11-Extended-Kalman-Filters.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
       "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
       "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
       "\n",
       "    div.cell{\n",
       "        width: 900px;\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",
       "        text-align: left;\n",
       "    } \n",
       "    h2 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "        text-align: left;\n",
       "    }\n",
       "    .text_cell_render h2 {\n",
       "        font-weight: 200;\n",
       "        font-size: 16pt;\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: wrap;\n",
       "        text-align: left;\n",
       "    } \n",
       "    h3 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h3 {\n",
       "        font-weight: 200;\n",
       "        font-size: 14pt;\n",
       "        line-height: 100%;\n",
       "        color:#d77c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 2em;\n",
       "        display: block;\n",
       "        white-space: wrap;\n",
       "        text-align: left;\n",
       "    }\n",
       "    h4 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h4 {\n",
       "        font-weight: 100;\n",
       "        font-size: 14pt;\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: 200;\n",
       "        font-style: normal;\n",
       "        color: #1d3b84;\n",
       "        font-size: 16pt;\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    div.text_cell_render{\n",
       "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
       "        line-height: 125%;\n",
       "        font-size: 120%;\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: 50000px;\n",
       "    }\n",
       "    div.output_subarea.output_stream.output_stdout.output_text {\n",
       "        overflow-x: auto;\n",
       "        overflow-y: scroll;\n",
       "        max-height: 50000px;\n",
       "    }\n",
       "    div.output_wrapper{\n",
       "        margin-top:0.2em;\n",
       "        margin-bottom:0.2em;\n",
       "}\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",
       "                    scale:100,\n",
       "                        availableFonts: [],\n",
       "                        preferredFont:null,\n",
       "                        webFont: \"TeX\",\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2  \n",
    "from __future__ import division, print_function\n",
    "import sys\n",
    "sys.path.insert(0,'./code')\n",
    "from book_format import load_style\n",
    "load_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point in the book we have developed the theory for the linear Kalman filter. Then, in the last two chapters we broached the topic of using Kalman filters for nonlinear problems. In this chapter we will learn the Extended Kalman filter (EKF). The EKF handles nonlinearity by linearizing the system at the point of the current estimate, and then the linear Kalman filter is used to filter this linearized system. It was one of the very first techniques used for nonlinear problems, and it remains the most common technique. Most filters in real world use are EKFs. \n",
    "\n",
    "The EKF provides significant mathematical challenges to the designer of the filter; this is the most challenging chapter of the book. To be honest, I do everything I can to avoid the EKF in favor of other techniques that have been developed to filter nonlinear problems. However, the topic is unavoidable; all classic papers and a majority of current papers in the field use the EKF. Even if you do not use the EKF in your own work you will need to be familiar with the topic to be able to read the literature. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearizing a System"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the function $f(x)=x^2−2x$. We want a linear approximation 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 (update) of the Kalman filter we know its 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−12.75 as the linearization, as in the plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu0AAAEWCAYAAADSA6kgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAwAAAH6O0A4AAAD4OUI7AAAA4Of+HyfFkOGO0XN/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6dda518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xs =  np.arange(0, 2, 0.01)\n",
    "ys = [x**2 - 2*x for x in xs]\n",
    "\n",
    "def y(x): \n",
    "    return 8*x - 12.75\n",
    "\n",
    "plt.plot(xs, ys)\n",
    "plt.plot([1.25, 1.75], [y(1.25), y(1.75)])\n",
    "plt.xlim(1, 2)\n",
    "plt.ylim([-1.5, 1]);"
   ]
  },
  {
   "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",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAu0AAAEWCAYAAADSA6kgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6dbefd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def y(x): \n",
    "    return x - 2.25\n",
    "\n",
    "plt.plot(xs, ys)\n",
    "plt.plot([1, 2], [y(1), y(2)])\n",
    "plt.xlim(1, 2)\n",
    "plt.ylim([-1.5, 1]);"
   ]
  },
  {
   "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. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearizing the Kalman Filter\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 ($\\mathbf{x}_t$). In other words we linearize the equations at time t by finding the slope (derivative) of the equations at that time. Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$ 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. We then use a computational technique, such as Taylor expansion, to turn this into a set of linear equations.\n",
    "\n",
    "For nonlinear problems our function $f()$ is a set of differential equations. Modeling physical systems with differential equations is well outside the scope of this book. You will need to be reasonably well versed in this branch of applied mathematics to successfully implement the EKF for your problem. If you have not read it yet, please read the section **Modeling Dynamic Systems** in the **Kalman Filter Math** chapter as it contains the math that you will need to complete this chapter.\n",
    "\n",
    "I think the easiest way to understand the EKF is to start off with an example. Perhaps the reason for some of my mathematical choices will not be clear, but trust that the end result will be an EKF.\n",
    "\n",
    "\n",
    "**orphan**\n",
    "The extended Kalman filter (EKF) linearizing the process model for each evolution. 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 1/100 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. More often you will have to perform numeric integration. 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. "
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAr8AAAERCAYAAABy58/tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABsg/ALAAAA2yD8AgAAwDb+Pxx+J0H6f6q5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x434c6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import ekf_internal\n",
    "ekf_internal.show_radar_chart()"
   ]
  },
  {
   "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",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
    "\\mathbf{\\bar{x}} = \\mathbf{Fx} & \\mathbf{\\bar{x}} = \\underline{f(x)} \\\\\n",
    "\\mathbf{\\bar{P}} = \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q} & \\mathbf{\\bar{P}} = \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "Update step:\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
    "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T}(\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf{R})^{-1}& \\mathbf{K} = \\mathbf{PH}^\\mathsf{T}(\\mathbf{HPH}^\\mathsf{T} + \\mathbf{R})^{-1}\\\\\n",
    "\\mathbf{x} = \\mathbf{\\bar{x}} + \\mathbf{K}(\\mathbf{z}-\\mathbf{H\\bar{x}}) & \\mathbf{x} = \\mathbf{\\bar{x}} + \\mathbf{K}(\\mathbf{z}-\\underline{h(x)}) \\\\\n",
    "\\mathbf{P} = \\mathbf{\\bar{P}}(\\mathbf{I} - \\mathbf{KH}) & \\mathbf{P} = \\mathbf{\\bar{P}}(\\mathbf{I} - \\mathbf{KH})\\\\\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see there are two minor changes to the Kalman filter equations, which I have underlined. 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 and 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",
    "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:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we want to track the position of an aircraft assuming a constant velocity and altitude, and measurements of the slant distance to the aircraft. That means we need 3 state variables - horizontal distance, velocity, and altitude.\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude\\end{bmatrix}=  \\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the System Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will model this as a set of differential equations. So we need an equation in the form \n",
    "$$\\dot{\\mathbf{x}} = \\mathbf{Ax} + \\mathbf{w}$$\n",
    "\n",
    "where $\\mathbf{w}$ is the system noise. \n",
    "\n",
    "Let's work out the equation for each of the rows in $\\mathbf{x}.$\n",
    "\n",
    "The first row is $\\dot{x}_{pos}$, which is the velocity of the airplane. So we can say \n",
    "\n",
    "$$\\dot{x}_{pos} = x_{vel}$$\n",
    "\n",
    "The second row is $\\dot{x}_{vel}$, which is the acceleration of the airplane. We assume constant velocity, so the acceleration equals zero. However, we also assume system noise due to things like buffeting winds, errors in control inputs, and so on, so we need to add an error $w_{acc}$ to the term, like so\n",
    "\n",
    "$$\\dot{x}_{vel} = 0 + w_{acc}$$\n",
    "\n",
    "The final row contains $\\dot{x}_{alt}$, which is the rate of change in the altitude. We assume a constant altitude, so this term is 0, but as with acceleration we need to add in a noise term to account for things like wind, air density, and so on. This gives us\n",
    "\n",
    "$$\\dot{x}_{alt} = 0 + w_{alt}$$\n",
    "\n",
    "We turn this into matrix form with the following:\n",
    "\n",
    "$$\\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 & 0 \\\\ 0& 0& 0 \\\\ 0&0&0\\end{bmatrix}\n",
    "\\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix} + \\begin{bmatrix}0 \\\\w_{vel}\\\\ w_{alt}\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Now we have our differential equations for the system we can somehow solve for them to get our familiar Kalman filter state equation\n",
    "\n",
    "$$ \\mathbf{x}=\\mathbf{Fx}$$\n",
    "\n",
    "Solving an arbitrary set of differential equations is beyond the scope of this book, however most Kalman filters are amenable to Taylor-series expansion which I will briefly explain here without proof. The section **Modeling Dynamic Systems** in the **Kalman Filter Math** chapter contains much more information on this technique.\n",
    "\n",
    "Given the partial differential equation \n",
    "\n",
    "$$\\mathbf{F} = \\frac{\\partial f(\\mathbf{x})}{\\partial x}$$\n",
    "\n",
    "the solution is $e^{\\mathbf{F}t}$. This is a standard answer learned in a first year partial differential equations course, and is not intuitively obvious from the material presented so far. However, we can compute the exponential matrix $e^{\\mathbf{F}t}$ using a Taylor-series expansion in the form:\n",
    "\n",
    "$$\\Phi = \\mathbf{I} + \\mathbf{F}\\Delta t + \\frac{(\\mathbf{F}\\Delta t)^2}{2!} +  \\frac{(\\mathbf{F}\\Delta t)^3}{3!} + \\ldots$$\n",
    "\n",
    "You may expand that equation to as many terms as required for accuracy, however many problems only use the first term\n",
    "\n",
    "$$\\Phi \\approx \\mathbf{I} + \\mathbf{F}\\Delta t$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then compute the system matrix by substituting $\\Phi$ in $x(t_k) = \\Phi(\\Delta t)x(t_{k-1})$. Thus, $\\Phi$ is our system matrix.\n",
    "\n",
    "We cannot use Greek symbols in Python, so the code uses the symbol `F` for $\\Phi$. This is admittedly confusing. In the math above $\\mathbf{F}$ represents the system of partial differential equations, and $\\Phi$ is the system matrix. In the Python the partial differential equations are not represented in the code, and the system matrix is `F`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The measurement function for our filter needs to take the filter state $\\mathbf{x}$ and turn it into a slant range distance. This is nothing more than the Pythagorean theorem.\n",
    "\n",
    "$$h(\\mathbf{x}) = \\sqrt{x_{pos}^2 + x_{alt}^2}$$\n",
    "\n",
    "The relationship between the slant distance and the position on the ground is nonlinear due to the square root term.\n",
    "So what we need to do is linearize the measurement function at some point. As we discussed above, the best way to linearize an equation at a point is to find its slope, which we do by taking its derivative.\n",
    "\n",
    "$$\n",
    "\\mathbf{H} \\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_x \n",
    "$$\n",
    "\n",
    "The derivative of a matrix is called a Jacobian, which in general takes the form \n",
    "\n",
    "$$\\frac{\\partial \\mathbf{h}}{\\partial \\mathbf{x}} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n",
    "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n",
    "\\vdots & \\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "In other words, each element in the matrix is the partial derivative of the function $h$ with respect to the variables $x$. For our problem we have\n",
    "\n",
    "$$\\mathbf{H} = \\begin{bmatrix}\\frac{\\partial h}{\\partial x_{pos}} & \\frac{\\partial h}{\\partial x_{vel}} & \\frac{\\partial h}{\\partial x_{alt}}\\end{bmatrix}$$\n",
    "\n",
    "where $h(x) = \\sqrt{x_{pos}^2 + x_{alt}^2}$ as given above.\n",
    "\n",
    "Solving each in turn:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x_{pos}} &= \\\\ &=\\frac{\\partial}{\\partial x_{pos}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{pos}}{\\sqrt{x^2 + x_{alt}^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x_{vel}} &=\\\\\n",
    "&= \\frac{\\partial}{\\partial x_{vel}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ \n",
    "&= 0\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x_{alt}} &=\\\\ &= \\frac{\\partial}{\\partial x_{alt}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "giving us \n",
    "\n",
    "$$\\mathbf{H} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{x_{pos}}{\\sqrt{x_{pos}^2 + x_{alt}^2}} & \n",
    "0 &\n",
    "&\n",
    "\\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "This may seem daunting, so step back and recognize that all of this math is doing something very simple. We have an equation for the slant range to the airplane which is nonlinear. The Kalman filter only works with linear equations, so we need to find a linear equation that approximates $\\mathbf{H}$ As we discussed above, finding the slope of a nonlinear equation at a given point is a good approximation. For the Kalman filter, the 'given point' is the state variable $\\mathbf{x}$ so we need to take the derivative of the slant range with respect to $\\mathbf{x}$. \n",
    "\n",
    "To make this more concrete, let's now write a Python function that computes the Jacobian of $\\mathbf{H}$. The `ExtendedKalmanFilter` class will be using this to generate `ExtendedKalmanFilter.H` at each step of the process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def HJacobian_at(x):\n",
    "    \"\"\" compute Jacobian of H matrix for state x \"\"\"\n",
    "\n",
    "    horiz_dist = x[0]\n",
    "    altitude   = x[2]\n",
    "    denom = sqrt(horiz_dist**2 + altitude**2)\n",
    "    return array ([[horiz_dist/denom, 0., altitude/denom]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's provide the code for $h(\\mathbf{x})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def hx(x):\n",
    "    \"\"\" compute measurement for slant range that\n",
    "    would correspond to state x.\n",
    "    \"\"\"\n",
    "    \n",
    "    return (x[0]**2 + x[2]**2) ** 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets write a simulation for our radar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "import math\n",
    "\n",
    "class RadarSim(object):\n",
    "    \"\"\" Simulates the radar signal returns from an object\n",
    "    flying at a constant altityude and velocity in 1D. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, dt, pos, vel, alt):\n",
    "        self.pos = pos\n",
    "        self.vel = vel\n",
    "        self.alt = alt\n",
    "        self.dt = dt\n",
    "        \n",
    "    def get_range(self):\n",
    "        \"\"\" Returns slant range to the object. Call once \n",
    "        for each new measurement at dt time from last call.\n",
    "        \"\"\"\n",
    "        \n",
    "        # add some process noise to the system\n",
    "        self.vel = self.vel  + .1*randn()\n",
    "        self.alt = self.alt + .1*randn()\n",
    "        self.pos = self.pos + self.vel*self.dt\n",
    "    \n",
    "        # add measurement noise\n",
    "        err = self.pos * 0.05*randn()\n",
    "        slant_dist = math.sqrt(self.pos**2 + self.alt**2)\n",
    "        \n",
    "        return slant_dist + err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can implement our filter. I have not yet designed $\\mathbf{R}$ and $\\mathbf{Q}$ which is required to get optimal performance. However, we have already covered a lot of confusing material and I want you to see concrete examples as soon as possible. Therefore I will use 'reasonable' values for $\\mathbf{R}$ and $\\mathbf{Q}$.\n",
    "\n",
    "The `FilterPy` library provides the class `ExtendedKalmanFilter`. It works very similar to the `KalmanFilter` class we have been using, except that it allows you to provide functions that compute the Jacobian of $\\mathbf{H}$ and the function $h(\\mathbf{x})$. We have already written the code for these two functions, so let's get going.\n",
    "\n",
    "We start by importing the filter and creating it. There are 3 variables in `x` and only 1 measurement. At the same time we will create our radar simulator.\n",
    "\n",
    "```python\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "```\n",
    "\n",
    "We will initialize the filter near the airplane's actual position\n",
    "\n",
    "```python\n",
    "rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
    "```\n",
    "\n",
    "We assign the system matrix using the first term of the Taylor series expansion we computed above.\n",
    "\n",
    "```python\n",
    "dt = 0.05\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]])*dt\n",
    "```\n",
    "\n",
    "After assigning reasonable values to $\\mathbf{R}$, $\\mathbf{Q}$, and $\\mathbf{P}$ we can run the filter with a simple loop\n",
    "\n",
    "```python\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    rk.predict()\n",
    "```\n",
    "\n",
    "Putting that all together along with some boilerplate code to save the results and plot them, we get"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwYAAAEtCAYAAACyMncIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEREREeD/Azzu2+m2NDlAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7539b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvoAAAEtCAYAAAB5zMTfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKNEnhBBCCCGkCvp/vJjwP3kb8r4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x758e898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwMAAAEtCAYAAABUG7xMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x75d6748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "from numpy import eye, array, asarray\n",
    "\n",
    "dt = 0.05\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "\n",
    "# make an imperfect starting guess\n",
    "rk.x = array([radar.pos-100, radar.vel+100, radar.alt+1000])\n",
    "\n",
    "\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]])*dt\n",
    "\n",
    "rk.R = radar.alt * 0.05 # 5% of distance\n",
    "rk.Q = array([[0, 0, 0],\n",
    "              [0, 1, 0],\n",
    "              [0, 0, 1]]) * 0.001\n",
    "rk.P *= 50\n",
    "\n",
    "xs = []\n",
    "track = []\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    track.append((radar.pos, radar.vel, radar.alt))\n",
    "    \n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    xs.append(rk.x)\n",
    "    rk.predict()\n",
    "\n",
    "xs = asarray(xs)\n",
    "track = asarray(track)\n",
    "time = np.arange(0, len(xs)*dt, dt)\n",
    "ekf_internal.plot_radar(xs, track, time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using SymPy to compute Jacobians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on your experience with derivatives you may have found the computation of the Jacobian above either fairly straightforward, or quite difficult. Even if you found it easy, a slightly more difficult problem easily leads to very difficult computations.\n",
    "\n",
    "As explained in Appendix A, we can use the SymPy package to compute the Jacobian for us. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAAmBAMAAAA2HDP0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUqOHbKQnT/0tv+59MpOT+AmTXbj1s0kQCQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡       x_pos                    x_alt        ⎤\n",
       "⎢────────────────────  0  ────────────────────⎥\n",
       "⎢   _________________        _________________⎥\n",
       "⎢  ╱      2        2        ╱      2        2 ⎥\n",
       "⎣╲╱  x_alt  + x_pos       ╲╱  x_alt  + x_pos  ⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "sympy.init_printing()\n",
    "\n",
    "x_pos, x_vel, x_alt = sympy.symbols('x_pos, x_vel x_alt')\n",
    "\n",
    "H = sympy.Matrix([sympy.sqrt(x_pos**2 + x_alt**2)])\n",
    "\n",
    "state = sympy.Matrix([x_pos, x_vel, x_alt])\n",
    "H.jacobian(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result is the same as the result we computed above, and at much less effort on our part!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Designing Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**author's note: ignore this, it  to be revised - noise in position and altitude is independent, not dependent**\n",
    "\n",
    "Now we need to design the process noise matrix $\\mathbf{Q}$. From the previous section we have the system equation\n",
    "\n",
    "$$\\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 & 0 \\\\ 0& 0& 0 \\\\ 0&0&0\\end{bmatrix}\n",
    "\\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix} + \\begin{bmatrix}0 \\\\w_{vel}\\\\ w_{alt}\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "where our process noise is\n",
    "\n",
    "$$w = \\begin{bmatrix}0 \\\\w_{vel}\\\\ w_{alt}\\end{bmatrix}$$\n",
    "\n",
    "We know from the Kalman filter math chapter that \n",
    "\n",
    "$$\\mathbf{Q} = E(ww^T)$$\n",
    "\n",
    "where $E(\\bullet)$ is the expected value. We compute the expected value as\n",
    "\n",
    "$$\\mathbf{Q} = \\int_0^{dt} \\Phi(t)\\mathbf{Q}\\Phi^T(t) dt$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rather than do this by hand, let's use sympy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{3} w_{vel}^{2}}{3} & \\frac{\\Delta{t}^{2} w_{vel}^{2}}{2} & \\frac{w_{alt} w_{vel}}{2} \\Delta{t}^{2}\\\\\\frac{\\Delta{t}^{2} w_{vel}^{2}}{2} & \\Delta{t} w_{vel}^{2} & \\Delta{t} w_{alt} w_{vel}\\\\\\frac{w_{alt} w_{vel}}{2} \\Delta{t}^{2} & \\Delta{t} w_{alt} w_{vel} & \\Delta{t} w_{alt}^{2}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡           3      2                2      2             2            ⎤\n",
       "⎢  \\Delta{t} ⋅w_vel        \\Delta{t} ⋅w_vel     \\Delta{t} ⋅w_alt⋅w_vel⎥\n",
       "⎢  ─────────────────       ─────────────────    ──────────────────────⎥\n",
       "⎢          3                       2                      2           ⎥\n",
       "⎢                                                                     ⎥\n",
       "⎢           2      2                                                  ⎥\n",
       "⎢  \\Delta{t} ⋅w_vel                       2                           ⎥\n",
       "⎢  ─────────────────       \\Delta{t}⋅w_vel      \\Delta{t}⋅w_alt⋅w_vel ⎥\n",
       "⎢          2                                                          ⎥\n",
       "⎢                                                                     ⎥\n",
       "⎢         2                                                           ⎥\n",
       "⎢\\Delta{t} ⋅w_alt⋅w_vel                                           2   ⎥\n",
       "⎢──────────────────────  \\Delta{t}⋅w_alt⋅w_vel     \\Delta{t}⋅w_alt    ⎥\n",
       "⎣          2                                                          ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "from sympy import Matrix\n",
    "sympy.init_printing(use_latex='mathjax')\n",
    "w_vel, w_alt, dt = sympy.symbols('w_vel w_alt \\Delta{t}')\n",
    "w = Matrix([[0, w_vel, w_alt]]).T\n",
    "phi = Matrix([[1, dt, 0], [0, 1, 0], [0,0,1]])\n",
    "\n",
    "q = w*w.T\n",
    "\n",
    "sympy.integrate(phi*q*phi.T, (dt, 0, dt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robot Localization\n",
    "\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. 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",
    "### Robot Motion Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhQAAAEWCAYAAAA+Wg5zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl0VGWexvHnVvYggUDCThJAkDVGpEVBEJKGhCU0CK3I\nCIqCwMycdsEg49KAPTrCIM30zFEc0AAy0gpCswjKFiBBgsKAoCAIhi0NBGiyEELWO38wqaas7JVU\nkarv55yc7rz3rVu/yFIP7/3d9xqmaZoCAABwgMXVBQAAgPqPQAEAABxGoAAAAA4jUAAAAIcRKAAA\ngMMIFAAAwGEECgAA4DACBQAAcBiBAgAAOIxAAQAAHEagAAAADiNQAAAAhxEoAACAwwgUAOAGevbs\nqa1btzp0jgsXLqhly5a1VBE8jberCwAAOG7SpElasmSJBg0aVObxxMRE7d27V2FhYfrpp5/05JNP\nWufeuHFDgYGBCgwMVG5urjPLhhsxTNM0XV0EAMAxmZmZioiI0MmTJxUSEmIdN01TEyZMUGFhoT75\n5BNZLBbl5OSoXbt22rdvnzp06KCEhAT9+7//uwoLC+Xv76+ioiIZhuHCnwb1EZc8AMANNG7cWCNG\njNDy5cttxhcsWKDNmzdryZIlslhu/ZXfsGFD3X///VqxYoVSU1P14IMPSpJ8fHzk5eWlgoICp9eP\n+o9AAQBuYvLkyVqyZIlKF54LCgo0d+5cTZw4UXfddZfN3GbNmuns2bNauXKlRo8ebR1v0KABlz1Q\nIwQKAHATDz/8sIqLi7V3715J0o8//qgrV66U2Vfh5eWlr776yiZMSAQK1ByBAgDchGEY1uZMSSou\nLpYktW3b1m6ul5eX+vTpo/79+9uMBwYG6saNG3VfLNwOgQIA3MiECRO0du1aZWdn695771XHjh11\n7Ngx63HTNPXnP/9ZZ8+etfZK7N+/33qcFQrUFLeNAoAbad68uWJiYrRy5UpNmTJFGzdu1KuvvqrD\nhw/L19dXJSUlGjFihFauXKnHHntMCQkJGjJkiPX1BArUFLeNAoCb+fLLL/XGG2/o22+/rfZrBw8e\nrOnTpys2NrYOKoM745IHALiZQYMGKSMjQ4cOHar2a1mhQE0RKADAzXh5eemZZ56xNmdWB4ECNUWg\nAAA3NHHiRK1cuVJ5eXnVeh13eaCmCBQA4IbCwsL0wAMP6PPPP6/W61ihQE0RKADATU2aNEmLFy+u\n1msIFKgpAgUAuKn4+HgdP35cJ06cqPJruOSBmiJQAICb8vX11YQJE/Thhx9W+TWsUKCmCBQA4Mae\nffZZLVu2TIWFhVWaT6BATREoAMCN3XPPPbrnnnu0YcOGKs3nkgdqikABAG7u9geGVYYVCtQUgQIA\n3Nzo0aO1b98+nTt3rtK5BArUFIECANxcYGCgxo4dq48++qhKc7nkgZogUACAB5g8ebI++ugjFRcX\nVziPFQrUFIECADxAVFSUQkNDtW3btgrnEShQUwQKAPAQVWnO5JIHasowTdN0dREAgLqXnZ2t8PBw\nHT9+XM2aNStzTlZWltq2bavs7GwnV4f6jhUKAPAQQUFBGjlypJYvX17unMDAQOXm5op/a6K6CBQA\n4EFKL3uUFxh8fHzk5eWlgoICJ1eG+o5AAQAepE+fPrJYLNqzZ0+5c2jMRE0QKADAgxiGUeljzQkU\nqAkCBQB4mPHjx2vdunXKzMws8zh3eqAmCBQA4GFCQ0M1ePBgrVy50u7Y+fPnlZubqx07drigMtRn\nBAoA8ECTJ0+2XvbIycnRsmXLNHPmTK1du1Zt2rRRcnKyiytEfcM+FADggQoKCtS2bVsNHTpUHTp0\n0KOPPqquXbtKkgYPHqy2bdtq7ty5CgkJcXGlqC8IFADgIUzT1Hfffad169apoKBAFy5ckJ+fn95/\n/32beaNGjVJsbKxM09S0adNcVC3qG29XFwAAqFvZ2dlasmSJMjIyFBUVpYSEBAUGBur8+fOKjIzU\nu+++q8DAQOv8Bg0aqEGDBvrhhx9cWDXqG3ooAMADZGVl6Z133tHYsWOt4aFNmzbq06ePVq1aZTO3\n9C6Pjh076sSJE64oF/UQgQIA3FxQUJDy8/NVUlJid6ysB4aV7kMxevRorV692lllop4jUACAB+jf\nv3+Zd24MGzZMJ0+e1I8//mgdKw0UjRs3VlZWVplBBPglAgUAeIDBgwdry5YtduM+Pj56+umn9eGH\nH1rHbt/Yql+/fhVu0w2UIlAAgAfw9vaWj4+P8vLy7I4988wzWr58ufWBYLdvvR0bG6uvvvrKqbWi\nfiJQAICHiI+P14YNG+zGO3bsqK5du2r9+vWSbANF6dNHb9686dRaUf8QKADAQ/Ts2VMHDhwo89jt\nzZmBgYE2DwcbPny4Nm7c6JQaUX8RKADAQxiGoWbNmikjI8Pu2OjRo7V//36dPn1aDRo0sHk4WK9e\nvfTtt986s1TUQwQKAPAgjz32mD777DO7cX9/f40bN06JiYl2jy83DEMhISG6fPmyM0tFPUOgAAAP\n0rZtW50/f77MY5MmTdJHH30kPz8/m0Ah3Qoiv9wAC7gdgQIAPMw999xjs+9EqcjISLVq1UqHDx+2\nueQhSeHh4Tp79qyzSkQ9RKAAAA9T0Q6YkyZN0rp16+xWKKRbd4McP368rstDPUWgAAAPExQUpNzc\n3DJ3wBw7dqy++eYbZWdn2x0bM2YMW3GjXAQKAPBA/fv31+7du+3GGzZsqPj4+DIDRaNGjZSTk8NW\n3CgTgQIAPNCgQYO0devWMo9NmTJFhYWFMk3T7li/fv2UkpJS1+WhHiJQAIAHqmgr7o4dOyokJKTM\n/SrKeyYIQKAAAA81YsQI63bbt/uXf/kXXb58WTNnzrQ7xlbcKA+BAgA81H333aeDBw/ajGVkZCgp\nKUmSlJSUpEuXLtm9rrxngsCzESgAwEMZhqHQ0FCb0DBz5kydPn1aknTmzJkyVynuv/9+7d+/31ll\nop4gUACAB3v88cetW3HfvjpRqqxVitIgwlbcuB2BAgA8WJs2bZSeni7JdnWiVHmrFOU9EwSei0AB\nAB6uc+fOSklJsVudKFXWKkVYWJjOnTvnjPJQTxAoAMDDjR49Ws8//7zd6kSp8lYpynsmCDyTYZa1\ncwkAwGPcvHlTHTt2VEREhHVs7969euihh6zfm6aprVu3KiAgwDqWnZ2t//zP/9Rrr73mzHJxh/J2\ndQEAANfy9/fX4sWL5efnp4EDB0q61XiZnJxc4euCgoJ0/fp1lZSUyGJhwdvT8TsAAKBf//rX2rZt\nW7Vf169fv0qDBzwDgQIAIG9vb/n6+urGjRvVeh1bcaMUgQIAIKn8rbgrcvbsWX3//fcqKiqqo6pQ\nX9BDAQCQJEVFRenTTz/V2LFjK5x37do1rVq1SqdOnVL79u2VmJgob28+TjwdvwMAAJJuNWI2a9as\nzOd3FBQUaPPmzfr6668VHBysMWPG6LnnnnNBlbhTcdsoAMDq/PnzWrt2rX73u9+ppKRE+/bt0xdf\nfCFJGjJkiB566CEZhuHiKnEnYoUCAGDVpk0bpaWlSbr1GPPevXvr9ddfl5+fn4srw52OFQoAgI3j\nx4+rc+fO4uMB1UGgAADYMQyDQIFq4bZRAADgMAIFAABwGIECAAA4jEABAAAcRqAAAAAOI1AAAACH\nESgAAIDDCBQAAMBhBAoAAOAwAgUAAHAYgQIAADiMQAEAABxGoAAAAA4jUAAAAIcRKAAAgMMIFAAA\nwGEECgAA4DACBQAAcBiBAgAAOIxAAQAAHEagAAAADiNQAAAAhxEoAACAwwgUAADAYQQKAADgMAIF\nAABwGIECAAA4jEABAAAcRqAAAAAOI1AAAACHESgAAIDDCBQAAMBhBAoAAOAwAgUAAHAYgQIAADiM\nQAEAABxGoAAAuNzjjz+uhx9+uFbOdfr0aVksFs2ZM6dWzldTS5culcVi0e7duyscu1MdOnSoWrV6\n13E9AABUaM+ePVq1apWSkpJq9byGYdTq+TxNVFSURo0apenTp+vbb7+tdD4rFAAAl3rzzTd13333\n6ZFHHnF1KfiFF154QQcOHNCmTZsqnUugAAC4zMmTJ7Vt2zZNmDDB1aWgDP369VNERIQWLVpU6VwC\nBQCgUmfOnJHFYtHs2bNtxmNjY2WxWLRw4UKb8d69e6tr166Vnnf16tUyTVNDhw61GZ84caICAgKU\nn59vHdu7d68sFouaNm0q0zSt45s3b5bFYtGqVatszmGapjZu3Khf/epXCggIUKtWrTRjxgwVFxfb\n1fHTTz9p/Pjxatmypfz8/NSuXTvNmDFDN27csJt74cIFTZs2TWFhYfLz81Pr1q01ZcoUXb58udKf\nt1RhYaFmz56t8PBw+fv7695779Wnn35qN2/Lli16/PHH1b59ewUGBio4OFixsbFl9jX88MMP+u1v\nf6vWrVvL399fLVu2VHR0tN3qQn5+vt5++21169ZNAQEBCg4O1ogRI3To0KEya42NjdWXX36p3Nzc\nCn8mAgUAoFLh4eFq3769duzYYR0rKChQSkqKLBaLzXh2drb+93//VzExMZWed9euXQoODlbHjh1t\nxmNiYpSfn689e/ZYx7Zv3y6LxaLMzEwdPHjQOr5jxw5ZLBYNHDjQ5hybNm3Ss88+q2HDhmnhwoW6\n9957NX/+fM2bN89m3oEDB9SrVy+lpKRo2rRpeu+99zR8+HD96U9/0qBBg1RUVGSde/bsWfXq1Utr\n1qzRk08+qffee0/jx4/Xn//8Z/Xt21fZ2dmV/syS9Morr+izzz7TP//zP+vNN99UQUGBnnjiCS1b\ntsxm3rJly5SZmamnn35a//Vf/6UXX3xRx44dU0xMjFJSUqzzrl69qujoaKWkpOi5557TokWL9NJL\nLyk0NFTffPONdV5hYaHi4uL05ptvqm/fvlq4cKFmzpypo0ePqm/fvjpw4IBdrQ8++KCKiops3q9M\nJgAAv1DWx8OkSZNMX19fMy8vzzRN09y1a5dpGIY5fvx4MygoyCwuLjZN0zTXr19vGoZhrlmzptL3\nCQsLM++//3678fPnz5uGYZivvfaadWzgwIHmb37zGzMoKMicN2+edbxnz55mZGSk9fu0tDTTMAzz\nrrvuMs+cOWNz3u7du5stW7a0GYuMjDS7dOliXr9+3WZ87dq1pmEY5tKlS61jI0aMMJs3b26mp6fb\nzN2/f7/p7e1tzp492zqWmJhoGoZh7tq1y24sIiLCzM7Oto5nZWWZ4eHhZpMmTaz/fU3TNHNzc+3+\n21y6dMkMCQkxhw4dah1bt26daRiGuWrVKrv5t1uwYIFpGIa5ZcsWm/Hs7GwzLCzMHDBggN1rkpOT\nTcMwzAULFlR4blYoAABVEhMTo8LCQiUnJ0u6tTLQvHlzPf/888rJybHeCZCUlCTDMOxWDMpy+fJl\nNWnSxG68devW6tSpk3Xl4+bNm0pNTVVcXJweeeQRbd++XZKUmZmp7777TtHR0XbnGDlypMLCwmzG\nBgwYoIsXL1ovZRw5ckRHjhzRE088oby8PF25csX61bdvXwUGBmrLli2SpKysLG3cuFEjRoyQr6+v\nzdzw8HB16NDBOrcy06ZNU8OGDa3fBwUFaerUqbp27Zp27txpHQ8MDLT+/+vXr+vq1auyWCx64IEH\ntG/fPuuxxo0bS7q1KpOTk1Pu+65YsUJdunRRz549berPz8/Xr3/9a6WkpNhcZpKkpk2bSpIyMjIq\n/JkIFACAKikNCKUf8jt27NDAgQPVs2dPBQcH24xHRUVZP+QqYhiGTT/EL99v//79un79ur7++mvd\nvHlT0dHRGjhwoFJSUlRYWKidO3eqpKSkzEDRvn17u7HSD8erV69Kko4dOyZJmjVrlpo1a2bz1bx5\nc924ccP6QXr8+HGZpqklS5bYzW3WrJlOnDhR6YduqS5dupQ7lpaWZh07deqUxo4dq+DgYAUFBSk0\nNFTNmjXT5s2blZmZaZ3Xv39/TZgwQUuXLlVISIgefvhhzZ492/rzlTp27JiOHTtmPc/tX4mJiSop\nKdGVK1dsXlP661PZbbjsQwEAqJLmzZura9eu2rFjh/Ly8rRv3z5NmDBBhmHokUce0bZt2zRlyhQd\nPnxY06dPr9I5Q0ND9be//a3MYzExMfrggw+0e/duff3119ZVi7y8PE2fPl2pqanasWOHvLy8yrzl\n1MvLq9z3Lf2QLP3fl19+WXFxcWXODQ4Otpk7fvx4PfXUU2XODQgIKPc9q+v69evq37+/8vLy9OKL\nL6pHjx5q2LChLBaL3n77bbt9O5YuXaqEhARt3rxZycnJevfdd/XWW29p4cKF+qd/+ifrzxAZGakF\nCxaU+74hISE235f++oSGhlZYL4ECAFBl0dHReu+997R+/XoVFhZaGy9jYmL08ssvW+8oKGvFoCzd\nu3e3XkL5pQEDBsgwDG3fvl179+61njMyMlIhISHavn27kpKS1LNnTwUFBdXo5+nUqZMkyWKxVFrz\n3XffLcMwlJ+fX+WfrzxHjx5VfHy83Zj095WV7du368KFC0pMTLQLMK+++mqZ5+3WrZu6deuml19+\nWVlZWerdu7dmzpxpDRSdOnVSRkaGBg4cWOWNv06ePCnp1q9VRbjkAQCosujoaJWUlOjNN99UeHi4\n2rVrZx3Pz8/XO++8Ix8fH/Xv379K5xs4cKBycnL0ww8/2B0LCQlRjx49tHHjRu3fv9/6IV7an7Fq\n1SodPXrUoQ/3++67T927d9eiRYtsLjWUKioq0rVr1yTdulwydOhQrVmzxqZ/oZRpmnaXC8rz/vvv\n29wRkpWVpUWLFik4ONi62lK6wlJSUmLz2i1bttjcuSFJ165ds5vXqFEjRUREKC8vz9oXMWHCBF28\neLHcFYpLly7ZjaWmpsrHx0d9+/at8GdihQIAUGWlqwbHjh3TxIkTreNdunRR8+bNdfToUT300ENq\n0KBBlc43evRovfLKK9q0aZO6detmdzw6OloLFy6UYRg2wSE6Otq674SjqwUff/yxoqOjFRkZqWee\neUZdu3bVjRs3dPLkSa1du1bvvPOOdeOt999/Xw8//LC1ZyEqKkolJSX6+eeftX79ej311FP6/e9/\nX+l7hoaGqnfv3po4caJM01RiYqLOnz+vJUuWyN/fX9KtTaVatGih6dOn6/Tp02rdurUOHTqkFStW\nqEePHjpy5Ij1fMuWLdMf//hHPfroo+rQoYN8fHy0a9cu6z4Wfn5+kqTnn39eW7duVUJCgrUHJigo\nSGfPntX27dsVEBBgcwuwaZr68ssvFRcXZ9MgWqYK7wEBAHikij4e7r//ftNisZgrVqywGf+Hf/gH\n02KxmK+//nq13mvo0KFmjx49yjy2YcMG0zAM8+6777YZ/+mnn0zDMEw/Pz+b2yxN8++3jc6ZM8fu\nfLNnzzYtFovd7aRnzpwxp06dakZERJi+vr5m06ZNzV69epmvvvqqef78eZu5V65cMRMSEsxOnTqZ\n/v7+ZuPGjc3IyEjzhRdeMI8dO2adl5iYaFosFrvbRi0Wi7l9+3Zz1qxZZlhYmOnn52dGRkaaK1eu\ntKv38OHDZlxcnBkcHGw2bNjQHDhwoJmSkmI+/fTTpsVisc47dOiQ+dRTT5l333232aBBAzMoKMiM\niooyFyxYYBYUFNics6ioyPzTn/5k/upXvzIbNGhgNmjQwOzUqZP55JNPmlu3brWZu3PnTtMwDHPT\npk12tf2SYZrltNcCADxWRXdf1LbU1FT16dNHW7durdJmWHCeUaNGKT093e4SS1kIFAAAO84MFJL0\nxBNP6Ny5c5XvxginOXjwoHr16qWdO3eqX79+lc4nUAAA7Dg7UKD+4y4PAADgMAIFAABwGIECAAA4\njEABAAAcRqAAAAAOI1AAAACHESgAAIDDCBQAAMBhBAoAAOAwAgUAAHAYgQIAADiMQAEAABzm7eoC\nAACuU1RUJG/vWx8FBQW3vnJyCiRJaWm3vi8ulrp2dWWVqA8IFADgYX78sUjHjp1SYaFkGAFq3DhM\nBQVSSUnpDF9J0vff3/rOYiFQoHIECgDwMFeueMvb+x79/8KEbt6seH5eXp4uXcpT8+ZN6r441Fv0\nUACAh/Hzq958i8Wiq1dz6qYYuA0CBQB4GF/f6s339vbV9ev5dVMM3AaBAgA8THFxbrXmG4ahJk1a\n1VE1cBcECgDwMPn5mdV+jbf3XXVQCdwJgQIAPExYWOtqvyafKx6oBIECADxMdZsypVv7UQAVIVAA\ngIepSaBghQKVIVAAgIepSaBIT/+rSv6+8xVgh0ABAB7GMApVVFS9JQdf3+A6qgbugkABAB4mPz9f\nN29erdZrDCNAFgsfGSgfvzsAwI0UFxfrZiV7afv6+sowqrdCUVh4+7M+AHsECgBwI4ZhqEuXLho2\nbJiWL1+uvLw8uzm+vr5q0KD6jRQ0ZqIiBAoAcCMWi0WhoaHatGmTnnnmGfXo0UNDhgzRhx9+qNzc\nv++Q2aZN9Xe+5NZRVIRAAQBupmnTppJuXf44deqUvvzyS02ePFk9evRQbGysPvjgAxUWVv9hX2lp\n52u7VLgRHl8OAG6mNFDczjRNpaWlKS0tTd99952mTw9Q584TqnXerKwbtVWineLiYnl5edXZ+VH3\nWKEAgHosIyNDS5cu1ZgxYxQUFCTDMPQ///M/Zc719vZW3759lZqaqrFjqxcmpLq75PHXv/5VU6ZM\nqZuTw2kIFABwh7t+/br+8pe/6Nlnn1WrVq1kGIb1q3Pnzvrqq680atQopaWlyTRNJSUl2f1rv2XL\nlkpISNDu3bsVERGhgoLqX/IIDm5TWz+SjYSEBG3atEnp6el1cn44B5c8AOAOUFhYqJSUFG3YsEFf\nfPGFTpw4YT3m5+enmJgYDRs2TL///e8VHh5e4bm6dOmikJAQXbp0SZIUFRWlxYsXq1evXtY5RUW5\nMs27ZBhGlWv08gqs5k9Vub/+9a9KTk7WhQsXNGPGjHJXV3DnI1AAgJOYpqmDBw9q48aN+uKLL/TN\nN9/YHO/bt6+GDRum1atXq3v37tX6sL9ds2bN1KhRIxUWFuo3v/mN3nvvPfn7+9vMCQtrodsyS5XU\nxW2jCQkJOnfunCQpOTlZ6enpat26+k9DhesRKACglp06dcoaGpKSklRUVGQ91r17dw0dOlTvvvuu\nHnzwQXl71/5fw4ZhqHXr1po/f77i4+PLnOPrW/3z1nagSE9PV3JysvX7c+fOsUpRjxEoAKAGMjIy\ntGnTJm3cuFFbtmxRTs7fexLCwsI0ZMgQPf/88/rLX/6iwMDav1RQmW3btlW4VbaXl+TtLd2WdSpV\n202ZM2bMsK5OlGKVov4iUABAOa5fv65t27Zpw4YN2rx5sy5cuGA9FhwcrNjYWI0aNUoffPBBmbdq\nulJVnrvh51e9QHHtWrayskw1atTIgcpu+eXqRClWKeovAgUAj1ZRM6S/v7+io6Or3AxZ3xQVZUsK\nqvJ8X99AeXubtfLeZa1OlGKVon4iUABwe1Vthvz888/VrVu3GjdD1jc5ORfl61v1QOHl5V0rDwhL\nT0/X1q1b5ePjYx0zTdP63/3ixYv63e9+p88//9zxN4PTECgAuI2qNEMuWLBAvXv3rpNmyPrmts/z\nKquNPgpfX19t2LDB+n1JSYn69Omj1NRU65ifX/UfXgbX4k8UgHqlKs2QL7zwgsuaIeuTJk2CdO1a\n9V5TG3d6hIaGKjQ01Pp9SUmJDMNQ7969HT85XIZAAeCOU5+bIeuTNm1auCRQwD0RKAC4RFWaIYcP\nH65Zs2YpLCzMhZW6r5pcVUhLO6t27fj1gD0CBYA6QzPkna0mm1tdv55X+4XALRAoADiMZsj6qSYr\nFHX1xFHUf/zJBlAlNEO6n5KSPBUWesnHp+pLFcHB7rUXB2oPgQKAVVWaIR999FH993//t5o0aeLC\nSlEbLJZimWaJpLIDxV13SZcvn1J4eIQCA73k6yvddZd/mXMBwzTN2tn2DEC9UNVmyGHDhtEM6QF2\n7fpZplkoX1+pc+e7FRDgJT8/ycvLkGmaNhtO1ZWSkhJ5e3urpDZ2zYLLECgAN1TVZsj4+HiaIVEm\nw7gVKJyBQOEeCBRAPXZ7M+TOnTtVWFhoPda9e3draKAZEtVFoEB1ESiAO1xVmiFHjBihAQMG0AyJ\nWkOgQHURKIA7QGXNkHFxcRo+fLji4uJohoRTuFugiIiIULt27ZSUlFRn7+HpWAMFnOT2ZshNmzbp\n+PHj1mPsDAnULcMw6BWqYwQKoBaVNkOWhobbmyENw7A2Q65evZpmSMCJWIyvewQKoAaq0gzJzpAA\nPInF1QUAd6qMjAwtXbpUY8aMUVBQkHXJ1DAMxcTE6Mcff9QLL7ygrKws6/36pmnqyJEjeuedd9S3\nb1/CBOBk586d02OPPaZGjRqpUaNGGjFihE6dOuXqsjwCf9vBo1WlGZKdIYH6ITMzU/3799f58+c1\nbdo0de3aVTt37lR0dLTy8nioWV0jUMDt0QwJeIZ58+bpzJkzSkxM1FNPPSVJmjp1ql588UX9x3/8\nh4urc3/cNgq3UNVmyOHDh9MMCVRBfbxttGvXrsrMzFR6errNn/GLFy+qVatWGjBggHbs2OFouSgH\nKxSoV2iGBFCen3/+Wb1797b7B0OLFi3UqFEjF1XlOfgbF3ecinaGDA8Ptz4me926dQoICHBhpQCA\nUgQKuATNkABqW/v27XXixAmVlJTIYvn7TYwXLlxQVlaWCyvzDNw2ijpTWFiopKQkvfTSS+rcubPN\nbZehoaFavHixevXqpdTUVJvbLv/2t7/pk08+0bhx4wgTAKps5MiRunTpkpYvX24zPnfuXBdV5Flo\nyoRDaIYE3FN9bMrMzMxUVFSU0tPTNXXqVOtto6mpqcrLy1O3bt14lkcd4pIHqqSiZsgePXpo6NCh\n+uMf/6jevXvLy8vLhZUC8FSNGzdWcnKyXnrpJesqxYABA5SUlKSYmBj+QVPHWKGAVVWaIePj4zVw\n4ECaIQE3MXv27DLH58yZo1mzZlX7dTXB48vdA4HCw1TUDNmkSRPFxsYqPj5esbGx9C8AHmD27Nll\nhoOKLnmFFxVvAAAGzUlEQVSU95qaIlC4By55uCF32xkyIyNDS5YskSQVFBQoKytL8+bNk4+Pj4sr\nAwCUIlDUU1Vphhw+fLg+//xzde3atd5eO0xLS9OqVav0yiuvWHszxowZo48++khTpkxxcXUAgFIE\nijucJzdDFhYWasOGDZoxY4bN+PHjxzVy5EgXVQUAKAuB4g7AzpBl+/TTT/Xkk0/ajXl7e+u3v/2t\ni6oCAJSFQOEkVWmGHD16NDtD3ubq1atq0qSJFi9erOPHj+ubb77Rzz//rMOHD8vPz8/V5QEAbsNO\nmbWopjtDXr16VZ988omeeOIJwsT/O3/+vFq3bi3p1oN9fHx8FBUVpZs3b/IYYgC4A7FCUU2e0gzp\nasnJyYqLi5MkxcfHKz4+XpLk7e2ttWvXas6cOa4sDwDwCwSKcnhyM+SdICcnR8HBwXbjWVlZTtsO\nGABQdR4dKCprhhw6dKhefPFFj2uGvBPcHuBul5qaqujoaCdXAwCojNsHCpoh659z587p559/thvf\nuXOnTp8+rZdfftkFVQH1j2maXHaF07hFoKhsZ8iYmJh6tTOkp9uzZ4/y8vJ06dIlNW/eXJKUnp6u\nyZMna8WKFQoPD3dxhUD9MG7cOHXo0EGvvfYaq6yoc/UmUNAM6TmysrI0f/58/du//Zv1X1gXL17U\nqlWrFBUV5erygHrj2rVreuutt7RmzRo9+uijBAvUqTsuUFTUDBkZGUkzpAfIz89XYGCg/vCHP7i6\nFMAtHDt2jGCBOueSQEEzJMpz7tw5tWjRwtVlAG6prGAB1BrTiSTxxRdffPF1h3y1bt3anDhxYpl/\nXw8aNKjcv8tnzZpVq58NxcXF5uDBg2v1nHA+p65QmOwfgEr867/+q15//XVXlwG4hbi4OH311Vd2\n40FBQbr33nv1xhtvaM+ePWW+dsuWLXVdnpXFYimzTtQvbL2NOwphAqg7QUFB6tevn1avXq3du3dr\n0KBBri4JbuSOa8oEANSu21ckCBGoKwQKAHBTBQUF6tevH0ECTuGSSx43btzQwoUL1a9fPzVt2lS+\nvr5q0aKFhg0bpmXLlqm4uNgVZQG1ZufOnbJYLDZfDRs2VM+ePTV//nwVFRW5ukR4gI8//phLG3Aa\np69QnDx5UsOGDdNPP/2kQYMG6dVXX1VISIgyMjK0detWTZw4UUePHtXcuXOdXRpQ68aNG6ehQ4fK\nNE1duHBBy5cv14wZM3TkyBEtW7bM1eXBzbVu3drVJcCDODVQ5OXlafjw4Tp9+rTWrFmjkSNH2hxP\nSEjQ/v37tX//fmeWBdSZnj17aty4cdbv//Ef/1GdO3fWxx9/rLlz57LnBgC34dRLHkuWLNGJEyc0\nffp0uzBRqlevXpo6daozywKcJjAwUL1795YknTlzxsXVAEDtcWqgWL16tQzD0HPPPefMtwXuKKdO\nnZJhGGrVqpWrSwGAWuPUSx7ff/+9goKCFBER4cy3BVwmNzdXV65ckWmaunjxohYtWqRDhw5p5MiR\natu2ravLA4Ba49RAkZ2drZYtWzrzLQGXmjVrlmbNmmUz9tJLL+ntt992UUUAUDeceskjKCjI5kFg\ngLubMmWKtm3bps2bN2vu3Llq0qSJPvvsM2VkZLi6NACoVU4NFN27d1dWVpbS0tKc+baAy3Ts2FHR\n0dGKjY1VQkKCNmzYoPT0dE2aNMnVpQFArXJqoBgzZoykW3d7AJ7ooYce0vjx47VlyxZt377d1eUA\nQK1xaqCYNGmS7rnnHs2fP1/r168vc86BAwf0/vvvO7MswKneeOMNeXl5ac6cOa4uBQBqjVMDRUBA\ngDZu3Kh27dpp5MiRiouL0/z585WYmKh58+ZpyJAheuCBB3T27FlnlgU4VYcOHTR27FilpKQoKSnJ\n1eUAQK1w+rM8OnTooIMHD2rBggXKzc3V22+/rSlTpujdd9+VJC1dulRvvfWWs8sCnOq1116TxWLR\nH/7wB1eXAgC1wjBN03R1EQAA15g9e7ZTXwf3RaAAAAAOc8njywEAgHshUAAAAIcRKAAAgMMIFAAA\nwGEECgAA4DACBQAAcBiBAgAAOIxAAQAAHEagAAAADiNQAAAAhxEoAACAwwgUAADAYQQKAADgMAIF\nAABwGIECAAA4jEABAAAcRqAAAAAOI1AAAACHESgAAIDDCBQAAMBhBAoAAOAwAgUAAHAYgQIAADiM\nQAEAABxGoAAAAA4jUAAAAIcRKAAAgMMIFAAAwGEECgAA4DACBQAAcBiBAgAAOIxAAQAAHEagAAAA\nDiNQAAAAhxEoAACAwwgUAADAYQQKAADgMAIFAABwGIECAAA4jEABAAAc9n8DNbNy7oW9RgAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x75015f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.plot_bicycle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At a first approximation n automobile steers by turning the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modelling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. \n",
    "\n",
    "I have depicted this model above. Here we see the front tire is pointing in direction $\\alpha$. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. If you google bicycle model you will find that we can compute the turn angle $\\beta$ with\n",
    "\n",
    "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n",
    "\n",
    "and the turning radius R is given by \n",
    "\n",
    "$$R = \\frac{d}{\\beta}$$\n",
    "\n",
    "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n",
    "\n",
    "If we let $\\theta$ be our current orientation then we can compute the position $C$ before the turn starts as\n",
    "\n",
    "$$ C_x = x - R\\sin(\\theta) \\\\\n",
    "C_y = y + R\\cos(\\theta)\n",
    "$$\n",
    "\n",
    "After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n",
    "\n",
    "$$\\begin{aligned} x &= C_x + R\\sin(\\theta + \\beta) \\\\\n",
    "y &= C_y - R\\cos(\\theta + \\beta) \\\\\n",
    "\\theta &= \\theta + \\beta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Once we substitute in for $C$ we get\n",
    "\n",
    "$$\\begin{aligned} x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\theta &= \\theta + \\beta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "You don't really need to understand this math in detail, as it is already a simplification of the real motion. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "For our robot we will maintain the position and orientation of the robot:\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n",
    "\n",
    "I could include velocities into this model, but as you will see the math will already be quite challenging.\n",
    "\n",
    "Our control input $\\mathbf{u}$ is the velocity and steering angle\n",
    "\n",
    "$$\\mathbf{u} = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the System Model\n",
    "\n",
    "In general we model our system as a nonlinear motion model plus noise.\n",
    "\n",
    "$$x^- = x + f(x, u) + \\mathcal{N}(0, Q)$$\n",
    "\n",
    "Using the motion model for a robot that we created above, we can expand this to\n",
    "\n",
    "$$\\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix}^- = \\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix} + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}$$\n",
    "\n",
    "We linearize this with a taylor expansion at $x$:\n",
    "\n",
    "$$f(x, u) \\approx \\mathbf{x} + \\frac{\\partial f(x, u)}{\\partial x}$$\n",
    "\n",
    "We replace $f(x, u)$ with our state estimate $\\mathbf{x}$, and the derivative is the Jacobian of $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Jacobian $\\mathbf{F}$ is\n",
    "\n",
    "$$\\mathbf{F} = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
    "\\frac{\\partial \\dot{x}}{\\partial x} & \n",
    "\\frac{\\partial \\dot{x}}{\\partial y} &\n",
    "\\frac{\\partial \\dot{x}}{\\partial \\theta}\\\\\n",
    "\\frac{\\partial \\dot{y}}{\\partial x} & \n",
    "\\frac{\\partial \\dot{y}}{\\partial y} &\n",
    "\\frac{\\partial \\dot{y}}{\\partial \\theta} \\\\\n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial x} & \n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial y} &\n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial \\theta}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "When we calculate these we get\n",
    "\n",
    "$$\\mathbf{F} = \\begin{bmatrix}\n",
    "1 & 0 & -R\\cos(\\theta) + R\\cos(\\theta+\\beta) \\\\\n",
    "0 & 1 & -R\\sin(\\theta) + R\\sin(\\theta+\\beta) \\\\\n",
    "0 & 0 & 1\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "We can double check our work with SymPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}1 & 0 & - \\frac{w \\cos{\\left (\\theta \\right )}}{\\tan{\\left (a \\right )}} + \\frac{w}{\\tan{\\left (a \\right )}} \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\0 & 1 & - \\frac{w \\sin{\\left (\\theta \\right )}}{\\tan{\\left (a \\right )}} + \\frac{w}{\\tan{\\left (a \\right )}} \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\0 & 0 & 1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                        ⎛t⋅v⋅tan(a)    ⎞⎤\n",
       "⎢                   w⋅cos⎜────────── + θ⎟⎥\n",
       "⎢        w⋅cos(θ)        ⎝    w         ⎠⎥\n",
       "⎢1  0  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(a)            tan(a)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎢                        ⎛t⋅v⋅tan(a)    ⎞⎥\n",
       "⎢                   w⋅sin⎜────────── + θ⎟⎥\n",
       "⎢        w⋅sin(θ)        ⎝    w         ⎠⎥\n",
       "⎢0  1  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(a)            tan(a)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎣0  0                  1                 ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import symbols\n",
    "a, x, y, v, w, theta, time = symbols('a, x, y, v, w, theta, t')\n",
    "d = v*time\n",
    "beta = (d/w)*sympy.tan(a)\n",
    "R = w/sympy.tan(a)\n",
    "\n",
    "fxu = Matrix([[x-R*sympy.sin(theta)+R*sympy.sin(theta+beta)],\n",
    "              [y+R*sympy.cos(theta)-R*sympy.cos(theta+beta)],\n",
    "              [theta+beta]])\n",
    "\n",
    "fxu.jacobian(Matrix([x, y, theta]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can turn our attention to the noise. Here, the noise is in our control input, so it is in *control space*. In other words, we command a specific velocity and steering angle, but we need to convert that into errors in $x, y, \\theta$. In a real system this might vary depending on velocity, so it will need to be recomputed for every prediction. I will choose this as the noise model; for a real robot you will need to choose a model that accurately depicts the error in your system. \n",
    "\n",
    "$$\\mathbf{M} = \\begin{bmatrix}0.01 vel^2 & 0 \\\\ 0 & \\sigma_\\alpha^2\\end{bmatrix}$$\n",
    "\n",
    "If this was a linear problem we would convert from control space to state space using the by now familiar $\\mathbf{FMF}^\\mathsf{T}$ form. Since our motion model is nonlinear we do not try to find a closed form solution to this, but instead linearize it with a Jacobian which we will name $\\mathbf{V}$. \n",
    "\n",
    "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
    "\\frac{\\partial \\dot{x}}{\\partial v} & \\frac{\\partial \\dot{x}}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial \\dot{y}}{\\partial v} & \\frac{\\partial \\dot{y}}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial \\dot{\\theta}}{\\partial v} & \\frac{\\partial \\dot{\\theta}}{\\partial \\alpha}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "Let's compute that with SymPy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}t \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} & \\frac{t v}{\\tan{\\left (a \\right )}} \\left(\\tan^{2}{\\left (a \\right )} + 1\\right) \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} - \\frac{w \\sin{\\left (\\theta \\right )}}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) + \\frac{w}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\t \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} & \\frac{t v}{\\tan{\\left (a \\right )}} \\left(\\tan^{2}{\\left (a \\right )} + 1\\right) \\sin{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )} + \\frac{w \\cos{\\left (\\theta \\right )}}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) - \\frac{w}{\\tan^{2}{\\left (a \\right )}} \\left(- \\tan^{2}{\\left (a \\right )} - 1\\right) \\cos{\\left (\\frac{t v}{w} \\tan{\\left (a \\right )} + \\theta \\right )}\\\\\\frac{t}{w} \\tan{\\left (a \\right )} & \\frac{t v}{w} \\left(\\tan^{2}{\\left (a \\right )} + 1\\right)\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡                           ⎛   2       ⎞    ⎛t⋅v⋅tan(a)    ⎞                 \n",
       "⎢                       t⋅v⋅⎝tan (a) + 1⎠⋅cos⎜────────── + θ⎟     ⎛     2     \n",
       "⎢     ⎛t⋅v⋅tan(a)    ⎞                       ⎝    w         ⎠   w⋅⎝- tan (a) -\n",
       "⎢t⋅cos⎜────────── + θ⎟  ───────────────────────────────────── - ──────────────\n",
       "⎢     ⎝    w         ⎠                  tan(a)                             2  \n",
       "⎢                                                                       tan (a\n",
       "⎢                                                                             \n",
       "⎢                           ⎛   2       ⎞    ⎛t⋅v⋅tan(a)    ⎞                 \n",
       "⎢                       t⋅v⋅⎝tan (a) + 1⎠⋅sin⎜────────── + θ⎟     ⎛     2     \n",
       "⎢     ⎛t⋅v⋅tan(a)    ⎞                       ⎝    w         ⎠   w⋅⎝- tan (a) -\n",
       "⎢t⋅sin⎜────────── + θ⎟  ───────────────────────────────────── + ──────────────\n",
       "⎢     ⎝    w         ⎠                  tan(a)                             2  \n",
       "⎢                                                                       tan (a\n",
       "⎢                                                                             \n",
       "⎢                                                                      ⎛   2  \n",
       "⎢      t⋅tan(a)                                                    t⋅v⋅⎝tan (a\n",
       "⎢      ────────                                                    ───────────\n",
       "⎣         w                                                                w  \n",
       "\n",
       "               ⎛     2       ⎞    ⎛t⋅v⋅tan(a)    ⎞⎤\n",
       "  ⎞          w⋅⎝- tan (a) - 1⎠⋅sin⎜────────── + θ⎟⎥\n",
       " 1⎠⋅sin(θ)                        ⎝    w         ⎠⎥\n",
       "────────── + ─────────────────────────────────────⎥\n",
       "                               2                  ⎥\n",
       ")                           tan (a)               ⎥\n",
       "                                                  ⎥\n",
       "               ⎛     2       ⎞    ⎛t⋅v⋅tan(a)    ⎞⎥\n",
       "  ⎞          w⋅⎝- tan (a) - 1⎠⋅cos⎜────────── + θ⎟⎥\n",
       " 1⎠⋅cos(θ)                        ⎝    w         ⎠⎥\n",
       "────────── - ─────────────────────────────────────⎥\n",
       "                               2                  ⎥\n",
       ")                           tan (a)               ⎥\n",
       "                                                  ⎥\n",
       "     ⎞                                            ⎥\n",
       ") + 1⎠                                            ⎥\n",
       "──────                                            ⎥\n",
       "                                                  ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fxu.jacobian(Matrix([v, a]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**authors note: explain FPF better**\n",
    "\n",
    "This gives us the final form of our prediction equations:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{\\bar{x}} &= \\mathbf{x} + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}\\\\\n",
    "\\mathbf{\\bar{P}} &=\\mathbf{FPF}^{\\mathsf{T}} + \\mathbf{VMV}^{\\mathsf{T}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "One final point. This form of linearization is not the only way to predict $\\mathbf{x}$. For example, we could use a numerical integration technique like *Runge Kutta* to compute the position of the robot in the future. In fact, if the time step is relatively large you will have to do that. As I am sure you are realizing, things are not as cut and dried with the EKF as it was for the KF. For a real problem you have to very carefully model your system with differential equations and then determine the most appropriate way to solve that system. The correct approach depends on the accuracy you require, how nonlinear the equations are, your processor budget, and numerical stability concerns. These are all topics beyond the scope of this book."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "Now we need to design our measurement model. For this problem we are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. Using $p$ be the position of a landmark, the range $r$ is\n",
    "\n",
    "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n",
    "\n",
    "We assume that the sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n",
    "\n",
    "$$\\phi = \\arctan(\\frac{p_y - y}{p_x - x}) - \\theta$$\n",
    "\n",
    "\n",
    "Thus our function is\n",
    "\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{x}& = h(x,p) &+ \\mathcal{N}(0, R)\\\\\n",
    "&= \\begin{bmatrix}\n",
    "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n",
    "\\arctan(\\frac{p_y - y}{p_x - x}) - \\theta \n",
    "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is clearly nonlinear, so we need linearize $h(x, p)$  at $\\mathbf{x}$ by taking its Jacobian. We compute that with SymPy below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{- px + x}{\\sqrt{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}}} & \\frac{- py + y}{\\sqrt{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}}} & 0\\\\- \\frac{- py + y}{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}} & - \\frac{px - x}{\\left(px - x\\right)^{2} + \\left(py - y\\right)^{2}} & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡         -px + x                     -py + y              ⎤\n",
       "⎢──────────────────────────  ──────────────────────────  0 ⎥\n",
       "⎢   _______________________     _______________________    ⎥\n",
       "⎢  ╱         2           2     ╱         2           2     ⎥\n",
       "⎢╲╱  (px - x)  + (py - y)    ╲╱  (px - x)  + (py - y)      ⎥\n",
       "⎢                                                          ⎥\n",
       "⎢       -(-py + y)                   -(px - x)             ⎥\n",
       "⎢  ─────────────────────       ─────────────────────     -1⎥\n",
       "⎢          2           2               2           2       ⎥\n",
       "⎣  (px - x)  + (py - y)        (px - x)  + (py - y)        ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px, py = symbols('px, py')\n",
    "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n",
    "            [sympy.atan2(py-y, px-x) - theta]])\n",
    "z.jacobian(Matrix([x, y, theta]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now we need to write that as a Python function. For example we might write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def H_of(x, landmark_pos):\n",
    "    \"\"\" compute Jacobian of H matrix where h(x) computes \n",
    "    the range and bearing to a landmark for state x \"\"\"\n",
    "\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n",
    "    dist = sqrt(hyp)\n",
    "\n",
    "    H = array(\n",
    "        [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0],\n",
    "         [ (py - x[1, 0]) / hyp,  -(px - x[0, 0]) / hyp, -1]])\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We also need to define a function that converts the system state into a measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import atan2\n",
    "def Hx(x, landmark_pos):\n",
    "    \"\"\" takes a state variable and returns the measurement\n",
    "    that would correspond to that state.\n",
    "    \"\"\"\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n",
    "\n",
    "    Hx = array([[dist],\n",
    "                [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]])\n",
    "    return Hx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Design Measurement Noise\n",
    "\n",
    "This is quite straightforward as we need to specify measurement noise in measurement space, hence it is linear. It is reasonable to assume that the range and bearing measurement noise is independent, hence\n",
    "\n",
    "$$R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$\n",
    "\n",
    "### Implementation\n",
    "\n",
    "We will use `FilterPy`'s `ExtendedKalmanFilter` class to implment the filter. The prediction of $\\mathbf{x}$ is nonlinear, so we will have to override the method `predict()` to implement this. I'll want to also use this code to simulate the robot, so I'll add a method `move()` that computes the position of the robot which both `predict()` and my simulation can call. You would not need to do this for a real robot, of course.\n",
    "\n",
    "The matrices for the prediction step are quite large; while trying to implement this I made several errors before I finally got it working. I only found my errors by using SymPy's `evalf` function, which allows you to evaluate a SymPy `Matrix` for specific values of the variables. I decided to demonstrate this technique, and to eliminate a possible source of bugs, by using SymPy in the Kalman filter. You'll need to understand a couple of points.\n",
    "\n",
    "First, `evalf` uses a dictionary to pass in the values you want to use. For example, if your matrix contains an x and y, you can write\n",
    "\n",
    "```python\n",
    "    M.evalf(subs={x:3, y:17})\n",
    "```\n",
    "    \n",
    "to evaluate the matrix for `x=3` and `y=17`. \n",
    "\n",
    "Second, `evalf` returns a `sympy.Matrix` object. You can convert it to a numpy array with `numpy.array(m)`, but the result uses type `object` for the elements in the array. You can convert the array to an array of floats with ``numpy.array(m).astype(float)`.\n",
    "\n",
    "So, here is the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from filterpy.kalman import ExtendedKalmanFilter as EKF\n",
    "from numpy import dot, array, sqrt\n",
    "class RobotEKF(EKF):\n",
    "    def __init__(self, dt, wheelbase, std_vel, std_steer):\n",
    "        EKF.__init__(self, 3, 2, 2)\n",
    "        self.dt = dt\n",
    "        self.wheelbase = wheelbase\n",
    "        self.std_vel = std_vel\n",
    "        self.std_steer = std_steer\n",
    "\n",
    "        a, x, y, v, w, theta, time = symbols(\n",
    "            'a, x, y, v, w, theta, t')\n",
    "        d = v*time\n",
    "        beta = (d/w)*sympy.tan(a)\n",
    "        r = w/sympy.tan(a)\n",
    "    \n",
    "        self.fxu = Matrix(\n",
    "            [[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)],\n",
    "             [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)],\n",
    "             [theta+beta]])\n",
    "\n",
    "        self.F_j = self.fxu.jacobian(Matrix([x, y, theta]))\n",
    "        self.V_j = self.fxu.jacobian(Matrix([v, a]))\n",
    "\n",
    "        # save dictionary and it's variables for later use\n",
    "        self.subs = {x: 0, y: 0, v:0, a:0, \n",
    "                     time:dt, w:wheelbase, theta:0}\n",
    "        self.x_x, self.x_y, = x, y \n",
    "        self.v, self.a, self.theta = v, a, theta\n",
    "\n",
    "    def predict(self, u=0):\n",
    "        self.x = self.move(self.x, u, self.dt)\n",
    "\n",
    "        self.subs[self.theta] = self.x[2, 0]\n",
    "        self.subs[self.v] = u[0]\n",
    "        self.subs[self.a] = u[1]\n",
    "\n",
    "        F = array(self.F_j.evalf(subs=self.subs)).astype(float)\n",
    "        V = array(self.V_j.evalf(subs=self.subs)).astype(float)\n",
    "\n",
    "        # covariance of motion noise in control space\n",
    "        M = array([[self.std_vel*u[0]**2, 0], \n",
    "                   [0, self.std_steer**2]])\n",
    "\n",
    "        self.P = dot(F, self.P).dot(F.T) + dot(V, M).dot(V.T)\n",
    "\n",
    "    def move(self, x, u, dt):\n",
    "        h = x[2, 0]\n",
    "        v = u[0]\n",
    "        steering_angle = u[1]\n",
    "\n",
    "        dist = v*dt\n",
    "\n",
    "        if abs(steering_angle) < 0.0001:\n",
    "            # approximate straight line with huge radius\n",
    "            r = 1.e-30\n",
    "        b = dist / self.wheelbase * tan(steering_angle)\n",
    "        r = self.wheelbase / tan(steering_angle) # radius\n",
    "        sinh = sin(h)\n",
    "        sinhb = sin(h + b)\n",
    "        cosh = cos(h)\n",
    "        coshb = cos(h + b)\n",
    "        return x + array([[-r*sinh + r*sinhb],\n",
    "                          [r*cosh - r*coshb],\n",
    "                          [b]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a bearing difference of $-358^\\circ$, which will throw off the computation of the Kalman gain. The correct angle difference in this case is $2^\\circ$. So we will have to write code to correctly compute the bearing residual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def residual(a, b):\n",
    "    \"\"\" compute residual (a-b) between measurements containing \n",
    "    [range, bearing]. Bearing is normalized to [-pi, pi)\"\"\"\n",
    "    y = a - b\n",
    "    y[1] = y[1] % (2 * np.pi)    # force in range [0, 2 pi)\n",
    "    if y[1] > np.pi:          # move to [-pi, pi)\n",
    "        y[1] -= 2 * np.pi\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the EKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from filterpy.stats import plot_covariance_ellipse\n",
    "from math import sqrt, tan, cos, sin, atan2\n",
    "dt = 1.0\n",
    "\n",
    "\n",
    "def z_landmark(lmark, sim_pos, std_rng, std_brg):\n",
    "    x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "    d = np.sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2)  \n",
    "    a = atan2(lmark[1] - y, lmark[0] - x) - sim_pos[2, 0]\n",
    "    z = np.array([[d + randn()*std_rng],\n",
    "                  [a + randn()*std_brg]])\n",
    "    return z\n",
    "\n",
    "def ekf_update(ekf, z, landmark):\n",
    "    ekf.update(z, HJacobian=H_of, Hx=Hx, \n",
    "               residual=residual,\n",
    "               args=(landmark), hx_args=(landmark))\n",
    "    \n",
    "                \n",
    "def run_localization(landmarks, std_vel, std_steer, \n",
    "                     std_range, std_bearing):\n",
    "    ekf = RobotEKF(dt, wheelbase=0.5, std_vel=std_vel, \n",
    "                   std_steer=std_steer)\n",
    "    ekf.x = array([[2, 6, .3]]).T\n",
    "    ekf.P = np.diag([.1, .1, .1])\n",
    "    ekf.R = np.diag([std_range**2, std_bearing**2])\n",
    "\n",
    "    sim_pos = ekf.x.copy() # simulated position\n",
    "    # steering command (vel, steering angle radians)\n",
    "    u = array([1.1, .01]) \n",
    "\n",
    "    plt.scatter(landmarks[:, 0], landmarks[:, 1],\n",
    "                marker='s', s=60)\n",
    "    for i in range(200):\n",
    "        sim_pos = ekf.move(sim_pos, u, dt/10.) # simulate robot\n",
    "        plt.plot(sim_pos[0], sim_pos[1], ',', color='g')\n",
    "\n",
    "        if i % 10 == 0:\n",
    "            ekf.predict(u=u)\n",
    "\n",
    "            plot_covariance_ellipse(\n",
    "                (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], \n",
    "                 std=6, facecolor='b', alpha=0.08)\n",
    "\n",
    "            x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "            for lmark in landmarks:\n",
    "                z = z_landmark(lmark, sim_pos,\n",
    "                               std_range, std_bearing)\n",
    "                ekf_update(ekf, z, lmark)\n",
    "\n",
    "            plot_covariance_ellipse(\n",
    "                (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2],\n",
    "                std=6, facecolor='g', alpha=0.4)\n",
    "    plt.axis('equal')\n",
    "    plt.show()\n",
    "    return ekf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiIKEcM00REREREOWKYJiIiIiLK0f8DFOtXWgWEMYwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4ffecc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.02356385  0.04184256  0.00219828]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
    "landmarks = array([[5, 10], [10, 5], [15, 15]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print(ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAKBIhGkAAACgSP8D90KwQZi0wAkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4ffe780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.02010224  0.02051038  0.00154269]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print(ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have plotted the landmarks as solid squares. The path of the robot is drawn with a dashed line, which is admittedly hard to see. The covariance after the predict step is drawn in a very light shade of blue, and the covariance after all of the landmark measurements are incorporated are shown in green. To make them visible at this scale I have set the ellipse boundary at 6$\\sigma$.\n",
    "\n",
    "From this we can see that there is a lot of uncertainty added by our motion model, and that most of the error in in the direction of motion. We can see that from the shape of the blue ellipses. After a few steps we can see that the filter incorporates the landmark measurements. \n",
    "\n",
    "We can see the fantastic effect that multiple landmarks has on our uncertainty by only using the first two landmarks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncyTBtBBCCCGEEOfo/wcw4X8B/URueQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4ffe080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.01975584  0.04575349  0.00022389]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:2], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print(ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the covariance gets smaller as it passes through the landmarks but quickly expands once past them. Let's see what happens with only one landmark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEREREZFJUpgWEREREZmk/w/2lO7DINsZjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9f749e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.26397302  0.7937892   0.00351629]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:1], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print(ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you probably suspected, only one landmark produces a very bad covariance. What is worse, the filter starts to diverge from the robot's path. On the other hand, a large number of landmarks allows us to make very accurate estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtMAAAEWCAYAAACkORurAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmUXFd99vvvqXnoquqxelYPUktqy5InGWTheBDYQZBX\niUniJFyuEZNXbsyNDeE6OCHIlxgTsohf3hBwEhKIr8GJDQTyZoGNEjAGRZ4kW2BZsqyh1ep5rO4a\nTw3nnPtH2x0LWYOru9Xd8vNZq5ZK55w6vWsvrapHu397b8NxHAcREREREXnDXIvdABERERGR5Uph\nWkRERESkTArTIiIiIiJlUpgWERERESmTwrSIiIiISJkUpkVEREREyqQwLSIiIiJSpjOG6S9/+ctc\ncsklxGIxYrEYmzdv5gc/+MFJ19x99900NzcTCoW4/vrrOXDgwII2WERERERkqThjmG5tbeUv//Iv\nef7559m7dy9btmzhN37jN/j5z38OwOc//3nuu+8+/uZv/oZnn32WeDzODTfcQDqdPi+NFxERERFZ\nTMYb3QGxpqaGv/iLv+DDH/4wTU1N/OEf/iF33XUXAKZpEo/H+cIXvsCtt966IA0WEREREVkqzrlm\n2rIs/uVf/gXTNLnmmmvo6elhZGSEG2+8cfaaQCDANddcw+7duxeksSIiIiIiS4nnbBe88MILXHXV\nVeTzeYLBII888ghr1qyZDcz19fUnXR+PxxkcHFyY1oqIiIiILCFnDdNr167lF7/4BdPT03zrW9/i\nd3/3d3n88cfP+BrDME45Nj09XX4rRUREREQWWSwWO+XYWcs8vF4vnZ2dXHbZZdx7771s2rSJL3/5\nyzQ2NgIwMjJy0vUjIyM0NDTMU5NFRERERJauN7zOtGVZ2LZNR0cHDQ0N7Ny5c/acaZrs2rWLzZs3\nz2sjRURERESWojOWeXzyk5/k137t12hpaSGVSvHQQw/xxBNP8NhjjwFwxx13cO+997J27Vq6urq4\n5557iEQivPe97z3jD33tEPmePXsA2Lhx41zfy5uS+q986ru5Uf/NjfqvfOq7uVH/zY36r3zLte/O\nVqp8xjA9MjLC+973PoaHh4nFYlxyySU89thj3HDDDQDceeed5HI5brvtNhKJBJs2bWLnzp2Ew+H5\newciIiIiIkvUGcP017/+9bPeYMeOHezYsWPeGiQiIiIisly84ZppERERERGZoTAtIiIiIlImhWkR\nERERkTIpTIuIiIiIlElhWkRERESkTArTIiIiIiJlUpgWERERESmTwrSIiIiISJkUpkVEREREyqQw\nLSIiIiJSJoVpEREREZEyKUyLiIiIiJRJYVpEREREpEwK0yIiIiIiZVKYFhEREREpk8K0iIiIiEiZ\nFKZFRERERMqkMC0iIiIiUiaFaRERERGRMilMi4iIiIiUSWFaRERERKRMCtMiIiIiImVSmBYRERER\nKZPCtIiIiIhImRSmRURERETKpDAtIiIiIlImhWkRERERkTIpTIuIiIiIlElhWkRERESkTGcM05/7\n3Oe48soricVixONxtm3bxosvvnjSNdu3b8flcp302Lx584I2WkRERERkKThjmH7iiSf46Ec/ypNP\nPsmPf/xjPB4P73jHO0gkErPXGIbBDTfcwPDw8OzjBz/4wYI3XERERERksXnOdPKxxx476e8PPvgg\nsViM3bt38+53vxsAx3Hw+XzE4/GFa6WIiMgSdvCgSW/v6c+3tUF3d+D8NUhEzpszhulflkwmsW2b\nqqqq2WOGYbBr1y7q6+uprKzk2muv5bOf/Sx1dXXz3lgREZGlqLcXtm49fVh+9FGT7u7z2CAROW/e\nUJi+/fbbueyyy7jqqqtmj73zne/kN3/zN+no6KCnp4dPfepTbNmyhb179+Lz+ea9wSIiIiIiS4Xh\nOI5zLhd+/OMf55FHHmHXrl20t7ef9rqhoSHa2tp4+OGHuemmm2aPT09Pzz4/fPhw+S0WERFZYnp6\n2rj55tP/RvaRR8bo6DhDHYiILFldXV2zz2Ox2Cnnz2lk+mMf+xiPPPIIjz/++BmDNEBjYyMtLS0c\nOXLkjbVURERERGSZOWuYvv322/nWt77F448/zurVq896w7GxMQYGBmhsbDztNRs3bpx9vmfPnlOO\nyblT/5VPfTc36r+5Uf+Vbyn23fi4ecbzkUhkybR3KfbfcqL+K99y7bvXVle8njMujXfbbbfxT//0\nT3zzm98kFovNLn2XyWQAyGQyfOITn+Cpp57i+PHj/OQnP2Hbtm3U19efVOIhIiIiInIhOmOYvv/+\n+0mn07z97W+nqalp9vFXf/VXALjdbvbv38+v//qvs2bNGrZv3053dzdPPvkk4XD4vLwBEREREZHF\ncsYyD9u2z/jiQCBwylrUIiIibzZtbTPL353pvIhcmN7Q0ngiIiJyqu7ugNaRFnmTOmOZh4iIiIiI\nnJ7CtIiIiIhImRSmRURERETKpDAtIiIiIlImhWkRERERkTIpTIuIiIiIlElhWkRERESkTArTIiIi\nIiJlUpgWERERESmTwrSIiIiISJkUpkVEREREyqQwLSIiIiJSJoVpEREREZEyKUyLiIiIiJRJYVpE\nREREpEwK0yIiIiIiZVKYFhEREREpk8K0iIiIiEiZFKZFRERERMqkMC0iIiIiUiaFaRERERGRMilM\ni4iIiIiUSWFaRERERKRMCtMiIiIiImVSmBYRERERKZPCtIiIiIhImRSmRURERETKpDAtIiIiIlKm\nM4bpz33uc1x55ZXEYjHi8Tjbtm3jxRdfPOW6u+++m+bmZkKhENdffz0HDhxYsAaLiIiIiCwVnjOd\nfOKJJ/joRz/KlVdeiW3bfPrTn+Yd73gHBw4coKqqCoDPf/7z3HfffTzwwAOsXr2az3zmM9xwww0c\nOnSIioqK8/ImRESWg4MHTXp7Z56nUm0AjI+bs+fb2qC7O7AYTRMRkTKdMUw/9thjJ/39wQcfJBaL\nsXv3bt797nfjOA5f/OIXueuuu7jpppsAeOCBB4jH4zz00EPceuutC9dyEZFlprcXtm59NSyfGpof\nfdSku/v8tklERObmDdVMJ5NJbNueHZXu6elhZGSEG2+8cfaaQCDANddcw+7du+e3pSIiIiIiS4zh\nOI5zrhfffPPNHD16lD179mAYBrt37+bqq6/mxIkTtLS0zF73wQ9+kMHBwZNGtqenp2efHz58eJ6a\nLyKyfPT0tHHzzXWnPf/II2N0dPSexxaJiMjZdHV1zT6PxWKnnD9jmcdrffzjH2f37t3s2rULwzDO\nev25XCMiIiIispydU5j+2Mc+xiOPPMLjjz9Oe3v77PGGhgYARkZGThqZHhkZmT33ejZu3Dj7fM+e\nPacck3On/iuf+m5u1H9v3GsnG76eSCSi/jwH+rc3N+q/uVH/lW+59t1rqytez1lrpm+//XYefvhh\nfvzjH7N69eqTznV0dNDQ0MDOnTtnj5mmya5du9i8eXOZTRYRERERWR7OODJ922238Y1vfIPvfe97\nxGIxhoeHgZnRk3A4jGEY3HHHHdx7772sXbuWrq4u7rnnHiKRCO9973vPyxsQEREREVksZwzT999/\nP4Zh8Pa3v/2k43fffTef/vSnAbjzzjvJ5XLcdtttJBIJNm3axM6dOwmHwwvXahGRZaitbWb5O4BU\nKgXMDE689ryIiCwvZwzTtm2f00127NjBjh075qVBIiIXqu7uwOw60nv27AeWX+2giIic7A2tMy0i\nIiIiIv9NYVpEREREpEwK0yIiIiIiZVKYFhEREREpk8K0iIiIiEiZFKZFRERERMqkMC0iIiIiUiaF\naRERERGRMilMi4iIiIiUSWFaRERERKRMCtMiInJBs20H23YWuxkicoHyLHYDRERE5lvJsjELJYol\ni2JpJkj7vC5iYT+GYSxy60TkQqIwLSIiFwzLssnmi+TyFrkcFIvg2AYODuGwjd9bIuj3LnYzReQC\nojAtIiIXhKxZJGsWyWShUAC/10sk4MbtdpHLF7Gsoso9RGTeKUyLiMiyZlk2yWyenOmQyYDX7aEy\n7D2pnKNk2fh94HFrqpCIzC+FaRERWbbyhRLpXIFUGgp5iIT8eD3uk65xHIeSbRH1gc/rPs2dRETK\nozAtIiLLUiZXYDJpMpGwcGwDv9fHdCZP0OchHPTNXpfNF/H5wOtxa/KhiMw7hWkREVlWbNthOlvg\nxEiaqSkHbC8uPBRNA9txcGIlAj4PbreLkmVTtEpUVkA4oImHIjL/FKZFRGTZKBYthqdyTCchY+VI\nJPOUbJtYKEBjTYyA14tt27w6zTBjFggGIeifCdciIvNNYVpERJaFTK7A0ESK/mGblweyBGI9JEsT\n5EoZ/O4g1f461jQ1sf35lQD0friA22MTChonlX2IiMwnhWkREVnyplI5hiazHD2e57kjUyTsURxX\nnqpKg4pKFzlzkgPjfXxu5Fd47rcT1FdFyBbyVMZmJiWKiCwUhWkREVmybNthIpllZMJkcKjEvsND\njFn95D1jXLG6Eb/v1dINh38c+n3+oPo7jE5liIR9RCJQEfJpOTwRWVAK0yIisiQVihaJVI7B0TyJ\nSRiezDKSGSbNKO0NDkODMyG5vR127Pl9PtT8P7FyBZI5k3AYKoIeAj59zYnIwtKnjIiILDlmocRk\n0mRoNM9UwgHbxcG+YXqmj1EZtSlacLzH4mfRP4Bx+OSGL9E/lKfCHaSuykc46FadtIicFwrTIiKy\npGTNItPpAr0DOQaGc6TSkM2XGJ6ewnAXmZoKsHevn951fwDAut4vcSxiUyr5uLg5zuoVlURCCtIi\ncn4oTIuIyJKRyRVIJPM8s3+EPS+NMZLIU3Ly5PMWg8lhIvUWzQ1F4vE8vUm4evpveNuv2RzuydNR\ntYYr1tbTUF2hzVlE5LxRmBYRkSUhnSswNpnlB0/28PPDYwwkR7DcSWIRH+mixaSZITGS5AelewC4\nOfK/yAdKHDqap6WinfUr2rj64lZcLgVpETl/FKZFRGTRJTN5hsYz7HzqBHuPDXBi6gQtjV4KZgVt\nreA4DhPTBZ6ungnS1+X/hEKwgAs/XVUXs661mff8yloCfu1yKCLnl8K0iIgsqslkluGJHM8dSLD3\n8AA9U8dpX+EhFjX4z502bStcGIbB09W3s3n0a3gth2jUpi3UTHN1FZs3NPGWNc14ve7Ffisi8iZ0\n1sU3f/rTn7Jt2zZaWlpwuVw88MADJ53fvn07LpfrpMfmzZsXrMEiInLhGJ/OcrhvmiefG+c/9h6j\nZ2KIyqjBxJiHXbvg4AGLXbvgLw9v5z2+++mI13F5WzNXrVzB7113KR9413quuqhVQVpEFs1ZR6Yz\nmQwbNmzg/e9/P7fccsspkzoMw+CGG27gwQcfnD3m82kWtYjIcnLwoElv7+nPt7VBd3dg3n6e4zj0\njU7z+HMneHpfgtHUNIeHhkg5w3iifoL8966Fu+u38+v8I8lkgfrKKJ31Fi31Xta2VxEN+zXZUEQW\n1VnD9NatW9m6dSswMwr9yxzHwefzEY/H571xIiJyfvT2wtatpw/Ljz5q0t09Pz+rVLJ4qW+ch3/8\nEoeOTzJpjpK3THKYlHxTTOQM6sMunm/9Y2iFj3d+jRcPZ6n2NrC+s4qm6BTVEQ+xivkL9yIi5Zpz\nzbRhGOzatYv6+noqKyu59tpr+exnP0tdXd18tE9ERC4gWbPA4f4JHtr5Mi/2n6DkTtLRHiCbDZMv\nOpg+D6adZCd/zK0Nf8vwsJv9h9P4rErWtDfwq5ubGe7L4vOorENElgbDcRznXC+ORCJ8+ctf5pZb\nbpk99vDDDxMOh+no6KCnp4dPfepTWJbF3r17Tyr3mJ6enn1++PDheWq+iIjMh56eNm6++fSDII88\nMkZHxxnqQM7CcRxSuSITyQKPPTvOodEhSt4kLQ0GwyMeSrkAeTvPvtY7Aejqv5N4pIJcxkPUW01X\nQ4xfvbyBltowbi19JyLnUVdX1+zzWCx2yvk5j0z/zu/8zuzzdevWccUVV9DW1sb3v/99brrpprne\nXkREljnLdphKFxieLPDC0Rz9k2nSpTQtcYNiAYYHfWB7WdlpA1D/wg7wVWC4YrQEQ1zUGeDq7jri\nlUHVR4vIkjPvS+M1NjbS0tLCkSNHTnvNxo0bZ5/v2bPnlGNy7tR/5VPfzY36b26WWv+Nj5tnPB+J\nRMpqa6FoMTiRZKonxXQ+y3hugJzLZmV7FY4VZP9+m6Mvl+A9t3IUWH/sb6mqqaK+qprNl9Zy+dpK\nrljTSDj43xMSl1rfLTfqv7lR/5Vvufbda6srXs+8h+mxsTEGBgZobGyc71uLiMgyksrkOTaU4Cd7\nB9l/JEnazHJkaJzJ4jCuCjddrR62bDE4vO5WAN5V/HtyNW46Kuv4zS2drGyrYFVTFW73WVdxFRFZ\nNOe0NN6rNc62bdPb28u+ffuoqamhurqaHTt28Fu/9Vs0NDRw/Phx7rrrLurr61XiISLyJjY2leGl\n3gn+7YkeekcnmS6N4/VbOG6DQiHLWMYkMOrih86dbC3+LRNTBcwAdFS1sO3aFi5dW0VjTURlHSKy\n5J01TD/77LNs2bIFmFm5Y8eOHezYsYPt27fzla98hf379/Pggw8yNTVFY2MjW7Zs4dvf/jbhcHjB\nGy8ispy8di3nVKoNOLm8Yr7Xcn4j2tpmlr870/lzYVk2A+MpDp+Y4juPH+F4oh+8GTrb/bjw4nYc\nXNPVPFv1Rxxw4J3Wl8nlSzRX1dNcVcu2qzu4fE09NbHQPL2zc3O+19kWkQvHWcP0ddddh23bpz3/\n2GOPzWuDREQuVCev5XxqMJvPtZzfqO7uwJx/tpkv0jOc4ER/nu8/eZzeySEsd4qVrX5cLnjuGTfr\n17v5d/cfAXB579cJN9TSUhliTXuEd1zZSmdTJdFFWD/6fK6zLSIXlnmvmRYRkTefiekMxwanOdxj\n8vyhCfrHp0iXpulq9WPbBmBzrAeebPo/eI/xNcZGvaxobOVtG+J0rghxUWcldVVhAj59LYnI8qJP\nLRERKVuxZDEwnuKZ/cPs/sU4k1N5+ibHGM4MUxvPg6uaF16A4z0GI2+b2aPguRdMruqu56qL69i4\nrpr2pgoqIwG82ohFRJYhhWkRESlLOpvnxMg03/tpDwd7x5nMTZAnxXjWIVEaJmA79I+72F13J9RB\nw9Nf5aJLcsTW1HBxex3v2FRPQ3WYaNiviYYismwpTIuIyBtiWTaTyRxDk1ke+c8jHBocJJEfpb7O\nzXQiSH2NjZXxMZ1JsK9iZkfD90X+jqcqTap9TVzS3sx73t5OW32UgN+7yO9GRGRuFKZFROScmYUS\niWSOobE8P3y6j8ODQ0yYw3S2eXEcg90H4NJL3FSYNRys/XMuGryXpuoqJnNB3raujSvW1LDt6lW0\nxmO4tC24iFwAFKZFROSsHMchnSswMW3y3MEJ9r08zp5DJxg2+1i9KsDIsJsTfTbHD7s4fskHoBYu\n7fk68WgtLYEIrc0+rrminsu7mqhchNU6REQWisK0iMh58tq1nFOpFDCzTfdrzy9FlmWTyhU42JPg\nP57t4dhAiiPDQwxNj+OLJJnKRAi66zAowm99gLUv/QM+v83Fza1csbaBS7qjrGgM0xqP4vMuza+d\n+VpnW0TefJbmp5qIyAXotWs579mzH4CNGzcuYovOrliySKRMnnxhiP98tocTkyNMFxKUXG4Mf4ai\nd5KkCT/03wntsOKFL9HQmSUebOHizmqufWsNrfEINbHQkp5kOB/rbIvIm5PCtIiIvK5cvshoIsPz\nByd47NljHJs8TkXUpru1gr5+m7zhJYuPJ/1/DsC7jS/RXwVNFSu4fGUL/+OaVlpqo4SCvkV+JyIi\nC0dhWkRETjGdNhmezHBioMDPfjHIiekBamsNink/A/1uqmJuktlq9sX+lLZjd1MbrsKorGbTqjib\n1tdz3WUttMZjuN2uxX4rIiILSmFaREROMppIMzppMjoKLxwZZzAxgePKUlvjY9d/FbCLIX7uvQVi\ncNHRvyVMDesbqunujHLtxiZWNlVSHQ0t9tsQETkvFKZFRAQA23YYmkiy7+UJDh5Nk81ZHOobZyAz\nStDv5dHHDI68DPzGLbQ//wAVlSYdtU28pbue69/SREdzlNpYCJ9XOxmKyJuHwrSIiFAsWew9NMjO\nZ/o41j9Fupgmky8wOOhgeie5ZmMNO4MfgYtgXc/9VK+cIuqOs649xrbrV9DRVElF0LekJxmKiCwE\nhWkRkTe5rFnk0WeO8KM9xzk+NkTRlaUy6iab9ON48li2wz+M3crvhP6enp4CObdDQ3AFl3bV89tb\numhrqNJotIi8aSlMi4i8iU0mc+x85ig79xzj6PgJmhs8FPMh4jUGR1/08cLKDwFw7fg3mPa7qAt7\naGqt4m2XxrlxYzsNtRGNRovIm5rCtIjIm5Bl2QxNpnnupVH+fdcxeqd76WjzUl3l4YeP2YSOuXl+\n5fsA2HTkUVZ2VFIRho42P1dtqGVDZwPBgHeR34WIyOJTmBYReZPJmgWeOTjAk78Y5T+e7WEg3Y+/\nIstLx/0UX6jk0NrfB6B171dZ0+WjqS3MFRdVs6rDz8rWCB0NlbhcWvJORAQUpkVE3jQsy2ZoPMW/\n/uwQPz8yQu/YGL2TCdLuYWLeFF5vlJ+v+CQAvxO+n5cbStQGVnDFuiouXx9iZXMVtUt8J0MRkfNN\nYVpE5E0gly/SOzzFQ/9xkP0n+hjPTlIV9eAb9VNV6eZQ5d8DsDl7L6VUlLGwi+76Nq5cF+e6K+tY\n2VRFWDsZioicQmFaROQCZts2o4ks41NZ/uVHh3mxr48sCS7qCtLX6yefydOz6i8BaDr2CcZdblbH\n66gNV3PdxgY2b2iko7EKj3YyFBF5XQrTIiIXqEyuwEgiw/ikxdP7R+kZmiBZStDV7qOvD/Y+azBy\n9Ufo/MU/UDQyRIMVtETruGJVnOuuaGBtWzX11RUq6xAROQOFaRGRC4xl2Uwmc7zcn+CFQ0kSUyWO\nDE8wkkxQ0+Chr9/gB96PwNUQ/9k3qO40CfmqaIk18OvXtbF+dRWt8RgVKusQETkrhWkRkQtI1izy\nzEsD/GRvH30jOTJmjnypwNCIRdJO8KPox8AD7439LXuecQi2T1MZjbCispGbrm/nkq46mmoiuFXW\nISJyThSmRUQuAMWSxfBkmn/b9TLPvzzCQGKUAjkiERdur5enV3wEgIv7v0C8Okhfqkg0HKEjXs3K\n5ire9bYVrO+sozISXOR3IiKyvChMi4gsY47jkEjlODGS5F+fOML+3n7GsqO0Nfsp5MOUCjbfZWYX\nw8v6vkrMaKDeHcbltWloDXLZ2hhvWVdPe0MVXo+2BBcReaMUpkVElqnptEnf2DSj43kee6qPgwP9\nTFmjdLb7iYTdfLnvAwB8qOpBEgmLVDRIZ7SO7pVVNDV4WNUeoq0+SlUkqEmGIiJlUpgWEVlGbNsh\nmTEZnEjx9IsjvHQsTc9gmp7REabtAVa1exgfDfD/eWbKOvjeP/KjTpNYZYm1DfV0rQyzYW2I9uYQ\njTVRAn59DYiIzIU+RUVElgHbdsiaBcamszy9f4j/+sUwQ1NTZAspEtkU47kcxeAoj3IfeOC2lq/y\n7LMuMust6hts4r52rlxbz5a31tFcW0FtpXYyFBGZDwrTIiJLmG07ZPNFplIm41N5dj7dy/4TAwyn\nRgiELOpqPUSzFTxV+38DsGLwdupCcfqMAjYGUX8lbbE6rr4kzrWXtdBSF8Xv00e/iMh8OevaRz/9\n6U/Ztm0bLS0tuFwuHnjggVOuufvuu2lubiYUCnH99ddz4MCBBWmsiMibheM4ZHIFJqaznBjKcKQ3\nx7d+dJTnjvVyYrqP+nqbliYPLx/08nDhA/wP62tcNvy/cGUa8eTqqbDaWNfYxa9uauf/fNdKtv3K\nKjqbqhSkRUTm2Vk/VTOZDBs2bOD9738/t9xyyym/Fvz85z/PfffdxwMPPMDq1av5zGc+ww033MCh\nQ4eoqKhYsIaLiPyygwdNentPf76tDbq7A+evQWUyCyUyuQLD4zn2H52kbzjNy/1THBkeJGWPsKYz\nRDDo4f6Bj0Aj3FrzDbK5IiPjfrqqm+lqbGB1e5SLV0Vpb47QWhfF5z3zx/2F0nciIufbWcP01q1b\n2bp1KwDbt28/6ZzjOHzxi1/krrvu4qabbgLggQceIB6P89BDD3HrrbfOf4tFRE6jtxe2bj194Hv0\nUZPu7vPYoDeoZNkkM3nGEjl+tq+f/cfGSWRyTKZT9I9PMWmOU11n8c3UH0EK4k/+HaPDDv8azxCp\nKnLZqnpW1jXyq29tp6XZR7wyTFX03NaNXu59JyKyWOb0+76enh5GRka48cYbZ48FAgGuueYadu/e\nrTAtInIOHMchmcmTSJkcH0jz2NM9nJgcZSQ1ht9vE6l04512ONH6Z5wAri3dQ2dDLaV32vz790us\nv8RNfbiZda2NvOvqduqrg9RXVeDxaBdDEZGFNqcwPTw8DEB9ff1Jx+PxOIODg6d93Z49e87pmJw7\n9V/51Hdzs5T6L5VqA04/uppKpdizZ//5a9A5+K8nn2YylSeZdhgYtXiuZ5yR3DAmGXwuL07JIOCG\nZxs+QXffpxnNJDnuzZEYHsPrClATqKUaH101Bhe3mKTHe7BTHobOULLxepZj3y2lf3vLkfpvbtR/\n5VtufdfV1XXG8ws2E0VLLomInF7JsplO5+kdzdE3YpPJQM/EFKP5YRxvlua4w3eK/8/s9TdZ/5MT\n2ITylYRLERrCIapjbtrW+lnfGaWhMkAk6MXl0meviMj5NKcw3dDQAMDIyAgtLS2zx0dGRmbPvZ6N\nGzfOPn/1fyevPSbnTv1XPvXd3CzF/hsfN894PhKJLHp7bdthZDLFV7/9OEf6sxiBSvLFPIm0yVBi\nCttn0hyr5jvF/2vmBd/9O1atDJFoLeEPFri0vZnLVtZx6boauturqKsKEA3757wV+HLou1ctxX97\ny4n6b27Uf+Vbrn03PT19xvNzCtMdHR00NDSwc+dOrrjiCgBM02TXrl184QtfmMutRUQuOMlMnmdf\n6mfnMz39SRoAAAAgAElEQVTsfamfRD5NVfU4oaCLRB4mi2MMtP+/vAjc1vR1dj9VwrnSYtXKDEMj\nRZqibVy+Js67NrfRGq8gFPAR0FJ3IiKL6pyWxjt8+DAAtm3T29vLvn37qKmpobW1lTvuuIN7772X\ntWvX0tXVxT333EMkEuG9733vgjdeRGQ5SL+yXvRP9/XzxM97OTreS8E1RXurgYsKinmDZ+s+AHWw\nou8TtNfVMZ4oEAiXyOQsUokYFzV08LYNDdywsZ2aWEjrRYuILBFn/TR+9tln2bJlCzBTB71jxw52\n7NjB9u3b+drXvsadd95JLpfjtttuI5FIsGnTJnbu3Ek4HF7wxouIvFZb28wSbmc6f744joNZKHG4\nb4IjfVM8tX+cfT0nmCwO0dESxIWB4zh8K/9BcMMHog/yi0MpkgWTzESQiUKAKr+f1fUxVq+IsOWK\nNi5dWU/A712Q9i6lvhMRWU7OGqavu+46bNs+4zWvBmwRkblyHAfHmfkTwAFchnFOE+u6uwNLYi3k\nrFlg78tD7Hqhn+OD04wnsxwdGieRH6EiWmIyU+DH7j+dufi7fweWn8dXOoQjflZUtNJYG6GuysPq\nzhAbVtVycUecaNi/oG1eKn0nIrLc6PeEIrKoSpZNsWS98qeNZc+EaWD2T5cL3C5j5uF24XW78Hnd\nS27VoGTaZHQ6y86nj/Hc0UH6EqOYhSx+v4GNDb40B+Jf4ADwK5k/Ix4Nc/gyh3whS0ODixpvM11N\ncTatr6WzJURzXZSaytBivy0RETkDhWkROe9se6YEwiyUKJYcikUolWYejm3wakZ+NSzbtgOGg9vt\n4HbbeL3g94HX4ybg8+Dzzm0li7m+l3Q2z0Qyx/hUge8+cZhDg/2Mm6M01/vIZcOYWQ8vtG4H4PL8\nHaSyJZJFGywbl69I1F1BS7iBy9fWc83lDTTXVVBXGcbj1qYrIiJLncK0iJw3tu2QzRcx8yXMPJgm\n4Bh43G68HhfBgAv3aQKk4ziUrJmR63zOIpOx8HotAgELv8+gIuib8/Jwb0TJskln8/QMTXF8KM3I\nSJFDAwlOTAwxURils82Pz+finzMfhiD8Bl9ndCrNeGaCvAlYISrCMVbXtbCiPsrmDXVsWF1HS21U\nkwtFRJYRfWKLyHlhFkpkcgWyOcjnweNyUxHwnvPoq2EYeD1uvEDA55md4JdOlch5HIqlPEG/m4qg\nb0HLP8xCifGpLM8eGmDfy2P0j2bJ5ooUShb9wxmmnAEuXhPinyZ+f+YF3/kHcNzs7/JS2xDGW/BQ\n660hErZprfPzzutXsW5lFS21UcIL3HYREZl/CtMisqAcxyGdK5A1LdJpcBtuokHfnHfqMwyDoN9L\n0O/FLJSYni6QD1gUSybhgHdeR3ctyyaTK5DImPSPpPnh08c5PDzEeHoSiyJBn0EJN4linsOr/piX\n8/Dh+q/idXn42WV5DGy6ugqMTTisjjazuiVOU0WKhloX113RQnUkqBAtIrJMKUyLyIIpWTapbJ50\nxiFvzoRfv3f+P3YCPg8+j5uMWSBRsChFCkQch+Acl5ErFC1y+SKJtMnEZIEjfWl+vO8oA8k+8naG\n5uYAVdEgX+z98Myn6Spo7/0z3B6H3lKGSCBAqKJIPg+5VCVtsTreelGcqy9tZGTgCJUhHzVRTTAU\nEVnOFKZFZEFYlk0ykyeZcrBLLqIh/5xHo8/E5TKIhPyYhRLJZAHHKeI4EAq88UBtFkoMTaTY+9Iw\nL52YZDxRIJVy6B2bZNoaIhaD9hV+fB5jJkgDt9Z8A9O0ecGdJp8HMxHGFwrSEvNS4Q/R2Rzhqg31\nrOuopa4yTCnZP99dICIii0BhWkTmnWXZTL8SpLHdC75G8msFfB4MA1KpAlDEcRzCQd8ZX/Pq5Map\nVI5EKsfel0d5+sUBBpPjTGfTmIUimXyRickSjm+KPfHPwujMa+NP/j2jQwbfi5doaXETivhoCDay\nqqmKaMRNa1OItW0R2pti1FeFF2zTFRERWRwK0yIyr2zbIZmdCdKO5SYSOn9B+lV+rwcDg1QqD5Tw\nuF0n1VBblk2hZFEs2eTyRaYyeRIpk+kpi5/uG+Dl4X6Gs0OEQ9DQ4KUiHGBw0M/euo/M3uPdni/Q\n2VBL6Sabb3+3wHVvLzIy5lDjbmFlQy1vXVdPe3OA2uoAddEgobMEehERWZ4UpkVkXqWyeVLpV0o7\nzuOI9C/zed04+EinC7hdeRwHSvbMBjGFok3fSIb9PaP0DE4xnS5RyHlJZnJMmJMk7WGa4l4qYx4c\nHL4yMFPKsXnqS4zn+ynYOaYqC0yHSqQyBaI1FuMjAZpDLXR31LBlYxNNtSFqY2EqQgrRIiIXMoVp\nEZk3+UKJXN6mkDeILWKQfpXb5SJnlkhmC4SCefweP5PJPM+/PMQvjg8xlBpmOpvFtsHAxfiERao4\nRUuzm2/nb58t5ajb9XV++z0+BuwCxbEWxjJJMnaUgYIXF0EuaQ/RFq9i0/o6Nq5poL664qylJSIi\ncmFQmBaReeE4DhmzSCYDQb/3vC/1VrLsVx4WGbNArlAkn7cxTYfJZAGf3yYYyPH8y4O8NNxHf7Kf\nSNhHW6sXrwcyORhPWBzp+CRHgPcEv8jQ8SiHjxYYG3H4zr86tLR68Aa9tFWspaaigvrqEE1xNxet\nrGTDqjjNddE5ryAiIiLLi8K0iMyLjFkkk3Vw4V6Q5e9+WemVuudSyZop3yg6pHMlsrkS2ZzD1HSR\nnpEJEukMqVwey3bImjmmi5NkXaN0toaprfJi23DsmM13+RA0werhP6VkpJmOm6zfEObiDS7+9/8u\n8SvXFJicdIi66qmP1nLdZU00N3lZUR+lvqqCgF8fpyIib0b69BeRObNtZ2aLcBNiC1gjbNsO+WKJ\nQsnCzFvkTJtSCXJ5i0LRwrZc2EUvJ8YnOTI8zFB2gERugpxpYRUNEtM2WWea+riB3x/CcRz+6tgH\nAbji2DfpWlvihD/N8Ykh+gs2mCaGyyAac2MmI7SEauhqq+HqS+M011bQGo9qdQ4RkTc5hWkRmTOz\nUCJngtftmfe1pC3LJlcokc7lyRctcqbFwGiK48PTTGZyOJaD3+0l5KugLV7DVGaa53uPcDz9En6f\ni9oaPz6vh2zWIpEqkSlO8lTkCzw1OHP/7kP/yMH9XvY6DsmUm+q6INW0U+2qosEfwu9zsfJSD421\nIS5bXUt3RxXNtRFCAdVEi4iIwrSIzAOzUCKfh4rA/HyklCybfLFELl8kmSmQzlqYOcjl4cjAGEdH\nBhg1h0iXprELXtx2kKivisP9CSazCSaco1TH3NRV+/B6XDz3vMMzTbdC+8z9O0b/gIZYDRetaKCy\n00VFpIhjGaxabdE/WGR9XSeXdDbQUBumMuqlodZPfY2f6miISMinrb9FRGSWwrSIzMnMUnMOOAYe\nt6vs+ziOw1Q6x3gyS6Fo48JDNmuTzRoYjpegz8fQ+DBHJ05wPHeISNhDkz+A1+PCskpMTA1yYGyI\nbNogGCsRDQcoWvCPEx+EJthe8U0mpooMTUwxnBtgwikyFi7gwU9llc1UqsDYaIBVtR1c1BZn87pG\nIhEPVVE3lZEA4YBvQXdwFBGR5UlhWkTmpFC0KBTAN4dJh32jU/xsfw/DiRTT2QyFkkPYiNEQreGS\nzhVUVYTImHmOjAzRM32IhtoA4aAXr8fAMAwcx8Hn85JIFEgUErxQ8yc8k565d+3uv2N8yMP3ax1W\ntHqoagiRSjfhpB2mxiI42QAhD8Qb66iPxrh8dRNXrKknFvFQEfIS8ntxz+E/CSIicmFTmBaRObFs\nB8sC/zkEzly+yIETI0xnTAI+Lz6PG5/HxRMvHOel0ZeYKkzi83iwCz5KBQ+TZhOZfJHLOluZyKQY\nS4/i8/iIhL0njYIf77WpqfbwX9UfgmpY2f8nrF0Rp7G6ktyNRX64s8g7f9WY2RUxY1FV5aLOt4KL\nVtQTCngIBdysaAyzfmUt8eogfp+HoM+jEC0iImelMC0ic2LZNpYFHt+Zg+f4dIYf7TvC8UQvU+YU\nOG68BJkY9TBZ6qeyNs/axtjMca8Ly4L+wUEOTEyRyKYI+0LkTINQ1I3H7WJgAP7V2T5zcw+QhPcF\nHuRwb5rebD9jCZPG6pkR87YVDm5vCcuySWQKxAJR1jTWc+OVnVRXuamMeIlFfAR8HgI+j2qiRUTk\nnClMi0jZHMehZDk4DmetJ37uyAAHxg6SdkaoqnRjmm5GxpMcGs6Qd0+wKlwJjpuA3w2A2wWdbX6G\nRk0ODx8iaK7ACDg4jsGX+rfP3veKE19j7x6D9Rd7mWx2UV8bZGwyTjJRorffxOczqGsscWKwhJmH\nmLealfEmtl7TxKqWAJXhAEG/B6/HvZBdJSIiFyiFaREp26slHi7jzKPS0xmTE+MTjKZHWLvKT6ng\nJex34TYK9I8VSKVMpswp+sbdrGyqxfXKyHBfH9TWuZhOOPxb8B0zNyvCFX3/xN49cOWV0LLCwbJt\nNqy3cCwH03QRDVYQMuoIFd0ks9MU7RyVER+rGqtZ3Rznyu4G1q+qoSoSXOguEhGRC5zCtIjM2dmK\nIoYmk4ykRgkFDayCD+8rtcilIrgdP1VRFxk7wUjKwBgyWNlYS38//LO5HfoAF9yQ/jpGph5fJI3R\nmsDAz6ZNMz/dcVwEgxaWXWJsqkBTbZyumlaiQT+ZYopozGZlSyUXtTVQHQnh8pTOyy6NIiJy4dO3\niYgsuIxZwMxbgB+vx4XLBTnTxi4F8LpKOLaHuhoPY+OT7M58Do688sLvfp2NGx2mEz4i6y1sHAJO\nI2YB3L5JppMeggE3jY2QNW2GR4vYhQCN4VouXVVPNGIQDFbR0hCisToKzEyCdBatJ0RE5EKjMC0i\nc2IYnDGcWpaNZTlYeR8EDNxug0LRplhwEQq4+WnkozMXpoEAdIz9AUaqmWM/r6euziCTdTh8pEgg\nZOB1T7Gpswm3twu/McLw4ChFJ4tFAZ/HS9RXSWNdC1d1d9BcG8LjNqir9RALB05qk+PM1HuLiIjM\nlcK0iJTtXFa9yJgFXLaPkK+CZH4mwNo2WCU3Xu/MpL91/V/AVz1MXaPJpFPCUzVN0BNkw+pqWltd\nRKM2l11uc/y4RTgCV3evon+ykqGpejK5PGaxQDjgp6U2yobOBiqCARxswmEI+U9eRs92HNyes0+Y\nFBERORcK0yJSNgNwucC2X3+U17Js8kWbWKiC+kg1fUNe8gUHx5lZAcQAPr7im/zbi1m8FSlSUxax\nqMPISJJgLEZzsw246OxwgWMT8vuJBfzEQgFCgQZW1sfxeMHjcQgEXPi9HgwgXyoSDkNFyEPQ7z2p\nTbbt4HMzp90aRUREXqUwLSJlc7kMPG4Dw+VgWfYpm5zkSzO7IwZ8XppqYlQmqkhMTVJd5cLjtTh2\n1MXgkIujLwXocBpIJi1qGw28ngzBYI6pTI6qihCNjXCkN0/MaKAqGqLoFPD6IOzjlY1f3HjcbrKF\nArZjEYlARdB7SpAGKFk2bje4XQrTIiIyd3P+Nrn77rtxuVwnPZqamuajbSKyDHjcLjweKNn2Kecc\nx8G2Z4JrS10lNYE4o+MlPG4Dn9+mY1WRt7y1xJVvMbh6U4D26maKqSpSkxWMjuc5MZhlZLzAsf4M\nhu2joaqS9auqiEVdVEa8VIaDVAT9WI5DMpfD47WIxSAa9r1ukHYcBwwHt0tlHiIiMj/mZWR67dq1\n/OQnP5n9u9utzQ9E3iy8Hjcej0WxYPM6+RXDmCmtaK6J0lJVy0i2mpHRJA31btxuB6+vSOdKqK83\nqIh66RusZjLjZ3BimrFJm+pAgFp/HS11rVx90UrqYpHZWu1CsUQuV8TjdYhGIeh3E/L7ThuUCyUL\nj0clHiIiMn/mJUy73W7i8fh83EpElhmP24XXC2bOOuWcz+PG6y2RyZTwezxctrKZ0eQ0B8Z+Tizm\nJhR0gRfWdjs4NgSDbqorgyTTXuyf+1hR0cU71q4hFg6ysqGWkN+H4zjkiyXyxRKGyyZcAQG/i3DA\nd9aQXCxZ+Pzg9y1OhdvBgya9vTPPU6k2AMbHzdnzbW3Q3R14vZe+6anvRGSpmpdvlGPHjtHc3Izf\n7+etb30r9957Lx0dHfNxaxFZ4jxuFz6vgcvtUCha+Lz//Zspr8dN0O+iVLJJm3mqoyG6WxrJFNMc\n7jnCmk4fgYAxs+Ph7MsMaqt9xKst1tU38bbuTmAmCKfNPCXLwuuFYAj8PoNQwHtOG7DYtkPRsqh4\npc56MfT2wtatrwa+U4Pfo4+adHef3zYtF+o7EVmq5hymN23axAMPPMDatWsZGRnhnnvuYfPmzbz4\n4otUV1fPRxtFZIkL+Dz4/UXyZumkMA0QCflxyJN12WRyJl1NtSTSOUq2xaGjx1izyk/A/99lGbbt\nkErZePDjdhmkzTyWbeP1gs/PbBj2ed1vaBdDs1jC5wO/z616aRERmTeGM887F2SzWTo6OvjkJz/J\nxz72sdnj09PTs88PHz48nz9SRBaZ4zgkc0WSSRchn+91V8owiyUKRZtCEQpFh+d7JumZHGW8NER1\npU1lFAzDwTAcBkYg4tRzeXM7XU1RvJ6ZzV68bhcet2tmJPsNsB2HtFkgHLaIhT2LVjPd09PGzTfX\nnfb8I4+M0dHRex5btHyo70RksXR1dc0+j8Vip5yf98LBUCjEunXrOHLkyNkvFpELgmEY+D1u/H4b\nM28RDpwaVgNeD36PQ9FnU7JsNl9URbTPpnfCzWh+mN6RNF6PjWNDyBWjMVzF2tYo4YAXj8s4pw1i\nTscslPD5bAI+lyYfiojIvJr3MG2aJgcPHmTLli2nvWbjxo2zz/fs2XPKMTl36r/yqe/m5pf7z3Ec\nptImU9MObsNL6PWW9vgl1wP9Y1M8f3SQ0akUJacIQH2sis0XtRGvrJhzOwtFi2whT1UlVEWCi1ri\n8doJc68nEono3+NpqO/mjz775kb9V77l2nevra54PXMO05/4xCfYtm0bra2tjI6O8ud//ufkcjne\n//73z/XWIrKMGIZBRdCHZeWZmi6+spHK2UeBW+oqaamrpFC0MAtFCiWLmmhoTiPRr3Ich2y+QLgC\nwsHTL5knIiJSrjmH6YGBAX7v936P8fFx6urquOqqq3jqqadobW2dj/aJyDLi9bgJBbwUikXSmTzR\nUOCcA6zP6z5l8uJcOI5DMpvH53cIBVwEFmk5PBERubDN+dvln//5n+ejHSJygQgFvBRLFpZlk8ya\nbyhQz6dUNo/HaxOpMIiG/ef957+etraZJdwAUqkUMFOe8Nrz8vrUdyKyVGmoRkTmXTQ8sxyeYdik\nciYVAT/u8zTxz3Ec0rkCLo9NNGIQCwfmpWRkPnR3B2bXQt6zZz+w/GoHF4v6TkSWKoVpEZl3hmEQ\nC/sxXg3U2TzhgA/vAm+WUrJsMmYej9eZGZEO+VUnLSIiC0phWkQWhGEYxCoCGEYel8sik8njKboJ\nB3wLMlKczRcplIqEwxAKuIgoSIuIyHmgMC0iCyoa9uP1FPF5i2SyFtMZk4DPO28TAvPFErl8EbfH\noTI2U7MdCpx9WT4REZH5oDAtIgsu6Pfi93rwegrk8hbZbAEzXcTrmdkS/I1upGJZNoWSRb5Ywu1x\nCFdAwG8QCfm1KYuIiJxXCtMicl64XDOragR8FgFfkXzRxjRLpM0SOMbMNuEuF26XcdJ25I7j4Dhg\n2TaWbVMs2RguB68XIlHw+1wEfR78WvpOREQWgb59ROS8enU96ZJlkw+UyBctSpZDqWRhWRZFC8yZ\njRAxjJkHgMsFvgCEPOBxG3g9M2tHL/SkRhERkTNRmBaRReFxu/AEfYSDM2Ublu1QsuxXRqAdAAyY\nnazods2MXns9bk0sFBGRJUNhWkQWndvtwu1mXndAFBEROR80U0dEREREpEwK0yIiIiIiZVKYFhER\nEREpk8K0iIiIiEiZFKZFRERERMqkMC0iIiIiUiaFaRERERGRMilMi4iIiIiUSWFaRERERKRMCtMi\nIiIiImVSmBYRERERKZPCtIiIiIhImRSmRURERETKpDAtIiIiIlImhWkRERERkTIpTIuIiIiIlElh\nWkRERESkTArTIiIiIiJlUpgWERERESmTwrSIiIiISJnmLUx/5StfoaOjg2AwyMaNG9m1a9d83VpE\nREREZEmalzD98MMPc8cdd/CpT32Kffv2sXnzZrZu3UpfX9983F5EREREZEmalzB933338YEPfIAP\nfehDrFmzhr/+67+msbGR+++/fz5uLyIiIiKyJM05TBcKBZ577jluvPHGk47feOON7N69e663FxER\nERFZsuYcpv//9u42pok7jgP49w5XsIMWH1ZBYBMdzg10MSjBZvFpaqyLhGW66QJkvhhZDMzpXuzJ\nTTRmzm1ZsmSSKSYLiZrp4vYG2cBE5EFqxrQoCroZiJpA6xiIlEjM2t9eGC6cFAeF5Ap8P8mF9H+/\nXn75cm3+lOv/2tvb4fP5MGPGDN24zWaD2+0e6eGJiIiIiEKWIiIykgO0trYiPj4eVVVVeOmll7Tx\nPXv24NixY7h27RoAoKura2SdEhEREREZyGq1Dhgb8SfT06dPR1hYGDwej27c4/EgNjZ2pIcnIiIi\nIgpZI55Mm0wmpKamory8XDd++vRp2O32kR6eiIiIiChkTRqNg+zYsQPZ2dlIS0uD3W7H999/D7fb\njXfeeUerCfSxOBERERHRWDYqk+nXX38d//zzD/bu3Yu2tjbMnz8fpaWlSEhIGI3DExERERGFpBF/\nAZGIiIiIaKIatduJD9fbb7+NZ599FmazGTabDZmZmWhqatLVdHZ2Ijs7G9HR0YiOjkZOTg5XBcHD\nXPLz8/H888/DbDbj6aefxtatW9HR0TGgjvkFdujQIaxYsQLR0dFQVRW3bt0aUMP8BldYWIjExERM\nnjwZixYtQk1NjdEthaSqqipkZGQgPj4eqqqiuLh4QE1BQQHi4uJgNpuxYsUKNDY2GtBp6Nm3bx8W\nL14Mq9UKm82GjIwMXL16dUAd8wvswIEDePHFF2G1WmG1WmG321FaWqqrYXZDt2/fPqiqivz8fN04\nMxyooKAAqqrqtpkzZw6oGU+5GTaZXrx4MYqLi3Ht2jWUlZVBRLBq1Sr8+++/Ws2bb76J+vp6lJWV\n4bfffsPFixeRnZ1tVMsho7W1Fa2trfjqq69w5coVHDlyBFVVVdi8ebOujvkN7v79+1i7di127949\naA3zC+z48eN47733sHPnTtTX18Nut8PhcOD27dtGtxZyenp6sGDBAnz77beYPHkyFEXR7d+/fz++\n+eYbfPfdd6irq4PNZsPq1avh9XoN6jh0VFZWIi8vD06nE2fOnMGkSZOwatUqdHZ2ajXMb3AJCQn4\n8ssv4XK5cOHCBaxcuRKZmZm4dOkSAGY3HOfPn0dRUREWLFigew0zw8HNmzcPbrdb2xoaGrR94zI3\nCRGXLl0SRVHkzz//FBGRxsZGURRFamtrtZqamhpRFEWuX79uVJshq7S0VFRVle7ubhFhfkNVV1cn\niqLIzZs3dePMb3BpaWmSm5urG0tKSpKPPvrIoI7GhsjISCkuLtYe+/1+iYmJkc8//1wbu3//vkRF\nRcnBgweNaDGkeb1eCQsLk5KSEhFhfsGYOnWqHDp0iNkNw927d2XOnDly9uxZWb58ueTn54sIz7/H\n2bVrl6SkpATcN15zM+yT6f56enrwww8/ICkpCYmJiQAAp9OJyMhILFmyRKuz2+148skn4XQ6jWo1\nZHV1dSE8PBxmsxkA8xsp5hfYgwcPcPHiRaxZs0Y3vmbNGtTW1hrU1djU0tICj8ejyzIiIgJLly5l\nlgHcu3cPfr8fU6ZMAcD8hsPn8+HHH39Eb28vli5dyuyGITc3Fxs3bsSyZcsg/b5ixgwfr7m5GXFx\ncZg9ezY2b96MlpYWAOM3N0Mn04WFhYiKikJUVBRKSkpw6tQpTJr0cIERt9uNp556SlevKApvUx7A\n3bt38emnnyI3Nxeq+vBXyvxGhvkF1t7eDp/PhxkzZujGJ3ouwejLi1kOzbZt27Bw4ULtD1zm9/8a\nGhoQGRmJiIgI5Obm4sSJE3juueeY3RAVFRWhubkZe/fuBQDdJR7McHDp6ekoLi5GWVkZioqK4Ha7\nYbfb0dHRMW5zG9XJ9M6dOwdcdP7oVlVVpdVnZWWhvr4elZWVeOGFF+BwONDd3T2aLY0pw80PALxe\nL9avX69dHzeRBZMfUSh69NrqiW7Hjh2ora3FyZMnh5QN83to3rx5uHz5Mn7//Xfk5eVh06ZN+OOP\nPx77HGb30PXr1/HJJ5/g6NGjCAsLAwCIiO7T6cFM9AzXrl2LDRs2ICUlBS+//DJOnToFv98f8AvY\n/Y3l3EZlnek+27dvR05OzmNr+q89bbFYYLFYMGfOHKSnp2PKlCn45ZdfkJOTg5iYGPz999+654oI\n7ty5g5iYmNFsO2QMNz+v14t169ZBVVWUlJTAZDJp+5hfYENd+3wi5jcU06dPR1hYGDwej27c4/Eg\nNjbWoK7Gpr7zyOPxID4+Xhv3eDwT+hx71Pbt23HixAlUVFRg1qxZ2jjz+39PPPEEZs+eDQBYuHAh\n6urqcODAAXz22WcAmN3jOJ1OtLe3Izk5WRvz+Xyorq7GwYMHceXKFQDMcCjMZjOSk5Nx48YNZGZm\nAhh/uY3qZHratGmYNm1aUM/1+/0QEfh8PgDAkiVL4PV64XQ6tX/rOZ1O9PT0jNvblA8nv+7ubjgc\nDiiKgl9//VW7VroP8xuZiZjfUJhMJqSmpqK8vByvvfaaNn769Gls3LjRwM7GnsTERMTExKC8vByp\nqakAgN7eXtTU1ODrr782uLvQsG3bNvz000+oqKjA3LlzdfuY3/D5fD74/X5mNwSvvvoq0tLStMci\ngi1btmDu3Ln4+OOPkZSUxAyHqLe3F01NTVi5cuX4PfeM+NbjjRs35IsvvpALFy7IzZs35dy5c7J+\n/apU1iAAAAI0SURBVHqZOnWq3LlzR6tzOBwyf/58cTqdUltbKykpKZKRkWFEyyHl3r17kp6eLsnJ\nyfLXX39JW1ubtj148ECrY36Da2trE5fLJUePHhVFUaS0tFRcLpd0dHRoNcwvsOPHj4vJZJLDhw9L\nY2OjvPvuuxIVFSW3bt0yurWQ4/V6xeVyicvlErPZLHv27BGXy6VltX//frFarfLzzz9LQ0ODvPHG\nGxIXFyder9fgzo23detWsVgscubMGd17XP9smN/gPvjgA6murpaWlha5fPmyfPjhh6KqqpSXl4sI\nswvGsmXLJC8vT3vMDAN7//33pbKyUpqbm+X8+fPyyiuviNVqHdfve4ZMpm/fvi0Oh0NsNpuYTCZJ\nSEiQrKysAUuOdXZ2SlZWllgsFrFYLJKdnS1dXV1GtBxSKioqRFEUUVVVFEXRNlVVpbKyUqtjfoPb\ntWuXLre+n/2XLmN+gyssLJRZs2ZJeHi4LFq0SKqrq41uKST1vVYffb1u2bJFqykoKJDY2FiJiIiQ\n5cuXy9WrVw3sOHQEeo9TFEV2796tq2N+gb311lvyzDPPSHh4uNhsNlm9erU2ke7D7Ian/9J4fZjh\nQJs2bZKZM2eKyWSSuLg42bBhgzQ1NelqxltuvJ04EREREVGQQmKdaSIiIiKisYiTaSIiIiKiIHEy\nTUREREQUJE6miYiIiIiCxMk0EREREVGQOJkmIiIiIgoSJ9NEREREREHiZJqIiIiIKEicTBMRERER\nBek/BNLkK80PtugAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9ea99e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.00871873  0.00883399  0.00077378]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10,  5], [15, 15], [20,  5], [15, 10], \n",
    "                   [10,14], [23, 14], [25, 25], [10, 20]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print(ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "I said that this was a 'real' problem, and in some ways it is. I've seen alternative presentations that used robot motion models that led to much easier Jacobians. On the other hand, my model of a automobile's movement is itself simplistic in several ways. First, it uses the *bicycle model* to compute how it moves. A real car has two sets of tires, and each travels on a different radius. The wheels do not grip the surface perfectly. I also assumed that the robot was able to instaneously respond to my control input changes. In fact, I didn't even bother changing the control input during the run. Sebastian Thrun writes in *Probabalistic Robots* that simplied models are justified because the filters perform well when used to track real vehicles. The lesson here is that while you have to have a reasonably accurate nonlinear model, it does not need to be perfect to operate well. As a designer you will need to balance the fidelity of your model with the difficulty of the math and the computation required to implement the equations. \n",
    "\n",
    "Another way in which this problem was simplistic is that we assumed that we knew the correspondance between the landmarks and measurements. But suppose we are using radar - how would we know that a specific signal return corresponded to a specific building in the local scene? This question hints at SLAM algorithms - simultaneous localization and mapping. SLAM is not the point of this book, so I will not elaborate on this topic. \n",
    "\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 an 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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\nVHwTQgghhBBiIX8D/gsX1H+aQ5UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x73db128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.13\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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\n30REREREUfILuNhOEyl1MXoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa0ce160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.14\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": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}