Added Ensemble Kalman Filter chapter.

Had to rename and move directories around to allow the new chapter to fit in.
2014-12-07 19:44:42 -08:00
1 parent 3c6abb8899
commit a27ebac336
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+      "%matplotlib inline\n",
+      "from __future__ import division, print_function\n",
+      "import matplotlib.pyplot as plt\n",
+      "import numpy as np\n",
+      "from numpy.random import randn\n",
+      "from numpy import array, asarray\n",
+      "\n",
+      "import sys\n",
+      "sys.path.insert(0, '../code') # allow us to import book_format\n",
+      "import book_format\n",
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+      "pos = 1\n",
+      "vel = 1\n",
+      "p_pos = 1\n",
+      "p_move = .5\n",
+      "\n",
+      "data = [(0,pos+randn()*p_pos) for i in range(1000)]\n",
+      "data = np.asarray(data)\n",
+      "\n",
+      "pos += vel\n",
+      "\n",
+      "\n",
+      "plt.scatter(data[:,0], data[:,1], marker=',')\n",
+      "plt.show()\n"
+     ],
+     "language": "python",
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+     ],
+     "prompt_number": 3
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+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from filterpy.kalman import KalmanFilter\n",
+      "from numpy.random import multivariate_normal\n",
+      "import matplotlib.cm as cm\n",
+      "\n",
+      "vel = 20.\n",
+      "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
+      "kf.F = array([[1, 1], [0, 1]], dtype=float)\n",
+      "kf.H = array([[1, 0]])\n",
+      "kf.x = array([[0., vel]]).T\n",
+      "kf.P *= 100\n",
+      "kf.R *= 10\n",
+      "kf.Q *= .0001\n",
+      "\n",
+      "steps = 6\n",
+      "colors = cm.winter(np.linspace(0, .5, steps))\n",
+      "pcolors = cm.Reds(np.linspace(.5, 1, steps))\n",
+      "for i in range(steps):\n",
+      "    kf.predict()\n",
+      "    x,y = multivariate_normal(mean=kf.x.T[0], cov=kf.P, size=1000).T\n",
+      "    plt.scatter(x,y, marker=',', c=pcolors[i])\n",
+      "    \n",
+      "    z = (i+1)*vel\n",
+      "    kf.update(z)\n",
+      "    x,y = multivariate_normal(mean=kf.x.T[0], cov=kf.P, size=1000).T\n",
+      "    plt.scatter(x,y, marker='.', c=colors[i], alpha=0.7)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f7ad12f6da0>"
+       ]
+      }
+     ],
+     "prompt_number": 99
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def update(mu1, var1, mu2, var2):\n",
+      "    if var1 == 0.0:\n",
+      "        var1=1.e-80\n",
+      "        \n",
+      "    if var2 == 0:\n",
+      "        var2 = 1e-80\n",
+      "        \n",
+      "    mean = (var1*mu2 + var2*mu1) / (var1+var2)\n",
+      "    variance = 1. / (1/var1 + 1/var2)\n",
+      "    return (mean, variance)\n",
+      "\n",
+      "\n",
+      "\n",
+      "def predict(mu1, var1, mu2, var2):\n",
+      "    return (mu1+mu2, var1+var2)\n",
+      "\n",
+      "pos = 0\n",
+      "pos_p = 100.\n",
+      "move = 1\n",
+      "move_p = .1\n",
+      "sense_p = 8\n",
+      "\n",
+      "N = 10\n",
+      "colors = cm.winter(np.linspace(0, .5, N))\n",
+      "pcolors = cm.Reds(np.linspace(.5, 1, N))\n",
+      "for i in range(N):\n",
+      "    pos, pos_p = predict(pos, pos_p, move, move_p)\n",
+      "    x,y = multivariate_normal(mean=(pos,i), cov=[[0.001, 0],[0, p_pos]], size=1000).T\n",
+      "    plt.scatter(x,y, marker=',', c=colors[i])    \n",
+      "    print(pos, pos_p)\n",
+      "    \n",
+      "    pos, pos_p = update(pos, pos_p, i, sense_p)\n",
+      "    x,y = multivariate_normal(mean=(i, pos), cov=asarray([[0.001, 0],[0, pos_p]]).T, size=1000).T\n",
+      "    plt.scatter(x,y, marker='.', c=pcolors[i], alpha=0.5)  \n",
+      "    \n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "1 100.1\n",
+        "1.0740055504162813 7.50795559666975\n",
+        "2.0381768183201006 3.9730859395971154\n",
+        "3.02550842348427 2.7546779733418045\n",
+        "4.018974755764885 2.1491012228687625\n",
+        "5.014956796940505"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        " 1.7940228898505703\n",
+        "6.012217081465885 1.5654022438192952\n",
+        "7.010217725218009 1.409220211690132\n",
+        "8.008687415099768 1.2981611057964606\n",
+        "9.007474523188765 1.2169185743509554\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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truncated
+       "text": [
+        "<matplotlib.figure.Figure at 0x7f7ac824d320>"
+       ]
+      }
+     ],
+     "prompt_number": 100
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}