Kalman-Filter-CV.ipynb

{
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  "signature": "sha256:956b0085c0ddddcd57260230295c06f2d02d2d1c806a06c3d530191dbb418f68"
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.stats import norm\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": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Kalman Filter Implementation for Constant Velocity Model (CV) in Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Image](http://www.cbcity.de/wp-content/uploads/2013/06/Fahrzeug_GPS_Tunnel-520x181.jpg)\n",
      "\n",
      "Situation covered: You drive with your car in a tunnel and the GPS signal is lost. Now the car has to determine, where it is in the tunnel. The only information it has, is the velocity in driving direction. The x and y component of the velocity ($\\dot x$ and $\\dot y$) can be calculated from the absolute velocity (revolutions of the wheels) and the heading of the vehicle (yaw rate sensor)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Kalman Filter](Kalman-Filter-Step.png)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "State Vector"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Constant Velocity Model for Ego Motion\n",
      "\n",
      "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\dot x \\\\ \\dot y} \\right] = \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Velocity in X} \\\\ \\text{Velocity in Y}}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Formal Definition (Motion of Law):\n",
      "\n",
      "$$x_{k+1} = \\textbf{A} \\cdot x_{k}$$\n",
      "\n",
      "$$x_{k+1} = \\begin{bmatrix}1 & 0 & \\Delta t & 0 \\\\ 0 & 1 & 0 & \\Delta t \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\end{bmatrix}_{k}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Observation Model:\n",
      "\n",
      "$$y = \\textbf{H} \\cdot x$$\n",
      "\n",
      "$$y = \\begin{bmatrix}0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1\\end{bmatrix} \\cdot x$$ means: You observe the velocity directly in the correct unit"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Initial State $x_0$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.matrix([[0.0, 0.0, 0.0, 0.0]]).T\n",
      "print(x, x.shape)\n",
      "plt.scatter(float(x[0]),float(x[1]), s=100)\n",
      "plt.title('Initial Location')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 0.],\n",
        "        [ 0.],\n",
        "        [ 0.],\n",
        "        [ 0.]]), (4, 1))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<matplotlib.text.Text at 0x107200810>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cAcyte+2K2H8A6G5/+lI6hw/P4MorX8yb3nQqPT0v4brrXsyll57KW97y2/zDP8yc6ulJ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\nJEmSJEmSJEkay/8HedkJdK8KM/0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x106eab550>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Initial Uncertainty $P_0$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = np.diag([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),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([[ 1000.,     0.,     0.,     0.],\n",
        "       [    0.,  1000.,     0.,     0.],\n",
        "       [    0.,     0.,  1000.,     0.],\n",
        "       [    0.,     0.,     0.,  1000.]]), (4, 4))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wzTffnIvvr9JwqT+gtCeXh+FiscjgwYNzMz/J4ay/r2rD5b/VLOen9Lizs5Oe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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107232750>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Dynamic Matrix $A$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is calculated from the dynamics of the Egomotion.\n",
      "\n",
      "$$x_{k+1} = x_{k} + \\dot x_{k} \\cdot \\Delta t$$\n",
      "$$y_{k+1} = y_{k} + \\dot y_{k} \\cdot \\Delta t$$\n",
      "$$\\dot x_{k+1} = \\dot x_{k}$$\n",
      "$$\\dot y_{k+1} = \\dot y_{k}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = 0.1 # Time Step between Filter Steps\n",
      "\n",
      "A = np.matrix([[1.0, 0.0, dt, 0.0],\n",
      "              [0.0, 1.0, 0.0, dt],\n",
      "              [0.0, 0.0, 1.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 1.0]])\n",
      "print(A, A.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 1. ,  0. ,  0.1,  0. ],\n",
        "        [ 0. ,  1. ,  0. ,  0.1],\n",
        "        [ 0. ,  0. ,  1. ,  0. ],\n",
        "        [ 0. ,  0. ,  0. ,  1. ]]), (4, 4))\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Measurement Matrix"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We directly measure the Velocity $\\dot x$ and $\\dot y$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H = np.matrix([[0.0, 0.0, 1.0, 0.0],\n",
      "              [0.0, 0.0, 0.0, 1.0]])\n",
      "print(H, H.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 0.,  0.,  1.,  0.],\n",
        "        [ 0.,  0.,  0.,  1.]]), (2, 4))\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Measurement Noise Covariance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ra = 10.0**2\n",
      "\n",
      "R = np.matrix([[ra, 0.0],\n",
      "              [0.0, ra]])\n",
      "print(R, R.shape)\n",
      "\n",
      "# Plot between -10 and 10 with .001 steps.\n",
      "xpdf = np.arange(-10, 10, 0.001)\n",
      "plt.subplot(121)\n",
      "plt.plot(xpdf, norm.pdf(xpdf,0,R[0,0]))\n",
      "plt.title('$\\dot x$')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.plot(xpdf, norm.pdf(xpdf,0,R[1,1]))\n",
      "plt.title('$\\dot y$')\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(matrix([[ 100.,    0.],\n",
        "        [   0.,  100.]]), (2, 2))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/iROwsEfN1C2n/DAMomMSjT3/9ulKgvISO0zw/blA+gRVKl61LtrTE+89hlj3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\nu2UPBpsh/wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107225750>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Process Noise Covariance"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Position of the car 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",
      "$$Q = \\begin{bmatrix}\\sigma_{x}^2 & \\sigma_{xy} & \\sigma_{x \\dot x} & \\sigma_{x \\dot y} \\\\ \\sigma_{yx} & \\sigma_{y}^2 & \\sigma_{y \\dot x} & \\sigma_{y \\dot y} \\\\ \\sigma_{\\dot x x} & \\sigma_{\\dot x y} & \\sigma_{\\dot x}^2 & \\sigma_{\\dot x \\dot y} \\\\ \\sigma_{\\dot y x} & \\sigma_{\\dot y y} & \\sigma_{\\dot y \\dot x} & \\sigma_{\\dot y}^2 \\end{bmatrix}$$\n",
      "\n",
      "One can calculate Q as\n",
      "\n",
      "$$Q = G\\cdot G^T \\cdot \\sigma_v^2$$\n",
      "\n",
      "with $G = \\begin{bmatrix}0.5dt^2 & 0.5dt^2 & dt & dt\\end{bmatrix}^T$ and $\\sigma_v$ as the acceleration process noise, which can be assumed for a vehicle to be $8.8m/s^2$, according to: Schubert, R., Adam, C., Obst, M., Mattern, N., Leonhardt, V., & Wanielik, G. (2011). [Empirical evaluation of vehicular models for ego motion estimation](http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5940526). 2011 IEEE Intelligent Vehicles Symposium (IV), 534\u2013539. doi:10.1109/IVS.2011.5940526"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sv = 8.8\n",
      "\n",
      "G = np.matrix([[0.5*dt**2],\n",
      "               [0.5*dt**2],\n",
      "               [dt],\n",
      "               [dt]])\n",
      "\n",
      "Q = G*G.T*sv**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import Symbol, Matrix\n",
      "from sympy.interactive import printing\n",
      "printing.init_printing()\n",
      "dts = Symbol('dt')\n",
      "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[dts],[dts]])\n",
      "Qs*Qs.T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/paul/anaconda/lib/python2.7/site-packages/IPython/core/formatters.py:239: FormatterWarning: Exception in image/png formatter: \n",
        "\\left[\\begin{smallmatrix}0.25 dt^{4} & 0.25 dt^{4} & 0.5 dt^{3} & 0.5 dt^{3}\\\\0.25 dt^{4} & 0.25 dt^{4} & 0.5 dt^{3} & 0.5 dt^{3}\\\\0.5 dt^{3} & 0.5 dt^{3} & dt^{2} & dt^{2}\\\\0.5 dt^{3} & 0.5 dt^{3} & dt^{2} & dt^{2}\\end{smallmatrix}\\right]\n",
        "      ^\n",
        "Expected \"\\right\" (at char 6), (line:1, col:7)\n",
        "  FormatterWarning,\n"
       ]
      },
      {
       "latex": [
        "$$\\left[\\begin{matrix}0.25 dt^{4} & 0.25 dt^{4} & 0.5 dt^{3} & 0.5 dt^{3}\\\\0.25 dt^{4} & 0.25 dt^{4} & 0.5 dt^{3} & 0.5 dt^{3}\\\\0.5 dt^{3} & 0.5 dt^{3} & dt^{2} & dt^{2}\\\\0.5 dt^{3} & 0.5 dt^{3} & dt^{2} & dt^{2}\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "\u23a1       4         4        3        3\u23a4\n",
        "\u23a20.25\u22c5dt   0.25\u22c5dt   0.5\u22c5dt   0.5\u22c5dt \u23a5\n",
        "\u23a2                                    \u23a5\n",
        "\u23a2       4         4        3        3\u23a5\n",
        "\u23a20.25\u22c5dt   0.25\u22c5dt   0.5\u22c5dt   0.5\u22c5dt \u23a5\n",
        "\u23a2                                    \u23a5\n",
        "\u23a2      3         3       2        2  \u23a5\n",
        "\u23a20.5\u22c5dt    0.5\u22c5dt      dt       dt   \u23a5\n",
        "\u23a2                                    \u23a5\n",
        "\u23a2      3         3       2        2  \u23a5\n",
        "\u23a30.5\u22c5dt    0.5\u22c5dt      dt       dt   \u23a6"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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 $P$')\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),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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i5RR6J+8rb3L4KHbqU+182s3Y+bL3YqdI9WKnt17b7gYWSbVzP4qbu7LuIEKL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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1087b0750>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Identity Matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "I = np.eye(4)\n",
      "print(I, I.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(array([[ 1.,  0.,  0.,  0.],\n",
        "       [ 0.,  1.,  0.,  0.],\n",
        "       [ 0.,  0.,  1.,  0.],\n",
        "       [ 0.,  0.,  0.,  1.]]), (4, 4))\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Measurement"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = 200 # Measurements\n",
      "vx= 20 # in X\n",
      "vy= 10 # in Y\n",
      "\n",
      "mx = np.array(vx+np.random.randn(m))\n",
      "my = np.array(vy+np.random.randn(m))\n",
      "\n",
      "measurements = np.vstack((mx,my))\n",
      "\n",
      "print(measurements.shape)\n",
      "\n",
      "print('Standard Deviation of Acceleration Measurements=%.2f' % np.std(mx))\n",
      "print('You assumed %.2f in R.' % R[0,0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(2, 200)\n",
        "Standard Deviation of Acceleration Measurements=0.94\n",
        "You assumed 100.00 in R.\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,5))\n",
      "\n",
      "plt.step(range(m),mx, label='$\\dot x$')\n",
      "plt.step(range(m),my, label='$\\dot y$')\n",
      "plt.ylabel('Velocity')\n",
      "plt.title('Measurements')\n",
      "plt.legend(loc='best',prop={'size':18})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<matplotlib.legend.Legend at 0x1073a6450>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bqYxp12S+hmRBp3afB149wOetBL7I7DDltwLLSebjHkmy+NRY+4smJyd3N1sH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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107266350>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Preallocation for Plotting\n",
      "xt = []\n",
      "yt = []\n",
      "dxt= []\n",
      "dyt= []\n",
      "Zx = []\n",
      "Zy = []\n",
      "Px = []\n",
      "Py = []\n",
      "Pdx= []\n",
      "Pdy= []\n",
      "Rdx= []\n",
      "Rdy= []\n",
      "Kx = []\n",
      "Ky = []\n",
      "Kdx= []\n",
      "Kdy= []"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Kalman Filter](Kalman-Filter-Step.png)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for n in range(len(measurements[0])):\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",
      "    # 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[:,n].reshape(2,1)\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",
      "    \n",
      "    # Save states for Plotting\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",
      "    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",
      "    Rdx.append(float(R[0,0]))\n",
      "    Rdy.append(float(R[1,1]))\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]))    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thats it."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Let's take a look at the filter performance"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Kalman Gains K"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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",
      "\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':22})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.legend.Legend at 0x1073bbdd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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s629/+ctfGDBgwFUzGrECVxERERGRWjgHrxMnTqwWvBYXFwOem+6eO3eOjz/+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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1075f6950>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Covariance Matrix"
     ]
    },
    {
     "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 $P$')\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),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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TzOJYiFuDE8U7gJ8Dm4HtwFLgQ8ApwC1+mVuA0/zjU4FFwFagG1gHHBX6HQqdKERE0tbg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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10765fcd0>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "plt.plot(range(len(measurements[0])),Px, label='$x$')\n",
      "plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
      "plt.plot(range(len(measurements[0])),Pdx, label='$\\dot x$')\n",
      "plt.plot(range(len(measurements[0])),Pdy, label='$\\dot y$')\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": 17,
       "text": [
        "<matplotlib.legend.Legend at 0x10888d8d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mM+nq6tp3+VVXXZXOzs7ccMMNBUc5NjOvgN4fKETtQRlqj3b2kY98JNdee22u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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107a9f9d0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "State Estimate"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\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.axhline(vx, color='#999999', label='$\\dot x_{real}$')\n",
      "plt.axhline(vy, color='#999999', label='$\\dot y_{real}$')\n",
      "\n",
      "plt.xlabel('Filter Step')\n",
      "plt.title('Estimate (Elements from State Vector $x$)')\n",
      "plt.legend(loc='best',prop={'size':22})\n",
      "plt.ylim([0, 30])\n",
      "plt.ylabel('Velocity')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<matplotlib.text.Text at 0x1087bd550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9Nxs3bswZZ5yRb37zm/nOd76TP/mTP0nSBODVq1dn3rx5ueWWW3LhhRdmyZIl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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109177410>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Position x/y"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,16))\n",
      "plt.scatter(xt,yt, s=20, label='State', c='k')\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.axis('equal')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/paul/anaconda/lib/python2.7/site-packages/IPython/core/formatters.py:239: FormatterWarning: Exception in image/png formatter: \n",
        "\\begin{pmatrix}-100.0, & 500.0, & -50.0, & 250.0\\end{pmatrix}\n",
        "^\n",
        "Unknown symbol: \\begin (at char 0), (line:1, col:1)\n",
        "  FormatterWarning,\n"
       ]
      },
      {
       "latex": [
        "$$\\begin{pmatrix}-100.0, & 500.0, & -50.0, & 250.0\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "(-100.0, 500.0, -50.0, 250.0)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ul7/tuXPn8s033wCQk5PDtddey8FKlOcM1wW2A+uBasAE4H6gO7AWGE705lm1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       "text": [
        "<matplotlib.figure.Figure at 0x108ee3ed0>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Conclusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It works pretty well."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}