{ "metadata": { "name": "", "signature": "sha256:19a3d772fa76b37c67099c864a0e134c9e4efb6833eae3b0a3dfb497b186c9b3" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.dates as mdates\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import norm\n", "from sympy import Symbol, symbols, Matrix, sin, cos\n", "from sympy.interactive import printing\n", "printing.init_printing()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "fw = 10 # figure width" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Extended Kalman Filter Implementation for Constant Turn Rate and Velocity (CTRV) Vehicle Model in Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Wikipedia](http://en.wikipedia.org/wiki/Extended_Kalman_filter) writes: In the extended Kalman filter, the state transition and observation models need not be linear functions of the state but may instead be differentiable functions.\n", "\n", "$\\boldsymbol{x}_{k} = g(\\boldsymbol{x}_{k-1}, \\boldsymbol{u}_{k-1}) + \\boldsymbol{w}_{k-1}$\n", "\n", "$\\boldsymbol{z}_{k} = h(\\boldsymbol{x}_{k}) + \\boldsymbol{v}_{k}$\n", "\n", "Where $w_k$ and $v_k$ are the process and observation noises which are both assumed to be zero mean Multivariate Gaussian noises with covariance matrix $Q$ and $R$ respectively.\n", "\n", "The function $g$ can be used to compute the predicted state from the previous estimate and similarly the function $h$ can be used to compute the predicted measurement from the predicted state. However, $g$ and $h$ cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian matrix) is computed.\n", "\n", "At each time step, the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Situation covered: You have a velocity sensor, which measures the vehicle speed ($v$) in heading direction ($\\psi$) and a yaw rate sensor ($\\dot \\psi$) which both have to fused with the position ($x$ & $y$) from a GPS sensor." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "State Vector - Constant Turn Rate and Velocity Vehicle Model (CTRV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Constant Turn Rate, Constant Velocity Model for a vehicle ![CTRV Model](CTRV-Model.png)\n", "\n", "$$x_k= \\left[ \\matrix{ x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi} \\right] = \\left[ \\matrix{ \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate}} \\right]$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "numstates=5 # States" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Intertial Measurement Unit (IMU) acquired data 50 times a second, the GPS sensor just with 10Hz, so we only have a position correction every 5th Kalman filter cycle." ] }, { "cell_type": "code", "collapsed": false, "input": [ "dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz\n", "dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "All symbolic calculations are made with [Sympy](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-5-Sympy.ipynb). Thanks!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "vs, psis, dpsis, dts, xs, ys, lats, lons = symbols('v \\psi \\dot\\psi T x y lat lon')\n", "\n", "gs = Matrix([[xs+(vs/dpsis)*(sin(psis+dpsis*dts)-sin(psis))],\n", " [ys+(vs/dpsis)*(-cos(psis+dpsis*dts)+cos(psis))],\n", " [psis+dpsis*dts],\n", " [vs],\n", " [dpsis]])\n", "state = Matrix([xs,ys,psis,vs,dpsis])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Dynamic Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This formulas calculate how the state is evolving from one to the next time step" ] }, { "cell_type": "code", "collapsed": false, "input": [ "gs" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\left[\\begin{matrix}x + \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\y + \\frac{v}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\T \\dot\\psi + \\psi\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "\u23a1 v\u22c5(-sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))\u23a4\n", "\u23a2x + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n", "\u23a2 \\dot\\psi \u23a5\n", "\u23a2 \u23a5\n", "\u23a2 v\u22c5(cos(\\psi) - cos(T\u22c5\\dot\\psi + \\psi)) \u23a5\n", "\u23a2y + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u23a5\n", "\u23a2 \\dot\\psi \u23a5\n", "\u23a2 \u23a5\n", "\u23a2 T\u22c5\\dot\\psi + \\psi \u23a5\n", "\u23a2 \u23a5\n", "\u23a2 v \u23a5\n", "\u23a2 \u23a5\n", "\u23a3 \\dot\\psi \u23a6" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Calculate the Jacobian of the Dynamic Matrix with respect to the state vector" ] }, { "cell_type": "code", "collapsed": false, "input": [ "state" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\left[\\begin{matrix}x\\\\y\\\\\\psi\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "\u23a1 x \u23a4\n", "\u23a2 \u23a5\n", "\u23a2 y \u23a5\n", "\u23a2 \u23a5\n", "\u23a2 \\psi \u23a5\n", "\u23a2 \u23a5\n", "\u23a2 v \u23a5\n", "\u23a2 \u23a5\n", "\u23a3\\dot\\psi\u23a6" ] } ], "prompt_number": 37 }, { "cell_type": "code", "collapsed": false, "input": [ "gs.jacobian(state)" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\left[\\begin{matrix}1 & 0 & \\frac{v}{\\dot\\psi} \\left(- \\cos{\\left (\\psi \\right )} + \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\cos{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 1 & \\frac{v}{\\dot\\psi} \\left(- \\sin{\\left (\\psi \\right )} + \\sin{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{1}{\\dot\\psi} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right) & \\frac{T v}{\\dot\\psi} \\sin{\\left (T \\dot\\psi + \\psi \\right )} - \\frac{v}{\\dot\\psi^{2}} \\left(\\cos{\\left (\\psi \\right )} - \\cos{\\left (T \\dot\\psi + \\psi \\right )}\\right)\\\\0 & 0 & 1 & 0 & T\\\\0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 38, "text": [ "\u23a1 v\u22c5(-cos(\\psi) + cos(T\u22c5\\dot\\psi + \\psi)) -sin(\\psi) + sin(T\u22c5\\dot\\psi + \n", "\u23a21 0 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n", "\u23a2 \\dot\\psi \\dot\\psi \n", "\u23a2 \n", "\u23a2 \n", "\u23a2 v\u22c5(-sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi)) cos(\\psi) - cos(T\u22c5\\dot\\psi + \\\n", "\u23a20 1 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n", "\u23a2 \\dot\\psi \\dot\\psi \n", "\u23a2 \n", "\u23a2 \n", "\u23a20 0 1 0 \n", "\u23a2 \n", "\u23a20 0 0 1 \n", "\u23a2 \n", "\u23a30 0 0 0 \n", "\n", "\\psi) T\u22c5v\u22c5cos(T\u22c5\\dot\\psi + \\psi) v\u22c5(-sin(\\psi) + sin(T\u22c5\\dot\\psi + \\psi))\u23a4\n", "\u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n", " \\dot\\psi 2 \u23a5\n", " \\dot\\psi \u23a5\n", " \u23a5\n", "psi) T\u22c5v\u22c5sin(T\u22c5\\dot\\psi + \\psi) v\u22c5(cos(\\psi) - cos(T\u22c5\\dot\\psi + \\psi)) \u23a5\n", "\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u23a5\n", " \\dot\\psi 2 \u23a5\n", " \\dot\\psi \u23a5\n", " \u23a5\n", " T \u23a5\n", " \u23a5\n", " 0 \u23a5\n", " \u23a5\n", " 1 \u23a6" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It has to be computed on every filter step because it consists of state variables!\n", "\n", "To Sympy Team: A `.to_python` and `.to_c` and `.to_matlab` whould be nice to generate code, like it already works with `print latex()`." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Initial Uncertainty $P_0$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initialized with $0$ means you are pretty sure where the vehicle starts" ] }, { "cell_type": "code", "collapsed": false, "input": [ "P = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0])\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 = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(6))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(6))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,4.5])\n", "plt.ylim([4.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax)\n", "\n", "\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(array([[ 1000., 0., 0., 0., 0.],\n", " [ 0., 1000., 0., 0., 0.],\n", " [ 0., 0., 1000., 0., 0.],\n", " [ 0., 0., 0., 1000., 0.],\n", " [ 0., 0., 0., 0., 1000.]]), (5, 5))\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Process Noise Covariance Matrix Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"*The state uncertainty model models the disturbances which excite the linear system. Conceptually, it estimates how bad things can get when the system is run open loop for a given period of time.*\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sGPS = 0.5*8.8*dt**2 # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n", "sCourse = 0.1*dt # assume 0.1rad/s as maximum turn rate for the vehicle\n", "sVelocity= 8.8*dt # assume 8.8m/s2 as maximum acceleration, forcing the vehicle\n", "sYaw = 1.0*dt # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle\n", "\n", "Q = np.diag([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sYaw**2])\n", "print(Q, Q.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(array([[ 3.09760000e-06, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00],\n", " [ 0.00000000e+00, 3.09760000e-06, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00],\n", " [ 0.00000000e+00, 0.00000000e+00, 4.00000000e-06,\n", " 0.00000000e+00, 0.00000000e+00],\n", " [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 3.09760000e-02, 0.00000000e+00],\n", " [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 4.00000000e-04]]), (5, 5))\n" ] } ], "prompt_number": 40 }, { "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 = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(8))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(7),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(8))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(7),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,4.5])\n", "plt.ylim([4.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+AXsT48NA8U1jz8Tmnwz8E3sFQ0vIS44UCk96PGkBP0ZQJC+/z1BuwY4Bvh8N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\nmYZlxhdjt2J+sLXVaZgJ2AW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"text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Real Measurements" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#path = './../RaspberryPi-CarPC/TinkerDataLogger/DataLogs/2014/'\n", "datafile = '2014-03-26-000-Data.csv'\n", "\n", "date, \\\n", "time, \\\n", "millis, \\\n", "ax, \\\n", "ay, \\\n", "az, \\\n", "rollrate, \\\n", "pitchrate, \\\n", "yawrate, \\\n", "roll, \\\n", "pitch, \\\n", "yaw, \\\n", "speed, \\\n", "course, \\\n", "latitude, \\\n", "longitude, \\\n", "altitude, \\\n", "pdop, \\\n", "hdop, \\\n", "vdop, \\\n", "epe, \\\n", "fix, \\\n", "satellites_view, \\\n", "satellites_used, \\\n", "temp = np.loadtxt(datafile, delimiter=',', unpack=True, \n", " converters={1: mdates.strpdate2num('%H%M%S%f'),\n", " 0: mdates.strpdate2num('%y%m%d')},\n", " skiprows=1)\n", "\n", "print('Read \\'%s\\' successfully.' % datafile)\n", "\n", "# A course of 0\u00b0 means the Car is traveling north bound\n", "# and 90\u00b0 means it is traveling east bound.\n", "# In the Calculation following, East is Zero and North is 90\u00b0\n", "# We need an offset.\n", "course =(-course+90.0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Read '2014-03-26-000-Data.csv' successfully.\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Measurement Function H" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matrix $J_H$ is the Jacobian of the Measurement function $h$ with respect to the state. Function $h$ can be used to compute the predicted measurement from the predicted state.\n", "\n", "If a GPS measurement is available, the following function maps the state to the measurement." ] }, { "cell_type": "code", "collapsed": false, "input": [ "hs = Matrix([[xs],\n", " [ys],\n", " [vs],\n", " [dpsis]])\n", "hs" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\left[\\begin{matrix}x\\\\y\\\\v\\\\\\dot\\psi\\end{matrix}\\right]$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "\u23a1 x \u23a4\n", "\u23a2 \u23a5\n", "\u23a2 y \u23a5\n", "\u23a2 \u23a5\n", "\u23a2 v \u23a5\n", "\u23a2 \u23a5\n", "\u23a3\\dot\\psi\u23a6" ] } ], "prompt_number": 43 }, { "cell_type": "code", "collapsed": false, "input": [ "JHs=hs.jacobian(state)\n", "JHs" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\left[\\begin{matrix}1 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0\\\\0 & 0 & 0 & 1 & 0\\\\0 & 0 & 0 & 0 & 1\\end{matrix}\\right]$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 44, "text": [ "\u23a11 0 0 0 0\u23a4\n", "\u23a2 \u23a5\n", "\u23a20 1 0 0 0\u23a5\n", "\u23a2 \u23a5\n", "\u23a20 0 0 1 0\u23a5\n", "\u23a2 \u23a5\n", "\u23a30 0 0 0 1\u23a6" ] } ], "prompt_number": 44 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If no GPS measurement is available, simply set the corresponding values in $J_h$ to zero." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Measurement Noise Covariance $R$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"In practical use, the uncertainty estimates take on the significance of relative weights of state estimates and measurements. So it is not so much important that uncertainty is absolutely correct as it is that it be relatively consistent across all models\" - Kelly, A. (1994). A 3D state space formulation of a navigation Kalman filter for autonomous vehicles, (May). Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA282853" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sGPS = 5.0 # Standard Deviation of GPS Measurement\n", "sspeed = 2.0 # Standard Deviation of the speed measurement\n", "syaw = 0.01 # Standard Deviation of the yawrate measurement\n", "R = np.matrix([[sGPS**2, 0.0, 0.0, 0.0],\n", " [0.0, sGPS**2, 0.0, 0.0],\n", " [0.0, 0.0, sspeed**2, 0.0],\n", " [0.0, 0.0, 0.0, syaw**2]])\n", "\n", "print(R, R.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(matrix([[ 2.50000000e+01, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00],\n", " [ 0.00000000e+00, 2.50000000e+01, 0.00000000e+00,\n", " 0.00000000e+00],\n", " [ 0.00000000e+00, 0.00000000e+00, 4.00000000e+00,\n", " 0.00000000e+00],\n", " [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 1.00000000e-04]]), (4, 4))\n" ] } ], "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(4.5, 4.5))\n", "im = plt.imshow(R, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Measurement Noise Covariance Matrix $R$')\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(5))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(4),('$x$', '$y$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(5))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(4),('$x$', '$y$', '$v$', '$\\dot \\psi$'), 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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8tQjzE7JT4mOuxYWy1FM5wuwoRygipddMgOvp6XFYksYUCCOyyLVksUc86qij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\nbMB2QQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Identity Matrix" ] }, { "cell_type": "code", "collapsed": false, "input": [ "I = np.eye(numstates)\n", "print(I, I.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(array([[ 1., 0., 0., 0., 0.],\n", " [ 0., 1., 0., 0., 0.],\n", " [ 0., 0., 1., 0., 0.],\n", " [ 0., 0., 0., 1., 0.],\n", " [ 0., 0., 0., 0., 1.]]), (5, 5))\n" ] } ], "prompt_number": 47 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Approx. Lat/Lon to Meters to check Location" ] }, { "cell_type": "code", "collapsed": false, "input": [ "RadiusEarth = 6378388.0 # m\n", "arc= 2.0*np.pi*(RadiusEarth+altitude)/360.0 # m/\u00b0\n", "\n", "dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m\n", "dy = arc * np.hstack((0.0, np.diff(latitude))) # in m\n", "\n", "mx = np.cumsum(dx)\n", "my = np.cumsum(dy)\n", "\n", "ds = np.sqrt(dx**2+dy**2)\n", "\n", "GPS=np.hstack((True, (np.diff(ds)>0.0).astype('bool'))) # GPS Trigger for Kalman Filter" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Initial State" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi]]).T\n", "print(x, x.shape)\n", "\n", "U=float(np.cos(x[2])*x[3])\n", "V=float(np.sin(x[2])*x[3])\n", "\n", "plt.quiver(x[0], x[1], U, V)\n", "plt.scatter(float(x[0]), float(x[1]), s=100)\n", "plt.title('Initial Location')\n", "plt.axis('equal')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(matrix([[ 0. ],\n", " [ 0. ],\n", " [-4.08756111],\n", " [ 0.67322222],\n", " [-0.32660346]]), (5, 1))\n" ] }, { "latex": [ "$$\\begin{pmatrix}-0.00015, & 0.00015, & -0.0003, & 0.0003\\end{pmatrix}$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 49, "text": [ "(-0.00015, 0.00015, -0.0003, 0.0003)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 49 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Put everything together as a measurement vector" ] }, { "cell_type": "code", "collapsed": false, "input": [ "measurements = np.vstack((mx, my, speed/3.6, yawrate/180.0*np.pi))\n", "# Lenth of the measurement\n", "m = measurements.shape[1]\n", "print(measurements.shape)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(4, 10800)\n" ] } ], "prompt_number": 50 }, { "cell_type": "code", "collapsed": false, "input": [ "# Preallocation for Plotting\n", "x0 = []\n", "x1 = []\n", "x2 = []\n", "x3 = []\n", "x4 = []\n", "x5 = []\n", "Zx = []\n", "Zy = []\n", "Px = []\n", "Py = []\n", "Pdx= []\n", "Pdy= []\n", "Pddx=[]\n", "Pddy=[]\n", "Kx = []\n", "Ky = []\n", "Kdx= []\n", "Kdy= []\n", "Kddx=[]\n", "dstate=[]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 51 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Extended Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![Extended Kalman Filter Step](Extended-Kalman-Filter-Step.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$x_k= \\begin{bmatrix} x \\\\ y \\\\ \\psi \\\\ v \\\\ \\dot\\psi \\end{bmatrix} = \\begin{bmatrix} \\text{Position X} \\\\ \\text{Position Y} \\\\ \\text{Heading} \\\\ \\text{Velocity} \\\\ \\text{Yaw Rate} \\end{bmatrix} = \\underbrace{\\begin{matrix}x[0] \\\\ x[1] \\\\ x[2] \\\\ x[3] \\\\ x[4] \\end{matrix}}_{\\textrm{Python Nomenclature}}$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "for filterstep in range(m):\n", "\n", " # Time Update (Prediction)\n", " # ========================\n", " # Project the state ahead\n", " # see \"Dynamic Matrix\"\n", " if np.abs(yawrate[filterstep])<0.0001: # Driving straight\n", " x[0] = x[0] + x[3]*dt * np.cos(x[2])\n", " x[1] = x[1] + x[3]*dt * np.sin(x[2])\n", " x[2] = x[2]\n", " x[3] = x[3]\n", " x[4] = 0.0000001 # avoid numerical issues in Jacobians\n", " dstate.append(0)\n", " else: # otherwise\n", " x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2]))\n", " x[1] = x[1] + (x[3]/x[4]) * (-np.cos(x[4]*dt+x[2])+ np.cos(x[2]))\n", " x[2] = (x[2] + x[4]*dt + np.pi) % (2.0*np.pi) - np.pi\n", " x[3] = x[3]\n", " x[4] = x[4]\n", " dstate.append(1)\n", " \n", " # Calculate the Jacobian of the Dynamic Matrix A\n", " # see \"Calculate the Jacobian of the Dynamic Matrix with respect to the state vector\"\n", " a13 = float((x[3]/x[4]) * (np.cos(x[4]*dt+x[2]) - np.cos(x[2])))\n", " a14 = float((1.0/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n", " a15 = float((dt*x[3]/x[4])*np.cos(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n", " a23 = float((x[3]/x[4]) * (np.sin(x[4]*dt+x[2]) - np.sin(x[2])))\n", " a24 = float((1.0/x[4]) * (-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n", " a25 = float((dt*x[3]/x[4])*np.sin(x[4]*dt+x[2]) - (x[3]/x[4]**2)*(-np.cos(x[4]*dt+x[2]) + np.cos(x[2])))\n", " JA = np.matrix([[1.0, 0.0, a13, a14, a15],\n", " [0.0, 1.0, a23, a24, a25],\n", " [0.0, 0.0, 1.0, 0.0, dt],\n", " [0.0, 0.0, 0.0, 1.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 1.0]])\n", " \n", " \n", " # Project the error covariance ahead\n", " P = JA*P*JA.T + Q\n", " \n", " # Measurement Update (Correction)\n", " # ===============================\n", " # Measurement Function\n", " hx = np.matrix([[float(x[0])],\n", " [float(x[1])],\n", " [float(x[3])],\n", " [float(x[4])]])\n", "\n", " if GPS[filterstep]:\n", " JH = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 1.0, 0.0, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 1.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 1.0]])\n", " else:\n", " JH = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 0.0],\n", " [0.0, 0.0, 0.0, 1.0, 0.0],\n", " [0.0, 0.0, 0.0, 0.0, 1.0]]) \n", " \n", " S = JH*P*JH.T + R\n", " K = (P*JH.T) * np.linalg.inv(S)\n", "\n", " # Update the estimate via\n", " Z = measurements[:,filterstep].reshape(JH.shape[0],1)\n", " y = Z - (hx) # Innovation or Residual\n", " x = x + (K*y)\n", "\n", " # Update the error covariance\n", " P = (I - (K*JH))*P\n", "\n", "\n", " # Save states for Plotting\n", " x0.append(float(x[0]))\n", " x1.append(float(x[1]))\n", " x2.append(float(x[2]))\n", " x3.append(float(x[3]))\n", " x4.append(float(x[4]))\n", " Zx.append(float(Z[0]))\n", " Zy.append(float(Z[1])) \n", " Px.append(float(P[0,0]))\n", " Py.append(float(P[1,1]))\n", " Pdx.append(float(P[2,2]))\n", " Pdy.append(float(P[3,3]))\n", " Pddx.append(float(P[4,4]))\n", " Kx.append(float(K[0,0]))\n", " Ky.append(float(K[1,0]))\n", " Kdx.append(float(K[2,0]))\n", " Kdy.append(float(K[3,0]))\n", " Kddx.append(float(K[4,0]))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Plots" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Uncertainties" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,9))\n", "plt.semilogy(range(m),Px, label='$x$')\n", "plt.step(range(m),Py, label='$y$')\n", "plt.step(range(m),Pdx, label='$\\psi$')\n", "plt.step(range(m),Pdy, label='$v$')\n", "plt.step(range(m),Pddx, label='$\\dot \\psi$')\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.title('Uncertainty (Elements from Matrix $P$)')\n", "plt.legend(loc='best',prop={'size':22})" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 53, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ODikpKcycOROA1atXAzBgwAD7Ovv27WPv3sZZTximIKu0VOodghBCCCEMasOGDfzyyy9E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"text": [ "" ] } ], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(6, 6))\n", "im = plt.imshow(P, interpolation=\"none\", cmap=plt.get_cmap('binary'))\n", "plt.title('Covariance Matrix $P$ (after %i Filter Steps)' % (m))\n", "ylocs, ylabels = plt.yticks()\n", "# set the locations of the yticks\n", "plt.yticks(np.arange(6))\n", "# set the locations and labels of the yticks\n", "plt.yticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "xlocs, xlabels = plt.xticks()\n", "# set the locations of the yticks\n", "plt.xticks(np.arange(6))\n", "# set the locations and labels of the yticks\n", "plt.xticks(np.arange(5),('$x$', '$y$', '$\\psi$', '$v$', '$\\dot \\psi$'), fontsize=22)\n", "\n", "plt.xlim([-0.5,4.5])\n", "plt.ylim([4.5, -0.5])\n", "\n", "from mpl_toolkits.axes_grid1 import make_axes_locatable\n", "divider = make_axes_locatable(plt.gca())\n", "cax = divider.append_axes(\"right\", \"5%\", pad=\"3%\")\n", "plt.colorbar(im, cax=cax)\n", "\n", "\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Jq1kjqVnAHU16LhERSaDMI6lmFalxwJomPVemlEk5vs27Z0WZlNH+4KgviqMZ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\nV6QOBzqb9FyZ0ry7o74w6ge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"text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Kalman Gains" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,9))\n", "plt.step(range(len(measurements[0])),Kx, label='$x$')\n", "plt.step(range(len(measurements[0])),Ky, label='$y$')\n", "plt.step(range(len(measurements[0])),Kdx, label='$\\psi$')\n", "plt.step(range(len(measurements[0])),Kdy, label='$v$')\n", "plt.step(range(len(measurements[0])),Kddx, label='$\\dot \\psi$')\n", "\n", "\n", "plt.xlabel('Filter Step')\n", "plt.ylabel('')\n", "plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n", "plt.legend(prop={'size':18})\n", "plt.ylim([-0.1,0.1]);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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BOF1+IVr34/kWol/VVWh9RdhAiB/fuX7TPgWxM/kQIvel3v8/gJb+iYnw9dO6COI0p+8q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\n+whzzc5DPc3raV5P83qat2OuB7Yjd31v2kcAAJi4uR7Ylja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"text": [ "" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "State Vector" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(fw,16))\n", "\n", "plt.subplot(411)\n", "plt.step(range(len(measurements[0])),x0-mx[0], label='$x$')\n", "plt.step(range(len(measurements[0])),x1-my[0], label='$y$')\n", "\n", "plt.title('Extended Kalman Filter State Estimates (State Vector $x$)')\n", "plt.legend(loc='best',prop={'size':22})\n", "plt.ylabel('Position (relative to start) [m]')\n", "\n", "plt.subplot(412)\n", "plt.step(range(len(measurements[0])),x2, label='$\\psi$')\n", "plt.step(range(len(measurements[0])),(course/180.0*np.pi+np.pi)%(2.0*np.pi) - np.pi, label='$\\psi$ (from GPS as reference)')\n", "plt.ylabel('Course')\n", "plt.legend(loc='best',prop={'size':16})\n", " \n", "plt.subplot(413)\n", "plt.step(range(len(measurements[0])),x3, label='$v$')\n", "plt.step(range(len(measurements[0])),speed/3.6, label='$v$ (from GPS as reference)')\n", "plt.ylabel('Velocity')\n", "plt.ylim([0, 30])\n", "plt.legend(loc='best',prop={'size':16})\n", "\n", "plt.subplot(414)\n", "plt.step(range(len(measurements[0])),x4, label='$\\dot \\psi$')\n", "plt.step(range(len(measurements[0])),yawrate/180.0*np.pi, label='$\\dot \\psi$ (from IMU as reference)')\n", "plt.ylabel('Yaw Rate')\n", "plt.ylim([-0.6, 0.6])\n", "plt.legend(loc='best',prop={'size':16})\n", "plt.xlabel('Filter Step')\n", "\n", "plt.savefig('Extended-Kalman-Filter-CTRV-State-Estimates.png', dpi=72, transparent=True, bbox_inches='tight')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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PdEitnmvw5aB5if3kDmIWPwl6A45Rd0Q6LCECMu/3lIgef/LRB8NynEcffZQZ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J/PuU9LyPn5Wrmn+oLMp/u3cH3nrQ7Pa0/sx++nxRRn/Q8rYKkANFAYBnqz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CmvSzaao8SGpVI7HxIwFdT6vVK8jKyiImpu9FsKqWZtfy2aNf4N3TWlVSe3slxsSORauEvo4Y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"text": [ "" ] } ], "prompt_number": 56 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Position x/y" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#%pylab --no-import-all" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(16,9))\n", "\n", "# EKF State\n", "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5)\n", "plt.plot(x0,x1, label='EKF Position')\n", "\n", "# Measurements\n", "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements')\n", "#cbar=plt.colorbar(ticks=np.arange(20))\n", "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n", "#cbar.ax.set_xlabel(u'm')\n", "\n", "# Start/Goal\n", "plt.scatter(x0[0],x1[0], s=60, label='Start', c='g')\n", "plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r')\n", "\n", "plt.xlabel('X [m]')\n", "plt.ylabel('Y [m]')\n", "plt.title('Position')\n", "plt.legend(loc='best')\n", "plt.axis('equal')\n", "#plt.tight_layout()\n", "\n", "#plt.savefig('Extended-Kalman-Filter-CTRV-Position.png', dpi=72, transparent=True, bbox_inches='tight')" ], "language": "python", "metadata": {}, "outputs": [ { "latex": [ "$$\\begin{pmatrix}-100.0, & 700.0, & -50.0, & 400.0\\end{pmatrix}$$" ], "metadata": {}, "output_type": "pyout", "prompt_number": 58, "text": [ "(-100.0, 700.0, -50.0, 400.0)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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TIcy8fiZ9kvoA0KFmB+yG/aRz2Awbl9S55LTi2LRpE5MnTyYrKwuAXbt2MX36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\nS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V1DXdEX6PXORNPAsiAhQeB2C1JTBdOnC9TTSdaU4taZbnpP55/J/cAzwPuBC//pQ5Le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"text": [ "" ] } ], "prompt_number": 58 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Detailed View" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=(9,4))\n", "\n", "# EKF State\n", "#plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.01, scale=0.2, label='Driving Direction')\n", "plt.plot(x0,x1, label='EKF Position', linewidth=5, alpha=0.8)\n", "\n", "# Measurements\n", "plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements')\n", "#cbar=plt.colorbar(ticks=np.arange(20))\n", "#cbar.ax.set_ylabel(u'EPE', rotation=270)\n", "#cbar.ax.set_xlabel(u'm')\n", "\n", "plt.xlabel('X [m]')\n", "plt.xlim(80, 120)\n", "plt.ylabel('Y [m]')\n", "plt.ylim(160, 180)\n", "plt.title('Position')\n", "plt.legend(loc='best');\n", "plt.savefig('EKF-Position.png', dpi=150)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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fAJDlXDWzNrGXZ3kDSVKxWER+IYFAUHIIQSMQlBPKhF/d7cS8LjfnjNkMFotKptOf9/55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"text": [ "" ] } ], "prompt_number": 59 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Conclusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, complicated analytic calculation of the Jacobian Matrices, but it works pretty well." ] } ], "metadata": {} } ] }