Appendix-D-HInfinity-Filters.ipynb

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    "[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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   "source": [
    "# H Infinity filter"
   ]
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   ],
   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "from __future__ import division, print_function\n",
    "from book_format import load_style\n",
    "load_style()"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am still mulling over how to write this chapter. In the meantime, Professor Dan Simon at Clevant State University 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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   "execution_count": 2,
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OhBBotLm73fH2T7ZjR7srvMZ3c7fjgzW+QyUGg2O/TUZkG1jjmyhdMJgTERHFgCwL1Fld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\nYWEoLS2FwWBAREQEuru7cenSJRgMBjQ1NSE/P1/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x232851c4f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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.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');"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}