Kalman-Filter-CV.ipynb

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  "name": ""
 },
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 "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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "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": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "State Vector"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Constant Velocity Model for Ego Motion\n",
      "\n",
      "$$x= \\left[ \\matrix{ x \\\\ y \\\\ \\dot x \\\\ \\dot y} \\right]$$\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Formal Definition:\n",
      "\n",
      "$$x_{k+1} = \\textbf{A} \\cdot x_{k}$$\n",
      "\n",
      "$$x_{k+1} = \\begin{bmatrix}1 & 0 & \\Delta t & 0 \\\\ 0 & 1 & 0 & \\Delta t \\\\ 0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\end{bmatrix}_{k}$$\n",
      "\n",
      "$$y = \\textbf{H} \\cdot x$$\n",
      "\n",
      "$$y = \\begin{bmatrix}0 & 0 & 1 & 0 \\\\ 0 & 0 & 0 & 1\\end{bmatrix} \\cdot x$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Initial State"
     ]
    },
    {
     "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": 8,
       "text": [
        "<matplotlib.text.Text at 0x1074eaf90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hx3o8HlJSUoa8X0NDA6tXryYmJobk5GRcLhetra2RRBARkXEQUbEJBAIkJiYG2wkJCQQC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\nr8DdIwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1075a2f50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Initial Uncertainty"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = 1.0*np.eye(4)\n",
      "print(P, P.shape)\n",
      "\n",
      "fig = plt.figure(figsize=(5, 5))\n",
      "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
      "plt.title('Initial Covariance Matrix $P$')\n",
      "ylocs, ylabels = yticks()\n",
      "# set the locations of the yticks\n",
      "yticks(arange(5))\n",
      "# set the locations and labels of the yticks\n",
      "yticks(arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = xticks()\n",
      "# set the locations of the yticks\n",
      "xticks(arange(5))\n",
      "# set the locations and labels of the yticks\n",
      "xticks(arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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)\n",
      "\n",
      "\n",
      "plt.tight_layout()"
     ],
     "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"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rKysRGhqKxMREJCYm4j/+4z9cjsmVMBH1ed5YCTscDuTl5WH79u0wmUxITk5G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\n1Vq00HatiQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1074f3810>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Dynamic Matrix"
     ]
    },
    {
     "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": 10
    },
    {
     "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": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Measurement Noise Covariance"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ra = 1.0**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([[ 1.,  0.],\n",
        "        [ 0.,  1.]]), (2, 2))\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1zQlteD/38KkASWpJkkY09vjafLzr1CwoQaUIRq1+D9yDzoQixil+HyRvL5gk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\n8v8DZujbS0BBWAQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107023c10>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "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": 13
    },
    {
     "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": [
      {
       "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",
       "png": "iVBORw0KGgoAAAANSUhEUgAAATsAAABlCAMAAAAF8bTGAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\n+N/jEf7Et4d/kakTUwH1v8fyH3f+AUVRxVBa5uQDAAAAAElFTkSuQmCC\n",
       "prompt_number": 14,
       "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": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(5, 5))\n",
      "im = plt.imshow(Q, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
      "plt.title('Process Noise Covariance Matrix $Q$')\n",
      "ylocs, ylabels = yticks()\n",
      "# set the locations of the yticks\n",
      "yticks(arange(5))\n",
      "# set the locations and labels of the yticks\n",
      "yticks(arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = xticks()\n",
      "# set the locations of the yticks\n",
      "xticks(arange(5))\n",
      "# set the locations and labels of the yticks\n",
      "xticks(arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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)\n",
      "\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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T/9NSKCfdi0bChBCrQSNhiaP+pxDlhE9O/U9LkVNOqCdMCCEikkJRNZWiRsLU/xSinPBR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\ncUQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108a7ea50>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "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": 16
    },
    {
     "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=1.00\n",
        "You assumed 1.00 in R.\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "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": 18,
       "text": [
        "<matplotlib.legend.Legend at 0x1075d3710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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r4os4A2pKc+uL8vLytH79+irr5s2bpwceeEDbt2/X/fffr3nz5rlVHMCzmt/T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\nAIBvkdQCAAAAAHyLpBYAAAAA4Fv/H6KLikB4ddz+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10747d6d0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "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": 19
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Kalman Filter"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Kalman Filter](https://raw.github.com/balzer82/Kalman/master/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": 20
    },
    {
     "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": 21,
       "text": [
        "<matplotlib.legend.Legend at 0x108be8f50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p0iV8/vnnGDJkCCWthJBm89FHHyEjIwOpqamqDkUtxcfHIzQ0lJJWQghRAzEx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\nAAAAAEBMo3AFAAAAAMS0/wdwD1Br7opAuQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10757ea90>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Covariance Matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(5, 5))\n",
      "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n",
      "plt.title('Covariance Matrix $P$')\n",
      "ylocs, ylabels = yticks()\n",
      "# set the locations of the yticks\n",
      "yticks(arange(5))\n",
      "# set the locations and labels of the yticks\n",
      "yticks(arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), fontsize=22)\n",
      "\n",
      "xlocs, xlabels = xticks()\n",
      "# set the locations of the yticks\n",
      "xticks(arange(5))\n",
      "# set the locations and labels of the yticks\n",
      "xticks(arange(4),('$x$', '$y$', '$\\dot x$', '$\\dot y$'), 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)\n",
      "\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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f4P6fRzSDBw9GYWGhTedt1kq4trYWERERMJlMKCsra85dpcFMWIyZsJjesk+1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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108bc0650>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = plt.figure(figsize=(16,9))\n",
      "plt.semilogy(range(len(measurements[0])),Px, label='$x$')\n",
      "plt.semilogy(range(len(measurements[0])),Py, label='$y$')\n",
      "plt.semilogy(range(len(measurements[0])),Pdx, label='$\\dot x$')\n",
      "plt.semilogy(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": 23,
       "text": [
        "<matplotlib.legend.Legend at 0x108bbac50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rfXLOAQAAAPTH2rVrO1czORpFkbQ+8MADWrJkiebPn99520ZHofyBbRKowbdx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\n/vjO+Vrp2k7dZ/KPlfobPx3yM3X6D/ncx6xUwFfma0uybCt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pa6ReG/y78OOPP1ZNTY2R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\nAADAs/4/Jw7UdwAljykAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10719ccd0>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "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": 24,
       "text": [
        "<matplotlib.text.Text at 0x108bc93d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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33XabGjdurBkzZig9PV3l5eWaNWuWpk+frueff14HDx7UoEGD1L9/fzmOo5kz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107f29710>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "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",
      "axis('equal')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}-100.0, & 500.0, & -50.0, & 250.0\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAATAAAAAaBAMAAADClR0kAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nl3Jq7T/m9GVXvlB2BAAAAABJRU5ErkJggg==\n",
       "prompt_number": 25,
       "text": [
        "(-100.0, 500.0, -50.0, 250.0)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AAF6HzjAAAAAAwCPRGQYAAAAAwAKGYcACei4wiTzBNDIF08gUTCNTsBOGYQAA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\nlGEAAAAaRxkGAACgcf4LJAmXosSDaVsAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108bfaf10>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Conclusion"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It works pretty well."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}