diff --git a/08_Designing_Kalman_Filters/README.md b/08_Designing_Kalman_Filters/README.md
deleted file mode 100644
index d041551..0000000
--- a/08_Designing_Kalman_Filters/README.md
+++ /dev/null
@@ -1,2 +0,0 @@
-You may read this book online via nbviewer by using this link:
-[*Read Online Now*](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)
diff --git a/09_Extended_Kalman_Filters.ipynb b/09_Extended_Kalman_Filters.ipynb
new file mode 100644
index 0000000..9528fae
--- /dev/null
+++ b/09_Extended_Kalman_Filters.ipynb
@@ -0,0 +1,1380 @@
+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:5995720ed3ceb08c4be39c6feddca4bc39bad7116b8f07678560ea256675af70"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "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": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "The Extended Kalman Filter"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#format the book\n",
+      "%matplotlib inline\n",
+      "from __future__ import division, print_function\n",
+      "import matplotlib.pyplot as plt\n",
+      "import sys\n",
+      "sys.path.insert(0,'./code') # allow us to format the book\n",
+      "import book_format\n",
+      "book_format.load_style()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "<style>\n",
+        "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
+        "@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: 850px;\n",
+        "        margin-left: 0% !important;\n",
+        "        margin-right: auto;\n",
+        "    }\n",
+        "    div.text_cell code {\n",
+        "        background: transparent;\n",
+        "        color: #000000;\n",
+        "        font-weight: 600;\n",
+        "        font-size: 11pt;\n",
+        "        font-style: bold;\n",
+        "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
+        "   }\n",
+        "    h1 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "\t}\n",
+        "\t\n",
+        "    div.input_area {\n",
+        "        background: #F6F6F9;\n",
+        "        border: 1px solid #586e75;\n",
+        "    }\n",
+        "\n",
+        "    .text_cell_render h1 {\n",
+        "        font-weight: 200;\n",
+        "        font-size: 30pt;\n",
+        "        line-height: 100%;\n",
+        "        color:#c76c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 1em;\n",
+        "        display: block;\n",
+        "        white-space: wrap;\n",
+        "    } \n",
+        "    h2 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h2 {\n",
+        "        font-weight: 200;\n",
+        "        font-size: 20pt;\n",
+        "        font-style: italic;\n",
+        "        line-height: 100%;\n",
+        "        color:#c76c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 1.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    } \n",
+        "    h3 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h3 {\n",
+        "        font-weight: 300;\n",
+        "        font-size: 18pt;\n",
+        "        line-height: 100%;\n",
+        "        color:#d77c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 2em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    h4 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h4 {\n",
+        "        font-weight: 300;\n",
+        "        font-size: 16pt;\n",
+        "        color:#d77c0c;\n",
+        "        margin-bottom: 0.5em;\n",
+        "        margin-top: 0.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    h5 {\n",
+        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "    }\n",
+        "    .text_cell_render h5 {\n",
+        "        font-weight: 300;\n",
+        "        font-style: normal;\n",
+        "        color: #1d3b84;\n",
+        "        font-size: 16pt;\n",
+        "        margin-bottom: 0em;\n",
+        "        margin-top: 1.5em;\n",
+        "        display: block;\n",
+        "        white-space: nowrap;\n",
+        "    }\n",
+        "    div.text_cell_render{\n",
+        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
+        "        line-height: 135%;\n",
+        "        font-size: 125%;\n",
+        "        width:750px;\n",
+        "        margin-left:auto;\n",
+        "        margin-right:auto;\n",
+        "        text-align:justify;\n",
+        "        text-justify:inter-word;\n",
+        "    }\n",
+        "    div.output_subarea.output_text.output_pyout {\n",
+        "        overflow-x: auto;\n",
+        "        overflow-y: scroll;\n",
+        "        max-height: 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",
+        "    code{\n",
+        "      font-size: 70%;\n",
+        "    }\n",
+        "    .rendered_html code{\n",
+        "    background-color: transparent;\n",
+        "    }\n",
+        "    ul{\n",
+        "        margin: 2em;\n",
+        "    }\n",
+        "    ul li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.5em; \n",
+        "    }\n",
+        "    ul li li{\n",
+        "        padding-left: 0.2em; \n",
+        "        margin-bottom: 0.2em; \n",
+        "        margin-top: 0.2em; \n",
+        "    }\n",
+        "    ol{\n",
+        "        margin: 2em;\n",
+        "    }\n",
+        "    ol li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.5em; \n",
+        "    }\n",
+        "    ul li{\n",
+        "        padding-left: 0.5em; \n",
+        "        margin-bottom: 0.5em; \n",
+        "        margin-top: 0.2em; \n",
+        "    }\n",
+        "    a:link{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    a:visited{\n",
+        "       font-weight: bold;\n",
+        "       color: #1d3b84;\n",
+        "    }\n",
+        "    a:hover{\n",
+        "       font-weight: bold;\n",
+        "       color: #1d3b84;\n",
+        "    }\n",
+        "    a:focus{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    a:active{\n",
+        "       font-weight: bold;\n",
+        "       color:#447adb;\n",
+        "    }\n",
+        "    .rendered_html :link {\n",
+        "       text-decoration: underline; \n",
+        "    }\n",
+        "    .rendered_html :hover {\n",
+        "       text-decoration: none; \n",
+        "    }\n",
+        "    .rendered_html :visited {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .rendered_html :focus {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .rendered_html :active {\n",
+        "      text-decoration: none;\n",
+        "    }\n",
+        "    .warning{\n",
+        "        color: rgb( 240, 20, 20 )\n",
+        "    } \n",
+        "    hr {\n",
+        "      color: #f3f3f3;\n",
+        "      background-color: #f3f3f3;\n",
+        "      height: 1px;\n",
+        "    }\n",
+        "    blockquote{\n",
+        "      display:block;\n",
+        "      background: #fcfcfc;\n",
+        "      border-left: 5px solid #c76c0c;\n",
+        "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
+        "      width:680px;\n",
+        "      padding: 10px 10px 10px 10px;\n",
+        "      text-align:justify;\n",
+        "      text-justify:inter-word;\n",
+        "      }\n",
+        "      blockquote p {\n",
+        "        margin-bottom: 0;\n",
+        "        line-height: 125%;\n",
+        "        font-size: 100%;\n",
+        "      }\n",
+        "</style>\n",
+        "<script>\n",
+        "    MathJax.Hub.Config({\n",
+        "                        TeX: {\n",
+        "                           extensions: [\"AMSmath.js\"]\n",
+        "                           },\n",
+        "                tex2jax: {\n",
+        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
+        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
+        "                },\n",
+        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
+        "                \"HTML-CSS\": {\n",
+        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
+        "                }\n",
+        "        });\n",
+        "</script>\n"
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 1,
+       "text": [
+        "<IPython.core.display.HTML at 0x7ffc0bc93400>"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "**Author's note: this is still being heavily edited and added to - there is a lot of duplicate material, incorrect code, and so on. The examples are just a brain dump, not fully formulated and not ready to be used.**\n",
+      "\n",
+      "**The Uncented Kalman filter (UKF) chapter is much further along. The UKF is almost always better performing than the Extended Kalman filter, and is much easier to implement, so if you have an urgenet need for nonlinear Kalman filter I'll point you towards that chapter for now.**\n",
+      "\n",
+      "The Kalman filter that we have developed to this point is extremely good, but it is also limited. Its derivation is in the linear space, and hence it only works for linear problems. Let's be a bit more rigorous here. You can, and we have in this book, apply the Kalman filter to nonlinear problems. For example, in the g-h filter chapter we explored using a g-h filter in a problem with constant acceleration. It 'worked', in that it remained numerically stable and the filtered output did track the input, but there was always a lag. It is easy to prove that there will always be a lag when $\\mathbf{\\ddot{x}}>0$. The filter no longer produces an optimal result. If we make our time step arbitrarily small we can still handle many problems, but typically we are using Kalman filters with physical sensors and solving real-time problems. Either fast enough sensors do not exist, are prohibitively expensive, or the computation time required is excessive. It is not a workable solution.\n",
+      "\n",
+      "The early adopters of Kalman filters were the radar people, and this fact was not lost on them. Radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n",
+      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
+      "\n",
+      "So shortly after the Kalman filter was enthusiastically taken up by the radar industry people began working on how to extend the Kalman filter into nonlinear problems. It is still an area of ongoing research, and in the Unscented Kalman filter chapter we will implement a powerful, recent result of that research. But in this chapter we will cover the most common form, the Extended Kalman filter, or EKF. Today, most real world \"Kalman filters\" are actually EKFs. The Kalman filter in your car's and phone's GPS is almost certainly an EKF, for example. \n",
+      "\n",
+      "With that said, there are new techniques that have been developed that both perform equal to or better than the EKF, and require much less math. The next chapter "
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "The Problem with Nonlinearity"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "You may not realize it, but the only math you really know how to do is linear math. Equations of the form \n",
+      "$$ A\\mathbf{x}=\\mathbf{b}$$.\n",
+      "\n",
+      "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n",
+      " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n",
+      "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n",
+      "\n",
+      "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n",
+      "\n",
+      "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n",
+      "\n",
+      "> If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if a sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n",
+      "\n",
+      "> $$\n",
+      "\\begin{aligned}\n",
+      "amp(roger) &= amp(roger + 0) \\\\\n",
+      "&= amp(roger) + amp(0) \\\\\n",
+      "&= amp(roger) + non\\_zero\\_value\n",
+      "\\end{aligned}\n",
+      "$$\n",
+      "\n",
+      ">which is clearly nonsense. Hence, an apparently linear equation such as\n",
+      "$$L(f(t)) = f(t) + 1$$\n",
+      "\n",
+      ">is not linear because $L(0) = 1$! Be careful!"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "The Effect of Nonlinear Transfer Functions on Gaussians"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian.  Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy as np\n",
+      "from numpy.random import normal\n",
+      "\n",
+      "data = normal(loc=0.0, scale=1, size=500000)\n",
+      "ys = 2*data + 1\n",
+      "\n",
+      "plt.hist(ys,1000)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkbkf5AAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbef0bfcc0>"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This is an unsuprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from nonlinear_plots import plot_transfer_func\n",
+      "\n",
+      "def g(x):\n",
+      "    return 2*x+1\n",
+      "\n",
+      "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAyQAAAGaCAYAAAD+VYcoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDIUEAAAAgDEUEgAAAADG/B/oE3S27Zv2cgAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbeedd1400>"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The plot labelled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n",
+      "\n",
+      "Now let's look at a nonlinear function and see how it affects the probability distribution."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from nonlinear_plots import plot_transfer_func\n",
+      "\n",
+      "def g(x):\n",
+      "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
+      "\n",
+      "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxgAAAGaCAYAAACMmuWeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlcVPXeB/DPmYVhBoZhGHZBRUXcl0RTSsQlEzMze+pq\ned0qM7Ordm+3W5lL9miZdbOuZVnXpeWxzPY0s8QtTcEF930BZR9g2GGYOc8fBDmy44FZ+LxfL17B\nOWfO+c5xOt/5nvNbBFEURRAREREREUlAZu8AiIiIiIjIdbDAICIiIiIiybDAICIiIiIiybDAICIi\nIiIiybDAICIiIiIiybDAICIiIiIiybDAICIiIvrDO++8g+7du0Oj0UAmk2Hx4sV2iSMhIQEjR46E\nv78/ZDIZwsLC7BKHFGQyGYYOHWrvMKgFscCgVs8RLtzr1q2zayIjImqsnTt3QiaTYdq0afYORTIb\nN27EnDlzYLFYMGfOHCxatMguX4zz8vJwzz33YM+ePbj//vuxaNEizJs3r8XjaKiG5FFBEFooGnIE\nCnsHQOQIHOXC5yhxEBE1lCtdt3744QcAwIYNGzBgwAC7xXHw4EFkZmZi5syZePfdd+0WR2PU9Tk4\nc+YMNBpNC0ZD9sYCg8iBiKJo7xCIiBrFla5bKSkpAICAgADGIaHOnTvbOwRqYWwiRU7hq6++wtCh\nQ6HT6aBWq9GtWzcsXLgQhYWFNtu1b9++1se0lc2Q1q9fD+DPx/sAcOXKFchksqqfGx/5Vz76NZlM\nmDVrFoKDg6FWq9GjR48a7yxV7re25k4xMTFVxwWAqVOnYvr06QCAxYsX28Sxe/fuRpwlIqKWsWjR\nIgwbNgwAsH79epvr1s3X2GnTpuHs2bN48MEH4efnB7lcjmPHjgEA4uLiMGPGDHTr1g06nQ4ajQY9\nevTAokWLUFJSUuNxK48RFxeHmJgYeHl5QafTYcyYMThz5ky112RkZOCf//wnunTpAk9PT+h0OnTu\n3BmPPPJIVRyV+925cycAICwsrOr93OjChQt47LHH0K5dO7i7u8Pf3x/jx4/HkSNH6ox1y5YtiI6O\nhpeXF3x8fGo9r5W5aOrUqQBsc8KGDRsAVM8hN6ot/1S+5urVq3j//ffRs2dPqNVqBAYG4oknnkBe\nXl6N+7t+/Trmzp2Lzp07Q6PRwMfHB5GRkVi4cCHKy8sblUdramqWn5+P+fPno0uXLlCr1dDr9Rg+\nfDi+++67Ws/N0KFDYTQaMWPGDAQFBcHd3R09evTAunXraj2v1PL4BIMc3oIFC/DKK6/AYDDg4Ycf\nhre3N37++WcsWbIE3333Hfbs2QNPT8+q7et7XF+5PiwsDAsXLsTixYuh0+ls2rf26dPH5jVlZWUY\nMWIE8vPzMWnSJJSUlGDTpk2YPXs2zp07h7feeqvW49QVAwDcf//9MJlM+PbbbxETE4OYmJiqde3a\ntavzvRAR2cPQoUNx9epVrF+/Hn369MG4ceOq1vXt29dm2wsXLmDgwIHo1q0bpkyZgry8vKrmMsuX\nL8fZs2cRFRWFe++9FyUlJdi7dy9efvllxMXFYceOHZDL5dWO/8MPP+Dbb7/F6NGj8eSTT+LkyZPY\nsmUL4uPjcerUKRgMBgBAUVERoqKicOnSJYwYMQJjx44FACQlJeHXX3/F8OHD0atXLwwdOhSCIGDd\nunW4evUq5s6dC29vb5tj7tixA/fddx/KysowZswYhIeH49q1a/jqq6+wdetWfPvttxg5cmS1WDdt\n2oRt27ZhzJgxeOqpp5Cenl7redXr9Vi4cCGOHj1aLSfcmJcamudu9uyzz+Lnn3/G2LFjMWrUKOzY\nsQNr1qzBhQsX8Ouvv9psm5CQgFGjRiE7OxvR0dEYP348SkpKcPr0abz66qv4+9//3qg8enNMJpMJ\nd955J06ePInbbrsNc+fORU5ODjZt2oRx48Zh8eLFeOmll6q9h9zcXNxxxx1QqVR46KGHUFpaii++\n+ALTp0+HTCbD5MmT6zw31EJEIge2f/9+URAEMTQ0VExNTbVZN2XKFFEQBHH27NlVy9q1ayeGhYXV\nuK+1a9eKgiCI69evt1kuCEKtr6lcLwiCOHjwYLGsrKxqeVZWlhgWFiYKgiDu27evanlcXJwoCIK4\nePHiGvc3ZMgQUSaT1Rhbba8hInI0O3fuFAVBEKdNm1bj+sproSAI4vz582vc5tKlSzUuf+mll0RB\nEMSNGzfaLF+4cKEoCIKoVCrFHTt22Kx7/vnnRUEQxOXLl1ct++6770RBEMR58+ZVO4bVahVzc3Nt\nlg0ZMkQUBEG8evWqzfLc3FzRYDCIvr6+4unTp23WnT59WtRqtWJwcLBYWlpaLVa5XC5u27atxvdZ\nm7pyQk05pFJt+afyfbVr105MTk6uWl5eXi5GR0eLgiCIBw8erFpeWloqtm/fXpTJZOLHH39c7Tjp\n6elieXl51d8NyaNDhw61WTZz5kxREATx0UcftVl+7do1MSgoSJTJZGJ8fHzV8suXL1d9nh5//HHR\narVWrTt16pSoUCjEbt261RoDtSw2kSKH9tFHHwEAXnjhBQQGBtqsW758Odzd3bFu3TpYLJZmjUMQ\nBCxbtgxKpbJqmcFgwPPPPw8AWLt2bbMen4jI0YgN7HsRGBiIBQsW1Liutiatc+fOBQBs3769xvUT\nJkyo1uRmxowZAID4+Phq27u7u1dbJggCdDpd7YHfYMOGDcjOzsbChQvRpUsXm3VdunTBY489htTU\n1GpPAQDgvvvuq/HJhj0sWLAAISEhVX/L5fKqpkw3nrfvv/8eV69exejRozFp0qRq+/H396/xyVJD\nmc1mbNiwAR4eHli+fLnNujZt2uCFF16AKIr48MMPq73Ww8MDb775ps0Tka5duyIqKgpnzpxBUVFR\nk+Mi6bCJFDm0w4cPA0BVW98b+fv7o2fPnoiPj8e5c+fQtWvXZotDoVAgKiqq2vIhQ4YAAI4ePdps\nxyYicma9e/e2uTlzo8LCQqxcuRJff/01zp07h4KCApvC5fr16zW+LjIystqyyi/OOTk5VctiYmLQ\npk0bvPbaa0hISMDo0aNxxx134LbbbmvUF+TffvsNAJCYmIhFixZVW3/27FkAwOnTpxEbG2uzzp6j\nUd2soeft999/B4Bq70UqZ86cQXFxMQYOHFhjn5QRI0YAQI19W8LDw22aRVcKDQ2FKIrIycnhiFUO\ngAUGOTSTyQRBEKo9vagUFBQEoKJNZnPy9fWtsU2rv78/gIo4iYioutqu32azGcOGDUN8fDx69uyJ\niRMnws/PD0qlEqIoYvHixSgtLa3xtTf3jwAqbgQBsHmirdVqceDAASxevBjfffcdfvnll6rXT58+\nHUuWLIFara73PRiNRgB/PlWviSAI1QYeAWp///bQ0PNWmVPbtGnTLHFU5szazk3l8ppye03vAaj5\nfZD9sMAgh1b5+Do1NRVeXl7V1qemptpsJ5PJUF5eXuO+bqUIycrKgiiK1YqMys56Nz5mrxxRozni\nICJyNrV1OP72228RHx+PadOmVfvinpqaKtnEo8HBwXj//ffx/vvv4+zZs9i5cydWr16NN998Ezk5\nOXUWDZUqr/GHDx+u1nm5PlLPE1KZY6xWa7XRpKTKL5Vf4q9duybJ/m5WeT7T0tJqXH9zbifnwz4Y\n5ND69esHURQRFxdXbV1GRgZOnDgBT09PREREAKgYgSM9Pb3GL/c1tcsFKi7+9d3xKC8vr3pEfqNd\nu3YBsB01Ra/XA6gYpeRmJpMJ586dq7a88lE977wQkbO41evWhQsXAADjx4+vtq7y2iq1iIgIPPHE\nE9izZw/c3NzwzTffNOh1lU1kHWHocL1eD1EUa8wxteW5xho0aBAAYOvWrQ3aviF59EZdu3aFWq3G\n8ePHq54O3aiyL0u/fv0avE9yLCwwyKFVzg+xdOlSm6H9RFHEc889h+LiYkyZMqUq0Q0cOBBmsxlr\n1qyx2c+2bduwcePGGo9hMBiQmZlZ45jrNx7vhRdeQFlZWdWyrKwsLFu2DIIg2Iz33bVrV+h0Onzz\nzTc2MZeXl2Pu3Lk1HsfX1xcAcPXq1VpjICJyJJVDwTb1ulXZwfvmG0iXLl3Cc889d2vB/eHUqVM1\n3iXPysqC2Wyusa1+TU8cpk2bBr1ejyVLllT1T7iRKIrYu3cvzGazJHHXZeDAgQCA9957z2b50aNH\nsXLlylpf15gnKffeey/at2+PLVu24JNPPqm2Pj093aagaEgevZFCocDkyZNRWFhYNVhKpZSUFCxb\ntgwymazqOwA5HzaRIoc2cOBAPP/881i2bBl69OiBBx98EF5eXti+fTuOHDmCXr16YdmyZVXb/+1v\nf8PatWsxe/Zs7NixA+3bt8epU6ewfft2PPDAA/jyyy+rHWPkyJH47LPPMGrUKAwePBgqlQp9+vTB\nmDFjqrYJCgpCcXExevbsibFjx6KkpARffvkl0tPTMWfOnKoLPlBx4Zw3bx4WLVqEvn37Yty4cRAE\nAXFxcRAEAb1790ZiYqJNDFFRUfDw8MDGjRuhVCrRtm1bCIKAyZMno23bts1wZomIbk2XLl0QGhqK\nPXv2YNKkSQgPD4dcLsd9992Hnj171vv6e++9F506dcKbb76J48ePo0+fPkhKSsKPP/6IMWPG1HpT\nqDF+/vln/OMf/0BUVBTCw8MREBCAtLQ0fPvttwBQ7cstUPPoWHq9Hps3b8a4ceMQFRWFYcOGoVu3\nblAqlUhOTsaBAweQnJyM3NzcWju0S2X69OlYsWIFXn/9dRw7dgw9e/bEpUuX8P333+OBBx6o9bw1\ndNQvAFAqldi0aRPuvvtuTJ48GR9++CFuv/12lJWV4ezZs/j111+RmZlZ1XS5IXn0Zq+++ir27NmD\nDz/8EEeOHMHw4cORm5uLTZs2ITc3FwsWLED//v0bd3LIcTTX+LdLly6tNkcBUVNt2rRJHDJkiOjl\n5SWqVCqxa9eu4ksvvSQWFBRU23b//v3isGHDRA8PD9HLy0scPny4uHfvXnHdunWiTCarNg9GZmam\nOHnyZDEoKEiUy+WiTCazGde9cnxvk8kkPvnkk2JwcLCoUqnE7t27i6tWrao15hUrVojh4eGim5ub\nGBwcLM6aNUvMzs4WY2JiahzDfPv27eKdd94parVaURAEUSaTibt27bqFs0bk2phn7O/w4cPiXXfd\nJXp7e4symczmGls5J0Nt82SIoigmJyeLjzzyiNimTRtRrVaLPXr0EF9//XWxvLy8xrkTFi1aVON1\nvNLNrzl9+rT4zDPPiP379xf9/f1FlUoltmvXThw7dqz4yy+/VHt95fX55nkwKiUlJYlz5swRIyIi\nRLVaLWq1WjEiIkKcOHGiuHHjRpu5GeqLtS6V+aq2uZHOnDkjjh07VtTpdKJGoxEHDRokfvvtt1Vz\nk9z8urreV11zNyUnJ4uzZ88WO3ToIKpUKtFgMIj9+/cXFy9eLJrN5qrtGpJHb/63FEVRNJlM4gsv\nvCBGRESIKpVK1Ol04tChQ8Wvv/662raV82DUtB9RFMWpU6fW+W9HLUsQxUaUtA30+++/4+GHH4aX\nlxeio6Px9ttvS30IohYjk8nQvn17XLp0yd6hENEfmGeIiByX5H0wTCYTJk2ahLVr11Z1diUiIpIK\n8wwRkWOTvMCYMWMGHnzwQQwZMqRR7f2IiIgagnmGiMixSdrJe82aNbh06RI+++wzADWPWMAJycgZ\nWa1WfnbJKbj6uPENyTMAcw0RUXNpSJ6RrMA4e/YsXnzxRezdu7dqyFBRFHl3iZxeTk6OvUMgIjDP\nEBE5C8k6ea9btw7Tp0+vuugDFZPvCIIAuVyOwsJCKJVK3lUiImpGrvwEo6F5BuATDCKi5tKQPCNZ\ngWEymXD9+vWqv0VRxLRp09C5c2e88MIL6NatW9V2DQ3weGYJNpzKwZzbfBGibd5xpRsrISEBkZGR\n9g7jlvA9OAa+B/tz9vgbc111Zg3NM5XbVnL0c9KSn7+8Ugsm/5SMq3lmDG/rieXRgZA1YgI2Z/p/\nxVlidZY4AcbaHJwlzsZeUyVrIqXT6aodUKPRQK/X21z0G0oURXQxqCACKLfy8TcRUWsndZ5pjbxU\ncrwVE4y/bk3Gr0kFeP9YNp7sbbB3WETkYiQfRepGgiA0amr6G2WXWDDhhyR08nZDe52bxJEREZEr\nuJU801q117nhtehAyATgg2PZ2HYl394hEZGLkXQUqZvFxcU1+bVaNxme7e+Hby+Y8PGpHAwN9XS4\nZlJERGRft5JnWrOoYA/8vZ8vXk/IwsJ96QjxVKK7r7u9wyIiF9GsTzBuhZtchoFBGiwcFIDefu5Y\neyIbrx7MsHdYRERELmFiF2+M7+SFUouIuTtTkFFUbu+QiMhFOGyBUcldIcOh9GIoZAJMpRZ7h0NE\nROQSBEHAvwb4o1+AGlnFFsyNS0FxudXeYRGRC3D4AgMA+vqr0cHbDSXl7OxNREQkFaVcwOvRQQjx\nVOJ0dile+i0dVs4rQkS3yCkKjD7+avwlwhshWiUu5JTaOxwiIiKXoXeX462hQfBUyvBrUgHeOWK0\nd0hE5OScosCoNCHCG19fyLN3GERERC6lo7cKrw8JgkIA1p3MwVfnOVEhETWdUxUYP1/Nh0EtR1Je\nGQrNbCdKREQklYFBGjx/uz8AYOmBDPyeUmjniIjIWTlVgXFHGw8EaBTYkVyAby/w7goREZGUxofr\nMLW7HhYReHZ3Gi7mslkyETWepAXGqlWr0Lt376rZVqOiorBlyxbJ9t9Zr8I9HbwwIcIbu64VYnWi\nEasTjdhzjXdZiIhag+bOMwQ83deA4W09UWC2YvavKUgvNNs7JCJyMpIWGKGhoVi+fDmOHDmCQ4cO\nYdiwYRg3bhwSExOlPAzcFTK8f1cIZvY2QKeSI4fD1xIRtQotlWdaM5kg4JU7KuagSisqx+wdKchj\nniWiRpC0wBg7dizuvvtudOjQAZ06dcIrr7wCrVaLgwcPSnkYGyGeSqQUmPF6fGazHYOIiByDPfJM\na+SukGHl0GCE6dxwIbcMc3emoIRzZBBRAzVbHwyLxYKNGzeipKQE0dHRzXUYDA7xwMzeBhSarUjj\nY1wiolajpfJMa6VTyfHu8GD4axQ4klGCF/emwcopMoioASQvMI4fPw5PT0+4u7tjxowZ+OKLLxAR\nESH1YaoZ01GLTefY8ZuIyNXZK8+0RoEeSrw7PBhaNxl2JBfi0zR3iJyIj4jqIYgSXynMZjOSk5Nh\nMpmwadMmvPPOO4iLi0NkZCQAwGT6swg4f/68lIfGj1kqFFkEtHO3oLfWDJVTjZFFRNQ04eHhVb/r\ndDo7RtIy6sszQPPmmtboXJEcbyV5wCwKuMunFA/6l0AQ7B0VEbWUxuYZyQuMm911110ICQnB2rVr\nAdhe9JsjEeaXWfD1hTwkZhbjoc7e6OPvDpVc+kojISHBJpk5I74Hx8D3YH/OHn9zX1cd3c15BnCu\nc+Isn7891wsxb8d1WCDgsR56PNXX194h1clZzquzxAkw1ubgLHE29pra7Pf4LRYLrNaW6ximdZNj\ncjc9ZvQ0YH9KEVYnZuOHS5z9m4jIVbV0nmmtBrfxwIw2RZALwIcncvDh8Wx7h0REDkoh5c7+9a9/\nYcyYMQgJCUF+fj4+++wz7Nq1Cz/99JOUh2mQCB8VOnm7wSKKWB6fif4BagR4KFs8DiIiko4j5ZnW\n6DavciwJC8SLe9Ow6qgRbnIBk7vp7R0WETkYSQuM9PR0TJo0CWlpadDpdOjduzd++ukn3HXXXVIe\npsHkMgFyCLi/kw6fnM6Fv0aBke084atWQC5j41EiImfjaHmmNYoN08JsFbFwXzr+fSgLVlHE1O4+\n9g6LiByIpAXGje1fHUl3X3d00rvhx0v5eOtwFu5ur0VMqKe9wyIiokZy1DzT2ozt6AWzRcT/HsjA\nysNGFJlFPNnbBwJ7fhMRJC4wHJlKLsP4cB2GhnpieXwGzmSXwioCw9p6oIuPu73DIyIicioPdNZB\npRCwcF861hzPRlG5FX/v58sig4haT4FRSe8ux7LBQQCAtEIzPjqRA4N7IXJLLXi4izfaernZOUIi\nIiLnMKaDF9QKGf61JxWfns5FkdmKF2/3ZzNkolauVc8UEeihxIu3+yPYU4nkfDNSCsy4mFtq80NE\nRES1G97WE2/FBEMlF/D1hTw8uzsVxWaO6kXUmrXqAqPSbf5qjOvkhXyzFZdMZbhkKsNPVwrw7O40\ne4dGRETk8O5o44H/DA+Gp1KGuORCPLb9GrKKy+0dFhHZSatrIlWTEK0SIVrbIWyzS3LRw6DC6kSj\nzfKSchGP9uSQfERERDeKDNBgfWwonv71Ok4ZS/HXrcl4Z2gwOulV9g6NiFoYC4xa/CXCG4iovnzv\n9UKsTsyGvkCB3lbbSdAFAAq2OyUiolaqg84NH8eGYu7OVBzPKsG0bdfw6uBA3NHGw96hEVELYoHR\nSHe28UAvX3f8Oy4N60/m2Kw7mVWCKd1tn254KGUI590bIiJqJXzUCnxwVxss2JeO7VcL8PSOFMzo\n5YPHe/qw8zdRKyFpH4xly5ahf//+0Ol08Pf3x9ixY3Hy5EkpD+EQvFRy3ONbisd6+tj8zOjlg5Jy\nq83P6kQjPjudU/9OiYioXq0lzzg7d4UMrw4OxMzeFRPwvX8sG0/vSEF2CftlELUGkhYYu3btwuzZ\ns7F//37s2LEDCoUCI0aMQE5O6/iC3dXgjoHBHjY/S+4IRKlFxOpEI945koVD6cX2DpOIyGm19jzj\nTGSCgCd6GfDu8GB4q+TYn1qEh39MRmIm8yCRq5O0idRPP/1k8/fHH38MnU6Hffv24Z577pHyUE5D\no5RhWo+KOzjZJeVYeyIH8WlF9b4uKc+MR3vq4eOugLtCgFrBAb+IiJhnnM/AYA9svCcUz+1JQ2Jm\nCR7ddg3Tuusxo5cBSjmbTBG5ombtg5GXlwer1Qq9nqMuAYCPuwJ/j/Rr0LYXc0sRn1Zxl+dYZgli\nO2ht1g9mhzkiIuYZJxHgocSakSFYdcSIDady8OGJHOy6XoglUYGI8GE/RSJX06wFxpw5c9C3b18M\nGjSoOQ/jkjp6q9DRu+Ki28O3xGbd5vMmnMwqqellVR7t4cM7Q0Tk8phnnIdSJmBuP18MCfXAwn3p\nOJ9ThklbkvBYLx9M786cReRKBFEUxfo3a7xnnnkGX3zxBfbu3Yv27dtXLTeZTFW/nz9/vjkO3er9\nblIitVSG+q7VvkororzNLRMUETWb8PDwqt91Op0dI2lZteUZgLnG0ZVagc0Z7ojLqbiRFuBmwYSA\nEvTwZCdwIkfU2DzTLAXGvHnz8MUXXyAuLg6dO3e2WXfjRd+ZE2FCQgIiIyPtHcYteX7LcbRrE1zr\n+vSickzvUX+zA6VMQKCHst7tmoMr/DvwPdifs8fvKtfVxqgrzwDOdU6c6fMndazxaUVYeiADV/Iq\nbnYNDfXAPyL9EOx56znFWc6rs8QJMNbm4CxxNvaaKnkTqTlz5mDTpk21XvTJcTzgX4rI3oZa1++5\nXojEzLqbYgFAXFIBRrTzrHFdN4M72nm5NTlGIqKbMc+4jv6BGnwxph0+O5OL948ZEZdciH0pRXi4\nizemdtfDSyW3d4hE1ASSFhhPPfUUPvnkE3zzzTfQ6XRIS0sDAGi1Wnh4sFOys2loR/IBgRoUl1ur\nLc8tteDtw1mNmmjQx12OhyK8G7w9EbUuzDOuRykXMKW7HrFhWrx1KAtbr+Rj7ckcbDpnwtTuekzs\n4g2NkiMpEjkTSQuM9957D4IgYPjw4TbLFy1ahAULFkh5KHIg/pqaP0btALwRo27UvtYcy8bqRGO9\n2xWXWzGvX8NG5CIi18E847r8NQosHRyIh7t64z9HsnAgrRj/OWrEZ2dyMaW7Hv8TrmOhQeQkJC0w\nrNbqd7GJGuPxXj4N2m7r5TysTjQiJVOFhAYUJABwIqsEs/rU3iSsMbRuMoRq2fSLqKUxz7i+Hr7u\nWH1XCA6mFuE/R404nlWCfx/KwkfHszGhizcmRHhD786mU0SOrFmHqSVqLrFhXgCABPPlOvuR3Ohs\ndinSCqUZNWvNsTwMCtZIsi91Ke/IERHdbECQBusD1dh7vQgfnchGYmYJPjiWjQ0nc3BfJy9M7OLN\nPn5EDooFBrUaET4qySZ06u2vhsV66wOwZRVb8OYZFa438CmMRQT6+btjYDDbmhOR6xMEAYNDPDA4\nxANHMoqx9kQ29lwvwudnTfjirAl3ttHg4S7euD1IA0HgPBpEjoIFBlETeEs0solBrcDjbYob/BSm\nyGzF20eycLQBo3vdzCoCU7tLO9uxAEDNNtFE1AL6+qvRd1gbnM8pxaenc7H1cj72XC/CnutFCNO5\n4S8ROtwTpoWnG5tPEdkbCwwiJ6JRyvCvAf5Neu1X50348pyp/g0bISG9CJO66nG2UA5ralGDXhPs\nqUSI1j7zphCR8wvXq7AoKgB/u82Ar8/n4fOzubhsKsOrBzOx8nAW7unghQc7O/bcJ0SujgUGUSsx\nPlz6hBsd4gFjiQVyAZDLGtY8Ycnv6bg9qHH9V/r6q9HXv3EjkhGRa/NxV+DRnj6Y3F2PnckF2HTW\nhPj0Ynx5ruJmSie1B6b55GFEO0+4yfmklaglscAgoiZrr3NDex0gJlvQL6BhBcDbw2qfPb4moggs\n3JeOA7U8IVHKBDzas2GjjxGR61HKBNzVTou72mlxMbcUX54z4YdL+bhQrMCLv6VjRUIW7utU8VRD\nihnCiah+LDCIqEWpmnAn8bXooFrXfX42t0FzpwAV/VAUMuDhLt5sp03kgjp6q/DcAH883dcXq3ce\nx8FSPc7mlGLdyRxsOJWD6DYemNjFG/0D1ewUTtSMJC0wdu/ejRUrVuDw4cNISUnB2rVrMWXKFCkP\nQURk4y+NmPndKor45kIeXv49A3e311Ytv5ingCmpoOrvAYFqaFmAOCTmGWoIjVKGaL0Z8/qF4lhW\nCTadNWHb1XzsvFaIndcK0VHnhgldvDGmgxbuCjafIpKapP9XFRYWolevXli5ciXUat4dICLHIhME\njA/X4bHT2KtVAAAgAElEQVSePgjVKqt+/N2sVb+nFpjxnyNGrE40YtWRLJRZOLGbI2GeocYQBAG9\n/dR45c5A/DQ+DE/29oGvWo6LpjL874EMjP7qCj44ZkRuqcXeoRK5FEmfYMTGxiI2NhYAMHXqVCl3\nTUQkmc562/lQPi9QIu2GJxiVswRnFltgufXpTkhCzDPUVAa1AjN6GTCtuw9+SSrAx6dycDq7FO8l\nZmPtiRyM6+SFKd31CPRgPw2iW8U+GETksvLLLMgoKq93u/PFckwJ06ItZwUmcnlKuYDYMC1GtfdE\nQnox1p3Mwb6UImw8a8Lm83m4v5MXpvfQI4CFBlGTscAgIpe1+1ohvjqfB7WiejOaYW09oXWraCUa\npSuDQc3LIVFrIggC+gdq0D9Qg3M5pfjoeDa2Xy3AF+dM+PpCHsaHe2F6Dx/4a3htIGosQRTFZmkA\noNVqsWrVKkyePNlmucn050Rf58+fb45DExEBAK6XyLDFqMLN9UVuuYBJgcXwc3ON9k/h4eFVv+t0\nrWeCsdryDMBcQ01zvVSGH7NUSMhTQoQAN0HEXT6lGGUohTvHfaBWrLF5xq5leWRkpD0Pf0sSEhKc\nOn6A78FR8D00jiiKVf0i9l4vxJGMYqhrGQWmWLDib3dq0d3gXuc+nf3f4MYv01Sdo//bOtPnz9Vj\njQRwH4CLuRV9M35NKsCPRnfsL/TAE718MD5cB0UDJxVtzjjthbFKz1nibGye4XM/InIqhzKKsfJQ\nFnSqituJf4nwhtZNBn+NgpNoEZEkOnqrsGJIEI5mFOPfh7NwLLMEyw5mYuNZE54f4If+gRp7h0jk\n0CQtMAoLC6seRVutVly9ehVHjx6FwWBAaGiolIciIhd0MqsERzOL69zGVGqtKi6Aion2AKCLjwqz\n+/o2a3xkf8wz1JL6+Kux7u4Q/JpUgLePGHHZVIYZ269jVHtPPNPPD37sn0FUI0n/z4iPj8ewYcMA\nVHSeWrhwIRYuXIipU6fiv//9r5SHIiIXsvJwFlRyAZdMZXiuvx/c5I1vgqCUuNkCOSbmGWppgiBg\nRDstokM8sOFULj48no2frhRgz/UiPNnbBxMivCHn9YfIhqQFRkxMDKxWTkpFRHWrnFE7Kc8Md4WA\njt5uGNPBy95hkRNgniF7cZPL8FhPH4wO02J5fCZ2XSvEioQs/HQ5H4uiAtDRW1X/TohaCT7bIyLJ\nmEotOJ5VUu92+WVW7E8pwuKoAGiUNXfQJiJyRMGeSrw1NBi7rxVg6YFMnDCWYuKPyXiilw8md9fz\naSoRWGAQkYQumcrwXqIR3qq6x3MM8VTiXwP8WFwQkdOKDvFEX3813jqUha8u5OE/R434NakAL0cF\noJOeTzOodWOBQUSSsFhFfH8xD4PbeNS/rQhObEdETk/rJsdLgwJwV3stluxPx+nsUjyyJRlzbjNg\nQhdvyAQ+zaDWiRmeiBolo6gcSXll+PK8Ce293AAAKZkqxB/PxvC2nrijAQUGEZErGRikwaZ72+GN\nhEx8dSEPrydk4beUIiwaFMCRpqhV4qeeiBrl1YMZKLOImN7DB7cFqAEACebLiOxtsHNkRET2o1HK\n8NKgANzRxgNLfk/HvpQiPPTDVSwcFICYUE97h0fUotgAmoga5dn+fvifzjrsSC6wdyhERA5nWFtP\nfD6mHQYFaZBbasW8nalYkZAJs0W0d2hELYZPMIioXh8dz4bZapscA/nYn4ioRv4aBf4zPBifnM7F\nO4ez8OnpXCRmFOO16CAEeyrtHR5Rs5P8Cca7776LsLAwqNVqREZGYu/evVIfgohamEYpw+nsUpzI\nKoFGKcPM3gZM6qa3d1jUijHXkKOTCQImd9Pjo7tDEOihwAljKSb8mIQ4Pv2lVkDSAuPzzz/H3Llz\nMX/+fBw9ehRRUVGIjY1FcnKylIchohYQl1yATedyselcLk5mlSAmxAP/01mHmBB24ib7Yq4hZ9LL\nT42N97RFdIgH8suseGZnKlYezkK5lU2myHVJWmC8+eabmDZtGh599FFERETg7bffRlBQEN577z0p\nD0NEzWxncgH2pRRhaKgnhoZ6Ym4/X4zt6IWYUE+0/WPkKCJ7Ya4hZ6NTyfFWTBDm3eYLuQCsO5mD\np369juzicnuHRtQsJCswysrKcPjwYYwcOdJm+ciRI7Fv3z6pDkNEEjJbRBSbrdV+8sqsUCsEvJmQ\nBV+1Ar5qBeScnZYcAHMNOStBEDC5ux6r72oDH3c5DqYVY+KWZFwsrntiUiJnJFkvzaysLFgsFgQE\nBNgs9/f3R1pamlSHISKJXMgpxbqTOQivZcZZg7sCbdgZkRxMk3KNg092FmnvABqBsd66SAC/3vD3\n3t5DsOmLb/A/4ToIDv5ZJWoouw4Dk5CQYM/D3zJnjx/ge3AULfEeLhbJca7oz//lLxTLcbehFJ2L\nLXW+rqGhOfu/gzPHHx4ebu8QiKiJ7kzchb4HMrH7zHU8HFgMpYNPIOBM10pnidUZ4mxsnpGswPD1\n9YVcLkd6errN8vT0dAQFBdX4mshIR72/UL+EhASnjh/ge3AULfUeks+b4JlXBtkfd8j6AciTC0gA\nEOypxNiOXk3et7P/Ozh7/CaTyd4htJim5BqIjt2Z1pk+f4xVYn9cj1VyAXtNbshVaLFiSBACPBzz\n6bFTnNM/OEuszhJnY/OMZHWym5sb+vXrh59//tlm+fbt2xEVFSXVYYiogSxWERlF5VU/d7TxwCNd\n9ZjYxRsTu3hjQhdvlP4x8ZNKzsfy5ByYa8gVrb07BEF/DGX78JZkHE4vtndIRLdE0iZSzzzzDP76\n179iwIABiIqKwurVq5GWloaZM2dKeRgiagBTmQUzf7mOIA/b/80FAENDPQEAHb3dMKZD059cENkD\ncw25mq4Gd3w6ui3+tScVB9OK8cT2a/hHfz881Jn9Msg5SVpgPPTQQzAajXjllVeQmpqKnj17YsuW\nLQgNDZXyMETUAF5uciy7MxAAUGC2YsOpHMgF4FqBGQ901tk5OqKmY64hV6R3l2PV8DZ4+0gWPj6V\ni1cPZuKUsQQv3O4PldzBO2YQ3UTyTt5PPvkknnzySal3S0SNpJAJiPCpGCEqu6QcBnc5/DUKdNar\nsDrRiFKLiP6BakQFc+I8cj7MNeSKFDIBz/TzQ1cfd7y8Px3fXczHhdwyrBgShCAH7ZdBVBO7jiJF\nRC3Dx12BBYMqhvUsKLMgvagcmUXlyKhnBCkiImp5sWFadNC54ZmdKThlLMUjPybj1cGBGBCksXdo\nRA3CAoPIhX13Ma/aslPGEgR7KBHooUA/f7UdoiIiovpE+Kjw6T1t8fyeNPyeWoQnf72Ov/X1xeRu\n3uyXQQ6PBQaRC/vmggnBnkrM6m2oWhYZoIafWgElR44iInJo3io5/jMsGO8lGvHRiRy8dTgLJ7JK\nsCgqAB6OPmEGtWr8dBK5sI9GhqCvnxqbzlUUGpU/LC6IiJyDXCZgdl9fvBkTBE+lDL8kFeCvW5Jw\nMbfU3qER1YoFBpGLyigqx7cX83A4oxhhOjd7h0NERLdgaKgnPhkdio46N1zOM2PSlmT8cKl6M1gi\nR8AmUkQu6vuLeTiUXoxuBhUKyiz47HSOzfoxHbzgpZLbKToiImqsdl5u+Dg2FP97MAM/XsrHS7+l\n40h6MZ7t7wd3Be8Zk+NggUHkoh7p6o0Ha5nvYn9qET44ng3PGtrwBnsqMbYjJ98jInJEaqUMS6IC\ncJu/GsvjM/HVhTycMJbgtcFBaM+n1eQgJC13P/jgAwwdOhTe3t6QyWRISkqScvdE1AjuChm8VHJ4\nqeQ4klGMNw9l4b1EI95LNOJoRjEsVhGmUku1n3KraO/QiWrFPEMECIKA8eE6rB8VirZaJc7llGHi\nj0n46rwJoshrONmfpAVGcXExRo0ahcWLF0u5WyK6Re283NBZr0Ko1q3Gn+R8M5LyzTibUwq1gh3A\nyXExzxD9KcJHhU9Hh+KeDlqUWEQs+T0D/9idClMp5zgi+5K0idScOXMAAAkJCVLulohuUXudW52P\nzjedy0UbTyVCtUoMDOLM3uS4mGeIbHm6yfHKHYGICtJg6cFM7EgqxImsJLwcFYDbOTEf2Ql7BBER\nvhrbDu8MC0awpxKfn83FysNZSEgrsndYRETUQKM7eOHze9qil587MorKMfOX6/jfAxkoNFvtHRq1\nQuzkTUR4LT4TBTckIYtVhLHEgmv55qplbTwVnD2WiMiBtdEq8dHIEKw9kYMPjhvx5TkTfrteiEWD\nAjCATzOoBQliPb2B5s+fj6VLl9a5k507dyI6Orrq74SEBAwYMABXrlxB27ZtbbY1mUxVv58/f74p\nMRORxM4UypFtlsFULsO5oupD12aYZXi5QwE4P59jCg8Pr/pdp6t55DBHJnWeAZhryDlE9u8PAEiI\nj5d839dKZFibokFSacU1Pdq7FOP9S+DB0cmpCRqbZ+otMIxGI4xGY507CQ0NhVqtrvq7oQWGMybC\nSgkJCYiMjLR3GLeE78ExONJ72JdSiE9P59Y4fG17nRusInB3O0900qts1jnSe2gKZ4/f2a+rUucZ\nwLnOiTN9/hirxCqfCjfTyE9mq4i1J7Kx5ng2yq2AXiXHvH6+GNNB26Qn0k5xTv/gLLE6S5yNvabW\n20TKYDDAYDDcWlRE5BSigj0QFVx7J++kvDJ8diYX3io5Si0i+vq7IzrEswUjJFfEPEPUPJQyATN6\nGTC8rSf+90AGjmSUYMG+dHx9wYQXBvhXu1lEJBVJO3mnpaXh6NGjOHfuHADg5MmTOHr0KHJycup5\nJRE5gxf3piGtsBxX88rgJhfgq2Y3LmpZzDNEjdfRW4WPRobg5agA6FVyHMkowYQfk7D0QAaMxeX2\nDo9ckKQFxurVq3Hbbbdh0qRJEAQB99xzD/r164fvv/9eysMQkZ3M6G3AfZ28UGYV4adW4JSxFF+e\nM2FXjhu+PGfCl+dMSC80178joiZiniFqGkEQcG9HL3xzXzs82FkHEcCmcyaM/eYKPjhmRDFHmyIJ\nSXr7cdGiRVi0aJGUuyQiBzK4TUXzqb7+apgtf7YZTjSa0TvEA2dzSvH+sWz4axSwisCsPmz2QtJi\nniG6NV4qOV643R9/idDh7cNG7L5eiPcSs7HpnAmP9vDB/eFeUMk5iwHdGrZvIKJG81bZDkPirRTh\np1HAT6PAnX8UIV+fN2F1ohGmUguiQzzQx19d064gAHBXMJkREbWkjt4qrBwWjIS0Irx5KAuns0vx\nWnwmPjqRjand9RgfroOa12ZqIhYYRNQs7g+vGGUis6gcP17Ow9mc0hq3O5xejL9201f93Vmvgk7F\ncRSJiFpCZKAGn4wORVxyIdYcy8bZnFKsSMjCf0/k4OEu3nigs67aTSWi+rDAIKJm5adRYGp3n1rX\nR4eUIbukopPhxdwy/HgpH9N76NHWy62lQiQiatVkgoDhbT0xLNQDu68VYs3xbJw0luI/R4348Hg2\n7umgxcQu3vYOk5wICwwisqvcEgv2XS+Cm1yARQQUMiCjqJwFBhFRCxMEAUNCPREd4oEDqUX45HQu\nfkspwubzedh8Pg9dPTSY5pePmBBPKDnzKtWBBQYR2ZVCBlzJK8Psvr7ooGNRQURkb4IgYGCwBwYG\ne+CyqQz/dyYX31/Mw+lCJf65Ow3eKjnu7ajF+E46tOd1m2rAAoOIWlRJuRX7U4pslnX1ccc/d6Xi\ny7Ht7BQVERHVJEznhhdu98fsPga8t+skDpXqcD63DB+fysXHp3LR09cdYzpoMbK9ln01qAoLDCJq\nNu8nGiHetKzAbIVWKUNM6J8zgAd7KjEktPYZxImIyL68VHIM9ynDP/u1xYmsUnx1wYSfr+TjeFYJ\njmeV4PWETNwZ7IHRHbQY3MaDowO2cpIVGDk5OViwYAF++eUXXL16Fb6+vhgzZgxeeeUV+PjU3sGT\niJzL0Yxi7EgugOaG5JGSqUJCorHatr5qBf6ns64lwyMXxjxDZH+CIKCnnzt6+rnjn5F+2HmtAD9c\nysfvqUXYea0QO68VwkMpw7BQD8SGadE/UAOFjP01WhvJCoyUlBSkpKTg9ddfR7du3XDt2jXMmjUL\nEydOxLZt26Q6DFGrYxVFXMmTZnbsuKQCmMosNsVBY5VbRUzqqoe/5s/LR4L5MiJ7c1I9al7MM0SO\nRa2UITbMC7FhXsgsKse2K/nYeiUfp4yl+P5SPr6/lA+Duxx3t9didJgW3QwqCAKLjdZAsgKje/fu\n2Lx5c9XfHTp0wOuvv44xY8agoKAAnp6edbyayPWdzS6tcS6IK7lKpFzMq/V1ZouIQ+nFkjQhCtEq\n8UiINx9dk1NiniFyXH4aBSZ102NSNz2u5pXhp8v52HI5H0n5Znx2JhefnclFOy8lRodpcW9HLwR5\nKO0dMjWjZu2DYTKZoFKpoNFomvMwRJL66rwJGUXlku/3lLEE/4j0g/ymuzfK9HL0qmWW60oj23tC\n68bOc0Q3Y54hcjztvNzwRG8DZvTywSljKbZczsdPV/JxNc+M9xKzsToxGwODNLivkxdiQj2gkvOm\nl6tptgIjNzcXL730EmbMmAGZjB8cqk4UxWodgBvLKlY0IQKANw9lwVN56581EcCTLdjcJ9VNRBst\n7+QQNRbzDJFjEwQB3X3d0d3XHfP6+eJgWhG+u5iHuKRC7E8twv7UIni5yXBfJy/8pbM3c6ELEURR\nrPM73vz587F06dI6d7Jz505ER0dX/V1QUIDY2FgolUr89NNPcHP7c4xkk8lU9fv58+ebGjc5uKQS\nGcxi3e0sE/KUUAgi3CRqjhngZsUAnTR9FYicSXh4eNXvOp3zdaqXOs8AzDXkHCL79wcAJMTH2zmS\nllVoAQ6a3PCbSYmrJRX3ugWI6OVZjmH6MnT1KAe7ajiWxuaZegsMo9EIo7H66DA3Cg0NhVpd0cSj\noKAAo0ePhiAI2Lp1a7XH1jde9J0xEVZKSEhAZGSkvcO4JTW9h5wSC7Zerr0/QEMdzSzBfR296t1u\nQKDmlmYDddV/B2fj7O/B2eN39uuq1HkGcK5z4kyfP8Yqscpv0XV/FXMYzXFOTxpLsPFMLrZdKYDZ\nWnEeOuvd8HhPHwxr6wlZEysNp/j3h/PE2dhrar1NpAwGAwyGhjUXyc/PR2xsbJ0XfWp+p4wl2H61\nAKp6vrjXNLRofpkVff3dMSDw1v7txnXSQSNBcyUicn3MM0StV3eDO5bcEYh5t5Vj8/k8fHEuF+dy\nyvDs7jR01Lnh8V4+GNHWE3IOdetUJOuDkZ+fj5EjRyI/Px/ffPMN8vPzkZ+fD6AieSiVbFfXFPll\nFlhrubHx8v50hOtV1ZYXlVsxIcIbwZ51n3MOLUpEzoR5hsh1+agVeLyXDyZ398Y3F/Kw9kQOLprK\n8K89FYXG3yN9MSiYE7I6C8kKjEOHDuHAgQMQBAGdO3euWi4IAuLi4mzazlLtyq0iDqQWVf29+bwJ\nkQE136Gb0l2PXn51jz5EROQqmGeIXJ9KLsNfIrxxfycvfH8xHx+dyMZFUxlm/ZqCwW00eKafH9rr\n3OrfEdmVZAVGTEwMrFarVLtzKR8dz0Z5A9tXmi0iCs1WxIZpAQCz+/qiA/9HIiJiniFqRdzkMjzQ\nWYcxHbX4vzO5+PB4DvZcL8L+lKv4S4Q3ZvUxsCm2A2vWeTBaqxXxmfB0+/ND762S46GIhncyFADO\ndElEREStnkouw9TuPri3gxfePWrE1xfy8OmZXMQlF2DBoADcHsR+WI6IBUYdsorLUVpe85OHzDIB\n1/MrhkQttYpYeTgLXX0q+kP08nPHyPbaFouTiIiIyJUZ1Aq8NCgAD0bo8PL+DJzOLsXMX67jgXAv\nzL3NF56cjNahsMCow/L4TEToVfDTVD9NV4oUMGcUV/39dB8DOtXQ4ZqIiIiIpNHFxx3rY0Ox/mQO\n3j9mxObzefjtehFeuTMQ/QLYL9VRsMC4QZnFivePZUP5x1BoVhHorFdhcEj1UQsScsyIbMA8D0RE\nREQkHaVMwGM9fRAT4oGF+9NxyliKJ7Zfw+y+Bkzupm/y3BkkHRYYAFb/MReERQQi9Co2byIiIiJy\ncJ30KqwfFYp3jxqx9mQOVh424khGCZZEBdg7tFavVRUYxeVWfHo6F9klFnjd0AnbT63AA50de6ZX\nIiIiIrKlkAn4222+6OPvjvm/pWP3tUJM/DEJ0/1kcPz5sV1XqykwjMXl+OxMLgRU9JdQc2gzIiIi\nIpcQHeKJ/xutwrO7U3E6uxTLizxhaF+AmFBPe4fWKkn6Lfvxxx9Hp06doNFo4O/vj3HjxuH06dNS\nHqLBkvLKsPJwFlYnGit+jmWjm8Edj/fyYXFBROSkHCnPEJFjaaNVYt2oENzbQYsyUcAzO1Pxf2dy\n7R1WqyTpN+3+/ftj/fr1OHPmDLZt2wZRFDFixAiUl5dLeZhaiaKIknIrSsqt+O+JHIxqr8XM3gbM\n7G3Ai7f7Y3hbT6jkLC6IiJyVvfMMETk2N7kMi6MCcJ9vCURUjAi6Ij4TFmvDJjwmaUjaRGrGjBlV\nv7dt2xZLlixBnz59cPnyZYSHh0t5KBvJ+WVILyyHVQT+eyIbtwdpMDjEAxE+HDaWiMiV2CvPEJHz\nEAQBY/xKERnRDov3p+PTM7lILTRj2eBAuPFGc4totj4YhYWFWLt2LcLDwxEWFtYsx0jKK8OO5AIc\nTC3G9B56yARgwaAABHsqm+V4RETkOFoizxCR8xrTwQsBGgX+visVO5ILMW9nKt4YEgR3BYuM5ib5\nGX733Xeh1Wqh1Wrxww8/4Mcff4RC0Tx1THpROUrKRbwRE4TIQA0iAzUsLoiIXFxL5hkicm79AzVY\nc1cIvFVy7Espwpy4FBSbrfYOy+UJoijW2Sht/vz5WLp0aZ072blzJ6KjowEAeXl5yMzMREpKClas\nWIFTp07h8OHD0Gor5pYwmUxVrzt//nyTAy8XgY1p7ghTW3CHt7nJ+yEicnY3Ng3S6ZxvyG2p8wwg\nXa4hak6R/fsDABLi4+0cieu7XirDm1c9kGeRIVxdjr+FFsJdbu+onEdj80y9BYbRaITRaKxzJ6Gh\noVCrq0/PbjabodfrsWrVKkyZMgWA7UW/sYnwpLEEGUUVHfkum8oAANN7+DRqH1JJSEhAZKRzj7DM\n9+AY+B7sz9njv5XrqiOQOs8AznVOnOnzx1glVjnjdN1fxRyGU5zTP9QU69W8MszYfh0ZReXo6euO\nVcODoXWzb5XhLOe0sdfUep8pGwwGGAyGJgVjtVohiiKsVmkeRX193oRyKzChiw5BHgqEsDkUEZHT\nc6Q8Q0Suq52XGz4aGYIZ26/heFYJ5sSlYNXwNlCzT4bkJDujFy9exGuvvYbDhw8jKSkJ+/btw4MP\nPgh3d3eMGTPmlve/4WQOfNUKeKlk6OLjji4+7vC0c9VJREQtp7nzDBG5vhCtEmvuCoG/RoEjGSV4\ndlcqzBbneILkTCQrMFQqFXbt2oXY2FiEh4djwoQJ0Ol02L9/P/z8/Jq836t5ZbhsKsOh9GLM7G3A\nM/2avi8iInJezZVniKh1aaNV4r0RbeCtkuG3lCLM/y2N82RITLJhN0JCQrBlyxapdlfl+T1p6O7r\njhm97dPXgoiIHENz5Rkian066NywangbPLH9On6+WgAPZQZeGugPobJfDN0Sh290NihYA5VMQHeD\nu71DISIiIiIX0c3gjpVDg6GSC/j6Qh7eOVL3YBPUcA5bYIiiiHeOZMFNLuAf/fnom4iIiIikdVuA\nGiuGBEEuAGtP5uDLc6b6X0T1csgCw1hcjsX7M9DOyw1P9GrayCJERERERPW5s40HXrzdHwCw7GAG\n9lwvtHNEzs8hC4wdyQVIKzTDy80hwyMiIiIiF3J/uA6P9dDDKgLP7U7FaWOJvUNyag75DX5sRy9E\nBXvgcEaxvUMhIiIiolZgVh8DRodpUVwu4m9xKUgtNNs7JKflcAWG2SrivydykG+2ckhaIiIiImoR\ngiBg4SB/RAaokVVswd92pKDQzEk8m8LhCowDqUVIzCjGyHae9g6FiIiIiFoRN7kMbwwJQnsvJS7k\nlmH+3jRYRc6R0ViSFxiiKCI2NhYymQybN29u9OvlAqCQCfj8bK7UoRERkQu41TxDRFQXL5Ucbw0N\nhtZNhp3XCvHuUQ5f21iSFxhvvPEG5HI5ADRpshJTqRXRIR544Y/e/ERERDe61TxDRFSfdl5uWD44\nEHIB+OhEDrZezrd3SE5F0gIjPj4eb7/9NtauXduk15tKLdielA+DWgEZkwYREd3kVvMMEVFDDQz2\nwN8jK/oDL96fjpNZHFmqoSQrMPLz8/Hwww9jzZo18PNrWufsa/lm3B6owfC27H9BRES2pMgzRESN\nMSFCh/GdvFBqETFvZwoyi8rtHZJTEERRmp4rjzzyCHx9fbFy5UoAgEwmw5dffonx48fbbGcycYZE\nIqLmotPp7B1Cs2longGYa4iImktD8oyirpXz58/H0qVL69xBXFwckpKScOzYMSQkJACo6IB343+J\niIhqwjxDROR66nyCYTQaYTTW3XM+NDQUs2bNwoYNGyCT/dniymKxQCaTISoqCrt3765azrtKRETN\nx9meYDRHngGYa4iImktD8owkTaRSUlKQm/vnsLKiKKJnz57497//jfvuuw/t27e/1UMQEVErxjxD\nROQ86mwi1VDBwcEIDg6utjw0NJQXfSIiumXMM0REzsPhZvImIiIiIiLnJdkoUkRERERERHyCQURE\nLk8URcTGxkImk2Hz5s32DqdGjz/+ODp16gSNRgN/f3+MGzcOp0+ftndY1eTk5ODpp59G165dodFo\n0LZtW8yaNQvZ2dn2Dq1GH3zwAYYOHQpvb2/IZDIkJSXZO6Qq7777LsLCwqBWqxEZGYm9e/faO6Rq\ndu/ejbFjxyIkJAQymQzr16+3d0i1WrZsGfr37w+dTgd/f3+MHTsWJ0+etHdY1axatQq9e/eGTqeD\nTjnQvX4AACAASURBVKdDVFQUtmzZYu+w6rVs2TLIZDI8/fTT9W7LAoOIiFzeG2+8AblcDgAQBMHO\n0dSsf//+WL9+Pc6cOYNt27ZBFEWMGDEC5eWONbFXSkoKUlJS8Prrr+PEiRP45JNPsHv3bkycONHe\nodWouLgYo0aNwuLFi+0dio3PP/8cc+fOxfz583H06FFERUUhNjYWycnJ9g7NRmFhIXr16oWVK1dC\nrVY77P8/ALBr1y7Mnj0b+/fvx44dO6BQKDBixAjk5OTYOzQboaGhWL58OY4cOYJDhw5h2LBhGDdu\nHBITE+0dWq1+//13rFmzBr169WrYZ0AkIiJyYQcPHhRDQ0PFjIwMURAEcfPmzfYOqUESExNFQRDE\nc+fO2TuUem3ZskWUyWRifn6+vUOpVXx8vCgIgnj16lV7hyKKoigOGDBAnDFjhs2y8PBw8fnnn7dT\nRPXz9PQU169fb+8wGqygoECUy+XiDz/8YO9Q6uXj4yN+8MEH9g6jRrm5uWLHjh3FnTt3ijExMeLT\nTz9d72v4BIOIiFxWfn4+Hn74YaxZswZ+fn72DqfBCgsLsXbtWoSHhyMsLMze4dTLZDJBpVJBo9HY\nOxSnUFZWhsOHD2PkyJE2y0eOHIl9+/bZKSrXk5eXB6vVCr1eb+9QamWxWLBx40aUlJQgOjra3uHU\naMaMGXjwwQcxZMiQBk9uKskwtURERI5o5syZGD16NO6++257h9Ig7777Lp577jkUFhaiY8eO2Lp1\nKxQKx07Vubm5eOmllzBjxgybiRCpdllZWbBYLAgICLBZ7u/vj7S0NDtF5XrmzJmDvn37YtCgQfYO\npZrjx49j0KBBKC0thVqtxhdffIGIiAh7h1XNmjVrcOnSJXz22WcAGt7ElFcCIiJyKvPnz4dMJqvz\nZ9euXfj4449x7NgxLF++HACq7rw19A5cS8V64yzkkyZNwtGjR7Fr1y5069YNsbGxyM/Pd8hYAaCg\noAD33ntvVZvyltKUWKl1eeaZZ7Bv3z5s3rzZIfuNdOnSBceOHcPBgwcxe/ZsTJgwAQkJCfYOy8bZ\ns2fx4osv4tNPP63qwyaKYoOuoRymloiInIrRaITRaKxzm9DQUMyaNQsbNmywuatusVggk8kQFRXV\nIl9AGxqrWq2uttxsNkOv12PVqlWYMmVKc4VYpbGxFhQUYPTo0RAEAVu3bm3R5lFNOa8JCQkYMGAA\nrly5grZt2zZ3iHUqKyuDh4cHNm7ciAceeKBq+VNPPYVTp04hLi7OjtH9f3v3Hh1lfeB//PPMZDKZ\n3CZhSMIlAQQSBKpIiVFRK3SFFhdR62ptpS34W/1xvBRr159WbS3nt6zWVrec34F1627Vaq21uEdd\nVwRbQ/ACalAQUSGiQLgEyH1yn8vz+4OSEhOSAE/ynZm8X+dwnDw+Ax8mF57PfC/PiWVkZGjlypX6\n/ve/bzpKr370ox/pueeeU2lpqYqKikzH6Zc5c+YoPz9fjz/+uOkonZ544gndcMMNneVCOvoz1LIs\nud1uNTc3y+Px9Pjc2B53BQDgSwKBgAKBQJ/nLV++XHfeeWfnx7Zt66yzztLDDz+sK664YiAjdupv\n1p5Eo1HZtq1oNOpwqp6dTNZgMKh58+YZKRfS6b2usSA5OVkzZszQunXruhSM1157Tddcc43BZPFv\n6dKl+tOf/hRX5UI6euE+WN/r/XXVVVeppKSk82PbtrV48WIVFRXpnnvuOWG5kCgYAIAENWrUKI0a\nNarb8YKCAo0bN27wA/Vi165dWr16tebMmaPhw4dr3759evDBB5WSkqL58+ebjtdFMBjU3LlzFQwG\n9cILLygYDHZO4woEAr1edJhQVVWlqqoq7dy5U5K0fft21dbWauzYsUYX/95xxx363ve+p5KSEs2c\nOVOPPvqoqqqqtGTJEmOZetLc3KyKigpJR0vvnj17tGXLFgUCARUUFBhO19Utt9yip59+Wi+88IL8\nfn/nepaMjAylpaUZTvc3d999t+bPn6/8/HwFg0E988wzKisr06uvvmo6WhfH7tNxvNTUVGVnZ2vK\nlCm9P3nA9rQCACDGxOo2tZWVlfa8efPs3NxcOzk52S4oKLAXLlxo79ixw3S0bkpLS23LsmyXy2Vb\nltX5y+Vy2WVlZabjdXP//fd3yXjsv7Gw3eqqVavscePG2V6v1y4uLrbfeOMN05G6Ofb5/vLnfPHi\nxaajddPT16VlWfayZctMR+ti0aJF9tixY22v12vn5ubac+bMsdetW2c6Vr/0d5ta1mAAAAAAcAy7\nSAEAAABwDAUDAAAAgGMoGAAAAAAcQ8EAAAAA4BgKBgAAAADHUDAAAAAAOIaCAQAAAMAxFAwAAAAA\njqFgAAAAAHAMBQMAAACAYygYAAAAABxDwQAAAADgGAoGAAAAAMdQMAAAAAA4hoIBAAAAwDEUDAAA\nAACOoWAAAAAAcAwFAwAAAIBjKBgAAAAAHEPBAAAAAOAYCgYAAAAAx1AwAAAAADiGggEAAADAMRQM\nAAAAAI6hYAAAAABwDAUDAAAAgGMoGAAAAAAcQ8EAAAAA4BgKBgAAAADHUDAAAAAAOIaCAQAAAMAx\nFAwAAAAAjqFgAAAAAHAMBQMAAACAYygYAAAAABxDwQAAADiB3bt3y+VyafHixaajAHGDggEAANAH\ny7JMR+jTsTI0e/Zs01EwxCWZDgAAABCr8vPz9emnn8rv95uO0qdjJSgeyhASGwUDAADgBJKSklRU\nVGQ6Rr/Ytm06AiCJKVIAAAAn1NMajEWLFsnlcqmsrEyrV69WSUmJ0tLSFAgE9J3vfEcHDhzo9vvM\nmjVLLpdLX3zxhX71q19p0qRJ8vl8GjNmjP7pn/5JTU1N3Z7T23Snn//853K5XNqwYYMk6YknntD4\n8eMlSevXr5fL5er8tWzZMideCqDfGMEAAADoQ0/TjlatWqWXXnpJV1xxhWbPnq1Nmzbpj3/8o7Zu\n3aotW7YoOTm523OWLl2qt956S9/+9rfl9/v1yiuv6JFHHtGbb76pDRs2dHtOf6c7TZ8+XUuXLtWK\nFSs0btw4LVq0qPP/zZo166T+rsDpomAAAACcgrVr16q8vFxTp07tPHb99dfrD3/4g1588UVdc801\n3Z6zadMmbd26Vfn5+ZKk5cuX6+qrr9aLL76oRx55RHffffcpZZk2bZpuv/32zoLxs5/97NT+UoAD\nmCIFAABwCn74wx92KReSdOONN0qS3nvvvR6fs3Tp0s5yIR2dBvWLX/xClmXpt7/97WnlYQ0GYgUF\nAwAA4BQUFxd3O3asPNTV1fX4nEsuuaTbsaKiIuXm5mrXrl1qbm52NiRgAAUDAADgFGRlZXU7lpR0\ndPZ5JBLp8Tl5eXm9Hm9sbHQoHWAOBQMAAGCQHDp0qNfjmZmZXY6Hw+Eez6+vr3c2GOAgCgYAAMAg\nWb9+fbdjO3bs0KFDhzRx4kSlpaV1Hs/OzlZlZWWPv09PazzcbrekE4+eAIOFggEAADBIVqxY0aU0\nRCIR3XXXXZLU5V4bknT++edrz549WrNmTZfjjz32mDZu3NhtC9vs7GxJOmEpAQYL29QCAAAMkgsv\nvFDnnHOOrr32WmVmZmrNmjX66KOPVFJSoh//+Mddzr3zzju1du1aXXXVVbr22muVk5OjzZs3a/Pm\nzZo/f75efvnlLuenp6dr5syZevvtt7VgwQJNnz5dHo9Hl1xyiS6++OLB/GtiiGMEAwAA4CRYltXv\nG+B9+Xm//vWv9ZOf/ESlpaVasWKF6uvrdccdd+gvf/mLPB5Pl/NnzZqll156Seecc45Wr16txx9/\nXFlZWXrnnXc0Y8aMHjM89dRTuvLKK7Vx40YtX75c999/v0pLS0/57wqcCstm02QAAIABNWvWLG3Y\nsEG7d+/WmDFjTMcBBhQjGAAAAIPgVEY9gHhEwQAAABgETBrBUMEibwBAwmloaDAdAegiEonIsiw1\nNjby9Ym45vf7+zyHNRgAgITDBRwADIz+FAymSAEAAABwDFOkAAAJrT/vtplUXl6u4uJi0zH6hazO\ni5ecElkHQrzkPNlRYUYwAAAAADiGggEAAADAMRQMAAAAAI6hYAAAAABwDAUDAAAAgGMoGAAAAAAc\nQ8EAAAAA4BgKBgAAAADHUDAAAAAAOIaCAQAAAMAxFAwAAADDalrD2l7dptrWsOkowGmjYAAAAAwC\n27Z1oCmkIy3dS8Rre5q0rbpNpZXNBpIBzkoyHQAAAGAoCEVtPbz5iDI8bt109jB9XNOm9o6/vdf7\n1Tyfth1pM5gQcAYjGAAAAANsfWWTVrxfowXjM+X3uvTirkZJ0ram7u/1/vztQ7r1L/vVGoqqPRJV\nKGIPdlzgtDCCAQAAMIAeLj8ij8vSDV/JVsCXpOwUt2rbIpoSSNETm5P04mcNXc4fkZakcX6PKptC\n+s9ttfJ73brnvFxD6YGTR8EAAAAYIM/tqFdtW0TLLxrReezsHF/n49vHtGh9XYeko1Okjre7oUNf\ny09TZTA0OGEBhzBFCgAAYIDsbwrpznNzej1n3vgMXTQ6Vemev12WzS5Il8dlaUaeT9kpbt20bt9A\nRwUcwwgGAACAwzbsa9Ib+1s0uyBNWV53r+dODaRIkg4ft7vU2Mxkjc1MliR9e1KW6toiAxcWcJhl\n2zYrhwAACaWh4W9z2isqKgwmwVD0abNb5Y0efS27Q2NSov1+XmtEWlvjVW5yVDOzuk6LeumIV5cP\nb9exizaX5WBgoA+FhYWdj/1+f5/nM4IBAEhoxcXFpiP0qry8POYzHkPWvm0+1Kpdnzfq3r8LKCvF\nLU8fTeDLOS8+0Xlba+Qfk67fflSrLK9bd587+Iu++fw7L15yHv+mTX+wBgMAAMAh/72rUd+a6FdO\nalKf5eJUzBmb0TnlqjUc1a769i5Tq4BYwAgGAADAafj15mqlJB0tE5eOTddZOSmO/xn5GR79z+eN\nmlWQrurWsH73cZ32NHQoK8WtqC0t/epwx/9M4FRRMAAAAE5DSpKlJdMCA/pnzB+f2fk42W0pFLG1\ncHKWLEn//mGtgh0RtYVt+b0uJbuZoAKzKBgAAAAnqSUU1Z7GoyMIg+3YrlPH++1HdQpFbc0qSFNx\nXuqgZwKOR8EAAAA4STvq2vVuVYv2NISU7Da/pZPXbWnmKIoFYgMFAwAA4BRMy/Hpf589sFOj+iMc\ntcU9BxBLKBgAAAB92BcM6dkd9RqXmaypAa82HWzR9Fyf6ViSpLy0JEX6f7sNYMBRMAAAAPoQ7Iio\nOM+nT2vb9XplWH9/RobyUmPjMuqaoixJ0ntVLZKkP+8Jyu2yNLsg3WQsDGFsMwAAANBPFfXt+qSm\nTeP8yfJ5YusyKseXpI0HWtTYEVV5VavpOBjCYqN6AwAAxIGHLxllOsIJjfMn67bpR++HsfKDau0L\nhpST6paXbWsxyPiKAwAASDAXjk7Tszvq9Vldh+koGIIoGAAAAL3YXtOm1yubTcc4Kefk+nTeiFQ1\nh6JqC7MCHIOLggEAAPAloaitA00h1baFtWFfs/6hMFPnj4yv+0yM9yeror5d/7mt1nQUDDGswQAA\nAPiSfcGQfv9JnZpDUaV5XMpL85iOdNJGZ3h0/eRsPbq1xnQUDDEUDAAAgB4U56Xqm2dkmI4BxB2m\nSAEAACS4D4+06rU9QQU7IqajYAhgBAMAAOA4L+1q1K76dl08Os10FEd8cLhVn9S069wRPh1qDisj\n2W06EhIcBQMAAOCvXv0iqD/vCerhS0bJ47ZMx3HEv106WpL0l71NKtvXrIgtTRrmNZwKicyybds2\nHQIAACc1NDR0Pq6oqDCYBPHmvw579Y1Ah1JdtqzE6Bed2qJSY9ildxo8ujyn3XQcxJHCwsLOx36/\nv8/zGcEAACS04uJi0xF6VV5eHvMZjxkKWcu31uiSaYEBSHSCP2+QX9OobatyW62Kzz75v+NQ+PwP\ntnjJefybNv1BwQAAAENeayiq0som1bezCBo4XewiBQAAhrz6jogONod1w1eGmY4CxD0KBgAAGNI+\nq2vX2t1BBXxu5aYm/uSO6taIHnrviOkYSGAUDAAAMGSV7m3Sox/W6uLRaZo7NvFvqueyLN17Xq4y\nk7kExMBJ/JoOAABwAtuq23R3SY6GpbjlSrRtowBDKBgAAGDIaQ1F9eTHdappC2u4b+hdDo1MS9Kd\nZQcV8Lk1qyBd549MNR0JCWTofUcBAIAhrzUSVXaKW0sGcUvaWHLFRL+umOhXSyiq1TsbKBhwFAUD\nAAAMKdWtYX1Sw43mgIHCCh8AADCkrK9sVlMoqq/lp5mOYpzHZaklHNV9b1aZjoIEQsEAAABDxrKN\nh3SkNayv5adpZJrHdBzjPG5LS6YFVDIyVUtLD6i6NWw6EhIAU6QAAMCQkZeaNGTXXfRmwYRMtUei\npmMgQTCCAQAAAMAxFAwAAABIkrZXt+lIC9OkcHooGAAAANDFo9PUHrH1z5sO64XPGkzHQRxjDQYA\nAAA0Is2jEWkezR2XoX/bWqNI1JbLkizucI6TxAgGAABIaNuOtGnF+9W6780qRW3TaeLD6HSPflh6\nQM0hFn7j5DGCAQAAEtqeYIe+VZipgoxk01HixoIJmWpoj5iOgTjFCAYAAEhYwY4I78Kfhtf2NGlf\nMGQ6BuIMBQMAACSslVtqJElZXrfhJPFnwYRMjUr36P3DraajIM5Ytm0zGxEAkFAaGv62A05FRYXB\nJDDtpSNeLchpNx0jblV3WNrRkqQLsxjFGMoKCws7H/v9/j7PZw0GACChFRcXm47Qq/Ly8pjPeEw8\nZX3vvXKtjRQofbhLxcU5puOcUKy/pgeaQuo41KriCZkxn/V48ZI1XnIe/6ZNf1AwAABAQsrxJel/\nTwuYjgEMOazBAAAAAOAYRjAAAEBCKd3bpJcOpejbX00xHSUhfFrbroq6I6o57NX0qC23ixvvoXeM\nYAAAgITxyueN+vPeJs3K7tD5o9JMx4l7w31uXT4+Q9dO8svrktjwF/1BwQAAAAljbzCk5ReN0Ggv\nl8JOSHa7NDmQwk0KcVKYIgUAABLCiverVd0aNh0DGPIoGAAAIK7VtUW0o7ZNSS5L//fCEabjJKxU\nl60V71crHLU1Ii1Ji6YOMx0JMYqCAQAA4tpHNW060hLWVRMzTUdJaLOHdXTeU+TRrTWG0yCWsQYD\nAADEvaJsr0ale0zHACAKBgAAAAAHUTAAAABwUiK21BFhpy70jIIBAACAkzIiNUk/fP2A6RiIURQM\nAAAQt7bXtGnL4VbTMYacq4v8OifXZzoGYhS7SAEAgLjU1BHRut1BXT4+U6MzWOBtwo7adj39SZ3y\nUpN06/ThpuMgRjCCAQAA4tJ9bx3SmIxkTcz2ypfEJc1gi9rSm/ubdemYdCW5LNNxEEMYwQAAAHHp\nzGFeXV3kNx1jyLpukl/1HVHlpSbpk9p203EQQygYAAAgbqzbHdTGgy2SpJmjUg2nGdqG+ZI07K/L\nMBraI/rnTYd03/l5ZkMhJlAwAABA3Pi8oUP3X8BFbKy5qySXu3ujk2Xbtm06BAAATmpoaOh8XFFR\nYTAJnPbSEa8W5DAdJxbxuUlchYWFnY/9/r6nJTKCAQBIaMXFxaYj9Kq8vDzmMx5jOuumgy2y2xtV\nXDyiz3NNZ+2veMkp9Z21fGuNxhb6VbavWROykjXd4Da28fK6xkvO49+06Q+2XAAAAHGhdG+Trp+c\nZToGTiDJZenfP6xRwOfW2wdaTMeBQYxgAACAuJCd4taZw1JMx8AJ/ONZwzof72BXqSGNEQwAABDT\n6tsjWvNFUG1hlo3Gi5117fqPbbWmY8AQCgYAAIhp+4IhtYSiWjiF6VHx4pFZoxSOUgiHKgoGAACI\neblpSRruY2Y3EA8oGAAAIGY9v7NBa3cHlZXsNh0FQD/xVgAAAIhZR1rD+nFxjukYAE4CIxgAACAm\n7W3sUH17xHQMACeJggEAAGJKY3tE/72rUSs+qNaMPHM3a8PpKcr26qdvVemt/c1qDUVNx8EgYooU\nAACIKYdawmoNR3VPSa4CLOyOW18fk67JAa/KKpv1/uFW3TZ9uOlIGCSMYAAAgJgzLMVNuUgAI9M8\nuu7MLHlclu7acNB0HAwSvnMBAEBMeGNfsz6pbVN1a0QlI5galUiWTAvo0a01pmNgkFAwAABATHjv\nUIuuLvSrIMMjy3QYOC47xa1/3nRICydna5w/2XQcDCCmSAEAgJiQmuTS2MxkuSxLlkXFSDTfnpSl\nC0eladPBFu1p7DAdBwOIggEAAIwKdkT07Kf1bEk7BHw1z6epgRS98kXQdBQMIAoGAAAwqr49Ipcl\n3XpOwHQUDDC/162zclKYApfgWIMBAACMeW1PUB8eadN5I1OVnuw2HQeAAxjBAAAARjSHovq8oUM3\nTwvootFppuNgEO1p7NDKD6pNx8AAoWAAAAAjfvHuYaV7XEpyM2FmqHng4pFqCdta80VQTR2svUk0\nlm3btukQAAA4qaGhofNxRUWFwSTozUtHvFqQ0246BgypC1l6t9GjaelhjfBGTcdBLwoLCzsf+/3+\nPs9nDQYAIKEVFxebjtCr8vLymM94jFNZm0NR/eHTermzQiouznMgWXfx8rrGS05pYLKGv2hUY0dU\nOSNTNTbTuXtjxMvrGi85j3/Tpj8oGAAAYFC1hKLKTHZp0Xm5pqPAsAtHpWl/U0gvftaomrawls0c\nYToSHEDBAAAAg+JfNx/RkZaIfjA1Wy7LUpKLtRdDXabXrUyvW5MDKXp0a43pOHAIi7wBAMCg8CW5\ntHBKlt7c36ypAa/pOAAGCAUDAAAMmimBFP2vs4ZpciDFdBTEmDEZHi0tPaBDzSHTUXCamCIFAAAA\n4y4bn6m2iK1t1W2yLEu5qVymxitGMAAAwIB552CLVrxfrfWVTaajIA5cNDpNbsvSn/cETUfBaaBg\nAACAAVPVHNL88Rl660ALi7rRp9zUJM3I85mOgdPE2BMAABhQviSX7mVLWpyEjQdblJLk0rcK+76p\nG2IPIxgAAGBA/O7jOn1wuI2RC5yUTK9b/+/ro7Wzrl1llU0KRWzTkXCSGMEAAACOsm1bh1rCqmuL\n6OczB+ZO3Uh8103K0pYjrfrX96tV3RrW+SNTGdGIExQMAADgqHBU+uV7RzR/QqbpKIhj4/zJGudP\n7vyYG/HFD6ZIAQAAx00JpGh2QbrpGEggextD+vetNQpFmTIV6ygYAADAMesrm/Sv71erMDu575OB\nk7D8ojx53JYiFIyYxxQpAADgiOd21Gt7TZtuPCug/AyP6ThIMJZlyZL01Mf1GpmepKJsr4qyvaZj\noQcUDAAAcNrufbNKI9KStGzmCNNRkMCun5ylYEdUXzR26H8+b1TRjBzTkdADpkgBAIDTVpDh0W3T\nh5uOgQSX7HYp4EtScV6qfElcxsYqRjAAAMAp2VHbrvJDLTrYHFZhFmsuABxFwQAAAKdk7e6g/m5M\nur41MVk+D+8mY3Cle1y65S/7NSnbq78bm66pgRTTkfBXlm3bLMUHACSUhoaGzscVFRUGkySe1oh0\nqMOtl6u9OsMX0d8PbzcdCUNcZZtLa2u8OjczpGkZYdNxElJhYWHnY7+/75sdUjAAAAnn+ILRn38M\nTSovL1dxcbHpGP3yL2s/lDcwUmf4kzUtJ0UTsmJ3B594eV3jJacUu1mjtq1Q1NZ/bKvTkrOHye2y\nYjbrl8VLzpP9mcp4JgAA6Je2qKUfF+foW4X+mC4XGFpcliWv26VAilu3vn7AdByIggEAAPrhcEtY\n7VHLdAzghK47M0tfGZ6if3nnsJ444NO/ba0xHWnIYpE3AADo0ZbDrXqnqkUN7VHVtYVVkBIxHQno\n1S3nBCRJ5eV7VW44y1BGwQAAAN38qvyImjqium16QBnJLiW7XSov3286FtBvEVu6+42DevDikaaj\nDDlMkQIAAN2ke1z6+cw8BXxJSnZzuYD4c8s5AZWMSNWD7x7WJzVtpuMMKYxgAACATo3tEW062KKW\ncNR0FOC0favQr3cPtuhIa1gth1qV4rY0dTj3yxhoFAwAAKDWcFSv723S9pp2nTnMq4WTs01HAhwx\nJtOj1/c2y+MO67O6Dr26O6hrJ/lVkMHd5wcKBQMAgCEqFLG1rymkpz+uU1MoqqnDU/R/zs0xHQtw\n1Ig0j747Oavz4w37mnSkJaIRqbY8bnZGGwgUDAAAhqjffVwnSbp+SrbG+3k3F0PDGf5kvb63WX/4\ntF5XFWZq5qg005ESDgUDAIAhpL49ov/cVquILTWHIrr3vFwWcWNIKchI1g+mJuuzunY9u6NeXrdL\nYzI88ntdfC84hIIBAMAQseaLRn1a264LR6Uq4EtSaziqJBdTRDA0Tcz26rpJWdpZ164th1sVsW3d\ndHbAdKyEQMEAACABhSK2bNmdHz/9Sb0q6tp1z3m5ykh2G0wGxI6J2V5NzPYqatv6VXm1fvZWlVrD\ntgI+tyZkJeuruT5NyPKajhl3KBgAACSgB949rNHpns6PR6Un6YavDDOYCIhdLsvqssFBOGpr48EW\nvfJFULvqa/T34zN01vAUjUjz9PK74BgKBgAACeCVzxv1RWNI/1CYqV+VV2vqcK8WTaVQAKciyWXp\n4tFpunh0mo60hPVxTZse2Vyts4anqCDDo4tGpzG9sBcUDAAA4kxVc0jvH2pVMBSVJemt/S06JzdF\nl+SnafXOBl1dmKnz2RkHcEROapIu9qXpnFyfqprDWr+vSR9Vt3UWjMMtYf1garZyfElK9bBIXKJg\nAAAQFw40hfRxTZu217SrpjWsc0ekau7YDNm2rfnjMzsvbL7CXYoBx7ksS36vW36vW5OGdV2TsbOu\nXW/tb9bnDR2qb4+qIMOjuWPTlZ/hGbLrnSgYAAAY9tKuRh1qDuureT61/fWO2o0dUfm9Ltn20XdQ\n69sjOn9kqhZPzVamd2hetACxqCjbq6Lso6UjFLW1u6FDH1W36X8+Dyo9+Wjxr2mLyLZtTQmknqI9\n6wAACBxJREFUaGogRbZsjUngO4lTMAAAOEW2bSsclWRJliRb0v5gSPubQgpFbUVsKRK1FbFt7Q2G\n1NgeVUs4qkjU1sh0jyxJ+494lWm3a/74DDWFospIdukfzx6mkSwmBeKOx2WpMNurwuyed54qq2zS\n/qaQvmjo0H+1NKqt1qvyrTWd/78lHNVwX5JCEVuhqK1zR6RqRp5P0tGfJfuaQvK6LeWlHr2Et6zY\nXAdi2bZt930aAADxo6GhwXQEAEhIfr+/z3NYiQIAAADAMRQMAAAAAI5hihQAAAAAxzCCAQAAAMAx\nFAwAAAAAjqFgAAAAAHAMBQMAkPBs29a8efPkcrn0/PPPm47ToxtvvFETJ05UamqqcnNzdeWVV+qT\nTz4xHauburo63XbbbZo8ebJSU1M1ZswY3XzzzaqtrTUdrUe/+c1vNHv2bGVlZcnlcmnv3r2mI3Va\ntWqVzjjjDPl8PhUXF+vNN980HambDRs2aMGCBcrPz5fL5dKTTz5pOtIJPfDAAzr33HPl9/uVm5ur\nBQsWaPv27aZjdbNy5UpNmzZNfr9ffr9fM2fO1CuvvGI6Vp8eeOABuVwu3XbbbX2eS8EAACS8hx9+\nWG730btfx+qNqc4991w9+eST+vTTT7V27VrZtq1LL71U4XDYdLQuDhw4oAMHDuiXv/ylPvroIz39\n9NPasGGDvvOd75iO1qPW1lZ985vf1LJly0xH6eKPf/yjbr/9dt13333asmWLZs6cqXnz5qmystJ0\ntC6am5t19tlna8WKFfL5fDH7/SNJZWVluvXWW7Vx40a9/vrrSkpK0qWXXqq6ujrT0booKCjQQw89\npA8++ECbN2/W17/+dV155ZXaunWr6WgntGnTJj322GM6++yz+/c1YAMAkMDeffddu6CgwD58+LBt\nWZb9/PPPm47UL1u3brUty7J37txpOkqfXnnlFdvlctnBYNB0lBN67733bMuy7D179piOYtu2bZeU\nlNg33XRTl2OFhYX2T37yE0OJ+paenm4/+eSTpmP0W1NTk+12u+2XX37ZdJQ+DRs2zP7Nb35jOkaP\n6uvr7QkTJtjr16+3Z82aZd922219PocRDABAwgoGg/rud7+rxx57TDk5Oabj9Ftzc7Mef/xxFRYW\n6owzzjAdp08NDQ3yer1KTU01HSUudHR06P3339fcuXO7HJ87d67efvttQ6kST2Njo6LRqLKzs01H\nOaFIJKJnn31WbW1t+trXvmY6To9uuukmXXPNNbrkkktk9/PuFkkDnAkAAGOWLFmiyy67TN/4xjdM\nR+mXVatW6a677lJzc7MmTJigNWvWKCkptv+prq+v109/+lPddNNNcrl437I/qqurFYlElJeX1+V4\nbm6uqqqqDKVKPEuXLtX06dN1wQUXmI7SzbZt23TBBReovb1dPp9Pzz33nCZNmmQ6VjePPfaYPv/8\ncz3zzDOS+j/FlJ8EAIC4ct9998nlcvX6q6ysTE899ZQ+/PBDPfTQQ5LU+c5bf9+BG6ysGzZs6Dx/\n4cKF2rJli8rKyjRlyhTNmzdPwWAwJrNKUlNTky6//PLOOeWD5VSyYmi544479Pbbb+v555+PyXUj\nZ555pj788EO9++67uvXWW3XdddepvLzcdKwuduzYoXvvvVe///3vO9ew2bbdr5+h3MkbABBXampq\nVFNT0+s5BQUFuvnmm/W73/2uy7vqkUhELpdLM2fOHJQL0P5m9fl83Y6HQiFlZ2dr5cqV+sEPfjBQ\nETudbNampiZddtllsixLa9asGdTpUafyupaXl6ukpES7d+/WmDFjBjpirzo6OpSWlqZnn31WV199\ndefxW265RR9//LFKS0sNpjuxjIwMrVy5Ut///vdNR+nVj370Iz333HMqLS1VUVGR6Tj9MmfOHOXn\n5+vxxx83HaXTE088oRtuuKGzXEhHf4ZaliW3263m5mZ5PJ4enxvb464AAHxJIBBQIBDo87zly5fr\nzjvv7PzYtm2dddZZevjhh3XFFVcMZMRO/c3ak2g0Ktu2FY1GHU7Vs5PJGgwGNW/ePCPlQjq91zUW\nJCcna8aMGVq3bl2XgvHaa6/pmmuuMZgs/i1dulR/+tOf4qpcSEcv3Afre72/rrrqKpWUlHR+bNu2\nFi9erKKiIt1zzz0nLBcSBQMAkKBGjRqlUaNGdTteUFCgcePGDX6gXuzatUurV6/WnDlzNHz4cO3b\nt08PPvigUlJSNH/+fNPxuggGg5o7d66CwaBeeOEFBYPBzmlcgUCg14sOE6qqqlRVVaWdO3dKkrZv\n367a2lqNHTvW6OLfO+64Q9/73vdUUlKimTNn6tFHH1VVVZWWLFliLFNPmpubVVFRIelo6d2zZ4+2\nbNmiQCCggoICw+m6uuWWW/T000/rhRdekN/v71zPkpGRobS0NMPp/ubuu+/W/PnzlZ+fr2AwqGee\neUZlZWV69dVXTUfr4th9Oo6Xmpqq7OxsTZkypfcnD9ieVgAAxJhY3aa2srLSnjdvnp2bm2snJyfb\nBQUF9sKFC+0dO3aYjtZNaWmpbVmW7XK5bMuyOn+5XC67rKzMdLxu7r///i4Zj/03FrZbXbVqlT1u\n3Djb6/XaxcXF9htvvGE6UjfHPt9f/pwvXrzYdLRuevq6tCzLXrZsmeloXSxatMgeO3as7fV67dzc\nXHvOnDn2unXrTMfql/5uU8saDAAAAACOYRcpAAAAAI6hYAAAAABwDAUDAAAAgGMoGAAAAAAcQ8EA\nAAAA4BgKBgAAAADHUDAAAAAAOIaCAQAAAMAx/x+DFGNITFQ31wAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbed899550>"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This result may be somewhat suprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian.  Recall the equations for multiplying two univariate Gaussians:\n",
+      "$$\\begin{aligned}\n",
+      "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
+      "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
+      "\\end{aligned}$$\n",
+      "\n",
+      "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n",
+      "\n",
+      "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "y=g(data)\n",
+      "plot_transfer_func (y, g, lims=(-4,4), num_bins=300)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxgAAAGaCAYAAACMmuWeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAANv8f6W5dr5KrNwGAAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffc0bc84978>"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As you can see the probability function is futher distorted from the original Gaussian. However, the graph is still somewhat symmetric around $0$, let's see what the mean is."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print ('input  mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n",
+      "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "input  mean, variance: 0.0009, 0.9984\n",
+        "output mean, variance: -0.0290, 2.2380\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n",
+      "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def h(x): return -1.5*x\n",
+      "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n",
+      "out = h(data)\n",
+      "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAxgAAAGaCAYAAACMmuWeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbee781c18>"
+       ]
+      },
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "output mean, variance: -0.0013, 2.2464\n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "out = h(data)\n",
+      "out2 = g(data)\n",
+      "\n",
+      "for i in range(10):\n",
+      "    out = h(out)\n",
+      "    out2 = g(out2)\n",
+      "print ('linear    output mean, variance: %.4f, %.4f' % \n",
+      "       (np.average(out), np.std(out)**2))\n",
+      "print ('nonlinear output mean, variance: %.4f, %.4f' % \n",
+      "       (np.average(out2), np.std(out2)**2))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "linear    output mean, variance: -0.0748, 7469.8042\n",
+        "nonlinear output mean, variance: -1.9234, 26155.6443\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. "
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "The Extended Kalman Filter"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n",
+      "\n",
+      "\n",
+      "Consider the function $f(x)=x^2\u22122x$, which we have plotted below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "xs =  np.arange(0,2,0.01)\n",
+      "ys = [x**2 - 2*x for x in xs]\n",
+      "plt.plot (xs, ys)\n",
+      "plt.xlim(1,2)\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQen/8TF/df2LO60AAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbee7b25f8>"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We want a linear appoximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation (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\u221212.75 as the linearization, as in the plot below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def y(x): \n",
+      "    return 8*x - 12.75\n",
+      "plt.plot (xs, ys,c='k')\n",
+      "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n",
+      "plt.xlim(1,2)\n",
+      "plt.ylim([-1.5, 1])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbee9f69e8>"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This is not a good linearization for $f(x)$. It is exact for $x=1.5$, but quickly diverges when $x$ varies by a small amount.\n",
+      "\n",
+      "A much better approach is to use the slope of the function at the evaluation point as the linearization. We find the slope by taking the first derivative of the function:\n",
+      "\n",
+      " $$f(x) = x^2 -2x \\\\\n",
+      " \\frac{df}{dx} = 2x - 2$$, \n",
+      " \n",
+      " so the slope at 1.5 is $2*1.5-2=1$. Let's plot that."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def y(x): \n",
+      "    return x - 2.25\n",
+      "\n",
+      "plt.plot (xs, ys,c='k')\n",
+      "plt.plot ([1,2], [y(1),y(2)], c='r')\n",
+      "plt.xlim(1,2)\n",
+      "plt.ylim([-1.5, 1])\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npEoMK0REREREpEp/ACi1cdz/Hkz+AAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbee8e8d30>"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. \n",
+      "\n",
+      "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$ we will need to include that term:\n",
+      "\n",
+      "$$\n",
+      "\\begin{aligned}\n",
+      "F \n",
+      "&\\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_{{x_t},{u_t}} \\\\\n",
+      "H &\\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_{x_t} \n",
+      "\\end{aligned}\n",
+      "$$\n",
+      "\n",
+      "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at  x. \n",
+      "\n",
+      "We approximate the state transition function $\\mathbf{F}$ by using the Taylor-series expansion \n"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "** orphan text\n",
+      "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n",
+      "\n",
+      "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n",
+      "\n",
+      "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathmatical choices will not be clear, but trust that the end result will be an EKF."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example: Tracking a Flying Airplane"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We will start by simulating tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
+      "\n",
+      "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import ekf_internal\n",
+      "ekf_internal.show_radar_chart()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAv4AAAGICAYAAAA59uT4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffc0bc84470>"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As discussed in the introduction, our measurement model is the nonlinear function $x=\\sqrt{slant^2 - altitude^2}$. Therefore we will need a nonlinear \n",
+      "\n",
+      "Predict step:\n",
+      "$$\n",
+      "\\begin{array}{ll}\n",
+      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
+      "x = Fx & x = \\underline{f(x)} \\\\\n",
+      "P = FPF^T + Q & P = FPF^T + Q\n",
+      "\\end{array}\n",
+      "$$\n",
+      "\n",
+      "Update step:\n",
+      "$$\n",
+      "\\begin{array}{ll}\n",
+      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
+      "K = PH^T(HPH^T + R)^{-1}& K = PH^T(HPH^T + R)^{-1}\\\\\n",
+      "x = x + K(z-Hx) & x = x + K(z-\\underline{h(x)}) \\\\\n",
+      "P = P(I - KH) & P = P(I - KH)\\\\\n",
+      "\\end{array}\n",
+      "$$\n",
+      "\n"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As we can see there are two minor changes to the Kalman filter equations, 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 use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system.  For example, consider the function $f(x) = x^2 -2x$\n",
+      "\n",
+      "\n",
+      "The rest of the equations are unchanged, so $f()$ and $h()$ must produce a matrix that approximates the values of the matrices $\\mathbf{F}$ and $\\mathbf{H}$ at the current value for $\\mathbf{x}$. We do this by computing the partial derivatives of the state and measurements functions:"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "### Design the State Variables\n",
+      "\n",
+      "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\n",
+      "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",
+      "\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. \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": [
+      "$\\Phi$ is our system matrix. 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\n",
+      "\n",
+      "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",
+      "\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",
+      "$$\\begin{aligned}\n",
+      "\\frac{\\partial h}{\\partial x_{alt}} &=\\\\ &= \\frac{\\partial}{\\partial x_{alt}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
+      "\\end{aligned}$$\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 just 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",
+     "collapsed": false,
+     "input": [
+      "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]])"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Finally, let's provide the code for $h(\\mathbf{x})$"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def hx(x):\n",
+      "    \"\"\" compute measurement for slant range that would correspond \n",
+      "    to state x.\n",
+      "    \"\"\"\n",
+      "    \n",
+      "    return (x[0]**2 + x[2]**2) ** 0.5"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Now lets write a simulation for our radar."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from numpy.random import randn\n",
+      "import math\n",
+      "\n",
+      "class RadarSim(object):\n",
+      "    \"\"\" Simulates the radar signal returns from an object flying \n",
+      "    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 for each\n",
+      "        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 measurment 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"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 15
+    },
+    {
+     "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 just 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",
+      "    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",
+      "We will initialize the filter near the airplane's actual position\n",
+      "\n",
+      "    rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
+      "    \n",
+      "We assign the system matrix using the first term of the Taylor series expansion we computed above.\n",
+      "\n",
+      "    dt = 0.05\n",
+      "    rk.F = eye(3) + array ([[0, 1, 0],\n",
+      "                            [0, 0, 0],\n",
+      "                            [0, 0, 0]])*dt\n",
+      "                            \n",
+      "After assigning reasonble values to $\\mathbf{R}$, $\\mathbf{Q}$, and $\\mathbf{P}$ we can run the filter with a simple loop\n",
+      "\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",
+      "Putting that all together along with some boilerplate code to save the results and plot them, we get"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "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",
+      "'''\n",
+      "wv = .1**2\n",
+      "wa = .1**2\n",
+      "rk.Q = array([[dt**3 * wv/3, dt**2*wv/2, 0],\n",
+      "              [dt**2*wv/2, dt*wv, 0],\n",
+      "              [0, 0, wa*dt]])'''\n",
+      "rk.P *= 50\n",
+      "\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",
+      "\n",
+      "xs = asarray(xs)\n",
+      "track = asarray(track)\n",
+      "time = np.arange(0,len(xs)*dt, dt)\n",
+      "\n",
+      "plt.figure()\n",
+      "plt.plot(time, track[:,0], label='track')\n",
+      "plt.plot(time, xs[:,0], label='filter')\n",
+      "plt.legend(loc=4)\n",
+      "plt.xlabel('time (sec)')\n",
+      "plt.ylabel('position (m)')\n",
+      "\n",
+      "\n",
+      "plt.figure()\n",
+      "plt.plot(time, track[:,1], label='track')\n",
+      "plt.plot(time, xs[:,1])\n",
+      "plt.legend(loc=4)\n",
+      "plt.xlabel('time (sec)')\n",
+      "plt.ylabel('velocity (m/s)')\n",
+      "\n",
+      "plt.figure()\n",
+      "plt.plot(time, track[:,2], label='track')\n",
+      "plt.plot(time, xs[:,2])\n",
+      "plt.ylabel('altitude (m)')\n",
+      "plt.legend(loc=4)\n",
+      "plt.xlabel('time (sec)')\n",
+      "plt.ylim((900,1600))\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAA0QAAAGkCAYAAAARwuWFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbee7c0cc0>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAzkAAAGkCAYAAAASdeutAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGHKIiIiIiMitMOQQEREREZFb+QfRQhaBZorE8gAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbed82fb38>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAA0EAAAGkCAYAAAD36y7BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAOBRKIIAAAAAeBSKIAAAAAAe5f8BL+NlJ3AduZ4AAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbed7ffbe0>"
+       ]
+      }
+     ],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "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",
+     "collapsed": false,
+     "input": [
+      "import sympy\n",
+      "sympy.init_printing(use_latex='mathjax')\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)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "latex": [
+        "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$"
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 17,
+       "text": [
+        "\u23a1       x_pos                    x_alt        \u23a4\n",
+        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  0  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
+        "\u23a2   _________________        _________________\u23a5\n",
+        "\u23a2  \u2571      2        2        \u2571      2        2 \u23a5\n",
+        "\u23a3\u2572\u2571  x_alt  + x_pos       \u2572\u2571  x_alt  + x_pos  \u23a6"
+       ]
+      }
+     ],
+     "prompt_number": 17
+    },
+    {
+     "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": "heading",
+     "level": 3,
+     "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",
+     "collapsed": false,
+     "input": [
+      "import sympy\n",
+      "sympy.init_printing(use_latex='mathjax')\n",
+      "w_vel, w_alt, dt = sympy.symbols('w_vel w_alt \\Delta{t}')\n",
+      "w = sympy.Matrix([[0, w_vel, w_alt]]).T\n",
+      "phi = sympy.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))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "latex": [
+        "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{3} w_{vel}^{2}}{3} & \\frac{\\Delta{t}^{2} w_{vel}^{2}}{2} & \\frac{w_{alt} w_{vel}}{2} \\Delta{t}^{2}\\\\\\frac{\\Delta{t}^{2} w_{vel}^{2}}{2} & \\Delta{t} w_{vel}^{2} & \\Delta{t} w_{alt} w_{vel}\\\\\\frac{w_{alt} w_{vel}}{2} \\Delta{t}^{2} & \\Delta{t} w_{alt} w_{vel} & \\Delta{t} w_{alt}^{2}\\end{matrix}\\right]$$"
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 18,
+       "text": [
+        "\u23a1           3      2                2      2             2            \u23a4\n",
+        "\u23a2  \\Delta{t} \u22c5w_vel        \\Delta{t} \u22c5w_vel     \\Delta{t} \u22c5w_alt\u22c5w_vel\u23a5\n",
+        "\u23a2  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500       \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500    \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
+        "\u23a2          3                       2                      2           \u23a5\n",
+        "\u23a2                                                                     \u23a5\n",
+        "\u23a2           2      2                                                  \u23a5\n",
+        "\u23a2  \\Delta{t} \u22c5w_vel                       2                           \u23a5\n",
+        "\u23a2  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500       \\Delta{t}\u22c5w_vel      \\Delta{t}\u22c5w_alt\u22c5w_vel \u23a5\n",
+        "\u23a2          2                                                          \u23a5\n",
+        "\u23a2                                                                     \u23a5\n",
+        "\u23a2         2                                                           \u23a5\n",
+        "\u23a2\\Delta{t} \u22c5w_alt\u22c5w_vel                                           2   \u23a5\n",
+        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \\Delta{t}\u22c5w_alt\u22c5w_vel     \\Delta{t}\u22c5w_alt    \u23a5\n",
+        "\u23a3          2                                                          \u23a6"
+       ]
+      }
+     ],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example: A falling Ball"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import ekf_internal\n",
+      "ekf_internal.plot_ball()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": "iVBORw0KGgoAAAANSUhEUgAAAyAAAAGNCAYAAADpbRVxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x7ffbee7f50b8>"
+       ]
+      }
+     ],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We can artifically force the Kalman filter to track the ball by making $Q$ large. That would cause the filter to mistrust its prediction, and scale the kalman gain $K$ to strongly favor the measurments. However, this is not a valid approach. If the Kalman filter is correctly predicting the process we should not 'lie' to the filter by telling it there are process errors that do not exist. We may get away with that for some problems, in some conditions, but in general the Kalman filter's performance will be substandard.\n",
+      "\n",
+      "Recall from the **Designing Kalman Filters** chapter that the acceleration is\n",
+      "\n",
+      "$$a_x = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_x \\\\\n",
+      "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n",
+      "$$\n",
+      "\n",
+      "These equations will be very unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n",
+      "\n",
+      "\n",
+      "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n",
+      "\n",
+      "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 19
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file
diff --git a/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb b/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb
deleted file mode 100644
index b3c526c..0000000
--- a/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb
+++ /dev/null
@@ -1,1380 +0,0 @@
-{
- "metadata": {
-  "name": "",
-  "signature": "sha256:50aa8b9428a821f428bc4db9096bcf449f706a919d8565e0afc8049759b110b0"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
-  {
-   "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": "heading",
-     "level": 1,
-     "metadata": {},
-     "source": [
-      "The Extended Kalman Filter"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "#format the book\n",
-      "%matplotlib inline\n",
-      "from __future__ import division, print_function\n",
-      "import matplotlib.pyplot as plt\n",
-      "import sys\n",
-      "sys.path.insert(0,'../code') # allow us to format the book\n",
-      "import book_format\n",
-      "book_format.load_style()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "html": [
-        "<style>\n",
-        "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
-        "@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: 850px;\n",
-        "        margin-left: 0% !important;\n",
-        "        margin-right: auto;\n",
-        "    }\n",
-        "    div.text_cell code {\n",
-        "        background: transparent;\n",
-        "        color: #000000;\n",
-        "        font-weight: 600;\n",
-        "        font-size: 11pt;\n",
-        "        font-style: bold;\n",
-        "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
-        "   }\n",
-        "    h1 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "\t}\n",
-        "\t\n",
-        "    div.input_area {\n",
-        "        background: #F6F6F9;\n",
-        "        border: 1px solid #586e75;\n",
-        "    }\n",
-        "\n",
-        "    .text_cell_render h1 {\n",
-        "        font-weight: 200;\n",
-        "        font-size: 30pt;\n",
-        "        line-height: 100%;\n",
-        "        color:#c76c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 1em;\n",
-        "        display: block;\n",
-        "        white-space: wrap;\n",
-        "    } \n",
-        "    h2 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h2 {\n",
-        "        font-weight: 200;\n",
-        "        font-size: 20pt;\n",
-        "        font-style: italic;\n",
-        "        line-height: 100%;\n",
-        "        color:#c76c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 1.5em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    } \n",
-        "    h3 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h3 {\n",
-        "        font-weight: 300;\n",
-        "        font-size: 18pt;\n",
-        "        line-height: 100%;\n",
-        "        color:#d77c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 2em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    }\n",
-        "    h4 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h4 {\n",
-        "        font-weight: 300;\n",
-        "        font-size: 16pt;\n",
-        "        color:#d77c0c;\n",
-        "        margin-bottom: 0.5em;\n",
-        "        margin-top: 0.5em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    }\n",
-        "    h5 {\n",
-        "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "    }\n",
-        "    .text_cell_render h5 {\n",
-        "        font-weight: 300;\n",
-        "        font-style: normal;\n",
-        "        color: #1d3b84;\n",
-        "        font-size: 16pt;\n",
-        "        margin-bottom: 0em;\n",
-        "        margin-top: 1.5em;\n",
-        "        display: block;\n",
-        "        white-space: nowrap;\n",
-        "    }\n",
-        "    div.text_cell_render{\n",
-        "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
-        "        line-height: 135%;\n",
-        "        font-size: 125%;\n",
-        "        width:750px;\n",
-        "        margin-left:auto;\n",
-        "        margin-right:auto;\n",
-        "        text-align:justify;\n",
-        "        text-justify:inter-word;\n",
-        "    }\n",
-        "    div.output_subarea.output_text.output_pyout {\n",
-        "        overflow-x: auto;\n",
-        "        overflow-y: scroll;\n",
-        "        max-height: 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",
-        "    code{\n",
-        "      font-size: 70%;\n",
-        "    }\n",
-        "    .rendered_html code{\n",
-        "    background-color: transparent;\n",
-        "    }\n",
-        "    ul{\n",
-        "        margin: 2em;\n",
-        "    }\n",
-        "    ul li{\n",
-        "        padding-left: 0.5em; \n",
-        "        margin-bottom: 0.5em; \n",
-        "        margin-top: 0.5em; \n",
-        "    }\n",
-        "    ul li li{\n",
-        "        padding-left: 0.2em; \n",
-        "        margin-bottom: 0.2em; \n",
-        "        margin-top: 0.2em; \n",
-        "    }\n",
-        "    ol{\n",
-        "        margin: 2em;\n",
-        "    }\n",
-        "    ol li{\n",
-        "        padding-left: 0.5em; \n",
-        "        margin-bottom: 0.5em; \n",
-        "        margin-top: 0.5em; \n",
-        "    }\n",
-        "    ul li{\n",
-        "        padding-left: 0.5em; \n",
-        "        margin-bottom: 0.5em; \n",
-        "        margin-top: 0.2em; \n",
-        "    }\n",
-        "    a:link{\n",
-        "       font-weight: bold;\n",
-        "       color:#447adb;\n",
-        "    }\n",
-        "    a:visited{\n",
-        "       font-weight: bold;\n",
-        "       color: #1d3b84;\n",
-        "    }\n",
-        "    a:hover{\n",
-        "       font-weight: bold;\n",
-        "       color: #1d3b84;\n",
-        "    }\n",
-        "    a:focus{\n",
-        "       font-weight: bold;\n",
-        "       color:#447adb;\n",
-        "    }\n",
-        "    a:active{\n",
-        "       font-weight: bold;\n",
-        "       color:#447adb;\n",
-        "    }\n",
-        "    .rendered_html :link {\n",
-        "       text-decoration: underline; \n",
-        "    }\n",
-        "    .rendered_html :hover {\n",
-        "       text-decoration: none; \n",
-        "    }\n",
-        "    .rendered_html :visited {\n",
-        "      text-decoration: none;\n",
-        "    }\n",
-        "    .rendered_html :focus {\n",
-        "      text-decoration: none;\n",
-        "    }\n",
-        "    .rendered_html :active {\n",
-        "      text-decoration: none;\n",
-        "    }\n",
-        "    .warning{\n",
-        "        color: rgb( 240, 20, 20 )\n",
-        "    } \n",
-        "    hr {\n",
-        "      color: #f3f3f3;\n",
-        "      background-color: #f3f3f3;\n",
-        "      height: 1px;\n",
-        "    }\n",
-        "    blockquote{\n",
-        "      display:block;\n",
-        "      background: #fcfcfc;\n",
-        "      border-left: 5px solid #c76c0c;\n",
-        "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
-        "      width:680px;\n",
-        "      padding: 10px 10px 10px 10px;\n",
-        "      text-align:justify;\n",
-        "      text-justify:inter-word;\n",
-        "      }\n",
-        "      blockquote p {\n",
-        "        margin-bottom: 0;\n",
-        "        line-height: 125%;\n",
-        "        font-size: 100%;\n",
-        "      }\n",
-        "</style>\n",
-        "<script>\n",
-        "    MathJax.Hub.Config({\n",
-        "                        TeX: {\n",
-        "                           extensions: [\"AMSmath.js\"]\n",
-        "                           },\n",
-        "                tex2jax: {\n",
-        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
-        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
-        "                },\n",
-        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
-        "                \"HTML-CSS\": {\n",
-        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
-        "                }\n",
-        "        });\n",
-        "</script>\n"
-       ],
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 1,
-       "text": [
-        "<IPython.core.display.HTML at 0x7f4bc93e3518>"
-       ]
-      }
-     ],
-     "prompt_number": 1
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "**Author's note: this is still being heavily edited and added to - there is a lot of duplicate material, incorrect code, and so on. The examples are just a brain dump, not fully formulated and not ready to be used.**\n",
-      "\n",
-      "**The Uncented Kalman filter (UKF) chapter is much further along. The UKF is almost always better performing than the Extended Kalman filter, and is much easier to implement, so if you have an urgenet need for nonlinear Kalman filter I'll point you towards that chapter for now.**\n",
-      "\n",
-      "The Kalman filter that we have developed to this point is extremely good, but it is also limited. Its derivation is in the linear space, and hence it only works for linear problems. Let's be a bit more rigorous here. You can, and we have in this book, apply the Kalman filter to nonlinear problems. For example, in the g-h filter chapter we explored using a g-h filter in a problem with constant acceleration. It 'worked', in that it remained numerically stable and the filtered output did track the input, but there was always a lag. It is easy to prove that there will always be a lag when $\\mathbf{\\ddot{x}}>0$. The filter no longer produces an optimal result. If we make our time step arbitrarily small we can still handle many problems, but typically we are using Kalman filters with physical sensors and solving real-time problems. Either fast enough sensors do not exist, are prohibitively expensive, or the computation time required is excessive. It is not a workable solution.\n",
-      "\n",
-      "The early adopters of Kalman filters were the radar people, and this fact was not lost on them. Radar is inherently nonlinear. Radars measure the slant range to an object, and we are typically interested in the aircraft's position over the ground. We invoke Pythagoras and get the nonlinear equation:\n",
-      "$$x=\\sqrt{slant^2 - altitude^2}$$\n",
-      "\n",
-      "So shortly after the Kalman filter was enthusiastically taken up by the radar industry people began working on how to extend the Kalman filter into nonlinear problems. It is still an area of ongoing research, and in the Unscented Kalman filter chapter we will implement a powerful, recent result of that research. But in this chapter we will cover the most common form, the Extended Kalman filter, or EKF. Today, most real world \"Kalman filters\" are actually EKFs. The Kalman filter in your car's and phone's GPS is almost certainly an EKF, for example. \n",
-      "\n",
-      "With that said, there are new techniques that have been developed that both perform equal to or better than the EKF, and require much less math. The next chapter "
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "The Problem with Nonlinearity"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "You may not realize it, but the only math you really know how to do is linear math. Equations of the form \n",
-      "$$ A\\mathbf{x}=\\mathbf{b}$$.\n",
-      "\n",
-      "That may strike you as hyperbole. After all, in this book we have integrated a polynomial to get distance from velocity and time:\n",
-      " We know how to integrate a polynomial, for example, and so we are able to find the closed form equation for distance given velocity and time:\n",
-      "$$\\int{(vt+v_0)}\\,dt = \\frac{a}{2}t^2+v_0t+d_0$$\n",
-      "\n",
-      "That's nonlinear. But it is also a very special form. You spent a lot of time, probably at least a year, learning how to integrate various terms, and you still can not integrate some arbitrary equation - no one can. We don't know how. If you took freshman Physics you perhaps remember homework involving sliding frictionless blocks on a plane and other toy problems. At the end of the course you were almost entirely unequipped to solve real world problems because the real world is nonlinear, and you were taught linear, closed forms of equations. It made the math tractable, but mostly useless. \n",
-      "\n",
-      "The mathematics of the Kalman filter is beautiful in part due to the Gaussian equation being so special. It is nonlinear, but when we add and multipy it using linear algebra we get another Gaussian equation as a result. That is very rare. $\\sin{x}*\\sin{y}$ does not yield a $\\sin(\\cdot)$ as an output.\n",
-      "\n",
-      "> If you are not well versed in signals and systems there is a perhaps startling fact that you should be aware of. A linear system is defined as a system whose output is linearly proportional to the sum of all its inputs. A consequence of this is that to be linear if the input is zero than the output must also be zero. Consider an audio amp - if a sing into a microphone, and you start talking, the output should be the sum of our voices (input) scaled by the amplifier gain. But if amplifier outputs a nonzero signal for a zero input the additive relationship no longer holds. This is because you can say $amp(roger) = amp(roger + 0)$ This clearly should give the same output, but if amp(0) is nonzero, then\n",
-      "\n",
-      "> $$\n",
-      "\\begin{aligned}\n",
-      "amp(roger) &= amp(roger + 0) \\\\\n",
-      "&= amp(roger) + amp(0) \\\\\n",
-      "&= amp(roger) + non\\_zero\\_value\n",
-      "\\end{aligned}\n",
-      "$$\n",
-      "\n",
-      ">which is clearly nonsense. Hence, an apparently linear equation such as\n",
-      "$$L(f(t)) = f(t) + 1$$\n",
-      "\n",
-      ">is not linear because $L(0) = 1$! Be careful!"
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "The Effect of Nonlinear Transfer Functions on Gaussians"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Unfortunately Gaussians are not closed under an arbitrary nonlinear function. Recall the equations of the Kalman filter - at each step of its evolution we do things like pass the covariances through our process function to get the new covariance at time $k$. Our process function was always linear, so the output was always another Gaussian.  Let's look at that on a graph. I will take an arbitrary Gaussian and pass it through the function $f(x) = 2x + 1$ and plot the result. We know how to do this analytically, but lets do this with sampling. I will generate 500,000 points on the Gaussian curve, pass it through the function, and then plot the results. I will do it this way because the next example will be nonlinear, and we will have no way to compute this analytically."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import numpy as np\n",
-      "from numpy.random import normal\n",
-      "\n",
-      "data = normal(loc=0.0, scale=1, size=500000)\n",
-      "ys = 2*data + 1\n",
-      "\n",
-      "plt.hist(ys,1000)\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3X90VPWd//HXnZmEhCQNQggBQSW7WKhVaqEqVK1WROmq\n1NMfHGmxdN2DPbVUZFfO2rqLu1/Fdde6itTWeo4rxaXanrq221qlVldBaCta7FbEWoe1ypiQGSBM\nJpnJ3B/fP4YZZvI7ZJJ778zzcQ7HYeYmfDJm5s7rfj7v98dwHMcRAAAAAHhMwO0BAAAAAEBfCCsA\nAAAAPImwAgAAAMCTCCsAAAAAPImwAgAAAMCTCCsAAAAAPImwAgAAAMCTBgwrd955pz72sY+pvr5e\njY2Nuuqqq/T666/3Ou62227TySefrPHjx+viiy/W3r17Cx5PpVJavXq1Jk+erNraWi1dulQHDhwo\nOObw4cNasWKFJkyYoAkTJujaa69Ve3t7EX5EAAAAAH40YFh54YUX9LWvfU27du3Sc889p1AopEWL\nFunw4cO5Y+666y7dc8892rRpk15++WU1Njbq0ksvVUdHR+6YNWvW6IknntBjjz2m7du36+jRo7ri\niitk23bumOXLl2vPnj165pln9PTTT+vVV1/VihUrRuFHBgAAAOAHxnB2sE8kEqqvr9dPfvIT/dVf\n/ZUcx9G0adP09a9/XbfccoskKZlMqrGxUXfffbdWrVql9vZ2NTY26pFHHtE111wjSXrvvfd06qmn\n6he/+IUWL16sN954Q2eccYZeeuklLViwQJL00ksv6YILLtC+fft0+umnj8KPDgAAAMDLhlWzcvTo\nUdm2rZNOOkmStH//frW2tmrx4sW5Y6qqqnThhRdq586dkqRXXnlF6XS64Jjp06drzpw52rVrlyRp\n165dqq2tzQUVSVq4cKFqampyxwAAAAAoL6HhHHzjjTfq7LPPzoWKlpYWSdKUKVMKjmtsbFQkEskd\nEwwGNWnSpIJjpkyZkvv6lpYWTZ48ueBxwzDU2NiYOyaLOhYAAADAf+rr64f9NUMOK2vXrtXOnTu1\nY8cOGYYx6PGDHTOM1WcAAAAAytCQloHddNNNevzxx/Xcc8/ptNNOy93f1NQkSWptbS04vrW1NfdY\nU1OTLMtSLBYb8Ji2traCxx3H0cGDB3PHAAAAACgvg86s3HjjjfrRj36k559/vleh+8yZM9XU1KRt\n27Zp3rx5kjIF9jt27NDdd98tSZo3b54qKiq0bdu2ggL7ffv2aeHChZKkBQsWqKOjQ7t27cotMdu1\na5cSiUTumL6cyFQSCu3evVvz5893exglg+ezeHgui4vns3h4LouL57N4eC6Li+ezOEZawjFgWLnh\nhhv06KOP6sknn1R9fX2ufqSurk41NTUyDENr1qzRhg0bNHv2bM2aNUu333676urqtHz5ckmZQHHd\ndddp3bp1amxs1MSJE7V27VrNnTtXixYtkiTNmTNHl19+ua6//np973vfk+M4uv7663XllVdq1qxZ\nI/oBAQAAAPjTgGHlO9/5jgzD0CWXXFJw/2233aZ//Md/lCStW7dOXV1duuGGG3T48GGdd9552rZt\nm2pqanLH33vvvQqFQlq2bJm6urq0aNEiPfroowV1LVu3btXq1at12WWXSZKWLl2qTZs2Fe0HBQAA\nAOAvA4aV/E0bB7J+/XqtX7++38crKyu1ceNGbdy4sd9jJkyYoC1btgzp3wMAAABQ+oa1zwoAAAAA\njBXCCgAAAABPIqwAAAAA8CTCCgAAAABPIqwAAAAA8CTCCgAAAABPIqwAAAAA8CTCCgAAAABPIqwA\nAAAA8CTCCgAAAABPIqwAAAAA8CTCCgAAAABPIqwAAAAA8CTCCgAAAABPIqwAAAAA8CTCCgAAAABP\nIqwAAAAA8CTCCgAAAABPIqwAAAAA8CTCCgAAAABPIqwAADwjHI0rHI27PQwAgEcQVgAAY8Y0zQEf\njyRMRRIDHwMAKB+EFQDAmBksrAAAkI+wAgAAAMCTCCsAAE+pCfW+j1oWAChPfZwSAABwT03I6HVf\nJGEqJFtSXM0NdWM/KACAK5hZAQC4Yij1K/nHxJIWxfcAUGYIKwCAohvKsq3hhpUT+TcAAP5GWAEA\nFN1YtCAe7N+g8xgA+B81KwCAEcnObgylluTd9qSCHelex/Y1QxKOxlUdsDW1qmrIYzFNU6FQqNdt\nAIA/8S4OABiR7OxGc8Pgx77faSkQcHod29cMSSRhqrHK0NS8+0Kyc8EmmTZVVVF4GiOgAEBp4R0d\nAOAbsaQlU5lgk7IcVVUUPt7fzA0AwJ+oWQEAjJpwNK4/x44O6diQbCXTI6szeb+TjmEAUEoIKwCA\nQZ1o561IwlTStId0bCxpKWU5w/43AACli7ACABjUWHT3AgCgJ2pWAACjLn9WJlskP622os9jO9NW\n7vj82wCA8kNYAQCMWDaA9FfYnj8rE0takrr7bUvc1mWrwzJ73QYAlB/CCgBgQOFovM82wfmyXbqG\n0r44e3xVUDrYdUiSlExbIxqfNLR9XgAA/kJYAQAMKJIw+2wT3J+hhBspM2vSbY+8oH44+7wQbADA\nXyiwBwAUVTbcuO3d9mRBvUs4Glf4SJJGAQDgI8ysAAB6GWgGIrtLfM/C95pBzigh2eq0htbGOCRb\nHen+j3WcwcPQ+52WAgEnN+My3BkiAID7CCsAgF4GWlqVDSuRhHlsI8dMqKgJGQN+z1jSUmVg4GPy\nj5XU5/Eh2eoc4t4tfRksVAEAvIO3bABAv7L1J/3Jhgqp/zbDnWkrF2iKYTihR1IfM0BD/1oAgLsI\nKwCAfg2n/qS/NsNDKaQPGtJIy1zC0bhMy1Zl4Hg5Zki2wkeSmlTN6Q4A/IgCewCA64LGyGc7Igmz\nV+CJJS2lLIfZFADwKcIKAGBQQQ981u9vDEMptgcA+BNhBQAg6Vhr3z5qTqTizHyMVH9j6BlWQrL1\n2oFDMofYeQwA4F0s4gWAMpcNKMPdXHGgwns3DdRJLB8bRAKA9xFWAKDMncgmiYMV3hdz2dhge66c\nqMHCGWEGANzHMjAAwLC8257Mzar0F0qKuWwsWyRfTH3NDJlm4d8jCZPd7gHAZYQVAMCwvN95PDwM\nFEoyG0aO7of9kOwTqk3JzgzlbxDZM6wAANxHWAEADFl2L5OhGI0Zkb7+jZH8E4Zj99tUoC/haFxO\n3RCKegAARUHNCgAgVxdSVTHwaaGvvUz8rK3LVtLqlhTXtNqKQY+PJEzF01znA4CxQlgBgDKVP6OQ\n7aBVNfjn9ZITS1oyZQ4prAAAxhZhBQDK1GDF4z27cA2lK9dode4CAJQnwgoAIKfKOF7DkZ1tyRrK\n/iVD3eOk2AhJAFCaCCsAgJzDKVtJx39dsYoRkt5tTyrYke61rwr7rQCAe6gSBABAmZbM2aVx+W2M\n2W8FANxDWAEAoAf2XAEAb2AZGAAAecLRuKoDfde/OE4J9W0GAB9gZgUAygSzBRmdaUvJdP/PRWYv\nleOhJD+gOI6j2qrKYW0kCQA4ccysAECJy+66bpqmQqFQ2X/Qbuuy1W33PUOS6yqWt+GM4zgyjOOF\n+4e7HRkJU81sZA8Ao46wAgAlrueu6xSL969nu2YAgLtYBgYAKHmDLf0a6fEAgNFBWAEAlLy2Llsp\na+jF8T2PD8ku++VzAOAGwgoAlLGQ7H5nEIJjuwm9q0KyZVp9dwCTMsvD8pfPEV4AYGwQVgCgjMWS\nVr8zDkGjfNJKLGlpGBMvvcILAGB0EFYAAAAAeBLdwACgRPW1TCkcjSuZNlVVwds/AMD7OFsBQInq\na5lSJGEqZTn524goaKhgCVRurxEoJFudA9SyAABGF8vAAKDM9axNGaiOpdwMt5YFAFBchBUAKBHh\naJwOVQCAkkJYAYASEUmYdKgCAJQUwgoAAAAATyKsAAAAAPAkwgoAlCDTzCwHy+5QX1tVqcOdqdzj\nNfSCHBXZ5x0AUByEFQAoQdkPzUdSmc5eh7sdxdPH21rVhMpnd/qxRFgBgOLi2hoAlLCgYchyevfe\n7UxbSrKXyrAMtudKOBpXV3da1ZVpNTfUjeHIAKB0MbMCAD7W15X8cDResOSrL21dNnupDNNAe66Y\npnmsG5tFRzYAKKJBw8qLL76oq666StOnT1cgENDmzZsLHl+5cqUCgUDBn4ULFxYck0qltHr1ak2e\nPFm1tbVaunSpDhw4UHDM4cOHtWLFCk2YMEETJkzQtddeq/b29iL8iABQuvoKK5GEWbDkC6OP5V8A\nMDoGDSuJREJnnXWW7rvvPlVXV8vosdOxYRi69NJL1dLSkvvz1FNPFRyzZs0aPfHEE3rssce0fft2\nHT16VFdccYVs+/h0+vLly7Vnzx4988wzevrpp/Xqq69qxYoVRfoxAaA8ZAvqAQAoBYPWrCxZskRL\nliyRlJlF6clxHFVWVqqxsbHPr29vb9fDDz+sRx55RJdccokkacuWLTr11FP17LPPavHixXrjjTf0\nzDPP6KWXXtK5554rSXrwwQd1wQUX6I9//KNOP/30E/35AKCsxJJWv49Rp1JcIdkKR+PUpwDAKBpx\nzYphGNqxY4emTJmiD37wg1q1apXa2tpyj7/yyitKp9NavHhx7r7p06drzpw52rVrlyRp165dqq2t\n1YIFC3LHLFy4UDU1NbljAAADc/oopM9HnUpxHUlRnwIAo23E3cAuv/xyfeYzn9HMmTO1f/9+3Xrr\nrfrkJz+pV155RZWVlWppaVEwGNSkSZMKvm7KlClqaWmRJLW0tGjy5MkFjxuGocbGxtwxAIDjwtG4\nJGlabUXuvsHCCooraND+GQBG24jDyrJly3K3zzjjDM2bN0+nnnqqfv7zn+vqq6/u9+uKcVLdvXv3\niL8HeB6LjeezeHgu+9dWdWzp7XhThw4dkiR1106TZWc+QHenUorHUwpUjJN1rN2ubdvHbyvA7RO8\nLUmWZclWQPF4XC+/2a5JtVWKx7sVqBineDyu3bvfHvT/IY7jtV48PJfFxfM5crNmzRrR1xd9n5Wp\nU6dq+vTp+tOf/iRJampqkmVZisViBbMrra2t+sQnPpE7Jn/pmJQJMwcPHlRTU1O//9b8+fOLPfyy\ns3v3bp7HIuL5LB6ey/6ZpqlfHzg2szKlWs3NzZKkF/fHlOrO1KxUjqtUXV2lurpNBWXIsiwFAgEF\nlQkzgYDB7RO8LctWMBhUIGCopq5OKUlmyFBd3Th1dZuqr6tRxUnNqhtXQT3LEPBaLx6ey+Li+SyO\nkXb3Lfo+K21tbTpw4ICmTp0qSZo3b54qKiq0bdu23DHvvfee9u3bl2txvGDBAnV0dBTUp+zatUuJ\nRKJXG2QAKHe0yfWeTPOCzP+XWNLSex0m9SwAUASDzqwkEgm99dZbkjJLCN555x3t2bNHkyZN0sSJ\nE7V+/Xp99rOfVVNTk/7v//5Pt9xyi6ZMmZJbAlZfX6/rrrtO69atU2NjoyZOnKi1a9dq7ty5WrRo\nkSRpzpw5uvzyy3X99dfre9/7nhzH0fXXX68rr7xyxFNHAFAOwtG4zAF2V8foauuy1W07qgwcr2Op\nMugWBgAjNejMyssvv6yPfvSj+uhHP6pkMqn169frox/9qNavX69gMKg//OEPWrp0qT74wQ9q5cqV\nuS5fNTU1ue9x77336uqrr9ayZct0/vnn6wMf+ID++7//u2DPlq1bt2ru3Lm67LLLdPnll+vss8/W\nli1bRuenBgCf6m93+kjC7Hd3dbjjcMpmdgUARmjQmZWLLrqoYPPGnp5++ulB/5HKykpt3LhRGzdu\n7PeYCRMmEE4AYBCRhKnGKrpQAQDKQ9EL7AEA7mMDSABAKSh6gT0AwH1sAOkd4Wg8ty8OAGB4CCsA\nAIyiSILOYABwoggrAAAAADyJsAIAPheOxnN7fMBbQrL5fwMAI0BYAQAfe7c9qfCRJPUpLhksjMSS\nllKWoxra2QDACeHtEwA8aKgF2e93WgQVF8WSliQVbAbZl5oQ7aYB4EQQVgDAgyjIBgCAZWAA4AuO\nw+wJAKD8EFYAwAcIK/7X134r7MECAAMjrACAx4Vky7TYjd7v+tpvhT1YAGBg1KwAgMdkWxHXVgTU\nkc7sRD9YATf8ISSbmRQAGAbCCgB4TCRhKmU5SllWwf0h2epI21JVRe7vncy4+EosackUMykAMFQs\nAwMAn8ju2ZH/d7oW+092zxU2jASAwTGzAgAeMpTd6DvTlpJpZlT8ynBsJY8t75NyE2UAgD4wswIA\nHpJdAjaQti6bjSB9rOf/P+pYAKB/hBUAAEZZZjas7xmzWNJSJGHKNFkSBgA9EVYAABhlQ5kNI6wA\nQG+EFQAAAACeRFgBAMAlQbbPAYABEVYAAHBJ0CCtAMBACCsA4FFcdQcAlDv2WQEAD+irdW3QMGQ5\ntCgGAJQvwgoAeEAkQScoFMoG2OaGOpdHAgDuYRkYAAAeFEmYhFgAZY+wAgAe4rDsCwCAHMIKAHgI\nYQVSZglYfzveA0A5IawAAOAxkYQ56I73AFAOCCsAAHgMM2wAkEFYAQDAYwgrAJBBWAEAwAPebU/2\n2m8nJLvPPXgAoFywzwoAjKG+9s7IFlNXVfCWXM7e77RUGbAkHQ8nsaQlU6aaG9wbFwC4iTMjAIyh\n7L4ZzQ2ZkBJPpdXWZSllOaqqcHlwcF02nOSr4UwNoIzxFggALokkTLUnaU+LgdWEDLeHAACuoWYF\nAMYYdQgAAAwNMysAMMb6WuoDAAB6Y2YFAAAAgCcRVgAAcFlItkzL7nUbAModYQUAXBY8Vj/Nh9Ty\nFUtaspzet/OFo3FqnQCUHcIKALgsaGTSSn8fUgEp0z0u2/oaAMoFYQUAxohp8kETAIDhIKwAwBgh\nrAAAMDyEFQAAPC4cjSuZJuwCKD+EFQAAPC6SMJWioAlAGSKsAAAAAPAkwgoAuKAm5PYIAADwPsIK\nAIySnvtivNuezNUd1IQMt4YFAIBvEFYAYJT03Bfj/U6LugMUDd3lAJQDwgoAAB7WmbbyZuSO309Y\nAVAOWDUNAKOov9qUzAdQe2wHA19q67LVbWdm5AzH1msHDkmSGquDmlpV5ebQAGDUEVYAYBT1V5uS\n/wEUGKr835vqUEBTXR4PAIw2wgoAjLL8InugmLK/W80NdS6PBABGB2EFAIqgvw+NnWlL0XhaVRW8\n3aL4sg0cmhtcHggAjBIK7AGgCHp2/gpH40qmTbV12UpZjkKyZVrUqAAAMByEFQAYBZGEWdCmOJa0\nRNdijBY6gwEoVYQVACiSkGzqU+AKwgqAUkVYAYAiiSUtRRImHxwBACgSwgoAFBlhBWMhf7NIAChV\nhBUAAHwov3nD24c6WYIIoCQRVgCgiEKydbgz5fYwUEYyyw+tgm50AFAqCCsAUESxpKV4mrZfAAAU\nA2EFAIASFo7GWSIGwLcIKwAAlIi+gknPDUsBwE8IKwAAlAiCCYBSQ1gBAKCEsDkpgFJCWAGAImP/\nC7gpuzkpAJQCwgoAjEBfNQLZ/S+AsRSSnQvJzK4AKBUhtwcAAH7GFWx4RSxpFdw2Zaq5wcUBAUAR\nMLMCAAAAwJMIKwAAlCjTZOYPgL8RVgDgBIWjcQrp4TlB4/htwgoAvyOsAMAJOtCRzhXSOw4F9fCG\noJFJKyHZOtyZyt1PcAHgR4QVADhB+QGFsAKviSUtxdPHfy8JKwD8iLACACcgHI3LtGxJmSvY2dsA\nAKB4CCsAcAIiCVPZrVRiSUtsqwIAQPERVgBgECyfAQDAHYQVABgEYQV+1Zm26FgHwNfYwR4Ahigc\njSueSqtuXIXbQwGGpK3LVrftqIpfWQA+NejMyosvvqirrrpK06dPVyAQ0ObNm3sdc9ttt+nkk0/W\n+PHjdfHFF2vv3r0Fj6dSKa1evVqTJ09WbW2tli5dqgMHDhQcc/jwYa1YsUITJkzQhAkTdO2116q9\nvX2EPx4AFE8kYeq9DlORBFeqAQAYC4OGlUQiobPOOkv33XefqqurZRhGweN33XWX7rnnHm3atEkv\nv/yyGhsbdemll6qjoyN3zJo1a/TEE0/oscce0/bt23X06FFdccUVsu3j3XOWL1+uPXv26JlnntHT\nTz+tV199VStWrCjijwoAQHnquecKAPjFoMvAlixZoiVLlkiSVq5cWfCY4zi69957dcstt+jqq6+W\nJG3evFmNjY3aunWrVq1apfb2dj388MN65JFHdMkll0iStmzZolNPPVXPPvusFi9erDfeeEPPPPOM\nXnrpJZ177rmSpAcffFAXXHCB/vjHP+r0008v5s8MACMSkq2ONK2K4R+xpKWJVUFNdXsgADBMIyqw\n379/v1pbW7V48eLcfVVVVbrwwgu1c+dOSdIrr7yidDpdcMz06dM1Z84c7dq1S5K0a9cu1dbWasGC\nBbljFi5cqJqamtwxAOAVsaSV27ke8KO329oVjsbdHgYADGpEYaWlpUWSNGXKlIL7Gxsbc4+1tLQo\nGAxq0qRJBcdMmTKl4JjJkycXPG4YRsH3AYCxFI7G+TCHknWA2isAPjFqrYt71rb05DhclQTgXZEE\nH+YAAHDbiFoXNzU1SZJaW1s1ffr03P2tra25x5qammRZlmKxWMHsSmtrqz7xiU/kjmlrayv43o7j\n6ODBg7nv05fdu3ePZPg4huexuHg+i8fN5zJe1XhsDG9r4sSJOnTokOJVjbICx3vA2grIsmxP3y64\nz7Y9My4/35Yky7IGf749drsjmdbLb/6fjHhU3bXTlDZN7d79tryA983i4bksLp7PkZs1a9aIvn5E\nYWXmzJlqamrStm3bNG/ePElSMpnUjh07dPfdd0uS5s2bp4qKCm3btk3XXHONJOm9997Tvn37tHDh\nQknSggUL1NHRoV27duXqVnbt2qVEIpE7pi/z588fyfChzIuQ57F4eD6Lx+3ncsc7hyVJ8z98ipLJ\npPSByTpyJCk7r1YlEDAUlOHp29n/WpalQCDgmXH5+bYsW8FgcMDn2+0x9nU71i1VV9Xr/A+ephf3\nx1RVXa35Hz5FbnP7tV5KeC6Li+ezOEa6FcmgYSWRSOitt96SlLkq984772jPnj2aNGmSZsyYoTVr\n1mjDhg2aPXu2Zs2apdtvv111dXVavny5JKm+vl7XXXed1q1bp8bGRk2cOFFr167V3LlztWjRIknS\nnDlzdPnll+v666/X9773PTmOo+uvv15XXnnliNMYAIzUu+1JvRNPK2U5ChoStfXws3A0LtOyVRkI\n5OqymhvqXB4VAPRt0LDy8ssv65Of/KSkTB3K+vXrtX79eq1cuVIPP/yw1q1bp66uLt1www06fPiw\nzjvvPG3btk01NTW573HvvfcqFApp2bJl6urq0qJFi/Too48W1LVs3bpVq1ev1mWXXSZJWrp0qTZt\n2lTsnxcAhu39zuPdv4KGIYuaO/hUSLbCR5LK/gpn67KaG1wcFAAMYNCwctFFFxVs3tiXbIDpT2Vl\npTZu3KiNGzf2e8yECRO0ZcuWwYYDAABOUCxpSZIqAwM3wQEArxi1bmAAAAAAMBKEFQAYQHZ9PwAA\nGHuEFQAYQCRhUlAPAIBLRtS6GABKTTgaVzyVVjJtqaqCt0iUvpq8X3PTNBUK8XsPwDt4RwIAKdfC\nNZIw1Z7MdEiqqhjoK4DSUBM6XmxPWAHgNbwjAYCOt3DNF5KtjjT1KihNud9vUjkADyOsAEA/aPOK\nUpb9/QYAL6PAHgAAAIAnMbMCAMew7AvlKttYorE6qKlVVW4PBwByCCsAcAzLYlCuso0lqkMBdR1r\nNpHV3FDn0qgAgLACADlBQ+ypgrLXs9lEc4NLAwEAUbMCoMyZ5vEPZkHDyLvtxmiAsdeZtpRM9+6G\nBwBeQFgBUNbyw0q+/OAClLK2LlspphQBeBRhBQAAFAjJZrYFgCcQVgAAQIFY0mK2BYAnUGAPoOyF\no3GuIgPK1q/QvhuAdzCzAqDshKNxhfPas0YSJleRAVG/AsB7CCsAyk4kYfZqzwoAALyHsAKgrL3b\nnmQJGAAAHkVYAVDW3u+kkBjoS/5eQ/21+AaA0UZYAVB2HIdwAgwmaBgKyVY4GiesAHANYQVA2cmG\nlXA0LtOi8xHQn1jSor4LgKsIKwDKViRhihVgwODebU8WdNADgLFCWAFQVphNAYbv/U5mWAC4g7AC\noKxkZ1NCsukCBgCAxxFWAJSlWJIuYMBwZIvtAWAsEVYAAMCgKLYH4AbCCgAAAABPCrk9AAAYbflL\nV6hTAYYnJFudx5pSZJeCNTfUuTwqAOWCsAKg5GTDSXNDncLRuMJHkqqqyLzdpSxHlQFjoC8HkCeW\ntHKvmVjSkilTzQ2Zx0zTVCjERwkAo4dlYABKTiRh5tbWRxImhfRAEeUX2rOzPYDRxuUQAAAwZNnZ\nFSmuru60qivTLAsDMGqYWQFQFmq4NAMURfDYKsrMDCYdwgCMLsIKgJIVjsZzBfU1IepUgGIIGryW\nAIwdwgqAknWgI029CgAAPkZYAVCyHIegAow2drYHMJpYxQ2gZOR/YMrfG0KSOtOWkmm7ry8DMAI9\n2xkDQDERVgCUjPxC3/y9ISSprctWt81MCwAAfsIyMAAAAACeRFgBAAAA4EmEFQAAMCwh2bm24AAw\nmggrAEoKH6KA0RdLWrQFBzAmCCsAfM80Cwvr+RAFAEBpIKwA8L38sAIAAEoHYQUAAACAJxFWAAAA\nAHgSYQUAABRdOBpXOBp3exgAfI4d7AH4Ss8PP80NdS6NBEBP4Whc8VRaJ1WFFElYkqTmBpcHBcDX\nCCsAfCWSyBTTO44jwzD4IAR4QEi2wtG4IglT7UlTjuMombZVVcHHDAAjwzIwAL7kOLQnBrwilrTU\nnjrela+ty6aFOICi4JIHAF8LR+OqDtjq6kizGSTgopqQoYRJQAFQXIQVAL4WSZiqDdqKJrmSCwBA\nqWEZGADfCslWMm0WLDkJGi4PCkBOtpYFAE4UYQWAb8WSVq/ZlKBBWgG8Ipa0ck0xAOBEEFYA+E5I\ntkzLdnsYAABglFGzAsA3wtG4kmlTKctRZYAZFMBLOtOWkmkuIgAoLsIKAN+IJEyK6AGPauuy1W3z\n+gRQXIS7DNOGAAAdrklEQVQVAJ5HgS7gXzXHPmlkX8fNDXUujgaA3xBWAHgeBbqAf9WEMks2s6/j\n5gY3RwPAbyiwBwAAoypbbwYAw0VYAeBp+R9yHIf18IDfdKYthY8klbKc3JIwABgqwgoAT3LqGhSO\nxguK6gkrgP/kb9qaXRIGAEPFNQ4AnhRNB5SiVgUAgLLGzAoAABgTnWmL7n4AhoWwAgAAxkRbl013\nPwDDQlgB4Fkh2XQQAkpMSDazKwCGjJoVAJ4VS1q52yHZ6rRsF0cDoBgyr+tuxVOHVDeuwu3hAPA4\nwgoATwsakuVkPuBUBugkBJSCWNJS0JDipqEqtwcDwNNYBgbA04IGAQUoRfmv7XA0ztIwAH1iZgWA\np/CBBSg/BzrSMgxDzQ1ujwSA1xBWAHgKnYKA8uM4jgxmUQH0gWVgADynhssoAABAhBUAHlQT4gor\nUA5CsuXUNeRuswwUQE+EFQCe05m2pCAtTYFSF0taSgarZFq2YkkrtwyUgnsAWYQVAJ4RjsaVTJtq\n67KVdtweDYCxcLjbkdXj9R5JmNSvAZBEWAHgEaaZ+XCS6vmpBQAAlC3CCgBPME2uogLlLiRb/3vg\nkJJp3g8AZNBzBwAAeEIsaSkeMNRtO6qibA2AmFkB4LJwNK7XDhzS4c6U20MB4CF0BwMgFSGs3Hbb\nbQoEAgV/pk2b1uuYk08+WePHj9fFF1+svXv3FjyeSqW0evVqTZ48WbW1tVq6dKkOHDgw0qEB8IFI\nwtR7HaZaO02WfgDIye8OBqB8FWVmZfbs2Wppacn9+d///d/cY3fddZfuuecebdq0SS+//LIaGxt1\n6aWXqqOjI3fMmjVr9MQTT+ixxx7T9u3bdfToUV1xxRWybbsYwwPgA21dNsX1AACgQFFqVoLBoBob\nG3vd7ziO7r33Xt1yyy26+uqrJUmbN29WY2Ojtm7dqlWrVqm9vV0PP/ywHnnkEV1yySWSpC1btujU\nU0/Vs88+q8WLFxdjiAA8ILuko7mhzuWRAAAAPyjKzEo4HNbJJ5+s5uZmXXPNNdq/f78kaf/+/Wpt\nbS0IHFVVVbrwwgu1c+dOSdIrr7yidDpdcMz06dM1Z86c3DEASgN7JwAYjhraAAFlb8Rh5bzzztPm\nzZv1zDPP6KGHHlJLS4sWLlyoQ4cOqaWlRZI0ZcqUgq9pbGzMPdbS0qJgMKhJkyYVHDNlyhS1traO\ndHgAAMCnakKG20MA4LIRX7O4/PLLc7c//OEPa8GCBZo5c6Y2b96sc889t9+vM4yRvwHt3r17xN8D\nPI/FxvPZv3hVZrno7t1vS5Kqq6sVd+pkBSpkKyDLytSp2ceuo1iW1et+bg/vdsF9tu2Zcfn5ttT/\n76ZXxui72/38bnanUrynDhPPV3HxfI7crFmzRvT1RZ9gHT9+vM444wz96U9/0qc//WlJUmtrq6ZP\nn547prW1VU1NTZKkpqYmWZalWCxWMLvS0tKiCy+8cMB/a/78+cUeftnZvXs3z2MR8XwObMc7hyVJ\nE5tOkpT5wFcRT8u2HAUChoLKXMQIBAzJshUMBnvdz+3h3c7+17IsBQIBz4zLz7cH+t30yhj9dHug\n383KcZX6MO+pQ8Y5qLh4Poujvb19RF9f9H1Wksmk3njjDU2dOlUzZ85UU1OTtm3bVvD4jh07tHDh\nQknSvHnzVFFRUXDMe++9p3379uWOAVA6QrIVPpJUJGHq/U6LDmAA+tWZtthrBShzI55Z+bu/+ztd\nddVVmjFjhg4ePKj/9//+n7q6uvSlL31JUqYt8YYNGzR79mzNmjVLt99+u+rq6rR8+XJJUn19va67\n7jqtW7dOjY2NmjhxotauXau5c+dq0aJFIx0eAI+JJS1JUm2FrU6L9uQA+tfWZavDMtXcQDdBoFyN\nOKwcOHBA11xzjaLRqCZPnqwFCxbo17/+tWbMmCFJWrdunbq6unTDDTfo8OHDOu+887Rt2zbV1NTk\nvse9996rUCikZcuWqaurS4sWLdKjjz5alLoWAN4SNCTLyYSWygCvcQBDk+0k2Nzg8kAAjKkRh5Uf\n/OAHgx6zfv16rV+/vt/HKysrtXHjRm3cuHGkwwHgcUHDkOWw9AvA0IWjcSXTpqoqQgX3Scy0AKWO\nDuYAAMCzsnVupp25yJENKcy0AOWBsAJgVHH1E8BIZOvcsstG2VgWKC+EFQCj6vgHi8wyDgA4USHZ\n6kjbqq0IqCNtFywLA1CaeJUDGHUh2dp/JKmU5VBUD+CEZWdZTNuS5UhVFS4PCMCoK/o+KwDQUyxp\nyaamHkCRBOkWCpQNwgqAUZPt4AMAoykcjbN5JFCiCCsAiir/Q0MkYbJDPYBRF0mYFN4DJYqaFQBF\nFUmYCslWPHVIybTl9nAAlImQbIWjcToPAiWGsAKg6LJFsAAwVmJJS6ZM9l0BSgzLwAAAAAB4EmEF\nAAD4UnbplyQFaRAGlCSWgQEAAF86krIkdSuZtgvaGWcDDPUrgP8xswIAAHwpaBiKJa2CroPhaFzh\nI0m6gwElgrACYNSwLAPAWArJVvhIMhde2H8F8D+WgQEoir4+EAQNQ5bDPisAxkbPToTZ2RU6hAH+\nxcwKgBHLLrs4mOhWih3rAXhIfhE+AP9hZgXACQtH44qn0mrryqwZT1mWKgOs/QLgHey/AvgbYQXA\nCYskTLUnmUkBAACjg2VgAIaMYlUAADCWCCsAhiySMHMFq+FoXEnqUwB4VEg271FACWAZGIATEkmY\nBXsbAICX9OwMBsCfmFkBMCx9ddZhPxUAXpX//sRSVsB/mFkBMCzZzjr52E8FgJcEDSk78Rs0jqeV\nAx1pGYZBZzDAR5hZAQAAJSU/oGSFo3GlTZaGAX5DWAEAACUvkjDVX5mdaVKID3gVy8AADCq7+WMy\nffyqpMOyLwA+EZKtjrSdu51ft9LcUCfTNBUK8ZEI8CJemQD6FY7GlUil1Xpsh/psoWpItjpN293B\nAcAQZTuDVQaMPuru4qoO2JpaVeXO4AAMiGVgAPoVSZhq6bRyLYqz68BjSavf5RQA4CeRhKl4mjc0\nwKuYWQHQC609AQCAFxBWAPQSSZjHdn9mqReA0hOSrUTa1rgKPgYBXscyMAA5+RumxZIWO9QDKEmx\npCXb0bGLMqY60xYzyoBHcUkBQA4zKgDKSbbwvq3LVodlqrnh+DLY5oY6N4cG4BjCCoCC1sTMpgAo\nZ5FEplMYu9wD3kBYAaBIwlR7kk3RAJSv7P4rjuPIONb5EID7qFkBylR+fUpPQc7TAMpMLGnpYKJb\nadPqtXEkAPcQVoAyFUmYueUOPQW5qgigDGX3kIolrYL3x4Eu7gAYXYQVAACAAQx0cQfA6CKsAGWs\nJpS5YphMmyz9AoAeTJOAAriNsAKUoWxAMRxb4SNJpSyHpV8AkCckW21HE24PAyh7hBWgDPS8OhhJ\nmEpZjtq6bFoVA0AfYklL8TTvj4DbCCtAGcgPK2+3tSuZZmkDAADwPsIKUGYOdJjMpgDAMNWwMx3g\nCl56QJmg7SYADF+2xq+xqiJ3n2ma+vORLklSc0OdW0MDygJhBSgD77Yn9U48raoKXvIAMFSdaUvR\neLpgNjocjaurO633Oy3VVgQkxQkswCjikwtQ4sLRuN49drKtrbDVadluDwkAfKGty1a3XbhsNpIw\n1dVtqdt2lLIsmTLV3ODSAIEyQM0KUOIiCVPZi4LZ3ZkBAMOXXRLW1/0stQVGBzMrQIkKR+OKp9JK\npi23hwIAJSHb9r0yYPS6XxIzLMAoIKwAJcQ0TYVCmZd1JGGqPZk5gfY8sQIAAPgBy8CAEpLdT6W/\npQoAgBPTmbb6fF/NtjQOyWYpGDAKmFkBSkD2BDmtNtNaM5IwZdoUpwBAsfRVbC9JhmMrmbaVspx+\ni+3zZ70BDA+vHKAEZNdLW5alYEdakhQ0DFkOgQUARlN+iMnOrvRsZUxYAU4crxzAZ8LRuEKGo1Mm\nfaDg/pBsvRu3VVlBQAEANxxJ0coYKDbCCuAzkYSpxqpMwXx+x69sh5qQbHWk2UsFAMZa0DBysyun\nTKjWn490KZ5Kq7E6qKlVVW4PD/AlwgrgY/kdv7JiyUyrYjqAAcDYiyUzsyuW1aF3jm3IWx0KaKrb\nAwN8irAC+EB+h5lk2pSqKuj4BQAelV2Wm+qxC2/2vbxnTQuA/hFWAB/IFtBLyp38spuTBQ2xKz0A\neEgsaRXMbnemLb124JDauixNquajFzAcvGIAn6gybB3pztSiZPr9Z27T9QsAvC2/Y1hNiCW6wHAQ\nVgAPyy+g73KUO9n11+8fAOBvLBUDChFWAA/LL6CnYB4ASkv2glTduIpcOMku+6X9MZBBWAE8zGF5\nFwCUnGxIiXZZSlqOJpmOpN6bSQIgrACu6+vKWva+tGm5PDoAQLFlZ82zM+axpKVxITPX5bGqgo9n\nQBavBsBl2ZNWvWmouUF6u61d+9u7c5s8AgBKn+HYCh9JKmU5qqpwezSAdxBWAA8IHssk4Whc7xwL\nKgCA0pPfzTHfQI1TKLpHOSOsAGOsr5NO0DAUUuaqGmUqAFC6htPNMXu+oOge5YywAoyBbA3KSVUh\nRRKZOpTmBhXsQh9LZu5n6RcAlLeaY5/OIglTIdlKpm3qWFC2+M0HxkC2LqU6FJCkzCxKNJ7bhZ6A\nAgDIqgkZuYtZ2WXB/dWxsEQMpY6wArggM4vS3ee6ZQBAeetMW4rG0wX1i9mLXFmnTKhWKBRiiRhK\nHmEFKJJwNC6nLnO2ME1ToVDvl1d+YWV22RcAAPny61qChmQ5x9sbJ8xMcOnqTqu6krZhKH2EFaBI\nIglT8XRmmdf+WIeCwaCaG+r0dlt7ri6lrxMQAAD9CRqGrGOdVwwnU7+SshzFuw1Vp1lCjNJHWAGK\nxHEc1VZVKhyN6/1OS5UBS/HUIcW6rD5bEeefgAAAGEzPTmIh2epI25pQGcgtEcvO7FPLglJBWAFG\n4O22dnV0W6obVyHHcXSk25GRoLsXAGD0Zc8zh1O2ko6pcXUNajua0NSJ9blaFql3aOlvqTLgRfym\nAv3o+Wae3374lEkfyG3g2GU5mmQ6Mq1MLUpItjotCucBAGMrmg6oPu1oat592dByyoTj5zTCCvwk\n4PYAAK/aH+vQawcOFWzK9V6HqaSZ6cgSPpLM1ZzEklaftwEAGAsh2VKwQp1pS68dOKRk2lSVYSuZ\nzuzV0nY00etrwtF4QYcxwIuI1UA/3u+0FO+2VG8avVpCsj8KAMBLshfK8utaDqcyt1OWpaqgdLDr\nkOrGVciyLAU70rQ9hi8QVlDWehYg5hcmmnlLufI7euW3HwYAwA+yIWaS6agzbauy4vgSgOwyZ0mq\nG1dBUT48hbCCshZJZKbJFY2ruaEu13I4kjBzS7lCsvVO+/FdhHt2YwEAwC9iSatgVUBNKHMubE9m\nLshNMh1JcQILPIOwgpLVX9vG7P2nTKiWlJkmN53uXJvh/KtNUu83dgAA/C7b9rg2GMitFgga2Q5j\nmXNidpYlu+rANE39+UhXwfch1GC0EVZQcvIL4iXJcdplGAE1N9TlCuNrKwKqDhxfypXfZjj7Bg4A\nQKnKnvcKNyvO7P8VS1oKGlKX6SieOqTG6qCmTqyXaZp5LZGPFfUzC4NRRliBrwy2yVU2jFRVHP/V\nPtBhKhAISIpr/5GkUtbxYsO+ak/YHwUAUO6ChpE7HzqOo4NdhxQypGTaUm1FQIm0rXbLkdStkHFU\np0z6QMHXsyklisVzrYsfeOABzZw5U9XV1Zo/f7527Njh9pDgEdkgkn9VxzRNhaNxvXbgkP4cO5rr\n0lVzLKuEZMu0bIVkK3wkqfxSk7Yuu8+d5QEAwHFtXbbe6zAVSVhKWZmZFzuvXf+hrnSu1X/2vNzz\nfJ09V9MqGcPlqZmVxx9/XGvWrNF3vvMdnX/++fr2t7+tJUuWaO/evZoxY4bbw8Mo6vnmlb0Sk39l\nJhtEJlTaeu3AIUlSyMi0GE5ZjhzHyc2UGI6tZNrOtRdmtgQAgNGR32msqzudOy9XVWQez4aX1LFN\nlBOpQ6rpUQ/TEzMzyPJUWLnnnnv05S9/Wdddd50kaePGjXr66af1ne98Rxs2bHB5dBiK/DeXgdoC\nZ8VTadWNq1Akkdm0KpG2VVMRUDx1SAFJrV2WqipCcpzjrYOzfeOlTPjI3s5fd0vHLgAAxlYsaSne\nffy8XGVkLi62dVkyj90XS1qKBwzVHauHCRmSeex0HZCUXZzdduz839ygPgNNOBpXyHB6LT9D6fFM\nWOnu7tarr76qdevWFdy/ePFi7dy506VRlZe3244XoufrGTr6CiRZ2dART2XenGqPBQ9JuTekti5L\nk6pDSphSe9LUFMvpdxak23ZUW1HYOhgAAHhfz4uLlnP8PN7zXN/ztiTVVmTCTvbzQ924zFRNPJVW\nW5elU+oqcnvEZDuX9fyM0t9j8A/DcRxPfAKMRCKaPn26XnzxRZ1//vm5+//5n/9ZW7du1b59+yRJ\n7e3tbg0RAAAAwAmqr68f9td4rsAeAAAAACQPhZWGhgYFg0G1trYW3N/a2qqpU6e6NCoAAAAAbvFM\nzUplZaXmzZunbdu26TOf+Uzu/l/+8pf63Oc+l/v7iUwfAQAAAPAfz4QVSVq7dq1WrFihc845RwsX\nLtR3v/tdtbS06Ctf+YrbQwMAAAAwxjwVVj7/+c8rFovp9ttv1/vvv68zzzxTTz31FHusAAAAAGXI\nM93AAAAAACCfZwrsT0QkEtEXvvAFTZ06VTU1NfrIRz6irVu3uj0s3/rtb3+rSy+9VHV1dfrABz6g\nj3/844rFYm4Py9ccx9GSJUsUCAT04x//2O3h+M7hw4e1evVqzZkzR+PHj9cpp5yir371qzp06JDb\nQ/ONBx54QDNnzlR1dbXmz5+vHTt2uD0kX7rzzjv1sY99TPX19WpsbNRVV12l119/3e1hlYQ777xT\ngUBAq1evdnsovvX+++/rS1/6khobG1VdXa0zzjhDL774otvD8h3TNPWNb3xDzc3Nqq6uVnNzs/7h\nH/5BlmW5PTRfePHFF3XVVVdp+vTpCgQC2rx5c69jbrvtNp188skaP368Lr74Yu3du3fQ7+vrsPLF\nL35Rb731ln7605/q9ddf17XXXqsVK1Zo+/btbg/Nd37zm9/osssu0yc/+Un95je/0auvvqqbb75Z\nFRUVbg/N1771rW8pGAxKkgzDcHk0/hOJRBSJRPRv//Zv+sMf/qBHH31UL774oq655hq3h+YLjz/+\nuNasWaNbb71Ve/bs0cKFC7VkyRK9++67bg/Nd1544QV97Wtf065du/Tcc88pFApp0aJFOnz4sNtD\n87Vf//rXeuihh3TWWWfxHnmCjhw5oo9//OMyDENPPfWU9u3bp02bNqmxsdHtofnOhg0b9OCDD+r+\n++/Xm2++qfvuu08PPPCA7rzzTreH5guJREJnnXWW7rvvPlVXV/d6Td9111265557tGnTJr388stq\nbGzUpZdeqo6OjoG/seNjtbW1ziOPPFJw36mnnup861vfcmlE/rVgwQLn1ltvdXsYJeW3v/2tM2PG\nDOfgwYOOYRjOj3/8Y7eHVBKeeuopJxAIOPF43O2heN4555zjrFq1quC+WbNmObfccotLIyodHR0d\nTjAYdH72s5+5PRTfOnLkiPMXf/EXzv/8z/84F110kbN69Wq3h+RLt9xyi3P++ee7PYyScMUVVzgr\nV64suO/aa691rrzySpdG5F+1tbXO5s2bc3+3bdtpampyNmzYkLuvq6vLqaurcx588MEBv5evZ1aW\nLFmixx9/XIcOHZJt2/rJT36iaDSqRYsWuT00Xzl48KB+/etfq6mpSeeff76mTJmiCy+8UM8995zb\nQ/OteDyu5cuX66GHHtLkyZPdHk5JaW9v17hx4zR+/Hi3h+Jp3d3devXVV7V48eKC+xcvXqydO3e6\nNKrScfToUdm2rZNOOsntofjWqlWr9LnPfU6f+MQn5FA+e8KefPJJnXPOOVq2bJmmTJmis88+W9/+\n9rfdHpYvLVmyRM8995zefPNNSdLevXv1/PPP61Of+pTLI/O//fv3q7W1teCcVFVVpQsvvHDQc5Kv\nw8rmzZuVTqfV0NCgqqoqffGLX9QPfvADnXXWWW4PzVfC4bAkaf369fqbv/kbbdu2TRdccIEuu+wy\n/f73v3d5dP70la98RZ/61Kd02WWXuT2UknLkyBH9wz/8g1atWqVAwNdvX6MuGo3KsixNmTKl4P7G\nxka1tLS4NKrSceONN+rss8/WggUL3B6KLz300EMKh8O6/fbbJbFMdiTC4bAeeOAB/eVf/qW2bdum\nG2+8UX//939PYDkBX/3qV/WFL3xBc+bMUWVlpT784Q9r5cqVbKFRBNnzzomckzx3tr/11lsVCAQG\n/JMtGvviF7+oeDyuX/3qV3rllVd08803a8WKFXzAPmaoz6Vt25IyH7BXrlypuXPn6o477tDHPvYx\nffe733X5p/COoTyfL7zwgrZs2aLf//73+td//VdJyl0x5MrhccN5nWd1dHToyiuv1IwZM3LPLeCG\ntWvXaufOnfrxj3/Mh+wT8Oabb+qb3/ym/vM//zNX0+c4Du+RJ8i2bc2bN0933HGH5s6dq5UrV+rr\nX/86YeUEbNy4Uf/xH/+hxx57TL/73e/0/e9/X9/+9rf18MMPuz20kjbY+6in9lmRpJtuuknXXnvt\ngMfMmDFDb7zxhv7rv/5Lr732ms4880xJ0plnnqnt27fr/vvv10MPPTQWw/W0oT6X2UT7oQ99qOCx\nOXPm6M9//vOojc9vhvp8PvLII9q7d69qa2sLHlu2bJkWLlxIhxYN/bnM6ujo0Kc+9SkFAgH97Gc/\nU2Vl5WgP0fcaGhoUDAbV2tpacH9ra6umTp3q0qj876abbtIPf/hDPf/88zrttNPcHo4v7dq1S9Fo\nVGeccUbuPsuytH37dj344INKJBI0dxmGadOm9Tp/z549m/P3Cbjjjjt066236vOf/7wk6YwzztA7\n77yjO++8U3/913/t8uj8rampSVLmHDR9+vTc/a2trbnH+uO5sDJp0iRNmjRp0OOyswE9l4IEAgGu\nzhwz1OfytNNO07Rp07Rv376C+//4xz9q7ty5ozU83xnq83nHHXfo5ptvzv3dcRydeeaZ+ta3vqWl\nS5eO5hB9Y6jPpZSp/1myZIkMw9AvfvELalWGqLKyUvPmzdO2bdv0mc98Jnf/L3/5S33uc59zcWT+\ndeONN+pHP/qRnn/+eZ1++uluD8e3rr76ap1zzjm5vzuOoy9/+cs6/fTT9Y1vfIOgMkwf//jH+zx/\nE6aHz3EcPleOkpkzZ6qpqUnbtm3TvHnzJEnJZFI7duzQ3XffPeDXei6sDNXs2bM1e/ZsffWrX9Xd\nd9+tiRMn6sknn9Szzz6rn/70p24Pz1cMw9DNN9+s9evX66yzztJHPvIR/fCHP9Rvf/tbPfDAA24P\nz3emTZumadOm9bp/xowZnDyGKR6Pa/HixYrH43ryyScVj8cVj8clZQIPH2oGtnbtWq1YsULnnHOO\nFi5cqO9+97tqaWlh/fUJuOGGG/Too4/qySefVH19fW5Guq6uTjU1NS6Pzl/q6+tVX19fcN/48eN1\n0kkn9ZohwOBuuukmLVy4UBs2bNDnP/95/e53v9P9999Pu90T8OlPf1r/8i//opkzZ+pDH/qQfve7\n3+nf//3f9aUvfcntoflCIpHQW2+9JSkzqfDOO+9oz549mjRpkmbMmKE1a9Zow4YNmj17tmbNmqXb\nb79ddXV1Wr58+cDfuMidysbU22+/7Xz2s591mpqanJqaGucjH/mI8/3vf9/tYfnWXXfd5ZxyyilO\nTU2Nc+655zq/+tWv3B5SyaB18Yl5/vnnHcMwnEAg4BiGkfsTCAScF154we3h+cIDDzzgnHbaac64\nceOc+fPnO9u3b3d7SL7U1++hYRjOP/3TP7k9tJJA6+KR+fnPf+7MnTvXqaqqcj74wQ86999/v9tD\n8qWOjg7nb//2b53TTjvNqa6udpqbm51vfvObTiqVcntovpA9Z/d8v/zyl7+cO+a2225zpk6d6lRV\nVTkXXXSR8/rrrw/6fQ3HYW4LAAAAgPd4rhsYAAAAAEiEFQAAAAAeRVgBAAAA4EmEFQAAAACeRFgB\nAAAA4EmEFQAAAACeRFgBAAAA4EmEFQAAAACe9P8BZm9Os9oNPYEAAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bacf8bba8>"
-       ]
-      }
-     ],
-     "prompt_number": 2
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This is an unsuprising result. The result of passing the Gaussian through $f(x)=2x+1$ is another Gaussian centered around 1. Let's look at the input, transfer function, and output at once."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from nonlinear_plots import plot_transfer_func\n",
-      "\n",
-      "def g(x):\n",
-      "    return 2*x+1\n",
-      "\n",
-      "plot_transfer_func (data, g, lims=(-10,10), num_bins=300)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAyQAAAGaCAYAAAD+VYcoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bacf25f28>"
-       ]
-      }
-     ],
-     "prompt_number": 3
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "The plot labelled 'input' is the histogram of the original data. This is passed through the transfer function $f(x)=2x+1$ which is displayed in the chart to the upper right. The red lines shows how one value, $x=0$ is passed through the function. Each value from input is passed through in the same way to the output function on the left. The output looks like a Gaussian, and is in fact a Gaussian. We can see that it is altered -the variance in the output is larger than the variance in the input, and the mean has been shifted from 0 to 1, which is what we would expect given the transfer function $f(x)=2x+1$ The $2x$ affects the variance, and the $+1$ shifts the mean.\n",
-      "\n",
-      "Now let's look at a nonlinear function and see how it affects the probability distribution."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from nonlinear_plots import plot_transfer_func\n",
-      "\n",
-      "def g(x):\n",
-      "    return (np.cos(4*(x/2+0.7)))*np.sin(0.3*x)-1.6*x\n",
-      "\n",
-      "plot_transfer_func (data, g, lims=(-4,4), num_bins=300)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAxgAAAGaCAYAAACMmuWeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bac74ae80>"
-       ]
-      }
-     ],
-     "prompt_number": 4
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This result may be somewhat suprising to you. The transfer function looks \"fairly\" linear - it is pretty close to a straight line, but the probability distribution of the output is completely different from a Gaussian.  Recall the equations for multiplying two univariate Gaussians:\n",
-      "$$\\begin{aligned}\n",
-      "\\mu =\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}\\mbox{, } \n",
-      "\\sigma = \\frac{1}{\\frac{1}{\\sigma_1^2} + \\frac{1}{\\sigma_2^2}}\n",
-      "\\end{aligned}$$\n",
-      "\n",
-      "These equations do not hold for non-Gaussians, and certainly do not hold for the probability distribution shown in the 'output' chart above. \n",
-      "\n",
-      "Think of what this implies for the Kalman filter algorithm of the previous chapter. All of the equations assume that a Gaussian passed through the process function results in another Gaussian. If this is not true then all of the assumptions and guarantees of the Kalman filter do not hold. Let's look at what happens when we pass the output back through the function again, simulating the next step time step of the Kalman filter."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "y=g(data)\n",
-      "plot_transfer_func (y, g, lims=(-4,4), num_bins=300)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAxgAAAGaCAYAAACMmuWeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ8EAAAAAYJn/D53izIyEuoOsAAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bc93e7c18>"
-       ]
-      }
-     ],
-     "prompt_number": 5
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "As you can see the probability function is futher distorted from the original Gaussian. However, the graph is still somewhat symmetric around $0$, let's see what the mean is."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "print ('input  mean, variance: %.4f, %.4f'% (np.average(data), np.std(data)**2))\n",
-      "print ('output mean, variance: %.4f, %.4f'% (np.average(y), np.std(y)**2))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "input  mean, variance: -0.0004, 1.0027\n",
-        "output mean, variance: -0.0268, 2.2466\n"
-       ]
-      }
-     ],
-     "prompt_number": 6
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Let's compare that to the linear function that passes through (-2,3) and (2,-3), which is very close to the nonlinear function we have plotted. Using the equation of a line we have\n",
-      "$$m=\\frac{-3-3}{2-(-2)}=-1.5$$"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def h(x): return -1.5*x\n",
-      "plot_transfer_func (data, h, lims=(-4,4), num_bins=300)\n",
-      "out = h(data)\n",
-      "print ('output mean, variance: %.4f, %.4f'% (np.average(out), np.std(out)**2))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAxgAAAGaCAYAAACMmuWeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bac6b50f0>"
-       ]
-      },
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "output mean, variance: 0.0006, 2.2561\n"
-       ]
-      }
-     ],
-     "prompt_number": 7
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Although the shapes of the output are very different, the mean and variance of each are almost the same. This may lead us to reasoning that perhaps we can ignore this problem if the nonlinear equation is 'close to' linear. To test that, we can iterate several times and then compare the results."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "out = h(data)\n",
-      "out2 = g(data)\n",
-      "\n",
-      "for i in range(10):\n",
-      "    out = h(out)\n",
-      "    out2 = g(out2)\n",
-      "print ('linear    output mean, variance: %.4f, %.4f' % \n",
-      "       (np.average(out), np.std(out)**2))\n",
-      "print ('nonlinear output mean, variance: %.4f, %.4f' % \n",
-      "       (np.average(out2), np.std(out2)**2))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "output_type": "stream",
-       "stream": "stdout",
-       "text": [
-        "linear    output mean, variance: 0.0360, 7502.2648\n",
-        "nonlinear output mean, variance: -1.7522, 26273.4649\n"
-       ]
-      }
-     ],
-     "prompt_number": 8
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Unfortunately we can see that the nonlinear version is not stable. We have drifted significantly from the mean of 0, and the variance is half an order of magnitude larger. "
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "The Extended Kalman Filter"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "The extended Kalman filter (EKF) works by linearizing the system model at each update. For example, consider the problem of tracking a cannonball in flight. Obviously it follows a curved flight path. However, if our update rate is small enough, say 1/10 second, then the trajectory over that time is nearly linear. If we linearize that short segment we will get an answer very close to the actual value, and we can use that value to perform the prediction step of the filter. There are many ways to linearize a set of nonlinear differential equations, and the topic is somewhat beyond the scope of this book. In practice, a Taylor series approximation is frequently used with EKFs, and that is what we will use. \n",
-      "\n",
-      "\n",
-      "Consider the function $f(x)=x^2\u22122x$, which we have plotted below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "xs =  np.arange(0,2,0.01)\n",
-      "ys = [x**2 - 2*x for x in xs]\n",
-      "plt.plot (xs, ys)\n",
-      "plt.xlim(1,2)\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQen/8TF/df2LO60AAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bac8c25c0>"
-       ]
-      }
-     ],
-     "prompt_number": 9
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We want a linear appoximation of this function so that we can use it in the Kalman filter. We will see how it is used in the Kalman filter in the next section, so don't worry about that yet. We can see that there is no single linear function (line) that gives a close approximation of this function. However, during each innovation (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\u221212.75 as the linearization, as in the plot below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def y(x): \n",
-      "    return 8*x - 12.75\n",
-      "plt.plot (xs, ys,c='k')\n",
-      "plt.plot ([1.25, 1.75], [y(1.25), y(1.75)], c='r')\n",
-      "plt.xlim(1,2)\n",
-      "plt.ylim([-1.5, 1])\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bac68e438>"
-       ]
-      }
-     ],
-     "prompt_number": 10
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "This is not a good linearization for $f(x)$. It is exact for $x=1.5$, but quickly diverges when $x$ varies by a small amount.\n",
-      "\n",
-      "A much better approach is to use the slope of the function at the evaluation point as the linearization. We find the slope by taking the first derivative of the function:\n",
-      "\n",
-      " $$f(x) = x^2 -2x \\\\\n",
-      " \\frac{df}{dx} = 2x - 2$$, \n",
-      " \n",
-      " so the slope at 1.5 is $2*1.5-2=1$. Let's plot that."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def y(x): \n",
-      "    return x - 2.25\n",
-      "\n",
-      "plt.plot (xs, ys,c='k')\n",
-      "plt.plot ([1,2], [y(1),y(2)], c='r')\n",
-      "plt.xlim(1,2)\n",
-      "plt.ylim([-1.5, 1])\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAysAAAGNCAYAAAARje6GAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlwVHW+9/FPZ0/IAoSQhYSwhB2yEUGQLYZFRDZRVFR0\nZp7Hmqm7uJTPnest751FZ2451rXEqdEpb90RrsuAyqCg7CKrAYkkLCFAIBCWLJAEEgLZ+zx/9KRJ\np0Nk6aRPJ+9X1aluzvmdzrfx6OQz53x/P4thGIYAAAAAwGS83F0AAAAAALSFsAIAAADAlAgrAAAA\nAEyJsAIAAADAlAgrAAAAAEyJsAIAAADAlAgrAAAAAEzJpWFl586dmjdvnmJjY+Xl5aUVK1b86DmH\nDx/W1KlTFRQUpNjYWL322muuLAkAAACAh3JpWLl27ZoSExO1bNkyBQYGymKxtDu+qqpKM2bMUHR0\ntLKysrRs2TK9+eabeuutt1xZFgAAAAAPZOmoFexDQkL0pz/9SUuXLr3pmPfee0+vvPKKSktL5e/v\nL0n63e9+p/fee0/nz5/viLIAAAAAeAi39qxkZmZq8uTJ9qAiSTNnzlRRUZEKCwvdWBkAAAAAd/Nx\n5w8vKSlR//79HfZFRkbaj8XHx9v3V1ZWdmptAAAAAO5eWFjYHZ/r1jsrP9bTAgAAAKD7cmtYiYqK\nUklJicO+0tJS+zEAAAAA3ZdbHwObMGGCfvnLX6qurs7et7Jlyxb169fP4RGw1u7mVhLQWlZWltLS\n0txdBroYrit0FK4tdASuK7iaq1o4XD51cU5OjnJycmS1WlVYWKicnBydO3dOkvTKK69o+vTp9vFL\nlixRUFCQnn32WeXm5upvf/ub3njjDb300kuuLAsAAACAB3JpWNm/f79SU1OVmpqq2tpa/epXv1Jq\naqp+9atfSbI1zRcUFNjHh4aGasuWLSoqKlJaWpr+6Z/+SS+//LJefPFFV5YFAAAAwAO59DGwadOm\nyWq13vT4Bx984LRv9OjR2rFjhyvLAAAAANAFuLXBHgAAAABuhrACAAAAwJQIKwAAAABMibACAAAA\nwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibAC\nAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABM\nibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAA\nAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQI\nKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAA\nwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibAC\nAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABM\nibACAAAAwJQIKwAAAABMibACAAAAwJQIKwAAAABMqUPCyrvvvquBAwcqMDBQaWlp2r17903Hnjlz\nRl5eXk7b5s2bO6I0AAAAAB7C5WFl1apVeuGFF/Tqq68qJydHEydO1OzZs3Xu3Ll2z9u0aZNKSkrs\nW3p6uqtLAwAAAOBBXB5W3nrrLf3kJz/Rz372Mw0bNkzvvPOOoqOj9d5777V7Xu/evdW3b1/75uvr\n6+rSAAAAAHgQl4aV+vp6HThwQDNnznTYP3PmTH333Xftnvvwww8rMjJSkyZN0urVq11ZFgAAAAAP\n5NKwUlZWpqamJkVGRjrs79u3r0pKSto8JyQkRP/1X/+lzz77TBs2bFBGRoYee+wxffzxx64sDQAA\nAICH8XF3AeHh4XrxxRftf05NTVV5ebn+8Ic/6Mknn2zznKysrM4qD90E1xQ6AtcVOgrXFjoC1xVc\naciQIS75HJeGlT59+sjb21ulpaUO+0tLSxUdHX3Ln3PPPffoL3/5y02Pp6Wl3XGNQGtZWVlcU3A5\nrit0FK4tdASuK7haZWWlSz7HpY+B+fn5aezYsU7TDm/ZskUTJ0685c/JyclRTEyMK0sDAAAA4GFc\n/hjYSy+9pKefflrjxo3TxIkT9ec//1klJSX6+c9/Lkl65ZVXtH//fm3dulWStGLFCvn5+Sk5OVle\nXl5at26d3n33Xf3hD39wdWkAAAAAPIjLw8rixYtVXl6u119/XcXFxRozZozWr1+vuLg4SVJJSYkK\nCgrs4y0Wi15//XUVFhbK29tbw4YN0wcffKAlS5a4ujQAAAAAHsRiGIbh7iJuRcvn3sLCwtxYCboa\nntNFR+C6Qkfh2kJH4LqCq7nqd3eXLwoJAAAAAK5AWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAA\nAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQV\nAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABg\nSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEA\nAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZE\nWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAA\nAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQV\nAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABgSoQVAAAAAKZEWAEAAABg\nSoQVAAAAAKZEWAEAAABgSoQVAAAAAKbk8rDy7rvvauDAgQoMDFRaWpp2797d7vjDhw9r6tSpCgoK\nUmxsrF577TVXlwQAAADAA7k0rKxatUovvPCCXn31VeXk5GjixImaPXu2zp071+b4qqoqzZgxQ9HR\n0crKytKyZcv05ptv6q233nJlWQAAAAA8kEvDyltvvaWf/OQn+tnPfqZhw4bpnXfeUXR0tN577702\nx3/88ceqra3VihUrNHLkSC1atEi//OUvCSsAAAAAXBdW6uvrdeDAAc2cOdNh/8yZM/Xdd9+1eU5m\nZqYmT54sf39/h/FFRUUqLCx0VWkAAAAAPJDLwkpZWZmampoUGRnpsL9v374qKSlp85ySkhKn8c1/\nvtk5AAAAALoHH3f+cIvFckfnZWVlubgSdHdcU+gIXFfoKFxb6AhcV3ClIUOGuORzXBZW+vTpI29v\nb5WWljrsLy0tVXR0dJvnREVFOd1BaT4/Kirqpj8rLS3tLqsFbsjKyuKagstxXaGjcG2hI3Bd4XZd\nvnxZp06duul1U1lZ6ZKf47LHwPz8/DR27Fht3rzZYf+WLVs0ceLENs+ZMGGCdu3apbq6Oofx/fr1\nU3x8vKtKAwAAAHCXmpqatHHjRj322GOKjo7W4sWLZbVaO/RnunQ2sJdeeknLly/X//zP/ygvL0/P\nP/+8SkpK9POf/1yS9Morr2j69On28UuWLFFQUJCeffZZ5ebm6m9/+5veeOMNvfTSS64sCwAAAMAd\nysvL07/+67+qf//+mj17tj799FPV19crISFBFRUVHfqzXdqzsnjxYpWXl+v1119XcXGxxowZo/Xr\n1ysuLk6SrWm+oKDAPj40NFRbtmzRP/zDPygtLU29e/fWyy+/rBdffNGVZQEAAAC4DZcvX9aqVau0\nfPly7du3z74/ISFBP/nJT/T000/bf8fvSC5vsP/FL36hX/ziF20e++CDD5z2jR49Wjt27HB1GQAA\nAABuQ2NjozZv3qzly5dr7dq19laNkJAQPfbYY3r22Wc1ceLEO54k6064dTYwAAAAAO51+PBhrVix\nQh9//LF98iuLxaLp06frmWee0cKFC9WjRw+31EZYAQAAALqZixcvauXKlVqxYoUOHDhg3z906FA9\n88wznfaY148hrAAAAADdQG1trb766iv97//+rzZs2KDGxkZJUs+ePfX444/rmWee0fjx4zv1Ma8f\nQ1gBAAAAuijDMLR3716tWLFCq1at0pUrVyRJ3t7eeuihh7R06VLNnTtXAQEBbq60bYQVAAAAoIsp\nKCjQhx9+qI8++kgnT560709JSdHSpUu1ZMkS9e3b140V3hrCCgAAANAFXL58WZ9++qk+/PBD7dmz\nx74/OjpaTz75pJYuXaoxY8a4scLbR1gBAAAAPFR9fb02bNigDz/8UOvWrVN9fb0kKSgoSAsXLtTS\npUuVkZEhb29vN1d6ZwgrAAAAgAdp7kP58MMPtWrVKvsq8haLRRkZGVq6dKkWLlyokJAQN1d69wgr\nAAAAgAfIz8/XRx99pI8++kgFBQX2/aNGjdLTTz+tJ598UrGxsW6s0PUIKwAAAIBJXbp0SatWrdJH\nH32kffv22ffHxMRoyZIleuqpp5SYmGiq6YZdibACAAAAmMi1a9f05Zdf6qOPPtLmzZvV1NQkSQoO\nDtaiRYv01FNPKT093WP7UG4HYQUAAABws8bGRm3dulUfffSRvvjiC127dk2SbT2UOXPm6Mknn9T8\n+fMVFBTk5ko7F2EFAAAAcAPDMLRv3z598sknWrVqlS5evGg/NmHCBD355JNavHixIiIi3FilexFW\nAAAAgE6Ul5enTz75RJ988olDo/zQoUP11FNPacmSJRo8eLAbKzQPwgoAAADQwc6fP6+VK1fq448/\nVk5Ojn1/dHS0nnjiCS1ZskSpqaldtlH+ThFWAAAAgA5QVlamzz//XH/961+1c+dO+/6wsDA98sgj\nWrJkiaZOndotGuXvFGEFAAAAcJHq6mp9+eWX+uSTT7R582Y1NjZKkgICAvTQQw9pyZIlevDBB+Xv\n7+/mSj0DYQUAAAC4C3V1ddqwYYNWrlyptWvXqqamRpJtJq8HHnhATzzxhBYsWKDQ0FA3V+p5CCsA\nAADAbWpsbNQ333yjlStXas2aNaqsrLQfmzRpkp544gk9+uij3XomL1cgrAAAAAC3wGq1avfu3Vq5\ncqU+++wzlZWV2Y+lpKToiSee0OLFixUfH+/GKrsWwgoAAABwE4Zh6Pvvv9eqVav06aef6sKFC/Zj\nw4YN0xNPPKHHH39cw4YNc2OVXRdhBQAAAGjBMAzl5ORo1apVWrVqlc6cOWM/Fh8fr8cff1xPPPGE\nEhMTmWq4gxFWAAAAAEm5ubn2gHLixAn7/piYGC1evFiPP/64xo0bR0DpRIQVAAAAdFvHjx+3P+KV\nm5tr3x8REaFHH31Ujz32mCZNmiQvLy83Vtl9EVYAAADQrZw8eVKffvqpVq1apUOHDtn39+rVSw8/\n/LAee+wxpaeny8eHX5XdjX8CAAAA6PJOnTqlzz77TJ9++qmys7Pt+8PCwrRw4UI99thjysjIkK+v\nrxurRGuEFQAAAHRJzQHls88+04EDB+z7Q0JCtGDBAi1evFgzZsxgNXkTI6wAAACgy2gvoMybN0+L\nFy/WzJkzFRAQ4MYqcasIKwAAAPBo+fn59oCSk5Nj3x8cHKz58+fr0Ucf1axZswgoncFqlQoKpIgI\nl3wcYQUAAAAe59ixY/r888/12WefOTTJh4SEaO7cuVq8eDEBpaPV10tHj0o5OVJ2tm3LyZGuXpWu\nXHHJjyCsAAAAwPQMw9CRI0e0evVqff755w7TDIeFhWn+/Pl65JFHNGPGDAJKR6iulg4evBFKsrOl\n3FxbYGktOtplP5awAgAAAFMyDEMHDhywB5T8/Hz7sZ49e2rBggV69NFHlZGRQZO8K1286BhKsrOl\nkyclw3AeO2SIlJwspaTc2CIjpcpKl5RCWAEAAIBpWK1W7du3T6tXr9bq1at15swZ+7E+ffpo4cKF\nWrRokdLT0+Xn5+e+QrsCw5BOn3YMJTk5UlGR81hfX2nUKMdQkpQkhYR0aImEFQAAALhVY2Ojdu3a\npdWrV2vNmjUqavHLclRUlB5++GE98sgjmjx5Mgs13qmGBikv70YgaX5t6w5IcLDz3ZKRIyU3hEP+\naQMAAKDT1dfX65tvvtHq1av15ZdfqqyszH6sf//+WrhwoR555BFNnDhRXl5ebqzUA127Zusvadn4\nfuSIVFfnPDYy0jGUJCdLgwdLJvk7J6wAAACgU1RXV2vjxo1as2aNvvrqK1VVVdmPDRkyRIsWLdKi\nRYs0duxYWSwWN1bqQcrKnPtLTpxou79k8GDHUJKS4tJm+I5AWAEAAECHKS8v17p167RmzRpt3rxZ\ntbW19mNjxoyxB5RRo0YRUNpjGFJhoXMwuXDBeayPz43+kuZQkpQkhYV1ft13ibACAAAAlzp//ry+\n+OILrVmzRjt27FBTU5P92IQJE/Twww9r4cKFGjx4sBurNLHGRunYMefG97bWLunRwxZEWj7KNWqU\n1EVmRyOsAAAA4K7l5eVpzZo1WrNmjbKysuz7vb29NX36dD388MOaP3++YmJi3FilCV2/Lh065BhK\nDh+WWtyBsouIcAwlKSlSQoJp+ks6AmEFAAAAt81qtWr//v1as2aNvvjiCx0/ftx+LDAwUA888IAW\nLFighx56SL1793ZjpSZSXu44G1d2tnT8uGS1Oo8dONA5mERHS93sUTnCCgAAAG5JXV2dtm3bpi+/\n/FJr165VcXGx/Vjv3r01d+5cLVy4UDNmzFBQUJAbK3Uzw5DOnXPuLzl3znmst7c0Zoxj43tystSz\nZ+fXbUKEFQAAANzUlStXtH79en3xxRfasGGDqqur7cf69++v+fPna+HChd13DZSmJtvdkdb9JRUV\nzmODgm70lzQ3vo8eLQUEdH7dHqIbXlEAAABoT2FhodauXau1a9dq+/btamxstB9LSkrSggULNH/+\nfCUnJ3evGbxqamz9JC2DyeHDtv2t9enjGEpSUqQhQ2x3UnDLCCsAAADdnGEYOnDggP3xrpycHPsx\nb29vTZs2zR5QBgwY4L5CO9Ply453SrKzbTN0tZjZzC4+3rm/pF+/btdf0hEIKwAAAN1QXV2dtm/f\nrrVr1+rzzz/XxYsX7ceCg4P1wAMPaN68eXrwwQcVHh7uxko7mGFI5887N74XFjqP9fa+sX5J85aU\nJDGBQIchrAAAAHQTZWVlWr9+vdauXatNmzY59J9ER0dr3rx5mj9/vtLT0xXQFfsompqk/Hznxvfy\ncuexgYFSYqJj4/uYMbb96DSEFQAAgC7KMAwdP35c69at09q1a/Xdd9/J2mKa3KSkJM2dO1cJCQl6\n+umn5dWV1uuorZWOHHEMJYcO2dY1aa13b8dQkpIiDR1qWwkebsU/AQAAgC6koaFBu3bt0rp16/TV\nV1/p5MmT9mO+vr6aPn265s6dq7lz5yo+Pl6SlJWV5dlB5coVx0e4srOlvLy2+0v693dsek9JkeLi\n6C8xKcIKAACAhysvL9eGDRu0bt06bdy4UVVVVfZj4eHhmj17tubNm6dZs2YpNDTUjZXeJcOQioqc\npwk+fdp5rJeXNGKEYyhJTpa6cv9NF0RYAQAA8DCGYSg3N1dfffWVvvrqK2VmZjo83jVy5EjNnTtX\nDz30kCZMmCBvT5wu12q90V/S8q7JpUvOYwMCHBdWTEmx/bk7L0zZRRBWAAAAPEBtba2+/fZbe0A5\ne/as/Zivr6/S09Ptj3cNGjTIjZXegbo6W39Jy1By8KB07Zrz2J49nacJHjaM/pIuin+qAAAAJnX2\n7FmtX79eX3/9tbZt26brLZrD+/btqzlz5mjOnDmaMWOG5zzeVVlpCyItH+U6elRqsfCkXWysc+N7\nfDz9Jd0IYQUAAMAkGhsblZmZqa+//lpff/21jhw54nA8NTVVDz30kObMmaO0tDTzN8UXFztPE1xQ\n4DzOYpGGD3cMJcnJUkRE59cMUyGsAAAAuNHFixe1ceNGrV+/Xps2bdKVK1fsx4KDgzVjxgzNmTNH\ns2fPVkxMjBsrbYfVKp065bzie2mp81g/P+f+ksREqUePzq8bpkdYAQAA6ERNTU3KysrS+vXrtX79\nemVlZTkcHzp0qP3xrkmTJsnf399Nld5Efb2Um+sYSg4elK5edR4bFuY8TfDw4ZKvb+fXDY9EWAEA\nAOhgZWVl2rRpkzZs2KCNGzeqvMWK6f7+/kpPT9eDDz6o2bNnKyEhwY2VtnL1qnN/SW6u1NDgPDYm\nxrnxfcAA+ktwVwgrAAAALtbU1KT9+/fbw8n+/ftlGIb9+IABA+yPdqWnpyvIDFPslpY695e0WFDS\nzmKxre7eev2Svn07v2Z0eYQVAAAAFygtLdXmzZu1YcMGbd682eHuiZ+fn6ZMmaLZs2frwQcf1LBh\nw2Rx1x0Hq9W2iGKLUJL4/fdSi3rt/Pyk0aMdG9+TkqTg4M6vG90SYQUAAOAONDQ0KDMzUxs3btSm\nTZt04MABh+MDBw7U7Nmz7XdPerijgbyhwTYtcMu7JQcPSi1WuJckP0kKCXHuLxkxwhZYADchrAAA\nANyiwsJCbdq0SRs3btTWrVt1tUVTeUBAgKZNm6ZZs2Zp9uzZGjp0aOfePamuvtFf0tz4fuSIrSG+\ntagoh1By2MdHY+bNk8w+FTK6HZeFlbq6Or388stauXKlampqlJGRoXfffVf9+vW76TnLly/XT3/6\nU4d9FotFNTU18iPFAwAAN7t27Zq2b9+uTZs2adOmTTpx4oTD8REjRuiBBx7QrFmzNGXKFAUGBnZO\nYRcvOoaS7GwpP19q0Rdjl5Dg3F8SFeUwpC4ri6ACU3JZWHnhhRe0du1arVy5Ur1799ZLL72khx56\nSD/88EO7CxYFBQXp9OnTDk1nBBUAAOAOVqtVhw4d0ubNm7Vp0ybt3r1b9S3uTISGhiojI8MeUOLj\n4zu2IMOw9Ze0DCXZ2VJRkfNYX19p1CjHUJKUJHnKyvZAG1wSViorK/WXv/xFy5cvV0ZGhiTpww8/\nVHx8vLZu3aqZM2fe9FyLxaIIVicFAABuUlxcrC1btmjz5s3asmWLLl68aD9msVg0btw4zZo1SzNn\nztT48ePl21FrhDQ0SMeOOYaSnBypstJ5bHCw40rvKSm2oML/4YsuxiVh5YcfflBDQ4NDKImNjdWI\nESP03XfftRtWampqNGDAADU1NSk5OVmvvfaakpOTXVEWAACAk5qaGu3atUubN2/W5s2bdfjwYYfj\n/fr108yZMzVr1ixNnz5d4eHhri/i2jXp0CHHYHLkiFRX5zy2b1/n9UsGD+axLXQLLgkrJSUl8vb2\ndvqXOTIyUqWlpTc9b/jw4frggw+UlJSkqqoqLVu2TPfdd58OHjxorgWRAACAx7JarcrOztaWLVu0\nZcsW7dmzR3UtQkFQUJCmTZummTNnasaMGRoxYoRrG+PLyhzvlGRnS8ePt91fMmiQczCJjnZdLYCH\nsRhGW/+m2Lz66qv6/e9/3+4HbN++XefPn9czzzyjhlarmWZkZGjo0KF67733bqkYq9WqlJQUTZs2\nTcuWLXM4VtniFmh+fv4tfR4AAOieioqKtG/fPn3//ffav3+/w+8RFotFw4YN0/jx43XvvfcqMTHR\nNf2yhiG/4mIFHT+uoBMnbK/Hj8uvxWNlzaze3qodNEjXhw7V9WHDdH3YMNUMHaom1i9BFzFkyBD7\n+7CwsDv+nHbvrLz44otaunRpux8QFxenxsZGNTU1qby83OHuSklJiaZMmXLLxXh5eSk1NfVHw0ha\nWtotfybwY7Kysrim4HJcV+goXFttKy8v17fffqutW7dq69atOnXqlMPx+Ph4zZgxQzNmzND999+v\nPn363N0PbGy03R1p3V9y+bLz2B49bI3uLe6WeI0apSB/f5lg3XpJXFdwvcq2eq3uQLthJTw8/Jae\n0xw7dqx8fX21efNmPfHEE5Kk8+fP69ixY5o4ceItF2MYhg4ePKjU1NRbPgcAAHQ/NTU12rNnjz2c\nHDhwwGFm0bCwMKWnp9sDSkJCwp0/2nX9unT4sGMwOXxYqq11HhsR4TgbV0qKbepgb+87/KZA9+aS\nnpWwsDD97Gc/07/8y7+ob9++9qmLk5KSNH36dPu4jIwMjR8/3v5o2W9+8xtNmDBBCQkJqqqq0jvv\nvKPc3Fy9//77rigLAAB0EY2Njdq/f7+++eYbffPNN/ruu+8cphT28/PTfffdp+nTp2v69OlKTU2V\nj88d/JpTUeEYSpr7S6xW57EDBzqv+B4TI3XmQpBAF+eydVbefvtt+fj46LHHHlNNTY2mT5+ujz76\nyOH/xSgoKHCYj7yyslLPPfecSkpKFBYWptTUVO3cuZPbkAAAdHNWq1W5ubn2cLJjxw6H1eItFotS\nUlI0Y8YMZWRkaNKkSQoKuo2HqgxDOnfOufH97Fnnsd7e0ujRzgsr9uzpgm8KoD3tNtibScvn3u6m\nSQdojed00RG4rtBRuuq1ZRiGTp48qW3btmnbtm369ttvdenSJYcxQ4YMUUZGhqZPn65p06bd+pTC\nTU03+ktaLq5YUeE8NihISkx0DCajR0sBAS74lubVVa8ruI+rfnd32Z0VAACA23H27Fl9++239oBy\n/vx5h+MxMTG6//77lZGRoYyMDMXFxf34h9bU2PpJWoaSQ4ds+1sLD3e+WzJ0KP0lgIkQVgAAQKco\nKirSt99+a98KCgocjvfp00fp6em6//77df/992vIkCHtN8VfvuwYSrKzbSvANzU5j42Pd258j42l\nvwQwOcIKAADoEKWlpdq+fbs9nJw4ccLheFhYmKZMmWIPJ6NHj5ZXW6uyG4Z04YJz43thofNYLy9p\n1CjHxvfkZKl37w76lgA6EmEFAAC4RElJiXbs2KHt27dr+/btOnbsmMPx4OBgTZ48Wenp6UpPT1dK\nSoq8Wz+4B2voAAAgAElEQVRy1dQk5ec7r19SVub8AwMCnPtLxoyRAgM78FsC6EyEFQAAcEeKi4u1\nY8cOe0BpHU6CgoI0adIkTZs2Tenp6fZ12exqa51n4zp40LauSWu9ejmGkpQUW3/JnUxPDMBj8G84\nAAC4JefOnbOHkx07dig/P9/heMtwMm3aNKWlpd0IJ1euSN9953jHJC/PthJ8a3FxzsEkLo7+EqAb\nIqwAAAAnhmHo9OnT2rlzpz2cnD592mFMcHCw7rvvPk2dOvVGOPHxkYqLbWHkjTduBJNW50qy9ZeM\nGOHc+H6rUxID6PIIKwAAQIZhKC8vTzt37rRvFy5ccBgTGhqqyZMna+rUqZo6dapSk5Plc+aMLYx8\n+aX061/b3rdaH0WS5O9/o7+kOZQkJtrWNQGAmyCsAADQDTU2Nio7O1u7du3Srl27tHv3bpW1amIP\nDw/XlClTNGXKFE29914lenvL+9AhWyB56SVbf0l1tfOH9+zpGEpSUqThw+kvAXDb+K8GAADdQE1N\njfbt26edO3dq165dyszM1LVr1xzGREdHa+rUqcq45x5lhIcr/vJleR08KC1fLv2//9d2f0m/fs79\nJfHx9JcAcAnCCgAAXVBZWZn27Nmj3bt3a/fu3frhhx/U0NDgMCYhIUEPjR2rB6Ojlerlpd5nz8qy\nf7+0cqXzB1os0rBhziu+R0R00jcC0B0RVgAA8HCGYejUqVMO4aT1NMJekuaOGKEF8fGaEBCgQZWV\n8j96VFq1yvkD/fxs65W0DCWJiVJwcOd8IQD4O8IKAAAepr6+XtnZ2dqzZ499Ky0ttR/3lTTOz08P\nDxyoKaGhGn79unqePStLXp5tuuCWwsJu9JY0v44YIbVcDwUA3ISwAgCAyZWXl2vv3r3as2ePNm7c\nqLy8PNXW1kqSgiUlSfpJjx7KCA/XmMZGRVy8KK/6eun4cccPiolxbHpPSZEGDqS/BIBpEVYAADAR\nq9Wq48eP67vvvrNvzY909ZWUImmWpCkhIUqxWBR59aoshiFdu2bbmg0Z4txfEhnpjq8EAHeMsAIA\ngBtdvXpV33//vTIzM5WZmam9e/eqoqJCg2QLJk9KGuvlpXt8fNSnvr7libZXX19p9GjHYJKYKIWE\nuOHbAIBrEVYAAOgkhmEoPz/fHkwyMzN17PBhDTcMJUuaIelfJKVYLAo1jBsnWq1Sfb0UEqKrCQkK\nmTz5xt2SkSNtDfEA0AURVgAA6CCVlZX6/vvvtXfvXu3du1eHMzMVe/myUiSlSfq/kkZL8m99omFI\nUVGOj3ClpEiDBun4gQNKS0vr7K8CAG5BWAEAwAWampp09OhR7du3T3v37tXx3bsVdPy4kmV7nOtR\nSUNlm0LYSUKC84rvUVGdWT4AmBJhBQCAO1BcXGwLJpmZKtyxQ14HD2p4ba2SJf1aUmwb5xg+PjJG\njZKlZX9JUpIUGtq5xQOAhyCsAADwI6qrq/XDDz9of2amirdtk/WHHxRXUaEUSb+U1KuNc5qCgmRJ\nSpLX2LH2YGIZOVLyd3roCwBwE4QVAABaaGho0JEjR5S9e7dKtmxRU1aWooqLlSzpHyUFtHFOXViY\nlJoq//Hj7cHEe/BgyavNh74AALeIsAIA6LasVqvy8/N1cNs2Xdq8WcaBA4o4f16JVquekeTdxjlV\nEREykpMVMnmyvFJTpZQU+UdHs7AiAHQAwgoAoFswDENnCwt1dONGlW3ZIiM7WxHnzml0Y6MWtzG+\n0WLRpehoGUlJ6pmeLr9x46TkZIWGhXV67QDQXRFWAABdUtHZszq+dq3Kt26V18GDirhwQaMaGjS7\njbG13t4qi4mRkZys3hkZ6jFpknxGjVJEQFsPfQEAOgthBQDg8YpPndLJNWtUuX27vA8fVmRxsUY0\nNCi9jbFXfH1VFhsra3Ky+kyfrt4ZGQpISFCsd1sPfQEA3ImwAgDwGIZhqOjIERV+8YWu7tolv6NH\nFVNaqoTGRkW3Mb44IEDlcXFSSor6zJihyFmz1DM2Vj3pLwEAj0BYAQCYkmG16lxmps6vW6ea775T\n4PHjiisrU5zVqn6txjZKKujRQ5fj42UZO1aRM2cqevZsRYeHtxliAACegbACAHC7pvp6nd60SSUb\nNqjh++8VWlCgAVeuqL9hqH+rsdclnQkNVeWgQfJJS1PU7NnqN2uWBvXo4Y7SAQAdiLACAOhU1ysq\ndPrvje/Kzlavs2c1qLpaCZISWo2tsFhU2KuXqocMkf+99ypmzhz1S0/XSB/+5wsAugP+aw8A6DCX\nTpxQ4Zdf6urOnfI5ckSRxcUaVFenUW2MPe/trQsREaodMUJB992nuHnzFDl2rHqzsCIAdFuEFQDA\nXWtqbFTBrl0qXr9edfv2KejECcWVlal/U5MiWo+VdNLfX6XR0WoYPVqhU6dq4MKFih08WLHuKB4A\nYFqEFQDAbblcVqb8DRtU/s030oED6lVYqMFVVRoiaUirsTWSCoKDVdG/v21GrunTNWDuXCWEhzs9\n8gUAQGuEFQBAmxoaGpR/5IjOrl+v63v2yO/oUUUVF2t4fb3GtTH+ipeXCnv3VnVCgnzHjVPUAw8o\nNiNDo/z8Or12AEDXQFgBgG7OMAwVFRUpb+9eXdqyRU1ZWQr7+2xcww1DI9s4p8TPTyVRUaofOdLe\nX9JzzBjWLwEAuBRhBQC6kcuXL+vI4cM6tXu3ru/ZI98jR9S3uFijGxo0vY3xVknngoN1OT5eRnKy\nemdkKObBBxUVGamozi4eANDtEFYAoAu6evWqjh49qtzDh1W6Z4+MAwcUUlCgIdXVSpE0uY1z6i0W\nFUdE6PqwYQq49171nTVLPe69V3E9eiius78AAAAirACAR6uurtaxY8eUm5ur44cOqfr77xWQl6e4\n8nKlSHpUUkgb51339VV5//5qSkpSz2nTFDZ1qvxGjFC8r28nfwMAAG6OsAIAHqCqqkp5eXnKy8vT\n0aNHVZCTI6/DhxVVUqIUSSmSnpDUVit7VWiorg8dKr/x4xU2bZq8x45V0IABCqK/BABgcoQVADCR\nS5cuOYSSvLw8XWoVSp6T80rvkmRYLKqKjpaRlKTgSZPknZYmpaQoNCJCoZ37NQAAcAnCCgB0MqvV\nqsLCQuXl5enYsWP2cHI8L09hFRX2UPKApH+VFN3GZzT5+Kjh73dLvMaOlVJSZElMVGhwcKd+FwAA\nOhJhBQA6yNWrV3XixAkdO3ZMx48ft7+eOHFCTbW1GilbKEmW9PTfX9u6A9IUHCyvlBRZUlOllBQp\nJUXeI0bIm/4SAEAXR1gBgLvQ1NSkM2fO2ENI8+uRI0d08eJFSVKwpETZgsmsv7+OkuTfxucZ0dGy\n/D2Q2IPJgAGSl1cnfSMAAMyDsAIAP8IwDJWUlOjEiRPKz8+3vx4/flynTp1SfX29fWyEbGHkJ5LG\nennpHh8f9a+vV5tRY8iQG6EkOdn2KFdkZOd8KQAAPABhBQBkCySXLl3SyZMnlZ+f77RVV1c7nTNQ\n0kOSpoaEaLyfn4bV1Kjn9es3BlitUn295OsrjR7tEEqUlCSFtDWpMAAAaEZYAdBtGIah0tJSnTx5\nUqdOndLJkycdwklVVVWb5/lImhQaqpkRERrn56fhNTWKvnhRfs3B5OrVG4ODg6XkZJX266fIWbNs\nwWTkSMmvrUmFAQBAewgrALqUxsZGnT17VgUFBTp16pQ9lDS/v3bt2k3PDQ0N1ZhBg3R/nz4a5+Oj\nYTU1ii4tVY/Tp2WpqpJah5nISIfeEqWkSIMGSV5eOpeVpci0tA7+tgAAdG2EFQAep7KyUgUFBTp9\n+rQ9lDS/FhYWqrGx8abn9urVSwkJCUpISNCYqCiN9fbW0OvXFVVcLP+jR2U5eFAyDOcTBw92DCXJ\nyVJ0W5MKAwAAVyGsADCduro6FRYW6vTp0zpz5ow9lDQHlIqKinbP79evnwYPHqxBgwZp8ODBGjxo\nkEb26KFBlZUKOXlSys6Wdu6ULlxwPtnHRxo1yjGUJCVJYWEd9G0BAMDNEFYAdLr6+nqdO3dOhYWF\nOnPmjD2QNIeToqIiGW3d3fi7wMBADRo0SIMGDdLAgQMdgsmA2FgFFhbaAkl2tvTNN9J//Zd05Yrz\nB/XoYQsjzU3vKSm2oOLf1qTCAACgsxFWALjc9evXdfbsWRUWFqqwsND+vjmYXLhwod0w4u3trbi4\nOA0cOFADBgzQwIED7eFk0KBB6tu3rywWi3T9unTokC2UrF1rez18WKqrc/7QiAjn/pKEBNYvAQDA\nxAgrAG6L1WrVxYsXdfbsWZ09e1bnzp2zv28OJ2VlZe1+hpeXl+Li4hQfH68BAwYoPj5eAwcOtIeT\nuLg4+fi0+s9TebktjPzv/0o5Obb3x4/bpgdubeBA52ASHS1ZLC78mwAAAB2NsALAzjAMVVRU6Ny5\nczp//rzOnTtn31r+ueUiiG3x8/Ozh5H4+Hj179/fHkwGDBig2NhY+fr63qwI6exZWxhpDiXZ2dK5\nc85jvb2lMWMcQ0lSktSzpwv+NgAAgLsRVoBuoqmpSZcuXdKFCxd0/vx5h63lvpqamh/9rD59+qh/\n//6Ki4tT//797e+bw0lkZKS8buXxqsZG292RlqEkJ0dqq4E+KMgWRFo2vo8eLQUE3MHfBgAA8ASE\nFcDDGYahq1evqqioyL5duHDBaSspKWl3St9moaGhiouLs2+xsbEOf46Li1NQUNDtF1pTY+snaQ4l\nzf0lbYWjPn0cQ0lKijRkiO1OCgAA6DYIK4BJGYahK1euqLi4WMXFxSopKbG/Ly4udggn7S102FJ4\neLj69eun2NjYNrd+/fopNDT07ouvqHC+W3LsmNTU5Dx2wADH2bhSUqR+/egvAQAAhBWgs9XU1Ki0\ntFSlpaUqKSlpd6utrb2lzwwMDFS/fv0UExOj6Oho+/t+/frZt5iYGAW4+pEpw5DOn3cMJdnZUmGh\n81hvb8f1S5rvmvTq5dqaAABAl0FYAe5S8x2QixcvOmylpaX215bb1atXb/mzg4ODFR0d3ebWr18/\nRUdHKyYmRqGhobapfDtSU5N04oRz43t5ufPYwEApMdExmIwebdsPAABwiwgrQCtNTU2qqKhQWVmZ\nysrKdOnSpXa3ixcv3lIvSDNfX19FRkYqMjJSUVFRbW6RkZGKjo5WcHBwB37TdtTWSkeOOPaXHDpk\nW9ektd69ne+WDBtGfwkAALhrhBV0afX19aqoqFB5eflNt1OnTqmxsdEeTioqKtpdsLAtoaGh6tu3\nr9MWGRlpf23eevbs2fF3QW7HlSuOd0qys6W8vLb7S/r3d258j4ujvwQAAHQIwgpMz2q1qqqqSpcv\nX77pVlFR0eZWXV19Rz+zd+/e6tOnj8LDwxUREdHu1rdvX9f3gnQEw5CKihxDSXa2dOaM81gvL2nk\nSMfG9+RkKTy808sGAADdl8vCyvvvv6+//vWvys7OVlVVlc6cOaP+/fv/6HmrV6/Wv//7v6ugoECD\nBw/W7373Oy1YsMBVZcHNDMNQbW2tqqqqVFVVpcrKSl25ckWVlZUOW/O+K1euOG2VlZW3faejmY+P\nj3r16qXw8PCbbpcvX9aECRPUp08f9enTR7169XJePd3TWK1Sfr5jKMnJkS5dch4bEOC8sOKYMbZ1\nTQAAANzIZb+R1dTU6IEHHtCCBQv04osv3tI5mZmZevzxx/Xb3/5WDz/8sFavXq1HH31Ue/bs0bhx\n41xVGm5TU1OTqqurHbarV6/aX2+2VVVV2V9bbg0NDXddU0hIiHr16mXfevfu7fDn5kDSu3dvhy0k\nJORHH7nKyspSWlraXdfoNnV1N/pLmh/nOnhQams64549HUNJSoqtv8TTwxkAAOiSXPYbyvPPPy/J\n9ovfrXr77bd1//3365VXXpEk/du//Zu+/fZbvf322/rkk09cVVqX0tjYqJqamptu169ft7+/du2a\nrl+/bn9tfn+zrbq6WteuXbvl6XJvlb+/v0JDQxUaGqqwsDCnrWfPnvb3vXr1Us+ePR220NBQz7/T\n4SqVlbZA0rLH5OhR20rwrcXGOje+x8fTXwIAADyGW38D3Lt3r/75n//ZYd/MmTP1pz/9qcN+pmEY\nMgxDTU1NslqtampqctgaGxud3jc2NqqxsVENDQ1O7xsaGtTQ0KD6+vqbvtbX16uurs7+vuWfa2tr\nVVdXp7q6Oof3zX+uqalxeG1qq+m5AwQHBys4OFghISH29y33hYaGKiQkxGlrDiTN4SQ0NFT+/v6d\nUnOXU1zs3F9SUOA8zmKRhg93bnzv06fzawYAAHAht4aVkpISRUZGOuyLjIxUSUlJu+f1+fsvYS37\nGAzDkNVqdXht+b45nFitVtd/kU7k5eWlwMBABQQEKDAwUEFBQQoMDGzzfY8ePRQUFOSwNe/r0aOH\nwxYcHGx/HxgYKC8vL3d/1e7DapVOnXLuLyktdR7r72/rJ2nZ+J6YKPXo0fl1AwAAdLB2w8qrr76q\n3//+9+1+wPbt2zVlyhSXFvVjyttahO42WCwWeXl5OW0+Pj72997e3vL29ra/9/Hxsb+2fO/t7S1f\nX1/7/uateZ+vr2+7m5+fn33z9fWVv7+/w35/f3/5+/vb33fE41DNd3Lu9u/Vk93O44t3w9LQoICC\nAgUdP27bTpxQUH6+vNvoL2kMDlbN0KG6PmyYfasdMEBG62sgL69Tasft66zrCt0P1xY6AtcVXGnI\nkCEu+Zx2f/N98cUXtXTp0nY/IC4u7o5/eFRUlNNdlNLSUkVFRbV73sWLF+1N0y2bp5uDhsVisQeS\n5vctw4ep1riA23VYg31Vla3RvWXje26u1NaEAzExTo3vPgMGKMRiUYjrK0Mn8PiJG2BaXFvoCFxX\ncLXKykqXfE67YaV5ateOMmHCBG3ZskUvv/yyfd+WLVt03333tXteREREh9UE3JGSEueFFU+edB5n\nsUhDhzo3vvft2/k1AwAAmJzLnikqKSlRSUmJTpw4IUnKzc1VRUWF4uPj1atXL0lSRkaGxo8fb3+0\n7Pnnn9eUKVP0xhtvaP78+VqzZo22b9+uPXv2uKoswLWsVun0aefG97b6rPz8pNGjHUNJUpIUHNz5\ndQMAAHggl4WVP//5z/rtb38ryfZo1pw5c2SxWPTBBx/YHyUrKChQfHy8/ZwJEyZo5cqVevXVV/Uf\n//EfSkhI0Keffqp77rnHVWUBd66hwTYtcMtQcvCg7fGu1kJDbWGkZeP7iBG2wAIAAIA74rKw8utf\n/1q//vWv2x1z+vRpp32LFi3SokWLXFUGcGeqq2/0lzT3mBw5ItXXO4+NjnYMJSkp0sCBEjOoAQAA\nuBQr7aH7uXjRIZSMzsyUzp2TWkyFbZeQ4Lzie6vptgEAANAxCCvougzjRn9Jy+b3oiKHYQGS5Osr\njRrlGEoSE22PdwEAAMAtCCvoGhoapGPHnBdWbGvavOBgh8e4cv38NOrRR+kvAQAAMBnCCjzPtWvS\noUOOweTIEamuznlsZOSNmbia75gMHuzQX1KTlUVQAQAAMCHCCsytrMx5muATJ9ruLxk82LnxPTq6\n82sGAACASxBWYA6GIRUWOj7ClZ0tnT/vPNbHRxo50jGUJCVJYWGdXzcAAAA6DGEFna+x0dZf0rLp\nPSdHunzZeWyPHrYg0jKYjBol+ft3ft0AAADoVIQVdKzr16XDhx0f4zp8WKqtdR4bEeE8TfDgwZK3\nd+fXDQAAALcjrMB1Kiqc+0uOH5esVuexAwfeCCTNfSYxMZLF0vl1AwAAwJQIK7h9hmFbRLH1NMFn\nzzqP9faWxoxxDCXJyVLPnp1fNwAAADwKYQXta2qy3R1p3fheUeE8NijItpBiy8e4Ro+WAgI6v24A\nAAB4PMIKbqipudFf0hxKDh2y7W8tPNy5v2TIEPpLAAAA4DKEle7q8mXH2biys20zdDU1OY+Nj3cM\nJcnJUmws/SUAAADoUISVrs4wpAsXnBvfCwudx3p52aYFbhlKkpOl3r07v24AAAB0e4SVrqSpScrP\nd258LytzHhsYaOsvabni+5gxtv0AAACACRBWPFVtrXTkiGMwOXTItq5Ja716OfeXDB1qWwkeAAAA\nMCl+W/UEV67c6C9pfs3Ls60E31pcnHMwiYujvwQAAAAeh7BiJoYhFRU5hpLsbOn0aeexXl7SiBHO\nje/h4Z1fNwAAANABCCvuYrVKJ086N75fuuQ8NiDgxsKKzaEkMdG2rgkAAADQRRFWOkNdnZSb6xhK\nDh6Url1zHtuzp2MoSUmRhg+nvwQAAADdDr8Bu1pVleMjXDk5tqDSVn9JbKzjbFwpKbY1TegvAQAA\nAAgrd6W42DGUZGdLp045j7NYpGHDnPtLIiI6v2YAAADAQxBWboXVagshrRvfS0udx/r5OfaXNK9f\nEhzc+XUDAAAAHoyw0lp9vXT0qHN/ydWrzmPDwhwf40pOts3Q5evb+XUDAAAAXUz3DitXr9qCSMtg\nkpsrNTQ4j42JcWx6T0mRBg6kvwQAAADoIN0nrJSWOk8TfPKk8ziLxba6e+vG9759O79mAAAAoBvr\nemHFMKSCAufG9+Ji57G+vtLo0Y6hJDFRCgnp/LoBAAAAOPDssNLQcKO/pDmU5OTYpg9uLSTE+W7J\niBG2hngAAAAApuOZYeX//B9bMDlyxNYQ31pUlPM0wYMGSV5enV8rAAAAgDvimWHlf/7nxvuEBOcV\n36Oi3FcbAAAAAJfwzLCybJktlCQlSaGh7q4GAAAAQAfwzLDyz//s7goAAAAAdDCaOAAAAACYEmEF\nAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACY\nEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAA\nAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkR\nVgAAAACYEmEFAAAAgCkRVgAAAACYEmEFAAAAgCkRVgAAAACYksvCyvvvv6/09HT17NlTXl5eOnv2\n7I+es3z5cnl5eTls3t7eqq+vd1VZAAAAADyUy8JKTU2NHnjgAf3mN7+5rfOCgoJUWlqqkpISlZSU\nqLi4WH5+fq4qCwAAAICH8nHVBz3//POSpKysrNs6z2KxKCIiwlVlAAAAAOgi3N6zUlNTowEDBigu\nLk5z585VTk6Ou0sCAAAAYAIWwzAMV35gVlaWxo0bpzNnzqh///7tjt27d6/y8/OVlJSkqqoqLVu2\nTOvXr9fBgweVkJDgMLaystKVZQIAAADoBGFhYXd8brt3Vl599VWnBvjW286dO+/4h9977716+umn\nlZiYqEmTJmnVqlVKSEjQH//4xzv+TAAAAABdQ7s9Ky+++KKWLl3a7gfExcW5rBgvLy+lpqYqPz/f\nZZ8JAAAAwDO1G1bCw8MVHh7eWbXIMAwdPHhQqampTsfu5vYRAAAAAM/jstnAmqcePnHihCQpNzdX\nFRUVio+PV69evSRJGRkZGj9+vH7/+99Lkn7zm99owoQJSkhIUFVVld555x3l5ubq/fffd1VZAAAA\nADyUy2YD+/Of/6zU1FQ99dRTslgsmjNnjsaOHat169bZxxQUFKikpMT+58rKSj333HMaOXKkZs2a\npeLiYu3cuVNpaWmuKgsAAACAh3L5bGAAAAAA4ApuX2dFknbu3Kl58+YpNjZWXl5eWrFixY+ec/jw\nYU2dOlVBQUGKjY3Va6+91gmVwpPc7nW1fft2zZ8/XzExMerRo4eSkpL0wQcfdFK18BR38t+rZvn5\n+QoJCVFISEgHVghPdafX1ttvv63hw4crICBAMTExeuWVVzq4UniSO7mu1q9fr3vvvVehoaGKiIjQ\nggULmPwIDv7zP/9T99xzj8LCwtS3b1/NmzdPubm5P3renfz+boqwcu3aNSUmJmrZsmUKDAyUxWJp\nd3xVVZVmzJih6OhoZWVladmyZXrzzTf11ltvdVLF8AS3e11lZmYqKSlJq1evVm5urn7xi1/oueee\n01//+tdOqhie4Havq2b19fV6/PHHNXXq1Fs+B93LnVxbL730kt577z29+eabOnbsmDZs2KCpU6d2\nQrXwFLd7XZ08eVILFizQtGnTlJOTo61bt6q2tlYPPvhgJ1UMT7Bjxw794z/+ozIzM7Vt2zb5+Pho\n+vTpunz58k3PuePf3w2TCQ4ONlasWNHumHfffdcICwszamtr7ftef/11o1+/fh1dHjzUrVxXbVm8\neLGxaNGiDqgIXcHtXFcvvPCC8dOf/tRYvny5ERwc3MGVwdPdyrV17Ngxw9fX1zh27FgnVQVPdyvX\n1WeffWZ4e3sbVqvVvm/btm2GxWIxysvLO7pEeKjq6mrD29vb+Oqrr2465k5/fzfFnZXblZmZqcmT\nJ8vf39++b+bMmSoqKlJhYaEbK0NXU1lZqd69e7u7DHi4r7/+Wl9//bX++Mc/yqBNEC7y5ZdfatCg\nQVq/fr0GDRqkgQMH6tlnn9WlS5fcXRo82H333afg4GD993//t5qamnT16lUtX75c48aN438PcVNV\nVVWyWq32GYDbcqe/v3tkWCkpKVFkZKTDvuY/t5xtDLgbX331lbZt26bnnnvO3aXAgxUVFem5557T\nxx9/rKCgIHeXgy6koKBAhYWF+vT/t3M3IcmsYRiAby2hIsmVpNEfSAs3URIkWCs3Cf0sKugPVIKQ\nIMld0EZduW4VBEXWoi9q2SZI+4cQGykpCIRqkbV3IZTvWTUcO9/5DlnnzPid+4IXdHyFZ+BBnxtm\n5scPrK+vIxqN4vb2Fv39/QzFVDKTyYS9vT0sLi6iqqoKBoMB6XS66OmuRB/5/X50dHTAbrf/7Z5S\n5/eyDCu83pv+baenp5iYmMDS0hIfpU1fMjU1BZ/Ph66uLqVLod9MoVBAPp9HNBqFw+GAw+FANBrF\nxcYQGjgAAALpSURBVMUFEomE0uVRmcpkMhgaGoLH40EikUA8Hoder8fo6ChDMP1UIBDA2dkZdnZ2\nfjmjlzq/l2VYqa+v/0sCe35+lj8j+oqTkxO4XC6Ew2HMzMwoXQ6VuVgshmAwCJ1OB51Oh+npaeRy\nOeh0OqysrChdHpUxk8mEyspKWCwW+ZjFYkFFRQUeHh4UrIzK2fLyMhobGxGJRNDe3o6enh5sbGzg\n8PAQ5+fnSpdHKjM/P4+trS0cHBygpaXll3tLnd/LMqzY7XYcHx8jn8/Lx/b399HQ0IDm5mYFK6Ny\nd3R0BJfLhWAwiLm5OaXLod/A9fU1UqmUvEKhEKqrq5FKpTA8PKx0eVTGHA4HXl9fkclk5GOZTAZv\nb2/8L6SSCSGg1RaPh+/vC4WCEiWRSvn9fjmotLW1/eP+Uud3VYSVXC4HSZIgSRIKhQLu7+8hSRIe\nHx8BAAsLC3A6nfL+8fFx1NTUwO12I51OY3d3F5FIBIFAQKlTIBX6bF/F43H09fXB5/NhbGwM2WwW\n2WyWN6tSkc/2ldVqLVpmsxlarRZWqxUGg0Gp0yAV+mxvOZ1OdHZ2wuv1QpIkXF5ewuv1oru7m5ev\nkuyzfTUwMIBkMolwOIy7uzskk0l4PB40NTXBZrMpdRqkMrOzs1hbW8Pm5ibq6urkmSmXy8l7vm1+\n/5bnlX1RLBYTGo1GaDQaodVq5dcej0cIIYTb7Ratra1F37m6uhK9vb2iqqpKmM1mEQqFlCidVOyz\nfeV2u4v2va+PvUf/b6X8Xv3Z6uqq0Ov1/1W5VEZK6a2npycxMjIi9Hq9MBqNYnJyUry8vChRPqlU\nKX21vb0tbDabqK2tFUajUQwODoqbmxslyieV+thP7ysYDMp7vmt+1wjBu6WIiIiIiEh9VHEZGBER\nERER0UcMK0REREREpEoMK0REREREpEoMK0REREREpEoMK0REREREpEoMK0REREREpEoMK0RERERE\npEoMK0REREREpEp/ACi1cdz/Hkz+AAAAAElFTkSuQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bac712cc0>"
-       ]
-      }
-     ],
-     "prompt_number": 11
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Here we can see that this linearization is much better. It is still exactly correct at $x=1.5$, but the errors are very small as x varies. Compare the tiny error at $x=1.4$ vs the very large error at $x=1.4$ in the previous plot. This does not constitute a formal proof of correctness, but this sort of geometric depiction should be fairly convincing. Certainly it is easy to see that in this case if the line had any other slope the errors would accumulate more quickly. \n",
-      "\n",
-      "To implement the extended Kalman filter we will leave the linear equations as they are, and use partial derivatives to evaluate the system matrix $\\mathbf{F}$ and the measurement matrix $\\mathbf{H}$ at the state at time t ($\\mathbf{x}_t$). Since $\\mathbf{F}$ also depends on the control input vector $\\mathbf{u}$ we will need to include that term:\n",
-      "\n",
-      "$$\n",
-      "\\begin{aligned}\n",
-      "F \n",
-      "&\\equiv {\\frac{\\partial{f}}{\\partial{x}}}\\biggr|_{{x_t},{u_t}} \\\\\n",
-      "H &\\equiv \\frac{\\partial{h}}{\\partial{x}}\\biggr|_{x_t} \n",
-      "\\end{aligned}\n",
-      "$$\n",
-      "\n",
-      "All this means is that at each update step we compute $\\mathbf{F}$ as the partial derivative of our function $f()$ evaluated at  x. \n",
-      "\n",
-      "We approximate the state transition function $\\mathbf{F}$ by using the Taylor-series expansion \n"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "** orphan text\n",
-      "This approach has many issues. First, of course, is the fact that the linearization does not produce an exact answer. More importantly, we are not linearizing the actual path, but our filter's estimation of the path. We linearize the estimation because it is statistically likely to be correct; but of course it is not required to be. So if the filter's output is bad that will cause us to linearize an incorrect estimate, which will almost certainly lead to an even worse estimate. In these cases the filter will quickly diverge. This is where the 'black art' of Kalman filter comes in. We are trying to linearize an estimate, and there is no guarantee that the filter will be stable. A vast amount of the literature on Kalman filters is devoted to this problem. Another issue is that we need to linearize the system using analytic methods. It may be difficult or impossible to find an analytic solution to some problems. In other cases we may be able to find the linearization, but the computation is very expensive. **\n",
-      "\n",
-      "In the next chapter we will spend a lot of time on a new development, the unscented Kalman filter(UKF) which avoids many of these problems. I think that as it becomes better known it will supplant the EKF in most applications, though that is still an open question. Certainly research has shown that the UKF performs at least as well as, and often much better than the EKF. \n",
-      "\n",
-      "I think the easiest way to understand the EKF is to just start off with an example. Perhaps the reason for some of my mathmatical choices will not be clear, but trust that the end result will be an EKF."
-     ]
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "Example: Tracking a Flying Airplane"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We will start by simulating tracking an airplane by using ground based radar. Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
-      "\n",
-      "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import ekf_internal\n",
-      "ekf_internal.show_radar_chart()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAv4AAAGICAYAAAA59uT4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bacf18eb8>"
-       ]
-      }
-     ],
-     "prompt_number": 12
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "As discussed in the introduction, our measurement model is the nonlinear function $x=\\sqrt{slant^2 - altitude^2}$. Therefore we will need a nonlinear \n",
-      "\n",
-      "Predict step:\n",
-      "$$\n",
-      "\\begin{array}{ll}\n",
-      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
-      "x = Fx & x = \\underline{f(x)} \\\\\n",
-      "P = FPF^T + Q & P = FPF^T + Q\n",
-      "\\end{array}\n",
-      "$$\n",
-      "\n",
-      "Update step:\n",
-      "$$\n",
-      "\\begin{array}{ll}\n",
-      "\\textbf{Linear} & \\textbf{Nonlinear} \\\\\n",
-      "K = PH^T(HPH^T + R)^{-1}& K = PH^T(HPH^T + R)^{-1}\\\\\n",
-      "x = x + K(z-Hx) & x = x + K(z-\\underline{h(x)}) \\\\\n",
-      "P = P(I - KH) & P = P(I - KH)\\\\\n",
-      "\\end{array}\n",
-      "$$\n",
-      "\n"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "As we can see there are two minor changes to the Kalman filter equations, 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 use $f()$ and $h()$ in the Kalman filter if they are nonlinear? We reach for the single tool that we have available for solving nonlinear equations - we linearize them at the point we want to evaluate the system.  For example, consider the function $f(x) = x^2 -2x$\n",
-      "\n",
-      "\n",
-      "The rest of the equations are unchanged, so $f()$ and $h()$ must produce a matrix that approximates the values of the matrices $\\mathbf{F}$ and $\\mathbf{H}$ at the current value for $\\mathbf{x}$. We do this by computing the partial derivatives of the state and measurements functions:"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "### Design the State Variables\n",
-      "\n",
-      "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\n",
-      "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",
-      "\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. \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": [
-      "$\\Phi$ is our system matrix. 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\n",
-      "\n",
-      "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",
-      "\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",
-      "$$\\begin{aligned}\n",
-      "\\frac{\\partial h}{\\partial x_{alt}} &=\\\\ &= \\frac{\\partial}{\\partial x_{alt}} \\sqrt{x_{pos}^2 + x_{alt}^2} \\\\ &= \\frac{x_{alt}}{\\sqrt{x_{pos}^2 + x_{alt}^2}}\n",
-      "\\end{aligned}$$\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 just 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",
-     "collapsed": false,
-     "input": [
-      "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]])"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 13
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Finally, let's provide the code for $h(\\mathbf{x})$"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "def hx(x):\n",
-      "    \"\"\" compute measurement for slant range that would correspond \n",
-      "    to state x.\n",
-      "    \"\"\"\n",
-      "    \n",
-      "    return (x[0]**2 + x[2]**2) ** 0.5"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 14
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "Now lets write a simulation for our radar."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "from numpy.random import randn\n",
-      "import math\n",
-      "\n",
-      "class RadarSim(object):\n",
-      "    \"\"\" Simulates the radar signal returns from an object flying \n",
-      "    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 for each\n",
-      "        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 measurment 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"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 15
-    },
-    {
-     "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 just 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",
-      "    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",
-      "We will initialize the filter near the airplane's actual position\n",
-      "\n",
-      "    rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
-      "    \n",
-      "We assign the system matrix using the first term of the Taylor series expansion we computed above.\n",
-      "\n",
-      "    dt = 0.05\n",
-      "    rk.F = eye(3) + array ([[0, 1, 0],\n",
-      "                            [0, 0, 0],\n",
-      "                            [0, 0, 0]])*dt\n",
-      "                            \n",
-      "After assigning reasonble values to $\\mathbf{R}$, $\\mathbf{Q}$, and $\\mathbf{P}$ we can run the filter with a simple loop\n",
-      "\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",
-      "Putting that all together along with some boilerplate code to save the results and plot them, we get"
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "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",
-      "'''\n",
-      "wv = .1**2\n",
-      "wa = .1**2\n",
-      "rk.Q = array([[dt**3 * wv/3, dt**2*wv/2, 0],\n",
-      "              [dt**2*wv/2, dt*wv, 0],\n",
-      "              [0, 0, wa*dt]])'''\n",
-      "rk.P *= 50\n",
-      "\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",
-      "\n",
-      "xs = asarray(xs)\n",
-      "track = asarray(track)\n",
-      "time = np.arange(0,len(xs)*dt, dt)\n",
-      "\n",
-      "plt.figure()\n",
-      "plt.plot(time, track[:,0], label='track')\n",
-      "plt.plot(time, xs[:,0], label='filter')\n",
-      "plt.legend(loc=4)\n",
-      "plt.xlabel('time (sec)')\n",
-      "plt.ylabel('position (m)')\n",
-      "\n",
-      "\n",
-      "plt.figure()\n",
-      "plt.plot(time, track[:,1], label='track')\n",
-      "plt.plot(time, xs[:,1])\n",
-      "plt.legend(loc=4)\n",
-      "plt.xlabel('time (sec)')\n",
-      "plt.ylabel('velocity (m/s)')\n",
-      "\n",
-      "plt.figure()\n",
-      "plt.plot(time, track[:,2], label='track')\n",
-      "plt.plot(time, xs[:,2])\n",
-      "plt.ylabel('altitude (m)')\n",
-      "plt.legend(loc=4)\n",
-      "plt.xlabel('time (sec)')\n",
-      "plt.ylim((900,1600))\n",
-      "plt.show()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAA0QAAAGkCAYAAAARwuWFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bac676048>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAzkAAAGkCAYAAAASdeutAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bab812e10>"
-       ]
-      },
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAA0EAAAGkCAYAAAD36y7BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4bab7e3b70>"
-       ]
-      }
-     ],
-     "prompt_number": 16
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "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",
-     "collapsed": false,
-     "input": [
-      "import sympy\n",
-      "sympy.init_printing(use_latex='mathjax')\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)"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "latex": [
-        "$$\\left[\\begin{matrix}\\frac{x_{pos}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}} & 0 & \\frac{x_{alt}}{\\sqrt{x_{alt}^{2} + x_{pos}^{2}}}\\end{matrix}\\right]$$"
-       ],
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 17,
-       "text": [
-        "\u23a1       x_pos                    x_alt        \u23a4\n",
-        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  0  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
-        "\u23a2   _________________        _________________\u23a5\n",
-        "\u23a2  \u2571      2        2        \u2571      2        2 \u23a5\n",
-        "\u23a3\u2572\u2571  x_alt  + x_pos       \u2572\u2571  x_alt  + x_pos  \u23a6"
-       ]
-      }
-     ],
-     "prompt_number": 17
-    },
-    {
-     "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": "heading",
-     "level": 3,
-     "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",
-     "collapsed": false,
-     "input": [
-      "import sympy\n",
-      "sympy.init_printing(use_latex='mathjax')\n",
-      "w_vel, w_alt, dt = sympy.symbols('w_vel w_alt \\Delta{t}')\n",
-      "w = sympy.Matrix([[0, w_vel, w_alt]]).T\n",
-      "phi = sympy.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))"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "latex": [
-        "$$\\left[\\begin{matrix}\\frac{\\Delta{t}^{3} w_{vel}^{2}}{3} & \\frac{\\Delta{t}^{2} w_{vel}^{2}}{2} & \\frac{w_{alt} w_{vel}}{2} \\Delta{t}^{2}\\\\\\frac{\\Delta{t}^{2} w_{vel}^{2}}{2} & \\Delta{t} w_{vel}^{2} & \\Delta{t} w_{alt} w_{vel}\\\\\\frac{w_{alt} w_{vel}}{2} \\Delta{t}^{2} & \\Delta{t} w_{alt} w_{vel} & \\Delta{t} w_{alt}^{2}\\end{matrix}\\right]$$"
-       ],
-       "metadata": {},
-       "output_type": "pyout",
-       "prompt_number": 18,
-       "text": [
-        "\u23a1           3      2                2      2             2            \u23a4\n",
-        "\u23a2  \\Delta{t} \u22c5w_vel        \\Delta{t} \u22c5w_vel     \\Delta{t} \u22c5w_alt\u22c5w_vel\u23a5\n",
-        "\u23a2  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500       \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500    \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
-        "\u23a2          3                       2                      2           \u23a5\n",
-        "\u23a2                                                                     \u23a5\n",
-        "\u23a2           2      2                                                  \u23a5\n",
-        "\u23a2  \\Delta{t} \u22c5w_vel                       2                           \u23a5\n",
-        "\u23a2  \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500       \\Delta{t}\u22c5w_vel      \\Delta{t}\u22c5w_alt\u22c5w_vel \u23a5\n",
-        "\u23a2          2                                                          \u23a5\n",
-        "\u23a2                                                                     \u23a5\n",
-        "\u23a2         2                                                           \u23a5\n",
-        "\u23a2\\Delta{t} \u22c5w_alt\u22c5w_vel                                           2   \u23a5\n",
-        "\u23a2\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500  \\Delta{t}\u22c5w_alt\u22c5w_vel     \\Delta{t}\u22c5w_alt    \u23a5\n",
-        "\u23a3          2                                                          \u23a6"
-       ]
-      }
-     ],
-     "prompt_number": 18
-    },
-    {
-     "cell_type": "heading",
-     "level": 2,
-     "metadata": {},
-     "source": [
-      "Example: A falling Ball"
-     ]
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "In the **Designing Kalman Filters** chapter I first considered tracking a ball in a vacuum, and then in the atmosphere. The Kalman filter performed very well for vacuum, but diverged from the ball's path in the atmosphere. Let us look at the output; to avoid littering this chapter with code from that chapter I have placed it all in the file `ekf_internal.py'."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [
-      "import ekf_internal\n",
-      "ekf_internal.plot_ball()"
-     ],
-     "language": "python",
-     "metadata": {},
-     "outputs": [
-      {
-       "metadata": {},
-       "output_type": "display_data",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAAyAAAAGNCAYAAADpbRVxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nE9j3bqBZOK4AAAAASUVORK5CYII=\n",
-       "text": [
-        "<matplotlib.figure.Figure at 0x7f4ba85b1f98>"
-       ]
-      }
-     ],
-     "prompt_number": 20
-    },
-    {
-     "cell_type": "markdown",
-     "metadata": {},
-     "source": [
-      "We can artifically force the Kalman filter to track the ball by making $Q$ large. That would cause the filter to mistrust its prediction, and scale the kalman gain $K$ to strongly favor the measurments. However, this is not a valid approach. If the Kalman filter is correctly predicting the process we should not 'lie' to the filter by telling it there are process errors that do not exist. We may get away with that for some problems, in some conditions, but in general the Kalman filter's performance will be substandard.\n",
-      "\n",
-      "Recall from the **Designing Kalman Filters** chapter that the acceleration is\n",
-      "\n",
-      "$$a_x = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_x \\\\\n",
-      "a_y = (0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}})*v*v_y- g\n",
-      "$$\n",
-      "\n",
-      "These equations will be very unpleasant to work with while we develop this subject, so for now I will retreat to a simpler one dimensional problem using this simplified equation for acceleration that does not take the nonlinearity of the drag coefficient into account:\n",
-      "\n",
-      "\n",
-      "$$\\ddot{x} = \\frac{0.0034ge^{-x/20000}\\dot{x}^2}{2\\beta} - g$$\n",
-      "\n",
-      "Here $\\beta$ is the ballistic coefficient, where a high number indicates a low drag."
-     ]
-    },
-    {
-     "cell_type": "code",
-     "collapsed": false,
-     "input": [],
-     "language": "python",
-     "metadata": {},
-     "outputs": [],
-     "prompt_number": 20
-    }
-   ],
-   "metadata": {}
-  }
- ]
-}
\ No newline at end of file
diff --git a/09_Extended_Kalman_Filters/README.md b/09_Extended_Kalman_Filters/README.md
deleted file mode 100644
index d041551..0000000
--- a/09_Extended_Kalman_Filters/README.md
+++ /dev/null
@@ -1,2 +0,0 @@
-You may read this book online via nbviewer by using this link:
-[*Read Online Now*](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)