Moved chapter 8 as part of reorg

08_Designing_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:a37ccdfe2b40c1c2e9e4dc6c1512db6c9e4c2398316fe30f509bed9c5a50579c"
+  "signature": "sha256:1e1380354f6dfc1cf9470d633eebdacba2529a712807045e1d9435b76c925336"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -32,7 +32,7 @@
       "from __future__ import division, print_function\n",
       "import matplotlib.pyplot as plt\n",
       "import sys\n",
-      "sys.path.insert(0,'../code') # allow us to format the book\n",
+      "sys.path.insert(0,'./code') # allow us to format the book\n",
       "import book_format\n",
       "book_format.load_style()"
      ],
@@ -261,7 +261,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f4026f471d0>"
+        "<IPython.core.display.HTML at 0x7fbb50f2e400>"
        ]
       }
      ],
@@ -354,9 +354,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400e344f28>"
+        "<matplotlib.figure.Figure at 0x7fbb50f29ac8>"
        ]
       }
      ],
@@ -555,8 +555,8 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "[[ 5.  0.]\n",
-        " [ 0.  5.]]\n"
+        "[[5 0]\n",
+        " [0 5]]\n"
        ]
       }
      ],
@@ -707,9 +707,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400e344be0>"
+        "<matplotlib.figure.Figure at 0x7fbb3409b080>"
        ]
       }
      ],
@@ -788,9 +788,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400e058630>"
+        "<matplotlib.figure.Figure at 0x7fbb33fd9fd0>"
        ]
       },
       {
@@ -875,7 +875,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f400264a780>"
+        "<matplotlib.figure.Figure at 0x7fbb34058128>"
        ]
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      ],
@@ -997,7 +997,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400264a6d8>"
+        "<matplotlib.figure.Figure at 0x7fbb34070b38>"
        ]
       }
      ],
@@ -1336,7 +1336,7 @@
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        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f400dfc5e10>"
+        "<matplotlib.figure.Figure at 0x7fbb33d7ea90>"
        ]
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@@ -1386,7 +1386,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000e202e8>"
+        "<matplotlib.figure.Figure at 0x7fbb2c687860>"
        ]
       }
      ],
@@ -1417,7 +1417,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f400e344940>"
+        "<matplotlib.figure.Figure at 0x7fbb33e4a2e8>"
        ]
       }
      ],
@@ -1450,7 +1450,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400dcd1128>"
+        "<matplotlib.figure.Figure at 0x7fbb33d3d470>"
        ]
       }
      ],
@@ -1481,7 +1481,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d92828>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5f32b0>"
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000cfb320>"
+        "<matplotlib.figure.Figure at 0x7fbb2c571da0>"
        ]
       }
      ],
@@ -1561,7 +1561,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d99e10>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5a9550>"
        ]
       }
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@@ -1601,7 +1601,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d7f898>"
+        "<matplotlib.figure.Figure at 0x7fbb33d3d4a8>"
        ]
       }
      ],
@@ -1638,7 +1638,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000cfb2e8>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5d5208>"
        ]
       }
      ],
@@ -1676,7 +1676,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d51c88>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5d5b00>"
        ]
       },
       {
@@ -1684,7 +1684,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f400dcac588>"
+        "<matplotlib.figure.Figure at 0x7fbb33d5fd68>"
        ]
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@@ -1724,7 +1724,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000c7b128>"
+        "<matplotlib.figure.Figure at 0x7fbb2ace9668>"
        ]
       },
       {
@@ -1732,7 +1732,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400e07e1d0>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5c0d30>"
        ]
       }
      ],
@@ -1765,7 +1765,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400de0bac8>"
+        "<matplotlib.figure.Figure at 0x7fbb34387da0>"
        ]
       }
      ],
@@ -1833,7 +1833,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000e0c710>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5d09b0>"
        ]
       }
      ],
@@ -1866,7 +1866,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000c7b2b0>"
+        "<matplotlib.figure.Figure at 0x7fbb3408ccf8>"
        ]
       },
       {
@@ -1874,7 +1874,7 @@
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        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f4014114470>"
+        "<matplotlib.figure.Figure at 0x7fbb33ffe908>"
        ]
       }
      ],
@@ -1909,7 +1909,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4014114e48>"
+        "<matplotlib.figure.Figure at 0x7fbb33ffef28>"
        ]
       },
       {
@@ -1917,7 +1917,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d20710>"
+        "<matplotlib.figure.Figure at 0x7fbb2c5f5b70>"
        ]
       }
      ],
@@ -1950,7 +1950,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d20ba8>"
+        "<matplotlib.figure.Figure at 0x7fbb2c58b9e8>"
        ]
       },
       {
@@ -1958,7 +1958,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f400dca50b8>"
+        "<matplotlib.figure.Figure at 0x7fbb2c58bc50>"
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@@ -2083,7 +2083,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f400de127b8>"
+        "<matplotlib.figure.Figure at 0x7fbb33e35978>"
        ]
       }
      ],
@@ -2262,7 +2262,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f400de12b38>"
+        "<matplotlib.figure.Figure at 0x7fbb33e35470>"
        ]
       }
      ],
@@ -2415,18 +2415,16 @@
      "metadata": {},
      "outputs": [
       {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "fusion std: 0.452\n"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000c60320>"
+       "ename": "LinAlgError",
+       "evalue": "singular matrix",
+       "output_type": "pyerr",
+       "traceback": [
+        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
+        "\u001b[1;32m<ipython-input-43-bda69a291b49>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     63\u001b[0m         \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     64\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 65\u001b[1;33m \u001b[0mfusion_test\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+        "\u001b[1;32m<ipython-input-43-bda69a291b49>\u001b[0m in \u001b[0;36mfusion_test\u001b[1;34m(wheel_sigma, ps_sigma, do_plot)\u001b[0m\n\u001b[0;32m     45\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     46\u001b[0m         \u001b[0mkf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 47\u001b[1;33m         \u001b[0mkf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mz\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mR\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     48\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     49\u001b[0m         \u001b[0mxs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkf\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+        "\u001b[1;32m/home/rlabbe/Dropbox/filterpy/filterpy/kalman/kalman_filter.py\u001b[0m in \u001b[0;36mupdate\u001b[1;34m(self, z, R, H)\u001b[0m\n\u001b[0;32m    166\u001b[0m         \u001b[1;31m# K = PH'inv(S)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    167\u001b[0m         \u001b[1;31m# map system uncertainty into kalman gain\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 168\u001b[1;33m         \u001b[0mK\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdot3\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mP\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mH\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlinalg\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minv\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mS\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    169\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    170\u001b[0m         \u001b[1;31m# x = x + Ky\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+        "\u001b[1;32m/home/rlabbe/anaconda3/lib/python3.4/site-packages/scipy/linalg/basic.py\u001b[0m in \u001b[0;36minv\u001b[1;34m(a, overwrite_a, check_finite)\u001b[0m\n\u001b[0;32m    381\u001b[0m         \u001b[0minv_a\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minfo\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgetri\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpiv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlwork\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlwork\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0moverwrite_lu\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    382\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0minfo\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 383\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"singular matrix\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    384\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0minfo\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    385\u001b[0m         raise ValueError('illegal value in %d-th argument of internal '\n",
+        "\u001b[1;31mLinAlgError\u001b[0m: singular matrix"
        ]
       }
      ],
@@ -2536,8 +2534,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 44
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -2576,25 +2573,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000c60438>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000c60198>"
-       ]
-      }
-     ],
-     "prompt_number": 45
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -2730,8 +2709,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 46
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -2769,17 +2747,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000da3e10>"
-       ]
-      }
-     ],
-     "prompt_number": 47
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -2919,8 +2887,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 48
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -2965,17 +2932,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f400dfb9da0>"
-       ]
-      }
-     ],
-     "prompt_number": 49
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -3108,17 +3065,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f400dfb0940>"
-       ]
-      }
-     ],
-     "prompt_number": 50
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -3191,8 +3138,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [],
-     "prompt_number": 51
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -3246,17 +3192,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f400dd9af60>"
-       ]
-      }
-     ],
-     "prompt_number": 52
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -3314,25 +3250,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000e1db38>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d92eb8>"
-       ]
-      }
-     ],
-     "prompt_number": 53
+     "outputs": []
     },
     {
      "cell_type": "markdown",
@@ -3352,25 +3270,7 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f40026658d0>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": 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truncated
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4000d101d0>"
-       ]
-      }
-     ],
-     "prompt_number": 54
+     "outputs": []
     },
     {
      "cell_type": "markdown",