Added derivation of Gaussian product from Bayes.

04_One_Dimensional_Kalman_Filters.ipynb

@@ -435,7 +435,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1YAAAEWCAYAAABlmwYuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e3b748>"
+       "<matplotlib.figure.Figure at 0x71310f0>"
       ]
      },
      "metadata": {},
@@ -475,9 +475,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8DOcfB/DPbCTZ3CRpJAiRyEFcdZ+JW+uqFHFUiSso\n6j7iTNG6i6Kt0hJt3epokWrdcZ8lQVDHzxlEDlfOfX5/jEyt3bA5N/i8X6+87MzzzMx3N7Ox331m\nvo8khBAgIiIiIiIio1IZOwAiIiIiIiJickZERERERFQgMDkjIiIiIiIqAJicERERERERFQBMzoiI\niIiIiAoAJmdEREREREQFAJMzogIuNDQUKpUKe/fuNXYoRJQL9uzZA5VKhS+++MLYoRARUQHD5Iyo\ngJMkSfmh3CeEQNOmTaFSqaBSqZCSkpLlfWzduhUNGzaEnZ0dbGxsUKtWLaxYsSIPoqW3Cd/TuevQ\noUNo2bIl7O3tYWlpiUqVKmH+/PnQaDRZ3tf58+cRGBgIJycnWFhYwMfHB6GhoUhKSsqDyImI/iNx\nEmqigi02NhaxsbFwdXWFhYWFscN568ybNw8jR46EmZkZkpKS8OzZM5iZmRm8/aJFizBo0CA4Ojqi\nY8eOMDMzw7p163Dz5k0MHz4cs2bNysPo6U307Nkz3LhxA46OjrC3tzd2OG+FzZs3o127drC0tETH\njh1hb2+PLVu2IDo6Gu3bt8fatWsN3tfRo0fRqFEjpKWloX379nB1dcXOnTtx/Phx1K1bFzt37szS\n3wgioqxgckZE76yoqChUr14dQ4cOxcqVK/G///0vS8nZtWvX4OPjAxsbG5w4cQIlS5YEAMTHx6N6\n9er4999/cfDgQdSqVSsvnwbROy0xMRFlypTBo0ePcODAAVSpUgUAkJycjEaNGuHQoUNYtWoVOnbs\n+Np9paeno0KFCoiOjsbmzZvRqlUrAPIIe2BgIDZs2IBp06Zh9OjRefqciOjdxcsaiTJx+PBhqFQq\ntGnTJtM+1apVg4mJCa5fvw4ASE1NxcKFC9GiRQuUKlUKarUa9vb2aNKkCbZu3ap3H25ubsrldKGh\nofD09IS5uTmGDh0K4L97zvbt26e13aZNm9C1a1d4eXnB2toa1tbWqFq1aqaX8QQFBSn3rq1fvx41\natSAlZUVHBwc0LlzZ9y+fVtvfHFxcZgwYQIqVKgAa2tr2NnZoUKFChg5ciTi4+O1+iYkJGDixIko\nX748rKysYGtri/r162P9+vWZv9BGkpKSorx+oaGhyM73VD/99BNSUlIwcOBAJTEDgMKFC2Ps2LEA\ngO+//z7Hsb54jowdOxZubm5Qq9Xw9PTE1KlTkZqaqrONSqVC6dKlkZiYiCFDhqBUqVIwNTXF/Pnz\nlT6//fabcjmmhYUFypUrh0mTJuHJkyd648jLc2HFihWoW7euchmZq6srGjdujKVLl2r1u3LlCvr2\n7QtPT09YWlrC3t4e5cqVQ69evXDjxo1Xvo5JSUkoUqQIHB0d9b5mADBixAioVCqty1Jz8l77+eef\nUb16dVhZWeH9998HkPk9ZydOnMDgwYNRqVIlODg4wMLCAl5eXhg2bBji4uJ0jrN8+XJlP6dPn0bL\nli1RuHBhWFlZoUGDBjh06JDe55ieno4ffvgB9evXR+HChWFpaQkPDw8EBQUhKipKq69Go8HSpUtR\nt25d5TypUKECpk+fnulrmN/Wr1+PBw8eoFOnTkpiBgDm5uaYOnUqAOC7774zaF979+7FhQsX4Ofn\npyRmgHwJ6syZMwHkznuaiChTgogyVbZsWWFqairu3bun0xYZGSkkSRINGzZU1t25c0eYmJgIPz8/\n0adPHzF27FgRFBQkHBwchCRJYvHixTr7KVWqlJAkSbRs2VIUK1ZM9OrVS4wePVp8//33QgghJk2a\nJCRJEnv37tXazsfHR/j6+opu3bqJkJAQ8dlnnwlvb28hSZLo0qWLznG6d+8uJEkSgYGBQq1Wi44d\nO4pRo0YJPz8/IUmSKFu2rEhOTtba5sqVK0p8VatWFcOHDxfDhw8XrVu3FpaWluKff/5R+t68eVN4\nenoKSZKEv7+/GDZsmAgODhbFixcXkiSJ0NDQrL34eWz06NHCzMxMeQ6lSpUSKpVK5zV4lbp16wpJ\nksThw4d12u7cuSMkSRIlS5bMcawZv4PWrVuL4sWLi8GDB4sRI0YIDw8PIUmSaNu2rc42kiQJFxcX\nUaVKFVGmTBnRv39/MXz4cLFhwwYhhBATJkwQkiQJR0dH0a9fPzFmzBhRpUoVIUmSqFy5snj06JHW\n/vLyXAgJCRGSJAl3d3cxYMAAMW7cONGrVy9RtWpV4efnp/S7ffu2sLe3F6ampqJNmzZi9OjRYujQ\noeLjjz8WhQsXFjt37nzta9mvXz8hSZL47bffdNrS0tKEs7OzsLGxEU+ePFHWZ/e91qpVK2FhYSE6\ndeokQkJCxPDhw4UQQuzevVtIkiS++OILre369u0rihYtKjp27ChGjBghhg0bprw/fXx8dH4ny5Yt\nU45jaWkpmjRpIkaOHCkCAwOFiYmJsLCwENHR0VrbJCcni6ZNmyrnZv/+/UVISIjo0qWLcHZ2FvPn\nz1f6pqamitatWyvH79+/vxg6dKh4//33hSRJokmTJiItLe21r3le++STT4QkSWL16tU6bWlpacLS\n0lKYmZmJlJSU1+5r3LhxQpIkMX36dL3tXl5eQqVSiX///TfHcRMR6cPkjOgVZsyYISRJEnPnztVp\nGzlypJAkSYSFhSnrkpOTxa1bt3T6JiQkiPLlywt7e3vx7NkzrbaMD7yVKlUSsbGxOttmlpxduXJF\np69Go1E+GL6cMGSst7OzE5GRkVptXbp0EZIkibVr12qtr127tpAkSUydOlXvc3r8+LGy3LhxY2Fi\nYqLzASkxMVFUqVJFqFQqrQ/wr7Jx40YxadIkg3+ymvjt27dPmJiYaD2v7CRnjo6OQqVSiYcPH+pt\nt7KyEiqVSud3nlUZ54i3t7eIj49X1j979kzUqFFDSJIkVq1apbWNJElCkiTRrFkzneMfOnRISJIk\nXF1dxZ07d7TaMs6TgQMHaq3Py3PB3t5elChRQjx9+lRn3w8ePFAef/PNN0KSJK0EIkNKSopWDJk5\ncuSIkCRJfPTRRzptW7duFZIkiR49emitz+57zdraWu85n1lydv36daHRaHT6//jjj3oThozk7OW/\nQ0IIsXjxYiFJkvjss8+01mckwq1atdI519PS0kRMTIyyPGXKFCFJkhg0aJBWXBqNRgQHBwtJksSC\nBQt04tXn1KlTWXpPT5o0SVy7ds2gfVerVk1IkiROnjypt93X11eoVCpx4cKF1+6rffv2mSbvQgjR\nsmVLIUmSCA8PNyg2IqKsYnJG9Aq3b98WhQoVEpUrV9Zan5aWJlxcXHS+YX+VOXPmCEmSxL59+7TW\nZ3zw3rJli97tMkvOMnPixAkhSZKYMmWK1vqMD4wTJkzQ2Sbjw+LIkSOVdcePH1eSxtc5c+aMkCRJ\ntGvXTm/7li1bhCRJYtSoUQY9h6CgIOVDpyE/KpXKoP0KIScSbm5uombNmiI9PV1Zn53kzNTUVKhU\nKq39vKhYsWJCpVKJu3fvGrxPfTLOkV9++UWnbceOHUKSJNG0aVOt9Rmvy5kzZ3S26d27t5AkSXz3\n3Xc6bTExMcLCwkLY2NiI1NRUIUTenwsODg7C3d39ta/9ggULMh2Bzopy5coJMzMzcf/+fa31HTp0\nyNX32rBhw/Rul1lylhmNRiNsbW1F48aNtdZnJGf169fX2SY1NVUUKlRIVK9eXVmXlpYm7OzshKWl\npbh58+Yrj5meni4cHR2Fs7Oz3vM7Li5OqFQqUbNmTYOew/Lly7P8njb09+Dp6fnK0aw6depkOsL9\nsoxRxcxGYTO+yNI3SkdElBsKGfuySqKCzMXFBU2bNkV4eDj++ecfVKpUCQCwY8cO3L17F0FBQbC0\ntNTaJioqCrNmzcK+fftw9+5dndLL+u7tkiQJNWrUyFJssbGxmDVrFrZt24YrV67g6dOnWu23bt3S\nu121atV01pUoUQIAtO5rOXz4MACgWbNmr43lwIEDAOT7jEJDQ3Xa79+/D0AuT22IZcuWYdmyZQb1\nzapBgwbh3r17CA8Ph0r15tx2K0kS/P39ddbXr18fAHD69GmdNrVajQoVKuisP3nyJACgUaNGOm1O\nTk6oUKECjh07hkuXLqFs2bJ5fi588sknWLBgAcqWLYsOHTqgXr16qFOnjk4lwzZt2mDs2LEYOHAg\nwsPD0axZM9SuXRsVK1bMUln67t27Y8yYMfj1118xePBgAPK5v2XLFri7u8PPz0+rf3bfa1l9T6em\npmLx4sVYvXo1zp07h8TERK172rLyni5UqBCKFi2q9Z6+cOECEhMTUa1aNRQvXvyVsVy8eBGxsbHw\n8PDA5MmT9fZRq9U4d+6cIU8N3bt3R/fu3Q3qS0T0LmNyRvQaPXr0QHh4OMLCwvD1118DAMLCwgDI\nN/6/6PDhw2jUqBE0Gg0aN26Mtm3bwtbWFiqVCqdOncLmzZuRnJys9zhFixY1OKaMaoDXrl1DzZo1\nERQUBHt7exQqVAhxcXGYP39+pscpXLiwzrpCheQ/Benp6VrHAPDaD3GA/OEVAHbu3ImdO3fq7SNJ\nUqaFJvLL77//jp9//hlz5syBt7e33j4iC4VB7Ozs8PDhQyQkJKBIkSI67QkJCUq/3KDvHFGr1bC1\ntVWO9SInJye9+0lISIAkSXB2dtbb7uLiAuC/cyCvz4W5c+eiTJkyWL58OWbNmoWZM2dCpVKhcePG\nmDVrFipWrAgAKFmyJI4dO4YvvvgC4eHh2LRpEwD5dRk0aBDGjBljUML96aefYty4cLine truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e482e8>"
+       "<matplotlib.figure.Figure at 0x71a3a58>"
       ]
      },
      "metadata": {},
@@ -527,9 +527,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e41cc0>"
+       "<matplotlib.figure.Figure at 0x7128358>"
       ]
      },
      "metadata": {},
@@ -550,9 +550,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x766b710>"
+       "<matplotlib.figure.Figure at 0x7922320>"
       ]
      },
      "metadata": {},
@@ -583,7 +583,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7911438>"
+       "<matplotlib.figure.Figure at 0x7bc16d8>"
       ]
      },
      "metadata": {},
@@ -615,7 +615,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7911668>"
+       "<matplotlib.figure.Figure at 0x7aada20>"
       ]
      },
      "metadata": {},
@@ -651,7 +651,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuAAAADaCAYAAADnoPfrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e1d6d8>"
+       "<matplotlib.figure.Figure at 0x7f13f28>"
       ]
      },
      "metadata": {},
@@ -688,7 +688,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e3b710>"
+       "<matplotlib.figure.Figure at 0x71310b8>"
       ]
      },
      "metadata": {},
@@ -743,9 +743,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "It is not particularly difficult to perform the algebra to derive the equation for multiplying two Gaussians, but I will just present the result. Here the subscript $\\mathtt{z}$ stands for the *measurement*.\n",
-    "$$\n",
-    "N(\\mu_\\mathtt{prior}, \\sigma_\\mathtt{prior}^2)\\times N(\\mu_\\mathtt{z}, \\sigma_\\mathtt{z}^2) = N(\\frac{\\sigma_\\mathtt{prior}^2 \\mu_\\mathtt{z} + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}}{\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2},\\frac{1}{\\frac{1}{\\sigma_\\mathtt{prior}^2} + \\frac{1}{\\sigma_\\mathtt{z}^2}}) $$ \n",
+    "The algebra for this is not extremely hard, but it is messy. It uses Bayes theorem to compute the posterior (new Gaussian) given the prior (old Gaussian) and evidence (the measurement. I've placed the math at the bottom of the chapter if you are interested in the details. Here I will present the results. The subscript $\\mathtt{z}$ stands for the *measurement*.\n",
+    "$$\\begin{aligned}\n",
+    "\\mathcal{N}(\\mu_\\mathtt{posterior}, \\sigma_\\mathtt{posterior}^2) &= \\mathcal{N}(\\mu_\\mathtt{prior}, \\sigma_\\mathtt{prior}^2)\\times \\mathcal{N}(\\mu_\\mathtt{z}, \\sigma_\\mathtt{z}^2) \\\\\n",
+    "&= \\mathcal{N}(\\frac{\\sigma_\\mathtt{prior}^2 \\mu_\\mathtt{z} + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}}{\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2},\\frac{1}{\\frac{1}{\\sigma_\\mathtt{prior}^2} + \\frac{1}{\\sigma_\\mathtt{z}^2}})\n",
+    "\\end{aligned}$$ \n",
     "\n",
     "In other words the result of multiplying two Gaussians is a Gaussian is \n",
     "\n",
@@ -767,7 +769,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -776,7 +778,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2MAAAEWCAYAAADrQU9SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b5a400>"
+       "<matplotlib.figure.Figure at 0x7b3f9e8>"
       ]
      },
      "metadata": {},
@@ -824,7 +826,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
@@ -833,7 +835,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b5a1d0>"
+       "<matplotlib.figure.Figure at 0x7c9d1d0>"
       ]
      },
      "metadata": {},
@@ -877,7 +879,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
@@ -886,7 +888,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAugAAAEWCAYAAAA0KmJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7d0a208>"
+       "<matplotlib.figure.Figure at 0x7d176a0>"
       ]
      },
      "metadata": {},
@@ -967,16 +969,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 111,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEPCAYAAACa3Kh2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEPCAYAAACa3Kh2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x98bbba8>"
+       "<matplotlib.figure.Figure at 0x7e77eb8>"
       ]
      },
      "metadata": {},
@@ -984,6 +986,9 @@
     }
    ],
    "source": [
+    "from IPython.html.widgets import interact, interactive, fixed\n",
+    "import IPython.html.widgets as widgets\n",
+    "\n",
     "def plot_products(mu_1, mu_2, var_1, var_2):\n",
     "    xs = np.arange(0, 20, min(var_1, var_2)/10)\n",
     "    ys = [stats.gaussian(x, mu_1, var_1) for x in xs]\n",
@@ -1023,7 +1028,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -1062,7 +1067,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
@@ -1180,7 +1185,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false
    },
@@ -1199,7 +1204,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false
    },
@@ -1225,7 +1230,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5AAAAESCAYAAACLqzreAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b47940>"
+       "<matplotlib.figure.Figure at 0x7eb06a0>"
       ]
      },
      "metadata": {},
@@ -1237,7 +1242,6 @@
     "np.random.seed(13)\n",
     "pos = (0., 400.)   # gaussian N(0, 400)\n",
     "velocity = 1.\n",
-    "horsey\n",
     "# variance in process model and the RFID sensor\n",
     "process_variance = 1.\n",
     "sensor_variance = 2.\n",
@@ -1275,11 +1279,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtYAAAEgCAYAAACQMzRfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8575978>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "from mkf_internal import show_residual_chart\n",
     "show_residual_chart()"
@@ -1386,7 +1401,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
@@ -1405,9 +1420,9 @@
     },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5wAAAEPCAYAAAAu38sVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5wAAAEPCAYAAAAu38sVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9955128>"
+       "<matplotlib.figure.Figure at 0x9b830f0>"
       ]
      },
      "metadata": {},
@@ -1498,7 +1513,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
@@ -1507,7 +1522,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvwAAAEtCAYAAAB00rSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x78a7630>"
+       "<matplotlib.figure.Figure at 0x7b465f8>"
       ]
      },
      "metadata": {},
@@ -1620,7 +1635,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
@@ -1658,7 +1673,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 25,
    "metadata": {
     "collapsed": false
    },
@@ -1667,7 +1682,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFoCAYAAAAhN0NQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x92ac208>"
+       "<matplotlib.figure.Figure at 0x866c358>"
       ]
      },
      "metadata": {},
@@ -1688,7 +1703,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 26,
    "metadata": {
     "collapsed": false
    },
@@ -1697,7 +1712,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvwAAAEtCAYAAAB00rSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7a70908>"
+       "<matplotlib.figure.Figure at 0x7af7630>"
       ]
      },
      "metadata": {},
@@ -1783,7 +1798,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
    "metadata": {
     "collapsed": false
    },
@@ -1813,7 +1828,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 28,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -1821,9 +1836,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6YAAAEPCAYAAABRDtnkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6YAAAEPCAYAAABRDtnkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x929b4a8>"
+       "<matplotlib.figure.Figure at 0x8587a58>"
       ]
      },
      "metadata": {},
@@ -1833,7 +1848,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvEAAAEjCAYAAAC7Jl5YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a88ef0>"
+       "<matplotlib.figure.Figure at 0x85fb9e8>"
       ]
      },
      "metadata": {},
@@ -1861,7 +1876,7 @@
        "        0.07327415,  0.07327415,  0.07327415,  0.07327415,  0.07327415])"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1966,7 +1981,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "metadata": {
     "collapsed": false
    },
@@ -1984,16 +1999,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 30,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEWCAYAAAAuFoLqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEWCAYAAAAuFoLqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a254a8>"
+       "<matplotlib.figure.Figure at 0x8020b70>"
       ]
      },
      "metadata": {},
@@ -2005,6 +2020,7 @@
     "actual_voltage = 16.3\n",
     "\n",
     "def VKF():\n",
+    "    N = 50\n",
     "    voltage = (14, 1000)\n",
     "    for i in range(N):\n",
     "        Z = volt(actual_voltage, variance)\n",
@@ -2047,16 +2063,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 31,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAucAAAEPCAYAAADh+Gq6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEPCAYAAAAKz9G5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9966128>"
+       "<matplotlib.figure.Figure at 0x9b4fd30>"
       ]
      },
      "metadata": {},
@@ -2105,16 +2121,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 32,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEPCAYAAACTNwgMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtwAAAEPCAYAAABx6xN1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7bfbd68>"
+       "<matplotlib.figure.Figure at 0x7c0e9e8>"
       ]
      },
      "metadata": {},
@@ -2168,16 +2184,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
+   "execution_count": 33,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEPCAYAAACA4Ej4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEPCAYAAACA4Ej4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9959710>"
+       "<matplotlib.figure.Figure at 0x85e1908>"
       ]
      },
      "metadata": {},
@@ -2227,16 +2243,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 88,
+   "execution_count": 34,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEUCAYAAABj3iPhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuQAAAEPCAYAAAAKz9G5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9959630>"
+       "<matplotlib.figure.Figure at 0x7b172e8>"
       ]
      },
      "metadata": {},
@@ -2273,16 +2289,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 90,
+   "execution_count": 35,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAucAAAEPCAYAAADh+Gq6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAucAAAEPCAYAAADh+Gq6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7830b38>"
+       "<matplotlib.figure.Figure at 0x9a81c88>"
       ]
      },
      "metadata": {},
@@ -2335,26 +2351,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 36,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<function __main__.plot_kalman_filter>"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "from IPython.html.widgets import interact, interactive, fixed\n",
-    "import IPython.html.widgets as widgets\n",
-    "\n",
     "def plot_kalman_filter(start_pos, \n",
     "                       sensor_noise, \n",
     "                       velocity, \n",
@@ -2364,7 +2366,7 @@
     "\n",
     "interact(plot_kalman_filter,\n",
     "         start_pos=(-10, 10), \n",
-    "         sensor_noise=widgets.IntSliderWidget(value=5, min=0, max=100), \n",
+    "         sensor_noise=widgets.FloatSliderWidget(value=5, min=0, max=100), \n",
     "         velocity=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n",
     "         process_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.));"
    ]
@@ -2385,16 +2387,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 101,
+   "execution_count": 37,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x786f6d8>"
+       "<matplotlib.figure.Figure at 0x7b46cf8>"
       ]
      },
      "metadata": {},
@@ -2444,8 +2446,10 @@
    "source": [
     "Our equations are linear:\n",
     "\n",
-    "$$\\begin{aligned}new\\_pos &= old\\_pos+dist\\_moved\\\\\n",
-    "new\\_position &= old\\_position*measurement\\end{aligned}$$\n",
+    "$$\\begin{aligned}\n",
+    "\\mathcal{N}(\\mu,\\, \\sigma^2) &= \\mathcal{N}(\\mu,\\, \\sigma^2) + \\mathcal{N}(\\mu_\\mathtt{move},\\, \\sigma^2_\\mathtt{move})\\\\\n",
+    "\\mathcal{N}(\\mu,\\, \\sigma^2) &= \\mathcal{N}(\\mu,\\, \\sigma^2)  \\times \\mathcal{N}(\\mu_\\mathtt{z},\\, \\sigma^2_\\mathtt{z})\n",
+    "\\end{aligned}$$\n",
     "\n",
     "Do you suppose that this filter works well or poorly with nonlinear systems?\n",
     "\n",
@@ -2458,7 +2462,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 38,
    "metadata": {
     "collapsed": false
    },
@@ -2476,20 +2480,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 39,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x8020ef0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "sensor_variance = 30\n",
-    "movement_variance = 2\n",
+    "process_variance = 2\n",
     "pos = (100,500)\n",
     "\n",
     "zs, ps = [], []\n",
     "\n",
     "for i in range(100):\n",
-    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+    "    pos = predict(pos[0], pos[1], velocity, process_variance)\n",
     "\n",
     "    Z = math.sin(i/3.)*2\n",
     "    zs.append(Z)\n",
@@ -2536,7 +2551,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 40,
    "metadata": {
     "collapsed": false
    },
@@ -2554,20 +2569,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 42,
    "metadata": {
     "collapsed": false
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0xa2d7780>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "sensor_variance = 30\n",
-    "movement_variance = 2\n",
+    "process_variance = 2\n",
     "pos = (100,500)\n",
     "\n",
     "zs, ps = [], []\n",
     "\n",
     "for i in range(100):\n",
-    "    pos = predict(pos[0], pos[1], movement, movement_variance)\n",
+    "    pos = predict(pos[0], pos[1], velocity, process_variance)\n",
     "\n",
     "    Z = math.sin(i/3.)*2 + randn()*1.2\n",
     "    zs.append(Z)\n",
@@ -2596,6 +2622,78 @@
     "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Derivation From Bayes Theorem (Optional)\n",
+    "\n",
+    "\n",
+    "I gave you the equations for the product of two Gaussians but did not derive them for you. They are a direct result of applying Bayes rules to Gaussians, however. You don't need to understand this section to read the rest of the book or to use Kalman filters. You may need to know this if you read the literature, much of which is written in terms of Bayes theorem. It's a bit of neat algebra, so why not read on?\n",
+    "\n",
+    "We can state the problem as: let the prior be $N(\\mu_p, \\sigma_p^2)$, and measurement be $z \\propto N(\\mu_z, \\sigma_z^2)$. What is the posterior  x given the measurement z?\n",
+    "\n",
+    "Write the posterior as $P(x|z)$. Now we can use Bayes Theorem to state\n",
+    "\n",
+    "$$P(x|z) = \\frac{P(z|x)P(x)}{P(z)}$$\n",
+    "\n",
+    "$P(z)$ is a normalizing constant, so we can create a proportinality\n",
+    "\n",
+    "$$P(x|z) \\propto P(z|x)P(x)$$\n",
+    "\n",
+    "Now we subtitute in the equations for the Gaussians, which are\n",
+    "\n",
+    "$$P(z|x) = \\frac{1}{\\sqrt{2\\pi\\sigma_z^2}}\\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]$$\n",
+    "\n",
+    "$$P(x) = \\frac{1}{\\sqrt{2\\pi\\sigma_p^2}}\\exp \\Big[-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big]$$\n",
+    "\n",
+    "We can drop the leading terms, as they are constants, giving us\n",
+    "\n",
+    "$$\\begin{aligned}\n",
+    "P(x|z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big]\\\\\n",
+    "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big] \\\\\n",
+    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z-x)^2-\\sigma_z^2(x-\\mu_z)^2]\\Big]\n",
+    "\\end{aligned}$$\n",
+    "\n",
+    "Now we multiply out the squared terms and group in terms of the posterior $x$.\n",
+    "\n",
+    "$$\\begin{aligned}\n",
+    "P(x|z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z^2 -2xz + x^2) - \\sigma_z^2(x^2 - 2x\\mu_z+\\mu_z^2)]\\Big ] \\\\\n",
+    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_z + \\sigma_p^2z) + (\\sigma_p^2z^2+\\sigma_z^2\\mu_z^2)]\\Big ]\n",
+    "\\end{aligned}$$\n",
+    "\n",
+    "The last parentheses do not contain the posterior $x$, so it can be treated as a constant and discarded.\n",
+    "\n",
+    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_z + \\sigma_p^2z)}{\\sigma_z^2\\sigma_p^2}\\Big ]\n",
+    "$$\n",
+    "\n",
+    "Divide numerator and denominator by $\\sigma_p^2+\\sigma_z^2$ to get\n",
+    "\n",
+    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n",
+    "$$\n",
+    "\n",
+    "Proportionality lets us create or delete constants at will, so we can factor this into\n",
+    "\n",
+    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n",
+    "$$\n",
+    "\n",
+    "A Gaussian is just\n",
+    "\n",
+    "$$N(m,\\, s^2) \\propto \\exp\\Big [-\\frac{1}{2}\\frac{(x - m)^2}{s^2}\\Big ]$$\n",
+    "\n",
+    "So we can see that $P(x|z)$ has a mean of\n",
+    "\n",
+    "$$\\mu_\\mathtt{posterior} =\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2}$$\n",
+    "\n",
+    "and a variance of\n",
+    "$$\\begin{aligned}\n",
+    "\\sigma_\\mathtt{posterior} &=\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2} \\\\\n",
+    "&= \\frac{1}{\\frac{1}{\\sigma_p^2}+\\frac{1}{\\sigma_z^2}}\n",
+    "\\end{aligned}$$\n",
+    "\n",
+    "which are the equations that we have been using."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},