From 43d6727995ccf65557a20c4e9685cd30fac43e1a Mon Sep 17 00:00:00 2001 From: Sylwester Arabas Date: Fri, 5 Jan 2018 17:51:36 +0200 Subject: [PATCH] Update 04-One-Dimensional-Kalman-Filters.ipynb --- 04-One-Dimensional-Kalman-Filters.ipynb | 632 +----------------------- 1 file changed, 3 insertions(+), 629 deletions(-) diff --git a/04-One-Dimensional-Kalman-Filters.ipynb b/04-One-Dimensional-Kalman-Filters.ipynb index e999d51..2eedd72 100644 --- a/04-One-Dimensional-Kalman-Filters.ipynb +++ b/04-One-Dimensional-Kalman-Filters.ipynb @@ -1,4 +1,4 @@ -{ +to { "cells": [ { "cell_type": "markdown", @@ -2164,7 +2164,7 @@ "source": [ "## Comparison with g-h and discrete Bayes Filters\n", "\n", - "Now is a good time to be understand the differences between these three filters in terms of how we model errors. For the g-h filter we modeled our measurements as shown in this graph:" + "Now is a good time to understand the differences between these three filters in terms of how we model errors. For the g-h filter we modeled our measurements as shown in this graph:" ] }, { @@ -2450,630 +2450,4 @@ "outputs": [ { "data": { - "image/png": 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Q5/Xq1euLj/tLIDg4mAEBARw1ahTd3d1ZoEAB8UHXJ2tarVZ8sP+XjXczGxn1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\nn5+fXLlyJd/PpKamynvvvSePPfaYdO/eXSIiIu54yai0Jr6UlJR87ZPc3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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sensor_var = 300**2\n", - "process_var = 2\n", - "process_model = (1, process_var)\n", - "pos = (0,500)\n", - "N = 1000\n", - "dog = DogSimulation(pos[0], 1, sensor_var, process_var)\n", - "zs = [dog.move_and_sense() for _ in range(N)]\n", - "ps = []\n", - "\n", - "for i in range(N):\n", - " prior = predict(pos, process_model) \n", - " pos = update(prior, (zs[i], sensor_var))\n", - " ps.append(pos[0])\n", - "\n", - "book_plots.plot_measurements(zs, lw=1)\n", - "book_plots.plot_filter(ps)\n", - "plt.legend(loc=4);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? \n", - "\n", - "We get a nearly straight line because our process error is small. A small process error tells the filter that the prediction is very trustworthy, and the prediction is a straight line, so the filter outputs a nearly straight line. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example: Incorrect Process Variance\n", - "\n", - "That last filter looks fantastic! Why wouldn't we set the process variance very low, as it guarantees the result will be straight and smooth?\n", - "\n", - "The process variance tells the filter how much the system is changing over time. If you lie to the filter by setting this number artificially low the filter will not be able to react to changes that are happening. Let's have the dog increase his velocity by a small amount at each time step and see how the filter performs with a process variance of 0.001 m$^2$." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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FihU5fPgwc+fOZfPmzeTm5tKhQwfeeecdGjVqdN/urTySQEMIIcQjIyIigmXLlnHy5Emc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\nLAwhBJs3b+ann37C1taWzz//nG7duhEcHExgYOBtx41CQ0NZtWoVbm5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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sensor_var = 20\n", - "process_var = .001\n", - "process_model = (1, process_var)\n", - "pos = (0,500)\n", - "N = 100\n", - "dog = DogSimulation(pos[0], 1, sensor_var, process_var*10000)\n", - "zs, ps = [], []\n", - "for _ in range(N):\n", - " dog.velocity += 0.04\n", - " zs.append(dog.move_and_sense())\n", - "\n", - "for z in zs:\n", - " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", - "\n", - "book_plots.plot_measurements(zs, lw=1)\n", - "book_plots.plot_filter(ps)\n", - "plt.legend(loc=4);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is easy to see that the filter is not correctly responding to the measurements. The measurements clearly indicate that the dog is changing speed but the filter has been told that it's predictions are nearly perfect so it almost entirely ignores them. I encourage you to adjust the amount of movement in the dog vs process variance. We will also be studying this topic much more in the later chapters. The key point is to recognize that math requires that the variances correctly describe your system. The filter does not 'notice' that it is diverging from the measurements and correct itself. It computes the Kalman gain from the variance of the prior and the measurement, and forms the estimate depending on which is more accurate." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example: Bad Initial Estimate\n", - "\n", - "\n", - "Now let's look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000 meters. Can the filter recover from a 1000 meter error?" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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wYAGHDh0CYMmSJSQnJ+faPiMjg+PHj7Njxw4uXbr0r5f3URqNBkdHR4NqYADq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\n7CUuXEtm8+bN9OnTh+TkZObOnQtA8+bN8x33Wg1bfhrdlOFrTtBn2Z9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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sensor_var = 5**2\n", - "process_var = 2\n", - "pos = (1000, 500)\n", - "process_model = (1, process_var)\n", - "N = 100\n", - "dog = DogSimulation(0, 1, sensor_var, process_var)\n", - "zs = [dog.move_and_sense() for _ in range(N)]\n", - "ps = []\n", - "\n", - "for z in zs:\n", - " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", - "\n", - "book_plots.plot_measurements(zs, lw=1)\n", - "book_plots.plot_filter(ps)\n", - "plt.legend(loc=4);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma^2=5^2$) after only the first step we have changed our position estimate from 1000 m to roughly 50 m. After another 5-10 measurements we have converged to the correct value. This is how we get around the chicken and egg problem of initial guesses. In practice we would likely assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges so long as the filter variances are chosen to match the actual process and measurement variances." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Example: Large Noise and Bad Initial Estimate\n", - "\n", - "What about the worst of both worlds, large noise and a bad initial estimate?" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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mZ6vMh7JK/+abb5iQkJBi4a1WrVoJK41CnhRS5eXlxQYNGggLCmB0s1y4cEFU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\nPKhTpw7Tpk0r9Pump6dz+vRpM3236Rvl0KpKi1JqE5AgIh8opfyBQ9itJ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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sensor_var = 30000\n", - "process_var = 2\n", - "pos = (1000, 500)\n", - "process_model = (1, process_var)\n", - "\n", - "N = 1000\n", - "dog = DogSimulation(0, 1, sensor_var, process_var)\n", - "zs = [dog.move_and_sense() for _ in range(N)]\n", - "ps = []\n", - "\n", - "for z in zs:\n", - " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", - "\n", - "book_plots.plot_measurements(zs, lw=1)\n", - "book_plots.plot_filter(ps)\n", - "plt.legend(loc=4);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This time the filter struggles. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", - "\n", - "Finally, let's implement the suggestion of using the first measurement as the initial position." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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bt2+vqJwrmxuWLFki2ozrtOTPn18wc61WS1tbW7q6urJ3794iB0flypXZo0cP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\n1E6upGnakeoF/53c3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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sensor_var = 30000\n", - "process_var = 2\n", - "process_model = (1, process_var)\n", - "N = 1000\n", - "dog = DogSimulation(0, 1, sensor_var, process_var)\n", - "zs = [dog.move_and_sense() for _ in range(N)]\n", - "\n", - "pos = (zs[0], 500)\n", - "ps = []\n", - "for z in zs:\n", - " prior = predict(pos, process_model) \n", - " pos = update(prior, (z, sensor_var))\n", - " ps.append(pos[0])\n", - "\n", - "book_plots.plot_measurements(zs, lw=1)\n", - "book_plots.plot_filter(ps)\n", - "plt.legend(loc='best');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on the amount of noise in the first measurement. A large amount of noise causes the initial estimate to be far from the dog's position.\n", - "\n", - "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser range finders, GPS satellites, computer vision, and so on. None have the enormous errors in these examples. A reasonable variance for a cheap thermometer might be 0.2 C$^{\\circ 2}$, and our code is using 30,000 C$^{\\circ 2}$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise: Interactive Plots\n", - "\n", - "Implement the Kalman filter using Jupyter Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the **Gaussians** chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have written the boilerplate for this; you fill in the required code." - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "7cdc56e40a90494cbaca4f5fb4d145e7", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "A Jupyter Widget" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from ipywidgets import interact, FloatSlider\n", - "\n", - "def plot_kalman_filter(start_pos, \n", - " sensor_noise, \n", - " velocity, \n", - " process_noise):\n", - " plt.figure()\n", - " # your code goes here\n", - " pass;\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10, 10), \n", - " sensor_noise=FloatSlider(value=5, min=0, max=100), \n", - " velocity=FloatSlider(value=1, min=-2., max=2.), \n", - " process_noise=FloatSlider(value=5, min=0, max=100.));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution\n", - "\n", - "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Process noise is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders." - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "c60f71af532746729d0fc85ce753d6c3", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "A Jupyter Widget" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from numpy.random import seed \n", - "from ipywidgets import interact, FloatSlider\n", - "\n", - "def plot_kalman_filter(start_pos, \n", - " sensor_noise, \n", - " velocity,\n", - " process_noise):\n", - " N = 20\n", - " zs, ps = [], [] \n", - " seed(303)\n", - " dog = DogSimulation(start_pos, velocity, sensor_noise, process_noise)\n", - " zs = [dog.move_and_sense() for _ in range(N)]\n", - " pos = (0., 1000.) # mean and variance\n", - " process_model = (velocity, process_noise)\n", - " \n", - " for z in zs: \n", - " pos = predict(pos, process_model)\n", - " pos = update(pos, (z, sensor_noise))\n", - " ps.append(pos[0])\n", - "\n", - " plt.figure()\n", - " plt.plot(zs, c='k', marker='o', linestyle='', label='measurement')\n", - " plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n", - " plt.legend(loc=4);\n", - "\n", - "interact(plot_kalman_filter,\n", - " start_pos=(-10, 10), \n", - " sensor_noise=FloatSlider(value=5, min=0., max=100, continuous_update=False), \n", - " velocity=FloatSlider(value=1, min=-2., max=2., continuous_update=False), \n", - " process_noise=FloatSlider(value=.1, min=0, max=40, continuous_update=False));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Exercise - Nonlinear Systems\n", - "\n", - "Our equations for the Kalman filter are linear:\n", - "\n", - "$$\\begin{aligned}\n", - "\\mathcal{N}(\\bar\\mu,\\, \\bar\\sigma^2) &= \\mathcal{N}(\\mu,\\, \\sigma^2) + \\mathcal{N}(\\mu_\\mathtt{move},\\, \\sigma^2_\\mathtt{move})\\\\\n", - "\\mathcal{N}(\\mu,\\, \\sigma^2) &= \\mathcal{N}(\\bar\\mu,\\, \\bar\\sigma^2) \\times \\mathcal{N}(\\mu_\\mathtt{z},\\, \\sigma^2_\\mathtt{z})\n", - "\\end{aligned}$$\n", - "\n", - "Do you suppose that this filter works well or poorly with nonlinear systems?\n", - "\n", - "Implement a Kalman filter that uses the following equation to generate the measurement value\n", - "\n", - "```python\n", - "for i in range(100):\n", - " z = math.sin(i/3.) * 2\n", - "```\n", - " \n", - "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "#enter your code here." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Solution" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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A+6pVKWBX0hwd3apgx/nHCpHzFvRSeKmA8qCs+LtPI1iYGqLRhN0YvfYcnr2P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\nt3Il7X8vXkxGRW2sgJSkUycyvqQ6ILYambfcQsG+8+ZRfIUtpaWXLKE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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import math\n", - "\n", - "sensor_var = 30\n", - "process_var = 2\n", - "pos = (100,500)\n", - "process_model = (1, process_var)\n", - "\n", - "zs, ps = [], []\n", - "\n", - "for i in range(100):\n", - " pos = predict(pos, process_model)\n", - "\n", - " z = math.sin(i/3.)*2 + randn()*1.2\n", - " zs.append(z)\n", - " \n", - " pos = update(pos, (z, sensor_var))\n", - " ps.append(pos[0])\n", - "\n", - "plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", - "plt.plot(ps, c='#004080', label='filter')\n", - "plt.legend(loc='best');" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Discussion\n", - "\n", - "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", - "\n", - "If we recall the **g-h Filter** chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", - "\n", - "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Later chapters are devoted to this problem." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Fixed Gain Filters\n", - "\n", - "Embedded computers usually have extremely limited processors. Many do not have floating point circuitry. These simple equations can impose a heavy burden on the chip. This is less true as technology advances, but do not underestimate the value of spending one dollar less on a processor when you will be buying millions of them.\n", - "\n", - "In the example above the variance of the filter converged to a fixed value. This will always happen if the variance of the measurement and process is a constant. You can take advantage of this fact by running simulations to determine what the variance converges to. Then you can hard code this value into your filter. So long as you initialize the filter to a good starting guess (I recommend using the first measurement as your initial value) the filter will perform very well. For example, the dog tracking filter can be reduced to this:\n", - "\n", - "```python\n", - "def update(x, z):\n", - " K = .13232 # experimentally derived Kalman gain\n", - " y = z - x # residual\n", - " x = x + K*y # posterior\n", - " return x\n", - " \n", - "def predict(x):\n", - " return x + vel*dt\n", - "```\n", - "\n", - "I used the Kalman gain form of the update function to emphasize that we do not need to consider the variances at all. If the variances converge to a single value so does the Kalman gain. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## FilterPy's Implementation\n", - "\n", - "FilterPy implements `predict()` and `update()`. They work not only for the univariate case developed in this chapter, but the more general multivariate case that we learn in subsequent chapters. Because of this their interface is slightly different. They do not take Gaussians as tuples, but as two separately named variables.\n", - "\n", - "`predict()` takes several arguments, but we will only need to use these four:\n", - "\n", - "```python\n", - "predict(x, P, u, Q)\n", - "```\n", - "\n", - "`x` is the state of the system. `P` is the variance of the system. `u` is the movement due to the process, and `Q` is the noise in the process. You will need to used named arguments when you call `predict()` because most of the arguments are optional. The third argument to `predict()` is **not** `u`.\n", - "\n", - "These may strike you as terrible names. They are! As I already mentioned they come from a long history of control theory, and every paper or book you read will use these names. So, we just have to get used to it. Refusing to memorize them means you will never be able to read the literature.\n", - "\n", - "Let's try it for the state $\\mathcal N(10, 3)$ and the movement $\\mathcal N(1, 4)$. We'd expect a final position of 11 (10+1) with a variance of 7 (3+4)." - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(11, 7.000)" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import filterpy.kalman as kf\n", - "kf.predict(x=10, P=3., u=1, Q=4)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`update` also takes several arguments, but for now you will be interested in these four:\n", - " \n", - "```python\n", - "update(x, P, z, R)\n", - "```\n", - " \n", - "As before, `x` and `P` are the state and variance of the system. `z` is the measurement, and `R` is the measurement variance. Let's perform the last predict statement to get our prior, and then perform an update:" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(11.364, 4.455)" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "x, P = kf.predict(x=10, P=3., u=1, Q=2**2)\n", - "x, P = kf.update(x=x, P=P, z=12, R=3.5**2)\n", - "x, P" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I gave it a noisy measurement with a big variance, so the estimate remained close to the prior of 11.\n", - "\n", - "One final point. I did not use the variable name `prior` for the output of the predict step. I will not use that variable name in the rest of the book. The Kalman filter equations just use $\\mathbf x$. Both the prior and the posterior are the estimated state of the system, the former is the estimate before the measurement is incorporated, and the latter is after the measurement has been incorporated." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Summary\n", - "\n", - "The Kalman filter that we describe in this chapter is a special, restricted case of the more general filter we will learn next. Most texts do not discuss this one dimensional form. However, I think it is a vital stepping stone. We started the book with the g-h filter, then implemented the discrete Bayes filter, and now implemented the one dimensional Kalman filter. I have tried to show you that each of these filters use the same algorithm and reasoning. The mathematics of the Kalman filter that we will learn shortly is fairly sophisticated, and it can be difficult to understand the underlying simplicity of the filter. That sophistication comes with significant benefits: the generalized filter will markedly outperform the filters in this chapter.\n", - "\n", - "This chapter takes time to assimilate. To truly understand it you will probably have to work through this chapter several times. I encourage you to change the various constants in the code and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of the position of a dog in a hallway, the position of an aircraft in the sky, or the temperature of a chemical reaction chamber. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians together updates your belief. \n", - "\n", - "Most of all, spend enough time with the **Full Description of the Algorithm** section to ensure you understand the algorithm and how it relates to the g-h filter and discrete Bayes filter. There is just one 'trick' here - selecting a value somewhere between a prediction and a measurement. Each algorithm performs that trick with different math, but all use the same logic." - ] - } - ], - "metadata": { - "anaconda-cloud": {}, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.3" - }, - "widgets": { - "state": { - "58ed37dc23fe44cc9a0e20ffc9c47414": { - "views": [ - { - "cell_index": 79 - } - ] - }, - "8b8fb12fbc4048a0af7d29dfc57d5fb9": { - "views": [ - { - "cell_index": 29 - } - ] - }, - "ec6802d3ecf14e67bbcf34b40aa0e3c4": { - "views": [ - { - "cell_index": 77 - } - ] - } - }, - "version": "1.2.0" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} + "image/png": 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Q5/Xq1euLj/tLIDg4mAEBARw1ahTd3d1ZoEAB8UHXJ2tarVZ8sP+XjXczGxn1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\n/vz5J8NPxqxX3e7p6Ynbt2/zLIk+ffpIWoJExIW