Moved chapter 6 as part of reorg.

06_Multivariate_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
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  "metadata": {
   "name": "",
-  "signature": "sha256:8a4a4e8740b8aaba558a875f4549818dbde8e67fe4e65bd3bee1b7293f4778af"
+  "signature": "sha256:cc93f0602c44f29149840aa5f8363ab5a6b42db6007e6e1c3826a7a4e7c742cd"
  },
  "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 import book_format\n",
+      "sys.path.insert(0, './code') # allow us to import book_format\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 0x7fc65bc4d160>"
+        "<IPython.core.display.HTML at 0x7f579724c438>"
        ]
       }
      ],
@@ -395,7 +395,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc65bc4d0f0>"
+        "<matplotlib.figure.Figure at 0x7f579724c4a8>"
        ]
       }
      ],
@@ -563,7 +563,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fc65bc3d3c8>"
+        "<matplotlib.figure.Figure at 0x7f577276bf28>"
        ]
       }
      ],
@@ -595,9 +595,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc65bc3d6d8>"
+        "<matplotlib.figure.Figure at 0x7f579723dc18>"
        ]
       }
      ],
@@ -655,7 +655,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636fe8ac8>"
+        "<matplotlib.figure.Figure at 0x7f577275d438>"
        ]
       }
      ],
@@ -666,7 +666,7 @@
      "metadata": {},
      "source": [
       "And for those of you viewing this online or in IPython Notebook on your computer, here is an animation.\n",
-      "<img src='ellipse.gif'>"
+      "<img src='animations/multivariate_ellipse.gif'>"
      ]
     },
     {
@@ -758,7 +758,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc63702fb00>"
+        "<matplotlib.figure.Figure at 0x7f5772358198>"
        ]
       }
      ],
@@ -785,7 +785,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636da5a20>"
+        "<matplotlib.figure.Figure at 0x7f5772413780>"
        ]
       }
      ],
@@ -812,7 +812,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636d9dfd0>"
+        "<matplotlib.figure.Figure at 0x7f57726016a0>"
        ]
       }
      ],
@@ -843,7 +843,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636dcc550>"
+        "<matplotlib.figure.Figure at 0x7f57721fd4e0>"
        ]
       }
      ],
@@ -908,7 +908,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636e8e438>"
+        "<matplotlib.figure.Figure at 0x7f57724a8400>"
        ]
       }
      ],
@@ -1744,6 +1744,10 @@
         "    Model. dim may be either 2 or 3, dt is the time step, and sigma is the\n",
         "    variance in the noise.\n",
         "    \n",
+        "    Q is computed as the G * G^T * variance, where G is the process noise per\n",
+        "    time step. In other words, G = [[.5dt^2][dt]]^T for the constant velocity \n",
+        "    model.\n",
+        "    \n",
         "    **Paramaeters**\n",
         "    \n",
         "    dim : int (2 or 3)\n",
@@ -2033,7 +2037,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 30
+     "prompt_number": 28
     },
     {
      "cell_type": "markdown",
@@ -2054,9 +2058,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636daef28>"
+        "<matplotlib.figure.Figure at 0x7f577239c470>"
        ]
       },
       {
@@ -2064,11 +2068,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc6370cee80>"
+        "<matplotlib.figure.Figure at 0x7f577b208400>"
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 29
     },
     {
      "cell_type": "markdown",
@@ -2144,7 +2148,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 32
+     "prompt_number": 30
     },
     {
      "cell_type": "markdown",
@@ -2173,7 +2177,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 33
+     "prompt_number": 31
     },
     {
      "cell_type": "markdown",
@@ -2231,9 +2235,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636e8e668>"
+        "<matplotlib.figure.Figure at 0x7f57725f0198>"
        ]
       },
       {
@@ -2241,11 +2245,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc6370c9fd0>"
+        "<matplotlib.figure.Figure at 0x7f5772446470>"
        ]
       }
      ],
-     "prompt_number": 34
+     "prompt_number": 32
     },
     {
      "cell_type": "markdown",
@@ -2409,7 +2413,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 35
+     "prompt_number": 33
     },
     {
      "cell_type": "markdown",
@@ -2475,13 +2479,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc637119a20>"
+        "<matplotlib.figure.Figure at 0x7f57724565c0>"
        ]
       }
      ],
-     "prompt_number": 36
+     "prompt_number": 34
     },
     {
      "cell_type": "markdown",
@@ -2547,7 +2551,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636e8ea20>"
+        "<matplotlib.figure.Figure at 0x7f577261e128>"
        ]
       },
       {
@@ -2555,11 +2559,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636ea3860>"
+        "<matplotlib.figure.Figure at 0x7f57721f5438>"
        ]
       }
      ],
-     "prompt_number": 37
+     "prompt_number": 35
     },
     {
      "cell_type": "markdown",
@@ -2598,11 +2602,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636e0e438>"
+        "<matplotlib.figure.Figure at 0x7f57726a82b0>"
        ]
       }
      ],
-     "prompt_number": 38
+     "prompt_number": 36
     },
     {
      "cell_type": "markdown",
@@ -2627,11 +2631,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636d8b668>"
+        "<matplotlib.figure.Figure at 0x7f577239d358>"
        ]
       }
      ],
-     "prompt_number": 39
+     "prompt_number": 37
     },
     {
      "cell_type": "markdown",
@@ -2656,11 +2660,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636ec4828>"
+        "<matplotlib.figure.Figure at 0x7f5772740fd0>"
        ]
       }
      ],
-     "prompt_number": 40
+     "prompt_number": 38
     },
     {
      "cell_type": "markdown",
@@ -2725,11 +2729,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc637089d68>"
+        "<matplotlib.figure.Figure at 0x7f57724c1ba8>"
        ]
       }
      ],
-     "prompt_number": 41
+     "prompt_number": 39
     },
     {
      "cell_type": "markdown",
@@ -2755,11 +2759,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636b7ada0>"
+        "<matplotlib.figure.Figure at 0x7f577260fc50>"
        ]
       }
      ],
-     "prompt_number": 42
+     "prompt_number": 40
     },
     {
      "cell_type": "markdown",
@@ -2827,11 +2831,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636f2d208>"
+        "<matplotlib.figure.Figure at 0x7f57725728d0>"
        ]
       }
      ],
-     "prompt_number": 43
+     "prompt_number": 41
     },
     {
      "cell_type": "markdown",
@@ -2857,11 +2861,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc63709c160>"
+        "<matplotlib.figure.Figure at 0x7f5772572940>"
        ]
       }
      ],
-     "prompt_number": 44
+     "prompt_number": 42
     },
     {
      "cell_type": "markdown",
@@ -2890,11 +2894,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc63714edd8>"
+        "<matplotlib.figure.Figure at 0x7f57723509e8>"
        ]
       }
      ],
-     "prompt_number": 45
+     "prompt_number": 43
     },
     {
      "cell_type": "markdown",
@@ -2921,11 +2925,11 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636dcc128>"
+        "<matplotlib.figure.Figure at 0x7f57725cda58>"
        ]
       }
      ],
-     "prompt_number": 46
+     "prompt_number": 44
     },
     {
      "cell_type": "markdown",
@@ -2992,28 +2996,28 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636f7eeb8>"
+        "<matplotlib.figure.Figure at 0x7f577260ff28>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636b74860>"
+        "<matplotlib.figure.Figure at 0x7f5772520470>"
        ]
       }
      ],
-     "prompt_number": 47
+     "prompt_number": 45
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "If you are viewing this in IPython Notebook or on the web, here is an animation of the filter filtering the data. I've tuned the filter parameters such that it is easy to see a change in $\\mathbf{P}$ as the filter progresses.\n",
-      "<img src='track1.gif'>"
+      "<img src='animations/multivariate_track1.gif'>"
      ]
     },
     {
@@ -3077,11 +3081,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636d35080>"
+        "<matplotlib.figure.Figure at 0x7f577b1bdbe0>"
        ]
       }
      ],
-     "prompt_number": 48
+     "prompt_number": 46
     },
     {
      "cell_type": "markdown",
@@ -3155,13 +3159,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636cc81d0>"
+        "<matplotlib.figure.Figure at 0x7f57722e9240>"
        ]
       }
      ],
-     "prompt_number": 49
+     "prompt_number": 47
     },
     {
      "cell_type": "heading",
@@ -3215,11 +3219,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636b94d68>"
+        "<matplotlib.figure.Figure at 0x7f57722e94e0>"
        ]
       }
      ],
-     "prompt_number": 50
+     "prompt_number": 48
     },
     {
      "cell_type": "markdown",
@@ -3259,11 +3263,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636b94198>"
+        "<matplotlib.figure.Figure at 0x7f57722e9e48>"
        ]
       }
      ],
-     "prompt_number": 51
+     "prompt_number": 49
     },
     {
      "cell_type": "markdown",
@@ -3293,11 +3297,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fc636ed7c88>"
+        "<matplotlib.figure.Figure at 0x7f577262b668>"
        ]
       }
      ],
-     "prompt_number": 52
+     "prompt_number": 50
     },
     {
      "cell_type": "heading",

06_Multivariate_Kalman_filter/README.md

@@ -1,2 +0,0 @@
-You may read this book online via nbviewer by using this link:
-[*Read Online Now*](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)

animations/multivariate_animations.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:df0ee24d44b70c6bc4ea7fc3b5ad7e572ad8bc3f6f2176128a5165d9cdb182b5"
+  "signature": "sha256:c82e943808236de492b791895b0610ea0864057ea274158ee910a721ed9ce67c"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -20,7 +20,7 @@
       "# use same formatting as rest of book so that the plots are\n",
       "# consistant with that look and feel.\n",
       "import book_format\n",
-      "book_format.load_style()"
+      "book_format.load_style('..')"
      ],
      "language": "python",
      "metadata": {},
@@ -245,13 +245,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 1,
+       "prompt_number": 2,
        "text": [
-        "<IPython.core.display.HTML at 0x7f5bb0483f60>"
+        "<IPython.core.display.HTML at 0x7effd802fa20>"
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 2
     },
     {
      "cell_type": "markdown",
@@ -335,7 +335,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 2
+     "prompt_number": 3
     },
     {
      "cell_type": "code",
@@ -363,7 +363,7 @@
       "\n",
       "fig = plt.figure()\n",
       "#ax = fig.add_subplot(111, projection='3d')\n",
-      "animate('ellipse.gif', ellipse_animate, 30, 125)"
+      "animate('multivariate_ellipse.gif', ellipse_animate, 30, 125)"
      ],
      "language": "python",
      "metadata": {},
@@ -372,7 +372,7 @@
        "metadata": {},
        "output_type": "display_data",
        "text": [
-        "<matplotlib.figure.Figure at 0x7f5b93fff5f8>"
+        "<matplotlib.figure.Figure at 0x7effd7d90630>"
        ]
       },
       {
@@ -380,17 +380,17 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f5b93fff6d8>"
+        "<matplotlib.figure.Figure at 0x7effd7d90898>"
        ]
       }
      ],
-     "prompt_number": 3
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "<img src='ellipse.gif'>"
+      "<img src='multivariate_ellipse.gif'>"
      ]
     },
     {
@@ -455,7 +455,7 @@
       "    plt.plot(xs, c='b')\n",
       "    f.predict()\n",
       "\n",
-      "animate('track1.gif', animate_track, 37, 200, figsize=(10.5, 10.5))"
+      "animate('multivariate_track1.gif', animate_track, 37, 200, figsize=(10.5, 10.5))"
      ],
      "language": "python",
      "metadata": {},
@@ -465,17 +465,17 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f5b8c272208>"
+        "<matplotlib.figure.Figure at 0x7effd05c44a8>"
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 5
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "<img src='track1.gif'>"
+      "<img src='multivariate_track1.gif'>"
      ]
     },
     {