ced..1cd691a 100644 --- a/Kalman_Filters.ipynb +++ b/Kalman_Filters.ipynb @@ -1,2179 +1,2053 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:7bcd692a8ae1a36e1bb14d78bc58a3b8d1234f768fb0d0c6c00dee4155fa0676" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "Kalman Filters" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "%matplotlib inline\n", - "from __future__ import division, print_function\n", - "import matplotlib.pyplot as plt\n", - "import book_format\n", - "book_format.load_style()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 2, - "text": [ - "" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "One Dimensional Kalman Filters" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking A Dog" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", - "\n", - "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Futhermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n", - "\n", - "Implementing and/or robustly modelling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function, division\n", - "\n", - "import numpy.random as random\n", - "import math\n", - "\n", - "class DogSensor(object):\n", - " \n", - " def __init__(self, x0=0, velocity=1, noise=0.0):\n", - " \"\"\" x0 - initial position\n", - " velocity - (+=right, -=left)\n", - " noise - scaling factor for noise, 0== no noise\n", - " \"\"\"\n", - " self.x = x0\n", - " self.velocity = velocity\n", - " self.noise = math.sqrt(noise)\n", - "\n", - " def sense(self):\n", - " self.x = self.x + self.velocity\n", - " return self.x + random.randn() * self.noise\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The constructor $\\verb,__init()__,$ initializes the DogSensor class with an initial position (x0), velocity (vel), and an noise scaling factor. The $\\verb,sense(),$ function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for $\\verb,sense(),$ you will see a call to $\\verb,numpy.random.randn(),$. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that.\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "for i in range(20):\n", - " print(\"%.4f\" % random.randn(),end='\\t')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "-0.8025\t0.4440\t1.6176\t-0.7325\t0.0304\t0.3592\t-0.1916\t1.3645\t0.2563\t-0.4732\t-0.3872\t0.2693\t0.4122\t0.1272\t0.7263\t-0.5945\t0.4633\t-1.5166\t0.5133\t1.1987\t" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n", - "\n", - "Okay, so lets look at the output of the $\\verb,DogSensor,$ class. We will start by setting the noise to 0 to check that the class does what we think it does" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib.pyplot as plt\n", - "import matplotlib.pylab as pylab\n", - "\n", - "dog = DogSensor (noise=0.0)\n", - "xs = []\n", - "for i in range(10):\n", - " x = dog.sense()\n", - " xs.append(x)\n", - " print(\"%.4f\" % x, end=' '),\n", - "plt.plot(xs)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that *sense()* returns the dog's position *after* updating his position, so the first postion is 0.0 + 1, or 1.0.\n", - "\n", - "Now let's inject some noise in the signal." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def test_sensor(noise_scale):\n", - " dog = DogSensor(noise=noise_scale)\n", - "\n", - " xs = []\n", - " for i in range(100):\n", - " x = dog.sense()\n", - " xs.append(x)\n", - " p1, = plt.plot(xs, c='b')\n", - " p2, = plt.plot([0,99],[1,100], 'r--')\n", - " plt.xlabel('time')\n", - " plt.ylabel('pos')\n", - " plt.ylim([0,100])\n", - " plt.title('noise = ' + str(noise_scale))\n", - " plt.legend([p1, p2], ['sensor', 'actual'], loc=2)\n", - " plt.show()\n", - " \n", - "test_sensor(4.0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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KaSxeHMCdd57LtlNDQnB268aURp9y/FAw1pCzvhqu+AmfJtrh4eEEBASQlJSE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\nyoWYUS7EjHIh/qZCux7xeuGuu2LZudPGypW1+2XGwoUO/v3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- "text": [ - "" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use $\\verb,numpy.random.seed(some_value),$ to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", - "\n", - "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", - "\n", - "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n", - "\n", - "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "test_sensor(100.0)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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qxAm0Pf442hcvlt0D+7XXwvHKK+EoLr6E6GiPvx07b78dhpISFq+80oonnuiF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1LrZvzyIgAFJTLRw8aOXgwQAOHgxgbXIscXGFJCVlULmyz+3rIGWEdh0RERER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\nIRcwQy5ghlwg2NjRjiAOl0uxjz4qe+URzb5qq17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- "text": [ - "" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply $\\verb,randn(),$ with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. DogSensor.$\\verb,__init__(),$ takes the square root of the noise setting so that the $\\verb,noise * randn(),$ call properly computes the normal distribution." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Math with Gaussians" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import stats\n", - "stats.norm_plot(23, 5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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GalwoFmbEyS6FiCRz6UgGEZGnVLVcRFO3BTMSdbJLIS+1IC0Wu443w6aM40RE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\nOp2289zpmTlz9kWh9OF0OOViz7T9fpIJ0/8cDr9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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", - "\n", - "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpertation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", - "\n", - "Let's look at 100 sensor readings in a plot:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(23, 0, 5)\n", - "xs = range(100)\n", - "ys = []\n", - "for i in xs:\n", - " ys.append(dog.sense())\n", - " \n", - "plt.plot(xs,ys)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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NMPkIE+1BceEsgiTrSiMyMX9Nl6O4IPSguCCcxLAirDE1NYX7778fBw8exLlz5/D1r38d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\nO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- "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", - "\n", - "\n", - "Recall the histogram code for adding a measurement to a pre-existing belief:\n", - "\n", - " def sense(pos, measure, p_hit, p_miss):\n", - " q = array(pos, dtype=float)\n", - " for i in range(len(hallway)):\n", - " if hallway[i] == measure:\n", - " q[i] = pos[i] * p_hit\n", - " else:\n", - " q[i] = pos[i] * p_miss\n", - " normalize(q)\n", - " return q\n", - " \n", - "Note that the algorithm is essentially computing:\n", - "\n", - " new_belief = old_belief * measurement * sensor_error\n", - " \n", - "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convience. \n", - " \n", - "If we are implementing this with gaussians, we might expect it to be implemented as:\n", - "\n", - " new_gaussian = measurement * old_gaussian\n", - " \n", - "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n", - "$$\n", - "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n", - "\n", - "In other words the result is a Gaussian with \n", - "\n", - "$$\\begin{aligned}\n", - "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", - "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", - "\\end{aligned}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", - "\n", - "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "\n", - "def multiply(mu1, sig1, mu2, sig2):\n", - " m = (sig1*mu2 + sig2*mu1) / (sig1+sig2)\n", - " s = 1. / (1./sig1 + 1./ sig2)\n", - " return (m,s)\n", - "\n", - "xs = np.arange(16, 30, 0.1)\n", - "\n", - "\n", - "m1,s1 = 23, 5\n", - "m, s = multiply(m1,s1,m1,s1)\n", - "\n", - "ys = [stats.gaussian(x,m1,s1) for x in xs]\n", - "p1, = plt.plot (xs,ys)\n", - "\n", - "ys = [stats.gaussian(x,m,s) for x in xs]\n", - "p2, = plt.plot (xs,ys)\n", - "\n", - "plt.legend([p1,p2],['original', 'multiply'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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K+TdEQCYf/ot+zF+s4fJPmBuMmspWNDd0CqjIfvDaF4v5SwsbZiKyWdXll9HZ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\nZSItykR0iF4uLERGmC+Z2+ujudtFg9VJo9VFg81Jo9VJg9VFk81JYri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- "text": [ - "" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplation is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", - "\n", - "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get $23m$ each time, I should conclude that the length is close to $23m$. So the mean should be $23$. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", - "\n", - "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", - "\n", - "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "xs = np.arange(16, 30, 0.1)\n", - "\n", - "m1,s1 = 23, 5\n", - "m2,s2 = 25, 5\n", - "m, s = multiply(m1,s1,m2,s2)\n", - "\n", - "ys = [stats.gaussian(x,m1,s1) for x in xs]\n", - "p1, = plt.plot (xs,ys)\n", - "\n", - "ys = [stats.gaussian(x,m2,s2) for x in xs]\n", - "p2, = plt.plot (xs,ys)\n", - "\n", - "ys = [stats.gaussian(x,m,s) for x in xs]\n", - "p3, = plt.plot(xs,ys)\n", - "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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XYnbWnn1tJ/nbFmmYhRCilrh6PJHsrbtoOm2c6lJqlZCJo7hy6CSX9vymuhQh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LTvY7keac8nbRiEzDDx//kvuP8f/1AOZi2Yu7q6uHTp0tT60NAQXV1dcx7b3d3N+Pj4nI5h2zY9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\nELOQglkIIYQQQohZSMEshBBCCCHELP4fMK5kG7vKF9gAAAAASUVORK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n", - "\n", - "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n", - "\n", - "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", - "\n", - "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", - "\n", - "One final test of your intuition. What if the two measurements are widely separated? " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "xs = np.arange(0, 60, 0.1)\n", - "\n", - "m1,s1 = 10, 5\n", - "m2,s2 = 50, 5\n", - "m, s = multiply(m1,s1,m2,s2)\n", - "\n", - "ys = [stats.gaussian(x,m1,s1) for x in xs]\n", - "p1, = plt.plot (xs,ys)\n", - "\n", - "ys = [stats.gaussian(x,m2,s2) for x in xs]\n", - "p2, = plt.plot (xs,ys)\n", - "\n", - "ys = [stats.gaussian(x,m,s) for x in xs]\n", - "p3, = plt.plot(xs,ys)\n", - "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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0i7lTj2RaMuLNnzE3BwZLDsLnB5MJjSTAsadtzF9mMcZz0SOPPAIAePXVV6HT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\ncLUJCQY1YgP5P9iP17VcABAfpEaUzheHq2fmUcM8dzddug7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- "text": [ - "" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", - "\n", - "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Futhermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", - "\n", - "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n", - "\n", - "$$\n", - "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", - "$$\n", - "\n", - "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n", - "\n", - "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n", - "\n", - "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", - "$\\sigma_1^2=0$, yielding\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n", - "\\text{or just}\\\\\n", - "\\mu&=\\mu_1\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n", - "\\text{or just}\\\\\n", - "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing the Sensing Step" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", - "\n", - "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the sense function for a Kalman filter:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def sense(mu, sigma, measurement, measurement_sigma):\n", - " return multiply(mu, sigma, measurement, measurement_sigma)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def sense_dog(dog_pos, dog_sigma, measurement, measurement_sigma):\n", - " return multiply(dog_pos, dog_sigma, measurement, measurement_sigma)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the $\\verb,sense_dog(),$ function should make what we are doing very clear. \n", - "\n", - "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a $\\verb,DogSensor,$ object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at postion 2.0, not 0.0." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(velocity=0, noise=1)\n", - "\n", - "pos,s = 2, 5\n", - "for i in range(20):\n", - " pos,s = sense(pos, s, dog.sense(), 5)\n", - " print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "time: 0 \tposition = 0.793 \tvariance = 2.500\n", - "time: 1 \tposition = 0.575 \tvariance = 1.667\n", - "time: 2 \tposition = 0.277 \tvariance = 1.250\n", - "time: 3 \tposition = 0.348 \tvariance = 1.000\n", - "time: 4 \tposition = 0.401 \tvariance = 0.833\n", - "time: 5 \tposition = 0.231 \tvariance = 0.714\n", - "time: 6 \tposition = 0.386 \tvariance = 0.625\n", - "time: 7 \tposition = 0.517 \tvariance = 0.556\n", - "time: 8 \tposition = 0.452 \tvariance = 0.500\n", - "time: 9 \tposition = 0.332 \tvariance = 0.455\n", - "time: 10 \tposition = 0.298 \tvariance = 0.417\n", - "time: 11 \tposition = 0.280 \tvariance = 0.385\n", - "time: 12 \tposition = 0.197 \tvariance = 0.357\n", - "time: 13 \tposition = 0.132 \tvariance = 0.333\n", - "time: 14 \tposition = 0.116 \tvariance = 0.312\n", - "time: 15 \tposition = 0.076 \tvariance = 0.294\n", - "time: 16 \tposition = 0.135 \tvariance = 0.278\n", - "time: 17 \tposition = 0.040 \tvariance = 0.263\n", - "time: 18 \tposition = 0.003 \tvariance = 0.250\n", - "time: 19 \tposition = 0.006 \tvariance = 0.238\n" - ] - } - ], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the intial value of 5.0 to 0.238.\n", - "\n", - "By now the fact that we converged to a position of 0.0 should not be terribly suprising. All we are doing is computing $\\verb,new_pos = old_pos * measurement,$ and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", - "\n", - "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", - "\n", - "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing Updates" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track nonmoving objects? The histogram used a loop of sense and update functions, and we must do the same to accomodate movement.\n", - "\n", - "How how do we perform the update function with gaussians? Recall the histogram method:\n", - "\n", - " def update(pos, move, p_correct, p_under, p_over):\n", - " n = len(pos)\n", - " result = array(pos, dtype=float)\n", - " for i in range(n):\n", - " result[i] = \\\n", - " pos[(i-move) % n] * p_correct + \\\n", - " pos[(i-move-1) % n] * p_over + \\\n", - " pos[(i-move+1) % n] * p_under \n", - " return result\n", - " \n", - " \n", - "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n", - "\n", - "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is $\\verb,new_pos = old_pos + dist_moved,$. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n", - "\n", - "How is addition for gaussians performed? It turns out to be very simple:\n", - "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n", - "\n", - "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", - "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the $\\verb,update(),$ function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n", - "\n", - "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", - "\n", - "So, here is our implementation of the update function:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def update(pos, sigma, movement, movement_sigma):\n", - " return (pos + movement, sigma + movement_sigma)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What is left? Just calling these functions. The histogram did nothing more than loop over the $\\verb,sense(),$ and $\\verb,update(),$ functions, so let's do the same. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# assume dog is always moving 1m to the right\n", - "movement = 1\n", - "movement_error = 2\n", - "sensor_error = 10\n", - "pos = (0, 500) # gaussian N(0,50)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(10):\n", - " pos = update(pos[0], pos[1], movement, movement_error)\n", - " print('UPDATE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - " \n", - " print('SENSE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n", - " print()\n", - " \n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "UPDATE: 1.0000,\t502.0000\n", - "SENSE: -0.9237,\t9.8047\n", - "\n", - "UPDATE: 0.0763,\t11.8047\n", - "SENSE: 0.1727,\t5.4138\n", - "\n", - "UPDATE: 1.1727,\t7.4138\n", - "SENSE: 3.2003,\t4.2574\n", - "\n", - "UPDATE: 4.2003,\t6.2574\n", - "SENSE: 6.5697,\t3.8490\n", - "\n", - "UPDATE: 7.5697,\t5.8490\n", - "SENSE: 7.6101,\t3.6904\n", - "\n", - "UPDATE: 8.6101,\t5.6904\n", - "SENSE: 8.2152,\t3.6267\n", - "\n", - "UPDATE: 9.2152,\t5.6267\n", - "SENSE: 6.5868,\t3.6007\n", - "\n", - "UPDATE: 7.5868,\t5.6007\n", - "SENSE: 6.4438,\t3.5900\n", - "\n", - "UPDATE: 7.4438,\t5.5900\n", - "SENSE: 7.7971,\t3.5856\n", - "\n", - "UPDATE: 8.7971,\t5.5856\n", - "SENSE: 7.7203,\t3.5838\n", - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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OD6fbvBkxb7+N/W++iaf79n3g8+5cIiztJg83b6pRrpw3wxXcUC0RJiepzymP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\nm5tRpYoXkyax4SWiKKXVwjF8OEwjRwZuQXkX1a1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- "text": [ - "" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n", - "\n", - " movement = 1 \n", - " movement_error = 2\n", - " \n", - "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the $\\verb,update(),$ step.\n", - "\n", - "For now let's walk through the code and output bit by bit.\n", - "\n", - " movement = 1\n", - " movement_error = 2\n", - " sensor_error = 10\n", - " pos = (0, 500) # gaussian N(0,500)\n", - " \n", - " \n", - "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we initialize the RFID simulator with\n", - "\n", - " dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "It may seem very 'convienent' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n", - "\n", - "The next code allocates an array to store the output of the measurements and filtered positions. \n", - "\n", - " zs = []\n", - " ps = []\n", - " \n", - "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we just enter our $\\verb,sense() - >update(),$ loop.\n", - "\n", - " for i in range(10):\n", - " pos = update(pos[0], pos[1], movement, sensor_error)\n", - " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", - "\n", - "Wait, why $\\verb,update(),$ before sense? It turns out the order does not matter once, but the first call to $\\verb,DogSensor.sense(),$ assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the $\\verb,sense(),$ first.\n", - "\n", - "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n", - "\n", - " UPDATE: 1.000 502.000\n", - "\n", - "What is this saying? After the update, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the update step.\n", - "\n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - "Here we sense the dog's position, and store it in our array so we can plot the results later.\n", - "\n", - "Finally we call the sense function of our filter, save the result in our *ps* array, and print the updated position belief:\n", - "\n", - " pos = sense(pos[0], pos[1], Z, movement_error)\n", - " ps.append(pos[0])\n", - " print 'SENSE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", - " \n", - "Your result will be different, but I get\n", - "\n", - " SENSE: 1.6279 , 9.8047\n", - " \n", - "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n", - "\n", - "Now the software just loops, calling $\\verb,update(),$ and $\\verb,sense(),$ in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n", - "\n", - "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%precision 2\n", - "# assume dog is always moving 1m to the right\n", - "movement = 1\n", - "movement_error = 2\n", - "sensor_error = 4.5\n", - "pos = (0, 100) # gaussian N(0,50)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "\n", - "for i in range(50):\n", - " pos = update(pos[0], pos[1], movement, movement_error) \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " vs.append(pos[1])\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - " \n", - "#plt.subplot(121) \n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()\n", - "\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()\n", - "print ([float(\"%0.4f\" % v) for v in vs])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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upO+Iv7VF8YMMC8N1xx040tPJ+8uSriWtMueF+I96jEVERMqBoPnzsS9fjmP5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\nCuNa4ti+XQ369VPEJ59Uv7Zpk0O9e8fpppv8WrW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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literatue, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Relationship to the g-h Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n", - "\n", - "The equation for our estimate is:\n", - "\n", - "$$\n", - "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", - "$$\n", - "\n", - "which I will make more friendly for our eyes as:\n", - "\n", - "$$\n", - "\\mu_{x'}=\\frac{ya + xb} {a+b}\n", - "$$\n", - "\n", - "We can easily put this into the g-h form with the following algebra\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n", - "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n", - "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n", - "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n", - "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "We are almost done, but recall that the variance of estimate is given by \n", - "\n", - "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n", - "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n", - "$$\n", - "\n", - "We can incorporate that term into our equation above by observing that\n", - "$$ \n", - "\\begin{aligned}\n", - "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n", - " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n", - " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n", - " &= \\frac{\\sigma^2_{x'}}{b}\n", - " \\end{aligned}\n", - "$$\n", - "\n", - "We can tie all of this together with\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", - "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n", - "&= x + g_n(y-x)\\\\\n", - "\\blacksquare\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "where\n", - "\n", - "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n", - "\n", - "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n", - "\n", - "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n", - "\n", - "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#####Excercise:\n", - "Modify the values of mov$\\verb,ement_error,$ and $\\verb,sensor_error,$ and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n", - "\n", - " movement_error = 40\n", - " sensor_error = 2\n", - " \n", - "or:\n", - "\n", - " movement_error = 2\n", - " sensor_error = 40 " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Introduction to Designing a Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equiped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n", - "\n", - "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "temp_variance = 2.13**2\n", - "def volt():\n", - " return random.randn()*temp_variance + 16.3" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We generate white noise with a given variance using the equation $\\verb,random.randn() * variance,$. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n", - "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performace will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", - "\n", - "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field \"Repeatability\", with the value \"$\\pm0.50\\%$ Reading\". Is this a Gaussian? Is there a bias? For example, perhaps the repeatibility is nearly $0.0\\%$ at low temperatures, and always nearly $+0.50$ at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", - "\n", - "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call $\\verb,volt(),$ to get the measurement, pass the result into $\\verb,sense(),$ function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", - "\n", - "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = temp_variance\n", - "movement_error = 0\n", - "movement = 0\n", - "voltage = (25,1000) #who knows what the first value is?\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "N=50\n", - "\n", - "for i in range(N):\n", - " Z = volt()\n", - " zs.append(Z)\n", - " \n", - " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n", - " ps.append(voltage[0])\n", - " vs.append(voltage[1])\n", - "\n", - " voltage = update(voltage[0], voltage[1], movement, movement_error)\n", - "\n", - "plt.scatter(range(N), zs, marker='+')\n", - "p1, = plt.plot(ps, c='g')\n", - "plt.legend([p1], ['filter'], 3)\n", - "plt.xlim((0,N));plt.ylim((0,30))\n", - "plt.show()\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()\n", - "print('Variance converges to',vs[-1])\n", - "print('Last voltage is',voltage[0])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - 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FWpyzWNuu2qYFWQuUHJvs9d9hsOY9EDhHIHzERMcMFj8peR4/VjjmItif8zab\nTSlxKUqJS1FBWsGw9zu3SD7VeUoT4icoLzkv6I7eX/JV8/7779eTTz6pjIwMVVVVSZKio6M1d+5c\nSdK1116rhx9+2LejPEeULUpfnPlFPfPRM3ow40G/rRfhbSQnUZ3bYrCrdpeqW6u1MGuhLptwmV6u\nfll7Tu5RUmySCjMKNTdzruZlztPcjLnKGpc1oj3a7r5u/f3U31VRN9gz+nb920qMSdTVOVdrcfZi\nbZ2/VTMnzvTq0cxAi4mO0az0WWoe16zCzMJR/WxKXIqyk7K1MGuh8ftdfV2qO1PnLoZr22u19/Te\nwZOdou2DvZGfnAiSFJvk7pN03Xbu52mp03TlxCt9NsWWK3+SQmZatXDCDgfgHSMtkgPtkm0Pu3fv\nVmxsrO666y538ZucnKz29vaLPrCv2h4k6VDzId38m5tV9aUqv77FywbSv84tSLdtG/uJAKNxfs+q\nq8VgV+0u1Z+p1+KcwRaDJTlLLmgxsCxLR9uOas/JPYMfp/bo/ZPvKzoqWnMz5qows3DwI6NQk5Mn\nq7W7VW/Xv6236t7SW/VvqepUlWaMn6Grc67WVdlXaXH2YuUm5/r0/4vgE+ytN+GI3zkQ2rze9rBk\nyRJVV1d7Miavu2zCZZqSMkWv1bymm6bd5Lf1Uvz6l7fO6nedmex6K3vI29qfnBzi/vqKw/r6q29o\nV+0uNXc3u1sMNszaoDnpcy565M9ms2lq6lRNTZ3qno7PsizVnqnV+yff155Te/TU3qe07dQ2dfR2\nyLIsLchaoKuyr9I3r/qmFmYt9Mnb6AgtbGP8x9O5bQGEpjE1CzqdTi1YsEAJCQn6t3/7N11zzTVe\nGcxoist1V6zTMx8945filw3kWZ29ndp7eq8aOhq0JGfJqHtcx9KrNdLf88nOk3rt6Gt69eir2lW7\nS+097e6zn4eb/9A1xZdrkvApqVO0LGOZvjbva15pMbDZbO6e08/M+Iz79tOdpzU+fnxQ9esGUjj2\n8I1VJG5XhuPrXATrRUxwcWwv4KkxvfLW1tYqMzNT77zzjm655RYdOnRIcXEXTqe0ZcsWORyD12dP\nTU3VnDlz3IEtLy+XpCHLTz+dr+LizGG/f+5yVmOWyj4uU7OzWRPiJ1zy/p4sD24c/6KamnyVlJwd\nX3m5b9YXLMtn+s4ocUai3j/1vsr2lulI1xGd7jut/An5snfbtaVjiwrSC3Tj1BuV0ZKhGYkztPya\n5Rd9fJcS0rGwAAAaGElEQVTR/v5N3++3+hV/WbxerX5V/2/v/1N9d71WTF2hVVNW6dMxn1aKPUXL\nly1XTHSMdr25a9T//13a5bPf777KfT7/+4XSsqulKljGw3JwLLv4en01NTUqLz8Q8P8vy2wvWB7Z\nclVVlVpbWyUNPn83bdqk0RjRVGfV1dVavXq1O3DnWrx4sXbs2KGCgqGNzWPp+R1t39WX//RlFecW\n68tzvzyq9YxVuPaFWZalho4GVZ2q0vun3nd/NHU1aVb6LBVmFmpOxhzNzZirgrQC93Q0Pf09eqvu\nLb1S/YpeqX5FLd0tWjllpW6YeoNWOFYoNS7V62M92XlSZUfL9Gr1q/rLsb8oJylHq6as0qopq3RV\n9lUBneYLQGiipQ0IbT6f6qypqUkJCQlKSEhQdXW1amtr3Ud3x2qslytdd8U6ba/Y7rfiN5w2jgPW\ngF4/9rqe+vApvX7sdQ1YA4MFbuZcff7yz+t7S7+n6eOnX/Rt/9joWC3PW67lecv1wDUP6GjrUb1S\n/Yqe+egZff3Vr2tuxlzdOO1GrZq6SlekXTGqOfwsy1JXX5c6ejt0uOWwu+CtbqvW8snLtWrqKj1w\nzQPKScrxxq8DQAQLp237uSjqYUIuRlD8bt26Vb/73e/U2NiovLw8ffWrX9VTTz2luLg4RUdH65e/\n/KUSEhIu9TAXNda+qxWOFbrvtfu07S/b9PUFX9fk5MkejeNSwiEsNW01evrDp/X0R08rLT5Nd1x5\nh/73sv/tlcn5p6RO0abCTdpUuEldfV0qP16uV6pf0foX1qt/oF+rpq5Sx6kOpWWl6UzvGXX0dLiv\nT37ux5meM+rs61RsVKzGxYxTbnKurndcrweXP6hFWYs4uhuGysvp4cOFyIVnwrXIIReeCddcjMYl\ni99HHnlEjzzyyJDb/uVf/sUngxntH8MeZddrt7+mR957RNc+c61Wz1itexfeq6mpU30yvlDV1del\nPxz+g5768ClVnarSFwq+oCc/+6TmZs712ToT7Am6YeoNumHqDfqh9UMdbD6o12pe00dNH2n6+OlK\ntCdqXMw4JcUmaVzMOOOHr+ZUBQAg0oz1XfZwFHKXNx5OU1eTfvb3n+m/qv5LN027SfcuvFeXT7jc\nb+sPNpZl6e8n/66nPnxKvzv4O83PnK87rrxDn57+acXb4wM9PACAjwRijnSEjnA8fynsL288nLSE\nNH1nyXd0T9E9enzP4/rM85/RtY5r9Y1F39AVE68I9PBGbaxvS5zuPK3n9z+vpz58Sp29nVp/5Xr9\ndd1ffd4SAgAIDkzhhothR0gKn+ukfiI1LlXfvOqbqryrUnPS5+iW392ijX/YqPdPvj/qx7IsSyc7\nT6r8eLn+7/v/Vz9996fq6uvywagv5LrU6UjVn6nXpv/ZpIU7FqrqVJV+eO0P9c6d7+j+q+4PqsL3\n/CmMAIlcwCzYczHa7bS/hWuRE+y5CHbhmovRCO5nrgeSY5P1zwv/WZsKN+lXH/xK615Yp7kZc3X/\nVfdrQdaCIfcdsAZ0rO2YDjQf0P6m/TrQdEAHmg/oQNMB2Ww2FaQVKH9Cvk53ndbvDvxOT9z8hM8K\nyrH05Pz+0O/1zT9/U3fOuVPvf+l9pcSl+GRsAICzgv3EoWAeWzgL9lwgjHp+L8XZ59STe5/Uv7/7\n78pPy9fi7MU62HxQB5oO6HDLYY2PH6/8CfnKT8t3F7v5aflKT0h3z4JgWZYeee8RPVL5iP7zU/+p\n4sm+O9t0JD05bd1t+vbr39ZbdW/p5zf+XIuyF/lsPACAQfTU4mLCsac22EVsz++lxNvjtalwkzbO\n3qhnP3pWH7d+rOunXK+vzfuaLp9w+YiOltpsNt1TdI9mp8/Wpv/ZpHsX3qvNhZs9niJsLHbX7tbd\nr9ytFY4V+uu6vyopNsnvYwCASERPLc7n2iGSxGwKISBiil+X2OhYbZy90aPHuM5xnV5a85I2/mGj\n9pzcox9f/2Ml2D2b6/h8wz1hevp7VPpWqZ756Bn95Pqf6FPTP+XV9foa8zPChFzAhFzAJBhzcX6h\ny05RcAu7E978ZUrqFP1pzZ/UN9CnTz//aR1rO+bVxzcVv/sa9+nGnTdqX9M+vb7+9ZArfAEgnHBU\nDybkIvhFTM+vr1iWpUffe1T/p/L/6PGbHtc1edd4fR0D1oD+c89/6kdv/0jfXfpdbZy1MSCtFgAA\nAMGGnl8/s9ls2lq0VbMzZuufXvon/fOCf9bX5n3Na8Vp3Zk63fPKPWrvaddLa1/S9PHTvfK4AAAA\nkYi2By+5Nu9avbz2ZT370bO6++W7vTIf8H8f/G+teGaFrs65Wn9a86ewKHyZnxEm5AIm5AIm5AKe\novj1IkeKQ39a8yf1W/1j6gPu7utWdWu1dtXu0t0v360Hdz+op1c/rW2Lt8kexUF6AAAwKNgvshLM\n+M15WWJMoh6/6XE9+t6jumHnDXr8pse1PG+5Ons7Vd9Rr7r2OtWdMX+0drdq0rhJyknK0aLsRfrL\nur9oXMy4QP+XvCrYztBFcCAXMCEXMCEXg7iYxthR/PrAuX3AX33pq+od6FVnb6eyx2UrJylHOck5\nyk3KVX5avq5zXDd4W1KOMhIzFGXjYDwAADA7/0qwEnMKjxbFrw9dm3et3t7wtnr6ezQxYSIzNCg4\n52dE4JELmJALmER6LrjIiucofn1sJFeOAwAAgH/wHjv8KpL31jE8cgETcgETcjGINoexo/gFAAAI\nMRS/Y0fxC79ifkaYkAuYkAuYkAt4iuIXAAAAEcNmWZbliwcuKytTUVGRLx4aAAAAkCRVVlZq5cqV\nI74/R34BAAAQMSh+4Vf0asGEXMCEXMCEXMBTEVv8ck1sIPLwvAcAUPzCr5ifESb+ygXP+9DC9gIm\n5AKeirhXgvOvic31sIHwd/7zXuK5DwCRKuKKX66JHViRfk12mPk6FzzvQxPbC5iQC3gqYtseOOID\nAAAQeZjnF0DEKC+3s+MLAGGGeX4BYBgUvgAAil/4FfMzwoRcwIRcwIRcwFMUv0CAMO0WAAD+R/EL\nv+IM3bMofs8iFzAhFzAhF/AUr76AnzHXNAAAgcORX/gVvVqDxW5JiVPbtnWppMRJ4StyATNyARNy\nAU9R/AIBQtELAID/UfzCz64L9ACCBsXvWfTwwYRcwIRcwFMUv/ArTvICAACBRPELvygvt6u0NF7b\ntyeotDSeIhhD0MMHE3IBE3IBT1GBwC9cMxrU1NSopCQz0MMBAAARiiO/8Kv163MCPQQEIXr4YEIu\nYEIu4CmKX/gVJ3kBAIBAoviFX9GrBRNyARNyARNyAU9R/AIAACBiUPzCr+jVgtl1gR4AghDbi7OY\nIecscgFPUfwCCDhe2IGL4zkCeM8li9/7779fWVlZmjNnjvu2nTt3Kj8/XwUFBXrxxRd9OkCEF3q1\n4OKa+5n5nzGcSN9ehPtzZKz/l0jPBTx3yeTddtttWrdune666y5JUk9Pj0pKSlRRUSGn06kVK1bo\n5ptv9vU4AYQZ19zPkpj/GTA49zkiSSUlzgCOxvvKy+3MAISAuGTxu2TJElVXV7uXKyoqNGvWLGVk\nZEiS8vLytGfPHhUWFvpskAg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LLldeKGXMVsGEXMCEXMCEXMAJWR1d4Fq6AAAAcEsWiy5ndEsZs1UwIRcwIRcwIRdwQnZn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\nuL0UAAAA5FhRF92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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Variance converges to 0.0907297673624\n", - "Last voltage is 15.6491261618\n" - ] - } - ], - "prompt_number": 21 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the $\\verb,volt(),$ function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n", - "\n", - "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n", - "\n", - "##### Exercise(optional):\n", - "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", - "\n", - "> use plt.hist(data,bins=100) to plot the histogram. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#Your code here" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 22 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Solution\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = temp_variance\n", - "\n", - "def VKF():\n", - " voltage=(14,1000)\n", - " for i in range(N):\n", - " Z = volt()\n", - " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n", - " return voltage[0]\n", - "\n", - "vs = []\n", - "for i in range (10000):\n", - " vs.append (VKF())\n", - "plt.hist(vs, bins=100) \n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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V5WcrtCknoBHZwtzpDmZZAADS2GhkKuYGvNNHdtIUAwuseJ1iuIe1Gm2jfraR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\nfeUrX5m7Ix6px+v8u337ts6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- "text": [ - "" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Discussion\n", - "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Explaining the Results - Multi-Sensor Fusion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focussed all of our attention on the position sensor. Let's change focus and see how the filter performs if the intertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_sensor = 30\n", - "pos = (0,500)\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "vs = []\n", - "\n", - "for i in range(100):\n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - " vs.append(pos[1])\n", - "\n", - " pos = update(pos[0], pos[1], movement+ random.randn(), movement_error)\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()\n", - "plt.plot(vs)\n", - "plt.title('Variance')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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5U5x9koih4wURU8AB8uTJk1GzZk20bNnS/dzatWvRtGlTNGvWDN99950oAySEEEJCwTJ9\nOqyTJkH19ddQf/xxpIdDCJGQgAPkgQMH4vvvv3c/ttlsmDp1Kvbt24cdO3YgNTVVlAGSyoFyx4gQ\nmhdEiNjzgtdqqdV0BUDHCyKmgAPkTp06eeQMHzx4EC1atECNGjVQr1491KtXD8eOHRNlkIQQQkjI\naDQAddIjhBQjWg7y9evXUatWLSxatAjr1q1DzZo18c8//4i1e1LBUe4YEULzgggRe17wajW1mq4A\n6HhBxCR6FYuxY8cCADZu3AiGWncSQgiROF6rpQCZEOJBtAC5du3aHivGRSvKQiZMmICkpCQArgYh\nLVu2dOcOFZ0B0mN6TI/pcdFzUhkPPa5Yjw/s3AmnXI774uLAVa0a8fHQYzpe0OPgHxf9f0ZGBgDg\n2WefRSAYPoj+zunp6ejTpw9OnDgBm82G5ORkHDx4EBaLBT169MC5c+dKbbNz5060bds20I8khBBC\nRKF77DFYpk2Do0uXSA+FEBIiR44cQc+ePf3eLuAc5IkTJ6Jz5844e/Ys6tWrh23btuGDDz5Aly5d\n0LNnT8ydOzfQXZNKqPiZHyFFaF4QIWLNC2o1XbHQ8YKISR7ohgsWLMCCBQtKPf/kk08GNSBCCCEk\nLKjVNCHEC+qkRySheA4ZIUVoXhAhYs0LxmqlFeQKhI4XREwUIBNCCKmUGFpBJoR4QQEykQTKHSNC\naF4QIWLNC14uB69WAzwP9uJFUfZJIoeOF0RMFCATQgiplAx//AG+Rg0AgL5DB8DpjPCICCFSQQEy\nkQTKHSNCaF4QIaLPC4ahdtMVAB0viJgoQCaEEFLp8RqNKyeZEEJAATKRCModI0JoXhAhIZkXajW1\nm45ydLwgYqIAmRBCSKXHa7WAyRTpYRBCJIICZCIJlDtGhHibF5q33gJ76VKYR0OkQpTjhdMJFBTc\nftioEcDzwe+XRAx9jxAxUYBMCIk6ssOHwV67FulhkCjGZmRAf9997sfGVavAJSdHcESEECmhAJlI\nQrTmjskPHIDs6NFID6PC8jYveL0eTH5+mEdDpEKU44XFAlAXvQolWr9HiDTJIz0AQqKZ/OefAZ0O\nztatIz2UysNgAJuTA8ZgiPRISBRjLBZXkxBCCBFAK8hEEqI2d0ylAozGSI+iwhKaF4p9+yD//Xda\nQa7ERDleWK20glzBRO33CJEkCpAJCYJm9mzKhQ0zJifH9V8KkEkQGIsFvEYT6WEQQiSKAmQiCVGZ\nO1bUlpalP6NQEZoXTE4O7A8+CNvjj0dgREQKRDleOJ3g4+LcD5nsbPfJF4lOUfk9QiSLvtkJCRBT\nWOj6LzUXCCsmNxeOe++ligMkKI6ePWFcutT9WD1vHpQrVkRuQIQQSaEAmUhCNOaOFV3it3fv7td2\nym++geb110MwoopHaF6wubngqlaNwGiIVITieMFrNGCoUUhUi8bvESJdFCATEiDGYICjRQvYRozw\nb7ucHCi3bIF8z54Qjaxi4+LjwSUlRXoYpILhtVowFkukh0EIkQgKkIkkRGXuWGEh+ABWMhmjEcz1\n61Bs3x6CQVUsQvPC8vrrcPTsGYHREKkIyfFCrQYoXSqqReX3CJEsCpAJCZCzY0cUbt7s93aM0Qhn\n+/aQnTkTglERQgLBazR0PwEhxI0C5Cgi++MP6AYO9Hs7+d69YDIzQzAi8URt7hjD+L9NYSEc7dpR\ngOwDr/PCaETMmDHhHQyRDFGOF2azqxbyLXyNGuCrVAl+vyRiovZ7hEgSBchRhL1+HbxC4fd2quXL\noaB8V8lgjEY4k5PB5OdTLd9AqVRQbNkCcFykR0KilPqTT6CeP9/92N67N8wzZkRwRIQQKaEAOYow\nWVngExL83o5LSABz/XoIRiSeqM0d43moFiwAeN7nTUyzZ8M2cCCczZqBpVXkMnmdF3I5oNUCt0rt\nkcpFjOMFY7GAp056FUrUfo8QSaIAOYqwWVngEhP93o5LTASblRWCEREwDDQzZgA2m+/bxMYCGg3M\nb75J1Rj8ZTJBdvw4AIDX68EYDBEeEIlaFovrxjxCiGSo5s4F7PZIDwMABchRhcnKgnLLFrCnT/u1\nHZ+YSDnIoWCxABwHPiYGjNHo9+aObt3A16oVgoFVHCXnhezCBWgnTADgCpBZSlGplMQ4XtAKcsUT\nld8j5DaOg3bGDLAZGZEeCQAKkKMKm5kJ2blzkP31l1/bcQkJtIIcAjFjx7ryYAMMkIn/mJwc8NWq\nAQD4uDhaQSaBs1oBjSbSoyCEFLl106xU7s2hADmKGBctgnXwYDB5eb5v5HSC1+v9SwGIgGjMHWMM\nBvBxceBjYigXNkRKzgsmJ8dde9o0YwacTZtGYlgkwkQ5Xsjl4LXa24/tdrAXLgS/XxIx0fg9QorR\naGDv0QPMzZuRHgkAQB7pARA/aDSudAk/AmT20iXEjB0Lw6FDIRxY5cTk57sCZJ2OWtSGCZOX515B\ndnboEOHRkGhm+vxzj8dMTg5iH3kE+WfPRmhEhBAuPh7sjRuRHgYAWkGOOlyVKmD9CJCZ3NyoqO0Z\njbljTH4+eL0etiFDwFev7vN2cS1aABRQ+6TkvGBzcsDdCpBJ5RWK4wU1Col+0fg9Ek4cB5w4IYv0\nMMpknjkTtn79Ij0MABQgRx2+ShUwubk+v5/Jy4uKADkaFaVYWJ99FlyDBr5t5HS6bpi8lfuoXLIE\nig0bQjfICoarXh1cs2aRHgapiDQa14mrHyUbCYkmn3yiRvfusZg+XQOHI9KjEcZXr+4q4SkBFCBH\nGUeXLrD50U2Pzctz52xKWdTljvE84HC48rv9YTS6/vhvdeBjrFbIDxwIwQArhpLzwjZqFGxPPhmh\n0RCpCMnxQqEAZDLJlJgi/ou675Ew2rlTjiVLVEhLM+DsWRmeeEKHnJwAOsFWIhQgR4tbqxpckyZw\ndOvm82ZMbi64KAiQow7DIP/SJcDPMlFMYSF4nc792Nm8ObWcJkQq1GpKsyAVTkYGiwkTYrB4sRHN\nm3P45ptCtGzpxAMPxOL0aemEgbKDB8H+/Xekh+Emnd8MKZNi82Zon3/e/w2tVvA1agAFBZIpnSKk\nsuSOMUajq+rFLc7kZMj+/JMu63pR1ryQ/f471B98EMbREKkQpQ5yfn6pVuWOFi1oBTmKeZsXUv7u\nCzWzGRgxIgYvvWRB586uvAq5HJgxw4xp0yzo2zcWW7cqIjxKF/X8+ZAdPRrpYbhRFYsowWZlBZRL\nbJ00CQCgfv99AIBl2jRRx0X8UzJALmodzmRlgQ+gS2JlxphMkP/2W6SHQaKUvlMnGHbu9GjWU/jD\nDxEcEQkF5sYNVGnWDLk5OREdx759cmg0PNq2dYbtM3kemDxZi0aNOIwfby31+hNP2NCkiRNPP63D\niRNWTJ1qARvBZVP2xg1wNWpEbgAl0ApylGCyslwrwQGServpaM4dk/3xB+R79vj0XmfLlijYsuX2\nEwzjSrP4888QjS66lTUv+Li4Sr0yVJmJcrygVtMVjtC8YAoKXP8Toat0PO+6Oe7552MwbJgO77yj\ngcUSns9etkyJP/6Q49//Nhbd9lJK69ZO7NxpwN69Crz9dmQb5zDZ2YBOB32rVhEdRxEKkKMEm5kJ\n7tZqYyCiod10tJIfOgTF1q2+vVkmA0rc2GeaNw+Odu1CMLIKhuMg37vX/ZACZBIMxmqlVtOVAGMw\nwHH33fAaIYaQ2QyMHavF998r8PPPBuzZY8CFCyzuv1+Po0dDW27t0CEZZs3SYPnyQhS77UVQQgKP\nJUsKsWKFErm5kbtxj71xA86kJNdingRKoVKAHCXYYpfgNa+/DvjZYlfq7aajLgfZYkHRMgAfZKtp\nrmFDIDZWrJFVKMXnBWMwIObpp92PKUCuvII+XvA8rSBXQELzgjEY/K82JILr1xn06RMLjmPw3XcF\nqF2bR0ICj2XLjHjlFTMGD9Zh1ix1SJrc3rjBYPRoHebONaFxY678DQDUrMnj4YftWL5cKf6AfGEy\nufL/Y2PBx8eDlUA3PQqQowSTne1eQVb89JPfnWb4mjXB0gqyaJSrV0N7K5872ACZ+KZ4m2kA4PV6\nMAYD3eBI/Ge3u8q6RTLhkoRFUUMnIaE6dBw9KsODD+rRu7cdixcbi8reu8bDAIMG2bF7twEnTsjw\nwAOxOHlSvNVkngfGjYvB4MFWPPKIfzecjh9vxeLF6ojcp8rY7bCOGAEwDLj4eDAS6KZHR4coUfDz\nz3C2bg3gVrMQH7vpMdnZAM+Dq1EDvEYj2WAi2nKQi9pMAwCv1VKAHCLF5wWTk+NuMw0AUChQuG6d\nZOc0CZ2gjxdWq2DKGnPtmvSuShgMYK5cifQoooLQvHC2agXrhAmC7//6ayXattVjyxaFaIeRb79V\n4MkndXj/fRNeecXiNbOjZk0eq1YZMX68Ff376/Dzz+LUTNiyRYHMTAZTp/qf6NyypRMNGzqxZUv4\nq1rwcXEwz57t+v/4eDASWEGmKhbRothKBx8X51uAzPOIu+su5F26BGg0MPz+ewgHWLl4XLbT6ShA\nDgMmN7dU0xtH9+6RGQyJbrGxMBw/XuppzYwZcNx/P2yDB0dgUMK006dDtWoVcm/ejEgebbTjkpLA\nJSUJvrZsmQqDB9swZ44aX36pwqxZZtx1V/lVJgwG4NIlGdLTWVy+zOLy5dv/b7cDGza46gyXh2GA\noUNtaNTIiaee0mHNmkK0axd4lQuzGXjzTQ0++8wEeYDR3fjxVnz0kRoDBtgjNt24+Hiw2dmR+fBi\naAU5Cvm8gmwyuW4K00T2zlRfRFsOMltsBdlZrx5s/fv7tJ161iyoFi4M5dAqlOLzghUIkEnlFLLj\nhVrtijKkhGXhaN0aku0NLCHe5oViwwYolyzxeO70aRbXr7OYPNmCXbsK0K+fDQMH6vDyy1rcuOEZ\nGTocwG+/yTBzpho9esTirruqYNIkLTZsUOLGDRbNmzsxbpwFq1cX4n//M/gUHBd3zz1OzJtnwvDh\nOly4EHhY9tlnarRu7UTXroHPlYcesiM/n8HBg6G9ibAsptmzYRs0KGKfX4RWkKMQX6WKT5cBmdzc\ngGonk/Ix+fngilIs6taF1ccmLkxurrv2cXHqjz4CHxMD6/jxoo6zIuH1ejjato30MEgFxms0YCRw\n93xxbEYGzP/6lytnmgSEMRggP3YMxe+HW7NGhSFDrJDdigPHjLFhwAA75sxRo3NnPV580YK4OB47\ndyqwZ48c9etz6NnTjvfeM6NDB4fo/xy9e9uRlWXGE0/o8NNPBUhI8C/n48oVBgsXqvDLLwVBjYNl\ngbFjrfj8czU6dozQldEI3FQphFaQo5B12DA4OnUq931sfn7UBMjRloMMng/od1uyUUgRLj4espMn\nxRhZhVJ8XtgffphOIAiA0B0veK0WTLiK1PqITU8H16CBePs7exbKtWtF25+UeJsXfPXqHjmtDgew\nbp0SQ4Z4lpCoUoXHrFlmfP99AQ4flmPvXgV697bjt98M2LWrAG+84epGF6pzlZEjbRg82IbBg3Uo\n8DPOfecdLcaMsaJ+fd+qVpRl6FAr9u+X4/Llyh0iVu6fPlrYbB4tUZ3t24Nr3rzczZjcXHB0STok\njF99BccDD/i9HVNYKBggO5s3h+zMGTGGRggJlNRSLHgeXP364OrVE22XyrVroVy9WrT9wWyG8r//\nFW9/IcCXyGn95Rc5kpI4NGkiHEw2bcph6VIjFi82YsgQGxITw3cj8JQpFrRq5cSoUTqfS8D99psM\nBw7IkZoqzsmdTgc89ZQNixaFr064/JdfwP79d9g+zxcUIEcB1aJF0Lz5pv8bWq2eB1aDAczVq+IN\nTETRloMcKG8BMpecDNlff3mcCJHy54Xqyy+h2Lw5TKMhUhH08cJmg9ASHVerVkRq5nrFMCjcvFnU\n9ArF7t3ilvxUKKCdPh0hKejrJ6F5oZ4zB8zNm2CKtZpetUqFoUNLt16WAoYBPvrIBLWax0svacut\nruF0AlOnavH22yYIfLUE7LnnLFizRulvy4WAqefPB3vuXHg+zEcUIEcBNisroC56jp49YfriC/dj\n5U8/Qfv22yKOjPjLW4oFHxcHPi4ObEZGBEYVvZjr1yGT2EGVSJ98717oRo0q9bxt+HBYJ00K/4B8\n5XR6dJPEy/4WAAAgAElEQVT0G8/D2awZUFgo3pjkcnCJiWAluvii+OknV275rRXknBwGu3bJMWBA\n5AN6b+RyYPFiIy5elGHKFE2Z6RYrVyqh0QADB4pbvLhuXR733+/AihXCq8g8D6xYocSDD8aK0jqb\nuXFD8P6cSKIAOQowxbroBYNLTAQj0W56UZeDXIJq8WLBFamSCjZtgrN9e8HXnMnJkjuDjrTy5gWv\n10uvbi0JuWCPF4zFAj4au+g5HIgZPx6yP/4IbHuGgWnBAsESd8Hg6teXxMm90LxgDAZw9eujcOVK\nAMCGDUr06mWXyn1gXmm1wOrVhcjLY9G2bRzmzFEjP9+zukZ+PoNZszR4/31TSEqyjR9vwX/+o4Kz\nRFGOs2dZ9Omjw9KlKhiNDPbuDb7eA5udDS4+3vXAaERc06ZB7zNYIQmQZTIZ2rRpgzZt2iA1NTUU\nH1GpBLqCXBKXkAD2+nURRkRKUn3+uW+tMbVaeCtQWbhiBRwPPijyyCoO+a5dgNXzsigfF+fqpkeI\nPywWQBW+/ErRqFSwvPgi1J98EumRuMl++w2yS5ckESALYW7drO7s2BEAsHq1EkOHSnf1uLhq1Xgs\nXmzEjz8W4PJlFu3a6TFzpho5Oa5o+MMP1ejVy47WrQOvnVyW9u2dSEzk8f33rhQfiwV4/301Hnss\nFn372rFtWwGGDLHixx+DbE/tdLoaQRUFyFotmIICV6naCApJmTetVos/Aj3DJaWwmZngiq0gM3l5\nUM+aBfOcOX7th69ZU7IryFGVg+x0uhqFFL8BUoxuetG4ohVixeeFbsQI5J086RHY8HFxtIJcCQV7\nvGCs1uhcQQZgffppqD/9FOzp0+DuvDPSw3HlNF+9KokAudS84HmPpk6nT7PIymLRrVt01ZRu3JjD\nggUmXL7MYu5cNTp00GPAABs2bVJi//7QLhCMH2/BF1+oUbUqj1de0SI52YlduwyoU8eVHN27tx39\n+qnBcYF3bmdyc13/RkWLRwzjurHy5k1wWq1IP4n/KMUiGhiN4GvUcD/kWRaqAO5C5qtUAWM2S+su\n7SjEXr6M2J49PZ7jY2LEzesjnmw21/JFbKzH0xQgk4BYrVFxQirftav0KppGA8v48dBIZBWZMZth\ne/RRONu1i/RQSrNYXM2ybp1Ur17tWfs42tSvz+HTT03YvdsAmQx4912z3/WS/fXYY3Zcu8ZgwoQY\nvPOOGcuXG93BMQA0acJBp+Nx9Ghwv1TrmDEej7n4eDA3bgS1z2CFJEC2WCxo164dUlJSsDeYGwoI\nAMBw7JhHgIzYWNcB3l52Uj6TleV5ZzHDwNGpk+vShcREUw4yU6yLXhE+JobaTYdA0bxwt5kukWjn\nbNsW5hkzIjE0EkFBHy8YBpxQHXOzGezFi8HtWyw8D93IkWCspastWEePhnzPHrDnz0dgYCWYTHB0\n7Qr7ww9HeiSl54VMBuOiRQBcX5dCtY+jUd26PD74wByWVBG5HNiypRD79+ejd2/hmKN3bzt+/DHw\nSit8fDws06eXeo7xJW0xhEISIF+9ehWHDx/G3LlzMWzYMFgF/sBJEBjGtXJWTrtp3ZAhpZpPFG7a\nJLk7RaNN8Ut2RXidjgLkEPLWFZKPi4OzZcsIjIh44Dhox49Hqbt5JMo2ahQsAqUzZefPI0agukUk\nMLm54FlWuL16bCwKvv3WrwYiqi++AHv6tOuBlzJ3AY3TaAQfwcvgZVIqYe/TBwDwyy8KNGjAoXFj\nKqXpr/r1uZIX7zz07m3DDz8EmYdcAleidnUkhCQHOeFWANa+fXvUrl0b6enpaNasmfv1CRMmICkp\nCQAQFxeHli1bunOHis4A6XHZjx+pUgVMbi72nj3r9f1Mbi7+d+ECTCZTxMdbkR7XOngQd99aQS56\n/f5+/cDdcUeZ2zPXrkH+4IP4ddEir/vf9+uvYO12dOrVSzI/byQfFz3XXSYDX61axMdDj4Uf9/zz\nT6i++Qb7uneHsU6diI8n0MeHTp3CPcXq5UZyPGx6Ogzx8UhLSxN8nbvzTt/316UL1PPn40B8PEw5\nOeh56hTYS5fw82OPBT3etn//jbgePSL++yri7fe15oPr6F3lN6SlxUlmvlWUx506pSA7m8H69UdQ\ns6Y48YZp7lyk/f474OXfs6zHRf+fcSsv/tlnn0UgGJ4vrwy1f3Jzc6FWq6HRaJCeno6UlBScO3cO\nGo0GALBz5060bdtWzI+slGIffBCmmTPhvOcer++Ju+MOGI4cEV6BIAFTrlgB+W+/wfTZZ35tx/71\nF3TDh8Pw++9e36N56y3wVarA8vLLwQ6zQpH98QcU27bBMnVqpIdCBOieeALyX3+FcelS2G8FXdGI\nuXIF+oceQv6pU2W+T7l8OWJSU5F79Spw67tNbIqNG6HcsgXGpUuD3hd75gx0Q4bA8McfAMNAsWmT\na99LlgQ/zg0b4GzRAlxyctD7CpWcHAbt7lLj7JNToJz7TqSHUyG9+KIWzZs7MX689DIGjhw5gp4l\n7hvyhegpFmfOnEGbNm3QqlUrDBgwAF999ZU7OCbiMb/+etmX15xOV9c2qRd7vKX4mZ/kOZ3gatb0\nezNvTUKK45KSJNduM5KK5oWzTRsKjiWMKSiAs337sLVLD9nxQquFL10PZLfylMtLcwuGLD3drxSK\nsij27IGjWzd3Dj+fkCBaRSP7wIGSCY69zYv165V4uNUVVDXQsTVUgs1DliK52Dvs1KkTzoTpIFkp\nFBQASmWpmp2O7t3L3IzJzwcfG4uovV1XwmwjRwa0nS8BsjMpCYoffwxo/4REClNQAHuPHmELkEOF\nV6tdlX7KUdS2mMnNBV+rVkjGwtWpA+6uu0TZl3z3btgGDLi974QEsCKX/JRv3w5otXAUS3eQitWr\nlZjR9x8wu3LKfzMJyH332TF2bAxycxlUrepfYoJiyxY42rYFX7duQJ9tsbjS6sVeD6QybxKnee89\nqAK5xGYygSuW9+1WUAD2zz+DHpfYUiR4UBUbYzQC5a0g161LK8jF+DIvtBMmgL10KQyjIV4VFsLR\noQPYMAXIQR8vDIZSTWcAAGo1nA0buvroluH8FQ3exb/AhnAF2TZ4MBy37kUoE8dBuXy59xskHQ7I\n9+1zrSAXbZKYCDYzU6SRushPnoRi505R9+mvkvNCsXUrvp50EmYzg67deXe7aSI+rRbo1s2On3/2\nfxVZPW8e2GvXfHpvXp6rc9/nn6swfrwWXbro0bBhFaxfL+5NggAFyJLHZmYG1EWPr1sXBQIrkbK/\n/kLMCy+IMTTir8JC8DpdmW/h6tUDe+VKuV/Q5DbZhQuSbYBTWTAFBXC0bw/z++9Heig+iUlNheL7\n70u/wLIoSEsrVU6wOKcTePbQJMzAmzh/2hHCUfqIZaFasQKKH34Qfp1hULhhQ6lSoVyVKj6lk/jK\nmZQE9vJl0fYnhp+/tWHWt62wenUhmITqvnU7JQHr3duOH34oO0DmeeCZZ2LQt68OGzYoYLUCTHa2\ncHUtzlVx5MQJGaZO1aBNGz3uvjsOM2dqkJ7OonNnBz7/3IiLF/MwZoz4Je8oQJY4JisLfLEuesHi\nEhMl2W46qnKQBbBnzkCxdWuZ77H36wfjggVl70inA1e/PjW/uMWXeUHtpiPP/P774BMS4OjaNSyf\nF/TxIohGIZ9/roLSaUJq4kp89UNScOMQiWX8eKgWLhR+USYr3cSDYWA4flzUZilcUlLEu+kVnxfH\njskw9scnsWbEt7jjDg58QgIK166N4OgqvocesmPXLrngxZkiK1cqcf48i5EjrVixQoWWLePw6rX/\nw5k8z/t6si+bsKz2bHTrFounnoqBXs9j9epCpKfn4aefCjBnjhlPP21Dq1bOkPX8oQBZ4tisrIBW\nkL3ha9RwXWbiKmctSLM5NIuzsvPnoSzv4CuT+fSFZNi/X7Dmb2Um37MHTG6u4GvUTS/ybIMH324T\nGwUYiwX8rfs6du6U48wZ374K//qLxb//rca81Vo8/U13rDrWClIof27v0weyjAzIjh4N+2erP/wQ\nsNslESAXuXKFwbBhOsxruxgd7rrV4VQup5rpIRYfz6N5cw579ggfCzIyWLzzjgZffGHEgAF2bNpU\niG0br0MFG/oOTcSjj+qwaJEKI0bEoP19tXDY0RrvvZGLo0cNmD7dguRkLuB21oGgAFnivAXIsuPH\noQ6k1ahK5WpqkRPmmxXMZjDZ2V5bR4YjB9luB+67T48XX9QG1c+AycwEHJ6XVvmYGDDUalp0RfNC\nO3Wq1xw1Li4OLAXIlUrQxwurFRZWiylTNHjxxRj07x+L06fL/jp0OoEXXojBa69ZkNStLurdHYeO\nHR1Yt0783Ee/yeWwPPec91XkUOF5qGfPBmQy8ImJrmNgCM8Y2IsXoSzjnpyUlBQYDMDgwbGYMMGC\nAfodpbqektDq3duGH38s/TfBccCkSVq88IIFd955e4GukS4T79X+DMeP52PcOCuOHpXhgQfsOH48\nH8tqTUH35H/CGhQXRwGylFks4KpWhVALG6awEPIdOwLarZglfnwVM3YsYh96CCoR6m4GauVKJRIS\nOPz9N4tx42LK69TtVWyvXmCvXvV4jtdqqZNeCDG5ua6/BQG8Xk8ryMQvZ/NqoserXXHjBov9+w14\n7z0TBg2KLXMlecECFdRqHs88c/v68TPPWPHVVyrRr0rJjh6F7PBhv7axjRgBxfbtrhP4cDGbXVWW\nWBZgGJg++ih0909YLGBu3oRqxQqvb7HZgJEjdUhJsWPCBKurmlOUlDqtKB55xI5t2xSlLlIvXqyC\nxcLghRc88y94lQrW556DQgH06WPHF1+YMGKEDXq9q5teJG+spABZytRqGI4dE7xhhKtSBayXS86A\nK3fZWytRe9euYMLcEpbNyID9sccgO35c8PVQ5yCbzcCHH2rw9ttmrF5dCIOBwejRMWXmSnnDGAyl\nVyWo1XRIpKWlATzvKqdVrZrge2yjR8M6eHCYR0YiKdDjBc+7TpTv/+srPDswE//9rxFxcTwGDrTj\nnXfMGDgwFud/uVbq2Hn2LIt589SYP9/ksZrVvbsDViuDgwfFLaep3LgRcj9/Rr5KFRTs2OF5s1Mg\nBzg/MCaTR5tp27BhQDk3Igf0Ofn5iGvdGtBqvada8cBTTxVAo+Exa5YZDANYpk6F8847RR8P8a5x\nYw46HY+jR2//TZw7x+LDD9X4/HNjqcqzfK1asE6cKLgvvnp1CpCJ//gqVcpcNdO88w6UmzcLvmae\nMyfsuVhsRgZsffpAfuxYWD+3yJdfqtC2rQPt2zuh0QBff10ImQwYNkwHk8mPHXEcmIICV43pYviY\nmJBeWpQK9vJlKNetc5XJChej0ZXf6iV/m6tXD3ydOuEbD/HO6URsz54I+PJMCBkMwPPPx2DBAjU2\n72YwYlp1j7WHJ56w4Y03zOg/LAGXtp51P+9wABMnxmDaNAvq1/dcFmNZYMwYK778Uty7hNj0dHD1\n6/u9HdewoceCSuzDD3vPSzabg15tLhkgh4pi0yY47r0XXJ06YLxUovj4YzUuX9Zj8eLbQZija1ev\nJ9YkdB555HbTEIcDGD8+BlOnWtCokX/3PnE1aoS0lGJ5KECOUnyVKmV2cWLy8qTTYtpgAGO3w9m2\nLVBQIHhGGMocZIMBmD9fjenTbzcAUCqBr74yIiGBw5NP6rwttpdWWOgq+FjiNJirVg3W0aPL3DRm\n9Gjh0lIlORxgz53zcUDhpf7gA8SMHQv5yZNh+byUlBSwubl006KEyY4cuZ37KpOByc8He+FCSD/T\n3+NFRgaL++/XIzaWx44dBjRvLvxFPWSIDW81XY7H3+yMixddX48LFqgQE8Nj9Gjh1dihQ23YuVOO\n69e9l4bzFytCFz3m5k3ILl6Es0ULwdcVv/wCbbAt7U2mkLXaLk61Zg1sQ4e60qlMplInYHv2yPHf\n/6qwZUvZpeZV//kPlBFM86ssHn7Yhh9+cOUh//vfasTG8hgzxv+rGaYFC2B74gmxh+czCpCjlUbj\nynr30vWJkVBQIcvIAJeUBLAsnK1aQRbmVeTPPlPjgQfspb4U5XJgwQITmjXj0L9/LPLyyv+CYwwG\n4Zw2vR7Wl14qe9v8fPA+VLFgjEboe/aUZC1kJi8PXHx82BpCAADPMLD17Ru2zyP+kZ0/D9mRI+7H\nzuRkyM6eLWOL8JszR43+/W345BMTylvwHNk4DVMfO4K+fWOxbZsC8+erMW/e7dQKxZYt0Lz9Npgr\nV6Dv1AlxcTz69bNj+XJV2Tv2Fc+L0mZavncv7J06AQrhurRidNPjq1aFZfz4oPZRHvbCBbCXLsHe\nsyfAsuCrVvW4yfzmTQbjx8dg/nwjatYs55hptUIW4pM3ArRv70R2NoPvvlNg4UIV5s83BnajXaTu\nziv6+Ih+Ogkcw8C4dKnXVtJsXp7Xm5rCjblxA86mTQEA9oceAiNw+dVbTqFu8GDIfv894M++cYPB\nV1+pMHWqcEF8lgU++siEjh0dePTRWJw6VXYuIWM2w9moUUBj8aXVNOAqWwaGKfMKQaQw+flw3Htv\n2FoKp6Wlga9bF+aZM8PyeSQAhYUeNxI7k5NDPj/8yUG+coXBDz8oMHGibytYvEaD0R2O4ZVXzBg6\nVIfp080eqRXslSuAxQJer3ffrPvss1YsW6YqM7PEbAbeekvjXpn2hsnJAS+XB73Aodi9G4777vP6\nOp+YGPTN2nxiImyjRgW1j/Io16yBbdAgd6Bvfv11d7oVz7sqIwwcaEPPno5y5wVfvbrXFA0iHpnM\nVRP5mWdiMGOGGXXrSm+xxxcUIEsYk5npdYUYAOwPP+zKFRDaNi9PMivIjvvvh/HWZS3rhAmucfvK\n6QyqCcQnn6gxaJANSUnec58YBnj3XTPGjrWgf38dZs5Ue20wxTVpgkIvud3lMhoFK5IIcUqopmhx\nbF6eK0CW2AohiRymoMCjQ2Q4AmR/LFigxlNP2VC1qm9f0rxGA8ZsxqhRNqSl5WPUKM8OXUxuLvjq\n1V1/y2YzYLejRQsnGjRweu0ilpvLYOBAHfbulWPYMF3ZKfxOJyypqb7+eMIKCqBatgz2MgJkrkYN\n1wqymFeqzGZoy7mS5i/G4XDd/HeLbcQI903SX36pwvXrLP71L+/fk8Vx8fFgqd10WAwbZsXw4TYM\nGVJ2hzvlypVgSlSFkgoKkCVMm5oKxa+/BrQtFx/vPUC2WCDfvz+IkYnPW05hMPWF//6bxdq1Srzy\nSvntVBkGGDHChj17DPjrLxm6ddNj/35xGx/4uoIM3Go5/fffon6+GJj8fDg6dgxbAORLrimTnw/d\ngAFhGA0RUvKmVS4MAbKvOcg3bzL45hslJkwodgzgea/12AGAq1/fHfDfeWfpxgTszZuuG78YxuNe\nkKKSbyVducKgd+9YtG/vxI4dBUhJsWPcuBivvZr4hARYX3zRp5/PK4UClokTwTVv7v09Gg14tVrc\nEolqNZQbNoh6E6/5rbcE86hPnpRhzhw1vvzS6F4nKj4v2MuXoZk2zWMbWkEOn44dnfj4Y1NZXdsB\nAOr58yVbppMCZAkLpotewZ498JZsx1gs0A0dGszQwobX6QIOkGfPVmPMGCsSEnxfIalZk8eyZUa8\n9ZYZzz0Xg5df1iI/X5ybbxij0WOlrSxS6kpVnLNhQziTk2F7/HHJVCrgVSrXCZ8Ec7YrA6aw0CNA\ndiYno2DTpgiO6LZFi1R4/HE7atUqNjfMZlfJMC+skybBNmSI19eZnBx3+hpftaq77Nhjj9lx/rwM\nf/55+2v11CkZHn5Yj5EjrZgxwwyWBWbNMsNgYDBrVoj64wKAWg3zu+8Klggtztmmjbht2hkGXL16\nkIX45N5oBJ55JgYzZ5rRsKHwmQbzzz+Q//GHx3N8hOvqktKY7GzP0oQllXEVPdQoQJYwNisLfGKi\n6Pvl4+JcFdX9qm8WWiVzx9j0dKhnzXIFyAGUTzt7lsX27YpSRcl99eijdhw4kA+WBTp31mPuXBW+\n/FKFZcuUWLVKifXrFdi8WYEff1SgKH5XLltW5qWi/BMnXJdmfeC86y5Jtu4t3LoV0Olg/vBDrzf/\niMmnXFO12pVM7i0vhoSU7YknXDdQFZHLwdesGdLP9GVeFBQAS5aoMGmS57wo3mY6EMVrchdfQVYq\ngaeftuK//3Xte88eOfr31+Hdd00YP/72cUipBJYuNWLdOiU2bgz931BZCjdtct1ALSJn/fohP7l/\n/XUt2rZ14MknPS/fF58XQjdUc7Vro1AiJ28EgMPh+nfydr9UQQGq3Lp/KRKk9w1MXG5dBuRq1BB/\n3wzjvoM52DulQ0W+ezfYjAxX3csAVpBnzdLghRcsiIsLfFVRrwc+/tiEJ56QYcsWJa5eBWw2Bg6H\n6792u2uF6LnnWDz/vBXKb74B16QJHN5q8vrxpWwbPjzgcVc08v374UxKAl+3rtf38HFxriohYSg5\nRTw527WL9BAELVumQteujtK1Vy0WrzW1fWFctMidA1uwaZNHmbORI63o0kWPFi2ceP99DZYsMaJL\nF0epfcTH81ixwogBA3Ro3LgQd98d3sZNYpHv2wdYrXD06OF+jktKAnv5csg+89tvFUhLk+PXX8te\n+RZs6KRQgAvwJmsiPiY723Wy6aXYAHQ6VyFlk8nrFfFQogBZopi8PNeXfRkHcsXmzWDM5jIvB3rD\nJyS4bgIUCJDZS5cg//VX2MaM8Xu/pdhsrj+C2rXdTzHXr0N+9KjHzXolcwrl+/bB0a0bbAMG+F3q\n5ehRGQ4dkuOLL8Rp3NGxoxMdO7ou8zA3b7pWn26lSqxYocTevbf+jLTaStEsJJxSUlKgHjwY1tGj\nYS8rQL7VbjrUK5dEGsrLQbZagS++UGP16tIn14zV6lO5RW885liJewpq1+bRvbsDH36owaZNBbjz\nTu83B7ds6cSHH5rw9NMx2LGjADVqRF+KkHzvXoDnSwfIIVpB/vtvFlP+T4mNz21AbOyDpV73yEGm\nNtOSx2Zng4uP9/4GhgEfHw/25k1wEQiQKcVCohiDAc4y8uQAgP3nH8hK5Fj5iqtZ02sNTMWWLZCd\nPo2YESPAXrwY0P6LyE6dKpXvzOTmQvPGG9434nko0tLgSElxBZ1+fpmtWaPEmDHWkJxwambMcN2E\ncku7dg4cOuQKkPmYGGo3HQJMbm65JQuLVpAJAVzHgDvvdAqvzFosfl3N8dfHH5uwZ4+hzOC4SL9+\ndjz5pA2jRsXAZgNgs0H94YchG5vYhDrp2R97DLYgW7+zf/8N7dixpZ6fNk2D8Q+dQcejX5Y/Nm81\n64lkcFWqwDpuXNnviWDeOAXIEsXVr19urhRftapgrVzm5s1y61s6Onf2WlFB+d13sD/6KJiCArCX\nLvk+aAHs5culWqZyTZqAvX7d407n4rlj7IULgEwWUKtVANi1S4EePUJzAxlTYlWiaVMO2dksbt5k\nAs6XJt6lpaV55Hx6Y/zsMzjvvDNMo5IOngf27ZPjwAE5LlxgUVAgoXsVnaFLGygrB9npdHXOfPll\n4Zx0huPAlXVvh8EQ1MJAtWo8qlf3/R9h2jRXKtjEiTE4vi0bstVrA/7ssDObS1365ho0gLNVq6B2\nq1yzplRwu3+/HCdOyPDC8CyvlSiKzwvb44/DGiU3o1dWfN265aYT8tWrRyxAphSLKMZXqSLYp1y5\nZg3Yq1dhnjXL67ZWL92PmGvXwF64AEdKCrhvvw261Bhb1EWvOLkczjvvhPzECTi6dCm1jTwtDfaU\nlHLvwBZy7RqD7GwmZDl9JfPaZDKgTRsHjhyRoa5W62qDKoTnA/p5pITJzARjMoG74w4AgGrRItiG\nDCmd5yf25+bklBsgcxG8kSNS7HZgyhQtdu+WIzGRR1YWg8xM15pHQgKHGjV4NGjgRPfuDtx/v738\nLmNicjgQ17gx8s+eDelqrZAtWxSoXp1Hp06lc38BwNmiBQq//dbr9vLff4d64UIUrl8fqiF6YFlg\n4UIjZs3SYPy/6uLataO4d4gSXbo4kJLiQMuWztDdr2s2g712LeC8XKEV5KDxPJRr1sC4eLH7KY4D\n3nxTgzffNENVy7OTnjeUa1wxcLVqgSkoiMhn0wpyFOPi4twlhopj8vK83xVaDuWPP8Leq5frZoak\nJMiCvNlCMEAG4CjRcrp47pj9scdgmTo1oM/bvVuBrl0dXnP+gyV040f79q40C/vDD8PhZeVEvm8f\ndP37+/VZ7F9/gfnnn4DHKjbF999D/dln7sfKjRshO306pJ+Z0rmz8M02lVxuLoNBg3S4fp3B7t0G\n/PhjAQ4fNuDKlTycOZOH9esL8c47JnTu7MBPPynQqZMeXbvG4u23NdizRw7rraIKTieQmcng+HEZ\ntm+XY/lyJebNU/lVWUk7cWLpCiJyOfjERNfVoBDwWjedB+bOda0eB3w+qtH4VxFFhCV7vR744AMz\nDr24GCcGTcfQoTb8/TeLiRNj0LhxHN56S+PXx1y6xGL06Bhcv172L0F27hxiRo8OeNyM0Sj6jbGy\nkycBhoGzTRv3c5s2KcDzQP/+dvDVq4P1soLsS31s1dy5UC5dKtZwSYiZ5s+HPUJ17ilAjmJ81aqC\neZfBdNFT3EqvAMQp1yMTSLEAAOfdd0N2/LjgNnx8fBDpFXLcd1/o6vOWTLEAgHbtnDh8WA5Hz55w\n3nOP8HZGo9+lpVT/+Q+U330X8FjFxublgSsWqDqbNQMb6oYhVitsTz0lyZJ3YWUwuCsDnDvH4sEH\nY9GqlRMrVhhLNWfU6YCGDTl07OjEyJE2LFtmxLlz+fjoIxOUSh4zZmjQpEkVtGgRh1q1qiAlRY+J\nE7X4z3/U+P13OVavVnntCFcKx0H5zTeCHT2dycmQ/flnsD+5X3bulMPhYNCrV+DHgKJOekLkaWnQ\nPv/87ce//IIYES/js+npqN68Ovr2tWPOHDP27zfgt98MOHBAjldf1XhtLlLcxYssHn88FiaT6yQq\nL/GrDBkAACAASURBVM97kOzuphcgW79+cLZsGfD2QmSHD8Nx773uK24WCzBjhsZdR5rX690dDAPB\ncJwka8wT6aEAOYpx9erBJHBDB+vDTU3emN97z13TlKtXz+9yPbt3316dAlxfNk6BShmOlBQ4unZ1\nP/aWU8ieOYPYB0vfrSyE510ryPffL3xpVQx8XFypk4927Rw4fFhW9pdXYWGpO97Lw9WrJ6kDeckT\nr3C0FE47fBimuXND+hmSZrOBvXQJin37oHntNfz6qxyPPRaL1FQLZsww+3ylRC4H7r3XienTLdix\nowBHj+Zj2zbXivO5c/nYu7cA69cX4rPPTHjpJQvWrxduYV9KYaErB1Wg0kx588NgACZO1AZU+MXb\n8WLuXDVSUy3+Fr7xwKvVXlOlmMxMMI7bxxc+NlbU1sVsenqpxYGaNXmsX1+A48flmDKl7CD54kUW\nffvG4pVXzFizphBduzowZIjO6++Yj493pSsEmC9u79cPXJMmAW3rjfzYMTjat3c/XrxYhZYtnbfL\n5TEMTB9/DKFfhC/1sblq1ajdNPEJBcgSxV64UH4HGa0Wjm7dSj3N5OUFfEna2aKF+6YLZ6tWMC5Z\n4vO2BgMwcKAOTz+tcw/duHw5uGbNSr2Xa9DAtTJYHrW6zLawxf35Jwutlkf9+j4sswSoYMcO8CVq\nUyck8NDreVy44P3PiSks9LmLXhGptZsuOa+czZqFreV0ZaX47jtoU1PB1amDhce7Yvz4GCxZYsTw\n4bbyNy5DtWo86tblhRZ+8cgjNuzfr0BOTvk5CiXbTBfnbNYMsrNnvW67ZYsS69Yp8dZb4lyiP3lS\nhvR0Gfr3D+53A63Wa4oFm5MDrlg+vLcbpQNlGzgQDoG60no9sH59AU6ckOPVV7WCQfKFC7eD41Gj\nbGAYYOZMM+64w4lRo3SuKhklKRSuZiciB4zKlSuhCDCH2/TRR7DdWpXPyWEwb54ab73l+V1oe/rp\ngHPb3ScFJOJUX3wB5vr1SA/DKwqQJSpm5EjIAszf4+LjfaoHq/juO8GzcDe1Gly9ej5/7r59CnTq\n5IBez2PYMO+rFkK85hT60Wr6118V6N49dKvHZSlKs/CGMRq9Vg3xhqtXD+yVK8EOTTRMfr5ngJyc\nXGYAJAZfcgoBQL5rV9mlA6OUaskSWEePxjvf3I1FWQPx008F6Nw5tHNcrwfuv9+OLVvKT7NgCgq8\nnvg5k5PBltFZcsMGJT7+2ITt2xXYvt2/FBqhebF8uRJPP20tPxvHaHS12fOC1+ncN6KWxOTkeNzf\nUbzVtBjs/fp5bYij1wPr1hXg5ElZqSC5KDiePNkVHBdhWWDePBMUCleVDKHDfVHTKDExBgPkhw4F\ntrFM5i7t+eGHavTrZ0OTJr4tehSfF9rnnxcMhLn4eFpBlgj155+DETxzk4bKFSDzPDRTpkD+yy+Q\nHT0a6dGUic3KAldWf/IymBYu9CkvTJuaKuqZ9O7dcvTo4cCiRUbUrs1h8GBdWd9DpfE8Si5z+FNb\nePduBbp3D13+cVnat3elWXgTcIAsoRQLrl49cMW+vPnatWFJTS37JCtcHI6w57uGGvvnn5BduICt\n8v5Y950ee5QPoEH18NR6HjTIho0by0+zYAoLva4gc82bo2DHDsHX/vmHwdGjMgwaZMMXX5iQmhqD\nGzcCr/JiMrkC7qeeKr+1vGrVKmjefdfr63x8PAo3bhR8jcnJ8WgXz8fFgTEYwvY3UBQknzolw+TJ\nriD5/HlXcDxlihkjR5YONhQK4KuvjPjnHwavvVb6Zj9nhw4B5/N6I0Y3vYsXWaxbp8SUKYG1kFf+\n+CN4gbMlvlo1r2XiSBjxPJjyGoUUvS9CK/7SD5ANBii+/16UXbHnzkH5ww+QHzkCxZYt/m2bkeHO\n0xJzxUCQ3e66nF3sQBwKfGJiufWS/bFnjwLdutkhkwHz55vQuDGHQYNii5c79iotLQ3sX39Bf999\nni+o1a5Wk+UcwK1W4Lff5OjaNVIryA4cPsBBuWyZ4OuWyZNhee01v/bJJyS4cvEckfmZSjK/9x6c\nxXIDwTCuIu/BJHyWw5ecQqBiNgpRLVmCi30nIHWyHosWGVGlrrbMFVkxPfCAHSdPynDtWtlBK9eg\nAczeVu4Zxmtpw02blHjkETs0GqBLFwcGD7YhNVXrc6WGkvPi22+VuOceB+rW9WEHQTQKYUuWHJTL\nXSfxvhzkRFIUJJ8+LcO4cVr06xeLqVPNGDHC+0qcRgOsWlWI//1Pjvff92y8ZPr0UzjbthV1jFz9\n+pAFeXI/Y4YGEyda/eow6J4XDocrRVHg6gZ3xx0o8PP7n4RAQYHr7K28MoGFhYi7++7wjKkEyQfI\nsowMqN9/X5R9KbZtg/2hh/z/4+V56Dt1cv3B8Tx0w4ZB9WX5nXwCxWRnu4LjUNUqu4VLSHA17ACC\nDpQzMxn88w+D1q1dJxEsC3z6qQlt2jjQv38scnPLXx1SpKXBUfJAzfjWgON//5OjaVMnqlaNTJeE\nu+924uwFFbil3wi/gWH8r8TAsjCuWlWpKzhUOXMGrA+l5Hi9PqxBSsgVFkK2biNGHX4Zzz1nRceO\nTjhSUsBYy18hFYNaDTzyiB2bNpW9iszHx8NR8qTWB+vXK/HEE7cDumnTzLhyhcXXX/t4c2AJS5eq\nBFdPhQTTatr48cewPfaYx3P5584FXDUoULGxriC5oIDB9Olmn3LSXYF1Ib79VomvvhKnNrV61izB\nxQtnUbvpAEvgHTwow+HDcowbF9jqMWMwuK5sCJ28KxTga9UKaL9EPOyNG+BK3M8jSKdzLU566zEQ\nQpIPkIO54awkxfbtsD30EJx+3vzE3LjhKoau0wEMA+PChVB/+ikUxVoOi8mf9Ar1xx9Dvn9/QJ/j\nbjftcEDfuTOYa9cC2g8A7N0rR5cunvWHZX+dxQev/YMuXRzo21eH7OwSQTLPQ/t//weYzUhJSYG8\nqL10CfnHj5c7B3bvloc+vcJg8HpDgUYDNLvDjD9uBlaejgjrcOYMFPv2lfu+iraCzNjteCflB7Aa\nFVJTXUGC6ZNPgu5Q5o9Bg2zYsCGwgLUs586x+Ocf1uNqj1IJLFpkxLvvasq82bVI8VzTU6dkuHqV\nxQMP+Pj3b7UG3rxEry+94qXwsSSeyGJjgdWrjRg2zPcczho1eKxZU4j331cHldICAOA4qD/5RHgh\nR68Hr1D4fWmcuXIFPMfjjTe0eP11M7yVWJbv3QvlunWlni+aF9RmWvqYGzfAl5deAbgWycqofR1K\n0g+Q8/NFOTtn8vJc5WO6dvW7OkDJdslc/fooWLcO2unTIfeSYxcUh8PzUnZZY7t4MeC2qHxCApjM\nTMj37weXlAS+du1S75H//DO0EyaUu6/duxXo1s0zFUA7dSrkRw7jnXfMeOghO556Sue5oMAwkB0+\nDNmpUwDPQ75vn2BnPcTGltuF7tdfFbjvvtCmIih27IB22jSvr7drZcX/DM1DOobKpmTVAG8qWoC8\n/0wNfHmoAxYuNIb6QpJXXbs6cO0ai/Pnxf2aWL9eif79baV+ruRkDq++asG4cTF+ZRUtX67E8OE+\n3Jx3C2Ox+F2TPByU//0vZIcPh/xzGjbk8OSTNnz4YWCr6G5ms+tSg5cUq8ING3DichVcuuTb/GGu\nXYO+e3ds3aqA1Qo8+aT3wJ+9cgXyX37xvi9qLiR5fO3asPgQWwCuet2+VrMSU1QEyMoff4TsxImg\n9iPfufP/2Tvv8CjKro3fz8xs3/SQ0EEgoDTpRboUUZASkCaiCCKCIMUCqFioKipFKSKC8gIiiK8C\nflSl+dJL6FV6D6nbd2fm+2OSkM22md3ZEuB3XV6X2Z2Z50mYcuY859w37M2aARoN+JIlhTdbkW5J\n1JUrLmoOXPXqMCxdCt0bb4DeuzeguRWFrV9f0HkUAR8b61wTnZsL6vx5Ufs6GjUCV7YsFOvXF5iD\nuBw/Pt6nlBfPAzt2MGjZ0jmDk++iRwgwfrwFmZkEe/Y4P8XYJ58EffQojqxYAV6rdeu654usLIKz\nZ2k0ahTcANnXTbdBQxZ7zfKK5j/sZF+8KM4VUq0WGsJkcDULNxkZBEOG6DB7thGlSoXv96FpoFu3\nALPIHAfq4sWCH3leaKbr2dN98DN4sBUxMTy+/NJ78JZfa2oyCQH3Sy+JLz3hVSqfwRN18qRvmU2Z\nUf72m+iG5EAZO9aCNWuUorL1niAmk1cXvX/j66Nbr3i89pp79YyiMIcOwVKnISZP0eLjj81eWxs4\nDxnF/POCrVgRphkzfA/6iLDBlS8Pe9euorblExLC0lgZ+QFynsZkoDWy9mefvW+qQdOwjBnjopjg\nCY9ucI0awThvXli1YIu66TEHDkD7zjui9rV36gR7aiqU69fD5iFAFtONfOkSBbudoFq1QndBlgV1\n/XrBiwVFAa+/bsW8ec6ZG/bJJ8EcOQLdrVuwd+woat5F2bmTQaNGDr9XTcXia9mufhOCvXZXDVMA\nxT9wMxo9Zre0Y8cGrXFVmZvr3BTlCUIEDW+//YUjA54HRo7UomtXG9q3D39zZo8eQoDs9+nLsohu\n1qwg2Dx0iAYhQN267o0pKAqYM8eIxYtV2L/fd+r899+VaNCAFdecl4flgw9gGzDA6zb6QYOcAvtQ\nQF+6BM6NqVIwSEjgMXy4FZMmaQCrFfShQ5KPQUwmofTQDUYj0L+/DmPHCkmoVat8v2TRhw7he+Z1\nlCnD+TR74uPjvZdvREd7dDV9RPGDrVjRo7tlMIn4AJmrVAkARGvhekSrddKXtLz7rlBPJgKeosBW\nr+72O0e7drC9/HJgcwsAPjbWSaieZGZKWlqijxwRMrduzDyAPFF1qxXepCi2b2fQooXdKTYhN28K\ngU2hZpg+fazYvZvBpUv3TztHnuV0ypgxME+fLnrehdm2LTTybkV1gItS+XEaueoSuH3T9WEd1aKF\nqGYzF3JywGzaJH0/maHPn4d29Gj33x07FrSXRL3NJi5AfkD4/nsVbtygMHFi6B8G7mjQgIXdDhw9\n6j5YVS5eDGbbNs8HUCjAPfYY6HPnAAjZ3h49bF7fY0qV4vHVVya8+qoe16+73zC/1vTHH1V4+WX5\nGxd5rRZE5AojgMBl3qxWkLt3wbkpcwsWr79uwf79DA7+j4W+Rw/pBzAa3SoQ8Dzw5ps61K7NYuhQ\nK6ZONeHTTzXw9Qi37DuJafs7upiCuMNTRlGsbrp6yhSPikMPNDwvlKZEiDKSWMwzZsDepUvIx434\nANnesSOs/fqBSBLUlRfrqFGw9eoVtvG9wcXGgiocIGdliVuSzt8+JwfWIUM8Z94I8WlYIci7OV9w\ndF55RWF0OqB/fxsWLLif6mVr1hQengF052/bxgTVXjofXyUWhCKo+5QCBw+7ZktIviWv1DFzc6Eb\nNUryfnLjrReArVYNVJACZHunTuCCLHcYKZw+TeHz6Up8v9Dg1uEOPA9mx46QrkYQIjTrebKeZnbv\n9mkywVatCurcOTgcgrybp/KKwjz3nB2vvWZB7956j+/mJ09SuHqVQocO8r8c82q1S8aKOnUKejcr\nbap58wI2qaFu3xYcOkOoWKPVCuohE2ckAUaT6JLDfPiEBFiGD3f5fOZMNa5epfDllyYQAjRqxKJZ\nMztmzfJSNsOy+OZAMzz1lKNACcnr2PHxgTVtURSoAJrSiy25udCOGYPoVq28v9g+AkAxCJCBPDe1\nMAbIkYyjZUtYCmX2qKwsSU2NjlatYB082Os2XPnyoD2UWXCcUOLQqpXrQ8reurXLZ4MHW7BypfL+\nQ0+jgWHFCvzjRYlDM2EClEuWuP3u8mUKBgPBE0/4vqkGjF4Pzoc8kCfDkMJGITwvXrFGar18sCBe\nzqtgOupt7tRJeLN6CFj6kxJvsN8gxXLc/QaEQPfyyyEXzU9NFUxD3CVJvVlN58NWqQL67Fns3Mmg\nTBkOVaqIy7aOGGFF06YOvPyy3kVJbNeuXfjpJxX69RPfnCcJjcblIqXu3XObSOBjYgK2mya5uWFR\nXejb14bMTApro/uBktgExScnw9a/v9Nnmzcz+P57FX780VB48RATJ5rxww8qXL3qPuS4dy4Ls/i3\n8MEkcecGHx0N07RpLi+LonXTH1a76eho5Bw+DPO4cdCOHg3diy+C8tOx92GgeATIUVGBl1gUI+i0\nNNENInxSklB7mQfJzAQnIYMsBsOiRbA/84zb706epBETw7vUADqeegqWceNcti9Thkfbtg4sXXo/\ni+xo2RK8N6kkhvGocbttmxCcB9GrogDzRx95bGbMp359h1vLaWI0FljyLligQufO3oOKAmgaXOnS\nITOI8ATJzvb4AGcffzysdfgPAryDxbrlFvQotcvpei4KV6ZMyM+FJ57gEB/PYfduN+e1Fye9fLiq\nVUGfO4fVq8VljwuOTYBp08zQaHgXExGrVXBZe+ml4NjUuiuxIEVNQvK3Ldoo7Qdc6dIwffJJQMfw\nB5oGPvrIjAmmD8HeDEwl4Px5CsOH67BokQFlygiuqFGtWwO88HwYMsSKjz5y39T3xZKy6DFQhYoV\nRZaqEALbiy/63XPAJSQ8vHbThMD+/PPI2b0bjkaNEPXMM2C2bw/5NNTTpkW8o2GxCJCtAwfC+uKL\n/u2ck+O1fjYS0Q0YAOr2bb/25ePj3TYUBoRe71HKZ/t2xqW8whdvvGHBd9+pnMqgvNWO8Xq9xxek\nbduCL+8mhfr1WRw6xOSbLgo4HEJDqFqN69cJZsxQ4+JFCpcvi7v8xMgSBprB8oXPDHKQAmSxNYUA\noJ4xA4rVq4Myj2BCnTyJMy1GQ2PPQcXl73vdlg9DgAzcb9YriqgMcvXqMClj8OefCnTvLi2gZRhg\n4UIjTp+m8fnn91OS6emtUa8ei/Llpdf+kvR0n86cbNWqLgoNHgPkuDhQAQbIfFwcHO3aBXQMf+nQ\nwY4EjRErfvV/pSYnB3jxRT0mTDCjSZO8m59SCer69YIG+xEjhJrnoi9aly4JLzv5DX2BkH+/UM2e\nDWbrVo/b8YmJER+cBR21Gta33kLOP//AEYaGRtV330V8U3WxCJD50qXdavSKQbVyJbQTJrh+YTRC\nNXNmgDMTILduQfPRR7IcC8jLyrixyBSDZfRo0dIpcpBvLy2FevVYlC7NY/16cQL7vE7nNkDOL+8I\nRYOeWOLjeSQlcThz5v6lVZA9JgTvv6/FoEFWPP+8HevWifv9ubJlBVcqT1itiKlRI6iyVHyJEh4b\nVfnSpWGcNy/sSh3EYAh7pl0qzJYtiOraFavKvIXOQ5PAP1bR6/Zc2bJh+R1TU+344w+Fi/CPqAC5\nRg381vEb1KnDomRJ6eeITgesWGHAzz8rsXy5EKT/+KPS7+Y8fc+egva6FywffOASsHrS5OZkyCCH\nE0KASd33YOqvtf0yK+M4YOhQHZo3d+CVV5xPEK5ChYJ7l1YLfPyxCRMmaJzKdaZOVeP116VZSvuC\nOXTIa1km/zBnkIvAJyfDoyNLsLDZhOei2HJQjgMJw30v4gNk5apVAT348+2lXVCpoJk+3afUG7l2\nzbepiFIpa0esmGXLSMBuB/bsYZwcscTyxhsWzJ17PyPkrXbMUwb56FEaCQm8sJwXISh/+QUNqmQ4\nlVnwMTHI/vdfbN7M4NgxGqNHW9C5sw1//ikuQLa3a+e99lmlApuSAvq4h9pVGbD16QNbv37uvyQE\njjZtgpINEFtTCBRPsxBH06bI3rYd/71YF126+n7RC0eJBQCULy/UDm/b5pz9M02fDq5kSZ/7e9M+\nFkNSEo+VKw345BMN5s9X4cwZFs8849+Lsb9GIeTePY8Z5OLeI1N7xgto2ILB/PnSzUNmzlQjI4PC\ntGmu0TVXrpzTy31qqh0qFQpedNLSaOzapcCwYfL0WOTfL7yVhAFCY3Hun3/KMuYj3EOuXYPmk0/c\nNuAXuOiJrY00GhHTuLHMM/RNxAfI2rFjfS6HecRgALNvn9tmMTAMuKQkn52sqv/8B8qffvK6DR8X\nB+JwyFPKkX8yRaDTU1EOHqRRsSKLhATpAWqnTnbcvk1w4IBvrVNer3croL9tW2RljwFAsWEDGiWc\nc6lDNlspvPeeFp9/boJaDbRs6cCJE7Qou1d79+5wtG/vdRu2bl0wR44ENPdIgz5xAvE+Mn2F4WJi\nQBWzABk6HY5llAPHAbVq+W40ddSuDS45OQQTc6VnTxu+/16NkyepgtuUo317n+osWVkEO3Yo8Pzz\ngdULV63KYckSIz7+WIN27a767/BstfqVMTNPnAjroEEun/PJycgO4stpqPjwQzPmzlUhPV3ciy6z\nYwcOfHMYCxaosGiRe+UV9vHHoSjUgE0IMHWqCVOnapCTA3zyiQZvv22GnwumHvHZ9Mgwsjj0FjeY\nTZtA79/vczty4wbUkyYFJAfHlywJ6tIl6FNTXcpZqPR0cCVKiD+YXi8sVfizxBEAkR0gOxxC9tjP\nbKpi2zY4GjTwuD9XvrzP7DB15Yrvml5ChKVPL1JoYiG5uZLLK7RDhoDcvBnw2F5hWRetT3fybkCe\nrfeOHV4PR9PAkCFWzJsnZCy81Zrau3SBcf58l8+3b1egdesQ1R9znCgpM16nQ8NSV1wC/6++UuPJ\nJ1m0bSvMV60G2rRxYMMGf5/yzjjq1AF9+LAsx4oUmC1bUF+CFFNxzCADwB9/KNCli11UAt7Rrh2s\nQ4cGf1Ju6NnThqgoHgMH6lGxYiwaN47GgAE6TJmixurVCuzZQ+PUKQo3bhAYjfcrbv74Q9Apl0Ok\noWlTB9avz8Xnn0t4uBaBWK3+WU2rVO4Da0IivpZSDJUqcXjxRRsGDdKJEs3J2XIIg2bUxaxZJo+r\neNZBg6DYsMEpeVSvHos2bex46SU9rlyh8Er13X5pxCvWrYPiv/91+iz/OfLIato9ynXrQIv4W/PR\n0WAOH4bu1Vf9V1BiGBgXLYKjcWNEPfMMqDwtdKBQBlkshAhlMSGuG4/oALnAuczPm4/H8oo8uPLl\nvdd24r5dsi/kCpDBsnA0ayZpF/r0ackSPVKJatfOZQnfnb00ANBHj0Kd71rohf79rfj7bwbXrvn4\n91UoUDRddPs2wcGDDJo1C00GmWRlIeq553xux+t0qB1zCZcu0QXC+GfPUli8WIUpU5zffjt3tomu\nw3YH9e+/BTcvtm5dMA9YgExJVGTho6Ox81IFDByow507xSdg+eMPZcDZ1VAQG8tj0SIj9u7NweXL\nWViyxIDUVBsYBli/XomJE7UYOFCPdu2iUbVqLJKTY1GlSgw++ECLXr3k+/3q12cRExNAWZXF4mRg\nFAkoly0Ds3lzuKeBiRPNSEzkMWiQzuvCLc8DQ9f1QNfqp9Gxo+cN+cREZO/f72LK9eGHZhw+zOCD\nD8yI+n6eX6tf1OXLYPbudfudrxKLhxVvzdZO6PUwrFgBMAz0vXv7vzpOUbBMnAjLW28hqnNnMHkl\nMFxKCixvvCHpUFxiIkiQ45yiRHaAnJUlZIVu3oSuTx/J+/MxMd4D5LJlfWaQPdlMuz2WDAEyn5wM\no4+SDpd98t30HA6PdsCBwpUu7fQyYTQCaWkMmjZ1zeBSly+LeqmIjgb69LFh4UK16FpTiwWYNUuF\nZs2i8eabFlmyUmIQm5Hg9XqobAZUr87iyBEGPA+8844WY8daULq080O9fXs7/vc/BfwqX+R56F5+\nGcw//wAA2CeeELJi/pYjRSAkIwPnJGQM9qhboffFz6HT8WjbNhqHDvku3wk16s8/d9L0Pn2agslE\nUL9+CHS8ZUSpFOTfunWz4733LFi82IhNm3KxZ08OTp7MxvXrWbh6NQu7d+dgx44cPNcyE4wXrXOp\nSKlNLwofE+Mzg0zS00FduuT3GFJh9u2LiAZTmgbmzTPC4SAYMULr0SDwu+9UuGGIwqSuu30f1E0J\nTsmSPA4fzka3bnbQhw7BUa+e5LnyCQkuWsb554Vx8eJi5cCp+OMPn/1QciDJSEylgnHhQnBVqiCq\na9eAVudsL70E43ffQZmnMsRVqCBZtcWTe2IwiewAOd+9S6EAc+CA5P3Nkyd79ba3d+wIx1NPeT6A\nzSbYf5Yp43Ms66BBcLRsKXmOcpCvw0nu3YPeUyNVgBRtttizh0GtWg63tWNis+4A8PrrVixbpoTZ\n7D2Y4XlhqbZp02js389g48ZcvPtu6MwzRGckdDrAaMzTQ6axerUSWZkErw12nWt0NNCokQNbt0rP\nIjM7doA4HHA8/bTwgUKB3G3bXDLtcsFs3+4z+NZ37ixrNz/JzIRNZHnViRM0XhxcAt/MteCbb0yY\nNs2E3r31Bc1AkQKzdy/4Qg2Xf/yhROfO3q2XiysqFVCiBI+KFTlQOdnQuanfDQc5hw/7rJtWbNwo\nahVMLsLemM3zgiwaz0OpBBYvNuDqVQrjxmlcxGnS0mh8+aUaSxvPhCLa/0x8QgIPcu8eqHv3wFWt\nKnl/LiEBlAezD8dTTwXtXig39JEj0L/yChSbNgV9LJKZKa32mqZhmjEDXIUKASffHK1awRSAchib\nkiL0eoWQiA6Q+ago2Lp186qDGwhsvXpeg1qSmysYQ4iwamJr1QJXpYqc0xNNfgbZ08k/ebIakyer\nRTWEeaJoOYqn+mNAZN12HhUqcGjWzIFZs9pj8mShlvH4cdqp8TUtjcbzz+vx+edqzJxpwn/+Y0Tl\nytL1TwOBZGeLyiDbW7SAo1UrNGjgwN9/K/DRRxrMbrca0W+7t4vu1MmG9et9B3GKDRtAXbxY8LN6\n7lxYhg0LTe0jzwvLbKz3LCexWkGfOiXbsCQjA4+LKDc6f57CCy/oMW2aqUDZoHNnO9auzcXXX6vx\n3nuayEis8zzoo0fhqF274KO1axXo2jXyyyvcQZ08CfWUKaK25UuXFu7hMmnSS9HH9gderXYxCvEK\nywa0eiNGLi+oEAL9K68gvy5MqxWk9fbvZzB16v0gODcXGDRIh+nTTahCXXTRipYKfegQHHXrixxF\nCAAAIABJREFUilczKAQfH++SQZZyXmgmTIBy6VLJ48qN+ssv4ahXryC7GkwoKRnkfAiBccmS+8kY\nsWNduSJrVtw8bRrszz4r2/HEENEBMlelCqwjRwqpCJ53KxcSTPiEBBgXLQrpmP5QECC7qS+6cIHC\nkiUqZGRQaNw4Gu+8o8GlS9L/2V0DZMajQQctssQinzlzjBg8WLCMXbdOicGDdahYMRaNGkWja1c9\n+vTRo2dPG7Zvzw2bKUhBPbwP2AYN8gJkFjt2KNCxox2NEi8U2EwX5dln7diyhfF5H1H8979gdgvL\nmdSZM6CPHIHthRck/x5+YTYLDzAfdZuO5s1lzYLYn3kGrI8XratXKaSm6jF+vBmpqc4ByuOPc9iy\nJReXLtHo1k3vV10yz8N3jbxIyPXrQvd8Xgb5wgUK6ekUGjWSVl5BHzni9LLkcbv9+8Fs2+bPVEVB\nXb8uvnaUEMFyulCjTkSj1TrJi5L0dMTUquV589GjoVy2zP/xDAa/m9HlgktKApVn6gEIK1yrVhnw\nxx9KzJ6tAs8DY8dq0aKFA6mpdth69gTr5W/ikUIpaebgQb/KK4DAl9x5tdrp9w0HJDMT9IULMCxd\nKrxsBFlL3vL66+ASEoI6Rj76rl0jomwoECI6QC6AEMFuuphrTQYL66BBsPXoASory6WpafZsNQYN\nsuKrr0zYsycH0dE82rWLwmuv6XD8uPgaTa5ChQJh9cxMggsXaNSv7z5YdTRoALZyZdHHjo4GEhP/\nxrhxFixZYsSePfebgIYMsWLv7iyMmpAImoQ2a+wEw4CVsAxYvjyHIUMsmDjRLAiiewiQS5bkkZLC\nYedO76sUhd301PPnwzpwYMgajcQ2dlj79IHyl18CkgZyOt7IkdjppQ701i2C7t31GDbM6tFyOCaG\nx4oVBjz1lANt20ZLOucBYOVKJRo0iMGFC4HfKpm0NLBFssedO9skJ8+UK1dCIULDVblmDeijR6VO\nUzRSs55sSopsAXIgNchi4NVqkMIB8r17XrOlfFxcQDWaYc8gA+CLBMgAkJjIY82aXPzwgwqvvqrD\niRMMpk4Vmo3tzz8PTsJ9HgA0778Pxbp1BT+ztWvD3rmzX/PlSpaEefJkp88k6aaHoabVZQ5xccjZ\ntQt8qVIwzZsX9BVB65tv+iwvkgvq3r2QBePBQvYA+ZdffkHVqlVRrVo1rCt0IQTKwxIgk2vXQF2+\nLGkfrkIF8GXLugQy168TrF2rwOuvC5n3pCQeH35owaFD2ahd24HevfXo0UOPNWsUPuUF2Zo1kbtx\nIwDBva5xY4db3UtAqP3mA9RqVSqB6tU5dOpkR3QsETKYIdZALIy9Y0dYJk4UvT0hwPTpZsTG8j6d\nEQU1C+9lFoVrwG3PPedWjzVYiK2/5qpVA1e6NJi//w76nDIyCFJTo9Cnjw1Dh3pfWaIo4P33LZgw\nwYxXX9WJ9h3KzCT4+GMNune34b33tJKSO9evE5dVAfrECTiefLLgZ0G9QvqyvFizEObIEbB16kg+\nvlikBnVcSoqT1FMkw2s0zgFyZqbXpWkuQLtp80cfgZWw6hYMuKQkkNu3XT4vU4bHmjVCTfKiRYaA\nTNfsrVtDM3lywUu0/bnnwPqZQYZa7XdwDUSQ3bQf5SURj9Uq/FcMDM+8Ieu/jM1mw7hx4/DPP/9g\ny5YtGDXKfd2lPxhWrPDuJlYE1cKFBfVUxQnV8uVQ/uc/fu3L63Rga9Ys+HnuXDX69rUhPt75yR4d\nDYwYYcWhQ9no1cuG5ctVqF49BkOHarF5M+O2lO5eBoUNG5X49FM1Jk/W4Omn5S3q9FU7Fqw69JBg\nNMKbEn6nTnb83/8pPHaMA3klLnkqKY727cF7EFmnjx3z7fwokYJmWRFY+/WDwocGthSKnhfXrxN8\n/70KnTpFoX17O8aOda4T1ffoIcjfuaFvXxtq1WIxdaq4J/wnn2jQpYsNs2ebcP06JVqS7/p1gpYt\no9G7t97pFmR55x1YxowBAFy5QuHaNQpPPSU92y4qQGZZ0CdOgC0UkMuNVM12R9Om4MqWlWVsv2uQ\n7XZRUlF8XBzYxx4r+NmTzXTh7QNpUHW0a+cihRZquORkjyUHlSoJ5UqPPx7YKp6jXTtwSUlQLl8e\n0HE80bx5czDbt0M9fbrPbbn4+Ed200GCpKeDT0gISkacOnMGMTVqQN+9OzTvvQfVokVgdu508WmQ\nZSw5D7Z3717UqFEDJUqUQLly5VCuXDmkpaXJcmzu8cclLSlrJk8G8dFUBACK1asLpLICRf3pp6AD\ndDMLpJvZ/vzzwhIKgHv3CFasUGL4cM+NJioV0Lu3DatXG7BvXw7q12cxY4YG1avH4O23NfjhByWG\nD9eiUaNo1KsXg4ULVVCpgM8+M+G110JcD+7BTa84QCwWjyUWAFC5MofYWN6rqyBXrhzMl3w/2JU/\n/wzFmjV+zdMjajXsIgMS28svwzxpkmxD8zxw5gyFr75So127KLRoEY0DB2h88IEZH39sdrn/kqws\nl8adwnz2mQmrVyuxd6/3Uou9e2ls2qTABx+YoVAAn39uwvvva3wuYjgcwJAhOgwdakW5chy6dYtC\nRkbeJAkpuIf98YcCzz5rF9P/64KYAJk6exZccnJQzRKkZpAdzZvDNnBg0OYjBvrMGehTU31ux1Wr\nJix550EyMrzKhgUaIEcCbIMG4KSYN/gDITBPnAjNZ59B9FKORKjLl0VJrgaaQdaMGwcih/dBccDh\nkLSyTWVkBK28gktJQe6GDbAMHy6oaxw7BvWsWcEJxuU82O3bt1GqVCksWLAAq1atQsmSJXEzAIc3\nZvNm/7QoWRYwmUTdvOnTpz3qcyrWrZNUT0lfuQL67FnR27vD13K8WBYsUKFLF7uL9q4nkpJ4vPaa\nFRs35mLz5lyULs3j4EEGDRo4sHixEf/+m4VffzXgvfcsaNPG4deD3Ru+aseKSwaZZGRANWuW02em\nb76BrXdvr/t17mzDn396LrPYeKYSSt5M81mr7AiCYQhbpw4sH3wgbmNaHu3ha9cIpk5Vo3ZtBXr0\niMLt2wQffmjGmTPZmD/fhE6d3DvP8dHRIF6UEhITeXz2mQkjRngutbDbhWakSZNMBUm9Fi0caNSI\nxddfe39JnzFDDaUSGDPGglmzTGje3IHnnovC9evOk127VokuXfzr8BYTIDNHjoB98klQJ09C9d13\nfo3jC1tqKmw9egTl2L7wuwbZYhEyAxIRFSD76zgWIdh69YJdxMtDoLANG8JRv76wyiszu3btEt9Q\nXbs2cjdskDwGuXOnQMtcVUjT/EGGZGQgqn178TvYbE6r2bJCUeDKlRNcRYcNg2nmTBhWrw5KgCxz\nmCPw+uuvAwDWrFkD4mbSw4YNQ/m8equYmBjUqlWrYMks/8bXvHlzqL/7DoeaNcOdBg3cfu/pZ0Vu\nLjro9QBF+dz+rMWCuKNHkR9KF3xfrx50Q4Zg3c8/AxQlanyuXDlc3bUL50qXljTfwj/fvXgRd+Li\nkL+4J3X/Xbt2wWRi8MMPz2DTply/9geAMWPu/5yZCdC0f7+P2J/z8fR9R50OxGAI2vhy/bx/5060\nmDMHeOstSfs/91wrDBmiQ9u2m0GI8/c7d5bGjz/WxUuv2jBxogWTJu3xeLx9LIsme/b4/HtG4s8s\nC8yZcxYbNlTAuTOJ6N3oPLp02Y2OHRPRooXI68dux419+1A5T5LI3fbx8UCtWs9gyhQNOnbc7PL9\nb79VQlJSVaSm2p32//RTE5o00aJKlcPo3buuy/H/+YfBwoUEX3/9N2i6IQCgXbvNyM6ujE6dqmH1\nagNu3dqB9HQ1zp9vi5YtHf79vVgWHZ5+GuB57Mpb/Sq6fauaNcE+9hjS9u/Hk/PnA0OGyP7vxVWr\nJvx8+3bIz5d8pO5//MABVLNaCzJDovd/803Abvf8fYsWMLRoEVHXU7B/1nz8Mba0aQOepiXv3/L9\n96H46y/Z53fs2DFUO3EC5fL8D7xuT9PYlacMJGW82LNn0XTZMhjnz4e6Qwf8r1kzPNWmjej9Nbdu\nodWyZTCsWeP2+q01dy7ipk8HV768rH8f+tAhnN20CTebN5e+f5MmIFlZ2LV9OyDy39tUv37Yzs/8\n/7+S17czePBg+APhefl0Rf755x9Mnz4da9euBQC0adMGs2bNQu1Cndtbt25FPZFF+VEdOsA0aRLY\nxo0lzYO6dAn6bt2QI6LcgfnrL6jnzIHht9+cj3HmDPQvvYScfftEj6v84Qcwx47B9PXXkuZbGF2/\nfrD17w+7CFvjAgwG6F96qeB3mD1bhWPHGCxcKHNJgt0uLKt6yaQo/u//4KhVC7xMtYYF2GyC8HuY\nHBWoc+fAlS4tGIF4IycHsTVrIsuHhXlReB6oVSsGq1bl4okn7tdSLVmixBdfaLBqVS6qVOHQoEE0\nFi82enZe4zjEVKqEnAMHpHndh5HbtwmWLVPhxx+VKFGCxyuvWNGLWoW4Lb/D+MMPko6lfestOOrW\nhe2VV7xul55O0KJFNJYsMaBx4/t/y2vXCFq3jsbGjblutba//VaFv/5SYPVqg9OpeO8eQatW0Zg5\n04h27VxXnZYuVWLaNA1+/tmAPXsYpKXR+PbbEDSdGo2ITUlB1tWrsmX3izPM1q1Qz50Lw6+/hnsq\nxRuWRWxSErLS08N2TwYA5dKl4JOSnBxzNePGgatQAVaJVsZiYbZtg/rrr2H4/XfoU1Nh69MHtl69\nRO+vHT0aXEKCx1U57dixYMuVg1XGHi4AUH33Hahz52D20wAnJiUFOf/7n8f+l0jm0KFDaNu2reT9\nZC2xaNiwIU6cOIG7d+/i6tWruHbtmlNwLBWx5gyB7FfUIS4f6soVcOXKSRpXDrtprnJlSc2IAACN\nRvA4Z1mYzcC8eWqMGiX/cp9iyxbofNx01F9+CerGDdnHhlIZ1huxbvBg0OfP+95QqxXUNiS+dxIi\nmIYULrOYPVuFWbPUWLs2F9Wrc1AqheZKr8v8FAW2Tp2Aa+FDxe7dDBo3jsblyxR+/NGILVty0b+/\nDVGmu16bojzBx8R4LbHIx1OpxfjxWgwZYvVoRDNkiBU3b1JYt+5+wx7PAyNGaJGaanMbHAPAgPZX\n8Nl0I3r21GPhQqH8KSTodIK+rURlnAcVYrWCD5E8olioixehkaCQExGYTMK9LswWkNSVKy5ShmJL\nLPylcJ+Q9bXXJJWKkGvXoPj9d6/Bu61nz6CYhkh20SsCn5goqsH1QULWAFmpVGL69Olo1qwZ2rZt\ni5kB2AoCzt3zyp9+gmrBAlH78XFxsPrIIOXDlS0rBHRFOiDpy5dFu8E5HStABQHzpElg69aVthNN\ng9frwWzdiuU/UqhTx4EaNaSZD4iBrVDB7ctEATk5oM6fB1epkuRjF106jTRE33QZRsh0+1GP2KmT\nHevXK8DzwKefqrF8uQrr1+eiUqX752b//lYcOMDg5EnPl66tb19Z6tgDgmWh/uwznzX8v/6qKKjX\nrVPn/jlLMjLAx8VJPi8sb70l+trv0sWOWrVYTJkiqFr83/8pcOYMjbfe8vxvp1AAX3whNOzl94x+\n950Kd+5Q+OADz01H0e3aoWvt81i40IioKB6tWoXO2o+rVg30mTMhG88b1MWLUPhR91kUv+8XFAU+\nKUnUpvShQ7JpenuDunUL9IEDQR9HTojJFLCLnhwUddPbtWsXLKNHwy6lXlYihfuE7B06gOTkQGyz\nnnrOHNj69xcUHjzgaNwYVHY2qJMnZZlvPmL17D3BJSaCigRZvBAiuwBfr169cPbsWZw9exadOnXy\n/0A8L/yD5mWCidEoumGPK19efLe0RgPjN9+42OhSV65I1qXkKlWCcc4cSfvIBR8bC3Wf/pjzrRaj\nRwenWaTArMJDdlT9zTewP/tssVnal4KUVQlep3NW3BBpt/nUUw5cvkzhtdd02L5dgfXrc12aLDUa\nYOhQC2bN8pwFs/XuDbZJE1FjioHetw9EqhwSTUOxebNXTWSeBzZvVqB9e9dg0VdTlMdjJiRIksv6\n7DMTfv1Vib//ZjBunAZffGHy2cPVrJkDTZo48NVXaqSl0ZgxQ43vvzd61AUnd+8CRiO4ChXQqpUD\nf/2VGyqPFwAAW7UqqEgJkG/cgDrAxEkg2Dt2FF0Cp+/ZU9RqRMDk5nqVgQwlzKZNgAi1IGI2gw+R\n4YQ33NlNcykpol+ChINIXO0rLG9I08j55x9RJYXk1i0oV62CZfhw7xtSFGypqVDKrEZEsrOl20wX\ngq1ePSA79eJI5CpUc5yQCcp7S5XLKITnhU7zwoII9h49hNRQIdgqVcA2aiTt4Go12IYNA56jP/Ax\nMfgZfVC+Ai/ZulY0UVGCw5SbYIncugXVokWwTJjg16Hzi+wjEp4XbooiAy/L+PHgC0VZsRUqiJI0\nYhghi3z7NsFvv+UiIcH9jfvVV63YulXhl2W4P2g++QT06dOS97P26wfVihUevz99mgLPw622KsnM\nBB8fH/TzIr/UondvPZo0cbi3Mud5KH/6ycnq/pNPzPjxRxVeflmH6dNNqFjRswYnnZYm6BGHaTna\n+uKLsHfoIPtxtcOHS35xYlNSQJ09G7ClbkjuFxrN/etWjMaq0ehXABEJLnr5aD/6SFw5Tn6JRZjh\n4uOdsppSzwvtyJFQerlHucNRuzbsHTve/0CkpBN15QqsI0aIMtGy9ewpy0pLYQItsTB/9hkcec3P\nvqDOnQuajF8oidwAmaZhLiT2zev1sgTIt28TTJ2qwbRp3peHbAMGwPHUUwGPFyo4WoFpGI/RY4Or\nT8yVL+/2BqqeORO2F1+UXLctiSD71HvEYBAeliJvhNZBg+47CNntwjKtyJThjBkm/P67wWsSNDoa\nGDjQitmzQ2Q1LcEopDD21FQotm4Fycpy+/3mzQp06OBers3Rpg0ctWpJHtMfunSxY+pUMyZP9nBD\nJwSKTZsErc08SpXiMXGiGZ0729Gjh/egiDl61MliWg7IzZtQrF/v9jvt6NFO1yj3+OPgqleXdXxA\naMiV6gLGlyghvHAGaalW+8YbXnWwpVDgpsfziC1TxmfwG9WzJ+iDByWPI9VwJZh4MwspDJ+YCMvI\nkSGYkY95JCQEpD/NR0dLPhfZxo0FYxeJsI0awTJ6tLhta9ZE7qZNksfwhq137+BJrxVBP2AAqIsX\nQzJWMIncALkIcmWQjx+nUbu2A7/+qsShQw9OV/cPTedCR1nQunVwa+bY2rXdLjtaxo2D+e23/T6u\nr5pC5ZIl0AZw/EAgViscUlcT8vc1GgWTEJHZQ6VSXMwxdKgV//2vAjduBD8rSRUqdZICHxsLe9u2\nHo1L8gNkd9j69AFXvXrIatMHD7aiRAnPL2Cm6dOFLvBCjZoDBtg8B9WFoI8ccbKYlgPqzh2hxrso\ndjuUq1YFTaS/gPxVFamBHSHgUlJAB2g57em8oE+ckM1JMj9AJjk5woWp8O6k6K/ddCDmUHLDlygh\nLkBOSoKtT58QzMg7bJUqMH/0UcHPUu8XEVtXS4jsGXp7t27gQmRnTjIyvNZZFxceygC5WTMHPv3U\njFGjtJFVUmOzeTQt8caWLQw+XF4H8x+bEvRVXNPMmW6XWfjY2OBapWo0YbMO5xMTBSFyfzAYfEvD\n+UFCAo8+fWyYOzf4WWSSkwPOT0c2a9++ULmxlc3OJkhLY9C8efCboAJBNWsWlMuWgS9bFpYxY4SX\nNKkrGTQNtk4dWeflySyEPn1asHMOdkbSbBYCRk+F114oKLMIAqJsuMWSV2JBfNhM58PHxvqVzbR3\n7Ahrv37+zFB2uISEoGX3g0J0NBwtW/q9Ox8fL72/4hHe4biCErniTrEJkNmaNWEUqWKh+P13UB5q\nJo8fZ1CrFosXXrAhKYnH3LniXJXWrVNgyhQ1fvpJie3bGVy8SMkeXJP0dOhee03SPnv20HjjDR2W\nTTmFGu2Knz5hPr5qx1wa34oJxGgM2vLp8OEWLF+uvG9lXAjq6lWo5s8PfBC7XQiG/MxwOdq0gfH7\n710+//tvBk2aOHwmSSTXmvI8ohs1AmRqrirsjGkdMgQkKwvKVaskHcO4eDG4ypVlmU8+fEKCsPxf\n5JqgDx+GQ6oKjh8E4vhp69EDXNWqAY3v6bzwFSCTrCzRL9qO2rUBpRLk3j1RD3t/A2SuSpWglMD4\ng7umt+JE87p1oe/WTfT2fGysbI2Y5Pp1qKdMEf4/PR2KP/+U5bjFDZKdLaya+lhxKQ4UmwAZWq1o\n+TDlihWgPTQaHDtGo2ZNFoQAX35pwpw5alzcnwmtF1HuxYuVGDdOC4oC9u5lMGOGGl276lG2bCxq\n1YpB9+56XLki/CmZXbugef996b8fpD90jh2jMWCAHvPnG9Gwb3mYp03za9ziQHGxmi4KMZuDpslZ\npgyPLl3sWLDA9SWPp2mov/oq8LptqxW27t39bzBjGHB5rlaF8aReETCEgNdqA17Cz4e6fRtcfkc8\nw8D09ddC7W24IcRtMMikpcmerXY7fACNZY6nn4ajaVP5JsPzBec57yNAVk+fDtXSpaIOa54xA2yd\nOqKzYXxcnMd6++KCo25d2V/mQgnJynJ6qfWFXCvTgPDSqvrpJzDbtyOqUyfQaWmyHDdisNtBnTrl\nczOSnv7AKFlFbIBMp6X5VW4ACDWT7paETSbg6lUKVasKKg8VKnAYNcqCMZNKQ7Hyl4KbLL1/f0Gz\nxdy5980axo+34NtvTVi71oCjR3Nw7VoW1q7NRePGDgwcqIPVCvBKJZi9e/2at5SavvPnKfTurccX\nX5jQtm1kL1OLwVftGJ9nNV0cUKxbBzrP7pmtUwe5mzcHbayRIy344QcVit7j+VKlAJoGCXS5Wa+H\n6bvvAjtGETgO2LLFc/1xYfypQeaqVBFn6iICcveuk2QUW7cujIsXy3LsQHEXIHuqd2a2bXNfs+zv\n2ElJMM2eLdvxpFL4vKD37oXupZcAiMgg+2EUQrKzRZVYcCVKgIiUdIxUHO3bR0Rtsb8c3r5dUkLC\n0aoVDBLl1JSLF4PcvOn6hVoNa//+0PfoAWv//rCMHy/puG4xGsEE8fkhBZKbiygx0r12OxwNGgR/\nQiEgYgNkxdatYLZu9WtfT5q1p07RqFKFdSqbGzrUiqxcBkuYQQUuMcpffwWzZw++/FKNxYtVWLcu\nF4895irzo1AAFStyeO89C8qW5TBhglYwC/EzKBGbQb52jSA1VY8JE8zo2jVMRdR2O3SvvAKSnR2S\n4Xi9PvQlFg6HX0v1zJ49YEIk/F+pEofWrR1YvLhIFpkQOOrUAXPoUEjmIYUjR2jExfGoUMG9dBa5\ncwfKJUv8Pj5bpYpTM10gUHfugItQa1Vbr14umRrj/PnujYZUKij++ku+waOi4GjWTL7jBYBq6VI4\nGjcGANhbt4blrbc8b2y1ilaUycfesydM8+b53M72yiswf/KJpGMXV5i//46YwK0wCqNR2oodRUle\nHVMvWOCxlMb65psw/PwzrCNGSDqmJ4jBAJ0MxyLXrkEV4AstHxsrJKl8vARy1auLul6KAxEbIBM/\nO+eBPNczN/seP06jVi1njWCGAWbONGG89RPcSxPeCsnlK/hoX1esXq3E2rW5KFvW+zI1IcCcOUbs\n2MFg5Y7ywsXjh5OamAD57l2C1NQoDB1qRf/+4clWUOfOQbVggd9W4O7wVWvKVauGnH/+kWUsUbAs\ntMOGQVNIalAsvFYb0mB+5EgLFi5Uu1RTsHXrRqTl9KZN3ssrqH//LWjs80fvlpVBJUE4ECvUn0Zq\ngNyvH9giUnhcSgrcOZ2w1aoJZiHhkkqUmfzzgmRnQ/Hnn7D17QtAUFfwJmVFLBYnjXLRSJSze9Bh\ndu+OmJdv1ezZYHbsAAA8WbFiUG2mgbzntIcx+Lg4vyTgPMHHxQnxRIDXLX3lCpSBloZRlND7UJya\nOAMkYq/6QIIvT8H18eO0WwvmJ59k8WKF7Rj/ZTnwPPDuvr7YeOoxrF2bi5IlxZ2Y0dHAjz8a8P6H\nOhxNaCXYV0uEj472ajNtMgEvvKBHt242DBsWXL1jb+jeeAOaSZNg/vjj0A1KUaF7SLEstG++Ceru\nXZg//FDy7qHOdtesyUKh4HHypLNsoaNuXTCHD4dsHl4xmwteGn2VV1CZmaKWtD3BpaTIk0EmBDl7\n9vjfbGIwREyWjY+PFxrObt0K91RkRblqFRxt2oivefQjgxxsNO+8I9qqOFIgJlNEOOkBAH3pUsH1\n7ik5JisGQ+icD5VK4YU3wPJCkpUFLgCTkHy4xERQD5HqR+QGyG6CXF2fPr7Fp3leEDB3c/HmK1i4\n44O2O7H/bDxSU/XYm/0E/lidgcREaW9t1atzmDTJjBcyv4fhrPQHkaNFC1i8aP1+/bUaFStyGD8+\nOFbSYuEqVoStWzfBHUwmQqV36xOOg3bkSFA3bsCwbFmBk6MkQqy4QQjQoYMdGzcWcYNs1AiWYcNC\nNg9v6EaMgGLdOty5Q3D+PIXGjT3XzRduivLnvGBr1JCn7puifDYGk1u3wHhY2WCOHIHmyy8Dn4dM\nsNWqgY4Qy2lm2zaPRidi2LVrV4HDoXXAANH78VFRopsLyfXrsmkqe0OxaRMIGyT30yBBTCZBqSAC\n4BISCrSMd2k0MPvZJC8Kng9IwcUfuNhYv/S1C0MyMwOymc6HT0x8qGTxIjdAzslxce+i7t71LaND\nCCzvvedSV8RxwIkTgoKFO+jXXsTs6XcRo7Zio747Ysr716Hdp48NzTrpMGxZG1lXM8+do7B4sQrT\nppnC5VhbgOnTT2GaMSO8kwgGHAftqFGgLl+GYflyv4XaeZ3uvvyW1QqE4OHXoYMdmzY5B8h8TAwc\n7dsHdFzq1ClhaT5AuKQkULduYcsWBVq1cniVzyUZGYHdzGnavxcbP6CuXoVu4EC3ur50WprsBiGB\nEEkBMnXjBhRr1wZ0DJKZCb5UKUk6uKb58+Fo0ULUtqqVKwOqhRdLJFlNA4Di1199lwgQwR0XAAAg\nAElEQVSazRFhNQ3kSdPlBcj26GjRalcFcJz4EgaTScjoinRVlYOCMosACKRktTByJsWKAxEbINs7\ndgT32GNOnwViN335MoWYGB5xce4vBK5yZTTvVQI/zrkJxdghfo2Rz9Q5FC5fU2LePD9q3dzA88C7\n72oxdqwFpUqFv4aQL13ab11cT/hTayo7PA+2ShUYfv45IHMPR716sHfvDgDQTJ0K1bffyjVDjzRr\n5sCpUzTu3ZP37Um1cqUssmb5Frbe3PPyKZztiIjzwgtsw4Ywf/gh9P37uzSs0mlpsltMe6SQ1Jkn\nLGPGwNarlyzDKZcuheK33/zeP9A68ebNm4OPj4dh5cqglV7xajWIyeSzKakw5O5dIeASPUjoM5K+\n0HzyCai8hnVPEKMxYkosCttN+3O/iG7YULwtMiEwjxsneYxAsHfs6F/dfCFIVpZLwtEfzB9/DEeb\nNl63oU6ehIusUjElYgNk6+uvg6tQwemzQDQLBf1j33JofGJiwB2oajWwZIkRs2apsWdP4HbWv/2m\nQHo6wWuvha/uOCIQEQQEBE3DOnJkwPVlXNWqsD/zDAChoSMYTnpFUamAli3t2LJFXnF2uW6sfHIy\nHLfuYds2Bu3aeQ+QHU2bwi4yyxcJ2F56CfbWraEbMsRptSAUmsSquXOBnBzQhw9D37mz12350qVl\nWWYFAPr4cZ9BlDcK7KaDcD2rFi2CcsWKgI/Da7UgFgti6tYVXSMc3aSJtGyfxSKsePjhSBgsCmdk\nPWHr29elQTRccHFxAdlFS0q8abWyKVSIxTJ+PLjHHw/oGPa2bQueScFGN2KEJC3qSCZiA2R38FFR\nfmvhHj/uubwiGFSowGHOHCMGDdLjxg3/s3o5OcCHH2rxxRemUK7qhBwxtaZRLVqIEiqPKIzGkNXq\ntW/vWmYRKCQrS5aucC4pCXvPlcBjj3FITvYeFDnatQObJ9sVMbXpPjBPmQKYTFDnm/UYDKCuXQMb\noGOcL1T/+Q/oK1dAp6VJX1oOgECznnxsLHiNxr2erAi8nhdmM+ijR/2cWSHUasBkEkp+RDaNSl0O\nj7TsMSAuQLY/+6zLCm+4YBs0KKg79ud+wUdHy+amF6mwTZqExEAIeGQUEjYCySCHOkAGgA4dHBg8\n2Ir+/fUwmXxvT6eluRTAT5+uwdNP29GkSfFq4ggKWq1srkehgoQ4QP7rL0ZWC3SSnS1LBpkrWRJ/\npjf2mT2WFTEXnRc077wj3i5WoYBx8eKCDC0xmWAZNSrodqtcmTKgrl0DEyKL6XzkqJtlU1JkM3Qp\njC+zELHwGo2QmaQo0fW2fGysJDc9Xq+HUWYjnkDh4+MDrnkNJXxcnFf1J5/7R0U98AFyKKHu3QtI\nhSiSKFYBsmXsWNheeMHrNvTevWA2bXL53J0GcigYNcqCqlVZvPmmzudqoubTT510a48fp7F6tRIf\nfWQO8izDj5jasbCYhQQIMRhCFiCXKsWjYkUO+/Y5LzWop0zxu15ULq1rrnp1rNf3FuWeVxh/a5DJ\n9euICdDNiT5/XpLrGp+YCOvw4cL/JyXB8s47AY0vhnxjIvrIkZA20MgRIFveew+sn1lvb+cFV6aM\nR5lNcv266BphLjlZUL2QUJYiuaFKo/FZ0xlqCqtCFDc6rFgB+sQJSfvw0dHFLvESsZhMQplZhK2K\n+EuxCpD55GSf2Sxm924oilhUZ2YSZGVRqFjR+41RPW2a3+59RYlq0wbkzh0QIhiRXLtG4fPPvT9s\nC1tNcxzw9ttaTJhgliw396DC6/WiSmzIjRug5DCKkAOOC+kSqju5Nz45GQo/z2tHkybgSpYMeF5X\nrlC4d4+gXr3QvKTypUoJWaEAMkPUnTtONtORCFemDKgLF0BfuAC2Ro2QjVv4XuUvjhYtwJctK3k/\n9YwZYHbu9Pi9twxyTNOmojVl2SZNYBk1SlI2jIuLAyUhgxyJOJo1Axsh5RNSYfwwRuKjo4td4iVs\n2GygvRjEFJQjhVtqSyYiMkAmt25B+fPPfu1LuRHEPnGCRvXqrM9mZ5KdDf1LL8nWOELlNXao1cDS\npQYsW6bEf//recmVGAwF6hDLlyvhcAADBoTHLS/UiKkdE5tBjurZEzF5NaxiUf70EzTvvitpH4/Y\n7dBMnAgAMPz+O9hGjeQ5rgjcyb3ZW7aEYvt2v85r89Sp4MuUCXhemzcr0LatXbLggN81yBQFtnJl\n0Bcu+Lc/BMtrrhgEyMyuXUJwLCLbrVy+HBo/zG+KYpo6Nej11Z5QrF+PI17k6viSJUEyMtyrT1it\nbp0GPUFyc8EnJ4venitbFrLWOIUBe5cucHToEO5p+IXt7l1wEle8zJ99BuugQaK2pfftg2LDBn+m\n5jfk9m0w27aFdEyPWCyI6tbN49fEboddguxipBORATJ94QKUS5f6ta+7JWGxChZQqUAsFlnefrhy\n5ZxE5pOTeSxbZsS772px5IgHZYu8ho2MDIJJkzSYMcP0yOG0ELxeL8gu+YBkZEg+NsnKks9hi6YF\ndQEpck8yUbcui8xMgkuX7p84XEoKwHGg/v035PPJZ/Nmxqu9dAEWC9RffCHLmFyVKv5Lidntwr0k\nIUGWuQQLR8OGsIwZg9yNG0VtzyUngz5+POBx2UaNBPvQUMNxoM+dg6F8ec/b0DRy//pLUIcoDMsC\nDockxQhH8+YwrFolenvLxImw9esnevviiub994W/ZYTBGI3Sm4olPO+ZPXs8GgMFC/rff6GZPt3/\nA/A8NO+8I0/iLypKeAH08BzmHnsMpnnzAh8nQojI8CuQxiCSne1ygYht0JOjGSmf/OaZwtSqxeLL\nL0146SU9bt1yvShzcilsPpSEYcO06NbNhjp1Hp7GPDG1pmLf9NknnoB5wgRJ48slZwZAaOrRaAJu\nEvN36HbtimSRCYG9dWswO3aEfD4sCyxapMKePQyeftr3A5Wkp0NVyJwhEB1ktkoVv0ttSHq6sFRY\nNMiKMLgqVWDv1k30Qz6SzEL8gbp6FXxsLJr4yHCyNWq4/tvl20w/IMu/YcPhgGrBgoi6NjQTJ4Le\nvx+M1RrU+tdwqI5wgRqF5OZCtXKlPOc9IeCLcY26VCIzQC7k+sJxwNq14jvB3QXXYgNky7BhyN6z\nR9pkPVA0g5zP88/b8corgrLFxYsU1qxR4L33NGjVKgrlDKcxa1Eiatdm8f77D35jnmREXuC8Wg1H\n06aSDu2uNCcQeK02bHVtzzzjWofsaNkSzP79ko7DsoLBztatDBYsUOHddzXo3l2PAQN02L6d8ZmQ\n2L+fRrt2UVizRoE//8xFLJXts8OfyswEJ5NWL/v44y7mHWLhk5OR46XOtbjClykDYjBIUlqIJKgz\nZ8D6qQlLrNaADRfkRvHbb1AuWxbuaUjDZBJUPSLoRYO6ckVoztPpgmYcA4TH9TBQJz25n21ciRKC\nIc5DQGQGyIWywKdPU3j5ZT1OnqRAnToFnY/lK1uvXmCrVbv/sw04f16oQfaJSgVOprq6/O5yd4wZ\nY0G1aiw6dIjCb78pUa4chy+/NOHCdQv+WGfEhAmWsKxehhM59W6NK1bA0ayZpH3ksuLMh9fpwhYg\nt25tx/79jFMvki01FaZvvhG1/9WrFNq0iUK5crHo3DkK33yjxvnzFCpV4jB8uAVPP23H+PFaNG8e\njR9/VLokytPTCUaM0OLll/UYNsyKdesMqF6dg3rOHKh8SFoV1ZwN5Lywd+8O8+ef+7czRYEvUcLv\nsSMWQsBWrSqLfbgcKBcvhuL330VvT58+DbZaNf/OC7sdXMWK4rdnWdB790ofRwL0qVMuK42RDjGZ\nIsZFLx8+IQHEYsH2yZODOk44Msh8XJzwQutniYSsq6PI+1s/JBnkiLSeKFxHvH8/A5rmsWKFClMG\nMD4dWmy9ezv9fO4cjbJluZDbxts7dID96afdfkcI8O23JvB8RL2EP9TIpfebD6/TCdJBRmNInPQK\nEx0N1K/vwPbtCnTqlFf3K1KPl2WBoUO1ePZZO9YvPIvoWxfgcFPm8PLLNmzfzuC771SYMkWD/v2t\nGDjQhk2bFPjsMzVeeMGGPXuynV70+KQkn4FZYZvpRwQHtmpVQfVCYiNrMCBmM+j//Q/2rl1FbW/r\n00eogRRrDVwIPilJqE0Wi8OBqC5dkHX7tuSxxEJyc8GVKxe04/sFx0H500+wvfKK26+J2Qxeownt\nnHzAxceD5OQgt2ZN6TvzvJBJE7G6EBZjF6VSKA3KzfWr7p9kZcl6T3U0bBh0ffdIISIzyI4GDeDI\ns5rdv5/B4MFWrF6thF0j3UkvHAYhAIQT2seF9Cg4vk8gtaZyYPjlFzhat5bteJZRowCOk6ymIRfu\n1CzEMHu2GjQNjB1rQczpg1DNn+92O0KA1q0dWL7ciA0bcmE2EzRrFo3fflPgv//NxZQpZpd7OZec\nDOrOHa/jFw2Qw31ePIiYvvoKtr59/d6funwZ2pEjZZkL+8QToE+eFL09n5QEvkyZ0JwXSiWI3e5e\nDcMTLAviQYPZHXLI5ckOIdCOH++xh4Lkl1hEEHx8PEhGhl/nBXXqFKJFalHbunUDW7u25DECxdqv\nHwjrXxxDMjNlXR21vPeex2clnZZWrExmfBGZAXK7dgVZqwMHGPTrZ0PZshy2HiohWdBbULB4eJrd\nHmh4Pnid0zQta9OJvUcP8FptyExCitKhgx2bNyskrcodOUJj3jwV5s41gqbFl51UqsRh2jQz/v03\nC2vXCuUU7uCSkkDduuX1WOyTT8LmRUboETIQYKMauXNHUlDrDbZ6ddCnTskmrZkPde4c9EVWEyWT\n9zdiJPSlkIwMRLdqJX57gyHkNa0+IaQg4HQHl5QE85gxIZ6UdwJpHJNiNW3v2hVclSp+jRMI5unT\n/c4CszVripaxCxTNhAmy3RsigYgMkPPJyiK4cYPCE0+w6NfPihW/RQmdyBKCpBMnREq8PSKsiKkp\npPfuRdTzz4s6nm7AAFCXLgU4q8AgRmPYskOVK3PQ63kcPSou6DeZgNdf12H6dBPKlhWCFakuegzj\nPe7ik5NBfGSQ2Xr1nLITctamP0Ie5GxU4pOSAEJAJJYx+Dov+NhY0AcPBjK1+8eSsKxdYDUtUuIx\nIjPIEEoWKA8BMl+iBOw9eoR4Rt6xP/00zG+/7df94kF30uMqV4ZDwktbIFDp6eAiXBpTChEdIB88\nSKNOHQcYBuje3Y6//1YgQ1dWdJkFzxefDDK5fdvJZvoRbtDpfLtgGQxAbi6oGzfC3mlLjMawZZAB\noH17VzUL6upVwW63CB9+qEXdug6kpt7XKpa7uYNLTg55PTYMBlCXL0veTd+7N5jdu4MwoeKPrFlP\nQiSXWYiBT0wUmmQDlFrM+ftvaRbeCoUg8SjyGWV+/32w9er5ObvgwSck+KUnHy74xERwhZrzJaHX\nC70iYdCtf9AgGRkRrx0vhbAEyGKNhvbvZ9CggZD9jY3l0aaNAz+N2Onx5kxu3HCqmbx5k4CigJIl\nw2jVLHLpkPnnH6hnzQryZCIXMbVjYpQhlL/8Au3Eifc7f8NIODPIgCD3VrQOWfnTT1AtXuz02YYN\nCmzdyuDzz52DCZKTI2uADK0WORJF9gOtNWX27YP2rbck70ddvizZkethQW6pK9PXXwuNPxLweV4Q\nAq50aVCF64GNRpD0dEnjsE8+KbkchYuLAyWyDpOtVy8iAwo+Lq7YKRUof/gBbU+flr4jRQk11RL7\nmx5RBJaVvSEw3IQlQD54UNyy74EDDBo2vJ/97dvXimUbS3usFaWuXIGykGTQ8eM0atRgw9YMp5o9\nG+qpU0VtG5bu2GIGr9f7XD2gbt8Gl5QEPjYWlNgAmedlr4EEANhsYb1ZNGniwPnzFO7cuX8BOFq1\ngqKQbemdOwSjR2sxf77RpamOrV5dMFwoxnApKX656ZG7dyVZDBc77HahK94P5A6QucqVBYcuH2je\neQeKtWvFH7eIWZNiyxZoQ1A7G6hubSRgf/bZyFPX8AF96ZLfKwZcCen9TQ8tNhsYN6UsJCtLKEdi\nIlIczS/CEiBv2+a9u141cyY4qx0HD9IFGWQAePppB65do3DunPtpU9nZTlmf48cZ1KoVvvIKPjFR\ntMZlRDZrhBAxtWO8Tuc7QL5zB1xysiT3Ifr4cUSJ7GIWC/P334BCAdO338p6XCkolYLSxDffqHHs\nGA2zWZDooc+eFeqLeWDECB3697eiSRPX68T28suS9aTlJtAaZK5MGcEsRMrDz2YTgsAHKBNSFPX0\n6VD70KT2hK1zZ1hfe03mGfmGOXwYXFISAHHnBVemjJMWPbFaQyJPxlWpIvTKFGNsvXoJduLFCJKd\njfM+ehw8kXPwIPgyZbxvZLNBHWSdZU9QZ8+ClsnELGDsduh79XJNKtlssHfsGJ45BYmwBMg7dnh5\nw3A4oJk8GecuKhEXx6NEifv/CAwD9Oxpw88/K93uWrTrPtz1x1zZstIC5EcZZO9otUKdmJcmTXLn\njiAFld8sIwKSlSX7354+edLtW3aoGTXKgqtXKQwdqkPlyrGo17QEOqs24ZM3jRg/XoP0dIJ337WE\ne5oFqKdMAcwyukhSFNhKlUCfPy96F3L3rmASEkRHrnDDx8b6neXky5YVsr6hhOdBnz0rqc7UPHky\nbKmp9z+wWERp3QaK8fvvI0JjOlgwmzdDsXFjuKfhAsnJgT2IPQ4kJ8elPC1UMAcOQPXjj37tq546\n1W3fid/odMIqfpFkFV+qVFgTQsEgLE+A40cpjwkdkpMDPjoa+w8o0LChayDUt68VK1eq4E4SsGjX\nfbgVLLhSpZxr4LzwsAfIompNCUHWzZtel3CoO3fAJSXBOmgQrB6E7l0OK7NJCBBeJ73C1KnDYvFi\nI/75JwdXrmRh5UoDBrS7jLjbZ2E2EyxcaIwczXeOE+rwC01IDr1bLiVFUoBM3bkD7kF00StEcSsD\noK5dA6/XF1ynonoWEhKEhrk8iNUKXq0O2hwfFph9+0AfPRruabig/P13PCHzfbww4VzlDeR6Vf7y\ni6DnLSNcYiIoifX8xZGwBMj1qmRi9273QU5+sHLgAIMGDVyj4OrVOSQmcm6z0IUzyEYjcP06hZSU\n8HWm8klJok8i9rHH/O/CfZjwVVDOMOBLlgSfnCxISIk5pMw20wCACAmQC8MwQEoKh45vVcDbXU9g\n1iwTKlUK7fVBsrJAPKyqkJwcwcJW5ho2x1NPSdqerVMHuX/+KescIo1IaGKVApVnMR0QIcogi4Vk\nZED36qvhnoZkiNEYcVbTAGAZNiyoS/zhTGJJafwsitxqRECeysmjADk4tH7ihsc65PxgZf9+xm0G\nWf3VV+hfeZfbMgt7y5awt28PADh5kkbVqmxYs2N8dLTgwmTxvYRtGzgQ9meeCcGsIhO59G5z/+//\nwJUvL2mfoNxAdLqAJaaCBff447AOHx6WsRV//gmNh8ZVkpEBPj7e6TM5zgvroEGwvfCC+B0IiTin\nMLkJpMQiGKi+/Rbqr7/2+D199qxTgOzXeaHRRNTKAMnMBJ2WFu5pSIaYzWGVr/SEefJk7JCzlKAo\nBoNPd9xg4XcGmWWFFxo/LKq9wZUo8SiDHCxaDK7osQ6ZZGcjW1cKV65QqFHDTR2F1YreZXdi40YF\niprfsE2aFDQW5CtYhBVCkHX1quBc9YiIheTmyp5B5rVaULdvi9c0jDRsNih/+UX2w3JJScLfxQ3u\nAuRHBAcuwv7OXHKy12DROmwYzBMnBjSGdfBgWGWyyJaDiC6rMxqhXLLE/Xcmk1PpygOB3e4zkRVO\nUxd/A2SSnS2UhcjcT+Fo2jQiVxHkJiwBcp06LK5fp3D7tutyOVemDHY3ehO1azvcZn95vR5J7C00\nb+7AH3+4b9bLyiLYsEEZVgWLAh4gyZNgIketqb9Yxo+H5e23ZT0mW60amEOHIrKZRQwkIwOaAAMS\nd/DJyR5d00hmpotyRDjPiwcZ7oknYPCzjET75pug/v1X9vnQp0553qBIVj+izwubTZSLp9xyebLC\ncdB++KHbr4jJFLHBkb/nhXrWLKhnzPC6DVepkui+Frnh4+Jg69pV8n7BWB0FAOvIkS7ufPTBg5Id\nMSOdsATINA00b+7Azp2uwSOXkoL/aZ52W38MAHxUFEhuLvr0sWHFCucA+epVChMmaFCvXjQSEzn0\n7GkLyvwfEUYcDklW46KR+Q2bL1UK9latInIpUgxBqctGXgbZgxQTV7kyrIMGyT7mI+SF2b1bdt1w\nNiUF1NWrosrRpBD17LOgvAXeQYC6fBn6nj19bhfR0p56vcfyQFv//mBr1w7DpIIHHxUFUnRJughc\n5cqwd+4cohkVQaGA2UcA7w4+Ph7mSZOCMCFXNFOngj52LCRjhYqw6Ri1auXA9u3uC4QFgxD3QRAf\nFQViMKBDBzvOnqVx6RKFY8doDBmiRevWUWAYYOfOHHz7rQkJCWF00HuEJMTWFGqHDYPyt998b+hw\nILpZs+AYgIiEGAzFN0AuoggjF3xiotAc5qb0hKtUyaXJRq7adEk8spz1SlAyn0oluIoVQZ89K2pz\nsecFr9WKltqUCy452eNLYGFIbm7Yalp9QohHu2n7M8+Aq1AhDJPyjb/3Cz462meAXBzhY2Nh79Qp\nJGORe/ci0hUyEMIWILdsace2bQqX+IXngQMHnA1CnL7PyyArlUCPHjY8/3wU+vTRo2ZNFocPZ+PT\nT80oU6b4BcbM5s3CG/sjvKPTCRIlbiDp6fc78xkG1OXLHrcNBeG2mvYFnZYGzYQJbr8LhvSdMCgN\nR7NmPg1f5Ia6cAHUyZOito1u2hSUBFm4h41glQawTzwBSmSALJaiZiEhISoKYFmf1sX2Fi1gHj06\nRJOSDhcfD8pNgPwgwkdHP3LSCxDq3j3wiYnhnoashCVApi5cQNXom+A44N9/nadw4QIFvZ5HyZLu\ng1xH8+Yw5olRv/mmBR9/bMLhw9kYOdKK5K8+ln2JLmB4XlTgqx84sNi7LwWC2NoxXq/3eCNTf/ut\nk5C7FLOQoGA0Rm6GCABbuTKUa9b8f3t3Hh9Vfe4P/HPOLMlk38MSQAgXKNdIA1QBI3BFxKpYqdq6\nL4UWFS43tdba/tr7sq1ttfeiWKu+7C22olertuhV0LZARUERRJDiwhI0gEAIEDLZZjLL+f7+mGTI\ncjJbzpxl5vN+vXy1k5zMPMrD5Dvf83yfB7aPP+73PTlJJRYA0PbyyzFPqdOq1tSxfj0ynnoqpmvl\nhoaUe6PXjM8XWvwl4eBx+2OPwX/VVf2/0dbWb1c/1rzouUCWjh/Xp7OMJEUsJeomhgyBMnFi8uNJ\nkCgqUt1BNrNE3y9SdQdZN0JAOnUKCneQBy/zsceQseY1zJ7t79fN4v331fsfh2VlhaZcAaioELjq\nKj+cTgCKgozf/hbmmXoQ4nzxRWRFOzkdDIYW9ha9Ha+nSAM4pK4hId2UwkLIsSyQk9Vpwm43d4lF\nTg68//EfyFRpu6ZUVMCv8fhtIwXHjo1tWIjHA3R2Ju3DgZlIbnfcUwvDdbPR+pEnIjNT9XmzfvhD\nOFetSugpleHDw8Oaspctg2PTpkGFGCtRXj5gtxar8H3jG73eT1OZyM9naVU8fD7Y//73M487OlKy\nPaYhC+RgZSXkujrMmhXo1w95x/Of4dwx8b+xSK2tZ0YgmohSXAz5xInIF7W3hxIrhUfbRhNzTWFO\nzoC35+Xjx3u9ocfUGkcIFFRUJOXOQ8sHH5i+Jqvztttg37ULtu3be309MGMGfNdfb1BUZ2hVg6yM\nGwfb/v1Rr5O7x0wnYwFoMllLl8Kxfn1cPyNyctD2wgtJikidbe/efkOUYs2LXiUWOk7SC0yaZN0W\nj118N94IZcIEo8OIS6LvF8FzzkHb2rURr3E+9xxsH32U0PNrwbZ1q6n6ZufceGP4Q4Xk8/Ue654i\nDFmRKZWVsH32GS64wI/Nm+29xka//0EGzq2I/1CF5HZDSeKYyUSJ0lJIURbIpm73YzIiN3fAXzxS\nYyNEefmZa2MZhtDREfpQla69qjMz4bn7brh+8QujI0Hm8uWQYhzNHi9l+PDQjmmUOkPp+HEoPXIo\nlSU0LMTpRHDq1OQEpEYI2PbuTXiKXqCmBm1d/bwlrxdCp0l6ngcfRGDmTF1eS2+ue+5Br1/aacLx\n6qu6H/js9frr18fdNjRj5UrY3ntP+2CcToisrNB7KkKbUR2PPqr96xjMuB3kAwcwdKhAWZnA7t2h\nXd+2NqDOW4GqyfHv3iSrLdVgxTJxxsgG5GYRa+2Y75Zb4HnwQdXvyY2NvSZldTzwAPwXXhjx+ZLV\nJ9JKfDfcEJq0ZHANnvPppyH1+fCjWb9bWUZw9GjYDhyIfFlTU/rcVrbAuGnp6FEIl6vfAJmY88Lh\nQKgGD6EzHun6QVgrfn/onIdJ73Ymsz+20YNdRGFh3DXh9o0bo9/BTjSe0tKUHzdtzA7yqFGhujCf\nD7Nm+fHWW6E65J077Zhk/xiO0vgXukk7dT9IoqQklESR6psyMuC/6CL9gkpFQkApKel1uEoMGxb1\nkFyy2plZisOB9qefBjQeRzqglhbVjhJyczOUGA/vJcL3zW9GHdzjnzcP7c8+m7QYzMSUC2S/P7wr\nBQC2PXsQ1Og2v+Tx6LaDHAvXj38M24cfGh1GfDye0BS9NChB6svovtWJ/H1VG76kWTwlJSk/blrT\nBbLNZkN1dTWqq6tRW1s78IVOJ3xXXgmppaVXHfL27XZMU96JumDJnTmzX9mCctZZ6Lz99kH/O2jO\n6QwtkiPszimjR8NjglvcRhp0rakkoXXz5rgPacrcQdad/eOPkf297/X+YvdQgj6/gLTsg9y5dCmC\nZ58d/UKT7o5pTSkshJzA+Npkyli5Epn33x9+LDc1IVhd3e+6RPJCKSkx1UFo+7ZtlmvtKbW3m/rg\ncTL7pht9p1cUFcX99zWZd0iV7s2/FKbpHOSsrCzs3Lkzpms7nngCAHD++X4sXgRhGzoAACAASURB\nVJwNrxd4/z0Jt0lbgcybI/6s1NYWStYet9OVESOgjBiRePBJ5I6x/yoZoL095VrTaMGxejUCF16Y\nlDdXpays30hSqakptNORhjtTRhFlZRAmO9QcnDgRjtdeCz/2XXONZs/dtmaNZs+lBaNv2UcjnTgB\nx+uvw3fLLWe+ZuIx04PW2hoqwRlgk8XoPy+loCDuEgu5uTlpZ7MCM2em/OaS4VsleXnAl74UxNat\ndmzf4UD1f5wX9Zdk97AQSh3JrB2LJDB3LtqfecaQ1zYz1333Ja0vaLhHbI8pQeEFch9G5UU68F96\nadzja50vvoiMlSuTFFFoWIjtk0+iTsCMKy+E0L+jRDAYtXxCam0N1f6blNTWhsyHH+79NY8HwuUy\nKKLoBvN+kfu1r8H2z38O+H3vPfcYuiBURo6E/9JL4/qZZO4gd3772whccAEAwLZtGyQDDzAmi6YL\nZK/XiylTpqCmpgab4ug3OXOmH6tWZcDhlFDy/26Jen33uGlKQ0JoPx2Pu5a9SM3NSR0Ugu4+uj3+\nDovSUngGmOpH5iEfOBC1K89giNJSwOmEdOyYZs+Z8eij+ndpEQK5F18cudtDW5upBwkpxcX9Jukp\n5eXwfv/7BkWUXNGm6XUuXAgYWMMuhg6FN57Ji0Kg/ZFHdCkryvzNb2C3Wj19DBJaIK9YsQJVVVW9\n/vnJT36CI0eO4IMPPsCKFStw/fXXozPGyXCzZwfwyisOfOUr6uOl++IOcuqJuXastRUFX/pSTJfK\ne/ci55vfHERU6Snr9tuB9vakHkjpO2lMlJbCf8UV/a5LZk2hqjgHZ6QbPVpSBidODO0iRxBPXojy\ncv3HTdvtoUNVA32YEMLwW/ZR5eaGzgX0qJMWpaXwf+1rBgYV2WDeL1Jump4khSZT6rABJJ86Zfqe\n/4lIqAa5trY24iG8qVOnYtiwYaivr8d4lf6Vd955J0aOHAkAyM/Px4QJk+ByXYqpUwPhBO++VaL2\nuNrrRWHXAjmW683+OO/zz/HlGTOgVFaaIh4jHneLdv07O3fiso6O0E6yJIW/P3PECIi8PGzqGptc\nU1MDuFzw79qFzZs3G/7vZ6XHRbNnY/rOnYAsJ+31Lp41C/D7o16/e/duTV//vb//HWP//GeU/O53\nqt/PHTsW6/7wB0y7+GLd/ntb6XFjXR1O2+0IvXsn5/XGDR2K4V2dLAb7frF582YUNzXhK10LZD3/\neyllZdj1t7+hpbKy//dnzEDbK69gc1ePWrP8+fZ6LEnozMnB+3/9K77S9eHVVPGpPB7M+4XIzUXd\nBx/gcFGRaf59rPL40q4x02aJp/v/Hzp0CACwaNEiJEISIkqxV4xOnz6NzMxMuFwu1NfXo6amBvv3\n74erT73Shg0bMHnyZACA45VX4J83D3C58OMfu3DjjZ2YMCH6uEepqSlUB9XjuTN+9zv4Z8405+Sf\nQCC0MzXAzovrBz+AMmYMOhcv1jkwayoYPhzN+/b1unWUvWgRfJdcAv/VV5+5sKUFBWefjeauvyQU\nO6mpqV/v2ZSgKMgfNw4tb70FMXx47++1taFg3Dg0HznCspsBZN92G3zz58Ovw9Qs+eDBUA/kQfal\nlj//HLnz56P19dehjBwZ/Qc0knP11fAuXozA3Lm6vabW8qZPR9vKlVAmTjQ6lKRz3XsvlFGj0HnH\nHUaHYjn5lZVo2bbNtLvIO3bswJw5c+L+Oc1qkPfs2YPq6mpMmjQJX//617Fy5cp+i+O+XL/+dbhx\n//33e2JaHAOhdifo89zOl182Xcuibo7XX0f2kiUDft/0t9pMRmRnQ+pThyw1NvbqagIg9IHE44l8\nQKejI3KP6jSVkotjAJBlBGpq4Hj77f7fOnEiNCQkjRbH0tGjcR1g03PqZ+bDD8PZo6NFopRhwyAf\nPYrcKEODtKaUl0Pu063FaryLF5v6IKGWRFlZaDOLYuP3w7F6NRAIQGppScmOFpotkKdPn449e/Zg\n165d2LFjB+bNmxf1Z4KVlZDr6sKP7f/4B+wbNyb0+pLbDcWkAx9EaWnEaTZG91c0g763TiMROTn9\nDmnKx4/3n4AmSaFxuhGaq+dedRXsW7fGFSvpJ568iJV/9mzYVRbIUmPjoHcrrSZ3wQLIn38e8/Ud\n99+P4LnnJjGiM2x79gw4YjquvOg6WNX3Q3WyBSdNMnXHh1j4br0VoqLC6DBiNpj3C+9dd6Hz3/9d\n9Xvyp5/C+Yc/JPzcWnG8/jrkKNNAdSNJyL79dqCjA77rrwdM1jJSC4a2eVMqK2H77LPwY8fGjRHb\nrEQiud2m/aSrlJREPPnNBXJ8RHFx6PBID9KJExDl5f2vjTJ9SGpuNu0Hq3SS8cQTsH30kS6vFZg5\nE4633urXSkxubEybMdPdREEBpDjuvCkTJugzeVIIyHv3ajZFz/3ee7r3ye/8zndCh6RSiONvf4Pj\njTeMDkN3tv374XjzTaPDgHP1ath37IjpWscbb8D5pz8lLxi7HSI/H1JnJzoeeSR5r2MgQxfIwcrK\nXp+GBrPINfMWvygri7yDzBKLcJF9LFrXretdE9fZGZrwpPLn3/rKK1DOOmvA5+KoaXNwrFmj+kEm\nnryIlTJ6NITdDnnfvl5fl9raoPStS05xSmEhZLONmwYgNTSEfgH3GB3fU7x5Ifl8phozbVW2bdui\ndhgxUjLeLwDzbGIphYUxf6C17doV192hRIgom39WZ/wOco8Si4QXK34/0NlpqjGiPYm8vNCOZ59d\nz26BadMghgzROarUIbW1ITBrluqIYDFsWMTx08lspE4RdHTA/s474YdyUxMUveqeJQntTz8NZdiw\nXl/2XXcdPA8+qE8MJiHi+IWrJ0ccffRj4vUa2sO2L/u6dchcvtzoMOImdXRYvmwkEVJbm26195HE\n8/dVj99tSkkJ5FOnkvoaRjJ2B3n8ePhnzQo/ltzumP5A7Vu2ILvH+EsIgY6HHjLv4RpJgjJ27IC3\n+j0//zmUUaN0DspcBlM7JoqL0fbii/H/oNcbauSfqqNTTUxyu5G9cOGZx6dPq07SS0YNMgAEq6sH\n7CqTTkR+vikXyEp5ObwD1IMCCeSFLJvqPdZ26BDko0eNDiNuZh81naz3C7Pc5Y1rgex2q76nahoP\nd5CTRxQXw9tjelasO8jCbu/d+N3phO/GG5MRomZa3nmHu8QmE76lbtYPVilMlJZCamoKfUARIrRA\nTtXOGSamjBxpysM1gVmz0LlsmWbPF5w8Ge1JHJEdN5Pcso9Grq+H83//N/xY6ugw7Z3aQVMUSAPs\nhurZvSUSUVQU+wL59Omk7yD758xRPfuTKgxdIPfV+a1vxfQpn5P0Uk+yasciESUlaInxwANprHvS\n2MmToZG7TqfqLXAj8iKddN55Jzq/852YrpVOnkTONdckOaLYWCUv7Fu2hMr/+jDLLftopMZGZPTs\n3uDxmLrEYjB5ITU0IO+CC1S/57vkEgR0bhOoJlBVhcC//VtM18rNzVCSvED23XgjhM1mns4aGjPV\nAtl3440xNZoWubn92nxRGvH5Qv2LydLC46btdrSvWGF0OBSF1NwMuUfXIYoua+lSyF980e/rZjn0\nFY0oLu61Y9l5660ITppkYETJE2nUdHDaNATPOUfniPpTJk6E79prY7rW86Mf6TI4LfP3v4+5s4bV\nmGqBHCvuIKeeeGrHM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lYblulk9DDL1dMCEXMCEXMCEXcFJalk9jRhgAAABuw8NySCt6u2BCLmBCLmBCLuAk1hEG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\nlOux5PNa8sVf90Rfj2/7PNG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- "text": [ - "" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distintly jagged. But, it still mostly tracks the dog. What is happening here?\n", - "\n", - "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n", - "\n", - "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n", - "\n", - "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematicall model this sort of reasoning." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "More examples" - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Extreme Amounts of Noise" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intution tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30000\n", - "movement_error = 2\n", - "pos = (0,500)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " pos = update(pos[0], pos[1], movement, movement_error)\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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kONRo3Dj2cjSSceuthnFEMS9cGNZpxvzhhzDrNfK1Wv2WldMnTlS0yVNry0aV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ho4VqxovhkxQhCkuGyNlcDarVtjnu0UCgpgU2ceCcwgC506NU9uGBzYps+fD+/11ys5zWXh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\nZ+3ffrKpOn/aP/4B9siRl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- "text": [ - "" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_error = 2\n", - "pos = (1000,500)\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(100):\n", - " pos = update(pos[0], pos[1], movement, movement_error)\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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I84JEmBckwrwgEW9bLPTevNnff/+Nxx57DIGBgdDpdPjiiy8QHh6OWbNmoUePHgCA5OTk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- "text": [ - "" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Example: Large Noise and Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What about the worst of both worlds, large noise and a bad initial estimate?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30000\n", - "movement_error = 2\n", - "pos = (1000,500)\n", - "\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " pos = update (pos[0], pos[1], movement, movement_error)\n", - " \n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " \n", - " pos = sense (pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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37gx4+xde0OPzzzWe8RFN9SyraM5lYwoLoZs6lepCCERzvfCJguigxGy9sCsr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\nk6bIlmXmvsKb1G6scakUtGbNbE35yuWXwzDXXy4SAW9CS7hkMid23vB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Be1XC5d4Cd9+N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437q14xyaTYXNrFxZNI7QAbT5hVkTY64N3pNuvESay1UkZeIlN9Ka4PhC4Vm2zFrEDAOxv/6V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\nR2jGDKPZlt+2LT0udk3CIxhkwe/YAWnZMmjZ2RC//x65NupHxZt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Pr7CLUYrm\nERzHxo2zNpX66OV7XWetbl2obdpUSWsfAJK/+x0xPrJlpLVwuEY40UqLFsR6HUDlyy9DZRUY/pcz\nt9yBA1DatUu7KmdcA9scpXTujNh99zmaqf9fRXz4cIirVnk+X6VxwVCnuDNnzEy3JFkDdtosbeMs\na7VqQb76al8Fj5SQZWRRmWEmASVs2QLhwAFLf4ID+jV3VFsz0HX3gtK+vbkepvlZnKY5Enrq+edD\nq1sX8SFDIPz4o/kEq9UtCAj//e+un0krc1xZGZKdOkHu3t2gmWqhEORevTI7sSrg3A2ieR5KixbE\nItTDPEBt3Nhodqk29JvFb4HnjxwhGQ+OAyfLiD7xBJJ+ZaIqljmSF1/smUnLBPGRI6G2aAGtYUOU\n+3SQa8GgK3/R8prata2SUlXMwEaef97dYS4vr8Z2huki+sQTpEkuDZSuXEnslm3gDx06a3SO+O23\nk2DmbJSPqxA4lq1dm5ZknBsMBY0qTuAZlURzcshCZ8t6AHDNCvFHjlRf7cAHbploT0gSUXzxGFNa\nXh60YBCBjz6yfQmf+ThMtQCnEeBqgkAaBd2Qanyl6KvwBVs11P9fU9W7+IgRSOoJAuXyyy2JnISu\nq/y/lcHlDxyAuHp1+rJ0tGrqci1i48f/V8jbAWQD5dnMXgUIGzdC2LzZmHuz77mH2EtDTwiw45bO\n0XY6R/36qHj//eodSDSK4Jtvkn8zKllGr4/fPUw3l/b+JI85WGnfHmq6ikatW0PW75Gkrt3sB2Oz\n5nHfcLEY6cuir2cpharqmQzjDx0iakZ0w8PMW8niYlTOmpXW+VQH524QrZctNZ73lFJTGzcmmdaa\nQDoBhZ690wIBkonVHQG94NeoxiI4YwZCzE6rYtGitIO7tMBxSPrtyAKBzMuTVd3NZthhXBMcR09k\n4LyntmvnKoGYNWGCfzagOggESINgDUvCASSz4sW7tUNp0wYV77xT5e+Su3dH8oorAACBefMg2rXD\n04HtOqUaF+EJE8C5UL2i48Y5NuWhV19F4IMPMj+mNJCKk+8Knw2O0rUrok8/7b4RrQIi//iHq0oL\nf/iwq0SlHWrbtij7+mvX55KXX47KV1/1fK/mQRlJB2qLFhZer1qnDpI9etT4fJF9660WiTtjE/a/\naftdlbL7fwv32QNuLp4sMh0Xeb17I+fee0mwHI9bJSklCcKuXea8rGei48OGEYv1GkSAqf6CTaik\nc13pumRPHHis3ckrr0TippvSPrbY8OEoX7DA4iTrBaNi73WNZNlCE0t2747/2969R0lRX3kA/1Z1\ndfe8Z3gMMMMMsoDADgoKyAkoGgEDRqKym/WBgs+EVVEnuskhx7DxGXGzKjlu2GUj8SxqFjFLdMFj\nNoLGYHRGcQyoARQQBoQZGObR8+pn/faP6urp6anurqquV3ffzz/JtN1Vv2Fud//qV/d3b+C73x1U\n3lNJZOZMIBAY2CsSf/Hv9VpykejYd5Y4bpyUB+v1SpvulBi5yUO+alNojQ0ACIUgNDQAPI/QsmVS\n6kGac4eWLFFuHpKIseSrORYI/v3fI6RxU5LW1s8xRpXpUaHv5z9HaO7cpP89MmMGul97LaNzMEFA\nX1zrYkOFw9IqggmxwfX1KZbB45ubUZr4oVhYiNCSJfpPFrdyw4YPR1CpXXkawRUr0Psf/6HtRUrx\nGb09aBWxthbdb7yh6TXB66+PVTNRpNDiWNi9G3zC5l9V5HJzCfoefxz+++5L/3qeR9GPfgSPvFoW\nr6RkyOZj7uzZgXHqTOcApD0SsSohJm72c7///uD3n5xPatFn2BAazyvW1CB83nn2tSm3SpK233qJ\nldHehG43+OPHwfn9sRXdWApg9O4ti1aWiMyYAZbkrrn+gQzEdXjOnIHFtYS7MCkl/ruIIkIKFxXi\n2LEQp05VPbTInDkIX365ugW/NKkfXDAo7TGLP/7550Osrk55F5K53dLFTVypXmHfPtW/gxEcO4mG\nyyXVsq2sRE/81Vg8hSYguvE8wtOnJw0irrcXfEfHQNBmcityyME5qbC4TfVHI7NmaU6lcO/cCeHj\nj7WfTOMkWs5lq6ishEvj+VhRUerNRoIg3frPhIlf4OLYsfA/8IApK9H969ahLyGvFgC4kycN22cg\nCy1cCHHUKABSXnnKDalJhC++eFB96bQ5jsk2CStc/AWvvFIqlWcGjkM4xYWckv7HH08dl6HQkC8j\nz7Zt+m5nR2vxJ2I1NWDRv1laGjaLCg0NKHziCekcZWVDqv7owYqKYpsNDakTPeQEcSu/Bk/WdNGS\nYz95MgK33qp5U3bWSWzck0BrXIRnz5b+jyiC6+qC0NQU26jGqqoGFxUQhIFJt9Hi/tb+++9HZMoU\n6Qf5sy1NFaa+p54aspfH89prUuO4BKElSxC4887MxpuEnM6RdEIcDA5ZMQ/cey/Cl1wyULJOASev\nqkfv0ARuuin5JkSTZPXlqVIzBd3STYbic8sYg/CnPxk6gfe8+Sb6jx2DKL9JLFY6fz56fvtb1Zsg\ndFdF0bkSzUUimmtkRubMQZ+OCZsmJk6i2ahRCK5cKU1mentTd9Q0SMkdd8T+tvyRIyhaswY9GaY6\nDKohrKeKhB5J4kwcOVKapMY/NmmS6lxAR1Ca+Orco8CGDYOY6aRQy10plwueN99E+LnnwEaPHqhX\nrIHn5ZchVlYiLHeoKyxEIL7kmIEYz0v9COQHXC70xVVIsJzWdA4AwdtvRzDhNZ5XXwVCIQSXLzdy\ndPZJcjGoV+9//if6urpQeuWVA/ul4i9E4i7S2Zgx6NbQuViTuL+bd9Mm8MePo//JJwGeh//7309+\n5zwqsHw5uMRStClqzZslUleH/n/6p6STfi4UGrISLRMnT0Y4oSvtwIGlO0PhOXPgF0UITU2xzxTu\n9Gl4/vu/EdDRl0AL565EB4MoTFMkPbh8uWEfApG6OnQnW/HGQJeu8Lx5QDiMoocfhuvw4bTl41Rx\nQN6aps1PkP4dAno6z4XD6NmyRfXTB+WyaXzjs/LylBcl7jfeSN/RMR15Z7ZZeB6FjzwyqIi/Vbgz\nZwYV5S+qr888d9jlMuQDPGWOoyjCFd+2OV5ZGUJyXXSZDV8qyXBnz6J00aKUzxHPPReBhLJV3pde\ngkdHalJwxQoE7r5b8+sG0bA/Qt7gxjc3J00lScd18CBcBw4o/jejc6J5n2/wplO325iW6zqJVVUQ\nmprA79+v7YUJF5RcS4vUvjzNhvJs4X73XbCysqT/XXNcFBeDVVdLK53y5C5+74CZFX3iDPqd4s4Z\nqauTuiamU1w8dKJtQMMg/osvpPrjarndUnnfJBfNwttvJ81fFkeOTL5CLt+BKCuD0NAgXRzKVUna\n2uDVMNfQy9GTaG+aPxJ/6JBxTRJcrrS39llJibQaGJ00cX6/Mfk3ScoQWUpjjjMTBF2bgooefhj8\n4cOaXyed1NiJTsG//Rt4HY0/4oljxpg/AbMwj3yQhHN6N2+Gq6kps2OafdEBDKwQJWtrntgEqbIy\n7YqOZSIRaYKZTE8PEAohpJBXrueWsvDWW8p1ojXQVLYwfsFAZ9tvxYY5//M/gMqNslqEzz9fqpYi\nn+fNN1GsUKLTKqymBuELL0zaJEf1cUpLwft8jujeaQRWVDSQ6mDogRmYIEAsK4NYWzvwuN49QVpP\nX1aG4Le/PXBOeTFv/nyE9KagGbBowB8/Ds/27RkdIx4bNmxQmh/X1RXbO8GqqhBMWDSQiePGQayu\nll4jitJ3S3SiLjQ1Dar4YRbnTqJVBCn/1VfwvP66NeOJrxkZzV0Oz5ljSGWGwJ13SnVJ7dxBrfVD\nQWdOeLKOa8mYkuMoj0UQMi7Q7/vwQ/PTLCz6wB5CZRc6LYLXXgu/AbfXUsYFx4G53Yqtz907dgxp\nPhC4+24ETWrdrlma2/Wuzz5DsUIDoc7PP5e6N2pUsHFjRjmEXHs7PNu2aUrnkF7I6c8vLiiQ2hPH\nfY4UPfww+K4uwz8vut99d/DiiigOrtZhBwMaPKUrOZZ1knUsjNIVF/L3W2HhkO+s8De+MeSzsPCh\nh/QvECUbwje/iV55odCo1W8dKUFD8Dzc77xjXP5xQilX1yefoOihh9K+LPCP/4jQsmXSD6IoNZKR\n0zksukB07CSab21N29ucM3hy4WpoAJK1gRaE2GYDt7zb3qjzC4I0GbdpEu368EPw7e3aJkh6c1sz\nySHW+MYveOyxlLechIYGlNxwg76xRHmff16xfbahLFyJjkyZgh65tqYJk2jXoUMofOYZza/zbN6M\nYVrylpN1LXS7Lftw1YXjpI2dyS7uknwBsqoqXRdzrLAwtiigC89DLCsb+CJLdz75li3HSRWJ9NQM\n93qlVbD4SVN/f/I7D0ZyQttvDekzXGsr3Ik1xYGBC4McKX3HvF7DOxZybW1AJCLd4Un4m/e88caQ\nz0Lh3XczvkOQitDUZEyH5v5+fUUB4sndQtvaMh8PMPR9xfMQ9uwB19Ki/hiiCLG8PNYpOXTppQgt\nWGDM+FJw7jtIzYaT+PasBih+8EHwx48r/8eCAvTIH0by5NHASbw4cWLSxHqzxfJtNfwu4Tlz4P/B\nD3ScTNuXkJzLFvzWt6S26Bpw/f3gUuWsM5b5h57aVvGZsHASLVZVpS5ZlOE4OJ9PVf3hRIkrHmlz\nHJOUT2Ner7NvYcv/vslW1QzIZxzE681oEi2X91IbF5ELLkDfY48BPI/urVsHqiBoIVfckc8ZDoNv\nbwcrLDS3rjzgiEk0p+F7jz9xAgXPPTfkwitWtzdHJtHpVqJ1xYV8wVpYiO7f/jb580QR3MmTUhm8\nNNUyMuH53/8d1NVPePvttHeDy887D9zp04MeC8+fb8hKNADj7mQkpphwHLjeXm2TfcYg/PWvsbs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- "text": [ - "" - ] - } - ], - "prompt_number": 27 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", - "\n", - "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30000\n", - "movement_error = 2\n", - "pos = None\n", - "\n", - "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "for i in range(1000):\n", - " Z = dog.sense()\n", - " zs.append(Z)\n", - " if pos == None:\n", - " pos = (Z, 500)\n", - " \n", - " pos = sense (pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - " pos = update (pos[0], pos[1], movement, movement_error)\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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pu56ifsEwqJkxA+wFFyRfIBOhS0vB7N6d8LhAz57i/zFGDwC2n36CfcWK2BON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\nC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TfZmGb+/ndo559vv9eaBrNePRTdcQfZxHXdlpH0gd65M7IBhW/6SSdBs96znFQxvwwP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YMQtjxnhZ/NZloh4fwLnMGBYWLyT58GYqnPEzcryfSZO8RNy6h7epqAgVz59PtWeeoeb27cix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- "text": [ - "" - ] - } - ], - "prompt_number": 28 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", - "\n", - "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise: Interactive Plots" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the $\\verb,interact(),$ function to call a calculation and plotting function. Each parameter passed into $\\verb,interact(),$ automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.html.widgets import interact, interactive, fixed\n", - "import IPython.html.widgets as widgets\n", - "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n", - " # your code goes here\n", - " pass\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10,10), \n", - " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", - " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", - " movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n", - " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 29, - "text": [ - "" - ] - } - ], - "prompt_number": 29 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Solution\n", - "One possible solution follows." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "zs = np.zeros(100)\n", - "ps = np.zeros(100)\n", - "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n", - " dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n", - " random.seed(303)\n", - " pos = (0,100)\n", - "\n", - " for i in range(100):\n", - " Z = dog.sense() + random.randn()*noise_scale\n", - " zs[i] = Z\n", - "\n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps[i] = pos[0]\n", - "\n", - " pos = update(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n", - "\n", - " p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - " p2, = plt.plot(ps, c='b')\n", - " plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", - " plt.show()\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10,10), \n", - " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", - " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", - " movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n", - " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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XroRPnIjtl19wDR5MoF69EoxQpPQ88kgk//ynm4svDpT4vTSCLCFBvWNiRnkh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\n2rf3afRok5v8Cgr0hxU2AAAATFWpdZD9fmncOLc2bIjUO+9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- "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 30, - "text": [ - "" - ] - } - ], - "prompt_number": 30 - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise - Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our equations are linear: \n", - "$$\\begin{aligned}new\\_pos&=old\\_pos+dist\\_moved\\\\\n", - "new\\_position&=old\\_position*measurement\\end{aligned}$$\n", - "\n", - "Do you suppose that this filter works well or poorly with nonlinear systems?\n", - "\n", - "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", - "\n", - " Z = math.sin(i/3.) * 2\n", - " \n", - "Adust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#enter your code here." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 31 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###### Solution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_error = 2\n", - "pos = (100,500)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "\n", - "for i in range(100):\n", - " pos = update(pos[0], pos[1], movement, movement_error)\n", - "\n", - " Z = math.sin(i/3.)*2\n", - " zs.append(Z)\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['input', 'filter'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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l+L//+z/ExcVh1KhRRX6elpaG+vXrF36uVi0BP/2UhZtuCuh0RERERERF7NmzB61bt/Z5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- "text": [ - "" - ] - } - ], - "prompt_number": 32 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Discussion\n", - "\n", - "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", - "\n", - "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the predition and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", - "\n", - "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Exercise - Noisy Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Implement the same system, but add noise to the measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#enter your code here" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 33 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "######Solution" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "sensor_error = 30\n", - "movement_error = 2\n", - "pos = (100,500)\n", - "\n", - "zs = []\n", - "ps = []\n", - "\n", - "\n", - "for i in range(100):\n", - " pos = update(pos[0], pos[1], movement, movement_error)\n", - "\n", - " Z = math.sin(i/3.)*2 + random.randn()*1.2\n", - " zs.append(Z)\n", - " \n", - " pos = sense(pos[0], pos[1], Z, sensor_error)\n", - " ps.append(pos[0])\n", - "\n", - "\n", - "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", - "p2, = plt.plot(ps, c='b')\n", - "plt.legend([p1,p2], ['measurement', 'filter'], 3)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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qBfMTT3js/e/fZ7BpkwYvvWTA779n4eRJHi+8EAhThQhaGS7FuIsXZdMkiG9o\nN20Cf+KES+eG9O1rc7FMlGuxzDAwjhxp8/3EqCiqNeyHjNOmQWjXzifXdisYNhgMGDZsGGbNmoU6\nMrcjpk6dipkzZ2LmzJnY8vLLuFqoR/jevXuLfLvb37w5DhXaFFf89cKPxbg47Llyxebraj7Ozx9+\n+20eP/540uPXK+uP83O9HkyZgsuFSqgUHJ9XR/LA1q0238/SoQMOm0xOXd9w9y6OFCqzU/z1Q/fu\nwVzow9Ff/r7Ky+P85+ReN/fujd3Xr3vs+kuX6tC+/Q2cPbsHYWESfv01E+fPZ2DIT/1hfvDQL/5+\nyuvj/M8LV86/1KgRxLxVJn/585Tnx6lHjkDIa7gh9/qV//wH/P79sq+LSUnYX+zOXf7rQr16MJ0+\nXeT4XRkZ2Naihc3xXOY43N2zx6/+fuix84/37t2LmTNnYurUqZg6dSrcwUiSawkAkiRh1KhR6Ny5\nM5577rkSr2/btg0tW7YseKz/9FOAYWCYPt310frQ8uVazJ6tx/btGc70hCA2BA8eDMO0abDIrPCH\ntmqFrJ9/ls33c1VYgwbI2LMHUpUq8geYTKhQsyYe3roF8Lxq1yX+zWQCmjcPw6+/ZiIu7u8cQqMR\nmDASMKXlYsmGAARSpUVC3BLSpQtyZs+GUChILUz/0UdAYCAMr7xS9IXcXFSoWxcPb9+Wb44kCNbN\nz6GhisfCb9kC/cKFyPr1V2f+CMTPHTt2DN1dKNcKuLEyvG/fPvz2229YuHAhWrRogRYtWuCunaLZ\nTFqaz1sxFxc0bpzivKGnnjKhbl0Bv/5K6RLuyP92xyYm2tzcIEZGgr1/X/F7MnfugHNw+41JT4dk\n78NSq4UQG0u3xX2k8Ld+b1q7VoP69YUigTBgrda35Beg4iPhGD48GBkZPhlemcfv2wfN2rU2X5ed\nFxYLgsaModripYkkOWyyZKslM3vnDsSqVYsEwkXmBcc5FQgDeZvuZCpQkPLL5WA4Pj4eJpMJx48f\nL/hf1apVbV8oJcXnrZiLE6OiwB86pPj4Z581YeVK54Jh3fz5BQ0iSB6z2foBV7Om7Mu5H30EoUED\nxW/HHzkC/X//a/sAk8m64U6vt/s+mXv2QLIzh0nZs3ChHpMmyVcZ4Xlg/vwc1K8v4vnn6XaQmtir\nVxH07LMImjChREt2h+fevg3+6FG3WqizSUngzpxx+XziHCYlBRLPQ6pQweYxtrrQubJHxBGxVi0w\n6enWW0Ma8TlfAAAgAElEQVSEwIsd6JjUVL9bGba0bQv+4EHFx3fvbsbFixwSE5X/tXEnT4LJzXVl\neGVSfHw82Js3IUZGyjZgAQChVStry0yFpPBwa+k0W7RaZBw/7uxQiRepUX/aWceOcbh7l0Hv3rZL\nQrIsMGNGDvbv53HtGtUcdxeTno6Ad95BSM+eEFq0QPqxY3bLXMrNC/bGDQjR0W6Ng9+9G7oFC9x6\nD+IEjkPuhx/aPUSsWhWsTPMMJj0dYt26RZ5z+/OC55F+5YrN30HE+5j7912vNqIC7wXDKqVJsFev\nIvCFF1QYkTUY5o4cUVxvUKsFnnzSudVhNjkZkl4P7sABV4dZ5rCJiRDzNlKoQaxUiUpglUGBL7zg\n0Q/HRYt0GD/eCI5zMI5A4OmnTfj2W53HxlIuCAJCevYEk5WFjL/+guGf/3SpdjSblGTzrpJSYmSk\n7Cok8QypYkWYnnnG7jFitWqy/ybmvn2RM3eu4mtxx49b+xY44sadBaI+7tQp6OfN89n1vRYMG6ZP\nh1Ds211x7NWrCBo3zv4xt26BvXZNlTFJVapAqlQJ7IULis8ZMcKEFSu0itPVmJQUQKNB8OjRVOQb\n1lwvS8eOyP7mG5fO544eLfFB53BlmPi9ErmhBgM0a9dCyGvso7b8cmqjRyu7TTp+vBE//6xFVpZH\nhlM+cBwytm5FzuzZtjeyFiOXM8zeuAExb2WYPX8e+s8+K3GMfsYMux0lpapVqSWzn5EiI5H72muK\njpXNJc9LedD+8YdTd3yJf2BTUiA6cUdY9et760Lm3r0dJrmLERHQbN1qN2h0txVzcZZ27cA50d6v\nRQsBPA8cOuRgOSkP++ABLM2aQapQAdzZs64Os2zR6VzOzdVs3lyieYZUsSKYhw+tu4pJmaDZuRNC\nkyYOOwu6aulSHQYNMqNiRfvfanVffw326lXUrCmiUyeL03sGSDFObnSSw964ATEqCgAgVa8O3aJF\nRTdDZWZCP3++3T0C1JLZD2k0MI0Z49KpzM2bCMurXsVSG+ZSiXnwwCvN1GzxryS40FBIISFgbt+2\neQiTmupUPqkjOXPmwDx0qOLjGQYYOdKEFSsU3DKVpIJueeYuXcDv2uXGSMsGd3O92Nu3S3af43mY\nBw0CDAa33huSZL1LQLvUva74vNCsXQvzgAEeuZbJBCxZosPEiY7ni2bHDnB59aknTTJi4UI9TQ8v\nkvu8ME6ZAnPPngAAKSwMxkmToC9Us5y7cgVCvXqwl/8iRUSAycigDVSlVPF5IVWvDiY1FcjKAkfB\ncKnEpqR4bPFD0fV9dmUbhPr1C375yGFTUuz2rnaaCzVlhw0z4vffNYpir8x164CAAFg6d4aGgmFl\nsrMRZKN7kK2dxdmLFsFWAWgmPd26cuwIwyBkyBDqROdrZjM0mzbB1K+fR97eVjk1OWJEBJgHDwAA\nnTpZwHHArl1Uh1pNuu++g97B5qrChEaNIBX6QmyYPBmabdvAJiQAsHaec1ijnGVhGj7c/S/QxD+w\nLMQ6dcCdOQP23r0Se1LMZuDyZbboF1lJAnPzJi1++AnmwQN1YzsnlbpgWO00CVdERUlo0kTAli3y\nfc8LMAyE1q0BAJZHH7XmMZXzlQhF9WQDAqDZudPa+aAY9s4dSE6W2dEuXQr9rFmKjrW0aAHu2DGn\n3p+4r/C84C5ehNC0KaQaNTxyrW++sV1OrbjC+egMA0yaZMDChbSRTint0qVgExPtHiNWrAju6lXZ\n1xR9XoSGwjh1KgLyVofZS5cUtWHOmTtXlbQN4kBODgJef921c0XRGrAWIzcvhJgYaDdutN4VKLbI\nNXOmHl26hKJVq1C8/XYA9u3jYbEAoY8+SvtN/ITQvDmERo18dn2/C4bF2FiwdoJh4+TJMA0a5MUR\nycvfSKeUVLEiDC++CIZ24DjGspAiImQbbzB37pRMk3CAycyEFBam6FihRQvwDhp4EM8SGjVC1qpV\nHnnvY8c43Ltnv5xaYWJEBNhCjViGDTPh8GHeqfKK5RWTno6Af/8bkoOKEWJ0tNt3YwwTJoC9cQPI\nzrZ+mYqNdev9iHrYxESX74oyd+8iNC8lxhEhJgZMcjIML79c5PlTpzj88IMOx46lY9mybISGSnj7\n7QA80rACxvL/w/plmbQx1g8YJ0yA0KqVz67vlU907sAB6BRWDzANH263ZbNYp06RW2S+0r+/Cfv2\n8UhOVl6exfDqqz5f1fa1Lno9gp980uFxolw3IlGEcdIkSBUrOnVNh93nCrE0bw6OahJ7XYncUA+U\nPZIkYPZsvaJyagXnREQUWTkKDARGjaIya0poly+HpXt3SJGRdo+zFwwr3mMQEoLMzZuBoCAYn3kG\nlg4dnB0u8RAuMRGCnc5zRY49eBDa778veCy7RwTy80KMiYEUHAzzkCEFz5nNwAsvBOKDD3IRGSmh\ncWMBb7xhwM6dmdi5MwMtayXj25WVERdXAf36BeOzz/Q4eJCDWdl3ZVKGeCcYPn8e3Pnzio6VKlTw\n/o5Ci8XpbkQhIUCvXmasWkW7y53BJiba7UKUT3a3N8vC8OabTgdKTEaGw2D41i0GP/6oxXcJncGd\nOEll8MqgBQt0uHaNxbhxylIkAMDSvj1MhX65AtYya8uXU5k1uyQJusWLYZgwwfGhlStbGxNlZqpy\naUuPHn6xYEKs2GvXFNeVZ1NTodm06e/Ht28r7j5nGjkSuf/5T5Hn5s3ToXJlCSNGlExPjIqSMLnP\nFWzs/QUuXHiIV14xIDubwRtvBKJ+/TCMGhWEb7/VwWJRdHlSynklGGZTU/2uFXMRBgNCeveWzVG1\nx9lUCQLc3LlT0SqB5GTpI/baNZsrukx6eok0iexsYOtWHm+9FYAOHULRpUsotm/XYOmvlTCu0mpY\n7qcpvjZRzlaNcEW5oW74808e//d/evz0UzaCg5WfJ9atC0v37kWei44W0bGjBb/8Qj/7tvC7dkHS\naiG0a+f4YIaBWLMmWAW5odply6BdtkytYTomiuD37/fe9cogNjERosKV4eItmVkbaXGynxfFFkku\nXWIxb54eX36ZY3P9RIiJAXv5MgIDgW7dLPjgg1zs3JmJI0cyMGyYCcuXa/HNN3QXqDzwSjDMpKY6\nfWvbq4KDrRv3nMwV7dLFgrt3WVy4IP/XqJs9G9fm/YnNmzXlfd9cgUCZnb5yDC+8AFPfvorfl9+3\nD7pvv5V/MTi4YJeqKALPPhuEhg0rYM4cPSIiJMyfn42EhHR89102/vgjE7diO2PUi7Vo5U9tJhOC\nBw3yeonBixdZTJ0ahMWLs1Czpjor/lRmzT7d//4H4/jxiu/iZOzcCbFhQ4fH8SdOgFHpw5S5d89h\nh0N+2zaEeKiqSXnBXb2qeGW4eBc6Z1aGi7yPCLz0UiBef91g92deaNBAtqJURISEwYPN+OabbHz5\npR43b1K3urLOe8GwD0tmKGFp2xb8oUNOncNxwNCh8u2ZTSbgP782RI+Z/fHll3o0bhyG6dMDcPIk\nV65/gVbLyVH0wehsbrgUEWGtMykje9EiCG3bAgD27+dx5QqHs2cfYu3aLPzrXwa0aCEU5JAGBwM/\n/piFyEgRAweG4MED+hBUjVaLnM8/R+A//1miO1h8fDzYS5fAb9mi6iXT0hiMGhWM997LRfv26jVl\niY+3gGWB3bupzJqc7C+/hMlGeURZNhpkFM8NZZOSIOR1n3OWJBWtosUmJSFgxgy75/DHj0PIa/BB\nXGN44QVY8j5/HZEqVwaTlob8pF2J42RXlR3lki9erIMkMRg/3v7dXvGRR5BdKEe5uJgYEZMmGTF9\neqDjwROXMXfvQrNxo0/H4LU0Cac3jslEjMytWwh69lmVRlWUpW1b8IcPO33eiBFGrFypK5JieuQI\nh8ceC8WRu7Ww94vt2LQpE1u2ZKJCBQnPPh2ALjFZmDdPh/v3y1+gxSUlKd5M4QyxUiWwCkrkrFih\nxYgRRoSE2D5GowHmzMlB9+5m9OkTgmvXqHKAO9jLlws2xVh69oSlTRsEfPppieO0y5eDP3BAteua\nzcC4cUHo3duMZ55R99YMwwATJ1KZNZtCQwEHVSRcUbj7nLPeeisA/fsHF3zuSsVuycvh//oLOV98\n4dL1iJWla1fld4Y5zrqwkVdJyPDeezAPHOjU9W7cYDFzph5ffZUNVoWP7pdeMuDSJQ7r1zsopUpc\nxp0+Dd3ixT4dg1d+yxtefhmWvFaJSvBbtyJo/PgSz7P378vmlanB0q6ddWXYyWXbuDgREREi9u7l\nkZ1t/cAdPToY//pXLtZUn4waj1gbQdSuLWL6dAOOH03DHMNknDtmQdu2oWWvgL/FAu2KFQUfZsVt\nmDPH5fqx2h9+sFl2TwoPt7kynM9gANat02DoUMeBEcMAb71lwPPPG9CvXwiOH1dYfoCUoNm2DfzJ\nkwWPcz/5BNpffwV35EjBc3v37IFW5a5z77wTAJ4HPvggV7X3LGzYMBMOHuRx7BjNDU8pkhsqSWBv\n3YJYs6bT73PzJoOVK7Vo1UpA9+6hOH6cg1ilCpjkZNubZQ0G8EePwtK+vYujJ67ImTULkr3VCtje\nYyBJwL/+FYipU42IjVUnJUqnA2bNysH06YFq7fEkxbDJyRBV7CzsCq9EYs6WuRFr1AB37lyJ55nk\nZI+VJpNq1IC5WzcgKwt2lw1ljBhhwsyZety+zaJjRwv27ctApUoSuPeSS3RUYXUadOosok2/X7Cg\nw1NYvlyLLl3KznZV7uxZBL72GiSOg6VdO5hGjIC5T5+C26CSRuNy2Szd99/bLKZfuDmCLZs2adCs\nmYDq1ZV/4Rk71oQqVSQMHx6Mnj3NyMlhkJ3NICsLyM5mkJ1mBpuZiV926lCrFlWgkMPv32+dA3mk\n8HDkzJiBgI8+QtbvvwMAQpKSAKMRQvPmqlxzyRItdu7UYOvWDMVl1GzRf/klTE88AbFevSLPBwUB\n77+fi9GjgxEcLKFvXzP69jWhVStBlRUpUhSTkgJJp3P68xkAZs0KwJgxRrz3ngFt21owfHgwPv6Y\nw6TgYOv7yrSBZe/ds9a0p8YcXmXu3dvlc1eu1OLePQYvvOBaZ8GAt9+2bviLioJYowbEOnVg7t8f\n8fEWdO5sxsyZAZgxwzNfrssz5sEDn6fS+uWypFi3Ltjr1633OTV/35pgU1M9166PYZAzf75Lpw4d\nasLatRrMmpWD7t3zAltJsgbvMt92LJ07Q7N7N/q9MQSffBIKo9H67bMsEKtWRdbixbB06ADt+vXQ\nLVsG3eLFyFq7FoATdUNlsHfuQLSxqiyFhsLcs6d1acBGsP3LL1oMG6bsdjl39CgAQGjVCn37mhEd\nnYUTJzgEBUkIDpYQFAQEBUmo9NNCfLW3PX7+uRXeeINau5YgSeAPHEBusXa75iefhLlHj4LH7W7e\nhLl/f1XqC+/fz2PmzABs2JCpShzD//UXLI0blwiGAWD0aBOeftqEEyc4bNigwYsvBuHhQwZ9+pgx\ncKCpTH3R9TiDoUTucOHPCyk01Nre3klJSSz++EODw4czAAD9+5tRr14mnnkmGBfwX7x3+z4YmWDY\nUrMWDk2ej3vbmL8/14lfyJ8XZjNw+jSH/ft5HDjAY+9eHqtXZxUOG5xiHD0a3OXLYG/eBHvzJvRz\n5iCzXj2IcXH48MNcdOwYihEjTGjaVL39BwRgU1IgyvwMepNfBsPQ6627Sq9fhxgTU/C0P7RillO5\nsoQNG0qWHsjYsUN2Y4i5SxfoFi1CtdkSHnlEwO7dPHr0KBsftlJkJCx5RfZNw4fDNHy40yXr8gUP\nG4bsefMgVakCWCzWb4+2CvizLHLkGrsYjWDv38eDwGjs3avBggXZJY+RwR89Cu78eeTkdcRp3FhA\n48YlPwBDXvofRk9oh/HztHj9dYMnekWUauzVqwDPl7y1zTBFVtw069YhJ6+drjuysoCpUwMxZ04O\n6tVTZ6VejIgA++CBzddZFmjZUkDLlgLeeceAK1dYbNigwdSpQfjyy2z07Fk2frYdYS9eBHv9OiyF\nvuQoJkmoUL8+Hp47Z3vlV6tVVHGiuFmz9Bg3zohKlf6+I9SwoYht2zIx8fF4PPl6ZXy3XEKlShIS\nE1ns2sVj1y4N9uzhUaGChPv3Wfz1Vzpq1CjHO59dYWdhwh2XLrFYtUqLAwd4HD3KIzpaQIcOFgwa\nZMJnn+WgWjXX/53ERx6B+Mgjfz9hNoNNT4cIIDxcwnvv5eKf/wzEli2Zbt9xIn9jkpMhKWih7kl+\nezNPrF8f3MWLRZ4rDVUpCjAMxLg42ZfEhg3BZGeDTUrCgAFm/P57Ga9XWmjZ25l6sszduwUbXJj7\n961fhJz8ys9duoSgp57CmjVa9OhhVrxSaGne3GGpPSZv9aDpM4+AZYGjR+nTsTh+/35rmpS9X4qS\nhKNPPgmhTRu3r/fBBwHo2NGCXr3UayElhYdbc0sVqldPxAsvGDFnTjamTw9Ebjm5q6pbtAi8q90b\nGQZijRrWlsqFuFt/OjGRxfr1GkydWvILeYUKEn4+GI6m7XXo0iUULVqEonfvEPz1F4/u3c3YsSMD\nhw9nYGTbi1j+eoJb4yiPAv/5T2jWrHH5fCYlBUyxPUKiCIwaFYwzZ+5iyhQjTp1Kx969mfj881wM\nGWJ2KxCWk/uf/xRJ8xw1yoSAAAmLF5eRW7l+wtKuHYQmTXw6Br8NhoX69UsU6DeOGwfjM8/4aEQq\nYhhkbtoEsXp1DBhgwsaNGmr/KEOKjAST13jDVvF1R/JbMa9caa0ioZTQpIn1y5jBduqDduNGmHv2\nBHfzBkY8ep2aMMiwdOoEw0sv2T+IYXC/TRu4u9SyZw+PjRu1+OQTdaNPMSJCUaWS4rp3t6BJEwFf\nfSVfNqys4Q8ehPnxx10+X4yOBmejLbOrvvjC2n67YkX5IInjrBssFy3Kwk8/ZeH8+XR8800Onn7a\nhKgo6znjWxzC0l31qROZMyQJmq1b3QpwNGvXIuCzz4o8t3WrBsHBEiZNOoNevcyoUMG7q/UMY91M\n99lnety5Q7cB1WJ69lkIzZr5dAweD4bZc+egL5YvqETu++/DOG1akeek6tUhVa2q1tB8SqxTB+B5\nREVJqFtXxJ49/pmxojZncobFyMiClWExMtJxUCWDycjAJf4RJCay6NrVid9mAQEQYmLAnT1r8xDN\n1q0w9+kDft8+PJ08B6tXa+lLTTFinToQGjd2eJw7ueSANT3ixRcD8d//ZiMsTN1fkM6uDBc2Y0YO\nvv1WV/bL85nN4C5fhlD4FrOThOhosMWCYXfmxdWrLDZtkl8VLq59ewENG4qyNzAaNWNQU3sXW7ZQ\naS2l2PPnIWm1EOvWdfpc5vZtBLz2mrXhRrEFkK+/1uG554x49FH3Pi/c0aCBiLFjjXj3Xao9XJZ4\n/BOau35dtjKEQ65mwLuJO30a+v/+F95cBnjiCRPWrqVVxeLEqlULWjJLUVEwDxpU5PVz51gsWWL/\n741JT8fy1D4YPNjk9JQSWrSwe9s3a8kSmHv2hBQRgXrG86hbV8SOHeXjS42/+fBDa3qEJ/JzLY8+\nCpOLd6SioiS8+KIBb7wRWKab7bBXrlg3twa6HiCIMsGwO774Qo9Jk4wufTnSLVwI5uFD67giIjCp\nwgp8/z3dGldKs307LN26uZYzrNVCu3q19W5goe5z586xSEjgMGiQ79u5vvyyAdu28eWyV0BZ5fFg\nuFTl+QIQ6tQBv38/gkaPBnJyvHLNJ54wY/16Tam/DcdeuICA99+3e4wzOYCF0yTkfPBBIN56KxB/\n/GGNctlz58AVD17TM/DTza4YPtz5D1DTiBEQ7G3YCQoCdDqI4eFgk5MxbJgJv/xCvzBd4U5u6J49\nPDZsUD89Ip9Yu7bT5SELmzLFiKQktkwX7efOnrX/s6KAWKsWmPT0Is8Vnhch8fFQ2iP90iUWW7dq\nMGWKCxVeMjIQ8PHHkPLLQVaujGHiChw7xuH69TK+wq8SzfbtMD/2mEvnSpUqgcnKspY4KxQML1hg\nTXnRat3PJXdXUBDQt68Zv/1Gi1hlhXeCYaXdZ/xBcDCyfvoJUsWKCBk0yGEjB1v0n30G7cqVio6t\nVUtEVJSI/ftL96oid/astSSeSkxDhsDwz3/Kvnb6NIfTpzmsWZOJV14JxIULLDQ7d5b4Oz90Jxqc\nhkOLFs6XwrF06ABLp04Oj8tv+DFokAlbt/JUmN2LPJke4ba8L9NaLfDFFzl4662A4l2oywyhYUMY\nJ0xw6z3MAwciZ+5c2deY9HRrPnFQkKL3+uILPaZMMTreMJudDe2PPxZ5SrN/v7VJVF4wLEZEICj1\nFoYPN2HZMgp+HBIEsNevw9y5s2vnsyzEKlXAnzgBKS8YfvCAwbp1Gowd61plInewCQklNnYCwMiR\nJvz8M82HssLzwXBaml+WQ7NLo0HOvHmwdOqEkD59ZH8QHGEvX1Z2YF73owEDzAUrnKUVd/UqBJla\nrIU5kwMohYcXfBgWN3u2Hs89Z0C7dgI++CAXzz4bjIeB1Up8efkxezCGTQ70aMkzMSICbHIywsMl\ndOxowfr19AHpLFdzQz2ZHuEWUUTFqKiCOxvx8RZ06GDBF1+o36LYH4hxcbC4GvzYkT8v2KQka3k+\nBT/ICQksduzQYOJEBavCkoTAN94o0nmU370blkcf/fuYkBBkffcdxo4x4McfdTD5/i69f+M4ZBw5\n4lazEqlqVWuFkbzP/yVLdBg40IzwcOu/k7t7DJyh+/FHaH77rcTznTpZkJrK4uxZqiLkDubmTbeq\njqjF8xvoUlMhuhoMm0xAhrVQOpOaiuB+/VQcmQMMY93E949/QLNli9Onsw8eOGwQov/iC+hnzgQA\nDBhgwrp1WpudQUsD9upVlzZMOOvKFRa7d/MFqwSjRpnQubMZk37qBST/HQybTMCaNcobbbgsJASm\n3r0BUcSwYSasXEnBMDIyrLe1PTihPZ0e4Q721i0A1tJ++T78MBc//KBFQgLdancWe+MGhOhoRcd+\n/nkApk41KIvFgoOtAXah2zn83r0wFw62GAaWHj0Q20BCbKyADRtK96KFV7i5+iBWrYrsuXMhVawI\no9EaDE+e7JumRkJsLLiEkqX1WBYYMcKIFSvo894d/Nmz0P30k6+H4flg2DhhgsvldnQLFyLg008B\nWIsy2yt87ynGKVNgHD/e6fNstfgsTKpYsaBkU0yMiIgIEYcOld5vmdyVKw6DYZdyvSQJAa+9hvxS\nDXPm6PGPfxiL1Ob/5JNcPMgJwmfn/95kt22bBvXrC6q3SeZOnUKR+90Mg5yFCwGWRe/eZhw/zpX7\nsjv8oUPW9CiFfYmdnRc5OX6cHgFA0ukgaTRgC9VKj4yU8OqrBrz+etneTKem/HlRsDJshyRZu0zu\n2cNjwgTlt9PFyMiCjbpMaiq4a9cgtGwpe+zYsUbaSOcFhtdeg6VtWwDAqlVaxMVZq33k82bOsNCg\nQYmeB/mGDzfh11+1pX6/jy8xyck+7z4HeCEYFho3hhQV5dq5sbEFKyulbSMem5zscGVYLFay6Ykn\nSncDDvbqVQieWBnOzIRuxQpAo8Ht2wzWrtVg8uSiv+y0WmDplzfx9YOh2LrVmnu9cqXWpY1zdkkS\ngp9+2uau94AAoF8/M1atKr3/jmrgDxyApX17j73/ypVaPPKI4LX0CH7nTugWLFB8vFSlCnLfe6/E\nL9Hx4414+JDBqlW0uugM9sYNu8FwWhqD8eODMGuWHitXZiE4WPl7Fw6GJZ5H9qJFNqsZ9e9vxvnz\nHC5dotV9TxKaNIFUrRokyVpOzaWNkGqNJT8YlrnLFRsronp1Ebt2le79Pr7EJCf7RWzn1z/RYv36\nYPOCYSXBpd+QJOvKcESE/cMiIsAUKuafX2KtVKZKSBKyly61tk62w5Vcr8L1JufN02PkSFNB7lhh\nkXEVsKzvMjz/fBBOneKwfbsGAwe6V/iXSUtD4MsvFzzmTp+21s+0U091+HBTuW/AUdB5TiGncskl\n4Ouv9Yrqx6rGbIZm2zanTjENHQrjlClFnuN54D//ycFHHwVAcH5PZ9mXlVUk7z9/XuS++SaMY8bI\nnrJ9O4/4+FBERorYsSMDzZo59xdbpGpNaCjMvXrZPFartaZlLV1Kq8PesG8fD4OBQffuRb/0ejNn\nGKGhkEJCwNy+LfuydSMdzQdXscnJEB3ESl4Zh68HYI8YHW1NjcjJsQaXpWgjXsbBg0XaEMsRw8OL\npH40aCAiJEQqnW19GcZaeUHlnWqBzz8P7W+/QaxeHampDJYv12LaNBurBEFBaLl0Il591YB+/ULQ\npYsZ4ckX4U4nDCk0FNpVq8CkpQEANBs2wNynj90/Z6dOFjx4wOLCBb/+8fIcoxH8qVOwqNBeWc6O\nHTw0Ggnx8d67NynWqVOiI6YjUmQkxNq1Szzfvr2AiAgJf/5ZNlaHdV9/DV6l29a6JUugnzWr5AvB\nwSU2ZOXkAG+8EYCXXgrCvHnZ+PTTXAS4sD/RNGCAwxSMwsaMseaJ2mlOWW7x27YV1GdWQ/6qsMJs\nK48xPv00GBv/4IMHW6sI5W1vKn9EEcydOy6frmTh0Bv8+7c1x0GsUwfclStg/SBNgj13DppVqxwf\nyDCyvwSLkyIiwBT7CRowwIQ//ii7q4pO53qZTOAPH4ZYrRoWLtShf38zatSwn3A5YYIR48YZMXmy\nESH9+rlcHg8AwHGwNG0K7sQJAIBm40aY+/Z1dAqGDrXmkpVH3PnzEGJjUSSp2wFn5sXXX1vLZnmy\nQkhxYnQ02Nu33fpiVdjEiUYsWlQ2VpM0f/wBtZKgxejoItV7bM2L48c5PPZYKNLSGOzZk+Fcd8li\nzIMHQ8jLT7VFs3YtdN9+CwCoXVtE06ZCmf6cdokgIGjSJKhVP/DaNRYHD/KyqW7erjNsePttiDEx\nsq+Fh0t49FFLuZ0PuvnzUaFRI5fPt3TuDEvz5iqOyDX+HQwDsLRtCyYlBcYxY2B47jmfjoW9dw+6\npZ87i98AACAASURBVEtVez8pIgLpxbrzDRxoxtq1Gtpgk0eKjAR//DjSw2vju+90ePFFx8sxDAN8\n8EEuOnU0g8nIgBQW5tYY8jvRsTdugL11q2BjR2Hs+fPgjh4teJyfKlEqU17cJDRvjsyNGz3y3hcv\nsjh5ksOQIV6ub6XVQqxWTbUOaQMHmnD6NIfLl/3+I9g+SQJ37hyEuDhV3k6MjnZYq/zKFRbDhgXj\njTdysXBhDipU8PyHJZORUaShzz/+YcSSJWXjy4xauBMnIEVGQqpRQ5X3++YbHUaPNiotLe1TI0aY\nym1VCc3mzdb/cPGXnWnkSIgqfX64w6OfxMzt2wicOtWt98j58ktYunaFVKmSw3xUTxPr1AGbmKje\nGzJMidvtcXECNBrg5MlSmCqhgLO5XmKVKrA0bYpF0kQ8+qgFMTFO/MDl39bKK57vKkvz5taVYbMZ\nue+8Y038LEazb1+R8jCNGgkICZFw8GA53Vihde4Xg9J5sXChDmPGGN39J3WJWKcO2KtXHR7HXr0K\n/Rdf2D1GrwdGjzbiu+9Kd0DF3LoFBAaqdtdOrFWryBeO4vNCEIBp04LwyisGPPmkOqv0isZVuXKR\nlLZevcxISmJx7lwp/zKjIs327TB366bKe2VkWDfJjh8vvy/AqznDCvToYcaFCxySksrXfGDS0sCf\nOoVMhQ3G/JlH/+XYe/fAFVv5LM3EGjWsu449WHWdYawb6Up7Aw61SFWrwhBRA/NW18bLLzuXpKfG\nqjAACC1bgj92DGLdujCNHSt7jBgeXmQzJAAMG2bC8uXlc7XAEx4+ZPDbb1qMG+f9LlQAkPPRRzZL\nbhXGnTxpLb/nwNixRqxcqVXaYdgv8Sq0YS5MqlgRjCAUbctc6DbZ/Pk6aDRSiWoyagjp08ca3MuN\nKyKiSOUfjcb6ZWbGjAAqq5XHnRbM9+8z2LhRg48/1mPw4GA0aVIBgwc7TonzFzqdNXe4vK0OazZu\nhLlbN1gef1xxGU13XLvG4vx5z1zHsyvDpa0VsyMajfVWqQsd6ZzxxBNmrF6tRVpa6alVG9KrF5T0\nIXY210uMjMQPZ1ohLk5A06aOd4lzhw+DO3kSgLWFq+RGF6SCMdSujaxvv7WbFynJBMMjRpiwdy+P\nwYODceBA2VzpV4uSebFsmRa9e5tRtapvfkGKcXGKVkC5y5ch5OUX8n/9ZfPuWFSUhE6dLKW68gh3\n7hwEN/IFS2AYWNq3L8jz37t3L7RLliDgnXdw4QKLr77SY+7cHNV/7zI3b4K9fBlSXtWa4qSIiBJ1\n7l9+2QCjkcHkyUEUEGdkgDt7FpaOHRWfYjIBzz8fiObNQ9GuXSi+/VYHlgWee86Ao0fTMWtWjs1z\nvZ0zrER+qkR5SnE0jRiBHLkNrx7y5psB2L7dMwuFHr2Hy6amlqoKEEqItWuDTUyEaKftsP7jjyHW\nqwfTU0+5dI2mTQX06mVGmzaheO45IyZPNjhVN9PbmLQ0cBcuwJ1Bzpqlx549PPR6CTodEBCQ9/+a\n7liX3ReL/qVsVVizbRsgSRCaNQMEAULjxi6PqQDDQHBQM1eMiChooJKvalUJBw9m4OeftZgyJQh1\n6oiYPj0X7dpRTS1nWSzAokV6/O9//r+Myl65UtCaWIyIAH/woM1jJ0404o03AjF2rMmrGwLVYho6\nVLXNc/myit1y5ZKSYK4QgWnTgvD227moXVv9RPyQESOsewFsRNkFd34kqSC1Ta8HfvghC6NHB2PS\npCAsXJgtl0FVLjAmE3I++gjOlPPYtYvH2bMcfvklC/XqiT6vGOEIv2ULxLp1bW6ka9lSAMcBhw9z\naNu2nHzGc5zXYrydO3lcusRh6VJ1NmgW5/GV4VJTG1gh4+TJEB20BeUSEyHZKNpegiCgeI0ehgFm\nzszF5s2ZOH+eQ5s2YVi4UAejb+4OO8ReuWJttqHgt7lcrldmprWr3LRpBowda8LgwSZ07WpBixYW\n1I5h8c57JnTooGzpRQoPL1hVEhs2RPaSJc79YVwktzIM5N9ONeHQoQwMHmzC5MlBePLJYBw8WDZX\nitmEBLgyUR3lAK5bp0HNmgKaN/f/XzKFV4bFOnXA3rlT4mc8X3y8BZJkradaGok1azr8PHRHfHw8\n2Bs38PnZAQgLkzB2rGdS1Ljz5yHGxto+ICgIWb/8UuJpvR743/+ykJXFYOLEILWKjZQ6UkQETDbq\nQNuyfr0WTz5pQv36zgfCvsgZ1m7YAM3OnTZfZ5j81eHSvQ/Am9gbN6D9+WeHxwkC8O67AXj//VxH\nFWtdH4tn3tZKrTQJ9sIFhNlZifUmc+/eEOvXt3uMMx1V9DNnQv/VV7Kv1asn4ttvs7FiRRb+/FOD\ndu1CsXy51u+K9XNXrzpsw2zP5s0adOhgRo8eFvTubcagQWaMHGnC2LEmTJlixMiRyn8BipUqlVih\n9QapUiW7Jde0WuDZZ61B8aBBJkyaFITZs8veh2bwsGFgb95U/X3zy6n5PUkCd+nS36tHGg3E6Ghw\nV67IHs4wwMSJhjJTZs1Z9+4x+OEHLXJzbR9zOkGP+TuaYs6cbI+tnpsGDoTx6aftHmOrjrpeDyxb\nloWcnPIdEDtDEICNGzXo37/0/GUJDRoUaa8uZ/hwI9as0fjtwpW/4c6ehWbNGofH/fSTFiEhEgYM\n8Nx88WgwbHrqKZhGjXL7fQI++QRsXtOD0oBJToaksNe2VLmy7IpiYU2bCli5MgsLFuTg++91mDo1\nUI1hqqZgZVgBuVyvNWu0GDRInUleeGXYqzQa5Hz5pcPD8oPi5cuz8N13+rJVes1sBnv/PsRatZw+\n1V4O4NGjHO7cYdC3byn4xSmKyJ43r8itQyE2FuyFCzZPGTbMhD17eNy8WQrzJNz01luBmDtXj5Yt\nwzB3rq7EZsIdO/Zh3MW38eFr9xEV5blkzOwlS2ze/lYiPyA2GIAJEyggduTwYQ6VK4uoU8e1D0Bf\n5AwXtGW2IypKQuPGAjZtKmcb4AUBoZ06wdnkeSULh5mZwKefBuDjj3M9mkrm0WBYrF3bpV+MxZW2\nvGNnWkeL4eFgC+1StqdDBwt++CELmzdr/Gp1mL12zW4OtT0ZGcCePRr06aNiMOyDlWFnxcWJqFhR\nLLW3x+Wwd+5YvwSqnDj5zTc6TJxo9It8zIDp08Hv22f7AI6DuX//Ik85+iUaEmKtS13eWvzu28fj\n8GEOO3Zk4JdfsnD8OI+WLcPwxRd6pKdbf+utXB6DaDERIyf7oJaek3Q6YOnSbJhMwPjxQZ4sOlTq\nrVunRb9+pesbgxAbCy4hweFxI0aYsHJl6d0UqwR3+HDRRSeOA7Kzna7DrmThcM4cPTp3NqNlS88G\nPX6esm5l6tsXghPtMn1KFK3pIQqDYSkiwqngrXJlCdWqSTh92n9yTnM//RSmfv0UHVs812vTJi06\ndTIjLEylDlbVqzvsEOcvhg8vW6V42Js3IUZFuXSurRzAO3cY/PmnBqNH+0dkwZhM1s2iTjC8+CIM\nr7xi95hx44xYtsx/9wWozWIBpk8PwIcf5iIwEGjcWMDixdlYty4TV6+waNUsEK+9FoDtu2Lx2fG2\nYHj/+byzR6cDvv/eusGnX7+Qsl131mwGd+yY06dJErB+vXspEr7IGZZq1ACTnV207J+M/v1N2LtX\ng5SUMnqnR5IQ9NxzJXouiPXqgbWRDmYL++CB3YXDmzcZLF6swzvv2MmjUkmp+Em19OyJjLxyWX6P\nYZB++rTipgNSRITileF88fFm7N3rB8tkeaTwcKda7xa2Zo1GtRSJ/LEY3nwTgDU5n/Hj9JohQ0xY\nv16DHNsVhEoVd4JhWxYv1mHYMJNqX5bcJdSp4/QHPkJCHH4exMaKaNRIwO+/l54vR4GTJ4M7cMCl\nc5ct06JCBQkDBxb92Y+NFTF/fjYOWVoBRhNmz85B1Zr+81mnRH5A/MQTJjz+eEiZrRmv/d//EDBj\nhtPnnTvHQZKsX4BKFYZB7rvvOkwFCA21NuFYs6b0/Cw7I78To9CiRZHnhZgYcJcvO/VeTEqK3ZXh\njz8OwLhxRo+mSOUrFcGwv9HNmWPdNS+HYSBFRip+LzE83OkmHp06Wf6fvTMPk+HqwvhbVb3OihmM\nbQzD2MUWRBBbEEKCEIlESGxBkEWQRYgIYo/EGoKQIPFZsxBLJCN2EruxDMMwmInZe62q7482Y5bq\n7uru6q7qnvt7nu95vuq6devInK4+de655/Xb5fWCtV4ZGRQOHlSja1fvZP1006c/kopUIBUq8Gjc\nOHDqy3iVCtamTd26VqgGMCODwurVWgwbppx0KRcbCzox0StzDx1q8quNdOr4ePAVK7p83YMHFGbN\n0mPmTDs1gBSFmKos5g37F6Gh+z03VCLU27ZBu2iRqLE0Dbz1lgnff5+NTz7RY/x4vb2GIv5JTg70\nc+bYgkMX2blTje7dLR7Vf8rVZ9g0dKioVd9+/UwBWyqh+eknmPv0KbaZ1J3MsKVzZ1iLBNV5nDzJ\n4M8/1Rg71jdfHBIMu4Hqn3/AnDkjyVx8VBQyjx1z6Zonn7Ti0CGVouqG3eHXX9Vo08YCCXQxBJFK\ngU4szD//gDl+3KVrAqm+zNK7N0wjRkg236JFWnTtakFsrHJ2GbLVqoERIcnsDp07W3DvHoWTJ5Vf\nEkA9eAAqKwucG+VrM2bo0LOnGfXq2X+AsdHRoG/c8MREyaFMJpef+82asfjjjyykptLo3DkUly8H\nxk+ubvlyWFu2BNuokcvXeloi4Q+0b29FYiKNxMTA+Hvnw7LQbNliC4aLnoqNtds1xx6W3r3B1apV\n7HOet7VSmzTJ4DONBa/+pUKef96b08sGW60aGC9lh8SgxLphsRSs9bKVSHhR2jojw6fBsOqvv6DZ\nssWla7p3N+PwYRXu3w/Q+jKRFK0BvHuXwrffajFhgvdrxVyBi4mxKVAKvYmazQjp1QvutghhGGDI\nEBOWLlV+dpg5f94mw+xieu/8eRpbt2owaZLjbA9XtSropCRZakPtwQmo0IkhPJzHqlU5eP11E7p1\nC/X7fQLUgwfQLl4Mw4cfunztjRs0UlJoNG/umWSfkvxCCLUa6N07cBIdeaji48FFRQn25LY++SRy\nVq2S5D47d6qRmUnh5Zd9t1fEq8GwmJ2X/ghXtWqx4nFfo5i6YTfVp9LTKRw6pEaXLt7LEFCZmZLI\nMYvF1c2QgE20r2tXC/73v8B6aHrKvHk69Otn9kmtmEvo9cj8+29BpTI6MdEWKAspCPC8KDGS114z\nYe9eNW7eVHZGyR0ZZp4HJk4MwoQJRpQp4/jvylWpYtuZnuMdtSl34MuWBeXi/o48KAoYNMiMbduy\nMH26zq/riLWLF8PSo4dbHYR27lSja1cLGP/L47hM375m/PhjYMkzcxUrwjBlivBJnU4SXQmzGZgy\nRY9p0ww+9ROvPnGl+A+jRLhq1WQPhpVSNxw0ciTUO3aIHp9X6/XLL2o89ZTF3X13DlH98QeYs2d9\nnhnmIiLcEvzo1y/wMgiuUrAGMCmJxk8/afCOSAluX8PFxAhmRJmrV/OV54qi2bgRQW+/7XTusDBg\nwAAzlixRdnaYOX8ebN26Ll2zfbsa//1H4bXXnL8UsPXrgy9TBrrGjRVTLuFKG0x71K3LYe3aHLz7\nbhAuXlT2C489TKNHu5UVBvJKJDzP9slVM+wKTZqwoGng+PHAify5mjVhfeopr95j3z41ypXj0a6d\nZ6sHruL2t3HTpk2Ii4tDrVq1sHPnTsExnJ/1BxYLFxMDxk4wrJ88GZq1a71ug1LqhplLl8BFRbl8\n3ZYtGq+VSKh374bqzz9tfa59GAy72+P4qaesuHOHRkKCf/44Ss2sWTq88YYJZcv6V0qFvnLFrnAD\nW7266JWy4cON2LBBg/R05ZbO5M6aBZMLgkq5ubYawJkzDaL6RVufegrGceOgSU8H58YmPW+Qv/Lj\noVJOo0Yspk41YODAEGRmSmScD+HDw0W3Di3IvXsUzp9n0Latb4McqdF+9RVoEV0TKOpRdpggnh07\n1OjVy/etNN369TWbzZg4cSIOHjyIPXv2YNy4cYLj/E0sQyxcxYrI/ewzwXN0cjL44GDXJjQYUEx6\nyQmKqBvmedDXrrm0XNa6dWv89x+Fo0dV6NzZOyUSeSp02du3w2u78+zd141gmGH8v76MevAAzIkT\nbl+fVwN48SKN339XY/RoZWaFHcFcvmw3M8zVqgXm8mVRZUWVKvHo2tWCb79VcHZYowGCxCthLlqk\nQ9OmLFq3Fh8I0XfugCpf3laAqQQ0GmTt3i3JVC+/bEbbthaMHBkcWCqUDvj1VzU6dLBCJ4F+ipw1\nw6pTp6AS2V+5b18ztmzREEVCAejERGjWrCn0mdkM/PabNKsHLtvjzkVHjhxBvXr1ULZsWVSpUgVV\nqlTBvwJ9gAO1TAIMA0uvXoKnxMgLFkU3Zw50S5e6bIbcdcNUWhpA0y6/9Pz8sxrt21u8tkvU3XIF\nj+9btiwsbm4azesq4a8/jMzx49DPnOnxPJ9/rsfo0UZfvsNIBuMgM8yHh4MPDgaVnCxqrtGjjVix\nIjBEOO7epbB8uRaffuraZkg6KUlxYktso0bCNeFu8PnnBty7R2P+fOWr60nBzz9r0L27MsRzPIGN\ni7PfWrUIMTEcatTgsHevQl7ofIHIHzHmwgWof/ut0Gd//aVCbCyHihV9vyro1rf67t27qFChApYt\nW4Yff/wRUVFRuHPnTrFxRjsZ40CGFiEvWBQ+IkL0xgz11q0IbdsWgPx1w/TVq+CqV3fpmvj4eGzd\n6r0SCcC2IiGLJHNwMAxTp4oaqv7pp0K1kPXrswgNBQ4flr8O3B08FdyIj4/HyZMMTpxQYehQ/4wA\ncxYtgrVJE7vn2Vq1RJdK1K1rE+Hw59WCPL7+WocXXjCjShXX3vTomzdxV4o0okLRaIDVq7OxcqUW\ne/b45/deLJmZtmfb009LkyKVs2bYmbx6UQK553BRmGPHENKjh6ixVGoq+MjIQp/t2KFBz57yvDB5\n9Io7fPhw9O3bFwBACWwoGTF7NmbOnImZM2diyZIlhRw4Pj4+II+ptDRwEREuXc9HRiL14kVR4zXb\ntkF19izi4+OhUh3MrxuW49975fffwT4MhsVen5mpwfHjKoSE/Ok1+/iICGRdu6YIf7B3zM6YgX/3\nPxIUOHgwHs2bX8pvuyS3fa4e3z50CIkFCthdvf7MmTN4910Txo83QK+X/9/j8Nhkgr56dcT/+Weh\n83+mpOSXDghdn1S6NOi7d0Xfr127Y/jqKx04TmH/fheO09IorFunQcuWf7l8feKpU8h+WC+slH+P\n1McVK/JYuTIHQ4dq8NNPJz2ez5vHlxYuRJ5cpqvXf/31NdSqdS9/xcdTe86cOSPbfw82Lg7mf/4R\nPf755y3YvZvCrl2HRY1X4vGNKVOQOnSo0/FclSpgEhJEzZ90/Di4h4nD+Ph4HDhwEL/8okaPHhbR\n9sXHx2PmzJkYOXIkRo4cCU+geN71xh8HDx7EzJkzseNhF4H27dtj4cKFaNiwYf6YvXv3oomDLElA\nwnEoFRWF9ORkl+rcVPv2QbdoEbJF9KjVLl+OoIkT8eC//wAATzwRhiVLctCokUw76cxm0dLTALBm\njQYHDqixapX3WiZRt29Ds327pAIQksLzKBUdjYyzZwt1u0hOptCmTRjOn8+QpK7OlwQNHw5r+/Yw\n9+/v1vV//qnC228H4fDhTMWUiDoivF49ZO7aBV5i+emC8DzQoUMoJkwwomtXBRUdZmdDbI3T9Ok6\npKbSmD8/QDTHvcTy5VqsW6fBb79luVKK7TtMJpSKjUX6xYui//YFeeONYLRta8Frr/l/mQRMJpSK\niUH69es27W0RvPpqMLp0seCVV/zz3x/09ttg69aFqUBALAjPo1TVqsg4fRp8qVIOh+o/+ABcpUow\njRoFwFYiMXmyHvv3Z7lt58mTJ9GxY0e3rnUrM/z444/j3LlzuH//Pm7evIlbt24VCoRLLBSF9KtX\nXd7w4Up/WnO3boV2V8tdN+xKIAzA6yUSAMBXrAhz375ek831FOr+ffBqNbRLlxbaUFWpEo/HHvNP\neWZPyiR4Hpg2zaY25A+BMOAb4R2KstUOL1qkrI10YR07gr5wwem4jAwKq1ZpfSan6s8MHWpC3bos\nBgwIwdmzymvFxZw9CzYmxq1A2GQC9u5V4ZlnFPRC5wlaLXJWrHCpx36/fv7dVYI5edKubHIhKAqs\nSFlmqkhJ6Y4dtqywXLgVDGs0GsycORNPPvkkOnbsiAULFkhtl+Khbt9G0MM3mkcfUnCncS4XGSl6\nUwZfujTMzzyTfyx33bArpKZSOH4c6NTJ+w6v3rMHulmzvH4fd6ATE8FVrw7d118DWYXfgvv29c+u\nEmzdumCrVXPr2l9+USM1NRe9e/vPjyVXrZqoB76nPPecBcnJtHJ6lRoMoG/etLtRsCDLltnktGNi\n3N8VWnBpVAmot26F7osvJJ+XooCFC3Px9NMW9O0bgoEDgxUVFKtOnADbtKlb1/75pwp16nAoV066\nTVFy+4Xl2WfhyvJd584WnD3L4NYt5bZLtIvBAObKFbD164sazomUZbY89xysD32K42wbLOWqFwY8\nqBnu168fEhISkJCQgO7du0tpk1/Ah4ZCs3Wr2wpsheaqWBFZf/whbnBwMAyzZ+cfKqXfsBg2btSg\nadO7PlkGpDIyfKo+lwdz+DCYY8ccj7l+HVy1auDKlwedklLoXI8eZhw8qEZysn89NA2zZ4OvVMnl\n67KygA8+0OP1189JtUnfJ3DVq/tEkl2lAt5804RFi5RRN8NcugQ2Ntbp6ldmJrBihRZvvx1gWWGO\nAyMiK+4OWi0wcqQJJ05koGVLq6KCYubECVibNXPr2p07A6OLhCdotUDPnhZs3ux/iQ7m9GmwcXGi\ng382Nha0iK45lu7d89uyHjvGoFQpHjVqyNdOybs/P/7YUVwsoaG2VkkPN8TIhSL6DYsgNZXCwoU6\nfP65FyTnBKAyM32qPpeHOj4e6l27HI5h4+Jg6t8fXLlyoO/dK3QuNBR4910DOncOw6FD/pHx94Tp\n0/Vo3dqKt96qLbcpLsEWUaEM6d4d9LVrXrnXgAEm/P23Cteuyf+2wFy4ALZOHafjvv1Wi3btrB7/\nuMnZT1YITySZxRIUJBwU37kj3wuy6sSJ/CyeK9y7R3lFREFpfiGGfv3M2LhR63fyzMyFC2Bd2P9l\nnDABRhFqmwXZvl2DHj3kfWHy7tNVkTsBpIOLiZFdlhmQqW7YYACM4rM+U6fq0bevGXXr+ubNj8rI\nAO8NrWcniJFsZRs3hrVjR/Dlywu+TI0ZY8KCBTkYPDgYX36p9dvew844coTB9u0afPaZa/1nlYCl\ne3fkfPut7YBloTp1SpQSI/XgAagiqwHOCAkBBg0yYfFi+WuHmYQEcLVqORyTkwMsWaLDO+/439/V\nGVxkJOj7931yr4JBcalSvHz9iFkWli5dnP7dhViwQId+/cyoVMnPIkAv0KKFFbm5tueeP2EeNAi5\nM2aIv8DFJT6eB3buVMtaIgF4OxgWo7vpx7BFZZm9/MrHnDkDzaZNxT6Xo25Ys2ULgkT2kT56lMG+\nfWpMmGDwWa2X5ocfQAv0vvY2eep3YuDKlctvtVWUp5+2Ys+eTOzcqcErrwQrWprXHYxGYMyYYMyY\nkYvSpXnZawBdRq3Of+jTSUm2un8RL/+adeugW7jQ5dsNHWrC5s0aXLokc3Y4JwdsbcdZ/DVrtGje\n3Io6dTx/i1OaX7iy2VkqgoKA9983YPNmTV5nM9/CMDBMn26TynSB5GQKGzdqvFIqozS/EANNAx9/\nbMD48UGw+psitYsb5V3hn38YaLWQ5HnhCfKvu/kxRTPD+kmToMnLFnkB1dGjUB0+XOxzOeqG6WvX\nRAlusCwwYUIQpkwx+FRVzPDRRzC/+KLvbvgQPjJS9DKqpUcPhyINlSvz2LkzCzExHNq1C8XJk/6V\nUXDE3Lk6xMWx6NnTfzbN2YO+ckW0JLkrwhsFKVeOx4wZBvTsGSrrhlnDF1/A4mCPiNFoE9l4770A\nqxV+CF+mDKiMDPg6mqlcmUeTJix27PCfmtN58/R49VUzypcPzKxw0Jtvgrp1y6Vreve2IDKSx7Jl\n8q/yKIW8EgkBqQqfQoJhDzANHAjzgAH5x/S9e+5v2srMtD1kHUAnJYGNjoYqPr7QTnY56oaZa9fy\nBTccsWaNBsHBPF54wbYE4qtaL/OgQTbpVB/DlSkjWgra+uSTYFu2dDhGo7HJtn76qQH9+4dg9Wrl\n/Rgyhw8XUtNzxrlzDNas0eKLL3LzH4D+WAOYB3P5MtiaNUWN5eLiXFKvKkj//mYsX24rn/npJ2X2\noFu/XouGDa1o2FCaN3PF+QXDIDM+XjJJZlcYONCEtWuV9/0X4sYNGlu3qjFmjHdeipTgF3RKissv\nthQFzJmTi/nzdf7ZWUICtMuXQ7tiBQDbYrrcLdXyIMGwB/CVK4OrUiX/WEheUCz6efOgXbXK4Rg6\nKQlclSrQbNwIVZFlIl/XDTMXLjjNhqWlUZg5U18o6Al0uIoVYe7XT/J5e/a04LffsvDZZ3okJirr\na6tbtAjMmTOixlqtwJgxQfjoIwMqVAiMjBFz9aqoVmMAwFWpAio9vVhLPbE89ZQVW7dmYdo0PebO\n1SlqM47ZDCxcqA3YrHAeXFycLMFwly4WXL3K4PJlZX3/hfjiCx2GDDGhTBkFOajEsDVqgLl82eXr\nYmM5DB1qwgcfBPCeKoPBbnJPs3Ej2IfPy/PnGVitwGOPyd8OS/nfKj+CTk3Nlxd0FS4iwunyOn3z\nJrjoaPClShVzNF/WDTPnzoHKygLrRGjl00/16NOn8KY5f6z1comwMBjffdfuaebYMWg2bHBr6urV\nOQwcaFLcEpsrghtLl2oREsLj1VcLb5bwS7/gOCA7G7kzZ8L06qvirmEYsLGxbv2I5lG3Lodd2zq5\nnwAAIABJREFUu7Kwc6caY8cGwSJ/UgUAsGGDBjVrcmjaVLofNr/0CwCq/fsR9M47COnVC/SVK5LM\nqdHYVgfWrVPW978oly/T2L1bjZEjTV67hxL8gqtRw+2/7dixRly4wCheYIm+ccOtkiDtsmXQzZ1b\nfL7ERNA3b8Lapg0AYNs2W1ZYCckyEgxLCJWaCj4iwq1rxWzMoG/eBFelCvjwcFBF2tb5sm6YvnQJ\npjfecLih4sQJBr//rsakSYG3o9wTVIcOgTl3zu3rhwwxYdMmDTIyFPD0eIjYYDgxkcaCBTosWBAY\nKwXqrVsRPGqUbTOdXi/6OkvHjqAMnn0voqJ47NiRhXv3KLz4YojsXSzNZmDePB3GjyffdwAIev99\ncBUrwjh6NLjy5Qudo2/ehOrQIbfmfeUVEzZs0MDso433qgMHoN6yxaVrZs3SY+RIE8LDAzcrDDzM\nDLsZDOt0wOzZuZgwQY+cHIkNk5DQbt1E9QwuCmdHhU69bRssPXrkN1fYsUP+lmp5kGBYKjgOVHo6\n+DJl3Ls8MtJxSy6eh3H8ePDlytmC4SKZYV/WDVt693bYR5BlgfffD8LkycU3zSmh1ktOmMREt5Xa\nAKBiRR6dO1uwZo1CagdzckAZjU5fAnkeePvtIIwbZ0S1asV3DfujX3DVq7sl+W2cPBnWJ5/0+P4h\nIcC6dTmIjWXx3HOhXu80QF++bLe8Y/16DWJjObRsKe3buD/6BXX7NqgHD2B85x1YO3YspkpKJyZC\n/+GHbs1dowaHuDjfSbard+4Effu26PHnzjGIj1dh6FDvlsoowS+4uDiPVnjatbOiRQsr5swR/yLt\nS6jbtwGTCVx0tMvXsrGxgi8Kmi1bYO7VCwCQkEAjM5NCs2byl0gAJBiWDppGenKyU2Ume/AREY4z\nwxQF05AhAE0LBsOAraZsxQr5l9C++04DjQZ48UVlvPEpCToxEVxMTP6xbu5cl5v4v/mmCcuX6xSx\nPE4nJ4OrVAnOUr27d6vx338URozw3tKpr2HzVOhkLNxVqYAvvjCgVi0W770X5FVTgkePhurs2WKf\nG43A3Ll6fPAByQoDgOrvv2Ft1cpuXbG1VSvQt265tOm0IK++asbatb55zrsqtjFzpg5jxhgREuJF\noxQCV6kSsr//3qM5pk0zYN06Dc6fdy8U033xBWDyzjNVdeqUTWzDjWU8rlo10ElJhUosqNRUUEYj\nrE88AeBRVlgpyqMKMcN/0S5eDM3atbYDNwNhwNZzlg8OFjWWrV0bVoEuBO+9Z8Dhwyrs2CFfHVJG\nBoUZM/SYPVt4KVwJtV5yQicmgiuQGVb//LPLP4qPPcaienUW27croN5MpYLp5ZedDlu1SosRI0x2\nW4/7pV+EhYHX60EVURH0NRQFzJ2bi3/+UeG777y0YsDzoO10zVizxtZBQspa4TyU6BfqLVugnzLF\n7nmuShWYBg+2P4FKBcszz0C9Y4db9+/Rw4xTpxjcvOnln2+DwSa//dhjooafOsXg5EkVBg/2/guv\nIvyCpkX/t7FH+fI8Jk0y4L33glwXV8rJgW7+fI/iDkcwp07B2rixexfr9bY++gVaz/GRkcg8fBgs\nGGzZosaqVVo895wCMjoPIcGwp1CURzWgefCVKyN7505RY9mGDWF+/fVin4eEAEuW5GD8+CCkpMhT\nlLlmjQbt2llQv74ylj7kQLVvH5jjx4ufMJtB371bqL5WSJJZDCNHmrB4sfzdBLjq1WFyIr6SlETj\nxAlGcklWJcBVqADGSzLMrhAcDKxZk41p0/T491/pS6Wo1FSAooqVw+Tm2lTGJk0K7A4ShVCpBOsh\n82BbtIC1fXuHU5h79oRm+3a3bq/XAy+8YMb69d4tlWL+/RdsXJzoevgZM/R4912DK+XzBACvvWaG\n2Uzh++9d+3vm79WgaSAzEyG9e0PKzQNiVwUsFuDwYaZYBZW1ZctCq55mM7BuvRYtW4ZhyRId5s3L\nxRNPKEd9hATDHsJVq2ZbKlUIzZuzGDjQhDFjgn0eKFmtwIoVOrz5pv3MgBJqvbyN6u+/of7jj+In\nOA45S5YUepO3J8nsjM6dLcjMpHD4sPJVHteu1aBfP7PDH0l/9Qu+VCnQbohoeIOaNTl88UUuBg+W\nXrGQuXwZXM2axZZMv/lGixYtrGjQwDsvv0r0C65sWY8lma1t24K+ehWU2M1JVitQYNPlq6+asX69\n1qsbplUnTsDarJmosYcPM0hIoPHKK7554VWiX7gLwwDz5uVi2jQ9HjwQ/72lb958lFgJCwNXuTKC\nJk+WzC6+VCmwIjLDs2fr8MYbIahbtxSefjoUU6fqsWePCnfnLAPbrBlycmxdhJo2Dcf//qfB/Pm5\n2LUrC126KCcrDJBg2GPYqlXdrv3yFuPHG5GWRmHVKgnryngeQe+847Cueft2NaKjWTRqVHKzwsBD\nlSqh/046HSwPNw/k4UiS2RE0DYwYYcLixfLXiDvCbAbWrdNi0KDAqRUuSPa2bTAPGuTydfT162CO\nHJHcnl69LOjc2YJRo9xYdnUAnZBQrEQiK8umNjdxYsmqFXZFZdIuajVyv/pKtMyt7vPPofv66/zj\n+vVZlC/PYd8+770MW7p2hWnoUKfjDAZg3LhgfPyxwZuqvQFNw4Ysnn3WglmzdKKvoW/dKqRzkPvZ\nZ1Dt3w/V779LYlPOt9+Cd9Iq9to1GitXarF7dyYSEtLxyScGaLU8Fi7UoW7dUujUKRRNmoTj779V\nWLs2G//7XzZat7YqspsQCYY9hKta1VYobjJ5dSON7rPPREs/qtXA0qU5mDFDJ1mDdub0aaj27QNf\nurTdMUuXOs4KAwqp9fIyYtrk5Y+NinKrTAIA+vc34fBhFa5dU+7X+Oef1ahVi0VcnOPIrCT4RUGY\nc+egF+jDKQWffmrA/fs0vvpKwhcljca2KawAy5bp0K6dBbVrSxh1F0GJfiFJMAzA8swzToON/HtW\nqAD6zp1Cn73yignffee9l2EuNtYmMOKEadP0qFuXRe/evsv0KdEvPGXSJAM2b9bg4kVxz/NCmWEA\nCAtD7qJFCB43DtSDB16y8hE8D0ycGISxY42oVImHXg+0bm3FxIlG7NiRjcuX0zF1qgE7dmRh7doc\nNG6s7CSZcn9F/YWgIPClSyN48GBoV6702m2069Y57OtblJo1OUyaZMSIEcGSdB3Q/PADzP37290h\nfewYg/v3KTzzjLKWPuSAK1PGcZu8AljatIG5Rw+37hMcDEWKcBRk9erAzQp7grVxYzCnTnnlBVqj\nAVatysbixTrJhHjML78M80sv5R+np1NYulSL998vQbXCD+HDw219or20i18IrkIFUEWC4T59zPjr\nLxXu3pUvzfbnnyps26bB3LmB0TvcZUwmhD3+OKRYhomM5PHOO0Z8+KG4rjDWp56CpUuXwp+1bQtz\njx7QT5zosT3O+PVXNZKSaLsdgnQ6m/5BbToB6p9/9ro9nkKCYQnI3L0bUKnAuSm4kQd1/75wRvGh\ntCFfoHm75ocfnEq6vv66TQ5z9mzxSy+CmEzQbN5c6MewKEuX6jBsmMlpvB5ItV724CMjQf33n6ix\nXFwcrO3auX2vPBEOqWtERcFx0C5dajegS0igkZDAoHt35y9IJcEvCsJXrAio1bZVJS9QuTKPr7/O\nwbBhwV7ZTPv111o884wFsbHeywoDCvULikLGiRPFdvFTKSkIGjnSK7fkKlQAnZJS6LPQUODZZy3Y\nsEGe2oSMDAqjRwdh4cIclC7t2w0qivELrRZUbq5bwhRCDBliwq1bNgU/Z1jbthXsZmGYPBmW55+X\nxB575OYCkybp8cUXuU5LYzTffw/VsWNetUcKSDAsAXzlyqAePAAfGenRPLovv4Rm/fpin+cvhxTI\nyurmzSv2cCwKRQGLFuVg7Votjh51f4e5etcusHXrgqtaVfD8rVsU9u9XYcAAkgEEAC46GmYR7cak\noEIFHl27WrB2re9/EKnUVOjmzbPbh3L1ai0GDDCROkI7WBs3BnPypNfm79jRiiFDTOjQIQwrVmgl\nUy3L248wfnzJywrnwRd5HgOA6uDBYsqgnkClpEA3cyaAh8FwkcwwYFsZ+u47raT14WKZOFGPzp0t\n6NRJOR0B5ICtWdMmSCMBajUwfXouPvxQ7/73NSgIlmeekcQee8yfr8Pjj7No29bx356+cAHa1avz\nhTaUDAmGJYK+f9/jzLA9FTo6KamY3K094Y2iREXxmD07F2++GQx3FWA1O3Y4zAqvWKFD//7mYmpz\nQgRirVdR+DJlYBo2rPCHHIfgV16BN7Z/yyXC4UiG2WAANm3SYOBAcU/0kuAXRWEbN4bq1Cmv3uPt\nt43YsCEbv/+uRvPmYfjhB43HLvjllzr06mVGdLT3IzB/8gv1wYPuKQvyvOBzQbd4Maj0dNuQcuUE\nxzVrxiI8nMeWLb7tOb59uxrHj6swdao8myeV5BdsjRoeKdEVpVMnK2rUYGUrf6Nu3XK4Ce/qVRrf\nfqvFp586l7wM7d0bdHo62IYNpTTRK5BgWCKotDTRmyHsYU+Fjr51q5gkIh8WJioYBoAePSyoXp3D\n5s3upehyFi+GuXdvwXPZ2TYp1uHDSVbYEdTt21CdPOlS3bdYGjZkERvLYts23/4g0rdu2dTnBNi6\nVYOmTVmfBEz+iqVzZ1h98CPRsCGLTZuysWRJLr77ToMnnwzDjh1qt8qV796lsG6dBu+8U3KzwvZQ\nHTwIqxvL9/oJE6ApomRGPXgAzfr1MI4e/XByFTIuXiz2/KAoYOpUA6ZN08Mo1Z+EZRH25JOwp++d\nkkLh/feDsHhxDkTqRAU0XM2aoAWkhz1h2jQDFi7U4d49xyVOmZnA6dMM9uxR4fvvNViwQItJk/QY\nMiQYw4cHuVXWrt6zB5otWwTP8TwwYUIQxo0zomJF5w8Qa5MmMD/7rFsqdr6GBMNSwHGgTCbwZcp4\nNA1vJzNsbdPGJsVccGx4eH7WQAzDhhmxYoXWvf06arXdFkAbNmjRqpUVVauKC3oUU+vlY5jr18EW\nkGGWmqFDTT6TaM3DUTC8apUWr78u/klcEv2CbdgQlhde8Nn9nnjCip9/zsa0abmYM0eHTp1CceaM\n85cz5tQp0Fev4tYtCn36hGDYMJOoH0Ip8Be/oO7eBXX/Pti6dV2+1vrEE8UEOLQrVti6TdhZeSlI\n69ZW1KvHYvlyab7/9KVLts2BQUHFzvE8MHZsMF591YTHH5evO4CS/ELqzDBg2wDfv78Z06cLN2fP\nzQXmzdOhceNwjBoVhCVLdPjrLxUePKBRuTKHrl3NSE6msWmT6wmwfBlmAX7+WY3kZFp08itn3Trk\nrFnjsg1yQIJhKaBppN+44XHWj7OTGeZiY8E2aFDoMz483KX6tI4drcjNpXDkiHSZSY4Dli3TOm2n\nRgDoa9cKyTAXRLt0KZizZz2av1MnC86cYXyqPGivTOL0aQYpKTQ6dSKdRZQGRQFPP23F/v1ZeOMN\nE3r3DsG6dY5/MLVLluDs5kR06RKGl14yl8gOEs5QHTwI6xNPuPUbYHn6aaiOHHmU3MjOhnbFChjH\njhU9x5QpBixapENamufff0fKY2vWaHDvHkV8oADWNm2QXSSzLwXjxxuxa5e6kKIkywLff69Bi0Y6\nnP3lNn7/PQt//ZWFzZttKz9TpxowapQJL7xgwYTxufjqS9eFWZiTJwVlmHNygA8+0GP27FzxCtAU\n5RdZYYAEw9IhwR+cj4oqJndqD0uHDuBq1BA9N03bdqouX+5hZ4kC/P67GiEhPFq2FL+BQkm1Xr6E\nvn4dnJ3MsOrECTDnz3s0v04HdO1qwfbtvtutZm3RQrBGcvVqLV57zXlnkYKUVL+QC5oGXn7ZjB07\nsrBokQ6jRwfZWxXHbyei8NyS5zBzZi5GjTL59LdNqX6h3rIF+gkT8o8t3bsj192+0SEhsLRtC/Vv\nv9nm/vNPWFu3tin+iaRmTQ69e5s97xwE2/OIFVCeu3KFxvTpeixZkiM+GPISivILjUYwi+4p4eE8\nJk0yYNIkPXge2L9fhfbtQ7FmjRbfdV+LH9osQvXq9ldkO/01DeG5d/DLLy78sXJywFy7BrZ+/WKn\n5s/XoWVLK1q3DswNkyQYVhBclSrI3rhR1FhLz56wtmnj0vwvvWTCH3+okJwsza/ZkiW2rLCfvPj5\nFPXOnWCOH88/ZhITwdrJDHMuSDLTiYl2+5v26mXGli2+C4Ytzz1XTK4zMxPYulWNV14hqwX+QO3a\nHPbuzYTRSKFLl1BcvVr4J2HFcg3evP4Bflidhh49SKY/H72+sPKoVgs+Ksrt6Sw9e0L9sFTC0q0b\nclascHmO8eON+OknDa5c8exnXXX0aLHMsMEADB4cjA8+MHhVZIVQmFdeMSM7m0L79qEYPz4I771n\nxG+/ZaEV/zfYAupzglSIwvg627BwoU50eSRz5gzY2rUBbeGSm6NHGaxdq5Vtw6QvIMFwCSIsDHjh\nBTNWrxZXW8YcPlys0Xse584xuHyZwfPPu9b/RUm1Xt5EdegQVIcO5R8bxo+320/YFUnm4EGDwFy4\nIHiuXTsrEhJo3Lol39vJTz9p0LatFVFRrtWUlhS/UCIhIcCKFTkYNMiMrl1DsWOHGixrWxJduYzB\nnxHPo9lT0q0ouYJS/cJe5x93MXftait7y+uRphIQSzGZQDlQq4yM5DFmjBFTpgjXmYqBSk0FlZZW\nrH/txIlBqFOHxaBBEvXn8xCl+oXUMAzw9de5eO01E/7+OxM9e1pAUQLqcwJwUVHoqfkVWVkU4uPF\nie/wpUvD+NZbhT5LS6MwZEgwFi7MRYUKvu0n7UtIMFzCGDLEttFKzM5j/cyZYC5eFDz31Ve2DVKk\nh6wwfEQE6ALCG1zdunb7UPPlyzv8kSsIFxNjyw4LoNEA3bpZsG2b+D8KdesW6Js3RY93aBsHrFyp\nw+DBJCssGp5H0LvvQrImwG5CUcAbb5iwYUM2PvpIj6eeCsXZswx+n/I7qtZRrsKhXPCRkaDu35du\nwrAwZO/caVfhE7C9YAcPHepwmmHDTDhzhnFbeZCPjETGP/8Uqn3esEGDw4dVmDevhKrMyUyDBiwG\nDzYX+q111NYyD65CBahSbuOtt4xYsEDcyyxXq1YhwQ6OA958MxjPP28JeHVZEgwrHOboUeg+/1yy\n+eLiONSvz2LrVucBE33nDrgiS38cB3z8sR6nTqlc6haQh6JqvbwIFxEBSmTmiCtfXnRmmKtWDcz1\n63bPu1oqofnpJ2i//FL0eEfs3KmGWs07bcQuREnxi2JQFFSHD3tcMy4VTZuy2L8/CwMHmvHjj9ko\nVUEHsw87XhRFqX7BRUaCFlIL9eY97QhvFESnAyZPNuDjj/XuC3HoH2WWL1yg8fHHenz7bTZCQtyc\nzwso0i98Jc/N87Zg2EmZBBcVBTolBX37mnHxIlNoI55Y5s/XITsb+PjjwC2PyIMEwwqHOX/eqdKc\nqwwbZsLy5c7brNF37thkYx9iNgMjRgTh2DEVfv01y+cSnP6EK5LMbP36j/qJOiDsiSfAh4fbzQwD\nQNu2ViQl0bhxQ9xX29KtGzS//GJXUlksLAvMmKHHhx8aSPbIRayNG4PxsviGK5Qpw2PYMBO0WoBt\n1gzmV1+V2yTlERxs+87k5LjU4tIT8oNhJ9/V3r0toGlbyZInZGcDgweH4NNPDahbl9QJO4I5fRqh\nTz/tm5txHHIWLrTpcTuAL1cOMJuhVbF4800jvvzStVKnv/5S4ZtvtPjmG/k3TPoCEgwrDOrWrUJL\n5vTNm8UENwAAmZnQfPedW/fo1MmC9HQKx445eFPMygI4DvxDWbnMTODFF0NgMFDYssX9QLik1Hpx\nERGiawr5yEhYnTxIqbQ0UHfuwNqkCWgHmWGVCnj2WQu2bhX39OLi4sAHB4P55x9R4/Ngjh7N3/0O\nAP/7nwbh4bzb0qwlxS+EsDZpYhNkIRRDsX5BUcg4exZUTg7CmjSBT/SQw8Js9SxZWc5Mw2ef5WLa\nNL3bqqM8D7z7bhAef9yKl15SRp1wQZTmF2y1amCuXfONHzCMuP7kKhUyrlwBGAavvWbCgQMqXLsm\nLuRLSaEwfHgwFi/O8VlPcbkhwbDC0C1eDM2mTfnHTFKSYDBMGQzQf/aZW/dgGFvt8IoV9t8U6ZQU\nW4kEReHuXQo9eoSienUOq1fnFFxFI9iBi42FaeBAyeZjLl0CV6sW2NhY8KVKORwrtlSCTkgAc+IE\nLN26Qf3LLy7Zo/7jDzAnTgAALBZg1iwdyQq7CethZli7ciU0a9dKaBFBDHzp0lAdOgRrixYOa32l\nhIuKAn37ttNxLVuyaNLEigULxHcSKMjatRqcO8dg1iznkrsEAKGhtlW75GS5LREkNBQYPNiEr75y\nnh22WoGhQ4MxcKAJ7dsHZhs1IUgwrDD4IrVodFKSYG0QHx5uk2N2c3l7wAAz9uxR2RdpoGmY+/TB\nlSs0unYNRY8eFsyZk+uxmrAia728AF+2LMwDBgAA9FOnOtR6FwN98SLY2rXBV66MHCeBT6tWVty9\nSxdrk1UU9W+/QbN1K8zPPGMrlXDFngLqcxs2aFC5Moc2bdx/cJYUvxCCrVfPVgeek+PW9eodO8CX\nLy+tUQpB6X6hOngQ1latfHY/tmFDUNnZosZ++qkBW7dq0Lt3CM6edf7gVv31F8BxOHOGwfTpenz7\nbY432udKghL9gq1RA7TESnRSMmyYCVu2qHH3rvBvPn3lCrRLl2LmTB1UKlurvpIECYYVRtGNV/St\nW8L9BHU623qYm+tg4eE8eve22G2zZomJxZZGk9GjRyjeftuI994zkqyfmzBHjsDTdDpz6RLYWrXE\njWWAnj2dZ4fp1FRwkZG2utBu3WwpAZHQycngKlWCyQTMnq3DpEmBv8HCa2g0yP7hB/cULHNyoDp5\nEhYB8ROC91HHx8PqwyX7nG++ERTEEKJqVQ7x8Zno3t2CPn1C8NZbQbhzR/ghTl2+gvOvL8FHk4Pw\nwgshmDEjFzVrkjphV2Br1gRz5YrcZtilbFkeffuasWyZ8G++6cQFrNsYjA0btFi+PMfjxJe/QYJh\nhcFHRhaSZM5etQp8hQrCY0uVsmWH3WTIECPWrNEW6up09SqNadN0aNgwHHPn6rBoUQ4GDpSuZkxp\ntV6+gLl+Hawd9TnRcyQkiA6GAeD55y1Og2EqLc2meMgwMH74oXBvUzvktfb57jst6tTh0KKFi5qf\nRSiJflEQa5s2thdcF1EdPAhro0Zwa6u/k1Ul5sQJqPbudX1eCVGyX1CpqaBu3wbboIHcpthFrbaV\nxB07loGICB6tW4dh1ixd/iLEhQs0pk/XoekzsRhg/hZBQcD27Vno00fZbbSU6Bdc7dqiOwjJxahR\nJqxZo0Vmpu345k0aK1dq8eKLIagx7kWsu98Vq1dno2zZklEnXBD3mhESvEbRjVdsixZ2x/JhYaAy\nMuwGy86oU4dD7dosvv9eA5XKpnl+9SqDvn3N+PHHLLKDWAoe7jYv2JVDCM0PP4AvXRqWrl0Fz2cX\nqCMXQ4sWVqSnU7h4kbarGEWnpoqW/y4Ez4NOTkZ2mcqYP1+H9evFLdsSpEe9bx+s7dsDAOhLl6Dd\nsAGGTz5xeh194waCBw1C1t69dutd1b/9BqhUsHbsKKnNgQJ96xYsvXu79BIpF2FhwJQpBrz+ugmf\nfqpH8+bhKF2aQ3o6jd69zfg+ZiLqjmsL67Pd5TbVbzENGeKT++gnToRp1CinrdUAABYLqKws8GXK\nALCtFnTsaMGgQSG4e5fG/fsUOnWyoH9/E9ZW/AhhNcvC1Gykl/8FyoRkhhUGX7Gi02baeZheew28\nh80fR4wwYfz4IPz6qxqjRplw9mwGPvvMe610lFjr5U3oGzdsDy0nG2zoGzfAOOoooFbDlf42NA08\n95zjUgkqLQ2cO8Ewy8Lw0UdY9WMkmja1olEjz7LCQMnzC6lQHTwIS4cOAGytt7SrVolq6af96itY\n2rd36JdMQgLYmjUls9UdlOwXbKNGyJ03T24zXCI6msM33+Rg/fpszJmTi9OnM/Dp+HtonvADrE+1\nlds80SjZL7yNZvNm8FpxQjiqAweKCbVMmmREy5ZWLFyYgwsXMrB4cS569bKgTOoV0bFHIKL8V9oS\nBhcdjZxVq0SNNY30/A2uSxcLEhPTFdVQPVDQbNoEOiEBbLVqTsdyUVFQie0okJkJ5uJFsM2bOxzW\nq5cZo0cHY+JE4Xpvy1NPicsuFEWlQuqAEVjUTIetWx23eSJ4l6zdu4G8H8awMFg6dYJ62zaYBw+2\new117x40mzcj8/Bhh3Mzly+Di4uT0lyCQij4Aqs+cADWpk2d9q0lKICcHFA5OXbVTIvCV6hQTKeg\nWjUO779ffHOcGFW7QIZkhgmCgbBm40a3N+c5Qom1Xt5CdeQI+PBwUdkjvlw50ZLMdHIygovoxwvR\nrBkLoxE4d674Toi7dym8nfs5olvWwQsvhOC77zT47z/xOySXL9ehXTsL6tSRZgWhJPmFpOj1hbK7\n5n79oHVSUqNdtgzmPn1sTfntYbWCvn4dbPXqUlnqFsQvisCyoCVWK+TLlIFp+HBJ5/Q2JdUv8jYu\ni23lx0VFgRIp2mUcMwZsjRqemOfXkGCYUByOQ9CYMSDtIzyDi4gAlZvrtF4YcFGSOSYGdFKSTfbN\nARSVt5HuUXnFf/9RmDJFj1atbGIqBw5kYsAAE/buVaNx4zC8WP0yvlsJh4FxejqFpUu1gtkFgvto\nV6yA9uuvPZrD0qED6CtX7AuzZGZCu2YNTEUUD+lLlwr1OqaTksCVKwfF9tYqqfA8wtq3d6nzizOs\nrVrZ3atAUBb0zZsuZW/5MmVA5eQARufPakuvXrbi8hIKCYYVTNCwYZJnAcRApaWBDw11a3e7M0pS\nrRcfEVGoM4gjHAXDxfpJ6/W2h9ydO07n7dXLjK1bNcjIoDBjhg7Nm4chK4vCn39mYsbr1EO1AAAg\nAElEQVQMA2JiOPTqZcHq1Tk4fz4Dg6J+xv4fM9G4cTjatw9F586h6No1FN27h6BnzxD06hWCHj1C\n8MwzFsTGSldXXpL8wh5cZCRUhw55NolaDXOvXnZFVOiUFJiGDwdXtWqhz5mEBASPGAGYTAAAPijI\n1mFEZohfFEGlsj1XRL44ByqK9YusLFBeFN5wNRgGRdl+W0Rmh0sypGZYwagPHoRh8mSf35e+c8em\nPkfwCC4yEqqjR0WN5cuXt1tOEdayJTJ//x18gYcgGxMDJjERVicPxsces2WPGzUKQ7duFuzdm4Wq\nVYWD2OBg4PnX9Ohz5gPc++krXLrEgGVtCqMsS4HjAO6/DLCh4WjRouQoE/kKtkkTqD76yON5DJ98\nYjejy8XFwTh+fLHPLc8+C82GDdAtWADjhAngo6Jg7tvXY1sI0sNFRYG+cwfsQ9EbgnLQ/Por1Lt2\nIWflSq/Mb+nUCdaWLV26hq1XD1ReLzWCXUgwrEDoa9cAhrFlaB0EpfT582CSkiRf4qJSUtxu1+aM\nklTrxZcpIzozDLUali5din1MPXhg2zBR5IePi4kBnZgItGnjcFqKApYty0F4OC+qib6lWzfo5sxB\nyEIWTZsWPsecPo2QIX2RuXcv+GBpN1qUJL+wBxcdDZhMoG7fdlpaQ1+6BK5CBeFlzeBg129OUcid\nNQth7drB3KuXYjbOEb8oDlehgi0YltsQGVGqX7A1akD71Vdem5+vXBmudgDO+f57r9gSaJAyCQWi\nXb4c2iVLbD92DnpYMpcuQfPDD5Lfn759m2SGJYCtUwcmB7v6xUBfugQ2Lq5Y/bb1qafAlyolao5m\nzdhigTB98SJUf/9dbCxXpQq4ChWKZbTpq1cR0r8/cufMKZShJkgIRYFt3FhUV5Hgt94S331EJHzl\nyjC+9x6C3nnHthxAUCR5wTBBebA1aoC5do18f/wQEgwrED4iAqqTJ522veJLlfLK8gcXEwNL586S\nzwsouNbLC/BRUbA895xHczAXLwoqz5n79YOlZ0+351Xv3w/19u2C5yzdukH155/5x9SdOwjp0weG\niRNh6dHD7Xs6oiT5hSMsHTpAdeCAwzFUejqYixdhdSDI4y6moUMBhgF96ZLkc7sD8YvisPXrg9c4\nVpcUg/rnnz3esCkXivWLsDCbGNbt23Jb4hLapUvBOGm1GOiQMgkFwkVGgjl5EuYXX3Q4jg8P90iO\n2R7Wdu0kn5PgHsylS2Br15Z83nwpZgGMb78NPPyxpdLTEfrCCzANGgTzwIGS20EojGnIEKcyyaoD\nB2x1g2I3uPI8kJ0tro8swyB761bSSUbBmAcNkmQe9bZtsLZqJclchEewNWuCSUhwup9DSah37ZJd\nYEduSGZYgfAREbC2aeN085y3gmFvotRaL6VC5eaCrVtX8nnptDRw9hq3a7X5wRCVmgpz794wjR0r\nuQ0FIX7xELU6/0XE7pB9+/JV5xxBPXgA9c8/Q717N0Jeflm8DQoKhIlfeAmWtfnR00/LbYlbKNkv\nrE8+CcpsltsMl6CTk0u04AZAMsOKhI+MBGU0gi9f3vG48HBQ6ek+sorgbdS7doG+fr1QA/zchQu9\nci9HmeGCcDVqwPjuu16xgeAGPA/V/v0wjhrlfCzLImjUKHCxsTBKoFZJCByY48fBVaxYbGMuwXOM\n77/vlXmZU6eg2bABhlmzXLvQagV94wa42Fjh8zxvU58r4b7gcmY4OTkZrVu3Rv369dG0aVPs2bPH\nG3aVaLiKFcHac9wC8OHhML3+ug8skg7F1nopgexsqI4c8cmtqNRU0ZKevoD4hUgMBli6dwcnYkmT\nj4yEtWVLUOnpHteuywXxC++g3rPHb7PCQMn0C+byZdBiuxMVJDcXYe3a2S2/otLSwOv1wlK0JQiX\nM8NqtRpLlixBgwYNkJSUhFatWuHWrVvesK3EwsXEIFdMexa1WhGN8QnS4IokMwAwR4+CDw0FV6eO\ny/eyPv002CLCCwQFkplp6yiT1zc4KAiGGTNEX26cNAlUdrbDrjSEkof6wAEYpkyR2wyCC9C3bjnd\nVC9I3l6BrCzBVoykRMKGy0/IcuXKodxDTfvo6GiYzWZYLBao1WonVxL8Aeq//6D+5ReYX3nFK/Mr\nudZLblyRZAYA9W+/AUFBMLoRDBvfftvla7wJ8Qth9J99Buh0MHz6qVvXs489JrFFvoX4hTDM6dNg\nY2Lcls/N+t//vKIw6itKol/QN2/C2qCB6xdSVH47Pk7AX7joaBhmzpTAQv/Gow10u3btQtOmTUkg\nHEDQV65Au2aN3GaUSHgXg+F84Q1CwGJ8/31oNm4E888/cptCUBD6jz7yrM90SAhZLfAzXJZiLgAX\nFWVXkpkvXRrWJ57wxLSAwGEwvGDBAjRo0KDQ/yY/7HCQkpKC9957D4sXL/aJoQTfQN+5YxP78BIl\nsdZLLHxYGGC1Ajk5AADmzBnAYLA7nqtWDfT16z6yzrsQvxCGj4yEYepUBI0dC1gscpvjc4hfCFPS\nhTf8wS9Ue/ZAJXZPlQiRDm8FwwQbDl8Nx40bh3HjxhX73Gg0om/fvpg7dy6qVatm9/qRI0ciOjoa\nABAeHo4GDRrkL2/kOTM59s1x6TJlsPvbb/H4w4009sZ3TEkBV6GC1+zJQ+7/Hko9brd5M6BWIz4+\nHp0GDwa/dy+46GjB8frUVHR4GAwrxX53j8+cOaMoe5R0bH7xReQuX47777+PCvPny26PL4/zUIo9\nSjm+ybKwHDqEqP79FWEPeV4UP6547BganjyJ7E6dHI6nUlOhat8efyxahCcf9vgXGh8ydiwaPdxY\n76o9V4ODYUpIQAygmP8+Uhzn/f+kpCQAwJAhQ+AuFM876fBeBJ7n8fLLL6Nt27Z488037Y7bu3cv\nmjRp4rZhBHGod+0CFxXluDbQYkHp8uWRtWkTrJ06OZxPP2UKuFKlYBJ4CSL4kMxMlKpXD+k3bgC0\nnQUclkWpKlWQfvUqoNf71j6CT6Fv3EB448ZIv3QJfNmycptDkBntsmWgr16F4Ysv5DaFYI+cHJSq\nWxcZJ086bGOpmzMH9M2bj9po8ryien37EydPnkTHjh3dutblmuGDBw9i8+bNWL58ORo3bozGjRsj\nhaTfZUO1bx9UzmQU1WoYhw8Hc/680/molBTwUVESWUdwF+bSJbBxcfYDYQBgGBjHjAFlNLo0N33h\nAkQv3xEUAVe1KtIvXyaBMAHAwzIJN3536evXbV0FCN4nOBiWjh2h3rHD/hizGdpVq2B82FueunMH\noU8/bSuXI/gUl4Ph1q1bw2w249SpU/n/iyLBk2zwYWGiVOjY+vXBnDvndJy1QwdYGzeWwjRBii5/\nEoRhLl4EW6uW03HGiRPBly7t0tyqQ4eg+eUXd03zCsQvnCNGJCXQIH4hDFujBriHJYiuEDR+PNT7\n93vBIt/iL35h7tULmq1b7Z7XbN0KtlYtcA9VRvkKFcBrtVBv2+YjA80IeeEFpxLwJQEix+zniFWh\nY+vXh+rsWafjzP36gRMRhBG8C3PpEtjatb0yN52aCq4EBlYEQqDA1a0Lw2efuXaR0QjVkSOwtm3r\nHaMIxbB06gTm339BCXUJ4nloly6FacSIQh8bx42Dbv58nwSo9J07oC9fJmUZIMGw38OHh4vLDNeu\njZx583xgkWPyCuAJjuEjIsA2a+aVuam0NEWpzwHELwjCEL+QDtWRI2Dr1AFfqpTcpniM3/iFXo+s\n3buFn7dZWWDr1CmmBGjt1AlgGKh37/a6eUSG+REkGPZz+FKlQGVmOh+o1YJt0cL7BhE8gjl5EvqJ\nE2F8+21YW7Xyyj3o1FRwCguGCQSCd1Hv2wdL+/Zym1Hi4GrWBBim+ImwMOR+/XXxfSEUBePYsYWy\nw0HjxkF14IBHdgi16qRv3SLqcw8hwbCfw9atC0uPHg7HqP74AzCbfWOQE/yl1ks2aBqqQ4e8egsq\nLQ18mTJevYerEL8gCEH8QjpU+/cHTDAc6H5hee45sDVrPuo5f/o0+JAQj+YMevNNMFeuFPqMBMOP\nIMGwn8PFxsLcr5/9AWYzQh72oiQoH658edD37om/gOehmz0bYFnRl1i6dbM9aAkEQsnAagXbqBHY\npk3ltoQgBoZB7qJFNqVAPBTcqFLFoyn5qChQRTqQkGD4ESQYDnDomzfBRUUBGo3Tsczx41B7ucuA\n39R6yQRftiyotDTxwS1FQbtmDejkZNH3MA0bBl5hD0DiFwQhiF/Yh750CXRCgrjBKhVyv/wyYCSY\nS5Rf5OSAysnxeJ8HFxVVTLXQOGYMLM8+69G8gQIJhgMcOjERnAOVwIKo4uOhOnLEyxYRHKJSgS9d\nGlRqquhL2GrVQCcmetEoAoGgNDTbt0OzcaPcZhBEQiUng/rvP1HSywWhk5Ntm9wc9ZwXgZCEN1et\nGvhy5TyaN1AgwXCAw1y/XigYDunWDdStW4Jj6ZQUWxbZiwR6rZcUUKmpYK5dEz2ei4nx+2CY+AVB\nCOIX9hEKbkoK/ugX+tmzoVm3DqEdOoB24flO37wpSSmDu0ItJQUSDAc4dGIi2JiYRx/odFDZEd+g\nb98GV6GCbwwj2CXr119dEj7hqlUD4+fBMIFAcI2SHAz7I+ZevaCfOxfgedGrtQBgbdMGOStWeHx/\nrmZNcETB0i4kGA4AtEuW2OpMBeCiowv1q2Xr1wdjR3zDF5nhElXr5SZs8+aATid+fABkholfEIQg\nfmGfkhwM+6NfWJ98ErxeD9Pw4a6JXGg0kvSFt7ZpA+MHH3g8T6BCguEAQPPDD6Bv3xY8Zxo+vFC/\nWofB8J074CtW9IqNBO/BPv44zM8/L2osffEi1Dt2eNkiAoHgbfiKFUUFw7qZM0EnJfnAIoJDVCpk\n7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- "text": [ - "" - ] - } - ], - "prompt_number": 34 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###### Discussion\n", - "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", - "\n", - "Very shortly after practioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Summary" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This information in this chapter takes some time to assimulate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", - "\n", - "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 34 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "author notes:\n", - " clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end.\n", - " \n", - " " - ] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "", + "signature": "sha256:7ef35bb11ab92ac993eeaa45ddc2bd139cb3a3842240266d90d82e6a0812daff" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Kalman Filters" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", + "import book_format\n", + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Installed secnum.py. To use it, type:\n", + " %load_ext secnum\n" + ] + }, + { + "javascript": [ + "console.log(\"Section numbering...\");\n", + "\n", + "function number_sections(threshold) {\n", + "\n", + " var h1_number = 0;\n", + " var h2_number = 0;\n", + "\n", + " if (threshold === undefined) {\n", + " threshold = 2; // does nothing so far\n", + " }\n", + "\n", + " var cells = IPython.notebook.get_cells();\n", + " \n", + " for (var i=0; i < cells.length; i++) {\n", + "\n", + " var cell = cells[i];\n", + " if (cell.cell_type !== 'heading') continue;\n", + " \n", + " var level = cell.level;\n", + " if (level > threshold) continue;\n", + " \n", + " if (level === 1) {\n", + " \n", + " h1_number ++;\n", + " var h1_element = cell.element.find('h1');\n", + " var h1_html = h1_element.html();\n", + " \n", + " console.log(\"h1_html: \" + h1_html);\n", + "\n", + " var patt = /^[0-9]+\\.\\s(.*)/; // section number at start of string\n", + " var title = h1_html.match(patt); // just the title\n", + "\n", + " if (title != null) { \n", + " h1_element.html(h1_number + \". \" + title[1]);\n", + " }\n", + " else {\n", + " h1_element.html(h1_number + \". \" + h1_html);\n", + " }\n", + " \n", + " h2_number = 0;\n", + " \n", + " }\n", + " \n", + " if (level === 2) {\n", + " \n", + " h2_number ++;\n", + " \n", + " var h2_element = cell.element.find('h2');\n", + " var h2_html = h2_element.html();\n", + "\n", + " console.log(\"h2_html: \" + h2_html);\n", + "\n", + " \n", + " var patt = /^[0-9]+\\.[0-9]+\\.\\s/;\n", + " var result = h2_html.match(patt);\n", + "\n", + " if (result != null) {\n", + " h2_html = h2_html.replace(result, \"\");\n", + " }\n", + "\n", + " h2_element.html(h1_number + \".\" + h2_number + \". \" + h2_html);\n", + " \n", + " }\n", + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" + ], + "metadata": {}, + "output_type": "display_data" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "One Dimensional Kalman Filters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now that we understand the histogram filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the histogram filter - rather than going into the theory we will just develop the code step by step. But first, let's set the book style." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking A Dog" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As in the histogram chapter we will be tracking a dog in a long hallway at work. However, in our latest hackathon someone created an RFID tracker that provides a reasonable accurate position for our dog. Suppose the hallway is 100m long. The sensor returns the distance of the dog from the left end of the hallway. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", + "\n", + "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is reasonably accurate, and while it had errors, the errors are small. Futhermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23m would be equally likely to be measured as 22.9 as 23.1.\n", + "\n", + "Implementing and/or robustly modelling an RFID system is beyond the scope of this book, so we will write a very simple model. We will start with a simulation of the dog moving from left to right at a constant speed with some random noise added. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import print_function, division\n", + "\n", + "import numpy.random as random\n", + "import math\n", + "\n", + "class DogSensor(object):\n", + " \n", + " def __init__(self, x0=0, velocity=1, noise=0.0):\n", + " \"\"\" x0 - initial position\n", + " velocity - (+=right, -=left)\n", + " noise - scaling factor for noise, 0== no noise\n", + " \"\"\"\n", + " self.x = x0\n", + " self.velocity = velocity\n", + " self.noise = math.sqrt(noise)\n", + "\n", + " def sense(self):\n", + " self.x = self.x + self.velocity\n", + " return self.x + random.randn() * self.noise\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The constructor $\\verb,__init()__,$ initializes the DogSensor class with an initial position (x0), velocity (vel), and an noise scaling factor. The $\\verb,sense(),$ function has the dog move by the set velocity and returns its new position, with noise added. If you look at the code for $\\verb,sense(),$ you will see a call to $\\verb,numpy.random.randn(),$. This returns a number sampled from a normal distribution with a mean of 0.0. Let's look at some example output for that.\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "for i in range(20):\n", + " print(\"%.4f\" % random.randn(),end='\\t')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "-0.8025\t0.4440\t1.6176\t-0.7325\t0.0304\t0.3592\t-0.1916\t1.3645\t0.2563\t-0.4732\t-0.3872\t0.2693\t0.4122\t0.1272\t0.7263\t-0.5945\t0.4633\t-1.5166\t0.5133\t1.1987\t" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You should see a sequence of numbers near 0, some negative and some positive. Most are probably between -1 and 1, but a few might lie somewhat outside that range. This is what we expect from a normal distribution - values are clustered around the mean, and there are fewer values the further you get from the mean.\n", + "\n", + "Okay, so lets look at the output of the $\\verb,DogSensor,$ class. We will start by setting the noise to 0 to check that the class does what we think it does" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib.pyplot as plt\n", + "import matplotlib.pylab as pylab\n", + "\n", + "dog = DogSensor (noise=0.0)\n", + "xs = []\n", + "for i in range(10):\n", + " x = dog.sense()\n", + " xs.append(x)\n", + " print(\"%.4f\" % x, end=' '),\n", + "plt.plot(xs)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see. If you thought the correct answer should have been 0..9 recall that *sense()* returns the dog's position *after* updating his position, so the first postion is 0.0 + 1, or 1.0.\n", + "\n", + "Now let's inject some noise in the signal." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def test_sensor(noise_scale):\n", + " dog = DogSensor(noise=noise_scale)\n", + "\n", + " xs = []\n", + " for i in range(100):\n", + " x = dog.sense()\n", + " xs.append(x)\n", + " p1, = plt.plot(xs, c='b')\n", + " p2, = plt.plot([0,99],[1,100], 'r--')\n", + " plt.xlabel('time')\n", + " plt.ylabel('pos')\n", + " plt.ylim([0,100])\n", + " plt.title('noise = ' + str(noise_scale))\n", + " plt.legend([p1, p2], ['sensor', 'actual'], loc=2)\n", + " plt.show()\n", + " \n", + "test_sensor(4.0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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KaSxeHMCdd57LtlNDQnB268aURp9y/FAw1pCzvhqu+AmfJtrh4eEEBASQlJSE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\n8O677zJy5Eg+//xzAHJzc5WLeu7QoUPExMTwzDPPkJeXR2pqKgkJCcp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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "> **Note**: numpy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use $\\verb,numpy.random.seed(some_value),$ to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", + "\n", + "So the output of the sensor should be a wavering blue line drawn over a dotted red line. The dotted red line shows the actual position of the dog, and the blue line is the noise signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", + "\n", + "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing Ctrl+Enter. Each time it runs you should see a different jagged blue line wavering over the top of the dotted red line.\n", + "\n", + "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show two extreme examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "test_sensor(100.0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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qxAm0Pf442hcvlt0D+7XXwvHKK+EoLr6E6GiPvx07b78dhpISFq+80oonnuiF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1LrZvzyIgAFJTLRw8aOXgwQAOHgxgbXIscXGFJCVlULmyz+3rIGWEdh0RERER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\nIRcwQy5ghlwg2NjRjiAOl0uxjz4qe+URzb5qq17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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply $\\verb,randn(),$ with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $\\mathcal{N}(0,100)$. Recall the notation for a normal distribution is $\\mathcal{N}(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. DogSensor.$\\verb,__init__(),$ takes the square root of the noise setting so that the $\\verb,noise * randn(),$ call properly computes the normal distribution." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Math with Gaussians" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's say we believe that our dog is at 23m, and the variance is 5, or $pos_{dog}=\\mathcal{N}(23,5)$). We can represent that in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import stats\n", + "stats.norm_plot(23, 5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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GalwoFmbEyS6FiCRz6UgGEZGnVLVcRFO3BTMSdbJLIS+1IC0Wu443w6aM40RE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\nOp2289zpmTlz9kWh9OF0OOViz7T9fpIJ0/8cDr9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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", + "\n", + "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpertation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", + "\n", + "Let's look at 100 sensor readings in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(23, 0, 5)\n", + "xs = range(100)\n", + "ys = []\n", + "for i in xs:\n", + " ys.append(dog.sense())\n", + " \n", + "plt.plot(xs,ys)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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NMPkIE+1BceEsgiTrSiMyMX9Nl6O4IPSguCCcxLAirDE1NYX7778fBw8exLlz5/D1r38d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\nO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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", + "\n", + "\n", + "Recall the histogram code for adding a measurement to a pre-existing belief:\n", + "\n", + " def sense(pos, measure, p_hit, p_miss):\n", + " q = array(pos, dtype=float)\n", + " for i in range(len(hallway)):\n", + " if hallway[i] == measure:\n", + " q[i] = pos[i] * p_hit\n", + " else:\n", + " q[i] = pos[i] * p_miss\n", + " normalize(q)\n", + " return q\n", + " \n", + "Note that the algorithm is essentially computing:\n", + "\n", + " new_belief = old_belief * measurement * sensor_error\n", + " \n", + "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convience. \n", + " \n", + "If we are implementing this with gaussians, we might expect it to be implemented as:\n", + "\n", + " new_gaussian = measurement * old_gaussian\n", + " \n", + "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is not particularly difficult to perform the algebra to derive the equation for multiplying two gaussians, but I will just present the result:\n", + "$$\n", + "N(\\mu_1, \\sigma_1^2)*N(\\mu_2, \\sigma_2^2) = N(\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1}{\\sigma_1^2 + \\sigma_2^2},\\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}) $$ \n", + "\n", + "In other words the result is a Gaussian with \n", + "\n", + "$$\\begin{aligned}\n", + "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", + "\\sigma &= \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n", + "\\end{aligned}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The expression for the mean is not particularly illuminating, except that it is a combination of the means and variances of the input. But the variance of the result is merely some combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", + "\n", + "Let's immediately look at some plots of this. First, let's look at the result of multiplying $N(23,5)$ to itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance by wider, narrower, or the same?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "\n", + "def multiply(mu1, sig1, mu2, sig2):\n", + " m = (sig1*mu2 + sig2*mu1) / (sig1+sig2)\n", + " s = 1. / (1./sig1 + 1./ sig2)\n", + " return (m,s)\n", + "\n", + "xs = np.arange(16, 30, 0.1)\n", + "\n", + "\n", + "m1,s1 = 23, 5\n", + "m, s = multiply(m1,s1,m1,s1)\n", + "\n", + "ys = [stats.gaussian(x,m1,s1) for x in xs]\n", + "p1, = plt.plot (xs,ys)\n", + "\n", + "ys = [stats.gaussian(x,m,s) for x in xs]\n", + "p2, = plt.plot (xs,ys)\n", + "\n", + "plt.legend([p1,p2],['original', 'multiply'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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K+TdEQCYf/ot+zF+s4fJPmBuMmspWNDd0CqjIfvDaF4v5SwsbZiKyWdXll9HZ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\nZSItykR0iF4uLERGmC+Z2+ujudtFg9VJo9VFg81Jo9VJg9VFk81JYri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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is either amazing or what you would expect, depending on your state of mind. I must admit I vacillate freely between the two! Note that the result of the multiplation is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", + "\n", + "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get the same value, I should be more confident in my answer than if I just measured once. If I measure twice and get $23m$ each time, I should conclude that the length is close to $23m$. So the mean should be $23$. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", + "\n", + "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is just a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", + "\n", + "Now let's multiply two gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(16, 30, 0.1)\n", + "\n", + "m1,s1 = 23, 5\n", + "m2,s2 = 25, 5\n", + "m, s = multiply(m1,s1,m2,s2)\n", + "\n", + "ys = [stats.gaussian(x,m1,s1) for x in xs]\n", + "p1, = plt.plot (xs,ys)\n", + "\n", + "ys = [stats.gaussian(x,m2,s2) for x in xs]\n", + "p2, = plt.plot (xs,ys)\n", + "\n", + "ys = [stats.gaussian(x,m,s) for x in xs]\n", + "p3, = plt.plot(xs,ys)\n", + "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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XYnbWnn1tJ/nbFmmYhRCilrh6PJHsrbtoOm2c6lJqlZCJo7hy6CSX9vymuhQh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LTvY7keac8nbRiEzDDx//kvuP8f/1AOZi2Yu7q6uHTp0tT60NAQXV1dcx7b3d3N+Pj4nI5h2zY9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\nELOQglkIIYQQQohZSMEshBBCCCHELP4fMK5kG7vKF9gAAAAASUVORK5CYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23m, and then a friend make the same measurement and got 25m, your best guess must be 24m. \n", + "\n", + "That is fairly counter-intuitive, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker just made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using. Humans make galling mistakes, physical sensors do not. \n", + "\n", + "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", + "\n", + "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", + "\n", + "One final test of your intuition. What if the two measurements are widely separated? " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xs = np.arange(0, 60, 0.1)\n", + "\n", + "m1,s1 = 10, 5\n", + "m2,s2 = 50, 5\n", + "m, s = multiply(m1,s1,m2,s2)\n", + "\n", + "ys = [stats.gaussian(x,m1,s1) for x in xs]\n", + "p1, = plt.plot (xs,ys)\n", + "\n", + "ys = [stats.gaussian(x,m2,s2) for x in xs]\n", + "p2, = plt.plot (xs,ys)\n", + "\n", + "ys = [stats.gaussian(x,m,s) for x in xs]\n", + "p3, = plt.plot(xs,ys)\n", + "plt.legend([p1,p2,p3],['measure 1', 'measure 2', 'multiply'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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0i7lTj2RaMuLNnzE3BwZLDsLnB5MJjSTAsadtzF9mMcZz0SOPPAIAePXVV6HT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\ncLUJCQY1YgP5P9iP17VcABAfpEaUzheHq2fmUcM8dzddug7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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", + "\n", + "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160lbs while the second read 170lbs, and both were equally accurate, the best estimate was 165lbs. Futhermore I should be a bit more confident about 165lbs vs 160lbs or 170lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", + "\n", + "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense.\n", + "\n", + "$$\n", + "\\mu=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", + "$$\n", + "\n", + "If both scales have the same accuracy, then $\\sigma_1^2 = \\sigma_2^2$, and the resulting equation is\n", + "\n", + "$$\\mu=\\frac{\\mu_1 + \\mu_2}{2}$$\n", + "\n", + "which is just the average of the two weighings. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", + "$\\sigma_1^2=0$, yielding\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{0*\\mu_2 + \\sigma_2^2 \\mu_1} { \\sigma_2^2}, \\\\\n", + "\\text{or just}\\\\\n", + "\\mu&=\\mu_1\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Finally, if we set $\\sigma_1^2 = 9\\sigma_2^2$, then the resulting equation is\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{9 \\sigma_2^2 \\mu_2 + \\sigma_2^2 \\mu_1} {9 \\sigma_2^2 + \\sigma_2^2} \\\\\n", + "\\text{or just}\\\\\n", + "\\mu&= \\frac{1}{10} \\mu_1 + \\frac{9}{10} \\mu_2\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing the Sensing Step" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", + "\n", + "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $dog_{pos} = \\mathcal{N}(\\mu,\\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the sense function for a Kalman filter:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def sense(mu, sigma, measurement, measurement_sigma):\n", + " return multiply(mu, sigma, measurement, measurement_sigma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog was with the new measurement. Perhaps this would be clearer if we used more specific names:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def sense_dog(dog_pos, dog_sigma, measurement, measurement_sigma):\n", + " return multiply(dog_pos, dog_sigma, measurement, measurement_sigma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the $\\verb,sense_dog(),$ function should make what we are doing very clear. \n", + "\n", + "Let's look at an example. We will suppose that our current belief for the dog's position is $N(2,5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a $\\verb,DogSensor,$ object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at postion 2.0, not 0.0." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(velocity=0, noise=1)\n", + "\n", + "pos,s = 2, 5\n", + "for i in range(20):\n", + " pos,s = sense(pos, s, dog.sense(), 5)\n", + " print('time:', i, '\\tposition =', \"%.3f\" % pos, '\\tvariance =', \"%.3f\" % s)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time: 0 \tposition = 0.793 \tvariance = 2.500\n", + "time: 1 \tposition = 0.575 \tvariance = 1.667\n", + "time: 2 \tposition = 0.277 \tvariance = 1.250\n", + "time: 3 \tposition = 0.348 \tvariance = 1.000\n", + "time: 4 \tposition = 0.401 \tvariance = 0.833\n", + "time: 5 \tposition = 0.231 \tvariance = 0.714\n", + "time: 6 \tposition = 0.386 \tvariance = 0.625\n", + "time: 7 \tposition = 0.517 \tvariance = 0.556\n", + "time: 8 \tposition = 0.452 \tvariance = 0.500\n", + "time: 9 \tposition = 0.332 \tvariance = 0.455\n", + "time: 10 \tposition = 0.298 \tvariance = 0.417\n", + "time: 11 \tposition = 0.280 \tvariance = 0.385\n", + "time: 12 \tposition = 0.197 \tvariance = 0.357\n", + "time: 13 \tposition = 0.132 \tvariance = 0.333\n", + "time: 14 \tposition = 0.116 \tvariance = 0.312\n", + "time: 15 \tposition = 0.076 \tvariance = 0.294\n", + "time: 16 \tposition = 0.135 \tvariance = 0.278\n", + "time: 17 \tposition = 0.040 \tvariance = 0.263\n", + "time: 18 \tposition = 0.003 \tvariance = 0.250\n", + "time: 19 \tposition = 0.006 \tvariance = 0.238\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the intial value of 5.0 to 0.238.\n", + "\n", + "By now the fact that we converged to a position of 0.0 should not be terribly suprising. All we are doing is computing $\\verb,new_pos = old_pos * measurement,$ and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", + "\n", + "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", + "\n", + "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing Updates" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a useless one - who would need to write a filter to track nonmoving objects? The histogram used a loop of sense and update functions, and we must do the same to accomodate movement.\n", + "\n", + "How how do we perform the update function with gaussians? Recall the histogram method:\n", + "\n", + " def update(pos, move, p_correct, p_under, p_over):\n", + " n = len(pos)\n", + " result = array(pos, dtype=float)\n", + " for i in range(n):\n", + " result[i] = \\\n", + " pos[(i-move) % n] * p_correct + \\\n", + " pos[(i-move-1) % n] * p_over + \\\n", + " pos[(i-move+1) % n] * p_under \n", + " return result\n", + " \n", + " \n", + "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with gaussians?\n", + "\n", + "It turns out that we just add gaussians. Think of the case without gaussians. I think my dog is at 7.3m, and he moves 2.6m to right, where is he now? Obviously, $7.3+2.6=9.9$. He is at 9.9m. Abstractly, the algorithm is $\\verb,new_pos = old_pos + dist_moved,$. It does not matter if we use floating point numbers or gaussians for these values, the algorithm must be the same. \n", + "\n", + "How is addition for gaussians performed? It turns out to be very simple:\n", + "$$ N({\\mu}_1, {{\\sigma}_1}^2)+N({\\mu}_2, {{\\sigma}_2}^2) = N({\\mu}_1 + {\\mu}_2, {{\\sigma}_1}^2 + {{\\sigma}_2}^2)$$\n", + "\n", + "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", + "${\\mu}_1$ is the old position, and ${\\mu}_2$ is the distance moved. Surely it makes sense that our new position is ${\\mu}_1 + {\\mu}_2$. What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the $\\verb,update(),$ function for the histogram filter we always lost information - our confidence after the update was lower than our confidence before the update. Perhaps this makes sense - we don't really know where the dog is moving, so perhaps the confidence should get smaller (variance gets larger). I assure you that the equation for gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using gaussians to model physical events, the results must correctly describe those events.\n", + "\n", + "I recognize the amount of hand waving in that argument. Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", + "\n", + "So, here is our implementation of the update function:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def update(pos, sigma, movement, movement_sigma):\n", + " return (pos + movement, sigma + movement_sigma)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is left? Just calling these functions. The histogram did nothing more than loop over the $\\verb,sense(),$ and $\\verb,update(),$ functions, so let's do the same. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# assume dog is always moving 1m to the right\n", + "movement = 1\n", + "movement_error = 2\n", + "sensor_error = 10\n", + "pos = (0, 500) # gaussian N(0,50)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(10):\n", + " pos = update(pos[0], pos[1], movement, movement_error)\n", + " print('UPDATE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + " \n", + " print('SENSE: %.4f,\\t%.4f' % (pos[0], pos[1]))\n", + " print()\n", + " \n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "UPDATE: 1.0000,\t502.0000\n", + "SENSE: -0.9237,\t9.8047\n", + "\n", + "UPDATE: 0.0763,\t11.8047\n", + "SENSE: 0.1727,\t5.4138\n", + "\n", + "UPDATE: 1.1727,\t7.4138\n", + "SENSE: 3.2003,\t4.2574\n", + "\n", + "UPDATE: 4.2003,\t6.2574\n", + "SENSE: 6.5697,\t3.8490\n", + "\n", + "UPDATE: 7.5697,\t5.8490\n", + "SENSE: 7.6101,\t3.6904\n", + "\n", + "UPDATE: 8.6101,\t5.6904\n", + "SENSE: 8.2152,\t3.6267\n", + "\n", + "UPDATE: 9.2152,\t5.6267\n", + "SENSE: 6.5868,\t3.6007\n", + "\n", + "UPDATE: 7.5868,\t5.6007\n", + "SENSE: 6.4438,\t3.5900\n", + "\n", + "UPDATE: 7.4438,\t5.5900\n", + "SENSE: 7.7971,\t3.5856\n", + "\n", + "UPDATE: 8.7971,\t5.5856\n", + "SENSE: 7.7203,\t3.5838\n", + "\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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OD6fbvBkxb7+N/W++iaf79n3g8+5cIiztJg83b6pRrpw3wxXcUC0RJiepzymP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\nm5tRpYoXkyax4SWiKKXVwjF8OEwjRwZuQXkX1a1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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is a fair bit of arbitrary constants code above, but don't worry about it. What does require explanation are the first few lines:\n", + "\n", + " movement = 1 \n", + " movement_error = 2\n", + " \n", + "For the moment we are assuming that we have some other sensor that detects how the dog is moving. For example, there could be an inertial sensor clipped onto the dog's collar, and it reports how far the dog moved each time it is triggered. The details don't matter. The upshot is that we have a sensor, it has noise, and so we represent it with a Gaussian. Later we will learn what to do if we do not have a sensor for the $\\verb,update(),$ step.\n", + "\n", + "For now let's walk through the code and output bit by bit.\n", + "\n", + " movement = 1\n", + " movement_error = 2\n", + " sensor_error = 10\n", + " pos = (0, 500) # gaussian N(0,500)\n", + " \n", + " \n", + "The first lines just set up the initial conditions for our filter. We are assuming that the dog moves steadily to the right 1m at a time. We have a relatively low error of 2 for the movement sensor, and a higher error of 10 for the RFID position sensor. Finally, we set our belief of the dog's initial position as $N(0,500)$. Why those numbers. Well, 0 is as good as any number if we don't know where the dog is. But we set the variance to 500 to denote that we have no confidence in this value at all. 100m is almost as likely as 0 with this value for the variance. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we initialize the RFID simulator with\n", + "\n", + " dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "It may seem very 'convienent' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position.\n", + "\n", + "The next code allocates an array to store the output of the measurements and filtered positions. \n", + "\n", + " zs = []\n", + " ps = []\n", + " \n", + "This is the first time that I am introducing standard nomenclature used by the Kalman filtering literature. It is traditional to call our measurement $Z$, and so I follow that convention here. As an aside, I find the nomenclature used by the literature very obscure. However, if you wish to read the literature you will have to become used to it, so I will not use a much more readable variable name such as $m$ or $measure$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we just enter our $\\verb,sense() - >update(),$ loop.\n", + "\n", + " for i in range(10):\n", + " pos = update(pos[0], pos[1], movement, sensor_error)\n", + " print 'UPDATE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", + "\n", + "Wait, why $\\verb,update(),$ before sense? It turns out the order does not matter once, but the first call to $\\verb,DogSensor.sense(),$ assumes that the dog has already moved, so we start with the update step. In practice you will order these calls based on the details of your sensor, and you will very typically do the $\\verb,sense(),$ first.\n", + "\n", + "So we call the update function with the gaussian representing our current belief about our position, the another gaussian representing our belief as to where the dog is moving, and then print the output. Your output will differ, but when writing this I get this as output:\n", + "\n", + " UPDATE: 1.000 502.000\n", + "\n", + "What is this saying? After the update, we believe that we are at 1.0, and the variance is now 502.0. Recall we started at 500.0. The variance got worse, which is always what happens during the update step.\n", + "\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + "Here we sense the dog's position, and store it in our array so we can plot the results later.\n", + "\n", + "Finally we call the sense function of our filter, save the result in our *ps* array, and print the updated position belief:\n", + "\n", + " pos = sense(pos[0], pos[1], Z, movement_error)\n", + " ps.append(pos[0])\n", + " print 'SENSE:', \"%.4f\" %pos[0], \", %.4f\" %pos[1]\n", + " \n", + "Your result will be different, but I get\n", + "\n", + " SENSE: 1.6279 , 9.8047\n", + " \n", + "as the result. What is happening? Well, at this point the dog is really at 1.0, however the predicted position is 1.6279. What is happening is the RFID sensor has a fair amount of noise, and so we compute the position as 1.6279. That is pretty far off from 1, but this is just are first time through the loop. Intuition tells us that the results will get better as we make more measurements, so let's hope that this is true for our filter as well. Now look at the variance: 9.8047. It has dropped tremendously from 502.0. Why? Well, the RFID has a reasonably small variance of 2.0, so we trust it far more than our previous belief. At this point there is no way to know for sure that the RFID is outputting reliable data, so the variance is not 2.0, but is has gotten much better.\n", + "\n", + "Now the software just loops, calling $\\verb,update(),$ and $\\verb,sense(),$ in turn. Because of the random sampling I do not know exactly what numbers you are seeing, but the final position is probably between 9 and 11, and the final variance is probably around 3.5. After several runs I did see the final position nearer 7, which would have been the result of several measurements with relatively large errors.\n", + "\n", + "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter shown to work!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%precision 2\n", + "# assume dog is always moving 1m to the right\n", + "movement = 1\n", + "movement_error = 2\n", + "sensor_error = 4.5\n", + "pos = (0, 100) # gaussian N(0,50)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "\n", + "for i in range(50):\n", + " pos = update(pos[0], pos[1], movement, movement_error) \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " vs.append(pos[1])\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + " \n", + "#plt.subplot(121) \n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()\n", + "\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()\n", + "print ([float(\"%0.4f\" % v) for v in vs])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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upO+Iv7VF8YMMC8N1xx040tPJ+8uSriWtMueF+I96jEVERMqBoPnzsS9fjmP5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\nCuNa4ti+XQ369VPEJ59Uv7Zpk0O9e8fpppv8WrW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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[102.0, 6.3099, 4.6267, 4.2812, 4.1939, 4.1708, 4.1646, 4.1629, 4.1624, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623, 4.1623]\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we can see that the variance converges very quickly to roughly 4.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literatue, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Relationship to the g-h Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the first chapter I stated that the Kalman filter is a form of g-h filter. However, we have been reasoning about the probability of Gaussians, and not used any of the reasoning or equations of the first chapter. A trivial amount of algebra will reveal the relationship, so let's do that now. It's not particularly illuminating algebra, so feel free to skip to the bottom to see the final equation that relates *g* to the variances.\n", + "\n", + "The equation for our estimate is:\n", + "\n", + "$$\n", + "\\mu_{x'}=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\n", + "$$\n", + "\n", + "which I will make more friendly for our eyes as:\n", + "\n", + "$$\n", + "\\mu_{x'}=\\frac{ya + xb} {a+b}\n", + "$$\n", + "\n", + "We can easily put this into the g-h form with the following algebra\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu_{x'}&=(x-x) + \\frac{ya + xb} {a+b} \\\\\n", + "\\mu_{x'}&=x-\\frac{a+b}{a+b}x + \\frac{ya + xb} {a+b} \\\\ \n", + "\\mu_{x'}&=x +\\frac{-x(a+b) + xb+ya}{a+b} \\\\\n", + "\\mu_{x'}&=x+ \\frac{-xa+ya}{a+b} \\\\\n", + "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We are almost done, but recall that the variance of estimate is given by \n", + "\n", + "$${\\sigma_{x'}^2} = \\frac{1}{ \\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\\\\\n", + "= \\frac{1}{ \\frac{1}{a} + \\frac{1}{b}}\n", + "$$\n", + "\n", + "We can incorporate that term into our equation above by observing that\n", + "$$ \n", + "\\begin{aligned}\n", + "\\frac{a}{a+b} &= \\frac{a/a}{(a+b)/a} = \\frac{1}{(a+b)/a}\\\\\n", + " &= \\frac{1}{1 + \\frac{b}{a}} = \\frac{1}{\\frac{b}{b} + \\frac{b}{a}}\\\\\n", + " &= \\frac{1}{b}\\frac{1}{\\frac{1}{b} + \\frac{1}{a}} \\\\\n", + " &= \\frac{\\sigma^2_{x'}}{b}\n", + " \\end{aligned}\n", + "$$\n", + "\n", + "We can tie all of this together with\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu_{x'}&=x+ \\frac{a}{a+b}(y-x)\\\\\n", + "&= x + \\frac{\\sigma^2_{x'}}{b}(y-x) \\\\\n", + "&= x + g_n(y-x)\\\\\n", + "\\blacksquare\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$g_n = \\frac{\\sigma^2_{x'}}{\\sigma^2_{y}}$$\n", + "\n", + "The end result is multipying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not truly a constant, as it varies with each time step as the variance changes, but it is truly the same formula. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n", + "\n", + "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n", + "\n", + "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and preditions at time *n*. In other words, we are just picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Excercise:\n", + "Modify the values of mov$\\verb,ement_error,$ and $\\verb,sensor_error,$ and note the effect on the filter and on the variance. Which has a larger effect on the value that variance converges to. For example, which results in a smaller variance:\n", + "\n", + " movement_error = 40\n", + " sensor_error = 2\n", + " \n", + "or:\n", + "\n", + " movement_error = 2\n", + " sensor_error = 40 " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Introduction to Designing a Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equiped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 2.13.\n", + "\n", + "We do not have a real sensor to read, so we will simulate the sensor with the following function. We have hard-coded the voltage to 16.3 - obviously the voltage will differ based on the temperature, but that is not important to our filter design." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "temp_variance = 2.13**2\n", + "def volt():\n", + " return random.randn()*temp_variance + 16.3" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We generate white noise with a given variance using the equation $\\verb,random.randn() * variance,$. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is just the square of the standard deviation. Hence we raise 2.13 to the second power.\n", + "> **Sidebar**: spec sheets are just what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Numbers given are often maximums - the spec is a guarantee that the performace will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that everything falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution. Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", + "\n", + "> For example, I just randomly looked up a data sheet for an airflow sensor. There is a field \"Repeatability\", with the value \"$\\pm0.50\\%$ Reading\". Is this a Gaussian? Is there a bias? For example, perhaps the repeatibility is nearly $0.0\\%$ at low temperatures, and always nearly $+0.50$ at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", + "\n", + "> As you might guess, modeling the performance of your sensors is one of the harder parts of creating good Kalman filter. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of sensing and updating. The sensing step probably seems clear - call $\\verb,volt(),$ to get the measurement, pass the result into $\\verb,sense(),$ function, but what about the update step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", + "\n", + "As always, we will trust in the math. We have no movement, and no error associated with them, so we will just set both to zero. Let's see what happens. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = temp_variance\n", + "movement_error = 0\n", + "movement = 0\n", + "voltage = (25,1000) #who knows what the first value is?\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "N=50\n", + "\n", + "for i in range(N):\n", + " Z = volt()\n", + " zs.append(Z)\n", + " \n", + " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n", + " ps.append(voltage[0])\n", + " vs.append(voltage[1])\n", + "\n", + " voltage = update(voltage[0], voltage[1], movement, movement_error)\n", + "\n", + "plt.scatter(range(N), zs, marker='+')\n", + "p1, = plt.plot(ps, c='g')\n", + "plt.legend([p1], ['filter'], 3)\n", + "plt.xlim((0,N));plt.ylim((0,30))\n", + "plt.show()\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()\n", + "print('Variance converges to',vs[-1])\n", + "print('Last voltage is',voltage[0])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + 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FWpyzWNuu2qYFWQuUHJvs9d9hsOY9EDhHIHzERMcMFj8peR4/VjjmItif8zab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\nZEiS8vLytGfPHhUWFvpskAg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LLldeKGXMVsGEXMCEXMCEXMAJWR1d4Fq6AAAAcEsWiy5ndEsZs1UwIRcwIRcwIRdwQnZn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\nUfq5uH34+8RsDTp+LGPtMVu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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Variance converges to 0.0907297673624\n", + "Last voltage is 15.6491261618\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first plot shows the individual sensor measurements marked with '+'s vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the $\\verb,volt(),$ function. On other runs I have gotten up to around $16.9$ as an output and also as low as 15.5 or so.\n", + "\n", + "The second plot shows how the variance converges over time. Compare this plot to the variance plot for the dog sensor. While this does converge to a very small value, it is much slower than the dog problem. The next section **Explaining the Results - Multi-Sensor Fusion** explains why this happens.\n", + "\n", + "##### Exercise(optional):\n", + "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", + "\n", + "> use plt.hist(data,bins=100) to plot the histogram. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Your code here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Solution\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = temp_variance\n", + "\n", + "def VKF():\n", + " voltage=(14,1000)\n", + " for i in range(N):\n", + " Z = volt()\n", + " voltage = sense(voltage[0], voltage[1], Z, sensor_error)\n", + " return voltage[0]\n", + "\n", + "vs = []\n", + "for i in range (10000):\n", + " vs.append (VKF())\n", + "plt.hist(vs, bins=100) \n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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V5WcrtCknoBHZwtzpDmZZAADS2GhkKuYGvNNHdtIUAwuseJ1iuIe1Gm2jfraR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\nfeUrX5m7Ix6px+v8u337ts6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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Discussion\n", + "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. We will discuss this more in a subsequent math chapter." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Explaining the Results - Multi-Sensor Fusion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So how does the Kalman filter do so well? I have glossed over one aspect of the filter as it becomes confusing to address too many points at the same time. We will return to the dog tracking problem. We used two sensors to track the dog - the RFID sensor that detects position, and the inertial tracker that tracked movement. However, we have focussed all of our attention on the position sensor. Let's change focus and see how the filter performs if the intertial tracker is also noisy. This will provide us with an vital insight into the performance of Kalman filters." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_sensor = 30\n", + "pos = (0,500)\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "vs = []\n", + "\n", + "for i in range(100):\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + " vs.append(pos[1])\n", + "\n", + " pos = update(pos[0], pos[1], movement+ random.randn(), movement_error)\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()\n", + "plt.plot(vs)\n", + "plt.title('Variance')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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5U5x9koih4wURU8AB8uTJk1GzZk20bNnS/dzatWvRtGlTNGvWDN99950oAySEEEJCwTJ9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\nmGqBHCvuIKeeeGrHM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lYblulk9DDL1dMCEXMCEXMCEXcFJalk9jRhgAAABuw8NySCt6u2BCLmBCLmBCLuAk1hEG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\nlOux5PNa8sVf90Rfj2/7PNG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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This result is worse than the example where only the measurement sensor was noisy. Instead of being mostly straight, this time the filter's output is distintly jagged. But, it still mostly tracks the dog. What is happening here?\n", + "\n", + "This illustrates the effects of *multi-sensor fusion*. Suppose we get a position reading of -28.78 followed by 31.43. From that information alone it is impossible to tell if the dog is standing still during very noisy measurements, or perhaps sprinting from -29 to 31 and being accurately measured. But we have a second source of information, his velocity. Even when the velocity is also noisy, it constrains what our beliefs might be. For example, suppose that with the 31.43 position reading we get a velocity reading of 59. That matches the difference between the two positions quite well, so this will lead us to believe the RFID sensor and the velocity sensor. Now suppose we got a velocity reading of 1.7. This doesn't match our RFID reading very well - it suggests that the dog is standing still or moving slowly.\n", + "\n", + "When sensors measure different aspects of the system and they all agree we have strong evidence that the sensors are accurate. And when they do not agree it is a strong indication that one or more of them are inaccurate. \n", + "\n", + "We will formalize this mathematically in the next chapter; for now trust this intuitive explanation. We use this sort of reasoning every day in our lives. If one person tells us something that seems far fetched we are inclined to doubt them. But if several people independently relay the same information we attach higher credence to the data. If one person disagrees with several other people, we tend to distrust the outlier. If we know the people that might alter our belief. If a friend is inclined to practical jokes and tall tales we may put very little trust in what they say. If one lawyer and three lay people opine on some fact of law, and the lawyer disagees with the three you'll probably lend more credence to what the lawyer says because of her expertise. In the next chapter we will learn how to mathematicall model this sort of reasoning." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "More examples" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Extreme Amounts of Noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intution tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = (0,500)\n", + "\n", + "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " pos = update(pos[0], pos[1], movement, movement_error)\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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kONRo3Dj2cjSSceuthnFEMS9cGNZpxvzhhzDrNfK1Wv2WldMnTlS0yVNry0aV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ho4VqxovhkxQhCkuGyNlcDarVtjnu0UCgpgU2ceCcwgC506NU9uGBzYps+fD+/11ys5zWXh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\nJIQQQgghxCAaRBNLo9kDosWq/ULo0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+ "text": [ + "" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? If you are not sure, don't worry, we will discuss it latter." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Bad Initial Estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_error = 2\n", + "pos = (1000,500)\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(100):\n", + " pos = update(pos[0], pos[1], movement, movement_error)\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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I84JEmBckwrwgEW9bLPTevNnff/+Nxx57DIGBgdDpdPjiiy8QHh6OWbNmoUePHgCA5OTk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+ "text": [ + "" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would probably just assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges very quickly." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example: Large Noise and Bad Initial Estimate" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about the worst of both worlds, large noise and a bad initial estimate?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = (1000,500)\n", + "\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error) \n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " pos = update (pos[0], pos[1], movement, movement_error)\n", + " \n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " \n", + " pos = sense (pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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37gx4+xde0OPzzzWe8RFN9SyraM5lYwoLoZs6lepCCERzvfCJguigxGy9sCsr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\nk6bIlmXmvsKb1G6scakUtGbNbE35yuWXwzDXXy4SAW9CS7hkMid23vB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Be1XC5d4Cd9+N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437q14xyaTYXNrFxZNI7QAbT5hVkTY64N3pNuvESay1UkZeIlN9Ka4PhC4Vm2zFrEDAOxv/6V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\nR2jGDKPZlt+2LT0udk3CIxhkwe/YAWnZMmjZ2RC//x65NupHxZt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Pr7CLUYrm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tlYSAghhBBCSLagSTQhhBBCCCEa0SSaEEIIIYQQjWgSTQghhBBCiEY0iSaEEEII\nIUQjmkQTQgghhBCiEU2iCSGEEEII0Ygm0YQQQgghhGj0/3Ckugs5ZiLiAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", + "\n", + "Finally, let's make the suggest change of making our initial position guess just be the first sensor measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30000\n", + "movement_error = 2\n", + "pos = None\n", + "\n", + "dog = DogSensor(0, velocity=movement, noise=sensor_error)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "for i in range(1000):\n", + " Z = dog.sense()\n", + " zs.append(Z)\n", + " if pos == None:\n", + " pos = (Z, 500)\n", + " \n", + " pos = sense (pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + " pos = update (pos[0], pos[1], movement, movement_error)\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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pu56ifsEwqJkxA+wFFyRfIBOhS0vB7N6d8LhAz57i/zFGDwC2n36CfcWK2BON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\nC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TfZmGb+/ndo559vv9eaBrNePRTdcQfZxHXdlpH0gd65M7IBhW/6SSdBs96znFQxvwwP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YMQtjxnhZ/NZloh4fwLnMGBYWLyT58GYqnPEzcryfSZO8RNy6h7epqAgVz59PtWeeoeb27cix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+ "text": [ + "" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $Z$ had a small amount or large amount of noise. \n", + "\n", + "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser rangefinders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable value for the variance for a cheap thermometer might be 10, for example, and our code is using 30,000 for the variance. " + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Exercise: Interactive Plots" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the $\\verb,interact(),$ function to call a calculation and plotting function. Each parameter passed into $\\verb,interact(),$ automatically gets a slider created for it. I have built the boilerplate for this; just fill in the required code." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.html.widgets import interact, interactive, fixed\n", + "import IPython.html.widgets as widgets\n", + "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise, noise_scale):\n", + " # your code goes here\n", + " pass\n", + "\n", + "interact(plot_kalman_filter,\n", + " start_pos=(-10,10), \n", + " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", + " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", + " movement_noise=widgets.FloatSliderWidget(value=5,min=0,max=100.),\n", + " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=2.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 29, + "text": [ + "" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Solution\n", + "One possible solution follows." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "zs = np.zeros(100)\n", + "ps = np.zeros(100)\n", + "def plot_kalman_filter(start_pos, sensor_noise, movement, movement_noise,noise_scale):\n", + " dog = DogSensor(start_pos, velocity=movement, noise=sensor_noise)\n", + " random.seed(303)\n", + " pos = (0,100)\n", + "\n", + " for i in range(100):\n", + " Z = dog.sense() + random.randn()*noise_scale\n", + " zs[i] = Z\n", + "\n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps[i] = pos[0]\n", + "\n", + " pos = update(pos[0], pos[1], movement + random.randn()*movement_noise, movement_noise)\n", + "\n", + " p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + " p2, = plt.plot(ps, c='b')\n", + " plt.legend([p1,p2], ['measurement', 'filter'], 2)\n", + " plt.show()\n", + "\n", + "interact(plot_kalman_filter,\n", + " start_pos=(-10,10), \n", + " sensor_noise=widgets.IntSliderWidget(value=5,min=0,max=100), \n", + " movement=widgets.FloatSliderWidget(value=1,min=-2.,max=2.), \n", + " movement_noise=widgets.FloatSliderWidget(value=2,min=0,max=100.),\n", + " noise_scale=widgets.FloatSliderWidget(value=1,min=0,max=20.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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XroRPnIjtl19wDR5MoF69EoxQpPQ88kgk//ynm4svDpT4vTSCLCFBvWNiRnkh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\n2rf3afRok5v8Cgr0hxU2AAAATFWpdZD9fmncOLc2bIjUO+9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+ "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 30, + "text": [ + "" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Exercise - Nonlinear Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our equations are linear: \n", + "$$\\begin{aligned}new\\_pos&=old\\_pos+dist\\_moved\\\\\n", + "new\\_position&=old\\_position*measurement\\end{aligned}$$\n", + "\n", + "Do you suppose that this filter works well or poorly with nonlinear systems?\n", + "\n", + "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", + "\n", + " Z = math.sin(i/3.) * 2\n", + " \n", + "Adust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#enter your code here." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 31 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###### Solution:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_error = 2\n", + "pos = (100,500)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "\n", + "for i in range(100):\n", + " pos = update(pos[0], pos[1], movement, movement_error)\n", + "\n", + " Z = math.sin(i/3.)*2\n", + " zs.append(Z)\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['input', 'filter'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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l+L//+z/ExcVh1KhRRX6elpaG+vXrF36uVi0BP/2UhZtuCuh0RERERERF7NmzB61bt/Z5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+ "text": [ + "" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Discussion\n", + "\n", + "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", + "\n", + "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the predition and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", + "\n", + "Maybe we just didn't adjust things 'quite right'. After all, the output looks like a sin wave, it is just offset some. Let's test this assumption." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Exercise - Noisy Nonlinear Systems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Implement the same system, but add noise to the measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#enter your code here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 33 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "######Solution" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "sensor_error = 30\n", + "movement_error = 2\n", + "pos = (100,500)\n", + "\n", + "zs = []\n", + "ps = []\n", + "\n", + "\n", + "for i in range(100):\n", + " pos = update(pos[0], pos[1], movement, movement_error)\n", + "\n", + " Z = math.sin(i/3.)*2 + random.randn()*1.2\n", + " zs.append(Z)\n", + " \n", + " pos = sense(pos[0], pos[1], Z, sensor_error)\n", + " ps.append(pos[0])\n", + "\n", + "\n", + "p1, = plt.plot(zs,c='r', linestyle='dashed')\n", + "p2, = plt.plot(ps, c='b')\n", + "plt.legend([p1,p2], ['measurement', 'filter'], 3)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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qBfMTT3js/e/fZ7BpkwYvvWTA779n4eRJHi+8EAhThQhaGS7FuIsXZdMkiG9o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\n7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QPvWv/RRx/RokULcnNzCQoKIj09nR07dnjWP/nkk2zZsgWXy8WMGTNYvHgxGzduBP5u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\nWiqGRURERMRr/Q+qK/+8gQ67GwAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###### Discussion\n", + "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", + "\n", + "Very shortly after practioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of this book is devoted to this problem and its various solutions." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Summary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This information in this chapter takes some time to assimulate. To truly understand this you will probably have to work through this chapter several times. I encourage you to change the various constants and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of something like the position of a dog in a hallway. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians correctly updates your belief. That is all the Kalman filter does. Even now I alternate between complacency and amazement at the results. \n", + "\n", + "If you understand this, you will be able to understand multidimensional Kalman filters and the various extensions that have been make on them. If you do not fully understand this, I strongly suggest rereading this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 34 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "author notes:\n", + " clean up the code - same stuff duplicated over and over - write a 'clean implemntation' at the end.\n", + " \n", + " " + ] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/Multidimensional_Kalman_Filters.ipynb b/Multidimensional_Kalman_Filters.ipynb index b8fa667..18c17bf 100644 --- a/Multidimensional_Kalman_Filters.ipynb +++ b/Multidimensional_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:472320d5c3e0702f2a18addf88f006b5f5a19a3f51784050f9346806d2cc46b3" + "signature": "sha256:9de522896a31234c5502f9ba39e27ca8fe00b307764f4a503b6b7ca27476e2b3" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 diff --git a/Preface.ipynb b/Preface.ipynb index b975e46..6c32141 100644 --- a/Preface.ipynb +++ b/Preface.ipynb @@ -13,8 +13,121 @@ "metadata": {}, "source": [ "

Kalman and Bayesian Filters in Python

\n", - "
Table of Contents
\n", - "\n", + "
Table of Contents
" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", + "import book_format\n", + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Installed secnum.py. To use it, type:\n", + " %load_ext secnum\n" + ] + }, + { + "javascript": [ + "console.log(\"Section numbering...\");\n", + "\n", + "function number_sections(threshold) {\n", + "\n", + " var h1_number = 0;\n", + " var h2_number = 0;\n", + "\n", + " if (threshold === undefined) {\n", + " threshold = 2; // does nothing so far\n", + " }\n", + "\n", + " var cells = IPython.notebook.get_cells();\n", + " \n", + " for (var i=0; i < cells.length; i++) {\n", + "\n", + " var cell = cells[i];\n", + " if (cell.cell_type !== 'heading') continue;\n", + " \n", + " var level = cell.level;\n", + " if (level > threshold) continue;\n", + " \n", + " if (level === 1) {\n", + " \n", + " h1_number ++;\n", + " var h1_element = cell.element.find('h1');\n", + " var h1_html = h1_element.html();\n", + " \n", + " console.log(\"h1_html: \" + h1_html);\n", + "\n", + " var patt = /^[0-9]+\\.\\s(.*)/; // section number at start of string\n", + " var title = h1_html.match(patt); // just the title\n", + "\n", + " if (title != null) { \n", + " h1_element.html(h1_number + \". \" + title[1]);\n", + " }\n", + " else {\n", + " h1_element.html(h1_number + \". \" + h1_html);\n", + " }\n", + " \n", + " h2_number = 0;\n", + " \n", + " }\n", + " \n", + " if (level === 2) {\n", + " \n", + " h2_number ++;\n", + " \n", + " var h2_element = cell.element.find('h2');\n", + " var h2_html = h2_element.html();\n", + "\n", + " console.log(\"h2_html: \" + h2_html);\n", + "\n", + " \n", + " var patt = /^[0-9]+\\.[0-9]+\\.\\s/;\n", + " var result = h2_html.match(patt);\n", + "\n", + " if (result != null) {\n", + " h2_html = h2_html.replace(result, \"\");\n", + " }\n", + "\n", + " h2_element.html(h1_number + \".\" + h2_number + \". \" + h2_html);\n", + " \n", + " }\n", + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" + ], + "metadata": {}, + "output_type": "display_data" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "### Version 0.0\n", "\n", "Not ready for public consumption. In development." diff --git a/Signals_and_Noise.ipynb b/Signals_and_Noise.ipynb index bede4e3..1e114f5 100644 --- a/Signals_and_Noise.ipynb +++ b/Signals_and_Noise.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:b884811797e64562baf3c2f742fbb57d9857907b27eeb0885fa24fc3a524bb18" + "signature": "sha256:a99c80ee33c889d337e7c98906135c5be7203be21423375ba59d0399563d8508" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 diff --git a/Unscented_Kalman_Filter.ipynb b/Unscented_Kalman_Filter.ipynb index d17f311..923470b 100644 --- a/Unscented_Kalman_Filter.ipynb +++ b/Unscented_Kalman_Filter.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:6f9ef48b22782824d2e9169118d616cce66aaf1365292e761e4d3ecfb022703b" + "signature": "sha256:66c26b5f12522984f5c0f4f1f89c03cd62b201e37c170c063437cb122ac1b054" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 diff --git a/Untitled0.ipynb b/Untitled0.ipynb index be13cf5..65557f8 100644 --- a/Untitled0.ipynb +++ b/Untitled0.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:5c99106a58fdfec14e71afe805a522f7a3f434845e28ce911f0640049674ed28" + "signature": "sha256:842d8c88675001eadf27bb53d68b649129f5e3c560cf8b43ccfab1ceb5f93bec" }, "nbformat": 3, "nbformat_minor": 0, @@ -17,230 +17,105 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], - "prompt_number": 1 + "prompt_number": 22 }, { "cell_type": "heading", @@ -262,16 +137,18 @@ "metadata": {}, "source": [] }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "One" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "test\n", - "-\n", - "\n", - "testtwp\n", - "--\n", - "\n", "\n", "# One\n", ">this is a big test asdf asdf asd fasd fasd;fj sadf;lkjas df;kasdj f;lasdkfj asd;lkfj asd;lkfj asd;lfkja sdf;ojasd f;lkasdj f;alsdkfj das;lkfjasdf; asdfkj; asf\n", @@ -297,230 +174,78 @@ { "cell_type": "code", "collapsed": false, - "input": [], + "input": [ + "xmax=500" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import *\n", + "\n", + "xs = [x for x in arange(0,xmax,0.1)]\n", + "ys = [x**1.3 for x in xs]\n", + "\n", + "plt.plot(xs,sin(radians(ys)))\n", + "plt.ylim((-2,2))\n", + "plt.show()" + ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" - ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, + "output_type": "display_data", + "png": 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osKnBZdPCMiu3w8MtocMMAFkqFk+ozxvSxZFgcigeTg7HV70hVTnMWliefHv64SVlWlhW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\nRU5ErkJggg==\n", "text": [ - "" + "" ] } ], - "prompt_number": 1 + "prompt_number": 20 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "xmax=50\n", + "print (xs[0:5])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[0.0, 0.10000000000000001, 0.20000000000000001, 0.30000000000000004, 0.40000000000000002]\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is where I explain the magic of how xs contains ....\n", + "blah\n", + "\n", + "##header" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Test" + ] }, { "cell_type": "markdown", diff --git a/discrete_bayes.ipynb b/discrete_bayes.ipynb index 1ee9d16..ed99de0 100644 --- a/discrete_bayes.ipynb +++ b/discrete_bayes.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:266729b27e2d51ad90c675d939766430799e16551541a85150394b3f7eead92e" + "signature": "sha256:6cc4195c7865759973fa69265113f14252ea1ccb05d16196c88fa00f18862420" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1 diff --git a/g-h_filter.ipynb b/g-h_filter.ipynb index ed630e9..78fc2c3 100644 --- a/g-h_filter.ipynb +++ b/g-h_filter.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:c95a43951094c5ec86b654934c7bbbd79ece1d3f2eb3fb3cf541ddc9d6483a2a" + "signature": "sha256:327668f3cfc21e289ec66ce5afcf96d3bdb9e2cc78fc817e634cd292d081ac7a" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,227 +25,101 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import book_format\n", - "book_format.load_style()" + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" ], "language": "python", "metadata": {}, "outputs": [ { - "html": [ - "\n", - "\n" + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" ], "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] + "output_type": "display_data" } ], "prompt_number": 1