diff --git a/Kalman Filters.ipynb b/Kalman Filters.ipynb index 117a30a..76b4d8b 100644 --- a/Kalman Filters.ipynb +++ b/Kalman Filters.ipynb @@ -50,7 +50,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 106 + "prompt_number": 1 }, { "cell_type": "markdown", @@ -74,11 +74,11 @@ "output_type": "stream", "stream": "stdout", "text": [ - "0.4069 0.2905 -1.7388 1.0792 -0.4538 0.5012 -0.5006 0.0431 0.4978 0.1898 -0.2238 -0.0177 -0.9256 1.1435 0.5238 0.3113 0.2732 0.5035 1.7994 -1.2416\n" + "1.2396 0.5610 -0.5456 -0.8361 -0.8521 0.4101 -0.4417 0.0910 -0.4968 0.5187 -1.9393 -0.3410 0.0943 1.1800 0.1204 -1.0427 1.2128 -2.2642 -1.7840 -0.0621\n" ] } ], - "prompt_number": 107 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -117,7 +117,7 @@ "output_type": "display_data", "png": 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"text": [ - "" + "" ] }, { @@ -128,7 +128,7 @@ ] } ], - "prompt_number": 108 + "prompt_number": 3 }, { "cell_type": "markdown", @@ -167,13 +167,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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kuDV6vSQJYRqSKIQwopEjoVcvuHLlwZ53c/2EEKYgiUIII8nIgC1b1LqHrl0h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\nnExgYGDhYGWvp0J274YRI9Q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WBWMVdkcShRCWpBTMnQtBQXrnuRYtAEhNheee0xsNXT9LvGpVPfGpWjULxSvs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\nYV1YNBUrWjoaIYQ9sdhgdlZ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VFYCxUe7Dh5NFYS8uXgT+8x/ghRfodWAgMHMmsGFD6wGtdRHhd49ETmiKTo+mnj0pXtLY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\nNJCVhfxuCepgNgAMHUrnHzmi2Xb2rKFQjBtHP3L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KrIHbSa3mQ6dravjs6oQE+FfL11GYilEAPBh99qz0PrIobAdZFAThIOrquAvI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\n0BcKxrhF4QyuJzm8vID8fN7UkCAIDv0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REcG//vUvU4bIqulJ7MVqhXbt4McfoVEjs6MRuTIV3kfRu3dvvL29efDBBzEM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\nmUFOcATjvulE54TRfP01xMd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"text": [ - "" + "" ] } ], - "prompt_number": 113 + "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ - "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply *randn()* with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $N(0,100)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$. *dog_sensor().__init__* takes the square root of the noise setting so that the noise * randn() call properly computes the normal distribution." + "You may not have a full understanding of the exact *meaning* of a noise value of 100.0, but as it turns out if you multiply *randn()* with a number $n$, the result is just a normal distribution with $\\sigma = \\sqrt{n}$. So the example with noise = 100 is using the normal distribution $N(0,100)$. Recall the notation for a normal distribution is $N(\\mu,\\sigma^2)$. If the square root is confusing, recall that normal distributions use $\\sigma^2$ for the variance, and $\\sigma$ is the standard deviation, which we do not use in this book. *dog_sensor.__init__()* takes the square root of the noise setting so that the *noise * randn()* call properly computes the normal distribution. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Math with Gaussians\n", + "\n", + "Let's say we believe that our dog is at 23m, and the variance is 5 ($N(23,5)$). We can represent that in a plot:\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import gaussian\n", + "gaussian.norm_plot (23, 5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position.\n", + "\n", + "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpertation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", + "\n", + "Let's look at this in a plot:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = dog_sensor (23, 0, 5)\n", + "ys = range (100)\n", + "xs = []\n", + "for i in ys:\n", + " xs.append (dog.sense())\n", + " \n", + "plot (xs,ys)\n", + "show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Implementing Sensing\n", + "\n", + "Recall the histogram filter uses a numpy array to encode our belief about the position of our dog at any time. That array stored our belief that the dog was in any position in the hallway using 10 positions. This was very crude, because with a 100m hallway that corresponded to positions 10m apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", + "\n", + "Therefore, let us use a single gaussian to reflect our current belief of the dog's position. Gaussians extend to infinity on both sides of the mean, so the single gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. \n", + "\n", + "So let us implement the sensing function, but using gaussians instead of the histogram array. First, here is the histogram code for reference:\n", + "\n", + " def sense (pos, measure, p_hit, p_miss):\n", + " q = array(pos, dtype=float)\n", + " for i in range(len(hallway)):\n", + " if hallway[i] == measure:\n", + " q[i] = pos[i] * p_hit\n", + " else:\n", + " q[i] = pos[i] * p_miss\n", + " normalize(q)\n", + " return q\n", + " \n", + "Note the algorithm is essentially computing:\n", + "\n", + " new_belief = old_belief * measurement * sensor_error\n", + " \n", + "The measurement term might not be clear, but recall that measurement in this case was always 1 or 0, and so it was left out for convience. \n", + " \n", + "If we are implementing this with gaussians, we might expect it to be implemented as:\n", + "\n", + " new_gaussian = measurement * old_gaussian\n", + " \n", + "where measurement is a gaussian returned from the sensor. But does that make sense? Can we multiply gaussians? If we multiply a gaussian with a gaussing is the result another gaussian, or something else?\n", + "\n", + "\n", + " \n", + "\n", + "\n", + "\n" ] }, { @@ -242,7 +358,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 111 + "prompt_number": 7 } ], "metadata": {} diff --git a/dog_track_1d.py b/dog_track_1d.py new file mode 100644 index 0000000..3b5bc44 --- /dev/null +++ b/dog_track_1d.py @@ -0,0 +1,35 @@ +# -*- coding: utf-8 -*- +""" +Created on Wed Apr 30 10:35:19 2014 + +@author: rlabbe +""" +import numpy.random as random + +class dog_sensor(object): + def __init__(self, x0 = 0, motion=1, noise=0.0): + self.x = x0 + self.motion = motion + self.noise = math.sqrt(noise) + + def sense(self): + self.x = self.x + self.motion + self.x += random.randn() * self.noise + return self.x + + +def measure_dog (): + if not hasattr(measure_dog, "x"): + measure_dog.x = 0 + measure_dog.motion = 1 + + +if __name__ == '__main__': + + dog = dog_sensor(noise = 1) + for i in range(10): + print (dog.sense()) + + + + diff --git a/gaussian.py b/gaussian.py index 60ae39f..5ac2999 100644 --- a/gaussian.py +++ b/gaussian.py @@ -1,6 +1,6 @@ import numpy as np import math - +import matplotlib.pyplot as plt def _to_array(x): """ returns any of a scalar, matrix, or array as a 1D numpy array @@ -63,6 +63,14 @@ def multivariate_gaussian (x, mu, cov): fprime = (x - mu)**2 return frac * np.exp(-0.5*np.dot(fprime, 1./np.diag(cov))) +def norm_plot (mean, var): + min_x = mean - var * 1.5 + max_x = mean + var * 1.5 + + xs = np.arange (min_x, max_x, 0.1) + ys = [gaussian (x,23,5) for x in xs] + plt.plot (xs,ys) + plt.show() if __name__ == '__main__': from scipy.stats import norm