diff --git a/Chapter09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb b/Chapter09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb
new file mode 100644
index 0000000..1ed9e6c
--- /dev/null
+++ b/Chapter09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb
@@ -0,0 +1,1041 @@
+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:3ee53e118c8313c872ece50f585d138691e58bd895a187ec935ce1a99a6fb7dd"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "The Extended Kalman Filter"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#format the book\n",
+      "%matplotlib inline\n",
+      "from __future__ import division, print_function\n",
+      "import matplotlib.pyplot as plt\n",
+      "import sys\n",
+      "sys.path.insert(0,'../') # allow us to format the book\n",
+      "import book_format\n",
+      "book_format.load_style()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "<style>\n",
+        "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "\n",
+        "    div.cell{\n",
+        "        width: 850px;\n",
+        "        margin-left: 0% !important;\n",
+        "        margin-right: auto;\n",
+        "    }\n",
+        "    div.text_cell code {\n",
+        "        background: transparent;\n",
+        "        color: #000000;\n",
+        "        font-weight: 600;\n",
+        "        font-size: 11pt;\n",
+        "        font-style: bold;\n",
+        "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
+        "   }\n",
+        "    h1 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "\t}\n",
+        "\t\n",
+        "    div.input_area {\n",
+        "        background: #F6F6F9;\n",
+        "        border: 1px solid #586e75;\n",
+        "    }\n",
+        "\n",
+        "    .text_cell_render h1 {\n",
+        "        font-weight: 200;\n",
+        "        font-size: 30pt;\n",
+        "        line-height: 100%;\n",
+        "        color:#c76c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 1em;\n",
+        "        display: block;\n",
+        "        white-space: wrap;\n",
+        "    } \n",
+        "    h2 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h2 {\n",
+        "        font-weight: 200;\n",
+        "        font-size: 20pt;\n",
+        "        font-style: italic;\n",
+        "        line-height: 100%;\n",
+        "        color:#c76c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 1.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    } \n",
+        "    h3 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h3 {\n",
+        "        font-weight: 300;\n",
+        "        font-size: 18pt;\n",
+        "        line-height: 100%;\n",
+        "        color:#d77c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 2em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    h4 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h4 {\n",
+        "        font-weight: 300;\n",
+        "        font-size: 16pt;\n",
+        "        color:#d77c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 0.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    h5 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h5 {\n",
+        "        font-weight: 300;\n",
+        "        font-style: normal;\n",
+        "        color: #1d3b84;\n",
+        "        font-size: 16pt;\n",
+        "        margin-bottom: 0em;\n",
+        "        margin-top: 1.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    div.text_cell_render{\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "        line-height: 135%;\n",
+        "        font-size: 110%;\n",
+        "        width:750px;\n",
+        "        margin-left:auto;\n",
+        "        margin-right:auto;\n",
+        "        text-align:justify;\n",
+        "        text-justify:inter-word;\n",
+        "    }\n",
+        "    div.output_subarea.output_text.output_pyout {\n",
+        "        overflow-x: auto;\n",
+        "        overflow-y: scroll;\n",
+        "        max-height: 300px;\n",
+        "    }\n",
+        "    div.output_subarea.output_stream.output_stdout.output_text {\n",
+        "        overflow-x: auto;\n",
+        "        overflow-y: scroll;\n",
+        "        max-height: 300px;\n",
+        "    }\n",
+        "    code{\n",
+        "      font-size: 70%;\n",
+        "    }\n",
+        "    .rendered_html code{\n",
+        "    background-color: transparent;\n",
+        "    }\n",
+        "    ul{\n",
+        "        margin: 2em;\n",
+        "    }\n",
+        "    ul li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.5em; \n",
+        "    }\n",
+        "    ul li li{\n",
+        "        padding-left: 0.2em; \n",
+        "        margin-bottom: 0.2em; \n",
+        "        margin-top: 0.2em; \n",
+        "    }\n",
+        "    ol{\n",
+        "        margin: 2em;\n",
+        "    }\n",
+        "    ol li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.5em; \n",
+        "    }\n",
+        "    ul li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.2em; \n",
+        "    }\n",
+        "    a:link{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    a:visited{\n",
+        "       font-weight: bold;\n",
+        "       color: #1d3b84;\n",
+        "    }\n",
+        "    a:hover{\n",
+        "       font-weight: bold;\n",
+        "       color: #1d3b84;\n",
+        "    }\n",
+        "    a:focus{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    a:active{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    .rendered_html :link {\n",
+        "       text-decoration: underline; \n",
+        "    }\n",
+        "    .rendered_html :hover {\n",
+        "       text-decoration: none; \n",
+        "    }\n",
+        "    .rendered_html :visited {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .rendered_html :focus {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .rendered_html :active {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .warning{\n",
+        "        color: rgb( 240, 20, 20 )\n",
+        "    } \n",
+        "    hr {\n",
+        "      color: #f3f3f3;\n",
+        "      background-color: #f3f3f3;\n",
+        "      height: 1px;\n",
+        "    }\n",
+        "    blockquote{\n",
+        "      display:block;\n",
+        "      background: #fcfcfc;\n",
+        "      border-left: 5px solid #c76c0c;\n",
+        "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "      width:680px;\n",
+        "      padding: 10px 10px 10px 10px;\n",
+        "      text-align:justify;\n",
+        "      text-justify:inter-word;\n",
+        "      }\n",
+        "      blockquote p {\n",
+        "        margin-bottom: 0;\n",
+        "        line-height: 125%;\n",
+        "        font-size: 100%;\n",
+        "      }\n",
+        "</style>\n",
+        "<script>\n",
+        "    MathJax.Hub.Config({\n",
+        "                        TeX: {\n",
+        "                           extensions: [\"AMSmath.js\"]\n",
+        "                           },\n",
+        "                tex2jax: {\n",
+        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
+        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
+        "                },\n",
+        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
+        "                \"HTML-CSS\": {\n",
+        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
+        "                }\n",
+        "        });\n",
+        "</script>\n"
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 1,
+       "text": [
+        "<IPython.core.display.HTML at 0x7fc4d817b9e8>"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The Kalman filter that we have developed to this point is extremely good, but it is also limited. Its derivation is in the linear space, and hence it only works for linear problems. Let's be a bit more rigorous here. You can, and we have in this book, apply the Kalman filter to nonlinear problems. For example, in the g-h filter chapter we explored using a g-h filter in a problem with constant acceleration. It 'worked', in that it remained numerically stable and the filtered output did track the input, but there was always a lag. It is easy to prove that there will always be a lag when $\\mathbf{\\ddot{x}}>0$. The filter no longer produces an optimal result. If we make our time step arbitrarily small we can still handle many problems, but typically we are using Kalman filters with physical sensors and solving real-time problems. Either fast enough sensors do not exist, are prohibitively expensive, or the computation time required is excessive. It is not a workable solution.\n",
+      "\n",
+      "The early adopters of Kalman filters were the radar people, and this fact was not lost on them. Radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n",
+      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
+      "\n",
+      "So shortly after the Kalman filter was enthusiastically taken up by the radar industry people began working on how to extend the Kalman filter into nonlinear problems. It is still an area of ongoing research, and in the Unscented Kalman filter chapter we will implement a powerful, recent result of that research. But in this chapter we will cover the most common form, the Extended Kalman filter, or EKF. Today, most real world \"Kalman filters\" are actually EKFs. The Kalman filter in your car's and phone's GPS is an EKF, for example. "
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "The Problem with Nonlinearity"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "You may not realize it, but the only math you really know how to do is linear math. Equations of the form \n",
+      "$$ A\\mathbf{x}=\\mathbf{b}$$.\n",
+      "\n",
+      "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n",
+      " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n",
+      "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n",
+      "\n",
+      "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n",
+      "\n",
+      "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n",
+      "\n",
+      "If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if a sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n",
+      "\n",
+      "$$\n",
+      "\\begin{aligned}\n",
+      "amp(roger) &= amp(roger + 0) \\\\\n",
+      "&= amp(roger) + amp(0) \\\\\n",
+      "&= amp(roger) + non\\_zero\\_value\n",
+      "\\end{aligned}\n",
+      "$$\n",
+      "\n",
+      "which is clearly nonsense. Hence, an apparently linear equation such as\n",
+      "$$L(f(t)) = f(t) + 1$$\n",
+      "\n",
+      "is not linear because $L(0) = 1$! Be careful!"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "The Effect of Nonlinear Transfer Functions on Gaussians"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian.  Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy as np\n",
+      "from numpy.random import normal\n",
+      "\n",
+      "data = normal(loc=0.0, scale=1, size=500000)\n",
+      "ys = 2*data + 1\n",
+      "\n",
+      "plt.hist(ys,1000)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtEAAAF2CAYAAACoOMTMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c24a4ef0>"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This is an unsuprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from nonlinear_plots import plot_transfer_func\n",
+      "\n",
+      "def g(x):\n",
+      "    return 2*x+1\n",
+      "\n",
+      "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAsoAAAGDCAYAAAAyKTZ5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c20c2208>"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The plot labelled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n",
+      "\n",
+      "Now let's look at a nonlinear function and see how it affects the probability distribution."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from nonlinear_plots import plot_transfer_func\n",
+      "\n",
+      "def g(x):\n",
+      "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
+      "\n",
+      "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAGDCAYAAAAlC6awAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAADCyv8AnI/h3w1eMLIAAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c1082c50>"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This result may be somewhat suprising 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",
+      "$$\\begin{aligned}\n",
+      "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
+      "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
+      "\\end{aligned}$$\n",
+      "\n",
+      "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n",
+      "\n",
+      "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "y=g(data)\n",
+      "plot_transfer_func (y, g, lims=(-4,4), num_bins=300)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAGDCAYAAAAlC6awAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAwAAwK9QgAEAAOBXKMAAAADwK/8fgHTmbOeK/F4AAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c10d0518>"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As you can see the probability function is futher distorted from the original Gaussian. However, the graph is still somewhat symmetric around $0$, let's see what the mean is."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print ('input  mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n",
+      "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "input  mean, variance: -0.0002, 1.0019\n",
+        "output mean, variance: -0.0272, 2.2486\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n",
+      "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def h(x): return -1.5*x\n",
+      "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n",
+      "out = h(data)\n",
+      "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAGDCAYAAAAlC6awAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c20b7208>"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "output mean, variance: 0.0004, 2.2543\n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "out = h(data)\n",
+      "out2 = g(data)\n",
+      "\n",
+      "for i in range(10):\n",
+      "    out = h(out)\n",
+      "    out2 = g(out2)\n",
+      "print ('linear    output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))\n",
+      "print ('nonlinear output mean, variance: %.4f, %.4f'% (np.average(out2), np.std(out2)**2))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "linear    output mean, variance: 0.0214, 7495.9793\n",
+        "nonlinear output mean, variance: -1.7468, 26292.6295\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. "
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "The Extended Kalman Filter"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n",
+      "\n",
+      "\n",
+      "Consider the function $f(x)=x^2\u22122x$, which we have plotted below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "xs =  np.arange(0,2,0.01)\n",
+      "ys = [x**2 - 2*x for x in xs]\n",
+      "plt.plot (xs, ys)\n",
+      "plt.xlim(1,2)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAF2CAYAAACh02S2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZYlDNRERERFRlv4H1uOEcHRL5gYAAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c20933c8>"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We want a linear appoximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation of the Kalman filter we know it's current state, so if we linearize the function at that value we will have a close approximation. For example, suppose our current state is $x=1.5$. What would be a good linearization for this function?\n",
+      "\n",
+      "We can use any linear function that passes through the curve at (1.5,-0.75). For example, consider using f(x)=8x\u221212.75 as the linearization, as in the plot below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def y(x): \n",
+      "    return 8*x - 12.75\n",
+      "plt.plot (xs, ys,c='k')\n",
+      "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n",
+      "plt.xlim(1,2)\n",
+      "plt.ylim([-1.5, 1])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAF2CAYAAACh02S2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nI0I1AAAAYCNCNQAAAGCj/w9NFFvbPPChxAAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c24d1908>"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This is not a good linearization for $f(x)$. It is exact for $x=1.5$, but quickly diverges when $x$ varies by a small amount.\n",
+      "\n",
+      "A much better approach is to use the slope of the function at the evaluation point as the linearization. We find the slope by taking the first derivative of the function:\n",
+      "\n",
+      " $$f(x) = x^2 -2x \\\\\n",
+      " \\frac{df}{dx} = 2x - 2$$, \n",
+      " \n",
+      " so the slope at 1.5 is $2*1.5-2=1$. Let's plot that."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def y(x): \n",
+      "    return x - 2.25\n",
+      "\n",
+      "plt.plot (xs, ys,c='k')\n",
+      "plt.plot ([1,2], [y(1),y(2)], c='r')\n",
+      "plt.xlim(1,2)\n",
+      "plt.ylim([-1.5, 1])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAF2CAYAAACh02S2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c20a49e8>"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. \n",
+      "\n",
+      "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$m we will need to include that term:\n",
+      "\n",
+      "$$\n",
+      "\\begin{aligned}\n",
+      "F \n",
+      "&\\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_{{x_t},{u_t}} \\\\\n",
+      "H &\\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_{x_t} \n",
+      "\\end{aligned}\n",
+      "$$\n",
+      "\n",
+      "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at  x. \n",
+      "\n",
+      "We approximate the state transition function $\\mathbf{F}$ by using the Taylor-series expansion \n"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "** orphan text\n",
+      "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n",
+      "\n",
+      "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n",
+      "\n",
+      "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathmatical choices will not be clear, but trust that the end result will be an EKF."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example: Tracking a Flying Airplane"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We will start by simulating tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
+      "\n",
+      "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import ekf_internal\n",
+      "ekf_internal.show_radar_chart()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAFwCAYAAACfCjKAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c10a5c50>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAFwCAYAAACfCjKAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c10a5dd8>"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As discussed in the introduction, our measurement model is the nonlinear function $x=\\sqrt{slant^2 - altitude^2}$. Therefore we will need a nonlinear \n",
+      "\n",
+      "Predict step:\n",
+      "$$\n",
+      "\\begin{array}{ll}\n",
+      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
+      "x = Fx & x = \\underline{f(x)} \\\\\n",
+      "P = FPF^T + Q & P = FPF^T + Q\n",
+      "\\end{array}\n",
+      "$$\n",
+      "\n",
+      "Update step:\n",
+      "$$\n",
+      "\\begin{array}{ll}\n",
+      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
+      "K = PH^T(HPH^T + R)^{-1}& K = PH^T(HPH^T + R)^{-1}\\\\\n",
+      "x = x + K(z-Hx) & x = x + K(z-\\underline{h(x)}) \\\\\n",
+      "P = P(I - KH) & P = P(I - KH)\\\\\n",
+      "\\end{array}\n",
+      "$$\n",
+      "\n"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As we can see there are two minor changes to the Kalman filter equations. The first change replaces the equation $\\mathbf{x} = \\mathbf{Fx}$ with $\\mathbf{x} = f(\\mathbf{x})$. In the Kalman filter, $\\mathbf{Fx}$ is how we compute the new state based on the old state. However, in a nonlinear system we cannot use linear algebra to compute this transition. So instead we hypothesize a nonlinear function $f()$ which performs this function. Likewise, in the Kalman filter we convert the state to a measurement with the linear function $\\mathbf{Hx}$. For the extended Kalman filter we replace this with a nonlinear function $h()$, giving $\\mathbf{z}_x = h(\\mathbf{x})$.\n",
+      "\n",
+      "The only question left is how do we implement use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system.  For example, consider the function $f(x) = x^2 -2x$\n",
+      "\n",
+      "\n",
+      "The rest of the equations are unchanged, so $f()$ and $h()$ must produce a matrix that approximates the values of the matrices $\\mathbf{F}$ and $\\mathbf{H}$ at the current value for $\\mathbf{x}$. We do this by computing the partial derivatives of the state and measurements functions:\n",
+      "\n",
+      "\n",
+      "$$\n",
+      "F \\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_x, \\\\\n",
+      "H \\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_x \n",
+      "$$\n",
+      "\n",
+      "All this means is that at each update step we compute F as the partial derivative of our function $f()$ evaluated at the point of f. "
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "xs =  np.arange(0,2,0.01)\n",
+      "ys = [x**2 - 2*x for x in xs]\n",
+      "plt.plot (xs, ys)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAF2CAYAAACh02S2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEemh/wfy5LGTmUX1AAAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c2097be0>"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Suppose we want to linearlize this equation so we can evaluate it's value at 1.5. In other words, we want to create a linear function of the form $y_l(x) = ax+b$ such that $y_l(1.5)$ gives the same value as $y(1.5)$. Obviously there is not single linear equation that will do this. But if we linearize $y(x)$ at 1.5, then we will have a perfect answer for $y_l(1.5)$, and a progressively worse answer as our evaluation point gets further away from 1.5.\n",
+      "\n",
+      "The simplest way to linearize a function is to take a partial derivative of it. In geometic terms, the derivative of a function at a point is just the slope of the function. Let's just look at that, and then reason about why this is a good choice.\n",
+      "\n",
+      "The derivative of $f(x) = x^2 -2x$ is $\\frac{\\partial{f}}{\\partial{x}} = 2x - 2$, so the slope at 1.5 is $2*1.5-2=1$. Let's plot that."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def y(x): \n",
+      "    return x - 2.25\n",
+      "\n",
+      "plt.plot (xs, ys)\n",
+      "plt.plot ([1,2], [y(1),y(2)], c='r')\n",
+      "plt.ylim([-1.5, 1])\n",
+      "\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAF2CAYAAACh02S2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ndHfrkQAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c1064eb8>"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This is a nice visual demonstration of how the slope of the function gives the ideal linear approximation of the function near a point. We could use any linear function such that $f(1.5)=-0.75$, here, but as x varies the value computed by the function would potentially be very far from the functions value. For example, consider using $f(x) = 8x - 12.75$ as the linearization, as in the plot below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def y(x): \n",
+      "    return 8*x - 12.75\n",
+      "plt.plot (xs, ys)\n",
+      "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n",
+      "plt.ylim([-1.5, 1])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAtUAAAF2CAYAAACh02S2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c20c51d0>"
+       ]
+      }
+     ],
+     "prompt_number": 15
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We can see that the linearization is exactly correct for $x=1.5$, but very quickly diverges as x varies from 1.5. This does not constitute a proof that taking the derivative is a good linearization, but it should be fairly convincing. "
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We will begin by writing a simulation for the radar."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import random\n",
+      "import math\n",
+      "\n",
+      "class Radar(object):\n",
+      "    def __init__(self, pos, vel, alt, dt):\n",
+      "        self.pos = pos\n",
+      "        self.vel = vel\n",
+      "        self.alt = alt\n",
+      "        self.dt = dt\n",
+      "        \n",
+      "    def get(self):\n",
+      "        \"\"\" Simulate radar range to object at 1K altidue and moving at 100m/s.\n",
+      "        Adds about 5% measurement noise. Returns slant range to the object.\n",
+      "        Call once for each new measurement at dt time from last call.\n",
+      "        \"\"\"\n",
+      "        \n",
+      "        # add some process noise to the system\n",
+      "        vel = self.vel  + 5*random.gauss(0,1)\n",
+      "        alt = self.alt + 10*random.gauss(0,1)\n",
+      "        self.pos = self.pos + vel*self.dt\n",
+      "    \n",
+      "        # add measurment noise\n",
+      "        err = self.pos * 0.05*random.gauss(0,1)\n",
+      "        return math.sqrt(self.pos**2 + alt**2) + err"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "$$F = I + \\begin{bmatrix}0 & 1 & 0\\\\ 0 & 0 & 0\\\\0&0&0\\end{bmatrix}dt$$"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "$$\n",
+      "\\begin{aligned}\n",
+      "H&=\\begin{bmatrix}\n",
+      "\\frac{\\partial h}{\\partial x_{pos}} & \n",
+      "\\frac{\\partial h}{\\partial x_{vel}} &\n",
+      "\\frac{\\partial h}{\\partial x_{alt}}\\end{bmatrix} \\\\\n",
+      "&= \\begin{bmatrix}\n",
+      "\\frac{x_{pos}}{\\sqrt{x_{pos}^2 + x_{alt}^2}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
+      "\\end{bmatrix}\n",
+      "\\end{aligned}\n",
+      "$$"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Example: A falling Ball"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import ekf_internal\n",
+      "ekf_internal.plot_ball()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF2CAYAAABtSl5dAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\na8ZxXqsAAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7fc4c2083198>"
+       ]
+      }
+     ],
+     "prompt_number": 17
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We can artifically force the Kalman filter to track the ball by making $Q$ large. That would cause the filter to mistrust its prediction, and scale the kalman gain $K$ to strongly favor the measurments. However, this is not a valid approach. If the Kalman filter is correctly predicting the process we should not 'lie' to the filter by telling it there are process errors that do not exist. We may get away with that for some problems, in some conditions, but in general the Kalman filter's performance will be substandard.\n",
+      "\n",
+      "Recall from the **Designing Kalman Filters** chapter that the acceleration is\n",
+      "\n",
+      "$$a_x = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_x \\\\\n",
+      "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n",
+      "$$\n",
+      "\n",
+      "These equations will be very unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n",
+      "\n",
+      "\n",
+      "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n",
+      "\n",
+      "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 17
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file
diff --git a/Extended_Kalman_Filters.ipynb b/Extended_Kalman_Filters.ipynb
deleted file mode 100644
index 219bdf1..0000000
--- a/Extended_Kalman_Filters.ipynb
+++ /dev/null
@@ -1,1039 +0,0 @@
-{
- "metadata": {
-  "name": "",
-  "signature": "sha256:ab67c51059a4e13a6e530ab9ac6055815a6e0856a34dcefe748088741a95b950"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
-  {
-   "cells": [
-    {
-     "cell_type": "heading",
-     "level": 1,
-     "metadata": {},
-     "source": [
-      "The Extended Kalman Filter"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "#format the book\n",
-      "%matplotlib inline\n",
-      "from __future__ import division, print_function\n",
-      "import matplotlib.pyplot as plt\n",
-      "import book_format\n",
-      "book_format.load_style()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "html": [
-        "<style>\n",
-        "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
-        "\n",
-        "    div.cell{\n",
-        "        width: 850px;\n",
-        "        margin-left: 0% !important;\n",
-        "        margin-right: auto;\n",
-        "    }\n",
-        "    div.text_cell code {\n",
-        "        background: transparent;\n",
-        "        color: #000000;\n",
-        "        font-weight: 600;\n",
-        "        font-size: 11pt;\n",
-        "        font-style: bold;\n",
-        "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
-        "   }\n",
-        "    h1 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "\t}\n",
-        "\t\n",
-        "    div.input_area {\n",
-        "        background: #F6F6F9;\n",
-        "        border: 1px solid #586e75;\n",
-        "    }\n",
-        "\n",
-        "    .text_cell_render h1 {\n",
-        "        font-weight: 200;\n",
-        "        font-size: 30pt;\n",
-        "        line-height: 100%;\n",
-        "        color:#c76c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 1em;\n",
-        "        display: block;\n",
-        "        white-space: wrap;\n",
-        "    } \n",
-        "    h2 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h2 {\n",
-        "        font-weight: 200;\n",
-        "        font-size: 20pt;\n",
-        "        font-style: italic;\n",
-        "        line-height: 100%;\n",
-        "        color:#c76c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 1.5em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    } \n",
-        "    h3 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h3 {\n",
-        "        font-weight: 300;\n",
-        "        font-size: 18pt;\n",
-        "        line-height: 100%;\n",
-        "        color:#d77c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 2em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    }\n",
-        "    h4 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h4 {\n",
-        "        font-weight: 300;\n",
-        "        font-size: 16pt;\n",
-        "        color:#d77c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 0.5em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    }\n",
-        "    h5 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h5 {\n",
-        "        font-weight: 300;\n",
-        "        font-style: normal;\n",
-        "        color: #1d3b84;\n",
-        "        font-size: 16pt;\n",
-        "        margin-bottom: 0em;\n",
-        "        margin-top: 1.5em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    }\n",
-        "    div.text_cell_render{\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "        line-height: 135%;\n",
-        "        font-size: 110%;\n",
-        "        width:750px;\n",
-        "        margin-left:auto;\n",
-        "        margin-right:auto;\n",
-        "        text-align:justify;\n",
-        "        text-justify:inter-word;\n",
-        "    }\n",
-        "    div.output_subarea.output_text.output_pyout {\n",
-        "        overflow-x: auto;\n",
-        "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
-        "    }\n",
-        "    div.output_subarea.output_stream.output_stdout.output_text {\n",
-        "        overflow-x: auto;\n",
-        "        overflow-y: scroll;\n",
-        "        max-height: 300px;\n",
-        "    }\n",
-        "    code{\n",
-        "      font-size: 70%;\n",
-        "    }\n",
-        "    .rendered_html code{\n",
-        "    background-color: transparent;\n",
-        "    }\n",
-        "    ul{\n",
-        "        margin: 2em;\n",
-        "    }\n",
-        "    ul li{\n",
-        "        padding-left: 0.5em; \n",
-        "        margin-bottom: 0.5em; \n",
-        "        margin-top: 0.5em; \n",
-        "    }\n",
-        "    ul li li{\n",
-        "        padding-left: 0.2em; \n",
-        "        margin-bottom: 0.2em; \n",
-        "        margin-top: 0.2em; \n",
-        "    }\n",
-        "    ol{\n",
-        "        margin: 2em;\n",
-        "    }\n",
-        "    ol li{\n",
-        "        padding-left: 0.5em; \n",
-        "        margin-bottom: 0.5em; \n",
-        "        margin-top: 0.5em; \n",
-        "    }\n",
-        "    ul li{\n",
-        "        padding-left: 0.5em; \n",
-        "        margin-bottom: 0.5em; \n",
-        "        margin-top: 0.2em; \n",
-        "    }\n",
-        "    a:link{\n",
-        "       font-weight: bold;\n",
-        "       color:#447adb;\n",
-        "    }\n",
-        "    a:visited{\n",
-        "       font-weight: bold;\n",
-        "       color: #1d3b84;\n",
-        "    }\n",
-        "    a:hover{\n",
-        "       font-weight: bold;\n",
-        "       color: #1d3b84;\n",
-        "    }\n",
-        "    a:focus{\n",
-        "       font-weight: bold;\n",
-        "       color:#447adb;\n",
-        "    }\n",
-        "    a:active{\n",
-        "       font-weight: bold;\n",
-        "       color:#447adb;\n",
-        "    }\n",
-        "    .rendered_html :link {\n",
-        "       text-decoration: underline; \n",
-        "    }\n",
-        "    .rendered_html :hover {\n",
-        "       text-decoration: none; \n",
-        "    }\n",
-        "    .rendered_html :visited {\n",
-        "      text-decoration: none;\n",
-        "    }\n",
-        "    .rendered_html :focus {\n",
-        "      text-decoration: none;\n",
-        "    }\n",
-        "    .rendered_html :active {\n",
-        "      text-decoration: none;\n",
-        "    }\n",
-        "    .warning{\n",
-        "        color: rgb( 240, 20, 20 )\n",
-        "    } \n",
-        "    hr {\n",
-        "      color: #f3f3f3;\n",
-        "      background-color: #f3f3f3;\n",
-        "      height: 1px;\n",
-        "    }\n",
-        "    blockquote{\n",
-        "      display:block;\n",
-        "      background: #fcfcfc;\n",
-        "      border-left: 5px solid #c76c0c;\n",
-        "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "      width:680px;\n",
-        "      padding: 10px 10px 10px 10px;\n",
-        "      text-align:justify;\n",
-        "      text-justify:inter-word;\n",
-        "      }\n",
-        "      blockquote p {\n",
-        "        margin-bottom: 0;\n",
-        "        line-height: 125%;\n",
-        "        font-size: 100%;\n",
-        "      }\n",
-        "</style>\n",
-        "<script>\n",
-        "    MathJax.Hub.Config({\n",
-        "                        TeX: {\n",
-        "                           extensions: [\"AMSmath.js\"]\n",
-        "                           },\n",
-        "                tex2jax: {\n",
-        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
-        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
-        "                },\n",
-        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
-        "                \"HTML-CSS\": {\n",
-        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
-        "                }\n",
-        "        });\n",
-        "</script>\n"
-       ],
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 1,
-       "text": [
-        "<IPython.core.display.HTML at 0x7f2d25427748>"
-       ]
-      }
-     ],
-     "prompt_number": 1
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "The Kalman filter that we have developed to this point is extremely good, but it is also limited. Its derivation is in the linear space, and hence it only works for linear problems. Let's be a bit more rigorous here. You can, and we have in this book, apply the Kalman filter to nonlinear problems. For example, in the g-h filter chapter we explored using a g-h filter in a problem with constant acceleration. It 'worked', in that it remained numerically stable and the filtered output did track the input, but there was always a lag. It is easy to prove that there will always be a lag when $\\mathbf{\\ddot{x}}>0$. The filter no longer produces an optimal result. If we make our time step arbitrarily small we can still handle many problems, but typically we are using Kalman filters with physical sensors and solving real-time problems. Either fast enough sensors do not exist, are prohibitively expensive, or the computation time required is excessive. It is not a workable solution.\n",
-      "\n",
-      "The early adopters of Kalman filters were the radar people, and this fact was not lost on them. Radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n",
-      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
-      "\n",
-      "So shortly after the Kalman filter was enthusiastically taken up by the radar industry people began working on how to extend the Kalman filter into nonlinear problems. It is still an area of ongoing research, and in the Unscented Kalman filter chapter we will implement a powerful, recent result of that research. But in this chapter we will cover the most common form, the Extended Kalman filter, or EKF. Today, most real world \"Kalman filters\" are actually EKFs. The Kalman filter in your car's and phone's GPS is an EKF, for example. "
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "The Problem with Nonlinearity"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "You may not realize it, but the only math you really know how to do is linear math. Equations of the form \n",
-      "$$ A\\mathbf{x}=\\mathbf{b}$$.\n",
-      "\n",
-      "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n",
-      " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n",
-      "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n",
-      "\n",
-      "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n",
-      "\n",
-      "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n",
-      "\n",
-      "If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if a sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n",
-      "\n",
-      "$$\n",
-      "\\begin{aligned}\n",
-      "amp(roger) &= amp(roger + 0) \\\\\n",
-      "&= amp(roger) + amp(0) \\\\\n",
-      "&= amp(roger) + non\\_zero\\_value\n",
-      "\\end{aligned}\n",
-      "$$\n",
-      "\n",
-      "which is clearly nonsense. Hence, an apparently linear equation such as\n",
-      "$$L(f(t)) = f(t) + 1$$\n",
-      "\n",
-      "is not linear because $L(0) = 1$! Be careful!"
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "The Effect of Nonlinear Transfer Functions on Gaussians"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian.  Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import numpy as np\n",
-      "from numpy.random import normal\n",
-      "\n",
-      "data = normal(loc=0.0, scale=1, size=500000)\n",
-      "ys = 2*data + 1\n",
-      "\n",
-      "plt.hist(ys,1000)\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAssAAAFyCAYAAAADJZf7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nANAHYRkAAADog7AMAAAA9PH/AQTVtAQWnH8sAAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0c3b6f60>"
-       ]
-      }
-     ],
-     "prompt_number": 2
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This is an unsuprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from nonlinear_plots import plot_transfer_func\n",
-      "\n",
-      "def g(x):\n",
-      "    return 2*x+1\n",
-      "\n",
-      "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAF9CAYAAADsuhWdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAADA9ijFAAAAsL3/ASpaa25FgskwAAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0bfbeb70>"
-       ]
-      }
-     ],
-     "prompt_number": 3
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "The plot labelled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n",
-      "\n",
-      "Now let's look at a nonlinear function and see how it affects the probability distribution."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from nonlinear_plots import plot_transfer_func\n",
-      "\n",
-      "def g(x):\n",
-      "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
-      "\n",
-      "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAF9CAYAAAAJJNDxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUe//AbYhT29XZGuUAAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0bf56320>"
-       ]
-      }
-     ],
-     "prompt_number": 4
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This result may be somewhat suprising 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",
-      "$$\\begin{aligned}\n",
-      "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
-      "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
-      "\\end{aligned}$$\n",
-      "\n",
-      "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n",
-      "\n",
-      "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "y=g(data)\n",
-      "plot_transfer_func (y, g, lims=(-4,4), num_bins=300)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAF9CAYAAAAJJNDxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0af77cf8>"
-       ]
-      }
-     ],
-     "prompt_number": 5
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "As you can see the probability function is futher distorted from the original Gaussian. However, the graph is still somewhat symmetric around $0$, let's see what the mean is."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "print ('input  mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n",
-      "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "input  mean, variance: -0.0016, 0.9985\n",
-        "output mean, variance: -0.0249, 2.2395\n"
-       ]
-      }
-     ],
-     "prompt_number": 6
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n",
-      "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def h(x): return -1.5*x\n",
-      "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n",
-      "out = h(data)\n",
-      "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAF9CAYAAAAJJNDxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wcc3ZZZ6gexPwAAAABJRU5ErkJggg==\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0afb9d30>"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "output mean, variance: 0.0025, 2.2465\n"
-       ]
-      }
-     ],
-     "prompt_number": 7
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "out = h(data)\n",
-      "out2 = g(data)\n",
-      "\n",
-      "for i in range(10):\n",
-      "    out = h(out)\n",
-      "    out2 = g(out2)\n",
-      "print ('linear    output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))\n",
-      "print ('nonlinear output mean, variance: %.4f, %.4f'% (np.average(out2), np.std(out2)**2))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "linear    output mean, variance: 0.1420, 7470.2773\n",
-        "nonlinear output mean, variance: -1.4736, 26191.9586\n"
-       ]
-      }
-     ],
-     "prompt_number": 8
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. "
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "The Extended Kalman Filter"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n",
-      "\n",
-      "\n",
-      "Consider the function $f(x)=x^2\u22122x$, which we have plotted below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "xs =  np.arange(0,2,0.01)\n",
-      "ys = [x**2 - 2*x for x in xs]\n",
-      "plt.plot (xs, ys)\n",
-      "plt.xlim(1,2)\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAs8AAAFyCAYAAAAKzjeBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0afbe5c0>"
-       ]
-      }
-     ],
-     "prompt_number": 9
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We want a linear appoximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation of the Kalman filter we know it's current state, so if we linearize the function at that value we will have a close approximation. For example, suppose our current state is $x=1.5$. What would be a good linearization for this function?\n",
-      "\n",
-      "We can use any linear function that passes through the curve at (1.5,-0.75). For example, consider using f(x)=8x\u221212.75 as the linearization, as in the plot below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def y(x): \n",
-      "    return 8*x - 12.75\n",
-      "plt.plot (xs, ys,c='k')\n",
-      "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n",
-      "plt.xlim(1,2)\n",
-      "plt.ylim([-1.5, 1])\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAs8AAAFyCAYAAAAKzjeBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAuInwDAAAALjp/wN8CdGvM9/CZQAAAABJRU5ErkJggg==\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0afd9978>"
-       ]
-      }
-     ],
-     "prompt_number": 10
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This is not a good linearization for $f(x)$. It is exact for $x=1.5$, but quickly diverges when $x$ varies by a small amount.\n",
-      "\n",
-      "A much better approach is to use the slope of the function at the evaluation point as the linearization. We find the slope by taking the first derivative of the function:\n",
-      "\n",
-      " $$f(x) = x^2 -2x \\\\\n",
-      " \\frac{df}{dx} = 2x - 2$$, \n",
-      " \n",
-      " so the slope at 1.5 is $2*1.5-2=1$. Let's plot that."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def y(x): \n",
-      "    return x - 2.25\n",
-      "\n",
-      "plt.plot (xs, ys,c='k')\n",
-      "plt.plot ([1,2], [y(1),y(2)], c='r')\n",
-      "plt.xlim(1,2)\n",
-      "plt.ylim([-1.5, 1])\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAs8AAAFyCAYAAAAKzjeBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEc8AAACAQcQzAAAAYBDxDAAAABj0/wGT4ivjb8R/WwAAAABJRU5ErkJggg==\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0ae82c50>"
-       ]
-      }
-     ],
-     "prompt_number": 11
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. \n",
-      "\n",
-      "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$m we will need to include that term:\n",
-      "\n",
-      "$$\n",
-      "\\begin{aligned}\n",
-      "F \n",
-      "&\\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_{{x_t},{u_t}} \\\\\n",
-      "H &\\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_{x_t} \n",
-      "\\end{aligned}\n",
-      "$$\n",
-      "\n",
-      "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at  x. \n",
-      "\n",
-      "We approximate the state transition function $\\mathbf{F}$ by using the Taylor-series expansion \n"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "** orphan text\n",
-      "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n",
-      "\n",
-      "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n",
-      "\n",
-      "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathmatical choices will not be clear, but trust that the end result will be an EKF."
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 3,
-     "metadata": {},
-     "source": [
-      "Example: Tracking a Flying Airplane"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We will start by simulating tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
-      "\n",
-      "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import ekf_internal\n",
-      "ekf_internal.show_radar_chart()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAFtCAYAAAAgQiPFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0c3d2f60>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAFtCAYAAAAgQiPFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d25427550>"
-       ]
-      }
-     ],
-     "prompt_number": 12
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "As discussed in the introduction, our measurement model is the nonlinear function $x=\\sqrt{slant^2 - altitude^2}$. Therefore we will need a nonlinear \n",
-      "\n",
-      "Predict step:\n",
-      "$$\n",
-      "\\begin{array}{ll}\n",
-      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
-      "x = Fx & x = \\underline{f(x)} \\\\\n",
-      "P = FPF^T + Q & P = FPF^T + Q\n",
-      "\\end{array}\n",
-      "$$\n",
-      "\n",
-      "Update step:\n",
-      "$$\n",
-      "\\begin{array}{ll}\n",
-      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
-      "K = PH^T(HPH^T + R)^{-1}& K = PH^T(HPH^T + R)^{-1}\\\\\n",
-      "x = x + K(z-Hx) & x = x + K(z-\\underline{h(x)}) \\\\\n",
-      "P = P(I - KH) & P = P(I - KH)\\\\\n",
-      "\\end{array}\n",
-      "$$\n",
-      "\n"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "As we can see there are two minor changes to the Kalman filter equations. The first change replaces the equation $\\mathbf{x} = \\mathbf{Fx}$ with $\\mathbf{x} = f(\\mathbf{x})$. In the Kalman filter, $\\mathbf{Fx}$ is how we compute the new state based on the old state. However, in a nonlinear system we cannot use linear algebra to compute this transition. So instead we hypothesize a nonlinear function $f()$ which performs this function. Likewise, in the Kalman filter we convert the state to a measurement with the linear function $\\mathbf{Hx}$. For the extended Kalman filter we replace this with a nonlinear function $h()$, giving $\\mathbf{z}_x = h(\\mathbf{x})$.\n",
-      "\n",
-      "The only question left is how do we implement use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system.  For example, consider the function $f(x) = x^2 -2x$\n",
-      "\n",
-      "\n",
-      "The rest of the equations are unchanged, so $f()$ and $h()$ must produce a matrix that approximates the values of the matrices $\\mathbf{F}$ and $\\mathbf{H}$ at the current value for $\\mathbf{x}$. We do this by computing the partial derivatives of the state and measurements functions:\n",
-      "\n",
-      "\n",
-      "$$\n",
-      "F \\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_x, \\\\\n",
-      "H \\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_x \n",
-      "$$\n",
-      "\n",
-      "All this means is that at each update step we compute F as the partial derivative of our function $f()$ evaluated at the point of f. "
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "xs =  np.arange(0,2,0.01)\n",
-      "ys = [x**2 - 2*x for x in xs]\n",
-      "plt.plot (xs, ys)\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAs8AAAFyCAYAAAAKzjeBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiIdNH/AxHFjmRS+CEYAAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0afc6eb8>"
-       ]
-      }
-     ],
-     "prompt_number": 13
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Suppose we want to linearlize this equation so we can evaluate it's value at 1.5. In other words, we want to create a linear function of the form $y_l(x) = ax+b$ such that $y_l(1.5)$ gives the same value as $y(1.5)$. Obviously there is not single linear equation that will do this. But if we linearize $y(x)$ at 1.5, then we will have a perfect answer for $y_l(1.5)$, and a progressively worse answer as our evaluation point gets further away from 1.5.\n",
-      "\n",
-      "The simplest way to linearize a function is to take a partial derivative of it. In geometic terms, the derivative of a function at a point is just the slope of the function. Let's just look at that, and then reason about why this is a good choice.\n",
-      "\n",
-      "The derivative of $f(x) = x^2 -2x$ is $\\frac{\\partial{f}}{\\partial{x}} = 2x - 2$, so the slope at 1.5 is $2*1.5-2=1$. Let's plot that."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def y(x): \n",
-      "    return x - 2.25\n",
-      "\n",
-      "plt.plot (xs, ys)\n",
-      "plt.plot ([1,2], [y(1),y(2)], c='r')\n",
-      "plt.ylim([-1.5, 1])\n",
-      "\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAs8AAAFyCAYAAAAKzjeBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAACGGJ4BAAAAQwzPAAAAgKE/jKzLnf2jXcwAAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0bfb07f0>"
-       ]
-      }
-     ],
-     "prompt_number": 14
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This is a nice visual demonstration of how the slope of the function gives the ideal linear approximation of the function near a point. We could use any linear function such that $f(1.5)=-0.75$, here, but as x varies the value computed by the function would potentially be very far from the functions value. For example, consider using $f(x) = 8x - 12.75$ as the linearization, as in the plot below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def y(x): \n",
-      "    return 8*x - 12.75\n",
-      "plt.plot (xs, ys)\n",
-      "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n",
-      "plt.ylim([-1.5, 1])\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAs8AAAFyCAYAAAAKzjeBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0afd5198>"
-       ]
-      }
-     ],
-     "prompt_number": 15
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We can see that the linearization is exactly correct for $x=1.5$, but very quickly diverges as x varies from 1.5. This does not constitute a proof that taking the derivative is a good linearization, but it should be fairly convincing. "
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We will begin by writing a simulation for the radar."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import random\n",
-      "import math\n",
-      "\n",
-      "class Radar(object):\n",
-      "    def __init__(self, pos, vel, alt, dt):\n",
-      "        self.pos = pos\n",
-      "        self.vel = vel\n",
-      "        self.alt = alt\n",
-      "        self.dt = dt\n",
-      "        \n",
-      "    def get(self):\n",
-      "        \"\"\" Simulate radar range to object at 1K altidue and moving at 100m/s.\n",
-      "        Adds about 5% measurement noise. Returns slant range to the object.\n",
-      "        Call once for each new measurement at dt time from last call.\n",
-      "        \"\"\"\n",
-      "        \n",
-      "        # add some process noise to the system\n",
-      "        vel = self.vel  + 5*random.gauss(0,1)\n",
-      "        alt = self.alt + 10*random.gauss(0,1)\n",
-      "        self.pos = self.pos + vel*self.dt\n",
-      "    \n",
-      "        # add measurment noise\n",
-      "        err = self.pos * 0.05*random.gauss(0,1)\n",
-      "        return math.sqrt(self.pos**2 + alt**2) + err"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "$$F = I + \\begin{bmatrix}0 & 1 & 0\\\\ 0 & 0 & 0\\\\0&0&0\\end{bmatrix}dt$$"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "$$\n",
-      "\\begin{aligned}\n",
-      "H&=\\begin{bmatrix}\n",
-      "\\frac{\\partial h}{\\partial x_{pos}} & \n",
-      "\\frac{\\partial h}{\\partial x_{vel}} &\n",
-      "\\frac{\\partial h}{\\partial x_{alt}}\\end{bmatrix} \\\\\n",
-      "&= \\begin{bmatrix}\n",
-      "\\frac{x_{pos}}{\\sqrt{x_{pos}^2 + x_{alt}^2}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
-      "\\end{bmatrix}\n",
-      "\\end{aligned}\n",
-      "$$"
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 3,
-     "metadata": {},
-     "source": [
-      "Example: A falling Ball"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import ekf_internal\n",
-      "ekf_internal.plot_ball()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAsIAAAFyCAYAAAD/MLwxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n9PGq1QAAAABJRU5ErkJggg==\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f2d0bfc6160>"
-       ]
-      }
-     ],
-     "prompt_number": 17
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We can artifically force the Kalman filter to track the ball by making $Q$ large. That would cause the filter to mistrust its prediction, and scale the kalman gain $K$ to strongly favor the measurments. However, this is not a valid approach. If the Kalman filter is correctly predicting the process we should not 'lie' to the filter by telling it there are process errors that do not exist. We may get away with that for some problems, in some conditions, but in general the Kalman filter's performance will be substandard.\n",
-      "\n",
-      "Recall from the **Designing Kalman Filters** chapter that the acceleration is\n",
-      "\n",
-      "$$a_x = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_x \\\\\n",
-      "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n",
-      "$$\n",
-      "\n",
-      "These equations will be very unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n",
-      "\n",
-      "\n",
-      "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n",
-      "\n",
-      "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 17
-    }
-   ],
-   "metadata": {}
-  }
- ]
-}
\ No newline at end of file