From 1fca1115678f16eabf47b04900622b76dc30f81b Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 14 Sep 2014 11:58:32 -0700 Subject: [PATCH] Added animation of dog tracking. I animate the dog update->predict cycle with both the estimate and variance being shown. --- Chapter05_Kalman_Filters/Kalman_Filters.ipynb | 27 ++- .../Kalman_Filters_Animations.ipynb | 169 ++++-------------- Chapter05_Kalman_Filters/dog_track.gif | Bin 0 -> 243822 bytes Chapter05_Kalman_Filters/volt_animate.gif | Bin 492577 -> 476390 bytes 4 files changed, 60 insertions(+), 136 deletions(-) create mode 100644 Chapter05_Kalman_Filters/dog_track.gif diff --git a/Chapter05_Kalman_Filters/Kalman_Filters.ipynb b/Chapter05_Kalman_Filters/Kalman_Filters.ipynb index 27e91f0..3bce71a 100644 --- a/Chapter05_Kalman_Filters/Kalman_Filters.ipynb +++ b/Chapter05_Kalman_Filters/Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:ce50ae76601ee29b27998c3d04ed65d7a05c21cf63a83e520527e96fff2359e3" + "signature": "sha256:6bbf3b69472f466f37cf43314d0391a512ece3f8f9592b3b02ec292d425f2c17" }, "nbformat": 3, "nbformat_minor": 0, @@ -1227,6 +1227,31 @@ "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets a bit more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurement means more data to work with. \"Measure twice, cut once!\"" ] }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Animating the Tracking" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n", + "\n", + "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement." + ] + }, { "cell_type": "heading", "level": 2, diff --git a/Chapter05_Kalman_Filters/Kalman_Filters_Animations.ipynb b/Chapter05_Kalman_Filters/Kalman_Filters_Animations.ipynb index bac67d5..df974e0 100644 --- a/Chapter05_Kalman_Filters/Kalman_Filters_Animations.ipynb +++ b/Chapter05_Kalman_Filters/Kalman_Filters_Animations.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:e4bf6588bd5504bdeff5802ced00bcc98d4cad46767b3d4f649b0fe63a2976cf" + "signature": "sha256:93eea406145c65de7a62ec1f5ec3c4d26d16c2116b86fa6bd9e80589122ce2c7" }, "nbformat": 3, "nbformat_minor": 0, @@ -241,13 +241,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 2, + "prompt_number": 64, "text": [ - "" + "" ] } ], - "prompt_number": 2 + "prompt_number": 64 }, { "cell_type": "code", @@ -274,7 +274,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 3 + "prompt_number": 65 }, { "cell_type": "code", @@ -341,7 +341,7 @@ " plt.tight_layout()\n", " \n", "N=12\n", - "animate('volt_animate.gif', volt_animate, N*3, 500)" + "animate('volt_animate.gif', volt_animate, N*3, 350)" ], "language": "python", "metadata": {}, @@ -349,13 +349,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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r4+Pj/VFGr2A2m4Hub5PzzrOxdavr62lUVDzRsbEAODpRR3099O9vbjqW4grK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\n9Stzc3MqylHKSwvtRqNRYrEY69cvX33jzZs39PT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07tA062LLFoVmLnWlcE5GwtPfHL6S3xScAsC4ccMfxPPrX5dy+eU9dzepqOjU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\nzJw09pTH504Zx5iKUvYdbub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"text": [ - "" + "" ] } ], - "prompt_number": 38 + "prompt_number": 69 }, { "cell_type": "markdown", @@ -368,164 +368,63 @@ "cell_type": "code", "collapsed": false, "input": [ - "class DogSensor(object):\n", - " \n", - " def __init__(self, x0=0, velocity=1, noise=0.0):\n", - " \"\"\" x0 - initial position\n", - " velocity - (+=right, -=left)\n", - " noise - scaling factor for noise, 0== no noise\n", - " \"\"\"\n", - " self.x = x0\n", - " self.velocity = velocity\n", - " self.noise = math.sqrt(noise)\n", - "\n", - " def sense(self):\n", - " self.x = self.x + self.velocity\n", - " return self.x + random.randn() * self.noise\n", - " \n", - " \n", "# assume dog is always moving 1m to the right\n", "movement = 1\n", - "movement_error = .2\n", + "movement_error = .05\n", "sensor_error = 4.5\n", - "pos = (0, 100) # gaussian N(0,50)\n", - "\n", - "dog = DogSensor(pos[0], velocity=movement, noise=sensor_error)\n", + "pos = (0, 100) # gaussian N(0,100)\n", "\n", + "# this is the recorded output of a run of the dog sensor with an initial\n", + "# seed of 200\n", + "ZS = [-2.07, 6.05, 4.51, 3.47, 5.76, 5.93, 6.53, 9.01, 7.53, 11.68, \n", + " 11.15, 14.76, 13.45, 16.15, 19.05, 14.87, 20.90, 15.75, \n", + " 17.16, 20.50]\n", "zs = []\n", "ps = []\n", - "vs = []\n", + "\n", + "N=20\n", "\n", "def dog_animate(frame):\n", - " global pos, zs, ps, vs\n", + " global pos, zs, ps, N, ZS\n", " pos = predict(pos[0], pos[1], movement, movement_error) \n", - " Z = dog.sense()\n", + " Z = ZS[frame]\n", " zs.append(Z)\n", - " vs.append(pos[1])\n", - " print(pos[1])\n", " \n", " pos = update(pos[0], pos[1], Z, sensor_error)\n", " ps.append(pos[0])\n", "\n", + "\n", " plt.subplot(211)\n", - " plt.scatter (frame, Z)\n", + " plt.plot(zs,c='r', linestyle='dashed')\n", + "\n", + " plt.xlim([0,N*1.2])\n", + " plt.ylim([0,N*1.2])\n", + "\n", + " if len(ps) > 1:\n", + " plt.plot(ps, c='#8EBA42')\n", + " \n", " plt.subplot(212)\n", " plt.cla()\n", - " stats.plot_gaussian(pos[0], pos[1], xlim=[0,32])\n", + " stats.plot_gaussian(pos[0], pos[1], xlim=[0,N*1.2])\n", " plt.ylim([0,1])\n", + " plt.tight_layout()\n", "\n", "\n", - "N=12\n", "animate('dog_track.gif', dog_animate, N, 200)" ], "language": "python", "metadata": {}, "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "100.2\n", - "4.506590257879656" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "2.451646358922152" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "1.7870209797122434" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "1.4790786661369082" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "1.3131905715360732" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "1.2165428948514319" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "1.1576492519214656" - ] - }, - { - "output_type": 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CglBUVCTWkEREZCNEu3GlTqeDRqOBVqtFYWEhamtrodFooNPp2ixr7zO2WSwWXLtmBgAM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\nHgVnJ2n/yi2aPRYA8LeDeWg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IkVw87jfExsbCU1B00l9weHDfZcrZZ7vCufDll71SvoiIOxSc0mcjr7qKstFD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\n1wOHgPF+LSg4HULfZZ/Td9n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