Lots of book formatting changes.

Changed default sizes of plots, changed the book template for
pdf creation, and lots of minor edits, most changing bold to
italic, and removing italic for emphasis.

01-g-h-filter.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -295,7 +300,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "** Try Another Scale**\n",
+    "**Try Another Scale**\n",
     "\n",
     "Is there any way we can improve upon this result? The obvious, first thing to try is get a better sensor. Unfortunately, your co-worker informs you that she has built 10 scales, and they all operate with about the same accuracy. You have her bring out another scale, and you weigh yourself on one, and then on the other. The first scale (A) reads \"160 lbs\", and the second (B) reads \"170 lbs\". What can we conclude about your weight?\n",
     "\n",
@@ -327,7 +332,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x491e048>"
+       "<matplotlib.figure.Figure at 0x4607c18>"
       ]
      },
      "metadata": {},
@@ -361,7 +366,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAxsAAAB6CAYAAADXnk6rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x73a7b38>"
+       "<matplotlib.figure.Figure at 0x72396d8>"
       ]
      },
      "metadata": {},
@@ -392,7 +397,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x76ed198>"
+       "<matplotlib.figure.Figure at 0x7eb5780>"
       ]
      },
      "metadata": {},
@@ -427,7 +432,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Average of measurements is 165.0058\n"
+      "Average of measurements is 165.0549\n"
      ]
     }
    ],
@@ -458,7 +463,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Average of measurements is 164.9607\n"
+      "Average of measurements is 165.0200\n"
      ]
     }
    ],
@@ -490,9 +495,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwkAAAERCAYAAAAwgetTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdYVGf2wPHvDB1FEBQUqWJBQezGWBAHFbDHig1RYzbR\nGF1josYk7G5MspuYtWyy2cSsPYpGo8aKZVQ0aqyo2AsWVOyKIH3m9we/jJmdMbFMoZzP8/A8znvP\nvXPmOgz3zH2LQqvVahFCCCGEEEKI/6e0dgJCCCGEEEKIkkWKBCGEEEIIIYQeKRKEEEIIIYQQeqRI\nEEIIIYQQQuiRIkEIIYQQQgihR4oEIYQQQgghhB4pEoQQQgghhBB6rFYkJCcn0717d3x8fFAqlcyf\nP19ve1ZWFmPGjMHX1xdnZ2eCg4OZMWOGXkxERARKpVLvZ+DAgZZ8GUIIIYQQQpQ5ttZ64uzsbMLC\nwhg6dChxcXEoFAq97ePHj2fr1q0sWrSIwMBAduzYwciRI6lSpQqDBw8GQKFQMHz4cD755BPdfk5O\nThZ9HUIIIYQQQpQ1VruTEBMTw9SpU+nduzdKpWEae/bsIS4ujnbt2uHn58eQIUNo2bIl+/bt04tz\ncnLC09NT9+Pi4mKplyCEEEIIIUSZVGLHJLRp04affvqJ9PR0AHbv3k1KSgrR0dF6cYmJiVStWpXQ\n0FDeeecdsrKyrJGuEEIIIYQQZYbVuhv9kVmzZvHaa6/h5+eHrW1xml9++SWdO3fWxQwcOJCAgAC8\nvb1JTU1l8uTJHD16lKSkJL1jPXjwwKK5CyGEEEIIYW2urq7PvW+JLhL27NnDmjVr8Pf3Z8eOHbz9\n9tv4+/sTFRUFwMiRI3XxISEhBAUF0aJFCw4fPkzjxo2tlboQQgghhBClWoksEnJycnjvvfdYvnw5\nXbp0ASA0NJSUlBSmTZumKxL+V5MmTbCxseHcuXNSJAghhBBCCPGcSmSRUFBQQEFBgcGAZqVSiVar\nfeJ+x44do6ioiOrVqz8x5kVuuwjjDhw4AECzZs2snEnZJOfXfOTcmpecX/OS82s+cm7NS86veZmq\nm71Vp0A9e/YsABqNhkuXLpGSkoKHhwe+vr60a9eOSZMmUbFiRfz8/NixYwcLFy7k888/B+DChQss\nWrSILl264OHhwYkTJ3j77bdp0qQJrVu3ttbLEkIIIYQQotSz2uxG+/fvp0mTJjRp0oTc3FwSEhJo\n0qQJCQkJQPGsRc2bN2fQoEGEhITw2WefMXXqVEaPHg2Avb09arWaqKgogoODGTt2LNHR0WzZssVg\nzQUhhBBCCCHE07PanYSIiAg0Gs0Tt3t5eTFnzpwnbvfx8WH79u1myEwIIYQQQojyrcSukyCEEEII\nIYSwDikShBBCCCGEEHqkSBBCCCGEEELokSJBCCGEEEIIoUeKBCGEEEIIIYQeKRKEEEIIIYQQeqRI\nEEIIIYQQQuiRIkEIIYQQQgihR4oEIYQQQgghhB4pEoQQQgghhBB6pEgQQgghhBBC6JEiQQghhBBC\nCKFHigQhhBBCCCGEHikShBBCCCGEEHqkSBBCCCGEEELokSJBCCGEEEIIoUeKBCGEEEIIIYQeKRKE\nEEIIIYQQeqRIEEIIIYQQQuixWpGQnJxM9+7d8fHxQalUMn/+fL3tWVlZjBkzBl9fX5ydnQkODmbG\njBl6MXl5eYwZM4aqVatSsWJFevTowdWrVy35MoQQQgghhChzrFYkZGdnExYWxsyZM3FyckKhUOht\nHz9+POvXr2fRokWcOnWKKVOmMGnSJBYtWqSLGTduHD/++COJiYns3LmTzMxMunbtikajsfTLEUII\nIYQQosywWpEQExPD1KlT6d27N0qlYRp79uwhLi6Odu3a4efnx5AhQ2jZsiX79u0D4MGDB8yZM4dp\n06YRGRlJ48aNWbhwIUePHmXLli2WfjlCCCGEEEKUGSV2TEKbNm346aefSE9PB2D37t2kpKQQHR0N\nwMGDBykoKKBTp066fXx8fKhXrx67d++2Ss5CCCGEEEKUBSW2SJg1axZhYWH4+flhb29PREQEn332\nGZ07dwYgIyMDGxsbPDw89Pbz8vLixo0b1khZCLPILMjktT2vseTYEh4VPLJ2OkIIIYQoB2ytncCT\nzJo1iz179rBmzRr8/f3ZsWMHb7/9Nv7+/kRFRT33cQ8cOGDCLMVvybl9ds2bN/vjoK5LodlhBv44\nEPKd4XQPSI2Fc1FQ5KAXun+//B88D3nvmpecX/OS82s+cm7NS86vedSuXdskxymRRUJOTg7vvfce\ny5cvp0uXLgCEhoaSkpLCtGnTiIqKolq1ahQVFXHnzh29uwkZGRmEh4dbK3UhTMv7ADSd/fix/SNo\nsKT458CfYO1/rJebEEIIIcqsElkkFBQUUFBQYDCgWalUotVqAWjatCl2dnZs2rSJAQMGAJCens6p\nU6do1arVE4/drNlTfHMrnsmv3wTIuX12//92fiKNtgk2fftBg6UG25Jm9KLTmv9tlf+DZyHvXfOS\n82tecn7NR86tecn5Na8HDx6Y5DhWKxKys7M5e/YsABqNhkuXLpGSkoKHhwe+vr60a9eOSZMmUbFi\nRfz8/NixYwcLFy7k888/B8DV1ZURI0bw7rvv4unpibu7O+PHj6dhw4Z06NDBWi9LCJNSKpSwYglk\nV4OWM3XtlR0rowpUGd0nflU8VZyrEBsaS9PqTQ2mFxZCCCGE+CNWKxL279+PSlV8kaNQKEhISCAh\nIYH4+HjmzJlDYmIikydPZtCgQdy9e5eAgACmTp3K6NGjdceYMWMGtra29O/fn5ycHDp06MCiRYvk\nokiUMQrYOB0KnKHtp7jYu5A0OAlbpeGv742sGyw8uhCNVsMXe74gqHIQsaGxxIbGEuoZaoXchRBC\nCFEaWa1IiIiI+N1Fz7y8vJgzZ87vHsPe3p5Zs2Yxa9YsU6cnRAmjgK0f8+lfKtHGrw3NazQ3GrXy\n1Eo02se/V+fvnefjnR/zzcFvuP72daOFhRBCiMceFTzibOZZalcyzeBPIUoruWIQotRQMKnNpN+N\nGNF4BAFuASSmJrLy1Eoy8zIB6Fu/r9ECQavVyp03IUS58rsfeY73YGBXqHoC5u2Ap5hR/Y/GlglR\nWpXYdRKEEM8mrzAPOxs7omtFM6/nPG5MuMHK/ivpF9KPQQ0GGd3nm4PfED43nK/3f83N7JsWzlgI\nIUoSLcT2BL/d4HQfBkcVFw1ClFNSJAhRBsw5PIfG3zTmauZVXZujrSM9g3uytM9SWvu1NrrfktQl\n7Ly8k1HrR+H9hTdRi6KYe3guD3JNMzOCEEKUNFrtk34UJP9lKo62jsWBuyZBbuXfiZe7CKJskyJB\niFJu8bHFvPrTq5y8fZLweeFcun/pqfa78+gOu6/s1j0u0hax6fwmhv80nJSMFHOlK4QQJVZb/7as\n6LcCVs6HX8ZaOx0hrEqKBCFKOXsbe2yUNgBcuHeB8HnhnLt77g/383D2IP3P6XwZ8yVt/Nro2r1d\nvPUe/1ZBUYFpkhZCiBKqc+3OcCTO2mkIYXVSJAhRyvWp34cf+/2IvY09AJcfXCZ8bjgnb538w329\nKnoxusVodg7byeVxl5nWcRoTW0/UFR2/lZ6Zjuc0T+JXxZN0LkkKBiFEqZaRlWHtFIQo0aRIEKIM\n6Fa3G2sGrMHJ1gmA3MJcCjTPdhHv6+rL263e5q2X3jK6fdnxZdzPvc/8I/OJ/j4a739688baN9ib\nvveF8xdCCEtadWoVNWfWZGmq4Wr2QohiUiQIUUZ0CurEhkEbqOFSg01DNhHmFWbS4/985We9x7cf\n3eY/B/9DYmqiSZ9HCCHMaV7KPHov601OYQ5DVg5h0/lN1k5JiBJJigQhypB2Ae0499Y5mnk3M/mx\nl/ddzv6R+xnfcjw1XGro2geEDjAafz/3PlqZ+kMIUYLM2DuDYauH6RadDHALoK5HXStnJUTJJIup\nCVHG6KbvMzGFQkEz72Y0827G550+5+fLP7Ph3AZa1GhhND5qURQP8x4yIHQA/UP7U8ejjlnyEkKI\np/GPXf9g0tbHC1I2qtaIjYM24lXRy4pZCVFyyZ0EIcqJr/d/bbLb6kqFkrb+bfkk8hOjKzZfuHeB\nfVf3cfL2ST7c/iF1v6xL02+b8vnPn5NXmGeSHIQQ4llE1oykon1FANr4tWHb0G1SIAjxO6RIEKIc\n+O7Qd4xaP4puS7qx5vQasz/f0RtHcbZz1ms7dP0Q/z7wb90sTEIIYUnNvJuxZsAaetXrRdLgJNwc\n3aydkhAlmhQJQpRxOQU5fLLzEwDyi/LptawXPxz/wazP2TO4Jzcn3CSxdyI9g3vqCoPYkFijdx7u\n5dzjXs49s+YkhBARARGs6LfC4EsMIYQhKRKEKOOc7JzYHr+doMpBABRqColdEcvCIwvN+rwV7CvQ\nP7Q/K/uv5OaEm8zrMY9hjYcZjf3m4Dd4TfOi25JufH/0e7Lys8yamxCibJN1XIR4cVIkCFEO+Ln6\nkTwsmeAqwQBotBre3fIuD/MeWuT5XR1dGdpo6BMHLy9JXUKBpoC1Z9YyeOVgPD/3pN8P/Th245hF\n8hNClB23sm/x8n9f5r+H/mvtVIQo1aRIEKKc8HbxZkf8DsK8wnB3cmfT4E24OLhYOy0y8zINZmTK\nKczhhxM/UKQtslJWQojS6PKDy7Sd25aD1w/y2trXWH5iubVTEqLUkiJBiHLEs4In24ZuY9vQbTTw\namDtdACo5FCJX179hfNvnedj1cc08CzOK7hKMA29GhrdZ8+VPRRppIAQQjx2+vZp2sxpw+k7p3Vt\nmXmZVsxIiNJN1kkQopxxd3LH3cnd2mkYqFm5Ju+1fY/32r7H8ZvHuZl90+gg55O3TLine truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwkAAADtCAYAAAD0pjmFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f23e48>"
+       "<matplotlib.figure.Figure at 0x7f41358>"
       ]
      },
      "metadata": {},
@@ -521,9 +526,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEtCAYAAABqG4QrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEPCAYAAAAgfyAWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fbf5f8>"
+       "<matplotlib.figure.Figure at 0x7fdc160>"
       ]
      },
      "metadata": {},
@@ -550,9 +555,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEtCAYAAABqG4QrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAEPCAYAAAAgfyAWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ffde48>"
+       "<matplotlib.figure.Figure at 0x804ef98>"
       ]
      },
      "metadata": {},
@@ -581,9 +586,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA48AAAEtCAYAAACoIlXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA48AAAEPCAYAAADiRvH+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f72a90>"
+       "<matplotlib.figure.Figure at 0x7fdc0b8>"
       ]
      },
      "metadata": {},
@@ -613,9 +618,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA48AAAEtCAYAAACoIlXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA48AAAEPCAYAAADiRvH+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x48ce240>"
+       "<matplotlib.figure.Figure at 0x72b7518>"
       ]
      },
      "metadata": {},
@@ -648,9 +653,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwkAAAEtCAYAAABDOSyFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwkAAAEPCAYAAAAJXYi4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xtc1FX+P/DXjII3MK4CigoGqZmoieAFRAdBUQZ1s+jG\nSNv+LK12XVrbeIjRrulj+6aW5mV3LS9htlmaO6QoeUEETUXxVmqigoqOcRFZMUBgfn98ZMbRGUSc\nGQ7D6/l48Hj4+cyZz+dM7wbmPed9zpFptVotiIiIiIiI7pA3dweIiIiIiEgsTBKIiIiIiMgAkwQi\nIiIiIjLAJIGIiIiIiAwwSSAiIiIiIgNMEoiIiIiIyACTBCIiIiIiMtCsSUJmZiZiYmLg7e0NuVyO\ntWvXGjweHx8PuVxu8DN8+HCDNufOncPkyZPRpUsXPPbYY4iNjcWvv/7a4H1XrlyJ0NBQuLi4wNnZ\nGQqFAtnZ2WZ/fURERERELVGzJgkVFRUICAjA4sWL0aFDB8hkMoPHZTIZIiIioNFodD9bt241eH5k\nZCRkMhl2796N7OxsVFdXQ6lUoqE94vbs2YMXXngBu3fvxoEDB9C7d2+MHTsWeXl5FnutREREREQt\nhUyUHZcdHR2xbNkyqFQq3bn4+HiUlJQgNTXV6HPS09MRFRWF0tJSPPbYYwCA8vJyODs7Iz09HeHh\n4Y2+v5eXF5KSkvDGG2882gshIiIiImrhhJ6TIJPJkJWVBQ8PD/Tu3RvTpk1DUVGR7vGqqirIZDK0\na9dOd65du3aQy+UPVT5UVVWFyspKODs7m7X/REREREQtkdBJwrhx45CSkoJdu3Zh4cKFOHjwIBQK\nBaqrqwEAw4YNg4ODA2bNmoVbt26hoqICf/nLX1BbW4urV682+j5JSUlwdHRETEyMpV4KEREREVGL\n0ba5O9CQ2NhY3b/79euHwYMHo2fPntiyZQsmT54MNzc3fPPNN5g+fTqWL18OuVyOF198EU8//TTk\n8sblP4sXL8a///1v7Ny5Ew4ODgaP3bhxw6yvh4iIiIjImupL8h+W0EnCvby8vODt7W0wwTgiIgJ5\neXkoLS1F27Zt0blzZ3h6euKFF1544PU++eQTvPfee9i2bRsCAwMt2XUiIiIiohajRSUJRUVFKCws\nhJeX132Pubi4AAB27tyJoqKiB5YOLVq0CO+//z62bt1637KqREREREStWbMmCRUVFTh79iwAoK6u\nDgUFBTh69ChcXV3h4uKC5ORkTJkyBZ6ensjPz0diYiI8PDwwefJk3TVWr16NPn36oEuXLti/fz9m\nzpyJhIQE+Pv769qEh4cjODgY8+fPBwB89NFHSEpKwrp16+Dn5weNRgMA6NixIzp37my0r00dqiEi\nIiIisiZzlMw36xKoGRkZUCgUUkdkMt3eBvHx8Vi+fDkmTZqE3NxclJWVwcvLCwqFAnPnzkW3bt10\n10hMTMSaNWtQWloKX19fvP7665g5c6bBfXx9fTF69GisWrVKd3zx4sX79lKIj4/XtQEM/wMzSSAi\nIiKilsAcn2GF2SdBREwSxJCTkwMAnDciAMZCDIyDOBgLMTAOYmAcxMEkwcKYJBARERFRS2OOz7BC\n75NARERERETWxySBiIiIiIgMMEkg4eXk5OjqHKl5MRZiYBzEwViIgXEQA+NgWzgnoQGck0BERERE\nLQ3nJBARERERkdkxSSAiIiIiIgNMEkh4rHEUB2MhBsZBHIyFGBgHMTAOtoVzEhrAOQlERERE1NJw\nTgIREREREZkdkwQiIiIiIjLAJIGExxpHcTAWYmAcxMFYiIFxEAPjYFs4J6EBnJNARERERC0N5yQQ\nEREREZHZMUkgIiIiIiIDTBJIeKxxFAdjIQbGQRyMhRgYBzEwDraFcxIawDkJRERERNTScE4CERER\nERGZHZMEIiIiIiIy0GxJQmZmJmJiYuDt7Q25XI61a9caPB4fHw+5XG7wM3z4cIM2586dw+TJk9Gl\nSxc89thjiI2Nxa+//vrAe2/cuBFPPvkk2rdvj379+mHz5s1mfW1kXqxxFAdjIQbGQRyMhRgYBzEw\nDralbXPduKKiAgEBAZg6dSpUKhVkMpnB4zKZDBEREUhJSdGds7e3N3h+ZGQkBgwYgN27d0Or1WLO\nnDlQKpX48ccf77tevf379+P555/H3//+d/zud7/Dxo0b8eyzzyI7OxtBQUGWebH0SAIDA5u7C3QH\nYyEGxkEcjIUYGAcxMA62RYiJy46Ojli2bBlUKpXuXHx8PEpKSpCammr0Oenp6YiKikJpaaluQkZ5\neTmcnZ2Rnp6O8PBwo8+LjY1FWVkZtm/frjsXEREBd3d3rF+/3qAtJy4TERERUUtj0xOXZTIZsrKy\n4OHhgd69e2PatGkoKirSPV5VVQWZTIZ27drpzrVr1w5yuRzZ2dkmr/vjjz8iMjLS4FxkZCT27dtn\n/hdBRERE1ArU1dWhqqAAVQUFqKura+7ukBkImySMGzcOKSkp2LVrFxYuXIiDBw9CoVCguroaADBs\n2DA4ODhg1qxZuHXrFioqKvCXv/wFtbW1uHr1qsnrajQaeHh4GJzz8PCARqOx6OuhpmONozgYCzEw\nDuJgLMTAODSvuro6VKWnw27oUNgNHYqq9HQmCjZA2CQhNjYW0dHR6NevH6Kjo5GWloYzZ85gy5Yt\nAAA3Nzd88803SEtLg6OjI5ycnFBeXo6nn34acrnlXta9v4R4bPnjwMBAXZ2jCP1pzceAYc1pc/en\ntR7XvydE6U9rPubvJzGOjdXCi9S/Fne8ZQs0KhWwfDmwZw9QUtJg+9uXLqHdK69ArtFArtGg3Suv\n4OLBg+K8nlZ4bA7NNnH5YXl5ecHb2xt5eXm6cxEREcjLy0NpaSnatm2Lzp07w9PTEy+88ILJ63h6\net43anDt2jV4enparO9ERERELUJ+PjBxIjxra4G7Fo8Z4OICdO0KdOkCLFrUfP0jqxF24vK9ioqK\n4O3tjc8//xwvv/yy0TY7d+5EZGQkTp8+DX9/f6Ntnn/+eVy/ft1g4nJkZCTc3d3x5ZdfGrTlxGUi\nIiJqVW7cALp1AyoqTLdxcQFKSnSH9eVG7V55BQBQtXo12kVGWrSygxpmjs+wzboE6tmzZwFI/3MV\nFBTg6NGjcHV1hYuLC5KTkzFlyhR4enoiPz8fiYmJ8PDwwOTJk3XXWL16Nfr06YMuXbpg//79mDlz\nJhISEgwShPDwcAQHB2P+/PkAgD/96U8YOXIkPvzwQ0ycOBHfffcdMjIyGpzsTM3r7hILal6MhRgY\nB3EwFmJgHMykthb4+WdApQI2bgRM7T1115L0ACCXy9EuMhIXv/sOANAjKIgJgg1otpGEjIwMKBQK\nqRMyGeq7ER8fj+XLl2PSpEnIzc1FWVkZvLy8oFAoMHfuXHTr1k13jcTERKxZswalpaXw9fXF66+/\njpkzZxrcx9fXF6NHj8aqVat05zZu3IikpCScP38efn5+mDdvHiZNmnRfHzmSQERERDatogL44QdA\nrQa+/x64ayVJo9zdgX37AD8/6/SPmsQcn2GFKDcSFZMEIiIisjmFhVJCoFYDO3cCVVXG27VtC9TU\n6I8HDgS2b5fmJZDQWnS5ERERERFZgVYLHDsmJQVqNXD4sOm2XboASqU0YvCPf+jPDxsGbN0KODlZ\nvr8kBCYJJDzWmoqDsRAD4yAOxkIMjIMRVVVARoaUFKSmApcumW771FNATIyUHAQFAXI5MGeO/vHw\ncGDzZsDBocFbMg62heVGDWC5EREREbUYxcXSt/1qtVQWdPOm8XZt2wJhYfrEwNf3/jYaDfD++9JK\nR7NmAe3bW7TrZF6ck2BhTBKIiIhIaGfO6MuI9u0DTO107OQEjB8vJQXjxrFsyMZxTgIRERFRa1JT\nIyUD9WVEv/xium2vXsDEiVJiEBIC2NlZr5/U4jFJIOGxxlEcjIUYGAdxMBZisPk4lJdL5UNqtVRO\nVFpqvJ1MJk0wri8j6ttXOmclNh+HVoblRg1guRERERE1i4ICaaRArZYmIN++bbxdx47A2LFSUjBh\nApcnJQAsNyIiIiKyDXV10tKk9WVEx46Zbtu1q360QKHgpGKyCCYJRERERM3ht9+kzczqdzu+etV0\n20GDpKQgJgZ4+mmrlhFR68QkgYTHGkdxMBZiYBzEwViIoUXF4do1KSFITQXS06VEwRh7e2mUQKmU\nfrp3t24/m6BFxYEeiHMSGsA5CURERPRItFrgp5/0ZUQHDkjnjHF1leYVxMQAkZGAo6N1+0o2g3MS\niIiIiERz+zaQmalPDC5cMN22Tx99GdGwYUCbNtbrJ1EDmCQQERERParr14G0NCkpSEsD7vom14Bc\nDoSG6suInnjCuv0kaiQmCSQ81jiKg7EQA+MgDsZCDM0Wh3Pn9KMFmZlAba3xdo6O0i7HMTFAVJRU\nVmSD+H6wLZyT0ADOSSAiIiKd2lppTkH9/gU//2y6bc+e+jKisDBpIjKRlXBOAhEREZElVVQAP/yg\nX6a0qMh02yFDpKQgJgbo35/LlFKLxiSBiIiI6G6FhVJCoFZL+xhUVRlv1749MGaMlBRERwNeXtbt\nJ5EFMUkg4bHGURyMhRgYB3EwFmJ45DhotcDRo/oyosOHTbf18JASgpgYKUHo2LFp97RBfD/YFs5J\naADnJBAREdmoqiogI0M/8fjSJdNtn3pKX0Y0ZIi0QhGRwMzxGbbZ/i/PzMxETEwMvL29IZfLsXbt\nWoPH4+PjIZfLDX6GDx9u0Eaj0SAuLg5eXl7o1KkTBg4ciPXr1z/w3osXL0afPn3QsWNHdO/eHW++\n+SYqKirM+vqIiIhIMMXFwBdfAFOmAG5u0opDy5ffnyC0bQuEhwOLFwPnzwMnTgDz5Line truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x739f518>"
+       "<matplotlib.figure.Figure at 0x7236b38>"
       ]
      },
      "metadata": {},
@@ -677,9 +682,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvwAAAEtCAYAAAB00rSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvwAAAEPCAYAAAA+thClAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x73d50b8>"
+       "<matplotlib.figure.Figure at 0x7f6ce80>"
       ]
      },
      "metadata": {},
@@ -720,9 +725,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvwAAAEtCAYAAAB00rSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x803d908>"
+       "<matplotlib.figure.Figure at 0x7f17358>"
       ]
      },
      "metadata": {},
@@ -777,9 +782,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6sAAAEICAYAAAC59WLsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x83d1f98>"
+       "<matplotlib.figure.Figure at 0x91ad390>"
       ]
      },
      "metadata": {},
@@ -818,7 +823,7 @@
     "    gh.plot_gh_results(weights, estimates, predictions)\n",
     "\n",
     "initial_guess = 160.\n",
-    "predict_using_gain_guess (weight=initial_guess, gain_rate=1)"
+    "predict_using_gain_guess(weight=initial_guess, gain_rate=1)"
    ]
   },
   {
@@ -841,9 +846,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6sAAAEmCAYAAACEUwaqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6sAAAEICAYAAAC59WLsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8363358>"
+       "<matplotlib.figure.Figure at 0x80807b8>"
       ]
      },
      "metadata": {},
@@ -883,9 +888,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6sAAAEmCAYAAACEUwaqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8397978>"
+       "<matplotlib.figure.Figure at 0x815a710>"
       ]
      },
      "metadata": {},
@@ -928,12 +933,10 @@
     "I think this is starting to look really good. We used no methodology for choosing our scaling factors of $\\frac{4}{10}$ and $\\frac{1}{3}$ (actually, they are poor choices for this problem), and we 'luckily' choose 1 lb/day as our initial guess for the weight gain, but otherwise all of the reasoning followed from very reasonable assumptions.\n",
     "\n",
     "One final point before we go on. In the prediction step I wrote the line\n",
-    "\n",
     "```python\n",
     "gain_rate = gain_rate\n",
-    "```\n",
-    "    \n",
-    "This obviously has no effect, and can be removed. I wrote this to emphasize that in the prediction step you need to predict next value for **all** variables, both *weight* and *gain_rate*. In this case we are assuming that the gain does not vary, but when we generalize this algorithm we will remove that assumption. "
+    "``` \n",
+    "This obviously has no effect, and can be removed. I wrote this to emphasize that in the prediction step you need to predict next value for all variables, both `weight` and `gain_rate`. In this case we are assuming that the gain does not vary, but when we generalize this algorithm we will remove that assumption. "
    ]
   },
   {
@@ -978,7 +981,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8046a20>"
+       "<matplotlib.figure.Figure at 0x7f816a0>"
       ]
      },
      "metadata": {},
@@ -993,7 +996,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let me introduce some more formal terminology. The predict step is known as **system propagation**. The *system* is whatever we are estimating - in this case my weight. We *propogate* it into the future. Some texts call this the **evolution**. It means the same thing. The update step is usually known as the **measurement update**. One iteration of the system propagation and measurement update is known as an **epoch**. \n",
+    "Let me introduce some more formal terminology. The *system* is the object that we want to estimate. In this chapter the system is whatever we are trying to weigh. \n",
+    "\n",
+    "The *state* of the system is the current configuration or values of that system that is of interest to us. If I put a 100 kg weight on the scale, its state is 100kg. We define the state based on what is relevant to us. The color, weight, and location of the scale is irrelevant to us so we do not include those values in the state. The *state estimate* is our filter's estimate of the state. For example, for the 100 kg weight weight our estimate might be 99.327 kg due to sensor errors and other factors.\n",
+    "\n",
+    "We use a *process model* to mathematically model the system. In this chapter our process model is the assumption that my weight today is yesterday's weight plus my weight gain for the last day. The process model does not model or otherwise account for the sensors. Another example would be a process model for an automobile. The process model might be \"distance equals velocity times time. This model is not perfect as the velocity of a car can vary over a non-zero amount of time, the tires can slip on the road, and so on. The *system error* or *process error* is the error in this model. We never know this value exactly; if we did we could refine our model to have zero error.\n",
+    "\n",
+    "The predict step is known as *system propagation*. It uses the *process model* to form a new *state estimate*. Because of the *process error* this prediction is normally imperfect. Assuming we are tracking data over time, we say we *propogate* the state into the future. Some texts call this the *evolution*. \n",
+    "\n",
+    "The update step is known as the *measurement update*. One iteration of the system propagation and measurement update is known as an *epoch*. \n",
     "\n",
     "Now let's explore a few different problem domains to better understand this algorithm. Consider the problem of trying to track a train on a track. The track constrains the position of the train to a very specific region. Furthermore, trains are large and slow. It takes them many minutes to slow down or speed up significantly. So, if I know that the train is at kilometer marker 23 km at time t and moving at 18 kph, I can be extremely confident in predicting its position at time t + 1 second. And why is that important? Suppose we can only measure its position with an accuracy of $\\pm$ 250 meters. The train is moving at 18 kph, which is 5 meters per second. So at t+1 second the train will be at 23.005 km yet the measurement could be anywhere from 22.755 km to 23.255 km. So if the next measurement says the position is at 23.4 we know that must be wrong. Even if at time t the engineer slammed on the brakes the train will still be very close to 23.005 km because a train cannot slow down very much in 1 second. If we were to design a filter for this problem (and we will a bit further in the chapter!) we would want to design a filter that gave a very high weighting to the prediction vs the measurement. \n",
     "\n",
@@ -1028,22 +1039,17 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Notation and Nomenclature"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "I'll begin to introduce the nomenclature and variable names used in the literature. Some of this was already used in the above charts. Measurement is typically denoted $z$ and that is what we will use in this book (some literature uses $y$). Subscript $k$ indicates the time step, so $z_k$ is the data for this time step. A bold font denotes a vector or matrix. So far we have only considered having one sensor, and hence one sensor measurement, but in general we may have *n* sensors and *n* measurements. $\\mathbf{x}$ denotes our data, and is bold to denote that it is a vector. For example, for our scale example, it represents both the initial weight and initial weight gain rate, like so:\n",
+    "## Notation\n",
+    "\n",
+    "I'll begin to introduce the notations and variable names used in the literature. Some of this was already used in the above charts. Measurement is typically denoted $z$ and that is what we will use in this book (some literature uses $y$). Subscript $k$ indicates the time step, so $z_k$ is the data for this time step. A bold font denotes a vector or matrix. So far we have only considered having one sensor, and hence one sensor measurement, but in general we may have *n* sensors and *n* measurements. $\\mathbf{x}$ denotes our state, and is bold to denote that it is a vector. For example, for our scale example, it represents both the initial weight and initial weight gain rate, like so:\n",
     "\n",
     "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n",
     "\n",
-    "So if the weight is 62 kg and the weight gain is 0.3 kg/day, the vector would be\n",
+    "For a weight of 62 kg with a gain of 0.3 kg/day we have\n",
     "\n",
     "$$\\mathbf{x} = \\begin{bmatrix}62 \\\\ 0.3\\end{bmatrix}$$\n",
     "\n",
-    "So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$. We then enter a loop, predicting the state for time $k$ from the values from time $k-1$. We then get the measurement $z_k$ and choose some intermediate point between the measurements and prediction, creating the estimate $\\mathbf{x}_k$."
+    "So, the algorithm is simple. The state is initialized with $\\mathbf{x_0}$, the initial estimate. We then enter a loop, predicting the state for time or step $k$ from the values from time/step $k-1$. We then get the measurement $z_k$ and choose some intermediate point between the measurements and prediction, creating the estimate $\\mathbf{x}_k$."
    ]
   },
   {
@@ -1059,7 +1065,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -1068,23 +1074,55 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[1 2 3]\n",
       "<class 'numpy.ndarray'>\n"
      ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([1, 2, 3])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
     "import numpy as np\n",
     "x = np.array([1, 2, 3])\n",
-    "print(x)\n",
-    "print(type(x))"
+    "print(type(x))\n",
+    "x"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "You can create a 2D array with nested lists:"
+    "You can also use tuples:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([4, 5, 6])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x = np.array((4,5,6))\n",
+    "x"
    ]
   },
   {
@@ -1138,6 +1176,93 @@
     "print(x)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can access the array elements using subscript location:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "6\n"
+     ]
+    }
+   ],
+   "source": [
+    "x = np.array([[1, 2, 3],\n",
+    "              [4, 5, 6]])\n",
+    "\n",
+    "print(x[1,2])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can access a column or row by using slices. A ':' used as a subscript is shorthand for all data in that row or column. So `x[:,0]` returns an array of all data in the first column (the 0 specifies the first column):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1, 4])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x[:, 0]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can get the second row with:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([4, 5, 6])"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x[1, :]"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1255,6 +1380,15 @@
     "print('\\neye\\n', np.eye(3))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "NumPy is part of the SciPy package. Both are well documented. You can find a tutorial and links to the full documentation at the following location:\n",
+    "\n",
+    "https://docs.scipy.org/doc/numpy-dev/user/quickstart.html"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1385,9 +1519,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5kAAADxCAYAAABBGXOMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x80120f0>"
+       "<matplotlib.figure.Figure at 0x7e461d0>"
       ]
      },
      "metadata": {},
@@ -1479,9 +1613,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5EAAAEPCAYAAADbIUClAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5EAAADxCAYAAABSzjN4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x809b5c0>"
+       "<matplotlib.figure.Figure at 0x91b0f28>"
       ]
      },
      "metadata": {},
@@ -1516,9 +1650,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuYAAAEWCAYAAAAq41LXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuYAAAD4CAYAAACg2iORAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7714278>"
+       "<matplotlib.figure.Figure at 0x8105dd8>"
       ]
      },
      "metadata": {},
@@ -1570,9 +1704,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5kAAADxCAYAAABBGXOMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x772f908>"
+       "<matplotlib.figure.Figure at 0x8047978>"
       ]
      },
      "metadata": {},
@@ -1633,9 +1767,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAEPCAYAAAC6OWLnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAADzCAYAAAB+HrAxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdYFFcXwOHf0quIBYgQO4q9YNRogg1LYkETY4+9JPbe\nY4uxa+zJp7HFXmOPvYsaxNhii4oFFYxKsdD3fn9MXCQ2wMUFPe/z7AN7d2b2DFyWOXObTimlEEII\nIYQQQgghTMDM1AEIIYQQQgghhHh/SVIqhBBCCCGEEMJkJCkVQgghhBBCCGEykpQKIYQQQgghhDAZ\nSUqFEEIIIYQQQpiMJKVCCCGEEEIIIUxGklIhhBBCCCGEECZjkVYHHjt2LEOGDKFLly7MmDHDUD5i\nxAjmzp1LWFgY5cqVY9asWRQuXNjwekxMDH379mXFihVERUVRrVo1Zs+ejbu7e5LjR0REpFXoQggh\nhBBCpDknJydThyBEupAmLaVHjx5l7ty5FC9eHJ1OZygfP348U6ZMYebMmQQEBODi4kL16tV59OiR\nYZuePXuybt06VqxYwcGDB4mMjKROnTro9fq0CFUIIYQQQgghhAkZPSmNiIigRYsWLFiwAGdnZ0O5\nUoqpU6cyaNAgGjRoQJEiRVi0aBEPHz5k2bJlhn3nz5/PpEmTqFatGqVKlWLx4sWcPn2aXbt2GTtU\nIYQQQgghhBAmZvTuux07duSrr76iUqVKKKUM5UFBQYSGhlKjRg1DmY2NDT4+Pvj7+9OxY0cCAwOJ\ni4tLso2HhweFChXC398/SfmzpOuDeJnjx48DUKZMGRNHItIzqSciOaSeiNeROiKSQ4agCfE8oyal\nc+fO5erVq4aWz2e77oaEhADg6uqaZB8XFxdu375t2Mbc3JysWbMm2cbV1ZXQ0FBjhiqEEEIIIYQQ\nIh0wWlJ68eJFhgwZwqFDhzA3Nwe0LrvPtpa+zLPJa2o8vTMpxMtIHRHJIfVEJIfUE/E6UkfEq3h6\nepo6BCHSHaONKT1y5Aj37t2jSJEiWFpaYmlpyYEDB5g9ezZWVlZky5YN4LkWz9DQUNzc3ABwc3Mj\nISGB+/fvJ9kmJCTEsI0QQgghhBBCiHeH0VpKGzRoQNmyZQ3PlVK0adOGAgUKMHjwYDw9PXFzc2PH\njh14e3sDEB0dzaFDh5g0aRIA3t7eWFpasmPHDpo2bQpAcHAwFy5coEKFCi99bxm7IV5GxveI5JB6\nYhxBQUHcvn0bT09PXFxcTB2O0Uk9Ea8jdUQkh4wpFeJ5RktKnZycnptwyM7ODmdnZ8M6pD179mTM\nmDF4eXnh6enJ6NGjcXR0pFmzZoZjtGvXjv79++Pi4kKWLFno3bs3JUqUwNfX11ihCiGEMKL4+Hg6\nduzIggULALCwsGDy5Ml0797dxJEJIYQQIiMw+uy7z9LpdEnGi/bv35+oqCi6dOlCWFgY5cuXZ8eO\nHdjb2xu2mTp1KhYWFjRu3JioqCh8fX1ZsmTJG487FUIIkTbGjRvHggULsLS0pHDhwpw6dYoePXpQ\nqFAhqlevburwhBBCCJHOGX2d0mft3buX6dOnJykbPnw4t2/fJioqir179xpaUZ+ysrJi+vTp3Lt3\nj8ePH7Nhwwbc3d3TMkwhhBBvYMOGDQAsW7aMkydP0qdPHwA2bdpkyrCEEEIIkUGkaVIqhBDi3Wdm\npv0riY2NTfJVergIIYQQIjkkKRVCCPFGvvzySwBatGiBp6cnM2bMQKfT8cUXX5g4MiGESBtBQUH0\n7duXr7/+mgkTJhAdHW3qkITI0NJ0TKkQQoh3X58+fbhx4wazZs3i8uXLWFtbM2PGDCpVqmTq0IQQ\nwujOnTtHxYoVCQ8PN5Rt2LCBPXv2YG1tbcLIhMi4pKVUCCHEGzE3N2fmzJncuXOHP//8k9DQUDp0\n6GDqsIQQIk3069eP8PBwqlatyk8//YS7uzv+/v7Mnz/f1KEJkWFJS6kQQgijcHNzw83NzdRhCCFE\nmrpw4QKgrRhRrFgx7t+/z9ChQ7l48aKJIxMi45KWUiGEEEIIIZIpZ86cAEycOJFdu3axbNmyJOVC\niJSTpFQIIYQQQohkGjlyJBYWFixevJjq1atz7tw58ufPT9u2bU0dmhAZliSlQgghhBBCJJOPjw/7\n9+/Hz8+P8uXL06FDBw4fPkzmzJlNHZoQGZaMKRVCCCGEECIFKlSowPr1600dhhDvDGkpFUIIIYQQ\nQghhMpKUCiGEEEIIIYQwGUlKhRBCCCGEEEKYjCSlQgghhBBCCCFMRpJSIYQQQgghhBAmI0mpEEII\nIYQQQgiTkaRUCCGEEEIIIYTJSFIqhBBCCCGEEMJkJCkVQgghhBBCCGEykpQKIYQQQgghhDAZoyal\ns2bNokSJEjg5OeHk5ESFChXYunVrkm1GjBiBu7s7dnZ2VKlShXPnziV5PSYmhm7dupE9e3YcHBzw\n8/Pj1q1bxgxTCCGEEEKINKGU4syZMxw8eJCwsDBThyNEhmDUpPTDDz9kwoQJ/PnnnwQGBlK1alXq\n16/PmTNnABg/fjxTpkxh5syZBAQE4OLiQvXq1Xn06JHhGD179mTdunWsWLGCgwcPEhkZSZ06ddDr\n9cYMVQghhBBCCKMKDw+nWrVqFC9eHB8fHzw8PFizZo2pwxIi3TNqUlqvXj1q1qxJ3rx5yZ8/P6NH\nj8bR0ZGjR4+ilGLq1KkMGjSIBg0aUKRIERYtWsTDhw9ZtmwZABEREcyfP59JkyZRrVo1SpUqxeLF\nizl9+jS7du0yZqhCCCGEEEIYVZcuXdi7dy+ZMmWiaNGiPHnyhObNm3Px4kVThyZEupZmY0oTEhJY\nsWIFjx8/pkKFCgQFBREaGkqNGjUM29jY2ODj44O/vz8AgYGBxMXFJdnGw8ODQoUKGbYRQgghhBAi\nPdq0aRMA/v7+nD59mnr16hEbG8vOnTtNHJkQ6ZuFsQ945swZPv74Y2JiYnBwcOC3336jSJEihqTS\n1dU1yfYuLi7cvn0bgJCQEMzNzcmaNWuSbVxdXQkNDTV2qEIIIYQQQhiNmZnW3hMVFYVSiujo6CTl\nQogXM3pS6uXlxenTp4mIiGD16tW0bNmSffv2vXIfnU73Ru95/PjxN9pfvPukjojkkHoikkPqiXgd\nqSPvrypVqrB+/Xo+/vhjsmTJwt27d7G1tcXDw8NQLzw9PU0cpRDpj9Fv21haWpI3b15KlSrFmDFj\nKFmyJD/++CMffPABwHMtnqGhobi5uQHg5uZGQkIC9+/fT7JNSEiIYRshhBBCCCHSo969e1O1alXi\n4+O5e/cuTk5OTJgwgRw5cpg6NCHSNaO3lP5XQkICsbGx5MmTBzc3N3bs2IG3tzcA0dHRHDp0iEmT\nJgHg7e2NpaUlO3bsoGnTpgAEBwdz4cIFKlSo8NL3KFOmTFqfhsignt6VlDoiXkXqiUgOqSfpk1KK\n0NBQbGxsyJw5s0ljSU0duXXrFps3byYmJoYqVapQrFixtApPvCW7d+/m1q1bREREkDdvXmxsbJK8\nHhERYaLIhEi/jJqUDhw4kDp16uDh4WGYVXf//v2GtUp79uzJmDFj8PLywtPT0zA7b7NmzQBwcnKi\nXbt29O/fHxcXF7JkyULv3r0pUaIEvr6+xgxVCCGESFNBQUHMnTuXe/fuUbp0adq3b4+FRZrfC36v\n/PXXXzRq1Miw5rmfnx+LFi3CycnJxJElz5EjR/j8888JDw8HwNzcnLlz59KmTRvDNk/HJP43sRHp\nm7u7O+7u7qYOQ4gMw6j/HUNDQ2nRogUhISE4OTlRokQJtm3bRvXq1QHo378/UVFRdOnShbCwMMqX\nL8+OHTuwt7c3HGPq1KlYWFjQuHFjoqKi8PX1ZcmSJW887lQIIYR4W06dOkWlSpWStIhs2bKF9evX\nY25ubsLI3h0PHz7ks88+4+bNm9jb2xMdHc2GDRto165dhlgXUq/X07RpU8LDw/Hx8cHV1ZXVq1fT\nqVMnfH19sba2plWrVmzbtg2Azz//nIULF5I9e3YTRy6EEManU0opUweRGs/+o88od0TF2yfd7URy\nSD0RyZGSelK5cmX279+Pr68vtWrVYsyYMTx48IAVK1bQuHHjtA71vbBlyxbq1KmDl5cXgYGB3L59\n2zCBzKNHj5Lc8H5bUlJHbt++jbu7O46Ojjx48AALCwt8fHw4ePAgv/32GxMnTnxuObxPP/2U/fv3\ny436DE6uYYV4nsxPLYQQQhjZX3/9BcDcuXPp06cP7dq1AzB0MxVvLjY2FgBnZ2dsbW3Jnj27oXt0\nfHy8KUNLFkdHR3Q6HQ8fPuTw4cNcuXKFS5cuARAZGYm/vz9OTk7cunWLmzdv4ujoyMGDB/n7779N\nHLkQQhifJKVCCCGEkT0dS/bjjz9y4MABNmzYACAzcBpR+fLlsbe358iRI5QtW5YSJUoQHx9P2bJl\nM0Trk6Ojo+FmReXKlcmfPz+hoaF4e3tToEABQEu4XV1d+eCDD3B2dgbgyZMnJotZCCHSiiSlQmQw\n8fHxjBw5kmLFilGkSBEGDx5saDEQQqQPI0eORKfTMX36dCpVqsSlS5fw8vIyTOwn3twHH3zAypUr\ncXBw4Pjx41y/fp0CBQqwfPlyU4eWbDNnzqRHjx5kyZIFBwcHGjRowNatWylevDjZs2fn2rVrVKhQ\ngY8//pgbN27g6uqKl5eXqcPOkB48eMCRI0e4fPmyqUMRQryATAMoRAbz7bff8ssvvxienzt3jmvX\nrrFs2TITRpUymzZtYtq0aYSFhVG2bFnGjh1r8qUchDAmPz8/tm7dyqRJk7h//z6lS5dm3LhxODo6\nmjq0d0rt2rW5evUqAQEB2NjYUKFChQw1S621tTVTp05l6tSpz722evVq6tevzx9//Line truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x95780f0>"
+       "<matplotlib.figure.Figure at 0x923f710>"
       ]
      },
      "metadata": {},
@@ -1643,7 +1777,7 @@
     }
    ],
    "source": [
-    "zs = gen_data (x0=5, dx=2, count=100, noise_factor=100)\n",
+    "zs = gen_data(x0=5, dx=2, count=100, noise_factor=100)\n",
     "data = g_h_filter(data=zs, x0=5., dx=2., g=0.2, h=0.02)\n",
     "plot_g_h_results(measurements=zs, filtered_data=data)"
    ]
@@ -1698,9 +1832,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5oAAAEPCAYAAAAjwbtSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9585080>"
+       "<matplotlib.figure.Figure at 0x925e6a0>"
       ]
      },
      "metadata": {},
@@ -1778,7 +1912,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x95d3cf8>"
+       "<matplotlib.figure.Figure at 0x924a080>"
       ]
      },
      "metadata": {},
@@ -1820,7 +1954,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x957a828>"
+       "<matplotlib.figure.Figure at 0x7fc3668>"
       ]
      },
      "metadata": {},
@@ -1865,7 +1999,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f25278>"
+       "<matplotlib.figure.Figure at 0x7f56f98>"
       ]
      },
      "metadata": {},
@@ -1912,7 +2046,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f243c8>"
+       "<matplotlib.figure.Figure at 0x728de48>"
       ]
      },
      "metadata": {},
@@ -1958,9 +2092,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvMAAAEWCAYAAADrZBh7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvMAAAD4CAYAAABhXWk9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x73db630>"
+       "<matplotlib.figure.Figure at 0x80d72e8>"
       ]
      },
      "metadata": {},
@@ -1979,11 +2113,11 @@
     "    plt.plot(data, color='b')\n",
     "    plt.show()\n",
     "\n",
-    "interact (interactive_gh,           \n",
-    "          x=FloatSlider(value=0., min=-50, max=50.), \n",
-    "          dx=FloatSlider(value=5., min=-50., max=50.), \n",
-    "          g=FloatSlider(value=0.1, min=0.01, max=2, step=.02), \n",
-    "          h=FloatSlider(value=0.02, min=0.0, max=0.5, step=0.01));"
+    "interact(interactive_gh,           \n",
+    "         x=FloatSlider(value=0., min=-50, max=50.), \n",
+    "         dx=FloatSlider(value=5., min=-50., max=50.), \n",
+    "         g=FloatSlider(value=0.1, min=0.01, max=2, step=.02), \n",
+    "         h=FloatSlider(value=0.02, min=0.0, max=0.5, step=0.01));"
    ]
   },
   {
@@ -2006,7 +2140,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAACXCAYAAADte/19AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9591278>"
+       "<matplotlib.figure.Figure at 0x92660f0>"
       ]
      },
      "metadata": {},
@@ -2042,7 +2176,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x80bc160>"
+       "<matplotlib.figure.Figure at 0x7f7f278>"
       ]
      },
      "metadata": {},
@@ -2106,9 +2240,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwMAAAEcCAYAAACbPWhEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x802aac8>"
+       "<matplotlib.figure.Figure at 0x92acc18>"
       ]
      },
      "metadata": {},
@@ -2157,9 +2291,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEjCAYAAABaRN5lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEFCAYAAACLsThOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdcVfX/wPHXuWwQcKCMZAWIkSPNvQeiuXe5LVc5Ek2z\n1NCGWVqpWYn6LUPUX84cYZYDceEsUwMBFVBUFEJwoMzz++PGrZuKTC/i+/l4nAf3fu45n/M+3CPe\n9/0sRVVVFSGEEEIIIYQQopRoDB2AEEIIIYQQQojyTRJPIYQQQgghhBClShJPIYQQQgghhBClShJP\nIYQQQgghhBClShJPIYQQQgghhBClShJPIYQQQgghhBClShJPIYR4img0Gtzd3Q0dhhBCCCGeMpJ4\nCiHEv4SEhNC2bVtsbW2xtramSZMmrFy5skh1hYeH06VLFypXroylpSV169Zl0aJF5Obm3rdvQkIC\nc+bMoV+/fnh6eqLRaNBoNERHRxf3ku6jKEqJ11kQkZGR9O/fn2rVqmFhYUHNmjWZPXs29+7dK3Rd\nCQkJjBgxAicnJ8zNzXF3d2fSpEmkpqY+9JjCvB95Vq5cSePGjbG2tqZixYq0bduWkJCQB+579OhR\n3n33XV566SUcHBzQaDQ4OjoW+tqEEEKI8khRVVU1dBBCCFEWfP3110yYMAE7OztefvllTE1NWb9+\nPQkJCbz11lvMnz+/wHVt2bKFPn36YGlpycsvv0zlypXZunUrUVFR9O3bl3Xr1untv3nzZnr37q1r\nkfzrr79IS0sjMjKSGjVqlNg1ajQa3NzcuHDhQonVWRBHjx6lXbt2ZGdn07dvX5ydndm9ezfHjx+n\nefPm7N69G1NT0wLVdeHCBZo1a8b169fp2bMnNWvW5MiRI4SGhuLt7c3BgwepXLmy3jGFfT8Apk6d\nyueff46zszN9+/YlIyODH374gZSUFBYvXsy4ceP09vf39+fLL7/E1NQUHx8fTp48iYODA1euXCn6\nL04IIYQoL1QhhBBqbGysamZmptrZ2anx8fG68hs3bqienp6qoihqeHh4gepKS0tTq1atqpqbm6sn\nTpzQld+7d09t1qyZqiiK+sMPP+gdk5CQoB44cEC9deuWqqqq2rp1a1VRFDUqKqoEru4fiqKo7u7u\nJVrno2RnZ6vPPfecqtFo1G3btunKc3Nz1b59+6qKoqiffPJJgevz8/NTFUVRv/rqK73yyZMnq4qi\nqK+//rpeeVHej4MHD6qKoqheXl5qamqqrjwuLk6tUqWKam5ursbFxekdc/LkSfXkyZNqVlaWqqra\n37Wjo2OBr0sIIYQoz6SrrRCizFFVlUWLFuHj44OFhQXVq1dnwoQJpKWl4ebmVipjFL/77jsyMzMZ\nP348Li4uuvKKFSsyffp0AAIDAwtU14YNG0hOTuaVV16hfv36unIzMzM++ugjAJYsWaJ3zDPPPEPz\n5s2pUKFCcS+lQNLT05k6dSouLi6Ym5vj5eXFvHnzSuVcYWFhnD17llatWtG1a1dduaIounMW9Hd7\n/vx5du7cibu7+30tju+//z6WlpasWrWK9PR0XXlR3o+8eGbMmIGtra2u3NXVlXHjxpGRkcGKFSv0\njqlbty5169bF2Ni4QNcihBBCPE0k8RRClDnjxo1j0qRJ3Lx5k9GjRzNgwAB27tyJn58f2dnZpTJG\ncc+ePQB06tTpvtdeeuklAEJDQ4tdV6tWrbCwsCA8PJysrKyihlssmZmZ+Pn5sWnTJrp06cKoUaO4\ne/cu77zzDh988EGJny+/34e7uzteXl5cvHixQN1/894DPz+/+16rUKECzZs3586dOxw+fLhA5//3\n+5GZmal3jKIoJXI/CCGEEALka1khRJmyf/9+AgMD8fLy4ujRo7rWpo8//hhfX1+uXLmCm5ub3jFp\naWksWLCgUOdp27YtrVu31j2PiopCUZQHjqd0cHDA0tKShIQE7t27h7m5eb51R0VFATywLiMjI9zd\n3YmMjOTChQt4e3sXKu6ScOXKFV544QV2796NmZkZAAEBAdSoUYMFCxYwffp0vVa7hQsX5jtpz3+5\nu7szbNgw3fP8fh8AXl5exMTEEBMTw7PPPptv3QWpa+fOncTExNCuXbtHHvPf96NmzZrcuXOHK1eu\nYG1tjb29/X3HeHp6ApTKxE9CCCFEeSWJpxCiTAkKCgLg3Xff1eviaGJiwty5c2nRosV9x9y4caNQ\nLXWKoqDRaPQSz7S0NAC9c/6bra0td+/eJS0t7ZGJZ1paGoqi5FuXqqqFSuZKkqIofPnll7qkE6Bq\n1ap0796d4OBgoqOj8fHx0b22aNEi4uPjC1x/mzZt9BLPgvxugQL9PopSV0Hfj7y6SzJeIYQQQmhJ\n4imEKFN+//13gAcmmI0bN8bIyOi+cjc3t3yXxBD6bG1tH9iy6OzsDGgT+X+LjY19LHEJIYQQovyS\nMZ5CiDIlr3XqQV0cjYyMqFKlSqmcN68VK6+160Fx/Xu/R9X17xa0h9VVsWLFooRabA87b1732pyc\nnBI9X0F/twX5fRSlrsK+HyUZrxBCCCG0pMVTCFGm2NjYAJCYmIi1tbXeazk5Ofz1119YWlrqlZfE\nGE9vb28OHTpEVFQUTZo00dv36tWrpKen4+zs/Mhutnl1nThxgqioKOrVq6f3WnZ2NrGxsZiYmDxy\nPGNZUdwxnjVr1gT+GWv5XzExMQ8dX/tfBakL9MdzFvb9sLKywsnJiatXr5KYmIiDg8MjzyGEEEKI\n/EniKYQoU+rXr8/Jkyc5cOAAXl5eeq8dPnz4ga1xeWM8FUVBVdVHnuNBYzzbt2/PoUOH2LFjx32J\n588//wygm6zmUdq3b8+aNWvYsWMHr7zyit5r+/bt4+7du7Ru3RoTE5MC1WdoxR3j2a5dO+bMmcOO\nHTt455139Pa9cOECMTExBV4mp23btgDs3LkTVVX1Zji+desWBw8exMrKSu89LMr70b59e4KDg9mx\nYwfDhw/XO6aw94MQQgghAAOuISqEEPcJCwtTFUVRvby81Bs3bujKMzIy1FatWqmKoqju7u4lft7Y\n2FjV3NxcrVKlihoXF6crT0lJUT08PFSNRqMePnxY75jk5GQ1MjJSvXr1ql75zZs31apVq6pmZmbq\n8ePHdeV3795VmzZtqiqKoq5duzbfeFq3bq0qiqKePXv2ofusWLFCVRRFbdOmTYGvM7/f36xZs1RF\nUdSwsLAC11cQOTk5qo+Pj6ooirp161a98r59+6qKoqiffvqp3jHp6elqZGSkev78+fvq69ixo6oo\nirp48WK98kmTJqmKoqhvvPGGXnlR3o9Dhw6piqKonp6eevdhbGysWrlyZdXCwkKNj4/P97oVRVEd\nHR3z3UcIIYR4WkiLpxCiTGnVqhWjR49m2bJl1KpVi969e2NmZsbWrVupVKkSTk5OaDQlPzzdzc2N\nzz77jAkTJtCgQQNefvllTExM2LBhA5cvX2bKlCk0btxY75jFixfzwQcfMGzYMFasWKErt7a25n//\n+x99+vShTZs2vPLKK1SqVImtW7cSHR1Nv3796N+//30x/Ltl7ezZs4B2dt+87se9evWiR48eun3y\nJlQyNTUtsd9DadBoNKxYsYJ27drRt29f+vbti7OzM7t37+bEiRO0aNGCSZMm6R1z5MgR2rVrh6ur\n632TG33zzTc0a9aMN998k927d1OzZk2OHDnC3r178fb2Zs6cOXr7F+X9aNq0KW+99Raff/45derU\noU+fPmRmZrJ27VpSU1NZvHgxLi4uesecPXuWTz75RK8sNTVV73199913DbKEjhBCCGFwhs58hRDi\nv3Jzc9UFCxaoNWvWVM3MzNRnnnlGHT9+vJqWlqZWqFBBrVevXqmdOyQkRG3durVqbW2tVqhQQW3U\nqJG6cuXKB+47e/ZsVaPRqK+++uoDXw8PD1c7d+6sVqpUSbWwsFDr1KmjLly4UM3NzX3g/oqiqBqN\nRvczb8t7/v777+vtP3HiRFVRFHXVqlUFvr78WjzzrqekWzzzREREqP3799e1Pnp7e6uzZ89W7927\nd9++e/fuzTfWhIQE9bXXXlMdHR1VU1NT1c3NTZ00aZKampr60PMX9v1QVVVduXKl2qhRI9XKykq1\nsbFR27Rpo4aEhDxw39DQ0Ee+h6X1uxVCCCHKOkVVCzAgSgghyoCYmBi8vb0ZMGAAq1evNnQ4BvfC\nCy+QmZnJn3/+qTfWUQghhBCirJGutkKIMuf69evY2dnpdalNT0/H398f0HY5fdqlpKRw+vRp1qxZ\nI0mnEEIIIco8afEUQpQ5M2fOJDg4mLZt2+Lg4EBiYiK7d+/m8uXLdO7cmZ9++snQIQohhBBCiEKQ\nFk8hRJnj6+vL77//zq+//kpKSgomJibUqFEDf39/XaunEEIIIYR4cpTpFs+0tDRDhyCEEEIIIUSR\n2draGjoEIcqEkl+TQAghhBBCCCGE+BdJPIUQQgghhBBClKonZoyndFMQD3P8+HEAGjRoYOBIRFkm\n94koCLlPREHIfSIeRYaLCXE/afEUQgghhBBCCFGqJPEUQgghhBBCCFGqJPEUQgghhBBCCFGqnpgx\nnkIIIZ4uubm5/Pnnn9y+fZtatWphbW1t6JCEEEIIUUTS4imEEKLMSU5OplWrVtSpU4dmzZrh7OzM\njh07DB2WEEIIIYpIEk8hhBBlzsiRIzl48CC2trbUqFGDtLQ0+vbty6VLlwwdmhBCCCGKQBJPIYQQ\nZUp2djY//fQTAH/88Qdnz56lTZs23Llzh9DQUANHJ4QQQoiikMRTCCFEmaIoChqN9r+nzMxMcnNz\nycrK0r0mhBBCiCePJJ5CCCHKFCMjI3r16gVA3bp1cXV11XW79fX1NXB0QgghhCgKSLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x83f6f60>"
+       "<matplotlib.figure.Figure at 0x92702e8>"
       ]
      },
      "metadata": {},
@@ -2183,14 +2317,15 @@
    "cell_type": "code",
    "execution_count": 48,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "scrolled": true
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5EAAAEjCAYAAACrT4XoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5EAAAEFCAYAAAB6umPDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x96009b0>"
+       "<matplotlib.figure.Figure at 0x9209358>"
       ]
      },
      "metadata": {},
@@ -2221,9 +2356,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEjCAYAAABaRN5lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEFCAYAAACLsThOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9418828>"
+       "<matplotlib.figure.Figure at 0x92fcf60>"
       ]
      },
      "metadata": {},
@@ -2271,9 +2406,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEjCAYAAABaRN5lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEFCAYAAACLsThOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8Tff/wPHXudmSiAhZiASRUOOLxGrsmFF7VWt8tUZr\nxirqq/hW1WoprdFhRNXsj6o9IkhiJLbIQIIgCJKIkUhyfn+kud/eIhKS3IT38/G4D+7nnPM573Pv\ncd33/SxFVVUVIYQQQgghhBAin2j0HYAQQgghhBBCiDebJJ5CCCGEEEIIIfKVJJ5CCCGEEEIIIfKV\nJJ5CCCGEEEIIIfKVJJ5CCCGEEEIIIfKVJJ5CCCGEEEIIIfKVJJ5CCPEW0Wg0uLi46DsMIYQQQrxl\nJPEUQoi/2bZtG82aNcPKygpLS0vq16/PqlWrXqmu4OBgfHx8KFmyJMWKFaNmzZosWLCAjIyMZ/aN\njY1lxowZdO/enUqVKqHRaNBoNERGRr7uJT1DUZQ8rzMnLly4QI8ePbC1tcXMzAx3d3emTp3KkydP\ncl1XbGwsH330EY6OjpiamuLi4oKvry8JCQkvPCY370eWVatWUa9ePSwtLSlRogTNmjVj27Ztz933\n2LFjTJw4kbZt22Jvb49Go8HBwSHX1yaEEEK8iRRVVVV9ByGEEIXB999/z/DhwylVqhQ9e/bE2NiY\nDRs2EBsby5gxY5gzZ06O69qyZQtdu3alWLFi9OzZk5IlS/LHH38QERFBt27dWL9+vc7+mzdvpkuX\nLtoWybt375KYmMiFCxeoXLlynl2jRqPB2dmZy5cv51mdOXHs2DGaN29OWloa3bp1o1y5cuzbt4+Q\nkBDeffdd9u3bh7GxcY7qunz5Mg0bNuT27dt06tQJd3d3jh49ir+/P25ubgQGBlKyZEmdY3L7fgCM\nGzeOefPmUa5cObp160ZKSgpr167l3r17LFy4kKFDh+rsP2rUKL777juMjY2pWrUqp06dwt7enhs3\nbrz6CyeEEEK8KVQhhBBqdHS0amJiopYqVUq9cuWKtvz+/ftqpUqVVEVR1ODg4BzVlZiYqJYuXVo1\nNTVVQ0NDteVPnjxRGzZsqCqKoq5du1bnmNjYWPXw4cPqgwcPVFVV1SZNmqiKoqgRERF5cHX/oyiK\n6uLikqd1vkxaWppapUoVVaPRqFu3btWWZ2RkqN26dVMVRVG//vrrHNfXqlUrVVEUddGiRTrlo0eP\nVhVFUYcMGaJT/irvR2BgoKooiurq6qomJCRoy2NiYlQbGxvV1NRUjYmJ0Tnm1KlT6qlTp9SnT5+q\nqpr5Wjs4OOT4uoQQQog3mXS1FUIUOqqqsmDBAqpWrYqZmRlly5Zl+PDhJCYm4uzsnC9jFH/55RdS\nU1MZNmwYTk5O2vISJUowadIkAJYsWZKjujZu3Eh8fDy9evWidu3a2nITExO+/PJLABYvXqxzTJky\nZXj33XexsLB43UvJkUePHjFu3DicnJwwNTXF1dWV2bNn58u5AgICCA8Pp3HjxrRv315briiK9pw5\nfW0vXbrEnj17cHFxeabFcdq0aRQrVozVq1fz6NEjbfmrvB9Z8Xz++edYWVlpy8uXL8/QoUNJSUlh\n+fLlOsfUrFmTmjVrYmhomKNrEUIIId4mkngKIQqdoUOH4uvrS1JSEoMGDeL9999nz549tGrVirS0\ntHwZo7h//34A2rRp88y2tm3bAuDv7//adTVu3BgzMzOCg4N5+vTpq4b7WlJTU2nVqhW///47Pj4+\nDBw4kMePHzNhwgSmT5+e5+fL7vVwcXHB1dWVq1ev5qj7b9Z70KpVq2e2WVhY8O677/Lw4UOOHDmS\no/P//f1ITU3VOUZRlDy5H4QQQggB8rOsEKJQOXToEEuWLMHV1ZVjx45pW5u++uorvL29uXHjBs7O\nzjrHJCYm8u233+bqPM2aNaNJkyba5xERESiK8tzxlPb29hQrVozY2FiePHmCqalptnVHREQAPLcu\nAwMDXFxcuHDhApcvX8bNzS1XceeFGzdu8K9//Yt9+/ZhYmICwJQpU6hcuTLffvstkyZN0mm1mz9/\nfraT9vyTi4sL/fr10z7P7vUAcHV1JSoqiqioKCpUqJBt3Tmpa8+ePURFRdG8efOXHvPP98Pd3Z2H\nDx9y48YNLC0tsbOze+aYSpUqAeTLxE9CCCHEm0oSTyFEobJy5UoAJk6cqNPF0cjIiJkzZ+Ll5fXM\nMffv389VS52iKGg0Gp3EMzExEUDnnH9nZWXF48ePSUxMfGnimZiYiKIo2dalqmqukrm8pCgK3333\nnTbpBChdujQdOnTAz8+PyMhIqlatqt22YMECrly5kuP6mzZtqpN45uS1BXL0erxKXTl9P7Lqzst4\nhRBCCJFJEk8hRKFy8uRJgOcmmPXq1cPAwOCZcmdn52yXxBC6rKysntuyWK5cOSAzkf+76OjoAolL\nCCGEEG8uGeMphChUslqnntfF0cDAABsbm3w5b1YrVlZr1/Pi+vt+L6vr7y1oL6qrRIkSrxLqa3vR\nebO616anp+fp+XL62ubk9XiVunL7fuRlvEIIIYTIJC2eQohCpXjx4gDExcVhaWmpsy09PZ27d+9S\nrFgxnfK8GOPp5uZGUFAQERER1K9fX2ffmzdv8ujRI8qVK/fSbrZZdYWGhhIREUGtWrV0tqWlpREd\nHY2RkdFLxzMWFq87xtPd3R3431jLf4qKinrh+Np/ykldoDueM7fvh7m5OY6Ojty8eZO4uDjs7e1f\neg4hhBBCZE8STyFEoVK7dm1OnTrF4cOHcXV11dl25MiR57bGZY3xVBQFVVVfeo7njfFs0aIFQUFB\n7Ny585nEc8eOHQDayWpepkWLFqxZs4adO3fSq1cvnW0HDx7k8ePHNGnSBCMjoxzVp2+vO8azefPm\nzJgxg507dzJhwgSdfS9fvkxUVFSOl8lp1qwZAHv27EFVVZ0Zjh88eEBgYCDm5uY67+GrvB8tWrTA\nz8+PnTt30r9/f51jcns/CCGEEALQ4xqiQgjxjICAAFVRFNXV1VW9f/++tjwlJUVt3LixqiiK6uLi\nkufnjY6OVk1NTVUbGxs1JiZGW37v3j21YsWKqkajUY8cOaJzTHx8vHrhwgX15s2bOuVJSUlq6dKl\nVRMTEzUkJERb/vjxY7VBgwaqoijqunXrso2nSZMmqqIoanh4+Av3Wb58uaooitq0adMcX2d2r98X\nX3yhKoqiBgQE5Li+nEhPT1erVq2qKoqi/vHHHzrl3bp1UxVFUWfNmqVzzKNHj9QLFy6oly5deqa+\n1q1bq4qiqAsXLtQp9/X1VRVFUT/55BOd8ld5P4KCglRFUdRKlSrp3IfR0dFqyZIlVTMzM/XKlSvZ\nXreiKKqDg0O2+wghhBBvC2nxFEIUKo0bN2bQoEEsW7aMatWq0aVLF0xMTPjjjz+wtrbG0dERjSbv\nh6c7Ozszd+5chg8fjoeHBz179sTIyIiNGzdy/fp1xo4dS7169XSOWbhwIdOnT6dfv34sX75cW25p\naclPP/1E165dadq0Kb169cLa2po//viDyMhIunfvTo8ePZ6J4e8ta+Hh4UDm7L5Z3Y87d+5Mx44d\ntftkTahkbGycZ69DftBoNCxfvpzmzZvTrVs3unXrRrly5di3bx+hoaF4eXnh6+urc8zRo0dp3rw5\n5cuXf2Zyox9++IGGDRsyYsQI9u3bh7u7O0ePHuXAgQO4ubkxY8YMnf1f5f1o0KABY8aMYd68edSo\nUYOuXbuSmprKunXrSEhIYOHChTg5OekcEx4eztdff61TlpCQoPO+Tpw4US9L6AghhBB6p+/MVwgh\n/ikjI0P99ttvVXd3d9XExEQtU6aMOmzYMDUxMVG1sLBQa9WqlW/n3rZtm9qkSRPV0tJStbCwUOvW\nrauuWrXquftOnTpV1Wg06r///e/nbg8ODlbbtWunWltbq2ZmZmqNGjXU+fPnqxkZGc/dX1EUVaPR\naP/MemQ9nzZtms7+I0eOVBVFUVevXp3j68uuxTPrevK6xTNLWFiY2qNHD23ro5ubmzp16lT1yZMn\nz+x74MCBbGONjY1VBwwYoDo4OKjGxsaqs7Oz6uvrqyYkJLzw/Ll9P1RVVVetWqXWrVtXNTc3V4sX\nL642bdpU3bZt23P39ff3f+l7mF+vrRBCCFHYKaqagwFRQghRCERFReHm5sb777/Pr7/+qu9w9O5f\n//oXqampnD9/XmesoxBCCCFEYSNdbYUQhc7t27cpVaqUTpfaR48eMWrUKCCzy+nb7t69e5w9e5Y1\na9ZI0imEEEKIQi/bgVIzZ87E09MTKysrbG1t6dChA+fPn39mv8jISLp06YK1tTXm5ubUqVNHOz7p\nRQICAqhTpw5mZmZUrFiRpUuXvt6VCCHeGN999x0uLi7079+fCRMm0L9/f9zc3NixYwft2rWjW7du\n+g5R70qWLEl6ejo9e/bUdyhCCCGEEC+VbeIZEBDAsGHDCA4OZv/+/RgaGuLt7c39+/e1+0RHR/Pu\nu+9SsWJF/P39OX/+PDNmzMDCwuKF9UZHR9OuXTu8vLw4deoUEydOZPjw4fz+++95d2VCiCLL29ub\natWqsXv3bubPn8+mTZuwtbVlzpw5bNmyRd/hCSGEEEKIXMrVGM+HDx9iZWXFli1b8PHxAaB3794Y\nGBjg5+eX45N+9tlnbN68WWcB8IEDB3L+/HmCgoK0ZYmJiTmuUwghhBBCiMLGyspK3yEIUSjkak2C\npKQkMjIysLa2BjKn8v/zzz+pUqUKbdq0wdbWlrp167J+/fps6wkODqZVq1Y6Za1atSIkJOS5i8ML\nIYQQQgghhCi6cpV4jhw5klq1atGgQQMgcwKQ5ORkvvrqK9q0acPevXt5//33+eCDDLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x96033c8>"
+       "<matplotlib.figure.Figure at 0x92d75f8>"
       ]
      },
      "metadata": {},
@@ -2302,9 +2437,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEjCAYAAABaRN5lAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA54AAAEFCAYAAACLsThOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x93e8940>"
+       "<matplotlib.figure.Figure at 0x80487b8>"
       ]
      },
      "metadata": {},
@@ -2357,7 +2492,7 @@
    "outputs": [],
    "source": [
     "from filterpy.gh import GHFilter\n",
-    "f = GHFilter (x=0., dx=0., dt=1., g=.8, h=.2)"
+    "f = GHFilter(x=0., dx=0., dt=1., g=.8, h=.2)"
    ]
   },
   {
@@ -2499,7 +2634,7 @@
     "x_0  = np.array([1., 10., 100.])\n",
     "dx_0 = np.array([10., 12., .2])\n",
     "               \n",
-    "f_air = GHFilter (x=x_0, dx=dx_0, dt=1., g=.8, h=.2)\n",
+    "f_air = GHFilter(x=x_0, dx=dx_0, dt=1., g=.8, h=.2)\n",
     "f_air.update(z=np.array((2., 11., 102.)))\n",
     "print(' x =', f_air.x)\n",
     "print('dx =', f_air.dx)"

02-Discrete-Bayes.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -273,7 +279,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The Kalman filter belongs to a family of filters called **Bayesian filters**. Most textbook treatments of the Kalman filter present the Bayesian formula, perhaps shows how it factors into the Kalman filter equations, but mostly keeps the discussion at a very abstract level. \n",
+    "The Kalman filter belongs to a family of filters called *Bayesian filters*. Most textbook treatments of the Kalman filter present the Bayesian formula, perhaps shows how it factors into the Kalman filter equations, but mostly keeps the discussion at a very abstract level. \n",
     "\n",
     "That approach requires a fairly sophisticated understanding of several fields of mathematics, and it still leaves much of the work of understanding and forming an intuitive grasp of the situation in the hands of the reader.\n",
     "\n",
@@ -330,9 +336,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In Bayesian statistics this is called our **prior**. It basically means the probability prior to incorporating measurements or other information. More completely, this is called the **prior probability distribution**, but that is a mouthful and so it is normally shorted to *prior*. A **probability distribution** is a collection of all possible probabilities for an event. Probability distributions always to sum to 1 because *something* had to happen; the distribution lists all the different *somethings* and the probability of each.\n",
+    "In Bayesian statistics this is called our *prior*. It basically means the probability prior to incorporating measurements or other information. More completely, this is called the *prior probability distribution*, but that is a mouthful and so it is normally shorted to prior. A *probability distribution* is a collection of all possible probabilities for an event. Probability distributions always to sum to 1 because something had to happen; the distribution lists all the different somethings and the probability of each.\n",
     "\n",
-    "I'm sure you've used probabilities before - as in \"the probability of rain today is 30%\". The last paragraph sounds like more of that. But Bayesian statistics was a revolution in probability because it treats the probability as a *belief* about a single event. Let's take an example. I know if I flip a fair coin a infinitely many times 50% of the flips will be heads and 50% tails. That is standard probability, not Bayesian, and is called **frequentist statistics** to distinguish it from Bayes. Now, let's say I flip the coin one more time. Which way do I believe it landed? Frequentist probablility has nothing to say about that; it will merely state that 50% of coin flips land as heads. Bayes treats this as a belief about a single event - the strength of my belief that *this specific* coin flip is heads is 50%.\n",
+    "I'm sure you've used probabilities before - as in \"the probability of rain today is 30%\". The last paragraph sounds like more of that. But Bayesian statistics was a revolution in probability because it treats the probability as a belief about a single event. Let's take an example. I know if I flip a fair coin a infinitely many times 50% of the flips will be heads and 50% tails. That is standard probability, not Bayesian, and is called *frequentist statistics* to distinguish it from Bayes. Now, let's say I flip the coin one more time. Which way do I believe it landed? Frequentist probablility has nothing to say about that; it will merely state that 50% of coin flips land as heads. Bayes treats this as a belief about a single event - the strength of my belief that this specific coin flip is heads is 50%.\n",
     "\n",
     "There are more differences, but for now recognize that Bayesian statistics reasons about our belief about a single event, whereas frequentists reason about collections of events. In this rest of this chapter, and most of the book, when I talk about the probability of something I am referring to the probability that some specific thing is true. When I do that I'm taking the Bayesian approach.\n",
     "\n",
@@ -368,7 +374,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x71f4a20>"
+       "<matplotlib.figure.Figure at 0x720c4a8>"
       ]
      },
      "metadata": {},
@@ -389,7 +395,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This distribution is called a **categorical distribution**, which is the term used to describe a discrete distribution describing the probability of observing $n$ outcomes. It is a **multimodal distribution** because we have multiple beliefs about the position of our dog. Of course we are not saying that we think he is simultaneously in three different locations, merely that so far we have narrowed down our knowledge in his position to be one of these three locations. My (Bayesian) belief is that there is a 33.3% chance of being at door 0, 33.3% at door 1, and a 33.3% chance of being at door 8.\n",
+    "This distribution is called a *categorical distribution*, which is the term used to describe a discrete distribution describing the probability of observing $n$ outcomes. It is a *multimodal distribution* because we have multiple beliefs about the position of our dog. Of course we are not saying that we think he is simultaneously in three different locations, merely that so far we have narrowed down our knowledge in his position to be one of these three locations. My (Bayesian) belief is that there is a 33.3% chance of being at door 0, 33.3% at door 1, and a 33.3% chance of being at door 8.\n",
     "\n",
     "A few words about the *mode* of a distribution. This terms from elementary statistics. Given a set of numbers, such as {1, 2, 2, 2, 3, 3, 4}, the *mode* is the number that occurs most often. For this set the mode is 2. A set can contain more than one mode. The set {1, 2, 2, 2, 3, 3, 4, 4, 4} contains the modes 2 and 4, because both occur three times. We say the former set is *unimodal*, and the latter is *multimodal*.\n",
     "\n",
@@ -455,7 +461,7 @@
    "source": [
     "Obviously I carefully constructed the hallway layout and sensor readings to give us an exact answer quickly. Real problems will not be so clear cut. But this should trigger your intuition - the first sensor reading only gave us very low probabilities (0.333) for Simon's location, but after a position update and another sensor reading we knew much more about where he is. You might suspect, correctly, that if you had a very long hallway with a large number of doors that after several sensor readings and positions updates we would either be able to know where Simon was, or have the possibilities narrowed down to a small number of possibilities. For example, suppose we had a long sequence of \"door, right, door, right, wall, right, wall, right, door, right, door, right, wall, right, wall, right, wall, right, wall, right, door\". Simon could only have started in a location  where his movements had a door sequence of [1,1,0,0,1,1,0,0,0,0,1] in the hallway. There might be only one match for that, or at most a few. Either way we will be far more certain about his position then when we started.\n",
     "\n",
-    "We could work through the code to implement this solution, but instead let us consider a real world complication to the problem."
+    "We could implement this solution now, but instead let us consider a real world complication to the problem."
    ]
   },
   {
@@ -499,7 +505,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7949908>"
+       "<matplotlib.figure.Figure at 0x756d748>"
       ]
      },
      "metadata": {},
@@ -549,7 +555,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e3b4e0>"
+       "<matplotlib.figure.Figure at 0x7e590b8>"
       ]
      },
      "metadata": {},
@@ -584,12 +590,11 @@
    "source": [
     " We can see from the output that the sum is now 1.0, and that the probability of a door vs wall is still three times larger. The result also fits our intuition that the probability of a door must be less than 0.333, and that the probability of a wall must be greater than 0.0. Finally, it should fit our intuition that we have not yet been given any information that would allow us to distinguish between any given door or wall position, so all door positions should have the same value, and the same should be true for wall positions.\n",
     " \n",
-    "This result is called the **posterior**, which is short for **posterior probability distribution**. All this means is a probability distribution *after* incorporating the measurement information (posterior means 'after' in this context). To review, the *prior* is the probability distribution before including the measurement's information. Another term is the **likelihood** - this is the probability for the **evidence** (the measurement in this case) being true. That gives us this equation:\n",
+    "This result is called the *posterior*, which is short for *posterior probability distribution*. All this means is a probability distribution *after* incorporating the measurement information (posterior means 'after' in this context). To review, the *prior* is the probability distribution before including the measurement's information. Another term is the *likelihood* - this is the probability for the *evidence* (the measurement in this case) being true. That gives us this equation:\n",
     "\n",
-    "$$ \\mathtt{posterior} = \\frac{\\mathtt{prior}\\times \\mathtt{likelihood}}{\\mathtt{normalization}}$$ \n",
+    "$$\\mathtt{posterior} = \\frac{\\mathtt{prior}\\times \\mathtt{likelihood}}{\\mathtt{normalization}}$$ \n",
     "\n",
-    "It is very important to learn and internalize these terms as most of the literature uses them exclusively. You will be unable to read it if these terms aren't crystal clear to you. \n",
-    "In this chapter I will keep slipping these terms in so you get used to them."
+    "It is very important to learn and internalize these terms as most of the literature uses them exclusively."
    ]
   },
   {
@@ -623,7 +628,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e977b8>"
+       "<matplotlib.figure.Figure at 0x7e61358>"
       ]
      },
      "metadata": {},
@@ -633,7 +638,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e7f6a0>"
+       "<matplotlib.figure.Figure at 0x7ef7d30>"
       ]
      },
      "metadata": {},
@@ -665,9 +670,17 @@
    "source": [
     "We can see that we correctly shifted all values one position to the right, wrapping from the end of the array back to the beginning.\n",
     "\n",
-    "You will often see this referred to as the state or system **evolution**, which is short for **time evolution** [7]. Another term is **system propogation**. This term refers to how the state of the system changes over time. For filters, this time is usually discrete. For our dog tracking, the system state is the position of the dog, so the state evolution is the position after a discrete amount of time has passed. I haven't defined 'state' or 'system' yet, but I hope it is clear in context. The **system** is what we are trying to model or filter, and the state is its current configuration or value. Except in simulations we rarely know the actual state, so we say our filters produce the **estimated state** of the system. In practice this often gets called the state, so be careful to understand if the reference is to the state of the filter (which is the estimated state), or the state of the system (which is the actual state).\n",
+    "## Terminology\n",
     "\n",
-    "More terminology - this prediction becomes our new **prior**. Time has moved forward and we made a prediction without benefit of knowing the measurements. "
+    "I introduced this terminology in the last chapter, but let's review to help solidify your knowledge. \n",
+    "\n",
+    "The *system* is what we are trying to model or filter. Here the system is our dog. The state is its current configuration or value. In this chapter the state is our dog's position. We rarely know the actual state, so we say our filters produce the *estimated state* of the system. In practice this often gets called the state, so be careful to understand if the reference is to the state of the filter (which is the estimated state), or the state of the system (which is the actual state).\n",
+    " \n",
+    "One cycle of prediction and updating with a measurement is called the state or system *evolution*, which is short for *time evolution* [7]. Another term is *system propogation*. This term refers to how the state of the system changes over time. For filters, this time is usually discrete. For our dog tracking, the system state is the position of the dog, so the state evolution is the position after a discrete amount of time has passed.\n",
+    "\n",
+    "We model the system behavior with the *process model*. Here, our process model is that the dog moves one position at each time step. This is not a particularly accurate model of how dog's behave. The error in the model is called the *system error* or *process error*. \n",
+    "\n",
+    "More terminology - the prediction is our new *prior*. Time has moved forward and we made a prediction without benefit of knowing the measurements. "
    ]
   },
   {
@@ -699,7 +712,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x797d128>"
+       "<matplotlib.figure.Figure at 0x75e4470>"
       ]
      },
      "metadata": {},
@@ -741,7 +754,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x797ab38>"
+       "<matplotlib.figure.Figure at 0x71f7080>"
       ]
      },
      "metadata": {},
@@ -758,9 +771,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here the results are more complicated, but you should still be able to work it out in your head. The 0.04 is due to the possibility that the 0.4 belief undershot by 1. The 0.38 is due to the following: the 80% chance that we moved 2 positions $(.4 * .8)$ and the 10% chance that we undershot $(.6*.1)$. Overshooting plays no role here because if we overshot both .4 and .6 would be past this position. **I strongly suggest working some examples until all of this is very clear, as so much of what follows depends on understanding this step.**\n",
+    "Here the results are more complicated, but you should still be able to work it out in your head. The 0.04 is due to the possibility that the 0.4 belief undershot by 1. The 0.38 is due to the following: the 80% chance that we moved 2 positions (0.4 $\\times$ 0.8) and the 10% chance that we undershot (0.6 $\\times$ 0.1). Overshooting plays no role here because if we overshot both 0.4 and 0.6 would be past this position. **I strongly suggest working some examples until all of this is very clear, as so much of what follows depends on understanding this step.**\n",
     "\n",
-    "If you look at the probabilities after performing the update you probably feel dismay. In the example above we started with probabilities of .4 and .6 in two fields; after performing the update the probabilities are not only lowered, but they are strewn out across the map."
+    "If you look at the probabilities after performing the update you probably feel dismay. In the example above we started with probabilities of 0.4 and 0.6 in two fields; after performing the update the probabilities are not only lowered, but they are strewn out across the map."
    ]
   },
   {
@@ -774,7 +787,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x491b748>"
+       "<matplotlib.figure.Figure at 0x75b22b0>"
       ]
      },
      "metadata": {},
@@ -803,7 +816,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x803b8d0>"
+       "<matplotlib.figure.Figure at 0x800b7f0>"
       ]
      },
      "metadata": {},
@@ -841,7 +854,7 @@
     "\n",
     "In the code above we made the assumption that the movement error is only one position. In any real problem it will almost always be possible for the error to be two, three, or more positions. \n",
     "\n",
-    "This is easily solved with **convolution**. Convolution is the mathematical technique we use to modify one function with another function. In our case we are modifying our probability distribution with the error function that represents the probability of a movement error. In fact, the implementation of `predict()` is a convolution, though we did not call it that. Formally, convolution is defined as\n",
+    "This is easily solved with *convolution*. Convolution is the mathematical technique we use to modify one function with another function. In our case we are modifying our probability distribution with the error function that represents the probability of a movement error. In fact, the implementation of `predict()` is a convolution, though we did not call it that. Formally, convolution is defined as\n",
     "\n",
     "$$ (f \\ast g) (t) = \\int_0^t \\!f(\\tau) \\, g(t-\\tau) \\, \\mathrm{d}\\tau$$\n",
     "\n",
@@ -853,7 +866,7 @@
     "\n",
     "If you look at that equation and compare it to the `predict()` function you can see that they are doing the same thing. \n",
     "\n",
-    "I would love to go on and on about convolution, but we have a filter to implement. Khan Academy [4] has a good mathematical introduction to convolution, and Wikipedia has some excellent animations of convolutions [5]. But the general idea is already clear to you. You slide across an array, multiplying the neighbors of the current cell with the values of a second array. This second array is called the **kernel**. In our example above we used .8 for the probability of moving to the correct location, .1 for undershooting, and .1 for overshooting. We make a kernel of this with the array `[0.1, 0.8, 0.1]`. So all we need to do is write a loop that goes over each element of our array, multiplying by the kernel, and summing the results. To emphasize that the belief is a probability distribution I have named the belief `distribution`."
+    "I would love to go on and on about convolution, but we have a filter to implement. Khan Academy [4] has a good mathematical introduction to convolution, and Wikipedia has some excellent animations of convolutions [5]. But the general idea is already clear to you. You slide across an array, multiplying the neighbors of the current cell with the values of a second array. This second array is called the *kernel*. In our example above we used 0.8 for the probability of moving to the correct location, 0.1 for undershooting, and 0.1 for overshooting. We make a kernel of this with the array `[0.1, 0.8, 0.1]`. So all we need to do is write a loop that goes over each element of our array, multiplying by the kernel, and summing the results. To emphasize that the belief is a probability distribution I have named the belief `distribution`."
    ]
   },
   {
@@ -895,7 +908,7 @@
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x80286d8>"
+       "<matplotlib.figure.Figure at 0x7fe4208>"
       ]
      },
      "metadata": {},
@@ -913,7 +926,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "All of the elements are unchanged except the middle ones, which is correct. The value in position 4 should be $0.1 * 0.05 + 0.8 * 0.05 + 0.1 * 0.55 = 0.1$, which it does. Position 5 should be $0.1 * 0.05 + 0.8 * 0.55 + 0.1 * 0.05 = 0.45$, which it does. Finally, position 6 is computed the same as position 4, and it is also correct.\n",
+    "All of the elements are unchanged except the middle ones, which is correct. The value in position 4 should be $(0.1 \\times 0.05)+ (0.8 \\times 0.05) + (0.1 \\times 0.55) = 0.1$, which it does. Position 5 should be $(0.1 \\times 0.05) + (0.8 \\times 0.55)+ (0.1 \\times 0.05) = 0.45$, which it does. Finally, position 6 is computed the same as position 4, and it is also correct.\n",
     "\n",
     "Finally, let's ensure that it shifts the positions correctly for movements greater than one."
    ]
@@ -929,7 +942,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x80286a0>"
+       "<matplotlib.figure.Figure at 0x7fe4198>"
       ]
      },
      "metadata": {},
@@ -994,7 +1007,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The problem of losing information during a prediction may make it seem as if our system would quickly devolve into no knowledge. However, recall that our process is not an endless series of predictions, but of *update->predict->update->predict->update->predict->update...* The output of the update step, where we measure the current position, is fed into the prediction. The prediction step, with a degraded certainty, is then fed back into the update step where we measure the position again.\n",
+    "The problem of losing information during a prediction may make it seem as if our system would quickly devolve into no knowledge. However, recall that our process is not an endless series of predictions, but a cycle of predictions followed by updates. The output of the update step, where we measure the current position, is fed into the prediction. The prediction step, with a degraded certainty, is then fed back into the update step where we measure the position again.\n",
     "\n",
     "Let's think about this intuitively. After the first update->predict round we have degraded the knowledge we gained by the measurement by a small amount. But now we take another measurement. When we try to incorporate that new measurement into our belief, do we become more certain, less certain, or equally certain? Consider a simple case - you are sitting in your office. A co-worker asks another co-worker where you are, and they report \"in his office\". You keep sitting there while they ask and answer \"has he moved\"? \"No\" \"Where is he\" \"In his office\". Eventually you get up and move, and lets say the person didn't see you move. At that time the questions will go \"Has he moved\" \"no\" (but you have!) \"Where is he\" \"In the kitchen\". Wow! At that moment the statement that you haven't moved conflicts strongly with the next measurement that you are in the kitchen. If we were modeling these with probabilities the probability that you are in your office would lower, and the probability that you are in the kitchen would go up a little bit. But now imagine the subsequent conversation: \"has he moved\" \"no\" \"where is he\" \"in the kitchen\". Pretty quickly the belief that you are in your office would fade away, and the belief that you are in the kitchen would increase to near certainty. The belief that you are in the office will never go to zero, nor will the belief that you are in the kitchen ever go to 1.0 because of the chances of error, but in practice your co-workers would be correct to be quite confident in their system.\n",
     "\n",
@@ -1015,7 +1028,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e9e4a8>"
+       "<matplotlib.figure.Figure at 0x75a6668>"
       ]
      },
      "metadata": {},
@@ -1040,7 +1053,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8050278>"
+       "<matplotlib.figure.Figure at 0x7ff0c50>"
       ]
      },
      "metadata": {},
@@ -1071,7 +1084,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8050438>"
+       "<matplotlib.figure.Figure at 0x7ff0d30>"
       ]
      },
      "metadata": {},
@@ -1101,7 +1114,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8105668>"
+       "<matplotlib.figure.Figure at 0x7e375c0>"
       ]
      },
      "metadata": {},
@@ -1132,7 +1145,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x81007f0>"
+       "<matplotlib.figure.Figure at 0x7eafe80>"
       ]
      },
      "metadata": {},
@@ -1165,7 +1178,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e85dd8>"
+       "<matplotlib.figure.Figure at 0x7f3fb70>"
       ]
      },
      "metadata": {},
@@ -1181,7 +1194,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This filter is a form of the g-h filter. Here we are using the percentages for the errors to implicitly compute the *g* and *h* parameters. We could express the discrete Bayes algorithm as a g-h filter, but that would obscure the logic of this filter.\n",
+    "This filter is a form of the g-h filter. Here we are using the percentages for the errors to implicitly compute the $g$ and $h$ parameters. We could express the discrete Bayes algorithm as a g-h filter, but that would obscure the logic of this filter.\n",
     "\n",
     "We can express this in pseudocode.\n",
     "\n",
@@ -1239,7 +1252,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x80d4080>"
+       "<matplotlib.figure.Figure at 0x7e102e8>"
       ]
      },
      "metadata": {},
@@ -1276,7 +1289,7 @@
      "data": {
       "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7faa7b8>"
+       "<matplotlib.figure.Figure at 0x80c0f98>"
       ]
      },
      "metadata": {},
@@ -1307,7 +1320,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8071320>"
+       "<matplotlib.figure.Figure at 0x80aa438>"
       ]
      },
      "metadata": {},
@@ -1349,9 +1362,9 @@
     "\n",
     "The first problem is scaling. Our dog tracking problem used only one variable, $pos$, to denote the dog's position. Most interesting problems will want to track several things in a large space. Realistically, at a minimum we would want to track our dogs $(x,y)$ coordinate, and probably his velocity $(\\dot{x},\\dot{y})$ as well. We have not covered the multidimensional case, but instead of a histogram we use a multidimensional grid to store the probabilities at each discrete location. Each `update()` and `predict()` step requires updating all values in the grid, so a simple four variable problem would require $O(n^4)$ running time *per time step*. Realistic filters can have 10 or more variables to track, leading to exorbitant computation requirements.\n",
     "\n",
-    "The second problem is that the histogram is discrete, but we live in a continuous world. The histogram requires that you model the output of your filter as a set of discrete points. In our dog in the hallway example, we used 10 positions, which is obviously far too few positions for anything but a toy problem. For example, for a 100 meter hallway you would need 10,000 positions to model the hallway to 1cm accuracy. So each update and predict operation would entail performing calculations for 10,000 different probabilities. It gets exponentially worse as we add dimensions. If our dog was roaming in a $100x100 m^2$ courtyard, we would need 100,000,000 bins ($10,000^2$) to get 1cm accuracy.\n",
+    "The second problem is that the histogram is discrete, but we live in a continuous world. The histogram requires that you model the output of your filter as a set of discrete points. In our dog in the hallway example, we used 10 positions, which is obviously far too few positions for anything but a toy problem. For example, for a 100 meter hallway you would need 10,000 positions to model the hallway to 1cm accuracy. So each update and predict operation would entail performing calculations for 10,000 different probabilities. It gets exponentially worse as we add dimensions. If our dog was roaming in a 100x100 m$^2$ courtyard, we would need 100,000,000 bins (10,000$^2$) to get 1cm accuracy.\n",
     "\n",
-    "A third problem is that the histogram is multimodal. This is not always a problem - an entire class of filters, the particle filters, are multimodal and are often used because of this property. But imagine if the GPS in your car reported to you that it is 40% sure that you are on D street, but 30% sure you are on Willow Avenue. I doubt that you would find that useful. Also, GPSs report their error - they might report that you are at $(109.878W, 38.326N)$ with an error of $9m$. There is no clear mathematical way to extract error information from a histogram. Heuristics suggest themselves to be sure, but there is no exact determination. You may or may not care about that while driving, but you surely do care if you are trying to send a rocket to Mars or track and hit an oncoming missile.\n",
+    "A third problem is that the histogram is multimodal. This is not always a problem - an entire class of filters, the particle filters, are multimodal and are often used because of this property. But imagine if the GPS in your car reported to you that it is 40% sure that you are on D street, but 30% sure you are on Willow Avenue. I doubt that you would find that useful. Also, GPSs report their error - they might report that you are at (109.878W, 38.326N) with an error of 9 meters. There is no clear mathematical way to extract error information from a histogram. Heuristics suggest themselves to be sure, but there is no exact determination. You may or may not care about that while driving, but you surely do care if you are trying to send a rocket to Mars or track and hit an oncoming missile.\n",
     "\n",
     "This difficulty is related to the fact that the filter often does not represent what is physically occurring in the world. Consider this distribution for our dog:"
    ]
@@ -1367,7 +1380,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x80c4e10>"
+       "<matplotlib.figure.Figure at 0x8032ba8>"
       ]
      },
      "metadata": {},
@@ -1385,7 +1398,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    " The largest probabilities are in position 0 and position 5. This does not fit our physical intuition at all. A dog cannot be in two places at once (my dog Simon certainly tries - his food bowl and my lap often have equal allure to him). We would have to use heuristics to decide how to interpret this distribution, and there is usually no satisfactory answer. This is not always a weakness - a considerable amount of literature has been written on **Multi-Hypothesis Tracking (MHT)**. We cannot always distill our knowledge to one conclusion, and MHT uses various techniques to maintain multiple story lines at once, using backtracking schemes to go *back in time* to correct hypothesis once more information is known. This will be the subject of later chapters. In other cases we truly have a multimodal situation - we may be optically tracking pedestrians on the street and need to represent all of their positions. \n",
+    " The largest probabilities are in position 0 and position 5. This does not fit our physical intuition at all. A dog cannot be in two places at once (my dog Simon certainly tries - his food bowl and my lap often have equal allure to him). We would have to use heuristics to decide how to interpret this distribution, and there is usually no satisfactory answer. This is not always a weakness - a considerable amount of literature has been written on *Multi-Hypothesis Tracking (MHT)*. We cannot always distill our knowledge to one conclusion, and MHT uses various techniques to maintain multiple story lines at once, using backtracking schemes to go *back in time* to correct hypothesis once more information is known. This will be the subject of later chapters. In other cases we truly have a multimodal situation - we may be optically tracking pedestrians on the street and need to represent all of their positions. \n",
     " \n",
     "In practice it is the exponential increase in computation time that leads to the discrete Bayes filter being the least frequently used of all filters in this book. Many problems are best formulated as discrete or multimodal, but we have other filter choices with better performance. With that said, if I had a small problem that this technique could handle I would choose to use it; it is trivial to implement, debug, and understand, all virtues."
    ]
@@ -1444,7 +1457,7 @@
     "            if r <= s:\n",
     "                break\n",
     "            offset += 1\n",
-    "        self.pos = (self.pos + offset) % self.track_len\n",
+    "        self.pos = int((self.pos + offset) % self.track_len)\n",
     "        return self.pos\n",
     "\n",
     "    def sense(self):\n",
@@ -1495,7 +1508,7 @@
     "        index = np.argmax(belief)\n",
     "        if do_print:\n",
     "            print('''        predicted position is {}'''\n",
-    "                  ''' with confidence {:.4}%:'''.format(\n",
+    "                  ''' with confidence {:.4f}%:'''.format(\n",
     "                  index, belief[index]*100))            \n",
     "        if i < iterations - 1:\n",
     "            predict(belief, move_distance, kernel)       \n",
@@ -1505,8 +1518,8 @@
     "        print()\n",
     "        print('final position is', robot.pos)\n",
     "        iindex = np.argmax(belief)\n",
-    "        print('''predicted position is {} with'''\n",
-    "              '''confidence {:.4}%:'''.format(\n",
+    "        print('''predicted position is {} with '''\n",
+    "              '''confidence {:.4f}%:'''.format(\n",
     "                index, belief[index]*100))"
    ]
   },
@@ -1529,31 +1542,24 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "time 0: pos 4.0, sensed 4.0, at position 4\n",
-      "        predicted position is 4 with confidence 91.07%:\n",
-      "time 1: pos 8.0, sensed 8.0, at position 8\n",
-      "        predicted position is 8 with confidence 99.99%:\n",
-      "time 2: pos 2.0, sensed 2.0, at position 2\n",
-      "        predicted position is 2 with confidence 100.0%:\n",
-      "time 3: pos 6.0, sensed 6.0, at position 6\n",
-      "        predicted position is 6 with confidence 100.0%:\n",
+      "time 0: pos 4, sensed 4, at position 4\n",
+      "        predicted position is 4 with confidence 91.0665%:\n",
+      "time 1: pos 8, sensed 8, at position 8\n",
+      "        predicted position is 8 with confidence 99.9902%:\n",
+      "time 2: pos 2, sensed 2, at position 2\n",
+      "        predicted position is 2 with confidence 100.0000%:\n",
+      "time 3: pos 6, sensed 6, at position 6\n",
+      "        predicted position is 6 with confidence 100.0000%:\n",
       "\n",
-      "final position is 6.0\n",
-      "predicted position is 6 withconfidence 100.0%:\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "C:\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
+      "final position is 6\n",
+      "predicted position is 6 with confidence 100.0000%:\n"
      ]
     },
     {
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e5a710>"
+       "<matplotlib.figure.Figure at 0x82e91d0>"
       ]
      },
      "metadata": {},
@@ -1587,31 +1593,24 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "time 0: pos 4.0, sensed 4.0, at position 4\n",
-      "        predicted position is 0 with confidence 84.11%:\n",
-      "time 1: pos 8.0, sensed 8.0, at position 8\n",
-      "        predicted position is 4 with confidence 43.44%:\n",
-      "time 2: pos 2.0, sensed 2.0, at position 2\n",
-      "        predicted position is 2 with confidence 81.09%:\n",
-      "time 3: pos 5.0, sensed 5.0, at position 5\n",
-      "        predicted position is 5 with confidence 47.83%:\n",
+      "time 0: pos 4, sensed 4, at position 4\n",
+      "        predicted position is 0 with confidence 84.1121%:\n",
+      "time 1: pos 8, sensed 8, at position 8\n",
+      "        predicted position is 4 with confidence 43.4416%:\n",
+      "time 2: pos 2, sensed 2, at position 2\n",
+      "        predicted position is 2 with confidence 81.0925%:\n",
+      "time 3: pos 5, sensed 5, at position 5\n",
+      "        predicted position is 5 with confidence 47.8278%:\n",
       "\n",
-      "final position is 5.0\n",
-      "predicted position is 5 withconfidence 47.83%:\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "C:\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
+      "final position is 5\n",
+      "predicted position is 5 with confidence 47.8278%:\n"
      ]
     },
     {
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x81f7780>"
+       "<matplotlib.figure.Figure at 0x8118be0>"
       ]
      },
      "metadata": {},
@@ -1645,7 +1644,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f2ce48>"
+       "<matplotlib.figure.Figure at 0x7dee278>"
       ]
      },
      "metadata": {},
@@ -1681,7 +1680,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We developed the math in this chapter merely by reasoning about the information we have at each moment. In the process we discovered **Bayes Theorem**. We will go into the specifics of the math of Bayes theorem later in the book. For now we will take a more intuitive approach. Recall from the preface that Bayes theorem tells us how to compute the probability of an event given previous information. That is exactly what we have been doing in this chapter. With luck our code should match the Bayes Theorem equation! \n",
+    "We developed the math in this chapter merely by reasoning about the information we have at each moment. In the process we discovered *Bayes Theorem*. We will go into the specifics of the math of Bayes theorem later in the book. For now we will take a more intuitive approach. Recall from the preface that Bayes theorem tells us how to compute the probability of an event given previous information. That is exactly what we have been doing in this chapter. With luck our code should match the Bayes Theorem equation! \n",
     "\n",
     "We implemented the `update()` function with this probability calculation:\n",
     "\n",
@@ -1691,11 +1690,11 @@
     "\n",
     "Bayes theorem is\n",
     "\n",
-    "$$P(A|B) = \\frac{P(B | A)\\, P(A)}{P(B)}\\cdot$$\n",
+    "$$P(A|B) = \\frac{P(B | A)\\, P(A)}{P(B)}$$\n",
     "\n",
     "If you are not familiar with this notation, let's review. $P(A)$ means the probability of event $A$. If $A$ is the event of a fair coin landing heads, then $P(A) = 0.5$.\n",
     "\n",
-    "$P(A|B)$ is called a **conditional probability**. That is, it represents the probability of $A$ happening *if* $B$ happened. For example, it is more likely to rain today if it also rained yesterday because rain systems tend to last more than one day. We'd write the probability of it raining today given that it rained yesterday as $P(\\mathtt{rain_{today}}|\\mathtt{rain_{yesterday}})$.\n",
+    "$P(A|B)$ is called a *conditional probability*. That is, it represents the probability of $A$ happening *if* $B$ happened. For example, it is more likely to rain today if it also rained yesterday because rain systems tend to last more than one day. We'd write the probability of it raining today given that it rained yesterday as $P(\\mathtt{rain_{today}}|\\mathtt{rain_{yesterday}})$.\n",
     "\n",
     "In the Bayes theorem equation above $B$ is the *evidence*, $P(A)$ is the *prior*, $P(B | A)$ is the *likelihood*, and $P(A|B)$ is the *posterior*. By substituting the mathematical terms with the corresponding words  you can see that Bayes theorem matches out update equation. Let's rewrite the equation in terms of our problem. We will use $x_i$ for the position at *i*, and $Z$ for the measurement. Hence, we want to know $P(x_i|Z)$, that is, the probability of the dog being at $x_i$ given the measurement $Z$. \n",
     "\n",
@@ -1721,7 +1720,7 @@
     "\n",
     "$$P(A|B) = \\frac{P(B | A)\\, P(A)}{\\int P(B|A) P(B) \\mathtt{d}y}\\cdot$$\n",
     "\n",
-    "In practice the denominator can be fiendishly difficult to solve analytically (a recent opinion piece for the Royal Statistical Society called it a \"dog's breakfast\" [8], and filtering textbooks are filled with integral laden equations which you cannot be expected to solve. We will learn more techniques to handle this in the **Particle Filtering** chapter. Until then, recognize that in practice it is just a normalization term over which we can sum. What I'm trying to say is that when you are faced with a page of integrals, just think of them of sums, and relate them back to this chapter, and often the difficulties will fade. Ask yourself \"why are we summing these values\", and \"why am I dividing by this term\". Surprisingly often the answer is readily apparent."
+    "In practice the denominator can be fiendishly difficult to solve analytically (a recent opinion piece for the Royal Statistical Society called it a \"dog's breakfast\" [8], and filtering textbooks are filled with integral laden equations which you cannot be expected to solve. We will learn more techniques to handle this in the **Particle Filters** chapter. Until then, recognize that in practice it is just a normalization term over which we can sum. What I'm trying to say is that when you are faced with a page of integrals, just think of them of sums, and relate them back to this chapter, and often the difficulties will fade. Ask yourself \"why are we summing these values\", and \"why am I dividing by this term\". Surprisingly often the answer is readily apparent."
    ]
   },
   {
@@ -1732,7 +1731,7 @@
    "source": [
     "## Total Probability Theorem\n",
     "\n",
-    "We know now the formal mathematics behind the `update()` function; what about the `predict()` function? `predict()` implements the **total probability theorem**. Let's recall what `predict()` computed. It computed the probability of being at any given position given the probability of all the possible movement events. Let's express that as an equation. The probability of being at any position $i$ at time $t$ can be written as $P(X_i^t)$. We computed that as the sum of the prior at time $t-1$ $P(X_i^{t-1})$ multiplied by the probability of moving from cell $x_j$ to $x_i$. That is\n",
+    "We know now the formal mathematics behind the `update()` function; what about the `predict()` function? `predict()` implements the *total probability theorem*. Let's recall what `predict()` computed. It computed the probability of being at any given position given the probability of all the possible movement events. Let's express that as an equation. The probability of being at any position $i$ at time $t$ can be written as $P(X_i^t)$. We computed that as the sum of the prior at time $t-1$ $P(X_i^{t-1})$ multiplied by the probability of moving from cell $x_j$ to $x_i$. That is\n",
     "\n",
     "$$P(X_i^t) = \\sum_j P(X_i^{t-1})  P(x_i | x_j)$$\n",
     "\n",
@@ -1759,7 +1758,7 @@
    "source": [
     "The code is very short, but the result is huge! We have implemented a form of a Bayesian filter. We have learned how to start with no information and derive information from noisy sensors. Even though the sensors in this chapter are very noisy (most sensors are more than 80% accurate, for example) we quickly converge on the most likely position for our dog. We have learned how the predict step always degrades our knowledge, but the addition of another measurement, even when it might have noise in it, improves our knowledge, allowing us to converge on the most likely result.\n",
     "\n",
-    "If you followed the math carefully you will realize that all of this math is exact. The bar charts that we are displaying are not an *estimate* or *guess* - they are mathematically exact results that exactly represent our knowledge. The knowledge is probabilistic, to be sure, but it is exact, and correct.\n",
+    "If you followed the math carefully you will realize that all of this math is exact. The bar charts that we are displaying are not an estimate or guess - they are mathematically exact results that exactly represent our knowledge. The knowledge is probabilistic, to be sure, but it is exact, and correct.\n",
     "\n",
     "Furthermore, through basic reasoning we were able to discover two extremely important theorems: Bayes theorem and the total probability theorem. I hope you spent time on those sections as in almost any other source they will express filtering algorithms in terms of these two theorems. It will be your job to understand what these equations mean and how to turn them into code.  \n",
     "\n",

04-One-Dimensional-Kalman-Filters.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -315,7 +321,7 @@
     "\n",
     "$$ z = h(x) + \\epsilon_z$$\n",
     "\n",
-    "Here $h(x)$ is the **measurement model** - a function which describes how measurements are made from the current system state. In other words, $h(x)$ is the measurement we would get for the state $x$ *if* the sensor was perfect. $\\epsilon_z$ is the error that is in the measurement, and hence $z$ is the actual measurement that results. This is not meant to imply that we can somehow measure or know the exact value of $\\epsilon_z$, it is a mathematical definition that can be restated as\n",
+    "Here $h(x)$ is the *measurement model* - a function which describes how measurements are made from the current system state. In other words, $h(x)$ is the measurement we would get for the state $x$ *if* the sensor was perfect. $\\epsilon_z$ is the error that is in the measurement, and hence $z$ is the actual measurement that results. This is not meant to imply that we can somehow measure or know the exact value of $\\epsilon_z$, it is a mathematical definition that can be restated as\n",
     "\n",
     "$$ \\epsilon_z =  z - h(x)$$\n",
     "\n",
@@ -442,9 +448,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x489e198>"
+       "<matplotlib.figure.Figure at 0x272b4c663c8>"
       ]
      },
      "metadata": {},
@@ -485,9 +491,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72039e8>"
+       "<matplotlib.figure.Figure at 0x272b4db64a8>"
       ]
      },
      "metadata": {},
@@ -530,9 +536,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7206128>"
+       "<matplotlib.figure.Figure at 0x272b4c6ef98>"
       ]
      },
      "metadata": {},
@@ -553,9 +559,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fe3470>"
+       "<matplotlib.figure.Figure at 0x272b5026978>"
       ]
      },
      "metadata": {},
@@ -584,9 +590,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x81606d8>"
+       "<matplotlib.figure.Figure at 0x272b5758470>"
       ]
      },
      "metadata": {},
@@ -616,9 +622,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x81609b0>"
+       "<matplotlib.figure.Figure at 0x272b5764a58>"
       ]
      },
      "metadata": {},
@@ -652,9 +658,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x814ca20>"
+       "<matplotlib.figure.Figure at 0x272b4fe3898>"
       ]
      },
      "metadata": {},
@@ -690,9 +696,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x4cfcda0>"
+       "<matplotlib.figure.Figure at 0x272b5d21320>"
       ]
      },
      "metadata": {},
@@ -785,9 +791,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8841a58>"
+       "<matplotlib.figure.Figure at 0x272b5d490f0>"
       ]
      },
      "metadata": {},
@@ -841,9 +847,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8916d68>"
+       "<matplotlib.figure.Figure at 0x272b6dc9c88>"
       ]
      },
      "metadata": {},
@@ -892,9 +898,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89346a0>"
+       "<matplotlib.figure.Figure at 0x272b6e49ac8>"
       ]
      },
      "metadata": {},
@@ -983,9 +989,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89b60b8>"
+       "<matplotlib.figure.Figure at 0x272b6e8cc88>"
       ]
      },
      "metadata": {},
@@ -1241,9 +1247,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a74cf8>"
+       "<matplotlib.figure.Figure at 0x272b5c57358>"
       ]
      },
      "metadata": {},
@@ -1302,9 +1308,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ae6588>"
+       "<matplotlib.figure.Figure at 0x272b6f188d0>"
       ]
      },
      "metadata": {},
@@ -1367,7 +1373,7 @@
     "The next line allocates an array to store the output of the filtered positions. \n",
     "\n",
     "```python\n",
-    "positions =  np.zeros(N)\n",
+    "positions = np.zeros(N)\n",
     "```"
    ]
   },
@@ -1412,14 +1418,14 @@
     "If we didn't use pre-written functions the the code would be:\n",
     "\n",
     "```python\n",
-    "    for i in range(N):\n",
-    "        # predict\n",
-    "        pos = pos + vel\n",
-    "        var = var + sensor_var\n",
+    "for i in range(N):\n",
+    "    # predict\n",
+    "    pos = pos + vel\n",
+    "    var = var + sensor_var\n",
     "\n",
-    "        # update\n",
-    "        pos  = (var*vel + process_var*pos) / (var + process_var)\n",
-    "        var = 1 / (1/var + 1/process_var)\n",
+    "    # update\n",
+    "    pos  = (var*vel + process_var*pos) / (var + process_var)\n",
+    "    var = 1 / (1/var + 1/process_var)\n",
     "```    \n",
     "\n",
     "Just 4 lines of very simple math implements the entire filter!"
@@ -1453,9 +1459,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a66f98>"
+       "<matplotlib.figure.Figure at 0x272b4d6dc88>"
       ]
      },
      "metadata": {},
@@ -1542,7 +1548,7 @@
    "source": [
     "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n",
     "\n",
-    "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement."
+    "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x = 15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement."
    ]
   },
   {
@@ -1568,9 +1574,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a4bac8>"
+       "<matplotlib.figure.Figure at 0x272b6d86198>"
       ]
      },
      "metadata": {},
@@ -1635,9 +1641,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x82dd0f0>"
+       "<matplotlib.figure.Figure at 0x272b6f27240>"
       ]
      },
      "metadata": {},
@@ -1665,9 +1671,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x880b438>"
+       "<matplotlib.figure.Figure at 0x272b576fc50>"
       ]
      },
      "metadata": {},
@@ -1730,9 +1736,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8974588>"
+       "<matplotlib.figure.Figure at 0x272b4c740b8>"
       ]
      },
      "metadata": {},
@@ -1764,9 +1770,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ae22e8>"
+       "<matplotlib.figure.Figure at 0x272b6e8c080>"
       ]
      },
      "metadata": {},
@@ -1807,9 +1813,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87f6080>"
+       "<matplotlib.figure.Figure at 0x272b6d40048>"
       ]
      },
      "metadata": {},
@@ -1975,9 +1981,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f2a7b8>"
+       "<matplotlib.figure.Figure at 0x272b6f34c88>"
       ]
      },
      "metadata": {},
@@ -1985,9 +1991,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b34e10>"
+       "<matplotlib.figure.Figure at 0x272b6f08080>"
       ]
      },
      "metadata": {},
@@ -2079,7 +2085,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. "
+    "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor $g$. The Kalman filter is doing exactly the same thing, except that the scaling factor $g$ varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. "
    ]
   },
   {
@@ -2093,7 +2099,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. Use plt.hist(data, bins=100) to plot the histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?"
+    "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. Use `plt.hist(data, bins=100)` to plot the histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?"
    ]
   },
   {
@@ -2123,9 +2129,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b34f98>"
+       "<matplotlib.figure.Figure at 0x272b5041cc0>"
       ]
      },
      "metadata": {},
@@ -2189,9 +2195,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8919ba8>"
+       "<matplotlib.figure.Figure at 0x272b6df6be0>"
       ]
      },
      "metadata": {},
@@ -2247,9 +2253,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89931d0>"
+       "<matplotlib.figure.Figure at 0x272b7083710>"
       ]
      },
      "metadata": {},
@@ -2310,9 +2316,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a2f9e8>"
+       "<matplotlib.figure.Figure at 0x272b712a128>"
       ]
      },
      "metadata": {},
@@ -2369,9 +2375,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8166940>"
+       "<matplotlib.figure.Figure at 0x272b7189d68>"
       ]
      },
      "metadata": {},
@@ -2415,9 +2421,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x885aa20>"
+       "<matplotlib.figure.Figure at 0x272b71be2e8>"
       ]
      },
      "metadata": {},
@@ -2514,9 +2520,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x82c7ba8>"
+       "<matplotlib.figure.Figure at 0x272b72652b0>"
       ]
      },
      "metadata": {},
@@ -2609,9 +2615,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ea97b8>"
+       "<matplotlib.figure.Figure at 0x272b7237208>"
       ]
      },
      "metadata": {},
@@ -2698,9 +2704,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9e642b0>"
+       "<matplotlib.figure.Figure at 0x272b718eef0>"
       ]
      },
      "metadata": {},

05-Multivariate-Gaussians.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -341,9 +347,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAv0AAADxCAYAAABYmwhGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x796de10>"
+       "<matplotlib.figure.Figure at 0x207fd4c4b00>"
       ]
      },
      "metadata": {},
@@ -463,9 +469,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c7af60>"
+       "<matplotlib.figure.Figure at 0x207fdd30e10>"
       ]
      },
      "metadata": {},
@@ -505,9 +511,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f817f0>"
+       "<matplotlib.figure.Figure at 0x207fe587048>"
       ]
      },
      "metadata": {},
@@ -517,8 +523,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 7.868  3.056]\n",
-      " [ 3.056  2.318]]\n"
+      "[[ 7.78   3.043]\n",
+      " [ 3.043  2.439]]\n"
      ]
     }
    ],
@@ -548,9 +554,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x71ef940>"
+       "<matplotlib.figure.Figure at 0x207fe593400>"
       ]
      },
      "metadata": {},
@@ -560,8 +566,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 1.003 -0.001]\n",
-      " [-0.001  1.   ]]\n"
+      "[[ 1.002  0.   ]\n",
+      " [ 0.     1.011]]\n"
      ]
     }
    ],
@@ -609,9 +615,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f81b38>"
+       "<matplotlib.figure.Figure at 0x207fe55db00>"
       ]
      },
      "metadata": {},
@@ -758,9 +764,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x4455b00>"
+       "<matplotlib.figure.Figure at 0x207fe53d048>"
       ]
      },
      "metadata": {},
@@ -801,9 +807,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87eae10>"
+       "<matplotlib.figure.Figure at 0x207fe53dc18>"
       ]
      },
      "metadata": {},
@@ -838,9 +844,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f84be0>"
+       "<matplotlib.figure.Figure at 0x207fe5485f8>"
       ]
      },
      "metadata": {},
@@ -850,7 +856,7 @@
    "source": [
     "from book_format import set_figsize, figsize\n",
     "\n",
-    "with figsize(y=5):\n",
+    "with figsize(y=4):\n",
     "    mkf_internal.plot_3_covariances()"
    ]
   },
@@ -881,9 +887,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9315b38>"
+       "<matplotlib.figure.Figure at 0x207811c4f98>"
       ]
      },
      "metadata": {},
@@ -915,9 +921,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x93074a8>"
+       "<matplotlib.figure.Figure at 0x207fe53deb8>"
       ]
      },
      "metadata": {},
@@ -950,9 +956,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9837128>"
+       "<matplotlib.figure.Figure at 0x20781203be0>"
       ]
      },
      "metadata": {},
@@ -995,9 +1001,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9d696a0>"
+       "<matplotlib.figure.Figure at 0x2078013f898>"
       ]
      },
      "metadata": {},
@@ -1040,9 +1046,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8d10828>"
+       "<matplotlib.figure.Figure at 0x207800d2438>"
       ]
      },
      "metadata": {},
@@ -1101,9 +1107,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8dae748>"
+       "<matplotlib.figure.Figure at 0x207fe5af860>"
       ]
      },
      "metadata": {},
@@ -1134,9 +1140,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8dd32b0>"
+       "<matplotlib.figure.Figure at 0x207fdd3cc88>"
       ]
      },
      "metadata": {},
@@ -1170,9 +1176,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8e3d978>"
+       "<matplotlib.figure.Figure at 0x207fe58d908>"
       ]
      },
      "metadata": {},
@@ -1294,9 +1300,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8e4a7b8>"
+       "<matplotlib.figure.Figure at 0x20780170ba8>"
       ]
      },
      "metadata": {},
@@ -1326,9 +1332,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8dd3c50>"
+       "<matplotlib.figure.Figure at 0x207812429e8>"
       ]
      },
      "metadata": {},
@@ -1371,9 +1377,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88c5198>"
+       "<matplotlib.figure.Figure at 0x2078005c588>"
       ]
      },
      "metadata": {},
@@ -1426,9 +1432,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8e46a20>"
+       "<matplotlib.figure.Figure at 0x2078003feb8>"
       ]
      },
      "metadata": {},
@@ -1457,9 +1463,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88894e0>"
+       "<matplotlib.figure.Figure at 0x20781316978>"
       ]
      },
      "metadata": {},
@@ -1491,9 +1497,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c9de48>"
+       "<matplotlib.figure.Figure at 0x207813f0ef0>"
       ]
      },
      "metadata": {},
@@ -1505,20 +1511,20 @@
     "\n",
     "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n",
     "\n",
-    "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.2)\n",
-    "plot_covariance_ellipse((10, 10), P1, fc='b', alpha=0.6)\n",
-    "plot_covariance_ellipse((10, 10), P2, fc='y')"
+    "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n",
+    "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.9)\n",
+    "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I have plotted the original estimate (prior) in a very transparent yellow, the radar reading in blue (evidence), and the finale estimate (posterior) in yellow.\n",
+    "I have plotted the original estimate (prior) in a very transparent yellow, the radar reading in green (evidence), and the finale estimate (posterior) in blue.\n",
     "\n",
     "The posterior retained the same shape and position as the radar measurement, but is smaller. We've seen this with one dimensional Gaussians. Multiplying two Gaussians makes the variance smaller because we are incorporating more information, hence we are less uncertain.  Another point to recognize is that the covariance shape reflects the physical layout of the aircraft and the radar system. The importance of this will become clear in the next step.\n",
     "\n",
-    "Now lets say we get a measurement from a second radar, this one to the lower right, which I will plot in blue against the yellow covariance of our current belief. "
+    "Now lets say we get a measurement from a second radar, this one to the lower right, which I will plot in green against the yellow covariance of our current belief. "
    ]
   },
   {
@@ -1530,9 +1536,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuIAAADaCAYAAADjVSfWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8d8b978>"
+       "<matplotlib.figure.Figure at 0x207813cd630>"
       ]
      },
      "metadata": {},
@@ -1541,8 +1547,8 @@
    ],
    "source": [
     "P3 = [[2, -1.9], [-1.9, 2.2]]\n",
-    "plot_covariance_ellipse((10, 10), P2, fc='y', alpha=0.6)\n",
-    "plot_covariance_ellipse((10, 10), P3, fc='b', alpha=0.6)"
+    "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n",
+    "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)"
    ]
   },
   {
@@ -1561,9 +1567,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8804240>"
+       "<matplotlib.figure.Figure at 0x207812ffd68>"
       ]
      },
      "metadata": {},
@@ -1572,9 +1578,9 @@
    ],
    "source": [
     "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n",
-    "plot_covariance_ellipse((10, 10), P2, fc='y', alpha=0.2)\n",
-    "plot_covariance_ellipse((10, 10), P3, fc='b', alpha=0.6)\n",
-    "plot_covariance_ellipse((10, 10), P4, fc='y')"
+    "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n",
+    "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n",
+    "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')"
    ]
   },
   {
@@ -1595,9 +1601,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8d73198>"
+       "<matplotlib.figure.Figure at 0x207813b4080>"
       ]
      },
      "metadata": {},
@@ -1628,9 +1634,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9324ba8>"
+       "<matplotlib.figure.Figure at 0x207811d8518>"
       ]
      },
      "metadata": {},
@@ -1640,9 +1646,9 @@
    "source": [
     "P1 = [[2, 0], [0, .2]]\n",
     "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n",
-    "plot_covariance_ellipse((10, 10), P0, facecolor='y', alpha=0.2)\n",
-    "plot_covariance_ellipse((10, 10), P1, facecolor='b', alpha=0.6)\n",
-    "plot_covariance_ellipse((10, 10), P2, facecolor='y')"
+    "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n",
+    "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.6)\n",
+    "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')"
    ]
   },
   {
@@ -1661,9 +1667,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8ea52e8>"
+       "<matplotlib.figure.Figure at 0x20780021710>"
       ]
      },
      "metadata": {},
@@ -1673,9 +1679,9 @@
    "source": [
     "P3 = [[2, -1.9], [-1.9, 2.2]]\n",
     "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n",
-    "plot_covariance_ellipse((10, 10), P2, facecolor='y', alpha=0.2)\n",
-    "plot_covariance_ellipse((10, 10), P3, facecolor='b', alpha=0.6)\n",
-    "plot_covariance_ellipse((10, 10), P4, facecolor='y')"
+    "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n",
+    "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n",
+    "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')"
    ]
   },
   {
@@ -1696,9 +1702,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu4AAAEPCAYAAAAd7UFwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmQnPd93/n3cz99Tc994RgABECAAMEL4qHLFCUqJdne\njWJnnVVKJGXvqmorG8e72XKVy6mSrHKpVlVcJX+E3thyrGLscrIq2ZajKHaomKYoUuIJkQCIa3DN\ngblnevp+7t/+0T2DGQDEPRfwfaGaz9O/frrnGXZP96d/z/f3ezSllEIIIYQQQgixrulrvQNCCCGE\nEEKIa5PgLoQQQgghxAYgwV0IIYQQQogNQIK7EEIIIYQQG4AEdyGEEEIIITYAc6134GqKxeJa74IQ\nQgghhBA3LZ/P37bHkh53IYQQQgghNgAJ7kIIIYQQQmwA67pUZqnbeZhBrL533nkHgIMHD67xnohb\nJc/lnUGexzuHPJd3Dnku7xwrVe4tPe5CCCGEEEJsABLchRBCCCGE2AAkuAshhBBCCLEBSHAXQggh\nhBBiA5DgLoQQQgghxAYgwV0IIYQQQogNQIK7EEIIIYQQG4AEdyGEEEIIITYACe5CCCGEEEJsABLc\nhRBCCCGE2AAkuAshhBBCCLEBSHAXQgghhBBiA5DgLoQQQgghxAYgwV0IIYQQQogNwFzrHRBCiLtV\nkigSpUgShVIX15culeJD2pe3LVBLHl8pteznLb16fqoCQG54Bk3TFtuXrDavL7ltSZumga5p6Lq2\nuNQ07bI2/Tq2FUIIcX0kuAshxA1QShHFCXHSWEZxQtxcLm2Pk+SaoVuhUCqhEbcX1pNm4E6aSVuh\nSJbd3tiPpdsuXFiezi/f+8W1qjcCwEzB4WIk55L1SyyGeA3QmqFeR9P05nX94m001xdvu/K2GksD\n/uWhf2FpGjqmoWPoS9aby4V27dJvHUIIcYeR4C6EuCtdbwBfCOFL15WKUaqxREVAgiJutsfN9mbY\nviR0XwzayZJgyuJS0zQ0faGH+mJPtQYXrzdvW9rzfXlP+ZL1i33li+1BsfEFYEffxYrJpZlfLQn5\nF9vV4vWFowGNLyHNLyhL1i9+aVlyPWk8auMLzMUjDksD/fJQfzH8a5px8YIBmgEsadN0TMO4PNzr\n+lVDvwR+IcRGIsFdCHFHieOEIIoJwpgwThrLKCaI4ktC+cXwrVQMxKDiKwZwRbR4XdMUpq5hGhqm\nrmGYjXVjoc3Q0XUwFnuMzWYgvzx0r6W00wjs2dTafwxcK/zHSUQch83nrXGJE0UcK6KFtkShlL4Y\n4jVMWFjXDDTNbHwRaAb9hdCva8ayEG+ZBpahY1sGtmlgmQa21WgzDBkWJoRYW2v/ji2EENcpuiSI\nXymcx0lMkoQoFaHUkmUSLQngCZqWLA/gxpUDuKnrmIaFoduYhtRkrwRN0zAMMK5WpnMd4magjxbL\nlcJGuF9ob64nzW3CZvvFwN/ozdd0C00z0TULNBNNs9B1C9P48FBvW43rpoR7IcQKumpwf/XVV3n+\n+ec5dOgQY2NjfOc73+HZZ59dts3XvvY1vv3tb1MoFHjsscd44YUXuO+++67rh7/22ms8+eST7N27\nlyNHjtz8byGE2PDCDwniS9vi5JIwriKSJAIVoQhJkghDT7BNHdvUsUytuWysm4aFKQH8jmUYjS9g\nduPadd9vaeAPo4Qo9gnCOkGUEMYJYaTw/IRE6ei6hYaJppuNXnzNal5MdN3C0JuB/gqhfqFNwr0Q\n4mZdNbhXq1UOHDjAs88+yzPPPHPZod1vfvObfOtb3+LFF19k9+7dfP3rX+fpp5/m5MmTZLPZq/7g\nQqHAM888w2c+8xnGxsZu/TcRQqxrSimCMMYLIvzmsrEeEUaN3lGlIlQSNnvGI5IkBBWRNEO6aYBt\nNnrDbUu/uG7qWKaNbboSyMUNWxb4nQ8P/HGsGl8io4QwCggjr7neCPxBqIhiFsM9moW+LOA3loZu\nYlsGjmXg2iaubeJYjaVtXf8XDiHE3eeqwf1zn/scn/vc5wB47rnnlt2mlOLf/Jt/w+/8zu/whS98\nAYAXX3yR7u5u/vzP/5yvfOUrV/3Bv/Ebv8GXv/xlkiThe9/73i38CkKI9SSMrhDOm9fjJCBJApRq\nLpOARAUoFWIZGralY1raYm+5tdhz7mCbqTWvC1/PkqQZKkNFEDVq+cNoYV0RhEkzdCqiKGHwTI0o\ngfPlCYKo0R5GSeMSL6w3S0ua9eZAczApiwNT1eJ6c0Drksltlk5CozUHxmpacwjqkgG1enNlYRyA\n1Rw3sHDkxDT1xdeHZSx9XVz8ErfQvniUxdCxLK2xbLbd6uunEfANXPvDw/Xy5yEgir1l/2+DUFGP\naZbi2Gi6ja7baJrTLMexcSxzeahvLqWnXghx0zXu586dY3Jyks9+9rOLba7r8slPfpKf/vSnVw3u\nf/AHf8D09DT/6l/9K37v937vZndBCLFG4kRR88JlveYLYT2MwmY491EqJEl8VDOc2ybYlo5rGTiW\njmPrOJaEcqUUNT+m5sXU/JiqFzWW9cb1xnpELWhs44fNEBhdDOdx3BjUGScaSQIq0YgTSGJIlEYS\nN9obF41SSZEkGun0/GJbHINSC/fTmjO/aKAaz40CUFpzyZK2hd/jw3/H5SH+kvUlbZqm0HWFpisM\nvTmTjq4uLg0as/AYCkNXjRl4dDCa21x2P+Pi/RfDvaFhWY1wn7J1Uo5BNmWScgwyrkHGbaxnXaPZ\nZpJxG6/Za71OdV3D0Q0c6+rPdxAleEFCENbxwipeEBOECfU6VHUbTWsE+ovh3sE0zCU99MZiT32S\nKDnSJMRd4qaD+8TEBAA9PT3L2ru7u69a+nLkyBG+/vWv8+abb97QB/U777xzczsq1hV5HjeOhXAR\nREkjkMfJYmAM45iTF34ENEpYIAAiUAGGobBN7YoXNI2gufWdSCmFHyrqgaIeJHhhc9m8Xg8U3sIy\nXN4WxxpRpBPFOnGkEcc6UawRRzpRpDdub96WJPpi2E6URpKYoJpzoms6i/80HW3Juk7zuqah04uG\nRnVZu46BjrVs++XTJWpceX359cZas2+++d9LTga1dLrJZVNPNqbQTEhIVMLCtUg12lSzfeGfUout\nzfWl912+rumqOcOPQtejZrBXmEaCYV66TDANhWEkmObFZcrWSdka7sLSaixTto57yTJlabh247V/\nPZ93GmAliiBWzR775Zck0UGzgMZF08zFdds0GPqbV3BMA8vUccyFcjIpvdmI5LNy49u1a9eKPO6K\nzCrzYW9Qvu/za7/2azz//PMMDAysxI8WQtyEJFF4YdwobwljvKDRq5uoRiBXzSWEoEI0Lca2NBxT\na5YhLFwsjDuw50+pRhgv1xNK9ZhKPWmuJ1S8hHI9puYrvDAhihoBO4quFMAN4rjZtnhbYzsdA1Oz\nMDUDQzMxMJvrFg6NNrPZrms6um6gG9piML80YIvlGl8I1OWhPoqJoojYi4lUSKRi6kTEKiJSETGN\n9ljFJFq8PNwvhHozwTAUphFjmmFjvdlmmAmWCSlbI23r5FI6ubROS8og6+q0pJptKR3H0tF1DVfX\ncK/QYx8t1NiHHn5Ubx5tUQQR+IGBH1pUaIR5rRnwDd1q9M5bjRKfhaNd8loRYmO66eDe29sLwOTk\nJJs3b15sn5ycXLztUuPj45w4cYIvf/nLfPnLXwYgSRonJLEsi7/5m7/hM5/5zBXve/DgwZvdVbEO\nLPQeyPO49qI4oeaF1PyQuh8ulry4SR078ckkHknioZSPY6UaJS2Wjmsb2KbOuTMnMQ3zumePWu+U\nUpTrEfOVcPFSrF5cL1RDipWQug+BrxMEBn6gE/gavq8RBDpBoBGGGlGsNQO3ialbmJqJpVuYmoW7\n0KabmKaJ5VrNbRrbrXaQKhQKALS1ta3qz93IEpUQqYgoCQlVSJxEhCokiiKiICRSIUHSCPxhEja/\nCEQoYkxTYdkK206wbYVjKxynsW4319MpaM1Y5DMWrVmLtuzF9YVL2jEue60cO3aMMFJs33kPQdgo\nwfHDxpEyP9QwdAdNdzF0F0130XWHlGORdi3SzWXKNmWe+nVAPivvHMVicUUe96aD+/bt2+nt7eWl\nl17ikUceAcDzPF577TWef/75K95n8+bNHD16dFnbCy+8wI9+9CO+//3vSy+8ELdZEMbUmuF8Iaj7\nYUgcN4J5Y9lYT9k6Gdcg7TTqelN27op1s6axcXrqkkRRrC2E8YVwHiy/Xg3xPAiCiyF8IZD7gUbg\nm/iBja5MHN3BXrgYDi0L646NnbIxtEZvuLgz6ZqOrdnYun1D90tUTJhEhCogiH2Cio+f+BSTgCBp\nrAeJj6ZHzSAf4zghtqNwmkF/Yd11NFqzdjPUm7RmLeZn6rSkdNp6Q1qzFh0t9mK4j+PG+AkvqFPz\nK9T9xtGhumczX3bR9YsX114e5NOuhSWlNkKsK9ecDnJwcBBo9IwPDQ3x3nvv0dHRwZYtW/it3/ot\nvvGNb7Bnzx527drF7//+75PL5fjiF7+4+BgL00i++OKLmOblvXRdXV04jnPH9N4JsVa8IFoM6DWv\nEdKDKCBp9qAniU+SeOhaSMo2SDUH3qUdC9d2Nuyhc6UU89WQ6fmAqXmfqXmf6XmfqfmA2VKA59Po\nHW+G8mAhlPsaQWASBDYGFrbu4BgXg3m+uXRSDnbGwdAkwIibo2sGjmHg4AC5K26jlCJW0WKID2oB\nfsWnHPvLwr3SokavvRPj2BG2XSMIYiwrpPPds9iOIu1CZ96hu9Whu9WmK+/Q1dq4nu1uvI7rQULd\nD6j5dep+TL2e4HkWRc3FMFw0rdEz71j2siCfdiwcW87dKMRauepf39tvv81TTz0FNLine truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8ea5cf8>"
+       "<matplotlib.figure.Figure at 0x2078017a390>"
       ]
      },
      "metadata": {},
@@ -1707,9 +1713,9 @@
    ],
    "source": [
     "P5 = multivariate_multiply((10,10), P2, (10.1, 9.97), P2)\n",
-    "plot_covariance_ellipse((10, 10), P2, fc='y', alpha=0.2)\n",
-    "plot_covariance_ellipse((10.1, 9.97), P2, fc='b', alpha=0.6)\n",
-    "plot_covariance_ellipse(P5[0], P5[1], fc='y')"
+    "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n",
+    "plot_covariance_ellipse((10.1, 9.97), P2, ec='k', fc='g', alpha=0.6)\n",
+    "plot_covariance_ellipse(P5[0], P5[1], ec='k', fc='b')"
    ]
   },
   {
@@ -1737,9 +1743,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9800ef0>"
+       "<matplotlib.figure.Figure at 0x207fe537b38>"
       ]
      },
      "metadata": {},
@@ -1767,9 +1773,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x97e04e0>"
+       "<matplotlib.figure.Figure at 0x207813af550>"
       ]
      },
      "metadata": {},
@@ -1803,9 +1809,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87ccd68>"
+       "<matplotlib.figure.Figure at 0x20781371908>"
       ]
      },
      "metadata": {},
@@ -1832,9 +1838,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x71ff358>"
+       "<matplotlib.figure.Figure at 0x2078117e8d0>"
       ]
      },
      "metadata": {},
@@ -1861,9 +1867,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c2b198>"
+       "<matplotlib.figure.Figure at 0x207814130f0>"
       ]
      },
      "metadata": {},
@@ -1892,9 +1898,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8846550>"
+       "<matplotlib.figure.Figure at 0x207800badd8>"
       ]
      },
      "metadata": {},

06-Multivariate-Kalman-Filters.ipynb

@@ -644,7 +644,7 @@
     "\n",
     "####  **Step 2:** Design the State Transition Function\n",
     "\n",
-    "In the univariate chapter we modeled the dog's motion with\n",
+    "In the univariate chapter we modeled the dog's motion (the process model) with\n",
     "\n",
     "$$ x = v \\Delta t + x_0$$\n",
     "\n",
@@ -682,7 +682,7 @@
     "\n",
     "$$\\mathbf{A} = \\begin{bmatrix}2& 3 \\\\ 3&-1\\end{bmatrix},\\, \\mathbf{x} = \\begin{bmatrix}x\\\\y\\end{bmatrix}, \\mathbf{b}=\\begin{bmatrix}8\\\\1\\end{bmatrix}$$\n",
     "\n",
-    "We call the set of equations that describe how the systems behaves the *process model*. We use the process model to perform the innovation, because the equations tell us what the next state will be given the current state. Kalman filters implement this using the linear equation, where $\\mathbf{\\bar{x}}$ is the *prior*, or predicted state:\n",
+    "We call the set of equations that describe how the systems behaves the *process model*. We use the process model to perform the *innovation*, because the equations tell us what the next state will be given the current state. Kalman filters implement this using the linear equation, where $\\mathbf{\\bar{x}}$ is the *prior*, or predicted state:\n",
     "\n",
     "$$\\mathbf{\\bar{x}} = \\mathbf{Fx}$$\n",
     "\n",
@@ -715,7 +715,7 @@
     "\\mathbf{\\bar{x}} &= \\mathbf{Fx}\n",
     "\\end{aligned}$$\n",
     "\n",
-    "$\\mathbf{F}$ is often called the **state transition function**. In the `KalmanFilter` class we implement the state transition function with"
+    "$\\mathbf{F}$ is often called the *state transition function*. In the `KalmanFilter` class we implement the state transition function with"
    ]
   },
   {
@@ -777,7 +777,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This worked. Note that the code does not distinguish between between the *prior* and *posterior* in the variable names, so after calling predict the prior $\\bar{\\mathbf{x}}$ is stored in `KalmanFilter.x`. If we call `predict()` several times in a row the value will be updated each time. "
+    "This worked. Note that the code does not distinguish between between the prior and posterior in the variable names, so after calling predict the prior $\\bar{\\mathbf{x}}$ is stored in `KalmanFilter.x`. If we call `predict()` several times in a row the value will be updated each time. "
    ]
   },
   {
@@ -894,7 +894,7 @@
    "source": [
     "#### Process Noise\n",
     "\n",
-    "A quick review on **process noise**. A car is driving along the road with the cruise control on; it should travel at a constant speed. We model this with $x=\\dot{x}\\Delta t + x_0$. However, it is affected by a number of unknown factors. The cruise control is not perfect, and cannot maintain a constant velocity. Winds affect the car, as do hills and potholes. Passengers roll down windows, changing the drag profile of the car. \n",
+    "A quick review on *process noise*. A car is driving along the road with the cruise control on; it should travel at a constant speed. We model this with $x=\\dot{x}\\Delta t + x_0$. However, it is affected by a number of unknown factors. The cruise control is not perfect, and cannot maintain a constant velocity. Winds affect the car, as do hills and potholes. Passengers roll down windows, changing the drag profile of the car. \n",
     "\n",
     "We can model this system with the differential equation\n",
     "\n",
@@ -902,7 +902,7 @@
     "\n",
     "where $\\mathbf{Fx}$ models the state transition and $w$ is white process noise.\n",
     "\n",
-    "To account for the unmodelled behavior in the system the filter adds a **process noise** covariance matrix $\\mathbf{Q}$ to the covariance $\\mathbf{P}$. We do not add anything to $\\mathbf{x}$ because the noise is *white* - which means that the mean of the noise will be 0. If the mean is 0, $\\mathbf{x}$ will not change."
+    "To account for the unmodelled behavior in the system the filter adds a process noise covariance matrix $\\mathbf{Q}$ to the covariance $\\mathbf{P}$. We do not add anything to $\\mathbf{x}$ because the noise is *white* - which means that the mean of the noise will be 0. If the mean is 0, $\\mathbf{x}$ will not change."
    ]
   },
   {
@@ -911,7 +911,7 @@
    "source": [
     "The univariate Kalman filter used `variance = variance + process_noise` to compute the variance for the variance of the prediction step. The multivariate Kalman filter does exactly the same thing, essentially `P = P + Q`. I say 'essentially' because there are other terms unrelated to noise in the covariance equation that we will see later.\n",
     "\n",
-    "Computing the process noise matrix can be quite demanding, and we will put it off until the Kalman math chapter. For now I will say that $\\mathbf{Q}$ equals the *expected value* of the white noise $w$, computed as $\\mathbf{Q} = E[\\mathbf{ww}^\\mathsf{T}]$. In this chapter we will focus on building an intuitive understanding on how modifying this matrix alters the behavior of the filter. FilterPy provides functions which compute $\\mathbf{Q}$ for the kinematic problems of this chapter."
+    "Computing the process noise matrix can be quite demanding, and we will put it off until the Kalman math chapter. For now know that $\\mathbf{Q}$ equals the expected value of the white noise $w$, computed as $\\mathbf{Q} = E[\\mathbf{ww}^\\mathsf{T}]$. In this chapter we will focus on building an intuitive understanding on how modifying this matrix alters the behavior of the filter. FilterPy provides functions which compute $\\mathbf{Q}$ for the kinematic problems of this chapter."
    ]
   },
   {
@@ -953,7 +953,7 @@
    "source": [
     "#### **Step 4**: Design the Control Function\n",
     "\n",
-    "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Suppose we are controlling a robot. At each time step we would send control signals to the robot based on its current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity *and* control inputs to the drive motors. Remember, we *never* throw information away.\n",
+    "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Suppose we are controlling a robot. At each time step we would send control signals to the robot based on its current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity and control inputs to the drive motors. Remember, we *never* throw information away.\n",
     "\n",
     "For a linear system the effect of control inputs can be described as a set of linear equations, which we can express with linear algebra as\n",
     "\n",
@@ -1008,7 +1008,7 @@
     "\n",
     "#### **Step 5**: Design the Measurement Function\n",
     "\n",
-    "The Kalman filter computes the update step in what we call **measurement space**. We mostly ignored this issue in the univariate chapter because of the complication it adds. We tracked our dog's position using a sensor that reported his position. Computing the *residual* was easy - subtract the filter's predicted position from the measurement:\n",
+    "The Kalman filter computes the update step in what we call *measurement space*. We mostly ignored this issue in the univariate chapter because of the complication it adds. We tracked our dog's position using a sensor that reported his position. Computing the *residual* was easy - subtract the filter's predicted position from the measurement:\n",
     "\n",
     "$$ \\mathtt{residual} = \\mathtt{measured\\, \\, position} - \\mathtt{estimated\\, \\, position}$$\n",
     "\n",
@@ -1449,7 +1449,7 @@
     "A word about my notation. I'm a programmer, and I am used to code reading `x = x + 1`. That is not an equation; the sides are not equal. If we wanted to write this in correct mathematical notation we'd write\n",
     "$$x_k = x_{k-1} + 1$$\n",
     "\n",
-    "The Kalman filter equations are traditionally *littered* with subscripts and superscripts to keep the equations mathematically consistent. This makes them very precise, but extremely hard to read. In most of the book I opt for subscriptless statements. As a programmer you should understand that I am showing you an algorithm that is to be executed step by step. I'll elaborate on this once we have a concrete example.\n",
+    "The Kalman filter equations are traditionally littered with subscripts and superscripts to keep the equations mathematically consistent. This makes them very precise, but extremely hard to read. In most of the book I opt for subscriptless statements. As a programmer you should understand that I am showing you an algorithm that is to be executed step by step. I'll elaborate on this once we have a concrete example.\n",
     "\n",
     "### Prediction Equations\n",
     "\n",
@@ -1603,7 +1603,7 @@
    "source": [
     "### Update Equations\n",
     "\n",
-    "The update equations look messier than the predict equations, but that is mostly due to the Kalman filter computing the update in **measurement space**. This is because measurements are not *invertible*. For example, later on we will be using sensors that only give you the range to a target. It is impossible to convert a range into a position - an infinite number of positions (in a circle) will yield the same range. On the other hand, we can always compute the range (measurement) given a position(state).\n",
+    "The update equations look messier than the predict equations, but that is mostly due to the Kalman filter computing the update in measurement space. This is because measurements are not *invertible*. For example, later on we will be using sensors that only give you the range to a target. It is impossible to convert a range into a position - an infinite number of positions (in a circle) will yield the same range. On the other hand, we can always compute the range (measurement) given a position (state).\n",
     "\n",
     "Before I continue, recall that we are trying to do something very simple: choose a new estimate chosen somewhere between a measurement and a prediction, as in this chart:"
    ]
@@ -1652,7 +1652,7 @@
     "\n",
     "You should recognize this $\\mathbf{ABA}^\\mathsf{T}$ form - the prediction step used $\\mathbf{FPF}^\\mathsf{T}$ to update $\\mathbf{P}$ with the state transition function. Here, we use the same form to update it with the measurement function. In a real sense the linear algebra is changing the coordinate system for us. \n",
     "\n",
-    "Once the covariance is in measurement space we need to account for the sensor noise. This is very easy  - we just add matrices. The result is variously called either the **system uncertainty** or **innovation covariance**.\n",
+    "Once the covariance is in measurement space we need to account for the sensor noise. This is very easy  - we just add matrices. The result is variously called either the *system uncertainty* or *innovation covariance*.\n",
     "\n",
     "I want you to compare the equation for the system uncertainty and the covariance\n",
     "\n",
@@ -1683,7 +1683,7 @@
     "\n",
     "$$\\mu = (1-K)\\mu_\\mathtt{prior} + K\\mu_\\mathtt{z}$$\n",
     "\n",
-    "Here $K$ is the Kalman gain, and it is a real number between 0 and 1. Examine this equation and ensure you understand how it selects a mean somewhere between the prediction and measurement. In this form the Kalman gain is essentially a *percentage* or *ratio* - if K is .9 it takes 90% of the measurement and 10% of the prediction. \n",
+    "Here $K$ is the Kalman gain, and it is a real number between 0 and 1. Examine this equation and ensure you understand how it selects a mean somewhere between the prediction and measurement. In this form the Kalman gain is a *percentage* or *ratio* - if K is .9 it takes 90% of the measurement and 10% of the prediction. \n",
     "\n",
     "For the multivariate Kalman filter $\\mathbf{K}$ is a vector, not a scalar. Here is the equation again: $\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} \\mathbf{S}^{-1}$. Is this a *ratio*? We can think of the inverse of a matrix as linear algebra's way of doing matrix division. Division is not defined for matrices, but it is useful to think of it in this way. So we can read the equation for $\\textbf{K}$ as meaning\n",
     "\n",
@@ -2753,7 +2753,7 @@
     "\n",
     "The case with $\\mathbf{Q}$ is more dire. I hope you were skeptical when I blithely assigned a noise matrix to my prediction about the movements of a dog. Who can say what a dog will do next? The Kalman filter in my GPS doesn't know about hills, the outside winds, or my terrible driving skills. Yet the filter requires a precise number to encapsulate all of that information, and it needs to work while I drive off-road in the desert, and when a Formula One champion drives on a closed circuit track.\n",
     "\n",
-    "These problems led some researchers and engineers to derogatorily call the Kalman filter a 'ball of mud'. In other words, it doesn't always hold together so well. Another term to know - Kalman filters can become **smug**. Their estimates are based solely on what you tell it the noises are. Those values can lead to overly confident estimates. $\\mathbf{P}$ gets smaller and smaller while the filter is actually becoming more and more inaccurate! In the worst case the filter diverges. We will see a lot of that when we start studying nonlinear filters. \n",
+    "These problems led some researchers and engineers to derogatorily call the Kalman filter a 'ball of mud'. In other words, it doesn't always hold together so well. Another term to know - Kalman filters can become *smug*. Their estimates are based solely on what you tell it the noises are. Those values can lead to overly confident estimates. $\\mathbf{P}$ gets smaller and smaller while the filter is actually becoming more and more inaccurate! In the worst case the filter diverges. We will see a lot of that when we start studying nonlinear filters. \n",
     "\n",
     "The Kalman filter is a mathematical model of the world. The output is only as accurate as that model. To make the math tractable we had to make some assumptions. We assume that the sensors and motion model have Gaussian noise. We assume that everything is linear. If that is true, the Kalman filter is *optimal* in a least squares sense. This means that there is no way to make a better estimate than what the filter gives us. However, these assumption are almost never true, and hence the model is necessarily limited, and a working filter is rarely optimal.\n",
     "\n",

07-Kalman-Filter-Math.ipynb

@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -256,7 +262,7 @@
        "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -280,224 +286,6 @@
     "I have illustrated the concepts with code and reasoning, not math. But there are topics that do require more mathematics than I have used so far. This chapter presents the math that you will need for the rest of the book."
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Computing Covariances\n",
-    "\n",
-    "You will not need to compute covariances by hand, but it is important to understand the computation. It only takes a few minutes to learn."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The *covariance* measures how much two random variables move in the same direction, and is defined as\n",
-    "\n",
-    "$$ COV(x,y) = E[(X-E[X])(Y-E[Y])] = \\frac{1}{N}\\sum_{i=1}^N (x_i - \\mu_x)(y_i - \\mu_y)$$\n",
-    "\n",
-    "If we compare this to the formula for the variance of a single variable we can see where this definition came from.\n",
-    "\n",
-    "$$\\sigma^2 = \\frac{1}{N}\\sum_{i=1}^N(x_i - \\mu)^2$$\n",
-    "\n",
-    "And indeed, the covariance of a variable with itself is the variance of the variable, which we can trivially prove with\n",
-    "\n",
-    "$$\\begin{aligned}\n",
-    "COV(x,x) &= \\frac{1}{N}\\sum_{i=1}^N (x_i - \\mu_x)(x_i - \\mu_x) \\\\\n",
-    "&= \\frac{1}{N}\\sum_{i=1}^N (x_i - \\mu_x)^2 \\\\\n",
-    "&= VAR(x)\n",
-    "\\end{aligned}$$\n",
-    "\n",
-    "\n",
-    "Let's build some familiarity with this by calculating the covariance for a random variable $X = [a\\, b\\, c]^\\mathsf{T}$ that has this sample space:\n",
-    "$$\\mathbf{x}_0 = \\begin{bmatrix}1 \\\\8\\\\3\\end{bmatrix},\\ \\  \\mathbf{x}_1 = \\begin{bmatrix}3\\\\7\\\\7\\end{bmatrix}$$\n",
-    "\n",
-    "The mean of multivariate variables is computed as the mean of each univariate variable:\n",
-    "\n",
-    "$$\\mu = \\begin{bmatrix}\\frac{1+3}{2}\\\\\\frac{8+7}{2}\\\\\\frac{3+7}{2}\\end{bmatrix} = \\begin{bmatrix}2\\\\7.5\\\\5\\end{bmatrix}$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Recall that we named the three variables as $a, b, c$. Let's start by computing the variance of $a$.\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "VAR(a) &= \\frac{1}{2}[(1-2)^2 + (3-2)^2] \\\\\n",
-    "&= \\frac{1}{2}[1+1] \\\\\n",
-    "&= 1\\end{aligned}$$\n",
-    "\n",
-    "\n",
-    "Using similar math we can compute that $VAR(b) = 0.25$ and $VAR(c)=4$. This allows us to fill in the covariance matrix with\n",
-    "\n",
-    "$$\\Sigma = \\begin{bmatrix}1 & & \\\\ & 0.25 & \\\\ &&4\\end{bmatrix}$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now we can compute the covariance of a and b.\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "COV(a,b) &= \\frac{1}{2}[(1-2)(8-7.5) + (3-2)(7-7.5)] \\\\\n",
-    "&= \\frac{1}{2}[(-1)(.5)+  (1)(-.5)] \\\\\n",
-    "&= -0.5\\end{aligned}$$\n",
-    "\n",
-    "We can fill in the $a^{th}$ row and $b^{th}$ column  in the covariance matrix with this value:\n",
-    "\n",
-    "$$\\Sigma = \\begin{bmatrix}1 & & \\\\ -0.5 & 0.25 & \\\\ &&4\\end{bmatrix}$$\n",
-    "\n",
-    "We already talked about the symmetry of the covariance matrix; $\\sigma_{ab}=\\sigma_{ba}$. We see now why this is true from the equation for the covariance.\n",
-    "\n",
-    "$$\\begin{aligned} COV(x,y) &= \\frac{1}{N}\\sum_{i=1}^N (x_i - \\mu_x)(y_i - \\mu_y) \\\\\n",
-    "&= \\frac{1}{N}\\sum_{i=1}^N (y_i - \\mu_y)(x_i - \\mu_x) \\\\\n",
-    "&= COV(y,x)\\end{aligned}$$\n",
-    "\n",
-    "This gives the covariance matrix\n",
-    "\n",
-    "$$\\Sigma = \\begin{bmatrix}1 &-0.5 & \\\\ -0.5 & 0.25 & \\\\ &&4\\end{bmatrix}$$.\n",
-    "\n",
-    "The arithmetic is a bit tedious, so let's use NumPy's `cov()` function to compute the entire covariance matrix. To compute the covariance in accordance with the equations above you will need to set the parameter `bias=1`.  The meaning of that parameter is not important to this book. If you are interested, wikipedia has a good article on it here http://en.wikipedia.org/wiki/Bias_of_an_estimator."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 1.   -0.5   2.  ]\n",
-      " [-0.5   0.25 -1.  ]\n",
-      " [ 2.   -1.    4.  ]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "x = [[1, 3], [8, 7], [3, 7]]\n",
-    "print(np.cov(x, bias=1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We said above that \"the *covariance* measures how much two random variables move in the same direction\", so let's see what that means in practice. If we start with the value $x_0 = (1, 2)$ we can create subsequent values that vary in the same direction with $x_1 = (2, 4)$, $x_2=(3,6)$, and $x_3=(4,8)$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 1.25  2.5 ]\n",
-      " [ 2.5   5.  ]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fcd978>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from filterpy.stats import plot_covariance_ellipse\n",
-    "\n",
-    "x = [[1, 2, 3, 4], [2, 4, 6, 8]]\n",
-    "cov = np.cov(x, bias=1)\n",
-    "plot_covariance_ellipse([0, 0], cov)\n",
-    "print(cov)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The values for $x$ are perfectly correlated, and the result is a covariance ellipse with zero width. We can see this by making the values not slightly uncorrelated."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x71ef6d8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "x = [[1, 2, 3, 4], [2, 4, 6, 8.4]]\n",
-    "plot_covariance_ellipse([0, 0], np.cov(x, bias=1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now lets make the second value go away from the first."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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truncated
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x869a470>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "x = [[1, 2, 3, 4], [-2, -4, -6, -8.4]]\n",
-    "plot_covariance_ellipse([0, 0], np.cov(x, bias=1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As we would hope, the covariance matrix is tilted in the opposite direction, indicating that the variables are inversely correlated. That is, as one gets larger, the other becomes smaller."
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -567,12 +355,9 @@
    "source": [
     "## Converting the Multivariate Equations to the Univariate Case\n",
     "\n",
+    "The multivariate Kalman filter equations look very different from the equations for the univariate filter. However, if we use one dimensional states and measurements the equations do reduce to the univariate equations. This section will provide you with a strong intuition into what the Kalman filter equations are actually doing. While reading this section is not required to understand the rest of the book, I recommend reading this section carefully as it should make the rest of the material easier to understand.\n",
     "\n",
-    "As it turns out the Kalman filter equations are quite easy to deal with in one dimension, so let's do the mathematical proof. \n",
-    "\n",
-    "> **Note:** This section will provide you with a strong intuition into what the Kalman filter equations are actually doing. While this section is not strictly required, I recommend reading this section carefully as it should make the rest of the material easier to understand. It is not merely a proof of correctness that you would normally want to skip past! The equations look complicated, but they are actually doing something quite simple.\n",
-    "\n",
-    "Let's start with the predict step, which is slightly easier. Here are the multivariate equations. \n",
+    "Here are the multivariate equations for the prediction. \n",
     "\n",
     "$$\n",
     "\\begin{aligned}\n",
@@ -581,9 +366,9 @@
     "\\end{aligned}\n",
     "$$\n",
     "\n",
-    "The state $\\mathbf{x}$ only has one variable, so it is a $1\\times 1$ matrix. Our motion $\\mathbf{u}$ is also a $1\\times 1$ matrix. Therefore, $\\mathbf{F}$ and $\\mathbf{B}$ must also be $1\\times 1$ matrices. That means that they are all scalars, and we can write\n",
+    "For a univariate problem the state $\\mathbf{x}$ only has one variable, so it is a $1\\times 1$ matrix. Our motion $\\mathbf{u}$ is also a $1\\times 1$ matrix. Therefore, $\\mathbf{F}$ and $\\mathbf{B}$ must also be $1\\times 1$ matrices. That means that they are all scalars, and we can write\n",
     "\n",
-    "$$x = Fx + Bu$$\n",
+    "$$\\bar{x} = Fx + Bu$$\n",
     "\n",
     "Here the variables are not bold, denoting that they are not matrices or vectors. \n",
     "\n",
@@ -595,7 +380,7 @@
     "\n",
     "$$ \\mu = \\mu_1+\\mu_2$$\n",
     "\n",
-    "Hopefully the general process is clear, so now I will go a bit faster on the rest. Our other equation for the predict step is\n",
+    "Hopefully the general process is clear, so now I will go a bit faster on the rest. We have\n",
     "\n",
     "$$\\mathbf{\\bar{P}} = \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}$$\n",
     "\n",
@@ -611,19 +396,19 @@
     "\n",
     "$$\\sigma^2 = \\sigma_1^2 + \\sigma_2^2$$\n",
     "\n",
-    "This proves that the multivariate equations are performing the same math as the univariate equations for the case of the dimension being 1."
+    "This proves that the multivariate prediction equations are performing the same math as the univariate equations for the case of the dimension being 1."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here our multivariate Kalman filter equations for the update step.\n",
+    "These are the equations for the update step:\n",
     "\n",
     "$$\n",
     "\\begin{aligned}\n",
-    "\\textbf{y} &= \\mathbf{z} - \\mathbf{H \\bar{x}}\\\\\n",
     "\\mathbf{K}&= \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf{R})^{-1} \\\\\n",
+    "\\textbf{y} &= \\mathbf{z} - \\mathbf{H \\bar{x}}\\\\\n",
     "\\mathbf{x}&=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n",
     "\\mathbf{P}&= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n",
     "\\end{aligned}\n",
@@ -633,18 +418,16 @@
     "\n",
     "$$\n",
     "\\begin{aligned}\n",
-    "y &= z - x\\\\\n",
-    "K &=P / (P + R) \\\\\n",
-    "x &=x +Ky \\\\\n",
-    "P &= (1-K)P\n",
+    "K &=\\frac{\\bar{P}}{\\bar{P} + R} \\\\\n",
+    "y &= z - \\bar{x}\\\\\n",
+    "x &=\\bar{x}+Ky \\\\\n",
+    "P &= (1-K)\\bar{P}\n",
     "\\end{aligned}\n",
     "$$\n",
     "\n",
-    "Before we continue with the proof, I want you to look at those equations to recognize what a simple concept these equations implement. The residual $y$ is nothing more than the measurement minus the previous state. The gain $K$ is scaled based on how certain we are about the last prediction vs how certain we are about the measurement. We choose a new state $x$ based on the old value of $x$ plus the scaled value of the residual. Finally, we update the uncertainty based on how certain we are about the measurement. Algorithmically this should sound exactly like what we did in the last chapter.\n",
+    "Before we continue with the proof, I want you to look at those equations to recognize what a simple concept these equations implement. The residual $y$ is nothing more than the measurement minus the prediction. The gain $K$ is scaled based on how certain we are about the last prediction vs how certain we are about the measurement. We choose a new state $x$ based on the old value of $x$ plus the scaled value of the residual. Finally, we update the uncertainty based on how certain we are about the measurement. Algorithmically this should sound exactly like what we did in the last chapter.\n",
     "\n",
-    "So let's finish off the algebra to prove this. It's straightforward, and not at all  necessary for you to learn unless you are interested. Feel free to skim ahead to the last paragraph in this section if you prefer skipping the algebra.\n",
-    "\n",
-    "Recall that the univariate equations for the update step are:\n",
+    "So let's finish off the algebra to prove this. Recall that the univariate equations for the update step are:\n",
     "\n",
     "$$\n",
     "\\begin{aligned}\n",
@@ -653,7 +436,7 @@
     "\\end{aligned}\n",
     "$$\n",
     "\n",
-    "Here we will say that $\\mu_1$ is the state $x$, and $\\mu_2$ is the measurement $z$. That is entirely arbitrary, we could have chosen the opposite assignment. Thus it follows that that $\\sigma_1^2$ is the state uncertainty $P$, and $\\sigma_2^2$ is the measurement noise $R$. Let's substitute those in.\n",
+    "Here we will say that $\\mu_1$ is the state $x$, and $\\mu_2$ is the measurement $z$. Thus it follows that that $\\sigma_1^2$ is the state uncertainty $P$, and $\\sigma_2^2$ is the measurement noise $R$. Let's substitute those in.\n",
     "\n",
     "$$ \\mu = \\frac{Pz + Rx}{P+R} \\\\\n",
     "\\sigma^2 = \\frac{1}{\\frac{1}{P} + \\frac{1}{R}}\n",
@@ -756,11 +539,11 @@
     "\n",
     "$$g_n = \\frac{\\sigma^2_{x}}{\\sigma^2_{y}}$$\n",
     "\n",
-    "The end result is multiplying the residual of the two measurements by a constant and adding to our previous value, which is the *g* equation for the g-h filter. *g* is the variance of the new estimate divided by the variance of the measurement. Of course in this case g is not a constant as it varies with each time step as the variance changes. We can also derive the formula for *h* in the same way but I don't find this a particularly interesting derivation. The end result is\n",
+    "The end result is multiplying the residual of the two measurements by a constant and adding to our previous value, which is the $g$ equation for the g-h filter. $g$ is the variance of the new estimate divided by the variance of the measurement. Of course in this case $g$ is not a constant as it varies with each time step as the variance changes. We can also derive the formula for $h$ in the same way but I don't find this a particularly interesting derivation. The end result is\n",
     "\n",
     "$$h_n = \\frac{COV (x,\\dot{x})}{\\sigma^2_{y}}$$\n",
     "\n",
-    "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and predictions at time *n*. In other words, we are picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
+    "The takeaway point is that $g$ and $h$ are specified fully by the variance and covariances of the measurement and predictions at time $n$. In other words, we are picking a point between the measurement and prediction by a scale factor determined by the quality of each of those two inputs. That is all the Kalman filter is. "
    ]
   },
   {
@@ -838,7 +621,7 @@
     "$$F(x) = t - t_0 + F(x_0) \\\\\n",
     "x = F^{-1}[t-t_0 + F(x_0)]$$\n",
     "\n",
-    "In other words, we need to find the inverse of $F$. This is not at all trivial, and a significant amount of course work in a STEM education is devoted to finding tricky, analytic solutions to this problem, backed by several centuries of research. \n",
+    "In other words, we need to find the inverse of $F$. This is not at all trivial, and a significant amount of course work in a STEM education is devoted to finding tricky, analytic solutions to this problem, backed by a few centuries of research. \n",
     "\n",
     "In the end, however, they are tricks, and many simple forms of $f(x)$ either have no closed form solution, or pose extreme difficulties. Instead, the practicing engineer turns to numerical methods to find a solution to her problems. I would suggest that students would be better served by learning fewer analytic mathematical tricks and instead focusing on learning numerical methods, but that is the topic for another book."
    ]
@@ -911,17 +694,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "estimate of sin(.3) is 0.30452025\n",
-      "exact value of sin(.3) is 0.295520206661\n"
+     "ename": "NameError",
+     "evalue": "name 'np' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[1;32m<ipython-input-3-9197b58f6ce0>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m.3\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mestimate\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mx\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m6\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m120\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mexact\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m.3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'estimate of sin(.3) is'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mestimate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;31mNameError\u001b[0m: name 'np' is not defined"
      ]
     }
    ],
@@ -994,7 +780,7 @@
     "\n",
     "$$ \\Phi(t) = \\mathcal{L}^{-1}[(s\\mathbf{I} - \\mathbf{F})^{-1}]$$\n",
     "\n",
-    "I have no intention of going into this other than to say that the inverse Laplace transform converts a signal into the frequency (time) domain, but finding a solution to the equation above is non-trivial. If you are interested, the Wikipedia article on LTI system theory provides an introduction [2]."
+    "I have no intention of going into this other than to say that the inverse Laplace transform converts a signal into the frequency (time) domain, but finding a solution to the equation above is non-trivial. If you are interested, the Wikipedia article on LTI system theory provides an introduction [2]. I mention LTI because you will find some literature using it to design the Kalman filter matrices for difficult problem. "
    ]
   },
   {
@@ -1014,7 +800,9 @@
     "  \n",
     "    F = np.array([[0,1],[-1,0]], dtype=float)\n",
     "    G = np.array([[0.],[2.]]) # white noise scaling\n",
-    "    phi, Q = van_loan_discretization(F, G, dt=0.1)"
+    "    phi, Q = van_loan_discretization(F, G, dt=0.1)\n",
+    "    \n",
+    "As with LTI system theory, I do not intend to teach the topic of solving differential equations in this book so I will not pursue this further."
    ]
   },
   {
@@ -1028,7 +816,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In the sections above I spoke of *first order* differential equations; these are equations with only first derivatives. However, physical systems often require second or higher order equations. Any higher order system of equations can be converted to a first order set of equations by defining extra variables for the first order terms and then solving. Let's do an example. \n",
+    "In the sections above I spoke of *first order* differential equations; these are equations with only first derivatives. However, models of physical systems often require second or higher order equations. Any higher order system of equations can be converted to a first order set of equations by defining extra variables for the first order terms and then solving. Let's do an example. \n",
     "\n",
     "Given the system $\\ddot{x} - 6\\dot{x} + 9x = t$ find the first order equations.\n",
     "\n",
@@ -1122,7 +910,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -1149,7 +937,7 @@
        "⎣    6           2                 ⎦       "
       ]
      },
-     "execution_count": 7,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1184,7 +972,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -1205,7 +993,7 @@
        "[\\Delta{t}⋅\\Phi_s]"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1220,7 +1008,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -1249,7 +1037,7 @@
        "⎣    2                 ⎦       "
       ]
      },
-     "execution_count": 9,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1299,7 +1087,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -1321,7 +1109,7 @@
        "⎣    2                 ⎦    "
       ]
      },
-     "execution_count": 10,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1361,7 +1149,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -1388,7 +1176,7 @@
        "⎣    2                             ⎦    "
       ]
      },
-     "execution_count": 11,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1426,7 +1214,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -1450,7 +1238,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -1479,7 +1267,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
@@ -1500,21 +1288,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 0.25  0.5   0.5 ]\n",
-      " [ 0.5   1.    1.  ]\n",
-      " [ 0.5   1.    1.  ]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "Q = Q_discrete_white_noise(3, var=1.)\n",
     "print(Q)"
@@ -1531,7 +1309,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
@@ -1540,16 +1318,20 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[ 0.     0.     0.   ]\n",
-      " [ 0.     0.     0.001]\n",
-      " [ 0.     0.001  0.05 ]]\n"
+      "[[ 0.00000002  0.00000078  0.00002083]\n",
+      " [ 0.00000078  0.00004167  0.00125   ]\n",
+      " [ 0.00002083  0.00125     0.05      ]]\n"
      ]
     }
    ],
    "source": [
+    "import numpy as np\n",
+    "\n",
+    "np.set_printoptions(precision=8)\n",
     "Q = Q_continuous_white_noise(\n",
     "    dim=3, dt=0.05, spectral_density=1)\n",
-    "print(Q)"
+    "print(Q)\n",
+    "np.set_printoptions(precision=3)"
    ]
   },
   {
@@ -1561,11 +1343,13 @@
     "$$ \\mathbf{P}=\\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}$$\n",
     "\n",
     "If the values for $\\mathbf{Q}$ are small relative to $\\mathbf{P}$\n",
-    "than it will be contributing almost nothing to the computation of $\\mathbf{P}$. Setting $\\mathbf{Q}$ to \n",
+    "than it will be contributing almost nothing to the computation of $\\mathbf{P}$. Setting $\\mathbf{Q}$ to the zero matrix except for the lower right term\n",
     "\n",
     "$$\\mathbf{Q}=\\begin{bmatrix}0&0&0\\\\0&0&0\\\\0&0&\\sigma^2\\end{bmatrix}$$\n",
     "\n",
-    "while not correct, is often a useful approximation. If you do this you will have to perform quite a few studies to guarantee that your filter works in a variety of situations. Given the availability of functions to compute the correct values of $\\mathbf{Q}$ for you I would strongly recommend not using approximations. Perhaps it is justified for quick-and-dirty filters, or on embedded devices where you need to wring out every last bit of performance, and seek to minimize the number of matrix operations required. "
+    "while not correct, is often a useful approximation. If you do this you will have to perform quite a few studies to guarantee that your filter works in a variety of situations. Given the availability of functions to compute the correct values of $\\mathbf{Q}$ for you I would strongly recommend not using approximations. Perhaps it is justified for quick-and-dirty filters, or on embedded devices where you need to wring out every last bit of performance, and seek to minimize the number of matrix operations required. \n",
+    "\n",
+    "If you do this, 'lower right term' means the most rapidly changing term for each variable. If the state is $x=\\begin{bmatrix}x & \\dot{x} & \\ddot{x} & y & \\dot{y} & \\ddot{y}\\end{bmatrix}^\\mathsf{T}$ Then Q will be 6x6; the elements for both $\\ddot{x}$ and $\\ddot{y}$ will have to be set to non-zero in $\\mathbf{Q}$."
    ]
   },
   {

08-Designing-Kalman-Filters.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -280,7 +286,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In the last chapter we worked with 'textbook' problems. These are problems that are easy to state, program in a few lines of code, and teach. Real world problems are rarely 'textbook'. In this chapter, and the remainder of the book, we will work with more realistic examples. \n",
+    "In the last chapter we worked with 'textbook' problems. These are problems that are easy to state, program in a few lines of code, and teach. Real world problems are rarely this simple. In this chapter, and the remainder of the book, we will work with more realistic examples. \n",
     "\n",
     "We will begin by tracking a robot in a 2D space, such as a field or warehouse. We will start with a simple noisy sensor that outputs noisy $(x,y)$ coordinates which we will need to filter to generate a 2D track. Once we have mastered this concept, we will extend the problem significantly with more sensors and then adding control inputs. \n",
     "\n",
@@ -346,9 +352,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAADTCAYAAABDa58YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7231518>"
+       "<matplotlib.figure.Figure at 0x7208f60>"
       ]
      },
      "metadata": {},
@@ -683,9 +689,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeMAAAEPCAYAAABx8azBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAADTCAYAAACbfYSmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x852c8d0>"
+       "<matplotlib.figure.Figure at 0x86bcc50>"
       ]
      },
      "metadata": {},
@@ -750,9 +756,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAEPCAYAAABvIiPGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8727d68>"
+       "<matplotlib.figure.Figure at 0x8731a20>"
       ]
      },
      "metadata": {},
@@ -848,9 +854,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86c2898>"
+       "<matplotlib.figure.Figure at 0x86bc470>"
       ]
      },
      "metadata": {},
@@ -908,7 +914,7 @@
    "source": [
     "We have only studied tracking position and velocity. It has worked well, but only because I have been selecting problems for which this is an appropriate choice. You now have enough experience with the Kalman filter to consider this in more general terms.\n",
     "\n",
-    "What do I mean by **order**? In the context of these system models it is the number of derivatives required to accurately model a system. Consider a system that does not change, such as the height of a building. There is no change, so there is no need for a derivative, and the order of the system is zero. We could express this in an equation as $x = 312.5$.\n",
+    "What do I mean by order? In the context of these system models it is the number of derivatives required to accurately model a system. Consider a system that does not change, such as the height of a building. There is no change, so there is no need for a derivative, and the order of the system is zero. We could express this in an equation as $x = 312.5$.\n",
     "\n",
     "A first order system has a first derivative. For example, change of position is velocity, and we can write this as\n",
     "\n",
@@ -918,7 +924,7 @@
     "\n",
     "$$ x = vt + x_0.$$\n",
     "\n",
-    "This is also called a **constant velocity** model, because of the assumption of a constant velocity.\n",
+    "This is also called a *constant velocity* model, because of the assumption of a constant velocity.\n",
     "\n",
     "A second order has a second derivative. The second derivative of position is acceleration, with the equation\n",
     "\n",
@@ -928,7 +934,7 @@
     "\n",
     "$$ x = \\frac{1}{2}at^2 +v_0t + x_0.$$\n",
     "\n",
-    "This is also known as a **constant acceleration** model.\n"
+    "This is also known as a *constant acceleration* model.\n"
    ]
   },
   {
@@ -958,9 +964,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86c2518>"
+       "<matplotlib.figure.Figure at 0x86bc668>"
       ]
      },
      "metadata": {},
@@ -1002,7 +1008,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I am satisfied with this plot. The track is not perfectly straight due to the noise that we added to the system - this could be the track of a person walking down the street, or perhaps of an aircraft being buffeted by variable winds. There is no *intentional* acceleration here, so we call it a constant velocity system. Again, you may be asking yourself that since there is in fact a tiny bit of acceleration going on why would we not use a second order Kalman filter to account for those changes? Let's find out.\n",
+    "I am satisfied with this plot. The track is not perfectly straight due to the noise that we added to the system - this could be the track of a person walking down the street, or perhaps of an aircraft being buffeted by variable winds. There is no intentional acceleration here, so we call it a constant velocity system. Again, you may be asking yourself that since there is in fact a tiny bit of acceleration going on why would we not use a second order Kalman filter to account for those changes? Let's find out.\n",
     "\n",
     "How does one design a zero order, first order, or second order Kalman filter? We have been doing it all along, but just not using those terms. It might be slightly tedious, but I will elaborate fully on each - if the concept is clear to you feel free to skim a bit."
    ]
@@ -1274,9 +1280,9 @@
    "outputs": [
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAADqCAYAAADJRsOsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x885a390>"
+       "<matplotlib.figure.Figure at 0x881db38>"
       ]
      },
      "metadata": {},
@@ -1298,7 +1304,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "It looks like the filter is performing well, but it is hard to tell exactly how well. Let's look at the residuals and see if they help. You may have noticed that in the code above I saved the covariance at each step. I did that to use in the following plot. The ConstantVelocityObject class returns a tuple of (position, velocity) for the real object, and this is stored in the array `xs`, and the filter's estimates are in `filter_xs1`."
+    "It looks like the filter is performing well, but it is hard to tell exactly how well. Let's look at the residuals and see if they help. You may have noticed that in the code above I saved the covariance at each step. I did that to use in the following plot. The `ConstantVelocityObject` class returns a tuple of (position, velocity) for the real object, and this is stored in the array `xs`, and the filter's estimates are in `filter_xs1`."
    ]
   },
   {
@@ -1326,9 +1332,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAEACAYAAADr3HqZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86e3828>"
+       "<matplotlib.figure.Figure at 0x8895400>"
       ]
      },
      "metadata": {},
@@ -1359,9 +1365,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAE8CAYAAACYZL1PAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAEACAYAAADr3HqZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x887c160>"
+       "<matplotlib.figure.Figure at 0x86bc5c0>"
       ]
      },
      "metadata": {},
@@ -1392,9 +1398,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAEmCAYAAAANwgSvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAADqCAYAAADJRsOsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99ffef0>"
+       "<matplotlib.figure.Figure at 0x9a06f98>"
       ]
      },
      "metadata": {},
@@ -1429,9 +1435,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAE7CAYAAACyihXqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAEACAYAAADcN+KEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a13940>"
+       "<matplotlib.figure.Figure at 0x9a1e208>"
       ]
      },
      "metadata": {},
@@ -1470,9 +1476,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAEmCAYAAAANwgSvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAADqCAYAAADJRsOsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99e7668>"
+       "<matplotlib.figure.Figure at 0x9b0c860>"
       ]
      },
      "metadata": {},
@@ -1505,9 +1511,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAE6CAYAAABOPV5SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAD+CAYAAABiMwlEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a802e8>"
+       "<matplotlib.figure.Figure at 0x9a8d1d0>"
       ]
      },
      "metadata": {},
@@ -1544,9 +1550,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAE6CAYAAABOPV5SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAD+CAYAAABiMwlEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x991aeb8>"
+       "<matplotlib.figure.Figure at 0x8911f98>"
       ]
      },
      "metadata": {},
@@ -1587,9 +1593,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAEmCAYAAAANwgSvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAADqCAYAAADJRsOsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b01f28>"
+       "<matplotlib.figure.Figure at 0x9b0cd30>"
       ]
      },
      "metadata": {},
@@ -1620,9 +1626,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAAEoCAYAAAC6pSKLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a2cb38>"
+       "<matplotlib.figure.Figure at 0x9b0c6a0>"
       ]
      },
      "metadata": {},
@@ -1630,9 +1636,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAD+CAYAAABiMwlEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a2c240>"
+       "<matplotlib.figure.Figure at 0x9b0cef0>"
       ]
      },
      "metadata": {},
@@ -1672,9 +1678,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArUAAAEmCAYAAAB8umgxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x884c438>"
+       "<matplotlib.figure.Figure at 0x8899f60>"
       ]
      },
      "metadata": {},
@@ -1682,9 +1688,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwoAAAD+CAYAAACa0/KzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87a35c0>"
+       "<matplotlib.figure.Figure at 0x9a21ef0>"
       ]
      },
      "metadata": {},
@@ -1724,9 +1730,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAAEWCAYAAAAw37JZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAADaCAYAAADwgmciAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8717ef0>"
+       "<matplotlib.figure.Figure at 0x8812f60>"
       ]
      },
      "metadata": {},
@@ -1765,9 +1771,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEWCAYAAAAuFoLqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAADaCAYAAADuS1eRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87b8d30>"
+       "<matplotlib.figure.Figure at 0x893eef0>"
       ]
      },
      "metadata": {},
@@ -1821,9 +1827,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7EAAAEmCAYAAAC03xeLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8717a20>"
+       "<matplotlib.figure.Figure at 0x9b1f390>"
       ]
      },
      "metadata": {},
@@ -1831,9 +1837,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAD+CAYAAABV2JFZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x883bef0>"
+       "<matplotlib.figure.Figure at 0x87a8ba8>"
       ]
      },
      "metadata": {},
@@ -1871,9 +1877,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7EAAAEmCAYAAAC03xeLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87c9630>"
+       "<matplotlib.figure.Figure at 0x99cefd0>"
       ]
      },
      "metadata": {},
@@ -1881,9 +1887,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAD+CAYAAABV2JFZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87c9400>"
+       "<matplotlib.figure.Figure at 0x99ce400>"
       ]
      },
      "metadata": {},
@@ -1916,9 +1922,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA7EAAAEmCAYAAAC03xeLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88db550>"
+       "<matplotlib.figure.Figure at 0x8864d68>"
       ]
      },
      "metadata": {},
@@ -1926,9 +1932,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwYAAAD+CAYAAACA7xI9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9925588>"
+       "<matplotlib.figure.Figure at 0x88649e8>"
       ]
      },
      "metadata": {},
@@ -2088,9 +2094,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAADaCAYAAAB+WC5eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99ff780>"
+       "<matplotlib.figure.Figure at 0x9acbd30>"
       ]
      },
      "metadata": {},
@@ -2115,9 +2121,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The likelihood gets larger as the filter converges during the first few iterations. After that the likelihood bounces around until it reaches the bad measurements, at which time it goes to zero, indicating that *if* the measurements are valid the filter is very unlikely to be optimal.\n",
+    "The likelihood gets larger as the filter converges during the first few iterations. After that the likelihood bounces around until it reaches the bad measurements, at which time it goes to zero, indicating that if the measurements are valid the filter is very unlikely to be optimal.\n",
     "\n",
-    "The **log likelihood** is somewhat more convienent to use in some cases. By taking the log we guarantee that the function is monotonically increasing, and its maximum values occur at the same points as the function itself. See how starkly it illustrates where the filter goes 'bad'."
+    "The *log likelihood* is somewhat more convienent to use in some cases. By taking the log we guarantee that the function is monotonically increasing, and its maximum values occur at the same points as the function itself. See how starkly it illustrates where the filter goes 'bad'."
    ]
   },
   {
@@ -2129,9 +2135,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwkAAADaCAYAAADt2Q6QAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ac3208>"
+       "<matplotlib.figure.Figure at 0x87a1e10>"
       ]
      },
      "metadata": {},
@@ -2222,9 +2228,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwEAAAEtCAYAAABQ7mxxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAADqCAYAAADAgaGTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdYVMfXwPHvsoiAAkoXNUqMvcVGxIItKvauid1YIzGx\n917Q2HvD2DX+7D1KjMaGRuy9xS69I4Kw7H3/INw3xIa4CMr5PA/Pwty7M3MZytnZuWc0iqIoCCGE\nEEIIIT4qRhndASGEEEIIIcS7k0BeCCGEEEKIj5AE8kIIIYQQQnyEJJAXQgghhBDiIySBvBBCCCGE\nEB8h44zuwIcQGRmZ0V0QQgghhBAizaysrF4qkxl5IYQQQgghPkISyAshhBBCCPERyhJLa/7tVW9L\nfAhnz54FoGLFihnSvsg4MvZZm4x/1iVjn3XJ2Gddhh77ty0Plxl5IYQQQgghPkISyAshhBBCCPER\nynJLa4QQQgghhHiTy5cvs3btWp4/f46bmxvt2rVDo9FkdLdeIoG8EEIIIYTIkh4/fszZs2exsLCg\nWrVqmJqa4u3tTZMmTYiPjwdgyZIl+Pj4MH/+/Azu7csybGnNsWPHaNq0Kfny5cPIyIg1a9a8dM74\n8ePJmzcv5ubm1KpVi+vXr6c4/uLFC/r164ednR05c+akWbNmPH369ENdghBCCCGE+Eht2LCBL774\ngpYtW1K3bl0qVKjAkydP6NGjB/Hx8bRr146JEydiYmLCggULOHPmTEZ3+SUZFsjHxMRQpkwZ5s2b\nh5mZ2UtvV/z888/Mnj2bhQsX4uvri729PXXr1uXZs2fqOf3792f79u1s2rSJ48ePExUVRePGjdHr\n9R/6coQQQgghxEfizp07dOvWjfj4eNzc3MifPz/Xr1+nY8eOPH78GCMjIzZu3MiYMWNo0qQJADdu\n3MjgXr8swwL5Bg0aMHnyZFq1aoWRUcpuKIrC3LlzGTFiBC1atKBkyZKsWbOG6OhoNm7cCCSl41m5\nciUzZ86kTp06lCtXjnXr1nH58mUOHTqUEZckhBBCCCE+AsePHychIYGGDRty9OhRNW3k8ePHsbS0\nRK/XM3fuXLy9vTl69CgATk5OGdnlV8qUWWvu379PYGAg9erVU8tMTU1xc3PDx8cHgHPnzpGQkJDi\nnHz58lG8eHH1HCGEEEIIIf4re/bsAAQEBBAXF8ejR48AMDExYcKECQAMGjSI+vXrExISQo0aNahV\nq1aG9fd1MuXNrgEBAQA4ODikKLe3t8fPz089R6vVYmNjk+IcBwcHAgMDP0xHhRBCCCHER8fd3R0H\nBwfOnz+PtbU1sbGxAHTu3Jn+/ftjbW2Nl5cXMTEx1KhRg8mTJ2NsnPnC5szXo7d439Q/yW+dZJSM\nbl9kHBn7rE3GP+uSsc+6ZOwzt1mzZjFq1CgePnyIRqOhYcOGdOrUibNnz1KiRAnmzJmjnvuu6+MN\nNfaFCxd+4/FMGcg7OjoCEBgYSL58+dTywMBA9ZijoyOJiYmEhoammJUPCAjAzc3tw3ZYCCGEEEJk\nKH9/f44dO0Z8fDwuLi4ULVr0jecXLVqULVu2EBkZiampKaamph+op4aTKQN5Z2dnHB0d8fb2pkKF\nCgDExcVx4sQJZs6cCUCFChXIli0b3t7efPvttwA8efKEmzdvUqVKldfWXbFixfS/gFdIfmWWUe2L\njCNjn7XJ+GddMvZZl4z9h3fs2DE6dOhAdHQ0AEZGRixdupSePXt+0H4YeuwjIyPfeDxD009evHiR\nixcvotfrefjwIRcvXuTx48doNBr69+/Pzz//zI4dO7h69Spdu3bFwsKC9u3bA2BlZUX37t0ZOnQo\nf/zxBxcuXKBTp06ULVuWr7/+OqMuSwghhBBCpJObN29SrVo1TExMcHBwwNPTE51OpwbxderUoUOH\nDuj1evr27cvjx4+BpIyI0dHRKIqSwVdgWBk2I+/r60vt2rWBpHXv48aNY9y4cXTt2pWVK1cydOhQ\nYmNj8fDwIDw8nMqVK+Pt7U2OHDnUOubOnYuxsTHt2rUjNjaWr7/+mvXr12fKLXSFEEIIIUTahYSE\nULt2bfz9/QEICgpi1KhRxMTE8OTJEywtLTl48CBarZbHjx9z7NgxLly4wMGDBxk6dCjh4eE4ODiw\nePFiWrZsmcFXYxgZNiNfs2ZN9Ho9er2exMRE9fOVK1eq54wbNw4/Pz9iY2M5cuQIJUqUSFGHiYkJ\n8+fPJyQkhJiYGHbt2kXevHk/9KUIIYQQQoh0tn37dvz9/alQoQLBwcGsXr0agNWrV6PRaIiKiuLw\n4cNcv35dvTn16tWr9OzZk/DwcLRaLYGBgbRp04aTJ09m4JUYTqbMIy+EEEIIIbK2u3fvcuzYMTUt\nefJ68S+//BJbW1s1r3t0dDS9evUCoF69epQsWZLg4GC++uorNWAfO3YsCQkJ9OrVC71ez6pVqzLg\nigwvU97sKoQQQgghsiadTkf37t1Zu3YtAFqtlhkzZuDq6grAmjVriI+P59y5cwC4uroyf/58LC0t\nWbduHfHx8dStW5dFixbRpk0bAEqWLIlGo6FkyZIAPH/+PAOuzPBkRl4IIYQQQqSrK1eusH79eg4e\nPEhCQsIbz506dSpr167FxMSE8uXLk5iYyMCBA3n+/Dljx45Fp9Oxbt06rl+/jrOzM8uWLcPExITp\n06fj7+9PaGgomzZtwsbGhho1agDQq1cv2rRpw/DhwwHU8o+dBPJCCCGEECLdTJgwgTJlytCpUyfc\n3d2pVq0a4eHhrz1/9+7dAGzcuJFz584xePBgAPbu3cuECRM4deoU8+bNY+3atVy8eJGCBQu+tq7h\nw4fTqFEjIiMj2bp1K7GxsXTp0uWDp6VML7K0RgghhBBCpItDhw4xfvx4tFotjRs35q+//uLMmTMM\nGDBAvVn1v4yMkuaZ4+LiUjwmZyWsXLkylStXTlX72bNnZ/fu3Rw7doyHDx9SuHBhXF1dP5kMhxLI\nCyGEEEJ8IpLzpVtYWGSKYPXPP/8EwMPDg3nz5uHr64uLi4ta/tdff7F9+3b0ej2NGjWiZs2atGnT\nhjNnztCpUyfGjh3LvXv30Gg0tGrVKk19MDIyombNmoa5oExGltYIIYQQQnwCtm/fjpOTE1ZWVtjY\n2ODl5ZUu7ezatYvu3bvTs2dPDh48mKJ9FxcXChYsSPPmzXnw4AHm5uYA3LlzB51Op6aFNDc3Z/36\n9VSpUoXp06czc+ZMatWqxaJFixg4cCD9+vVDURTu3buHqakpXl5euLm5pcv1fMxkRl4IIYQQ4iPn\n4+NDmzZt0Ov1aLVawsPD6dWrF7a2trRo0cJg7Xh6ejJq1Cj16xUrVrBw4ULy5MmTYsb84cOHnD17\nlu3bt+Pp6clvv/2GmZkZOp0OgI4dO9K7d2/0ej3du3fH3NycBQsW0L9/f1q3bs38+fMZM2YM/v7+\nODs7Y2FhYbBr+JTIjLwQQgghxEdu1apV6PV6evXqRUJCAuPHjweSAm1D8ff3Z8yYMUBSXvahQ4cC\nMHDgQCZNmgTAkCFDuHLlCuXLl+fp06ecOHGC3377DWdnZ3Q6HWZmZowbN47GjRvz/PlzChYsyIoV\nK5g/fz7ly5dHp9Nx69YtAOzs7ChTpowE8W8gM/JCCCGEEB+55LzoJUqUSLd86Xfu3EGv11OhQgUm\nTJgAwLZt2/j777/VTZu6du1KiRIlaNCgAefPnycwMJDq1atz7949oqKiyJEjB1qtlqCgICBp5n7r\n1q2YmZlx7do1ABwdHQ3W50+dBPJCCCGEEB+5mjVrsnHjRkaMGMHx48c5dOgQYNh86fnz5wfg0qVL\nrFu3jri4OP7++280Gg1lypQhICCArl274u7uzqJFi4CkXViTWVpaqp/b29vz/fffs2TJEnXTJoB2\n7dpRpEgRg/X5UyeBvBBCCCHER6579+74+PiwevVqtm3bBkCjRo0YMWKEwdpwdnamV69eLF++nM6d\nO6vlgwcPpk+fPlSrVg1fX198fX0BaNmyJe3atXttfQsWLCBv3rxs3rwZRVFo3LixuiRIpI4E8kII\nIYQQHzkjIyNWrlxJr169uH37NgUKFMDNzQ0jIyPi4+OZOnUq3t7eZMuWjU6dOvHdd9+9NT3ljRs3\nuH79Ok5OTnz11VcYGRmxePFiihQpwp49e9BoNLRp04bvv/8ejUbDxYsXWbNmDUFBQXz55Zd8++23\nak74V9FqtYwaNSrFzbPi3UggL4QQQgjxCdBoNLi6uuLq6qqWKYpChw4d2Lp1q1p29OhR/P39GT16\n9GvrGj16NFOmTFG/btCgAdu2bcPMzIxBgwYxaNCgl55jb2/PkCFDDHQ1IjUka40QQgghxCfqwoUL\nbN26FXNzc7Zu3cqCBQsAmDRpErGxscTFxbFv3z7Wr1/P9evXgaQ88VOmTEGr1VK/fn0sLS357bff\nGDt2bEZeingFmZEXQgghhEhnoaGhHDhwgLi4OKpVq0bRokU/SLtPnjwBoHLlyrRq1QpFURg3bhxh\nYWFcv36dbt26ceXKFSBpRn/mzJncv38fgOHDhzN58mQOHDhAgwYN1BtoReYhM/JCCCGEEOno8uXL\nlCxZko4dO9KjRw9KlSrFmjVr1OMPHjzgzz//5OHDh2rZ8+fPGTJkCC4uLtSsWZP169enqe3kFwxH\njx5l0qRJ9O3bl7CwMCwtLZkwYQJXrlzhs88+o0mTJgAMGjSIsLAwAB49eoSiKDx69AiA7Nmzp6kP\nIv1IIC+EEEIIkU4UReGbb74hMDCQcuXK0aRJE3Q6HT179uT+/fsMGDAAZ2dnatWqRcGCBRk2bBg6\nnY6mTZsyc+ZMfH19OXr0KJ06dWL+/Pnv3H7RokUZPnw4iYmJjB07lqVLl2JkZMSSJLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88d23c8>"
+       "<matplotlib.figure.Figure at 0x86c2ef0>"
       ]
      },
      "metadata": {},
@@ -2253,7 +2259,7 @@
     "    xs.append(kf.x[0])\n",
     "\n",
     "plt.plot(xs, label='Kalman Filter')\n",
-    "plt.plot(zs, marker='x', color='k', ls='', label='Measurements')\n",
+    "bp.plot_measurements(zs)\n",
     "plt.xlabel('time')\n",
     "plt.legend(loc=4)\n",
     "plt.ylabel('distance');"
@@ -2324,9 +2330,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAADxCAYAAACpkFPLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x886ada0>"
+       "<matplotlib.figure.Figure at 0x86c2438>"
       ]
      },
      "metadata": {},
@@ -2407,9 +2413,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAADaCAYAAAB+WC5eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86c29e8>"
+       "<matplotlib.figure.Figure at 0x9f67898>"
       ]
      },
      "metadata": {},
@@ -2443,9 +2449,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAADaCAYAAAB3s44kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a46390>"
+       "<matplotlib.figure.Figure at 0x88e2588>"
       ]
      },
      "metadata": {},
@@ -2495,9 +2501,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAADaCAYAAAB3s44kAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a98a20>"
+       "<matplotlib.figure.Figure at 0x9f8f128>"
       ]
      },
      "metadata": {},
@@ -2581,9 +2587,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6gAAAE6CAYAAAAbcH9JAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4FNXbxvHvbDot1NAMPXSQItIE6Yh0BelVwBeQIgoa\nkN6LoICgSFUEDb2ICEj70VRAqtIJSgsCIZBA+rx/LGxYKSakbELuz3XtlZyZ2ZlnmZDsvWfmHMM0\nTRMRERERERERB7M4ugARERERERERUEAVERERERGRZEIBVURERERERJIFBVQRERERERFJFhRQRURE\nREREJFlQQBUREREREZFkQQFVREREREREkgUFVBGRVMpisWCxPP7PgL+/P0WKFMFisdCvXz8eTJld\no0YN2/Me92jevHlSvgQRERF5zjg7ugAREXEcwzAeWXb48GEaNGhAQEAA48eP58MPP3xkm86dO5Mv\nX75HlhctWjQxyhQREZFUQgFVRERstm3bRrNmzQgNDWXhwoV06NDhsdt17tyZ6tWrJ3F1IiIi8rzT\nJb4iIgKAn58fr732GqZpsm7duieGUxEREZHEooAqIiLMmDGDNm3akClTJrZt20a9evWeuv2De1JF\nREREEpIu8RURSeV8fX2ZOHEiBQsW5KeffqJAgQL/+ZyFCxeybds2u2WGYfDRRx/h5uaWWKWKiIjI\nc84w9TG4iEiq9PAIvi4uLhw/fpxChQo99Tk1atRg586dj11nGAaBgYFkyJAhQesUERGR1EOX+IqI\npHKvvfYaERERtG3blsDAwFg9Z/v27URHR9s9oqKiFE5FREQkXhRQRURSMcMwWLt2Lc2aNWP//v3U\nqFGDf/75x9FliYiISCqlgCoikso5OzuzbNky2rZty9GjR6levTqXLl1ydFkiIiKSCimgiogITk5O\nfPPNN3Tr1o2TJ09SvXp1/P39HV2WiIiIpDIKqCIiAlgv950zZw79+vXj/PnzVKtWjVOnTjm6LBER\nEUlFFFBFRMTOtGnT8PX15dKlS7z66qscO3bM0SWJiIhIKqGAKiIijxg7dixjx44lICCAmjVrcvDg\nQcDay2oYhoOrExERkeeV5kEVERERERGRZEE9qCIiIiIiIpIsKKCKiIiIiIhIsqCAKiIiIiIiIsmC\ns6MLSAhBQUGOLkFERERE5Jl5eno6ugSRZEE9qCIiIiIiIpIsKKCKiIiIiIhIsvBcXOL7sIS+PGL/\n/v0AvPTSSwm6X0l8Oncpl85dyqVzl3Lp3KVcOncpl25TE3mUelBFREREREQkWVBAFRERERERkWRB\nAVVERERERESSBQVUERERERERSRYUUEVERERERCRZUEAVERERERGRZEEBVURERERStLCwMHx9fSlf\nvjyVKlVi5syZmKbp6LJE5Bk8d/OgioiIiEjqYZomrVq1Ys2aNbZlv/zyCwEBAYwePdqBlYnIs1AP\nqoiIiIikWAcPHmTNmjWkS5eO9evXM3fuXAAmTJjA3bt3HVydiMSVAqqIiIiIpFiXL18GoEKFCjRs\n2JCuXbuSJUsWIiMjuX79uoOrE5G40iW+IiIiIpJiFStWDIAdO3YwZMgQrly5wo0bN8iYMSM5c+Z0\ncHUiElcKqCIiIiKSYhUqVIgRI0YwYsQIxo0bB4CTkxNz5szBxcUlVvuIijIJvAM3guDGbbh+69Gv\nMweAu5uRmC9FRFBAFREREZEUbvjw4ZQrV45NmzZhcXLjtcZtyVugLDsPmdwIgutB2L7efOj7B18D\n78B/Dfo74m14wStpXo9IaqaAKiIiIiIpniVLI7Zcb8TJv2DGbwm//xtBCqgiSUEBVURERERSrPAI\nE98vYNp38duPZzrI6glZPGO+ZnmonTNrwtQrIk+ngCoiIiIiKdK5SyZthsNvf8YsMwzInAGyZICs\nGa1f/x027b5mhMzpwdlZ95eKJAcKqCIiIiKS4ny/xeSdSXA7JGZZwyqwYAhkzZgwYXPixIlUqFCB\nWrVqJcj+ROS/aR5UEREREUkx7oaa9Jho7Tl9EE5dnGFKH1g7Kf7h9N69e7bvc+bMydixY+O1PxGJ\nGwVUEREREUkR/jhvUrEbzF0bs6xALtj1BQxobWAY8Qunu3fvpkaNGpj3h/Rt06YNM2bMiNc+RSRu\nFFBFREREJFkzTZN560wqvA3Hz8csb1UbDiyACsWeLZiapsnWrVuJjo4GoHLlykRGRnLmzBkAXFxc\nKF68eLzrF5HYU0AVERERkWTrdohJ+5HQfQLcC7Muc3eFLz+EJSPBM138ek0HDhzIunXrALBYLPz6\n66/4+PjEt2wReUYaJElEREREkqUDJ6z3mp65GLOseD74bjSULPBswXTDhg1ERUXRuHFjDMNg9OjR\nBAUF2dY7OTnFs2oRiQ8FVBERERFJVkzTZPoyGPQ5RETGLO/aCKa/B2nc4xZOTdO03Z9qsVgYNGgQ\nDRs2xGKx8Prrrydk6SISTwqoIiIiIpJs3AgyeXscrN0Vsyx9GvhiELSpG/de08uXL9O0aVP27t2L\ns7Mz9evXJyIiIgErFpGEpHtQRURERCTJHDp0iEWLFrFhwwbCw8Pt1u06bFK2s304LV/EOhBSXMLp\nxYsXCQ0NBSBXrlx4eHiwefNmAAzDoHHjxlgssXsb/Ouvv9KnTx+6devGkiVLbCP8ikjiUA+qiIiI\niCSJ4cOHM2rUKFu7fPnybNq0CU/PTExYDCPmQVRUzPb93oIJPcHNNW49p7169aJRo0b06NEDgPXr\n15MhQ4Y417t69WpatGhB1P2i5s2bxy+//MJnn30W532JSOyoB1VEREREEt3mzZsZNWoUTk5ONG/e\nnFy5cnHgwAF69B7GawNg6JyYcJo5A6yeANP6GbEKp8eOHWPlypW29qBBg2xTxQDPFE5N0+Sdd94h\nKiqKLl26MHbsWFxdXZk+fTq///57nPcnIrGjgCoiIiIiiW7nzp0AvPvuu6xcudI6tUvGeqw+P4yf\n98ds90pp+H0hNKn29GD68KW2kZGR9OnTx3bJ8CuvvMKkSZPiVe/Nmze5du0a7u7uzJs3j8GDB1O/\nfn0ATp48Ga99i8iTJZuAOn78eCwWC3369LFbPmLECHLnzk2aNGmoWbMmf/zxh4MqFBEREZFnlTZt\nWgBOnDhByN1whs51xii+kWinbAAYBgzpBFtngHf2p4fTe/fuUb58eYKDgwEoU6YMY8aMSdDBjzJm\nzEjatGkJDQ1l6tSprF271hayc+fOnWDHERF7ySKg7tu3j6+++orSpUvbhgAHmDhxIlOnTmXmzJn8\n9ttveHl5UbduXdsvIxERERFJGd566y3Sp0/PT9tPk77Sfn48XMq2LkcW2PQpjO5h4Oz8+HDq7+/P\nzZs3AfDw8KBAgQL4+fnZ1nfp0sUWghOCk5MTo0ePBuCDDz6gadOmBAUF0aBBA6pWrZpgxxERew4P\nqEFBQbRv354FCxaQKVMm23LTNPn000/x9fWlefPmlChRgkWLFnHnzh2WLFniwIpFREREJK5y5s5P\nywHHsJQ7Dukr25bXfdl6SW/tl57eazpu3Dhmzpxpa8+dO5fOnTsnUrVW/fv35+uvv6ZmzZpUqlQJ\nX19fVq5cGesRgEUk7hz+v6tHjx60bNmSV1991e5egvPnzxMQEEC9evVsy9zd3alevTp79uxxRKki\nIiIi8gx+2GNSqj0s2OyNabgB4ORkMr4n/PgJZM/8aDg9cuQIs2bNsrXfe+89AgMDbe2MGTMmelA0\nDIMOHTqwdetW9u7dy7hx43B3d0/UY4qkdg4NqF999RXnzp1jzJgxAHaX9169ehWA7Nmz2z3Hy8vL\ntk5EREQkNbt8+TLffPMNs2fPZsOGDY4u5xHnL5s0+9Ck8UA4dzlm+UtFYe+XBh+2N7BYYt7/RUZG\n2r7PnDkzH3/8Mbdu3QKgWLFiTJs2LclqFxHHcNg8qCdPnmTIkCHs2rULJycnwHpZb2wmP344yP7b\n/v37n7guPhJrv5L4dO5SLp27lEvnLuXSuUs5Tp8+Tc+ePQkKCgJg/vz5tGnThgEDBji4MgiLMFi8\nNTsLN+ckLCKmPyRDmkh6NbpE08rXIQQe/nGLjIykRYsWzJ07l6xZswLWwTKPHTv23PZa+vj4OLoE\nkWTHYT2oe/fu5fr165QoUQIXFxdcXFzYuXMns2bNwtXV1faLKSAgwO55AQEB5MiRwxEli4iIiCQb\nY8eOJSgoiDJlytC2bVtcXV1ZunQpBw4ccGhde/7IQJsJxflyQ267cNq08j8sH3KMN6pex+n+4jNn\nztiujHN2dqZKlSps27bN9pwqVao8t+FURB7PYT2ozZs35+WXX7a1TdOkS5cuFC5cmMGDB+Pj40OO\nHDnYtGkT5cuXByA0NJRdu3YxZcqUJ+73pZdeStA6H3ySnND7lcSnc5dy6dylXDp3KZfOXcpz6tQp\nAKZMmYKnpydubm4sWLCA0NBQh5xH/ysmA6bD6p32y8sVgZkDoFJJL8DLbt3q1asJDAzk888/B2Dx\n4sW4uromUcWO96D3W0RiOKwH1dPTk+LFi9seJUqUIE2aNGTKlInixYtjGAb9+/dn4sSJrFq1imPH\njtG5c2fSp09P27ZtHVW2iIiISLKQLZt1/tAff/yRM2fOsGvXLgDbVWhJJSzcZOwikxLt7MNpxvTw\n+Qfwy1dQqaT19qzDhw8zaNAg2zbvvvsunp6etnZqCqci8ngO60F9HMMw7O4vHTRoEPfu3aN3794E\nBgZSqVIlNm3alKBzXImIiIikRIMGDaJ///588skntmVFihShadOmSVbDT7+Y9J0Gp/+2X96lEUz4\nP8iWyeDvv//G29sbgPz58zN37lz69u3LCy+8QI4cORg3blyS1SsiyV+yCqgP33PwwLine truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b4f940>"
+       "<matplotlib.figure.Figure at 0x9af0da0>"
       ]
      },
      "metadata": {},
@@ -2591,9 +2597,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b4f048>"
+       "<matplotlib.figure.Figure at 0x9f8f160>"
       ]
      },
      "metadata": {},
@@ -2601,9 +2607,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6gAAAD+CAYAAAA3fihfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b165f8>"
+       "<matplotlib.figure.Figure at 0x99e5e80>"
       ]
      },
      "metadata": {},
@@ -2660,9 +2666,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6gAAAE6CAYAAAAbcH9JAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9c7a7b8>"
+       "<matplotlib.figure.Figure at 0x9a5c3c8>"
       ]
      },
      "metadata": {},
@@ -2670,9 +2676,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x879fc18>"
+       "<matplotlib.figure.Figure at 0x9a5c438>"
       ]
      },
      "metadata": {},
@@ -2680,9 +2686,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b01470>"
+       "<matplotlib.figure.Figure at 0x9acfc18>"
       ]
      },
      "metadata": {},
@@ -2789,9 +2795,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a886a0>"
+       "<matplotlib.figure.Figure at 0x872b8d0>"
       ]
      },
      "metadata": {},
@@ -2960,9 +2966,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAADxCAYAAACpkFPLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8705b70>"
+       "<matplotlib.figure.Figure at 0x87226d8>"
       ]
      },
      "metadata": {},
@@ -3150,9 +3156,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAAERCAYAAAAgxPKmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAucAAADaCAYAAAAFfOySAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9af6550>"
+       "<matplotlib.figure.Figure at 0x87cd160>"
       ]
      },
      "metadata": {},
@@ -3457,9 +3463,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAAEWCAYAAAAw37JZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAADaCAYAAADwgmciAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87ae320>"
+       "<matplotlib.figure.Figure at 0x88d1550>"
       ]
      },
      "metadata": {},
@@ -3578,9 +3584,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAADaCAYAAAAIYpzVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8718128>"
+       "<matplotlib.figure.Figure at 0x9a4a6a0>"
       ]
      },
      "metadata": {},
@@ -3727,9 +3733,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAADaCAYAAAAIYpzVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8723eb8>"
+       "<matplotlib.figure.Figure at 0x9a5ecf8>"
       ]
      },
      "metadata": {},
@@ -3797,9 +3803,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9918908>"
+       "<matplotlib.figure.Figure at 0x8752358>"
       ]
      },
      "metadata": {},
@@ -3807,9 +3813,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAADaCAYAAAAIYpzVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a10b70>"
+       "<matplotlib.figure.Figure at 0x9f830b8>"
       ]
      },
      "metadata": {},
@@ -3871,9 +3877,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9be49e8>"
+       "<matplotlib.figure.Figure at 0x881d668>"
       ]
      },
      "metadata": {},
@@ -3881,9 +3887,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAADaCAYAAADwgmciAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b014a8>"
+       "<matplotlib.figure.Figure at 0x9a2be10>"
       ]
      },
      "metadata": {},

10-Unscented-Kalman-Filter.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -292,9 +298,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7990320>"
+       "<matplotlib.figure.Figure at 0x721fb00>"
       ]
      },
      "metadata": {},
@@ -322,9 +328,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "I generated this by taking 500,000 samples from the input, passing it through the nonlinear transform, and building a histogram of the result. We call these points **sigma points**. From the output histogram we can compute a mean and standard deviation which would give us an updated, albeit approximated Gaussian.\n",
+    "I generated this by taking 500,000 samples from the input, passing it through the nonlinear transform, and building a histogram of the result. We call these points *sigma points*. From the output histogram we can compute a mean and standard deviation which would give us an updated, albeit approximated Gaussian.\n",
     "\n",
-    "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a **Monte Carlo** approach, and it used by some Kalman filter designs, such as the **Ensemble filter** and **particle filter**. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the function is, as long as we sample with enough sigma points we will build an accurate output distribution.\n",
+    "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a *Monte Carlo* approach, and it used by some Kalman filter designs, such as the Ensemble filter and particle filter. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the function is, as long as we sample with enough sigma points we will build an accurate output distribution.\n",
     "\n",
     "\"Enough points\" is the rub. The graph above was created with 500,000 sigma points, and the output is still not smooth. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you only needed 500 points for 1 dimension, you'd need 500 squared, or 250,000 points for two dimensions, 500 cubed, or 125,000,000 points for three dimensions, and so on. So while this approach does work, it is very computationally expensive. Ensemble filters and particle filters use very clever techniques to significantly reduce this dimensionality, but the computational burdens are still very large. The Unscented Kalman filter uses sigma points but drastically reduces the amount of computation by using a deterministic method to choose the points."
    ]
@@ -353,9 +359,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x71f3518>"
+       "<matplotlib.figure.Figure at 0x7205f98>"
       ]
      },
      "metadata": {},
@@ -364,7 +370,9 @@
    ],
    "source": [
     "import ukf_internal\n",
-    "ukf_internal.show_2d_transform()"
+    "\n",
+    "with figsize(y=4.3):\n",
+    "    ukf_internal.show_2d_transform()"
    ]
   },
   {
@@ -401,14 +409,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Difference in mean x=0.062, y=45.093\n"
+      "Difference in mean x=0.052, y=42.864\n"
      ]
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x90fd7b8>"
+       "<matplotlib.figure.Figure at 0x4817710>"
       ]
      },
      "metadata": {},
@@ -461,9 +469,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x83b9908>"
+       "<matplotlib.figure.Figure at 0x81f9e10>"
       ]
      },
      "metadata": {},
@@ -499,9 +507,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8742a90>"
+       "<matplotlib.figure.Figure at 0x915b6a0>"
       ]
      },
      "metadata": {},
@@ -544,9 +552,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87e8f28>"
+       "<matplotlib.figure.Figure at 0x87cde80>"
       ]
      },
      "metadata": {},
@@ -579,7 +587,7 @@
    "source": [
     "For the moment assume an algorithm exists for selecting the sigma points and weights. How are the sigma points used to implement a filter?\n",
     "\n",
-    "The **unscented transform** is the core of the algorithm yet it is remarkably simple. For each dimension in the state space we deterministically choose 3 sigma points and corresponding weights. We pass the sigma points through a (usually nonlinear) function yielding a transformed set of points.\n",
+    "The *unscented transform* is the core of the algorithm yet it is remarkably simple. For each dimension in the state space we deterministically choose 3 sigma points and corresponding weights. We pass the sigma points through a (usually nonlinear) function yielding a transformed set of points.\n",
     "\n",
     "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n",
     "\n",
@@ -595,9 +603,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8716dd8>"
+       "<matplotlib.figure.Figure at 0x87f3940>"
       ]
      },
      "metadata": {},
@@ -644,9 +652,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x897d748>"
+       "<matplotlib.figure.Figure at 0x89326a0>"
       ]
      },
      "metadata": {},
@@ -860,9 +868,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x890b6a0>"
+       "<matplotlib.figure.Figure at 0x90e9a58>"
       ]
      },
      "metadata": {},
@@ -983,9 +991,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x838bb38>"
+       "<matplotlib.figure.Figure at 0x915b828>"
       ]
      },
      "metadata": {},
@@ -1108,9 +1116,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x83309b0>"
+       "<matplotlib.figure.Figure at 0x8990e80>"
       ]
      },
      "metadata": {},
@@ -1163,7 +1171,7 @@
    "source": [
     "Let's tackle our first nonlinear problem. To minimize the number of things that change I will keep the problem formulation very similar to the linear tracking problem above. For this problem we will write a filter to track a flying airplane using a stationary radar as the sensor. To keep the problem as close to the previous one as possible we will track in two dimensions, not three. We will track one dimension on the ground and the altitude of the aircraft. The second dimension on the ground adds no difficulty or different information, so we can do this with no loss of generality.\n",
     "\n",
-    " Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the **slant distance** - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. True integration of sensors for applications like military radar and aircraft navigation systems have to take many factors into account which I am not currently interested in trying to cover in this book. So if any practitioners in the the field are reading this they will be rightfully scoffing at my exposition. My only defense is to argue that I am not trying to teach you how to design a military grade radar tracking system, but instead trying to familiarize you with the implementation of the UKF. \n",
+    " Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. True integration of sensors for applications like military radar and aircraft navigation systems have to take many factors into account which I am not currently interested in trying to cover in this book. So if any practitioners in the the field are reading this they will be rightfully scoffing at my exposition. My only defense is to argue that I am not trying to teach you how to design a military grade radar tracking system, but instead trying to familiarize you with the implementation of the UKF. \n",
     " \n",
     "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
    ]
@@ -1178,9 +1186,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8728320>"
+       "<matplotlib.figure.Figure at 0x87c61d0>"
       ]
      },
      "metadata": {},
@@ -1356,9 +1364,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x897d6a0>"
+       "<matplotlib.figure.Figure at 0x89325f8>"
       ]
      },
      "metadata": {},
@@ -1366,9 +1374,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8a11588>"
+       "<matplotlib.figure.Figure at 0x895e240>"
       ]
      },
      "metadata": {},
@@ -1376,9 +1384,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8a07a58>"
+       "<matplotlib.figure.Figure at 0x89dc5f8>"
       ]
      },
      "metadata": {},
@@ -1455,9 +1463,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89880b8>"
+       "<matplotlib.figure.Figure at 0x8f89630>"
       ]
      },
      "metadata": {},
@@ -1555,9 +1563,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89881d0>"
+       "<matplotlib.figure.Figure at 0x8f89940>"
       ]
      },
      "metadata": {},
@@ -1626,9 +1634,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8aa5710>"
+       "<matplotlib.figure.Figure at 0x8762cc0>"
       ]
      },
      "metadata": {},
@@ -1675,9 +1683,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8aa5240>"
+       "<matplotlib.figure.Figure at 0x8a53d68>"
       ]
      },
      "metadata": {},
@@ -1733,7 +1741,7 @@
    "source": [
     "By incorporating the velocity sensor we were able to reduce the standard deviation from 3.5 m/s to 1.3 m/s. \n",
     "\n",
-    "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to something called the **Complementary filter**, which uses the high update rate of the inertial sensor with the position accurate but slow estimates of the GPS to produce very high rate yet very accurate position and velocity estimates."
+    "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to something called the *Complementary filter*, which uses the high update rate of the inertial sensor with the position accurate but slow estimates of the GPS to produce very high rate yet very accurate position and velocity estimates."
    ]
   },
   {
@@ -1769,9 +1777,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87974a8>"
+       "<matplotlib.figure.Figure at 0x879cf98>"
       ]
      },
      "metadata": {},
@@ -1813,9 +1821,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87961d0>"
+       "<matplotlib.figure.Figure at 0x8a537f0>"
       ]
      },
      "metadata": {},
@@ -1912,9 +1920,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8378d30>"
+       "<matplotlib.figure.Figure at 0x7b54a58>"
       ]
      },
      "metadata": {},
@@ -1960,9 +1968,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x881eb70>"
+       "<matplotlib.figure.Figure at 0x823ec50>"
       ]
      },
      "metadata": {},
@@ -2013,9 +2021,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8868518>"
+       "<matplotlib.figure.Figure at 0x888aa58>"
       ]
      },
      "metadata": {},
@@ -2052,9 +2060,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87a1780>"
+       "<matplotlib.figure.Figure at 0x88d3518>"
       ]
      },
      "metadata": {},
@@ -2084,9 +2092,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8a3d710>"
+       "<matplotlib.figure.Figure at 0x89878d0>"
       ]
      },
      "metadata": {},
@@ -2207,7 +2215,7 @@
     "\\Sigma = SS^\\mathsf{T} \\\\\n",
     "$$\n",
     "\n",
-    "This method is frequently chosen in computational linear algebra because this expression is easy to compute using something called the **Cholesky decomposition** [3]. \n",
+    "This method is frequently chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition* [3]. \n",
     "SciPy provides this with the `scipy.linalg.cholesky()` method. If your language of choice is Fortran, C, or C++, libraries such as LAPACK provide this routine. Matlab provides `chol()`.\n",
     "\n",
     "```python\n",
@@ -2451,9 +2459,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8aa5d30>"
+       "<matplotlib.figure.Figure at 0x8a53470>"
       ]
      },
      "metadata": {},
@@ -2461,9 +2469,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9001c50>"
+       "<matplotlib.figure.Figure at 0x8aa0f28>"
       ]
      },
      "metadata": {},
@@ -2471,9 +2479,9 @@
     },
     {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9012e80>"
+       "<matplotlib.figure.Figure at 0x8ab4828>"
       ]
      },
      "metadata": {},
@@ -2558,9 +2566,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8fc5198>"
+       "<matplotlib.figure.Figure at 0x8a7ff28>"
       ]
      },
      "metadata": {},
@@ -2568,9 +2576,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89cccc0>"
+       "<matplotlib.figure.Figure at 0x898c9b0>"
       ]
      },
      "metadata": {},
@@ -2578,9 +2586,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89a8a58>"
+       "<matplotlib.figure.Figure at 0x8a0fa20>"
       ]
      },
      "metadata": {},
@@ -2838,9 +2846,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x89b7b70>"
+       "<matplotlib.figure.Figure at 0x8a70978>"
       ]
      },
      "metadata": {},
@@ -2855,7 +2863,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler **bicycle model** has been found to perform well. \n",
+    "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. \n",
     "\n",
     "I have depicted this model above. Here we see the front tire is pointing in direction $\\alpha$ relative to the wheelbase. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. We can compute the turn angle $\\beta$ with\n",
     "\n",
@@ -3268,9 +3276,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8f9c0b8>"
+       "<matplotlib.figure.Figure at 0x8912518>"
       ]
      },
      "metadata": {},
@@ -3358,9 +3366,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87aff98>"
+       "<matplotlib.figure.Figure at 0x87f4940>"
       ]
      },
      "metadata": {},
@@ -3398,9 +3406,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAADnCAYAAADcgNqjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87de080>"
+       "<matplotlib.figure.Figure at 0x8a005c0>"
       ]
      },
      "metadata": {},

11-Extended-Kalman-Filters.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -303,9 +309,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7200160>"
+       "<matplotlib.figure.Figure at 0x720fbe0>"
       ]
      },
      "metadata": {},
@@ -351,9 +357,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74fc978>"
+       "<matplotlib.figure.Figure at 0x720f978>"
       ]
      },
      "metadata": {},
@@ -429,9 +435,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAr8AAADVCAYAAABe6Zj7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x4b0a6d8>"
+       "<matplotlib.figure.Figure at 0x8664550>"
       ]
      },
      "metadata": {},
@@ -603,21 +609,21 @@
     "Solving each in turn:\n",
     "\n",
     "$$\\begin{aligned}\n",
-    "\\frac{\\partial h}{\\partial x_{pos}} &= \\\\ &=\\frac{\\partial}{\\partial x_{pos}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{pos}}{\\sqrt{x^2 + x_{alt}^2}}\n",
+    "\\frac{\\partial h}{\\partial x_{pos}} &=\\frac{\\partial}{\\partial x_{pos}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{pos}}{\\sqrt{x^2 + x_{alt}^2}}\n",
     "\\end{aligned}$$\n",
     "\n",
     "and\n",
     "\n",
     "$$\\begin{aligned}\n",
-    "\\frac{\\partial h}{\\partial x_{vel}} &=\\\\\n",
-    "&= \\frac{\\partial}{\\partial x_{vel}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ \n",
+    "\\frac{\\partial h}{\\partial x_{vel}} &=\n",
+    "\\frac{\\partial}{\\partial x_{vel}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ \n",
     "&= 0\n",
     "\\end{aligned}$$\n",
     "\n",
     "and\n",
     "\n",
     "$$\\begin{aligned}\n",
-    "\\frac{\\partial h}{\\partial x_{alt}} &=\\\\ &= \\frac{\\partial}{\\partial x_{alt}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
+    "\\frac{\\partial h}{\\partial x_{alt}} &= \\frac{\\partial}{\\partial x_{alt}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
     "\\end{aligned}$$\n",
     "\n",
     "giving us \n",
@@ -775,9 +781,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x873a1d0>"
+       "<matplotlib.figure.Figure at 0x75acd68>"
       ]
      },
      "metadata": {},
@@ -785,9 +791,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e7cd68>"
+       "<matplotlib.figure.Figure at 0x7246710>"
       ]
      },
      "metadata": {},
@@ -795,9 +801,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87c3588>"
+       "<matplotlib.figure.Figure at 0x87d2278>"
       ]
      },
      "metadata": {},
@@ -1015,9 +1021,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7e69710>"
+       "<matplotlib.figure.Figure at 0x75a22b0>"
       ]
      },
      "metadata": {},
@@ -1634,9 +1640,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa5e51d0>"
+       "<matplotlib.figure.Figure at 0xa6064e0>"
       ]
      },
      "metadata": {},
@@ -1646,7 +1652,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.024  0.043  0.002]\n"
+      "[ 0.024  0.042  0.002]\n"
      ]
     }
    ],
@@ -1669,9 +1675,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa5e5a58>"
+       "<matplotlib.figure.Figure at 0xa606438>"
       ]
      },
      "metadata": {},
@@ -1681,7 +1687,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.02   0.02   0.002]\n"
+      "[ 0.02   0.021  0.002]\n"
      ]
     }
    ],
@@ -1715,9 +1721,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa5e5f28>"
+       "<matplotlib.figure.Figure at 0xa606048>"
       ]
      },
      "metadata": {},
@@ -1727,7 +1733,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.02   0.045  0.   ]\n"
+      "[ 0.019  0.046  0.   ]\n"
      ]
     }
    ],
@@ -1755,9 +1761,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa5e5860>"
+       "<matplotlib.figure.Figure at 0xa5dc0f0>"
       ]
      },
      "metadata": {},
@@ -1767,7 +1773,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.305  0.753  0.004]\n"
+      "[ 0.283  0.753  0.004]\n"
      ]
     }
    ],
@@ -1795,9 +1801,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa9adb70>"
+       "<matplotlib.figure.Figure at 0xa55f438>"
       ]
      },
      "metadata": {},
@@ -1807,7 +1813,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.009  0.008  0.001]\n"
+      "[ 0.009  0.009  0.001]\n"
      ]
     }
    ],
@@ -1858,9 +1864,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa9ad320>"
+       "<matplotlib.figure.Figure at 0x87d2208>"
       ]
      },
      "metadata": {},
@@ -1898,9 +1904,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa869c50>"
+       "<matplotlib.figure.Figure at 0xab2dac8>"
       ]
      },
      "metadata": {},
@@ -1910,7 +1916,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "actual mean=1.31, std=1.14\n",
+      "actual mean=1.30, std=1.13\n",
       "UKF    mean=1.30, std=1.08\n"
      ]
     }

12-Particle-Filters.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -320,9 +326,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAADaCAYAAADwgmciAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x79722b0>"
+       "<matplotlib.figure.Figure at 0x4707b38>"
       ]
      },
      "metadata": {},
@@ -350,13 +356,12 @@
     "\n",
     "I then showed how poorly the EKF did at estimating the new mean and covariance compared to the UKF.\n",
     "\n",
-    "This technique of using a finite number of randomly sampled to compute a result is called a **Monte Carlo** (MC) method. The idea is simple. Generate *enough* points to get a representative sample of the problem, run the points through the system you are modeling, and then compute the results on the transformed points. \n",
-    "\n",
+    "This technique of using a finite number of randomly sampled to compute a result is called a *Monte Carlo* (MC) method. The idea is simple. Generate enough points to get a representative sample of the problem, run the points through the system you are modeling, and then compute the results on the transformed points. \n",
     "\n",
     "In a nutshell this is what particle filtering is. A bit later I'll demonstrate how MC can integrate over a probability distribution, but you don't need that formality to understand how they work. It's very simple. It is the Bayesian filter algorithm we have been using throughout the book applied to thousands of particles, where each particle represents a *possible* state for the system. We extract the estimated state from the thousands of particles using weighted statistics of the particles.\n",
     "\n",
     "\n",
-    "** Generic Particle Filter Algorithm**\n",
+    "**Generic Particle Filter Algorithm**\n",
     "\n",
     "1. **Randomly generate a bunch of particles**\n",
     "    \n",
@@ -394,9 +399,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d6cf98>"
+       "<matplotlib.figure.Figure at 0x82a6e80>"
       ]
      },
      "metadata": {},
@@ -413,7 +418,7 @@
    "source": [
     "After the first iteration the particles are still largely randomly scattered around the map, but you can see that some have already collected near the robot's position. The computed mean is quite close to the robot's position. This is because each particle is weighted based on how closely it matches the measurement. The measurement (with noise) says the robot is near (1,1), so particles that are near (1, 1) will have a high weight, and particles at, say, (15, 19.5) will have a very low weight. The estimated  is computed as the weighted mean of all of the particle's positions, so the estimate is quite accurate. This is partially the result of the random number generation - other runs could produce a poor estimate if no particles were particularly near the robot.\n",
     "\n",
-    "Several iterations later you can see that all the particles have clustered around the robot. This is due to the **resampling** step. Resampling discards particles that are very improbable (very low weight) and replaces them with particles with higher probability. There are multiple algorithms for this, and we will discuss them later. \n",
+    "Several iterations later you can see that all the particles have clustered around the robot. This is due to the *resampling* step. Resampling discards particles that are very improbable (very low weight) and replaces them with particles with higher probability. There are multiple algorithms for this, and we will discuss them later. \n",
     "\n",
     "I haven't fully shown *why* this works nor fully explained the algorithms for particle weighting and resampling, but it should make intuitive sense. Make a bunch of random particles,  move them so they 'kind of' follow the robot, weight them according to how well they match the measurements, only let the likely ones live, and continue. It seems like it should work, and it does. "
    ]
@@ -423,9 +428,9 @@
    "metadata": {},
    "source": [
     "## Probability distributions via MC\n",
-    "Suppose we want to know the area under the curve $y= \\mathrm{e}^{\\sin(x)}$ in the interval [0, $\\pi$]. We can compute the area with the definite integral $\\int_0^\\pi  \\mathrm{e}^{\\sin(x)}\\, \\mathrm{d}x$. As an exercise, go ahead and compute the answer; I'll wait. If you are wise you did not take that challenge; $y=  \\mathrm{e}^{\\sin(x)}$ cannot be integrated and so you can not find the answer this way. \n",
+    "Suppose we want to know the area under the curve $y= \\mathrm{e}^{\\sin(x)}$ in the interval [0, $\\pi$]. We can compute the area with the definite integral $\\int_0^\\pi  \\mathrm{e}^{\\sin(x)}\\, \\mathrm{d}x$. As an exercise, go ahead and compute the answer; I'll wait. If you are wise you did not take that challenge; $y=  \\mathrm{e}^{\\sin(x)}$ cannot be integrated analytically.\n",
     "\n",
-    "The world is filled with equations which we cannot integrate. We cannot integrate something as simple as $\\int_a^b  x^x\\, \\mathrm{d}x$. For a realistic example from physics, think of how we calculate luminosity of an object. An object reflects light. Some of that light bounces off of other objects and *restrikes* the original object, increasing the luminosity. This creates a **recursive integral**. Good luck with that one.\n",
+    "The world is filled with equations which we cannot integrate. We cannot integrate something as simple as $\\int_a^b  x^x\\, \\mathrm{d}x$. For a realistic example from physics, think of how we calculate luminosity of an object. An object reflects light. Some of that light bounces off of other objects and restrikes the original object, increasing the luminosity. This creates a *recursive integral*. Good luck with that one.\n",
     "\n",
     "However, these are trivial to compute using a Monte Carlo technique. Create a bounding box that contains the curve in the desired interval, generate random pairs $(x,y)$, and count how many fall under the curve. Multiply the area of the bounding box by the ratio of points that were under the curve vs the total number of points and you will have computed the are under the curve. As you tend towards infinite points you can achieve any arbitrary precision. In practice, a few thousand points will give you a fairly accurate result.\n",
     "\n",
@@ -472,9 +477,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x82e1a20>"
+       "<matplotlib.figure.Figure at 0x878b828>"
       ]
      },
      "metadata": {},
@@ -528,7 +533,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.axes._subplots.AxesSubplot at 0x8395908>"
+       "<matplotlib.axes._subplots.AxesSubplot at 0x82837f0>"
       ]
      },
      "execution_count": 5,
@@ -537,9 +542,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7db4518>"
+       "<matplotlib.figure.Figure at 0x7eb4780>"
       ]
      },
      "metadata": {},
@@ -571,9 +576,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8331908>"
+       "<matplotlib.figure.Figure at 0x879c860>"
       ]
      },
      "metadata": {},
@@ -601,7 +606,7 @@
     "\n",
     "Before I continue let me point out that the filter I am going to develop next is a specific form of particle filter that is intuitive to grasp and relates to the problems we have studied in this book. In other words, particle filters are a family of algorithms. A more academic approach would give you a better grasp of this family and the interrelationships between the algorithms, but as in previous chapters I choose to develop concepts based on examples and basic reasoning, and only once that is done go back and develop the theory. This will leave a few of the steps seeming a bit 'magical' since I haven't offered full explanation for their use. Full explanations will follow later in the chapter.\n",
     "\n",
-    "Taking insight from the discussion in the previous section we start by creating several thousand **particles**. Each particle has a position that represents a possible belief of where the robot is in the scene, and perhaps a heading and velocity. Suppose that when we initialize the filter we have no knowledge of the location of the robot. We would want to scatter the particles uniformly over the entire scene. If there was a large clump of particles near a specific location that would imply that we were more certain that the robot is there. If you think of all of the particles representing a probability distribution, locations where there are more particles represent a higher belief, and locations with fewer particles represents a lower belief.\n",
+    "Taking insight from the discussion in the previous section we start by creating several thousand *particles*. Each particle has a position that represents a possible belief of where the robot is in the scene, and perhaps a heading and velocity. Suppose that when we initialize the filter we have no knowledge of the location of the robot. We would want to scatter the particles uniformly over the entire scene. If there was a large clump of particles near a specific location that would imply that we were more certain that the robot is there. If you think of all of the particles representing a probability distribution, locations where there are more particles represent a higher belief, and locations with fewer particles represents a lower belief.\n",
     "\n",
     "Think back to the *Discrete Bayes* chapter. In that chapter we modeled positions in a hallway as discrete and uniformly spaced. This is very similar except the particles are randomly distributed.\n",
     "\n",
@@ -681,7 +686,7 @@
     "\n",
     "Next we get a set of measurements - one for each landmark currently in view. How should these measurements be used to alter our probability distribution as modeled by the particles?\n",
     "\n",
-    "Think back to the *Discrete Bayes* chapter. In that chapter we modeled positions in a hallway as discrete and uniformly spaced. We assigned a probability to each position. When a new measurement came in we multiplied the current probability of that position by the probability that the measurement matched that location. We implemented that like this:\n",
+    "Think back to the **Discrete Bayes** chapter. In that chapter we modeled positions in a hallway as discrete and uniformly spaced. We assigned a probability to each position. When a new measurement came in we multiplied the current probability of that position by the probability that the measurement matched that location. We implemented that like this:\n",
     "\n",
     "```python\n",
     "def update(map_, belief, z, prob_correct):\n",
@@ -704,7 +709,7 @@
     "    self.weights /= sum(self.weights) # normalize\n",
     "```\n",
     "\n",
-    "In the literature this part of the algorithm is called **Sequential Importance Sampling**, or SIS, and the equation for the weights is called the **importance density**. I will give it theoretical underpinnings in a following section. For now I hope that this makes intuitive sense. If we weight the particles according to how how they match the measurements they *probably* are a good sample for the probability distribution of the system after incorporating the measurements. Theory changes 'probably are a good sample' to 'are a good sample'. Different problems will need to tackle this step in slightly different ways.\n",
+    "In the literature this part of the algorithm is called *Sequential Importance Sampling*, or SIS, and the equation for the weights is called the *importance density*. I will give it theoretical underpinnings in a following section. For now I hope that this makes intuitive sense. If we weight the particles according to how how they match the measurements they probably are a good sample for the probability distribution of the system after incorporating the measurements. Theory changes 'probably are a good sample' to 'are a good sample'. Different problems will need to tackle this step in slightly different ways.\n",
     "\n",
     "** AUTHORS NOTE: NO. WE ARE SAMPLING FROM EVOLUTION USING IS TO GET POSTERIOR**\n",
     "\n",
@@ -736,11 +741,11 @@
    "source": [
     "### Particle Resampling\n",
     "\n",
-    "I mentioned problems that the SIS algorithm has. One is called the **degeneracy problem**. We initialize a large area with uniformly distributed particles. The number of particles near the robot are likely to be low. As we perform the algorithm above any particle modestly far from the robot will quickly acquire an extremely low weight, and only one or two particles near the robot with has an appreciable weight. The filter requires hundreds to thousands of particles to adequately sample the probability distribution.  Only one or two near the robot are not enough.\n",
+    "I mentioned problems that the SIS algorithm has. One is called the *degeneracy problem*. We initialize a large area with uniformly distributed particles. The number of particles near the robot are likely to be low. As we perform the algorithm above any particle modestly far from the robot will quickly acquire an extremely low weight, and only one or two particles near the robot with has an appreciable weight. The filter requires hundreds to thousands of particles to adequately sample the probability distribution.  Only one or two near the robot are not enough.\n",
     "\n",
-    "This problem is solved by some form of **resampling** of the particles. If most of the particles have a very small weight this means that most particles are not a very good representation of the probability distribution of the robot. The simplest resampling algorithm endevours to discard particles with very low probability (low weights) and replaces them with particles with higher probability. These particles are taken from the current particle set. This means that some of our particles will be duplicated, but this is not a problem because during the predict step we will be adding random noise to each, so they will separate from their twins. \n",
+    "This problem is solved by some form of *resampling* of the particles. If most of the particles have a very small weight this means that most particles are not a very good representation of the probability distribution of the robot. The simplest resampling algorithm endevours to discard particles with very low probability (low weights) and replaces them with particles with higher probability. These particles are taken from the current particle set. This means that some of our particles will be duplicated, but this is not a problem because during the predict step we will be adding random noise to each, so they will separate from their twins. \n",
     "\n",
-    "One way to accomplish this is to sample from the current particle set `N` times, making a new set of particles from the sample. For this to work the probability of selecting any given particle should be proportional to its weight. The easiest way to accomplish this is to use NumPy's `cumsum` function. `cumsum` computes the *cumulative* sum of an array. That is, element one is the sum of elements zero and one, element two is the sum of elements zero and one, etc. Then we generate random numbers in the range of 0.0 to 1.0 and do a binary search to find the weight that most closely matches that number. This algorithm is variously called **multinomial resampling** or **simple random resampling**.  Here is my implementation:\n",
+    "One way to accomplish this is to sample from the current particle set `N` times, making a new set of particles from the sample. For this to work the probability of selecting any given particle should be proportional to its weight. The easiest way to accomplish this is to use NumPy's `cumsum` function. `cumsum` computes the cumulative sum of an array. That is, element one is the sum of elements zero and one, element two is the sum of elements zero and one, etc. Then we generate random numbers in the range of 0.0 to 1.0 and do a binary search to find the weight that most closely matches that number. This algorithm is variously called *multinomial resampling* or *simple random resampling*.  Here is my implementation:\n",
     "\n",
     "```python\n",
     "def resample(self):\n",
@@ -756,7 +761,7 @@
     " \n",
     "There are many resampling algorithms. Each has different properties with respect to which particles are sampled, execution time, and memory required. I will share a few of them in a later section.\n",
     "\n",
-    "You will not necessarily want to resample every iteration. For example, if you received no new measurements you have not received any information from which the resample can benefit. We can determine when to resample by using something called the **effective N**, which is meant to approximate the number of particles with have an appreciable weight which meaningfully contributes to the probability distribution. The equation for this is\n",
+    "You will not necessarily want to resample every iteration. For example, if you received no new measurements you have not received any information from which the resample can benefit. We can determine when to resample by using something called the *effective N*, which is meant to approximate the number of particles with have an appreciable weight which meaningfully contributes to the probability distribution. The equation for this is\n",
     "\n",
     "$$\\hat{N}_{eff} = \\frac{1}{\\sum w^2}$$\n",
     "\n",
@@ -778,7 +783,7 @@
    "source": [
     "## SIR Filter  - A Complete Example\n",
     "\n",
-    "There is more, but we have covered enough to implement a full particle filter. The filter in this form is called the **Sampling Importance Resampling filter**, or SIR.\n",
+    "There is more, but we have covered enough to implement a full particle filter. The filter in this form is called the *Sampling Importance Resampling filter*, or SIR.\n",
     "\n",
     "The code above has been placed in the file *./code/RobotLocalizationParticleFilter.py* which we will import. If you want to read the source code, comment out the %load command in the next cell and press ctrl-return to execute it.\n",
     "\n",
@@ -814,9 +819,9 @@
     },
     {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b69630>"
+       "<matplotlib.figure.Figure at 0x8c8e7b8>"
       ]
      },
      "metadata": {},
@@ -926,9 +931,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ad2978>"
+       "<matplotlib.figure.Figure at 0x8c7e5f8>"
       ]
      },
      "metadata": {},
@@ -945,7 +950,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "From the plot it looks like there are only a few particles at the first two robot positions. This is not true; there are 5,000 particles, but due to resampling most are duplicates of each other. The reason for this is the Gaussian for the sensor is very narrow. This is called **sample impoverishment** and can lead to filter divergence. I'll address this in detail below. For now, looking at the second step at x=2 we can see that the particles have dispersed a bit. This dispersion is due to the motion model noise. All particles are projected forward according to the control input `u`, but noise is added to each particle proportional to the error in the control mechanism in the robot. By the third step the particles have dispersed enough to make a convincing cloud of particles around the robot. \n",
+    "From the plot it looks like there are only a few particles at the first two robot positions. This is not true; there are 5,000 particles, but due to resampling most are duplicates of each other. The reason for this is the Gaussian for the sensor is very narrow. This is called *sample impoverishment* and can lead to filter divergence. I'll address this in detail below. For now, looking at the second step at x=2 we can see that the particles have dispersed a bit. This dispersion is due to the motion model noise. All particles are projected forward according to the control input `u`, but noise is added to each particle proportional to the error in the control mechanism in the robot. By the third step the particles have dispersed enough to make a convincing cloud of particles around the robot. \n",
     "\n",
     "The shape of the particle cloud is an ellipse. This is not a coincidence. The sensors and robot control are both modeled as Gaussian, so the probability distribution of the system is also a Gaussian. The particle filter is a sampling of the probability distribution, so the cloud should be an ellipse.\n",
     "\n",
@@ -981,9 +986,9 @@
     },
     {
      "data": {
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+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8918320>"
+       "<matplotlib.figure.Figure at 0x87eed30>"
       ]
      },
      "metadata": {},
@@ -1037,9 +1042,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9995470>"
+       "<matplotlib.figure.Figure at 0xc97ccf8>"
       ]
      },
      "metadata": {},
@@ -1055,7 +1060,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Here the initial sample of points did not generate any points near the robot. The particle filter does not create new points during the resample operation, so it ends up duplicating points which are not a representative sample of the probability distribution. As mentioned earlier this is called **sample impoverishment**. The problem quickly spirals out of control. The particles are not a good match for the landscape measurement so they become dispersed in a highly nonlinear, curved distribution, and the particle filter diverges from reality. No particles are available near the robot, so it cannot ever converge.\n",
+    "Here the initial sample of points did not generate any points near the robot. The particle filter does not create new points during the resample operation, so it ends up duplicating points which are not a representative sample of the probability distribution. As mentioned earlier this is called *sample impoverishment*. The problem quickly spirals out of control. The particles are not a good match for the landscape measurement so they become dispersed in a highly nonlinear, curved distribution, and the particle filter diverges from reality. No particles are available near the robot, so it cannot ever converge.\n",
     "\n",
     "Let's make use of the `create_gaussian_particles()` method to try to generate more points near the robot. We can do this by using the `initial_x` parameter to specify a location to create the particles."
    ]
@@ -1077,9 +1082,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xbbba0b8>"
+       "<matplotlib.figure.Figure at 0xc97c668>"
       ]
      },
      "metadata": {},
@@ -1108,7 +1113,7 @@
     "\n",
     "But our difficulty is that in many problems, including this one, we don't know that distribution. For example, the tracked object might move very differently than we predicted with our state model. How can we draw a sample from a probability distribution that is unknown? \n",
     "\n",
-    "There is a theorem and associated techniques from statistics called **importance sampling**[1]. It somewhat remarkably gives us a way to draw samples from a *different* and known probability distribution compute the properties of the known one. It's a fantastic theorem that brings joy to my heart. \n",
+    "There is a theorem and associated techniques from statistics called *importance sampling*[1]. It somewhat remarkably gives us a way to draw samples from a different and known probability distribution compute the properties of the known one. It's a fantastic theorem that brings joy to my heart. \n",
     "\n",
     "The idea is simple, and we already used it. We draw samples from the known probability distribution, but *weight the particles* according to the distribution we are interested in. We can then compute properties such as the mean and variance by computing the weighted mean and weighted variance of the samples.\n",
     "\n",
@@ -1140,7 +1145,7 @@
     "\n",
     "which is the equation I gave you earlier in the chapter.\n",
     "\n",
-    "It is required that the weights be *proportional* to the ratio $\\frac{\\pi(x)}{q(x)}$. We normally do not know the exact value, so in practice we normalize the weights by dividing them by $\\sum w(x^i)$.\n",
+    "It is required that the weights be proportional to the ratio $\\frac{\\pi(x)}{q(x)}$. We normally do not know the exact value, so in practice we normalize the weights by dividing them by $\\sum w(x^i)$.\n",
     "\n",
     "When you formulate a particle filter algorithm you will have to implement this step depending on the particulars of your situation. For robot localization the best distribution to use for $q(x)$ is the particle distribution from the `predict()` step of the filter. Let's look at the code again:\n",
     "\n",
@@ -1207,7 +1212,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8871240>"
+       "<matplotlib.figure.Figure at 0xc97c780>"
       ]
      },
      "metadata": {},
@@ -1250,7 +1255,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d2b400>"
+       "<matplotlib.figure.Figure at 0x878e710>"
       ]
      },
      "metadata": {},
@@ -1266,7 +1271,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This is an O(n log(n)) algorithm. That is not terrible, but there are O(n) resampling algorithms with better properties with respect to the uniformity of the samples. I show it to you first merely because you can understand the other algorithms as variations on this one. There is a faster implementation of this algorithm that uses the inverse of the CDF of the distribution, but since we will not be using this much, if ever, I won't cover it. You can search on the internet if you are interested.\n",
+    "This is an $O(n \\log(n))$ algorithm. That is not terrible, but there are $O(n)$ resampling algorithms with better properties with respect to the uniformity of the samples. I show it to you first merely because you can understand the other algorithms as variations on this one. There is a faster implementation of this algorithm that uses the inverse of the CDF of the distribution, but since we will not be using this much, if ever, I won't cover it. You can search on the internet if you are interested.\n",
     "\n",
     "You may import this from FilterPy using\n",
     "\n",
@@ -1281,7 +1286,7 @@
    "source": [
     "### Residual Resampling\n",
     "\n",
-    "Residual resampling both improves the run time of multinomial resampling, and ensures that the sampling is uniform across the population of particles. It's fairly ingenious: the normalized weights are multiplied by *N*, and then the integer value of each weight is used to define how many samples of that particle will be taken. For example, if the weight of a particle is 0.0012 and $N$=3000, the scaled weight is 3.6, so 3 samples will be taken of that particle. This ensures that all higher weight particles are chosen at least once, and has O(N) running time.\n",
+    "Residual resampling both improves the run time of multinomial resampling, and ensures that the sampling is uniform across the population of particles. It's fairly ingenious: the normalized weights are multiplied by *N*, and then the integer value of each weight is used to define how many samples of that particle will be taken. For example, if the weight of a particle is 0.0012 and $N$=3000, the scaled weight is 3.6, so 3 samples will be taken of that particle. This ensures that all higher weight particles are chosen at least once, and has $O(N)$ running time.\n",
     "\n",
     "However, this does not make *N* selections. To select the rest, we take the *residual*: the weights minus the integer part, which leaves the fractional part of the number. We then use a simpler sampling scheme such as multinomial, to select the rest of the particles based on the residual. In the example above the scaled weight was 3.6, so the residual will be 0.6 (3.6 - int(3.6)). This residual is very large so the particle will be likely to be sampled again. This is reasonable because the larger the residual the larger the error in the round off, and thus the particle was relatively under sampled in the integer step.\n",
     "\n",
@@ -1324,7 +1329,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d84da0>"
+       "<matplotlib.figure.Figure at 0x82b98d0>"
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@@ -1369,7 +1374,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d339b0>"
+       "<matplotlib.figure.Figure at 0xc933278>"
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@@ -1432,7 +1437,7 @@
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x890bf28>"
+       "<matplotlib.figure.Figure at 0x91ab668>"
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      "metadata": {},
@@ -1498,7 +1503,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xbb13cf8>"
+       "<matplotlib.figure.Figure at 0x914f7b8>"
       ]
      },
      "metadata": {},
@@ -1508,7 +1513,7 @@
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x938a710>"
+       "<matplotlib.figure.Figure at 0x91e2cc0>"
       ]
      },
      "metadata": {},
@@ -1518,7 +1523,7 @@
      "data": {
       "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8848860>"
+       "<matplotlib.figure.Figure at 0x8cc1e10>"
       ]
      },
      "metadata": {},
@@ -1528,7 +1533,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAABCCAYAAACSCTtfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x88c0a90>"
+       "<matplotlib.figure.Figure at 0xc7d2f98>"
       ]
      },
      "metadata": {},

13-Smoothing.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -292,9 +298,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAucAAAEWCAYAAADFITnpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAucAAADaCAYAAAAFfOySAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7211630>"
+       "<matplotlib.figure.Figure at 0x720c0f0>"
       ]
      },
      "metadata": {},
@@ -337,9 +343,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x725cc88>"
+       "<matplotlib.figure.Figure at 0x75dff98>"
       ]
      },
      "metadata": {},
@@ -369,9 +375,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74718d0>"
+       "<matplotlib.figure.Figure at 0x7e82b38>"
       ]
      },
      "metadata": {},
@@ -396,11 +402,11 @@
    "source": [
     "## An Overview of How They Work\n",
     "\n",
-    "The Kalman filter is a **recursive** filter - it's estimate at step `k` is partially based on its estimate from step `k-1`. But this means that the estimate from step `k-1` is partially based on step `k-2`, and so on back to the first measurement. Hence, the estimate at step `k` depends on *all* of the previous measurements, though to varying degrees. `k-1` has the most influence, `k-2` has the next most, and so on. \n",
+    "The Kalman filter is a *recursive* filter - it's estimate at step `k` is partially based on its estimate from step `k-1`. But this means that the estimate from step `k-1` is partially based on step `k-2`, and so on back to the first measurement. Hence, the estimate at step `k` depends on all of the previous measurements, though to varying degrees. `k-1` has the most influence, `k-2` has the next most, and so on. \n",
     "\n",
     "Smoothing filters incorporate future measurements into the estimate for step `k`. The measurement from `k+1` will have the most effect, `k+2` will have less effect, `k+3` less yet, and so on. \n",
     "\n",
-    "This topic is called **smoothing**, but I think that is a misleading name. I could smooth the data above by passing it through a low pass filter. The result would be smooth, but not necessarily accurate because a low pass filter will remove real variations just as much as it removes noise. In contrast, Kalman smoothers are *optimal* - they incorporate all available information to make the best estimate that is mathematically achievable."
+    "This topic is called *smoothing*, but I think that is a misleading name. I could smooth the data above by passing it through a low pass filter. The result would be smooth, but not necessarily accurate because a low pass filter will remove real variations just as much as it removes noise. In contrast, Kalman smoothers are *optimal* - they incorporate all available information to make the best estimate that is mathematically achievable."
    ]
   },
   {
@@ -513,9 +519,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7ec72e8>"
+       "<matplotlib.figure.Figure at 0x7f67080>"
       ]
      },
      "metadata": {},
@@ -588,9 +594,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7eab198>"
+       "<matplotlib.figure.Figure at 0x7eb5898>"
       ]
      },
      "metadata": {},
@@ -617,9 +623,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8732320>"
+       "<matplotlib.figure.Figure at 0x8760ac8>"
       ]
      },
      "metadata": {},
@@ -656,9 +662,9 @@
     },
     {
      "data": {
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74ad588>"
+       "<matplotlib.figure.Figure at 0x87b57f0>"
       ]
      },
      "metadata": {},
@@ -698,7 +704,7 @@
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x882fc18>"
+       "<matplotlib.figure.Figure at 0x883f4e0>"
       ]
      },
      "metadata": {},
@@ -745,9 +751,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuYAAADaCAYAAADqvoesAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99b3f60>"
+       "<matplotlib.figure.Figure at 0x99bca90>"
       ]
      },
      "metadata": {},

14-Adaptive-Filtering.ipynb

@@ -30,6 +30,9 @@
        "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
        "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n",
        "\n",
+       ".CodeMirror pre {\n",
+       "    font-family: 'Source Code Pro', Consolas, monocco, monospace;\n",
+       "}\n",
        "    div.cell{\n",
        "        width: 900px;\n",
        "        margin-left: 0% !important;\n",
@@ -49,7 +52,7 @@
        "\t\n",
        "    div.input_area {\n",
        "        background: #F6F6F9;\n",
-       "        border: 1px solid #586e75;\n",
+       "        border: 1px solid #586e75;      \n",
        "    }\n",
        "\n",
        "    .text_cell_render h1 {\n",
@@ -108,6 +111,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -142,7 +146,8 @@
        "}\n",
        "\n",
        "    code{\n",
-       "      font-size: 70%;\n",
+       "        font-size: 6pt;\n",
+       "\n",
        "    }\n",
        "    .rendered_html code{\n",
        "    background-color: transparent;\n",
@@ -235,7 +240,8 @@
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
-       "                           extensions: [\"AMSmath.js\", \"autobold.js\"]\n",
+       "                           extensions: [\"AMSmath.js\"],\n",
+       "                           equationNumbers: { autoNumber: \"AMS\", useLabelIds: true}\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
@@ -243,7 +249,7 @@
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
-       "                    scale:100,\n",
+       "                    scale:95,\n",
        "                        availableFonts: [],\n",
        "                        preferredFont:null,\n",
        "                        webFont: \"TeX\",\n",
@@ -406,9 +412,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvAAAAD+CAYAAABcMzEjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72136a0>"
+       "<matplotlib.figure.Figure at 0x721df60>"
       ]
      },
      "metadata": {},
@@ -468,9 +474,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAE6CAYAAACWFK1xAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvUAAAD+CAYAAAC6GvpnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7206c18>"
+       "<matplotlib.figure.Figure at 0x7225cc0>"
       ]
      },
      "metadata": {},
@@ -561,9 +567,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAAE6CAYAAACmmLxQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAAD+CAYAAACKlutGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x74281d0>"
+       "<matplotlib.figure.Figure at 0x73aebe0>"
       ]
      },
      "metadata": {},
@@ -607,9 +613,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x747a358>"
+       "<matplotlib.figure.Figure at 0x75b71d0>"
       ]
      },
      "metadata": {},
@@ -650,9 +656,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xt8z+X/x/HH+7OZHZ1pRtg053NzlmMoZ98ip5wqQjkl\npcjIIRJCSRSLKORQaMihcsghKYechYalnGY2O12/P/bb+LRhsu2z2fN+u7m1va/r/f68Phdtz127\n3tfbMsYYREREREQkU7E5ugAREREREbl3CvIiIiIiIpmQgryIiIiISCakIC8iIiIikgkpyIuIiIiI\nZEIK8iIiIiIimZCCvIiI3NaxY8fInj07Y8eOdXQpD5zFixdjs9nYsGGDo0sRkUxKQV5EMj2bzYbN\nlrW/nJ0/f5433niDypUrkytXLtzc3PD19eXZZ59l69at//m6Q4YMIVeuXAwcODAVq80YQkJCmDFj\nBs2bN8fPzw83Nzfy5MlD/fr1+eyzz/7TNf/880+ee+45fHx8cHV1xdfXl0GDBnH58uUkfdu3b0/F\nihUZNGgQcXFx9/t2RCQLsvRAKBHJ7Gw2G5ZlERsb6+hSHGLFihU8++yzhIeHU7lyZerWrYubmxuH\nDh0iODiYyMhI+vTpw7Rp03ByckrxdXfs2EHNmjUZNWoUI0aMSMN34Bivv/46EydOpGjRotSvX59C\nhQoREhLCsmXLCAsLo127dnz55Zcpvt6JEyeoVasWf/31F23atKFUqVLs2LGDTZs2UbJkSbZu3Uqe\nPHnszlm8eDEdOnTgs88+o0uXLqn9FkXkQWdERDI5y7KMzWZzdBkOsXnzZuPs7Gzc3NzMokWLkrSf\nOnXKVKpUyViWZQYNGnRP1+7cubNxcnIyp06dSq1yM5Rly5aZzZs3Jzl+9uxZ8/DDDxvLssyyZctS\nfL0mTZoYy7LMjBkz7I4PHjzYWJZlXnzxxSTnREZGmty5c5saNWrc+xsQkSxPQV5EMr17CfIbN240\nL7zwgildurTJkSOHcXNzM2XLljUjR440ERERSfqPHDnSWJZl5s2bZ1avXm0ee+wx4+XlZXLnzp3Y\n5+zZs6Z79+4mf/78xs3NzVSqVMkEBQWZTZs2GcuyTGBgYJLrXr582YwYMcKULVvWuLu7Gy8vL1On\nTh2zZMmSFL/v2NhYU7JkSWNZlpk5c+Zt+4WEhJhcuXIZy7LMr7/+mqJrX7lyxbi4uJhatWolaStV\nqpTJli2bCQ0NTfbc6dOnG8uyzKhRoxKPpcW4p6Vx48YZy7JM//79U9T/2LFjxrIs4+fnl6QtLCzM\neHh4GE9PTxMeHp6kvUePHsayLHPgwIH7rltEspasvahURLKciRMn8t1331GlShVefPFFXnjhBbJn\nz87o0aNp2rTpbZfnLFmyhNatW5M3b1769etHmzZtAPjrr7+oWbMmQUFBlC5dmkGDBlG5cmX69u3L\n+++/D4BlWXbXCgkJoWrVqowZM4Z8+fLx4osv0rFjR06ePEn79u0ZNWpUit7L999/z5EjR/Dx8aFX\nr1637efj48MLL7wAwMyZM1N07R9++IHo6Gjq1KmTpK179+7ExMTw+eefJ3tuUFAQNpuNbt26JR5L\n7XFPa87Oznb/vZtNmzYB0KRJkyRtnp6e1K5dm/DwcH766ack7bVr1wZg/fr1/7VcEcmiUvYVSkTk\nAfHhhx/i6+ub5Phbb73FmDFjWLp0Kc8880yS9uDgYNasWZMkqA0bNozTp0/zyiuv8O677yYeHzhw\nINWqVUu2hm7dunHixAkWLVpk91phYWHUr1+f0aNH07ZtWypUqHDH97JlyxYAGjRocNebfRs3bsyk\nSZP48ccf79jv39cOCAhI0ta1a1eGDx9OUFAQgwYNsms7ePAgP//8M/Xr16do0aKJx1N73AGmTp2a\n7E2kt+Pr62v3w8XtxMTEJN7s+sQTT6To2ocPHwagRIkSybb7+/uzfv16jh49SsOGDe3aEsb4xx9/\nZMCAASl6PRERUJAXkSwmuTAJ8cF7zJgxrF+/PtlA2bp16yRhMioqikWLFpEjRw7eeustu7YKFSrQ\ntWtX5syZY3d83759bNy4kf/9739JXsfLy4vAwEBat27N559/ftcgf+7cOQAefvjhO/YDKFy4MBC/\nq0pKnD59GoCCBQsmaStYsCCNGzcmODiYvXv3UqlSpcS2efPmAfGz9rdKzXFP8P7773Pq1KmUvB0A\n6tevn6IgP2TIEA4cOECLFi1o3Lhxiq595coVAHLmzJlse8Lx5H7w8Pb2Bm6OuYhISinIi0iWEh4e\nzvvvv8/y5cs5cuQI165dw9yyeVdISEiy5yU3u3748GEiIyOpUqUKXl5eSdpr166dJMgnbAV55coV\nAgMDk5xz4cIFAH7//fcUv6d7ERkZmaJ+//zzDwC5c+dOtr179+4EBwcTFBSUGORjY2NZsGABnp6e\nPP3003b9U3PcE5w8eTJF7+VejB8/nmnTplGuXDnmz5+f6tdPTsJONn///Xe6vJ6IPDgU5EUky4iO\njqZhw4bs2rWL8uXL07FjR/Lnz0+2bNkwxjBq1Chu3LiR7LkJs6a3SpiFfeihh5I9J7njCQF5w4YN\nt30QkGVZhIeH3/X9+Pj4ACmbyT1z5gwABQoUuGtfADc3N+D2wb9Nmzbkzp2bhQsX8u677+Ls7Mz6\n9es5f/483bt3x93dPbFvao97Whk7diwjRoygYsWKfPfdd7edXU9OQt+EfxP/lnA8V65cSdoiIiKA\nm2MuIpJSCvIikmWsXLmSXbt20aNHDz755BO7tnPnzt3xJtN/37AKkCNHDgBCQ0OTPSe54wmBb/Lk\nyff9kKWEG1E3b95MbGzsHfeI/+6774Dk17wnJyHwJ/zg8W8uLi506NCBmTNnsmbNGlq1anXbZTWp\nPe4JUnON/PDhwxk3bhwBAQGsW7cu2cB9J6VKlQJurpX/t6NHjwLJr6FPGOOU/pAlIpJAQV5Esoxj\nx44B8L///S9J2/fff3/P1ytdujSurq7s37+fq1evJgb7BAk3jN6qVq1aQPyuMPcb5OvVq0fJkiU5\nfPgwc+bMoXfv3sn2O3fuHLNnzwagU6dOKbp2xYoVATh06NBt16h3796dmTNnEhQURP369Vm5ciV+\nfn7UrVvXrl9qj3uC1FojP3jwYKZOnUrNmjUJDg5OdpnU3TRo0ACI33nGGGP3A0hYWBhbt27Fw8OD\nGjVqJDn30KFDAHb3GoiIpIS2nxSRLCPhhsuErQITnDhxgtdee+2er5ctWzY6dOjA1atXefvtt+3a\nfv3118SdT25VpUoV6tWrx8qVK5Osn09w5MiRxKUwd2JZFh999BHOzs4MGjSIJUuWJOlz+vRpWrRo\nwZUrV2jYsGGSteu3U79+fQC2b99+2z5Vq1alTJkyrF69mhkzZnDjxg26du2apF9qj3uCkydPEhcX\nl+I/GzdutDvfGEOfPn2YOnUq9erVY/369XcN8RERERw6dIgTJ07YHffz86NJkyacPHmSDz74wK5t\n5MiRXL9+nWeffTbZ5TMJW1Im/DAgIpJSmpEXkQeCMSbJko4ElmUxadIkWrZsySOPPMLkyZPZt28f\nlSpV4vTp06xevZoWLVrwxRdf3PPrvvPOO2zcuJH33nuPnTt3Urt2bc6fP8/ixYtp3rw5K1asSLI1\n5MKFC2nUqBG9evVi+vTpVK9enTx58hASEsKBAwfYu3cvK1asSNFuNPXq1ePLL7+ka9euPPPMM0yY\nMIE6derg5ubGkSNH+Pbbb4mMjKR8+fJ89dVXKX5fZcuWpWTJkmzcuJGYmJjb7qfevXt3hg4dSmBg\nYJK94xOkxbinhtGjRzNr1ixcXFyoVq0aEydOTNLn38txduzYQcOGDSlatGiSm20//PBDatWqRf/+\n/dmwYQOlSpVix44dbN68mZIlSzJ27Nhk61i7di05c+ZM8Q45IiKJHPgwKhGRVJHwZFfLsuz+JByz\n2Wzm1KlTxhhjzpw5Yzp37mwKFSpk3NzcTLly5cy7775rYmJijGVZpkGDBnbXDgwMNDabzQQFBd32\n9UNCQky3bt0Sn+xauXJl89lnn5mlS5cay7LM+++/n+Sc8PBwM2HCBFO1alXj5eVlXF1dja+vr2na\ntKmZMWOGuXTp0j2Nwblz58zrr79uKlWqZHLkyGE3DqNGjTJRUVH3dD1jjJk2bZqxLMt8/fXXt+1z\n/vx54+zsbGw2W5Kxu1VajPv96t69u7HZbMn+20n48++6Nm/ebCzLMr6+vsle888//zQ9e/Y0BQsW\nNC4uLqZYsWJm0KBB5vLly8n2P3To0D09QVZE5FaWMbfs/yUiIqnmzTffZPz48axdu9Yhs61Dhgxh\n8uTJdOzYkQULFtzxxtHkhIWF8cgjjxAQEMDq1avTqMqsbdCgQcycOZODBw/i5+fn6HJEJJNRkBcR\nuU9nz55N3Aoywb59+6hVqxaurq6EhITg4uKS7nUZY2jXrh3Lli1LdseYlPj444958cUX2bp1KzVr\n1kyDKrOukJAQ/P396du3L5MmTXJ0OSKSCWmNvIjIfapRowbFihWjXLlyeHh4cPTo0cQZ7NmzZzsk\nxEP8vQELFixgypQpREdHs3//fsqVK3dP13j++ee5ePGiHlaUBk6dOsWwYcMYMGCAo0sRkUxKM/Ii\nIvdpzJgxLF++nJMnTxIWFkbu3LmpUaMGQ4YMSbIVo4iISGp5IIL87Z6kJyIiIiKSGdzL06QTaB95\nEREREZFMSEFeRERERCQTeuBudv0vv5aQ5O3evRuAgIAAB1fy4NHYpg2Na9rQuKYNjWva0LimDY1r\n2rjf5eGakRcRERERyYQU5EVEREREMiEFeRERERGRTEhBXkREREQkE1KQFxERERHJhLine truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x724d4e0>"
+       "<matplotlib.figure.Figure at 0x7566c18>"
       ]
      },
      "metadata": {},
@@ -689,9 +695,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd0VNXexvHvmXQSCKGESG+hg/R+6SBSVCz0JioqHVQQ\nFUGugiCXagEFkRdFKUqx0KRDKCJI771IpIQQQvrs94/I4JgAoSSTwPNZK+sye+9zzm8OrsuTPXv2\nsYwxBhERERERyVBsri5ARERERETunIK8iIiIiEgGpCAvIiIiIpIBKciLiIiIiGRACvIiIiIiIhmQ\ngryIiIiISAakIC8i8pB74YUXyJ49OxEREa4u5aF36tQpvL29eeedd1xdiohkAAryIpLh2Gw2bLZb\n/99XvXr1sNlsrFmzJo2qSn0LFy7k6aefJk+ePHh7e5M9e3Zq1qzJqFGjuHr16l2dc9u2bcyYMYNB\ngwaROXPm+1yx6y1dupQ+ffpQsWJFsmfPjre3N0WLFuXVV1/l+PHjNz0uLCyM/v37U7BgQby9vcmT\nJw8vvPACZ86cueMaoqKiGDZsGMWLF8fHx4dcuXLRpk0b9u/fn2Rsvnz5eOWVVxg7diwnT56842uJ\nyMPF0gOhRCSjsdlsWJZFQkLCTcfUq1ePdevWsWrVKurUqZOG1d1/V65coW3btixZsoQsWbLQrFkz\nChUqREREBMuXL+fAgQPkzp2bhQsXUqlSpTs69+OPP05ISAh//vknmTJlSqV34BrR0dFkypQJT09P\nateuTfny5bEsi/Xr17N582b8/PxYvnw51apVczru4sWL1KpVi4MHD9KwYUOqVKnCvn37WLhwIYGB\ngWzcuJFChQqlqIaYmBgaNWrEhg0bqFKlCg0aNODkyZPMnTsXT09PVq5cSdWqVZ2OOXv2LAUKFKBL\nly5MnTr1vt0PEXkAGRGRDMayLGOz2W45pm7dusayLLNmzZo0qip1JCQkmCZNmhjLskzjxo3NhQsX\nkowZP368sdlsJlu2bOb48eMpPvfBgweNzWYz3bp1u58lpxtxcXHmgw8+MJcuXUrS99///tdYlmXK\nlSuXpK979+7Gsizz+uuvO7VPnDjRWJZlmjZtmuIaRowYYSzLMq1bt3ZqX7hwobEsy5QuXdrY7fYk\nxzVt2tRkypTJhIWFpfhaIvLwUZAXkQznXoK8ZVmmXr16yR4zdOjQm4b/r7/+2lSoUMH4+PiYwMBA\n06lTJ3PmzBnHdZKzcuVK07JlS5MjRw7j6elpChQoYHr06GHOnTuXwneaeF3LskyRIkVMZGTkTce9\n8cYbxrIs06pVqxSfe9CgQcayLLNs2TKn9m+//dZYlmV69+6d7HFxcXEmKCjI+Pn5OWoKDw83o0eP\nNvXr1zd58uQxnp6eJmfOnKZly5YmJCQk2fNYlmUKFixowsPDTd++fU3+/PmNu7u7GT9+fIrfw92K\nj483Pj4+xmazOQX9iIgI4+PjYzJnzmyuXr3qdIzdbjcFChQwlmWZo0eP3vYadrvd5M+f39hstmR/\nwapTp46xLMusWrUqSd+MGTOMZVnmk08+ufM3JyIPDa2RF5GHjmVZdzR+9OjRdOrUiRMnTtClSxe6\ndevGnj17qF27NuHh4cmeb9SoUTRs2JCNGzfSvHlz+vfvT8mSJfnss8+oXLlyitdaf/755wC8/vrr\nt1z6MnjwYDw9PVm0aBHnzp1L0bl//fVX3NzcqFGjhlN7q1atyJo1K9999x1xcXFJjlu6dCmhoaE8\n99xzjpr27t3LO++8g7u7Oy1btuS1116jcePGjqVNixcvTraGmJgY6tevz88//0zz5s3p27cv+fLl\nS1H998KyLNzd3QFwc3NztG/atIno6Ghq1aqFr69vkmOaNm0KwKpVq257jSNHjnDq1CmKFStGgQIF\nkvQ//vjjAKxcuTJJX61atQBYvnx5Ct+RiDyM3F1dgIjI3TDG8N5772Fu8jWfW32R8U4cPXqUt99+\nm+zZs7Nt2zZHyBw5ciTt27fnu+++SxLk165dy+DBg6lRowaLFy8mS5Ysjr6vv/6azp0707dvX+bN\nm3fLa8fHx7Np0yYsy6Jx48a3HBsQEEDFihXZtGkT69at47nnnrvl+MjISP744w+KFy+On5+fU5+X\nlxdt27Zl8uTJ/Pzzzzz11FNO/TNmzACga9eujrZSpUrx559/ki1bNqexZ86coWrVqgwYMMARXP/p\n3LlzlC1blg0bNuDt7e3U98cff7BgwYJbvo9/e/7555MNzf82Z84crl69So0aNZz+fg4cOABAsWLF\nkj2uaNGiABw6dOi217iXcxUpUgR/f3/WrVt32+uIyMNLQV5EMqz33nsv1a8xa9YsEhIS6NmzZ5KZ\n4g8//JA5c+Yk+WViwoQJAEyZMsUpJAJ07NiRsWPHsnDhQiIjI5PM+v7TpUuXiIuLw7KsFM1S58uX\nj02bNqVotv/MmTPY7XYeeeSRZPu7du3K5MmT+eqrr5yCfFhYGIsWLaJw4cJOXyL+9/u8Lk+ePDzz\nzDN8/PHHnD59mrx58zr1W5bFmDFjkoR4gB07djB8+PDbvpd/nqtBgwa3DfKHDx+md+/eeHh4MG7c\nOKe+8PBwAPz9/ZM99nr75cuXb1vPvZ4rKCiIgwcPcu3atQfui8gicn8oyItIhpSSXWvWrl17z9fZ\nvn07ALVr107Slz9/fvLly5dkm8ANGzbg7u7O999/n+yse0xMDAkJCRw4cICKFSvec43/Fh0dfdsx\nFy9eBBJn8pNTtWpVSpYsyeLFi7lw4QI5cuQA4LvvviM2NpbOnTsnOWbDhg1MmDCBjRs3cv78eWJj\nY536z5w5kyTIe3t7U7Zs2WRr6NKlC126dLnte7kTp0+f5rHHHuPSpUtMmTIlyY4x6cn1TzcuXLhA\n/vz5XVyNiKRHCvIiIrdwfVY1V65cyfbnypUrSZC/ePEiCQkJt/zEwLIsIiMjb3ntbNmy4eHhQXx8\nPCdPnnQsxbiZU6dOARAYGHjLcQA+Pj7ArUN/165dGTRoELNmzaJPnz5A4rIam82WJGDPnz+fZ599\nlkyZMtG4cWOKFCmCr68vNpuNVatWsWbNGmJiYpJcIyW13i8nT56kQYMGnDhxgk8//ZQXX3wxyZjr\ns+TX/97/7Xp71qxZb3u9ez1XVFQUcOPvSkTk3xTkReShEx8fn2x7ckscri8ZCQ0NTXbmODQ0NEmb\nv78/8fHxKVp+cSvu7u7UqFGDtWvXsnz58lsG+UuXLrFt2zYsy6Jy5cq3Pff1AH19Zj45nTp14q23\n3uKrr76iT58+7N+/ny1btlCvXr0ky1eGDBmCt7c3W7dupXjx4k59Z86cuemDuW71xeP7uUb+yJEj\nNGzYkDNnzjB16lSn9f3/VKJECQAOHjyYbP/19ew3W/d+P8918eJFbDab49MQEZF/U5AXkYdKQECA\nY+b633777bckbRUrVmTBggWsW7eORo0aOfWdOHEi2XPVrFmTn376iZ07d1KuXLl7qrd79+6sXbuW\n//3vf3Tt2vWms7OjRo0iNjaW0qVLp+iajzzyCDly5LhpyITENdpNmjRh8eLF7Nq1i1mzZgEkG4IP\nHz5M2bJlk4R4u93O+vXrb1tPcu7XGvl9+/bRqFEjzp8/z8yZM2nbtu1Nz1G9enW8vb3ZsGEDV69e\ndfoisN1uZ9myZViWRf369W9bT5EiRcifPz8HDhzg+PHjFCxY0Kn/+k4+DRo0SHLs1atXOXPmDGXL\nlr3jXZZE5CHi4u0vRUTu2L3sI9+sWTNjWZb55ZdfnNo///xzx3n/ecyRI0eMh4eHyZ49uzlx4oSj\n3W63m3bt2iVby6pVq4xlWaZatWrm9OnTSWqLiooy69atS9F7tdvt5rHHHjOWZZkmTZokeSCU3W43\nEydONDabzXh4eJgVK1ak6LzGGPPss88ay7LM/v37bzpm7ty5xrIs069fP5M3b16TOXPmZPezL1Gi\nhMmSJYs5e/asU21DhgxJ9r4ak/j3WKhQoRTXezd27NhhcubMaby8vMwPP/yQomNefvllY1mWee21\n15zaJ0yYYCzLMo8//niSY/bt22f2799v4uLinNpHjhxpLMsyzz33nNODnxYsWGAsyzJlypRJtoaV\nK1cay7JM//79U1SziDycLGNusnebiEg6ZbPZUvxl19WrVzvtrrJ69WoaNWqEu7s7rVu3JmfOnPz+\n++/8/vvv1K9fn59++inJMR9++CFvvfUWWbNmpU2bNvj7+7N8+XLCwsLw9/dn165dSZbr/O9//2PQ\noEF4enrSrFkzChUqRFRUFCdPnmTt2rUULlyYbdu2pej9RkRE0KZNG5YsWUKWLFlo1qwZBQsWJCIi\nghUrVrB//37c3Nz49NNPeemll1J8H7/77jvat2/P+PHjHWvg/y02NpbcuXMTERFBXFwcXbt25csv\nv0wy7vPPP+eVV14hMDCQp59+Gg8PDzZs2OCYDf/xxx+T3FebzUbBggU5evRoimu+E2FhYRQtWpSw\nsDBq166d7Mw3JF2Oc+nSJWrVqsWBAwdo0KABVapUYd++fSxatIhcuXIREhJCoUKFnM5hsyU+luX4\n8eNOX0yNjY2lYcOGbNiwgcqVK9OgQQNOnjzJ3Llz8fb2ZuXKlVSpUiVJTW+++SajR49m3bp1jj3l\nRUSScPVvEiIidyolM/L16tVLdhbYGGN+/vlnU61aNePj42MCAgLMk08+afbs2WOGDRt202Nmzpxp\nKlSoYLy9vR1Pdj179qwpXbq0CQgISLaGTZs2mXbt2pm8efMaT09PkyNHDlOuXDnTq1evFM/I/9P8\n+fPNU089ZXLnzm08PDyMZVmOWd3t27ff8fliY2NNUFCQqVix4i3H9erV66az6v/01Line truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87d34e0>"
+       "<matplotlib.figure.Figure at 0x7edac88>"
       ]
      },
      "metadata": {},
@@ -754,9 +760,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87ef588>"
+       "<matplotlib.figure.Figure at 0x87c3ba8>"
       ]
      },
      "metadata": {},
@@ -797,11 +803,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Before we discuss how to create an adaptive filter we have to ask *how do we detect a maneuver?* We cannot reasonably adapt a filter to respond to maneuvers if we do not know when a maneuver is happening.\n",
+    "Before we discuss how to create an adaptive filter we have to ask \"how do we detect a maneuver?\" We cannot reasonably adapt a filter to respond to maneuvers if we do not know when a maneuver is happening.\n",
     "\n",
     "We have been defining *maneuver* as the time when the tracked object is accelerating, but in general we can say that the object is maneuvering with respect to the Kalman filter if its behavior is different than the process model being used by the filter. \n",
     "\n",
-    "What is the mathematical consequence of a maneuvering object for the filter? The object will be behaving differently than predicted by the filter, so the *residual* will be large. Recall that the residual is the difference between the current prediction of the filter and the measurement. "
+    "What is the mathematical consequence of a maneuvering object for the filter? The object will be behaving differently than predicted by the filter, so the residual will be large. Recall that the residual is the difference between the current prediction of the filter and the measurement. "
    ]
   },
   {
@@ -813,9 +819,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAADlCAYAAAB3YbDsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x87ec0f0>"
+       "<matplotlib.figure.Figure at 0x87fcf28>"
       ]
      },
      "metadata": {},
@@ -843,9 +849,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x742b278>"
+       "<matplotlib.figure.Figure at 0x9a470b8>"
       ]
      },
      "metadata": {},
@@ -911,7 +917,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The first approach we will consider will use a lower order model and adjust the process noise based on whether a maneuver is occurring or not. When the residual gets *large* (for some reasonable definition of large) we will increase the process noise. This will cause the filter to favor the measurement over the process prediction and the filter will track the signal closely. When the residual is small we will then scale back the process noise.\n",
+    "The first approach we will consider will use a lower order model and adjust the process noise based on whether a maneuver is occurring or not. When the residual gets \"large\" (for some reasonable definition of large) we will increase the process noise. This will cause the filter to favor the measurement over the process prediction and the filter will track the signal closely. When the residual is small we will then scale back the process noise.\n",
     "\n",
     "There are many ways of doing this in the literature, I will consider a couple of choices."
    ]
@@ -953,9 +959,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvoAAAD+CAYAAABLEaHqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a23160>"
+       "<matplotlib.figure.Figure at 0x98f40b8>"
       ]
      },
      "metadata": {},
@@ -1004,9 +1010,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAAE6CAYAAABAsXcUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuoAAAD+CAYAAABsvyACAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9930c50>"
+       "<matplotlib.figure.Figure at 0x98f46d8>"
       ]
      },
      "metadata": {},
@@ -1089,9 +1095,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99bc278>"
+       "<matplotlib.figure.Figure at 0x723f940>"
       ]
      },
      "metadata": {},
@@ -1189,9 +1195,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl4TGf7wPHvmZnsISJEYkkiBKX2rbXVVktLUUpLa21R\nuumiqjSklmoVvypKF1RrrbVVL69Saxdeak/ssSSCyL7PzPP7I83IyCIhMkncn+vKJXOes9xnZM65\n5znPoimlFEIIIYQQQohiRWfrAIQQQgghhBD5J4m8EEIIIYQQxZAk8kIIIYQQQhRDksgLIYQQQghR\nDEkiL4QQQgghRDEkibwQQgghhBDFkCTyokhasmQJOp2OpUuX5ms7nU5Hu3btHlBUedOhQwdq1aqF\nLUZ2bdu2LTpd0fhYjxo1Cnd3dyIjI20dihDiAbPFtcfPz4+qVasWyrHOnj2Lg4MDU6dOLZTjZXbx\n4kV0Oh1Dhgwp9GPfKSEhAU9PT1588UVbhyL+VTTu+ELcQdM0y09mOp3urhfuO7cpTBs2bGDnzp0E\nBQXdcxx5OcfcPIjzP3PmDJ9++ikdO3bEx8cHBwcHPD096dq1Kz///HO220ycOJGUlBQmTpxY4PEI\nIYqewr72ZnePmDRp0j1VAt3Nu+++S5kyZXjrrbfuafuMyqnJkyffcwwP4v3dunUrb7zxBo0aNcLD\nwwNHR0eqV6/Oq6++ysWLF7Os7+Liwvjx41mxYgV//fVXgccj8k8SeVEk9erVi1OnTtGzZ88sZbld\nzIKDg/n+++8fZGg5Ukoxfvx4qlWrRt++fe9rX7b8MpKdiRMnMm7cOMLCwujSpQvvvvsuHTp0YOfO\nnfTo0YOxY8dm2cbb25vBgwfz9ddfZ3tDEEKI+7Fjxw5+++23bMsK8hr6119/sWnTJl577TVcXFzu\na19F6dqenJxM165dWbRoEWXLlmXIkCG8/vrrlC9fnoULF1KvXr1sk/VXX30VNzc3PvzwQxtELe4k\nibwokkqXLk2NGjUoXbp0vrarUaMGlStXfkBR5e63334jODiYgQMH2uT4D1KXLl04ePAgJ0+eZNGi\nRUydOpUVK1bwv//9j9KlSzNz5kwOHz6cZbtBgwZhMplYuHChDaIWQpRkVatWzfHpZUE2bZw7dy46\nnY5Bgwbd975s0eQyJwaDgSlTphAeHs727duZOXMmn332GX/88QdBQUHEx8czfPjwLNs5ODjQr18/\nduzYQXBwsA0iF1aUEP+6cOGC0jRNtW3bVl25ckX1799flStXTjk5OakmTZqoVatWZdnGbDarr7/+\nWjVv3ly5uroqZ2dn1bBhQ/X555+rtLS0LOsfOXJEvfDCC8rPz085OjqqcuXKqXr16qlRo0apmJgY\ny3qLFy9WmqapJUuWKKWU2rlzp9I0LdufwYMHW7bLiP9OsbGx6sMPP1Q1a9ZUjo6OqkyZMqp9+/Zq\n48aNub4PN2/eVK+88ory8vJSDg4Oqk6dOmrx4sXZvn/9+vVTmqap06dPZylLSUlRX3zxhWrUqJHy\n8PBQTk5OysfHR3Xt2lWtW7cuX+eolFIrVqxQjRo1Uk5OTsrT01O99NJL6urVq+qJJ55QOp0u2/ge\nlOHDhytN09SsWbOyLffz81MVKlRQZrO5UOMSQqT7448/lKZpqnv37jmu07hxY6XT6dTFixcty3bs\n2KG6d++uypUrp+zt7ZWvr68aNWqUunbtWpbtc7r25PceoZRSV65cUW+++aYKCAhQTk5Oyt3dXTVu\n3Fh99NFHVtv4+voqPz8/qxhyuoZevHhRjRs3TmmappYuXZrtcU+dOqU0TVOtWrWyLIuJiVH29vaq\nRYsW2W5z7tw5NXz4cFW9enVLrI888ogaOnSounTpklJKqUGDBuUY165duyz7io2NVWPGjFGVKlVS\njo6OqlatWmrWrFnq3LlzStM0NWTIkGxjeBCMRqNycnJSOp1O3bp1K0v5rl27lKZp6r333iu0mET2\nDLb+IiGKnqioKFq1akXZsmV5+eWXuXXrFqtXr+b5558nLCzMqo3goEGD+OGHH6hcuTLDhg3Dzs6O\nTZs28e6777Jt2zY2b96MXq8H4OjRozRv3hy9Xk+3bt2oVq0a8fHxnD9/nqVLl/LOO+9kqYHPeAxZ\ntWpVAgMDmTx5Mm5ubowZM8ayToMGDbLdJkNMTAytWrXixIkTNGrUiLfeeouoqCjWrFlDz549mTx5\ncrbtuKOjo2nZsiUODg707duXlJQUVq9ezdChQ9HpdFY170opduzYgaenJwEBAVn2NXjwYFauXEmd\nOnV48cUXcXFx4erVq/z999+sX7+eXr165fkcZ8+ezTvvvEOZMmUYOHAg7u7ubN26lZYtW+Lm5pbz\nf+wDYjAYrP69U8uWLVm+fDlHjx6lfv36hRmaEAJ47LHHqFWrFv/5z3+4ceMG5cuXtyo/ceIEhw4d\nom3btvj6+gIwY8YMPvjgAzw8PHj66afx8vLiyJEjLFiwgE2bNvHnn39SqVKlux47P/cIgIMHD9Kl\nSxdu3bpFmzZtePbZZ0lOTubUqVN88sknWe4Tma/3Q4YMQdM0du3aRc+ePa2um2XKlGHkyJF89tln\nLFy4MNsnpxlPDl999VXLst27d5OWlkarVq2yrB8eHk7Tpk2Ji4uja9eu9O7dm9TUVEJDQ1m3bh0D\nBgygSpUq9OrVi5iYGDZu3Ejbtm1p27atZR8Z73dKSgodOnTg4MGD1KtXj5deeono6GimTJnC77//\nftf3uaBpmobBYCAlJcXq/ydD06ZNsbOzY/v27YUem7iDrb9JiKIjoyZa0zT1/PPPW5WdO3dOlSlT\nRjk4OKjQ0FCllFIrV65UmqapBg0aqLi4OMu6qampqkOHDkrTNDVz5kzL8rfffltpmpZtLXh8fLxK\nSUmxvM6okb+z5kTTNFW1atUcz0HTNNWuXTurZSNHjlSapqlhw4ZZLb9y5Yry9vZWOp1OHThwINv3\n4ZVXXrGqST558qQyGAyqdu3aVvvKqMl56qmnssQUHR2tNE1TTZs2VSaTKUv5zZs383yOFy5cUHZ2\ndsrd3V1duHDBstxsNqu+ffsqTdOyrRULDAzM18+GDRuyPX5251ahQgVlMBhUcHBwtuvMmTNHaZqm\n5s6dm6d9CiEK3owZM5SmaWr27NlZyt577z2r621GbWuLFi2snpQqpdSyZcuUpmmqd+/eVsuzq5HP\n7z0iJSVF+fn5KZ1Op5YtW5YlzoiICGU0Gi2vfX19s1wrAwMDc61179atm9I0TR09etRqeVJSknJ3\nd1fly5dXqampluXvv/++0jRNrV69Osu+vvjiC6Vpmvq///u/LGWpqakqPj7e8jrjnjZ58uRs45o6\ndarSNE316tXLanloaKgqV65ctjXyhw8fzve1PfMTl9ysWLHC8jeQkwYNGiidTpflb0QULknkhUVG\nAmtnZ5fth338+PFK0zQ1depUpZRSHTt2VJqmqS1btmRZ9+jRo0rTNFWzZk3LsoxEfuvWrXeNpaAS\n+dTUVOXs7KxcXV1VZGRklvXnzp2rNE1TI0aMsCzLeB9cXV2tbj4Z2rRpo3Q6nUpISLAs27p1a7Zf\nFpRKfzSraZpq2bJl7iedh3OcMmWK0jRNTZgwIUvZhQsXlF6vzzaRz0jwc3q8m/lHp9Pl6RGuyWRS\nvXr1Upqmqddffz3H9TJu5vIIVgjbCQsLUwaDQTVo0MBqudFoVN7e3qpUqVKWa9qzzz6rNE1Tx44d\ny3ZfDRs2VAaDwer6mF0in997xE8//aQ0TVPdunXL0zndSyL/66+/Kk3T1OjRo62WL126NNvr1Asv\nvKA0TVN79uzJsq+M+8fChQvvGuvdEvnq1asrvV6fbdPMoKCgbBP5JUuW5OmanvnanrkpT07OnDlj\naU71119/5bhely5dlKZp6sSJE3fdp3hwpLOryMLHx8fyuC+zNm3aAPDPP/8AcOjQITRNy3bc9rp1\n61K+fHnOnDlDYmIiAM8//zx6vZ6ePXvy0ksvsXjx4gfeUSY4OJikpCTq1q1L2bJls5R37NgRINuO\nmgEBAbi6umZZXqVKFZRSREVFWZZljJXu7u6eZf3SpUvTvXt39u/fT7169Zg0aRLbt28nPj4+3+dz\n6NAhAJ544oksZX5+flSpUiXb7cxmMyaTCbPZfNcfk8nEd999l2scSilGjRrFhg0baNeuHbNmzcpx\n3Yz3/ebNm3k9TSFEAfP29ubJJ5/kyJEjHDlyxLJ827ZtXLt2jT59+uDs7AzAvn37MBgMrF27lkmT\nJmX5SUlJwWQycfr06VyPmd97xJ9//glA165dC+q0s+jSpQv+/v788MMPluNCerManU7HiBEjrNbP\n7dr+zDPP4Orqymuvvcazzz7LV199xZEjR/LdoTUuLo5z587h5eWVbdPMjHvvnQYNGpSna3rma3tO\n+8pw5coVOnfuzK1bt5g3bx7NmjXLcV25thcNksiLLCpUqJDr8piYGMu/bm5uODg4ZLu+t7e31fpN\nmzZl7969PPnkk6xfv55hw4ZRu3Zt/P39H9ioJhnH9vLyyrY8Y3l0dHSWsjJlymS7TUZbcJPJZFnm\n5OQEpA/nlZ1Vq1YxefJk0tLSCAoKolOnTnh4eNCnTx9CQ0PzeDa3z+du/0cPklKKkSNHsmjRIjp2\n7MjmzZtzbB8PkJSUBNx+j4QQtpExoVDmMdYzfh88eLBlWWRkJEajkcmTJxMUFJTl59SpU2iaRkJC\nQq7Hy+89IuM6nJe29/dK0zRGjBhBbGwsK1asAODYsWP88ccftG/fnmrVqlmtn9u13cfHhwMHDtCn\nTx9+//13Ro0aRcOGDalYsSLTpk3DbDbnKaaicF0HuHTpEm3btiU0NJT58+fz8ssv5Line truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72bc6a0>"
+       "<matplotlib.figure.Figure at 0x7510710>"
       ]
      },
      "metadata": {},
@@ -1218,9 +1224,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99b46a0>"
+       "<matplotlib.figure.Figure at 0x8887160>"
       ]
      },
      "metadata": {},
@@ -1247,9 +1253,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99e5048>"
+       "<matplotlib.figure.Figure at 0x9a1db70>"
       ]
      },
      "metadata": {},
@@ -1257,9 +1263,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4FFX3wPHvbHpPSIHQEgKE3gnw0qRIFRQQQUWaKAhY\nEBUV6UpREVAE5WehGhBeaQoIr9JFEKWXhBBCDYQQ0nt27++PmIUljUBgN+F8nieP2bl3Zs5uZObs\nnTN3NKWUQgghhBBCCFGi6MwdgBBCCCGEEKLoJJEXQgghhBCiBJJEXgghhBBCiBJIEnkhhBBCCCFK\nIEnkhRBCCCGEKIEkkRdCCCGEEKIEkkReWKQlS5ag0+lYunRpkdbT6XS0b9/+AUV1dzp27EjNmjUx\nx8yu7dq1Q6ezjH/Wo0aNwsPDg5iYGHOHIoR4wMxx7PH396dKlSoPZV9nz57Fzs6O6dOnP5T93e78\n+fPodDqGDh360Pd9p+TkZHx8fHjhhRfMHYr4l2Wc8YW4g6Zpxp/b6XS6Qg/cd67zMK1fv54dO3Yw\nbdq0e47jbt5jQR7E+8/KyuLzzz9n6NChNGzYEFtbW3Q6HYsWLcp3nYkTJ5Kens7EiROLPR4hhOV5\n2MfevM4RU6ZMuadBoMK8/fbbuLu7M2bMmHtaP2dwaurUqfccw4P4fE+fPs3kyZN56qmnqFy5Mjqd\nDp1OR0ZGRp79nZycGD9+PCtXruTAgQPFHo8oOknkhUXq3bs3p0+fplevXrnaCjqYhYSEsGzZsgcZ\nWr6UUowfP56qVavSr1+/+9qWOb+M5CUpKYk333yTZcuWcf36dXx9fYGC4/T19WXIkCF88803nD9/\n/iFFKoR4VGzfvp3ff/89z7biPIYeOHCAjRs38uqrr+Lk5HRf27K0Y/vWrVv58MMP2bJlCy4uLtjb\n2xca48iRI3Fzc+ODDz54SFGKgkgiLyySq6srgYGBuLq6Fmm9wMBAKlas+ICiKtjvv/9OSEgIgwYN\nMsv+HyQnJye2bNlCZGQkkZGRd32Jd/Dgwej1+gJH7oUQ4l5UqVIl36uXxVnaOH/+fHQ6HYMHD77v\nbZmj5LIg3bt358CBAyQmJnLy5El8fHwKXcfOzo7+/fuzfft2QkJCHkKUoiCSyAujnDq89u3bc+XK\nFQYMGIC3tzeOjo4EBQWxevXqXOsopfj2229p0aIFLi4uODk50bhxY+bMmUNWVlau/seOHeP555+n\nSpUqODg44O3tTYMGDRg9ejQJCQnGfnfWyO/cudNYf5kTZ87P7UllfjXyiYmJTJgwgZo1a+Lg4ICH\nhwcdO3Zk48aNBX4OMTExDB8+HF9fX+zt7albty5LlizJ8/P79ttvAXj22WdztWVkZDB//nyaNGmC\nl5cXjo6O+Pn50b17d9atW1ek9wiwatUqmjRpgqOjI2XLlmXQoEFERkbmGVdxsLGxoUuXLpQtW7ZI\n6zVv3hw/Pz8WL15scScwIR4V+/fvR6fT8eSTT+bbp2nTplhZWXHhwgXjsh07dvDkk0/i7e2NnZ0d\n/v7+jB49mqioqLved1HPEQBXrlxhzJgxBAYG4ujoSJkyZWjatCmTJ082WefOGvl27doxbdo0AIYO\nHWpyDL1w4QLvv/8+Op0u36u2ISEh6HQ62rRpY1yWkJDAmjVraN68OZUrV861zrlz5xgxYgTVq1c3\nxlq7dm2GDRvGpUuXABgyZAgvvvgiAFOnTjWJa/fu3cZtJSYmMnbsWCpWrIiDgwO1atVi7ty5GAyG\nu/24iywwMJCgoCDs7OyKtN5zzz0HwPfff/8gwhJFYG3uAITliY2NpXXr1pQpU4aXXnqJmzdvsnr1\nap599lkiIyNNagQHDx7MihUrqFixIsOGDcPGxoaNGzfy9ttvs23bNjZt2oSVlRWQncQ3b94cKysr\nevToQdWqVUlKSuLcuXMsXbqUt956K9cIfM4lvipVqjB58mSmTp2Km5sbb775prFPw4YN81wnR3x8\nPK1bt+bkyZM0btyYMWPGEBsby5o1a+jVqxdTp07Ns447Li6OVq1aYWdnR79+/UhPT2f16tW8+OKL\n6HQ6k5F3pRTbt2/Hx8eH6tWr59rWkCFDWLVqFXXq1OGFF17AycmJK1eu8Ndff7Fu3Tp69+591+9x\n7ty5vPXWW7i7uzNo0CA8PDzYunUrrVq1ws3NLf8/rJm0atWK4OBgjh07RoMGDcwdjhCPnBYtWlCz\nZk1+/fVXoqOj8fb2Nmk/efIkhw4dol27dvj5+QHw8ccf8/777+Pp6ckTTzxBuXLlOHr0KF999RUb\nN25k//79VKhQodB9F+UcAfD333/TtWtXbt68Sdu2benTpw9paWmcPn2aWbNm5TpP3H68Hzp0KJqm\nsWvXLnr16mVy3HR3d+eVV17h008/ZdGiRXleOc25cjhy5Ejjst27d5OZmUnr1q1z9b969SpBQUEk\nJibSrVs3nn76aTIyMrhw4QJr165lwIABVKpUid69exMfH8+GDRto164d7dq1M24j5/NOT0+nY8eO\n/P3339SvX5+BAwcSFxfHRx99xM6dOwv9nB+2oKAgbGxs+O2338wdilBC/CsiIkJpmqY0TVPPPvus\nSVt4eLhyd3dXdnZ26sKFC0oppVatWqU0TVMNGzZUiYmJxr4ZGRmqY8eOStM0NXv2bOPysWPHKk3T\n1IYNG3LtOykpSaWnpxtfL168WGmappYuXWrST9M0VaVKlXzfg6Zpqn379ibLXnnlFaVpmho2bJjJ\n8suXLytfX1+l0+nUwYMH8/wcXn75ZWUwGIxtp06dUtbW1qp27dom2zp9+rTSNE117949V0xxcXFK\n0zQVFBSk9Hp9rvYbN27c9XuMiIhQNjY2ysPDQ0VERBiXGwwG1a9fP6VpmtLpdLnWmzx5cpF+1q9f\nn+f+b9+epmlq0aJFBfZTSql58+YpTdPU/PnzC+0rhHgwPv74Y6Vpmpo7d26utnfeecfkeLtr1y6l\naZpq2bKlio+PN+m7fPlypWmaevrpp02WP/bYY7mOPUU9R6Snpyt/f3+l0+nU8uXLc8UZFRWlsrKy\njK/9/PxyHStzjk13njty9OjRQ2mapo4dO2ayPDU1VXl4eChvb2+VkZFhXP7uu+8qTdPU6tWrc23r\niy++UJqmqc8//zxXW0ZGhkpKSjK+zjmnTZ06Nc+4pk+frjRNU7179zZZfuHCBeXl5aU0TVNDhw41\naTt8+HCRj+3nz5/Pc/85/Pz8lE6nMzkf56dhw4ZKp9Pl+n9EPFySyAujnATWxsYmz3/s48ePV5qm\nqenTpyullHr88ceVpmlqy5YtufoeO3ZMaZqmatSoYVyWk8hv3bq10FiKK5HPyMhQjo6OytnZWcXE\nxOTqP3/+fKVpmhoxYoRxWc7n4OzsbHLyydG2bVul0+lUcnKycdnWrVvz/LKglFLx8fFK0zTVqlWr\ngt/0XbzHjz76SGmapiZMmJCrLSIiQllZWeWZyOck+DlfUAr60el0uU4YdypKIp9zMn/nnXcK7SuE\neDAiIyOVtbW1atiwocnyrKws5evrq1xcXIzHtD59+ihN09Tx48fz3FajRo2UtbW1yfExr0S+qOeI\n//73v0rTNNWjR4+7ek/3kshv3rxZaZqmRo8ebbJ86dKleR6nnnvuOaVpmtqzZ0+ubeWcP+7mOFhY\nIl+tWjVlZWWlzpw5k6tt2rRpeSbyS5Ysuatj+u3H9l27dhUYZ1ES+a5duypN09TJkycL7SseHKmR\nF7lUrlzZeLnvdm3btgXgyJEjABw6dAhN0/KsSa9Xrx7e3t6EhYWRkpICZNeOW1lZ0atXLwYOHMji\nxYsf+I0yISEhpKamUq9ePcqUKZOr/fHHHwfg8OHDudqqV6+Os7NzruWVKlVCKUVsbKxxWc5c6R4e\nHrn6u7q60rNnT/bt20f9+vWZMmUKv/32G0lJSUV+P4cOHQLgsccey9Xm7+9PpUqV8lzPYDCg1+sx\nGAyF/uj1+mKte8z53G/cuFFs2xRCFI2vry+dOnXi6NGjHD161Lh827ZtXLt2jb59++Lo6AjAH3/8\ngbW1NT/99BNTpkzJ9ZOeno5er+fMmTMF7rOo54j9+/cD0K1bt+J627l07dqVgIAAVqxYYdwvZJfV\n6HQ6RowYYdK/oGP7k08+ibOzM6+++ip9+vTh66+/5ujRo0W+HygxMZHw8HDKlSuXZ2lmzrn3ToMH\nD76rY/rtx/b8tnUv5NhuGSSRF7nkd0NjzvL4+Hjjf93c3PK9SSZnisKc/kFBQezdu5dOnTqxbt06\nhg0bRu3atQkICHhgs5rk7LtcuXJ5tucsj4uLy9Xm7u6e5zrW1tm3luj1euMyBwcHANLS0vJc58cf\nf2Tq1KlkZmYybdo0OnfujKenJ3379jW5uawwOe+nsL+RJUlNTQVufUZCCPPIuWn+9jnWc34fMmSI\ncVlMTAxZWVlMnTqVadOm5fo5ffo0mqaRnJxc4P6Keo7IOQ7fTe39vdI0jREjRpCQkMDKlSsBOH78\nOH/++ScdOnSgatWqJv0LOrZXrlyZgwcP0rdvX3bu3MmoUaNo1KgR5cuXZ8aMGXd9k2pJPK6DHNst\nhdzsKnLJb0aCnOU5N1S6ubkRFxdHenp6ngfqq1evmvSH7FlMNmzYQFZWFocOHeJ///sfX375JSNH\njsTR0ZGBAwcW63vJ2fe1a9fybM8rxnuRM2VXfk8xtbe3Z+LEiUycOJGrV6+yZ88egoODWbt2LSdP\nnuT48ePGLwgFyYkzKiqKevXq5WrP7283ZcqUu3wn2Ro1asRTTz1VpHXyk/OZ3M20ZkKIB+epp57C\nw8OD4OBgZs+eTUJCAhs2bCAgIMBkpNbNzY2srKw8BziKoqjniJzBk8uXL9/XfgszbLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x729e198>"
+       "<matplotlib.figure.Figure at 0x73997b8>"
       ]
      },
      "metadata": {},
@@ -1289,9 +1295,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b73cf8>"
+       "<matplotlib.figure.Figure at 0x75478d0>"
       ]
      },
      "metadata": {},
@@ -1299,9 +1305,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x882bef0>"
+       "<matplotlib.figure.Figure at 0x88d88d0>"
       ]
      },
      "metadata": {},
@@ -1309,9 +1315,9 @@
     },
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72e0e80>"
+       "<matplotlib.figure.Figure at 0x9a377f0>"
       ]
      },
      "metadata": {},
@@ -1319,9 +1325,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99bcda0>"
+       "<matplotlib.figure.Figure at 0x8870240>"
       ]
      },
      "metadata": {},
@@ -1329,9 +1335,9 @@
     },
     {
      "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9baea58>"
+       "<matplotlib.figure.Figure at 0x9a7ce80>"
       ]
      },
      "metadata": {},
@@ -1402,9 +1408,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEkCAYAAADti70NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAADoCAYAAAAt1mh2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99fd940>"
+       "<matplotlib.figure.Figure at 0x8870f98>"
       ]
      },
      "metadata": {},
@@ -1563,9 +1569,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72c15f8>"
+       "<matplotlib.figure.Figure at 0x87716d8>"
       ]
      },
      "metadata": {},
@@ -1594,9 +1600,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAD+CAYAAABYxuEeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b781d0>"
+       "<matplotlib.figure.Figure at 0x9c452b0>"
       ]
      },
      "metadata": {},
@@ -1651,9 +1657,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8U9X7B/DPTUe60r0H3ZQ9pKyyQaZQBARUEApqVRAF\nBwoiFEWU8QWxzB+oVBRURIaKiLKHLJmlpYzS0j2T7jZtcn5/hOT2knRQ2iZtn/frxYvcc9dpxs2T\nc59zDscYYyCEEEIIIYQ0KSJ9V4AQQgghhBDy+CiQJ4QQQgghpAmiQJ4QQgghhJAmiAJ5QgghhBBC\nmiAK5AkhhBBCCGmCKJAnhBBCCCGkCaJAXs+OHz8OkUiEpUuX6rsqhBBCSLNSl+/YiIgIiEQinDx5\nsgFrptvAgQMhElFoRmqP3i0NTH0RmTFjRrXbcRzXSDWqHfXF5MGDB/quCiEGpbafaUKI4TC079jq\nNKW6Ev0z1ncFWoqqPpg9e/bErVu34Ojo2Mg1qhldTAipGn0+CDF8hvwdS0h9oEC+kVQ1ga65uTla\nt27dyLWpHcZYlfUmpKWjzwYhhs+Qv2MJqQ+UWlPJ5cuX8fzzz8Pd3R1isRju7u6YNm0a7t27p7Vt\nZmYm5s+fjzZt2sDKygo2NjZo3bo1pkyZguvXrwNQ5dkNHjwYABAVFQWRSKT5FxUVBaDq/D11aktC\nQgLWr1+Pdu3awdzcHL6+vvj888812+3evRs9e/aElZUVXFxcMGfOHJSWlmrVd9++fZg6dSpat24N\nKysrWFlZoVu3bli3bh2USqVg28q5gb6+vpo6+/r6CrbLy8vD4sWL0aFDB1haWsLa2hr9+vXDL7/8\novP5/e6779CnTx84OzvD3NwcXl5eGDJkCLZt21bt6wIAX3zxBUQiEdasWaNzfW5uLsRiMfz9/TVl\nBQUFWLZsGTp27AhbW1tIJBL4+flhwoQJOHHiRI3nBICwsDCIRCKcOHECu3btQrdu3WBpaQkPDw+8\n++67kMvlAICjR49i0KBBsLa2hq2tLV566SXk5ubqPGZ6ejrmzp2LwMBAmJubw97eHsOHD8fRo0e1\nts3Pz8eqVaswePBgeHp6QiwWw9nZGaGhofj33391Hv/UqVMIDQ2Fl5cXzMzM4OLigu7du+O9997T\n+bfpSp9KSEjQmT5S+fnYsWMHunfvDisrK3Tt2lWzzeO8Lyqnqdy7dw/PPfccHBwcYG1tjeHDh+Pm\nzZsAgKysLISHh8Pd3R3m5ubo3r07jh8/rvPvVyqV2LZtG/r06QMbGxuYm5ujY8eO+OKLL1BeXq61\nvfq9XVxcjPfffx+tWrWCmZkZAgMDsXLlSsG2tflMA0/2XiekOVJfUwYNGoTU1FTMnDkTbm5uMDY2\nxv79+wEAx44dQ2hoKJycnCAWi+Hj44PZs2cjIyND63jx8fF47bXXEBgYCAsLC9jb26Ndu3Z4+eWX\nkZSUpNmuuhz5//77DyNGjIBEIoGNjQ2GDh2Kc+fOVVv/qlLqqrqebt++HRMmTICfnx8sLCxgY2OD\nvn37YseOHbV+7gC6ppCqUYv8Qz/88APCwsJgZmamCYLu3LmDXbt24bfffsPx48fRuXNnAEBxcTFC\nQkIQHx+Pp59+GqGhoQCABw8e4MiRIxgyZAg6deqEQYMGITExEVFRUejSpQueffZZzfkqBz5A1bfp\n33vvPZw6dQpjxozB0KFDsXv3bnz00UeoqKiARCLB4sWLMW7cOPTt2xe//fYbNmzYAIVCgY0bNwqO\ns2DBAhgZGaF3797w8PBAXl4ejhw5gnnz5uHChQv44YcfNNsuWbIE27dvR2JiIubOnQtbW1sA0PwP\nACkpKRg0aBDu3r2L/v37Y/jw4SgsLMQff/yBSZMmYcmSJViyZIlm+4ULF+KLL76Ar68vJk2aBFtb\nW6Snp+Pq1avYsWMHXnnllWpfn2nTpmHRokWIiorCO++8o7V+165dKC8vx/Tp0wGoWktHjBiBf//9\nFz179sTLL78MU1NTJCcn4/Tp0zhy5AgGDBhQ7Tkri4yMxOHDhzFu3DgMHDgQBw4cwNq1ayGTyTBq\n1Ci89NJLCA0NxWuvvYZ//vkHP/zwA3JycnDw4EHBcW7cuIGhQ4ciKysLw4cPx7hx45CdnY19+/Zh\n6NCh2LZtm+CLIiYmBosWLcKAAQMwZswY2NnZITExEQcOHMCff/6JAwcOYOTIkZrtDx06hGeeeQY2\nNjYIDQ2Fp6cnpFIpbt++jcjISKxcuVLQkaqm9JCq1q9evRpHjhzB2LFjMXToUM0Pmsd9X6glJCSg\nV69e6Ny5M15++WXcvHkTf/75JwYNGoQzZ85gxIgRcHR0xAsvvICUlBTs3r0bI0eOxO3bt+Hl5aU5\nTkVFBcaPH4/ff/8dQUFBmDJlCszMzHD8+HEsXLgQR44cwaFDh2BkZCQ4f3l5OYYNG4a0tDQ888wz\nMDY2xt69e/Hhhx+itLQUixcvBoBafaaf9L1OSHOWk5ODkJAQ2NraYvLkyVAqlbC3t8eKFSuwYMEC\nODg44JlnnoGrqyuuXbuGTZs24cCBAzh37hw8PDwAAGlpaejevTsKCgowcuRITJgwAXK5HImJifj1\n118xZcoUwXUB0L6WnT17Fk8//TTKy8sxfvx4BAYG4tq1axg4cKDmx7ou1V0zda2bNWsWOnTogIED\nB8LNzQ3Z2dk4ePAgpk+fjlu3buGzzz6r8TmjawqpFiPszp07TCwWs4CAAJaamipYd/z4cWZsbMy6\ndeumKTtw4ADjOI7NmzdP61hKpZLJZDLB/hzHsRkzZug897FjxxjHcWzp0qWC8gEDBjCO41hgYCDL\nzMzUlCckJDBTU1NmZWXFXFxc2N27dzXr8vLymJOTExOLxYJ9GGMsPj5eZ12nT5/OOI5j586d03n+\nxMREnfUeMmQIMzIyYj/++KOgPD8/nz311FNMJBKxa9euacrt7e2Zp6cnKy4u1jpWTk6OznM8auTI\nkYzjOHblyhWtdd27d2dGRkYsISGBMcbY9evXGcdxbNy4cTqPVdtzqp8fBwcHdu/ePU25+rk2MjJi\njo6O7Pz585p1crmcdejQgXEcx65evaopr6ioYK1bt2bm5ubs5MmTgvOkpaUxLy8vZmFhIXjt8vLy\ndNY1OTmZubu7szZt2gjKx48fzziOEzz3arm5uTr/Nl2v8f3793W+b9X7WFlZ6TzH474v1O9/juPY\nmjVrBPuEh4czjuOYvb09mzt3rmDd8uXLdX4GP/30U8ZxHJszZw5TKpWacqVSqTleZGSkYB/1+Z95\n5hlWWlqqKc/MzGS2trbM1taWlZeXa8pr+kzXx3udkOZGfU3hOI5Nnz6dKRQKzboTJ04wjuNYSEgI\ny8vLE+y3Y8cOxnEcmzBhgqbsq6++YhzHsXXr1mmdRy6Xs8LCQs2yru9YpVLJgoKCmEgkYr/++qtg\n/w0bNjCO45hIJGInTpzQqn9Vn/uqrqe6vnvlcjkbMmQIMzY2ZsnJyYJ1AwYMYCKRSFBG1xRSHUqt\nAbBp0ybI5XKsXbsWbm5ugnXqltDLly8jNjZWsM7MzEzrWBzHwcbGRrPMnjCPdtGiRXByctIse3t7\no1+/figqKsKsWbMEqSTW1tYYPXo05HI5bt26JTjOo2kx6rq+9dZbAIC///671nW6ceMGjh49imef\nfRaTJ08WrJNIJIiIiABjTNDKz3EcTE1NtVpCAcDe3r5W5w0LCwOgulVZWUxMDC5duoT+/fvD29tb\nsE7Xa/Q451R766234Ofnp1m2trZGaGgolEolxowZgx49emjWmZiYYNKkSQCgSbMCgIMHD+LOnTuY\nNWsW+vXrJzi+q6sr3n//fZSUlAhSUKytrXXW1cPDAxMmTEBcXBySk5O11uv6u+3s7B7jL65eeHg4\nOnXqJCiry/tCzc/PD/PmzROUvfTSSwBUreXLly8XrJs6dSoA4Nq1a5oypVKJdevWwcXFBV9++aWg\ndYzjOKxYsQIcx+H777/XOj/Hcfjqq68gFos1ZU5OTggNDUVeXh5u376tKa/pM10f73VCmiuxWIzV\nq1cL7gyuW7cOALBlyxZYW1sLtp86dSq6dOmC/fv3o6ioSLBO13XOxMQElpaW1dbh7NmzuH37NkJC\nQjBu3DjBujfeeAMBAQH11gdG13eviYkJZs2aBYVCoTOl8lF0TSHVodQaAGfOnAEAnDhxApcuXdJa\nr87Pi42NRdu2bTFw4EB4eHhgxYoVuHTpEkaNGoU+ffrgqaee0vlBexKPpuAAqqCvqnXu7u4AoBXc\n5eTkYNWqVTh48CDi4+NRXFwsWJ+SklLrOqmfr7y8PERERGitz8rKAgDBD58pU6YgMjISbdu2xcSJ\nE9G3b1+EhIQ81kXo2Wefha2tLXbu3InVq1fD2Fj19lXnJqsDfQBo3749unTpgh9//BEJCQkYO3Ys\n+vTpg+Dg4CqD++o87uug/kFY+XVQP2+JiYk6n7c7d+4AgNYPxjNnzmDdunX4999/kZWVpUljUUtJ\nSYGnpycA1Zfe3r170bNnT0yaNAkDBw5E79694ePjU8u/tHYq/3CpXE/g8d4Xauq0tcrUz6+6L0Fl\nup7f27dvIycnB/7+/vjkk0901tvMzAwxMTFa5TY2NoIfamrq2/NSqVTn8XSpj/c6Ic2Vj4+P1ggy\nZ86cgbGxMfbs2aOzL01ZWRkUCgXi4uLw1FNPYezYsfjoo4/w5ptv4tChQxg2bBh69+6NTp061Wo0\nqcuXLwOAzvRKjuPQp08f3L17t45/odCDBw+wYsUKHDlyBElJSSgpKRGsT01NrfEYdE0h1aFAHqog\nFwD+97//VbkNx3Ga1gCJRILz589j6dKlOHDgAP755x8AqhzymTNn4tNPP9UKPOqqcLine truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b44c88>"
+       "<matplotlib.figure.Figure at 0x8832ac8>"
       ]
      },
      "metadata": {},
@@ -1677,9 +1683,13 @@
    "source": [
     "## MMAE\n",
     "\n",
-    "The core idea of using several filters to detect a maneuver is sound, but the estimate is jagged when we abruptly transition between the filters. Choosing one filter over the other flies in the face of this entire book, which uses probability to determine the *likelihood* of measurements and models. We don't choose *either* the measurement or prediction, depending on which is more likely, we choose a *blend* of the two in proportion to their likelihoods. We should do the same here. This approach is called the **Multiple Model Adaptive Estimator**, or MMAE.\n",
+    "The core idea of using several filters to detect a maneuver is sound, but the estimate is jagged when we abruptly transition between the filters. Choosing one filter over the other flies in the face of this entire book, which uses probability to determine the *likelihood* of measurements and models. We don't choose *either* the measurement or prediction, depending on which is more likely, we choose a *blend* of the two in proportion to their likelihoods. We should do the same here. This approach is called the *Multiple Model Adaptive Estimator*, or MMAE.\n",
     "\n",
-    "In the **Designing Kalman Filters** chapter we learned the **likelihood function** $\\mathcal{L} = \\frac{1}{\\sqrt{2\\pi S}}\\exp [-\\frac{1}{2}\\mathbf{y}^\\mathsf{T}\\mathbf{S}^{-1}\\mathbf{y}]$, which tells us how likely a filter is to be performing optimally given the inputs. We can use this to compute the probability that each filter is the best fit to the data. If we have N filters, we can compute the probability that filter i is correct in relation to the rest of the filters with\n",
+    "In the **Designing Kalman Filters** chapter we learned the *likelihood function* \n",
+    "\n",
+    "$$\\mathcal{L} = \\frac{1}{\\sqrt{2\\pi S}}\\exp [-\\frac{1}{2}\\mathbf{y}^\\mathsf{T}\\mathbf{S}^{-1}\\mathbf{y}]$$\n",
+    "\n",
+    "which tells us how likely a filter is to be performing optimally given the inputs. We can use this to compute the probability that each filter is the best fit to the data. If we have N filters, we can compute the probability that filter i is correct in relation to the rest of the filters with\n",
     "\n",
     "$$p_k^i = \\frac{\\mathcal{L}_k^ip_{k-1}^i}{\\sum\\limits_{j=1}^N \\mathcal{L}_k^jp_{k-1}^j}$$\n",
     "\n",
@@ -1699,9 +1709,9 @@
    "outputs": [
     {
      "data": {
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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9b46f98>"
+       "<matplotlib.figure.Figure at 0x8779400>"
       ]
      },
      "metadata": {},
@@ -1774,9 +1784,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72e04a8>"
+       "<matplotlib.figure.Figure at 0x99b9898>"
       ]
      },
      "metadata": {},
@@ -1812,7 +1822,7 @@
     "\n",
     "This naive approach leads to combinatorial explosion. At step 1 we generate $N$ hypotheses, or 1 per filter. At step 2 we generate another $N$ hypotheses which then need to be combined with the prior $N$ hypotheses, which yields $N^2$ hypothesis. Many different schemes have been tried which either cull unlikely hypotheses or merge similar ones, but the algorithms still suffered from computational expense and/or poor performance. I will not cover these in this book, but prominent examples in the literature are the generalized pseudo Bayes (GPB) algorithms.\n",
     "\n",
-    "The **interacting multiple Models** algorithm was invented by Blom [4] to solve the combinatorial problem of multiple models. The IMM algorithm uses $N$ Kalman filters to represent the various possible modes of the system. It models the transition between these modes as a **Markov chain**, as in this illustration:"
+    "The *Interacting Multiple Models* (IMM) algorithm was invented by Blom [4] to solve the combinatorial problem of multiple models. The IMM algorithm uses $N$ Kalman filters to represent the various possible modes of the system. It models the transition between these modes as a *Markov chain*, as in this illustration:"
    ]
   },
   {
@@ -1826,7 +1836,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEuCAYAAAB7xO7rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9871f98>"
+       "<matplotlib.figure.Figure at 0x7515978>"
       ]
      },
      "metadata": {},
@@ -1846,13 +1856,13 @@
     "\n",
     "The algorithm is not sensitive to the exact numbers, and you will typically use simulation or trials to choose appropriate values. However, these values are quite representative.\n",
     "\n",
-    "We represent Markov chains with a **transition probability matrix**, which we will call $p$. For the Markov chain in the illustration we would write\n",
+    "We represent Markov chains with a *transition probability matrix*, which we will call $p$. For the Markov chain in the illustration we would write\n",
     "\n",
     "$$p = \\begin{bmatrix}.97 & .03\\\\.05 & .95\\end{bmatrix}$$\n",
     "\n",
     "This should be clear, but formally $p_{ij}$ is the probability of transitioning from state $i$ to state $j$.\n",
     "\n",
-    "Next, the algorithm defines a vector of **mode probabilities**. This is merely a list containing the probability that the system is in any given mode. In the example above we have two modes straight and turn, so we will have a vector of two elements. In the absence of any any additional information we start by assigning equal probability to each mode:\n",
+    "Next, the algorithm defines a vector of *mode probabilities*. This is merely a list containing the probability that the system is in any given mode. In the example above we have two modes straight and turn, so we will have a vector of two elements. In the absence of any any additional information we start by assigning equal probability to each mode:\n",
     "\n",
     "$$\\mu = \\begin{bmatrix} 0.5 & 0.5\\end{bmatrix}$$\n",
     "\n",

Appendix-A-Installation.ipynb

@@ -25,7 +25,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -117,6 +117,7 @@
        "    h5 {\n",
        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
        "    }\n",
+       "\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 200;\n",
        "        font-style: normal;\n",
@@ -265,7 +266,7 @@
        "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -442,7 +443,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -484,7 +485,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -498,7 +499,7 @@
        "\\phi"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -520,7 +521,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -537,7 +538,7 @@
        "2⋅╲╱ φ "
       ]
      },
-     "execution_count": 4,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -555,7 +556,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -570,7 +571,7 @@
        "(\\phi - 1)⋅⎝\\phi  + 1⎠"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -588,7 +589,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -603,7 +604,7 @@
        "\\phi  - 3⋅\\phi - 4"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -621,7 +622,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -635,7 +636,7 @@
        "8"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -654,7 +655,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -668,7 +669,7 @@
        "2⋅t + 2"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -691,7 +692,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -709,7 +710,7 @@
        "⎣╲╱  x  + z       ╲╱  x  + z  ⎦"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -740,7 +741,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -767,7 +768,7 @@
        "⎣    6           2                 ⎦"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }

book_format.py

@@ -67,7 +67,7 @@ def equal_axis():
 
 
 def reset_axis():
-    pylab.rcParams['figure.figsize'] = 11, 4
+    pylab.rcParams['figure.figsize'] = 11, 3
 
 def set_figsize(x=11, y=4):
     pylab.rcParams['figure.figsize'] = x, y
@@ -135,7 +135,6 @@ def load_style(directory = '.', name='code/custom.css'):
     if version[0] > 1 or (version[0] == 1 and version[1] >= 5):
         style["axes.prop_cycle"] = "cycler('color', ['#6d904f','#013afe', '#202020','#fc4f30','#e5ae38','#A60628','#30a2da','#008080','#7A68A6','#CF4457','#188487','#E24A33'])"
         style.pop("axes.color_cycle", None)
-
     plt.rcParams.update(style)
     reset_axis ()
     np.set_printoptions(suppress=True)

code/book_plots.py

@@ -101,17 +101,6 @@ def plot_measurements(xs, ys=None, color='k', lw=2, label='Measurements',
     """
 
     plt.autoscale(tight=True)
-    '''if ys is not None:
-        plt.scatter(xs, ys, marker=marker, c=c, s=s,
-                    label=label, alpha=alpha)
-        if connect:
-           plt.plot(xs, ys, c=c, lw=1, alpha=alpha)
-    else:
-        plt.scatter(range(len(xs)), xs, marker=marker, c=c, s=s,
-                    label=label, alpha=alpha)
-        if connect:
-           plt.plot(range(len(xs)), xs, lw=1, c=c, alpha=alpha)'''
-
     if lines:
         if ys is not None:
             plt.plot(xs, ys, color=color, lw=lw, ls='--', label=label, **kwargs)

code/custom.css

@@ -4,6 +4,9 @@
 @import url('http://fonts.googleapis.com/css?family=Arimo');
 @import url('http://fonts.googleapis.com/css?family=Fira_sans');
 
+.CodeMirror pre {
+    font-family: 'Source Code Pro', Consolas, monocco, monospace;
+}
     div.cell{
         width: 900px;
         margin-left: 0% !important;
@@ -23,7 +26,7 @@
 	
     div.input_area {
         background: #F6F6F9;
-        border: 1px solid #586e75;
+        border: 1px solid #586e75;      
     }
 
     .text_cell_render h1 {
@@ -82,6 +85,7 @@
     h5 {
         font-family: 'Open sans',verdana,arial,sans-serif;
     }
+
     .text_cell_render h5 {
         font-weight: 200;
         font-style: normal;
@@ -116,7 +120,8 @@
 }
 
     code{
-      font-size: 70%;
+        font-size: 6pt;
+
     }
     .rendered_html code{
     background-color: transparent;
@@ -209,7 +214,8 @@
 <script>
     MathJax.Hub.Config({
                         TeX: {
-                           extensions: ["AMSmath.js", "autobold.js"]
+                           extensions: ["AMSmath.js"],
+                           equationNumbers: { autoNumber: "AMS", useLabelIds: true}
                            },
                 tex2jax: {
                     inlineMath: [ ['$','$'], ["\\(","\\)"] ],
@@ -217,7 +223,7 @@
                 },
                 displayAlign: 'center', // Change this to 'center' to center equations.
                 "HTML-CSS": {
-                    scale:100,
+                    scale:95,
                         availableFonts: [],
                         preferredFont:null,
                         webFont: "TeX",

pdf/book.tplx

@@ -1,10 +1,12 @@
 % Inherit from report
-((* extends 'report.tplx' *))
+%((* extends 'report.tplx' *))
  
+((* set cell_style = 'style_ipython.tplx' *))
  
 ((* block docclass *))
 \documentclass{book}
 \setcounter{chapter}{0}
+\raggedbottom
 ((* endblock docclass *))
  
 ((* block preamble *))
@@ -14,7 +16,9 @@
 \title{Kalman and Bayesian Filters in Python}
 \author{Roger R Labbe Jr}
 ((* endblock title *))
- 
+
 ((* block markdowncell scoped *))
+\setlength{\parindent}{0em}
+\setlength{\parskip}{0.5em}
     ((( cell.source | citation2latex | strip_files_prefix | markdown2latex(extra_args=["--chapters"]) )))
 ((* endblock markdowncell *))

pdf/book6x9.tplx

@@ -1,7 +1,6 @@
 % Inherit from report
 ((* extends 'report.tplx' *))
  
-((* set cell_style = 'style_ipython.tplx' *))
 
 ((* block margins *))
 \geometry{verbose,papersize={6in, 9in}, tmargin=.5in,bmargin=.5in,lmargin=.75in,rmargin=.75in}
@@ -11,7 +10,11 @@
 ((*- endblock in_prompt -*))
 
 ((* block input scoped *))
-    ((( cell.source | highlight2latex | indent(3) )))
+$\fontsize{5}{1.5}
+\selectfont$
+$\noindent\rule{8cm}{0.4pt}$
+    ((( cell.source | highlight2latex | indent(0) )))
+$\noindent\rule{8cm}{0.4pt}$
 ((* endblock input *))
 
 ((* block output_prompt *))
@@ -21,10 +24,11 @@
 ((* block docclass *))
 \documentclass{book}
 \setcounter{chapter}{0}
+\raggedbottom
 ((* endblock docclass *))
  
-((* block preamble *))
-((* endblock preamble *))
+((* block document *))
+((* endblock document *))
  
 ((* block title *))
 \title{Kalman and Bayesian Filters in Python}
@@ -32,6 +36,10 @@
 ((* endblock title *))
  
 ((* block markdowncell scoped *))
+\fontsize{10}{1.5}
+\selectfont
+\setlength{\parindent}{0em}
+\setlength{\parskip}{0.5em}
     ((( cell.source | citation2latex | strip_files_prefix | markdown2latex(extra_args=["--chapters"]) )))
 ((* endblock markdowncell *))
 

pdf/merge_book.py

@@ -1,6 +1,6 @@
 from __future__ import print_function
 import io
-import IPython.nbformat as nbformat
+import nbformat
 import sys
 from formatting import *
 
@@ -28,10 +28,8 @@ def merge_notebooks(outfile, filenames):
 
 if __name__ == '__main__':
     f = open('book.ipynb', 'w', encoding='utf-8')
-    '''merge_notebooks(
-        ['../00_Preface.ipynb',
-         '../01_g-h_filter.ipynb',
-         '../Appendix_A_Installation.ipynb'])'''
+    '''merge_notebooks(f,
+        ['../02-Discrete-Bayes.ipynb'])'''
 
     merge_notebooks(f,
         ['../00-Preface.ipynb',