{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "from __future__ import division, print_function\n", "import book_format\n", "book_format.load_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last chapter we discussed the difficulties that nonlinear systems pose. This nonlinearity can appear in two places. It can be in our measurements, such as a radar that is measuring the slant range to an object. Slant range requires you to take a square root to compute the x,y coordinates:\n", "\n", "$$x=\\sqrt{slant^2 - altitude^2}$$\n", "\n", "The nonlinearity can also occur in the process model - we may be tracking a ball traveling through the air, where the effects of gravity and air drag lead to highly nonlinear behavior. The standard Kalman filter performs poorly or not at all with these sorts of problems.\n", "\n", "In the last chapter I showed you a plot like this. I have altered the equation somewhat to emphasize the effects of nonlinearity." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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BQerPeZtyIiLzwJHqBiqtLMS+lLUorsivdbvczh1yOzfYWTshsEUYWjj5NKsi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\nxbNWJnSdOtUU3/A7h3doglbLtjozuatlDG1N8mq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.random import normal\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from nonlinear_plots import plot_nonlinear_func\n", "\n", "gaussian=(0., 1.)\n", "data = normal(loc=gaussian[0], scale=gaussian[1], size=500000)\n", "\n", "def g(x):\n", " return (np.cos(4*(x/2 + 0.7))) - 1.3*x\n", "\n", "with book_format.figsize(y=5):\n", " plot_nonlinear_func(data, g, gaussian=gaussian)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I generated this by taking 500,000 samples from the input, passing it through the nonlinear transform, and building a histogram of the result. We call these points **sigma points**. From the output histogram we can compute a mean and standard deviation which would give us an updated, albeit approximated Gaussian.\n", "\n", "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a 'Monte Carlo' approach, and it used by some Kalman filter designs, such as the **Ensemble filter** and **particle filter**. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the function is, as long as we sample with enough sigma points we will build an accurate output distribution.\n", "\n", "\"Enough points\" is the rub. The graph above was created with 500,000 sigma points, and the output is still not smooth. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you only needed 500 points for 1 dimension, you'd need 500 squared, or 250,000 points for two dimensions, 500 cubed, or 125,000,000 points for three dimensions, and so on. So while this approach does work, it is very computationally expensive. The Unscented Kalman filter uses a similar technique but reduces the amount of computation needed by a drastic amount by using a deterministic method of choosing the points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sigma Points - Sampling from the Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the problem in terms of a 2D covariance ellipse. I choose 2D merely because it is easy to plot; this will extend to any number of dimensions. Assuming some arbitrary nonlinear function, we will take random points from the first covariance ellipse, pass them through the nonlinear function, and plot their new position. Then we can compute the the mean and covariance of the transformed points, and use that as our estimate of the mean and probability distribution." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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wWq243e7YfaJtyKJMJhMOhwO/38/48eMpLi5m3rx5TJ06VUpsblA4HGbTrk1k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\n7ASG6V2Wzt4G/p5HK+FPB8W6QmJrB0X9w2m4aOmgqCgKmqY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import ukf_internal\n", "ukf_internal.show_2d_transform()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the left we show an ellipse depicting the $1\\sigma$ distribution of two state variables. The arrows show how several randomly sampled points might be transformed by some arbitrary nonlinear function to a new distribution. The ellipse on the right is drawn semi-transparently to indicate that it is an *estimate* of the mean and variance of this collection of points - if we were to sample, say, a million points the shape of the points might be very far different than an ellipse. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at that by running a bunch of points through a nonlinear function. We will write a function to pass randomly generated points with a Gaussian distribution through the system\n", "\n", "$$\\begin{aligned}x&=x+y\\\\\n", "y &= 0.1x^2 + y^2\\end{aligned}$$ \n", "\n", "for the mean and covariance \n", "\n", "$$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}, \n", "\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean x=-0.022, y=43.053\n" ] }, { "data": { "image/png": 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kk0nVp2VZKlZTXrvX63W8L05xsbkmBCzqniuz3Ol+F4uOcq0bGBgYGBgYolmG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u65527FcBO0b+94fiBMUOmjVCppbW1N6+vrocYwDUNckUTdJINd2k8sRSXtdDohu511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\nOEYzS8meVi5p2r4nfZ+QkJBwO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy.random import multivariate_normal\n", "from nonlinear_plots import plot_monte_carlo_mean\n", "\n", "def f(x,y):\n", " return x+y, .1*x**2 + y*y\n", " \n", "mean = (0, 0)\n", "p = np.array([[32, 15], [15., 40.]])\n", "\n", "# Compute linearized mean\n", "mean_fx = f(*mean)\n", "\n", "#generate random points\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=10000).T\n", "plot_monte_carlo_mean(xs, ys, f, mean_fx, 'Linearized Mean');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot shows the strong nonlinearity that occurs with this function, and the large error that would result if we linearized the function at (0,0), which is what filters like the Extended Kalman filters do (we will be learning this in the next chapter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing Sigma Points\n", "\n", "I used 10,000 randomly selected sigma points to generate this solution. While the computed mean is quite accurate, computing 10,000 points for every update would cause our filter to be very slow. So, what would be fewest number of sampled points that we can use, and what kinds of constraints does this problem formulation put on the points? We will assume that we have no special knowledge about the nonlinear function as we want to find a generalized algorithm that works for any function.\n", "We can visualize this algorithm using the following diagram." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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ZBsaD/Hj7iofaB+zz+fj000955513+OSTT0ilUqTTaRKJbMCy2WwYhkF5eTkv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\nbVte2hnuxEQwylR8CqdDwW4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oHpokFBqlo+8kj1Q8gXYftxvMBoqiUFJSQklJfvaVWpaJ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\ny8zf/PGDOT0SKh6Ps3//fr7//e/zzz/4IdFYlFQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_transform()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's consider the simplest possible case and see if it offers any insight. The simplest possible system is the *identity function*. In mathematical notation this is $f(x) = x$. It should be clear that if our algorithm does not work for the identity function then the filter will never converge. In other words, if the input is 1 (for a one dimensional system), the output must also be 1. If the output was different, such as 1.1, then when we fed 1.1 into the transform at the next time step, we'd get out yet another number, maybe 1.23. The filter would run away (diverge). \n", "\n", "The fewest number of points that we can use is one per dimension. This is the number that the linear Kalman filter uses. The input to a Kalman filter for the distribution $\\mathcal{N}(\\mu,\\sigma^2)$ is $\\mu$ itself. So while this works for the linear case, it is not a good answer for the nonlinear case.\n", "\n", "Perhaps we can use one point per dimension, but altered somehow. However, if we were to pass some value $\\mu+\\Delta$ into the identity function $f(x)=x$ it would not converge, so this is not a possible algorithm. We must conclude that a one point sample will not work.\n", "\n", "So, what is the next lowest number we can choose? Consider the fact that Gaussians are symmetric, and that we probably want to always have one of our sample points be the mean of the input for the identity function to work. Two points would require us to select the mean, and then one other point. That one other point would introduce an asymmetry in our input that we probably don't want. It would be very difficult to make this work for the identity function $f(x)=x$.\n", "\n", "The next lowest number is 3 points. 3 points allows us to select the mean, and then one point on each side of the mean, as depicted on the chart below." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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jxsr4hSgsVgIAjA2bYcrgt9Fcbi5yMmroPJ07YFSvqUI7/UwKdqVtFDERETUG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\nmDb0/7D3WDy27F2FSrUKanUVtqf+iMO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JoivfVBzCZ+e7XrrwfguUKxGi7ANVJ5fk+gRH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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_3_sigma_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we can take those three points, pass them through a nonlinear function f(x), and compute a new mean and variance. We can compute the mean as the average of the 3 points, but that is not very general. For example, for a very nonlinear problem we might want to weight the center point much higher than the outside points, or we might want to weight the outside points higher if the distribution is not Gaussian. A more general approach is to compute the mean as $\\mu = \\sum_i w_if(\\mathcal{X}_i)$.\n", "\n", "\n", "For this to work for identity we will want the sums of the weights for the mean to equal one. We can always come up with counterexamples, but in general if the sum is greater or less than one the sampling will not yield the correct output. Given that, we then have to select *sigma points* $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the input Gaussian. It is possible to use different weights for the mean ($w^m$) and for the variance ($w^c$). So we can write\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{Constraints:}\\\\\n", "\\sum_i{w_i^m}&=1 \\\\\n", "\\mu &= \\sum_i w_i^mf(\\mathcal{X}_i) \\\\\n", "\\Sigma &= \\sum_i w_i^c{(f(\\mathcal{X})_i-\\mu)(f(\\mathcal{X})_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "If we look at this is should be clear that there is no one unique answer - the problem is unconstrained. For example, if you choose a smaller weight for the point at the mean for the input, you could compensate by choosing larger weights for the rest of the $\\mathcal{X}$, and vice versa. We can use different weights for the mean and variances, or the same weights. Indeed, these equations do not require that any of the points be the mean of the input at all, though it seems 'nice' to do so, so to speak.\n", "\n", "But before we go on I want to make sure the idea is clear. We are choosing 3 points for each dimension in our covariances. That choice is *entirely deterministic*. Below are three different examples for the same covariance ellipse." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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aGhr42te+utUrGAqF8Ps/fmVSOV6ttNtSagKnp0BDtdd095TmCypX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\nD0l8jPtbmd2vWv1UqlZ5V2ox8Z2njtDRDguxe9L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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_selections()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The points do not lie along the major and minor axis of the ellipse; nothing in the constraints above require me to do that. Furthermore, in each case I show the points evenly spaced; again, the constraints above do not require that. \n", "\n", "We can see that the arrangement and spacing of the sigma points will affect how we sample our distribution. Points that are close together will sample local effects, and thus probably work better for very nonlinear problems. Points that are far apart, or far off the axis of the ellipse will sample non-local effects and non Gaussian behavior. However, by varying the weights used for each point we can mitigate this. If the points are far from the mean but weighted very slightly we will incorporate some of the knowledge about the distribution without allowing the nonlinearity of the problem to create a bad estimate. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Van der Merwe's Scaled Sigma Point Algorithm\n", "There are several published ways for selecting the sigma points for the Unscented Kalman filter, and you are free to invent your own. However, since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1] because it performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", "\n", "Before we work through the derivation, let's look at an example. I will plot the sigma points on top of a covariance ellipse showing the first and second standard deviations, and size them based on the weights assigned to them." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Ti/lDXakUV1bIJrAci3AYSJItxCRs7+612uiwZq2RSUecnMvJhBRxRZmUwSgc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\nWS2WOdcsHvf5i7NCkuwpSMb140qHNO6J2zcYeWzt27TMFq1imQutkgR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "3.91\n" ] } ], "source": [ "ukf_internal.plot_sigma_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the sigma points lie between the first and second deviation, and that the larger $\\alpha$ spreads the points out further. Furthermore, the larger $\\alpha$ weighs the mean (center point) higher than the smaller $\\alpha$, and weighs the rest of the sigma points less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know *how* these weights and sigma points are selected yet, but the choices look reasonable.\n", "\n", "Van der Merwe's formulation uses 3 parameters to control how the sigma points are distributed and weighted: $\\alpha$, $\\beta$, and $\\kappa$. We will go into detail with these later. For now, $\\beta=2$ is a good choice for Gaussian problems, $\\kappa=3-N$ is a good choice for $\\kappa$, and $0 \\le \\alpha \\le 1$ is an appropriate choice for $\\alpha$, where a larger value spreads the sigma points further from the mean.\n", "\n", "Our first sigma point is always going to be the mean of our input. This is the sigma point displayed in the center of the ellipses in the diagram above. We will call this $\\boldsymbol{\\chi}_0$. So,\n", "\n", "$$ \\mathcal{X}_0 = \\mu$$\n", "\n", "For notational convenience we define $\\lambda = \\alpha^2(n+\\kappa)-n$. Then the remaining sigma points are computed as\n", "\n", "$$ \n", "\\begin{aligned}\n", "\\boldsymbol{\\chi}_i &= \\mu + (\\sqrt{(n+\\lambda)\\Sigma})_i\\,\\,\\,\\, &\\text{for}\\text{ i=1 .. n} \\\\\n", "\\boldsymbol{\\chi}_i &= \\mu - (\\sqrt{(n+\\lambda)\\Sigma})_{i-n}\\,\\,\\,\\,\\, &\\text{for}\\text{ i=(n+1) .. 2n} \\\\\n", "\\end{aligned}$$\n", "\n", "In other words, we scale the covariance matrix by a constant, take the square root of it, and then to ensure symmetry both add and subtract if from the mean. We will discuss how you take the square root of a matrix later.\n", "\n", "Van der Merwe's forumation uses one set of weights for the means, and another set for the covariance. The weights for the mean of $\\mathcal{X}_0$ is computed as\n", "\n", "$$W^m_0 = \\frac{\\lambda}{n+\\lambda}$$\n", "\n", "The weight for the covariance of $\\mathcal{X}_0$ is\n", "\n", "$$W^c_0 = \\frac{\\lambda}{n+\\lambda} + 1 -\\alpha^2 + \\beta$$\n", "\n", "The weights for the rest of the sigma points $\\boldsymbol{\\chi}_1 ... \\boldsymbol{\\chi}_{2n}$ are the same for the mean and covariance. They are\n", "\n", "$$W^m_i = W^c_i = \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n$$\n", "\n", "It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to 1 standard deviation. However, there is an $n$ term in there - the more dimensions there are the more the points will be spread out and weighed less." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The update step converts the sigmas into measurement space via the `h(x)` function.\n", "\n", "\n", "$$\\mathcal{Z} = h(\\mathcal{Y})$$\n", "\n", "The mean and covariance of those points is computed with the unscented transform. The residual and Kalman gain is then computed. The cross variance is computed as:\n", "\n", "$$\\mathbf{P}_{xz} =\\sum W(\\mathcal{X}-x)(\\mathcal{X_z}-\\mathbf{x}_z)^\\mathsf{T}$$\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "$$\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\mathbf{P} = \\mathbf{P}^- - \\mathbf{PKP}_z\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This function can be implemented as follows, assuming it is a method of a class that stores the necessary matrices and data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The computation of the new mean and covariance is called the *unscented transform*. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Unscented Transform" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The unscented transform is the core of the algorithm yet it is remarkably simple. For each dimension in the state space we deterministically choose 3 sigma points and corresponding weights using the algorithm above. We pass the sigma points through the nonlinear function yielding a transformed set of points\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZBsaD/Hj7iofaB+zz+fj000955513+OSTT0ilUqTTaRKJbMCy2WwYhkF5eTkv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\nbVte2hnuxEQwylR8CqdDwW4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oHpokFBqlo+8kj1Q8gXYftxvMBoqiUFJSQklJfvaVWpaJ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\nir17/5rBwTfQ6SwUFrawYsXfUVjYPOV19oe7iFmP8ul7qnl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_transform(with_text=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then compute the new mean and covariance using these equations.\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_i w_i\\boldsymbol{\\mathcal{Y}}_i \\\\\n", "\\Sigma &= \\sum_i w_i{(\\boldsymbol{\\mathcal{Y}}_i-\\mu)(\\boldsymbol{\\mathcal{Y}}_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "These equations should be familar - they are the constraint equations we developed above. They perhaps don't look like much, but let's see an example of their power.\n", "\n", "Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now use 5 sigma points - we will pass them through the nonlinear function, and compute their mean with the unscented transform. This code is below. Under the comment `### create sigma points` I use code from FilterPy to generate the sigma points. It uses functionality which you will learn later in this chapter; pass by it for now. The key points are we generate 5 points deterministically, pass them through the nonlinear function, and then run the unscented transform on them to generate the estimated mean." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean x=-0.074, y=-0.566\n" ] }, { "data": { "image/png": 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fhsKIESPw/PPPY+7cuTYBYuHChejbt68ttGtvh3ad74VwIlJMhJEkLptq6NSf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\n8Prrr9ec63keXnvtNSxbtmwyY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import unscented_transform, MerweScaledSigmaPoints\n", "import scipy.stats as stats\n", "\n", "def f_nonlinear_xy(x, y):\n", " return np.array([x + y, .1*x**2 + y*y])\n", "\n", "mean = (0, 0)\n", "p = np.array([[32., 15],\n", " [15., 40.]])\n", "\n", "### create sigma points\n", "points = MerweScaledSigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n", "Wm, Wc = points.weights()\n", "sigmas = points.sigma_points(mean, p)\n", "\n", "### pass through nonlinear function\n", "sigmas_f = np.zeros((5, 2))\n", "for i in range(5):\n", " sigmas_f[i] = f_nonlinear_xy(sigmas[i, 0], sigmas[i ,1])\n", "\n", "### pass through unscented transform\n", "ukf_mean, _ = unscented_transform(sigmas_f, Wm, Wc)\n", "\n", "#generate random points\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=5000).T\n", "\n", "plot_monte_carlo_mean(xs, ys, f, ukf_mean, 'UKF Mean')\n", "plt.subplot(121)\n", "plt.scatter(sigmas[:,0], sigmas[:,1], c='r', s=40);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I find this result remarkable. Using only 5 points we were able to compute the mean with amazing accuracy. The error in x is only 0.054, and the error in y is 0.408. In contrast, a linearized approach (used by the predominant EKF filter) gave an error of over 43 in y. I told you to ignore the code to generate the sigma points, but if you look at it you'll see that it has no knowledge of the nonlinear function, only of the mean and covariance of our initial distribution. The same 5 sigma points would be generated if we had a completely different nonlinear function. \n", "\n", "I will admit to choosing a nonlinear function that makes the performance of the unscented tranform striking compared to the EKF. But the physical world is filled with very nonlinear behavior, and the UKF takes it in stride. You will see in the next chapter how more traditional techniques struggle with strong nonlinearities. This graph is the foundation of why I advise you to use the UKF or similar modern technique whenever possible.\n", "\n", "> The UKF belongs to a family of filters called sigma point filters. By the end of this chapter you will be prepared to do a literature search and learn about the various sigma point filters that have been invented." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Unscented Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can present the entire Unscented Kalman filter algorithm. As discussed earlier assume that there is a function $f(x, dt)$ that performs the state transition for our filter - it predicts the next state given the current state. Also assume there is a measurement function $h(x)$ - it takes the current state and computes what measurement that state corresponds to. These are nonlinear forms of the $\\mathbf{F}$ and $\\mathbf{H}$ matrices used by the linear Kalman filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As with the linear Kalman filter, the UKF's predict step computes the mean and covariance of the system for the next epoch using the process model. However, the computation is quite different.\n", "\n", "First, we generate the weights and sigma points as specified above.\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X} &= sigma\\_function(\\bf{\\mu}, \\bf{\\Sigma}) \\\\\n", "W &= weight\\_function()\\end{aligned}$$\n", "\n", "We pass each sigma point through the function f. This projects the sigma points forward in time according to our process model.\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we compute the predicted mean and covariance using the *unscented transform *on the transformed sigma points. I've dropped the subscript $i$ for readability.\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{\\mu}^- &= \\sum w^m\\boldsymbol{\\mathcal{Y}} \\\\\n", "\\mathbf{\\Sigma}^- &= \\sum w^c({\\boldsymbol{\\mathcal{Y}}-\\bf{\\mu}^-)(\\boldsymbol{\\mathcal{Y}}-\\bf{\\mu}^-)^\\mathsf{T}} + \\mathbf{Q}\n", "\\end{aligned}\n", "$$\n", "\n", "This computes the mean and covariance represented by the green ellipse above, and corresponds with the linear Kalman filter equations of\n", "\n", "$$ \\begin{aligned}\n", "\\mathbf{x}^- &= \\mathbf{Fx}\\\\\n", "\\mathbf{P}^- &= \\mathbf{FPF}^\\mathsf{T}+\\mathbf{Q}\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can perform the update step of the filter. Recall that Kalman filters perform the update state in measurement space. So, the first thing we do is convert the sigma points from the predict step into measurements using the $h(x)$ function that you define.\n", "\n", "$$\\boldsymbol{\\mathcal{Z}} = h(\\boldsymbol{\\mathcal{Y}})$$\n", "\n", "Now we can compute the mean and covariance of these points using the unscented transform.\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{\\mu}_z &= \\sum w^m\\boldsymbol{\\mathcal{Z}} \\\\\n", "\\mathbf{P}_z &= \\sum w^c{(\\boldsymbol{\\mathcal{Z}}-\\mu^-)(\\boldsymbol{\\mathcal{Z}}-\\mu^-)^\\mathsf{T}} + \\mathbf{R}\n", "\\end{aligned}\n", "$$\n", "\n", "The $z$ subscript denotes that these are the mean and covariance for the measurements.\n", "\n", "All that is left is to compute the residual and Kalman gain. The residual is trivial to compute:\n", "\n", "$$\\mathbf{y} = \\boldsymbol{\\mathcal{Z}} - \\boldsymbol{\\mu}_z$$\n", "\n", "\n", "The Kalman gain is not much worse. We have to compute the cross variance of the state and the measurements, which we state without proof to be: \n", "\n", "$$\\mathbf{P}_{xz} =\\sum w^c(\\boldsymbol{\\chi}-\\mu)(\\boldsymbol{\\mathcal{Z}}-\\mathbf{\\mu}_z)^\\mathsf{T}$$\n", "\n", "And then the Kalman gain is defined as\n", "\n", "$$K = \\mathbf{P}_{xz} \\mathbf{P}_z^{-1}$$\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "$$\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\hat{\\mathbf{P}} = \\mathbf{\\Sigma}^- - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. We convert the mean and covariance into measurement space, add the measurement error into the measurement covariance, compute the residual and kalman gain, compute the new state estimate as the old estimate plus the residual times the Kalman gain, and then convert both back into state space. The linear algebra is slightly different from the linear Kalman filter, but the algorithm is the same." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the UKF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now ready to consider implementing an unscented Kalman filter. All of the math is above is already implemented in FilterPy, and you are perhaps a bit lost at this point, so lets launch into solving some problems so you can gain confidence in how easy the UKF actually is. Later we will revisit how the UKF is implemented in Python.\n", "\n", "\n", "Let's start by solving a problem you already know how to do. Although the UKF was designed for nonlinear problems, it works fine on linear problems. In fact, it is guaranteed to get the same result as the linear Kalman filter for linear problems. We will write a solver for the linear problem of tracking using a constant velocity model in 2D. This will allows us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", "\n", "To design a linear Kalman filter you need to design the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times already so let me present a design to you without a lot of comment. We want a constant velocity model, so we can define $\\bf{x}$ to be\n", "\n", "$$ \\mathbf{x} = \\begin{bmatrix}x & \\dot{x} & y & \\dot{y} \\end{bmatrix}^\\mathsf{T}$$.\n", "\n", "With this ordering of state variables we can define our state transition model to be\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix}1 & \\Delta t & 0 & 0 \\\\\n", "0&1&0&0 \\\\\n", "0&0&1&\\Delta t\\\\\n", "0&0&0&1\n", "\\end{bmatrix}$$\n", "\n", "which implements the Newtonian equation\n", "\n", "$$x_k = x_{k-1} + \\dot{x}_{k-1}\\Delta t$$\n", "\n", "Our sensors provide position measurements but not velocity, so the measurement function is\n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}1&0&0&0 \\\\ 0&0&1&0\n", "\\end{bmatrix}$$\n", "\n", "Let's say our sensor gives positions in meters with an error of $1\\sigma=0.3$ meters in both the *x* and *y* coordinates. This gives us a measurement noise matrix of \n", "\n", "$$\\mathbf{R} = \\begin{bmatrix}0.3^2 &0\\\\0 & 0.3^2\\end{bmatrix}$$\n", "\n", "Finally, let's assume that the process noise can be represented by the discrete white noise model - that is, that over each time period the acceleration is constant. We can use `FilterPy`'s `Q_discrete_white_noise()` method to create this matrix for us, but for review the matrix is\n", "\n", "$$\\mathbf{Q} = \\begin{bmatrix}\n", "\\frac{1}{4}\\Delta t^4 & \\frac{1}{2}\\Delta t^3 \\\\\n", "\\frac{1}{2}\\Delta t^3 & \\Delta t^2\\end{bmatrix} \\sigma^2$$\n", "\n", "Our implementation might look like this:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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3K0H9xIkTOnDggPLz8yc8NW/fvn165plndPDgQWVmZuqJJ57QrbfeqrKyMgUF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\nEgR1aMw+qlMlb+uPp19VW0/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import KalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", "from numpy import random\n", "from numpy.random import randn\n", "\n", "sigma_x, sigma_y = .3, .3\n", "dt = 1.0\n", "\n", "random.seed(1234)\n", "kf = KalmanFilter(4, 2)\n", "kf.x = np.array([0., 0., 0., 0.])\n", "kf.R = np.diag([sigma_x**2, sigma_y**2])\n", "kf.F = np.array([[1, dt, 0, 0], \n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])\n", "kf.H = np.array([[1, 0, 0, 0],\n", " [0, 0, 1, 0]])\n", " \n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "\n", "zs = [np.array([i + randn()*sigma_x, i + randn()*sigma_y]) for i in range(100)] \n", "xs, _, _, _ = kf.batch_filter(zs)\n", "plt.plot(xs[:, 0], xs[:, 2]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should hold no surprises for you. Now let's implement this filter as an Unscented Kalman filter. Again, this is purely for educational purposes; using a UKF for a linear filter confers no benefit.\n", "\n", "The equations of the UKF are implemented for you with the `FilterPy` class `UnscentedKalmanFilter`; all you have to do is specify the matrices and the nonlinear functions `f(x)` and `h(x)`. `f(x)` implements the state transition function that is implemented by the matrix $\\mathbf{F}$ in the linear filter, and `h(x)` implements the measurement function implemented with the matrix $\\mathbf{H}$. In nonlinear problems these functions are nonlinear, so we cannot use matrices to specify them.\n", "\n", "For our linear problem we can define these functions to implement the linear equations. The function `f(x)` takes the signature `def f(x,dt)` and `h(x)` takes the signature `def h(x)`. Below is a reasonable implementation of these two functions. Each is expected to return a 1-D NumPy array with the result." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "def f_cv(x, dt):\n", " \"\"\" state transition function for a constant velocity aircraft\"\"\"\n", " \n", " F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])\n", " return np.dot(F, x)\n", "\n", "def h_cv(x):\n", " return np.array([x[0], x[2]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You need to tell the filter how to compute the sigma points and weights. We gave the Van der Merwe's scaled unscented transform version above, but there are many different choices. FilterPy uses a `SigmaPoints` class which must implement two methods:\n", "\n", " def sigma_points(self, x, P)\n", " def weights(self)\n", " \n", "FilterPy provides the class `MerweScaledSigmaPoints`, which implements the sigma point algorithm in this chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Other than these two functions, everything else is nearly the same. When you create the UKF you will pass in the two functions and sigma point class object like so:\n", "\n", " from filterpy.kalman import MerweScaledSigmaPoints\n", " from filterpy.kalman import UnscentedKalmanFilter as UKF\n", " \n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1)\n", " ukf = UKF(dim_x=4, dim_z=2, fx=f_cv, hx=h_cv, dt=dt, points=points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rest of the code is the same as for the linear kalman filter. Let's just implement it! I'll use the same measurements as used by the linear Kalman filter, and compute the standard deviation of the difference between the two solution. I will use the `batch_filter` method to keep the code succinct; for clarity I put the equivalent iterative loop in a comment. As with all the filters we have done to date you ju" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "UKF standard deviation 0.013\n" ] }, { "data": { "image/png": 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zs1OrV6/Wvn37lJOTM11tAMBfbHBoQMVVhTpW8o4uXrowbk1cZLJW53xWK7Nv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\nRjkcIzpeeliHTvxaHT0t15z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import MerweScaledSigmaPoints\n", "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "\n", "import numpy as np\n", "\n", "sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=1.)\n", "ukf = UKF(dim_x=4, dim_z=2, fx=f_cv, hx=h_cv, dt=dt, points=sigmas)\n", "ukf.x = np.array([0., 0., 0., 0.])\n", "ukf.R = np.diag([0.09, 0.09]) \n", "ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "ukf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "\n", "uxs = []\n", "for z in zs:\n", " ukf.predict()\n", " ukf.update(z)\n", " uxs.append(ukf.x.copy())\n", "uxs = np.array(uxs)\n", "\n", "plt.plot(uxs[:, 0], uxs[:, 2])\n", "print('UKF standard deviation {:.3f}'.format(np.std(uxs - xs)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gave me a standard deviation 0f 0.013 which is quite small. \n", "\n", "You can see that there is not much difference in the implementation of the UKF vs linear Kalman filter. We merely replace $\\mathbf{F}$ with the function *f(x)*, and the matrix $\\mathbf{H}$ with the function *h(x)*. The rest of the theory and implementation remains the same. Well, of course under the hood the `FilterPy` implementation is quite different than the Kalman filter code, but from a designer's point of view the problem formulation and filter design is very similar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking a Flying Airplane" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First Attempt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's tackle our first nonlinear problem. To minimize the number of things that change I will keep the problem formulation very similar to the linear tracking problem above. For this problem we will write a filter to track a flying airplane using a stationary radar as the sensor. To keep the problem as close to the previous one as possible we will track in two dimensions, not three. We will track one dimension on the ground and the altitude of the aircraft. The second dimension on the ground adds no difficulty or different information, so we can do this with no loss of generality.\n", "\n", " Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object. We also get the bearing to the target. For this 2D problem that will be the angle above the ground plane. True integration of sensors for applications like military radar and aircraft navigation systems have to take many factors into account which I am not currently interested in trying to cover in this book. So if any practitioners in the the field are reading this they will be rightfully scoffing at my exposition. My only defense is to argue that I am not trying to teach you how to design a military grade radar tracking system, but instead trying to familiarize you with the implementation of the UKF. \n", " \n", "For this example we want to take the slant range measurement from the radar and compute the horizontal position (distance of aircraft from the radar measured over the ground) and altitude of the aircraft, as in the diagram below." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import ekf_internal\n", "ekf_internal.show_radar_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will assume that the aircraft is flying at a constant altitude, so a three variable state vector will work.\n", "\n", "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude\\end{bmatrix}= \\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our state transition function is linear \n", "\n", "$$\\mathbf{x}^- = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x_{pos} \\\\x_{vel}\\\\ x_{alt}\\end{bmatrix} \n", "$$\n", "\n", "and we can implement that very much like we did for the previous problem." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "def f_radar(x, dt):\n", " \"\"\" state transition function for a constant velocity aircraft\n", " with state vector [x, velocity, altitude]'\"\"\"\n", " \n", " F = np.array([[1, dt, 0],\n", " [0, 1, 0],\n", " [0, 0, 1]], dtype=float)\n", " return np.dot(F, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is to design the measurement function. As in the linear Kalman filter the measurement function converts the filter's state into a measurement. So for this problem we need the position and velocity of the aircraft and convert it to the bearing and range from the radar station.\n", "\n", "If we represent the position of the radar station with an (x,y) coordinate computation of the range and bearing is straightforward. To compute the range we use the Pythagorean theorem:\n", "\n", "$$range = \\sqrt{(x_{ac} - x_{radar})^2 + (z_{ac} - z_{radar})^2}$$\n", "\n", "To compute the bearing we need to use the arctangent function.\n", "\n", "$$bearing = \\tan^{-1}{\\frac{z_{ac} - z_{radar}}{x_{ac} - x_{radar}}}$$\n", "\n", "As with the state transition function we need to define a Python function to compute this for the filter. I'll take advantage of the fact that a function can own a variable to store the radar's position." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "def h_radar(x):\n", " dx = x[0] - h_radar.radar_pos[0]\n", " dz = x[2] - h_radar.radar_pos[1]\n", " slant_range = math.sqrt(dx**2 + dz**2)\n", " bearing = math.atan2(dz, dx)\n", " return slant_range, bearing\n", "\n", "h_radar.radar_pos = (0, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Important Note**: There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem.\n", "\n", "We need to simulate the Radar station and the movement of the aircraft. By now this should be second nature for you, so I will present the code without much discussion." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "from numpy.linalg import norm\n", "from math import atan2\n", "\n", "class RadarStation(object):\n", " \n", " def __init__(self, pos, range_std, bearing_std):\n", " self.pos = np.asarray(pos)\n", " \n", " self.range_std = range_std\n", " self.bearing_std = bearing_std\n", "\n", " \n", " def reading_of(self, ac_pos):\n", " \"\"\" Returns actual range and bearing to aircraft as tuple. \n", " Bearing is in radians.\n", " \"\"\"\n", " \n", " diff = np.subtract(ac_pos, self.pos)\n", " rng = norm(diff)\n", " brg = atan2(diff[1], diff[0])\n", " return rng, brg\n", "\n", "\n", " def noisy_reading(self, ac_pos):\n", " \"\"\" Compute range and bearing to aircraft with simulated noise\"\"\"\n", " \n", " rng, brg = self.reading_of(ac_pos) \n", " rng += randn() * self.range_std\n", " brg += randn() * self.bearing_std \n", " return rng, brg\n", " \n", " \n", "class ACSim(object):\n", " \n", " def __init__(self, pos, vel, vel_std):\n", " self.pos = np.asarray(pos, dtype=float)\n", " self.vel = np.asarray(vel, dtype=float)\n", " self.vel_std = vel_std\n", " \n", " \n", " def update(self, dt):\n", " \"\"\" compute next position. Incorporates random variation in\n", " velocity. Returns new position.\"\"\"\n", " \n", " vel = self.vel*dt + (randn() * self.vel_std) * dt \n", " self.pos += vel\n", " \n", " return self.pos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's put it all together. A military grade radar system can achieve 1 meter RMS range accuracy, and 1 mrad RMS for bearing [1]. We will assume a more modest 5 meter range accuracy, and 0.5$^\\circ$ angular accuracy as this provides a more challenging data set for the filter.\n", "\n", "I'll start with the aircraft positioned directly over the radar station, flying away from it at 100 m/s. A typical radar might update only once every 12 seconds and so we will use that for our update period. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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2WXwWvaeHN9ITs6FW5kIRk8blUkREDmZzuH/zzTfx7//+7wgPD8f8+fMxb968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\nGo0G+fn5Ldbc//rrr9BoNNi+fTsyMjIQFBSEnj1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dgl+urn5fZV/Pljxx3z/1PrD3XgX7duLpMfNYsOYdSsqKKCot4IsVb/DEyDm3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\nPadmzZrJZrNp0qRJLivs4sWLKigokJ+fn9Nxf39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3q0znrPFyrVq1MmPGjHE6FhMTYyZM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\nAAAWQfgHAAAALOL/AUuzy/gfMeJRAAAAAElFTkSuQmCC\n", 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KUVyRi6LOFoHyPCiri3Qa2C0e39wKHi6+4lP/zt9ujp6wt3HUy7+1IAi4lX8F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\nHD16VFy/fl1+PRo35uyTaymuzNm2e+edd0RGRoYoKCgQ58+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import book_plots\n", "from filterpy.common import Q_discrete_white_noise\n", "import math\n", "\n", "dt = 12. # 12 seconds between readings\n", "\n", "range_std = 5 # meters\n", "bearing_std = math.radians(0.5)\n", "\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", "h_radar.radar_pos = radar_pos\n", "\n", "points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n", "kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2, 2] = 0.1\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2])\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", "\n", "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "xs = []\n", "for i in range(len(t)):\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x) \n", "ukf_internal.plot_radar(xs, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This may or may not impress you, but it impresses me! In the Extended Kalman filter chapter we will solve the same problem, but it will take significant amounts of mathematics to handle the same problem. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tracking Manuevering Aircraft" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous example produced extremely good results, but it also relied on an assumption of an aircraft flying at a constant speed with no change in altitude. I will relax that assumption by allowing the aircraft to change altitude. First, let's see the performance of the previous code if the aircraft starts climbing after one minute." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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oqCjNONHR0bCysoJcLmc4ICLqQ3FFPg6deQ/FFXlax50krlgx81kE+05/oP8+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\nIQQAwMvLCwYGBlCpVNL2oqIinD17Fn5+fm03ASI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Actual altitude: 2561.9\n", "UKF altitude : 1107.2\n" ] } ], "source": [ "# reset aircraft position\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "xs = []\n", "for i in t:\n", " if i >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=False, plot_alt=True)\n", "print('Actual altitude: {:.1f}'.format(ac.pos[1]))\n", "print('UKF altitude : {:.1f}'.format(xs[-1][2]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "the performance is terrible as the filter is completely unable to track the changing altitude. What do we have to change to allow the filter to track the aircraft?\n", "\n", "I hope you answered add climb rate to the state, like so:\n", "\n", "\n", "$$\\mathbf{x} = \\begin{bmatrix}distance \\\\velocity\\\\ altitude \\\\ climb rate\\end{bmatrix}= \\begin{bmatrix}x \\\\\\dot{x}\\\\ z \\\\ \\dot{z}\\end{bmatrix}$$\n", "\n", "This requires the following change to the state transition function, which is still linear.\n", "\n", "$$\\mathbf{x}^- = \\begin{bmatrix} 1 & \\Delta t & 0 &0 \\\\ 0& 1& 0 &0\\\\ 0&0&1&dt \\\\ 0&0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\\\dot{x}\\\\ z\\\\ \\dot{z}\\end{bmatrix} \n", "$$\n", "\n", "The measurement function stays the same, but we will have to alter Q to account for the state dimensionality change." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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Ef39/4uPjOXbsmFObgoICEhISCAwMJDAwkNGjR1NYeOl6zyIiIjeagpITfLRq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\nQBARERERdRedFgiRkZHQaO5/Ks2douFejIyMkJSUhKSkpHv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Actual altitude: 2561.9\n", "UKF altitude : 2432.9\n" ] } ], "source": [ "def f_cv_radar(x, dt):\n", " \"\"\" state transition function for a constant velocity aircraft\"\"\"\n", " \n", " F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]], dtype=float)\n", " return np.dot(F, x)\n", "\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", "kf = UKF(4, 2, dt, fx=f_cv_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2])\n", "kf.x = np.array([0., 90., 1100., 0.])\n", "kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", "\n", "random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "xs = []\n", "for i in t:\n", " if i >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=False, plot_alt=True)\n", "print('Actual altitude: {:.1f}'.format(ac.pos[1]))\n", "print('UKF altitude : {:.1f}'.format(xs[-1][2]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that a significant amount of noise has been introduced into the altitude, but we are now accurately tracking the altitude change. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sensor Fusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's consider a simple example of sensor fusion. Suppose we have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system, where you have to account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", "\n", "The accuracy of the radar system in the last examples allowed us to estimate velocities to within a m/s or so, so we have to degrade that accuracy to be able to easily see the effect of the sensor fusion. Let's change the range error to 500 meters and then compute the standard deviation of the computed velocity. I'll skip the first several measurements because the filter is converging during that time, causing artificially large deviations." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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ntjP/txvfq6SkJIYPHw4YvjGIjY0lNjaWGTNm8NlnnzFnzhzKy8uZ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\nANjzy2eICI5uN/pffK0An3z/plSqNcjaFQ/P/DPkMoOpziMiIiI9p/f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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Velocity standard deviation 3.4 m/s\n" ] } ], "source": [ "range_std = 500.\n", "bearing_std = math.degrees(0.5)\n", "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", "kf = UKF(4, 2, dt, fx=f_cv_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2])\n", "kf.x = np.array([0., 90., 1100., 0.])\n", "kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", "\n", "random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "xs = []\n", "for i in t:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", "xs = np.asarray(xs)\n", "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=True, plot_alt=False)\n", "print('Velocity standard deviation {:.1f} m/s'.format(np.std(xs[10:, 1])))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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b7ij4NwHVTWUa7RrRbYh7ukb59PRjCmU+h4oLp9V+iSb+qP/8mUtga21nxN5M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\nvr6+WL9+vdbjOnUlXnzt0b2X1q9HRERE1BRPJ1881ne8uB0d9xXulpe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Velocity standard deviation 1.3 m/s\n" ] } ], "source": [ "def h_vel(x):\n", " dx = x[0] - h_vel.radar_pos[0]\n", " dz = x[2] - h_vel.radar_pos[1]\n", " slant_range = math.sqrt(dx**2 + dz**2)\n", " bearing = math.atan2(dz, dx)\n", " return slant_range, bearing, x[1], x[3]\n", "\n", "h_vel.radar_pos = (0, 0)\n", "\n", "range_std = 500.\n", "bearing_std = math.degrees(0.5)\n", "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "vel_std = 2.\n", "\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "points = MerweScaledSigmaPoints(n=4, alpha=.2, beta=2., kappa=-1.)\n", "kf = UKF(4, 4, dt, fx=f_cv_radar, hx=h_vel, points=points)\n", "\n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2, vel_std**2, vel_std**2])\n", "kf.x = np.array([0., 90., 1100., 0.])\n", "kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", "\n", "random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "xs = []\n", "for i in t:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " vx = ac.vel[0] + randn()*vel_std\n", " vz = ac.vel[1] + randn()*vel_std\n", " kf.predict()\n", " kf.update([r[0], r[1], vx, vz]) \n", " xs.append(kf.x)\n", "xs = np.asarray(xs)\n", "ukf_internal.plot_radar(xs, t, plot_x=False, plot_vel=True, plot_alt=False)\n", "print('Velocity standard deviation {:.1f} m/s'.format(np.std(xs[10:,1])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By incorporating the velocity sensor we were able to reduce the standard deviation from 3.5 m/s to 1.3 m/s. \n", "\n", "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to something called the *Complementary filter*, which uses the high update rate of the inertial sensor with the position accurate but slow estimates of the GPS to produce very high rate yet very accurate position and velocity estimates. This will be the topic of a future chapter. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multiple Position Sensors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The last sensor fusion problem was somewhat a toy example due to the existence of techniques like the *Complementary filter*. Let's tackle a problem that is not so toy-like. Before the advent of GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. I do not intend to cover the intricacies of these systems - Wikipedia will fill the basics if you are interested. In general these systems are beacons that allow you to extract either the range, bearing, or range and bearing to the beacon. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays what is called the \"radial\" - the direction from the VOR station on the ground to the aircraft. Using a chart they can extend these two radials - the intersection point is the position of the aircraft.\n", "\n", "That is a very manual and low accuracy approach. We can use a Kalman filter to filter the data and produce far more accurate position estimates. Let's work through that." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below. In the chart the width of the circle is intended to denote a different amount of sensor noise." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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YVBN9S1VVvPHlTs36Z9oHXUigdI+Z43Kw4+X7sXByLtq/Wdbl/olxZphz81Fp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\njs9KT+JwrS2k80iyGvDAlaOQkSxgA5miwLJjA0z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_two_sensor_bearing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compute the bearing between a sensor and the target as follows:\n", "\n", " def bearing(sensor, target):\n", " return math.atan2(target[1] - sensor[1], target[0] - sensor[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So our filter will need to receive a vector of 2 measurements during each update, one for each sensor. We can implement that as:\n", "\n", " def measurement(A_pos, B_pos, pos):\n", " angle_a = bearing(A_pos, pos)\n", " angle_b = bearing(B_pos, pos)\n", " return [angle_a, angle_b]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The design of the measurement function and state transition function can remain the same as nothing has changed that would affect them. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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HBi2Xej8pB4iPruR/PDyURdlgi9KHO0VEBisFdBGRm5BhGOw9Chu2wqYdUH0R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\nqm4EJ8tmUHzuTto6Qj1ec/Qw1/SVtOg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "from filterpy.common import Q_discrete_white_noise\n", "\n", "sa_pos = [-400, 0]\n", "sb_pos = [400, 0]\n", "\n", "def bearing(sensor, target_pos):\n", " return math.atan2(target_pos[1] - sensor[1], target_pos[0] - sensor[0])\n", "\n", "def measurement(A_pos, B_pos, pos):\n", " angle_a = bearing(A_pos, pos)\n", " angle_b = bearing(B_pos, pos)\n", " return [angle_a, angle_b]\n", "\n", "def fx_VOR(x, dt):\n", " x[0] += x[1]\n", " x[2] += x[3]\n", " return x\n", "\n", "\n", "def hx_VOR(x):\n", " # measurement to A\n", " pos = (x[0], x[2])\n", " return measurement(sa_pos, sb_pos, pos)\n", "\n", "\n", "def moving_target_filter(target_pos, std_noise, Q, dt=0.1, kappa=0.0):\n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n", " f = UKF(dim_x=4, dim_z=2, dt=dt, hx=hx_VOR, fx=fx_VOR, points=points)\n", " f.x = np.array([target_pos[0], 1., target_pos[1], 1.])\n", "\n", " q = Q_discrete_white_noise(2, dt, Q)\n", " f.Q[0:2, 0:2] = q\n", " f.Q[2:4, 2:4] = q\n", "\n", " f.R *= std_noise**2\n", " f.P *= 1000\n", " \n", " return f\n", "\n", "\n", "def plot_straight_line_target(f, std_noise):\n", " xs = []\n", " txs = []\n", "\n", " for i in range(300):\n", " target_pos[0] += 1 + randn()*0.0001\n", " target_pos[1] += 1 + randn()*0.0001\n", " txs.append((target_pos[0], target_pos[1]))\n", "\n", " z = measurement(sa_pos, sb_pos, target_pos)\n", " z[0] += randn() * std_noise\n", " z[1] += randn() * std_noise\n", "\n", " f.predict()\n", " f.update(z)\n", " xs.append(f.x)\n", "\n", " xs = np.asarray(xs)\n", " txs = np.asarray(txs)\n", "\n", " plt.plot(xs[:, 0], xs[:, 2])\n", " plt.plot(txs[:, 0], txs[:, 1])\n", " plt.show()\n", " \n", "np.random.seed(123)\n", "target_pos = [100, 200]\n", "\n", "std_noise = math.radians(0.5)\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", "plot_straight_line_target(f, std_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks quite good to me. There is a very large error at the beginning of the track, but the filter is able to settle down and start producing good data.\n", "\n", "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors with the same y-coordinate. This will cause a nonlinearity in the computation of the sigma means and the residuals because the mean angle will be near zero. As the angle goes below 0 the measurement function will compute a large positive angle of around $2\\pi$. The residual between the prediction and measurement will thus be very large, nearly $2\\pi$ instead of nearly 0. This makes it impossible for the filter to perform accurately, as seen in the example below." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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iUg42713HywvXsTb+H2Rkh7qMhTfdwA0RC/D1TsNkMjP8xodo4BsAQAPfABr4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\n1klsbKzExsZKeXm5DA0N6bbV3d0tJSUlYrFYJD4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "target_pos = [0, 0]\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", "plot_straight_line_target(f, std_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is untenable behavior for a real world filter. `FilterPy`'s UKF code allows you to provide it a function to compute the residuals in cases of nonlinear behavior like this, but this requires more knowledge about `FilterPy`'s implementation than we yet process.\n", "\n", "Finally, let's discuss the sensor fusion method that we used. We used the measurement from each bearing and had the Kalman filter's equations compute the world position from the measurements. This is equivalent to doing a weighted least squares solution. In the *Kalman Filter Math* chapter we discussed the limited accuracy of such a scheme and introduced an *Iterative Least Squares* (ILS) algorithm to produce greater accuracy. If you wanted to use that scheme you would write an ILS algorithm to solve the geometry of your problem, and pass the result of that calculation into the `update()` method as the measurement to be filtered. This imposes on you the need to compute the correct noise matrix for this computed positions, which may not be trivial. Perhaps in a later release of this book I will develop an example, but regardless it will take you a significant amount of research and experiment to design the best method for your application. For example, the ILS is probably the most common algorithm used to turn GPS pseudoranges into a position, but the literature discusses a number of alternatives. Sometimes there are faster methods, sometimes the iterative method does not converge, or does not converge fast enough, or requires too much computation for an embedded system. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Track a target moving in a circle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Change the simulated target movement to move in a circle. Avoid angular nonlinearities by putting the sensors well outside the movement range of the target, and avoid the angles $0^\\circ$ and $180^\\circ$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "# your solution here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have a few choices here. First, if we know the movement of the target we can design our filter's state transition function so that it correctly predicts the circular movement. For example, suppose we were tracking a boat race optically - we would want to take track shape into account with our filter. However, in this chapter we have not been talking about such constrained behavior, so I will not build knowledge of the movement into the filter. So my implementation looks like this." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "def plot_circular_target(kf, std_noise, target_pos):\n", " xs = []\n", " txs = []\n", " radius = 100\n", " for i in range(300):\n", " target_pos[0] = math.cos(i/10)*radius + randn()*0.0001\n", " target_pos[1] = math.sin(i/10)*radius + randn()*0.0001\n", " txs.append((target_pos[0], target_pos[1]))\n", "\n", " z = measurement(sa_pos, sb_pos, target_pos)\n", " z[0] += randn() * std_noise\n", " z[1] += randn() * std_noise\n", "\n", " kf.predict()\n", " kf.update(z)\n", " xs.append(kf.x)\n", "\n", " xs = np.asarray(xs)\n", " txs = np.asarray(txs)\n", "\n", " plt.plot(xs[:, 0], xs[:, 2])\n", " plt.plot(txs[: ,0], txs[:, 1], linestyle='-.')\n", " plt.axis('equal')\n", " plt.show()\n", "\n", "sa_pos = [-240, 200]\n", "sb_pos = [240, 200]" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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InZaZfY7v1s0vtc/EgTMYdNG0hPJKzzDoe2F++bdrYMt+SP4RZlyjYF4feLib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\ntm3btDFCCFhaWuKbb77B6NGjtdsvXbp00ydHRERERGSq7O3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(12283)\n", "std_noise = math.radians(0.5)\n", "target_pos = [0, 0]\n", "f = moving_target_filter(target_pos, std_noise, Q=1.1)\n", "plot_circular_target(f, std_noise, target_pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filter tracks the movement of the target, but never really converges on the track. This is because the filter is modeling a constant velocity target, but the target is anything but constant velocity. As mentioned above we could model the circular behavior by defining the `fx()` function, but then we would have problems when the target is not moving in a circle. Instead, lets tell the filter we are are less sure about our process model by making $\\mathbf{Q}$ larger. Here I have increased the variance from 0.1 to 1.0" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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8q/nBRO+ONa+Ln55h+UCi3cc3lEBmIlJWqDgXkTIhM/sChmG5DKIJEwGVClaA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\npBFszomIiIiINILNORERERGRRrA5JyIiIiLSCDb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(12283)\n", "std_noise = math.radians(0.5)\n", "cf = moving_target_filter(target_pos, std_noise, Q=10.)\n", "target_pos = [0, 0]\n", "plot_circular_target(cf, std_noise, target_pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The convergence is not perfect, but it is far better. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Sensor Position Effects" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is the behavior of the filter invariant for any sensor position? Find a sensor position that produces bad filter behavior." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "# your answer here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have already discussed the problem of angles being modal, so causing that problem by putting the sensors at `y=0` would be a trivial solution. However, let's be more subtle than that. We want to create a situation where there are an infinite number of solutions for the sensor readings. We can achieve that whenever the target lies on the straight line between the two sensors. In that case there is no triangulation possible and there is no unique solution. My solution is as follows." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "std_noise = math.radians(0.5)\n", "sa_pos = [-200, 200]\n", "sb_pos = [200, -200]\n", "plt.scatter(*sa_pos, s=200)\n", "plt.scatter(*sb_pos, s=200)\n", "target_pos = [0, 0]\n", "cf = moving_target_filter(target_pos, std_noise, Q=10.)\n", "plot_circular_target(cf, std_noise, target_pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I put the sensors at the upper left hand side and lower right hand side of the target's movement. We can see how the filter diverges when the target enters the region directly between the two sensors. The state transition always predicts that the target is moving in a straight line. When the target is between the two sensors this straight line movement is well described the bearing measurements from the two sensors so the filter estimate starts to approximate a straight line. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Compute Position Errors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The position errors of the filter vary depending on how far away the target is from a sensor. Write a function that computes the distance error due to a bearing error. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "# your solution here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Basic trigonometry gives us this answer." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Error of 1 degree at 100km is 1.75km\n" ] } ], "source": [ "def distance_error(target_distance, angle_error):\n", " x = 1 - math.cos(angle_error)\n", " y = math.sin(angle_error)\n", " return target_distance*(x**2 + y**2)**.5\n", "\n", "d = distance_error(100, math.radians(1.))\n", "print('\\n\\nError of 1 degree at 100km is {:.3}km'.format(d))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is an inherent physical limitation that is extremely difficult to deal with when designing filters. We can see that a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. For example, here is a scatter plot that shows the error distribution for a $1^\\circ$ standard deviation in bearing for a $30^\\circ$ bearing." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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HU5NBTU2MXbscLc5du9bF5ZenSKUcXHut/f/Z3LkxwuEUOTkNnHGGRZ8+XTCM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\nbuAirUQ/JoqIiMgpYxgGLtc+XK59R5y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p06fp+PHjlJ2d7a+YqmYwGCg6OprOnz9PlZWV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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d = 100\n", "xs, ys = [], []\n", "\n", "for i in range (3000):\n", " a = math.radians(30) + randn() * math.radians(1) \n", " xs.append(d*math.cos(a))\n", " ys.append(d*math.sin(a)) \n", "plt.scatter(xs, ys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Explain Filter Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that for even very small angular errors the (x, y) positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer this for the one sensor problem as well as the multiple sensor problem. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> This is **very** important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you really need to revisit some of the earlier Kalman filter material in the Multidimensional Kalman filter chapter.\n", "\n", "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible positions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target to form an intuition." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pos = np.array([5., 5.])\n", "for i in range(5):\n", " pos += (0.5, 1.) \n", " actual_angle = math.atan2(pos[1], pos[0])\n", " d = math.sqrt(pos[0]**2 + pos[1]**2)\n", "\n", " xs, ys = [], []\n", " for i in range (100):\n", " a = actual_angle + randn() * math.radians(1)\n", " xs.append(d*math.cos(a))\n", " ys.append(d*math.sin(a))\n", " plt.scatter(xs, ys)\n", "\n", "plt.axis('equal')\n", "plt.plot([5.5, pos[0]], [6, pos[1]], c='g', linestyle='--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that each individual measurement has a very large position error. However, when we plot successive measurements we suddenly have a clear trend - the target is obviously moving towards the upper right. When the Kalman filter (whether a linear KF, an EKF, or UKF) computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately $45^\\circ$ degree line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will be taking that into account. The end result is the track can be computed even with this sort of noise distribution. Of course, this graph makes it look easy because we have computed 100 possible measurements for each position update and plotted them all. This makes it easy for us to see where the target is moving. In contrast, the Kalman filter only gets 1 measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", "\n", "The next interaction we must think about is the fact that the bearing gives us no distance information. Suppose in the example above we told the filter that the initial position of the target was 1000km away from the sensor (vs the actual distance of 7.07 km), and that we were highly confident in that guess by setting $\\mathbf{P}$ very small. At that distance a $1^\\circ$ error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's consider the effect of adding a second sensor. Again, I will start by plotting the measurements so we can form an intuition about the problem." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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evSVav96h4cOTJUljxwY0aZJHM2b4lZpqq9+uv8rw+xN7AABQj9WoR7mwsFBt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\ngC+//FKRSEStWrWqsj0tLU3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sin, cos, atan2, pi\n", "\n", "def isct(pa, pb, alpha, beta):\n", " \"\"\" Returns the (x, y) intersections of points pa and pb\n", " given the bearing ba for point pa and bearing bb for\n", " point pb.\n", " \"\"\"\n", " \n", " B = [pb[0] - pa[0], pb[1] - pa[1]]\n", " AB = math.sqrt((pa[0] - pb[0])**2 + (pa[1] - pb[1])**2) \n", " ab = atan2(B[1], B[0])\n", " a = alpha - ab \n", " b = pi - beta - ab\n", " p = pi - b - a\n", " \n", " AP = (sin(b) / sin(p)) * AB \n", " x = cos(alpha) * AP + pa[0]\n", " y = sin(alpha) * AP + pa[1]\n", " return x, y\n", "\n", "\n", "def plot_iscts(pos, N=4):\n", " for i in range(N):\n", " pos += (0.5, 1.) \n", " actual_angle_a = math.atan2(pos[1] - sa[1], pos[0] - sa[0])\n", " actual_angle_b = math.atan2(pos[1] - sb[1], pos[0] - sb[0])\n", "\n", " da = math.sqrt((sa[0] - pos[0])**2 + (sa[1] - pos[1])**2)\n", " db = math.sqrt((sb[0] - pos[0])**2 + (sb[1] - pos[1])**2)\n", "\n", " xs, ys, xs_a, xs_b, ys_a, ys_b = [], [], [], [], [], []\n", "\n", " for i in range (300):\n", " a_a = actual_angle_a + randn() * math.radians(1)\n", " a_b = actual_angle_b + randn() * math.radians(1)\n", "\n", " x,y = isct(sa, sb, a_a, a_b)\n", " xs.append(x)\n", " ys.append(y)\n", "\n", " xs_a.append(da*math.cos(a_a) + sa[0])\n", " ys_a.append(da*math.sin(a_a) + sa[1])\n", "\n", " xs_b.append(db*math.cos(a_b) + sb[0])\n", " ys_b.append(db*math.sin(a_b) + sb[1])\n", "\n", " plt.scatter(xs, ys, c='r', marker='.')\n", " plt.scatter(xs_a, ys_a)\n", " plt.scatter(xs_b, ys_b)\n", " plt.axis('equal')\n", " plt.show()\n", "\n", "pos = np.array([4., 4.])\n", "sa = [0., 2.]\n", "sb = [8., 2.]\n", "\n", "plt.scatter(*sa, s=100)\n", "plt.scatter(*sb, s=100)\n", "plot_iscts(pos, N=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I placed the sensors nearly orthogonal to the target's initial position so we get these lovely 'x' shape intersections. I then computed the (x, y) coordinate corresponding to the two noisy bearing measurements and plotted them with red dots to show the distribution of the noisy measurements in x and y. We can see how the errors in x and y change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the y coordinate of sensor B the shape becomes strongly elliptical.\n", "\n", "Next I will alter the starting positions and rerun the simulation. Here the shape of the errors in x and y changes radically as the target position changes relative to the two sensors. " ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sa = [3, 4]\n", "sb = [3, 9]\n", "pos= np.array([4., 4.])\n", "\n", "plt.scatter(*sa, s=100)\n", "plt.scatter(*sb, s=100)\n", "plot_iscts(pos, N=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation of the UKF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's implement these equations with Python. As you have seen FilterPy already implements this code for you, but it is instructive to learn how to go from equations to code. Plus, if you encounter a problem and need to debug your code you will likely need to step through the code with the debugger.\n", "\n", "Implementing the UKF is quite straightforward. First, let's write the code to compute the mean and covariance given the sigma points. \n", "\n", "We will store the sigma points and weights in matrices, like so:\n", "\n", "$$ \n", "\\begin{aligned}\n", "weights &= \n", "\\begin{bmatrix}\n", "w_1&w_2& \\dots & w_{2n+1}\n", "\\end{bmatrix} \n", "\\\\\n", "sigmas &= \n", "\\begin{bmatrix}\n", "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} & \\mathcal{X}_{0,2} \\\\\n", "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} & \\mathcal{X}_{1,2} \\\\\n", "\\vdots & \\vdots & \\vdots \\\\\n", "\\mathcal{X}_{2n+1,0} & \\mathcal{X}_{2n+1,1} & \\mathcal{X}_{2n+1,2}\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "In other words, each column contains the $2n+1$ sigma points for one dimension in our problem. The $0th$ sigma point is always the mean, so first row of sigma's contains the mean of each of our dimensions. The second through nth row contains the $\\mu+\\sqrt{(n+\\lambda)\\Sigma}$ terms, and the $n+1$ to $2n$ rows contains the $\\mu-\\sqrt{(n+\\lambda)\\Sigma}$ terms. the choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code a bit easier to code as I can refer to the ith sigma point for all dimensions as `sigmas[i]`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weights" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Computing the weights in numpy is extremely simple. Recall that for the Van der Merwe scaled sigma point implementation\n", "\n", "$$\n", "\\begin{aligned}\n", "W^m_0 &= \\frac{\\lambda}{n+\\lambda} \\\\\n", "W^c_0 &= \\frac{\\lambda}{n+\\lambda} + 1 -\\alpha^2 + \\beta \\\\\n", "W^m_i = W^c_i &= \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n\n", "\\end{aligned}\n", "$$\n", "\n", "with $\\lambda=\\alpha^2(n+\\kappa)-n$.\n", " \n", "Our code will look something like this.\n", "\n", " lambda_ = alpha**2 * (n +kappa) - n\n", " Wc = np.full(2*n + 1, 1. / (2*(n+lambda_))\n", " Wm = np.full(2*n + 1, 1. / (2*(n+lambda_))\n", " Wc[0] = lambda_ / (n + lambda_) + (1. - alpha**2 + beta)\n", " Wm[0] = lambda_ / (n + lambda_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sigma Points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###### The equations for the sigma points are:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\mathcal{X}_0 &= \\mu \\\\\n", "\\mathcal{X}_i &= \\mu + \\bigg[\\sqrt{(n+\\lambda)\\Sigma} \\bigg]_i\\,\\,\\,\\, &\\text{for}\\text{ i=1 .. n} \\\\\n", "\\mathcal{X}_i &= \\mu - \\bigg[\\sqrt{(n+\\lambda)\\Sigma}\\bigg]_{i-n}\\,\\,\\,\\,\\, &\\text{for}\\text{ i=(n+1) .. 2n}\n", "\\end{aligned}\n", "$$\n", "\n", "The Python for this is not much more difficult once we wrap our heads around the $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ term.\n", "\n", "The term $[\\sqrt{(n+\\kappa)\\Sigma}]_i$ has to be a matrix because $\\Sigma$ is a matrix. The subscript $i$ is choosing the column vector of the matrix. What is the square root of a matrix? There is no unique definition. A typical definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$.\n", "\n", "$$\n", "\\begin{aligned}\n", "\\text{if }\\Sigma = SS \\\\\n", "\\\\\n", "\\text{then }S = \\sqrt{\\Sigma}\n", "\\end{aligned}\n", "$$\n", "\n", "However there is an alternative definition, and we will chose it because it has numerical properties that makes it much easier for us to compute its value. We can define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n", "\n", "$$\n", "\\Sigma = SS^\\mathsf{T} \\\\\n", "$$\n", "\n", "This method is frequently chosen in computational linear algebra because this expression is easy to compute using something called the *Cholesky decomposition* [3]. \n", "SciPy provides this with the `scipy.linalg.cholesky()` method. If your language of choice is Fortran, C, or C++, libraries such as LAPACK provide this routine. Matlab provides `chol()`.\n", "\n", " sigmas = np.zeros((2*n+1, n))\n", " U = scipylinalg.cholesky((n+kappa)*P)\n", "\n", " sigmas[0] = X\n", " for k in range (n):\n", " sigmas[k+1] = X + U[k]\n", " sigmas[n+k+1] = X - U[k]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's implement the unscented transform. Recall the equations\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_i w_i^m\\mathcal{X}_i \\\\\n", "\\Sigma &= \\sum_i w_i^c{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "We implement the sum of the means with\n", "\n", " X = np.dot (Wm, sigmas)\n", "\n", "If you are not a heavy user of NumPy this may look foreign to you. NumPy is not just a library that make linear algebra possible; under the hood it is written in C to achieve much faster speeds than Python can reach. A typical speedup is 100x. To get that speedup we must avoid using for loops, and instead use NumPy's built in functions to perform calculations. So, instead of writing a for loop to compute the sum, we call the built in `numpy.dot(x,y)` method. If passed a 1D array and a 2D array it will compute the sum of inner products:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "array([410, 520, 630])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.array([10, 100])\n", "b = np.array([[1, 2, 3],\n", " [4, 5, 6]])\n", "np.dot(a,b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All that is left is to compute $\\mathbf{P} = \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}} + \\mathbf{Q}$\n", "\n", " kmax, n = sigmas.shape\n", " P = zeros((n, n))\n", " for k in range(kmax):\n", " y = sigmas[k] - x\n", " P += Wc[k] * np.outer(y, y) \n", " P += Q\n", "\n", "This introduces another feature of NumPy. The state variable $X$ is one dimensional, as is $sigmas[k]$, so the difference $sigmas[k]-X$ is also one dimensional. NumPy will not compute the transpose of a 1-D array; it considers the transpose of `[1,2,3]` to be `[1,2,3]`. So we call the function `np.outer(y,y)` which computes the value of $\\mathbf{yy}^\\mathsf{T}$ for a 1D array $\\mathbf{y}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the predict step, we will generate the weights and sigma points as specified above. We pass each sigma point through the function f.\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n", "\n", "Then we compute the predicted mean and covariance using the unscented transform. In the code below you can see that I am assuming that this is a method in a class that stores the various matrices and vectors needed by the filter.\n", "\n", " def predict(self):\n", " \"\"\" Performs the predict step of the UKF. On return, self.xp and\n", " self.Pp contain the predicted state (xp) and covariance (Pp). 'p'\n", " stands for prediction.\n", " \"\"\"\n", "\n", " # calculate sigma points for given mean and covariance\n", " sigmas = sigma_points(self.x, self.P, self.kappa)\n", "\n", " for i in range(self._num_sigmas):\n", " self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n", "\n", " self.xp, self.Pp = unscented_transform(\n", " self.sigmas_f, self.W, self.W, self.Q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The update step converts the sigmas into measurement space via the `h(x)` function.\n", "\n", "\n", "$$\\mathcal{Z} = h(\\mathcal{Y})$$\n", "\n", "The mean and covariance of those points is computed with the unscented transform. The residual and Kalman gain is then computed. The cross variance is computed as:\n", "\n", "$$\\mathbf{P}_{xz} =\\sum w^c(\\boldsymbol{\\chi}-\\mu)(\\boldsymbol{\\mathcal{Z}}-\\mathbf{\\mu}_z)^\\mathsf{T}$$\n", "\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "\n", "$$K = \\mathbf{P}_{xz} \\mathbf{P}_z^{-1}\\\\\n", "\\hat{\\mathbf{x}} = \\mathbf{x}^- + \\mathbf{Ky}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\mathbf{P} = \\mathbf{P}^- - \\mathbf{KP}_z\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This function can be implemented as follows, assuming it is a method of a class that stores the necessary matrices and data." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [], "source": [ "def update(self, z):\n", " \"\"\" Update the UKF with the given measurements. On return,\n", " self.x and self.P contain the new mean and covariance of the filter.\n", "\n", " **Parameters**\n", "\n", " z : numpy.array of shape (dim_z)\n", " measurement vector\n", " \"\"\"\n", "\n", " # rename for readability\n", " sigmas_f = self.sigmas_f\n", " sigmas_h = self.sigmas_h\n", "\n", " # transform sigma points into measurement space\n", " for i in range(self._num_sigmas):\n", " sigmas_h[i] = self.hx(sigmas_f[i])\n", "\n", " # mean and covariance of prediction passed through inscented transform\n", " zp, Pz = unscented_transform(sigmas_h, self.W, self.W, self.R)\n", "\n", " # compute cross variance of the state and the measurements\n", " Pxz = zeros((self._dim_x, self._dim_z))\n", " for i in range(self._num_sigmas):\n", " Pxz += self.W[i] * np.outer(sigmas_f[i] - self.xp,\n", " sigmas_h[i] - zp)\n", "\n", " K = dot(Pxz, inv(Pz)) # Kalman gain\n", "\n", " self.x = self.xp + dot(K, z-zp)\n", " self.P = self.Pp - dot3(K, Pz, K.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Batch Processing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kalman filter is designed as a recursive algorithm - as new measurements come in we immediately create a new estimate. But it is very common to have a set of data that have been already collected which we want to filter. Kalman filters can always be run in a *batch* mode, where all of the measurements are filtered at once. We have implemented this in `UnscentedKalmanFilter.batch_filter()`. Internally, all the function does is loop over the measurements and collect the resulting state and covariance estimates in arrays. It may seem a bit trivial, but you will almost always want to do this if you can for several reasons. First, it will execute a bit quicker than if you implement the loop yourself. Second, the logic in your code will be a bit cleaner, and you will have a reduced chance of bugs. Third, and most importantly, it you batch process your data you can then use an extremely powerful technique to generate far smoother results than you have seen so far. We will present that technique in the next section; here I will show you how to use `UnscentedKalmanFilter.batch_filter()`.\n", "\n", "All you have to do is collect your measurements into an array or list. Maybe it is in a CSV file, for example.\n", "\n", " zs = read_altitude_from_csv()\n", "\n", "Or maybe you will generate it using a generator:\n", "\n", " zs = [some_func(i) for i in range(1000)]\n", " \n", "Now we call the `batch_filter()` method.\n", "\n", " Xs, Ps = ukf.batch_filter(zs)\n", " \n", "The function takes the list/array of measurements, filters it, and returns an array of state estimates (Xs) and covariance matrices (Ps) for the entire data set. \n", "\n", "Here is a complete example drawing from the radar tracking problem above." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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2WXwWvaeHN9ITs6FW5kIRk8blUkREDmZzuH/zzTfx7//+7wgPD8f8+fMxb968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\nGo0G+fn5Ldbc//rrr9BoNNi+fTsyMjIQFBSEnj1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dgl+urn5fZV/Pljxx3z/1PrD3XgX7duLpMfNYsOYdSsqKKCot4IsVb/DEyDm3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\nPadmzZrJZrNp0qRJLivs4sWLKigokJ+fn9Nxf39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3q0znrPFyrVq1MmPGjHE6FhMTYyZM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\nAAAWQfgHAAAALOL/AUuzy/gfMeJRAAAAAElFTkSuQmCC\n", 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KUVyRi6LOFoHyPCiri3Qa2C0e39wKHi6+4lP/zt9ujp6wt3HUy7+1IAi4lX8F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\nHD16VFy/fl1+PRo35uyTaymuzNm2e+edd0RGRoYoKCgQ58+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = 12. # 12 seconds between readings\n", "range_std = 5 # meters\n", "bearing_std = math.radians(0.5)\n", "\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", "h_radar.radar_pos = radar_pos\n", "\n", "points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n", "kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2 ,0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2, 2] = 0.1\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2])\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", "radar = RadarStation(pos=(0, 0), range_std=range_std, bearing_std=bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "zs = []\n", "for i in range(len(t)):\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " zs.append([r[0], r[1]])\n", "\n", " \n", "xs, covs = kf.batch_filter(zs)\n", "ukf_internal.plot_radar(xs, t)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 543.42853628, 87.77491996, -5.26709207],\n", " [ 87.77491996, 14.51416192, 0.01521311],\n", " [ -5.26709207, 0.01521311, 195.7945557 ]])" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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nOjVh84dDn8gcWKWOxe27Gbw4fxtHL0YD0K2lB0sm98G7Xs1KzVHVVNffjXZt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\nAyn48UAKgPrZKoYGemJoDy8M7uEJB1terr45yr9aiT0nMrA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import filterpy.stats as stats\n", "P = np.array([[kf.P[0,0], kf.P[0, 2]], [kf.P[0,2], kf.P[2,2]]])\n", "stats.plot_covariance_ellipse((0, 0), P, variance=[1, 4, 9])\n", "kf.P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing the Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Briefly, the recursive form of Kalman filtering that we have been using up to now use information from the past to generate the current estimate. Recall the last section, where we used batch processing to filter a collection of measurements. This implies that we know now only the past, but the future! This is a key insight.\n", "\n", "Let's assume that we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n", "\n", "However, if we have measurements from the future we can often figure out if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a true indication that a turn was initiated. On the other hand, if the subsequent measurements continued on in a straight line we would know that the measurement was noisy and should be mostly ignored.\n", "\n", "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `FilterPy`. The algorithm that we have implemented is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n", "\n", "The routine is `UnscentedKalmanFilter.rts_smoother()`. Using it is trivial; we pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in position in meters: [-0.7717 -0.1195 0.0426 -1.1727 -1.0871]\n" ] }, { "data": { "image/png": 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42rVr1ZqfiIiIKkculyMl7Qh+2bMTp46dRUFeoTBn3NgI/exs4DFsNNq16ihiSqLqY2lp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\nQqfT4dlnn0VjY2OnY2ZnZyMqKgoODg5wcHDA008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fCfXMmTN8+eWXbN68WWu5gYEB7777Lv369aNFixYcv7SbP3ctkNPbLM1s+ajL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dBFEUjR0K0aBgZuwAaGAoqy5CY0s9AMDW2gFujp4GP6e1pQ0mj74X+xL/CwDYl/hfjA6N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\nSfj5+SEtLQ0+Pj4AgKKioua8LCIiIiIirbK0tGzyMQy+OLi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ms, P, K = kf.rts_smoother(xs, covs)\n", "ukf_internal.plot_rts_output(xs, Ms, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From these charts we can see that the improvement in the position is small, but the improvement in the velocity is good, and spectacular for the altitude. The difference in the position are very small, so I printed the difference between the UKF and the smoothed results for the last 5 points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing the Sigma Parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "** author's note: this entire section needs a lot of work. Ignore for now.**\n", "\n", "I have found the literature on choosing values for $\\alpha$, $\\beta$, and $\\kappa$ to be rather lacking. Van der Merwe's dissertation contains the most information, but it is not exhaustive. So let's explore what they do. \n", "\n", "Van der Merwe suggests using $\\beta=2$ for Gaussian problems, and $\\kappa=3-n$. So let's start there and vary $\\alpha$. I will let $n=1$ minimize the size of the arrays we need to look at and to avoid having to compute the square root of matrices" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 3. -3.]\n", "mean weights: [ 0.6667 0.1667 0.1667]\n", "cov weights: [ 2.6667 0.1667 0.1667]\n", "lambda: 2\n", "sum cov 3.0\n" ] } ], "source": [ "ukf_internal.print_sigmas(mean=0, cov=3, alpha=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So what is going on here? We can see that for a mean of 0 the algorithm choose sigma points of 0, 3, and -3, but why? Recall the equation for computing the sigma points:\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= \\mu\\\\\n", "\\mathcal{X}_i &= \\mu \\pm \\sqrt{(n+\\lambda)\\Sigma}\n", "\\end{aligned}$$\n", "\n", "Here you will appreciate my choice of $n=1$ as it reduces everything to scalars, allowing us to avoid computing the square root of matrices. So, for our values the equation is\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= 0 \\\\\n", "\\mathcal{X}_i &= 0 \\pm \\sqrt{(1+2)\\times 3} \\\\\n", "&= 0 \\pm \\sqrt{9} \\\\\n", "&= \\pm 3\n", "\\end{aligned}$$\n", "\n", "So as $\\alpha$ gets larger the sigma points get more spread out. Let's set it to an absurd value." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 600. -600.]\n", "mean weights: [ 1. 0. 0.]\n", "cov weights: [-39996. 0. 0.]\n", "lambda: 119999\n", "sum cov -39996.0\n" ] } ], "source": [ "ukf_internal.print_sigmas(mean=0, cov=3, alpha=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the sigma point spread over 100 standard deviations.If our data was Gaussian we'd be incorporating data many standard deviations away from the mean; for nonlinear problems this is unlikely to produce good results. But suppose our distribution was not Gaussian, but instead had very fat tails? We might need to sample from those tails to get a good estimate, and hence it would make sense to make $kappa$ larger (not 200, which was absurdly large to make the change in the sigma points stark). \n", "\n", "With a similar line of reasoning, suppose that our distribution has nearly no tails - the probability distribution looks more like an inverted parabola. In such a case we'd probably want to pull the sigma points in closer to the mean to avoid sampling in regions where there will never be real data.\n", "\n", "Now let's look at the change in the weights. When we have $k+n=3$ the weights were 0.6667 for the mean, and 0.1667 for the two outlying sigma points. On the other hand, when $\\alpha=200$ the mean weight shot up to 0.99999 and the outlier weights were set to 0.000004. Recall the equations for the weights:\n", "\n", "$$\\begin{aligned}\n", "W_0 &= \\frac{\\lambda}{n+\\lambda} \\\\\n", "W_i &= \\frac{1}{2(n+\\lambda)}\n", "\\end{aligned}$$\n", "\n", "We can see that as $\\lambda$ gets larger the fraction for the weight of the mean ($\\lambda/(n+\\lambda)$) approaches 1, and the fraction for the weights of the rest of the sigma points approaches 0. This is invariant on the size of your covariance. So as we sample further and further away from the mean we end up giving less weight to those samples, and if we sampled very close to the mean we'd give very similar weights to all.\n", "\n", "However, the advice that Van der Merwe gives is to constrain $\\alpha$ in the range $0 \\gt \\alpha \\ge 1$. He suggests $10^{-3}$ as a good value. Lets try that." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 0.3606 -0.3606]\n", "mean weights: [-99. 50. 50.]\n", "cov weights: [-96.01 50. 50. ]\n", "lambda: -0.99\n", "sum cov 3.99\n" ] } ], "source": [ "ukf_internal.print_sigmas(mean=0, cov=13, alpha=.1, kappa=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I must admit to not fully understanding this advice. " ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 0.3 -0.3]\n", "mean weights: [-32.3333 16.6667 16.6667]\n", "cov weights: [-29.3433 16.6667 16.6667]\n", "lambda: -0.97\n", "sum cov 3.99\n" ] } ], "source": [ "ukf_internal.print_sigmas(mean=0, cov=3, alpha=.1)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 3. -3.]\n", "mean weights: [ 0.6667 0.1667 0.1667]\n", "cov weights: [ 2.6667 0.1667 0.1667]\n", "lambda: 2\n", "sum cov 3.0\n" ] } ], "source": [ "ukf_internal.print_sigmas(mean=0, cov=3, alpha=1)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 0.2449 -0.2449]\n", "mean weights: [-49. 25. 25.]\n", "cov weights: [-46.01 25. 25. ]\n", "lambda: -0.98\n", "sum cov 3.99\n" ] } ], "source": [ "ukf_internal.print_sigmas(mean=0, cov=3, alpha=.1, beta=2, kappa=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Robot Localization - A Fully Worked Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is time to try a real problem. I warn you that this is far from a simple problem. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world solution. \n", "\n", "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape with sensors that give range and bearings to various landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. Or, it might be one of those small robots that vacuum your house. It could be a search and rescue device meant to go into dangerous areas to search for survivors. It doesn't matter too much. \n", "\n", "Our robot is wheeled, which means that it manuevers by turning it's wheels. When it does so, the robot pivots around the rear axle while moving forward. This is nonlinear behavior which we will have to account for. The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", "\n", "### Robot Motion Model" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ekf_internal.plot_bicycle()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At a first approximation n automobile steers by turning the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modelling steering requires an ugly set of differential equations. For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. \n", "\n", "I have depicted this model above. Here we see the front tire is pointing in direction $\\alpha$. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. If you google bicycle model you will find that we can compute the turn angle $\\beta$ with\n", "\n", "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n", "\n", "and the turning radius R is given by \n", "\n", "$$R = \\frac{d}{\\beta}$$\n", "\n", "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n", "\n", "If we let $\\theta$ be our current orientation then we can compute the position $C$ before the turn starts as\n", "\n", "$$ C_x = x - R\\sin(\\theta) \\\\\n", "C_y = y + R\\cos(\\theta)\n", "$$\n", "\n", "After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n", "\n", "$$\\begin{aligned} x &= C_x + R\\sin(\\theta + \\beta) \\\\\n", "y &= C_y - R\\cos(\\theta + \\beta) \\\\\n", "\\theta &= \\theta + \\beta\n", "\\end{aligned}\n", "$$\n", "\n", "Once we substitute in for $C$ we get\n", "\n", "$$\\begin{aligned} x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", "\\theta &= \\theta + \\beta\n", "\\end{aligned}\n", "$$\n", "\n", "You don't really need to understand this math in detail, as it is already a simplification of the real motion. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the State Variables\n", "\n", "For our robot we will maintain the position and orientation of the robot:\n", "\n", "$$\\mathbf{x} = \\begin{bmatrix}x & y & \\theta\\end{bmatrix}^\\mathsf{T}$$\n", "\n", "I could include velocities into this model, but as you will see the math will already be quite challenging.\n", "\n", "Our control input $\\mathbf{u}$ is the velocity and steering angle\n", "\n", "$$\\mathbf{u} = \\begin{bmatrix}v & \\alpha\\end{bmatrix}^\\mathsf{T}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the System Model\n", "\n", "In general we model our system as a nonlinear motion model plus noise.\n", "\n", "$$x^- = x + f(x, u) + \\mathcal{N}(0, Q)$$\n", "\n", "Using the motion model for a robot that we created above, we can write:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from math import tan, sin, cos, sqrt\n", "\n", "def move(x, u, dt, wheelbase):\n", " hdg = x[2]\n", " vel = u[0]\n", " steering_angle = u[1]\n", "\n", " dist = vel*dt\n", " if abs(steering_angle) > 0.001:\n", " beta = dist / wheelbase * tan(steering_angle)\n", " r = wheelbase / tan(steering_angle) # radius\n", "\n", " sinh, sinhb = sin(hdg), sin(hdg + beta)\n", " cosh, coshb = cos(hdg), cos(hdg + beta)\n", " return x + np.array([-r*sinh + r*sinhb, r*cosh - r*coshb, beta])\n", " else:\n", " # moving in straight line\n", " return x + np.array([dist*cos(hdg), dist*sin(hdg), 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can use this function to implement the function `f(x)` which implements the system model." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fx(x, dt, u):\n", " return move(x, u, dt, wheelbase)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the Measurement Model\n", "\n", "Now we need to design our measurement model. For this problem we are assuming that we have a sensor that receives a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. Using $p$ be the position of a landmark, the range $r$ is\n", "\n", "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n", "\n", "We assume that the sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n", "\n", "$$\\phi = \\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$$\n", "\n", "Thus our function is\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{x}& = h(x,p) &+ \\mathcal{N}(0, R)\\\\\n", "&= \\begin{bmatrix}\n", "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", "\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta \n", "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n", "\\end{aligned}$$\n", "\n", "I will not implement this in Python yet as there is a difficulty that will be discussed in the *Implementation* section below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design Measurement Noise\n", "\n", "This is quite straightforward as we need to specify measurement noise in measurement space, hence it is linear. It is reasonable to assume that the range and bearing measurement noise is independent, hence\n", "\n", "$$R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we begin coding the main loop we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a bearing difference of $-358^\\circ$. this will throw off the computation of the Kalman gain because the correct angle difference in this case is $-2^\\circ$. So we will have to write code to correctly compute the bearing residual." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def normalize_angle(x):\n", " x = x % (2 * np.pi) # force in range [0, 2 pi)\n", " if x > np.pi: # move to [-pi, pi]\n", " x -= 2 * np.pi\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state vector has the bearing at position 2, but the measurement vector has it at position 1, so we need to write functions to handle each. Furthermore, the function for the residual in the measurement will be passed an array of several measurements, one per landmark. These will be passed into the `UnscentedKalmanFilter.__init__()` function." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def residual_h(a, b):\n", " y = a - b\n", " # data in format [dist_1, bearing_1, dist_2, bearing_2,...]\n", " for i in range(0, len(y), 2):\n", " y[i + 1] = normalize_angle(y[i + 1])\n", " return y\n", "\n", "def residual_x(a, b):\n", " y = a - b\n", " y[2] = normalize_angle(y[2])\n", " return y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The modularity of angles kept me from implementing the measurement model. The equation is\n", "$$h(x,p)\n", "= \\begin{bmatrix}\n", "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", "\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta \n", "\\end{bmatrix}$$\n", "\n", "The expression $\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$ can produce a result outside the range $[\\pi, \\pi)$, so we should normalize the angle to that range.\n", "\n", "The function will be passed an array of landmarks and needs to produce an array of measurements in the form `[dist_to_1, bearing_to_1, dist_to_2, bearing_to_2, ...]`." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def Hx(x, landmarks):\n", " \"\"\" takes a state variable and returns the measurement that would\n", " correspond to that state.\n", " \"\"\"\n", " hx = []\n", " for lmark in landmarks:\n", " px, py = lmark\n", " dist = sqrt((px - x[0])**2 + (py - x[1])**2)\n", " angle = atan2(py - x[1], px - x[0])\n", " hx.extend([dist, normalize_angle(angle - x[2])])\n", " return np.array(hx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our difficulties are not over. The unscented transform computes the average of the state and measurement vectors, but each contains a bearing. There is no unique way to compute the average of a set of angles. For example, what is the average of 359$^\\circ$ and 3$^\\circ$? Intuition suggests the answer should be 1$^\\circ$, but a naive sum/count approach yields 181$^\\circ$.\n", "\n", "One common approach is to take the arctan of the sum of the sins and cosines.\n", "\n", "$$\\bar{\\theta} = atan2\\left(\\frac{\\sum_{i=1}^n \\sin\\theta_i}{n}, \\frac{\\sum_{i=1}^n \\cos\\theta_i}{n}\\right)$$\n", "\n", "We have not used this feature yet, but the `UnscentedKalmanFilter.__init__()` method has an argument `x_mean_fn` that allows you to provide a function which compute the mean for the state, and `z_mean_fn` for a function which computes the mean of the measurement. We will code these function as:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def state_mean(sigmas, Wm):\n", " x = np.zeros(3)\n", "\n", " sum_sin = np.sum(np.dot(np.sin(sigmas[:, 2]), Wm))\n", " sum_cos = np.sum(np.dot(np.cos(sigmas[:, 2]), Wm))\n", " x[0] = np.sum(np.dot(sigmas[:, 0], Wm))\n", " x[1] = np.sum(np.dot(sigmas[:, 1], Wm))\n", " x[2] = atan2(sum_sin, sum_cos)\n", " return x\n", "\n", "\n", "def z_mean(sigmas, Wm):\n", " z_count = sigmas.shape[1]\n", " x = np.zeros(z_count)\n", "\n", " for z in range(0, z_count, 2):\n", " sum_sin = np.sum(np.dot(np.sin(sigmas[:, z+1]), Wm))\n", " sum_cos = np.sum(np.dot(np.cos(sigmas[:, z+1]), Wm))\n", "\n", " x[z] = np.sum(np.dot(sigmas[:,z], Wm))\n", " x[z+1] = atan2(sum_sin, sum_cos)\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These functions take advantage of the fact that NumPy's trigometric functions operate on arrays, and `dot` performs element-wise multiplication. NumPy is implemented in C and Fortran, so `sum(dot(sin(x), w))` is much faster than writing the equivalent loop in Python. Once you are used to seeing it, I think it is as readable as the loop form.\n", "\n", "With that done we are now ready to implement the UKF. You've seen this sort of code many times, so I will not describe it in detail. There is one new thing here that is important to discuss. When we construct the sigma points and filter we have to provide it the functions that we have written to compute the residuals and means.\n", "\n", " points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", " subtract=residual_x)\n", "\n", " ukf = UKF(dim_x=3, dim_z=2, fx=fx, hx=Hx, dt=dt, points=points,\n", " x_mean_fn=state_mean, z_mean_fn=z_mean,\n", " residual_x=residual_x, residual_z=residual_h)\n", "\n", "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the EKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "\n", "dt = 1.0\n", "wheelbase = 0.5\n", "\n", "def run_localization(cmds, landmarks, sigma_vel, sigma_steer, sigma_range, \n", " sigma_bearing, ellipse_step=1, step=10):\n", "\n", " points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, subtract=residual_x)\n", " ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=fx, hx=Hx, dt=dt,\n", " points=points, x_mean_fn=state_mean, z_mean_fn=z_mean,\n", " residual_x=residual_x, residual_z=residual_h)\n", " ukf.x = np.array([2, 6, .3])\n", " ukf.P = np.diag([.1, .1, .05])\n", " ukf.R = np.diag([sigma_range**2, sigma_bearing**2]*len(landmarks))\n", " ukf.Q = np.eye(3)*0.0001\n", " \n", " sim_pos = ukf.x.copy()\n", " \n", " # plot landmarks\n", " if len(landmarks) > 0:\n", " plt.scatter(landmarks[:, 0], landmarks[:, 1], marker='s', s=60)\n", " \n", " track = []\n", " for i, u in enumerate(cmds): \n", " sim_pos = move(sim_pos, u, dt/step, wheelbase) # simulate robot\n", " track.append(sim_pos)\n", "\n", " if i % step == 0:\n", " ukf.predict(fx_args=u)\n", "\n", " if i % ellipse_step == 0:\n", " plot_covariance_ellipse((ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,\n", " facecolor='b', alpha=0.08)\n", "\n", " x, y = sim_pos[0], sim_pos[1]\n", " z = []\n", " for lmark in landmarks:\n", " d = sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2) + randn()*sigma_range\n", " bearing = atan2(lmark[1] - y, lmark[0] - x)\n", " a = normalize_angle(bearing - sim_pos[2] + randn()*sigma_bearing)\n", " z.extend([d, a]) \n", " ukf.update(z, hx_args=(landmarks,))\n", "\n", " if i % ellipse_step == 0:\n", " plot_covariance_ellipse((ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,\n", " facecolor='g', alpha=0.4)\n", " track = np.array(track)\n", " plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n", " plt.axis('equal')\n", " plt.title(\"UKF Robot localization\")\n", " plt.show()\n", " return ukf" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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VKwdMnefz+dR5553Xm2u6J4VYf/mfv6wDtdPV1aUyMjKUwWCIyAG9fPlyNXfuXBUfH6/M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\ne2WKtoumRfCDkDAMV5zimC8EJIwEdVUx4lGTWFzBMg2qq5rYvr6BbMG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ 0.0092 0.0187 0.0007]\n" ] } ], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15]])\n", "cmds = [np.array([1.1, .01])]*200\n", "ukf = run_localization(cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1)\n", "print(ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the EKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Steering the Robot\n", "\n", "While the robot was turning in the example above, we really can't say it was being driven realistically. The velocity and steering angles never changed, which doesn't pose much of a problem for the Kalman filter. We could implement a complicated PID controlled robot simulation, but I will just generate varying steering commands using NumPy's `linspace` method. I'll also add more landmarks as the robot will be travelling much further than in the first example." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": true }, "outputs": [], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15], [20, 5],\n", " [0, 30], [50, 30], [40, 10]])\n", "dt = 0.1\n", "wheelbase = 0.5\n", "sigma_range=0.3\n", "sigma_bearing=0.1\n", "\n", "# accelerate from a stop\n", "cmds = [[v, .0] for v in np.linspace(0.001, 1.1, 30)]\n", "cmds.extend([cmds[-1]]*50)\n", "\n", "# turn left\n", "v = cmds[-1][0]\n", "cmds.extend([[v, a] for a in np.linspace(0, np.radians(2), 15)])\n", "cmds.extend([cmds[-1]]*100)\n", "\n", "#turn right\n", "cmds.extend([[v, a] for a in np.linspace(np.radians(2), -np.radians(2), 15)])\n", "cmds.extend([cmds[-1]]*200)\n", "\n", "cmds.extend([[v, a] for a in np.linspace(-np.radians(2), 0, 15)])\n", "cmds.extend([cmds[-1]]*150)\n", "\n", "cmds.extend([[v, a] for a in np.linspace(0, np.radians(1), 25)])\n", "cmds.extend([cmds[-1]]*100)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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PTcfRuypUeBvDfyxRl9qr0L4PVlZmKgV68FRlP4q6/t+wPw8PD4YMGcLx48eZ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\nu8ePGDECCxYswLx58xAVFQUAUBQVx89VId4o8ND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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final covariance [ 0.0013 0.0043 0.0004]\n" ] } ], "source": [ "ukf = run_localization(cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1, step=1,\n", " ellipse_step=20)\n", "print('final covariance', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that the uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can force some error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further from the landmarks." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RhPqef65l6NChzJkzBzj/ieCXX33L5yu/JiX+JKnRiaRGJ4JmIyWhXajqfxtT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\nH2b+/Plo2qlDsqIoEqKFEEII0SUSpsWAt/dwNevWLeXollUUbd6JaZg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final covariance [ 0.0026 0.0657 0.0008]\n" ] } ], "source": [ "ukf = run_localization(cmds, landmarks[0:2], sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1, step=1,\n", " ellipse_step=20)\n", "print('final covariance', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working. On the other hand, if you have implemented an EKF or linearized Kalman filter you are perhaps bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. As you will see in the next chapter the EKF for the same problems requires some fairly difficult mathematics. In fact, for many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", "\n", "However, the advantage of the UKF over the EKF is not only the relative ease of implementation. It is somewhat premature to discuss this because you haven't learned the EKF yet, but the EKF linearizes the problem at one point and passes that point through a linear Kalman filter. In contrast, the UKF takes $2n+1$ samples. Therefore the UKF is almost always more accurate than the EKF, especially when the problem is highly nonlinear. While it is not true that the UKF is guaranteed to always outperform the EKF, in practice it has been shown to perform at least as well, and usually much better than the EKF. \n", "\n", "Hence my recommendation is to always start by implementing the UKF. If your filter has real world consequences if it diverges (people die, lots of money lost, power plant blows up) of course you will have to engage in a lot of sophisticated analysis and experimentation to chose the best filter. That is beyond the scope of this book, and you should be going to graduate school to learn this theory in much greater detail than this book provides. \n", "\n", "I have spoken of the UKF I presented in this chapter as *the* way to perform sigma point filters. This is not true. The specific version I chose is Julier's scaled unscented filter as parameterized by Van der Merwe in his 2004 dissertation. If you search for Julier, Van der Merwe, Uhlmann, and Wan you will find a family of similar sigma point filters that they developed. Each technique uses a different way of choosing and weighting the sigma points. But the choices don't stop there. For example, there is the SVD Kalman filter that uses singular value decomposition (SVD) to find the approximate mean and covariance of the probability distribution. There are many more. Think of this chapter as an introduction to the sigma point filters, rather than a definitive treatment of how they work. If you have been reading carefully and writing your own code you should be able to read the literature and implement your own filters without needing FilterPy, which does not implement every possible sigma point filter. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [1] Rudolph Van der Merwe. \"Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models\" dissertation (2004).\n", "\n", "- [2] Simon J. Julier. \"The Scaled Unscented Transformation\". Proceedings of the American Control Conference 6. IEEE. (2002)\n", "\n", "- [1] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n", "\n", "- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n", "\n", "- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition" ] } ], "metadata": { "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }