{ "metadata": { "name": "", "signature": "sha256:591ba66f323dfa03634bdaa3e988af4c6915ddac2bcde78256906da145966f3e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from IPython.display import YouTubeVideo\n", "from scipy.stats import norm" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 58 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "fw=10 # figure width" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 59 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Multidimensional Kalman Filter" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "for a Constant Acceleration Model (CA)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Situation covered: You have a Position Sensor (e.g. a Vision System) and try to calculate velocity ($\\dot x$ and $\\dot y$) as well as position ($x$ and $y$) of a ball in 3D space.\n", "\n", "Additionally, we estimate the gravitational acceleration g. :)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "YouTubeVideo(\"tIIJME8-au8\")" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 60, "text": [ "" ] } ], "prompt_number": 60 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "State Vector - Constant Acceleration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Constant Acceleration Model for Motion in 3D\n", "\n", "$$x= \\left[ \\matrix{ x \\\\ y \\\\ z \\\\ \\dot x \\\\ \\dot y \\\\ \\dot z \\\\ \\ddot x \\\\ \\ddot y \\\\ \\ddot z} \\right]$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Formal Definition:\n", "\n", "$$x_{k+1} = A \\cdot x_{k}$$\n", "\n", "Hence, we have no control input $u$.\n", "\n", "$$x_{k+1} = \\begin{bmatrix}1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 & 0 \\\\ 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 & \\frac{1}{2}\\Delta t^2 \\\\ 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 & 0 \\\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t & 0 \\\\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & \\Delta t \\\\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\end{bmatrix} \\cdot \\begin{bmatrix} x \\\\ y \\\\ z \\\\ \\dot x \\\\ \\dot y \\\\ \\dot z \\\\ \\ddot x \\\\ \\ddot y \\\\ \\ddot z\\end{bmatrix}_{k}$$\n", "\n", "$$y = H \\cdot x$$\n", "\n", "Position ($x$ & $y$ & $z$) is measured with vision system:\n", "\n", "$$y = \\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\end{bmatrix} \\cdot x$$" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Initial Uncertainty" ] }, { "cell_type": "code", "collapsed": false, "input": [ "P = 100.0*np.eye(9)\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(10))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), 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(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,8.5])\n", "plt.ylim([8.5, -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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PP/zwuBlT09LSUu8IZW3cuHH4B4mIAAsXLqSrq6uqz/Kenp7+s846q6blffe73616eUmw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\nAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 61 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 61 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Dynamic Matrix" ] }, { "cell_type": "code", "collapsed": false, "input": [ "dt = 1.0/100.0 # Time Step between Filter Steps, 100Hz\n", "\n", "A = np.matrix([[1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2, 0.0, 0.0],\n", " [0.0, 1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2, 0.0],\n", " [0.0, 0.0, 1.0, 0.0, 0.0, dt, 0.0, 0.0, 1/2.0*dt**2],\n", " [0.0, 0.0, 0.0, 1.0, 0.0, 0.0, dt, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, dt, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, dt],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n", "print(A.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(9, 9)\n" ] } ], "prompt_number": 62 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Measurement Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here you can determine, which of the states is covered by a measurement. In this example, the position ($x$ and $y$) is measured." ] }, { "cell_type": "code", "collapsed": false, "input": [ "H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])\n", "print(H, H.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(matrix([[ 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n", " [ 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n", " [ 0., 0., 1., 0., 0., 0., 0., 0., 0.]]), (3, 9))\n" ] } ], "prompt_number": 63 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Measurement Noise Covariance Matrix $R$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rp = 5.0**2 # Noise of Position Measurement\n", "R = np.matrix([[rp, 0.0, 0.0],\n", " [0.0, rp, 0.0],\n", " [0.0, 0.0, rp]])\n", "print(R, R.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(matrix([[ 25., 0., 0.],\n", " [ 0., 25., 0.],\n", " [ 0., 0., 25.]]), (3, 3))\n" ] } ], "prompt_number": 64 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(4, 4))\n", "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Measurement Noise Covariance Matrix $R$')\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(4))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(3),('$x$', '$y$', '$z$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(4))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(3),('$x$', '$y$', '$z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,2.5])\n", "plt.ylim([2.5, -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": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 65 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Process Noise Covariance Matrix $Q$ for CA Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Position of the ball 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", "To easily calcualte Q, one can ask the question: How the noise effects my state vector? For example, how the acceleration change the position over one timestep dt.\n", "\n", "One can calculate Q as\n", "\n", "$$Q = G\\cdot G^T \\cdot \\sigma_a^2$$\n", "\n", "with $G = \\begin{bmatrix}0.5dt^2 & 0.5dt^2 & 0.5dt^2 & dt & dt & dt & 1.0 &1.0 & 1.0\\end{bmatrix}^T$ and $\\sigma_a$ as the acceleration process noise." ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Symbolic Calculation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sympy import Symbol, Matrix\n", "from sympy.interactive import printing\n", "printing.init_printing()\n", "dts = Symbol('\\Delta t')\n", "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[0.5*dts**2],[dts],[dts],[dts],[1.0],[1.0],[1.0]])\n", "Qs*Qs.T" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\left[\\begin{matrix}0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0 & 1.0\\end{matrix}\\right]$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 66, "text": [ "\u23a1 4 4 4 3 3 \n", "\u23a20.25\u22c5\\Delta t 0.25\u22c5\\Delta t 0.25\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \n", "\u23a2 \n", "\u23a2 4 4 4 3 3 \n", "\u23a20.25\u22c5\\Delta t 0.25\u22c5\\Delta t 0.25\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \n", "\u23a2 \n", "\u23a2 4 4 4 3 3 \n", "\u23a20.25\u22c5\\Delta t 0.25\u22c5\\Delta t 0.25\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \n", "\u23a2 \n", "\u23a2 3 3 3 2 2 \n", "\u23a20.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \\Delta t \\Delta t \n", "\u23a2 \n", "\u23a2 3 3 3 2 2 \n", "\u23a20.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \\Delta t \\Delta t \n", "\u23a2 \n", "\u23a2 3 3 3 2 2 \n", "\u23a20.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \\Delta t \\Delta t \n", "\u23a2 \n", "\u23a2 2 2 2 \n", "\u23a20.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t \n", "\u23a2 \n", "\u23a2 2 2 2 \n", "\u23a20.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t \n", "\u23a2 \n", "\u23a2 2 2 2 \n", "\u23a30.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t \n", "\n", " 3 2 2 2\u23a4\n", " 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \u23a5\n", " \u23a5\n", " 3 2 2 2\u23a5\n", " 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \u23a5\n", " \u23a5\n", " 3 2 2 2\u23a5\n", " 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t 0.5\u22c5\\Delta t \u23a5\n", " \u23a5\n", " 2 \u23a5\n", " \\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t \u23a5\n", " \u23a5\n", " 2 \u23a5\n", " \\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t \u23a5\n", " \u23a5\n", " 2 \u23a5\n", " \\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t 1.0\u22c5\\Delta t \u23a5\n", " \u23a5\n", " \u23a5\n", " 1.0\u22c5\\Delta t 1.0 1.0 1.0 \u23a5\n", " \u23a5\n", " \u23a5\n", " 1.0\u22c5\\Delta t 1.0 1.0 1.0 \u23a5\n", " \u23a5\n", " \u23a5\n", " 1.0\u22c5\\Delta t 1.0 1.0 1.0 \u23a6" ] } ], "prompt_number": 66 }, { "cell_type": "code", "collapsed": false, "input": [ "sa = 0.5\n", "G = np.matrix([[1/2.0*dt**2],\n", " [1/2.0*dt**2],\n", " [1/2.0*dt**2],\n", " [dt],\n", " [dt],\n", " [dt],\n", " [1.0],\n", " [1.0],\n", " [22.0]]) # because we want to estimate g, \n", " # here we use a huge value to give the \n", " # Kalman Filter the possibility to\n", " # 'breath'\n", "Q = G*G.T*sa**2\n", "\n", "print(Q.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(9, 9)\n" ] } ], "prompt_number": 67 }, { "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 $Q$')\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(10))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), 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(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,8.5])\n", "plt.ylim([8.5, -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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pjTGH8ZoL/GZTrnBesylXqTrUpK4GfgHMAJ4D/g9wDnAANgV9/2QZYB6wDKtJ/RA4HlhT\nKW90w30iIlK9OtSkjhpifWeZddcnp9Sia6Q0xhzGay7wm025wnnNplylYjt2X0gj1Qp8HRgPbIi1\nnusLzr8EeAc4NrN0IiIyqoXUpM4GTgeOAw5n8B7GE4Cjgbeyi1aexpjDeM0FfrMpVziv2ZSrVGzH\n7kvbk5qBTSl8Djg4Wbe64Py9sd7V3dlFExGRrDXrcN/m2HAewKewKYP3F5w/L/l7T0a5hqQx5jBe\nc4HfbMoVzms25SoVWyOVdrjvHuBZ7NAWB2IHFCw0Nzn/+eyiiYjIaBe6n9Th2I5Y1xWs2xAb7huR\noT6NMYfxmgv8ZlOucF6zKVepZq1J5e2FHXvpyYJ1s4CNUT1KRMS92Ib7QhupLYBnitbNT/5WrEd1\ndXXR1tYGQEtLC+3t7f3jsvlvFWmWOzo6gi4/kst5XvJ4f7y8LufXeckTy3KelzzeX/95oddfvHgx\nuVyu//N07ty5hIitkQpN+xXgGOwotu8As4H/B/wZ24+qrO7u7r758+cPdbaIiFRp6dKldHZ2pvos\n7+7u7vvsZz9b0/a+9a1vpd5eFkJrUmcD3cDNwHewH7JaD9ybca4hFX8L8UK5wnnNplzhvGZTrlLN\nXpPqZeDItgBzgNOwhktERJyLbbgvtJGagDVUeYcmy9dklmgYhXUDT5QrnNdsyhXOazblKhVbIxUy\n3Hcr9sNVk5Llqdhx+r4KvJhxLhERkaBGag/sN0PeADYBfoAdcv3MOuQaksaYw3jNBX6zKVc4r9mU\nq1Qz16SOBD4InI8deWIJcFUdMomISJ3ENtwX0kgtTU4NpTHmMF5zgd9syhXOazblil90P3ooIiLV\ni60nFbqfVMNpjDmM11zgN5tyhfOaTblKNXNNSkREIqeeVJ15HctVrnBesylXOK/ZlCt+6kmJiIwi\n6knVmcaYw3jNBX6zKVc4r9mUq5RqUiIi4pZ6UnXmdSxXucJ5zaZc4bxmU674qSclIjKKqCdVZxpj\nDuM1F/jNplzhvGZTrlKqSYmIiFvqSdWZ17Fc5QrnNZtyhfOaTbnip56UiMgoop5UnWmMOYzXXOA3\nm3KF85pNuUqpJiUiIm6pJ1VnXsdylSuc12zKFc5rNuWKX3SNlIiIVK9Ow32fBR4BHk3+B2gFbgee\nAG4DWqrJG10jpTHmMF5zgd9syhXOazblKlWHRmom8ClgNrA78BFgR+BUrJHaGftV91OryRtdIyUi\nItWrQyP1V8AvgbeA9cCdwGHAIcDlyWUuBxZWkze6RsrrWK5yhfOaTbnCec2mXCPiUWAuNry3MXAg\nsB2wJbAqucyqZDmYZveJiIwidZjd9xhwLlZ3ehPIYT2qQn3JKVh0PSmNMYfxmgv8ZlOucF6zKVep\n0OG9NWvWsGLFiv5TLpcrd7OXAnsA+wKvYZMlVgFbJedvDbxUTV71pERERpHQnlRrayutra39y+3t\n7eUutgXWCL0b+Ftgb2AasAjrZS0Cbqgmb3SNlNexXOUK5zWbcoXzmk25RsyPgM2APwOfBtYC5wDX\nAZ8EVgBHVnPD0TVSIiJSvTodcWJemXWvAp213nA1NakZwC+APwIXAxOBDYFrgffUGmg4GmMO4zUX\n+M2mXOG8ZlOuUrEduy+0kZoI/ARYDVwDbA5cDTyFzZP/fabpREQkU7E1UqHDfZtiO2T9umDdV5O/\n38gk0TC8juUqVziv2ZQrnNdsyhW/0EbquaLlc4APAAuyiSMiIvUU21HQq504MQa4AKtPLQB6h7tC\nV1cXbW1tALS0tNDe3t7/bSI/PptmuXAst5rr12s5l8tx4oknusmTX/b6eBVm8pInv7x48eKqX5/1\nXM6v85JHr//ql2t5vBYvXkwul+v/PJ07dy4hYmukqkk7FrgMG/o7HFg33BW6u7v75s+fX8WmSvX0\n9PQ/WZ4oVziv2ZQrnNdsoyHX0qVL6ezsTPVZ3t3d3fe1r32tpu2dfPLJqbeXhdCJE2OAi7DjMx3K\nQAM1Dhv2qzuPLzhQrmp4zaZc4bxmU674hTZS5wFTgaMYODbTOOBMbO9iERFxLLbZfSGN1BHA+4Fv\nYvWoq5LTY9ghMH6QeboyCseYPVGucF6zKVc4r9mUq1RsjVTaiRMbYI3UAcA72H5R12M/bPVD4HN1\nSSciIqPaiDSLWU6cEBGRAaETJ775zW/WtL2TTjppRCdO6Nh9IiKjSGxT0PV7UhlRrnBesylXOK/Z\nlKtUbDWp6BopEREZPaIb7vO6f4FyhfOaTbnCec2mXKViG+6LrpESEZHqxdZIRTfcpzHmMF5zgd9s\nyhXOazblKqWalIiISEaiG+7TGHMYr7nAbzblCuc1m3KVim24L7pGSkREqhdbIxXdcJ/GmMN4zQV+\nsylXOK/ZlKuUalIiIiIZiW64T2PMYbzmAr/ZlCuc12zKVSq24b7oGikREalebI1UdMN9GmMO4zUX\n+M2mXOG8ZlOuUqpJiYiIZCS64T6NMYfxmgv8ZlOucF6zKVep2Ib7omukRESkerE1UtEN92mMOYzX\nXOA3m3KF85pNuUqpJiUiIpKR6Ib7NMYcxmsu8JtNucJ5zaZcpWIb7ouukRIRkerF1kiFDveNBe4C\nlgGTso8zPI0xh/GaC/xmU65wXrMpV6lmr0lNAvYEZgLbZB9HRERkQOhw31qgE2usHs8+zvA0xhzG\nay7wm025wnnNplyl6tAbmgFcU7D8HuB0YFPgU8DqZP1pwC2hN15NTeruKq4jIiIO1KGRehx4f/L/\nWOAF4HrgGOAbyalq0U1B1xhzGK+5wG825QrnNZtylapzTaoT+B3wHDAmOdUkpJHaDDg/Od0CHAZM\nAb4LfBu4Ati61kAiIhKtjwFXJ//3ASdgE+0uAVqqucG0rdxGwLXAZ4Dngd2AB4CbgOOBhcDFwMmU\n6dp1d3f3zZ8/v5p8IiJSwdKlS+ns7Ez1Wd7d3d135ZVX1rS9o48+eqjtjceG+nbB6lBbMFCP+grW\niflk6PbS1qT+CViMNVAAvcCGwMPAK1iLuQxrtERExKnQmtSLL77IypUr+5dnzpw51EU/DDzIQMP0\nUsF536PK9iHtcN9q4I6C5VnJ3/xMjUuxwtmT1YQIoTHmMF5zgd9syhXOazblKhVag9pmm22YNWtW\n/6m9vX2omz6KgaE+GFz+ORR4pJq8aXtSxf3D/bDp6A9Vs1EREWkqm2CTJo4tWHcu0I6NtD2NlYaC\nVXtYpP2xqeh9aa/Q1dVFW1sbAC0tLbS3t/fvK5D/VpFmuaOjI+jyI7mc5yWP98fL63J+nZc8sSzn\necnj/fWfF3r9xYsXk8vl+j9P586dS4g6HTXiTWDzonWfyOKGq0m7HfAscArwtYL1x2DDfiU0cUJE\npD5CJ05cc801w1+wgo997GOpt5eFNDWpqcD9wJnJ8oLk768KLjMd2+u47oq/hXihXOG8ZlOucF6z\nKVf80jRS+wJ7AOuwcceDgJeBycn5rcBZwNn1CCgiItmJ7QCzaba4CTb9fB2wMfBlYAfg37BhvzHJ\nuhVD3YCG+0RE6iN0uO+6666raXtHHnnkiA73pZk48SaDZ2yANUh3Zp5GRETqqtl/T6rhvI7lKlc4\nr9mUK5zXbMoVP/0yr4jIKBJbT2pE0qomJSJSH6E1qR//+Mc1be+www5zV5MSEZEmEVtPSjWpjChX\nOK/ZlCuc12zKFT/1pERERpHYelKqSYmIRCy0JnXDDTfUtL2FCxeqJiUiIvURW09KNamMKFc4r9mU\nK5zXbMoVP/WkRERGkdh6UqpJiYhELLQmddNNVf2Ke7+DDz5YNSkREamP2HpSqkllRLnCec2mXOG8\nZlOu+KknJSIyisTWk1JNSkQkYqE1qZ/+9Kc1be/AAw9UTUpEROojtp6UalIZUa5wXrMpVziv2ZQr\nfupJiYiMIrH1pFSTEhGJWGhN6tZbb61pex/60IdUkxIRkfqIrSelmlRGlCuc12zKFc5rNuWKn3pS\nIiKjSGw9qWrSjgV6gCnAPsDrw11BNSkRkfoIrUl1d3fXtL3Ozk73NalJwJ7AhsA2wOOZJhIRkbqJ\nrSdVTU1qLdAJfIQGNFBex3KVK5zXbMoVzms25YpftTWpuzNNISIiIyK2npT2kxIRiVhoTeqOO+6o\naXv77bef25pUK/B1YDxWjzoKWF9w/iXAO8CxmaUTEZFMxdaTCqlJnQ2cDhwHHA4sKDhvAnA08FZ2\n0crzOparXOG8ZlOucF6zKVf80jZSM4BVwHPA/sm61QXn7431rlSrEhFxbMyYMTWdhtAC/Aj4LfAb\nYC9s9O124AngtuQywdI2Uptjw3kAnwJ+D9xfcP685O891YQI0dHRUe9NVEW5wnnNplzhvGZTrlJ1\naqS+BfwUeC+wG/AYcCrWSO0MLE2Wg6VtpO4BngW2BA4ELis6f25y/vPVhBARkZFRh0ZqCtYGXJos\n/wXbVekQ4PJk3eXAwmryhk5BPxwYB1xXsG5DbLjvhkpX7Orqoq2tDYCWlhba29v7v03kx2fTLBeO\n5VZz/Xot53I5TjzxRDd58steH6/CTF7y5JcXL15c9euznsv5dV7y6PVf/XItj9fixYvJ5XL9n6dz\n586lwaZh5Z/LgN2BB4ETsU7NquQyq5LlYKHTPK7AalLbFazbC7gX+DRwYbkrZTkFvaenp//J8kS5\nwnnNplzhvGYbDblCp6DffXdtUwf22Wef4u3tgbUBc4AHgMXY4fL+Gdi04HKvYnWqIKE9qS2AZ4rW\n5VufutejQGPMobzmAr/ZlCuc12zKVSp0CvrTTz/NihUr+pcnTpxYfJHnk9MDyfKPgNOAlcBWyd+t\ngZeqyRvaSD0AHIP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"text": [ "" ] } ], "prompt_number": 68 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Identity Matrix" ] }, { "cell_type": "code", "collapsed": false, "input": [ "I = np.eye(9)\n", "print(I, I.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(array([[ 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n", " [ 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n", " [ 0., 0., 1., 0., 0., 0., 0., 0., 0.],\n", " [ 0., 0., 0., 1., 0., 0., 0., 0., 0.],\n", " [ 0., 0., 0., 0., 1., 0., 0., 0., 0.],\n", " [ 0., 0., 0., 0., 0., 1., 0., 0., 0.],\n", " [ 0., 0., 0., 0., 0., 0., 1., 0., 0.],\n", " [ 0., 0., 0., 0., 0., 0., 0., 1., 0.],\n", " [ 0., 0., 0., 0., 0., 0., 0., 0., 1.]]), (9, 9))\n" ] } ], "prompt_number": 69 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Measurements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Synthetically created Data of the Position of the Ball" ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = pd.read_csv('Ball.csv')\n", "data.head()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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XmYmZmXrYrZr
0 0.035 0.006 1.048 0.099 0 0.999
1 0.189-0.063 0.895 0.197 0 0.997
2 0.250 0.067 0.950 0.294 0 0.994
3 0.461 0.049 1.078 0.390 0 0.990
4 0.580-0.026 0.944 0.485 0 0.985
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 70, "text": [ " Xm Ym Zm Xr Yr Zr\n", "0 0.035 0.006 1.048 0.099 0 0.999\n", "1 0.189 -0.063 0.895 0.197 0 0.997\n", "2 0.250 0.067 0.950 0.294 0 0.994\n", "3 0.461 0.049 1.078 0.390 0 0.990\n", "4 0.580 -0.026 0.944 0.485 0 0.985" ] } ], "prompt_number": 70 }, { "cell_type": "markdown", "metadata": {}, "source": [ "m = Measurements, r= real values (unknown, just for plotting)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "[Xm, Ym, Zm, Xr, Yr, Zr] = data.T.values" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 71 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(12,6))\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(Xm, Ym, Zm, c='gray')\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Y')\n", "ax.set_zlabel('Z')\n", "plt.title('Ball Trajectory observed from Computer Vision System (with Noise)')\n", "\n", "#ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 1.0))\n", "\n", "# Axis equal\n", "max_range = np.array([Xm.max()-Xm.min(), Ym.max()-Ym.min(), Zm.max()-Zm.min()]).max() / 3.0\n", "mean_x = Xm.mean()\n", "mean_y = Ym.mean()\n", "mean_z = Zm.mean()\n", "ax.set_xlim(mean_x - max_range, mean_x + max_range)\n", "ax.set_ylim(mean_y - max_range, mean_y + max_range)\n", "ax.set_zlim(mean_z - max_range, mean_z + max_range)\n", "#plt.savefig('BallTrajectory-Computervision.png', dpi=150, bbox_inches='tight')" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\begin{pmatrix}-1.75807666667, & 2.94725666667\\end{pmatrix}$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 72, "text": [ "(-1.75807666667, 2.94725666667)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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nst/n5+ejf//+MBgMbDaZ6upqZGRkIDMzs1cwLvc4ubm5ePjhh/Hcc8/hgQce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\nI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"text": [ "" ] } ], "prompt_number": 72 }, { "cell_type": "code", "collapsed": false, "input": [ "measurements = np.vstack((Xm,Ym,Zm))\n", "m = len(measurements[0]) # short it\n", "print(measurements.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(3, 100)\n" ] } ], "prompt_number": 73 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Initial State" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.matrix([0.0, 0.0, 1.0, 10.0, 0.0, 0.0, 0.0, 0.0, -15.0]).T\n", "print(x, x.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(matrix([[ 0.],\n", " [ 0.],\n", " [ 1.],\n", " [ 10.],\n", " [ 0.],\n", " [ 0.],\n", " [ 0.],\n", " [ 0.],\n", " [-15.]]), (9, 1))\n" ] } ], "prompt_number": 74 }, { "cell_type": "code", "collapsed": false, "input": [ "# Preallocation for Plotting\n", "xt = []\n", "yt = []\n", "zt = []\n", "dxt= []\n", "dyt= []\n", "dzt= []\n", "ddxt=[]\n", "ddyt=[]\n", "ddzt=[]\n", "Zx = []\n", "Zy = []\n", "Zz = []\n", "Px = []\n", "Py = []\n", "Pz = []\n", "Pdx= []\n", "Pdy= []\n", "Pdz= []\n", "Pddx=[]\n", "Pddy=[]\n", "Pddz=[]\n", "Kx = []\n", "Ky = []\n", "Kz = []\n", "Kdx= []\n", "Kdy= []\n", "Kdz= []\n", "Kddx=[]\n", "Kddy=[]\n", "Kddz=[]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 75 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Kalman Filter](Kalman-Filter-Step.png)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "hitplate=False\n", "for filterstep in range(m):\n", " \n", " # Model the direction switch, when hitting the plate\n", " if x[2]<0.01 and not hitplate:\n", " x[5]=-x[5]\n", " hitplate=True\n", "\n", " \n", " # Time Update (Prediction)\n", " # ========================\n", " # Project the state ahead\n", " x = A*x #+ B*u # we have no Control Input\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[:,filterstep].reshape(H.shape[0],1)\n", " y = Z - (H*x) # Innovation or Residual\n", " x = x + (K*y)\n", " \n", " # Update the error covariance\n", " P = (I - (K*H))*P\n", " \n", " \n", " \n", " # Save states for Plotting\n", " xt.append(float(x[0]))\n", " yt.append(float(x[1]))\n", " zt.append(float(x[2]))\n", " dxt.append(float(x[3]))\n", " dyt.append(float(x[4]))\n", " dzt.append(float(x[5]))\n", " ddxt.append(float(x[6]))\n", " ddyt.append(float(x[7]))\n", " ddzt.append(float(x[8]))\n", " \n", " Zx.append(float(Z[0]))\n", " Zy.append(float(Z[1]))\n", " Zz.append(float(Z[2]))\n", " Px.append(float(P[0,0]))\n", " Py.append(float(P[1,1]))\n", " Pz.append(float(P[2,2]))\n", " Pdx.append(float(P[3,3]))\n", " Pdy.append(float(P[4,4]))\n", " Pdz.append(float(P[5,5]))\n", " Pddx.append(float(P[6,6]))\n", " Pddy.append(float(P[7,7]))\n", " Pddz.append(float(P[8,8]))\n", " Kx.append(float(K[0,0]))\n", " Ky.append(float(K[1,0]))\n", " Kz.append(float(K[2,0]))\n", " Kdx.append(float(K[3,0]))\n", " Kdy.append(float(K[4,0]))\n", " Kdz.append(float(K[5,0]))\n", " Kddx.append(float(K[6,0]))\n", " Kddy.append(float(K[7,0]))\n", " Kddz.append(float(K[8,0]))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 76 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 76 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Plots" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Estimated State" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,9))\n", "plt.subplot(211)\n", "plt.title('Estimated State (elements from vector $x$)')\n", "plt.plot(range(len(measurements[0])),dxt, label='$\\dot x$')\n", "plt.plot(range(len(measurements[0])),dyt, label='$\\dot y$')\n", "plt.plot(range(len(measurements[0])),dzt, label='$\\dot z$')\n", "plt.legend(loc='best',prop={'size':22})\n", "\n", "plt.subplot(212)\n", "plt.plot(range(len(measurements[0])),ddxt, label='$\\ddot x$')\n", "plt.plot(range(len(measurements[0])),ddyt, label='$\\ddot y$')\n", "plt.plot(range(len(measurements[0])),ddzt, label='$\\ddot z$')\n", "\n", "plt.xlabel('Filter Step (100 = 1 Second)')\n", "plt.ylabel('$m/s^2$')\n", "plt.legend(loc='best',prop={'size':22})\n", "\n", "print('Estimated g= %.2f m/s2' % ddzt[-1])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Estimated g= -9.83 m/s2\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ZM2f2eFo6SoI5IYQQ0cEdg9VvLFa/sS1/HqxRwVzhTowTO9Vz0X51b93q01B9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\n", "text": [ "" ] } ], "prompt_number": 84 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Uncertainty" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,9))\n", "plt.subplot(311)\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])),Pz, label='$z$')\n", "plt.title('Uncertainty (Elements from Matrix $P$)')\n", "plt.legend(loc='best',prop={'size':22})\n", "plt.subplot(312)\n", "plt.plot(range(len(measurements[0])),Pdx, label='$\\dot x$')\n", "plt.plot(range(len(measurements[0])),Pdy, label='$\\dot y$')\n", "plt.plot(range(len(measurements[0])),Pdz, label='$\\dot z$')\n", "plt.legend(loc='best',prop={'size':22})\n", "\n", "plt.subplot(313)\n", "plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n", "plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n", "plt.plot(range(len(measurements[0])),Pddz, label='$\\ddot z$')\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.legend(loc='best',prop={'size':22})" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 78, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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41WycRkRERKRHsnZZsIvuAeqB78YL1q5d6zz44IOMHz8egIqKCubMmZP4phAf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\nD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V4u6N253Dpx5b4vu93j21dccJs9b/YdF9xufwZ+7nGBY3ni/ccK3tbevyfOv41vuccT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\nEREREREREZGG8P8uZemtp7M4uwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 78 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Kalman Gains" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,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])),Kz, label='Kalman Gain for $z$')\n", "plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n", "plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n", "plt.plot(range(len(measurements[0])),Kdz, label='Kalman Gain for $\\dot z$')\n", "plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n", "plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n", "plt.plot(range(len(measurements[0])),Kddz, label='Kalman Gain for $\\ddot z$')\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n", "plt.legend(loc='best',prop={'size':18});" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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1jT+M+ua5wQFx2cpAjbRsQY2kjkGNhhyk9VMDn6AS2A9R73Eoakc7F/hVK687j9qGnkJ9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\ntxE/b0Rq+pXrwtU2FVdNsc1o3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"text": [ "" ] } ], "prompt_number": 79 }, { "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 $P$ (after %i Filtersteps)' % m)\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(10))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), 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(9),('$x$', '$y$', '$z$', '$\\dot x$', '$\\dot y$', '$\\dot z$', '$\\ddot x$', '$\\ddot y$', '$\\ddot z$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,8.5])\n", "plt.ylim([8.5, -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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YrJ0g+Pun2CHojzPMQRMQvyf1PHaMfGjH4Hf45JcEPyIiUjy3U7lTM9xBdGcG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\nERERERERERERERERERERkUL6/10XQzS6LNaiAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 80 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Position in x/z Plane" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,4))\n", "\n", "plt.plot(xt,zt, label='Kalman Filter Estimate')\n", "plt.scatter(Xm,Zm, label='Measurements', c='gray', s=30)\n", "plt.plot(Xr, Zr, label='Real')\n", "plt.title('Estimate of Ball Trajectory (Elements from State Vector $x$)')\n", "plt.legend(loc='best',prop={'size':14})\n", "plt.axhline(0, color='k')\n", "plt.axis('equal')\n", "plt.xlabel('X ($m$)')\n", "plt.ylabel('Y ($m$)')\n", "plt.ylim([0, 1]);\n", "plt.savefig('Kalman-Filter-CA-Ball-StateEstimated.png', dpi=72, bbox_inches='tight')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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gEAgEHUh3HB79EJgI+ANXgecAVe21jcDdwB+BGqQh0vldIGO3pavfwrsKobdz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\nSkpobW1Faa7E9vbfEP9vMzEfXUu7Rc/OZeP530cDlMWXoVesjEv6ax4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QQgghhBBCCCGE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\nRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 81 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Position in 3D" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(16,9))\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.plot(xt,yt,zt, label='Kalman Filter Estimate')\n", "ax.plot(Xr, Yr, Zr, label='Real')\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Y')\n", "ax.set_zlabel('Z')\n", "ax.legend()\n", "plt.title('Ball Trajectory estimated with Kalman Filter')\n", "\n", "# Axis equal\n", "max_range = np.array([Xm.max()-Xm.min(), Ym.max()-Ym.min(), Zm.max()-Zm.min()]).max() / 3.0\n", "mean_x = Xm.mean()\n", "mean_y = Ym.mean()\n", "mean_z = Zm.mean()\n", "ax.set_xlim(mean_x - max_range, mean_x + max_range)\n", "ax.set_ylim(mean_y - max_range, mean_y + max_range)\n", "ax.set_zlim(mean_z - max_range, mean_z + max_range)\n", "plt.savefig('Kalman-Filter-CA-Ball-Trajectory.png', dpi=150, bbox_inches='tight')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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WYsOGDcjKyvLp9epO0+vcd999iI2NxUMPPYS6ujrMnDkTBw8exAMPPACr1Yqr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\nIhGZncLCQrz//vv44osvEBwcjJEjR2LKl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"text": [ "" ] } ], "prompt_number": 82 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Conclusion" ] }, { "cell_type": "code", "collapsed": false, "input": [ "dist = np.sqrt((Xm-xt)**2 + (Ym-yt)**2 + (Zm-zt)**2)\n", "print('Estimated Position is %.2fm away from ball position.' % dist[-1])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Estimated Position is 0.06m away from ball position.\n" ] } ], "prompt_number": 83 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kalman Filter is just for linear dynamic systems. The drag resistance coefficient is nonlinear with a state, but the filter can handle this until a certain amount of drag.\n", "\n", "But at this time the ball is hitting the ground, the nonlinearity is too much and the filter is providing a wrong solution. Therefore, one have to model a switch in the filter loop, which helps the filter to get it." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 83 } ], "metadata": {} } ] }