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     "source": [
      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
     ]
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     "metadata": {},
     "source": [
      "$H_\\infty$ filter"
     ]
    },
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     "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()"
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     "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."
     ]
    },
    {
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     "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, 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",
      "\n",
      "f.P = 0.01\n",
      "f.W = array([[0.0003, 0.005],\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",
      "    xs.append(f.x[0,0])\n",
      "    vs.append(f.x[1,0])\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.title('velocity')\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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xxOX24FRDuzCWOLDEc3ePK6RsaqIaBf4wXGjwDaOYpNUwFFPURCQon30BL1u2DD/4wQ8Q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\nQmdnJ+Li4uByuWA2m/nbUYR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+wCiXSiCTiCGT+relZ21LJJCfvc8fVmV9jvWdyx9C/cfJ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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fbdaa100c50>"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}