Extended-Kalman-Filter-CTRA.ipynb

{
 "metadata": {
  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.dates as mdates\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.stats import norm\n",
      "from sympy import Symbol, symbols, Matrix, sin, cos, latex\n",
      "from sympy.interactive import printing\n",
      "printing.init_printing()\n",
      "%pylab inline --no-import-all"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Extended Kalman Filter Implementation for Constant Turn Rate and Acceleration (CTRA) Vehicle Model in Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Situation covered: You have an velocity and acceleration sensor which measures the vehicle speed ($v$) and acceleration ($a$) in heading direction ($\\psi$) and a yaw rate sensor ($\\dot \\psi$) which both have to fused with the position ($x$ & $y$) from a GPS sensor."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "State Vector - Constant Turn Rate and Velocity Vehicle Model (CTRA)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Constant Turn Rate, Constant Acceleration Model for a vehicle ![CTRV Model](https://raw.github.com/balzer82/Kalman/master/CTRV-Model.png)\n",
      "\n",
      "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\psi \\\\ v \\\\ a \\\\ \\dot\\psi} \\right] = \\left[ \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Acceleration} \\\\ \\text{Yaw Rate}} \\right]$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numstates=6 # States"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz\n",
      "dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All symbolic calculations are made with [Sympy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb). Thanks!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "vs, axs, psis, dpsis, dts, xs, ys, lats, lons = symbols('v a_x \\psi \\dot\\psi T x y lat lon')\n",
      "\n",
      "As = Matrix([[xs+(axs/dpsis**2)*(cos(psis+dpsis*dts)-cos(psis))+((vs+axs*dts)/dpsis)*(sin(psis+dpsis*dts)-vs*sin(psis))],\n",
      "             [ys+(axs/dpsis**2)*(sin(psis+dpsis*dts)-sin(psis))-((vs+axs*dts)/dpsis)*(cos(psis+dpsis*dts)-vs*cos(psis))],\n",
      "             [psis+dpsis*dts],\n",
      "             [vs+axs*dts],\n",
      "             [axs],\n",
      "             [dpsis]])\n",
      "state = Matrix([xs,ys,psis,vs,axs,dpsis])\n",
      "state"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\a_{x}\\\\\\dot\\psi\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACUAAACWCAMAAABuHrHqAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nR5Iq/91XKfoLomQqST1G724AAAAASUVORK5CYII=\n",
       "prompt_number": 5,
       "text": [
        "\u23a1   x    \u23a4\n",
        "\u23a2        \u23a5\n",
        "\u23a2   y    \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a2  \\psi  \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a2   v    \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a2   a\u2093   \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a3\\dot\\psi\u23a6"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Initial Uncertainty"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Initialized with $0$ means you are pretty sure where the vehicle starts"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0])\n",
      "print(P, P.shape)\n",
      "\n",
      "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),('$x$', '$y$', '$\\psi$', '$v$', '$a_x$', '$\\dot \\psi$'), 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),('$x$', '$y$', '$\\psi$', '$v$', '$a_x$', '$\\dot \\psi$'), 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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([[ 1000.,     0.,     0.,     0.,     0.,     0.],\n",
        "       [    0.,  1000.,     0.,     0.,     0.,     0.],\n",
        "       [    0.,     0.,  1000.,     0.,     0.,     0.],\n",
        "       [    0.,     0.,     0.,  1000.,     0.,     0.],\n",
        "       [    0.,     0.,     0.,     0.,  1000.,     0.],\n",
        "       [    0.,     0.,     0.,     0.,     0.,  1000.]]), (6, 6))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zIOeZCyGE4vSeet60aRPLly/n008/5fTp0xw9epRJkyZht9s5ePAg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\nXGkil1J/WUwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109601a50>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Dynamic Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This formulas calculate how the state is evolving from one to the next time step"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "As"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}x + \\frac{1}{\\dot\\psi} \\left(T a_{x} + v\\right) \\left(- v \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{a_{x}}{\\dot\\psi^{2}} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\y - \\frac{1}{\\dot\\psi} \\left(T a_{x} + v\\right) \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{a_{x}}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\T \\dot\\psi + \\psi\\\\T a_{x} + v\\\\a_{x}\\\\\\dot\\psi\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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NBik8DO9ubRi+OtnWQYvwjYi2br6eXXen4D5fNnW7Z2ctwjft/QvdYNJ84b0F\n+Ga0twjfjGrj6Px1ft5PPJnStm0YaBG+Dc/By+Ec5Catz0CL8PU5lh5o3dm2bchAi/ANyTauzGz4\n1k537K9F+Nad356c3ZZxG+Fv3o7bem7eGgMrM/Bt4pqfBDqZrc1grUx4M78xA3cb2N3/AxQ+KCJk\nj33eAAAAAElFTkSuQmCC\n",
       "prompt_number": 7,
       "text": [
        "\u23a1    (T\u22c5a\u2093 + v)\u22c5(-v\u22c5sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))   a\u2093\u22c5(-cos(\\psi) + cos\n",
        "\u23a2x + \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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2                         \\dot\\psi                                            \n",
        "\u23a2                                                                        \\dot\\\n",
        "\u23a2                                                                             \n",
        "\u23a2    (T\u22c5a\u2093 + v)\u22c5(-v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi))   a\u2093\u22c5(-sin(\\psi) + sin\n",
        "\u23a2y - \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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2                         \\dot\\psi                                            \n",
        "\u23a2                                                                        \\dot\\\n",
        "\u23a2                                                                             \n",
        "\u23a2                                        T\u22c5\\dot\\psi + \\psi                    \n",
        "\u23a2                                                                             \n",
        "\u23a2                                            T\u22c5a\u2093 + v                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                               a\u2093                            \n",
        "\u23a2                                                                             \n",
        "\u23a3                                            \\dot\\psi                         \n",
        "\n",
        "(T\u22c5\\dot\\psi + \\psi))\u23a4\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "   2                \u23a5\n",
        "psi                 \u23a5\n",
        "                    \u23a5\n",
        "(T\u22c5\\dot\\psi + \\psi))\u23a5\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "   2                \u23a5\n",
        "psi                 \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a5\n",
        "                    \u23a6"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Calculate the Jacobian of the Dynamic Matrix with respect to the state vector"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "state"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\a_{x}\\\\\\dot\\psi\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACUAAACWCAMAAABuHrHqAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nR5Iq/91XKfoLomQqST1G724AAAAASUVORK5CYII=\n",
       "prompt_number": 8,
       "text": [
        "\u23a1   x    \u23a4\n",
        "\u23a2        \u23a5\n",
        "\u23a2   y    \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a2  \\psi  \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a2   v    \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a2   a\u2093   \u23a5\n",
        "\u23a2        \u23a5\n",
        "\u23a3\\dot\\psi\u23a6"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "As.jacobian(state)\n",
      "#print(latex(JAs))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}1 & 0 & \\frac{1}{\\dot\\psi} \\left(T a_{x} + v\\right) \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{a_{x}}{\\dot\\psi^{2}} \\left(\\sin{\\left (\\psi \\right )} - \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & - \\frac{1}{\\dot\\psi} \\left(T a_{x} + v\\right) \\sin{\\left (\\psi \\right )} + \\frac{1}{\\dot\\psi} \\left(- v \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T}{\\dot\\psi} \\left(- v \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{1}{\\dot\\psi^{2}} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T}{\\dot\\psi} \\left(T a_{x} + v\\right) \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{T a_{x}}{\\dot\\psi^{2}} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{1}{\\dot\\psi^{2}} \\left(T a_{x} + v\\right) \\left(- v \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) - \\frac{2 a_{x}}{\\dot\\psi^{3}} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 1 & - \\frac{1}{\\dot\\psi} \\left(T a_{x} + v\\right) \\left(v \\sin{\\left (\\psi \\right )} - \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{a_{x}}{\\dot\\psi^{2}} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(T a_{x} + v\\right) \\cos{\\left (\\psi \\right )} - \\frac{1}{\\dot\\psi} \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & - \\frac{T}{\\dot\\psi} \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{1}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T}{\\dot\\psi} \\left(T a_{x} + v\\right) \\sin{\\left (T \\dot\\psi + \\psi \\right )} + \\frac{T a_{x}}{\\dot\\psi^{2}} \\cos{\\left (T \\dot\\psi + \\psi \\right )} + \\frac{1}{\\dot\\psi^{2}} \\left(T a_{x} + v\\right) \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) - \\frac{2 a_{x}}{\\dot\\psi^{3}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 0 & 1 & 0 & 0 & T\\\\0 & 0 & 0 & 1 & T & 0\\\\0 & 0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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tYJyxR5qKm8EDCqbTnqEEzI21ltyAlZUZrLCJJciZwbKqYiqMuKgZ4gUyC20D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\ngg==\n",
       "prompt_number": 22,
       "text": [
        "\u23a1       (T\u22c5a\u2093 + v)\u22c5(-v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi))   a\u2093\u22c5(sin(\\psi) - s\n",
        "\u23a21  0   \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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2                            \\dot\\psi                                         \n",
        "\u23a2                                                                           \\d\n",
        "\u23a2                                                                             \n",
        "\u23a2        (T\u22c5a\u2093 + v)\u22c5(v\u22c5sin(\\psi) - sin(T\u22c5\\dot\\psi + \\psi))   a\u2093\u22c5(-cos(\\psi) + \n",
        "\u23a20  1  - \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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2                             \\dot\\psi                                        \n",
        "\u23a2                                                                           \\d\n",
        "\u23a2                                                                             \n",
        "\u23a20  0                                                1                        \n",
        "\u23a2                                                                             \n",
        "\u23a20  0                                                0                        \n",
        "\u23a2                                                                             \n",
        "\u23a20  0                                                0                        \n",
        "\u23a2                                                                             \n",
        "\u23a30  0                                                0                        \n",
        "\n",
        "in(T\u22c5\\dot\\psi + \\psi))     (T\u22c5a\u2093 + v)\u22c5sin(\\psi)   -v\u22c5sin(\\psi) + sin(T\u22c5\\dot\\ps\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "      2                          \\dot\\psi                        \\dot\\psi     \n",
        "ot\\psi                                                                        \n",
        "                                                                              \n",
        "cos(T\u22c5\\dot\\psi + \\psi))   (T\u22c5a\u2093 + v)\u22c5cos(\\psi)   -v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "      2                         \\dot\\psi                        \\dot\\psi      \n",
        "ot\\psi                                                                        \n",
        "                                                                              \n",
        "                                                       0                      \n",
        "                                                                              \n",
        "                                                       1                      \n",
        "                                                                              \n",
        "                                                       0                      \n",
        "                                                                              \n",
        "                                                       0                      \n",
        "\n",
        "i + \\psi)   T\u22c5(-v\u22c5sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))   -cos(\\psi) + cos(T\u22c5\\do\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                             \\dot\\psi                                        2\n",
        "                                                                     \\dot\\psi \n",
        "                                                                              \n",
        " + \\psi)     T\u22c5(-v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi))   -sin(\\psi) + sin(T\u22c5\\d\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                              \\dot\\psi                                        \n",
        "                                                                      \\dot\\psi\n",
        "                                                                              \n",
        "                                                   0                          \n",
        "                                                                              \n",
        "                                                   T                          \n",
        "                                                                              \n",
        "                                                   1                          \n",
        "                                                                              \n",
        "                                                   0                          \n",
        "\n",
        "t\\psi + \\psi)   T\u22c5(T\u22c5a\u2093 + v)\u22c5cos(T\u22c5\\dot\\psi + \\psi)   T\u22c5a\u2093\u22c5sin(T\u22c5\\dot\\psi + \\p\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                              \\dot\\psi                                 2      \n",
        "                                                               \\dot\\psi       \n",
        "                                                                              \n",
        "ot\\psi + \\psi)  T\u22c5(T\u22c5a\u2093 + v)\u22c5sin(T\u22c5\\dot\\psi + \\psi)   T\u22c5a\u2093\u22c5cos(T\u22c5\\dot\\psi + \\p\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "2                             \\dot\\psi                                 2      \n",
        "                                                               \\dot\\psi       \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "\n",
        "si)   (T\u22c5a\u2093 + v)\u22c5(-v\u22c5sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))   2\u22c5a\u2093\u22c5(-cos(\\psi) + \n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                  2                                           \n",
        "                          \\dot\\psi                                         \\do\n",
        "                                                                              \n",
        "si)   (T\u22c5a\u2093 + v)\u22c5(-v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi))   2\u22c5a\u2093\u22c5(-sin(\\psi) + \n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                  2                                           \n",
        "                          \\dot\\psi                                         \\do\n",
        "                                                                              \n",
        "                   T                                                          \n",
        "                                                                              \n",
        "                   0                                                          \n",
        "                                                                              \n",
        "                   0                                                          \n",
        "                                                                              \n",
        "                   1                                                          \n",
        "\n",
        "cos(T\u22c5\\dot\\psi + \\psi))\u23a4\n",
        "\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",
        "     3                 \u23a5\n",
        "t\\psi                  \u23a5\n",
        "                       \u23a5\n",
        "sin(T\u22c5\\dot\\psi + \\psi))\u23a5\n",
        "\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",
        "     3                 \u23a5\n",
        "t\\psi                  \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a5\n",
        "                       \u23a6"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It has to be computed on every filter step because it consists of state variables."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Control Input"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Matrix G is the Jacobian of the Dynamic Matrix with respect to control (the translation velocity $v$ and the rotational\n",
      "velocity $\\dot \\psi$)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "control = Matrix([axs,dpsis])\n",
      "control"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}a_{x}\\\\\\dot\\psi\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAAyBAMAAAAgiK9pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhAiq3bdRLtm\nmc0lg57xAAABJklEQVQoFWOQ//+JAQ6Y/v8XYBB2cYULMLC6OAswiCD4IBYLdUXYilqmQi2Amrww\ngfsDigirDAPvBhQR3q8MnA0oIowbGOIdUETiFRjsGQKYej1KYG6ON2DYx5zQyv5gFkyEr4FnOhOD\nA98BoE6I7awVKuldDAz8CXARIAME/BkcYGrAfLYPmgwKKCKsFYs6AlBEwAppIzIdbDZSXLD+Qxch\n03YODHOYMEQiMESWYIgooIiw6jYwKHBMAIrB3MzE/IH1AMdXJJFk3gnMCQwCSCIBjApAyy8giTCs\nT2BiYG1AFtFkiGFgCkAWuc1wlMEKKAC3i2EhQwPPAhQR5st72kACCDUMLAZgASQRDpCxQABzMwMD\nJCyQRSDhhSwC0QMWwcxNGDkOAJBCOZb1nH7HAAAAAElFTkSuQmCC\n",
       "prompt_number": 15,
       "text": [
        "\u23a1   a\u2093   \u23a4\n",
        "\u23a2        \u23a5\n",
        "\u23a3\\dot\\psi\u23a6"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Calculate the Jacobian of the Dynamic Matrix with Respect to the Control"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Gs=As.jacobian(control)\n",
      "Gs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}\\frac{T}{\\dot\\psi} \\left(- v \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{1}{\\dot\\psi^{2}} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T}{\\dot\\psi} \\left(T a_{x} + v\\right) \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{T a_{x}}{\\dot\\psi^{2}} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{1}{\\dot\\psi^{2}} \\left(T a_{x} + v\\right) \\left(- v \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) - \\frac{2 a_{x}}{\\dot\\psi^{3}} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\- \\frac{T}{\\dot\\psi} \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) + \\frac{1}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T}{\\dot\\psi} \\left(T a_{x} + v\\right) \\sin{\\left (T \\dot\\psi + \\psi \\right )} + \\frac{T a_{x}}{\\dot\\psi^{2}} \\cos{\\left (T \\dot\\psi + \\psi \\right )} + \\frac{1}{\\dot\\psi^{2}} \\left(T a_{x} + v\\right) \\left(- v \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) - \\frac{2 a_{x}}{\\dot\\psi^{3}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & T\\\\T & 0\\\\1 & 0\\\\0 & 1\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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iKx710hKfP7dFak+BfmD6QHQdntcLr9X1c0zz6qVW40Hg0zi9ms3JIexx+qbq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\nZoO/eQAAAABJRU5ErkJggg==\n",
       "prompt_number": 16,
       "text": [
        "\u23a1 T\u22c5(-v\u22c5sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))   -cos(\\psi) + cos(T\u22c5\\dot\\psi + \\p\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2                  \\dot\\psi                                        2          \n",
        "\u23a2                                                          \\dot\\psi           \n",
        "\u23a2                                                                             \n",
        "\u23a2  T\u22c5(-v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi))   -sin(\\psi) + sin(T\u22c5\\dot\\psi + \\\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2                   \\dot\\psi                                        2         \n",
        "\u23a2                                                           \\dot\\psi          \n",
        "\u23a2                                                                             \n",
        "\u23a2                                        0                                    \n",
        "\u23a2                                                                             \n",
        "\u23a2                                        T                                    \n",
        "\u23a2                                                                             \n",
        "\u23a2                                        1                                    \n",
        "\u23a2                                                                             \n",
        "\u23a3                                        0                                    \n",
        "\n",
        "si)   T\u22c5(T\u22c5a\u2093 + v)\u22c5cos(T\u22c5\\dot\\psi + \\psi)   T\u22c5a\u2093\u22c5sin(T\u22c5\\dot\\psi + \\psi)   (T\u22c5a\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\n",
        "                    \\dot\\psi                                 2                \n",
        "                                                     \\dot\\psi                 \n",
        "                                                                              \n",
        "psi)  T\u22c5(T\u22c5a\u2093 + v)\u22c5sin(T\u22c5\\dot\\psi + \\psi)   T\u22c5a\u2093\u22c5cos(T\u22c5\\dot\\psi + \\psi)   (T\u22c5a\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\n",
        "                    \\dot\\psi                                 2                \n",
        "                                                     \\dot\\psi                 \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "\n",
        "\u2093 + v)\u22c5(-v\u22c5sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))   2\u22c5a\u2093\u22c5(-cos(\\psi) + cos(T\u22c5\\dot\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                        2                                                3    \n",
        "                \\dot\\psi                                         \\dot\\psi     \n",
        "                                                                              \n",
        "\u2093 + v)\u22c5(-v\u22c5cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi))   2\u22c5a\u2093\u22c5(-sin(\\psi) + sin(T\u22c5\\dot\n",
        "\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\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                        2                                                3    \n",
        "                \\dot\\psi                                         \\dot\\psi     \n",
        "                                                                              \n",
        "         T                                                                    \n",
        "                                                                              \n",
        "         0                                                                    \n",
        "                                                                              \n",
        "         0                                                                    \n",
        "                                                                              \n",
        "         1                                                                    \n",
        "\n",
        "\\psi + \\psi))\u23a4\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "\\psi + \\psi))\u23a5\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a5\n",
        "             \u23a6"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It has to be computed on every filter step because it consists of state variables."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Process Noise Covariance Matrix Q"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Matrix Q is the expected noise on the State.\n",
      "\n",
      "One method is based on the interpretation of the matrix as the weight of the dynamics prediction from the state equations\n",
      "Q relative to the measurements.\n",
      "\n",
      "As you can see in [Schubert, R., Adam, C., Obst, M., Mattern, N., Leonhardt, V., & Wanielik, G. (2011). Empirical evaluation of vehicular models for ego motion estimation. 2011 IEEE Intelligent Vehicles Symposium (IV), 534\u2013539. doi:10.1109/IVS.2011.5940526] one can assume the velocity process noise for a vehicle with $\\sigma_v=1.5m/s$ and the yaw rate process noise with $\\sigma_\\psi=0.29rad/s$, when a timestep takes 0.02s (50Hz)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "control"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}a_{x}\\\\\\dot\\psi\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACEAAAAyBAMAAAAgiK9pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMA74lUMhAiq3bdRLtm\nmc0lg57xAAABJklEQVQoFWOQ//+JAQ6Y/v8XYBB2cYULMLC6OAswiCD4IBYLdUXYilqmQi2Amrww\ngfsDigirDAPvBhQR3q8MnA0oIowbGOIdUETiFRjsGQKYej1KYG6ON2DYx5zQyv5gFkyEr4FnOhOD\nA98BoE6I7awVKuldDAz8CXARIAME/BkcYGrAfLYPmgwKKCKsFYs6AlBEwAppIzIdbDZSXLD+Qxch\n03YODHOYMEQiMESWYIgooIiw6jYwKHBMAIrB3MzE/IH1AMdXJJFk3gnMCQwCSCIBjApAyy8giTCs\nT2BiYG1AFtFkiGFgCkAWuc1wlMEKKAC3i2EhQwPPAhQR5st72kACCDUMLAZgASQRDpCxQABzMwMD\nJCyQRSDhhSwC0QMWwcxNGDkOAJBCOZb1nH7HAAAAAElFTkSuQmCC\n",
       "prompt_number": 17,
       "text": [
        "\u23a1   a\u2093   \u23a4\n",
        "\u23a2        \u23a5\n",
        "\u23a3\\dot\\psi\u23a6"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "svQ = (1.5)**2\n",
      "syQ = (0.29*dt)**2\n",
      "\n",
      "Q = np.matrix([[svQ, 0.0],\n",
      "               [0.0, syQ]])\n",
      "\n",
      "print(Q, Q.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[  2.25000000e+00,   0.00000000e+00],\n",
        "        [  0.00000000e+00,   3.36400000e-05]]), (2, 2))\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(4, 4))\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(3))\n",
      "# set the locations and labels of the yticks\n",
      "plt.yticks(np.arange(2),('$v$', '$\\dot \\psi$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = plt.xticks()\n",
      "# set the locations of the yticks\n",
      "plt.xticks(np.arange(3))\n",
      "# set the locations and labels of the yticks\n",
      "plt.xticks(np.arange(2),('$v$', '$\\dot \\psi$'), fontsize=22)\n",
      "\n",
      "plt.xlim([-0.5,1.5])\n",
      "plt.ylim([1.5, -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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SyhuIjZTqpjU5HX1dyaxbtw4BAQEICAjAoEGDYGdnh/LycgCAt7c3/P39ERAQ\ngOHDh+stJ7V0CLESprZ0GruSOX78OHr06IFhw4YhMjJS44NcixYtwqJFiwAAhw8fxr/+9S+4urpy\n283MzIS7u7tB26OWDg+klDcQGynVjamd7RnblcyuXbvw1ltvaYwz5sPtFHQIsRKmXl611MWMNlVV\nVTh27BgmT56ssd3Q0FAEBgZi69atestJl1c8kNJ3eMVGSnWjLahcunQJ+fn53PDIkSObdUFjzGXZ\noUOHMGbMGO7SCgCys7Ph6emJO3fuICwsDH5+fggKCmpxHRR0CLES2oLHwIEDMXDgQG5YW96laRcz\nurqS2b17d7NLK09PTwBAly5dEBUVBZVKpTPo0OUVD6TySypGUqobUy+vDO1K5uHDh8jKysKkSZO4\ncVVVVaisrAQAPH78GBkZGRg0aJDOclJLhxArYerDgS11JfPVV18BaOiGBgD279+PCRMmoEOHDtyy\nt2/fRlRUFACgrq4OsbGxGD9+vM7tyVgr+gt9+vQpQkJC8PDhQ5w5cwbOzs4GLXfixAm89NJLpm5W\ncKwtbyCWh8wMYW11c+LECa3dAp84cQIVFRV6l3/uuedM6laYT61q6VRWVkKlUqG2thalpaXo27cv\nX+UihBhJLD8WrQo6Li4uOH78OCorKyUdcKzpl9TaSKluJBF0AGDMmDF8lIMQ0kpieeFTHKUUOCm9\n3yM2UqobsXxPh9eg8+DBAyxevJjPVRJCDCSWoMPrLfPs7GwEBgbyuUpRkFLeQGykVDdCCSr68NrS\nOXPmjM4nEQkhbcfUFz7NjddSqNVqdO/enc9VioKU8gZiI6W6kdzlVXV1NTp27MjX6gghRhJKUNGH\nt6CTk5ODF154ga/ViYqU8gZiI6W6EUvQMeryqry8HHFxcYiNjUVMTAyePn3KTTtz5gyCg4MBAPfv\n30efPn24L40RQtqeVeZ0li1bhuXLlyMpKQnfffcd0tPTuWnXrl2Dr68vgIY3T0tLS5GRkcFvaQVK\nSnkDsZFS3VhdTuf69etwcnKCl5cXDh06BADch3zq6upgb2/PzSuXy7Fq1Srs2bOnxfW9/fbb8Pb2\nBtDwOsXgwYO5pnDjiSKW4by8PEGVh4atZzgzMxPbt28H0PABdF13hw0JKq14v5s3Br9lfvr0aXTv\n3h29e/dGdHQ0zp8/j6KiIgAN31hVqVSYN28eN39+fj42bNjAvR7/LGt7y9zaCOUXkTSn6y1zW1tb\nvcvX19fyxJHMAAAKkElEQVRb/C1zgy+vgoKC0Lt3b9y/fx9HjhzB1KlTuWnP5nMaFRcX48UXX+Sv\npIQQnVqT09HXBU1mZiZcXFy4bmhWrVpl8LLNymnsjh06dAi1tbV47bXXuHEXL16Ev7+/xnxHjhzB\nxIkTjV29KEkpbyA2UqobU3M6jV3QpKenIz8/H6mpqbh8+XKz+caOHYvc3Fzk5uZi6dKlRi37LKOD\nTm5uLjp06MAFGcZYs+vEc+fOwcvLC05OTsaunhBiIlODjqFd0GjLxBjbfQ1gQtBxcnJC+/btueH8\n/HwMGDCAG75x4waSkpLwwQcfGLtq0ZLSsyBiI6W6acsuaGQyGc6ePQulUomIiAiuhwljuq9pZPTD\ngTNmzMDmzZtx4MABTJo0CadPn+Yy6ocPH8bRo0exceNGwTwTQIhUaPs/d/78eeTm5nLD/fv3N6kL\nmiFDhkCtVsPR0RFHjx7Fq6++imvXrplUTqODjre3N3JycrBq1SqcPXsWZ8+exW+//Ybk5GSEhYVh\n48aNJhVEzKztO7zWREp1oy14DB06FEOHDuWGHz9+3GweQ7qgefb75+Hh4Xjvvfdw//59yOVyg7uv\naWTSaxAKhQLffvstAGD69OlITEw0ZTWEEB6Z+qjDs13QdO/eHXv27EFqaqrGPLdv30bXrl0hk8mg\nUqnAGIO7u7tByzbVqnev7t69i06dOrVmFVZBKr+kYiSlujE16BjSBc3evXuxefNm2NnZwdHREbt3\n79a5rM5ytqYLmiNHjqCyshIxMTFGLUcPBwobPRwoXLoeDnzuuef0Ll9RUSGehwO1ycnJwfDhw/kq\ni2hJ6VkQsZFS3Yjlhc9WXV6VlJTAx8eHr7IQQlpBLC3UVgWd5ORkvsohalLKG4iNlOpGEkGHECIc\nYgk6wrjIEzkp5Q3ERkp1I4mcDiFEOMTS0qGgwwMp5Q3ERkp1Q0GHEGJWYgk6wrjIEzkp5Q3ERkp1\nQzkdQohZiaWlQ0GHB1LKG4iNlOqGgg4hxKzEEnSEcZEnclLKG4iNlOqGcjqEELOilo6ESClvIDZS\nqpvW9PCprxuZlJQUKJVK+Pv7Y/To0bh48SI3zdvbG/7+/ggICDDoqxPU0iHESpja0mnsRub48ePo\n0aMHhg0bhsjISI2Pcfn4+CArKwsuLi5IT0/HrFmzkJOTw203MzMT7u7uBm2PWjo8kFLeQGykVDem\n5nQM6UZm5MiRcHFxAQCMGDECJSUlGtON+RYgBR1CrERbdkHzrK+//hoREREa2w0NDUVgYCC2bt2q\nt5x0ecUDKeUNxEZKdaMtqPz000/cZRDQEFBM6YKm0cmTJ/HNN98gOzubG5ednQ1PT0/cuXMHYWFh\n8PPz47ql0oaCDiFWQlvwGDVqFEaNGsUNX716tdk8hnRBAzR0Hz5z5kykp6fDzc2NG+/p6QkA6NKl\nC6KioqBSqXQGHbq84oGU8gZiI6W6MfXy6tluZGpqarBnzx5ERkZqzFNcXIzo6Gjs3LkTvr6+3Piq\nqipUVlYCaOhTKyMjA4MGDdJZTmrpEGIlTH34z5AuaBISEvDgwQPMmTMHAGBvbw+VSoWysjJER0cD\nAOrq6hAbG4vx48fr3F6ruqAxFXVBI2xiechMinR1QTNgwAC9y1+6dMniXdBQS4cQKyGWHwvK6fBA\nSnkDsZFS3bTmiWRzopYOIVZCKC906kNBhwdSehZEbKRUN0JpyehDQYcQKyGWoCOO9pjASSlvIDZS\nqhvK6RBCzIpyOhIipbyB2EipboTSktGHgg4hVkIsQUcc7TGBk1LeQGykVDeU0yGEmBXldCRESnkD\nsZFS3QilJaMPBR1CrIRYgo442mMCJ6W8gdhIqW7EktOhoMODvLw8SxeBtEBKddOazvb0dUEDAPPn\nz4dCoYBSqURubq5Ry2qU0/hdI009fPjQ0kUgLSgvL7d0EczG1JZOYxc06enpyM/PR2pqKi5fvqwx\nT1paGgoLC1FQUICkpCTuY16GLNsUBR1CrISpQceQLmgOHjyIadOmAWjogqa8vBxlZWUGLdsUBR0e\nFBUVWboIpAVSqpu27IKmpXlKS0uN6r4GsODdq//+97+W2jTvpkyZYlX7Y02mTJmCEydOWLoYZnHy\n5Mlm4y5cuIALFy5ww0OGDDG5Cxq+vmxskaBj6W+0EmJtWvo/Zcj/NUO6oGk6T0lJCeRyOWpraw3q\nvuZZdHlFiMQZ0gVNZGQkduzYAQDIycmBq6srunXrZtCyTdHDgYRInCFd0ERERCAtLQ2+vr7o2LEj\nkpOTdS6ri0W6oCGESBddXhFCzIqCjgkqKysxc+ZMxMbG4vXXX0d9fT037f3334e3tzeePHliwRKS\np0+fIjg4GEqlkuv2lggD5XRMsGLFCsTHx8PT0xNOTk5IT0/Hyy+/DKDhuZDi4mJcunQJQ4cOtXBJ\npauyshIqlQq1tbUoLS1F3759LV0k8n+opWOkW7dugTGG3r17IysrCwDg7u7OTd+0aRMcHR3RsWNH\nSxWRAHBxccHx48dx+PBhCjgCQ4lkI+Xm5qJDhw7w8/PDlClTkJWVhT/++ENjnpdeegn/+c9/YGtr\na6FSEiJcdHllpICAAAANzfcff/wRCxYsaDZP7969KeAQ0gK6vDJRWloaqqurMWnSJI3x58+fx5Ah\nQyxUKtKSBw8eYPHixZYuBgEFHZP98ssvsLOzQ2BgoMb4Xbt24c0337RQqUhLsrOzm9UVsQwKOiZ6\n8uQJOnfurHEZdf36dTg4OGgklokwnDlzBkFBQZYuBgEFHZOFhITgzp07uHXrFgCgoqICK1euRHx8\nvIVLRrRRq9Xo3r27pYtBQIlkk02ePBlr167FlClT4OvrCwBYs2YNnJycLFwy0lR1dTU9wiAgdMuc\nWL2TJ0/ixo0beOeddyxdFAK6vCJWory8HHFxcYiNjUVMTAyePn3KTTtz5gyCg4MBAPfv30efPn2w\naNEiSxVV8ujyiliFZcuWYfny5ejUqROcnZ0xdepUREREAACuXbvGXQJXVVWhtLQUGRkZliyupFFL\nh4je9evX4eTkBC8vL+6zsa6urgCAuro62Nvbc/PK5XKsWrWKcjwWRC0dInqlpaWYMWMGACA5ORle\nXl4YNWoUAO0Pa44fP15vNymk7VDQIaLX+PzN/fv3ceTIEXz00UfctDNnziA0NFRj/uLiYrz44otm\nLSP5/+jyiliNQ4cOoba2Fq+99ho37uLFi/D399eY78iRI5g4caK5i0f+DwUdYjUavwDQGGQYY826\nTTl37hy8vLzoeSoLossrYjWcnJzQvn17bjg/Px8DBgzghm/cuIGkpCRs3brVEsUj/4daOsRqzJgx\nAzKZjOvW9vTp01y+5/Dhw1i3bh02btwIGxs67S2JnkgmVqWgoACrVq2Ch4cHzp49C6VSiZqaGoSF\nheH111+3dPEIKOgQKzZ9+nRs377d0sUgTVA7k1ilu3fvolOnTpYuBtGCgg6xSufOncOwYcMsXQyi\nBQUdYpVycnIwfPhwSxeDaEFBh1ilkpIS+Pj4WLoYRAtKJBNCzIpaOoQQs6KgQwgxKwo6hBCzoqBD\nCDErCjqEELOioEMIMSsKOoQQs6KgQwgxKwo6hBCzoqBDCDGr/wdsmSL/hrXg1wAAAABJRU5ErkJg\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cac0390>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Real Measurements"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#path = './../RaspberryPi-CarPC/TinkerDataLogger/DataLogs/2014/'\n",
      "datafile = '2014-02-14-002-Data.csv'\n",
      "\n",
      "date, \\\n",
      "time, \\\n",
      "millis, \\\n",
      "ax, \\\n",
      "ay, \\\n",
      "az, \\\n",
      "rollrate, \\\n",
      "pitchrate, \\\n",
      "yawrate, \\\n",
      "roll, \\\n",
      "pitch, \\\n",
      "yaw, \\\n",
      "speed, \\\n",
      "course, \\\n",
      "latitude, \\\n",
      "longitude, \\\n",
      "altitude, \\\n",
      "pdop, \\\n",
      "hdop, \\\n",
      "vdop, \\\n",
      "epe, \\\n",
      "fix, \\\n",
      "satellites_view, \\\n",
      "satellites_used, \\\n",
      "temp = np.loadtxt(datafile, delimiter=',', unpack=True, \n",
      "                  converters={1: mdates.strpdate2num('%H%M%S%f'),\n",
      "                              0: mdates.strpdate2num('%y%m%d')},\n",
      "                  skiprows=1)\n",
      "\n",
      "print('Read \\'%s\\' successfully.' % datafile)\n",
      "\n",
      "# A course of 0\u00b0 means the Car is traveling north bound\n",
      "# and 90\u00b0 means it is traveling east bound.\n",
      "# In the Calculation following, East is Zero and North is 90\u00b0\n",
      "# We need an offset.\n",
      "course =(-course+90.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Read '2014-02-14-002-Data.csv' successfully.\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Measurement Noise Covariance R (Adaptive)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\"In practical use, the uncertainty estimates take on the significance of relative weights of state estimates and measurements. So it is not so much important that uncertainty is absolutely correct as it is that it be relatively consistent across all models\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sp = 6.0**2\n",
      "R = np.matrix([[sp, 0.0],\n",
      "               [0.0, sp]])\n",
      "\n",
      "print(R, R.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 36.,   0.],\n",
        "        [  0.,  36.]]), (2, 2))\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Measurement Function H"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Matrix H is the Jacobian of the Measurement function h with respect to the state."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hs = Matrix([[xs],\n",
      "             [ys]])\n",
      "Hs=hs.jacobian(state)\n",
      "Hs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAyBAMAAACqi/RtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrxBf4sJ7tfwE7VnUUnyUAR4AAAAASUVORK5CYII=\n",
       "prompt_number": 16,
       "text": [
        "\u23a11  0  0  0  0\u23a4\n",
        "\u23a2             \u23a5\n",
        "\u23a30  1  0  0  0\u23a6"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Identity Matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I = np.eye(numstates)\n",
      "print(I, I.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([[ 1.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  1.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  1.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  1.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  1.]]), (5, 5))\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Lat/Lon to Meters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "RadiusEarth = 6378388.0 # m\n",
      "arc= 2.0*np.pi*RadiusEarth/360.0 # m/\u00b0\n",
      "\n",
      "dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m\n",
      "dy = arc * np.hstack((0.0, np.diff(latitude))) # in m\n",
      "\n",
      "mx = np.cumsum(dx)\n",
      "my = np.cumsum(dy)\n",
      "\n",
      "ds = np.sqrt(dx**2+dy**2)\n",
      "\n",
      "GPS=np.hstack((True, (np.diff(ds)>0.0).astype('bool'))) # GPS Trigger for Kalman Filter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Initial State"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi]]).T\n",
      "print(x, x.shape)\n",
      "\n",
      "U=float(np.cos(x[2])*x[3])\n",
      "V=float(np.sin(x[2])*x[3])\n",
      "\n",
      "plt.quiver(x[0], x[1], U, V)\n",
      "plt.scatter(float(x[0]), float(x[1]), s=100)\n",
      "plt.title('Initial Location')\n",
      "plt.axis('equal')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[  0.00000000e+00],\n",
        "        [  0.00000000e+00],\n",
        "        [  1.57079633e+00],\n",
        "        [  1.00000000e-03],\n",
        "        [  1.49592170e-02]]), (5, 1))\n"
       ]
      },
      {
       "latex": [
        "$$\\begin{pmatrix}-0.00015, & 0.00015, & -0.0003, & 0.0003\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAAaBAMAAABP+FpwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nvA+Xwid7vTojAR/0eszwfCfDy31T/Q83afS6ajCW+AAAAABJRU5ErkJggg==\n",
       "prompt_number": 19,
       "text": [
        "(-0.00015, 0.00015, -0.0003, 0.0003)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zMXv2bCiVSkRGRkKj0aC4uBi9e/fGz3/+cwCAUqnE6NGjYbfbfZ0+ERFJCvZ1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ceb67d0>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Add some Error"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#my[200:300]+=2.0 # Static Drift"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(9,9))\n",
      "plt.scatter(mx,my, s=20, label='GPS Position', c='k')\n",
      "plt.scatter(mx[0],my[0], s=100, label='Start', c='g')\n",
      "plt.scatter(mx[-1],my[-1], s=100, label='Goal', c='r')\n",
      "plt.xlabel('E [m]')\n",
      "plt.ylabel('N [m]')\n",
      "plt.axis('equal')\n",
      "plt.legend(loc='best')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<matplotlib.legend.Legend at 0x10cdf4a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jIiIiMgwVOhKR5pqNoyyNpTyNpTyNoyyjiwodERERiVnq0REREZGopR4dERER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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cab6fd0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Put everything together as a measurement vector"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "measurements = np.vstack((mx,my))\n",
      "# Lenth of the measurement\n",
      "m = measurements.shape[1]\n",
      "print(measurements.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(2, 1500)\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Preallocation for Plotting\n",
      "x0 = []\n",
      "x1 = []\n",
      "x2 = []\n",
      "x3 = []\n",
      "x4 = []\n",
      "x5 = []\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",
      "dstate=[]\n",
      "K = np.matrix([[0.0], [0.0], [0.0], [0.0], [0.0]])\n",
      "Z = np.matrix([[0.0],[0.0],[0.0]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Extended Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Extended Kalman Filter Step](https://raw.github.com/balzer82/Kalman/master/Extended-Kalman-Filter-Step.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Constant Turn Rate, Constant Velocity Model for a vehicle\n",
      "\n",
      "$$x_k= \\begin{bmatrix} x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\end{bmatrix} = \\begin{bmatrix} \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\end{bmatrix} =  \\underbrace{\\begin{matrix}x[0] \\\\ x[1] \\\\ x[2] \\\\ x[3] \\\\ x[4]  \\end{matrix}}_{\\textrm{Python Nomenclature}}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for filterstep in range(m):\n",
      "    \n",
      "    # Data (Control)\n",
      "    vt=speed[filterstep]/3.6\n",
      "    yat=yawrate[filterstep]/180.0*np.pi\n",
      "    \n",
      "   \n",
      "    # Time Update (Prediction)\n",
      "    # ========================\n",
      "    # Project the state ahead\n",
      "    # see \"Dynamic Matrix\"\n",
      "    if np.abs(yat)<0.0001: # Driving straight\n",
      "        x[0] = x[0] + vt*dt * np.cos(x[2])\n",
      "        x[1] = x[1] + vt*dt * np.sin(x[2])\n",
      "        x[2] = x[2]\n",
      "        x[3] = vt\n",
      "        x[4] = 0.0000001 # avoid numerical issues in Jacobians\n",
      "        dstate.append(0)\n",
      "    else: # otherwise\n",
      "        x[0] = x[0] + (vt/yat) * (np.sin(yat*dt+x[2]) - np.sin(x[2]))\n",
      "        x[1] = x[1] + (vt/yat) * (-np.cos(yat*dt+x[2])+ np.cos(x[2]))\n",
      "        x[2] = (x[2] + yat*dt + np.pi) % (2.0*np.pi) - np.pi\n",
      "        x[3] = vt\n",
      "        x[4] = yat\n",
      "        dstate.append(1)\n",
      "    \n",
      "    # Calculate the Jacobian of the Dynamic Matrix A\n",
      "    # see \"Calculate the Jacobian of the Dynamic Matrix with respect to the state vector\"\n",
      "    a13 = float((x[3]/x[4]) * (np.cos(x[4]*dt+x[2]) - np.cos(x[2])))\n",
      "    a14 = float((1.0/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
      "    a15 = float((dt*x[3]/x[4])*np.cos(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
      "    a23 = float((x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n",
      "    a24 = float((1.0/x[4]) * (-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
      "    a25 = float((dt*x[3]/x[4])*np.sin(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n",
      "    JA = np.matrix([[1.0, 0.0, a13, a14, a15],\n",
      "                  [0.0, 1.0, a23, a24, a25],\n",
      "                  [0.0, 0.0, 1.0, 0.0, dt],\n",
      "                  [0.0, 0.0, 0.0, 1.0, 0.0],\n",
      "                  [0.0, 0.0, 0.0, 0.0, 1.0]])\n",
      "    \n",
      "    # Calculate the Jacobian of the Control Input G\n",
      "    # see \"Calculate the Jacobian of the Dynamic Matrix with Respect to the Control\"\n",
      "    g11 = float(1.0/x[4]*(-np.sin(x[2])+np.sin(dt*x[4]+x[2])))\n",
      "    g12 = float(dt*x[3]/x[4]*np.cos(dt*x[4]+x[2]) - x[3]/x[4]**2*(-np.sin(x[2])+np.sin(dt*x[4]+x[2])))\n",
      "    g21 = float(1.0/x[4]*(np.cos(x[2])-np.cos(dt*x[4]+x[2])))\n",
      "    g22 = float(dt*x[3]/x[4]*np.sin(dt*x[4]+x[2]) - x[3]/x[4]**2*(np.cos(x[2])-np.cos(dt*x[4]+x[2])))\n",
      "    JG = np.matrix([[g11, g12],\n",
      "                    [g21, g22],\n",
      "                    [0.0, dt],\n",
      "                    [1.0, 0.0],\n",
      "                    [0.0, 1.0]])\n",
      "    \n",
      "    # Project the error covariance ahead\n",
      "    P = JA*P*JA.T + JG*Q*JG.T\n",
      "    \n",
      "    # Because GPS is sampled with 10Hz and the other Measurements, as well as\n",
      "    # the filter are sampled with 50Hz, one have to wait for correction until\n",
      "    # there is a new GPS Measurement\n",
      "    if GPS[filterstep]:\n",
      "        \n",
      "        # Measurement Update (Correction)\n",
      "        # ===============================\n",
      "        \n",
      "        # Measurement Function\n",
      "        hx = np.matrix([[float(x[0])],\n",
      "                        [float(x[1])]])\n",
      "        \n",
      "        # Calculate the Jacobian of the Measurement Function\n",
      "        # see \"Measurement Matrix H\"\n",
      "        H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0],\n",
      "                       [0.0, 1.0, 0.0, 0.0, 0.0]])\n",
      "        \n",
      "       \n",
      "        S = H*P*H.T + R\n",
      "        K = (P*H.T) * np.linalg.inv(S)\n",
      "    \n",
      "        # Update the estimate via\n",
      "        Z = measurements[:,filterstep].reshape(H.shape[0],1)\n",
      "        y = Z - (hx)                         # Innovation or Residual\n",
      "        x = x + (K*y)\n",
      "        \n",
      "        # Update the error covariance\n",
      "        P = (I - (K*H))*P\n",
      "    \n",
      "\n",
      "    # Save states for Plotting\n",
      "    x0.append(float(x[0]))\n",
      "    x1.append(float(x[1]))\n",
      "    x2.append(float(x[2]))\n",
      "    x3.append(float(x[3]))\n",
      "    x4.append(float(x[4]))\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",
      "    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]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Plots"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Uncertainty"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "plt.semilogy(range(m),Px, label='$x$')\n",
      "plt.step(range(m),Py, label='$y$')\n",
      "plt.step(range(m),Pdx, label='$\\psi$')\n",
      "plt.step(range(m),Pdy, label='$v$')\n",
      "plt.step(range(m),Pddx, label='$\\dot \\psi$')\n",
      "\n",
      "plt.xlabel('Filter Step')\n",
      "plt.ylabel('')\n",
      "plt.title('Uncertainty (Elements from Matrix $P$)')\n",
      "plt.legend(loc='best',prop={'size':22})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.legend.Legend at 0x10d05c590>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NhUlNTUVUVBT69+9v+k27tWvXYtCgQejWrZtjWktERJe1oqIirFmzBt9++y0eeeQRm9/3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\nfF7YiE6j5vU9VQAseWAwNpOuizO7MCdPHGXVZ58we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BoN+/btZPbse9n6xQbcLhf33fcI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\n9mwGmAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cdf4c90>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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(6))\n",
      "# set the locations and labels of the yticks\n",
      "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = plt.xticks()\n",
      "# set the locations of the yticks\n",
      "plt.xticks(np.arange(6))\n",
      "# set the locations and labels of the yticks\n",
      "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n",
      "\n",
      "plt.xlim([-0.5,4.5])\n",
      "plt.ylim([4.5, -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()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RURF69+7t3iiJiKha1KiZ1sWLFxEfHw8A+OSTTxAREYHu3btr95et4/bq1cuN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\nh2BKKvco9GSmgmUmKo+Xyr6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Uzgt7WkRERG5iyeVBldeb9cbcyDEvcsyLnMp5MfvyoCWL\nFhERyZm9aFlyeVDl9Wa9MTdyzIsc8yLHvJSXkpKCtm3bIjIyEgsXLqzycSxZtIiISE6PEzFKSkow\nefJkpKSk4ODBg/j8889x6NChKsVnyaKl8nqz3pgbOeZFjnmRUzkvehSt3bt3o1WrVggPD4eXlxdG\njx6Nr7/+ukrxsadFRESayva0tm/f7rAc2rBhQ8TGxjrs8+9//xvNmzfXtkNCQrBr164qxWfJmRbX\nm51jbuSYFznmRc5Keenbty9mzZql/bPb7eX2cefJHZxpERGRRo+zBx944AHk5ORo2zk5OQgJCanS\nsSw501J5vVlvzI0c8yLHvMipnBc9elpdu3bF0aNHcfLkSRQWFuKLL77A8OHDqxQfZ1pERKTRY6ZV\nq1YtLFmyBIMGDUJJSQni4+PRrl27Kh3LkjMtK603VxZzI8e8yDEvcsxLeYMHD8bhw4dx7NgxzJgx\no8rHsWTR2rdvn9EhmBZzI8e8yDEvcirnxexfmGvJ5cFr164ZHYJpMTdyzIsc8yKncl74NU5ERERu\nYsmZ1qlTp4wOwbSYGznmRY55kVM5L2afadmEEKI6nig1NbU6noaIiO5y9zdUOOOO39O1atVCTEzM\nfR/HmWorWkRERPeLPS0iIlIGixYRESmDRYuIiJTBokVERMpg0SIiImVYpmhdunQJL7zwAl544QU8\n+uij+Pvf/45r167h17/+NX73u99h3LhxOHfunNFhVrvLly/jueeew5gxYzBq1CiUlJQ43B8fH4+J\nEycaFJ35XLlyBdOmTTM6DMNcv34dEydOxJgxY/Dkk086jJcpU6YgPDwct27dMjBC45WWlqJv376w\n2+24fv260eHUPMICCgoKxPDhw0VOTo4QQoh9+/aJ2rVriyeeeEJcvHhRfPLJJ8Jms4n333/f4Eir\n369//Wtx+vRpcePGDWGz2cSGDRu0+/Lz80Xt2rXF5MmTDYzQXNavXy9Wr15tdBiGmTp1qjh27Ji4\nefNmufHy+OOPC5vNJjIzMw2M0HhXr14V3t7ewsPDQ/zrX/8yOpwaxxIzrY8++ggvvfSS9kfHfH19\nUVRUhKioKAQGBsJms8Fut2PYsGEGR1q9Dh8+jCZNmqB58+b47rvvAACNGzfW7s/IyEBRURF69+5t\nVIimk5aWhj59+hgdhiHOnTsHIQRatmypfYt5QECAdv+yZctQp04d1K1b16gQTaFBgwbYvHkzNmzY\ngDZt2hgdTo1jia9xaty4Mfr3769tZ2VlAQAeffRRAMCECRMwYcIEQ2Iz0sWLFxEfHw8A+OSTTxAR\nEYHu3btr95f9YurVq5ch8ZlRTk4OmjVrZnQYhvjPf/6DSZMmAQBWrVqF5s2bo2fPntr9wcHB6N69\nOyIjI40K0TT4QU8/lihazzzzjMP2li1b0KBBA3Tp0sWgiMyhrBjl5uYiOTkZb7zxhsP9O3bsQGho\naJX/LHZNU1BQYOlZRFRUFIA7fa3//d//xYsvvlhun5YtW8LT07O6QyMLscTy4N2+++479O7d2/Rf\nDFldvvrqK5SUlGDUqFHabUVFRcjIyOAnxp/JyMhAjx49jA7DcMnJySgoKMBjjz3mcHtWVpblPwjK\nWP3kHXezXNE6c+YMjh07Vu4LHf/yl78YFJHxdu3ahWbNmjks62RlZSE/P99yRevq1auIj4/HmDFj\nMHr0aJSWlmr3paWloW/fvgDunHXZunVrvPLKK0aFapjMzEzUqlULXbt2dbj9s88+w69+9SuDojKv\nnTt3lssVVV2NL1oXLlxA9+7dMWvWLABASkoKADgMoqNHj+Lw4cOGxGcG58+fR1hYmMNtZd/2bLV+\n1uzZszFnzhwkJibiyy+/1MYLABw5cgStWrUCAOTn5+Ps2bPYtGmTUaEa5tatW2jUqJHDMmB2djZ8\nfHwcTsygO6x88o4eanzR2rZtGzIzM1G7dm3cvHkTGzduRKNGjZCXlwfgzifm3//+95g5c6bBkRqn\nW7duOHnypDar2LNnDxYsWAB/f3907NjR4OiqT3Z2Nvz8/BAaGqqdTenv7w8AKC4uhpeXl7ZvSEgI\n5s2bZ8keV79+/XDhwgXtusa8vDy8+eabmD59usGRmZOVT97RQ40/EWPw4MGIj49Hbm4uJk+ejA8+\n+ACnTp3CW2+9hbVr10IIgXfffRcNGjQwOlTDzJw5E6dPn8aQIUMQEREBf39/eHp6OpwZZgVnz55F\nQkICAGD58uUIDQ1FdHQ0AHm/ZuDAgTh06FC1x2m0J554AgsXLsTYsWO1meeCBQvg5+dncGTmY/WT\nd/TAv6dF5aSnp6N37954//33MWXKFKPDqXaXL19GcHAwXnvtNcydOxcA8Ic//AEDBgxAp06dtP1S\nUlJw9epVjB492qhQyeS2bNmCEydOWPKSGr3U+OVBqlhBQYHD9po1a+Dr62vZX8br169HUVERRo4c\nqVEgTiEAAAIPSURBVN22f/9+h4IFABs3bsTQoUOrOzwyGZ68U71YtCxu0KBBCAoK0r4j7cKFC0hK\nSsKMGTMQHBxscHTG+OGHH+Dr66sVKSEE7l6Q2LVrF0JDQ7kkRjx5p5qxaFlcZmYmoqOj4efnh5s3\nb+Lpp5/GiBEjtLMtrcjPzw/e3t7a9sGDB9GhQwdt+8SJE0hMTMTLL79sRHhkIjx5p/qxaFncl19+\nic6dO+OFF17A+PHjMX78eEtfswYACQkJsNls+PrrrwHc+WaQslOWN2zYgEWLFmHp0qXw8OCPj9VV\n5eSdu5eZqXJ4IgaRxNGjRzFv3jw0bdoU6enpsNvtKCwsRFxcHJ588kmjwyOT4ck71afGn/JOVBWR\nkZFYsWIFAGD8+PFYsmSJwRGRmTk7eWfq1KkO+23cuBELFiyo7vBqFK5vEN3DxYsXERgYaHQYZHI8\neaf6cKZFdA+7du1Ct27djA6DTM7Vk3eSkpKMCK9G4UyL6B4yMjIc/sYYkQxP3qk+PBGD6B6ee+45\nLF++3OgwSAE8ead6sGgREbnZ+PHj8de//tXoMGokzlWJiNyIJ+/oi0WLiMiNePKOvli0iIjciCfv\n6ItFi4jIjc6cOYOIiAijw6ixeCIGEREpgzMtIiJSBosWEREpg0WLiIiUwaJFRETKYNEiIiJlsGgR\nEZEyWLSIiEgZLFpERKQMFi0iIlLG/wFdrKyoef9IbgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cec9890>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Kalman Gains"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "plt.step(range(len(measurements[0])),Kx, label='$x$')\n",
      "plt.step(range(len(measurements[0])),Ky, label='$y$')\n",
      "plt.step(range(len(measurements[0])),Kdx, label='$\\psi$')\n",
      "plt.step(range(len(measurements[0])),Kdy, label='$v$')\n",
      "plt.step(range(len(measurements[0])),Kddx, label='$\\dot \\psi$')\n",
      "\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(prop={'size':18})\n",
      "plt.ylim([-0.5,0.5])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}-0.5, & 0.5\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG4AAAAaBAMAAACkxnQfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMkS7zRCZdiKJ71Rm\nq90icBAQAAACEklEQVQ4EZ2SP4gTURDGf5vbXTfJZi9Y2F5KG7mAWCprJSLCFoeghVlFkatM4ymC\nEBCuTQrhqsMIFtddeotLJxyKEUULLRT/IIiCh6cnh8SZ3exuvLBC/GDfzHzfzHtvZh+wn2nR1AKj\nPm0Zh7TCDKauK/al5EpWZi0uVTUyrxkXMzbyzqxciOyJ4EANPoCznWWYPeuTRqXhMGohUzjF+ZaG\n68Ofsi5BMdQwxibcUc9cvTFiEuN2KfoanHzZkrUte/c0jHEUNrTbSkKkdmZAObrYIKK8PnOaOMJv\nmNdtJutmBxR2NSuus+vI3RJYP6SuKVHlUTyfRIBGSEEb4/VDnc++Lpcy0fkFcx2JZwJnK6PVa3cw\nRIUjtGtQ2OawRjHSOgmPJWRs0zrZ9I28lW+cFmHhq+K4JTtG9xTqakuWDI3O6J5g78jP2+JjJiL9\nbehcnsPd2hgPsyFlnUvFpygtOLvReUnKO3gSSHBfzlObwavj6n8o+dhi5Ty9Z4KbxGMK4X3CxVYG\naPvi2uCJNXZ4FgvR6vWsezR8lnHX1I7hM+eq1neckM1WNE85I4W1cquKN8BZfBHgjT1cOHv9KXyB\n5dXLki7Pbv7vRtI94OCYv8eV91Kq7eHSsJ96E47ZxO5MsDFh9XMEoRsBRjdHdnN4pR/L9+ofep70\nVoSFPDGfd7W3cpifkKPcjvgHOWo+rb/wP/EHCDJ1QmcOuEYAAAAASUVORK5CYII=\n",
       "prompt_number": 27,
       "text": [
        "(-0.5, 0.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gh1ItmaZJx44defnll/2+SBJCFCU9sUKIGuuRRx5h8+bNrF27NtihVEtff/01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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d06ff50>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "State Vector"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,16))\n",
      "\n",
      "plt.subplot(411)\n",
      "plt.step(range(len(measurements[0])),x0-mx[0], label='$x$')\n",
      "plt.step(range(len(measurements[0])),x1-my[0], label='$y$')\n",
      "\n",
      "plt.title('Extended Kalman Filter State Estimates (State Vector $x$)')\n",
      "plt.legend(loc='best',prop={'size':22})\n",
      "plt.ylabel('Position (relative to start) [m]')\n",
      "\n",
      "plt.subplot(412)\n",
      "plt.step(range(len(measurements[0])),x2, label='$\\psi$')\n",
      "plt.step(range(len(measurements[0])),(course/180.0*np.pi+np.pi)%(2.0*np.pi) - np.pi, label='$\\psi$ (from GPS as reference)')\n",
      "plt.ylabel('Course')\n",
      "plt.legend(loc='best',prop={'size':16})\n",
      "           \n",
      "plt.subplot(413)\n",
      "plt.step(range(len(measurements[0])),x3, label='$v$')\n",
      "plt.step(range(len(measurements[0])),speed/3.6, label='$v$ (from GPS as reference)')\n",
      "plt.ylabel('Velocity')\n",
      "plt.ylim([0, 30])\n",
      "plt.legend(loc='best',prop={'size':16})\n",
      "\n",
      "plt.subplot(414)\n",
      "plt.step(range(len(measurements[0])),x4, label='$\\dot \\psi$')\n",
      "plt.step(range(len(measurements[0])),yawrate/180.0*np.pi, label='$\\dot \\psi$ (from IMU as reference)')\n",
      "plt.ylabel('Yaw Rate')\n",
      "plt.ylim([-0.6, 0.6])\n",
      "plt.legend(loc='best',prop={'size':16})\n",
      "plt.xlabel('Filter Step')\n",
      "\n",
      "plt.savefig('Extended-Kalman-Filter-CTRV-State-Estimates.png', dpi=72, transparent=True, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xf/rF3F2hhlrIZYeh5Gw3F7/FmTBUlVptpgUYzUVvTBJUYzJMQd0BOyy7yvzp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NjNfu5tZBFbT8v1mAM5R/cJ+cEJgS8l0i5Py3ZH3qOxvZiUzHA7bW94nccLKVlH+GU8ORwTwpgg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yHnroIbZu3cqIESO45557WL9+PbNnz2bdunVMmzaN5557ri3rPa6WPIeYR2KoDIEVZ0N52PEX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\nAAAAGYmEGAAAAACQkUiIAQAAAAAZ6StUYHZ5fvJD/wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d0495d0>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Position x/y"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab --no-import-all"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using matplotlib backend: TkAgg\n",
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "\n",
      "# EKF State\n",
      "plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n",
      "plt.scatter(x0,x1, c=dstate, s=30, label='EKF Position')\n",
      "\n",
      "# Measurements\n",
      "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', c=epe[::5], cmap='autumn_r')\n",
      "cbar=plt.colorbar(ticks=np.arange(20))\n",
      "cbar.ax.set_ylabel(u'EPE', rotation=270)\n",
      "cbar.ax.set_xlabel(u'm')\n",
      "\n",
      "# Start/Goal\n",
      "plt.scatter(x0[0],x1[0], s=60, label='Start', c='g')\n",
      "plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r')\n",
      "\n",
      "plt.xlabel('X [m]')\n",
      "plt.ylabel('Y [m]')\n",
      "plt.title('Position')\n",
      "#plt.legend(loc='best')\n",
      "plt.axis('equal')\n",
      "#plt.tight_layout()\n",
      "\n",
      "plt.show()\n",
      "#plt.savefig('Extended-Kalman-Filter-CTRV-Position.png', dpi=72, transparent=True, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('Done.')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Done.\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Conclusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As you can see, complicated analytic calculation of the Jacobian Matrices, but it works pretty well."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Write Google Earth KML"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Convert back from Meters to Lat/Lon (WGS84)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "latekf = latitude[0] + np.divide(x1,arc)\n",
      "lonekf = longitude[0]+ np.divide(x0,np.multiply(arc,np.cos(latitude*np.pi/180.0)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Create Data for KML Path"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Coordinates and timestamps to be used to locate the car model in time and space\n",
      "The value can be expressed as yyyy-mm-ddThh:mm:sszzzzzz, where T is the separator between the date and the time, and the time zone is either Z (for UTC) or zzzzzz, which represents \u00b1hh:mm in relation to UTC."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import datetime\n",
      "car={}\n",
      "car['when']=[]\n",
      "car['coord']=[]\n",
      "car['gps']=[]\n",
      "for i in range(len(millis)):\n",
      "    d=datetime.datetime.fromtimestamp(millis[i]/1000.0)\n",
      "    car[\"when\"].append(d.strftime(\"%Y-%m-%dT%H:%M:%SZ\"))\n",
      "    car[\"coord\"].append((lonekf[i], latekf[i], 0))\n",
      "    car[\"gps\"].append((longitude[i], latitude[i], 0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from simplekml import Kml, Model, AltitudeMode, Orientation, Scale"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The model path and scale variables\n",
      "car_dae = r'http://simplekml.googlecode.com/hg/samples/resources/car-model.dae'\n",
      "car_scale = 1.0\n",
      "\n",
      "# Create the KML document\n",
      "kml = Kml(name=d.strftime(\"%Y-%m-%d %H:%M\"), open=1)\n",
      "\n",
      "# Create the model\n",
      "model_car = Model(altitudemode=AltitudeMode.clamptoground,\n",
      "                            orientation=Orientation(heading=75.0),\n",
      "                            scale=Scale(x=car_scale, y=car_scale, z=car_scale))\n",
      "\n",
      "# Create the track\n",
      "trk = kml.newgxtrack(name=\"EKF\", altitudemode=AltitudeMode.clamptoground,\n",
      "                     description=\"State Estimation from Extended Kalman Filter with CTRV Model\")\n",
      "gps = kml.newgxtrack(name=\"GPS\", altitudemode=AltitudeMode.clamptoground,\n",
      "                     description=\"Original GPS Measurements\")\n",
      "\n",
      "# Attach the model to the track\n",
      "trk.model = model_car\n",
      "gps.model = model_car\n",
      "\n",
      "trk.model.link.href = car_dae\n",
      "gps.model.link.href = car_dae\n",
      "\n",
      "# Add all the information to the track\n",
      "trk.newwhen(car[\"when\"])\n",
      "trk.newgxcoord(car[\"coord\"])\n",
      "\n",
      "gps.newwhen(car[\"when\"][::5])\n",
      "gps.newgxcoord((car[\"gps\"][::5]))\n",
      "\n",
      "# Style of the Track\n",
      "trk.iconstyle.icon.href = \"\"\n",
      "trk.labelstyle.scale = 1\n",
      "trk.linestyle.width = 4\n",
      "trk.linestyle.color = '7fff0000'\n",
      "\n",
      "gps.iconstyle.icon.href = \"\"\n",
      "gps.labelstyle.scale = 0\n",
      "gps.linestyle.width = 3\n",
      "gps.linestyle.color = '7fffffff'\n",
      "\n",
      "\n",
      "# Saving\n",
      "#kml.save(\"Extended-Kalman-Filter-CTRV.kml\")\n",
      "kml.savekmz(\"Extended-Kalman-Filter-CTRV.kmz\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('Exported KMZ File for Google Earth')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Exported KMZ File for Google Earth\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    }
   ],
   "metadata": {}
  }
 ]
}