{ "metadata": { "name": "", "signature": "sha256:84d00c91b233d9282556386810d014ee3915939bfca14bff1985550d5c28171f" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Kalman Filter in 1 Dimension (=Distance)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import matplotlib.mlab as mlab\n", "import seaborn as sb\n", "from scipy import stats\n", "import time\n", "sb.set() # Reset Style\n", "#sb.set(style=\"white\")\n", "sb.set_context(\"talk\")" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "fw = 10 # figure width" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the Distributions in this range:\n", "x = np.linspace(-100,100,1000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "In the beginning" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mean0 = 0.0 # e.g. meters or miles\n", "var0 = 20.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 43 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(fw,5))\n", "plt.plot(x,mlab.normpdf(x, mean0, var0), label='Normal Distribution')\n", "plt.ylim(0, 0.1);\n", "plt.legend(loc='best');\n", "plt.xlabel('Position');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JkqQEMZxJkiQliOFMkiQpQQxnkiRJCWI4kyRJShDDmSRJUoIYziRJkhLEcCZJkpQghjNJ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\nWto6AZgwtoK3nbw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"text": [ "" ] } ], "prompt_number": 44 }, { "cell_type": "markdown", "metadata": {}, "source": [ "You are at position `0` and you are pretty unsure (flat normal distribution)" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Now we have something, which estimates the moved distance" ] }, { "cell_type": "code", "collapsed": false, "input": [ "meanMove = 25.0 # e.g. meters, calculated from velocity*dt or step counter or wheel encoder ...\n", "varMove = 10.0 # Estimated or determined with static measurements" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(fw,5))\n", "plt.plot(x,mlab.normpdf(x, meanMove, varMove), label='Normal Distribution')\n", "plt.ylim(0, 0.1);\n", "plt.legend(loc='best');\n", "plt.xlabel('Distance moved');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ERETERRTORERERFxE4UxERETERRTORERERFxE4UxERETERRTORERERFxE4UxERETERRTO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\n0IUA4fp0T8P0yQB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"text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Both Distributions have to be merged together" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\mu_\\text{new}=\\mu_\\text{0}+\\mu_\\text{move}$ is the new mean and $\\sigma^2_\\text{new}=\\sigma^2_\\text{0}+\\sigma^2_\\text{move}$ is the new variance." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def predict(var, mean, varMove, meanMove):\n", " new_var = var + varMove\n", " new_mean= mean+ meanMove\n", " return new_var, new_mean" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 47 }, { "cell_type": "code", "collapsed": false, "input": [ "new_var, new_mean = predict(var0, mean0, varMove, meanMove)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(fw,5))\n", "plt.plot(x,mlab.normpdf(x, mean0, var0), label='Beginning Normal Distribution')\n", "plt.plot(x,mlab.normpdf(x, meanMove, varMove), label='Movement Normal Distribution')\n", "plt.plot(x,mlab.normpdf(x, new_mean, new_var), label='Resulting Normal Distribution')\n", "plt.ylim(0, 0.1);\n", "plt.legend(loc='best');\n", "plt.title('Normal Distributions of 1st Kalman Filter Prediction Step');\n", "plt.savefig('Kalman-Filter-1D-Step.png', dpi=150)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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o0KARy5d/jtZ7cDgcfPfdt7Rp05yTJ6OpW7cBP/64nR07fiAhIYGPP16SjaDo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\nfQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What you see: The resulting distribution is flat > uncertain.\n", "\n", "The more often you run the `predict` step, the flatter the distribution get" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "First Sensor Measurement (Position) is coming in..." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Sensor Defaults for Position Measurements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(Estimated or determined with static measurements)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "meanSensor = 25.0\n", "varSensor = 12.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 50 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(fw,5))\n", "plt.plot(x,mlab.normpdf(x, meanSensor, varSensor))\n", "plt.ylim(0, 0.1);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 51 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Now both Distributions have to be merged together" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\sigma^2_\\text{new}=\\cfrac{1}{\\cfrac{1}{\\sigma^2_\\text{old}}+\\cfrac{1}{\\sigma^2_\\text{Sensor}}}$ is the new variance and the new mean value is $\\mu_\\text{new}=\\cfrac{\\sigma^2_\\text{Sensor} \\cdot \\mu_\\text{old} + \\sigma^2_\\text{old} \\cdot \\mu_\\text{Sensor}}{\\sigma^2_\\text{old}+\\sigma^2_\\text{Sensor}}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def correct(var, mean, varSensor, meanSensor):\n", " new_mean=(varSensor*mean + var*meanSensor) / (var+varSensor)\n", " new_var = 1/(1/var +1/varSensor)\n", " return new_var, new_mean" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "code", "collapsed": false, "input": [ "var, mean = correct(new_var, new_mean, varSensor, meanSensor)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(fw,5))\n", "plt.plot(x,mlab.normpdf(x, new_mean, new_var), label='Beginning (after Predict)')\n", "plt.plot(x,mlab.normpdf(x, meanSensor, varSensor), label='Position Sensor Normal Distribution')\n", "plt.plot(x,mlab.normpdf(x, mean, var), label='New Position Normal Distribution')\n", "plt.ylim(0, 0.1);\n", "plt.legend(loc='best');\n", "plt.title('Normal Distributions of 1st Kalman Filter Update Step');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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dao4e/ct+BarImLu7BT+/vHcdW8myphBCiCy5cuUKPXu+y6VLl0hMTOTrr78g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\nSOqsMqVFTpbPLx1osSjxje+aj+N6/UQv3991N/FMAp/dy2fXfGzUsUu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"text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "You see: Sensor readings increase the certainty!" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "This is called the Measurement or Correction step! The Filter get's more serious about the actual state." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Let's put everything together: The 1D Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*\"Kalman-Filter: Predicting the Future since 1960\"*\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's say, we have some measurements for position and for distance traveled. Both have to be fused with the 1D-Kalman Filter." ] }, { "cell_type": "code", "collapsed": false, "input": [ "positions = (10, 20, 30, 40, 50)+np.random.randn(5)\n", "distances = (10, 10, 10, 10, 10)+np.random.randn(5)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 55 }, { "cell_type": "code", "collapsed": false, "input": [ "positions" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 56, "text": [ "array([ 10.05476138, 20.28458674, 29.49295574, 38.62625017, 49.53275068])" ] } ], "prompt_number": 56 }, { "cell_type": "code", "collapsed": false, "input": [ "distances" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 57, "text": [ "array([ 10.98636654, 10.00344322, 10.93369829, 9.85055967, 10.33031138])" ] } ], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "mean = mean0\n", "var = var0\n", "\n", "plt.figure(figsize=(fw,5))\n", "for m in range(len(positions)):\n", " \n", " # Predict\n", " var, mean = predict(var, mean, varMove, distances[m])\n", " #print('mean: %.2f\\tvar:%.2f' % (mean, var))\n", " plt.plot(x,mlab.normpdf(x, mean, var), label='%i. step (Prediction)' % (m+1))\n", " \n", " # Correct\n", " var, mean = correct(var, mean, varSensor, positions[m])\n", " print('After correction: mean= %.2f\\tvar= %.2f' % (mean, var))\n", " plt.plot(x,mlab.normpdf(x, mean, var), label='%i. step (Correction)' % (m+1))\n", " \n", "plt.ylim(0, 0.1);\n", "plt.xlim(-20, 120)\n", "plt.legend(); " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "After correction: mean= 10.32\tvar= 8.57\n", "After correction: mean= 20.30\tvar= 7.29\n", "After correction: mean= 30.21\tvar= 7.08\n", "After correction: mean= 39.22\tvar= 7.05\n", "After correction: mean= 49.54\tvar= 7.04\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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X32jW7P+VKFMqFSiVSgoLb5cov3ecB8nNLcBoNJmP29k54enpyY4de8x1MjMz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Ft1WO0jnwowFBatmUqTJHbqBh7/VEOpVORq6+TUpsz1wmOPfZJXXnn5Wi/jmvHaa7/n/e9/aMTC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"text": [ "" ] } ], "prompt_number": 60 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Conclusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sensors are represented as normal distributions with their parameters ($\\mu$ and $\\sigma^2$) and are calculated together with addition or convolution. The prediction decreases the certainty about the state, the correction increases the certainty.\n", "\n", "* Prediction: Certainty $\\downarrow$\n", "* Correction: Certainty $\\uparrow$\n", "\n", "If you have more than one state (here: position), than you have to use the multidimensional Kalman Filter, which is pretty much the same, but with matrices:\n", "\n", "![Kalman Filter](Kalman-Filter-Step.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to use the Kalman filter to estimate the internal state $x$ of a process given only a sequence of noisy observations $z$, one must model the process in accordance with the framework of the Kalman filter. This means specifying the following matrices:\n", "\n", "* $A$, the state-transition model, which is applied to the previous state $x$\n", "* $H$, the observation model, which maps the true state space into the observed space\n", "* $Q$, the covariance of the process noise\n", "* $R$, the covariance of the observation noise\n", "* $P$, the error covariance matrix (a measure of the estimated accuracy of the state estimate)\n", "* $K$, the Kalman-Gain, which weights between the model and the observation\n", "* and sometimes $B$, the control-input model, which is applied to the control vector $u$\n", "\n", "for each time-step, $k$.\n", "\n", "*Source: [Wikipedia](http://en.wikipedia.org/wiki/Kalman_filter)*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And you can run the `Prediction` in high update rate Open-Loop mode (means: without `Correction`) and use a correction, only if it is available.\n", "\n", "Typical Example: You have a high update rate acceleration sensor (typical 100Hz) and a low update rate GPS sensor (typical 1Hz). Then you run the `Prediction` with 100Hz (mean 100 times a second) and only correct every 100th filter step." ] } ], "metadata": {} } ] }