Typos, and reran cells so numbering is sequential.

08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:e85081e9a12a7b03474c63a61f6724d276f456f0553ec94cff97e897f4b08075"
+  "signature": "sha256:53ed1038531ab2e0f1c6f53a7e50712c5b86128a3451c66ae19912cb6b7f0203"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -261,7 +261,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f7f48720208>"
+        "<IPython.core.display.HTML at 0x7fed72695208>"
        ]
       }
      ],
@@ -354,9 +354,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAx4AAAGNCAYAAACfV6f6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f48720828>"
+        "<matplotlib.figure.Figure at 0x7fed72695e48>"
        ]
       }
      ],
@@ -707,9 +707,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f48720940>"
+        "<matplotlib.figure.Figure at 0x7fed72695438>"
        ]
       }
      ],
@@ -788,9 +788,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b8069e8>"
+        "<matplotlib.figure.Figure at 0x7fed557d2208>"
        ]
       },
       {
@@ -875,7 +875,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f23ebfcc0>"
+        "<matplotlib.figure.Figure at 0x7fed4de1f828>"
        ]
       }
      ],
@@ -997,7 +997,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f23ebfba8>"
+        "<matplotlib.figure.Figure at 0x7fed4de1f438>"
        ]
       }
      ],
@@ -1336,7 +1336,7 @@
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        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b542e80>"
+        "<matplotlib.figure.Figure at 0x7fed557e4dd8>"
        ]
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@@ -1386,7 +1386,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b535630>"
+        "<matplotlib.figure.Figure at 0x7fed4c5805f8>"
        ]
       }
      ],
@@ -1417,7 +1417,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2c6ca320>"
+        "<matplotlib.figure.Figure at 0x7fed5580a278>"
        ]
       }
      ],
@@ -1450,7 +1450,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b7f05f8>"
+        "<matplotlib.figure.Figure at 0x7fed55484550>"
        ]
       }
      ],
@@ -1481,7 +1481,7 @@
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        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2261d828>"
+        "<matplotlib.figure.Figure at 0x7fed4c5745c0>"
        ]
       }
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@@ -1520,7 +1520,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f225906a0>"
+        "<matplotlib.figure.Figure at 0x7fed4c4e2d30>"
        ]
       }
      ],
@@ -1561,7 +1561,7 @@
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        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f22617a90>"
+        "<matplotlib.figure.Figure at 0x7fed4c4df550>"
        ]
       }
      ],
@@ -1601,7 +1601,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f22620be0>"
+        "<matplotlib.figure.Figure at 0x7fed4c5d1898>"
        ]
       }
      ],
@@ -1638,7 +1638,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f225904e0>"
+        "<matplotlib.figure.Figure at 0x7fed4c4e7588>"
        ]
       }
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@@ -1676,7 +1676,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f225d2780>"
+        "<matplotlib.figure.Figure at 0x7fed4c574588>"
        ]
       },
       {
@@ -1684,7 +1684,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b55ca90>"
+        "<matplotlib.figure.Figure at 0x7fed4c499d68>"
        ]
       }
      ],
@@ -1724,7 +1724,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f224f2668>"
+        "<matplotlib.figure.Figure at 0x7fed4c47a518>"
        ]
       },
       {
@@ -1732,7 +1732,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f225fcd68>"
+        "<matplotlib.figure.Figure at 0x7fed557b0f60>"
        ]
       }
      ],
@@ -1765,7 +1765,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b893208>"
+        "<matplotlib.figure.Figure at 0x7fed4c5c84e0>"
        ]
       }
      ],
@@ -1833,7 +1833,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b887518>"
+        "<matplotlib.figure.Figure at 0x7fed55732b38>"
        ]
       }
      ],
@@ -1866,7 +1866,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f48714f60>"
+        "<matplotlib.figure.Figure at 0x7fed4c47ae48>"
        ]
       },
       {
@@ -1874,7 +1874,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b5e39b0>"
+        "<matplotlib.figure.Figure at 0x7fed4c5a28d0>"
        ]
       }
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b505160>"
+        "<matplotlib.figure.Figure at 0x7fed4c52b860>"
        ]
       },
       {
@@ -1917,7 +1917,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f225d9198>"
+        "<matplotlib.figure.Figure at 0x7fed4c3af400>"
        ]
       }
      ],
@@ -1950,7 +1950,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f224958d0>"
+        "<matplotlib.figure.Figure at 0x7fed4c52b780>"
        ]
       },
       {
@@ -1958,7 +1958,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f225d94a8>"
+        "<matplotlib.figure.Figure at 0x7fed5554d780>"
        ]
       }
      ],
@@ -2081,9 +2081,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b827208>"
+        "<matplotlib.figure.Figure at 0x7fed5551ec50>"
        ]
       }
      ],
@@ -2119,7 +2119,8 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [],
+     "prompt_number": 39
     },
     {
      "cell_type": "heading",
@@ -2139,9 +2140,9 @@
       "\n",
       "Inputs to the Kalman filter must be *Gaussian* and *time independent*. The output of the GPS is *time dependent* because the filter bases it's current estimate on the recusive estimates of all previous measurements. Hence, the signal is not white, it is not time independent, and if you pass that data into a Kalman filter you have violated the mathematical requirements of the filter. So, the answer is no, you cannot get better estimates by running a KF on the output of a commercial GPS. \n",
       "\n",
-      "Another way to think of it. Kalman filters are optimal in a least squares sense. There is no way to take an optimal solution, pass it through a filter, any filter, and get a 'more optimal' answer because it is a logical impossibility. At best the signal will be unchanged, in which case it will still be optimal, or it will be changed, and hence no longer optimal.\n",
+      "Another way to think of it is that Kalman filters are optimal in a least squares sense. There is no way to take an optimal solution, pass it through a filter, any filter, and get a 'more optimal' answer because it is a logical impossibility. At best the signal will be unchanged, in which case it will still be optimal, or it will be changed, and hence no longer optimal.\n",
       "\n",
-      "This is a difficult problem that hobbiests face when trying to integrate GPS, IMUs and other off the shelf sensors. It is too early in the book to try to address this problem."
+      "This is a difficult problem that hobbyists face when trying to integrate GPS, IMUs and other off the shelf sensors. It is too early in the book to try to address this problem, hence the 'PS' in the this section."
      ]
     },
     {
@@ -2182,7 +2183,7 @@
        ]
       }
      ],
-     "prompt_number": 39
+     "prompt_number": 40
     },
     {
      "cell_type": "markdown",
@@ -2261,11 +2262,11 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2256bcc0>"
+        "<matplotlib.figure.Figure at 0x7fed56657d30>"
        ]
       }
      ],
-     "prompt_number": 40
+     "prompt_number": 41
     },
     {
      "cell_type": "markdown",
@@ -2299,7 +2300,8 @@
      ],
      "language": "python",
      "metadata": {},
-     "outputs": []
+     "outputs": [],
+     "prompt_number": 42
     },
     {
      "cell_type": "heading",
@@ -2422,13 +2424,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f221f1240>"
+        "<matplotlib.figure.Figure at 0x7fed4c5c3278>"
        ]
       }
      ],
-     "prompt_number": 104
+     "prompt_number": 43
     },
     {
      "cell_type": "markdown",
@@ -2535,7 +2537,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 41
+     "prompt_number": 44
     },
     {
      "cell_type": "markdown",
@@ -2580,19 +2582,19 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2247f278>"
+        "<matplotlib.figure.Figure at 0x7fed4c3eb358>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f23ecf5f8>"
+        "<matplotlib.figure.Figure at 0x7fed4c3ebda0>"
        ]
       }
      ],
-     "prompt_number": 42
+     "prompt_number": 45
     },
     {
      "cell_type": "markdown",
@@ -2729,7 +2731,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 43
+     "prompt_number": 46
     },
     {
      "cell_type": "markdown",
@@ -2773,11 +2775,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2242eeb8>"
+        "<matplotlib.figure.Figure at 0x7fed4c4d3b70>"
        ]
       }
      ],
-     "prompt_number": 44
+     "prompt_number": 47
     },
     {
      "cell_type": "markdown",
@@ -2918,7 +2920,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 45
+     "prompt_number": 48
     },
     {
      "cell_type": "markdown",
@@ -2967,13 +2969,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f222e60b8>"
+        "<matplotlib.figure.Figure at 0x7fed5546f748>"
        ]
       }
      ],
-     "prompt_number": 46
+     "prompt_number": 49
     },
     {
      "cell_type": "markdown",
@@ -3112,11 +3114,11 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b51fc50>"
+        "<matplotlib.figure.Figure at 0x7fed55799f28>"
        ]
       }
      ],
-     "prompt_number": 47
+     "prompt_number": 50
     },
     {
      "cell_type": "markdown",
@@ -3190,7 +3192,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 48
+     "prompt_number": 51
     },
     {
      "cell_type": "markdown",
@@ -3248,13 +3250,13 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b860550>"
+        "<matplotlib.figure.Figure at 0x7fed554d3ef0>"
        ]
       }
      ],
-     "prompt_number": 49
+     "prompt_number": 52
     },
     {
      "cell_type": "markdown",
@@ -3316,21 +3318,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b51f160>"
+        "<matplotlib.figure.Figure at 0x7fed557c7e10>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b824438>"
+        "<matplotlib.figure.Figure at 0x7fed4c570a20>"
        ]
       }
      ],
-     "prompt_number": 50
+     "prompt_number": 53
     },
     {
      "cell_type": "markdown",
@@ -3354,21 +3356,21 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2242eba8>"
+        "<matplotlib.figure.Figure at 0x7fed5578f320>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f7f2b50ebe0>"
+        "<matplotlib.figure.Figure at 0x7fed5578f710>"
        ]
       }
      ],
-     "prompt_number": 51
+     "prompt_number": 54
     },
     {
      "cell_type": "markdown",