From 18549e81377b33f882e62d7d41b9e88529716eb4 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sat, 6 Sep 2014 09:25:28 -0700 Subject: [PATCH] Added HIfinity placeholder chapter. Just pointed to Dan Simon's H Infinity PDF for now. --- .../HInfinity_Filters.ipynb | 389 ++++++++++++++++++ 1 file changed, 389 insertions(+) create mode 100644 Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb diff --git a/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb b/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb new file mode 100644 index 0000000..2bfd24c --- /dev/null +++ b/Chapter12_HInfinity_Filters/HInfinity_Filters.ipynb @@ -0,0 +1,389 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:7d487f11e312a7f42c8b0f26c54306db69a8a6b3fcec7863bf7db4070d9fc17e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" + ] + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "$H_\\infty$ filter" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import sys\n", + "sys.path.insert(0,'../code') # allow us to format the book\n", + "import book_format\n", + "book_format.load_style()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I am still mulling over how to write this chapter. In the meantime, Dan Simon has an accessible introduction here:\n", + "\n", + "http://academic.csuohio.edu/simond/courses/eec641/hinfinity.pdf\n", + "\n", + "In one sentence the $H_\\infty$ (H infinity) filter is like a Kalman filter, but it is robust in the face of non-Gaussian, non-predictable inputs.\n", + "\n", + "\n", + "My filterpy library contains an H-Infinity filter. I've pasted some test code below which implements the filter designed by Simon in the article above. Hope it helps." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import (absolute_import, division, print_function,\n", + " unicode_literals)\n", + "\n", + "from numpy import array\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from filterpy.hinfinity import HInfinityFilter\n", + "\n", + "dt = 0.1\n", + "f = HInfinityFilter(2, 1, 0, gamma=.4)\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", + "\n", + "f.P = 0.01\n", + "f.W = array([[0.0003, 0.005],\n", + " [0.0050, 0.100]])/ 1000\n", + "\n", + "f.V = 0.01\n", + "f.Q = 0.01\n", + "\n", + "xs = []\n", + "vs = []\n", + "\n", + "for i in range(1,40):\n", + " f.update (5)\n", + " print(f.x.T)\n", + " xs.append(f.x[0,0])\n", + " vs.append(f.x[1,0])\n", + " f.predict()\n", + "\n", + "plt.subplot(211)\n", + "plt.plot(xs)\n", + "plt.subplot(212)\n", + "plt.plot(vs)\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", + "[[ 5.06377767 4.66521177]]\n", + "[[ 5.56265755 4.7024333 ]]\n", + "[[ 6.06190354 4.73459514]]\n", + "[[ 6.5614219 4.76262524]]\n", + "[[ 7.0611432 4.78722492]]\n", + "[[ 7.56101536 4.80893611]]\n", + "[[ 8.06099891 4.828186 ]]\n", + "[[ 8.56106372 4.8453174 ]]\n", + "[[ 9.06118672 4.86060987]]\n", + "[[ 9.56135018 4.87429471]]\n", + "[[ 10.06154053 4.88656573]]\n", + "[[ 10.56174736 4.89758722]]\n", + "[[ 11.06196277 4.9074998 ]]\n", + "[[ 11.5621808 4.9164249]]\n", + "[[ 12.06239701 4.92446815]]\n", + "[[ 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