Added UKF/EKF comparison.

Had to adjust some examples and rerun notebooks in several places
to account for some code chantes that I made.

08_Nonlinear_Filtering.ipynb

@@ -370,9 +370,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6eae978>"
+       "<matplotlib.figure.Figure at 0x6ec9908>"
       ]
      },
      "metadata": {},
@@ -423,16 +423,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAAFSCAYAAACpCIpkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuwAAAEWCAYAAAA9wcIeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7893eb8>"
+       "<matplotlib.figure.Figure at 0x6eb7a58>"
       ]
      },
      "metadata": {},
@@ -460,7 +460,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -470,19 +470,25 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "6069\n",
-      "0.398942280401\n"
+      "6687\n"
      ]
     },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAACZCAYAAACMhumhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XdYVFf+P/D3ncowwIA0ka5iQbFEbNjAqFGDLUbTjIXd\nuOlGd/NL2STGbxKTNbvZZLNxSzagKcZYEo0FSyKKDRVssROxgCBSh95m7u8Pw8TJACoMc4fh/Xoe\nH5lzzsx9X8GZD2fOnCuIoiiCiIiIiIiaTSZ1ACIiIiKito5FNRERERFRC7GoJiIiIiJqIRbVRERE\nREQtxKKaiIiIiKiFWFQTEREREbUQi2qS3OXLlyGTyTBv3jypoxARERE1C4tqshuCIEgd4bbqfwGI\niYmROgoRERHZEYXUAYgCAgJw7tw56HQ6qaPcVn3h3xZ+ASAiIiLbYVFNklMoFOjWrZvUMe4IL0BK\nREREDeHyD5JcQ2uq586dC5lMhj179mDdunUYNGgQtFotPD098cgjjyA7O9vicaKjoyGTyXDp0iX8\n9a9/Rffu3aHRaBAUFIQ//elPKCsrs7hPU0s53nzzTchkMiQnJwMAVqxYgc6dOwMAdu/eDZlMZvqz\nZMkSa/xTEBERURvFmWqyGw0tqVi+fDm+//57TJkyBTExMUhJScE333yDEydO4Pjx41CpVBb3WbBg\nAfbv34+HHnoIOp0OW7duxQcffIB9+/YhOTnZ4j53upSjf//+WLBgAT766COEhIRg7ty5pr7o6Oi7\nOlciIiJyLCyqya5t374dqamp6NWrl6ntsccew9dff42NGzdixowZFvdJSUnBiRMnEBAQAAB45513\nMH36dGzcuBEffPABXn755WZl6du3L1544QVTUf3GG28076SIiIjI4XD5B9m1559/3qygBoAnnngC\nAHDkyJEG77NgwQJTQQ3cXOLxl7/8BYIgID4+vkV5uKaaiIiIGsKimuxaZGSkRVt9wVxUVNTgfUaN\nGmXR1q1bN/j4+ODixYsoLy+3bkgiIiJq91hUk11zd3e3aFMobq5aMhgMDd7H19e3yfaSkhIrpSMi\nIiK6iUU1OZzc3Nwm293c3Mza6+rqGhxfXFxs3WBERETksFhUk8PZvXu3Rdv58+eRm5uLrl27QqvV\nmto9PDyQmZnZ4OM0tGZbLpcDaHyWnIiIiNonFtXkcD766COzQtlgMOCll14CALO9sAFgyJAhuHLl\nChITE83aP/30Uxw8eNBiuz0PDw8AaLQQJyIiovaJW+qRwxk2bBj69euHmTNnws3NDYmJiTh16hQG\nDRqEP/7xj2ZjX3zxRWzfvh3Tpk3DzJkz4e3tjbS0NKSlpSE2NhabN282G+/i4oKoqCgcOHAAkydP\nRv/+/aFUKjFq1CiMGDHClqdJREREdoQz1WSXBEG444uy/PZ+H374IV555RUkJSXho48+QnFxMRYt\nWoQff/wRSqXSbHx0dDS+//579OvXD+vWrUNCQgLc3d1x6NAhDBgwoMEMX3zxBaZOnYqDBw/inXfe\nweLFi5GUlNTscyUiIqK2TxC58S45iOjoaCQnJ+Py5csICgqSOg4RERG1I5ypJofSnNltIiIiopZi\nUU0OhW+8EBERkRRYVJPDaO46bCIiIqKWsvmaar1eb8vDERFJSqfTSR2BiIhsgDPVREREREQtxKKa\niIiIiKiFJL34i6O8LZqamgoAiIyMlDiJdfB87BvPx/5xmRsRUfvDmWoiIiIiohZiUU1ERERE1EIs\nqomIiIiIWohFNRERERFRC7GoJiIiIiJqIRbVREREREQtxKKa2h2D0SB1BCIiInIwku5TTWQtF6+d\nxsmLh+DvHYo+XYYgp+AqFHIlAn06m8aIoojdxzZh26HVUCmdEHf//0OoXw8JUxMREZGjYFFNbd7V\n3J/xz28Xw2Cs+6XlI1PfkF5jEOjcGwVlOTj47UakZ/0EAKisqUD81vexeO6/oZArJUhNREREjkQQ\nRVG05QFvvdJYenq6LQ9NDirp7BpkFl5o1n2jusaig4sf8kqyAAAh3uFQKzTWjEftUFhYmOlrR7ly\nLBERNY0z1dSm6SsKml1QA8CBnzeb3T5+dQ+6+PSBztkLfroQuDi5tzQiERERtQOSzlQ7ygxOamoq\nACAyMlLiJNZhr+dTW1eDzBsX4ePhD4VciR/TvsX2w2tb7XgqhRpx978EmSCDXC5HF/9ekAnSf7bX\nXr8/zeVo5wM45vMcERE1jTPVZPdEUcSJnw9i3Z5PUVJeBEGQQRSNDY59dMxzCAvojZq6any8/nWU\nVd4sbjRKF3QL6g03bQdk5JzFtbxLtz1uTV01/r3x/0y3R/WLxfRRv7fOSREREZFDYVFNdi8xZTW2\nHf7GdLuxgrqDqzcG9oyGXCYHAPx59j9x9Pxe5OcWw9+9CwYNGgwAyM6/jPdX/wkGw80PNioVKmhU\nWpRUFDWZY8/xzejTZQjCAnpb47SIiIjIgbCoJruWU3AV2w+vue04tUqDR8Y8ayqoAUDr5IoRfSea\nlhfU6+QVgqenLkba+WT4eARgcM8YaDVuKCy5gbQL+3DkbBKuF2Y2eJw1Sf/GS4/+nTuGEBERkRkW\n1WTXEg+thojGl/1r1FrMnfAndO7UE2ql0x0/blhABMICIszaOrj5YGzkAxgb+QC2H16DLQdXWdwv\ntzALK7d9gFnjFtzV8YiIiMixsagmu1NZXYGdR9Zh19ENMP5mqUfvzoNwIfMkamqr0MHNB8898BY8\ndb5Wz3DfoJnoFRqJotJ8HDi1A6cv/TrbfeLngyjQ5+LJKW/ATcvdQYiIiIhFNdmBG0XXkFNwFR3c\nfJBTcBVbDnyForJ8i3H+3qF4IvYVlFYUI6fgKoI7doOTqvX2lA7w7owA784I6dgdy75eBH1Zgakv\nKy8Dr/1vLtQqDQK9O+PRsc/BS9ex1bIQERGRfWNRTZI6f/UE/rVhicWMdEMmDH4YgiDATesBN62H\nDdLd5OqswwsPLsWnm5Yiu+CKWV91TSV+vnYa/97wf3jpsY+gVHCtNRERUXsk/aa71K5tP7L2jgrq\nIeH3IqLzIBskapinzhcLZ76HnsH3NNh/ozgbP6Sut3EqIiIishecqSbJFJXm42LW6Qb7BEGGYb3H\nYUivMdBpO0Dn0sHG6SypVRo8MekVfLnjIxy9sM+iP/HQapy+lIoJQx5Gr1DHuZAJERER3R6LapLM\n0Qv7LHb26ODqjYgugzGizwT4ePhLlKxxCrkSc8b/EYN6xiCnIBMb960w679642f8b/N7+H+PfgA/\nzyBpQhIREZHNsagmSRhFI7YdWm3WNm1kHGL6T5Yo0Z0TBAHhIQMQHjIArs46fLnjI7N+g7EOO4+s\nx+zxCyVKSERERLYmiKLY+CbArUCv15u+Tk9Pt+WhSWKVNWU4nLEdheXXUVplfvVCAQKmD3wezipX\nidI1jyiKOH3tII5e2WXRN/Wep+Cm8ZQgFUktLCzM9LVOp5MwCRER2QpnqqlVVddWIrs4A24aTxzK\nSER+6bUGx3XUhbS5ghq4OWvdOyAKvfyHYt2Rj1BZW2bq23D0X/B06YQR3abCTSP9mnAiIiJqPZLO\nVDvKDE79ZbAjIx3jw2nWOp+K6jL8/ZuXkVuUdduxT055A+EhDe+s0VK2+v4cOrMLX+38h0W7t84P\nf3z4fTg7uVjlOPx5s3+O+DxHRERN45Z61Gq2pXzTZEGtUjphQLcRWPDg0lYrqG0psvtIeLpZXt0x\nT5+DZasW4lj6ARiMBgmSERERUWvj8g9qFdcLM5F8cmuj/Qtn/gVBPl0glzvOj6BcrsDvY1/Guj3/\nw8Vr5lsFFpbmIWHrMnQL7IOnpy6GTCaXKCURERG1Bs5UU6vYsHcFjI3Myk4bGYdQv+4OVVDX8/cO\nxYIH38HfnlmLUL8eFv0XMk/i9OU0CZIRERFRa2JRTVZXoM/Fmd8Ujhq1Ft7unTBu4IMY1S9WomS2\no1Qo8bv7X0Znv54WfXuObZIgEREREbUmx5sqJMmlnt9jdjvYNwyLHloGQRAkSiQNN607np/xDvad\n3IZ1u/9rar+Q9ROy8jIQ4N1ZwnRERERkTZypJqsSRRFHzu42axscfm+7K6jryQQZRvadiC6dws3a\nl61ahB1H1vGDi0RERA6CRTVZ1cmLh3CjONt0Wy5ToH9YlISJ7EN0/0kWbZsPfImvdv4DRtEoQSIi\nIiKyJhbVZBWiKCLx0Df4bMt7Zu29QgdAq3GTKJX9iOg8CB07BFq0p57bg+/3rZQgEREREVkTi2qy\nipQzPyIx5WuL9sjuoyRIY39kMjmemroYQ3qNgSCY/7fbdXQjTl5MkSgZERERWQM/qEgtVlNXja0N\nFNQhHbsjostgCRLZJw9XLzw65lncO2Aa/rHuzyitKDb1/W/ze/D3CoFvh0BMH/U7uDq7S5iUiIiI\n7paklylPT0+35aHJykRRRGbhBRz4eRNq6qrM+gaEjEEPv0jIZfy9rSEFZTnYejIBYgPrqQM7dENM\nz5kSpCJrCQsLM33Ny5QTEbUPXP5BzXbk0g7sPrfWoqAO7zQEvfyHsKBugqeLH3r7D22wL7PwAkoq\nC22ciIiIiFpC0qonMjJSysNbTWpqKoD2dT7nr57Auf1HLNqdVM54PPZpu/pwor1+f/r264Nlq64g\ntyjLoi+r4jSmR/4Ozk6uFtsR2uv5NJejnQ9g/o4cERG1D5ypprtWXVuF1T8ub7BvyvA5dlVQ2zOl\nQoU/THkNvUIsi8nUc3vwyn9n39xyj3tZExER2T2+P093RRRFrE36DwpKcs3aB/ccjej+k+DvHSpR\nsrbJS9cRf5jyGuoMtVgc/4TZhxcB4PDZJHQL7INBPWMkSkhERER3gjPVdFf2HN+MwLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9bc2f60>"
+       "<matplotlib.figure.Figure at 0xa311908>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "fuck\n"
+     ]
     }
    ],
    "source": [
@@ -510,20 +516,34 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "7451\n"
+     ]
+    },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9ac2ac8>"
+       "<matplotlib.figure.Figure at 0xa48a470>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "fuck\n"
+     ]
     }
    ],
    "source": [
@@ -538,7 +558,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This result may be somewhat surprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian.  Recall the equations for multiplying two univariate Gaussians:\n",
+    "This result may be somewhat surprising to you. The function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian.  Recall the equations for multiplying two univariate Gaussians:\n",
     "\n",
     "$$\\begin{aligned}\n",
     "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
@@ -552,20 +572,34 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "7324\n"
+     ]
+    },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a514e0>"
+       "<matplotlib.figure.Figure at 0xa48ab70>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "fuck\n"
+     ]
     }
    ],
    "source": [
@@ -584,7 +618,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -593,8 +627,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "input  mean, variance: 0.0036, 0.9998\n",
-      "output mean, variance: -0.1305, 2.4019\n"
+      "input  mean, variance: -0.0019, 0.9983\n",
+      "output mean, variance: -0.1220, 2.4022\n"
      ]
     }
    ],
@@ -614,16 +648,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "6687\n"
+     ]
+    },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9bc5a90>"
+       "<matplotlib.figure.Figure at 0xa57f358>"
       ]
      },
      "metadata": {},
@@ -633,7 +674,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "output mean, variance: -0.0055, 2.2496\n"
+      "fuck\n",
+      "output mean, variance: 0.0028, 2.2462\n"
      ]
     }
    ],
@@ -656,7 +698,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -665,8 +707,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "linear    output mean, variance: -0.3155, 7480.4651\n",
-      "nonlinear output mean, variance: -9.7978, 30473.9682\n"
+      "linear    output mean, variance: 0.1624, 7469.2910\n",
+      "nonlinear output mean, variance: -8.7963, 30432.7878\n"
      ]
     }
    ],
@@ -694,20 +736,34 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "79428\n"
+     ]
+    },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFfCAYAAACBcDBIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9c05080>"
+       "<matplotlib.figure.Figure at 0x8873b38>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "fuck\n"
+     ]
     }
    ],
    "source": [
@@ -752,7 +808,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtcAAAEWCAYAAACt0rvRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7cb3d30>"
+       "<matplotlib.figure.Figure at 0x7aa04a8>"
       ]
      },
      "metadata": {},
@@ -783,7 +839,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtcAAAEWCAYAAACt0rvRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x91d52b0>"
+       "<matplotlib.figure.Figure at 0x7be1a20>"
       ]
      },
      "metadata": {},
@@ -819,7 +875,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtcAAAEWCAYAAACt0rvRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x91e7cc0>"
+       "<matplotlib.figure.Figure at 0x7c4c7b8>"
       ]
      },
      "metadata": {},
@@ -855,7 +911,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtcAAAEWCAYAAACt0rvRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x99f04e0>"
+       "<matplotlib.figure.Figure at 0x6f61940>"
       ]
      },
      "metadata": {},

09_Unscented_Kalman_Filter.ipynb

@@ -3941,7 +3941,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3"
+   "version": "3.4.1"
   }
  },
  "nbformat": 4,

10_Extended_Kalman_Filters.ipynb

@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
@@ -250,7 +250,7 @@
        "<IPython.core.display.HTML object>"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 1,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -312,7 +312,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu0AAAEWCAYAAADSA6kgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6b5f2b0>"
+       "<matplotlib.figure.Figure at 0x6f67e80>"
       ]
      },
      "metadata": {},
@@ -352,7 +352,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -361,7 +361,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu0AAAEWCAYAAADSA6kgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6b4ccf8>"
+       "<matplotlib.figure.Figure at 0x6f67908>"
       ]
      },
      "metadata": {},
@@ -427,7 +427,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -436,7 +436,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAr8AAAERCAYAAABy58/tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6b4cb00>"
+       "<matplotlib.figure.Figure at 0x451e2b0>"
       ]
      },
      "metadata": {},
@@ -642,7 +642,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
@@ -667,7 +667,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
@@ -690,7 +690,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
@@ -765,16 +765,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwYAAAEtCAYAAACyMncIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwYAAAEtCAYAAACyMncIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7c636a0>"
+       "<matplotlib.figure.Figure at 0x81d6630>"
       ]
      },
      "metadata": {},
@@ -782,9 +782,9 @@
     },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvoAAAEtCAYAAAB5zMTfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvoAAAEtCAYAAAB5zMTfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72e16d8>"
+       "<matplotlib.figure.Figure at 0x8202780>"
       ]
      },
      "metadata": {},
@@ -792,9 +792,9 @@
     },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwMAAAEtCAYAAABUG7xMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwMAAAEtCAYAAABUG7xMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xt4FPXd///n7OZIIgnEbAIGURAwpYISBBNFORlCbw5y\nF8WAoVSqabVoym1puS9t0FZbrbdfwCP4E0mj3NgqbaW1EMEDB2Pl0NwoQgEPaMCEACGYkOPu/P7Y\n7CabbGCBhN1kX4/r2is7M5+Zec/u7Gbf8zmMYZqmiYiIiIiIBB2LvwMQERERERH/UDIgIiIiIhKk\nlAyIiIiIiAQpJQMiIiIiIkFKyYCIiIiISJBSMiAiIiIiEqSUDIiIiIiIBCm/JQObNm1iypQpJCUl\nYbFYyMvLa1Vm3759/Od//ic9evQgKiqKlJQU9u7d615eW1vLvHnziI+PJzo6mqlTp3Lo0CGPbZSX\nl5OVlUVsbCyxsbHMnj2bioqKDj8+EREREZFA57dkoKqqiiFDhrBkyRIiIyMxDMNj+RdffMH1119P\n//79effdd9m9ezePPvoo0dHR7jI5OTmsWbOG1atXs3nzZk6ePMmkSZNwOBzuMjNnzqSoqIj169ez\nbt06du7cSVZW1gU7ThERERGRQGUEwh2IL7roIp599llmz57tnjdz5kysViv5+fle16moqMBms7Fy\n5UoyMzMBKC4upm/fvvzjH/8gPT2dPXv2MHjwYLZu3UpqaioAW7duZdSoUezdu5eBAwd2/MGJiIiI\niASogOwz4HA4+Nvf/kZycjIZGRnYbDZGjBjBH//4R3eZHTt2UF9fT3p6unteUlISycnJFBYWAlBY\nWEh0dLQ7EQBIS0sjKirKXUZEREREJFgFZDJw5MgRKisreeyxx8jIyGDDhg1kZmYya9Ys3nrrLQBK\nSkqwWq3ExcV5rJuQkEBJSYm7THx8vMdywzCw2WzuMiIiIiIiwSrE3wF442rzf8stt5CTkwPAkCFD\n2L59O8888wzf+9732lz3XFs9qVOxiIiIiHRmMTExZ71OQNYMXHzxxYSEhPCd73zHY/6VV17JV199\nBUBiYiJ2u51jx455lCktLSUxMdFdpqyszGO5aZocOXLEXUZEREREJFgFZDIQFhbGtdde6zGMKDiH\nGr3ssssASElJITQ0lIKCAvfy4uJi9u7dS1paGgCpqalUVlZ69A8oLCykqqrKXUZEREREJFj5rZlQ\nVVUV+/fvB5zNgg4ePEhRURFxcXH06dOHBQsWcNtttzFq1CjGjBnDu+++y2uvvcZf//pXwFkNMnfu\nXBYsWIDNZqNnz57Mnz+foUOHMn78eAB3B+Ts7GyWL1+OaZpkZ2czefJkBgwY0GZs51LFInIhbd++\nHYDhw4f7ORIR3+iclc5E56t0Jufb1N1vNQPbtm1j2LBhDBs2jJqaGnJzcxk2bBi5ubkATJ06leXL\nl/Pkk08yZMgQnn32WfLz85k4caJ7G4sXL2batGnMmDGDG264ge7du7N27VqPexasWrWKoUOHMmHC\nBDIyMrjmmmvaHK5URERERCSYBMR9BgJB86xKNQMS6HTVSjobnbPSmeh8lc7kfH/DBmSfARERERER\n6XhKBkREREREgpSSARERERGRIKVkQEREREQkSCkZEBEREREJUkoGRERERESClJIBEREREZEgpWRA\nRERERCRIKRkQEREREQlSSgZERERERIKUkgERERERkSClZEBEREREJEgpGRARERERCVJKBkRERERE\ngpSSARERERGRIKVkQEREREQkSCkZEBEREREJUkoGRERERESClJIBEREREZEgpWRARERERCRIKRkQ\nEREREQlSSgZERERERIKUkgERERERkSDlt2Rg06ZNTJkyhaSkJCwWC3l5eR7L58yZg8Vi8XikpaV5\nlKmtrWXevHnEx8cTHR3N1KlTOXTokEeZ8vJysrKyiI2NJTY2ltmzZ1NRUdHhxyciIiIiEuj8lgxU\nVVUxZMgQlixZQmRkJIZheCw3DIObb76ZkpIS9+Ott97yKJOTk8OaNWtYvXo1mzdv5uTJk0yaNAmH\nw+EuM3PmTIqKili/fj3r1q1j586dZGVlXZBjFBEREREJZCH+2vHEiROZOHEi4KwFaMk0TcLCwrDZ\nbF7Xr6ioYMWKFaxcuZJx48YBkJ+fT9++fdmwYQPp6ens2bOH9evXs3XrVkaOHAnAsmXLGDVqFPv2\n7WPgwIEdc3AiIiIiIp1AwPYZMAyDLVu2kJCQwKBBg7j77rspKytzL9+xYwf19fWkp6e75yUlJZGc\nnExhYSEAhYWFREdHk5qa6i6TlpZGVFSUu4yIiIiISLDyW83AmWRkZPD973+fyy+/nC+++IIHH3yQ\nsWPHsmPHDsLCwigpKcFqtRIXF+exXkJCAiUlJQCUlJQQHx/vsdwwDGw2m7uMiIiIiEiwCthkYMaM\nGe7ngwcPJiUlhb59+/L3v/+dadOmtbmeaZrnve/t27ef9zZELgSdq9LZ6JyVzkTnq3QGAwYMOK/1\nA7aZUEu9evUiKSmJAwcOAJCYmIjdbufYsWMe5UpLS0lMTHSXad60CJzJwpEjR9xlvPnqSHg7Ry8i\nIiIiEngCtmagpbKyMg4dOkSvXr0ASElJITQ0lIKCAjIzMwEoLi5m79697iFIU1NTqayspLCw0N1v\noLCwkKqqqlbDlDZ3xcDvMuQKo83lIv7mulo1fPhwP0ci4huds9KZ6HyVzuR8h8z3WzJQVVXF/v37\nAXA4HBw8eJCioiLi4uLo2bMnubm5TJ8+ncTERL788ksWLlxIQkKCu4lQTEwMc+fOZcGCBdhsNnr2\n7Mn8+fMZOnQo48ePByA5OZmMjAyys7NZvnw5pmmSnZ3N5MmTT1ulUlPX8ccvIiIiIuJvfmsmtG3b\nNoYNG8awYcOoqakhNzeXYcOGkZubi9Vq5ZNPPmHq1KkMGjSIOXPmuEcJioqKcm9j8eLFTJs2jRkz\nZnDDDTfQvXt31q5d63HPglWrVjF06FAmTJhARkYG11xzDfn5+aeNrVbJgIiIiIgEAcNsjx63XUDz\nKpaP/t2dm0eomZAELlVhS2ejc1Y6E52v0pk0/w0bExNz1ut3mg7EF5KaCYmIiIhIMFAy4IWSARER\nEREJBkoGvKit93cEIiIiIiIdT8mAFzW1/o5ARERERKTjKRnwQs2ERERERCQYKBnwQsmAiIiIiAQD\nJQNeqM+AiIiIiAQDJQNeqM+AiIiIiAQDJQNeqJmQiIiIiAQDJQNeKBkQERERkWCgZMAL9RkQERER\nkWCgZMCLWtUMiIiIiEgQUDLghZoJiYiIiEgwUDLghUYTEhEREZFgoGTAC/UZEBEREZFgoGTACzUT\nEhEREZFgoGTACyUDIiIiIhIMlAx4oWRARERERIKBkgEvNLSoiIiIiAQDJQNeqGZARERERIKBkgEv\nlAyIiIiISDBQMuCFkgERERERCQZKBrxQnwERERERCQZ+SwY2bdrElClTSEpKwmKxkJeX12bZ7Oxs\nLBYL//M//+Mxv7a2lnnz5hEfH090dDRTp07l0KFDHmXKy8vJysoiNjaW2NhYZs+eTUVFxWljq6kD\n0zTP/eBERERERDoBvyUDVVVVDBkyhCVLlhAZGYlhGF7Lvf7662zbto3evXu3KpOTk8OaNWtYvXo1\nmzdv5uTJk0yaNAmHw+EuM3PmTIqKili/fj3r1q1j586dZGVlnTG+Ot2FWERERES6uBB/7XjixIlM\nnDgRgDlz5ngtc/DgQXJycti4cSMZGRkeyyoqKlixYgUrV65k3LhxAOTn59O3b182bNhAeno6e/bs\nYf369WzdupWRI0cCsGzZMkaNGsW+ffsYOHBgm/HV1EF4WDscqIiIiIhIgArYPgMNDQ1kZmby0EMP\nMWjQoFbLd+zYQX19Penp6e55SUlJJCcnU1hYCEBhYSHR0dGkpqa6y6SlpREVFeUu05Za1QyIiIiI\nSBcXsMlAbm4uNpuN7Oxsr8tLSkqwWq3ExcV5zE9ISKCkpMRdJj4+3mO5YRjYbDZ3mbbU1J5H8CIi\nIiIinYDfmgmdznvvvUdeXh5FRUUe833p1NteHX+37fyEIzZlBBLYtm/f7u8QRM6KzlnpTHS+Smcw\nYMCA81o/IGsG3n//fb755ht69epFaGgooaGhHDx4kF/84hdceumlACQmJmK32zl27JjHuqWlpSQm\nJrrLlJWVeSw3TZMjR464y7Slrj4gXxoRERERkXYTkDUD99xzD7feeqt72jRNJkyYwMyZM7nrrrsA\nSElJITQ0lIKCAjIzMwEoLi5m7969pKWlAZCamkplZSWFhYXufgOFhYVUVVW5y7TlioHfYXiy9xGO\nRPzNdbVq+PDhfo5ExDc6Z6Uz0fkqncmZhsw/E78lA1VVVezfvx8Ah8PBwYMHKSoqIi4ujj59+rRq\n6x8aGkpiYqK7KiQmJoa5c+eyYMECbDYbPXv2ZP78+QwdOpTx48cDkJycTEZGBtnZ2SxfvhzTNMnO\nzmby5MlnrFJRnwERERER6er81hZm27ZtDBs2jGHDhlFTU0Nubi7Dhg0jNzfX520sXryYadOmMWPG\nDG644Qa6d+/O2rVrPe5HsGrVKoYOHcqECRPIyMjgmmuuIT8//4zbrtFdiEVERESki/O5ZuDo0aNs\n3bqVPXv2cPToUQzD4OKLLyY5OZm0tDQuvvjis9rx6NGjPW4OdiZffPFFq3lhYWEsXbqUpUuXtrle\nbGysTz/+W1IyICIiIiJd3WmTgdraWl599VVefvlltm7detoNpaWl8cMf/pA77riD8PDwdg3SH3Sf\nARERERHp6tpsJvT888/Tv39/7rnnHnr06MHixYvZvHkzhw4d4tSpU1RVVVFcXMzmzLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x6bf02b0>"
+       "<matplotlib.figure.Figure at 0x81463c8>"
       ]
      },
      "metadata": {},
@@ -889,7 +889,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -897,7 +897,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEO+Zu3ZEIokyq83d\nZlSLRjhlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD0ElEQVRYCcWXPWgUQRTH/5v72s19ZIlN0MiF\nWKa5RkQEOSEiVhrkRIRoqmihcAErFbzCYAoTDkQIKBiLKCLiaSPhUC74UeqCBNIEAiJYWEREtBDj\nzNzO7Oz59uP8wIHczr73n//88mbCvaB/eAf+20gMD9voJ7af3n28ToT/RaiHJEjZ93MT/2I7wpMm\nsPCU0P5eKKqcNAHwNfZ2W6Z3h2lVOW86tCyAwNqw8HZ8DoXxEs6u0Evd6DMMVkMEqpzJOs5TOprg\nktky8b42iHcYx93t1EIZyw/BbMgX8umWswcgfxWaYOvR6TEk6zewhFlcWyKN3WByAYVPYQJeznxl\nH87BfE4dBE0gHHvY7o+MZbM6ELZB3wLSP0IEopwfMIRVoEXpQgguVhzMr1bza2PUQhkrlpD+Il+I\npyjnkrWAOzDI0wohYNAxxqUarG9RumXzBJbXC6XuTiHzIspX5GMRnF55gJlqZrFKWIbUgFAToWIt\n/BSIJf6QS9C32c3Y0Dz6SijoN7Frpz+uQa6MfOhfo0ZLTjsIMrFKodcgNYREg7CO7dRB0DvBzeYv\nU1eG2IaHXqO/TqRiO3UQXBBe5XRLPH0fQVgDlXs+nfsS4mTNHNBWdBDsFamGQZxsOd0SyZgfIU5J\nnNFM/ASGu0nBfTJhWopJLJn85Uk4YcJVZVG0vQV+gsR6O7PNuwdJpdWwVCxwQjihrNQf1QzwEwy2\nM8ZtT+ERaFheOmhGOHkExhNtmZ9gFuBN1ZapmpIIAh7UsVQ2cEI4CQLzyPV72Kodgr8G7PBEU/Vm\ns6WsOYEI6lgqGzShnATBWG/jlbFL/7731SDlQDVV0psTiKCOJZOBT8pJENSzDnKb37WFimCSBXM8\n4etR7zcfN5tOR1BbTk1pp95mc6TJOvA+75K3F0uC1Ah7r7Af3lTxIVtbcQ9kUGQiPgKd2jfxFup+\nA0kwdXJCdFGiqeIS2dpyAhXkiagR6MQJMhtXUfM7SAIU2Xccy4mmikt63NaWE4hgzOYdgU6cwFg8\nXbHzO1fX8f4t0muH+Ubyv7bEV+RsFuBDb23FKfBgvOadCYOc2qfABIVjRqtQSjm9Uw57UwSZz7yb\nbQ+9tU3IYLzmnamDnFCSVgetRrZuOtaeOosoAjy0l6WCbG3jNe/cIsoJQ6aTtQftK0aNqT2CW3OK\nkWxt4zXvnCDKKfNyHNbsFayt2D6C7Ah/F4NsbdUZSVXgM8qJ33hveDUofPaixCxm885XRjjhYln3\n9wigf2Hpku7nXTkxguLo/u43+VsrUqOHbKQnT/0tv+59MpOT+AmTXbj1s0kQCQAAAABJRU5ErkJg\ngg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUqOHbKQnT/0tv+59MpOT+AmTXbj1s0kQCQAAAABJRU5ErkJggg==\n",
       "text/latex": [
        "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$"
       ],
@@ -909,7 +909,7 @@
        "⎣╲╱  x_alt  + x_pos       ╲╱  x_alt  + x_pos  ⎦"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -974,7 +974,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -1001,7 +1001,7 @@
        "⎣          2                                                          ⎦"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1027,7 +1027,7 @@
     "\n",
     "So, time to try a real problem. I warn you that this is far from a simple problem. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world solution. \n",
     "\n",
-    "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. Or, it might be one of those small robots that  vacuum your house. It could be a search and rescue device meant to go into dangerous areas to search for survivors. It doesn't matter too much. \n",
+    "We will consider the problem of robot localization. We already implemented this in the **Unscented Kalman Filter** chapter, and I recommend you read that first. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. Or, it might be one of those small robots that  vacuum your house. It could be a search and rescue device meant to go into dangerous areas to search for survivors. It doesn't matter too much. \n",
     "\n",
     "Our robot is wheeled, which means that it manuevers by turning it's wheels. When it does so, the robot pivots around the rear axle while moving forward. This is nonlinear behavior which we will have to account for. The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from  a range and bearing requires square roots and trigonometry. \n",
     "\n",
@@ -1036,7 +1036,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1046,7 +1046,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhQAAAEWCAYAAAA+Wg5zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x72e1cc0>"
+       "<matplotlib.figure.Figure at 0x81e0a58>"
       ]
      },
      "metadata": {},
@@ -1171,7 +1171,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -1198,7 +1198,7 @@
        "⎣0  0                  1                 ⎦"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1238,7 +1238,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
@@ -1288,7 +1288,7 @@
        "                                                  ⎦"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1348,7 +1348,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
@@ -1371,7 +1371,7 @@
        "⎣  (px - x)  + (py - y)        (px - x)  + (py - y)        ⎦"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1394,7 +1394,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 15,
    "metadata": {
     "collapsed": true
    },
@@ -1428,7 +1428,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
    "metadata": {
     "collapsed": true
    },
@@ -1479,7 +1479,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -1556,7 +1556,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "metadata": {
     "collapsed": true
    },
@@ -1582,7 +1582,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1632,7 +1632,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1640,9 +1640,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9c1b400>"
+       "<matplotlib.figure.Figure at 0x6ff1240>"
       ]
      },
      "metadata": {},
@@ -1652,7 +1652,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.02427096  0.04335114  0.00222081]\n"
+      "[ 0.02479667  0.03958041  0.00220384]\n"
      ]
     }
    ],
@@ -1667,16 +1667,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 21,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9e2d400>"
+       "<matplotlib.figure.Figure at 0xa2c0668>"
       ]
      },
      "metadata": {},
@@ -1686,7 +1686,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.01981129  0.02080953  0.001537  ]\n"
+      "[ 0.02026067  0.0203502   0.00153694]\n"
      ]
     }
    ],
@@ -1711,7 +1711,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1719,9 +1719,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAEWCAYAAABL+3CVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86db438>"
+       "<matplotlib.figure.Figure at 0x6ff12b0>"
       ]
      },
      "metadata": {},
@@ -1731,7 +1731,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.01938022  0.04634068  0.00022408]\n"
+      "[ 0.02037772  0.04521487  0.00022534]\n"
      ]
     }
    ],
@@ -1750,7 +1750,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {
     "collapsed": false,
     "scrolled": false
@@ -1758,9 +1758,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x86dbf60>"
+       "<matplotlib.figure.Figure at 0xa2b1278>"
       ]
      },
      "metadata": {},
@@ -1770,7 +1770,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.29442198  0.82419287  0.00369511]\n"
+      "[ 0.2560811   0.81614092  0.00355988]\n"
      ]
     }
    ],
@@ -1789,7 +1789,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -1797,9 +1797,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmUXNV99vvvqTo1V3X1WD2r1RItqREgCyQjFMxoiPXa\nweYmIYlvgvEQnAS/Bvv69TXrelm8DsZ2YrOcwcaZcLjYxODc146TAJHfmMGKwCAwkxBoarXUU/Vc\nXXPVGe4fDW1koZao7lZ3i+ezVq0unX361K69tKoebe3z24brui4iIiIiIvKWeRa7AyIiIiIiy5XC\ntIiIiIhIhRSmRUREREQqpDAtIiIiIlIhhWkRERERkQopTIuIiIiIVEhhWkRERESkQrOG6W9+85ts\n2LCBeDxOPB5n69atPPjgg8ecc9ttt9Ha2ko4HObyyy/n5ZdfXtAOi4iIiIgsFbOG6fb2dv7sz/6M\nX/ziFzzzzDNcccUVfOADH+D5558H4Ktf/Sp33nknf/3Xf83TTz9NIpHgqquuIpPJnJbOi4iIiIgs\nJuOt7oBYV1fHV77yFT72sY/R0tLCJz/5SW699VYACoUCiUSCr33ta9x4440L0mERERERkaXilNdM\n27bN97//fQqFApdccgk9PT0kk0muvvrqmXOCwSCXXHIJu3btWpDOioiIiIgsJebJTnjxxRe56KKL\nKBaLhEIhHnjgAdauXTsTmBsbG485P5FIMDAwsDC9FRERERFZQk4aptetW8cLL7xAKpXiBz/4Ab/7\nu7/LI488MuvvGIZx3LFUKlV5L0VEREREFlk8Hj/u2EmXefh8PlatWsXGjRu544472LJlC9/85jdp\nbm4GIJlMHnN+MpmkqalpnrosIiIiIrJ0veU607Zt4zgOnZ2dNDU1sWPHjpm2QqHAzp072bp167x2\nUkRERERkKZp1mcfnPvc53ve+99HW1kY6nea+++7jscce4+GHHwbglltu4Y477mDdunV0dXVx++23\nE4vF+OAHPzjri75xinz37t0AbNq0aa7v5W1J41c5jd3caPzmRuNXOY3d3Gj85kbjV7nlOnYnW6o8\na5hOJpP8/u//PkNDQ8TjcTZs2MDDDz/MVVddBcBnP/tZ8vk8N910ExMTE2zZsoUdO3YQiUTm7x2I\niIiIiCxRs4bp73znOye9wPbt29m+ffu8dUhEREREZLl4y2umRURERERkmsK0iIiIiEiFFKZFRERE\nRCqkMC0iIiIiUiGFaRERERGRCilMi4iIiIhUSGFaRERERKRCCtMiIiIiIhVSmBYRERERqZDCtIiI\niIhIhRSmRUREREQqpDAtIiIiIlIhhWkRERERkQopTIuIiIiIVEhhWkRERESkQgrTIiIiIiIVUpgW\nEREREamQwrSIiIiISIUUpkVEREREKqQwLSIiIiJSIYVpEREREZEKKUyLiIiIiFRIYVpEREREpEIK\n0yIiIiIiFVKYFhERERGpkMK0iIiIiEiFFKZFRERERCqkMC0iIiIiUiGFaRERERGRCs0apr/85S+z\nefNm4vE4iUSCa665hj179hxzzg033IDH4znmsXXr1gXttIiIiIjIUjBrmH7sscf4xCc+wRNPPMFP\nf/pTTNPk3e9+NxMTEzPnGIbBVVddxdDQ0MzjwQcfXPCOi4iIiIgsNnO2xocffviYP997773E43F2\n7drFe9/7XgBc18Xv95NIJBaulyIiIkvY3r0FentP3N7RAd3dwdPXIRE5bWYN079qamoKx3GoqamZ\nOWYYBjt37qSxsZHq6mouvfRSvvSlL9HQ0DDvnRUREVmKenth27YTh+WHHirQ3X0aOyQip81bCtM3\n33wzGzdu5KKLLpo59p73vIff/M3fpLOzk56eHj7/+c9zxRVX8Mwzz+D3++e9wyIiIiIiS4Xhuq57\nKid++tOf5oEHHmDnzp2sXLnyhOcNDg7S0dHB/fffz7XXXjtzPJVKzTzfv39/5T0WERFZYnp6Orju\nuhP/j+wDD4zQ2TnLOhARWbK6urpmnsfj8ePaT2lm+lOf+hQPPPAAjzzyyKxBGqC5uZm2tjYOHDjw\n1noqIiIiIrLMnDRM33zzzfzgBz/gkUceYc2aNSe94MjICP39/TQ3N5/wnE2bNs08371793HH5NRp\n/CqnsZsbjd/caPwqtxTHbnS0MGt7LBZbMv1diuO3nGj8Krdcx+6NqyvezKyl8W666Sb+8R//ke99\n73vE4/GZ0nfZbBaAbDbLZz7zGZ588kkOHz7Mo48+yjXXXENjY+MxSzxERERERM5Es4bpu+66i0wm\nw5VXXklLS8vM4+tf/zoAXq+Xl156ife///2sXbuWG264ge7ubp544gkikchpeQMiIiIiIotl1mUe\njuPM+svBYPC4WtQiIiJvNx0d0+XvZmsXkTPTWyqNJyIiIsfr7g6qjrTI29SsyzxEREREROTEFKZF\nRERERCqkMC0iIiIiUiGFaRERERGRCilMi4iIiIhUSGFaRERERKRCCtMiIiIiIhVSmBYRERERqZDC\ntIiIiIhIhRSmRUREREQqpDAtIiIiIlIhhWkRERERkQopTIuIiIiIVEhhWkRERESkQgrTIiIiIiIV\nUpgWEREREamQwrSIiIiISIUUpkVEREREKqQwLSIiIiJSIYVpEREREZEKKUyLiIiIiFRIYVpERERE\npEIK0yIiIiIiFVKYFhERERGpkMK0iIiIiEiFFKZFRERERCqkMC0iIiIiUiGFaRERERGRCs0apr/8\n5S+zefNm4vE4iUSCa665hj179hx33m233UZrayvhcJjLL7+cl19+ecE6LCIiIiKyVJizNT722GN8\n4hOfYPPmzTiOwxe+8AXe/e538/LLL1NTUwPAV7/6Ve68807uuece1qxZwxe/+EWuuuoqXn31VaLR\n6Gl5EyIiy8HevQV6e6efp9MdAIyOFmbaOzqguzu4GF0TEZEKzRqmH3744WP+fO+99xKPx9m1axfv\nfe97cV2Xb3zjG9x6661ce+21ANxzzz0kEgnuu+8+brzxxoXruYjIMtPbC9u2vR6Wjw/NDz1UoLv7\n9PZJRETm5i2tmZ6amsJxnJlZ6Z6eHpLJJFdfffXMOcFgkEsuuYRdu3bNb09FRERERJYYw3Vd91RP\nvu666zh48CC7d+/GMAx27drFxRdfzJEjR2hra5s57yMf+QgDAwPHzGynUqmZ5/v375+n7ouILB89\nPR1cd13DCdsfeGCEzs7e09gjERE5ma6urpnn8Xj8uPZZl3m80ac//Wl27drFzp07MQzjpOefyjki\nIiIiIsvZKYXpT33qUzzwwAM88sgjrFy5cuZ4U1MTAMlk8piZ6WQyOdP2ZjZt2jTzfPfu3ccdk1On\n8aucxm5uNH5v3RtvNnwzsVhM43kK9HdvbjR+c6Pxq9xyHbs3rq54MyddM33zzTdz//3389Of/pQ1\na9Yc09bZ2UlTUxM7duyYOVYoFNi5cydbt26tsMsiIiIiIsvDrDPTN910E9/97nf50Y9+RDweZ2ho\nCJiePYlEIhiGwS233MIdd9zBunXr6Orq4vbbbycWi/HBD37wtLwBEREREZHFMmuYvuuuuzAMgyuv\nvPKY47fddhtf+MIXAPjsZz9LPp/npptuYmJigi1btrBjxw4ikcjC9VpEZBnq6JgufweQTqeB6cmJ\nN7aLiMjyMmuYdhznlC6yfft2tm/fPi8dEhE5U3V3B2fqSO/e/RKw/NYOiojIsd5SnWkREREREfkl\nhWkRERERkQopTIuIiIiIVEhhWkRERESkQgrTIiIiIiIVUpgWEREREamQwrSIiIiISIUUpkVERERE\nKqQwLSIiIiJSIYVpEREREZEKKUyLiIiIiFRIYVpEREREpELmYndARERkITiOS9mycQHT68H0av5I\nROafwrSIiJxRiiWLfMmibDmUy+A4EAxAVSSA3+dd7O6JyBlGYVpERM4IZcsmWyhTKDrkcuDYBqbX\ng+O4WJZDwG8pTIvIvFOYFhGRZc11XbKFMrmCRS4HVtkgFPARCE1/xZXKNiWniOsuckdF5IykMC0i\nIsuWZTukc0WyOZd8HoI+H9Go75hzSpaN6QefqTXTIjL/FKZFRGRZKpQsMrkSU2mXQtElaJoUShb5\nYhmf10s07AfAsm3CfvCbWuIhIvNPYVpERJadXNEilSkxMlrGdsCLj8m8g2WB60I4ZOPxlMEAn98l\n6PfiVTUPEVkACtMiIrJsOI5LOl9mKmOz/3CGsckCmbxDPBSmuaaKWDDA2Q9Mh+b91+fA41IdhUjQ\nd5Iri4hURmFaRESWBdt2mMwU6B8psfdIFrtnH+lSCpsyUX+M+nAdt/Zu5JkPFPGa0+Xxamu8hAKm\nZqVFZMEoTIuIyJJn2Q5jqRwHjqR5/KUxRnPjuPFDRKIOwYCHvqzN10du4c86n6dsWbhmieqQSThk\nEAn5F7v7InIGU5gWEZElzbIdBsfS9A0U+MnTRxnI9lP0jXD+Wc1EXrvJcPvuj/ObkW+QTI8znp2i\nMeQnXuUhFg4scu9F5EynMC0iIktWqWzTPzJFctTm2VfHSWYHKfpHaG92CQYNtu/+OAD/c9PfsK8n\nT7o4Rd7K0dgQJRb2awtxEVlwCtMiIrIkFUoWfcNTDA07pKcc+kYn6Mscprbaoa/Pz3dG/hiA/7np\n27iuSzpjURvy0dYUpDrqJ+DXV5yILDx90oiIyJJTLFn0DafoH3Qo5LykMjmSmRFMn41hGOw/EIb1\nwL/9Ff855VBdVwYnSGtDNWvaa7VOWkROG4VpERFZUgrFMn0jUzz1YoqR8SIhM8TA2BS5Up5cyceP\nzNthPWwZ/WumznHZ9E6LvQcKrKldxyUb2ohHtU5aRE4fhWkREVkyCiWLp/YO8B9P9Line truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xa642940>"
+       "<matplotlib.figure.Figure at 0xa26b9b0>"
       ]
      },
      "metadata": {},
@@ -1809,7 +1809,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[ 0.00881439  0.0086407   0.00077058]\n"
+      "[ 0.00865132  0.00887946  0.00077272]\n"
      ]
     }
    ],
@@ -1834,6 +1834,100 @@
     "\n",
     "However, this example should underscore how difficult EKFs can be. EKF have a well deserved reputation for difficulty. Especially when the problem is highly nonlinear you must design "
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## UKF vs EKF\n",
+    "\n",
+    "I implemented this tracking problem using and unscented Kalman filter in the previous chapter. The difference in implementation should be very clear. Computing the Jacobians for the state and measurement models was not trivial and we used a very rudimentary model for the motion of the car. I am justified in using this model because the research resulting from the DARPA car challenges has shown that it works well in practice. Nonetheless, a different problem, such as an aircraft or rocket will yield a very difficult to impossible to compute Jacobian. In contrast, the UKF only requires you to provide a function that computes the system motion model and another for the measurement model. This is will always be easier than deriving a Jacobian analytically. In fact, there are many physical processes for which we cannot find an analytical solution. It is beyond the scope of this book, but in that case you have to design a numerical method to compute the Jacobian. That is a very nontrivial undertaking, and you will spend a significant portion of a master's degree at a STEM school learning various techniques to handle such situations. Even then you'll likely only be able to solve problems related to your field - an aeronautical engineer learns a lot about Navier Stokes equations, but not much about modelling chemical reaction rates. \n",
+    "\n",
+    "So, UKFs are easy. Are they accurate? Everything I have read states that there is no way to prove that a UKF will always perform as well or better than an EKF. However, in practice, they do perform better. You can search and find any number of research papers that prove that the UKF outperforms the EKF in various problem domains. It's not hard to understand why this would be true. The EKF works by linearizing the system model and measurement model at a single point. \n",
+    "\n",
+    "Let's look at a specific example. I will take the function $f(x) = x^3$ as our nonlinear function and pass a Gaussian distribution through it. I will compute an accurate answer using a monte carlo simulation. I do this by generating 50,000 points distributed according to the Gaussian, passing each point through the function, and then computing the mean and variance of the result. \n",
+    "\n",
+    "First, let's see how the EKF fairs. The EkF linearizes the function by taking the derivative and evaluating it the mean $x$ to get the slope tangent to the function at that point. This slope becomes the linear function that we use to transform the Gaussian. Here is a plot of that."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0xa257c50>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "actual mean=1.30, std=1.12\n",
+      "EKF    mean=1.00, std=0.95\n"
+     ]
+    }
+   ],
+   "source": [
+    "import nonlinear_plots\n",
+    "nonlinear_plots.plot_ekf_vs_mc()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can see from both the graph and the print out at the bottom that the EKF has introduced quite a bit of error.\n",
+    "\n",
+    "In contrast, here is the performance of the UKF evaluated with the same Gaussian and function.b"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAt8AAAEWCAYAAAC+BfslAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x43aeda0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "actual mean=1.29, std=1.12\n",
+      "UKF    mean=1.30, std=1.08\n"
+     ]
+    }
+   ],
+   "source": [
+    "nonlinear_plots.plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here we can see that the computation of the UKF's mean is accurate to 2 decimal places. The standard deviation is slightly off, but you can also fine tune how the UKF computes the distribution by using the $\\alpha$, $\\beta$, and $\\gamma$ parameters for generating the sigma points. Here I used $\\alpha=0.001$, $\\beta=3$, and $\\gamma=1$. Feel free to modify them in the function call to see the result - you should be able to get better results than I did. However, ovoid overtuning the UKF for a specific test - it may perform better for your test case, but worse in general.\n",
+    "\n",
+    "This is one contrived example, but as I said the literature is filled with detailed studies of real world problems that exhibit similar performance differences between the two filters."
+   ]
   }
  ],
  "metadata": {

Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb

@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
@@ -29,8 +29,8 @@
      "output_type": "stream",
      "text": [
       "50000\n",
-      "3.00761397\n",
-      "1.99265941012\n"
+      "3.00043200502\n",
+      "2.01072423406\n"
      ]
     }
    ],
@@ -59,7 +59,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -68,7 +68,7 @@
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x85bfd30>"
+       "<matplotlib.figure.Figure at 0x79d6550>"
       ]
      },
      "metadata": {},
@@ -99,7 +99,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -107,9 +107,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9bf1588>"
+       "<matplotlib.figure.Figure at 0x46db518>"
       ]
      },
      "metadata": {},
@@ -130,16 +130,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAEKZJREFUeJzt3W2sHNddx/Gvsa+BPCiJwcTUudVtUVEtIbdFwXWUQBwe\nopsI1eJVX0RA6zbyC8KDiKhrKjUXqUI8CBVVPChKAzIQcKFKUIpSElvqFVGUOJj6oYU42I5NbNcq\nFqSWqFTVFcOLM5c7u569s7NP5+ye70ca+czszO7fO7O/PXtmdi9IkiRJkiRJkiRJkiRJkiRphBaB\nU8BpYF/N7Q8BJ4CTwEvA9spt58vlx4BXx1qlJGlg64EzwAIwBxwHtnWtcxdwS9leBF6p3HYO2DTe\nEiVJTb6r4fYdhLA/D1wDDgK7u9Z5Gbhato8Ad3Tdvm64EiVJw2oK+63Ahcr8xXJZLx8BnqvMF8Bh\n4Cjw8CAFSpKGt6Hh9qLFfd0H7AHuriy7G7gMbAYOEcb+X2xToCRpeE1hfwmYr8zPE3r33bYDTxDG\n7N+qLL9c/nsFeIYwLNQd9m3eUCRJq0Y2TL4BOEs4QbuR+hO0byeM6+/sWn4DcHPZvpFwpc79NY+R\nYtgvxS6gh6XYBdRYil1AjaXYBdRYil1AjaXYBfSwFLuAGkuxC6jRKjubevbfAR4BnidcmfMk8Bqw\nt7z9ceCTwG3An5bLrhF68FuApyuP8xTwQpviJEmj0RT2AF8sp6rHK+2PllO3N4D3DliXJGmEmq7G\nydVy7AJ6WI5dQI3l2AXUWI5dQI3l2AXUWI5dQA/LsQuosRy7gFmQ4pi9JKWuVXbas5ekDBj2kpQB\nw16SMmDYS1IGDHtJyoBhL0kZMOwlKQOGvSRlwLCXpAwY9pKUAcNekjJg2EtSBgx7ScqAYS9JGTDs\nJSkDhr0kZcCwl6QMGPaSlAHDXpIyYNhLUgYMe0nKgGEvSRkw7CUpA4a9JGXAsJekDBj2kpQBw16S\nMmDYS1IGDHtJyoBhL0kZMOwlKQOGvSRlYEPsAqTIikp7XbQqpDGzZy915L00m/oJ+0XgFHAa2Fdz\n+0PACeAk8BKwvcW2kqQErAfOAAvAHHAc2Na1zl3ALWV7EXilxbZgt0pxFVAUeBxq+rQ6Zpt69jsI\ngX0euAYcBHZ3rfMycLVsHwHuaLGtNA2KyiRNpaaw3wpcqMxfLJf18hHguQG3lRJmzmu6NV2N0+YI\nvw/YA9w9wLZLlfZyOUmxmOxK0a5yGkhT2F8C5ivz84QeerftwBOEMfu3Wm4LnWEvxVJcP9vzasyV\ndb1cU5OyTGdH+LFR3vkG4CzhJOtG6k+yvp0wNr9zgG3BXpTiqIzDF23a3dtLsYz8+HsAeJ0Q6PvL\nZXvLCeCzwH8Bx8rp1YZtu/mC0Tj1OrlaCXDDXlOp1fGXwkfQNT8rS0MqKofYuvrl1UOwsV1dQOUO\nuu9fGrdW2ek3aKV21upN2dtXsgx7aWTMeaXLsJfaM9U1dfzVS+VkRCHtaSZNH3v2yoydcuXJsJeG\n47uHpoJhLw2lNut9A1ByDHtJyoBhL0kZMOwlKQOGvSRlwLCXpAwY9po1Kf0+TUq1KHN+g1azypCV\nKuzZa0aZ9VKVYS9JGXAYR7Mita5891+1gvo/fCJNhD17zZCU8r4u66V4DHtJyoBhL02OXXxFY9hL\nUgYMe80Ce8xSA8NekjJg2EtSBgx7ScqAYS9JGfAbtJpmnpiV+mTPXtOq6PhH0poMe0nKgGEvTZYf\nRRSFYS9NlFmvOAx7ScqAV+NI8VW7+/7GvcbCnr0UT+UPkju8o/Ey7KVoDHhNTj9hvwicAk4D+2pu\nfzfwMvAt4NGu284DJ4FjwKsDVymtqvSGJY3KeuAMsADMAceBbV3rbAbuBD7F9WF/DtjU8Bi+cNVG\nAcVK4I+oPer7G6ot9avV8dLUs99BCPvzwDXgILC7a50rwNHy9jqecJKkyJrCfitwoTJ/sVzWrwI4\nTHgzeLhdaZKkUWm69HLYj5V3A5cJQz2HCGP/Lw55n5KklprC/hIwX5mfJ/Tu+3W5/PcK8AxhWKgu\n7Jcq7eVykiSt2lVOY7EBOEs4QbuR+hO0K5boPEF7A3Bz2b4ReAm4v2Y7T0qpDU/QSsHIj5cHgNcJ\nJ2r3l8v2lhPAFsK4/lXgLeBN4CbgnYQ3h+PAVyvbjr1gzTTDXgpaHS8pXClTkEYdmg5F5yEzivao\n72/YNnTPSDVaZaffoJWSYude42HYS1IGDHspTXbxNVKGvZQuT9pqZAx7KVnmvEbHsJekDBj2kpQB\nw17TxHENaUCGvSRlwD84rlTZi5dGyJ69Elb0aGen8hs60mAMe2kqmPMajmEvSRlwzF4psfvarPoc\n+cuY6ps9eyXGvG/mc6T2DHtJyoBhL0kZMOyl6eV4jvpm2EtSBgx7ScqAYS9JGTDsJSkDhr0kZcCw\nl6QM+HMJis3LB6UJsGevBJj30rgZ9pKUAcNemm7+URP1xbCXppo5r/4Y9pKUAcNekjJg2EuzwfEc\nrcmwV0wGlDQhhr0kZcCwl6QMGPaSlIF+wn4ROAWcBvbV3P5u4GXgW8CjLbeVJCVgPXAGWADmgOPA\ntq51NgN3Ap+iM+z72RY8SZez8tufRRG3HfvxR1WLMtNqnzf17HcQAvs8cA04COzuWucKcLS8ve22\nkqQJaAr7rcCFyvzFclk/htlWs8ceqBRRU9gP88L0Ra0uRbXh8SFNUNMfL7kEzFfm5wk99H602Xap\n0l4uJ820AlgXuwhpmuwqp7HYAJwlnGTdSO+TrBACu3qCtt9t7eHlIYGTn56g1UwZ+T5/AHidcLJ1\nf7lsbzkBbCGMzV8F3gLeBG5aY9uxF6wkJRCkhr1mSqt9nsLn6II06tB4FZ27OqV27McfVS2+jjLT\nKjv9Bq0kZcCwl2aLQzqqZdhLUgaaLr2UhmEPU0qEPXtNgJk/IT7R6smwl2aGWa/eDHtJyoBj9tJs\nqnbzvf5e9uyl2VR0zzjGkznDXpp55rwMe0nKgmP2Gge7klJi7NlrTMx7KSWGvSRlwLCXpAwY9pKU\nAcNekjJg2GvUPDMrJciwl/LhG3HGDHtJyoBfqtKo2GucDiv7yR9Hy4w9e42QeZ8+91GuDHtJyoBh\nL0kZMOwlKQOGvUbBgeDp4z7LjGEvSRkw7KV8+ecKM2LYa1AGxdRz9+XEsJekDBj2kpQBfy5Bw3Is\nYPpV96E/ozCj7NlrSGb9bHA/zjp79mrLVJCmkD17DcC8l6aNYS9JGegn7BeBU8BpYF+PdT5T3n4C\neF9l+XngJHAMeHXgKiVNSoHfocjSeuAMsADMAceBbV3rPAg8V7bfD7xSue0csKnhMTyopksBRSUQ\n2rQH3W7c7diPn2otSlyrfdTUs99BCPvzwDXgILC7a50PAAfK9hHgVuD2yu1eyiVJkTWF/VbgQmX+\nYrms33UK4DBwFHh48DIVWaXXp4y4z2dI06WX/e7oXr33e4CvAZuBQ4Sx/xdr1luqtJfLSUkp8ENa\nbtznidlVTgNpCvtLwHxlfp7Qc19rnTvKZRCCHuAK8AxhWKgp7JUWe3ZSGpbp7Ag/1mbjpmGco8C7\nCCdoNwIfBJ7tWudZ4BfK9k7gG8DXgRuAm8vlNwL3A19pU5wkaTSaevbfAR4BnidcmfMk8Bqwt7z9\nccKVOA8STuR+E/hwedsW4OnK4zwFvDCqwiVJ/UthQM6BwbQVq/+sY7j2KO5jHO3Yj598Lb4+09Qq\nO/0GrSRlwLBXHS+5Ux2Piynmr16qyhey6nhczAB79upS9JxRzq47Ljw2poxhrzX4elYdj4tpZNhr\nha9gaYYZ9pKUAcNekjLg1Thy+EbKgD17Yd5Ls8+wl6QMGPaSBuVHwinimH2efJFKmbFnny3zXiPh\nt2mnhGGfH1+YGiEPp2lh2EtSBgx7ScqAYS9pFBzPSZxX4+TDF6PGbeUY888YJsiefR6Kjn+ksfD4\nSplhL0kZcBhnttnVUgy9jjuHdyKyZz/zzHvFUPRoKxZ79rPHk2RKVTX1PT4nzJ797LI7pQR5WMZi\n2M+Ort8o8UUlaZXDONOtuH7WT8eSrmfPfurZg5fUzLCXFIO9lAkz7CUpA47ZTy97Rpp2fvlqggz7\n6WPIa0ZULyjouLig7hj3DWBIDuNMh4KOSyvNe80yv307Dvbs0+VllZJGxp590uzVSBX+cfMh9BP2\ni8Ap4DSwr8c6nylvPwG8r+W2OStqJvCAlrp1vyYM/hFbD5wBFoA54DiwrWudB4Hnyvb7gVdabAtp\n7rBdI7qf7hCvW15AURf6XcsHbY/iPtZqfymhWlJ9jlKtpWnfxXou6urqeI1QaVeXjdOuCTxGW63+\n3009+x2EwD4PXAMOAru71vkAcKBsHwFuBbb0uW2qdo3uropqo3Jg9tpPkzhuR2k5dgEa2HLsAnpY\nblqhqGl2h3/dNIxdQ24fXVPYbwUuVOYvlsv6WedtfWw7K+oOqpqDa9qCXEpRPx2l2nY/wT/JTwsT\n1RT2/f6Hx3mZyNtYffL3DHE/vXZiXQ/gsR7LG3oMxXUNSSlp/CTAAC/fSQ8pDaTp0stLwHxlfp7Q\nQ19rnTvKdeb62HZFv0/Qk+U0rDHtkLr3vHWR2+N+nN9KqJZUn6NUa2nad7Gei7q6xvE4vfT8ctdj\nfWxct91U2ACcJZxk3UjzCdqdrJ6g7WdbSVIiHgBeJ5xs3V8u21tOK/6ovP0E8KMN20qSJEmaZb8M\nvAZ8FfjdyLVUPQr8L7ApdiHA7xOeoxPA08AtEWtJ8Qtz88CXgH8lHEe/ErecDuuBY8AXYhdSuhX4\nPOF4+jfCEGxs+wn77ivAXwPfHaGGPwO+XtawYhNwCPh34AXCc5dCXSnlQd/uIzyZcLine truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x861ca90>"
+       "<matplotlib.figure.Figure at 0x7fd8b00>"
       ]
      },
      "metadata": {},
@@ -160,16 +160,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x9a4e780>"
+       "<matplotlib.figure.Figure at 0x82595f8>"
       ]
      },
      "metadata": {},
@@ -190,16 +190,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x830f6d8>"
+       "<matplotlib.figure.Figure at 0x851f860>"
       ]
      },
      "metadata": {},
@@ -208,6 +208,7 @@
    ],
    "source": [
     "plt.hist(data, bins=200, normed=True, histtype='step')\n",
+    "norm = stats.norm(mean, std)\n",
     "plt.plot(xs, norm.pdf(xs), color='k', lw=2)\n",
     "plt.show()"
    ]
@@ -221,16 +222,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x8531710>"
+       "<matplotlib.figure.Figure at 0x7a13710>"
       ]
      },
      "metadata": {},
@@ -259,16 +260,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xaf517f0>"
+       "<matplotlib.figure.Figure at 0x859ba90>"
       ]
      },
      "metadata": {},
@@ -278,8 +279,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "mean = 14.01\n",
-      "std  = 2.80\n"
+      "mean = 13.96\n",
+      "std  = 2.81\n"
      ]
     }
    ],
@@ -323,16 +324,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xb0126d8>"
+       "<matplotlib.figure.Figure at 0x95bb7f0>"
       ]
      },
      "metadata": {},
@@ -342,7 +343,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "mean = -1.60\n",
+      "mean = -1.57\n",
       "std  = 2.10\n"
      ]
     }
@@ -378,7 +379,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -389,7 +390,7 @@
        "-1.5*sin(x/3)*sin(1.5*x + 2.1) + cos(x/3)*cos(1.5*x + 2.1)/3 - 1.6"
       ]
      },
-     "execution_count": 75,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -411,7 +412,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
@@ -422,7 +423,7 @@
        "-1.66528051815545"
       ]
      },
-     "execution_count": 95,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -441,30 +442,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEACAYAAABS29YJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0xb0c47b8>"
+       "<matplotlib.figure.Figure at 0xaa5bac8>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/plain": [
-       "-2.33139272541763"
-      ]
-     },
-     "execution_count": 112,
-     "metadata": {},
-     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -472,8 +463,7 @@
     "plot_normal(xs, f2(mean), abs(float(m)*std), color='k', lw=3, label='EKF')\n",
     "plot_normal(xs, d_t.mean(), d_t.std(), color='r', lw=3, label='MC')\n",
     "plt.legend()\n",
-    "plt.show()\n",
-    "m*stdb"
+    "plt.show()"
    ]
   },
   {

code/nonlinear_plots.py

@@ -8,6 +8,7 @@ Created on Sun May 18 11:09:23 2014
 from __future__ import division
 import matplotlib.pyplot as plt
 import numpy as np
+from numpy.random import normal
 import scipy.stats
 
 
@@ -84,6 +85,90 @@ def plot_nonlinear_func(data, f, gaussian, num_bins=300):
     print("fuck")
 
 
+import math
+def plot_ekf_vs_mc():
+
+    def fx(x):
+        return x**3
+
+    def dfx(x):
+        return 3*x**2
+
+    mean = 1
+    var = .1
+    std = math.sqrt(var)
+
+    data = normal(loc=mean, scale=std, size=50000)
+    d_t = fx(data)
+
+    mean_ekf = fx(mean)
+
+    slope = dfx(mean)
+    std_ekf = abs(slope*std)
+
+
+    norm = scipy.stats.norm(mean_ekf, std_ekf)
+    xs = np.linspace(-3, 5, 200)
+    plt.plot(xs, norm.pdf(xs), lw=2, ls='--', color='b')
+    plt.hist(d_t, bins=200, normed=True, histtype='step', lw=2, color='g')
+
+    actual_mean = d_t.mean()
+    plt.axvline(actual_mean, lw=2, color='g', label='Monte Carlo')
+    plt.axvline(mean_ekf, lw=2, ls='--', color='b', label='EKF')
+    plt.legend()
+    plt.show()
+
+    print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std()))
+    print('EKF    mean={:.2f}, std={:.2f}'.format(mean_ekf, std_ekf))
+
+
+from filterpy.kalman import MerweScaledSigmaPoints, unscented_transform
+
+def plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.):
+
+    def fx(x):
+        return x**3
+
+    def dfx(x):
+        return 3*x**2
+
+    mean = 1
+    var = .1
+    std = math.sqrt(var)
+
+    data = normal(loc=mean, scale=std, size=50000)
+    d_t = fx(data)
+
+
+    points = MerweScaledSigmaPoints(1, alpha, beta, kappa)
+    Wm, Wc = points.weights()
+    sigmas = points.sigma_points(mean, var)
+
+    sigmas_f = np.zeros((3, 1))
+    for i in range(3):
+        sigmas_f[i] = fx(sigmas[i, 0])
+
+    ### pass through unscented transform
+    ukf_mean, ukf_cov = unscented_transform(sigmas_f, Wm, Wc)
+    ukf_mean = ukf_mean[0]
+    ukf_std = math.sqrt(ukf_cov[0])
+
+    norm = scipy.stats.norm(ukf_mean, ukf_std)
+    xs = np.linspace(-3, 5, 200)
+    plt.plot(xs, norm.pdf(xs), ls='--', lw=1, color='b')
+    plt.hist(d_t, bins=200, normed=True, histtype='step', lw=1, color='g')
+
+    actual_mean = d_t.mean()
+    plt.axvline(actual_mean, lw=1, color='g', label='Monte Carlo')
+    plt.axvline(ukf_mean, lw=1, ls='--', color='b', label='UKF')
+    plt.legend()
+    plt.show()
+
+    print('actual mean={:.2f}, std={:.2f}'.format(d_t.mean(), d_t.std()))
+    print('UKF    mean={:.2f}, std={:.2f}'.format(ukf_mean, ukf_std))
+
+
+
 def test_plot():
     import math
     from numpy.random import normal
@@ -124,8 +209,9 @@ if __name__ == "__main__":
     from numpy.random import normal
     import numpy as np
 
+    plot_ukf_vs_mc()
 
-    x0 = (1, 1)
+    '''x0 = (1, 1)
     data = normal(loc=x0[0], scale=x0[1], size=500000)
 
     def g(x):
@@ -137,3 +223,4 @@ if __name__ == "__main__":
     #plot_transfer_func (data, g, lims=(-3,3), num_bins=100)
     plot_nonlinear_func (data, g, gaussian=x0,
                         num_bins=100)
+    '''

code/particle_filter.py

@@ -30,11 +30,13 @@ class ParticleFilter(object):
 
 
 
-    def create_particles(self, mu, var):
-        self.particles[:, 0] = mu[0] + randn(self.N)* np.sqrt(var)
-        self.particles[:, 1] = mu[1] + randn(self.N)* np.sqrt(var)
+    def create_particles(self, mean, variance):
+        """ create particles with the specied mean and variance"""
+        self.particles[:, 0] = mean[0] + randn(self.N) * np.sqrt(variance)
+        self.particles[:, 1] = mean[1] + randn(self.N) * np.sqrt(variance)
 
     def create_particle(self):
+        """ create particles uniformly distributed over entire space"""
         return [uniform(0, self.x_range), uniform(0, self.y_range), 0, 0]
 
 
@@ -49,23 +51,22 @@ class ParticleFilter(object):
         self.particles[:, 1] += dx[1]
 
 
-    def move(self, h, v, t=1.):
+    def move(self, hdg, vel, t=1.):
         """ move the particles according to their speed and direction for the
         specified time duration t"""
-        h = math.atan2(h[1], h[0])
+        h = math.atan2(hdg[1], hdg[0])
         h = randn(self.N) * .4 + h
-        vs = v + randn(self.N) * 0.1
-        vx = v * np.cos(h)
-        vy = v * np.sin(h)
+        vs = vel + randn(self.N) * 0.1
+        vx = vel * np.cos(h)
+        vy = vel * np.sin(h)
 
-
-        #vx = self.particles[:, 2] * np.cos(self.particles[:, 3]) + randn(self.N)*0.5
-        #vy = self.particles[:, 2] * np.sin(self.particles[:, 3]) + randn(self.N)*0.5
         self.particles[:, 0] = (self.particles[:, 0] + vx*t)
         self.particles[:, 1] = (self.particles[:, 1] + vy*t)
 
 
     def move2(self, u):
+        """ move according to control input u"""
+
         dx = u[0] + randn(self.N) * 1.9
         dy = u[1] + randn(self.N) * 1.9
         self.particles[:, 0] = (self.particles[:, 0] + dx)
@@ -87,11 +88,12 @@ class ParticleFilter(object):
         self.weights *= prob
         self.weights /= sum(self.weights) # normalize
 
+
     def neff(self):
         return 1. / np.sum(np.square(self.weights))
 
-    def resample(self):
 
+    def resample(self):
         p = np.zeros((self.N, 4))
         w = np.zeros(self.N)
 
@@ -104,6 +106,7 @@ class ParticleFilter(object):
         self.particles = p
         self.weights = w / np.sum(w)
 
+
     def estimate(self):
         """ returns mean and variance """
         pos = self.particles[:, 0:2]
@@ -140,14 +143,15 @@ def plot(pf, xlim=100, ylim=100, weights=True):
 
 if __name__ == '__main__':
     pf = ParticleFilter(5000, 100, 100)
-    pf.particles[:,3] = np.random.randn(pf.N)*np.radians(10)  + np.radians(45)
+    pf.particles[:,3] = np.random.randn(pf.N)*np.radians(10) + np.radians(45)
 
     z = np.array([20, 20])
-    pf.create_particles(z, 40)
+    pf.create_particles(mean=z, variance=40)
 
     mu0 = np.array([0., 0.])
+    plot(pf, weights=False)
 
-    for x in range(60):
+    for x in range(10):
 
         z[0] += 1.0 + randn()*0.3
         z[1] += 1.0 + randn()*0.3
@@ -170,7 +174,7 @@ if __name__ == '__main__':
         plt.scatter(mu[0], mu[1], c='g', s=100)#,
                     #s=min(500, abs((1./np.sum(var)))*20), alpha=0.5)
         plt.tight_layout()
-        plt.pause(.02)
+        plt.pause(.22)
 
         #pf.assign_speed_by_gaussian(1, 1.5)
         #pf.move(h=[1,1], v=1.4, t=1)