Added Adaptive filtering chapter to PDF.

15_Adaptive_Filtering/Adaptive_Filtering.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:f928a92fe960eb385a50a836c0b47cedfffbe6063f78ac7a646541eb2cb1a951"
+  "signature": "sha256:c029584dd374b0f2f2bec0b527d961fdac43c5e14ab9d708333e9400e6d719f1"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -260,13 +260,13 @@
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 1,
+       "prompt_number": 2,
        "text": [
-        "<IPython.core.display.HTML at 0x7fabfb8831d0>"
+        "<IPython.core.display.HTML at 0x7f3c6cf44630>"
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 2
     },
     {
      "cell_type": "heading",
@@ -363,7 +363,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 2
+     "prompt_number": 3
     },
     {
      "cell_type": "markdown",
@@ -389,7 +389,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 3
+     "prompt_number": 4
     },
     {
      "cell_type": "markdown",
@@ -442,11 +442,11 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde9df3c8>"
+        "<matplotlib.figure.Figure at 0x7f3c6cf5de80>"
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 5
     },
     {
      "cell_type": "markdown",
@@ -471,13 +471,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde9ec7f0>"
+        "<matplotlib.figure.Figure at 0x7f3c6ceebb70>"
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 6
     },
     {
      "cell_type": "markdown",
@@ -509,7 +509,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 6
+     "prompt_number": 7
     },
     {
      "cell_type": "markdown",
@@ -556,13 +556,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde7b60f0>"
+        "<matplotlib.figure.Figure at 0x7f3c6ccc7a90>"
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 8
     },
     {
      "cell_type": "markdown",
@@ -596,13 +596,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde7c7240>"
+        "<matplotlib.figure.Figure at 0x7f3c6ccd5b38>"
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 9
     },
     {
      "cell_type": "markdown",
@@ -633,13 +633,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabe8147a58>"
+        "<matplotlib.figure.Figure at 0x7f3c6ce4b208>"
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 10
     },
     {
      "cell_type": "markdown",
@@ -670,13 +670,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAyQAAAGkCAYAAADAJeH1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabd70082e8>"
+        "<matplotlib.figure.Figure at 0x7f3c6ce1ceb8>"
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 11
     },
     {
      "cell_type": "markdown",
@@ -703,7 +703,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 11
+     "prompt_number": 12
     },
     {
      "cell_type": "code",
@@ -722,13 +722,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde72b588>"
+        "<matplotlib.figure.Figure at 0x7f3c6ce4b7f0>"
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -775,11 +775,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabd7008d30>"
+        "<matplotlib.figure.Figure at 0x7f3c6cc8e438>"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 14
     },
     {
      "cell_type": "markdown",
@@ -824,13 +824,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde7d2240>"
+        "<matplotlib.figure.Figure at 0x7f3c6ce71d30>"
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 15
     },
     {
      "cell_type": "markdown",
@@ -876,6 +876,11 @@
       "\n",
       "$$\\mathbf{S} = \\mathbf{HPH^\\mathsf{T}} + \\mathbf{R}$$\n",
       "\n",
+      "\n",
+      "If the linear algebra used to compute this confuses you, recall that we can think of matrix inverses as division, so $\\epsilon = \\mathbf{y^\\mathsf{T}S}^{-1}\\mathbf{y}$ can be thought of as computing\n",
+      "\n",
+      "$$\\epsilon=\\frac{\\mathbf{y}^2}{\\mathbf{S}}$$\n",
+      "\n",
       "Both $\\mathbf{y}$ and $\\mathbf{S}$ are attributes of `filterpy.KalmanFilter` so implementation is of this computation will be straightforward.\n",
       "\n",
       "Let's look at a plot of $\\epsilon$ against time."
@@ -911,13 +916,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde74ce10>"
+        "<matplotlib.figure.Figure at 0x7f3c6cde05f8>"
        ]
       }
      ],
-     "prompt_number": 33
+     "prompt_number": 16
     },
     {
      "cell_type": "markdown",
@@ -973,25 +978,16 @@
      "language": "python",
      "metadata": {},
      "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "4.0 1\n",
-        "4.1 2\n",
-        "6.9 1\n"
-       ]
-      },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7fabde6ccda0>"
+        "<matplotlib.figure.Figure at 0x7f3c6cbeac18>"
        ]
       }
      ],
-     "prompt_number": 40
+     "prompt_number": 17
     },
     {
      "cell_type": "markdown",
@@ -999,96 +995,6 @@
      "source": [
       "The performance of this filter is markedly better than the constant velocity filter. The constant velocity filter took roughly 10 seconds to reacquire the signal after the start of the manuever. The adaptive filter takes under a second to do the same. "
      ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
     }
    ],
    "metadata": {}

merge_book.py

@@ -57,5 +57,6 @@ if __name__ == '__main__':
          '12_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb',
          '13_HInfinity_Filters/HInfinity_Filters.ipynb',
          '14_Smoothing/Smoothing.ipynb',
+         '15_Adaptive_Filtering/Adaptive_Filtering.ipynb',
          'Appendix_A_Installation/Appendix_Installation.ipynb',
          'Appendix_B_Symbols_and_Notations/Appendix_Symbols_and_Notations.ipynb'])