{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Kalman Filter Implementation for Constant Acceleration Model (CA) in Python\n",
    "\n",
    "Multisensor Data Fusion with acceleration ($\\ddot x$ and $\\ddot y$) and position ($x$ and $y$).\n",
    "\n",
    "`CC-BY-SA2.0 Lizenz Paul Balzer, Motorblog http://www.cbcity.de`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![Kalman Filter](Kalman-Filter-Step.png)\n",
    "\n",
    "First, we have to initialize the matrices and vectors. Setting up the math."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## State Vector\n",
    "\n",
    "Constant Acceleration Model for Ego Motion in Plane\n",
    "\n",
    "$$x_k= \\left[ \\begin{matrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y \\end{matrix} \\right]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Motion\n",
    "\n",
    "Formal Definition:\n",
    "\n",
    "$$x_{k+1} = A \\cdot x_{k} + B \\cdot u$$\n",
    "\n",
    "Hence, we have no control input $u$:\n",
    "\n",
    "$$x_{k+1} = \\begin{bmatrix}1 & 0 & \\Delta t & 0 & \\frac{1}{2}\\Delta t^2 & 0 \\\\ 0 & 1 & 0 & \\Delta t & 0 & \\frac{1}{2}\\Delta t^2 \\\\ 0 & 0 & 1 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 1 & 0 & \\Delta t \\\\ 0 & 0 & 0 & 0 & 1 & 0  \\\\ 0 & 0 & 0 & 0 & 0 & 1\\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y\\end{bmatrix}_{k}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Measurement\n",
    "\n",
    "$$y = H \\cdot x$$\n",
    "\n",
    "Acceleration ($\\ddot x$ & $\\ddot y$) as well as position ($x$ & $y$) is measured.\n",
    "\n",
    "$$y = \\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 \\\\0 & 1 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1\\end{bmatrix} \\cdot x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Setting up the math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Initial State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.],\n",
      "        [ 0.]]), (6, 1))\n"
     ]
    }
   ],
   "source": [
    "x = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]).T\n",
    "print(x, x.shape)\n",
    "n=x.size # States\n",
    "#plt.scatter(float(x[0]),float(x[1]), s=100)\n",
    "#plt.title('Initial Location')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Initial Uncertainty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 100.,    0.,    0.,    0.,    0.,    0.],\n",
      "       [   0.,  100.,    0.,    0.,    0.,    0.],\n",
      "       [   0.,    0.,   10.,    0.,    0.,    0.],\n",
      "       [   0.,    0.,    0.,   10.,    0.,    0.],\n",
      "       [   0.,    0.,    0.,    0.,    1.,    0.],\n",
      "       [   0.,    0.,    0.,    0.,    0.,    1.]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([100.0, 100.0, 10.0, 10.0, 1.0, 1.0])\n",
    "print(P, P.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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TJCRpoHZ2UZPcFug9wN9X1U8BPwPcALwVuLyqng5c3i5PZLGn+N4PfBTYvsjtSJKmbJan\n+JI8Bngx8BqAqroPuC/JscDh7csuAq4A3jLJeywqoKpqO4aTJHXSIgPqwCQbR5Y3VNWGkeWDgW3A\nnyf5GWAT8CZgTVVtbV9zO7Bm0gKcJCFJ2p3tVbVunvV7Az8L/E5VXZPkPexyOq+qKklNWoBjUJI0\nUDMeg7oVuLWqrmmXP0kTWHckWdu+/1rgzknrX3BAJXl7O2Pv87tZlyQXt+svTbLPpAVJkhZvMeG0\nkICqqtuBzUme2T51BHA9cAlwUvvcScBnJt2HcU7xnQv8JnBEkvVVNRpU7wNOAK4EXllV909akCRp\nOpbgc1C/A1yc5JHATcBv0DQ+H09yMnAL8KpJN77ggKqqu9vPO30AOBv4PECStwGn0gyQHVNVP5i0\nGEnS9Mw6oKrqWmB341RHTGP7445BbQC+BqxL8stJ3gScQTP3/eiqunu+H05ySpKNSTZu27Ztsool\nSSvCWAFVVQ/w8Hz2C4DzgW8DR7ZTzvf08xuqal1VrVu9evW4tUqSxrAEH9SdqbGnmVfVJUmuB55F\nMztjfVVtmXplkqRF6UrQTGrsgEryRppwAtgPmPe0niRp6XWpE5rUWKf4kpwEvBvYAnwWOAA4cwZ1\nSZJWuHE+B3Uc8CHgLuBImpl7O4DXJXnGbMqTJE2q72NQCwqoJOuBjwD30szWu6GqNtNcLHZv4JzZ\nlShJmsTgAyrJocCn28Vjq2r04oFnA98DjkvywhnUJ0ma0KADKslzgEuBfYHjq+qLo+ur6i6aK0wA\nnDeTCiVJK9K8s/iq6qvAqj285myaTkqS1CFd6YQm5ddtSNIAdelU3aQMKEkaqL4HlN8HJUnqJDso\nSRqovndQBpQkDZQBJUnqJANKktQ5Q5jF5yQJSVIn2UFJ0kD1vYMyoCRpoAwoSVIn9T2gHIOSJHWS\nHZQkDVTfOygDSpIGaAjTzA0oSRqovgeUY1CSpE6yg5Kkgep7B2VAaSJr165d7hJmZuvWrctdwkwN\n+djp/2dASZI6qe8B5RiUJKmT7KAkaYCcZi5J6iwDSpLUSQaUJKmT+h5QTpKQJHWSHZQkDVTfOygD\nSpIGyFl8kqTO6ntAOQYlSeokOyhJGqi+d1AGlCQNlAElSeqkvgeUY1CSpE6yg5KkAXKauSSpswwo\nSVIn9T2gHIOSJHWSHZQkDdSK7qCSnJWkkpw1pXokSVOyc6LEJLcusIOSpAHqUtBMarEB9X7go8D2\nKdQiSZqiFR1QVbUdw0mSNAOe4pOkgVrRHZQkqbv6HlALmsWX5Jh2tt6X53nNM5PsSHJbkgOmV6Ik\naRJ9n8W30GnmXwIKeF6S/eZ4zQXAvsBpVXX3NIqTJK1cCwqoqroLuA54JLBu1/VJTgReAlxWVR+b\naztJTkmyMcnGbdu2TViyJGlPFtM99a2DAriqvX/B6JNJVgHnATuAU+fbQFVtqKp1VbVu9erVYxUq\nSRrPSgqoK9v7w3Z5/p3AauAdVfWtqVQlSVq0pQioJHsl+UqSv22XVyX5XJJvtvePm7T+RXVQSV4E\nvBb4OnDupEVIknrrTcANI8tvBS6vqqcDl7fLE1lwQFXVFuBmYE2SpyXZB/ggEOANVXXfpEVIkqZv\n1h1UkicD/wm4cOTpY4GL2scXAa+YtP5xPwd1JXAwzWm+g4BDgIur6guTFiBJmo1FjiUdmGTjyPKG\nqtqwy2veDbwZ+PGR59ZU1db28e3AmkkLGDegrgJOAk4ADge+C5w+6ZtLkmZjCpMdtlfVj8zaHtn+\nLwF3VtWmJIfv7jVVVUlq0gImCSiAl7X3p1fVnZO+uSSpt14IvDzJLwL7AQck+SvgjiRrq2prkrXA\nxBkx1vdBVdU3gDvaxWuAXds9SVJHzHIMqqr+oKqeXFVPBV4NfKGqfg24hOZMG+39Zyatf6wOKsn+\n7cMHgddX1UOTvrEkabaW6fNM5wAfT3IycAvwqkk3NO4pvjNoBrzOr6prJ31TSdLsLVVAVdUVwBXt\n438FjpjGdhccUEleSjMh4iaaoJIkdVhXrggxqXkDKskhwGnAE4CjgPuB46vqniWoTZK0gu2pgzoK\nOBn4Ps0MvjOqauP8PyJJWm5duqbepOYNqKp6F/CuJapFkjRFgw4oSVJ/9T2gxvoclCRJS8UOSpIG\nqu8dlAElSQM0+EkSkqT+6ntAOQYlSeokOyhJGqi+d1AGlCQNlAElSeokA0qS1DlDmMXnJAlJUifZ\nQUnSQPW9gzKgpF2sXbt2uUuYqYceGvYXYT/iEZ4Y2smAkiR1Ut8Dyj81JEmdZAclSQPV9w7KgJKk\nARrCNHMDSpIGqu8B5RiUJKmT7KAkaaD63kEZUJI0UAaUJKmT+h5QjkFJkjrJDkqSBshp5pKkzjKg\nJEmdZEBJkjqp7wHlJAlJUifZQUnSQPW9gzKgJGmAnMUnSeqsvgeUY1CSpE6aKKCSfDhJJTmrXX5N\nu3zFNIuTJE1u52m+SW5dMOkpvqvb+2vb+xuBi4CvLboiSdJUdCVoJjVRQFXVhcCFI8tX83BoSZI6\noO8B5RiUJKmTnMUnSQPUpbGkSRlQkjRQfQ+oBZ/iS/L2dqbe53ezLkkubtdfmmSf6ZYpSRpX32fx\njTMGdS6wDTgiyfpd1r0POAG4EnhlVd0/pfokSSvUggOqqu4GzmoXz975fJK3AacCm4BjquoHc20j\nySlJNibZuG3btskqliQtyErqoAA20HzWaV2SX07yJuAM4Abg6DbE5lRVG6pqXVWtW7169WQVS5IW\npO8BNdYkiap6IMlbgM8AFwCPB74NHFlV26dfniRpEl0KmkmNPYuvqi5Jcj3wLOBOYH1VbZl6ZZKk\nRel7QI39Qd0kb6QJJ4D9gHlP60mSNImxAirJScC7gS3AZ4EDgDNnUJckaZH6PgY1zuegjgM+BNwF\nHEkzc28H8Lokz5hNeZKkSa2IgGo/9/QR4F6a2Xo3VNVm4P0041jnzK5ESdIkBh9QSQ4FPt0uHltV\nG0dWnw18DzguyQtnUJ8kaYWaN6CSPAe4FNgXOL6qvji6vqruornCBMB5M6lQkjS2xXRPXemg5p1m\nXlVfBVbt4TVnM3JlCUlSN3QlaCbl1cwlaaD6HlB+YaEkqZPsoCRpoOygJEmdNMtJEkkOSvLFJNcn\nua69eDhJViX5XJJvtvePm7R+A0qSBmgJZvE9APzXqnoWcChwapJnAW8FLq+qpwOXt8sTMaAkSWOr\nqq1V9U/t4+/TfO3Sk4BjgYval10EvGLS93AMSpIGapFjUAcmGb0ww4aq2jDH+zwVeB5wDbCmqra2\nq24H1kxagAElSQO1yIDaXlXrFvAe+wN/A/xuVd09+p5VVUlq0gIMKEkaqFnP4kuyD004XVxVn2qf\nviPJ2qrammQtzfcGTsQxKEkaqBnP4gvNN1zcUFXvGll1CXBS+/gkmm9gn4gdlCRpEi8Efh34apJr\n2+f+kObbLT6e5GTgFuBVk76BASVJAzTri75W1dXAXG9wxDTew4CSpIHq+5UkDChJGqi+B5STJCRJ\nnWQHJUkD1fcOyoCSpIEyoCT1yiMeMewz+w899NByl9AJXfrq9kkN+79USVJv2UFJ0kD1vYMyoCRp\noAwoSVIn9T2gHIOSJHWSHZQkDVTfOygDSpIGaAjTzA0oSRooA0qS1El9DygnSUiSOskOSpIGqu8d\nlAElSQNlQEmSOmcIs/gcg5IkdZIdlCQNVN87KANKkgbKgJIkdVLfA8oxKElSJ9lBSdJArcgOKsmH\nk1SSs9rl17TLV0yzOEnSZHZOM5/01gWTdlBXt/fXtvc3AhcBX1t0RZKkqehK0ExqooCqqguBC0eW\nr+bh0JIkadEcg5KkgVqRHZQkqfsMKElSJ/U9oBY0iy/JMe0svS/P85pnJtmR5LYkB0yvREnSuIYw\ni2+h08y/BBTwvCT7zfGaC4B9gdOq6u5pFCdJWrkWFFBVdRdwHfBIYN2u65OcCLwEuKyqPjbXdpKc\nkmRjko3btm2bsGRJ0kKslA4K4Kr2/gWjTyZZBZwH7ABOnW8DVbWhqtZV1brVq1ePVagkaTwrKaCu\nbO8P2+X5dwKrgXdU1bemUpUkadFWUkD9SAeV5EXAa4GvA+dOsS5J0gq34GnmVbUlyc3AwUmeBmwG\nPggEeENV3TejGiVJE+hKJzSpcT8HdSVwMM1pvoOAQ4CLq+oL0y5MkjS5Lp2qm9S4AXUVcBJwAnA4\n8F3g9CnXJEmagpUYUAAva+9Pr6o7p1iPJEnAmAFVVd9IcgewBrgG2DCTqiRJi7aiOqgk+7cPHwRe\nX1UPTb8kSdI0rKiAAs6g6Z7Or6pr9/RiSdLyGMIkiQV/DirJS2kmRNxEE1SSJM3MvB1UkkOA04An\nAEcB9wPHV9U9S1CbJGkR+t5B7ekU31HAycD3aWbwnVFVG2delSRp0QYdUFX1LuBdS1SLJGmKBh1Q\nkqT+6ntAjXOxWEmSlowdlCQN0BCmmRtQkjRQBpQkqZP6HlCOQUmSOskOSpIGqu8dlAElSQNlQEmS\nOmcIs/gcg5IkdZIBJUkDtbOLmuS2wO0fneTrSW5M8tZp1+8pPkkaqFme4kuyF/AB4EjgVuAfk1xS\nVddP6z0MKEkaqBmPQf08cGNV3dS+10eBY4H+B9SmTZu2J7llCd/yQGD7Er7fUhvy/g1538D967ul\n3r+nLORFmzZtuizJgYt4n/2SjH690oaq2jCy/CRg88jyrcB/XMT7/YhlC6iqWr2U75dkY1WtW8r3\nXEpD3r8h7xu4f33X1f2rqqOXu4bFcpKEJGkSW4CDRpaf3D43NQaUJGkS/wg8PcnBSR4JvBq4ZJpv\nsJImSWzY80t6bcj7N+R9A/ev74a+f7tVVQ8k+W3gMmAv4M+q6rppvkeqaprbkyRpKjzFJ0nqJANK\nktRJBpR6IclZSSrJWctdixYmyYdHj1mS17TLVyxvZeqLlTRJQtLSurq9v7a9vxG4CPja8pSjvrGD\n6pkkx7R/hX55ntc8M8mOJLclOWAp65uh9wM/3d4PylC7w6q6sKpeU1WfbpevbpfPWe7apsEOcfbs\noPrnS0ABz0uyX1Xt2M1rLgD2BU6rqruXtLoZqartDPtyOeofO8QZG+Q08yRvB/4QuLyq1u+yLsBf\nAScAfwccW1X3L32Vk0vyVeDZwC9U1dW7rDuR5n+Sy4ZwqZOVoL1e2oHA9jaIJTHcU3znAtuAI5Ks\n32Xd+2jC6UrglX0Lp9ZV7f0LRp9Msgo4D9gBnLrURWkyVbW9qr5mOEn/v0EGVHta66x28eydzyd5\nG80v7k3AMVX1g6WvbiqubO8P2+X5dwKrgXdU1beWtqTpSfL29lz+53ezLkkubtdfmmSf5ahRu+ex\n0zQN8hQfQJK9ga8CPwX8Cs2l4d8N3AC8uM9/rSZ5Es2l7e+oqie0z72IJri+AfyHqrpvGUtclHZi\nx400YXtkVX1+ZN37af7IuBI4usd/ZAySx07TNMgOCprrRAFvaRcvAM4Hvk3zP01vwwmgqrYANwNr\nkjyt/Uv0g0CAN/Q5nGC4HfBKmIE51GMHK+P4dc1gO6idklwHPAu4Ezisz6e+RiX5MHAS8Os0l7x/\nB3BxVf3actY1LUPsgNsxwu3A/cBjdjcDM8kXgJcAr66qjy1xiVMxxGMHK+f4dUpVDfYGvJFmSnYB\n3wNWL3dNU9y3k9v9uhS4F/g/wL9b7rqmvI8vb/dxG/AQTdf4pOWua5H79NV2n160m3Untuv+frnr\n9Nit7OPXldtgT/ElOYnmr7YtwGeBA4Azl7Wo6do5k+9lwKOAP6iqO5exnqmrqkuA62mmYG8D1ldz\nerPPVsQMzIEeO1ghx68rBhlQSY4DPgTcBRxJ8x/MDuB1SZ6xnLVNS1V9A7ijXbyGAX4nTZI30pye\nBdgPGMKHjgc9A3OngR47WCHHrysGF1Dt554+QnPa6+iquqGqNtNcImdvYCiXWdm/ffgg8Pqqemg5\n65m2AXfAP/IXeDsD87XA12k+w9drAz52sAKOX5cMapJEkkOBz9ME0cuq6osj61YBNwGPoTl//KXl\nqXI6kpwLvBk4v6pOX+56pqntgD8BfBf4BeDfaKbP7w0c0naPvZXkJuBg4CeBzcBXgEOAI6rqC8tZ\n22IN/dglajvBAAABPklEQVTBsI9f1wymg0ryHJoJA/sCx4+GE0BV3cXDf92ct8TlTVWSlwKn0wTu\nGctczlStkA549DTR79H8cru477/cVsixg4Eevy4aVAc1ZEkOAU4DngAcRTPV9cVVtXFZC5uildIB\nJzkZuJDmWpCHAz8EntnnSS4r5djBMI9fVw2mg1oBjqKZWv5imvPgRw4snFZMB8zAZmCusGMHAzt+\nXWYHJS2DJLcDa2hmYB42tEkuQ+fxWxp2UNISG/oMzKHz+C0dA0paemfQ/PX93qq6dk8vVud4/JaI\np/ikJdTOwLwM+A7NVefvWeaSNAaP39LyK9+lGZtjBubx/nLrB4/f8vEUnzR7g56BuQJ4/JaJp/gk\nSZ1kByVJ6iQDSpLUSQaUJKmTDChJUicZUJKkTjKgJEmdZEBJkjrJgJIkddL/BVUVAPswlwJbAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a1f2710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Initial Covariance Matrix $P$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,5.5])\n",
    "plt.ylim([5.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Dynamic Matrix\n",
    "\n",
    "It is calculated from the dynamics of the Egomotion.\n",
    "\n",
    "$$x_{k+1} = x_{k} + \\dot x_{k} \\cdot \\Delta t +  \\ddot x_k \\cdot \\frac{1}{2}\\Delta t^2$$\n",
    "$$y_{k+1} = y_{k} + \\dot y_{k} \\cdot \\Delta t +  \\ddot y_k \\cdot \\frac{1}{2}\\Delta t^2$$\n",
    "\n",
    "$$\\dot x_{k+1} = \\dot x_{k} + \\ddot x \\cdot \\Delta t$$\n",
    "$$\\dot y_{k+1} = \\dot y_{k} + \\ddot y \\cdot \\Delta t$$\n",
    "\n",
    "$$\\ddot x_{k+1} = \\ddot x_{k}$$\n",
    "$$\\ddot y_{k+1} = \\ddot y_{k}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 1.   ,  0.   ,  0.1  ,  0.   ,  0.005,  0.   ],\n",
      "        [ 0.   ,  1.   ,  0.   ,  0.1  ,  0.   ,  0.005],\n",
      "        [ 0.   ,  0.   ,  1.   ,  0.   ,  0.1  ,  0.   ],\n",
      "        [ 0.   ,  0.   ,  0.   ,  1.   ,  0.   ,  0.1  ],\n",
      "        [ 0.   ,  0.   ,  0.   ,  0.   ,  1.   ,  0.   ],\n",
      "        [ 0.   ,  0.   ,  0.   ,  0.   ,  0.   ,  1.   ]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "dt = 0.1 # Time Step between Filter Steps\n",
    "\n",
    "A = np.matrix([[1.0, 0.0, dt, 0.0, 1/2.0*dt**2, 0.0],\n",
    "              [0.0, 1.0, 0.0, dt, 0.0, 1/2.0*dt**2],\n",
    "              [0.0, 0.0, 1.0, 0.0, dt, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1.0, 0.0, dt],\n",
    "              [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(A, A.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurement Matrix $H$\n",
    "\n",
    "Here you can determine, which of the states is covered by a measurement. In this example, the position ($x$ and $y$) as well as the acceleration is measured ($\\ddot x$ and $\\ddot y$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 1.,  0.,  0.,  0.,  0.,  0.],\n",
      "        [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
      "        [ 0.,  0.,  0.,  0.,  1.,  0.],\n",
      "        [ 0.,  0.,  0.,  0.,  0.,  1.]]), (4, 6))\n"
     ]
    }
   ],
   "source": [
    "H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(H, H.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurement Noise Covariance $R$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[ 10000.,      0.,      0.,      0.],\n",
      "        [     0.,  10000.,      0.,      0.],\n",
      "        [     0.,      0.,    100.,      0.],\n",
      "        [     0.,      0.,      0.,    100.]]), (4, 4))\n"
     ]
    }
   ],
   "source": [
    "ra = 10.0**2   # Noise of Acceleration Measurement\n",
    "rp = 100.0**2  # Noise of Position Measurement\n",
    "R = np.matrix([[rp, 0.0, 0.0, 0.0],\n",
    "               [0.0, rp, 0.0, 0.0],\n",
    "               [0.0, 0.0, ra, 0.0],\n",
    "               [0.0, 0.0, 0.0, ra]])\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7q+rKxe4sSVo+BtQ8kryApiHiepqgkiStIgNqRJL9gNcBjwMOB+4FXl5V96zC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\n1HKkewmfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114f28d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Measurement Noise Covariance Matrix $R$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(4),('$x$', '$y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(5))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(4),('$x$', '$y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,3.5])\n",
    "plt.ylim([3.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Process Noise Covariance Matrix $Q$\n",
    "\n",
    "The Position of an object can be influenced by a force (e.g. wind), which leads to an acceleration disturbance (noise). This process noise has to be modeled with the process noise covariance matrix Q.\n",
    "\n",
    "$$Q = \\begin{bmatrix}\\sigma_{x}^2 & \\sigma_{xy} & \\sigma_{x \\dot x} & \\sigma_{x \\dot y} & \\sigma_{x \\ddot x} & \\sigma_{x \\ddot y} \\\\ \\sigma_{yx} & \\sigma_{y}^2 & \\sigma_{y \\dot x} & \\sigma_{y \\dot y} & \\sigma_{y \\ddot x} & \\sigma_{y \\ddot y} \\\\ \\sigma_{\\dot x x} & \\sigma_{\\dot x y} & \\sigma_{\\dot x}^2 & \\sigma_{\\dot x \\dot y} & \\sigma_{\\dot x \\ddot x} & \\sigma_{\\dot x \\ddot y} \\\\ \\sigma_{\\dot y x} & \\sigma_{\\dot y y} & \\sigma_{\\dot y \\dot x} & \\sigma_{\\dot y}^2 & \\sigma_{\\dot y \\ddot x} & \\sigma_{\\dot y \\ddot y} \\\\ \\sigma_{\\ddot x x} & \\sigma_{\\ddot x y} & \\sigma_{\\ddot x \\dot x} & \\sigma_{\\ddot x \\dot y} & \\sigma_{\\ddot x}^2 & \\sigma_{\\ddot x \\ddot y} \\\\ \\sigma_{\\ddot y x} & \\sigma_{\\ddot y y} & \\sigma_{\\ddot y \\dot x} & \\sigma_{\\ddot y \\dot y} & \\sigma_{\\ddot y \\ddot x} & \\sigma_{\\ddot y}^2\\end{bmatrix}$$\n",
    "\n",
    "To easily calcualte Q, one can ask the question: How the noise effects my state vector? For example, how the acceleration change the position over one timestep dt.\n",
    "\n",
    "One can calculate Q as\n",
    "\n",
    "$$Q = G\\cdot G^T \\cdot \\sigma_a^2$$\n",
    "\n",
    "with $G = \\begin{bmatrix}0.5dt^2 & 0.5dt^2 & dt & dt & 1.0 & 1.0\\end{bmatrix}^T$ and $\\sigma_a$ as the acceleration process noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yVN1mN1SoNHh50cXbxQ4NpCHUyaOj9bIXioCB8NiJoBrthgqVBZwXokNDgdwEdcJ0t0rZ\nTBEwIjx0IriWf7IaV05EZ8KCGdXTiVVVrxyMFkwsbMnDHYdNEcNmB4JOb4WLVstfSIcbYQTCJ046\n3VBhdtrXrB6pbQu2Sx0aSACoUyLraP3dhSJgIDxyIqi2uqHCZBwaTdz9rrnKP0jfV0OdgqzvqhxZ\noQgYCg+MAxreDRUmxyAv9oAvdmggtZBOgI5WKlkoAobCAyeCblVfKwXPKBIt2fiiCX0h7vgsHfwC\nZRLETgYiGVN0tFLJQhEwFL4bKlyyl0zyOTQcWc0k6GidooUiYET4hqYH0ZCdNBRQfSDsQKRiko7W\nKlgoBEaEL2isr3rYDHThDytdXeBd+Lr8HXbrLvxhpasLvAtfl7/Dbt2FP6x0dYEb4Wc1ga8l6ph9\n67+dgeXzrXrqlZ7a1Ef/7Rz8J6N7G73F/wAZ83oZDIXzRAAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡             4               4              3              3              2  \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢             4               4              3              3              2  \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢            3               3             2              2                   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t     1.0⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢            3               3             2              2                   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t     1.0⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢            2               2                                                \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t        1.0       \n",
       "⎢                                                                             \n",
       "⎢            2               2                                                \n",
       "⎣0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t        1.0       \n",
       "\n",
       "            2⎤\n",
       "0.5⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "            2⎥\n",
       "0.5⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "1.0⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "1.0⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "     1.0     ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "     1.0     ⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Symbol, Matrix\n",
    "from sympy.interactive import printing\n",
    "printing.init_printing()\n",
    "dts = Symbol('\\Delta t')\n",
    "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[dts],[dts],[1.0],[1.0]])\n",
    "Qs*Qs.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(matrix([[  2.50000000e-11,   2.50000000e-11,   5.00000000e-10,\n",
      "           5.00000000e-10,   5.00000000e-09,   5.00000000e-09],\n",
      "        [  2.50000000e-11,   2.50000000e-11,   5.00000000e-10,\n",
      "           5.00000000e-10,   5.00000000e-09,   5.00000000e-09],\n",
      "        [  5.00000000e-10,   5.00000000e-10,   1.00000000e-08,\n",
      "           1.00000000e-08,   1.00000000e-07,   1.00000000e-07],\n",
      "        [  5.00000000e-10,   5.00000000e-10,   1.00000000e-08,\n",
      "           1.00000000e-08,   1.00000000e-07,   1.00000000e-07],\n",
      "        [  5.00000000e-09,   5.00000000e-09,   1.00000000e-07,\n",
      "           1.00000000e-07,   1.00000000e-06,   1.00000000e-06],\n",
      "        [  5.00000000e-09,   5.00000000e-09,   1.00000000e-07,\n",
      "           1.00000000e-07,   1.00000000e-06,   1.00000000e-06]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "sa = 0.001\n",
    "G = np.matrix([[1/2.0*dt**2],\n",
    "               [1/2.0*dt**2],\n",
    "               [dt],\n",
    "               [dt],\n",
    "               [1.0],\n",
    "               [1.0]])\n",
    "Q = G*G.T*sa**2\n",
    "\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LGtmmVts16bAd6X5tA33tWWH5Fm0kjQJ2Al4EjgUWRcQrEfEKcCfwyVo764AyM8ushQH1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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114d2b590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "plt.title('Process Noise Covariance Matrix $Q$')\n",
    "ylocs, ylabels = plt.yticks()\n",
    "# set the locations of the yticks\n",
    "plt.yticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "xlocs, xlabels = plt.xticks()\n",
    "# set the locations of the yticks\n",
    "plt.xticks(np.arange(7))\n",
    "# set the locations and labels of the yticks\n",
    "plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "plt.xlim([-0.5,5.5])\n",
    "plt.ylim([5.5, -0.5])\n",
    "\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "divider = make_axes_locatable(plt.gca())\n",
    "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "plt.colorbar(im, cax=cax)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Identity Matrix $I$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([[ 1.,  0.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  1.,  0.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  1.,  0.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  1.,  0.],\n",
      "       [ 0.,  0.,  0.,  0.,  0.,  1.]]), (6, 6))\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(n)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Measurements\n",
    "\n",
    "Typical update rates:\n",
    "\n",
    "* Acceleration from IMU with `10Hz`\n",
    "* Position from GPS with `1Hz`\n",
    "\n",
    "Which means, that every 10th of an acceleration measurement, there is a new position measurement from GPS. The Kalman Filter can perfectly handle this unsynchronous measurement incoming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "m = 500 # Measurements\n",
    "\n",
    "sp= 1.0 # Sigma for position\n",
    "px= 0.0 # x Position\n",
    "py= 0.0 # y Position\n",
    "\n",
    "mpx = np.array(px+sp*np.random.randn(m))\n",
    "mpy = np.array(py+sp*np.random.randn(m))\n",
    "\n",
    "# Generate GPS Trigger\n",
    "GPS=np.ndarray(m,dtype='bool')\n",
    "GPS[0]=True\n",
    "# Less new position updates\n",
    "for i in range(1,m):\n",
    "    if i%10==0:\n",
    "        GPS[i]=True\n",
    "    else:\n",
    "        mpx[i]=mpx[i-1]\n",
    "        mpy[i]=mpy[i-1]\n",
    "        GPS[i]=False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Accelerations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Acceleration\n",
    "sa= 0.1 # Sigma for acceleration\n",
    "ax= 0.0 # in X\n",
    "ay= 0.0 # in Y\n",
    "\n",
    "mx = np.array(ax+sa*np.random.randn(m))\n",
    "my = np.array(ay+sa*np.random.randn(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 500)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mpx,mpy,mx,my))\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_m():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.subplot(211)\n",
    "    plt.step(range(m),mpx, label='$x$')\n",
    "    plt.step(range(m),mpy, label='$y$')\n",
    "    plt.ylabel(r'Position $m$')\n",
    "    plt.title('Measurements')\n",
    "    plt.ylim([-10, 10])\n",
    "    plt.legend(loc='best',prop={'size':18})\n",
    "\n",
    "    plt.subplot(212)\n",
    "    plt.step(range(m),mx, label='$a_x$')\n",
    "    plt.step(range(m),my, label='$a_y$')\n",
    "    plt.ylabel(r'Acceleration $m/s^2$')\n",
    "    plt.ylim([-1, 1])\n",
    "    plt.legend(loc='best',prop={'size':18})\n",
    "\n",
    "    plt.savefig('Kalman-Filter-CA-Measurements.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MGMEf/vAHFi9ezOrVqx1ivQWZyerVq1m8eDF/+MMfGDFiRN2eu2/dnkmSJEmStN369+/P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\nAklEQVR4xukaKcEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114cc3450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_m()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Preallocation for Plotting\n",
    "xt = []\n",
    "yt = []\n",
    "dxt= []\n",
    "dyt= []\n",
    "ddxt=[]\n",
    "ddyt=[]\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "Kddy=[]\n",
    "\n",
    "\n",
    "def savestates(x, Z, P, K):\n",
    "    xt.append(float(x[0]))\n",
    "    yt.append(float(x[1]))\n",
    "    dxt.append(float(x[2]))\n",
    "    dyt.append(float(x[3]))\n",
    "    ddxt.append(float(x[4]))\n",
    "    ddyt.append(float(x[5]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))\n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Pddy.append(float(P[5,5]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))\n",
    "    Kddy.append(float(K[5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Kalman Filter\n",
    "\n",
    "![Kalman Filter](https://raw.github.com/balzer82/Kalman/master/Kalman-Filter-Step.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "for filterstep in range(m):\n",
    "    \n",
    "    # Time Update (Prediction)\n",
    "    # ========================\n",
    "    # Project the state ahead\n",
    "    x = A*x\n",
    "    \n",
    "    # Project the error covariance ahead\n",
    "    P = A*P*A.T + Q    \n",
    "    \n",
    "    \n",
    "    # Measurement Update (Correction)\n",
    "    # ===============================\n",
    "    # if there is a GPS Measurement\n",
    "    if GPS[filterstep]:\n",
    "        # Compute the Kalman Gain\n",
    "        S = H*P*H.T + R\n",
    "        K = (P*H.T) * np.linalg.pinv(S)\n",
    "    \n",
    "        \n",
    "        # Update the estimate via z\n",
    "        Z = measurements[:,filterstep].reshape(H.shape[0],1)\n",
    "        y = Z - (H*x)                            # Innovation or Residual\n",
    "        x = x + (K*y)\n",
    "        \n",
    "        # Update the error covariance\n",
    "        P = (I - (K*H))*P\n",
    "\n",
    "   \n",
    "    \n",
    "    # Save states for Plotting\n",
    "    savestates(x, Z, P, K)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Thats it.\n",
    "\n",
    "![Job done](http://www.troll.me/images/the-chuck-norris/job-done.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Let's take a look at the filter performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Uncertainty $P$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_P():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.subplot(211)\n",
    "    plt.plot(range(len(measurements[0])),Px, label='$x$')\n",
    "    plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
    "    plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.subplot(212)\n",
    "    plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n",
    "    plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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QClq/R8XKd+hCI7bRN2Jz+QAI+rObNlx/7BAlLWvYkn8BkN1rEG/b4mcoUK2EavfkFC+E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\nwQArX/wl9cfSV6+FEEK0Fz91+De/+Q2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VNwtJt/S8jjN81rup7K4o93vM2fI3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\nSZJK3v8FCoRLl6ySGV4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116cbaa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_P()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_P2():\n",
    "    fig = plt.figure(figsize=(6, 6))\n",
    "    im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
    "    plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n",
    "    ylocs, ylabels = plt.yticks()\n",
    "    # set the locations of the yticks\n",
    "    plt.yticks(np.arange(7))\n",
    "    # set the locations and labels of the yticks\n",
    "    plt.yticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "    xlocs, xlabels = plt.xticks()\n",
    "    # set the locations of the yticks\n",
    "    plt.xticks(np.arange(7))\n",
    "    # set the locations and labels of the yticks\n",
    "    plt.xticks(np.arange(6),('$x$', '$y$', '$\\dot x$', '$\\dot y$', '$\\ddot x$', '$\\ddot y$'), fontsize=22)\n",
    "\n",
    "    plt.xlim([-0.5,5.5])\n",
    "    plt.ylim([5.5, -0.5])\n",
    "\n",
    "    from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "    divider = make_axes_locatable(plt.gca())\n",
    "    cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n",
    "    plt.colorbar(im, cax=cax)\n",
    "\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.savefig('Kalman-Filter-CA-CovarianceMatrix.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NzAqu20N8kvYE/icVHRNgJtnIGen+uIr2myLitYhYQTbCdkg7++UiCTOzAuvA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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1170d1bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_P2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Kalman Gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_K():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "    plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "    plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "    plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "    plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
    "    plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "    plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EhcUlSiVhBWJealK8erXJ1Bdr6GEFAEQexgMCMSivqFiSlMaiSwDkzWN97pPV\nOuHBmUGVv+TYbP3P6V1CHBUAACSsQEwqTVhTSFgBSLp0QDvtziuSr8QFXHbhup16ZcE63Ti4s8ys\nFqIDAMQyElYgBuUVegkrQ4IBSFL7Zul68Be9gyr74mdrdPdbS7R+R57aNU0LbWAAgJjHHFYgBjEk\nGECoDOzQVJI0P3d7mCMBANRHJKxADKKHFUCodGnRQI3TEjU/l0WbAAChR8IKxKDShJXb2gA4UnFx\npgEdmtDDCgCoFcxhBWIQQ4IBhNLADk01Y8kWTf9mkzJSEwMu3yozRR2bN6iFyAAA0Y6EFYhBpQlr\nKgkrgBA4sUszSdL1Ly8MqnxaUrwW3nUmoz4AAIcgYQVi0AHmsAIIoa4tG+r9/z1Je/J8AZddvGGX\n7nt3qRau26njOzWrhegAANGMhBWIQfn0sAIIse5ZGUGV69GqoR6YvkyfrdpOwgoAOASLLgExiFWC\nAUSKhimJOqpNpj5dxaJNAIBDkbACMegAqwQDiCCDOjXV1+t3aX9B4EOKAQD1GwkrEIPyi4qVnBCn\n+DgLdygAoOM7NZWvxOnzNdzLFQBQHnNYgRiUV1TM/FUAEaN/ThMlxpuu//tCpSQG/lt6WlKCXr32\nOGU3SauF6AAA4UTCCsSgA4XFzF8FEDFSk+J1/0VH6duNuwMu6ytxemX+Os1YslmjTupYC9EBAMKJ\nhBWIQfSwAog0v+yfrV/2zw6q7LzV2/Xf77eRsAJAPcQcViAG5dPDCqAeOalzM81fvUOFvpJwhwIA\nCDESViAGMSQYQH1yQudmyisq1sJ1O8MdCgAgxEhYgRjEkGAA9clxnZoqPs7035Xbwh0KACDEmMMK\nxKD8omK1aJgc7jAAICQyUhJ1dNtMPT83V9O/3RRw+Tgz3f7z7hrcvWUtRAcAOBIkrEAMOlBIDyuA\n+uWmM7rq9S/WB1X20++36ZX560hYASACkbACMSivqFhpJKwA6pFTujbXKV2bB1X2j//6Rv9cuFGF\nvhIlJTBbCgAiCd/KQAzKLyxWCosuAYAk6eQuzXWgsFhfrN0R7lAAABWQsAIxxjmnA0WsEgwApQZ1\naqqEONOcFSzaBACRhoQViDFFxU7FJY4hwQDg1zAlUcfkNNacFVvDHQoAoALmsAIxJq+oWJIYEgwA\nZZzctbkenrFc7W97N6jyQ/u01uOX9A1xVAAAElYgxuQVegkrqwQDwE8uH9hOzjkVFruAy36eu0Pv\nfbNZfxlgpySMAAAgAElEQVTmU1oSl1YAEEp8qwIxprSHlTmsAPCTRmlJunFwl6DKzv1+my6fNF+f\nfr9dZ/Tk1jgAEErMYQViTGkPK3NYASA0jm3fROlJ8frP8h/DHQoA1DskrECMySvySWIOKwCESlJC\nnE7s0kz/WfajnAt8SDEAoGoMCQai1Kbdedq4My/gcos37JbEkGAACKXTurXQjCVb9Nwnq9UoLSng\n8q0zU3Vil2a1EBkARDcSViBKDZ0wV1v2FARdvmmDwC+oAACVG9y9hZIS4vSX95YFVd5M+vS2wWqV\nmRriyAAgupGwAlFqx/5CnX90a/2yf9uAyzZMSVTnFg1rISoAiE0tMlL0+R1naG9BUcBl1+/I06XP\nzdPHS3/UFcfl1EJ0ABC9SFiBKFRc4lRU7NS5eQOd1KV5uMMBAEjKTEtUZlpiwOXaNEpVuyZp+njp\nFhJWAKiARZeAKFTg81b6TU7kIwwA0c7MdHqPFpq7arsOFPrCHQ4ARBSudoEolF9UIklKSeAjDAD1\nwRk9WqrQV6L/rtwW7lAAIKIwJBiIQj/1sLLSLwDUB8e2b6KGyQm6/uWFSoizgMsnJ8TplWuOU682\nmbUQHQCEDwkrEIUO9rAyJBgA6oWkhDiN/+XR+nLdzsALO+n5T9fozUUbSVgB1DskrEAUOtjDmkAP\nKwDUF0N+lqUhP8sKquyKLXv1wXeb9cdze8gs8B5aAIhUdM8AUajA38OazBxWAIC8ZHf9jjwt37I3\n3KEAQEhxtQtEofwir4c1hTmsAABJp/doITPpgyVbwh0KAIQUQ4KBKFTgo4cVAPCTFg1T1K9dY039\ndI3mrd4ecHkzadRJHXVatxa1EB0ABI+rXSAK0cMKAKjoulM6qXPzBioqLgn4v2837tHE/6wK9ykA\nwCHoYQWiED2sAICKzuzZUmf2bBlU2cc/WqEnPl6prXsL1LxhcogjA4DgcbULRCF6WAEAoXR2ryw5\nJ33w3eZwhwIA5ZCwAlGIHlYAQCh1a9lQHZql6/1vSVgBRBaGBANRqLSHNZkeVgBACJiZzvpZliZ9\nslrXvvhFUHUM6tRUV5/QIcSRAYh1JKxAFKKHFQAQar/s31afrd6udTsOBFx2x/5CzVqxVRf3z1aD\nZC4vAYQO3yhAFCoo7WElYQUAhEjH5g301pgTgiq7IHeHfvnsZ/p46RZd2KdNiCMDEMu42gWiUIGv\nRMkJcTKzcIcCAID65zRWi4bJmv4Nc2ABhBYJKxCFShNWAAAiQVyc6ZxeWfrP8h+1v8AX7nAA1CMM\nCQaiUH5RMbe0AQBElHN7t9YLn63V0AlzlRbEPNbmDZL01GX9+PcNQDkkrEAUKvCVKDmRHlYAQOTo\nn9NYlw5opx925QVcNq+wWB8t/VGzlv+os3u1qoXoAEQrElYgCuUXFSslgV+g4dm9e7e2bdumwsLC\ncIcCxKSkpCQ1a9ZMmZmZ4Q4lrOLiTA8MOyqosr7iEg38y8f699ebSFgBlEPCCkQhelhRKj8/X1u2\nbFHbtm2VmprKQlxAHXPOKS8vTxs2bFBycrJSUlLCHVJUSoiP08+PaqU3vlyv/QU+pXNrHAB+XPEC\nUYgeVpTaunWrmjdvrrS0NJJVIAzMTGlpaWrWrJm2bt0a7nCi2vlHt1Z+UYne/3az8ouKA/6v0H+P\ncgD1Cz9fAVGowFeiFHpYIa+HNSsrK9xhADGvYcOG2r59e7jDiGr9cxorKyNFv3/ja/3+ja8DLh9n\n0uQRx+q0bi1qIToA4ULCCkSh/KJiNUpNDHcYiAA+n08JCXyVA+GWkJAgn4/buRyJuDjThMv7akHu\nzqDKT/7var26YB0JK1DPcJUDRCHmsKIshgID4cfnMDSOyWmiY3KaBFV2694C/X3eWu0+UKTMNH7U\nBeoLrniBKMQcVgAAyruwT2sVFpfo/SWbwh0KgBCihxWIQvSwAgBQXu+2mWrfNE0vfLpWBUEuwHRq\n1xZq1zQtxJEBOBIkrEAUyi8qVjI9rEBIzJo1S6eddpqef/55jRgxItzhRLzabK/c3FyNHTtWc+fO\n1bZt23TVVVdp6tSpIT0G6i8z06+Obaf/e3+Z7n5rSVB1nNB5s14edVyIIwNwJEhYgShEDytiUWmi\n9PDDD+vmm28ut2327Nm64IILlJaWphkzZqh3795hijIy5Ofna8qUKZo2bZq++eYb7dq1S+np6erS\npYsGDx6sq6++Wt27dw93mIcYMWKEFi9erDvvvFNZWVnq1KlTuENClLnulI665NhslTgXcNnnPsnV\ns3NWafPufGVlcj9dIFKQsAJRxjmnQl8JPayA3zvvvKOLL75YWVlZ+uijj2I+yVm9erXOO+88LV26\nVKeccorGjh2rVq1aad++ffrqq680ZcoUPfLII1q3bp3atGkTcP0nn3yy8vLylJgY2kVtCgoK9Mkn\nn+jGG2885AcJoKbMTI3Tk4Iq+6tjs/XM7FV666uNGn1KbH+PAJGEhBWIMqXzcrgPKyC98soruuqq\nq9StWzd98MEHat26dbhDCqu8vDyde+65WrVqlf75z3/qoosuOmSf/Px8PfbYY0GvahsXF6eUlND3\nPm3ZskXOOTVpEtwKsVUpLi5WQUGB0tKYl4jD69AsXX2yG+nNRSSsQCThiheIMgVFXsJKDyti3cSJ\nE3XFFVeoX79+mjNnTrlkde/evfrjH/+ogQMHqlmzZkpOTlbnzp1122236cCBA9XWPXXqVJmZPv74\nY91zzz3KyclRamqqBg4cqHnz5knyhiGfeOKJSk9PV6tWrXTvvfceUk8gcZQec+bMmXrkkUfUqVMn\nJScnq2vXrnrhhRdq1CaTJk3SsmXLdMstt1SarEpSSkqKbr/99qDba9asWTKzcnNLjzT2ESNGKCcn\nR5I0btw4mZnMTLNmzZIkbdu2TWPGjFF2draSkpKUnZ2tMWPGaPv27eXqKY3jo48+0r333qtOnTop\nJSVFr7/++mGPn5eXp7Zt26pdu3YqKCgot23UqFGKj4/Xq6++Wu15IPoN69dGyzbvVZ97PlDfIP4b\nOfVzuSCGIwOoGj2sQJTJ9xVLoocVse2BBx7QHXfcocGDB+utt95SgwYNym3fuHGjJk2apF/84he6\n7LLLlJCQoNmzZ+uhhx7SokWLNGPGjBod57bbblNxcbFuuukmFRYWavz48RoyZIhefPFFjRw5Utde\ne60uv/xyvf7667r77rvVoUMHXXHFFUcUxx133KG8vDyNHj1aycnJmjhxokaMGKHOnTvrhBNOOGy8\n06ZNk+QlWYEIVXsFG/vo0aPVp08fjR07VhdddJGGDRsmSerRo4d2796t448/Xt9//71+85vfqF+/\nflq0aJEmTpyomTNnasGCBWrYsGG5+m6++WYVFRXpmmuuUUZGhrp163bYuFNTUzVu3DiNGjVKTz/9\ntMaOHStJuv322zV58mRNmDBBl1xySY3aANHtF/3aauPOPOUVFQdcdv2OA/p42Y9a8sMe9WqTWQvR\nAbGJhBWIMvSwoibG/XuJvvthT7jDKKdn6wz96fyfHXE9EydO1OrVqzV06FC9+uqrSk5OPmSfjh07\nav369eXmWY4ZM0Z33XWX7rvvPi1YsEADBgyo9ljFxcWaN2+ekpK8OXE9e/bUhRdeqIsvvlifffaZ\n+vfvL0kaOXKkcnJyNGHChHIJazBxFBQU6PPPPz94zOHDh6tjx4566qmnqk1Yv/32W2VkZKhDhw6H\nnMfOnTvLPZeenq7U1NSQtlewsQ8aNEitWrXS2LFj1bt373JteOedd2rlypWaMGGCbrjhhoPP9+nT\nRzfeeKMeeuihQ3q38/LytGjRooCGAY8YMUKPPfaYHnjgAV1zzTWaNGmSHnzwQY0bN67ccVG/pScn\n6Paf9wiq7K4DhRpw/8f6x8INJKxACNFFA0QZelgR6zZt2iRJB4edViYpKelg8uXz+bRz505t27ZN\nZ5xxhiRp/vz5NTrW9ddffzD5kqSTTjpJkjRw4MCDyWrp8QYMGKCVK1cecRw33HBDuWO2adNGXbt2\nPaTuyuzZs0cZGRmHPL906VI1b9683H8TJkw4ojgrcySxV+XNN99U8+bNde2115Z7fvTo0WrevLne\nfPPNQ8pcf/31Ac9ZjY+P14MPPqitW7fqwgsv1O9+9zv9z//8j+6+++6gY0dsaZSWpNN7tNDbX/2g\nouLg7gML4FD0sAJRhh5W1EQoejIj1W233abZs2dr/Pjxcs5p/Pjxle739NNP65lnntGSJUtUUlL+\n4rFib2NVOnbsWO5x48aNJemQHszSbRXnVAYTR8VjSlLTpk21du3aauPNyMjQnj2H9qx36NBBH374\noSTp66+/rnQV3tpor0Bir0pubq769++vhITylywJCQnq2rWrFi5ceEiZrl27BnWs8847T3379tXM\nmTN1ySWX6IknngiqHsSuX/Rrq+nfbtat0xarecPKf1A7nMzURI0+uaMS4vlRGihFwgpEGXpYEevS\n0tL0zjvv6Pzzz9ejjz6qkpISPfbYY+X2efTRR/X73/9eQ4YM0W9/+1u1bt1aSUlJ2rhxo0aMGHFI\nQlaV+PjKfxiq6vmKgomjqrprspBLr169NGfOHOXm5pZLqtPT0w/2llZM/IKNszJHEnsoBbsi8Guv\nvaavv/5aktSwYcOgV1JG7DqlW3P1bJWh97/dHHDZEudU4CtRp+YNdHavrFqIDohOJKxAlKGHFfAW\nyfn3v/+tCy64QI8//ricc3r88ccPbn/ppZfUvn17TZ8+XXFxP/248/7779dpnHUdx/DhwzVnzhxN\nmjRJ999/f43LRUp7VaZjx45avny5fD5fuWTb5/NpxYoVlfbqBuODDz7Qr3/9a1100UVKTEzUlClT\nNHbsWPXoEdx8RsSmxPg4vXfTSUGVLS5xOv7Bj/XGF+tJWIEyatRFY2Znm9lyM/vezG6rZHt3M/vM\nzArM7OYK29aY2Tdm9pWZfRGqwIFYlV9EDysgeUnr22+/rTPPPFNPPPGEbrrppoPb4uPjZWblevZ8\nPp8efPDBOo2xruMYNWqUunfvrocffrjSuZ1S5b2dkdJelRk6dKi2bt2qSZMmlXv+ueee09atW6u8\nfU8g5s+fr2HDhumEE07Qyy+/rPvuu09xcXG6/fbbj7huoKbi40zD+rXVf5b/qB/35Ic7HCBiVNvD\nambxkiZIOlPSBkmfm9nbzrnvyuy2Q9JvJQ2toprTnHPbjjRYAFKBjx5WoFRp0nrhhRfqySefVElJ\nif76179q+PDhuv3223XOOedo2LBh2rNnj1555ZVyq+DWhbqOIzU1Ve+++67OO+88DRs2TKeeeqqG\nDBmirKws7dmzR8uWLdNrr72m+Ph4ZWdnhy3OQNx666164403NGbMGC1cuFB9+/bVokWLNHnyZHXr\n1k233nrrEdX/3Xff6ec//7m6du2qf/3rX0pOTlanTp00cuRIPfPMM5o7d261qzMDoXLxMW01cdYq\nPT1rlU7v0SLg8vFxpv45TZSUwI/aqD9qMiR4gKTvnXOrJcnMXpV0oaSDCatz7kdJP5rZubUSJYCD\n6GEFyktJSdFbb72loUOH6qmnnlJJSYmefPJJOec0efJk3XTTTcrKytKvfvUrXX311erZs2edxXbL\nLbfUeRwdO3bUl19+qSlTpmjatGkaP368du/erfT0dHXu3FmjRo3SyJEjy92bNBxx1lRmZqbmzp2r\nP/3pT3r77bf1/PPPq2XLlrruuus0bty4Q+7BGoh169bprLPOUuPGjTV9+vRyKyzfddddeuGFF3Tr\nrbdq7ty5oTgVoFodmzfQwA5NNPXTNZr66Zqg6rjlrG4ac1rn0AYGhJFVtxCCmQ2XdLZzbpT/8ZWS\nBjrnbqxk3z9L2uece6TMc7mSdksqlvSsc+5vVRznWknXSlK7du2OOZIVBYH67JX563THm99o3u2n\nKyszJdzhIMyWLl3KHDsgQvB5RCjsPlCklT/uDarsg9OXacvefM2++TTFxbFoGCKXmX3pnOtf/Z51\ns+jSic65jWbWQtKHZrbMOTen4k7+RPZvktS/f/+6XU4QiCIF/lWCkxnuAwBAvZOZlqj+7ZsEVfbK\nQTm66dWv9Nnq7Tqhc7MQRwaER00S1o2Ssss8but/rkaccxv9///RzN6UN8T4kIQVQM3k+1cJTklk\nDisAAPjJWT/LUmZqov4+b626tGgQVB1NGyQrnt5ZRJCaJKyfS+piZh3kJaqXSLqsJpWbWbqkOOfc\nXv/fQyTdE2ywAOhhBQAAlUtJjNdFfdto6qdrND2Ie8FK0vlHt9ZfL+0b4siA4FWbsDrnfGZ2o6QZ\nkuIlTXHOLTGz6/zbnzGzLElfSMqQVGJm/yupp6Rmkt7033g7QdIrzrnw39QNiABFxSUqLgl89Pv+\nAp+S4uOYmwIAAA4x9oyu6p7VUMXVrFNTmU9WbNN732zSH8/toZYZrJOByFCjOazOufckvVfhuWfK\n/L1Z3lDhivZIOvpIAgTqo4278nT6+FkHh/cGKjM1/LeaAAAAkSczLVGXDGgXVNkTOjXT+0s2640v\n1uvGwV1CHBkQnLpYdAlABT/sylN+UYl+1T9b7ZulB1y+e1bwt3EAAACoTPtm6Tqhc1P9vwXrNeqk\njoqzwEdzJcQZo8AQUiSsQBgU+HtWh/Vro4Edm4Y5GgAAAM+lA9rpxlcWqftdwc3i69gsXTPGnqzE\neNbaQGiQsAJhUFjsXziJlX4BAEAEOadXK427oFD7CnwBl928O18vzVurj77bonOOalUL0SEWkbAC\nYVDaw8pKvwAAIJLEx5muOr59UGWLS5xmLvtRf5+/loQVIUPCCoRBYbGXsCaRsAIAgHoiPs502cB2\nenjGci3bvEc5TQJfpyM+zrg+QjkkrEAY0MMKAADqo4v7t9VjH67Q2Y9/ElT5pPg4vXXjCerRKiPE\nkSFakbACYVDg889hTWAOKwAAqD9aNEzR3359jFZs2RdwWeekJz9eqalz1+j/hveuhegQjUhYgTAo\n8DEkGAAA1E+Du7fU4O4tgyq7bsd+vbloo+74eQ9lpnHfeZCwAmFRmrAyJBgAAOAnVx7XXv9vwXpN\nmZuroX3bBFw+zqTsxmncC7YeIWEFwoCEFYgcs2bN0mmnnabnn39eI0aMCHc4Ea822ys3N1djx47V\n3LlztW3bNl111VWaOnVqSI8BILL1bJ2hY9s31hMfr9QTH68Mqo7fn9lV/3N6lxBHhnAhYQXCoNBX\noqT4OJnx6x9QU6WJ0sMPP6ybb7653LbZs2frggsuUFpammbMmKHevWN77lN+fr6mTJmiadOm6Ztv\nvtGuXbuUnp6uLl26aPDgwbr66qvVvXv3cId5iBEjRmjx4sW68847lZWVpU6dOoU7JABh8MQlfbUg\nd0dQZV+ev1YvfLZWo0/pxNSreoKEFQiDAl8xvatAiLzzzju6+OKLlZWVpY8++ijmk5zVq1frvPPO\n09KlS3XKKado7NixatWqlfbt26evvvpKU6ZM0SOPPKJ169apTZvAh9udfPLJysvLU2JiaOeWFRQU\n6JNPPtGNN954yA8SAGJL60apQQ0HlqTG6Um6asoCvffNpqDrQGQhYQXCoMBXouREElbgSL3yyiu6\n6qqr1K1bN33wwQdq3bp1uEMKq7y8PJ177rlatWqV/vnPf+qiiy46ZJ/8/Hw99thjQY/wiIuLU0pK\nypGGeogtW7bIOacmTZqEtN7i4mIVFBQoLS0tpPUCiEwndW6mjs3S9bc5q4PuYT2qTaaym/CdESm4\nYgbCoHRIMIDgTZw4UVdccYX69eunOXPmlEtW9+7dqz/+8Y8aOHCgmjVrpuTkZHXu3Fm33XabDhw4\nUG3dU6dOlZnp448/1j333KOcnBylpqZq4MCBmjdvniRvGPKJJ56o9PR0tWrVSvfee+8h9QQSR+kx\nZ86cqUceeUSdOnVScnKyunbtqhdeeKFGbTJp0iQtW7ZMt9xyS6XJqiSlpKTo9ttvD7q9Zs2aJTMr\nN7f0SGMfMWKEcnJyJEnjxo2TmcnMNGvWLEnStm3bNGbMGGVnZyspKUnZ2dkaM2aMtm/fXq6e0jg+\n+ugj3XvvverUqZNSUlL0+uuvH/b41113ncxMP/zwwyHbli9frqSkJP32t7+t9jwAhF9cnOnqEzvo\nu017dMPLC4P676rnF6ikxIX7VOBHDysQBl4PK/dgBYL1wAMP6I477tDgwYP11ltvqUGDBuW2b9y4\nUZMmTdIvfvELXXbZZUpISNDs2bP10EMPadGiRZoxY0aNjnPbbbepuLhYN910kwoLCzV+/HgNGTJE\nL774okaOHKlrr71Wl19+uV5//XXdfffd6tChg6644oojiuOOO+5QXl6eRo8ereTkZE2cOFEjRoxQ\n586ddcIJJxw23mnTpkmSRo0aVaPzO5I4KxNs7KNHj1afPn00duxYXXTRRRo2bJgkqUePHtq9e7eO\nP/54ff/99/rNb36jfv36adGiRZo4caJmzpypBQsWqGHDhuXqu/nmm1VUVKRrrrlGGRkZ6tat22Hj\nHjRokJ599lktWLBAQ4cOLbdt7NixysjI0Lhx42rUBgDC7/IB7XR8p6byFQeedM79fpvueec7zV65\nVad1a1EL0SFQJKxAGBQyhxW1bfpt0uZvwh1FeVlHSec8eMTVTJw4UatXr9bQoUP16quvKjk5+ZB9\nOnbsqPXr15ebZzlmzBjddddduu+++7RgwQINGDCg2mMVFxdr3rx5SkpKkiT17NlTF154oS6++GJ9\n9tln6t+/vyRp5MiRysnJ0YQJE8olrMHEUVBQoM8///zgMYcPH66OHTvqqaeeqjZh/fbbb5WRkaEO\nHTocch47d+4s91x6erpSU1ND2l7Bxj5o0CC1atVKY8eOVe/evcu14Z133qmVK1dqwoQJuuGGGw4+\n36dPH91444166KGHDundzsvL06JFi2o8DPi4446TpEMS1nfffVfTp0/XhAkT1Lhx4xrVBSD84uJM\nnZo3qH7HSnRolq5nZq/SlP/mkrBGCBJWIAwKfCWsXAcEadOmTZJ0cNhpZUoTJkny+Xzau3eviouL\ndcYZZ+i+++7T/Pnza5SAXX/99eXqOumkkyRJAwcOPJislh5vwIABmjt37hHHccMNN5Qr16ZNG3Xt\n2lUrV1Z/e4c9e/YoKyvrkOeXLl2qo446qtxzZVdbDlV7HUnsVXnzzTfVvHlzXXvtteWeHz16tMaN\nG6c333zzkIT1+uuvD2jOateuXdWkSRMtWLDg4HNFRUX63e9+p169emn06NFBxw8guiQlxOnXg3L0\nyAcrdOu0rxUfF/j1WtvGqbrh1E7cDSJESFiBMCgoKqGHFbUrBD2Zkeq2227T7NmzNX78eDnnNH78\n+Er3e/rpp/XMM89oyZIlKikpKbetYm9jVTp27FjucWkvW8UezNJtFedUBhNHxWNKUtOmTbV27dpq\n483IyNCePXsOeb5Dhw768MMPJUlff/11pavw1kZ7BRJ7VXJzc9W/f38lJJS/ZElISFDXrl21cOHC\nQ8p07do1oGOYmY477jjNnTtXzjmZmZ544gmtWLFCH330keLjmcIBxJLLBubo319v0n+Wbw24bFFx\niXYdKNKx7ZtoQIfQLiIXq0hYgTAoLC5RCqsEA0FJS0vTO++8o/PPP1+PPvqoSkpK9Nhjj5Xb59FH\nH9Xvf/97DRkyRL/97W/VunVrJSUlaePGjRoxYsQhCVlVqkpUaprABBNHVXU7V/1crF69emnOnDnK\nzc0tl1Snp6frjDPOkKRDEr9g46zMkcQeSsGsCHzcccfpvffe0/Lly9WkSRPde++9Gjp0qE4//fRa\niBBAJGuSnqQZY08OqmxeYbEGPfixJv93NQlriJCwAmFQ4CtWZmpo72EIxJLU1FT9+9//1gUXXKDH\nH39czjk9/vjjB7e/9NJLat++vaZPn664MsO53n///TqNs67jGD58uObMmaNJkybp/vvvr3G5SGmv\nynTs2FHLly+Xz+crl2z7fD6tWLGi0l7dYAwaNEiSN491zpw5KigoqLL3HgCqkpoUrysG5mjCrO+1\ndvt+5TRND3dIUY+EFQgDhgQDRy41NVVvv/22LrzwQj3xxBNyzumJJ56Q5PX0mVm5nj2fz6cHH6zb\nodJ1HceoUaP09NNP6+GHH1b//v0rvbVNZb2dkdJelRk6dKj+8pe/aNKkSbruuusOPv/cc89p69at\nIZtfOmDAAMXFxWnSpEmaO3eubrnllpAlwwBiy68H5ejZOas05LE5Qd3GMDkxTlOvHqBebTJrIbro\nQ8IKhEFhMYsuAaFQNml98sknVVJSor/+9a8aPny4br/9dp1zzjkaNmyY9uzZo1deeaXcKrh1oa7j\nSE1N1bvvvqvzzjtPw4YN06mnnqohQ4YoKytLe/bs0bJly/Taa68pPj5e2dnZYYszELfeeqveeOMN\njRkzRgsXLlTfvn21aNEiTZ48Wd26ddOtt94akuNkZGSoZ8+e+uSTT5SVlaU777wzJPUCiD0tMlL0\nyMVH6+v1u4Mq/8aX6zVx1ipNuLxfiCOLTiSsQBjQwwqETkpKit566y0NHTpUTz31lEpKSvTkk0/K\nOafJkyfrpptuUlZWln71q1/p6quvVs+ePesstltuuaXO4+jYsaO+/PJLTZkyRdOmTdP48eO1e/du\npaenq3Pnzho1apRGjhxZ7t6k4YizpjIzMzV37lz96U9/0ttvv63nn39eLVu21HXXXadx48Ydcg/W\nIzFgwAB9++23euCBB0JaL4DYc2GfNrqwT5ugyiYlxOlvc1Zp3fYDatc08Dn59Y3V9UIINdG/f3/3\nxRdfhDsMoNb0vecDnde7te4d2ivcoSDKLV26VD169Ah3GEDUKyoqUvfu3Q/e3iaY21HweQQQClv2\n5OvE/5up07u31Fm9WgZVR5cWDSN6SLGZfemc61/9nvSwAmFRyH1YASCiPPLII8rNzdXLL7/MvRMB\nhJhWtE0AACAASURBVFXLjBQNP6at/t+C9Xp/yeag6rj25I4RnbAGgoQVCIMCH0OCASDcduzYoRkz\nZmjx4sV6+OGH9bvf/U7HHXdcuMMCAN17YS+NPrlT0OUz6tHdKEhYgTpWXOLkK3FKTuBG9AAQTjNm\nzNBll12mFi1aaOzYsRGxKjIASFJCfJzaN+OWOBIJK1DnCn0lksSQYAAIs0svvVSXXnppuMMAABwG\nV8xAHSvwFUsSQ4IBAACAanDFDNSx0h7W5EQ+fgAAAMDhcMUM1LGC0iHB8Xz8AAAAgMPhihmoYweH\nBCey6BIAAABwOCSsQB0r7WFlDisAAABweFwxA3WsgFWCAQAAgBrhihmoYwVF9LACAAAANcEVM1DH\nCotLE1bmsAIAAACHQ8IK1LGCIu7DCgAAANQEV8xAHWPRJQCIbLNmzZKZaerUqeEOBQBiHlfMQB0r\n9DEkGAAAAKgJElagjrFKMBBZ6E0LTG22V25uroYOHarmzZvLzDRixIiQH6MmTj75ZOXl5enKK68M\ny/EBAD/hihmoYwU+5rACwShNlB555JFDts2ePVuZmZlq1aqVFi9eHIboIkt+fr6efvppDR48WM2b\nN1diYqIaNWqkY489Vn/4wx+0bNmycIdYqREjRmj27Nn6wx/+oJdeekmjR48OSxxxcXFKSUlRfDwj\nYQAg3BLCHQAQaw4OCU4kYQVC4Z133tHFF1+srKwsffTRR+rUqVO4Qwqr1f+fvXuPi6rO/wf+OgzM\nMCAoIAoiEZdAzFo0BC9dXBfZLpZItmmxRUmi4epSXsBMH6StboK3VOwrXtLNX5nfSLNMMxX8WokX\ntFTwipfMEi/JbRiYmc/vD4NtAoU5DDMM83o+Hj5Wz5zP57w4D9jOm8/lnD2LoUOHoqioCI888ghS\nU1Ph6+uLiooKHD58GKtWrUJmZiYuXLgAPz8/k/uvG310cnIya26tVos9e/Zg/PjxmDRpkln7JiIi\n28WClcjC6qcEK1iwErXU+vXr8eKLLyIsLAzbt29Ht27drB3JqjQaDZ544gmcOXMGn3zyCYYPH97g\nnOrqaixYsACSJMm6Rt3oo7n98ssvEELA09PTrP3q9XpotVq4uLiYtV8iIrIMPjETWViNzgCFgwRH\nFqxELZKdnY2EhAT06dMH+fn5RsVqeXk5pk+fjujoaHTu3BkqlQohISFIS0tDVVVVk32vWbMGkiTh\n66+/xltvvYWAgACo1WpER0fju+++A3BrGvKDDz4IV1dX+Pr6YtasWQ36MSVH3TV37tyJzMxMBAcH\nQ6VSITQ0FO+//36z7klOTg6Ki4sxefLkRotVAHB2dkZ6errs+9XYGtaWZk9MTERAQAAAICMjA5Ik\nQZIk7N69GwBw9epVpKSkwN/fH0qlEv7+/khJScG1a9eM+qnLsWPHDsyaNQvBwcFwdnbGhg0b7nh9\njUaD7t2746677oJWqzX6LCkpCQqFAh9++GGTXwcREZkfR1iJLEyr03P9KlELzZkzB9OmTcPgwYOx\nadMmdOjQwejzS5cuIScnB08//TSee+45ODo6Ii8vD++88w4KCwuxbdu2Zl0nLS0Ner0eEydORE1N\nDbKyshAbG4u1a9di9OjRGDNmDJ5//nls2LABM2bMQGBgIBISElqUY9q0adBoNEhOToZKpUJ2djYS\nExMREhKCgQMH3jHvxo0bAdwqskxhrvslN3tycjIiIiKQmpqK4cOHIz4+HgAQHh6OmzdvYsCAATh9\n+jRefvll9OnTB4WFhcjOzsbOnTtRUFAANzc3o/4mTZqE2tpavPLKK3B3d0dYWNgdc6vVamRkZCAp\nKQnLli1DamoqACA9PR0rV67E0qVLMXLkyGbdAyIiMjMhRJv788ADDwii9urNT38Qf8rYZu0Y1E4c\nP37c2hEsZteuXQKACAoKEgBEXFycqK6ubvRcrVYrampqGhyfPn26ACD27dvXoN/Vq1fXH1u9erUA\nIHr37i20Wm398U2bNgkAwtHRUezfv9/oej4+PqJfv36yc9RdMyIiwuiaP/74o1AqlWLkyJF3uDu3\neHp6Cnd39wbHdTqdKC0tNfpTVVUlK+ed7ldLspeUlAgAYubMmUbHp02bJgCIpUuXGh1fsmSJACCm\nT5/eIEdoaKiorKxs8pq/p9PpxL333iu8vb1FeXm5WLBggQAgMjIymt2HPf08EhG1BIADopm1IUdY\niSysRmfgCCu1un8X/BvF19vWTrA9PHtgatTUFvdz+fJlAKifdtoYpVJZ/3edTofy8nLo9XrExMRg\n9uzZ2LdvH6Kiopq81rhx44z6euihhwAA0dHRiIyMNLpeVFQU9u7d2+Icr776qlE7Pz8/hIaG4tSp\nU03mLSsrg4+PT4PjRUVFuO+++4yOzZs3r35zI3Pdr5Zkv53c3Fx4e3tjzJgxRseTk5ORkZGB3Nzc\nBtOxx40bZ/KaVYVCgblz5+LJJ5/EsGHDsGvXLvzjH//AjBkzZGcnIqKW41MzkYVpdQaoHPmqBCK5\n0tLSMHjwYGRlZeH111+/7XnLli3D/fffD5VKBU9PT3h7e2PQoEEAgBs3bjTrWkFBQUb/9vDwAAAE\nBgY2ONfDw6PBmko5Of54TQDw8vJqtO8/cnd3R1lZWYPjgYGB+Oqrr/DVV181+logOTkb05Lst1NS\nUoKwsDA4Ohr/jt3R0RGhoaE4e/ZsgzahoaGyrjV06FD07t0bO3fuxLPPPotFixbJ6oeIiMyHI6xE\nFqbV6aHkCCu1MnOMZLZVLi4u2LJlC5588knMnz8fBoMBCxYsMDpn/vz5eP311xEbG4sJEyagW7du\nUCqVuHTpEhITE2EwGJp1rdu9h7O57+eUk+N2fd+aQXVnvXr1Qn5+PkpKSoyKaldXV8TExABAg8JP\nbs7GtCS7OcndEfijjz7CkSNHAABubm6yd1ImIiLzYcFKZGGcEkzUcmq1Gp999hmeeuopLFy4EEII\nLFy4sP7zdevW4e6778bWrVvh4PDfn7cvv/zSojktnWPEiBHIz89HTk4O3n777Wa3ayv3qzFBQUE4\nceIEdDqdUbGt0+lw8uTJRkd15di+fTteeOEFDB8+HE5OTli1ahVSU1MRHh5ulv6JiEgePjUTWZiW\nBSuRWajVamzevBlDhgzBokWLMHHixPrPFAoFJEkyGtnT6XSYO3euRTNaOkdSUhJ69OiBefPmITc3\nt9FzGhvtbCv3qzFxcXEoLS1FTk6O0fEVK1agtLT0tq/vMcW+ffsQHx+PgQMH4oMPPsDs2bPh4OCA\n9PT0FvdNREQtwxFWIgvT1ho4JZjITOqK1mHDhmHx4sUwGAx49913MWLECKSnp+Oxxx5DfHw8ysrK\nsH79ejg5OVk0n6VzqNVqfP755xg6dCji4+MxaNAgxMbGwsfHB2VlZSguLsZHH30EhUIBf39/q+U0\nxZQpU/Dxxx8jJSUFhw4dQu/evVFYWIiVK1ciLCwMU6ZMaVH/x48fx+OPP47Q0FB8+umnUKlUCA4O\nxujRo7F8+XLs3bu3ydcJERFR62HBSmRhWr0BnZTWfwgkai+cnZ2xadMmxMXFYcmSJTAYDFi8eDGE\nEFi5ciUmTpwIHx8fPPvss3jppZfQs2dPi2WbPHmyxXMEBQXh4MGDWLVqFTZu3IisrCzcvHkTrq6u\nCAkJQVJSEkaPHm30blJr5Gyujh07Yu/evZg5cyY2b96M1atXo2vXrhg7diwyMjIavIPVFBcuXMBf\n//pXeHh4YOvWrXB3d6//7M0338T777+PKVOmNNj9mYiILEey9EYIzREZGSkOHDhg7RhEt3Xyl3Is\n2Xkaehk/P/knS9E/yAv/80Jk0ycTNaGoqIhr7IjaCP48EhE1jyRJB4UQzXoY5ggrkQxfHv0Zm4/8\nhCBvV5i6h2QXNxUeCfNulVxERERERO0JC1YiGbQ6PRwkYOfrg6wdhYiIiIio3eLOL0Qy3Ho1TfPe\nw0hERERERPKwYCWSQaszQOXEHx8iIiIiotbEJ24iGbS1BigV/PEhIiIiImpNfOImkqFGzxFWIiIi\nIqLWxiduIhm0Oj3XsBIRERERtTIWrEQycEowEREREVHr4xM3kQycEkxERERE1Pr4xE0kg7bWAJUj\nf3yIiIiIiFoTn7iJZNDq9FByDSsRERERUatiwUokg1bHEVYiIiIiotbGJ24iGWpYsBIRERERtTo+\ncRPJoNUZoGTBSkRERETUqvjETSTDrSnBXMNKRNQe7d69G5IkYc2aNdaOQkRk91iwEsmg1ek5JZiI\niIiIqJXxiZtIBq5hJWo/OJpmmta8XyUlJYiLi4O3tzckSUJiYqLZr9EcDz/8MDQaDf7+979b5fpE\nRPRffOImMpEQgrsEE1lBXaGUmZnZ4LO8vDx07NgRvr6++P77762Qrm2prq7GsmXLMHjwYHh7e8PJ\nyQmdOnVC3759MXXqVBQXF1s7YqMSExORl5eHqVOnYt26dUhOTrZKDgcHBzg7O0Oh4NIPIiJrc7R2\nACJbU6M3AABUTnyQIWoLtmzZgmeeeQY+Pj7YsWMHgoODrR3Jqs6ePYuhQ4eiqKgIjzzyCFJTU+Hr\n64uKigocPnwYq1atQmZmJi5cuAA/Pz+T+68bfXRycjJrbq1Wiz179mD8+PGYNGmSWfsmIiLbxYKV\nyEQ1ulsFq1LBEVYia1u/fj1efPFFhIWFYfv27ejWrZu1I1mVRqPBE088gTNnzuCTTz7B8OHDG5xT\nXV2NBQsWQJIkWdeoG300t19++QVCCHh6epq1X71eD61WCxcXF7P2S0RElsEnbiITaXV1I6z88SGy\npuzsbCQkJKBPnz7Iz883KlbLy8sxffp0REdHo3PnzlCpVAgJCUFaWhqqqqqa7HvNmjWQJAlff/01\n3nrrLQQEBECtViM6OhrfffcdgFvTkB988EG4urrC19cXs2bNatCPKTnqrrlz505kZmYiODgYKpUK\noaGheP/995t1T3JyclBcXIzJkyc3WqwCgLOzM9LT02Xfr8bWsLY0e2JiIgICAgAAGRkZkCQJkiRh\n9+7dAICrV68iJSUF/v7+UCqV8Pf3R0pKCq5du2bUT12OHTt2YNasWQgODoazszM2bNhwx+uPHTsW\nkiThp59+avDZiRMnoFQqMWHChCa/DiIiMj+OsBKZqL5g5RpWIquZM2cOpk2bhsGDB2PTpk3o0KGD\n0eeXLl1CTk4Onn76aTz33HNwdHREXl4e3nnnHRQWFmLbtm3Nuk5aWhr0ej0mTpyImpoaZGVlITY2\nFmvXrsXo0aMxZswYPP/889iwYQNmzJiBwMBAJCQktCjHtGnToNFokJycDJVKhezsbCQmJiIkJAQD\nBw68Y96NGzcCAJKSkpr19bUkZ2PkZk9OTkZERARSU1MxfPhwxMfHAwDCw8Nx8+ZNDBgwAKdPn8bL\nL7+MPn36oLCwENnZ2di5cycKCgrg5uZm1N+kSZNQW1uLV155Be7u7ggLC7tj7v79++O9995DQUEB\n4uLijD5LTU2Fu7s7MjIymnUPiIjIzIQQbe7PAw88IIjaqrOlFSJg6hbxyaGL1o5CJI4fP27tCBaz\na9cuAUAEBQUJACIuLk5UV1c3eq5WqxU1NTUNjk+fPl0AEPv27WvQ7+rVq+uPrV69WgAQvXv3Flqt\ntv74pk2bBADh6Ogo9u/fb3Q9Hx8f0a9fP9k56q4ZERFhdM0ff/xRKJVKMXLkyDvcnVs8PT2Fu7t7\ng+M6nU6UlpYa/amqqpKV8073qyXZS0pKBAAxc+ZMo+PTpk0TAMTSpUuNji9ZskQAENOnT2+QIzQ0\nVFRWVjZ5zTrFxcUCgEhPTzc6vmXLlkavfTv29PNIRNQSAA6IZtaGHGElMpFWpwcAqBy56RK1XT//\n61/QFrWtnWBV4T3gM21ai/u5fPkyANRPO22MUqms/7tOp0N5eTn0ej1iYmIwe/Zs7Nu3D1FRUU1e\na9y4cUZ9PfTQQwCA6OhoREZGGl0vKioKe/fubXGOV1991aidn58fQkNDcerUqSbzlpWVwcfHp8Hx\noqIi3HfffUbH5s2bV7+5kbnuV0uy305ubi68vb0xZswYo+PJycnIyMhAbm5ug+nY48aNM2nNamho\nKDw9PVFQUFB/rLa2Fq+99hp69epltd2KiYiIU4KJTKat5ZRgImtKS0tDXl4esrKyIIRAVlZWo+ct\nW7YMy5cvx7Fjx2AwGIw+u3HjRrOuFRQUZPRvDw8PAEBgYGCDcz08PBqsqZST44/XBAAvLy+cP3++\nybzu7u4oKytrcDwwMBBfffUVAODIkSON7sLbGvfLlOy3U1JSgsjISDg6Gj+yODo6IjQ0FIcOHWrQ\nJjQ01KRrSJKEfv36Ye/evRBCQJIkLFq0CCdPnsSOHTv4ehsiIitiwUpkorrX2ihZsFIbZo6RzLbK\nxcUFW7ZswZNPPon58+fDYDBgwYIFRufMnz8fr7/+OmJjYzFhwgR069YNSqUSly5dQmJiYoOC7HZu\nV6g0t4CRk+N2fd+aQXVnvXr1Qn5+PkpKSoyKaldXV8TExABAg8JPbs7GtCS7OcnZEbhfv3744osv\ncOLECXh6emLWrFmIi4vDX/7yl1ZISEREzcWClchE/x1h5W/ciaxFrVbjs88+w1NPPYWFCxdCCIGF\nCxfWf75u3Trcfffd2Lp1Kxwc/vvLpS+//NKiOS2dY8SIEcjPz0dOTg7efvvtZrdrK/erMUFBQThx\n4gR0Op1Rsa3T6XDy5MlGR3Xl6N+/PwCgoKAA+fn50Gq1tx29JyIiy+EQEZGJ/ruGlT8+RNakVqux\nefNmDBkyBIsWLcLEiRPrP1MoFJAkyWhkT6fTYe7cuRbNaOkcSUlJ6NGjB+bNm4fc3NxGz2lstLOt\n3K/GxMXFobS0FDk5OUbHV6xYgdLS0tu+vsdUUVFRcHBwQE5ODlavXo1//vOfZiuGiYhIPo6wEpmo\nhu9hJWoz6orWYcOGYfHixTAYDHj33XcxYsQIpKen47HHHkN8fDzKysqwfv16ODk5WTSfpXOo1Wp8\n/vnnGDp0KOLj4zFo0CDExsbCx8cHZWVlKC4uxkcffQSFQgF/f3+r5TTFlClT8PHHHyMlJQWHDh1C\n7969UVhYiJUrVyIsLAxTpkwxy3Xc3d3Rs2dP7NmzBz4+PnjjjTfM0i8REbUMC1YiE9W9h1WpYMFK\n1BY4Oztj06ZNiIuLw5IlS2AwGLB48WIIIbBy5UpMnDgRPj4+ePbZZ/HSSy+hZ8+eFss2efJki+cI\nCgrCwYMHsWrVKmzcuBFZWVm4efMmXF1dERISgqSkJIwePdro3aTWyNlcHTt2xN69ezFz5kxs3rwZ\nq1evRteuXTF27FhkZGQ0eAdrS0RFReHo0aOYM2eOWfslIiL5JEtvhNAckZGR4sCBA9aOQdSoj/Zf\nwNT//QF70wbDr5Pa2nHIzhUVFSE8PNzaMYhsXm1tLXr06FH/ehtJkkzugz+PRETNI0nSQSFEZNNn\ncoSVyGT1U4K5hpWIqN3IzMxESUkJPvjgA1nFKhERtQ4WrEQmqp8SzIKViMimXb9+Hdu2bcP333+P\nefPm4bXXXkO/fv2sHYuIiH6HBSuRibQcYSUiahe2bduG5557Dl26dEFqamqb2BWZiIiMsWAlMhE3\nXSIiah9GjRqFUaNGWTsGERHdQbOeuCVJelSSpBOSJJ2WJCmtkc97SJL0rSRJWkmSJpnSlsjWaHV6\nKB0duMaJiIiIiKiVNVmwSpKkALAUwGMAegIYJUnSH/e4vw5gAoBMGW2JbEqNzsDpwEREREREFtCc\np+4oAKeFEGeFEDUAPgQw7PcnCCGuCCH2A6g1tS2RrdHqDFA5Kqwdg4iIiIio3WtOweoH4OLv/v3j\nb8eao9ltJUkaI0nSAUmSDpSWljazeyLL09ZyhJWIiIiIyBLazFO3EOJ/hBCRQohIb29va8chuq0a\nPQtWIiIiIiJLaM5T9yUA/r/7d/ffjjVHS9oStUnaWj3fwUpEREREZAHNeereD+AeSZICJUlSAhgJ\nYHMz+29JW6I2SctNl4iIiIiILKLJ97AKIXSSJI0HsA2AAsAqIcQxSZLG/vb5ckmSfAAcAOAOwCBJ\n0j8B9BRClDXWtrW+GCJLqOGmS0REREREFtFkwQoAQogvAHzxh2PLf/f3n3Frum+z2hLZMq1OD1dV\ns350iIiIiIioBTivkchEWp0BSgV/dIiIiIiIWhufuolMVKMzQOXEHx0iIiIiotbGp24iE2m5hpWI\nqN06d+4cJElCYmIiACAxMRGSJOHcuXNWzUVEZK+4EI/IRFqdnlOCiYjaKW9vb6xbtw7BwcEAgOTk\nZMTExIDviCcisg4+dROZiFOCidqX3bt3Q5IkrFmzxtpRbEJr3q+SkhLExcXB29vbaJTTklxdXZGQ\nkID+/fsDAPr374+EhAS4urpaPAsREbFgJTIZ38NKZB11hVJmZmaDz/Ly8tCxY0f4+vri+++/t0K6\ntqW6uhrLli3D4MGD4e3tDScnJ3Tq1Al9+/bF1KlTUVxcbO2IjUpMTEReXh6mTp2KdevWITk52dqR\niIjIyjglmMhEWp0BShasRG3Gli1b8Mwzz8DHxwc7duyon8ppr86ePYuhQ4eiqKgIjzzyCFJTU+Hr\n64uKigocPnwYq1atQmZmJi5cuAA/Pz+T+3/44Yeh0Wjg5ORk1txarRZ79uzB+PHjMWnSJLP2TURE\ntosFK5EJdHoD9AbBTZeI2oj169fjxRdfRFhYGLZv345u3bpZO5JVaTQaPPHEEzhz5gw++eQTDB8+\nvME51dXVWLBgASRJknUNBwcHODs7tzRqA7/88guEEPD09DRrv3q9HlqtFi4uLmbtl4iILIPDREQm\nqNEbAIBTgonagOzsbCQkJKBPnz7Iz883KlbLy8sxffp0REdHo3PnzlCpVAgJCUFaWhqqqqqa7HvN\nmjWQJAlff/013nrrLQQEBECtViM6OhrfffcdgFvTkB988EG4urrC19cXs2bNatCPKTnqrrlz505k\nZmYiODgYKpUKoaGheP/995t1T3JyclBcXIzJkyc3WqwCgLOzM9LT02Xfr8bWsLY0e2JiIgICAgAA\nGRkZkCQJkiRh9+7dAICrV68iJSUF/v7+UCqV8Pf3R0pKCq5du2bUT12OHTt2YNasWQgODoazszM2\nbNhwx+trNBp0794dd911F7RardFnSUlJUCgU+PDDD5v8OoiIyPw4wkp26eL1Khy6cMPkdlU1egDg\nlGAiK5szZw6mTZuGwYMHY9OmTejQoYPR55cuXUJOTg6efvppPPfcc3B0dEReXh7eeecdFBYWYtu2\nbc26TlpaGvR6PSZOnIiamhpkZWUhNjYWa9euxejRozFmzBg8//zz2LBhA2bMmIHAwEAkJCS0KMe0\nadOg0WiQnJwMlUqF7OxsJCYmIiQkBAMHDrxj3o0bNwK4VWSZwlz3S2725ORkREREIDU1FcOHD0d8\nfDwAIDw8HDdv3sSAAQNw+vRpvPzyy+jTpw8KCwuRnZ2NnTt3oqCgAG5ubkb9TZo0CbW1tXjllVfg\n7u6OsLCwO+ZWq9XIyMhAUlISli1bhtTUVABAeno6Vq5ciaVLl2LkyJHNugdERGReLFjJLr256Sh2\nnyiV3b6ru/mnwxFR82RnZ+Ps2bOIi4vDhx9+CJVK1eCcoKAgXLx40WidZUpKCt58803Mnj0bBQUF\niIqKavJaer0e3333HZRKJQCgZ8+eGDZsGJ555hl8++23iIyMBACMHj0aAQEBWLp0qVHBKieHVqvF\n/v376685YsQIBAUFYcmSJU0WrEePHoW7uzsCAwMbfB03bhj/ks7V1RVqtdqs90tu9v79+8PX1xep\nqam4//77je7hG2+8gVOnTmHp0qV49dVX649HRERg/PjxeOeddxqMbms0GhQWFpo0DTgxMRELFizA\nnDlz8MorryAnJwdz585FRkaG0XWJiMiyWLCSXSrT1CIywAP/HnG/yW2VCgd091C3Qioi89mz4SSu\nXqywdgwjnf074KG/hba4n8uXLwNA/bTTxtQVTACg0+lQXl4OvV6PmJgYzJ49G/v27WtWATZu3Dij\nvh566CEAQHR0dH2xWne9qKgo7N27t8U5Xn31VaN2fn5+CA0NxalTp5rMW1ZWBh8fnwbHi4qKcN99\n9xkdmzdvXv3mRua6Xy3Jfju5ubnw9vbGmDFjjI4nJycjIyMDubm5DQrWcePGmbxmVaFQYO7cuXjy\nyScxbNgw7Nq1C//4xz8wY8YM2dmJiKjlWLCSXaquNaBbJzWCvTs0fTIRtSlpaWnIy8tDVlYWhBDI\nyspq9Lxly5Zh+fLlOHbsGAwGg9FnfxxtvJ2goCCjf3t4eABAgxHMus/+uKZSTo4/XhMAvLy8cP78\n+Sbzuru7o6ysrMHxwMBAfPXVVwCAI0eONLoLb2vcL1Oy305JSQkiIyPh6Gj8yOLo6IjQ0FAcOnSo\nQZvQUHm/GBk6dCh69+6NnTt3YuTIkVi0aJGsfoiIyHxYsJJd0ur0UDlxHSq1X+YYyWyrXFxcsGXL\nFjz55JOYP38+DAYDFixYYHTO/Pnz8frrryM2NhYTJkxAt27doFQqcenSJSQmJjYoyG5HoWh8R/Db\nHf8jOTlu17cQosnr9erVC/n5+SgpKTEqql1dXRETEwMADQo/uTkb05Ls5iR3R+CPPvoIR44cAQC4\nubnJ3kmZiIjMhwUr2aXqWgOc+WoaIpulVqvx2Wef4amnnsLChQshhMDChQvrP1+3bh3uvvtubN26\nFQ4O//3l1JdffmnRnJbOMWLECOTn5yMnJwdvv/12s9u1lfvVmKCgIJw4cQI6nc6o2NbpdDh58mSj\no7pybN++HS+88AKGDx8OJycnrFq1CqmpqQgPDzdL/0REJA+HmMguaXUGjrAS2Ti1Wo3NmzdjyJAh\nWLRoESZOnFj/mUKhgCRJRiN7Op0Oc+fOtWhGS+dISkpCjx49MG/ePOTm5jZ6TmOjnW3lfjUmy5Nu\nVgAAIABJREFULi4OpaWlyMnJMTq+YsUKlJaW3vb1PabYt28f4uPjMXDgQHzwwQeYPXs2HBwckJ6e\n3uK+iYioZTjCSnZJW6vnCCtRO1BXtA4bNgyLFy+GwWDAu+++ixEjRiA9PR2PPfYY4uPjUVZWhvXr\n1xvtgmsJls6hVqvx+eefY+jQoYiPj8egQYMQGxsLHx8flJWVobi4GB999BEUCgX8/f2tltMUU6ZM\nwccff4yUlBQcOnQIvXv3RmFhIVauXImwsDBMmTKlRf0fP34cjz/+OEJDQ/Hpp59CpVIhODgYo0eP\nxvLly7F3794md2cmIqLWw4KV7BJHWInaD2dnZ2zatAlxcXFYsmQJDAYDFi9eDCEEVq5ciYkTJ8LH\nxwfPPvssXnrpJfTs2dNi2SZPnmzxHEFBQTh48CBWrVqFjRs3IisrCzdv3oSrqytCQkKQlJSE0aNH\nG72b1Bo5m6tjx47Yu3cvZs6cic2bN2P16tXo2rUrxo4di4yMjAbvYDXFhQsX8Ne//hUeHh7YunUr\n3N3d6z9788038f7772PKlCkNdn8mIiLLkSy9EUJzREZGigMHDlg7BrVTeoNA8LQvkBoTiokx91g7\nDlGLFBUVcY0dURvBn0ciouaRJOmgECKy6TO5hpXsUI3u1m6XHGElIiIiImrb+MROdqe6Vg8AcHbk\ntz8RERERUVvGJ3ayO9r6EVZuukRERERE1JaxYCW7Uz/CyinBRERERERtGp/Yye7Uj7DytTZERERE\nRG0aC1ayOxxhJSIiIiKyDXxiJ7vDEVYiIiIiItvAgpXsDkdYiYiIiIhsA5/Yye7UFawcYSUiIiIi\nattYsJLdqZsSzBFWIiIiIqK2jU/sZHc4wkpEREREZBtYsJLdqd90iSOsRERERERtGp/Yye5whJWI\niIiIyDawYCW7wzWsRERERES2gU/sZHe0tXpIEqBU8NufiIiMnTt3DpIkITExEQCQmJgISZJw7tw5\nq+YiIrJXjtYOQGRpWp0BKkcHSJJk7ShERNTGeHt7Y926dQgODgYAJCcnIyYmBt7e3lZORkRknzjE\nRHanulbP9atEVG/37t2QJAlr1qyxdhSb0Jr3q6SkBHFxcfD29jYa5bQkV1dXJCQkoH///gCA/v37\nIyEhAa6urhbPQkRELFjJDml1Bq5fJbJBdYVSZmZmg8/y8vLQsWNH+Pr64vvvv7dCuraluroay5Yt\nw+DBg+Ht7Q0nJyd06tQJffv2xdSpU1FcXGztiI1KTExEXl4epk6dinXr1iE5OdnakYiIyMo4JZjs\nDkdYidqXLVu24JlnnoGPjw927NhRP5XTXp09exZDhw5FUVERHnnkEaSmpsLX1xcVFRU4fPgwVq1a\nhczMTFy4cAF+fn4m9//www9Do9HAycnJrLm1Wi327NmD8ePHY9KkSWbtm4iIbBcLVrI7dWtYicj2\nrV+/Hi+++CLCwsKwfft2dOvWzdqRrEqj0eCJJ57AmTNn8Mknn2D48OENzqmursaCBQtkr+N3cHCA\ns7NzS6M28Msvv0AIAU9PT7P2q9frodVq4eLiYtZ+iYjIMvjUTnanulYPZyeOsBLZuuzsbCQkJKBP\nnz7Iz883KlbLy8sxffp0REdHo3PnzlCpVAgJCUFaWhqqqqqa7HvNmjWQJAlff/013nrrLQQEBECt\nViM6OhrfffcdgFvTkB988EG4urrC19cXs2bNatCPKTnqrrlz505kZmYiODgYKpUKoaGheP/995t1\nT3JyclBcXIzJkyc3WqwCgLOzM9LT02Xfr8bWsLY0e2JiIgICAgAAGRkZkCQJkiRh9+7dAICrV68i\nJSUF/v7+UCqV8Pf3R0pKCq5du2bUT12OHTt2YNasWQgODoazszM2bNhwx+uPHTsWkiThp59+avDZ\niRMnoFQqMWHChCa/DiIiMj+OsJLd4Qgrke2bM2cOpk2bhsGDB2PTpk3o0KGD0eeXLl1CTk4Onn76\naTz33HNwdHREXl4e3nnnHRQWFmLbtm3Nuk5aWhr0ej0mTpyImpoaZGVlITY2FmvXrsXo0aMxZswY\nPP/889iwYQNmzJiBwMBAJCQktCjHtGnToNFokJycDJVKhezsbCQmJiIkJAQDBw68Y96NGzcCAJKS\nkpr19bUkZ2PkZk9OTkZERARSU1MxfPhwxMfHAwDCw8Nx8+ZNDBgwAKdPn8bLL7+MPn36oLCwENnZ\n2di5cycKCgrg5uZm1N+kSZNQW1uLV155Be7u7ggLC7tj7v79++O9995DQUEB4uLijD5LTU2Fu7s7\nMjIymnUPiIjIzIQQbe7PAw88IIhay/Cl/yeeX/GdtWMQmcXx48etHcFidu3aJQCIoKAgAUDExcWJ\n6urqRs/VarWipqamwfHp06cLAGLfvn0N+l29enX9sdWrVwsAonfv3kKr1dYf37RpkwAgHB0dxf79\n+42u5+PjI/r16yc7R901IyIijK75448/CqVSKUaOHHmHu3OLp6encHd3b3Bcp9OJ0tJSoz9VVVWy\nct7pfrUke0lJiQAgZs6caXR82rRpAoBYunSp0fElS5YIAGL69OkNcoSGhorKysomr1mnuLhYABDp\n6elGx7ds2dLotW/Hnn4eiYhaAsAB0czakCOsZHe0OgM8XDjCSu3brjX/gyvnz1o7hpEuAUH4c+KY\nFvdz+fJlAKifdtoYpVJZ/3edTofy8nLo9XrExMRg9uzZ2LdvH6Kiopq81rhx44z6euihhwAA0dHR\niIyMNLpeVFQU9u7d2+Icr776qlE7Pz8/hIaG4tSpU03mLSsrg4+PT4PjRUVFuO+++4yOzZs3r35z\nI3Pdr5Zkv53c3Fx4e3tjzBjj753k5GRkZGQgNze3wXTscePGmbRmNTQ0FJ6enigoKKg/Vltbi9de\new29evXibsVERFbEgpXsDtewEtm2tLQ05OXlISsrC0IIZGVlNXresmXLsHz5chw7dgwGg8Hosxs3\nbjTrWkFBQUb/9vDwAAAEBgY2ONfDw6PBmko5Of54TQDw8vLC+fPnm8zr7u6OsrKyBscDAwPx1Vdf\nAQCOHDnS6C68rXG/TMl+OyUlJYiMjISjo/Eji6OjI0JDQ3Ho0KEGbUJDQ026hiRJ6NevH/bu3Qsh\nBCRJwqJFi3Dy5Ens2LEDCgX/m0FEZC0sWMnucA0r2QNzjGS2VS4uLtiyZQuefPJJzJ8/HwaDAQsW\nLDA6Z/78+Xj99dcRGxuLCRMmoFu3blAqlbh06RISExMbFGS3c7tCpbkFjJwct+v71gyqO+vVqxfy\n8/NRUlJiVFS7uroiJiYGABoUfnJzNqYl2c1Jzo7A/fr1wxdffIETJ07A09MTs2bNQlxcHP7yl7+0\nQkIiImouFqxkd6prDVBxhJXIpqnVanz22Wd46qmnsHDhQgghsHDhwvrP161bh7vvvhtbt26Fg8N/\nf0H15ZdfWjSnpXOMGDEC+fn5yMnJwdtvv93sdm3lfjUmKCgIJ06cgE6nMyq2dTodTp482eiorhz9\n+/cHABQUFCA/Px9arfa2o/dERGQ5HGYiu6PV6TnCStQOqNVqbN68GUOGDMGiRYswceLE+s8UCgUk\nSTIa2dPpdJg7d65FM1o6R1JSEnr06IF58+YhNze30XMaG+1sK/erMXFxcSgtLUVOTo7R8RUrVqC0\ntPS2r+8xVVRUFBwcHJCTk4PVq1fjn//8p9mKYSIiko8jrGR3tLUGrmElaifqitZhw4Zh8eLFMBgM\nePfddzFixAikp6fjscceQ3x8PMrKyrB+/Xo4OTlZNJ+lc6jVanz++ecYOnQo4uPjMWjQIMTGxsLH\nxwdlZWUoLi7GRx99BIVCAX9/f6vlNMWUKVPw8ccfIyUlBYcOHULv3r1RWFiIlStXIiwsDFOmTDHL\nddzd3dGzZ0/s2bMHPj4+eOONN8zSLxERtQwLVrIrBoNAjZ5rWInaE2dnZ2zatAlxcXFYsmQJDAYD\nFi9eDCEEVq5ciYkTJ8LHxwfPPvssXnrpJfTs2dNi2SZPnmzxHEFBQTh48CBWrVqFjRs3IisrCzdv\n3oSrqytCQkKQlJSE0aNHG72b1Bo5m6tjx47Yu3cvZs6cic2bN2P16tXo2rUrxo4di4yMjAbvYG2J\nqKgoHD16FHPmzDFrv0REJJ9k6Y0QmiMyMlIcOHDA2jGoHdLU6BE+40tMfbQHxg0KtnYcohYrKipC\neHi4tWMQ2bza2lr06NGj/vU2kiSZ3Ad/HomImkeSpINCiMimz+QIK9kZrU4PABxhJSIiI5mZmSgp\nKcEHH3wgq1glIqLWwYKV7Ep17a1XM3ANKxERXb9+Hdu2bcP333+PefPm4bXXXkO/fv2sHYuIiH6H\nBSvZFY6wEhFRnW3btuG5555Dly5dkJqa2iZ2RSYiImMsWMmucISViIjqjBo1CqNGjbJ2DCIiugMO\nM5Fd4QgrEREREZHt4FM72RWOsBIRERER2Q4WrGRX6kdYnfitT0RERETU1vGpnexK/QirI0dYiYiI\niIjaOm66RDbp8MVfcfF6lcntCi/8CoAjrEREREREtoAFK9kcvUHgb+99ixqdQVZ7hYMET1elmVMR\nWY8QApIkWTsGkV0TQlg7AhFRu8SClWxOda0eNToDxjwchL9Fdje5vbvaCZ07qFohGZHlOTk5QaPR\nwMXFxdpRiOyaRqOBk5OTtWMQEbU7LFjJ5lTV3No4yd9DjZAublZOQ2RdXbp0waVLl+Dn5we1Ws2R\nViILE0JAo9Hg0qVL6Nq1q7XjEBG1OyxYyeZU194qWNVKfvsSubu7AwB++ukn1NbWWjkNkX1ycnJC\n165d638eiYjIfPjETzanboRVzXepEgG4VbTyQZmIiIjaI26VSjZHUz/Cym9fIiIiIqL2jE/8ZHM0\n9SOsnCBARERERNSesWAlm6Op1QEA1EpOCSYiIiIias9YsJLN0dTcev+qCwtWIiIiIqJ2jQUr2Zz6\nNazcdImIiIiIqF1jwUo2R1Nza0qwMwtWIiIiIqJ2jQUr2Zy6EVZOCSYiIiIiat9YsJLNqXsPK0dY\niYiIiIjaNxasZHM0tXqoHB2gcJCsHYWIiIiIiFoRC1ayOdU1er7ShoiIiIjIDrBgJZtTVaPnDsFE\nRERERHaABSvZHE0tR1iJiIiIiOwBC1ayORqOsBIRERER2QUWrGRzNLUsWImIiIiI7AELVrI5nBJM\nRERERGQfWLCSzeGUYCIiIiIi+8CClWyOplYPF46wEhERERG1eyxYyeZU8T2sRERERER2gQUr2Zzq\nGj2cOSWYiIiIiKjdY8FKNodTgomIiIiI7AMLVrIpNToDdAbBTZeIiIiIiOwAC1ayKZpaPQBArXS0\nchIiIiIiImptLFjJplTXFawcYSUiIiIiavdYsJJNqaqpG2Hlty4RERERUXvHp36yKZq6gtWJU4KJ\niIiIiNq7ZhWskiQ9KknSCUmSTkuSlNbI55IkSYt/+/x7SZL6/O6zc5Ik/SBJ0mFJkg6YMzzZH02t\nDgD4HlYiIiIiIjvQ5DCVJEkKAEsBDAHwI4D9kiRtFkIc/91pjwG457c/0QCyf/vfOn8WQlw1W2qy\nW5oaAwDwtTZERERERHagOSOsUQBOCyHOCiFqAHwIYNgfzhkGYK245TsAnSRJ8jVzVqL/7hLMTZeI\niIiIiNq95hSsfgAu/u7fP/52rLnnCAA7JEk6KEnSmNtdRJKkMZIkHZAk6UBpaWkzYpE9qqq5NSXY\nmQUrEREREVG7Z4lNlx4UQkTg1rThFEmSHm7sJCHE/wghIoUQkd7e3haIRbao7rU2nBJMRERERNT+\nNadgvQTA/3f/7v7bsWadI4So+98rAHJxa4oxkSz1r7XhCCsRERERUbvXnIJ1P4B7JEkKlCRJCWAk\ngM1/OGczgBd+2y24H4CbQojLkiS5SpLkBgCSJLkCiAVw1Iz5yc7Ur2HlCCsRERERUbvX5C7BQgid\nJEnjAWwDoACwSghxTJKksb99vhzAFwAeB3AaQBWAl35r3hVAriRJdddaL4T40uxfBdmN6ho9JAlQ\nOfIVwkRERERE7V2TBSsACCG+wK2i9PfHlv/u7wJASiPtzgL4UwszEtWrqtFD7aTAb78EISIiIiKi\ndqxZBSuROQkhcPjir9D8th7VFOeuVXHDJSIiIiIiO8GClSzu4PkbGLH8W9ntQ7t2MGMaIiIiIiJq\nq1iwksWVlmsBAPNG3I+7PF1Mbh/g5WruSERERERE1AaxYCWLK9fqAAD9grzgL6NgJSIiIiIi+8Ct\nVsniKqpvFaxuzvx9CRERERER3R4LVrK4it9GWF1VLFiJiIiIiOj2WLCSxVVodXB2coCTgt9+RERE\nRER0e6wYyOLKq3XooHKydgwiIiIiImrjWLCSxVVodVy/SkRERERETWLBShZXUV2LDly/SkRERERE\nTWDBShZXodWxYCUiIiIioiaxYCWLK6/WoQOnBBMRERERURNYsJLFVWh1cOMIKxERERERNYEFK1lc\nhZYjrERERERE1DQWrGRRQghUVHMNKxERERERNY0FK1mUVmeAziA4wkpERERERE1iwUoWVV6tAwCu\nYSUiIiIioiaxYCWLqtDeKlhdWbASEREREVETWLCSRVX8NsLKNaxERERERNQUFqxkUXUjrFzDSkRE\nRERETWHBShZVV7C6qZysnISIiIiIiNo6FqxkURXaWgAcYSUiIiIioqaxYCWL4hpWIiIiIiJqLhas\nZFHldVOCOcJKRERERERNYMFKFlVRrYOjgwSVI7/1iIiIiIjozlg1kEVVaHXo4OwISZKsHYWIiIiI\niNo4FqxkURXVOq5fJSIiIiKiZmHBShZVrmXBSkREREREzcOClSyqolrHDZeIiIiIiKhZWDmQRVVo\ndejcQWntGGQGtYZaHL16FDqDTlZ7FycXdFF3gVIh7/tB7aiW3ZaIiIiIbAMLVjLZ1Qotvi76BQZh\netvLN6txd2dX84cii7pRfQOpu1Nx8JeDVsvgrnTH2w++jUH+g6yWgYiIiIhaFwtWMtmKPWfxXt5Z\n2e0DPF3MmIbkyj6cjY2nNspqW1lbiVp9Ld7s9yYCOwaa3F4IgfLacpRWlUIv9LLabz6zGf/Y+Q+E\neYTBQTJ9dYOrkyveiH4DIR4hJrclIiIiIstgwUomKy3XwrejM3JfHWhyW0kCuripWiEVmeLnyp+x\n4ocV6OHZA/d43GNyewfJAU/f8zR6de7VCuma55mwZ7Ds8DKc/VXeL0+OlB7B+J3jsf6J9fB09jRz\nOiIiIiIyBxasZLLrlTXo3EEFn47O1o5CMq38YSUEBDIfyUS3Dt2sHUcWlUKF1AdSZbf/ofQHvLTt\nJcR9Ggd3lbvJ7R0kB4y9fyweD3pcdgYiIiIiujMWrGSyG5U18HDlZjfW9kHRBzh546TJ7YQQ2HJ2\nC4YFD7PZYtUc7vO+D4v/vBibzmyCgOkLsk/dOIWZ38xEuFe4rGnRRERERNQ0FqxksmuVNQjy7mDt\nGHbtquYq5hbMhbvSHc6Opo90d3frjlfuf6UVktmWAX4DMMBvgKy2V6quIH5zPF7b/Roe6f6IrD76\ndeuHfr79ZLUlIiIisgcsWMlkNypr4OHCEVZryruYBwBY9ddVCPMMs3Ia+9TFpQtmDZiFN/a+gbXH\n15rc3iAMWHd8HT5+6mMEdQxqhYREREREto8FK5mkulaPyho9vPguVavafXE3url2Q6hHqLWj2LU/\n3/VnfHPXN7LaXtVcxbBPh2HG3hnIjsmGBMnkPlSOKjg5OMm6PhEREZEtYMFKJrlRVQMAHGG1Io1O\ng28vf4v4e+IhSaYXOdQ2dFZ3RlpUGqb93zQM+H/ypiV3VnfGfx7/D/w6+Jk5HREREVHbwIKVTHKt\n4lbB6slNl1rs2NVjqKitMLnd8WvHodVrMch/kPlDkUUNDRoKZ0dn/FTxk8lthRDIPpKNjG8y8N6Q\n9/jLCyIiImqXWLCSSepGWFmwtszRq0cx6vNRstu7K93Rt2tfMyYia5AkCUMChshu7+zojLf3vY3J\n+ZNlvUvWxdEFL977IjycPWRnICIiImpNLFjJJNcrWbCaw4GfDwAAlv5lKVwcXUxu79vBF04Krl20\nd38L+xsOXTmEb36St462vKYcZ26eweI/L+YILREREbVJLFjJJCxYzeNw6WHc5XYXHu7+sLWjkA1z\nkBzwzsPvyG7//rH3kXkgE+uL1yPaJ9rk9pIkIbBjIBwkB9kZiIiIiO6EBSuZ5HplDRwkoKOao3ty\nCSFw+MphDPQbaO0oZOcSwhOw88JOzC2YK7uPwf6DsfDPCzlCS0RERK2CBSuZ5HplDTq5KKFw4MOp\nXD9W/Ihr1dfwJ+8/WTsK2TmFgwLLYpbhm5++gUEYTG5/9OpRrDm2BhtObMCzPZ5thYRERERk71iw\nkkmuV9bAw4Wjqy1x+MphAEBElwgrJyECXJ1cZW/8NCRgCE7dOIW5BXOx4ocVsvro06UP/vXQv+Do\nwP8cERERUUN8QiCTXK+sgZerytox2oRfq3+FXuhNbrf/5/3o4NQBwR2DWyEVkeU4SA54+8G3kfND\nDiprK01uX1lbia3ntsLPzQ8T+0xshYRERERk61iwkkluVNUgsLOrtWNY3caTG5HxbYbs9gO7DYTC\nQWHGRETW4aX2wtSoqbLbZ3ybgZwfclB4pVDW5k2dnTvjjX5voKOqo+wMRERE1HaxYCWTXK+swQMB\npr/vsb0puFwAL2cvjP3TWFnt+3frb+ZERLYpLSoNOoMOF8svylpHu+PCDvyq/RXLYpZxWjEREVE7\nxP+6U7MZDAI3qmrh6co1rEXXixDRJQIje4y0dhQim6ZSqDBr4CzZ7XNP5WLGNzPwty1/g5uTm8nt\nlQolxvcez03QiIiI2igWrHZIbxCoqNaZ3K6suhZ6g4Cnna9hraipwLmycxgaNNTaUYjs3vB7hqOs\npgz5P+bLan/m1zNI+ToFax9bi6COQWZOR0RERC3FgtUOjVl7AF8XX5HdvnMHpRnT2J4TN04AAMK9\nwq2chIgA4MV7X8SL974oq+3F8otI+CIBf/vsb3B1krc+//HAxzG572RZa3CJiIjozliw2qHDF39F\n37s98FgvX5PbqpwcENvTpxVS2Y6ia0UAgJ5ePa2chIhayt/NHzmxOfj45Mey1tCWVpXiP0X/gc6g\nw7CQYbIy+Lr6wkvtJastERFRe8eC1c5UanW4VlmDlx8MxMsPBlo7jk0qul4Eb7U3Oqs7WzsKEZnB\nPR73YFr0NFlthRB4Z/87+E/Rf/DhiQ9l9aF2VGPZX5Yh0idSVnsiIqL2jAWrnfnxhgYA4O/pYuUk\ntuv4teOcDkxEAABJkjCl7xTEBMTIehet3qDHwkMLMW7HOAwJGAJJkkzuw13pjuT7k9HJuZPJbYmI\niNo6Fqx25sL1KgCAv4faykmsa33RenxR8oWstmdvnkVMQIyZExGRrZIkCQ90fUB2+/u970fanjQc\n/OWgrPZXNFfwf5f+D3MemiNrHa6j5Ijubt1lFctEREStjQWrnblYV7Da+Qjr+uL10NRqENwp2OS2\nA7sNxKN3P9oKqYjIHnmpvbAidoXs9gd+PoAJOydg1OejZPcxqPsgzH14ruyNp4iIiFoLC1Y7c/FG\nFdROCni52u9Ov5W1lThfdh7jI8Yj+U/J1o5DRNQikT6R2PjURhy+clhW+/Pl5/Hekfcw7NNh6OLS\nRVYfUT5RSOmdAicHvqebiIjMiwWrnbl4XQN/T7VdT/06cZ2vpSGi9qVbh27o1qGb7PZ/8v4T1het\nh06Y/o7ual01Vh5diUNXDiHaN1rW9X1dfTEseBgUDgpZ7YmIqP1iwWpnfrxRhbvsfDpw0fVbr6UJ\n8wizchIiorZhQLcBGNBtgOz2X5z9ArP3zUbhlcIW9TEqfBQkmP4LVWdHZ0T7RLPgJSJqh1iw2hEh\nBC5er0K/IPt+31/x9WJ4OnvKnvpGRETGHg96HI8HPS6rrRACn57+FP/a9y/s+3mf7Ax9uvRB6gOp\nUDuavqmgg+SAuzvezSnNRERtEAtWO3KjqhaVNXq733Cp+Hoxenj2sOtp0UREbYUkSRh+z3A83P1h\nXKm6IquPoutFmLd/Hv6+9e+yc9zjcQ/eiH4D3VzlTa32UntBqbDf/SGIiFoLC1Y7cpGvtEGtvhan\nfz2NF3q+YO0oRET0O15qL3ip5c0ACvcKx0N+D+FI6RFZ7X/V/orsw9lI/DJRVnsA6KzujCl9p6B3\nl96y2rs6ucJN6Sb7+kRE7RULVhsjhMD6ggv4+Wa1yW3PXr31Uvv2MMJ67uY5Wb+Jv1RxCTqDDuGe\n3HCJiKg98XbxbtE7smPvjkXexTzoDKZvPKUXemw4sQFT8qfIvr6TgxNevPdFPBH4BBwkB9PbK5zQ\nvQPfp0tE7Q8LVhtz9mol3sg9CkmCjG0pAL9OagR2tu337Gl0Gjzz2TOo1ptetNe5t/O9ZkxERES2\nzl3pjieDn5TdfnjIcOy6uAtlNWWy2u//eT9yfshBzg85sjNE+0TjhXtfkLWOFwB6ePbgKC8RtTks\nWG1MQcl1AMCO1x5BsHcHK6exjhPXT6BaX43XHngNvTr3Mrl9R1VH+Lv5t0IyIiKyVwoHRYtGeOPv\niccLPV/A+bLzstpfrryMVUdXIeXrFNkZ3JXuSAhPQFfXrrLa3+V2Fx7o+gBHeYnIrFiw2ph9Z6+h\ncwcVgmx8lLQlfrj6AwBgaNBQeLt4WzkNERGReYR7hbfoHeEjQkeg+HqxrLYanQbri9dj2ZFlsq8P\n3NqtuadXT1lt3ZRuiL8nHj6uPi3KQETtCwtWGyKEwL6S64gO9LTr314evXoUXVy6sFglIiL6HTel\nG/r69JXd/uHuD+Oq5qqsdbxCCOz+cTfWHluLkzdOyrp+la4KK35YgZ5ePeEA09fxKhwUiLkrBvH3\nxMPZ0VlWBjnrh4modbFgtSE/3tDg8s1qRAd5WjuKVR27dgy9vEyfCkxERER31lndWXZq+q8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qRtKsYrMGERsScifpEsH1bxA9pCEY+ooyg6kqy2Jj8h4hANYHuRpN+T9N2SYmIRWdFUsUjCWp2F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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11744dd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_K()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## State Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_x():\n",
    "    \n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "\n",
    "    plt.subplot(311)\n",
    "    plt.step(range(len(measurements[0])),ddxt, label='$\\ddot x$')\n",
    "    plt.step(range(len(measurements[0])),ddyt, label='$\\ddot y$')\n",
    "\n",
    "    plt.title('Estimate (Elements from State Vector $x$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel(r'Acceleration $m/s^2$')\n",
    "    plt.ylim([-.1,.1])\n",
    "\n",
    "    plt.subplot(312)\n",
    "    plt.step(range(len(measurements[0])),dxt, label='$\\dot x$')\n",
    "    plt.step(range(len(measurements[0])),dyt, label='$\\dot y$')\n",
    "\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel(r'Velocity $m/s$')\n",
    "    plt.ylim([-1,1])\n",
    "\n",
    "    plt.subplot(313)\n",
    "    plt.step(range(len(measurements[0])),xt, label='$x$')\n",
    "    plt.step(range(len(measurements[0])),yt, label='$y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.ylabel(r'Position $m$')\n",
    "    plt.ylim([-1,1])\n",
    "\n",
    "    plt.savefig('Kalman-Filter-CA-StateEstimated.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2tom8p0E11eq+/U5kv3wR1r3YpAoqxu43ot+jZxr1PfTXfT+p/4/aBz/1z8zu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n+Rmb+I96EGLCKeFxGnlI+B1wLfZMzuRcuzR0xmHomIdwBfAJYAn8rMe4fcLI2xiPhT4HzgtIj4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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116b7eb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_x()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Position x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_xy():\n",
    "\n",
    "    fig = plt.figure(figsize=(16,16))\n",
    "    plt.plot(xt,yt, label='State',alpha=0.5)\n",
    "    plt.scatter(xt[0],yt[0], s=100, label='Start', c='g')\n",
    "    plt.scatter(xt[-1],yt[-1], s=100, label='Goal', c='r')\n",
    "\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Y')\n",
    "    plt.title('Position')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlim([-5, 5])\n",
    "    plt.ylim([-5, 5])\n",
    "    plt.savefig('Kalman-Filter-CA-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Mzp07T+rZsy4tBgAAGEWzZs3Kxo0bs2PHjtEeypumqakps2bNOuH9hSwAAMAoqq+vz/z5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\nAKoiZAEAAKiKkAUAAKAq/x/7iNWXO93v6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11709cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_xy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![Nice](http://www.troll.me/images/stifler-thumbs-up/nice.jpg)\n",
    "\n",
    "It works pretty well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As you can see, good idea to measure the position as well as the acceleration to try to estimate the position."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your drifted 12m from origin.\n"
     ]
    }
   ],
   "source": [
    "dist=np.cumsum(np.sqrt(np.diff(xt)**2 + np.diff(yt)**2))\n",
    "print('Your drifted %dm from origin.' % dist[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "To use this notebook as a presentation type:\n",
    "\n",
    "`jupyter-nbconvert --to slides Kalman-Filter-CA-2.ipynb --reveal-prefix=reveal.js --post serve` \n",
    "\n",
    "Questions? [@Balzer82](https://twitter.com/balzer82)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}