From 9a8616a508318c4102e4fa03b7fb4f517ecbe2b0 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Mon, 8 Sep 2014 22:04:42 -0700 Subject: [PATCH] Work on animations. Experimented with adding animations to the book. Also, fixed the H-Infinity code a bit to more close reflect Simon's code. --- Chapter02_Discrete_Bayes/discrete_bayes.ipynb | 112 +++++++++++------- .../discrete_bayes_animations.ipynb | 23 ++++ .../HInfinity_Filters.ipynb | 74 +++--------- 3 files changed, 105 insertions(+), 104 deletions(-) create mode 100644 Chapter02_Discrete_Bayes/discrete_bayes_animations.ipynb diff --git a/Chapter02_Discrete_Bayes/discrete_bayes.ipynb b/Chapter02_Discrete_Bayes/discrete_bayes.ipynb index c0c6732..74b946f 100644 --- a/Chapter02_Discrete_Bayes/discrete_bayes.ipynb +++ b/Chapter02_Discrete_Bayes/discrete_bayes.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:8c25e49f13c73dcadcb995b7316539e0f420423df6a8583eb5ec8e7a3f0baf6d" + "signature": "sha256:3fd1875f54e8ffeb8fd85aa2109497a1ecb4090bbdb017910763f76e12562c32" }, "nbformat": 3, "nbformat_minor": 0, @@ -259,7 +259,7 @@ "output_type": "pyout", "prompt_number": 1, "text": [ - "" + "" ] } ], @@ -356,9 +356,9 @@ { "metadata": {}, "output_type": "display_data", - "png": 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"text": [ - "" + "" ] } ], @@ -433,7 +433,7 @@ ] } ], - "prompt_number": 4 + "prompt_number": 6 }, { "cell_type": "markdown", @@ -594,8 +594,12 @@ " \n", "pos = np.array([.4, .1, .2, .3])\n", "print('pos before predict =', pos)\n", + "bar_plot.plot (pos, title='Before prediction')\n", + "\n", + "\n", "pos = perfect_predict(pos, 1)\n", - "print('pos after predict =', pos)\n" + "print('pos after predict =', pos)\n", + "bar_plot.plot (pos, title='After prediction')\n" ], "language": "python", "metadata": {}, @@ -605,7 +609,22 @@ "stream": "stdout", "text": [ "pos before predict = [ 0.4 0.1 0.2 0.3]\n", - "pos after predict = [ 0.3 0.4 0.1 0.2]\n" + "pos after predict =" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " [ 0.3 0.4 0.1 0.2]\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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YAAAARiOIAQAAYDSCGAAAAEYjiAEAAGA0ghgAAABGI4gBAABgNIIYAAAARiOIAQAAYDSC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\nH7WokSOa/dtCAAAAAElFTkSuQmCC\n", + "text": [ + "" ] } ], @@ -681,7 +700,8 @@ "input": [ "p = np.array([0, 0, .4, .6, 0, 0, 0, 0])\n", "res = predict (p, 2, .8, .1, .1)\n", - "print(res)" + "print(res)\n", + "bar_plot.plot(res)" ], "language": "python", "metadata": {}, @@ -692,6 +712,14 @@ "text": [ "[ 0. 0. 0. 0.04 0.38 0.52 0.06 0. ]\n" ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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6663vuzepn/dBDAAAA0nzb+UAAPC/BDEAAEkTxAAAJE0QAwCQNEEMAEDSBDEA\nAEkTxAAAJE0QAwCQNEEMAEDS/h96A1+XD3/SYwAAAABJRU5ErkJggg==\n", "text": [ - "" + "" ] } ], @@ -1055,10 +1083,11 @@ "input": [ "measurements = [0,1,0,1,0,0]\n", "\n", - "for m in measurements:\n", + "for i,m in enumerate(measurements):\n", " pos = update(pos, m, .6, .2)\n", " pos = predict(pos, 1, .8, .1, .1)\n", - "bar_plot.plot(pos)" + " plt.subplot(3,2, i+1)\n", + " bar_plot.plot(pos, title='step{}'.format(i+1))" ], "language": "python", "metadata": {}, @@ -1066,13 +1095,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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FlixZgrCwMMjlcrz88ssdO3MiImoVc5uIyDKSvLy8to9lEIBKpYKvr6+YUyAieiC5ublw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\niRMnkJSUhKlTp4pe2+Fw4MyZM/Dz80NYWBiee+450WsCwK1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"text": [ - "" + "" ] } ], - "prompt_number": 21 + "prompt_number": 23 }, { "cell_type": "markdown", @@ -1176,15 +1205,6 @@ "**If you can understand this chapter you will be able to understand and implement Kalman filters** I cannot stress this enough. If anything is murky, go back and reread this chapter and play with the code. The rest of this book will build on the algorithms that we use here. If you don't intuitively understand why this histogram filter works, and can at least work through the math, you will have little success with the rest of the material. However, if you grasp the fundamental insight - multiplying probabilities when we measure, and shifting probabilities when we update leads to a converging solution - then you understand everything important you need to grasp the Kalman filter. " ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "**Author notes:**\n", - " Do I want to go to the multidimensional case? At least describe it, but why not implement it as well" - ] - }, { "cell_type": "heading", "level": 2, diff --git a/Chapter02_Discrete_Bayes/discrete_bayes_animations.ipynb b/Chapter02_Discrete_Bayes/discrete_bayes_animations.ipynb new file mode 100644 index 0000000..70dbc73 --- /dev/null +++ b/Chapter02_Discrete_Bayes/discrete_bayes_animations.ipynb @@ -0,0 +1,23 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:fea22f31f443e23e2d336a0742e6bf9a559c588029a2d3c2e8e69066e08c2fe5" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb b/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb index 2bfd24c..a97cd9e 100644 --- a/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb +++ b/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:7d487f11e312a7f42c8b0f26c54306db69a8a6b3fcec7863bf7db4070d9fc17e" + "signature": "sha256:8c68f422d155e6e256b984c1601ed17d878240844f686e8559510bac3b24b183" }, "nbformat": 3, "nbformat_minor": 0, @@ -256,13 +256,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 4, + "prompt_number": 2, "text": [ - "" + "" ] } ], - "prompt_number": 4 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -291,96 +291,54 @@ "from filterpy.hinfinity import HInfinityFilter\n", "\n", "dt = 0.1\n", - "f = HInfinityFilter(2, 1, 0, gamma=.4)\n", + "f = HInfinityFilter(2, 1, dim_u=1, gamma=.01)\n", "\n", "f.F = array([[1., dt],\n", " [0., 1.]])\n", "\n", "f.H = array([[0., 1.]])\n", "f.x = array([[0., 0.]]).T\n", - "#f.G = array([[dt**2 / 2, dt]]).T\n", + "f.G = array([[dt**2 / 2, dt]]).T\n", "\n", "f.P = 0.01\n", "f.W = array([[0.0003, 0.005],\n", - " [0.0050, 0.100]])/ 1000\n", + " [0.0050, 0.100]])/ 1000 #process noise\n", "\n", "f.V = 0.01\n", "f.Q = 0.01\n", + "u = 1. #acceleration of 1 f/sec**2\n", "\n", "xs = []\n", "vs = []\n", "\n", "for i in range(1,40):\n", " f.update (5)\n", - " print(f.x.T)\n", + " #print(f.x.T)\n", " xs.append(f.x[0,0])\n", " vs.append(f.x[1,0])\n", - " f.predict()\n", + " f.predict(u=u)\n", "\n", "plt.subplot(211)\n", "plt.plot(xs)\n", + "plt.title('position')\n", "plt.subplot(212)\n", - "plt.plot(vs)\n", + "plt.plot(vs) \n", + "plt.title('velocity')\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 0.250005 2.50005 ]]\n", - "[[ 0.66806083 3.34442646]]\n", - "[[ 1.1284151 3.77161316]]\n", - "[[ 1.60570517 4.03126553]]\n", - "[[ 2.09144161 4.20685183]]\n", - "[[ 2.58197401 4.33419113]]\n", - "[[ 3.07547127 4.4312003 ]]\n", - "[[ 3.57091268 4.50783208]]\n", - "[[ 4.06768385 4.57005637]]\n", - "[[ 4.56539275 4.62167173]]\n", - "[[ 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42dAWtJrd8dMm2J3ukLLp+hhfKM7unatYF6eKQq2JiIgmrmENysXFxThy5Agk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\nQmdnJ+Li4uByuWA2m/nbUYR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+wCiXSiCTiCGT+relZ21LJJCfvc8fVmV9jvWdyx9C/cfJ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\nkSNHLDrwZ599hri4OMTGxmL9+vXdKrJVp8fHBy8AaFtNFol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