spell check

01_g-h_filter.ipynb

@@ -1,7 +1,7 @@
 {
  "metadata": {
   "name": "",
-  "signature": "sha256:a976736be24f72af59769341dfd37ad1abad6c84a0de77c22512e24bb78eb8d7"
+  "signature": "sha256:0d1f24892de42157a6296f36d36e9d36d65f432da422fa1fcad38359bb995fbe"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -259,7 +259,7 @@
        "output_type": "pyout",
        "prompt_number": 1,
        "text": [
-        "<IPython.core.display.HTML at 0x7f25ddc7e6a0>"
+        "<IPython.core.display.HTML at 0x7f7634845438>"
        ]
       }
      ],
@@ -333,7 +333,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c17c66a0>"
+        "<matplotlib.figure.Figure at 0x7f76179b44a8>"
        ]
       }
      ],
@@ -370,7 +370,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c14799b0>"
+        "<matplotlib.figure.Figure at 0x7f761794b940>"
        ]
       }
      ],
@@ -404,7 +404,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c17c6588>"
+        "<matplotlib.figure.Figure at 0x7f76179b4438>"
        ]
       }
      ],
@@ -446,7 +446,7 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "Average of measurements is 165.0186\n"
+        "Average of measurements is 164.9546\n"
        ]
       }
      ],
@@ -458,7 +458,7 @@
      "source": [
       "The exact number printed depends on your random number generator, but it should be very close to 165.\n",
       "\n",
-      "This code makes one assumption that probably isn't true - that the scale is just as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `random.gauss()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy meaurements very similar to how a real scale would."
+      "This code makes one assumption that probably isn't true - that the scale is just as likely to read 160 as 165 for a true weight of 165 lbs. This is almost never true. Real sensors are more likely to get readings nearer the true value, and are less and less likely to get readings the further away from the true value it gets. We will cover this in detail in the Gaussian chapter. For now, I will use without further explanation the `random.gauss()` function, which will produce more values nearer 165 lbs, and fewer further away. Take it on faith for now that this will produce noisy measurements very similar to how a real scale would."
      ]
     },
     {
@@ -482,7 +482,7 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "Average of measurements is 164.9325\n"
+        "Average of measurements is 164.9443\n"
        ]
       }
      ],
@@ -498,7 +498,7 @@
       "\n",
       "So, let's play 'what if' again. What if you measured your weight once a day, and got the readings 170, 161, and then 169. Did you gain weight, lose weight, or is this all just noisy measurements? \n",
       "\n",
-      "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the weighings along with the error bars, and then some possible weight gain/lossses that could be explained by those measurements in dotted green lines."
+      "We really can't say. The first measurement was 170, and the last was 169, implying a 1 lb loss. But if the scale is only accurate to 10 lbs, that is explainable by noise. I could have actually gained weight; maybe my weight on day one was 165 lbs, and on day three it was 172. It is possible to get those weight readings with that weight gain. My scale tells me I am losing weight, and I am actually gaining weight! Let's look at that in a chart. I've plotted the weighings along with the error bars, and then some possible weight gain/losses that could be explained by those measurements in dotted green lines."
      ]
     },
     {
@@ -525,7 +525,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c140d208>"
+        "<matplotlib.figure.Figure at 0x7f76179a5d30>"
        ]
       }
      ],
@@ -535,9 +535,9 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a human's weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n",
+      "As we can see there is an extreme range of weight changes that could be explained by these three measurements. Shall we give up? No. Recall that we are talking about measuring a humans' weight. There is no way for a human to weigh 180 lbs on day 1, and 160 lbs on day 3. or to lose 30 lbs in one day only to gain it back the next (we will assume no amputations or other trauma has happened to the person). The behavior of the physical system we are measuring should influence how we interpret the measurements. \n",
       " \n",
-      "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based soley on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, just one that is reasonable and could be explained by the measurement."
+      "Suppose I take a different scale, and I get the following measurements: 169, 170, 169, 171, 170, 171, 169, 170, 169, 170. What does your intuition tell you? It is possible, for example, that you gained 1 lb each day, and the noisy measurements just happens to look like you stayed the same weight. Equally, you could have lost 1 lb a day and gotten the same readings. But is that likely? How likely is it to flip a coin and get 10 heads in a row? Not very likely. We can't prove it based solely on these readings, but it seems pretty likely that my weight held steady. In the chart below I've plotted the measurements with error bars, and a likely true weight in dashed green. This dashed line is not meant to be the 'correct' answer to this problem, just one that is reasonable and could be explained by the measurement."
      ]
     },
     {
@@ -561,7 +561,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c13ff080>"
+        "<matplotlib.figure.Figure at 0x7f7617881780>"
        ]
       }
      ],
@@ -596,7 +596,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c13a4a58>"
+        "<matplotlib.figure.Figure at 0x7f76187c4cf8>"
        ]
       }
      ],
@@ -634,7 +634,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1451358>"
+        "<matplotlib.figure.Figure at 0x7f7617921d30>"
        ]
       }
      ],
@@ -672,7 +672,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c129ae48>"
+        "<matplotlib.figure.Figure at 0x7f761773f208>"
        ]
       }
      ],
@@ -711,7 +711,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c14249b0>"
+        "<matplotlib.figure.Figure at 0x7f7617921fd0>"
        ]
       }
      ],
@@ -738,7 +738,7 @@
        "output_type": "display_data",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAzoAAAGkCAYAAAD5QlCuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XtcVHX+x/H3IKAIclHAS2ioeVcyFHI1FMwLWKG5pa2W\nkP26aLW6VpbZhrnqblpbVnbR0kxrw9rKzTU1CaXMTDQqb6Et2k0TFVFJVGR+f5wYueqMMAxzfD0f\nDx4M5/Kdz8yBmrffy7FYrVarAAAAAMBEPFxdAAAAAADUNIIOAAAAANMh6AAAAAAwHYIOAAAAANMh\n6AAAAAAwHYIOAAAAANMh6AAAAAAwHZcGnYyMDCUmJiosLEweHh5avHhxhWOys7M1fPhwBQUFydfX\nVz169NCuXbts+2NjY+Xh4VHma9SoUbX5MgAAAADUMS4NOgUFBYqIiNDcuXPl4+Mji8VSZn9OTo76\n9Omjtm3bKj09Xdu3b9fMmTPl5+dnO8ZisWjs2LE6cOCA7euVV16p7ZcCAAAAoA7xdOWTJyQkKCEh\nQZKUnJxcYf/UqVMVHx+vOXPm2LaFh4dXOM7Hx0ehoaHOKhMAAACAm6mzc3SKi4u1YsUKderUSfHx\n8QoNDVV0dLSWLVtW4di3335bISEh6tq1qx566CGdOHHCBRUDAAAAqCtc2qNzPgcPHtSJEyc0a9Ys\nzZgxQ7Nnz1ZaWppGjx4tPz8/DRkyRJI0atQohYeHq0WLFtq2bZumTJmib775RqtXr7a1lZ+f76qX\nAQAAAKAaAgICLuq8Oht0iouLJUnDhg3TxIkTJUkRERHKzMzUCy+8YAs6d955p+2cLl26qG3btoqO\njtZXX32lq666qvYLBwAAAOBydXboWnBwsDw9PdW5c+cy2zt27KgffvihyvMiIyNVr1497dmzx9kl\nAgAAAKij6myPjre3t6KiososJS0Zy01XtiBBiW+//VZnz55V8+bNK91/sV1fqD2ZmZmSpJ49e7q4\nElwI18q9cL3cB9fKfXCt3AvXy33UxNQTlwadgoIC7d69W5IxVG3fvn3KyspSkyZN1LJlS02ePFkj\nRoxQTEyM4uLilJ6ertTUVC1fvlyS9L///U9Lly7VddddpyZNmmjHjh164IEHFBkZqT59+rjypQEA\nAABwIZcOXdu8ebMiIyMVGRmpwsJCpaSkKDIyUikpKZKkoUOHav78+XrqqacUERGhefPmacmSJbYl\nqb29vfXJJ59o8ODB6tixoyZMmKD4+HitXbu2wj15AAAAAFw6XNqjExsba1t0oCpJSUlKSkqqdF9Y\nWJjWrVvnhMoAAAAAuLM6uxgBAAAAAFwsgg4AAAAA0yHoAAAAADAdgg4AAAAA0yHoAAAAACaybZvk\n6SmlpTl23vLlUv360p49zqmrthF0AAAAgDomK0uaNk3at8/xcydNkmJipGuvdey8oUOlbt2khx92\n/DnrIoIOAAAAUMdkZUnTpzsedDZulNauNcLOxZgwQXr/fWnHjos7vy4h6AAAAMCtnT0rnTzp6iqc\nw2p17PgXX5RCQqQhQy7u+YYPlxo2lF5++eLOr0sIOgAAAG7s9dclDw/pk0+kGTOk8HDjg+rVV0sb\nNhjHrFsnXXON5OcntWhhHFfeqVPSrFlSly6Sj48UFCQlJho9C6WdOCE99pjRfkiI1KCB1K6dNGVK\nxbBRWGgMv+rQQfL1NdqMiJAmTy573LRpxmv44YeKdYWHS3FxFV9vWpr0t79Jbdsa9S5b5tjrqKn3\n7WKeMz1deuopo/YGDYz35403yr4fY8caj+PijHM8PKTbb6/8+UsUFUkffCANGCDVq3f+Y6vi62sM\ne3v33Ys7vy7xdHUBAAAAqL5HHpGKi6WJE40P3k8/LcXHS6+9Jo0bJ91zj3TbbVJqqvT441Lr1tLo\n0ca5Z84Yx27cKI0ZI/35z9LRo9KCBVKfPlJGhtSjh3HsTz8Zbd50k3Trrcak93XrpNmzpa++klat\nOlfTvfdKixZJSUlS797GB/HsbOODvr0sFuOrvAcfNNq7+27J31/q2PHCr+PllxuqU6ffaux9c/S9\nK/Hoo0YIHDdO8vaWXnpJSk6WrrjCeJ/++EfpwAFp/nxp6lSpUyfjvLZtz/9ebdkiFRRI0dH2v7+V\n6dVLWr1a+u47I4S5K4IOAACACRQXS198YQQPSerc2ZhcPnq0tGmTFBlpbB87Vrr8cmnevHMf2F94\nQVq/3vhwO3DguTbHj5e6djVCRUk4advWCDulewzGjTNCwIwZ0ubNUlSUsf39940hVIsWXfzrqmro\nVmGhEawaNDi37Zlnzv865s4N08svZ5dppzrvm+TYe1fi9GnjfSp5zptuktq0Mdrq3dtYEKBXLyPo\nDBwo9e1r33tVMq+mqkB04oQRxtLSpJkzpfvuM3qSunQpG8ZKzt+xw72DDkPXAAAATGDcuHMfnCVj\nyJUk/eEP5z6sS5KXlxFEdu8+t23pUqPXIDJSOnTo3NepU8YwqM8+Mx6XnF8ScoqKpLw849iSFb6+\n/PJcu4GBxlLH27c75/WWDjn2vI6sLD+dPm2p0M7Fvm/2PGfp967E+PFln7NFC6l9++ov65yba3xv\n3Ljy/U8+aby+11+Xfv5ZGjVKOnKkYo9TkybG94MHq1ePq9GjAwAAYAJt2pT9OSjI+N66dcVjg4Kk\nw4fP/bxzp9FDEhJSedsWi/Hh/bLLjJ9ffNGYrL5jh9EjUlpe3rnHzz5rDPvq1s2oLy5OuuEG46uy\n4WiOaN++4rYLvw6Ljh4t+/G3Ou+bfc9Z9r2r7DklI5z8+GPlbdir5D2tqhds0qRzr69VK6MXauLE\niseVnF/da+RqBB0AAAATqGryuT2T0q1WY5GAf/6z6mOCg43v//ynMRxr8GDjQ3KLFsY8k59+MuaZ\nlA4+iYnS3r3SypXG8K61a425LzExxmMvL+O4832gLiqqfHvDho6/ju++y1ZgYNkGq/O+2fOc0rn3\n7kJtO7rCWnklYevIkcr3l4ScNWuMgPboo5UfV3J+VeHNXRB0AAAALnHt2xvDlOLiLvyv+EuWGL0d\nH31UdnvpRQhKCwoy5rSUzGt55BFj4YLly425KdK5oVZHjhg9DSUKC6X9+yvvvbmY1+Hvf9y+hhzg\nyHvniItpq1s343v54XWl/etfxnLcEyZUfUzJELquXR2voS5hjg4AAMAlqPQH6TFjjFW+quqV+PXX\nc49L5paU7rkpKpL+8Y+y5xQXG6uPlde9u/G99BC3kgnvH39c9thnnnGsl+NCr+Pw4er/G3/5AOLI\ne+cIPz/je/mhcufTvbuxAt3GjZXvf/11Y/noW281frZajWXBy/viC6lZM2PZcHdGjw4AAMAlqHSA\nmDDBCBkPPWTcVyYuzvjA/MMPxgpdPj7GdsnohZkyRUpIkG68UTp2THrrLWP4WmnHjknNmxsrmHXv\nLoWGSjk5xlLKjRsb83RKDBhghJ3HHzc+2IeHG5P4N20yhn3ZG3Yu9DqKitropZeyL9yQne+bPc9Z\n+r1zpO3oaOPeOTNnGj1dvr7G3J7zLR1dr55xw88PPjBWdit9Td57z+hFCw83FiLw95fefNNYnru0\nEyekTz+V/u//7Ku5LiPoAAAAuDlHhzmVvzeNp6f03/8aiwwsWWLcsFIyJtBHRxv3wSnx0EPGB/LX\nXjPm6DRvLo0caczP6dz53HG+vtJf/mJ82F+71vgA3aKFNGyYEZSaNTt3rIeH9J//GPegef554wP6\n4MHGvJ4+fSq+vqpe74VeR69e++1qpyqV3dPHkffufM9Zvu2WLaWFC42V0saPN+7Xk5x84XvkjBtn\n9NysWGGEHsnoVfruO2O575wc4xocOmQMIRw6tOz5//63cePX8gHIHVms1upOe6r78vPzbY8DAgJc\nWAnskZmZKUnq2bOniyvBhXCt3AvXy31wrdwH18q9XCrXKyHBuHFoRobj50ZGGj1H775b83U5oiY+\nvzNHBwAAADCRp5825umsXevYeR98YCwZ/uSTzqmrtjF0DQAAADCRzp2NoW6OGjbMWOnOLOjRAQAA\nAGA6BB0AAAAApkPQAQAAAGA6zNEBAACAaVmtVh07VqRt24qUnd1GknTq1El17eopf39PWRxdYxpu\ng6ADAAAAU7Jardq0qVApKV5as6aBJJ+SPRo8+KyeeKJQ0dENCDsmxdA1AAAAmE5JyImPb6A1azwl\nlQ4zFq1e7anBgxto06ZCXQK3lbwkEXQAAABgOseOFSklxUv5+VX31uTnWzRtmpeOHSuqxcpQWwg6\nAAAAMJ1t24q0Zk29Cx63enU9bd9O0DEjgg4AAABM56efLCo7XK0qFv34I3N0zIigAwAAAMB0CDoA\nAAAwnbAwqyR7FhmwqmVLFiMwI4IOAAAATKdrV08NGnT2gscNHnxWXbpwxxUzIugAAADAdPz9PTV9\n+hkFBFTdWxMYWKxp087I35+gY0YuCzoZGRlKTExUWFiYPDw8tHjx4grHZGdna/jw4QoKCpKvr696\n9OihXbt2VTjOarUqISFBHh4e+ve//10b5QMAAKAOs1gsio5uoFWrCjV4cJHKDmOzKj6+SB99dEpX\nX80NQ83KZfG1oKBAERERSkpK0pgxYyr8guXk5KhPnz5KTk7W448/rsDAQO3atUt+fn4V2nr66adV\nr56xfCC/qAAAAJCMz4VXX91AqalF2r69UN99d1KS1KGDj7p08ZS/PyHHzFwWdBISEpSQkCBJSk5O\nrrB/6tSpio+P15w5c2zbwsPDKxy3efNmPffcc9qyZYuaNm3qrHIBAADghiwWiwICvNS7t5e8vbdL\nknr27OniqlAb6uQcneLiYq1YsUKdOnVSfHy8QkNDFR0drWXLlpU57vjx4xo1apQWLFigkJLine truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11a4dd8>"
+        "<matplotlib.figure.Figure at 0x7f7617641cf8>"
        ]
       }
      ],
@@ -752,7 +752,7 @@
       "\n",
       "> The key insight to this entire book is in the next paragraph. Read it carefully!\n",
       "\n",
-      "So what do we do? If we only take data from the measurement than the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italized the key point)."
+      "So what do we do? If we only take data from the measurement than the prediction will not affect the result. If we only take data from the prediction then the measurement will be ignored. If this is to work we need to take some kind of *blend of the prediction and measurement* (I've italicized the key point)."
      ]
     },
     {
@@ -778,7 +778,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c12b6f98>"
+        "<matplotlib.figure.Figure at 0x7f7617713080>"
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@@ -848,7 +848,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c14e90b8>"
+        "<matplotlib.figure.Figure at 0x7f761792f048>"
        ]
       }
      ],
@@ -877,7 +877,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c13ae0b8>"
+        "<matplotlib.figure.Figure at 0x7f761779b438>"
        ]
       }
      ],
@@ -949,7 +949,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1514828>"
+        "<matplotlib.figure.Figure at 0x7f76178d9b00>"
        ]
       }
      ],
@@ -1013,7 +1013,7 @@
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c13cb710>"
+        "<matplotlib.figure.Figure at 0x7f7617884780>"
        ]
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@@ -1155,7 +1155,7 @@
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1398898>"
+        "<matplotlib.figure.Figure at 0x7f76178b47b8>"
        ]
       },
       {
@@ -1239,9 +1239,9 @@
       {
        "metadata": {},
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c120db00>"
+        "<matplotlib.figure.Figure at 0x7f7617918cc0>"
        ]
       }
      ],
@@ -1295,9 +1295,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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+       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1414ba8>"
+        "<matplotlib.figure.Figure at 0x7f76176d7b70>"
        ]
       }
      ],
@@ -1307,7 +1307,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "The filter starts out with estimates that are far from the measured data due to the bad initial guess of 100. You can see that it 'rings' before settling in on the measured data. 'Ringing' means that the signal overshoots and undershoots the data in a sinusodial type pattern. This is a very common phenomena in filters, and a lot of work in filter design is devoted to minimizing ringing. That is a topic that we are not yet prepared to address, but I wanted to show you the phenomenon."
+      "The filter starts out with estimates that are far from the measured data due to the bad initial guess of 100. You can see that it 'rings' before settling in on the measured data. 'Ringing' means that the signal overshoots and undershoots the data in a sinusoidal type pattern. This is a very common phenomena in filters, and a lot of work in filter design is devoted to minimizing ringing. That is a topic that we are not yet prepared to address, but I wanted to show you the phenomenon."
      ]
     },
     {
@@ -1358,9 +1358,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11e2978>"
+        "<matplotlib.figure.Figure at 0x7f763484b780>"
        ]
       }
      ],
@@ -1434,7 +1434,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1442a90>"
+        "<matplotlib.figure.Figure at 0x7f7617880240>"
        ]
       }
      ],
@@ -1507,25 +1507,25 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1220a90>"
+        "<matplotlib.figure.Figure at 0x7f76177014e0>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c15262b0>"
+        "<matplotlib.figure.Figure at 0x7f7617701128>"
        ]
       },
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11b2160>"
+        "<matplotlib.figure.Figure at 0x7f76176537f0>"
        ]
       }
      ],
@@ -1564,7 +1564,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c118ed30>"
+        "<matplotlib.figure.Figure at 0x7f7617777048>"
        ]
       },
       {
@@ -1572,7 +1572,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11c8710>"
+        "<matplotlib.figure.Figure at 0x7f76178eaf98>"
        ]
       },
       {
@@ -1580,7 +1580,7 @@
        "output_type": "display_data",
        "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c118e9b0>"
+        "<matplotlib.figure.Figure at 0x7f7617844e80>"
        ]
       }
      ],
@@ -1592,7 +1592,7 @@
      "source": [
       "Here we can see the effects of ignoring the signal. We not only filter out noise, but legitimate changes in the signal as well. \n",
       "\n",
-      "Maybe we need a 'Godilocks' filter, where is not too large, not too small, but just right? Well, not exactly. As alluded to earlier, different filters choose g and h in different ways depending on the mathematical properties of the problem. For example, the Benedict-Bordner filter was invented to minimize the transient error in this example, where $\\dot{x}$ makes a step jump. We will not discuss this filter in this book, but here are two plots chosen with different allowable pairs of g and h. This filter design minimizes transient errors for step jumps in $\\dot{x}$ at the cost of not being optimal for other types of changes in $\\dot{x}$."
+      "Maybe we need a 'Goldilocks' filter, where is not too large, not too small, but just right? Well, not exactly. As alluded to earlier, different filters choose g and h in different ways depending on the mathematical properties of the problem. For example, the Benedict-Bordner filter was invented to minimize the transient error in this example, where $\\dot{x}$ makes a step jump. We will not discuss this filter in this book, but here are two plots chosen with different allowable pairs of g and h. This filter design minimizes transient errors for step jumps in $\\dot{x}$ at the cost of not being optimal for other types of changes in $\\dot{x}$."
      ]
     },
     {
@@ -1615,7 +1615,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1233828>"
+        "<matplotlib.figure.Figure at 0x7f76178d3390>"
        ]
       },
       {
@@ -1623,7 +1623,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11a4fd0>"
+        "<matplotlib.figure.Figure at 0x7f7615d77a20>"
        ]
       }
      ],
@@ -1671,7 +1671,7 @@
        "output_type": "display_data",
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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c00beb00>"
+        "<matplotlib.figure.Figure at 0x7f7615d5cfd0>"
        ]
       },
       {
@@ -1679,7 +1679,7 @@
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c00c3d30>"
+        "<matplotlib.figure.Figure at 0x7f7615d88d30>"
        ]
       },
       {
@@ -1687,7 +1687,7 @@
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1262eb8>"
+        "<matplotlib.figure.Figure at 0x7f7617696278>"
        ]
       }
      ],
@@ -1765,9 +1765,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11a4048>"
+        "<matplotlib.figure.Figure at 0x7f761781fd30>"
        ]
       }
      ],
@@ -1779,7 +1779,7 @@
      "source": [
       "We can see from the chart how poor the measurements are. No real train could ever move like that. \n",
       "\n",
-      "So what should we set *g* and *h* to if we want to filter this data? We have not developed the theory for this, but let's try to get a reasonable answer by the seat of our pants. We know that the measurements are very inaccurate, so we don't want to give them much weight at all. To do this we need to choose a very small *g*. We also know that trains can not accelerate or deaccelerate quickly, so we also want a very small *h*. For example:"
+      "So what should we set *g* and *h* to if we want to filter this data? We have not developed the theory for this, but let's try to get a reasonable answer by the seat of our pants. We know that the measurements are very inaccurate, so we don't want to give them much weight at all. To do this we need to choose a very small *g*. We also know that trains can not accelerate or decelerate quickly, so we also want a very small *h*. For example:"
      ]
     },
     {
@@ -1796,9 +1796,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11ddb70>"
+        "<matplotlib.figure.Figure at 0x7f76176d2198>"
        ]
       }
      ],
@@ -1825,9 +1825,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c145f9e8>"
+        "<matplotlib.figure.Figure at 0x7f7615df2cf8>"
        ]
       }
      ],
@@ -1837,7 +1837,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "We made `g=0.2` and we can see that while the train's position is smoothed, the estimated position (and hence velocity) fluctuates a lot in a very tiny frame, far more than a real train can do. So emperically we know that we want `g<<0.2`.\n",
+      "We made `g=0.2` and we can see that while the train's position is smoothed, the estimated position (and hence velocity) fluctuates a lot in a very tiny frame, far more than a real train can do. So empirically we know that we want `g<<0.2`.\n",
       "\n",
       "Now let's see the effect of a poor choice for *h*."
      ]
@@ -1856,9 +1856,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c11f92e8>"
+        "<matplotlib.figure.Figure at 0x7f7617909278>"
        ]
       }
      ],
@@ -1904,9 +1904,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
+       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c1372048>"
+        "<matplotlib.figure.Figure at 0x7f7615e32c50>"
        ]
       }
      ],
@@ -1933,9 +1933,9 @@
       {
        "metadata": {},
        "output_type": "display_data",
-       "png": 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truncated
        "text": [
-        "<matplotlib.figure.Figure at 0x7f25c008e828>"
+        "<matplotlib.figure.Figure at 0x7f7615daac18>"
        ]
       }
      ],
@@ -1945,7 +1945,7 @@
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "There are two lessons to be learned here. First, use the *h* term to respond to changes in velocity that you are not modelling. But, far more importantly, there is a tradeoff here between responding quickly and accurately to changes in behavior and producing ideal output for when the system is in a steady state that you have. If the train never changes velocity we would make *h* extremely small to avoid having the filtered estimate unduly affected by the noise in the measurement. But in an interesting problem there is almost always changes in state, and we want to react to them quickly. The more quickly we react to it, the more we are affected by the noise in the sensors. \n",
+      "There are two lessons to be learned here. First, use the *h* term to respond to changes in velocity that you are not modeling. But, far more importantly, there is a trade off here between responding quickly and accurately to changes in behavior and producing ideal output for when the system is in a steady state that you have. If the train never changes velocity we would make *h* extremely small to avoid having the filtered estimate unduly affected by the noise in the measurement. But in an interesting problem there is almost always changes in state, and we want to react to them quickly. The more quickly we react to it, the more we are affected by the noise in the sensors. \n",
       "\n",
       "I could go on, but my aim is not to develop g-h filter theory here so much as to build insight into how combining measurements and predictions lead to a filtered solution, so I will stop here. Do understand that there is extensive literature on choosing *g* and *h* for problems such as this, and that there are optimal ways of choosing them to achieve various goals. In the subsequent chapters we will learn how the Kalman filter solves this problem in the same basic manner, but with far more sophisticated mathematics. "
      ]
@@ -1982,7 +1982,7 @@
       "Another advantage of this form of filter, even if the data fits a *n*-degree polynomial, is that it is *recursive*. That is, we can compute the estimate for this time period knowing nothing more than the estimate and rate from the last time period. In contrast, if you dig into the implementation for `polyfit()` you will see that it needs all of the data before it can produce an answer. Therefore algorithms like `polyfit()` are not well suited for real-time data filtering. In the 60's when the Kalman filter was developed computers were very slow and had extremely limited memory. They were utterly unable to store, for example, thousands of readings from an aircraft's inertial navigation system, nor could they process all of that data in the short period of time needed to provide accurate and up-to-date navigation information. \n",
       "\n",
       "\n",
-      "Up until the mid 20th century various forms of Least Squares Estimation was used for this type of filtering. For example, for NASA's Apollo program had a ground network for tracking the Command and Service Model (CSM) and the Lunar Module (LM). They took measurements over many minutes, batched the data together, and slowly computed an answer. In 1960 Stanley Schmidt at NASA Ames recognized the utility of Rudolf Kalman's seminal paper and invited him to Ames. Schmidt applied Kalman's work to the onboard navigation systems on the CSM and LM, and called it the \"Kalman filter\".[1] Soon after, the world moved to this faster, recursive filter.\n",
+      "Up until the mid 20th century various forms of Least Squares Estimation was used for this type of filtering. For example, for NASA's Apollo program had a ground network for tracking the Command and Service Model (CSM) and the Lunar Module (LM). They took measurements over many minutes, batched the data together, and slowly computed an answer. In 1960 Stanley Schmidt at NASA Ames recognized the utility of Rudolf Kalman's seminal paper and invited him to Ames. Schmidt applied Kalman's work to the on board navigation systems on the CSM and LM, and called it the \"Kalman filter\".[1] Soon after, the world moved to this faster, recursive filter.\n",
       "\n",
       "The Kalman filter only needs to store the last estimate and a few related parameters, and requires only a relatively small number of computations to generate the next estimate. Today we have so much memory and processing power that this advantage is somewhat less important, but at the time the Kalman filter was a major breakthrough not just because of the mathematical properties, but because it could (barely) run on the hardware of the day. \n",
       "\n",