diff --git a/KalmanFilter.py b/KalmanFilter.py index 53fcc0c..027f1fe 100644 --- a/KalmanFilter.py +++ b/KalmanFilter.py @@ -12,7 +12,7 @@ import numpy.random as random class KalmanFilter: - def __init__(self, dim, use_short_form=False): + def __init__(self, dim_x, dim_z, use_short_form=False): """ Create a Kalman filter of dimension 'dim', where dimension is the number of state variables. @@ -29,14 +29,14 @@ class KalmanFilter: """ self.x = 0 # state - self.P = np.matrix(np.eye(dim)) # uncertainty covariance - self.Q = np.matrix(np.eye(dim)) # process uncertainty - self.u = np.matrix(np.zeros((dim,1))) # motion vector + self.P = np.matrix(np.eye(dim_x)) # uncertainty covariance + self.Q = np.matrix(np.eye(dim_x)) # process uncertainty + self.u = np.matrix(np.zeros((dim_x,1))) # motion vector self.B = 0 self.F = 0 # state transition matrix self.H = 0 # Measurement function (maps state to measurements) - self.R = np.matrix(np.eye(1)) # state uncertainty - self.I = np.matrix(np.eye(dim)) + self.R = np.matrix(np.eye(dim_z)) # state uncertainty + self.I = np.matrix(np.eye(dim_x)) if use_short_form: self.update = self.update_short_form @@ -94,7 +94,7 @@ class KalmanFilter: if __name__ == "__main__": - f = KalmanFilter (dim=2) + f = KalmanFilter (dim_x=2, dim_z=2) f.x = np.matrix([[2.], [0.]]) # initial state (location and velocity) diff --git a/Multidimensional_Kalman_Filters.ipynb b/Multidimensional_Kalman_Filters.ipynb index 6609f8c..d7b23b5 100644 --- a/Multidimensional_Kalman_Filters.ipynb +++ b/Multidimensional_Kalman_Filters.ipynb @@ -1,1785 +1,1729 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:ee354a137c73da1b0d79cd4e4c09611cc5b303ad4e9e60867dd39eb48f08ddf5" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "Multidimensional Kalman Filters" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "%matplotlib inline\n", - "from __future__ import division, print_function\n", - "import matplotlib.pyplot as plt\n", - "import book_format\n", - "book_format.load_style()\n", - "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", - "%load_ext secnum\n", - "%secnum" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Installed secnum.py. To use it, type:\n", - " %load_ext secnum\n" - ] - }, - { - "javascript": [ - "console.log(\"Section numbering...\");\n", - "\n", - "function number_sections(threshold) {\n", - "\n", - " var h1_number = 0;\n", - " var h2_number = 0;\n", - "\n", - " if (threshold === undefined) {\n", - " threshold = 2; // does nothing so far\n", - " }\n", - "\n", - " var cells = IPython.notebook.get_cells();\n", - " \n", - " for (var i=0; i < cells.length; i++) {\n", - "\n", - " var cell = cells[i];\n", - " if (cell.cell_type !== 'heading') continue;\n", - " \n", - " var level = cell.level;\n", - " if (level > threshold) continue;\n", - " \n", - " if (level === 1) {\n", - " \n", - " h1_number ++;\n", - " var h1_element = cell.element.find('h1');\n", - " var h1_html = h1_element.html();\n", - " \n", - " console.log(\"h1_html: \" + h1_html);\n", - "\n", - " var patt = /^[0-9]+\\.\\s(.*)/; // section number at start of string\n", - " var title = h1_html.match(patt); // just the title\n", - "\n", - " if (title != null) { \n", - " h1_element.html(h1_number + \". \" + title[1]);\n", - " }\n", - " else {\n", - " h1_element.html(h1_number + \". \" + h1_html);\n", - " }\n", - " \n", - " h2_number = 0;\n", - " \n", - " }\n", - " \n", - " if (level === 2) {\n", - " \n", - " h2_number ++;\n", - " \n", - " var h2_element = cell.element.find('h2');\n", - " var h2_html = h2_element.html();\n", - "\n", - " console.log(\"h2_html: \" + h2_html);\n", - "\n", - " \n", - " var patt = /^[0-9]+\\.[0-9]+\\.\\s/;\n", - " var result = h2_html.match(patt);\n", - "\n", - " if (result != null) {\n", - " h2_html = h2_html.replace(result, \"\");\n", - " }\n", - "\n", - " h2_element.html(h1_number + \".\" + h2_number + \". \" + h2_html);\n", - " \n", - " }\n", - " \n", - " }\n", - " \n", - "}\n", - "\n", - "number_sections();\n", - "\n", - "// $([IPython.evnts]).on('create.Cell', number_sections);\n", - "\n", - "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", - "\n" - ], - "metadata": {}, - "output_type": "display_data" - } - ], - "prompt_number": 1 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Introduction" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n", - "\n", - "In this chapter I am purposefully glossing over many aspects of the mathematics behind Kalman filters. If you are familiar with the topic you will read statements that you disagree with because they contain simplifications that do not necessarily hold in more general cases. If you are not familiar with the topic, expect some paragraphs to be somewhat 'magical' - it will not be clear how I derived a certaina result. I prefer that you develop an intuition for how these filters work through several worked examples. If I started by presenting a rigorous mathematical formulation you would be left scratching your head about what all these terms mean and how you might apply them to your problem. In later chapters I will provide a more rigorous mathematical foundation, and at that time I will have to either correct approximations that I made in this chapter or provide additional information that I did not cover here. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Multivariate Normal Distributions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What might a *multivariate normal distribution* look like? In this context, multivariate just means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that $x = 2$ and $y = 7$. Therefore we can see that for $N$ dimensions, we need $N$ means, like so:\n", - "\n", - "$$\n", - "\\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix}\n", - "$$\n", - "\n", - "Therefore for this example we would have\n", - "\n", - "$$\n", - "\\mu = \\begin{bmatrix}2\\\\7\\end{bmatrix} \n", - "$$\n", - "\n", - "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 8, like so. \n", - "\n", - "$$\\sigma^2 = \\begin{bmatrix}10\\\\8\\end{bmatrix}$$ \n", - "\n", - "While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use the following matrix to denote *covariances* with multivariate normal distributions. You might guess, correctly, that *covariance* is short for *correlated variances*." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\Sigma = \\begin{pmatrix}\n", - " \\sigma_1^2 & p\\sigma_1\\sigma_2 & \\cdots & p\\sigma_1\\sigma_n \\\\\n", - " p\\sigma_2\\sigma_1 &\\sigma_2^2 & \\cdots & p\\sigma_2\\sigma_n \\\\\n", - " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", - " p\\sigma_n\\sigma_1 & p\\sigma_n\\sigma_2 & \\cdots & \\sigma_n^2\n", - " \\end{pmatrix}\n", - "$$\n", - "\n", - "If you haven't seen this before it is probably a bit confusing at the moment. Rather than explain the math right now, we will take our usual tactic of building our intuition first with various physical models. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements are a product of the $\\sigma$ corresponding to the $i$th (row) and $j$th (column) state variable multiplied by a constant $p$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, without explanation, here is the full equation for the multivarate normal distribution in $n$ dimensions.\n", - "\n", - "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n", - "\n", - "I urge you to not try to remember this function. We will program it in a Python function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the *univarate normal distribution* except it uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. Here is the *univariate* equation for reference:\n", - "\n", - "$$ \n", - "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 }\n", - "$$\n", - "\n", - "If you are reasonably well-versed in linear algebra this equation should look quite managable; if not, don't worry! If you want to learn the math we will cover it in detail in the next optional chapter. If you choose to skip that chapter the rest of this book should still be managable for you\n", - "\n", - "I have programmed it and saved it in the file *stats.py* with the function name *multivariate_gaussian*. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of numpy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner. If you wish to view the code, I urge you to either load it in an editor, or load it into this worksheet by putting $\\verb,%load -s multivariate_gaussian stats.py,$ in the next cell and executing it with ctrl-enter. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - ">As of version 0.14 scipy.stats has implemented the multivariate normal equation with the function $\\verb,multivariate_normal(),$. It is superior to my function in several ways. First, it is implemented in Fortran, and is therefore faster than mine. Second, it implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use $\\verb,scipy.version.version,$ to get the version number. I deliberately named my function $\\verb,multivariate_gaussian(),$ to ensure it is never confused with the built in version.\n", - "\n", - "> If you intend to use Python for Kalman filters, you will want to read the tutorial for the $\\verb,scipy.stats,$ module, which explains 'freezing' distributions and other very useful features. As of this date, it includes an example of using the multivariate_normal function, which does work a bit differently from my function." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from stats import gaussian, multivariate_gaussian" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n", - "\n", - "First, let's find the probability for our dog being at (2.5, 7.3) if we believe he is at (2,7) with a variance of 8 for $x$ and a variance of 10 for $y$. This function requires us to pass everything in as numpy arrays (we will soon provide a more robust version that works with numpy matrices, numpy arrays, and/or scalars in any combinations. That code contains a lot of boilerplate which obscures the algorithm).\n", - "\n", - "Start by setting $x$ to (2.5,7.3):" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "x = np.array([2.5, 7.3])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we set the mean of our belief:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mu = np.array([2,7])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances. I will use the seemingly arbitrary name $\\textbf{P}$ for the covariance matrix. The Kalman filters use the name $\\textbf{P}$ for this matrix, so I will introduce the terminology now to avoid explaining why I change the name later. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "P = np.array([[8.,0],[0,10.]])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now just call the function" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print(multivariate_gaussian(x,mu,P))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.0174395374407\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's check the probability for the dog being at exactly (2,7)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function\n", - "\n", - "x = np.array([2,7])\n", - "print(\"Probability dog is at (2,7) is %.2f%%\" % (multivariate_gaussian(x,mu,P) * 100.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Probability dog is at (2,7) is 1.78%\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These numbers are not easy to interpret. Let's plot this in 3D, with the $z$ (up) coordinate being the probability." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib.pylab as pylab\n", - "from matplotlib import cm\n", - "from mpl_toolkits.mplot3d import Axes3D\n", - "import numpy as np\n", - "\n", - "pylab.rcParams['axes.color_cycle'] = '348ABD, 7A68A6, A60628, 467821, CF4457, 188487, E24A33'\n", - "\n", - "P = np.array([[8.,0],[0,4.]])\n", - "mu = np.array([2,7])\n", - "\n", - "xs, ys = np.arange(-8, 13, .5), np.arange(-8, 20, .5)\n", - "xv, yv = np.meshgrid (xs, ys)\n", - "\n", - "zs = np.array([100.* multivariate_gaussian(np.array([x,y]),mu,P) \\\n", - " for x,y in zip(np.ravel(xv), np.ravel(yv))])\n", - "zv = zs.reshape(xv.shape)\n", - "\n", - "ax = plt.figure().add_subplot(111, projection='3d')\n", - "ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n", - "\n", - "ax.set_xlabel('X')\n", - "ax.set_ylabel('Y')\n", - "\n", - "ax.contour(xv, yv, zv, zdir='x', offset=-9, cmap=cm.autumn)\n", - "ax.contour(xv, yv, zv, zdir='y', offset=20, cmap=cm.BuGn)\n", - "plt.xlim((-10,15))\n", - "plt.ylim((-10,20))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 8, - "text": [ - "(-10, 20)" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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ZvabmLeoS47hs1pl4ysUiAeVYZWvZV5amuZM49QEFV5UGiVWP8IMwsymlLenT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- "text": [ - "" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange.\n", - "\n", - "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance or not. So for most of the rest of this book we will display multidimensional Gaussian using contour plots. I will use some helper functions in $\\verb,gaussian.py,$ to plot them. If you are interested in linear algebra go ahead and look at the code used to produce these contours, otherwise feel free to ignore it." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import stats\n", - "\n", - "P = np.array([[2,0],[0,2]])\n", - "plt.subplot(131)\n", - "stats.plot_covariance_ellipse((2,7), cov=P, title='|2 0|\\n|0 2|')\n", - "\n", - "plt.subplot(132)\n", - "P = np.array([[2,0],[0,9]])\n", - "stats.plot_covariance_ellipse((2,7), P, title='|2 0|\\n|0 9|')\n", - "\n", - "plt.subplot(133)\n", - "P = np.array([[2,1.2],[1.2,2]])\n", - "stats.plot_covariance_ellipse((2,7), P, title='|2 1.2|\\n|1.2 2|')\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ssQj06eNEp04u0V1RDa6ZIqJg8ifn8M4UEanKyJEjcebMGVgsFkydOlV0d1Rr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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "From a mathematical perspective these display the values that the multivariate gaussian takes for a specific sigma (in this case $\\sigma^2=1$. Think of it as taking a horizontal slice through the 3D surface plot we did above. However, thinking about the physical interpretation of these plots clarifies their meaning.\n", - "\n", - "The first plot uses the mean and covariance matrices of\n", - "$$\n", - "\\begin{aligned}\n", - "\\mathbf{\\mu} &= \\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", - "\\mathbf{\\sigma}^2 &= \\begin{bmatrix}2&0\\\\0&2\\end{bmatrix}\n", - "\\end{aligned}\n", - "$$ \n", - "\n", - "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for the $1\\sigma^2$ probability - points where the dog is quite likely to be based on our current knowledge. Of course, the dog might be very far from this point, as Gaussians allow the mean to be any value. For example, the dog could be at (3234.76,189989.62), but that has vanishing low probability of being true. Generally speaking displaying the $1\\sigma^2$ to $2\\sigma^2$ contour captures the most likely values for the distribution. An equivelent way of thinking about this is the circle/ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The second plot uses the mean and covariance matrices of\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", - "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "This time we use a different variance for $x$ (2) vs $y$ (9). The result is an ellipse. When we look at it we can immediately tell that we have a lot more uncertainty in the $y$ value vs the $x$ value. Our belief that the value is (2,7) is the same in both cases, but errors are different. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object, or is closer, than another sensor, and so we end up with different error rates in the different axis." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The third plot uses the mean and covariance matrices of:\n", - "$$\n", - "\\begin{aligned}\n", - "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", - "\\sigma^2 &= \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "This is the first contour that has values in the off-diagonal elements of $cov$, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling use the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal. What does this mean in physical terms? Think of trying to park your car in a parking spot. You can not pull up beside the spot and then move sideways into the space because most cars cannot go purely sideways. $x$ and $y$ are not independent. This is a consequence of the steering system in a car. When your tires are turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk straight forward to to the side. If $x$ changes, $y$ must also change in a defined way. \n", - "\n", - "So when we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how strongly correlated the values are.\n", - "\n", - "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Unobserved Variables" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's say we are tracking an aircraft and we get the following data for the $x$ coordinate at time $t$=1,2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import mkf_internal\n", - "mkf_internal.show_position_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It appears that the aircraft is flying in a straight line because we can draw a line between the three points, and we know that aircraft cannot turn on a dime. The most reasonable guess is that $x$=4 at $t$=4. I will depict that with a green arrow." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mkf_internal.show_position_prediction_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If this is data from a Kalman filter, then each point has both a mean and variance. Let's try to show that by showing the approximate error for each point. Don't worry about why I am using a covariance matrix to depict the variance at this point, it will become clear in a few paragraphs. The intent at this point is to show that while we have $x$=1,2,3 that there is a lot of error associated with each measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mkf_internal.show_x_error_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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gl2/Yib3iYuC008LYsMHaxlu97+MJUZnGUjby8ssvY9myZbj55puhqvqXnHDC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\n1ETH93v2z0EX793hYNVJTJizlOh6ULNbyESddku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- "text": [ - "" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see that there is a lot of error associated with each value of $x$. We could write a 1D Kalman filter as we did in the last chapter, but suppose this is the output of that filter, and not just raw sensor measurements. Are we out of luck?\n", - "\n", - "Let us think about how we predicted that $x$=4 at $t$=4. In one sense we just drew a straight line between the points and saw where it lay at $t$=4. My constant refrain: what is the physical interpretation of that? What is the difference in $x$ over time? In other words, what is $\\frac{\\partial x}{\\partial t}$? The derivative, or difference in distance over time is *velocity*. \n", - "\n", - "This is the **key point** in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). It does not have any kind of sensor that provides velocity to us. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity an *unobserved variable*. Unobserved means what it sounds like - there is no sensor that is measuring velocity directly. Since the velocity is based on the position, and the position has error, the velocity will have error as well. What happens if we draw the velocity errors over the positions errors?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mkf_internal.show_x_with_unobserved()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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3wj1Fabzs3h35Hrf+RJ8oE2aKvbHOfrDYQFbGqCQKYnbQ1+vDA1jFo/Ejbuai668HxM0c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042/+i5bUTfE8+AYXyXuE/XJ9qVh/l0zmlgYKErW4QMPTW5rxTmrs5h3NAZ6E8YhNlAr9Ef/mMt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\nYLPZ0NjYiKKiIvT39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- "text": [ - "" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n", - "\n", - "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Kalman Filter Algorithm" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the *measurement function*. Then we predict the next position by using the current estimate and something called the *state transition function*. In our example above,\n", - "\n", - "$$new\\_position = old\\_position + velocity*time$$ \n", - "\n", - "Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the *residual*. Finally, we use something called the *Kalman gain* to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. \n", - "\n", - "The chart shows a prior estimate of $x=1$ and $\\dot{x}=1$ ($\\dot{x}$ is the shorthand for the derivative of x, which is velocity). Therefore we predict $\\hat{x}=2$. However, the new measurement $x^{'}=1.3$, giving a residual $r=0.7$. Finally, Kalman filter gain $k$ gives us a new estimate of $\\hat{x^{'}}=1.8$.\n", - "\n", - "** CHECK SYMBOLOGY!!!!**" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from mkf_internal import *\n", - "show_residual_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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DD376/PPP1bBhngYN6iGbrfT2kJAwxcR01zfflL48t2hRpJCQkot+vMzM+rLb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\nLrmEygMAAIC34ZPgXEhJSXEsq6N6yNI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- "text": [ - "" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "The Equations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The brilliance of the Kalman filter is taking the insights of the chapter up to this point and finding an optimal mathematical solution. The Kalman filter finds what is called a *least squared fit* to the set of measurements to produce an optimal output. We will not trouble ourselves with the derivation of these equations. It runs to several pages, and offers a lot less insight than the words above, in my opinion. Furthermore, to create a Kalman filter for your application you will not be manipulating these equations, but only specifing a number of parameters that are used by them. It would be going too far to say that you will never need to understand these equations; but to start we can pass them by and I will present the code that implements them. So, first, let's see the equations. \n", - "> Kalman Filter Predict Step:\n", - "\n", - "> $$\n", - "\\begin{aligned}\n", - "\\hat{\\mathbf{x}}_{t|t-1} &= \\mathbf{\\Phi_t}\\hat{\\mathbf{x}}_{t-1} + \\mathbf{B u}_t\\;\\;\\;&(1) \\\\\n", - "\\mathbf{P}_{t|t-1} &= \\mathbf{\\Phi_tP}_{t-1}\\mathbf{\\Phi}^T_t + \\mathbf{Q}_t\\;\\;\\;&(2)\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "> Kalman Filter Update Step:\n", - "\n", - ">$$\n", - "\\begin{aligned}\n", - "\\mathbf{\\gamma} &= \\mathbf{z}_t - \\mathbf{H}_t\\hat{\\mathbf{x}}_t\\;\\;\\;&(3) \\\\\n", - "\\mathbf{K}_t &= \\mathbf{P}_t \\mathbf{H}^T_t (\\mathbf{H}_t \\mathbf{P}_t \\mathbf{H}^T_t + \\mathbf{R}_t)^{-1}\\;\\;\\;(4) \\\\\n", - "\\\\\n", - "\\hat{\\mathbf{x}}_t &= \\hat{\\mathbf{x}}_{t|t-1} + \\mathbf{K}_t \\gamma \\;\\;\\;&(5) \\\\\n", - "\\mathbf{P}_{t|t} &= (\\mathbf{I} - \\mathbf{K}_t \\mathbf{H}_t)\\mathbf{P}_{t|t-1} \\;\\;\\;&(6)\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Dash off, wipe the blood out of your eyes, and we'll disuss what this means. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These are nothing more than linear algebra equations that implement the algorithm we used in the last chapter, but using multidimensional Gaussians instead of univariate Gaussians, and optimized for a least squares fit. Each capital letter denotes a matrix or vector. The subscripts indicate which time step the data comes from; $t$ is now, $t-1$ is the previous step. $A^T$ is the transpose of A, and $A^{-1}$ is the inverse. Finally, the hat denotes an estimate, so $\\hat{x}_t$ is the estimate of $x$ at time $t$." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Kalman Equations Expressed as an Algorithm" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Different texts use different notation and variable names for the Kalman filter. Later we will expose you to these different forms to prepare you for reading the original literature. However, I find much of the notation very dense, and unnecessary for writing code. The subscripts indicate the time step, but we know the left hand side is for this time step, and the right hand side is for the previous step. For most of this book I'm going to use the following simplified equations, which express an algorithm.\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\text{Predict Step}\\\\\n", - "\\mathbf{x}' &= \\mathbf{F x} + \\mathbf{B u}\\;\\;\\;&(1) \\\\\n", - "\\mathbf{P} &= \\mathbf{FP{F}}^T + \\mathbf{Q}\\;\\;\\;&(2) \\\\\n", - "\\\\\n", - "\\text{Update Step}\\\\\n", - "\\mathbf{\\gamma} &= \\mathbf{z} - \\mathbf{H x} \\;\\;\\;&(3)\\\\\n", - "\\mathbf{K}&= \\mathbf{PH}^T (\\mathbf{HPH}^T + \\mathbf{R})^{-1}\\;\\;\\;&(4) \\\\\n", - "\\mathbf{x}&=\\mathbf{x}' +\\mathbf{K\\gamma} \\;\\;\\;&(5)\\\\\n", - "\\mathbf{P}&= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P}\\;\\;\\;&(6)\n", - "\\end{aligned}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is an algorithm, so $=$ denotes assignment, not equality. For example, equation (6) has P on both sides of the $=$. This equation updates the value of P by the computation on the right hand side. \n", - "\n", - "Here, a $'$ means estimate, so $\\mathbf{x}'$ is the estimate of the state $\\mathbf{x}$. Many texts use $\\hat{\\mathbf{x}}$ or $\\mathbf{x}^*$ to express this. I find these choices unfortunate because we will often want to express these in matrix form. The notation of a hat over a matrix is clumsy at best, and an asterisk followin a matrix normally means the *complex congugate* of the matrix, which is *not* what is intended. So I use $'$. \n", - "\n", - "What do all of the variables mean? What is $\\mathbf{P}$, for example? Don't worry right now. Instead, I am just going to design a Kalman filter, and introduce the names as we go. Then we will just pass them into Python function that implement the equations above, and we will have our solution. Later sections will then delve into more detail about each step and equation. I think learning by example and practice is far easier than trying to memorize a dozen abstract facts at once. \n", - "\n", - "Look at the code below for the predict step (which we will present a bit later). \n", - "\n", - " def predict():\n", - " x = F*x + B*u # equation (1)\n", - " P = F*P*F.T + Q # equation (2)\n", - " \n", - "Notice how simple it really is. It really isn't much different from the predict step in the previous chapter, and it is a nearly exact transliteration of the equations above. As you become familiar with this notation you will find yourself able to read textbooks and paper and implement the equations without much difficulty. \n", - " \n", - "> Later, if you become interested in the details of numerical computation you may change the implementation to be faster or more numerically stable than this written form, but for most of this book our code will follow the Kalman filter equations almost exactly. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking a Dog" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of this chapter - that of using *unobserved variables* to improve our estimates. In simple terms, our algorithm is:\n", - "\n", - " 1. predict the next value for x with \"x + vel*time\"\n", - " 2. get measurement for x\n", - " 3. compute residual as: \"x - x_prediction\"\n", - " 4. compute kalman gain based on noise levels\n", - " 5. compute new position as \"residual * kalman gain\"\n", - " \n", - "That is the entire Kalman filter algorithm. It is both what we described above in words, and it is what the rather obscure Kalman Filter equations do. The Kalman filter equations just express this algorithm by using linear algebra. \n", - "\n", - "As I mentioned above, there is actually very little programming involved in creating a Kalman filter. We will just be defining several matrices and parameters that get passed into the Kalman filter algorithm code. Rather than try to explain each of the steps ahead of time, which can be a bit abstract and hard to follow, let's just do it for our by now well known dog tracking problem. Naturally this one example will not cover every use case of the Kalman filter, but we will learn by starting with a simple problem and then slowly start addressing more complicated situations.\n", - "\n", - "\n", - "##### **Step 1:** Choose the State Variables\n", - "\n", - "*State variables* are the variables that the Kalman filter estimates. They include the *observed variables* - the data that is directly measured by a sensor, and the *unobserved variables*, which we can infer from the observed variables.\n", - "\n", - "For our dog tracking problem, our observed state variable is position, and the unobserved variable is velocity. \n", - "\n", - "The Kalman filter is implemented using linear algebra. We use an $n\\times 1$ matrix to store $n$ state variables. For the dog tracking problem, we use $x$ to denote position, and the first derivative of $x$, $\\dot{x}$, for velocity. The Kalman filter equations use $\\mathbf{x}$ for the state, so we define $\\mathbf{x}$ as:\n", - "\n", - "$$\\mathbf{x} =\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 2:** Design State Transition Function\n", - "\n", - "\n", - "The next step in designing a Kalman filter is designing what is called the *State Transition Function.* This is a set of equations that mathematically describe the behavior of the system we are filtering. So, for the dog tracking problem we are tracking a moving object, so we just need the Newtonian equations for motion. In other words, these are the equations that we use to predict the next state from the current state. \n", - "\n", - "We know from elementary physics how to compute a new position given a previous position, velocity, and time, like so:\n", - "\n", - "$$ x' = {velocity}*{time} + x_{previous}$$\n", - "\n", - "In more formal mathematics we would write:\n", - "\n", - "$$x' = \\dot{x}(\\Delta t) + x$$\n", - "\n", - "where $\\dot{x}$ is velocity, and $\\Delta t$ is the amount of time between $t-1$ and $t$. In our problems we will be running the Kalman filter at fixed time intervals, so $\\Delta t$ is a constant for us. We will just set it to $1$ and worry about the units later.\n", - "\n", - "As in step one we must express this in the form of matrices so that our linear algebra software and solve the equations for us. The Kalman filter equations require that we write it in the form:\n", - "\n", - "$$ \\mathbf{x}' = \\mathbf{Fx}$$\n", - "\n", - "where as in step 1 $\\mathbf{x}$ is the matrix containing the state variables, and $\\mathbf{F}$ is the matrix that when multiplied by $\\mathbf{x}$ yields our equations. Note that this is just part of the Kalman filter equation (1) above. We will deal with the second half of equation (1) in the next step.\n", - "\n", - "Since $\\mathbf{x}$ is a $2{\\times}1$ matrix $\\mathbf{F}$ must be a $2{\\times}2$ matrix to yield another $2{\\times}1$ matrix as a result. The first row of the F is easy to derive:\n", - "\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}' &=\\begin{bmatrix}1&\\Delta t \\\\ ?&?\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "When we multiply the first row of $\\mathbf{F}$ that out we get:\n", - "$$ \n", - "\\begin{aligned}\n", - "x' &= 1 \\times x + \\Delta t * \\dot{x} \\mbox{, or} \\\\\n", - "x' &= \\dot{x}(\\Delta t) + x\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Now we have to account for the second row. I've let it somewhat unstated up to now, but we are assuming constant velocity for this problem. Naturally this assumption is not true; if our dog moves it must accelerate and deaccelerate. If you cast your mind back to the $g-h Filter$ chapter we explored the effect of assuming constant velocity. So long as the acceleration is small compared to $\\Delta t$ the filter will still perform well. \n", - "\n", - "Therefore we will assume that\n", - "\n", - "$$\\dot{x}' = \\dot{x}$$\n", - "\n", - "which gives us the second row of $\\mathbf{F}$ as follows, once we set $\\Delta t = 1$:\n", - "\n", - "\n", - "$$\n", - "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}' =\\begin{bmatrix}1&1 \\\\ 0&1\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", - "$$\n", - "\n", - "Which, when multiplied out, yields our desired equations:\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "x' &= x + \\dot{x} \\\\\n", - "\\dot{x}' &= \\dot{x}\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "In the vocabulary of Kalman filters we call this *transforming the state matrix*. We take our state matrix, which for us is $(\\begin{smallmatrix}x \\\\ \\dot{x}\\end{smallmatrix})$,and multipy it by a matrix we will call $F$ to compute the new state. In this case, $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$. \n", - "\n", - "\n", - "You will do this for every Kalman filter you ever design. Your state matrix will change depending on how many state random variables you have, and then you will create $F$ so that it updates your state based on whatever the physics of your problem dictates. $F$ is always a matrix of constants. If this is not fully clear, don't worry, we will do this many times in this book.\n", - "\n", - "Refer back to the first Kalman filter equation $\\hat{\\mathbf{x}}_{t|t-1} = \\mathbf{F_t}\\hat{\\mathbf{x}}_{t-1} + \\mathbf{B u}_t$. There is an unexplained $\\mathbf{B u}_t$ term in there, but shorn of all the diacritics it should be clear that we just designed $F$ for this equation!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 3**: Design the Motion Function\n", - "\n", - "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Consider the state transition function we wrote for the dog:\n", - "\n", - "$$x_t = \\dot{x}(\\Delta t) + x_{t-1}$$\n", - "\n", - "Suppose that instead of passively tracking our dog we were actively controlling a robot. At each time step we would send control signals to the robot based on our current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity *and* control inputs to the drive motors. \n", - "\n", - "We will cover this use case later, but for now passive tracking applications we set those terms to 0. In step 2 there was the unexplained term $\\mathbf{Bu}$ in equation (1):\n", - "\n", - "$$\\mathbf{x}' = \\mathbf{Fx} + \\mathbf{Bu}$$.\n", - "\n", - "Here $\\mathbf{u}$ is the control input, and $\\mathbf{B}$ is its transfer function. For example, $\\mathbf{u}$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf{B}$ yields $\\begin{smallmatrix}x\\\\\\dot{x}\\end{smallmatrix}$. Since we do not need these terms we will set them both to zero and not concern ourselves with them for now.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 4**: Design the Measurement Function\n", - "\n", - "Now we need a way to compute the state variables to our measurements. In our problem we have one sensor for the position, and it outputs position directly. We do not have a sensor for velocity. If we put this in linear algebra terms we get:\n", - "\n", - "$$\n", - "z = \\begin{bmatrix}1&0\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", - "$$\n", - "\n", - "In other words, the measurement sensor provides one times the sensor's measurement of $x$, and zero times the nonexistent velocity measurement. This is simple, because the problem is simple! A slightly more complicated problem might use a temperature sensor might, for example, output a voltage, and we would need to provide an equation to convert from voltage to temperature. \n", - "\n", - "In the nomenclature of Kalman filters the $[1\\space\\space0]$ matrix is called $H$. If you scroll up to the Kalman filter equations you will see an $H$ term in the update step.\n", - "\n", - "$$\\mathbf{\\gamma} = \\mathbf{z} - \\mathbf{H x}\\tag{3}$$\n", - "\n", - "Believe it or not, we have designed the majority of our Kalman filter!! All that is left is to model the noise in our sensors." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 5**: Design the Measurement Noise Matrix\n", - "\n", - "The *measurement noise* is a matrix that models the noise in our sensors as a covariance matrix. This can be admittedly a very difficult thing to do in practice. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to already read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean. Later we will address this topic in detail. For now I just want you to get used to the idea of the measurement noise matrix so we will keep it deliberately simple.\n", - "\n", - "In the last chapter we used a variance of 5 for our position sensor. Let's use the same value here. The Kalman filter equations uses the symbol $R$ for this matrix.\n", - "\n", - "$$R = 5$$\n", - "\n", - "In general the matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is $m{\\times}m$ because it is a covariance matrix, as there may be correlations between the sensors. We have only 1 sensor here so we write:\n", - "\n", - "$$R = \\begin{bmatrix}5\\end{bmatrix}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 6**: Design the Process Noise Matrix\n", - "\n", - "What is *process noise*? Consider the motion of a thrown ball. In a vacuum and with constant gravitational force it moves in a parabola. However, if you throw the ball on the surface of the earth you will also need to model factors like rotation and air drag. However, even when you have done all of that there is usually things you cannot account for. For example, consider wind. On a windy day the ball's trajectory will differ from the computed trajectory, perhaps by a significant amount. Without wind sensors, we may have no way to model the wind. Wind can come from any direction, so it is likely to have a near Gaussian distribution. The Kalman filter models this as *process noise*, and calls it $\\small\\mathbf{Q}$.\n", - "\n", - "Astute readers will realize that we can inspect the ball's path and extract wind as an unobserved state variable, but the point to grasp here is there will always be some unmodelled noise in our process, and the Kalman filter gives us a way to model it.\n", - "\n", - "Designing the process noise matrix can be quite demanding. For our first example, we will set it to 0, like so: $\\small\\mathbf{Q}=0$. It is unlikely that you would do that for a real filter.\n", - "\n", - "> Some books and papers use $\\small\\mathbf{R}$ for measurement noise and $\\small\\mathbf{Q}$ for the process noise. Others do the opposite, using $\\small\\mathbf{Q}$ for measurement noise and $\\small\\mathbf{R}$ for the process noise! Read carefully, and make sure you don't get confused. I use the following mnemonic. Radars are used to measure positions, and they have measurement error. So, for me, $\\small\\mathbf{R}$ is the **R**adar's measurement noise. I've read a lot of Kalman filter literature in the context of radar tracking, so it makes sense to me. I don't have a good one for $\\small\\mathbf{Q}$, other than to note that it alphabetically follows the p in **P**rocess." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### **Step 7**: Design Initial Conditions\n", - "\n", - "Finally, we need to specify the initial conditions for the state variables and their associated covariance matrix. If you have a rough idea of the values you can use that as your initial settings, or, you could always read the sensors for the first time, and calculate a initial value. The Kalman filter will converge and find the solution even if your initial conditions are far off, but the more accurate they are the faster and better the output will be. \n", - "\n", - "The covariance matrix ($\\small{\\mathbf{P}}$) is a $n{\\times}n$ matrix that specifies the variances and covariances of each state variable. This is a complicated topic, and I'd rather demostrate the matrix rather than talk about it abstractly here. For now, recognize that the Kalman filter will be calculating the covariance matrix at each step, just like the 1-D filter computed the variance of the mean at each step. So as with those examples we can make an initial guess and trust that $\\small{\\mathbf{P}}$ will converge to a smaller value as the filter progresses. I find this description somewhat unsatisfactory for several reasons, but until you've seen some examples it is hard to talk about in an understandable way." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implementing the Kalman Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As promised, the Kalman filter equations are already programmed for you. In many circumstances you will never have to write your own Kalman filter equations. We will look at the code later, but for now we will just import the code and use it. I have placed it in *KalmanFilter.py*, so let's start by importing it and creating a filter." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "from KalmanFilter import KalmanFilter\n", - "dog_filter = KalmanFilter (dim=2)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That's it. We import the filter, and create a filter that uses 2 state variables. We specify the number of state variables with the 'dim=2' expression (dim means dimensions).\n", - "\n", - "The Kalman filter class contains a number of variables that you need to set. x is the state, F is the state transition function, and so on. Rather than talk about it, let's just do it!" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog_filter.x = np.matrix([[0], [0]]) # initial state (location and velocity)\n", - "dog_filter.F = np.matrix([[1,1], [0,1]]) # state transition matrix\n", - "dog_filter.H = np.matrix([[1,0]]) # Measurement function\n", - "dog_filter.R = 5 # measurement noise\n", - "dog_filter.Q = 0 # process noise\n", - "dog_filter.P *= 500. # covariance matrix \n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's look at this line by line. \n", - "\n", - "**1**: We just assign the initial value for our state. Here we just initialize both the position and velocity to zero. \n", - "\n", - "**2**: We set $\\textbf{F}=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$, as in design step 2 above. \n", - "\n", - "**3**: We set $\\textbf{H}=(\\begin{smallmatrix}1&0\\end{smallmatrix})$, as in design step 3 above.\n", - "\n", - "**4**: We set $\\textbf{R} = 5$ and $\\mathbf{Q}=0$ as in steps 5 and 6.\n", - "\n", - "**5**: Recall in the last chapter we set our initial belief to $\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(0,500)$ to signify our lack of knowledge about the initial conditions. We implemented this in Python with a list that contained both $\\mu$ and $\\sigma^2$ in the variable $pos$:\n", - "\n", - " pos = (0,500)\n", - " \n", - "Multidimensional Kalman filters stores the state variables in $\\mathbf{x}$ and their *covariance* in $\\mathbf{P}$. These are $\\verb,f.x,$ and $\\verb,f.P,$ in the code above. Notionally, this is similar as the one dimension case, but instead of having a mean and variance we have a mean and covariance. For the multidimensional case, we have\n", - "\n", - "$$\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(\\mathbf{x},\\mathbf{P})$$\n", - "\n", - "$\\mathbf{P}$ is initialized to the identity matrix of size $n{\\times}n$, so multiplying by 500 assigns a variance of 500 to $x$ and $\\dot{x}$. So $\\verb,f.P,$ contains\n", - "\n", - "$$\\begin{bmatrix} 500&0\\\\0&500\\end{bmatrix}$$\n", - "\n", - "This will become much clearer once we look at the covariance matrix in detail in later sessions. For now recognize that each diagonal element $e_{ii}$ is the variance for the $ith$ state variable. \n", - "\n", - "> Summary: For our dog tracking problem, in the 1-D case $\\mu$ was the position, and $\\sigma^2$ was the variance. In the 2-D case $\\mathbf{x}$ is our position and velocity, and $\\mathbf{P}$ is the *covariance* of the position and velocity. It is the same thing, just in higher dimensions!\n", - "\n", - "\n", - "All that is left is to run the code! The $\\tt DogSensor$ class from the previous chapter has been placed in $\\verb,DogSensor.py,$." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from DogSensor import DogSensor\n", - "\n", - "def dog_tracking_filter(R,Q=0,cov=1.):\n", - " dog_filter = KalmanFilter (dim=2)\n", - " dog_filter.x = np.matrix([[0], \n", - " [0]]) # initial state (location and velocity)\n", - " dog_filter.F = np.matrix([[1,1],\n", - " [0,1]]) # state transition matrix\n", - " dog_filter.H = np.matrix([[1,0]]) # Measurement function\n", - " dog_filter.R = R # measurement uncertainty\n", - " dog_filter.P *= cov # covariance matrix \n", - " if np.isscalar(Q):\n", - " dog_filter.Q = np.matrix([[0,0],\n", - " [0,Q]])\n", - " else:\n", - " dog_filter.Q = Q\n", - " return dog_filter\n", - "\n", - "\n", - "def filter_dog(noise=0, count=0, R=0, Q=0, data=None):\n", - " \"\"\" Kalman filter 'count' readings from the DogSensor.\n", - " 'noise' is the noise scaling factor for the DogSensor.\n", - " 'data' provides the measurements. If set, noise will\n", - " be ignored and data will not be generated for you.\n", - " \n", - " returns a tuple of (positions, measurements, covariance)\n", - " \"\"\"\n", - " if data is None: \n", - " dog = DogSensor(velocity=1, noise=noise)\n", - " zs = [dog.sense() for t in range(count)]\n", - " else:\n", - " zs = data\n", - "\n", - " dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", - "\n", - " pos = [None] * count\n", - " cov = [None] * count\n", - " \n", - " for t in range(count):\n", - " z = zs[t]\n", - " pos[t] = dog_filter.x[0,0]\n", - " cov[t] = dog_filter.P\n", - " \n", - " # perform the kalman filter steps\n", - " dog_filter.update (z)\n", - " dog_filter.predict()\n", - " \n", - " return (pos, zs, cov)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is the complete code for the filter, and most of it is just boilerplate. The first function $\\verb,dog_tracking_filter(),$ is a helper function that creates a $\\verb,KalmanFilter,$ object with specified $\\mathbf{R}$, $\\mathbf{Q}$ and $\\mathbf{P}$ matrices. We've shown this code already, so I will not discuss it more here. \n", - "\n", - "The function $\\verb,filter_dog(),$ implements the filter itself. Lets work through it line by line. The first line creates the simulation of the DogSensor, as we have seen in the previous chapter.\n", - "\n", - " dog = DogSensor(velocity=1, noise=noise)\n", - "\n", - "The next line uses our helper function to create a Kalman filter.\n", - "\n", - " dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", - " \n", - "We will want to plot the filtered position, the measurements, and the covariance, so we will need to store them in lists. The next three lines initialize empty lists of length *count* in a pythonic way.\n", - "\n", - " pos = [None] * count\n", - " zs = [None] * count\n", - " cov = [None] * count\n", - " \n", - "Finally we get to the filter. All we need to do is perform the update and predict steps of the Kalman filter for each measurement. The $\\verb,KalmanFilter,$ class provides the two functions $\\verb,update(),$ and $\\verb,predict(),$ for this purpose. $\\verb,update(),$ performs the measurement update step of the Kalman filter, and so it takes a variable containing the sensor measurement. \n", - "\n", - "Absent the bookkeeping work of storing the filter's data, the for loop reads:\n", - "\n", - " for t in range (count):\n", - " z = dog.sense()\n", - " dog_filter.update (z)\n", - " dog_filter.predict()\n", - " \n", - "It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the $\\verb,KalmanFilter,$ variables; executing the filter is trivial.\n", - "\n", - "Now let's look at the result. Here is some code that calls $\\verb,filter_track(),$ and then plots the result. It is fairly uninteresting code, so I will not walk through it." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def plot_track(noise=None, count=0, R=0, Q=0, data=None, plot_P=True, title='Kalman Filter'):\n", - " \n", - " ps, zs, cov = filter_dog(noise=noise, data=data, count=count, R=R, Q=Q)\n", - " \n", - " p0, = plt.plot([0,count],[0,count],'g')\n", - " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", - " p2, = plt.plot(range(1,count+1),ps, c='b')\n", - " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", - " plt.ylim((0-10,count+10))\n", - " plt.title(title)\n", - " plt.show()\n", - " \n", - " if plot_P:\n", - " plt.subplot(121)\n", - " plot_covariance(cov, (0,0))\n", - " plt.subplot(122)\n", - " plot_covariance(cov, (1,1))\n", - " plt.show()\n", - " \n", - "def plot_covariance(P, index=(0,0)):\n", - " ps = []\n", - " for p in P:\n", - " ps.append(p[index[0],index[1]])\n", - " plt.plot(ps)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, call it. We will start by filtering 100 measurements with a noise factor of 30, $\\mathbf{R}=5$ and $\\mathbf{Q}=0$." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plot_track (noise=30, R=5, Q=0, count=100)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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jmkbDZ7PkzI/4JfoxsPZAulTqgkFryLV+yFLTD7B06VJat25NjRo16N+/P7169aJatWqc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- "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Nobert Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n", - "\n", - "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n", - "\n", - "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that.\n", - "\n", - "In the previous chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filter with this code merely by altering are assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Walking Through the KalmanFilter Code (Optional)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The code in the $\\verb,KalmanFilter,$ is a nearly verbatim transcription of the linear algebra equations. I take advantage of numpy matrices to implement the linear algebra. It is worth looking at this code if for no other reason than to realize how easy it is to implement linear algebra with Python and numpy. For most of this book you will only really need to know how to call this class, not how to implement it from scratch.\n", - "\n", - "> **sidebar**: numpy provides two data structures which can be used to perform linear algebra: $\\verb,numpy.array,$ and $\\verb,numpy.matrix,$. The usual advice is to use $\\verb,numpy.array,$, not $\\verb,numpy.matrix,$. Ever the contrarian, I have chosen to use $\\verb,numpy.matrix,$, but for what I think are good pedalogical reasons. $\\verb,numpy.array,$ is usually recommended because it can be sized to any arbitrary number of dimensions, and $\\verb,numpy.matrix,$ is constrained to two dimensions. However, for Kalman filters we only need 2 dimensions. More importantly, $\\verb,numpy.matrix,$ allows you to use very natural sytax. Multipying a by b is written $\\verb,a*b,$ if using $\\verb,numpy.matrix,$, but $\\verb,a.dot(b),$ if they are $\\verb,numpy.array,$. It is also more natural to mix scalars and matrices using $\\verb,numpy.matrix,$. Finally, the resulting code is extremely close to the equivalent Matlab code; if you are more familiar with Matlab than Python this code should feel very familiar to you.\n", - "\n", - "\n", - "The constructor of the class creates variables for each of the Kalman filter variables, and assigns them a reasonable default value. This is the code in its entirety:\n", - "\n", - " def __init__(self, dim):\n", - " \"\"\" Create a Kalman filter of dimension 'dim'\"\"\"\n", - " \n", - " self.x = 0\n", - " self.P = np.matrix(np.eye(dim))\n", - " self.Q = np.matrix(np.eye(dim))\n", - " self.u = np.matrix(np.zeros((dim,1)))\n", - " self.B = 0\n", - " self.F = 0\n", - " self.H = 0\n", - " self.R = np.matrix(np.eye(1))\n", - " self.I = np.matrix(np.eye(dim))\n", - "\n", - "The function $\\verb,predict(),$ implements the Kalman filter prediction equations.\n", - "\n", - " def predict(self):\n", - " self.x = (self.F*self.x) + (self.B * self.u)\n", - " self.P = (self.F * self.P * self.F.T) + self.Q\n", - "\n", - "This is nothing more than a transliteration of these equations.\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "\\mathbf{x}' &= \\mathbf{F x} + \\mathbf{B u}\\\\\n", - "\\mathbf{P} &= \\mathbf{FP{F}}^T + \\mathbf{Q}\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Finally, the $\\verb,update(),$ function implements the Kalman filter update equations in an equally straightforward way:\n", - "\n", - " def update(self, Z):\n", - " \"\"\"\n", - " Add a new measurement to the kalman filter.\n", - " \"\"\"\n", - " y = Z - (self.H * self.x)\n", - " S = (self.H * self.P * self.H.T) + self.R\n", - "\n", - "\n", - " K = self.P * self.H.T * linalg.inv(S)\n", - " self.x = self.x + (K*y)\n", - " self.P = (self.I - (K*self.H))*self.P\n", - " \n", - "Finally, for those reading this online or in a printed form, here is the code in $\\verb,KalmanFilter.py,$ absent the unit testing code that is included in that file. It has also been simplified slightly; the actual code uses a more complicated way to compute $\\mathbf{P}$ in the update step that is more numerically stable. We are not yet prepared to discuss the numerical performance of the filter, so I have elided that code here. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "import scipy.linalg as linalg\n", - "\n", - "class KalmanFilter:\n", - "\n", - " def __init__(self, dim):\n", - " \"\"\" Create a Kalman filter of dimension 'dim'\"\"\"\n", - " \n", - " self.x = 0 # state\n", - " self.P = np.matrix(np.eye(dim)) # uncertainty covariance\n", - " self.Q = np.matrix(np.eye(dim)) # process uncertainty\n", - " self.u = np.matrix(np.zeros((dim,1))) # motion vector\n", - " self.B = 0\n", - " self.F = 0 # state transition matrix\n", - " self.H = 0 # Measurement function (maps state to measurements)\n", - " self.R = np.matrix(np.eye(1)) # state uncertainty\n", - " self.I = np.matrix(np.eye(dim))\n", - "\n", - "\n", - " def update(self, Z):\n", - " \"\"\"\n", - " Add a new measurement to the kalman filter.\n", - " \"\"\"\n", - "\n", - " # measurement update\n", - " y = Z - (self.H * self.x) # error (residual) between measurement \n", - " # and prediction\n", - " S = (self.H * self.P * self.H.T) + self.R # project system uncertainty into \n", - " # measurment space + measurement noise(R)\n", - "\n", - "\n", - " K = self.P * self.H.T * linalg.inv(S) # map system uncertainty into kalman gain\n", - "\n", - " self.x = self.x + (K*y) # predict new x with residual scaled \n", - " #by the kalman gain\n", - " self.P = (self.I - (K*self.H))*self.P # and compute the new covariance\n", - "\n", - " def predict(self):\n", - " # prediction\n", - " self.x = (self.F*self.x) + self.u\n", - " self.P = self.F * self.P * self.F.T + self.Q" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 8 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Adjusting the Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Your results will vary slightly depending on what numbers your random generator creates for the noise componenet of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n", - "\n", - "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the ${\\mathbf{H}}$ and ${\\mathbf{F}}$ matrices - they develop in an obvious manner based on the physics of the system we are modelling. The art comes in modelling the sensors and selecting appropriate values for the rest of our variables.\n", - "\n", - "Let's look at the effects of the noise parameters ${\\mathbf{R}}$ and ${\\mathbf{Q}}$. I will only run the filter for twenty steps to ensure we can see see the difference between the measurements and filter output. I will start by holding ${\\mathbf{R}}$ to 5 and vary ${\\mathbf{Q}}$. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "dog = DogSensor(velocity=1, noise=30)\n", - "zs = [dog.sense() for t in range(30)]\n", - "\n", - "plot_track (data=zs, R=5, Q=10,count=30, plot_P=False, title='R = 5, Q = 10')\n", - "plot_track (data=zs, R=5, Q=.02,count=30, plot_P=False, title='R = 5, Q = 0.02')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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SpYmKimLHjh2ULl2a69ev2zye1Wp1eGtl4f4kvkIIIbxFXJyT64utVsdLIvz8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WhiXKlSJdy9ezfv8d27d1GpUqVC24UnhqPW/Vo4e/IsbvjfQEhISJ5PYO6VmZzHRiOD5cvbw9vb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\noRkzZrj1p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/t1M8sDhPVX6KqCpRNCrVCJ1Wl+P9+bJiLIQQQggh8k/K3Llemddety7Jn3+O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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n", - "\n", - "In the Kalman filter ${\\mathbf{R}}$ is the *measurement noise* and ${\\mathbf{Q}}$ is the *process uncertainty*. ${\\mathbf{R}}$ is the same in both plots, so ignore it for the moment. Why does ${\\mathbf{Q}}$ affect the plots this way?\n", - "\n", - "Let's remind ourselves of what the term *process uncertainty* means. Consider the problem of tracking a ball. We can accurately model its behavior in statid air with math, but if there is any wind our model will diverge from reality. \n", - "\n", - "In the first case we set ${\\mathbf{Q}}=10$, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\". Strictly speaking, we are telling the filter there is a lot of external noise that we are not modeling with $\\small{\\mathbf{F}}$, but the upshot of that is to not trust the motion prediction step. So the filter will be computing velocity ($\\dot{x}$), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n", - "\n", - "In the second case we set ${\\mathbf{Q}}=0.02$, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". Again, more strictly this actually says there is very small amounts of process noise, so the motion computation will be accurate. So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our trustworthy velocity prediction.\n", - "\n", - "**AUTHOR'S NOTE: move covariance matrix coverage here, then do R, then Q. Order as below is confusing.**" - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Designing $\\textbf{Q}$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "But what does \"quite large\" and \"quite small\" mean, and what should $\\textbf{Q}$ contain? The numbers in the $\\textbf{Q}$ matrix are not arbitrary, but the variances of the process noise. This means that they have the same units as the rest of the system. So, suppose the noise of our sensor has a standard deviation of $0.5m$, and the rest of our system is specified in meters as well. Variance is the standard deviation squared, so if $\\sigma=0.5$, then $\\sigma^2 = 0.25$.\n", - "\n", - "If we have $m$ state variables then $\\textbf{Q}$ will be an $m{\\times}m$ matrix. $\\textbf{Q}$ is a covariance matrix for the state variables, so it will contain the variances and covariances for the process noise for each state variable. \n", - "\n", - "Let's make this concrete. Assume our state variables are $x=\\begin{bmatrix}x&\\dot{x}\\end{bmatrix}^T$. (**note**: it is customary to use this transpose form of writing an matrix in text. It is how we denote that $x$ is a column matrix without taking up a lot of line space). Then $\\textbf{Q}$ will contain:\n", - "\n", - "$$Q = \\begin{bmatrix}\n", - "\\sigma_x^2 & p\\sigma_x\\sigma_{\\dot{x}} \\\\\n", - "p\\sigma_x\\sigma_{\\dot{x}}& \\sigma_{\\dot{x}}^2\n", - "\\end{bmatrix}\n", - "$$\n", - "\n", - "But again, what does this *mean*? This is a one dimensional problem, where our variables are $x$ and $\\dot{x}$. Assume we are tracking a person walking in 1D, so $x$ is their position, and $\\dot{x}$ is their velocity. We have no state variable for $\\ddot{x}$, so we are assuming aceleration is zero, and thus their velocity is constant. No one walks with constant velocity, even if they are trying to do so. The *process noise* specifies how much variance there is in each state variable due to the changes in velocity that inevitably happen.\n", - "\n", - "You will very typically see Q expressed in this form (indeed, this is what the code immediately above does):\n", - "\n", - "$$\\begin{bmatrix}\n", - "0&0 \\\\\n", - "0&0.1\n", - "\\end{bmatrix}\n", - "$$\n", - "\n", - "Why all zeros but in the last row and column. This is a useful approximation that we can use for $\\textbf{Q}$ under certain circumstances. Think about the person. As they accelerate, that will also alter their velocity, and eventually their position. But if the acceleration is small compared to our time sample rate, then the changes to distance will small. This follows from the Newtonian equations:\n", - "$$\n", - "\\begin{aligned}\n", - "v&=a\\Delta t \\\\\n", - "d&=\\frac{a}{2}{\\Delta t}^2\n", - "\\end{aligned}\n", - "$$\n", - "If t is small and a is small than the contribution of $\\frac{a}{2}{\\Delta t}^2$ will be extremely small. In this case it is safe to set all of the terms in $\\mathbf{Q}$ to 0 except the variance for the last term. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "On the other hand, let's suppose this is not the case. How should Q be designed? Our design of the system is:\n", - "\n", - "$$ X_{n+1} = \\Phi X_n + U_n$$\n", - "\n", - "where $\\Phi X_n$ is our state transition, which computes $\\mathbf{x}$ at time $n+1$ using Newtonan equations, and $U_n$ is the white noise associated with the process. For a walking human, based on the equations above we get\n", - "\n", - "$$U_n = \\begin{bmatrix}\\frac{a{\\Delta t}^2}{2} \\\\ \\Delta t\\end{bmatrix}$$\n", - "\n", - "So white noise has the variance $U_n$ and a mean of 0, which we notate as $w \\sim \\mathcal{N}(0,Q)$. \n", - "\n", - "Finding an analytic value for $\\textbf{Q}$ in a simple problem like this is not difficult, but it quickly becomes difficult to impossible as the number of state variables increase. So in this chapter we will use the simplification that only the variance of the last term is important. In the Kalman filter math chapter we will discuss finding an analytic solution ofr $\\textbf{Q}$, and then present C. F. van Loan's extremely useful numerical technique for finding $\\textbf{Q}$, which is what you will typically use in practice. \n", - "\n", - "**author's note: text needs to move to kalman math chapter. leaving here for now **" - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Designing R" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's leave ${\\mathbf{Q}}=0.1$, but bump ${\\mathbf{R}}$ up to $1000$. This is telling the filter that the measurement noise is very large. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plot_track (data=zs, R=1000, Q=0.1,count=30, plot_P=False, title='R = 1000, Q = 0.1')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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HH0V35gzaM2c8HYqqSGEsRDEha6mqm+RPvSR3KnTPmsWqzZ/BgLlPH4zff+/pSFRFCmMh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- "text": [ - "" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The filter output should be much closer to the green line, especially after 10-20 cycles. If you are running this in Ipython Notebook, I strongly urge you to run this many times in a row (click inside the code box, and press CTRL-Enter). Most times the filter tracks almost exactly with the actual position, randomly going slightly above and below the green line, but sometimes it stays well over or under the green line for a long time. What is happening in the latter case?\n", - "\n", - "The filter is strongly preferring the motion update to the measurement, so if the prediction is off it takes a lot of measurements to correct it. It will eventually correct because the velocity is a hidden variable - it is computed from the measurements, but it will take awhile.\n", - "\n", - "To some extent you can get similar looking output by varying either ${\\mathbf{R}}$ or ${\\mathbf{Q}}$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary ${\\mathbf{R}}$ and/or ${\\mathbf{Q}}$ based on your knowledge of the system you are filtering." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "A Detailed Examination of the Covariance Matrix" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So far I have not given a lot of coverage of the covariance matrix. $\\mathbf{P}$, the covariance matrix is nothing more than the variance of our state - such as the position of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9{\\times}9$ covariance matrix, or even larger.\n", - "\n", - "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n", - "\n", - "$$\n", - "\\mathbf{P} = \\begin{pmatrix}\n", - " {{\\sigma}_{1}}^2 & p{\\sigma}_{1}{\\sigma}_{2} & \\cdots & p{\\sigma}_{1}{\\sigma}_{n} \\\\\n", - " p{\\sigma}_{2}{\\sigma}_{1} &{{\\sigma}_{2}}^2 & \\cdots & p{\\sigma}_{2}{\\sigma}_{n} \\\\\n", - " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", - " p{\\sigma}_{n}{\\sigma}_{1} & p{\\sigma}_{n}{\\sigma}_{2} & \\cdots & {{\\sigma}_{n}}^2\n", - " \\end{pmatrix}\n", - "$$\n", - "\n", - "(I have subtituted $\\mathbf{P}$ for $\\Sigma$ because of the nomenclature used by the Kalman filter literature).\n", - "\n", - "The diagonal contains the variance of each of our state variables. So, if our state variables are\n", - "\n", - "$$\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}$$\n", - "\n", - "and the covariance matrix happens to be\n", - "$$\\begin{pmatrix}2&0\\\\0&6\\end{pmatrix}$$\n", - "\n", - "we know that the variance of $x$ is 2, and the variance of $\\dot{x}$ is 6. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "P = np.array([[2,0],[0,6]])\n", - "stats.plot_covariance_ellipse ((0,0), P, title='|2 0|\\n|0 6|')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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S0axZ+3XZZdn65z+ZkgNghqScrT788EN1795daWns5egUzDaZi+zqrVrl0cSJmZozp0oF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\nSLW1Li1Z4rW6FDSTxx7za/j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- "text": [ - "" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "P = np.array([[2,2.4],[2.4,6]])\n", - "stats.plot_covariance_ellipse ((0,0), P, title ='|2.0 2.4|\\n|2.4 6.0|')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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Vr15AX35ZoL59rWt4D2vbtloTJpRq2LAklZZaW8uJcO+Zjfycj5VeAIhy69a59fvfJykQ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\nRn7Ox5ZlAKLSvn0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- "text": [ - "" - ] - } - ], - "prompt_number": 28 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, dependent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n", - "\n", - "$$\n", - "\\mathbf{P} = \\begin{pmatrix}\n", - " \\sigma_1^2 & p\\sigma_1\\sigma_2 \\\\\n", - " p\\sigma_2\\sigma_1 &\\sigma_2^2 \n", - " \\end{pmatrix}\n", - "$$\n", - "\n", - "Look at the computation for the off diagonal elements. \n", - "\n", - "$$\\begin{aligned}\n", - "\\mathbf{P}_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", - "\\mathbf{P}_{1,0}&=p\\sigma_2\\sigma_1.\n", - "\\end{aligned}$$\n", - "\n", - "If we re-arrange terms we get\n", - "$$\\begin{aligned}\n", - "\\mathbf{P}_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", - "\\mathbf{P}_{1,0}&=p\\sigma_1\\sigma_1 \\mbox{, yielding} \\\\\n", - "\\mathbf{P}_{0,1}&=P_{1,0}\n", - "\\end{aligned}$$\n", - "\n", - "In general, we can state that $\\small\\mathbf{P}_{i,j}=\\small\\mathbf{P}_{j,i}$.\n", - "\n", - "So for my example I multiplied the diagonals, 2 and 6, to get 12, and then scaled that with the arbitrarily chosen $p=.2$ to get 2.4.\n", - "\n", - "Let's get back to concrete terms. Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def plot_track(noise, count, R, Q=0, plot_P=True, title='Kalman Filter'):\n", - " dog = DogSensor(velocity=1, noise=noise)\n", - " f = dog_tracking_filter(R=R, Q=Q, cov=20.)\n", - "\n", - " ps = []\n", - " zs = []\n", - " cov = []\n", - " for t in range (count):\n", - " z = dog.sense()\n", - " f.update (z)\n", - " ps.append (f.x[0,0])\n", - " cov.append(f.P)\n", - " zs.append(z)\n", - " f.predict()\n", - "\n", - " p0, = plt.plot([0,count],[0,count],'g')\n", - " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", - " p2, = plt.plot(range(1,count+1),ps, c='b')\n", - " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", - " plt.title(title)\n", - "\n", - " for i,p in enumerate(cov):\n", - " stats.plot_covariance_ellipse ((i+1, ps[i]), cov=p)\n", - "\n", - " if i == len(cov)-1:\n", - " s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n", - " plt.text (30,1,s,fontsize=18)\n", - " s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n", - " plt.text (30,-4,s,fontsize=18)\n", - " plt.xlim((0,40))\n", - " plt.ylim((0,40))\n", - " plt.axis('equal')\n", - " \n", - " plt.show()\n", - "\n", - "\n", - "plot_track (noise=5, R=5, Q=5, count=20, title='R = 5')\n", - "plot_track (noise=5, R=.5, Q=5, count=20, title='R = 0.5')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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mtQjFgDci+Si+M+PrO5Nfd2JnszmvW6ZM1iUQBw9qqVdP6n/zSkG99woqbWYb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\nkEIIoXCnT59m+/bt9OvXj8zMT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bbinHZKrTx4qLpKVr3xdpNX8pdIUQQjSIlBQdbdvaCAmp/VyTyV65kUN2tsLw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\nLkJvuqmcH37w49QppXKJrwq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fUNsJCxcuZOHChU7H5syZ02ADEkIIUf8SE/XExblvQ3Cn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- "text": [ - "" - ] - } - ], - "prompt_number": 30 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $\\mathbf{P}=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slighly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n", - "\n", - "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n", - "\n", - "The first plot, with $\\mathbf{R}=5$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85, and the variance for velocity is 3.0. \n", - "\n", - "In contrast, the second plot, with $\\mathbf{R}=0.5$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $\\small\\mathbf{R}$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. " - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Question: Explain Ellipse Differences" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Why are the ellipses for $\\mathbf{R}=5$ shorter, and more tilted than the ellipses for $\\mathbf{R}=0.5$. Hint: think about this in the context of what these ellipses mean physically, not in terms of the math. If you aren't sure about the answer,change $\\mathbf{R}$ to truly large and small numbers such as 100 and 0.1, observe the changes, and think about what this means. " - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The $x$ axis is for position, and $y$ is velocity. An ellipse that is vertical, or nearly so, says there is no correlation between position and velocity, and an ellipse that is diagnal says that there is a lot of correlation. Phrased that way, it sounds unlikely - either they are correlated or not. But this is a measure of the *output of the filter*, not a description of the actual, physical world. When $\\mathbf{R}$ is very large we are telling the filter that there is a lot of noise in the measurements. In that case the Kalman gain $\\mathbf{K}$ is set to favor the prediction over the measurement, and the prediction comes from the velocity state variable. So, there is a large correlation between $x$ and $\\dot{x}$. Conversely, if $\\mathbf{R}$ is small, we are telling the filter that the measurement is very trustworthy, and $\\mathbf{K}$ is set to favor the measurement over the prediction. Why would the filter want to use the prediction if the measurement is nearly perfect? If the filter is not using much from the prediction there will be very little correlation reported. \n", - "\n", - "**This is a critical point to understand!**. The Kalman filter is just a mathematical model for a real world system. A report of little correlation *does not mean* there is no correlation in the physical system, just that there was no correlation in the mathematical model. It's just a report of how much measurement vs prediction was incorporated into the model. \n", - "\n", - "Let's bring that point home with a truly large measurement error. We will set $\\mathbf{R}=500$. Think about what the plot will look like before scrolling down. To emphasize the issue, I will set the amount of noise injected into the measurements to 0, so the measurement will exactly equal the actual position. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plot_track (noise=0, R=500, Q=5, count=7, title='R = 500')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ysrKYO3cu7du391axhSjxsrNh40Yzq1ZZWLnSzNGjKnfd5SQhwcWwYdnUrCmT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\nWj76yEmLFk5Kl8653oJWK0RFiWzcKLJ1q8grr3ho1MhJ5TI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6f15Lv35+SJKGiAgzb76Z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BwwYYKO+fP9Et1V19dQasjSFmX+FRQUfBVF8HmImzcFGjXKQIMGdgYNssYtFOrXd7B+vdxeftq0\ntEvBkiTZ123ECD2FCrlS1UsvMdy+LRAermf58me7MSYFSYI9e9RMnKjj0iWRsDArP/xg93ht3IMH\nAh07+uN0wu+/mxIUzTt2qAkP15Mpk+wtV7Kk70dm7pw/Rqtt7WlRurXPiD0AkwnOnxfRaCQuXxbJ\nmdN7c2m1wtGjqqcEnhqrlcepmS4GDLBSqpTTKzWmL+LePYGbN0WKFvWd88jplKOO69Zp2LBBg8MR\nQrNmAt9+a6ZkyaQZot+7J4u9pk3t9OzpOVFrscBPP2mZM0eHRiPRtauNpUuffC8cOqSiTx8DuXJJ\n7Njh+xsyCgoKCgoKSUGp4fMA167JYq9FCzt9+jzbNtxkgmrVMtK/v5XmzVM/De34cRVffqnn0SOB\nUaMsVK2aNp03X0T79v7ky+dm+HDLy5/8HGJNkSdN0nHnjkivXvJce6NZzsmTKtq08adOHQcjRlie\nW4/1zz8iw4bpOXNGxYgRFurX9y2LhYS4c+4omnof8OcndQgdtCithxOPL74w4HZDaKiDCRP07Nxp\n9IiQd7ng3DmRY8fUREbKIu/0aRWFCrniBF6ZMk7y50/7RikbN2qYP9+PlSuj03QcFgvs3Klh3ToN\nmzdryJvXTd26DurXtyc6kvdvHj4U+N//AqhRw0F4uNUjc33jhsCCBX58/70fwcFOuna1UbnyE1/L\nBw8ERo7Us3mzhhEjLDRrlv6iegoKCjJKDZ+CQsIoEb4UcvGiSOPGAXTqZKNbt+fvSGfIAIsWmWnS\nJACdTqJBg9Sp57t7V2DMGD0bNmj48ks5RUmlSpWXThLr1mk4cULFrFlJT+WUJNi5UzYqj44W6NPH\nQqNGDq91bly1SkP//ga++sryXPH+dG3kF1/4bufN5xEr9s7Vr+RzYm/jRg27dqnZtctIQIDsEzlx\noo7Bg5Pmy2a3w5kzKo4eVXHsmIqjR9WcOqUiZ043QUEuSpZ0Mnp0DEFBriR1zkwtDh5UU65c2mzY\nPHoksGWLLPJ27NAQFOSkbl0H/ftbefPNlGULGI3QrFkAlSo5PSL2jh5VMXu2H5s3a2je3M6GDfG9\nMCUJli3TMnKknoYN7ezbZ3yhFYaCgoKCgkJ6RhF8KeD2bXlHOizMSocOL47cFSvmYsWKaD78MAC7\nPYamTb0n+hwOGDToOqtXF6VZMzsHDhjJnNk3FzMPHggMGGBgwYLoJNfXHTyoYswYPVFRIgMHerfD\nqMsFo0bpWb1aw6+/RhMUFD+lzm6Hb7/1Y8oUHeXKXWb//iw+UxuZGJ4We6ltvfAy7twR6N3bwHff\nRcd1M/366xiqVMlIw4YOiheP/7eIraOJiYG//34i7I4dU/HPPyry5XNTooSToCAX//ufheLFUz81\nM7kcOKCif//UMx+/cUNgwwYt69drOHxYTaVKDurVczBpUkyC53dS65iio+WuxrLYtiRb7LlcsGmT\nhtmz/bh0SUWnTlbGjbM889136pRI374GLBaBZcu82wE0tVFqyNIWZf4VFBR8FUXwJRO7XU5D/Ogj\n+0vFXixBQS5WrjTRrFkGrl+30qNHwh0dk8v27WoGDTIQEOBg7VoTRYr4Tp3e8wgP11O/vp3y5RO/\n6Dp5UsWYMTqOH1fTv7+FFi28a1R+/77AZ5/5P274YCJbticLSEmSo0/DhukJDHSzdq2Ju3dPkD17\n+vmnf/vySbQ+KvYkCcLC5M6tT58juXNLDBtm4fPPDWzbZiImBo4fl0Xdtm0l6d8/I5cvixQq5CIo\nyEWJEk5at7ZRrJhvRu4Sg9EIJ06oCQ72boTv7FmR9es1rF+v5fx5kZo1HbRrZ+P776M92t0W5NTQ\nVq0CKFjQxYQJyRN7JpNslD53rh9Zs0p07WqlYUPHM+nc0dHw9dd6li7VMnCglXbtbD6Z8aCgoKCg\noOBpFMGXTMLD9WTMKPHll0nbbS9a1M2mTSY6dvRn924Ns2aZyZEj5ZGgy5dFvvxSrhkbM8ZCrVoa\nBMG3xd5ff6n44w8NBw8+StTzz58XGTfuiVH5woXet5I4cUKu12vQwMHQofHr9Y4fVxEeruf2bZFx\n42KoXj12IZ5+xN6N6Bs0/qMdQ7s3pm7POWk9nGdYskTLtWsi3333JN333j2Bo0dV3LkjcP26SNGi\nmbBYBIoWlYVdo0ZZKVHCTJEirhQ1API1NmzQ8t57Do97NkqSbF0SK/KMRoG6de0MGmThvfecSZ7D\nxEY4bDZo0yaAXLncTJ0ak+TNrytXRObN82PZMi3vv+9k9mwzZcs+2yRGkohrnPXeew4iIowv9MlM\nzyjRpbRFmX8FBQVfRRF8yWDJEi07d2rYutWYrAjdm2+6WbfOxLhxOqpWzcjUqWZq1kzerr3TCbNn\nyzYL3bvb+O679FMzNmaMnj59rC+NGly7JhuVr1unoWtXG1OmeNZHLyF+/VXDwIEGxo2Ln4J786Zc\nG7l1q4YBA+TaSG9GGL1FnPVCsZbU9aFunLGcPSsyfLievn2tTJ6s48QJOTXTZJKj5UFBLjp0sLF4\nsR+nTz9MVduTtGDlSi0ffuiZzpUOB+zdq44Tef7+EvXqOZgxw0zp0i6vW0vEZkgEBEjMnBmT6Eib\nJMlprXPm6Ni9W03LlnZ27EjYK+/yZZEBA/RcvCjXCFeu7HsNqxQUFBQUFLxNspept27dIiwsDJPJ\nhFarpW/fvlSsWNGTY/NJDh1SMWqUnvXrTSmq+9FoYMgQK++/76RfPwPz57sZNSomSVYJf/2lIizM\nQJYsElu3mggMfPK7vl5LsHevmrNnRX78MeEF7N27AlOm6Fi+XMsnn9g4dMhIlize35l3u2V/vZUr\ntaxaFc2778qphHY7zJrlx/TpusfG6Y+eew74+tyDb/nsuVxw6ZLI6dMqTp1SPf4p386SRWLvXjVF\nirho1szOqFEW8uWL73V3/LiKJUv86NJFPpfSw/wnlXv3BA4cULNwYfK7cz54IPD772q2btWwdauG\nwEA39eo5WLnSsxYtL5t/hwM6dfJHEGD+fHOiNktMJtmnc+FCPywWgY4dbUyfbk4w2mm3w4wZOmbN\n8qNbNxvff29+paK9CfEqnvvpCWX+FRQUfJVkCz61Ws3w4cMpXLgwUVFRfPzxx+zatcuTY/M5bt4U\naNcugOnTY3j7bc8skKpUcRIRYeTbb/2oX1/2n+rd20rOnAkLG7MZxo7Vs2KFlhEjLHz0UfpqJS5J\nMHq0joEDrc9dhBmN8mJtwQI/mjWzs2ePkVy5UicFy2aDzz83cPmyim3bntTr7dqlpl8/A4GBLrZt\niy+u0xtpJfbcbrh6VXws6mRBd/q0irNnVeTI4aZIERdFiripUcNBliwqsmWTWL06+qXRpsGDrTRt\nGkDr1rZUifymBWvWaKhRw5Gk9ydJckpyrMA7eVJFpUoOatRwMGSIJU285iwW+PRTf9xuWLzY/FLb\nlJMnVSxc6MeqVRoqVXIycqSFKlWcLzwndu9W07ev/Fndvt1Evnzp97OqoKCgoKDgCTzmw1ehQgV2\n7dqF5vF/8FfNh0+SoFUrf4oVcyW5FXxiuXdPbun/889a6tZ10Lmz7ZlukNu2yYuZ8uXljnbpqRNk\nLFu3qhkyxMCePcZ4qVwxMXKnyxkzdNSs6WDAgJS3e08Kjx4JtGnjT+bMEnPnmtHr5S6FQ4YYOHRI\nxdixFurUSR9+eglx59xR/uncgMiRn9PzvX5eeQ1JguvXhbhoXezln39UZMokUaSIi3fecT0WeC4K\nF3bFEzJHj6po3jyAP/5IvAF2x47+FCnieq4P5qtAgwYBdOlio169F3f3NZl4nG6uYds2DTqdRM2a\nDmrWdPDee06v17y+CKNRbtCSK5fErFkJiz2rFX77TY7mXbsm0ratjTZtbOTJ8+Jz4dYtgaFD9ezb\np2bsWAt166bvz6qCgkLSUHz4FBQSxiOVR7t376ZYsWJxYu9V5LffNFy8qIrXPMLTZMsmMX68hQED\nrHz/vZYWLQIIDHTRpYuNkBAnQ4fqOXRIzeTJMVSrlj5rUeR0ST2DB1vixJ7dDkuW+DFpko6yZZ2s\nXevZFLPEcO2aQPPmGaha1cHo0RYkSa6NnDRJxyef2PjmG3O6rxG7c+4o6nof4Fe/kkfEntMpR+zO\nnxc5e/ZJOuaZMyoMBilO0JUt66RtWxvvvON6aRq0xQKdO/szdmxMkiJQAwdaqFUrAx062FIl7Tc1\niYoSOHlSRY0az4o9SZJrHbdskQXekSNqypRxUrOmg549rRQo4BvRrXv3BD78MICSJV1MmPD8mr0L\nF0QWLfJj+XItxYu76NnTSq1aL/fUtFhg9mw5fbN1a9lTL71/VhUUFBQUFDxJigXfnTt3mDBhArNm\nzfLEeHySBw8EBg0ysGhRdKo0RMmaVSIszEb37jbWrtUwdKieK1dEKlRwsnx5dKLEkK/WEqxZo0EU\noX59B243rFihZexYHW+/7Wbp0mhKlkx9T6xjx1S0aBFAjx5Wuna1sX+/in79DGTPLrFhg4lChZK2\naPbFuY8Ve+eTaL3gcDwRdRcvqrhwQeTCBRUXL4pcuyaSM6ebt95y8/bbsml5ixZ2ihRxJVt0jRih\n5913XUn2qSxQwE39+g6mT/ejWrVtPjf/KWHVKjniH/vdExMDe/Y8qcVzOAQ++EDOCKhc2fPWCUnl\n3+d/VJRAkyYZqFfP/oyputMpe+ctXOjHiRMqWrSws2mTibfeevlnTpLkxkojR+opVcr1TB3zfxFf\n/O75L6HMv4KCgq+SIsFns9n44osvGDBgwHPD6N26dePNN98EIFOmTBQvXjzuyzAiIgIgXdweOVJP\ncPBl7PYTxLbcT43Xj4oysHTp+2TKJNGz558cO5aDBg3ykj27xDvvXKRMmdt8+uk7aDTP/v7x48d9\nZv5ib0sSfP11XUaMiGHu3L9ZsKAYWbL4MWtWDG73DqKjSdX5BbDZqtK1qz+ffXaEN9+8R/fuVdmx\nQ0Pr1n9SqVIUhQr5zvwl9/adc0dR1a3J4crvUvOx2Hv6cYcDVq36k6gof/T64ly8KHL4sJEbNwzc\nv+/Pa6+5yZr1Prlzm6lYMSdVqzp58OAQuXLFEBpaMd7xKlRI/nj//DM769aVY/duY7J+v2pVHb16\nVadsWY1PzX9Kb//6q5aqVY/x5Zcazp8vwv79avLlu09IyFV+/DEv77zjZs8e+fkBAWk/3qdv58r1\nPs2bB1C16hlCQ88jCPLjv/12mM2b32Tnzrd54w037713jB49blCtWsVEHX/+/JMsWFAMg0HHnDny\n98f16xAY6FvvP7Vvx+Ir4/mv3Y7FV8bzqt+OvX7lyhUAPvvsMxQUFJ5Psmv4JEmiT58+hISE0LJl\ny2cef1Vq+C5fFqlWLQORkUYyZ06dVDGHQ25aMnOmH716Wenc2RaX1uRyyZ5ZsTU6Fy6IVKkip3DV\nqOHwaX+pffvUdOtmoHhxF0ePqhg61EKTJmlXZ7NkiZYxY/QsXBjNmTMqxo7V07y5nQEDLCnqwOpL\n3Ii+wR+fVaJg7pJk7b4qXoTu/Hn55/XrIrlzy5G6t95yERjopkABN4GBLvLlc6dKVPvBA4HKlTMy\nY4aZqlWdyT5Ox47+BAc74zp2plfsdvnzsmSJlrVrtWTOLFGjhlyLFxrqJFMm3/2cx3LkiIpWrQL4\n8ksLbdvacbth5041333nR0SEmiZN7LRvb6dYscRH9a9cERkxQs+BA2qGDLHQvLnd6xYSCgoK6QOl\nhi/9sWXLFqKiojh69CgFChSgR48eaT2kVxZ1cn8xMjKSLVu2cOHCBX7++WcA5s+fT44cOTw2OF9g\n6lQdHTrYUk3sHT2qont3A7lzS8/tMKdSQUiIi5AQF19+aeX2bYFt2+TUrvBwPYGBcpfDGjUclCjh\n8hlPvkePBMLC9Ny5I1KqlD2uKUpaIEkwbpyOFSu0TJgQw5AhBrRaWLUqOkmLT19BkuD+fdmE/Pp1\nOdXy+nWRc7du8vubjfBT98aybDB5dsYXddWrOwgMdJMvnzvNW9a3a+dPgwb2FN8uXbwAACAASURB\nVIk9gPbtbfTqZaBzZ1u6a9hx5YrIH3+o2b5dw65dat5+243JBF262Bg2zJKuhM22bWq6dvVn2rQY\nypVzMn26H4sX+2EwSHToYGPmzIQtFZ6H0Sh/Fy9e7EfnzjamTUv/NbUKCgoK/2WuXLmC0WikXbt2\n2Gw2ateuTb58+WjQoEFaD+2VxGNdOv/NqxDhu3ZNoEqVjBw6ZCRrVu8KPrdb9nibNk3H6NHyznVS\nF6wOBxw8KNf2rFlj4+bNjAQGuilWzMm777ooVky+vPaalGqLYYcDFi3yY8IEHUajQESE0WOWFskd\nT1iYgZMnVRQt6uL33zUMHWrh4489FymIiPBsHYfRSJyYe94lKkrEz08ib17344tExrzXWOZXh1qv\ntSQsuBd586a9qEuIZcu0DB2q59ixRyneBJAkKFlSzaxZ8N57KROP3ubRI4Hdu9Xs2KFmxw4NJpPA\n++87qVHDQfXqDh49EqhdOwN//fUoXYmbUaMusWRJCfr3txAZqWbTJg116jho185GmTKuJH33OJ3w\nww9axo/XU62ag/BwC7lz+350M63w9HePQtJQ5j9tUSJ86Ytt27YxatQodu7cCUDPnj3Jli0bw4YN\nS+ORvZokO8L3X2DxYj8++sjudbF386ZAt27+xMQIbNtmSrYVgUYjL3Lfe89JjRoRhIRU4swZFSdO\nqDh5UsX27RpOnFChUhEn/mKFYKFCno0GStIT+4U8edx8+KGNhw/FNBV7Nhu0b+/PtWsit26JhIQ4\n2b8/9VJ1/43dLncvvHdP5O5dgRs3nhVz166JuFyQN6+bPHncvP66LOrKl3c+JfDc8Rp1xPrsdX6n\nBb3KfAH4biOLqVP9mDhRT0yMwDff6KhUyUmlSskXaoIAtWtfZtGiQj4n+Ox2OHz4icA7fVpFmTJO\nqlZ1sGiRmaJFXfE2HcaN09GunS1dib3Ro3XMnVuMrFklvv1WR+vWNsaMsSTrO/SPP9SEhxvImtXN\n8uXRlCiR/qLvCgoKCgrPp0qVKnF9PgBu3bpF2bJl03BErzZKhC8BJAnKl8/IrFlmgoO9t9DYvFlD\nWJiBtm1t9OtnfWkL8pQiSbK33MmTsgg8cULNyZMqLl8WH9duuciVy03u3NLjn08uGTKQqN35v/8W\nGTzYQFSUyKhRMVSv7qRcuYzMnm2mTJm0WbTFxEDz5gGcP68iZ043U6fGULq0Z8ditcLdu08E3JOf\nAnfvytfv3hUf3xaIiRHImlUiWzaJ7Nnd5Mr1JEIXK+zy5nWTOXPiI7J3zh2l9ZYO1C7TOlVN1ZPD\n3r1qPvnEn6VLo9m+XcPAgZ7x0Hv4UKBUqYwcPGgkR460iwZJEpw5I7Jjh4YdO9Ts26fhrbdcVK0q\ni7xy5RL2xbt7V6BMmYwcOGAkZ07fjmjZbLBunYYRI/RERYk0bWqnY0cbwcFJi+bFcuaMyNChBs6f\nFxkxQvHTU1BQSBxKhC/9curUKcLCwvjtt9/QpaFh7Pnz5/nqq6/o2rUrISEhzzy+adMm/vrrL/z8\n/Hjw4AFFihSJ18fk0KFDhIeHU6pUKTJnzozJZOLSpUsMGTKEIkWKvPC1bTYbK1as4N69e7hcLk6f\nPk2VKlVo1apVvOetWbOGPXv2kCdPHqKioqhZsyY1atR46XtTInwJcPq0SEyM4HFREIvVCsOG6dm4\nUcPChWYqVEidaIQgQJ48EnnyOKlZ0wnY4sZz+rQs/G7cELl5U+T0aXXc9Rs35NDD0yIwVy7p8U/5\ntkolG6f//ruGPn2sdOhgQ6OBHTvU+PtLhISkjdgzGqFatYxcuybSt6+VL76wPmP6LEmyn5fZLMRd\noqPj346978EDkTt3ngi52CidzQbZs0tky+Z+LOLk69mzS5Qq5SRbNokcOZ48limT5NG6rFjrhUGt\na1HFx8XeX3+paNfOn/nz5U0Am81zK/rMmSXq1XOwbJmWnj1Tt3nLtWsCu3bJNXi7d2tQqSSqVnXy\n4Yd2Zs6MIVu2xIm3BQv8aNjQ4bNiT5JkO5OlS7X88osWSZKj0Fu3PuS115J3zHv3BMaP17F6tZZe\nvawsWWLz2TRkBQUFBQXPYLVamTZtGgsWLEgzsffHH3+wZcsW/P392bNnD126dHnmOTt37uTevXsM\nHDgw7r6RI0eyfPlyPv74YwDcbjcxMTFs27YNtVpNhQoVGD16NIGBgS8dw+TJk4mMjGTZsmVoNBqO\nHz9O8+bNMZvNdOrUCYDFixezePFi1q1bh8FgwGKxUL16dbJly0apUqVeeHxF8CXAxo1a6tVLeh1d\nYvj7b5GOHQMoVMjFrl0mr6QUJrWWQKeDkiVdCfrgSRKYTHDjhhhPBF68KLJ7t5qjR9XcvCnELdAG\nDdIzcqQeg0EiJkYgUyaJmjUz4O8vYTBIGAxgMEjxbsdef9qUOXb+//1TkuSOpfJFwOWS631cLrke\n0umU77tyRWDFCj9UKqhUycHBg2oaNQr4l4gTiIkBrVYeg3x5cj0gIP59WbJIvPWWK07Q5cghR+hi\nI6BpUcfxtM9elSHfp+prJ5V//hFp0SKAyZNj4pq0pCSN899ERETQvn0VOnb0p0cPm1ebndy7J9fh\n7d4ti7yHDwUqVXJSpYqD/v2tBAa6k/wdYrHAwoV+rF1r8s6gU8C9ewIrVmj58UctRqNA7doOMmSQ\nBfbIkRZUqqSf/2YzzJsnG6c3bWpn/37v10y/qig1ZGmLMv8KCkln9uzZDB06lNy5c3P58mXy5cuX\n6mMIDQ0lNDSU69ev88MPPzz3Ob/88gudO3eOd1+rVq2YMGFCnOATBIE+ffrQqFGjJI/B7Xbz4MED\nXC4XGo2GggULAnD48GE6deqExWJh2rRp1K9fH4PBAIBeryckJIRFixYpgi+5nDqlokaNpJk/vwxJ\nkhdy48bpGD7cQsuW3hGU3kAQIGNGyJjRHWf8LkmwcqWGTZv0lC7tZPhwS5xhststp1HeuiVQpUom\nFi0yIQhyGqN8eRI9i719964cVXU/LjmT/rXm+/dtUQS1Wu5cqlbL0TL5OgiCxMGD6seeZW569rSS\nMWOseHta2Mn3GQx4PZ3WWyTXVD0tuHpVpGnTDAwdaqF+fc9+vp6mdGkXOh0cOqSiXDnPRZajo2W7\nhNgo3sWLKipUcFK5styUpFgxV4oF5vLlWoKDnRQq5Bu1l04n/P67mh9/9GPnTjW1azsYM8aC3Q7d\nu/sTHm6hTRt7ko9rs8l10lOm6HjvPScbN5ooWNA33rOCgoKCgvdZtmwZVatWRa1Wc+vWLfbu3Zsm\ngi8W6d8LzafQaDR89dVXzJgxg6xZswLw999/88477yT6GC9i8ODBDB48OO72xYsXAeLK486dO4fZ\nbCZbtmzxfi9XrlysWrUKt9uN+IIFSDpd4nqf8+dFOnf23ELx3j2Bnj0N3LghpsrCxtu7jCdPqujb\n14DVCrNmxTzTIEMUISAAtm9XU6GCk7JlU28hd+KEiq5dDVy6JNKmjZ0pU2JSVVin5g7vrWun0KYT\nsXf7tkCTJgF0726lRYukC4TEEjv/derY2bJFkyLBZzLBoUNq9u1TExEhNz0qUcLJ++87GT8+huBg\n1zPpwSnB6YSZM3V8802M5w6aTM6eFVm61I+fftKSN6+bVq1sTJ8u2ynMny8Lte++M1OxYvzP/svO\nf6cTfvpJy4QJOooWdfHzz9EUL640ZPEESnQpbVHmX0EB7HY78+bN49dff+XGjRvxHtNoNOzZs4eM\nGTNy+PBhRo0ahdv9ZH04bdq01B5uomnfvj1t27alTp069O3bl8DAQPbt28fIkSPjPe/SpUuMHz8e\nf39/Ll26RLVq1ahbt26SX2/+/PlUrlyZDh06AKB9nEL3b0HpdDoxmUxERUXx+uuvJ3g8RfAlwLlz\nKo+Jsp071XTr5k+zZna++86crutSTCYYP17Pzz9rGTRI3tl/OgXz32zZoqFWLe9Fcp7GZoOJE3V8\n950fGo3sXzZokDXdRFGTyo3oGzTa1pbwL5rRoNvMtB7OC3n4UKBp0wCaNbOnmin6Bx846NPHwJAh\niW8Gc/++wP79avbulaPDp0+rCApyUrGik759LZQv7/Rq18wfftDy+uvuZ0RUamE0wurVWpYu9ePS\nJZGPPrKzcqWJIkXk70KHA/r0MbB/v5pNm571CX0RbjesWaNh7Fg9OXO6mTfP7NHoq4KCgoJC2mK3\n2+nYsSMajYbJkycjCAJffvklZcqUoUuXLuj1ejJmzAhASEgIf//9dxqPOPEUL16c+fPn06VLF4YM\nGUL27NlZuHAh6n+lh507d44ZM2YgCALR0dF88MEHaLXaRDVWAfjxxx+5evUqdrud8ePHxwm9QoUK\nkStXLu7cuRPv+WfPngXgwYMHiuBLDnY76PUpqyORJFmALFrkx8yZ5hSbSicFT9cSSBKsXath0CAD\nVao42LPn5R0QXS7YutVz3RdfxKFDKj7/3J/XX3cRECDRtq2d3r29/7rPIzXqOGKtF1oUa0kDH2/Q\nYjbDRx8FULmyk/79vf83iZ3/kBAXt26JXL0q8sYbzxcmUVEC+/bJEby9ezVcuyZSpows8EaOtFC6\ndMKdND2N2Qxff61nyZLoVN2kcLvljqlLl2rZsEHD++87CQuzUr26I1708v59gXbt/PH3l9i0ycjj\n/9nP8O/zX5JkI/YxY/SoVDBunFy7+apuxKQlSg1Z2qLMv8J/nWnTpmGxWFi4cCGqx9GAVq1asXLl\nSvLkyePV1x4wYAD37t1L1HOzZs3KhAkTknT8R48esWzZMsaNG8fx48dZsGABzZo1Y8qUKVSvXh2A\nokWLMn78eITH/+ACAgIoU6YMU6dOTbTgi+3KGRkZSa1atZg6dSrvvfcegiAwbNgwhg8fzoMHD8iS\nJQtHjhzB4ZCDKqoXRV9QBF+C+PtLmM0Cfn7JE30WC/Ts6c+lSyK//27ktdfSbxOCixdFBgwwcPWq\nyLx5z6ZwJURkpGyBkNBi2xOYzTBmjJ5Vq7T06WNh+nQdnTvb6NYtdbszpiZxYu+dFj5vvWCzQZs2\nARQs6GL0aEuqLvJVKqhZ08HmzRo++8yGJMnn8t696jiRZzQKlC/vpEIFJ61amSle3JVmtZxz5ugo\nV87ptc7A/+bMGZFffpG7bBoM0KqVjREjLM/dyDl9WqRVqwAaNHAwZIjlhVH9p9m3T82oUToePBAZ\nPNhCvXqKxYKCgoLCq4jJZGLJkiVMmzYtnviw2+1xosSbjB8/3mvHliSJHj168Pnnn1O2bFlq1KhB\nw4YNGTBgAIMGDWLnzp3odDoCnjZFfoxer+fcuXMYjca46GZiCA4OpkCBAvTu3ZsdO3ag1+sJDQ0l\ne/bsLFiwgIwZM1KoUCFKlSrF0aNHXxjdA0XwJYi/v0R0tJCsbnG3bgm0bh1A/vxu1qwxodd7YYAv\nwRO7jDYbTJumY+5cP3r2tNKlS9LapHs7nXPXLjVhYQbKlnWycqWJVq0C6NHDRseOaSv2vLnDm57E\nntMJnTr5ExAg8c03MV7tlvk0sfPvdkPRoi6+/dYvLkVTEKBiRScVKjjo0cNK4cLuVBvXi7h3T2D2\nbD82b/ZuZ87r1wVWrpRF3t27Io0b21m0yExQUMKeeVu3qune3Z+RIy18/PHLay8rVarEX3+pGDNG\nz7lzIgMHWmnW7MWp3wqeQYkupS3K/Cv8lzl8+DAul4sKFSrEu//IkSMv7SDp65w/fx6TyRTPGL5A\ngQIsWrSI6tWrc+7cOfLnz0/Dhg2pWbMmX375ZdzzoqOjEQThmdTPp7lz5w5NmjQhNDQ0Xk1g3rx5\n+euvvzh37hzFixcH5NTS2OsAq1atonjx4i8Vk4rgS4B8+dycOyfy5ptJi06dOKGiZUt/Wre2069f\n+q0f27FDTb9+BgoXdvHHH6ZkRek2b9YwcaLnm0/ExMDw4Xo2btQyebKZ4GAX9etnoG3btBd73uTO\nuaNc+7Q+bUd/Tg8fF3tuN4SFGTCZBJYti06VqJnDAUePquLE3f79ajJnlrh2TaRzZytDh1rIly/p\nNgmpwYQJOpo0sVOggOej4Q8fCqxZo+GXX7ScOKGifn0Ho0ZZeO895wtFmCTBzJl+zJqlY8mS6ETV\n2505I/LVV3oOH1bTp4+F1q3t6bpmWUFBQUEhcVitVrJkyRJXcwZw69Yt9uzZwy+//OL11/dmSqcg\nCFgslmfuDwgIIHfu3Lz22muIoojdbn/Gc+/SpUuUKFEizkrhedy7d487d+7w8OHDePffvXsXtVpN\n3rx5ARg9ejQHDhxg7dq1gBw9PXToEIMGDXrpe1AEXwKUK+dk71411aolvu5u40YNPXsamDAhhsaN\nU6dRSUIkt5bg5k2B8HADhw+rGDfOQu3ayXsfV6/KXn2eNls/elRFp07+lCjhJCLCiChKNG6cgQ8+\ncBAW5htizxt1HLHWC0L9SvSo3N+jx/Y0kgRDhuj55x8VK1ea8PPzzus8eCAQGakiMlIWd5GRavLl\nc5Ev31WaN8/B5Mkx5Mol0bhxADlzSuTP75st/0+fFlm5Usv+/UaPHdNikTdcfv1Vy65dGkJDHXTq\nZKNGDUeiahKNRvj8c3+uXBHZvPnlGz5XroiMH69j61YN9euf5tCh3Lzgf5uCl1BqyNIWZf4V/suU\nLVsWm83Gw4cPyZw5M3a7nUGDBtG3b18KFCjg9df3REpnbAdMlyv+2rVAgQIEBgby448/xtXYAWzd\nupUyZcqQI0cOAJo0aUL58uXjHj927BhXr17lxx9/jLtv586dDBgwgMmTJ1OxYkUAihQpQqVKleje\nvXvc865fv05kZCTt27ePs4Ewm82UKFEi7jnTpk0jODiY+vXrv/S9KYIvAWrUcNC7tz+DB788SidJ\nMH26H3Pn6vjpp+hUq8HxJE4nLFjgx9df6/jkExvTpplTtGCLiFDz/vsvjiAkBZdLTi+dPduPsWNj\naNrUgdUqNwMpXtzFsGHP7ry8KqQnnz2QGxXt3Klm3bponpPOniwcDtkKJDJSzeHD8s+bN0VKlnQS\nHOyic2cb5cqZyZJFIiLiRLxFV2iog9271dSrl7abMM9DkiA83EDv3layZUtZna/TKac5//qr3Hyl\nZEkXzZvbmTnTnGCDledx/LiK9u39CQ11MHeu+YUCMSpKYOpUHb/+quWzz2wcPvyIY8fOYzDkTtF7\nUVBQUFBIX2TLlo3JkyczatQo8uXLx61bt2jdujWhoaHxnnf79m02btzI9evXKVasGA6Hg6ioKHr2\n7Bln6ZA7d25u3bpF2bJlCQkJwe12s2zZMrJkycL169dp0aLFc+vlkktkZCRLlizh1KlTCILAwIED\nCQoKomHDhnHNVqZNm8acOXPo168fmTNnxmq1UqBAgXjRtR49ejB37lzu3r2LVqvl/v37/PTTTxQp\nUiTe67lcLpzO+AGlqVOnMnfuXJYvX44gCFy9epVhw4bRvHnzuOeEhYUxY8YMRo8ejclkIk+ePEye\nPDlR71E4c+aMV7qJXL16Nc4sMD3ickHFihn56qsYqldPOMpns0Hv3gZOnlTx44/R5M2b/pqzHD4s\ne+plzCjx9dcxccbqKWHgQD1587r5/POUR90uXxbp2tWARgMzZ5p5/XUJhwPatfNHr4e5c82vbH1Q\nehN7c+f6MX++H+vXm5LdqEiS5Fqzw4fVHD4sR+5OnFDxxhtugoOdhIQ4CQlxUaSIK1F/91271Iwb\np2PDhuhkjcebbN2qJjzcQESEMVl+fpIER46oWLFCy+rVsqVD06Z2Gje2kytX0uZfkmDJEi2jRukZ\nN07eVEmIq1dFpk7VsWqVhpYt7YSFWcmePf199ykoKLw6HDlyhDfeeCOth6HwEn777Tfq1KlDzZo1\nWb9+PQEBAXz00UfMnDmTESNG0LJlSypUqIDFYuHDDz9k7dq17Nq1izNnztCxY0dGjx5NixYtUiVq\n+CqhRPgSQKWCAQMsjB2rp1o103OjfPfuCbRt60+2bBLr15u86s/lDYxGGD7cwMaNGkaMsNC8ud1j\n9U3HjqmoWzdlERVJguXLtQwdqueLL6x062ZDFOX6sB49DLhcMHv2qyv2bkTfYP3IZpRMJ2Jv+XIt\nM2bokiz2oqPhr7/UREaq4gSey8Vjcedi4EALpUo5kxSlepqgIBcnTqhxu/GJBi2x2GxydG/UqJgk\ni72zZ+UOm7/+qkUQoFkzO+vWmZLtHWo2Q9++Bo4dU7N+vYlChZ5/nAsXRKZM0bFhg4ZPPrFx8KBR\nEXoKCgoKCommRo0anDx5krJly8ZF6W7fvs2VK1e4fv16XNOXR48ecfv2bUCuuZs/fz6RkZF88skn\nithLBj60/PE9GjWS0wZXrnx2NXbxokjNmhmoUMHJokVmnxN7ERERL3x861Y1FStmQpJg3z4jH37o\nObHncsGJE2pKlEh+auv9+wLt2/szY4aO1auj6dFDFnuSBAMG6Ll+XeS778zJiop4m5fNfWKI7cZp\n6tE1XYi99es1jBih55dfTC9sdOR2w6lTIj/8oCUszEDlyhkoUiQzI0fquXVLpFEjO5s2mTh9+hFL\nl5rp3dtKlSpJE3v/nv/MmSWyZZObMPkSkybpePttFzVrJq5O+MYNgZkz/ahWLQMNG2bAZBKYP9/M\nwYNGBgywJlvsnTkjUqNGRkQRtm41PlfsnTkj0qWLgQ8+yECePG4OHzYydOjzo3qeOP8Vkocy92mL\nMv8KCi/H39+fv/76i5CQEACuXbuG3W7nzz//pFy5cnHP279/P2XKlAHg3Xff5bfffqN8+fKEh4en\nybjTO0qE7wWIIkyfHsOHHwbw7rumuFTHK1dEGjUKICzMSvv2L29T7ks8fCgwaJCeffvUzJpl5v33\nPW8Gf/68SPbsbjJlSt7O/++/q/n8c38aN7YzZ078GqIxY3RERqpZvTpt7C5Sg/RkvQCwc6eaXr0M\n/Pxz9DPpwLdvCxw58qTu7sgRNdmzuwkJkWvv2ra18e67Lq93cgwKcnHsmCrByFVqc+KEikWL/Ni5\n0/jCjZY7dwTWr9ewerU2Lmo+bJiFSpU8Ux/7yy8avvzSwLBhckfNf3PypIqJE3Xs3aumc2cbEyY8\nSnakVUFBQUFBAeCvv/6Ka36yfPlyevTogV6vJzpaLr2w2+38/PPPjBs3joMHDzJ37lwWLFhAu3bt\nOHnyZFoOPd2i1PAlgh9+0DJ9uo6tW40YjQINGmSgW7f0ZwGwcaOGvn0NNGhgJzzc4rGGGv/ml180\nrFunZdEic5J+z2KBESP0rFunZeZMM1WqxBej06f78eOPcn1YShtc+CrpTewdPqyiZcsAvvvOTN68\nbo4dU3H8uIpjx9QcP67CaoVSpVwEBzspU0Y2FU+Lv92UKTru3xcYNSrtm/s4nVCzZgY+/dT2XJF1\n86bA+vVa1qzRcPSoiho1nDRsaOeDDxLXYTMxWK0waJCB3bvVLFpkplix+NH4P/9UMWmSvLnSvbuV\ndu1sXvu+UFBQUPAESg1f+qF+/fq0bt0at9uN1WqlQ4cOuN1upk6dSv78+bly5Qp16tShcOHC3Lx5\nk82bN5MpUybu379P1apVeeutt9L6LaQ7lAhfImjd2s6JEyoaNMiA0SjQsWP6Env37wsMHKjnyBE1\n8+ebqVjR81G9pzl6NOnpnMePy3YL77zjYvduI1myxBcFq1ZpmDdPx6ZNRkXspTFOJ/zzj8icOX78\n+qsf+fO7aNXKH39/CApyUry4izZtbAQFuXjjDd/wvQsKcjJtmofUUgqZMcOPLFkkWrV6IvauXRNY\nt04WeadOqahVy0HnzjZCQx0ej2RfvCjSvr0/gYFutm83xovYHTigYuJEPadOqejZ08r8+eZXNpKu\noKCgoJD63Lx5k6xZs/Lxxx/Hu18URXr37v3M83PlysUnn3ySWsN7ZVEEXyLp1cvKihVynUuDBr7X\n3v3fxPoBrV+voV8/A40b29m1y5gq3ljHjqn44gtrop7rdssL4OnTdYwZ8/zGMZGRKvr3N7ByZfro\ngpocLyZfFXsxMfD33/GjdqdPq8iRw8316yING9pp2dJOUJDLZ5p3PG/+g4JcHD2qQpJIUwF69qzI\nzJk6tm83cfWqyJo1Gtas0XL+vEjt2g7CwuSaRW95F65bp6F3bwP9+ln57DMbgiDXxe7Zo2biRB2X\nLomEhVn54Qd7ssegeJGlHcrcpy3K/CsovJw///yT4sWLp/Uw/nMogi8R3L0r0LhxBrp0sZExo0Tt\n2hmYMcNMaKh3I2UpITpaTbduBg4eVLNwYTTly6eeN+Dff6ueSRF7Hg8eCHTtauDBA5Ht25/f7OPa\nNYG2bQOYNi2G4sXTn79hYvAVsffwocCxY6p4aZlXroi8/baL4sVdBAW5qFfPxrJlfmzcqMXpFChY\n0I1Wi8+IvYTIkUNCr5ftHl5/PW3G6nZDp07+lC3rpH172dS8bl0HAwZYqFzZ6dU6xth06U2bNCxb\nFk1wsAtJgu3b1UyapOPOHZFevaw0b273yUZICgoKCgrpn7Nnz7J48WL0ej2XL18mX758aT2k/wxK\nDd9LuH9f4H//C6B2bQeDB8tRqz/+UNOzpz+1atkZPtx7tXDJJXZ8derYGTbMkqodRG02ePPNzNy4\n8fCFLfAjI1V06OBPgwZyE4rnLTKjo6Fu3Qw0b273iJ+fL5IWYs/phEuXRE6fVj0VvVPx4IFIsWKu\nuLTMEiVcFC4sN1Qxm2H+fD9mztRRq5aD/v2tLF2qZeDAxEVyfYHq1TMwfnwMISGpu3Hwzz8ia9dq\nWbjQj7t3BVq3tvG//zmoWNGJOhW23I4dU9G5sz9Fi7qYNCmGTJkkNm/WMHGiDrNZoE8fC40aOVJl\nLAoKCgreQqnhU1BIGOVf/At49EigadMAqld3MmjQk4VtaKiTiAgjgwbpef/9jIwaZaFuXUea1ypF\nR8Pw4Xq2bNEwfbqZqlVTPwJ5+7ZIjhxSgmJPkmThMHGijsmTY6hf//npE7YTdAAAIABJREFUsS4X\ndO7sT4kSLnr0UMRecnA45Hqt06dVnDkjX06fFrlwQUWuXG4KF3ZRpIibxo3tDBvm4q233M/83Ww2\nmDfPjylTdFSo4HyhR5uv89prbm7dEgHvCj5Jkq0n1qzRsmaNlkePBKpUcRAdDbt2GZ/pZOotXC45\nXXrmTDldukEDOytXyl6JarVEnz5WGjRw+JQ3oYKCgoKCgoLnUQRfAtjt8NFHAVSo4GTYMMszYi5T\nJomZM2PYtk3NyJF6pkzRER5uSRORBbB/v4ru3f0pX14Wo8eORQCpX0tw86ZArlzPX9AajfDFF/5c\nvCiyebOJwMCEF74jR+oxGgW++86c5kI6qSSmjsOTYs/hkK0wZEH3RNxdvCiSO7ebIkXkSF3Nmg4+\n/9xFwYKul0Z9nU7ZSP3rr3UUKeLmp5+iCQqKL5QqVfLNlOaE5v+11yRu3fLOySRJstVCbE1eTIxA\nw4Z2pkwxExzsonnzAPr0saaa2Lt6VaRrVwOCAKtWmdi2TUNwcCYKF3YxZkwMVas6vfa5UuqY0g5l\n7tMWZf4VFBR8FUXwJcCwYXqyZ3czZsyzYu9patRwUq2aidWr5eYouXO76djRRu3ajlSphXG5YOJE\nHYsW+TFpUgx166ZtQ5lbt0Ree+3ZRe2JEyratfOnShUns2ebXthefskSLevXa9iyxeR1f7a0ILli\nz26Hc+fEp6J18s/Ll0Xy5n0i7OrUcdCrl5WCBV1J7rDodsPq1RrGjdOTM6ebuXPNCdZ/+qrgS4jX\nXnNz86bnwlkuFxw8qGbDBg0bNmhwu6FhQwezZpkpXdoV970xfbofZrNAt27ej1RLEqxYoSU8XE/r\n1jasVtlG5oMPHPz0UzTvvvtq1sEqKCgoKCgoJIxSw/cc1qzRMHSonh07TGTOnPjpcTph5Uotixdr\nuXBBxccf22nTxsZbb3lnV//mTYHOnf0RBJgzx0yuXGnfOGPBAj9OnlQxeXIMIC9Af/hBy8iResaO\njaFZsxcL0ogINZ9+6s/atek3dfBFvEzsSZJsVn7xosjFiyouXHgi8K5cEXnzTTkVU07HdFG4sJuC\nBV0p9meTJNi6Vc3o0Xo0Ghg82EJoqPeiQGnBokVa/vxTzTffxCT7GGYz/PGHho0bNWzZoiF3bjd1\n6jioW9dBUJDrmfk6eFBFmzYBbN9u9HqzmIcPBfr0MXDkiIq333YTGamiZUs7nTtb06xRjYKCgkJq\nodTwKSgkjBLh+xcXL4r07Wtg+fLoJIk9ALUaPvzQzocf2vnnH5ElS/yoXTsD77zjom1bG/Xqec44\n+Y8/1HTv7k+7djb69LGiUnnmuCnl5k0hLsJnNkP//gaOHFGzbp3ppels58+LfPqpP3Pnml9psfdR\n4RY0ydmHHTvEOGF36ZJ8/dIlFTqdRP78bgIDXQQGumnUyE6RIi4KFHB7pV1/RISaUaP0mEwCgwZZ\nqFcv7etRvUFyUzpv3RLYtEkWeXv3aggOdlKnjoOBA6288UbC5+mDBwKffebP1KkxXhdcO3ao+ewz\nf/R6CZdLoFIlB99+Gx3PY09BQUFBQUHhv4ki+J7CaoX27f3p29dK6dIpS30qVMjNqFEWwsMtbNig\nYckSP3r3lluyV67soFIlJ0FBriR3xnM6Yfx4HUuX+jFvnjnBtLq0qiW4dUukdGkn//wj0q5dACVK\nONm2zfjSmrGYGGjTJoABA9KuDtJTREREEBxcicuXZQF34YLIySs3+S1zI3Rn2jFxwCAWZZfiBF1g\noIvSpZ1x11NrkR4ZqWL0aD2XL4sMHGilaVO7z2wcpISEa/him7a8GEmCM2dENm7UsmGDhnPnRKpX\nd9K8uZ25c+Uul4k5RrduBho2dFCnjvfSrI1G6NDBn127NOTJ42bgQCtNmtjTNBVaqWNKO5S5T1uU\n+VdQUPBVFMH3FOHhevLnl2vwPIWfHzRu7KBxYwf37wvs2aMmIkJNjx7+REUJVKjgpFIlJ5UrO3n3\nXdcLO+Zdvy7QqZM/Oh3s2GEkRw7fS9O6fVvgwgUVY8boGTLEQps2zxqpP48BAwwUL+6kfXu79wfp\nAex2uHlTJCpK4Pp1kcuXVY8jdCJnztTAZNLxxhtu8ud381rBq2zNU5sG2VsS1rgH+WY/9FikN6lE\nRKjJmtXNV1/p+fNPNf36WWjV6r/hvfYiwWe3w969ajZv1rB5swaHQ6BuXTuDBll4772ke+TNnOnH\nnTsiixebPTDyZzEaYcIEHfPm6cicWWLePDP/+9+rGZlVUFBQUFBQSBnJruHbsGED33zzDQADBw4k\nNDQ03uPprYZv5041PXsa2L3bmGoRljt3ngjA3bs13LkjULGiLADLl3dSsKArzuNv61bZW69TJxtf\nfGH1yVbqTieULJkRSRJYvjw60UbpP/+sZdIkHdu3G33C09BkgqgokRs3xLifN24I8e57+FAgZ06J\n3Lnd5MkjC7v8+eWI3VtvyfepVL5jqm63wz//qOjSxcCdOyI9e1rp0MGW5KYu6ZmHDwVKlszIpUuP\nALh7V2DbNg2bNmnYsUPN22+7qV3bQa1aDooVe7YeL7EcOqSidesAtm418eabnk1NvnZNYM4cHd99\n54fLBb17W+nXz6oIPQUFhf88Sg2fgkLCJCvCZ7fbmTRpEitWrMBms9G2bdtnBF96wm6XI0xffWVJ\n1ZqXHDkkGjVy0KiRA7Bw86YsAHfv1vDDD1ouXlSRObOESiVx/75Iy5Y2ihZ1cfGi3LzDl6Iyjx4J\ndOjgj9ksMHeuOdFi759/RAYP1rN6dbTXxZ7bDffuCc+IuNhLrJhzuyFPHnecmJOtDdyEhjrj7suR\nQ3pp+mNqiz27Ha5cEblwQfbau3BB5Px5FadOqbhzRyBDBomHD0W++MJCiRJJ7+CZ3hFFCYdDYMoU\nHZs3azh1SkWVKrLAmzAhhpw5Ux4xj63bmzw5xqNi78QJFTNm+LFxowaDAd55x8mCBTHky/fq1boq\nKCgoKCgoeJZkCb5jx47x9ttvkzVrVgBy5crF6dOnKVKkiEcHl1rMmePHm2+609zSIFcuiaZNHTRt\nKo/jyhWBtm0DUKvh008t3Lgh8u23fpw/L4uTN95wU6CA3MyjYEHZODt7djeZM0ucPr2HatUqpsq4\nz50TadUqgGrVHJhMQqJqnAAsFrn+KDzcQrFiSauZjImB+/cFHj4UuX9feHxd4P59+faDB/Ll/n0x\n7vrDhwIZM0qPRZwUJ+bKl3fGXc+bVyJjRilFEZOIiAgKlCzgMbEXEaGOq9W02+HyZbnBy/nzqng/\no6JE8uRxExgonxeBgW5q1HAQGOgmXz43Wi2MG6dj4EBrisbj6zxdR2OxwJ49arZulSN5FovcWKh/\nfzlV05NNcCQJevQwULeug3r1Uv5d4nTCxo0a5s/349w5FUWLulCpoE8fOTrri1F+UOqY0hJl7tMW\nZf4VFBR8lWQJvrt375IjRw6WL19OpkyZyJEjB7dv306Xgu/2bYFp03Rs2WLyqbSojRs1hIUZ6NHD\nSvfuzy7ubDbiFvvnz4scOaLm119F7t2T0w3v3q2NViuSJYtElixusmaVyJJFImtWiaxZZVEoX5cf\nz5JFQqcDlUpCrf4/e/cd3mT1/nH8/WQ3TcseIrts2aPsPSpLZSobFBRUFBG//kQEGTJUEJRpQUFA\ncLBHGTLbsjfIkj0KFaGlKzvP749HCpUCHUkT6HldV642bZqcHlPMJ+ec++bfi4xKRfJ1tZqH5mj7\ndg1vveXP8OFm+vSx0aJFwEOFaBwOZbx2u4TVCjabRFISjBvnR758MoULu1i7VovZLJGYCGazhNks\nER9/L7TdD3AxMUqAA/79fVz//o5y8vUCBVyUK/fw75ozp5wlxSxu224zdPlQt4S9efP0/Pyzjpw5\n5ceGupIlXRQt6nom+xamhyzDlSsmZszQs2WLlgMHNFSq5KBFCweLFiXQtGkgkyaZPfLYs2bpiY5W\n8eOPmTu3d/u2xMKFOn74QU+hQjIhIbbk5/yOHfGPrQwqCIIgCILwX5kq2vLaa68BsHnzZiRfSkvp\nEBqq55VXbB7rlZdeLhdMmGDg1191LFyYQHBw6itfej2UK6dsNUyNLCttEWJi7q94KR+V69euqTh+\nXErxfatVwuVSAppykXA6lc+dTnA6peRAqFYrY7VaIUcOmS+/9GPyZAPR0Sq6dDHhcinBzma7P16t\nVv73o3J/MTESVao4mDnTgNEo4+cnYzTy70eZgACZYsWcyUH1wfDqq9sR46xxfHHti0yHvYgI5Wxn\nZKSGw4c1dOpkpWtXKx062DMV6p62ZulpERsrsX27hi1btGzbpkWtbkTz5g5ef93K/Pn3WxM4HMrf\nhSfs3Klh2jTljaOM/vc5dkzN99/rWbdOS5s2dubOTWTjRi2zZhkYPdrMa6+lrQCSt4kVDu8Rc+9d\nYv4FQfBVGQp8+fLl49atW8nXb926Rb58+R663dtvv03RokUByJEjB5UqVUr+BzEiIgLAq9ctFjXz\n57/Ixo3xPjEeq1XNokUtuHFDxfjxf2Cz2YCM3V9k5P3rRYoo38+fHzp2zPj4ZBnq1m2A2Qz9+8dx\n8mRuFi5Utkbu3r0fp1Ni2rQmDB9uRpYj0GplmjSpi1qd8v7OnVPRsqWBr77aQ69eldP8+LGxULGi\n7zx/Urtev359pjSbApdSbu9J7/3Bdho0gP/7vwZMnGigQYM/ANDpfOv39cZ1pxN+/PEEhw7l59y5\nIE6fVlOu3N9Uq3aLFSuKUKqUK/n5Hxh4/+dtNhVabRu3j+fcORV9+ugYNmwPxYqVT9fP167dgNWr\ntUyebOOff7QMGuRi//44Vqw4Qf/+VahWTU14eBx//RVOZKRvzL+4Lq6L6+K6L1y/9/mVK1cA6N+/\nP4IgpC5DVTptNhutW7dOLtrSp08fNm3alOI2T0OVztBQPeHhGn76yTOl09Pj5k2Jnj1NlCrlZOrU\npEyX7X8wbLhTTIxEv37+GAxKKfj/Frlp08bEZ59ZqFvXkerPWyzQqlUAr79upW/fp6MFQ3q5e+4f\nPMOXXV2/LrF1q5atW7Xs3KnhuedcNGvmoFkzO3XqOFL8vTxq/hMSoHz5nFy9Guu2ccXESLRqFcC7\n71ro0yftz+foaIkFC/QsWKAnKMjJgAFWWre2Y7EoW51Xr9YxcWISL73k3XPFGeGpf3uEJxNz711i\n/r1LVOkUhEfTZOSHdDodH374Id26dQNg+PDhbh1UVvn5Zx2jR3vmPE96nDihpnt3f3r3tvHhh75b\nYv3MGaU4S5s2dkaNMqdapVKjUbbOPcrnn/tRurQrXS+Os7vsGPYsFqUv3r2QFx0t0aSJgxYt7Hzx\nRRKFCqV/b+a9LcnuYrdD377+hITY0/x8PnBATWionk2btLzyip3ffounQgVlW/a2bRo++MBI/foO\nIiPjyJXL9/psCoIgCILw9MlwH74n8fUVvhs3JOrXD+Ts2bsPFRnJShs2aHnvPSOTJiXRoYPvvpv/\nxx8a3n7bn88/N9O9+6Nf3HbpYmLAAAutWj0cUvbsUfPGGyYiI+PImVO8mBXuk2WlRce9gLd3r4YK\nFZw0a2anWTM71ao5n9gG40lu3JBo2jSQ06fvumW8Q4YY+ftviUWLEh87NqsVVq7UERqq5/ZtiTfe\nsNKzpy35byA2VmLECD927tQwZUoSLVpkv4AvCIKQWWKFTxAezYtRx7s2b9bStKnDa2FPlmHmTD0z\nZxpYsiSBGjXS15YgK82Zo2faNAM//ZRAnTqPH2f+/C6iox+uF282w3vv+fPll0ki7AmAsq0xIkLp\nO7l1qwZZlmjWzE7PnlZCQxPd/jz5+28V+fO7pzjTzJl6Dh1Ss359/CPDXlSUxI8/6lm4UE+FCk6G\nDbPQsqU9xe3XrdPyv/8ZadvWRmRkHAEBbhmeIAiCIAhCsmwb+CIiNDRr5p0VNbsdPvrIyMGDajZu\njKNwYfcHIHecJXC5YORIP7Zu1bJxY9rKwRcsmHrgmzTJj4oVnW7pT+brxDmO1P3zjxLw7oW8v/+W\nqFfPQYMGDgYOtFC2rMst25kfNf/R0RIFCmT+b23DBi0zZhjYuDH+oYAmy7B7t4bQUD07dmjo3NnG\n6tXxlCmT8m/n+nWJ4cONnDypZu7cxEeeeX0aiee/94i59y4x/4Ig+KpsG/guXVLz+uvWLH/c2FiJ\nvn398fOTWb/+4ReMvsJmU5pIX7umYv36+DSvthQoIPPXXykD3+HDapYu1REeHueJoQo+KiZGIjLy\nfsC7dk1FnToOGjSw07NnIpUqZX6bZnrcvKmiQIHMrfD9+aeawYON/PxzQoo3QO7ckVi6VMeCBUon\n99dftzJt2sNFjex2pV/ft98aeOMNK7NnJ/psixFBEARBEJ4N2TbwXb+uonDhrO29d+GCitdeM9Gy\npZ0xY1IveuIumXmXMT4e+vQx4e8vs2xZQrpekBYo4CIi4v7TymaDwYONjB1rJl++7LGVM7u+wxsX\nB7t2aQkPV0LexYtqatVy0LChnWnTEqla1ZklW6gfNf/R0SoKFsz433x0tET37v5MnJhErVpOZBki\nIzUsWKBn82YNL75oZ+rUJOrUcaS6UhkZqWHYMCOFC7vYtCneZ3p/ult2ff77AjH33iXmXxAEX5Ut\nA58su297V1qdOaOiY8cAhg0z06+f71ao/PtviddeM1G1qpOvvkpKdygtUMDFzZv3V/i++cZAkSIu\nOnf23d9ZyJj4eNizR0NEhJaICA1nz6qpUUPZojlpUhLVqzsz1STe3aKjJcqWzVjIiouD7t1NdOtm\no1EjB99+q5zN02qhTx8rX36Z9MiqmtHREqNG+REZqWX8+CTatbP7bCVeQRAEQRCePQ8ftsoGJAmM\nRkhKyppXXadOqejQIYCRI7Mu7D3YmDStLl1S0bp1ACEhdiZPTn/YAyhYUCY6WpnXkydVzJ2rZ/Lk\npGz1Ajcjc/80SEpSWgeMHWugVasAKlTIybRpBvz8ZMaMMfPXX7GsXJnAsGEW6tTxXth71PxHR2ds\nS6fZrIS9/PldnDmjplatQM6cUTN9eiKRkXG89ZY11bDncMD33+tp0CCQggVldu++S/v2z37Ye1af\n/08DMffeJeZfEARflS1X+ADy5nVx+7ZEjhyeXeU7eVJFp04BjB2bROfOvluw5ORJFV26BPDhh2Ze\nfz3jobRAARd//63Cbleqco4YYc5QzzTB++Li4MABDXv2aIiM1HDsmIYXXnDSsKGdTz81ExzseKrO\nn2XkDN/16xIdO5qIilJTvLiTvn1tTJ2a9MR/N/bvVzNsmJEcOWTWrImnXLlnc/umIAiCIAi+L9sG\nvnz5ZKKiVB49R3PihJouXUx88UUSHTtmbdhLz1mCgwfV9OihjLNTp8yN088PDAaZqVMNmEwyvXtn\nv62cT+M5DlmGy5dV7NunYe9eDfv2qbl0SU2VKg5q13YwdKiF2rUdmEzeHumTPWr+b95UUbDgk998\ncDqVlcwFC5QG6fnzu/j993iCg51PXJ27fVti9Gg/tmzRMnq08vf0rK/o/dfT+Px/Voi59y4x/4Ig\n+KpsG/hq13YQGamhQQPPlEM/elTNq6+amDgxiVde8d2VvZ07NfTv78/06YmpNkvPiKAgF9On69my\nJT7bvdh9WthscOyY+t9wp1wkCYKDHQQHO+je3UqlSr51Bi8zYmMl7t6VHluoKSpK4uef9SxcqCN3\nbhmjUaZ6dQfLlz+5cJHLBQsX6hg/3o+OHW3s3n33oQqdgiAIgiAI3pAtz/ABhITYWbdO65H7PnxY\nTdeuJr76ynthLy1nCdav19K/vz8//ui+sAfKWa9KlZyUKpU9t7H54jmOO3ckNmzQMmaMgbZtTQQF\n5WToUCMXL6po187Oxo3x/PnnXebPT+Ttt63UqPH0hr3U5v/4cTUvvPBwGwinEzZt0tCjhz8NGgQS\nFaViwYJEmja1Y7FI/PLLk8Pe0aNqQkIC+PlnPb//nsCECeZsHfZ88fmfXYi59y4x/4Ig+Kpsu8JX\np46DuDiJXbs01KvnvrBz8KCabt1MTJ2aRJs2vruyt3Kllv/7PyO//JJAtWpOt93v8eNqrl9XUaaM\n7/7uzzpZhr/+enB7poabN1XUqKGs3g0bZqFGDUe2CiVHjijbU+85f17F0qU6lizRU7Cgiz59rMyZ\nk4jJBNOm6QkL07F2bfxj5+jOHYmJEw2sXq1jxAgz3bvbUGXbt9AEQRAEQfBV0pkzZzxSUePq1atU\nr17dE3ftNr/9pmP2bD2bN8e75YXa/v3KWbjvvksiJMR3A8/69VqGDjWybFkCL7zgvrAny/DSSybq\n1nWwapWOvXtFo/WskJQER49q2LtXnbw9099fpnZtB7VrOwkOdlChQtY2Ofc1Awb4U6eOHY0GlizR\nc/Giis6dbXTvbkvxNzB/vo5p0wysWxf/yGJDNhvMnatn6lQDr7xi45NPLI9sySAIgiBkjUOHDlGk\nSBFvD0MQfFK2XeED6NTJxuzZepYu1dG9e+aKi5w+raJHDxMzZiTSsqVnzgW6w+bNGoYMMfLrr+4N\newBhYVru3FExdKiFmTMNxMdDQIBbHyLbs1jgzz/VHDmi4fBhNUeOqLl4UU358kqw69rVxtdfJ4nK\nqP9yOmHHDg2bNmnYuFFLkyZ2hgyx0Ly5He1/dnQvW6blq6/8WLs29bAny8pzfNQoP0qWdLF6tai+\nKQiCIAiC78vWgU+lgqlTk+jY0US5ck6qV89YALpzR6JHDxOjR5t9JuxFREQ8VDFsxw4N77zjz6JF\nCVSt6t6w53DAmDF+jB2bhMEA5co5+fNPNXXquPdxngapzX1G2Gxw8qQS6g4f1nDkiJpz59SUKuWk\nalUnNWs66N/fSvnyTvR6Nwz8GREREUGBAo1YulTH0qV68uZ1YbFIHD9+l/z5Uw/Cq1Zp+fRTI8uX\nx1OixMMh7vhxNSNG+HHrlopJk5Jo1sw3/s59kbue/0L6ibn3LjH/giD4qmwd+EApLjJtWhK9epnY\nuDGOwoXTtzJit0O/fv60bWunWzffbUGwe7eGAQP8mT8/keBg94ewJUt05MvnokUL5YVwlSpOjh7V\nZMvAlxF2O5w+rYS7I0eUcHf6tJrixV1UreqgWjUnvXpZeeEF51PV+y4rxcRIrFihJTS0PrGxAXTp\nYuO33+KJi5MYMcL4yLD32286Ro704/ffE6hQIWXYu3lT4osv/Ni8Wcv//Z+Znj1taLL9v5qCIAiC\nIDxNxEsXoE0bO1evWmjbNoDFixOpWDHtIWX4cD8MBhg1yuzBEabfg+8y7t+vpk8ff77/PtGtBWru\nSUqCiRP9WLAgIbkNQ+XKDvbsyZ5Prye9w+twwNmzquRgd/iwhlOn1BQu7KJaNQdVqzrp2tVKxYpO\n/P2zaNBPKasVNm/W8uuvOnbs0NKihZ3Ro100a3Y3OZjNnq2nSpXU/6YXLtQxcaIfK1ak3J5pNsOM\nGQZmz9bTs6eNfftEm4W0Eisc3iPm3rvE/AuC4Kuy5yvyVLz1lpW8eV106GBi2rS0Vdj88Ucd4eFa\nNm2K89mCGEePqunZUzlb2KSJZ7ahhYbqqVnTQc2a919U16/v4Msv/ZBlsnUvvsREOHNGzcmTak6c\nUHP0qIYTJ9QULOiialUnVas6eOUVM5UqOcR5xzSSZThwQM0vv+hYuVJHuXJOXn3VxvTpiamGsh07\nNHTu/PDq+9y5er79Vs/q1fEEBSlhz+WCZct0jBnjR82aDrZsiadYMXFOTxAEQRCEp5cIfA/o1MlO\n8eIJ9O5tYts2G5999uh+WhERGiZO9CMs7PGl270lIiKC3Lkb8eqrJqZMSfLY2UKLBWbNMrBiRXyK\nr5cq5cJolDl+XE3lys/+tk6HAy5cUHHypJqNG6NISCjOyZNqbtxQUaqUkwoVlEvbtmYqV3aSI4co\nqpJely+r+PVXHb/+qkOSoGtXG1u3xlO0aMpA9uA5mqQkiIzUMmtWUorbTJ+uZ948PWvWJCQHur17\n1Xz6qRFZhtDQBLEdOYPEOSbvEXPvXWL+BUHwVSLw/UeNGk4iI+MYPdqPunVzMG6c0jz9wVWqS5dU\n9O+vbJEsWdI33/2/etXEm28GMH58Em3beq5FxC+/6KhSxUn58g/PQ6tWdjZu1D5TgU+WISpK4tQp\nZdXu3sdz59QUKOCiQgUnJhN07GhjxAgnJUu6HqoGKaTdrVsSq1frWLZMy19/qenQwcasWYnUqOFM\n08pxeLiWKlUc5Mx5P2BPnmxg6VKlz97zz8tcuaLi88/92LdPw2efmenSRfTTEwRBEATh2ZGt+/A9\nyZ49aj780B9/f5kPPrAQEmInMRFefDGQvn2tDBhg9fYQU3XtmsSLLwby2WdmXn3Vc4VkXC6oWzeQ\nyZOTaNDg4RXEnTs1jBnjxx9/xKfy077v7l2JU6dUyaHuXsDTaqFCBSflyt1fuStbVgl6QubFxEis\nWaNlxQodhw+radXKTocOdpo3t6PTpe++hg41UqKEk8GDrcgyjB9vYO1aHStWxGMwwLRpBn76Scdb\nb1l5910LRqNnfidBEATBs0QfPkF4NLHC9xh16jjZuTOONWu0TJpkYNw4P/LkcVGpklIO3xclJED3\n7iYGDrR4NOwBbNyoxd9fpn791LeL1q3r4Px5FdHREgUK+OYWRqcTrl9Xcf68igsX1Jw/r+L8eSXc\nxcZKlC2rBLry5Z20a2enQgUn+fL55u/yNIuLgw0bdCxfrmXXLi1Nm9rp08fK4sX2DIcwWVaeoytX\nWpBlGDnSj507NfzySzxLluiZOVNP69Z2wsPjRN9CQRAEQRCeWSLwPYFaDa+8Yufll+3MnKlj7Fgj\nBoPMO+8Y6djRRpMmDp8p0+50wltv+VO1qpMqVbYAnj1LMH26nnfesTxya51WC02bOti8WUvPnt5r\nWeFyKdswL1xQc+GCEujufbxyRUWuXDJBQcr2y5IlnTRo4KB8eSdPi9D3AAAgAElEQVTFirkytLVP\nnONIm6Qk2LRJy/LlOrZv11K/vp2OHe18/33qxVfS6t78Hz+uxs9PpmRJFx9/7MeBAxo6dbLx4ouB\n1KnjYP36eEqX9s0t2U8z8fz3HjH33iXmXxAEX+UjUcX32e2waJGBOXMSCQ52sHKlUs797bdVvPyy\njU6dbAQHO7169mfMGD/i4iR+/DGRffs8+1gHDqi5dk3Fyy8//nxgSIiddes8H/hkWemZdm+V7sFw\nd+mSisBAmZIllVAXFOSkVi0HQUEuihcXrQ+yktUKW7cqIW/zZg3Vqzvp0MHGtGlJ5Mrl3lW2jRu1\nNG9uZ+BAI4cPa7DZlDN9S5YkPLJNgyAIgiAIwrNGnOFLo8mTDRw4oObnnxNTrGhdvKhi+XIdv/+u\n459/JGrUcFC9upPq1R3UqOF0+4vYR1m8WMc33xjYtCme3Lk9/5j9+vlTu7aDgQMfv7X19m2J6tVz\ncOZMLAZDxh/P4VACXVSUKsXl2jUVFy6ouHhRjdEoJ6/SBQXd/1i8uFO0PPAiu105z7l8uY6wMC0V\nKjjp0MFO+/a2RzZDd4fGjQO4e1ciJkaibFkXn39u9kgfSkEQBMH7xBk+QXg0EfjS4Px5FSEhAWzb\nFk+RIo/eAnb9usShQxoOHdJw8KCaI0c05M/vSg5/1as7qFTJmangk5rISA2vv+7PmjXxlCnj+S1q\nly6paNEigCNH7qapUEmnTiZee81Gly6pr/LZ7XDzporr1+8HuuvXUwa7f/6RyJtX5rnnXBQqdP9S\nuLArOeT5YnuM7MrphN27lZC3Zo2W4sVddOhg4+WXbTz/vOffkPj2Wx2ff24kd26Z775L5MUXHdm6\nH6QgCMKzTgQ+QXg0saUzDT7+2MiQIZbHhj2A55+Xef55O+3bK9scnU44e1bFwYNKCFyyRMdff6kp\nV85JqVJOChWSKVTIxfPP3w8wefPK6doWevGiijfe8GfOnMQUYc+TZwlmz9bTu7f1sWHP5YLYWInb\ntyXq17czebIeq1VZ8btxQ5Ui2N25I5EvX8q5KFzYRXCwI/lrBQrIT017g+x6jsPphP371axcqWP1\nah1587ro2NHG5s0WihfPmrNyhw6pefttJ3/9ZaR8eSfh4fGixUIWy67Pf18g5t67xPwLguCrROB7\ngr171fz1l4olS9JflVOthvLlXZQvb0s+w5aUBMeOqbl0SU1UlIozZ1Rs3apJDkDx8RIFC94LgHJy\nEHzuORcmk4yfH/j5yRgMMg6HRN++/gwebKZuXQeyTIZXMWRZecFus4HdLmGzKZ87HMrnSUkSd+9K\n3Lkj8fPPOt5808r48Qbi4pSvK1vnlPB2545EbKxEQIBMnjwyuXLJXL6sZsMGLSVLuihWzEXduo7k\ncJc/v+wzhW+E9LFale2a69bp2LBBS548Mu3b21i5MmtWm+85fVrF+PF+7NqlISnJiZ+fzC+/JIiw\nJwiCIAhCtie2dD7Bq6+aePFFG/36ZU2VSYuFFCtgUVES16+ruHFDRUKChMUiYbGA2Sxx5YoKSQKN\nRvk5hwP8/MBgkDEY7gdDvV7ZNmmzSf9+VELdf7+mUoFOp9yfTiej04FWq3w0GGRy5pSxWuHCBTVd\nu9rIkUNOccmZUyZ3bhd58iifPxjiJkwwEBMj8eWX5iyZR8Fz4uPhjz+0rFunY8sWDWXLumjb1kbb\ntnZKlszaqpdXrqiYNMnA5s1Klc9du7T06GHl1Ck1S5YkZulYBEEQBO8RWzoF4dHEuspjHD2q5sQJ\nNQsWZF1LAYMBSpRwUaLE4184f/GFgUOHNPzyS0JysHI6wWwmRSi0WJQVOq32fnhTQl3KQKfVKiuS\nT/LOO0Y6dLA/sVjLf/XqZaVRo0BGjjSLBuVPoVu3JMLClJC3e7eG4GAH7drZ+OKLJK/0WLx2TWLa\nNAPLl+t44w0r3bpZWbtWx7p18Qwc6M///ifeWBAEQRAEQQBI94an6OhounXrRrt27ejYsSO7du3y\nxLh8wty5et56y+L2IiuZtWePmkWL9MyalZhiFU2tBpMJ8uaVuXQpnNKlXVSq5KRGDSeVKzspX95F\nUJCLIkVcPPecst0yMFAJmWkJexYLrF+v5eWX0x+ACxeWqVvXwfLlunT/7NMmIiLC20Nwi8uXVcyc\nqadtWxM1a+Zg2zYtXbtaOXEilt9/T6BvX1uWh71r1yQ+/NBI48aB+PvDzp1xXLumIjJSy4YN8SQk\nSFy9aqN5c1GN01uelef/00jMvXeJ+RcEwVele4VPo9Hw+eefU7ZsWaKionjttdfYuXOnJ8bmVRYL\nrFunJTzct1YK4uJg0CB/pkxJ8mhJ+9Rs3qylcmUnzz2Xscft29fKhAl+9O7tvSbswqPJMpw8qWbt\nWi3r1mm5eVPFiy/aee89K40bJ3j1jY8rV1R8842B1au19OljZe/eODQapT2I0SizalU8/v7wxRd6\nQkIuolYX8N5gBUEQBEEQfEi6A1+ePHnIkycPAIUKFcJut2O329E+LSUU0+iPP7RUrOjMkhLy6TF8\nuJFGjRy0bv34hueeqBS2bJmOjh0zHtaaNXPw0UcSe/eqqV372W18/TRVabtXWXPdOh3r1mlxOqFt\nWzsTJ5qpXduRppVfT7p8WcWUKQbWrtXSr5+V/fvjyJ1b5uRJFb16mQgJsTN2rBm1Gu7ckVi1Ssvu\n3QUB3/q7zU6epuf/s0bMvXeJ+RcEwVdl6gxfeHg4L7zwwjMX9gDWrNHSoYNvrUStWaNl924NO3bE\nZfljx8fDtm1apkxJyvB9qNXwwQcWJk70Y8WKBDeOTkiPhATYuVPLpk1aNmzQkjevi7Zt7SxYkEjF\nik6f6Fd34YKyohcWpgS9AwfiyJVLCXGrVmkZNszIF1+Y6dr1/t/otGkGOna0U7CgCHuCIAiCIAj3\nPPYM3/z582nfvn2Ky7Rp0wC4desWX375JaNGjcqSgWa1gwc11K3rO+eAbt6U+OgjI7NmJaap6Im7\nzxKEhemoW9dO7tyZezHdvbuNq1dV7Njx7NYL8rVzHLKs9IOcOVNPhw4mKlTISWiontKlnYSFxRMR\nEc8nn1ioVMn7Ye/UKRVvvmkkJCSA5593ceBAHJ9+aiFXLhmnE8aMMTBypB+//56QIuzduCGxaJGO\nDz80+9z8Zzdi/r1HzL13ifkXBMFXPfZVd9++fenbt+9DX7darbz//vt8/PHHjy2B+/bbb1O0aFEA\ncuTIQaVKlZK3PNz7h9EXr8fGSty4IRMdvZNy5bw/HllWqlw2bXqO4OB8afr548ePu3U8ixfHUq3a\nLaBYpu/vk0/MfPyxg6++iqBhQ+/P77N4fcuW3Rw/noeoqCps3qwlMdFGjRp/M2BAHn76KYGjR5Xb\nlyjhG+NdsOA4v/5amvPnCzBokIXOnbdiNDrImVP5fljYXr7+ujoBASa2bInn9OlwIiLu//ywYbE0\nafIPhQrl4cIF7/8+4rq47o3r9/jKeLLb9Xt8ZTzP+vV7n1+5cgWA/v37IwhC6tLdh0+WZT788ENq\n1qxJ9+7dH3m7p7kPX3i4hvHj/QgLi/f2UACYN0/Pzz/r2LAhHm/tnq1YMQerV8e7pc+aywWNGgXw\n6aeWJ55FFNLu4kUVf/yhZfNmLXv2aKhSxUGLFnZatrRTvrzL66t3qdm3T83kyX6cOKFm8GALvXtb\nMRpT3ubkSRU9e5po3drO6NHmFJVpAS5dUtGiRQB798aRJ4/YzikIgpAdiT58gvBomiffJKWDBw+y\nadMmLly4wK+//gpAaGgo+fLlc/vgvCUmRiJfvqxtIP0o165JTJhgICzMe2Hv2jWlOfuTegOmlUoF\nI0ZYGDvWj5AQO6p0NwcRAKxW2LVLw+bNWv74Q0t8vETz5nZ69LASGppIjhy+GX5kGXbs0DB1qoHL\nl1W8/76Fn36yodc/fNsVK7T8739Gxo8306VL6mdqJ00yMGCAVYQ9QRAEQRCEVKQ78NWsWZMTJ054\nYiw+w2yWMBh848XjhAl+9OtnpXTp9IWtiIiI5O0PmbV3r4batR1uXSEKCbEzZYqB5cu1dO78bK3y\nuXPu/+vqVRV//KGEvMhILeXLO2nZ0s7cuUrBFV8Oz3Y7rFihY/p0PQ6HxODBFjp3tqX6RobTCWPH\n+rFypZZlyxKoXDn1qq6nTqnYulXL/v13k7/myfkXnkzMv/eIufcuMf+CIPiqdAe+7MBqxWuraQ86\neVLFli1a9u27++Qbe9DevRqCgx1uvU9Jgs8+MzNkiJGXXrKje/b7sWdIYiLs2aNhxw5lFe/WLWUV\nr1MnG9OnJ2W6iE5WiIuDBQv0zJljoHRpJyNHmmne/NFvINy5IzFggD8uF2zZEv/Ylbvx4/0YPNhC\nYKCHBi8IgiAIgvCUE4EvFc895yIqyvtLJWPG+PHBBxl7MevOdxn37tXQpUvG2zE8SsOGDsqWdfLN\nNwY+/tji9vv3lszMvc2mVIjduVO5HDumoXJlB40aOfjuu0SqVnV6vTdeWl27JvH99wYWL9bRvLmd\nxYsTqFLl8f0X9+xR8+ab/rzyip2RIx8+r/egsDAtJ0+q+f77xBRfF++we5eYf+8Rc+9dYv4FQfBV\nIvClonRpF+fPezfwRUZqOHNGzYIFiU++sQfFx8OFC+pHbqnLrK++SqJJk0Dat7dRoYJvnJvMSk4n\nHD+u/jfgadm3T0OpUk4aNnQwdKiFOnUc+Pt7e5Tpc/y4mhkz9GzapKVbNxs7dsRRuPDjVyKdTpg6\n1UBoqJ5p05IICXn8Nt+7dyWGDTMyZ04ifn7uHL0gCIIgCMKzxfvLWD6oSBEXsbEq7tzxTllDWYZR\no/wYMcKcaiGLtPhvmeiMOnBAQ6VKjgyP40mef15mxAgzgwf743DvrlGvedzc3+uJN3eunt69/Sld\nOgdvveXPtWsq+va1cvToXbZujWf0aGXb49MS9mQZtm7V0KGDiddeM1GhgpPDh+P44gvzE8PezZsS\nnTub2LZNw5YtcU8MewCffebHiy/aadDg4SeNu577QsaI+fceMffeJeZfEARfJVb4UqFWQ9Omdtau\n1dK7d+qVAT1p9WotTid06OD9YibHj6upWtUzq3v39O5tY+VKHTNn6nnvPatHH8sbrl2T2LFDS3i4\nhvBwLWq1TKNGDtq1szNpUhLPPef75/AexWaD5cuVQiwA775rpWNHW5rPZG7ZomHwYH9697by0UeW\nNG1X3bZNw/btGiIi4jIxckEQBEEQhOwh3X340upp7sMHsGGDlsmTDWzaFJ+l/cvsdqhXL/DfrY7e\nX/IaPtyPQoVcvPuuZ4PY5csqmjcPICwsPt0VSX3N339LREYqWzR37tQQFyfRsKGDRo3sNG7soHhx\n3+yJlx5370osWKBjzhwDZco4efddC82apb2Sq9V6rwqnjtmzE1NdqUtNQgI0aBDI118n0aKF9/8+\nBEEQBN8g+vAJwqOJFb5HaNnSzqhRfqxbp6Vdu6xbaVu3TkvBgi6fCHsA0dEqatTw/FiKFXPx0UcW\n3n/fyNq1CT7dXuBBLhecPq1i3z4Ne/dq2LdPw507ErVrK4VW+ve3Ur68b7dLSI+//lIxb56eX3/V\n0bKlnSVLHt0y4VFOn1bx5pv+FC/uYufOuHRVGh071o/69R0i7AmCIAiCIKTRM/Iy1P3UavjmmyT+\n7/+MxMdn3eP+9puOHj0yv43UXWcJbt6UKFAga7YcDhhgxeWSCA310IFBN0hMhPBwDZMnG+ja1URQ\nUA569TKxb5/Sq3DhwgQWLFjH0qWJvP22lRdeePrDntMJ69dr6djRRLt2Afj7y+zcGcecOUnpCnuy\nDD/8oKN9+wD697eyYEFiusLerl0a1qzRMW6c+bG3E+dovEvMv/eIufcuMf+CIPgqscL3GPXqOWja\n1M6HHxqZPTvJ4y/cb99WtgLOnu3dypwPio5WUbBg1myxVKlgxoxEWrcOoGpVB7Vre/bsYFpERUkp\nVu/OnFFToYKT4GAHvXpZ+e47x0OB+Fn5f/4//0gsXKjnxx91FCwo07+/lZdftmWogM+tWxJDhhiJ\nilKxfn36t+3euKH05ps2LZFcuZ7eM4+CIAiCIAhZTZzhe4KkJOjUSQkg48ebPXr26ocfdOzapWXu\nXN8IfLIMRYrk5NSpWAICsu5xN23S8MEH/vzxR1yWFjRxOuHUKTV792rYu1f5mJAgERzsoHZtJYBW\nrep4ptsAyDIcPKhm3jw9GzZoadvWTv/+1gwX7pFlWLZMy6efGune3cYnn5jTXNDlHqsV2rULoHVr\nO0OHPjv9GgVBEAT3EWf4BOHRxArfExiNsHRpAu3amRg1yo9Ro8wea3z96696hg59/Ha1rBQfr6y6\nZWXYA2jVykG/flb69DGxZk28R1pCyDJcu6biyBE1x46pOXhQw8GDGgoUcBEc7KBhQwfDhlkoVcr1\n1G/JTAuzWam2OW+enthYiX79rHzxhTldWy7/68YNpVfexYtqlixJoHr19IdGWYaPPjJSqJCLDz4Q\nYU8QBEEQBCG9ssFL2czLkUNmxYoEjh1T07mzidu33b/Md+mSigsXVDRt6p5iFO44SxAdraJAAe9U\nzBw61ELBgi7+9z8jciYX+WQZLlxQsWKFltGj/ejQwUSpUjkICQlg8WIdkqScHzx48C779sUxfXoS\nvXrZKFMmY2HvaTrHcfmyilGj/KhcOQerVun45BMzBw7EMXiwNcNhT5Zh8WIdjRsHUrGik23b4jIU\n9gB+/FHHwYMaZsxITPPq+tM0/88iMf/eI+beu8T8C4Lgq8QKXxrlzSvz++8JjB9voEmTQCZOTKJN\nG7vbtnj+9puODh1saLXuuT93kGW81j7g3nm+kJBA5s/X0a9f2grZuFxw/ryKo0fVHD2q4ehRZQUv\nIACqVHFQpYqTQYMsVK7spGDB7HkWzOVS+t/Nm6fnwAEN3brZ2LQpnhIlMh/ur12TeP99f27flli2\nLIFKlTJ+DnP3bg2TJvmxYUM8JlOmhyYIgiAIgpAtiTN8GbBjh4ZPPjFSoICL8eOTKF8+8y+UmzcP\nYOxYM/Xq+U65+agoiRYtAjl58q7XxnDhgorWrQNYsCCBOnVShgeHQ2kTcC/YHT2q5sQJDXnyuKhc\n2UnVqk4qV3ZQubKTfPmyZ7h7UHS0xC+/6PjpJz0BATJvvKE0STcaM3/fLhcsWKBj/Hg/Bg2yMniw\nJVNvXly7JtGqVSDffZdI8+a+8zchCIIg+CZxhk8QHk2s8GVA48YOdu6M44cf9Lz8cgD16jkYONBC\n7drODK2IuVxw9qyaihV964WtySSTkODdDuElS7qYNi2RXr1MDBtmJj5exdmzKs6eVXP+vJqCBZVw\nV6WKgxdftFO5slNUcXyA3Q6bN2tZtEjH7t0a2re3M2tWIjVrZuy5mpqLF1W8/74Rs1lizZp4ypXL\n3Bsgd+9K9OhhYuBAiwh7giAIgiAImSQCXwZpNPDmm1a6dbOydKmewYP9CQiQ6dvXSps2dvLmTXvo\nuH5dRWCgTGCg+8YXERFBgwYNMnUf/v5KlVKXiywpXJKQAH/9pebsWXVyqDt7Vs2VK8r8jB5tpFs3\nK02bOnjrLSulSzvdOmfu4o65z6zTp1X8/LPSID0oyEmPHja+/z7RrVsjnU74/ns9kycb+OADCwMH\nWjNd0CghAbp2NVGvnoPBg60Zug9fmP/sTMy/94i59y4x/4Ig+CoR+DIpIEAp+PHGG1Y2b9aydKmO\nkSP9eOEFJ23a2Gnb1k7x4o9f8ThzRkWZMt7vOfdfajUYDEroc1dQkGWl3+C9UHfmjDo52N25I1Gy\npJOyZV2UKeOkUycbZco4CQpyoddDaKie2bP1DBtmydJ2DU+LuDhYsULH4sV6rl9X8dprVtaujadU\nKfcX3tm/X83HHxvx85PZuDGeoKDMP4bFAj17mihb1unxFiiCIAiCIAjZhTjD5wEWC4SHa1i3TkdY\nmJZ8+Vy0bOmgYkUH5cs7KV3aleJ808yZei5fVjFpku+0ZLinXLkcbN8el+YCJ7IMMTESV66oki9X\nr977XM3VqyrUapnSpZVQV6bM/YBXtKjriStE33xjYOlSHatXxz/U8Dw7kmXYtUvD4sU61q/X0qiR\ng549rTRr5kDjgbdz/v5bYswYP7Zu1TJqlJmuXW1uCWYWC/TpY8Jkkvn++0SPtT4RBEEQnk3iDJ8g\nPJpY4fMAgwFatnTQsqWDyZPhwAE127ZpWbVKx8SJaq5fV1GypJMKFZTL/v0aypd3erUq5qOYTDLx\n8RIFC8o4HBAbK3HzpoqoKImoKBXXr6uIikp5UamgWDElwBUp4qJ4cReNGjkoWtRF0aIucuTIeFD7\n4AMLTie89FIAK1fGZ9uVvuvXJX75Rc/ixTr0eujZ08qYMeZ0bSVOD4cD5s5Vtm++9pqNPXvuum07\nrdkMvXsrYW/2bBH2BEEQBCE72LRpE1FRURw9epSgoCDeffddbw/pmSUCn4ep1VC7tpPate9v2UxK\nUoq0nDypXI4dUxMRoSU01ECpUkrRkVy5ZHLndpEzp5x8PVcu1wOfy+TIIT+0iiPLyiU8PJJ69erj\ncpF8kWXlo9MpcfeuRGyscomJuX89JkaV/PXYWIlbtyTatAnAapUwmyEwUKZgQZlChVwUKuTi+edd\n1K3rSL5eqJDL4+fqhg2zoFYroW/VqngKFfKt0OepcxwWC2zcqGXxYj0HDqjp0MFOaGgi1aq5rwBL\naiIiNHz8sZH8+V2sXRtP2bLu2yKalKRs48ydWwl77liVFOdovEvMv/eIufcuMf+CkHZXrlwhLi6O\nvn37YrVaefHFFylWrBjt27f39tCeSSLweYHRCFWrKm0DAMxmiQoVnLzyio2LF1XExEjExiof79yR\nuHRJxeHDShiLiZGSL3FxEmo1D4Q65VW/JMlIUltUKpIvknT/o1otExiohMacOZXgeO/zXLlclCgh\nJwfNtWu12GwSY8cmYTJlTfGWtPjgAwtqtUybNgH8/HMCFSp4p0G8p9ntShuQ5cuV7cFVqjjp3t3G\n/PnuaafwONevS4wcaWT/fjXjxplp3959fScB/vlHondvf4oUcTFjRpJHtqAKgiAIguB7zp49y3ff\nfUfnzp3R6/VUqlSJQ4cOicDnIeIllg/QaGRsNsiTRyZPnrQXb3G5lEDwYKi7d3EXlQrGjfPzyWqY\n771npUABmVdeCWDGjERatvSNEv6ZfYfX5YI9ezQsX65l9WodxYq56NTJxsiR5ixpFm+1wqxZeqZP\nN/D661a++y7R7eHy5EkVPXqY6NTJxvDhFre+kSDeYfcuMf/eI+beu8T8C0LaNW7cmKJFiyZfj46O\nJjg42IsjeraJwOcDihRxcfVq+l/xqlSg13tgQA+oVs3Bn3+qsVo9/1gZ8eqrNkqUcNK3r4l337Uw\naJDV585BpoUsw5EjapYv17FihY6cOV106mRn06b4J1Z5decYNm7U8tlnfpQp4+SPPzzz2Js2aXj3\nXX/GjVOKvgiCIAiCkL1otVrKlCkDwKlTp4iNjaVz585ZOga73c6iRYu4efMmUVFR/P333/Tq1Yt2\n7do9dNvz588zfvx4Bg0aRM2aNZ943/v372fEiBFUq1aNnDlzEh8fz6VLl/jss88oV64cAFarld9+\n+43bt2/jdDo5ffo0jRs3pkePHm7/XUXg8wHFirnYvdu9/yncdZbAZILSpZ0cPaomONj3WkcABAc7\n2bgxnu7d/TlzRs1XXyWh03lvPOmZ+zNnVCxbpoQ8pxM6dbLx22/xlC+ftVtUd+/WMGaMH3fvSowf\nn+SR1VJZVirSzphhYNGiBI89n8Q5Gu8S8+89Yu69S8y/IKSfxWLh22+/Zd68eRgMhix97OnTp/Py\nyy9TsmRJALZt28agQYOIiYmhV69eyV/btGkT/v7+REZGMnDgwDTdt8vlIikpiT/++AONRkPdunUZ\nN24cJUqUSL7NlClTOHjwIEuWLEGr1XL8+HG6dOlCYmIib775plt/Vx85kZW9lSvn5OhRDbJv1R5J\nVquWg337fPu9gSJFXISFxfPPPxKdOpm4c8d3l/muXFExdaqehg0D6NgxgMREiTlzEjl4MI5PP7Vk\nadg7flxN164mBg0y0revlfDwOI+EPZsNhgwxsnSpjo0b4332zQNBEARBELLOrFmzGDlyJIULF+by\n5ctZ9rgJCQn8+OOPzJ8/P/lrTZs2pWLFikyfPj3F1yZMmEC/fv3Sdf+SJPHhhx9y4MAB9uzZwzff\nfJMi7IESCmNiYnA6lddEpUqVAuDAgQMZ/K0eTQQ+H1CqlAudTubPP91Xj96d7zI2buxg3TovLpml\nkckEP/2USI0aTlq2DODwYe/U909t7i9eVDFjhp6QkACaNQvg8mU1EyaYOXbsLl98YaZ6dc9W2vyv\nCxdU9O/vT9euJlq2tLN3bxyvvmrzSEuEa9ckOnY08c8/EmFh8RQp4tlAK95h9y4x/94j5t67xPwL\nQvosWbKEJk2aoNFoiI6OZteuXVn22CqVinz58pGYmJji60WKFOHu3bvcuXMnxdflDKzKPOlnPv30\nU7Zs2ZK8snnx4kUAj/Qx9+1lm2xCkqBVKzthYVoqVvS9lY+QEDvDh/tx8KCaGjV8b3wPUqvh88/N\nVK7s4NVXTfTrZ2XYMEuKRvdZweWCw4fVhIVpWb9ex+3bEiEhdoYNM9OkiSPLx3PPjRsSX33lx+rV\nWgYOtDJ1aiImk2ceS5Zh6VIdI0f6MXCglSFDLKLHniAIgiA8w2w2G99//z3Lli3jxo0bKb6n1WqJ\njIwkMDCQAwcOMHbsWFyu+28Cf/vtt1k2TqPRyJYtWx76+uXLl8mRIwc5c+bM9GNcunSJSZMm4e/v\nz6VLl2jWrBlt2rR55O1DQ0Np2LAhr7/+eqYf+79E4PMRr75qo08ff4YMcU84cedZAo0G3nzTyqxZ\nBubOTXzyD/iAjh3t1K0bx5Ah/rRsGcDMmYkeb91gtcLOnXDpphEAABaUSURBVBp+/PE2R48WxWSS\nad3azjffJFKzptOrYScmRmLaNAM//aSjZ08b+/bFkTu35/YQ//23xNChRi5fVrF8e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- "text": [ - "" - ] - } - ], - "prompt_number": 31 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I hope the result was what you were expecting. The ellipse quickly became very wide and not very tall. It did this because the Kalman filter mostly used the prediction vs the measurement to produce the filtered result. We can also see how the filter output is slow to acquire the track. The Kalman filter assumes that the measurements are extremely noisy, and so it is very slow to update its estimate for $\\dot{x}$. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Keep looking at these plots until you grasp how to interpret the covariance matrix $\\mathbf{P}$. When you start dealing with a, say, $9{\\times}9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9{\\times}9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intution and understanding in this simple, 2-D case. \n", - "\n", - "> **sidebar**: when plotting covariance ellipses, make sure to always use *plt.axis('equal')* in your code. If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall." - ] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "", + "signature": "sha256:9099cd7daae7d707a0f40a82136404f387af52df47c58d57a63f06db7c28b2bc" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Multidimensional Kalman Filters" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", + "import book_format\n", + "book_format.load_style()\n", + "%install_ext https://raw.github.com/dpsanders/ipython_extensions/master/section_numbering/secnum.py\n", + "%load_ext secnum\n", + "%secnum" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Installed secnum.py. To use it, type:\n", + " %load_ext secnum\n" + ] + }, + { + "javascript": [ + "console.log(\"Section numbering...\");\n", + "\n", + "function number_sections(threshold) {\n", + "\n", + " var h1_number = 0;\n", + " var h2_number = 0;\n", + "\n", + " if (threshold === undefined) {\n", + " threshold = 2; // does nothing so far\n", + " }\n", + "\n", + " var cells = IPython.notebook.get_cells();\n", + " \n", + " for (var i=0; i < cells.length; i++) {\n", + "\n", + " var cell = cells[i];\n", + " if (cell.cell_type !== 'heading') continue;\n", + " \n", + " var level = cell.level;\n", + " if (level > threshold) continue;\n", + " \n", + " if (level === 1) {\n", + " \n", + " h1_number ++;\n", + " var h1_element = cell.element.find('h1');\n", + " var h1_html = h1_element.html();\n", + " \n", + " console.log(\"h1_html: \" + h1_html);\n", + "\n", + " var patt = /^[0-9]+\\.\\s(.*)/; // section number at start of string\n", + " var title = h1_html.match(patt); // just the title\n", + "\n", + " if (title != null) { \n", + " h1_element.html(h1_number + \". \" + title[1]);\n", + " }\n", + " else {\n", + " h1_element.html(h1_number + \". \" + h1_html);\n", + " }\n", + " \n", + " h2_number = 0;\n", + " \n", + " }\n", + " \n", + " if (level === 2) {\n", + " \n", + " h2_number ++;\n", + " \n", + " var h2_element = cell.element.find('h2');\n", + " var h2_html = h2_element.html();\n", + "\n", + " console.log(\"h2_html: \" + h2_html);\n", + "\n", + " \n", + " var patt = /^[0-9]+\\.[0-9]+\\.\\s/;\n", + " var result = h2_html.match(patt);\n", + "\n", + " if (result != null) {\n", + " h2_html = h2_html.replace(result, \"\");\n", + " }\n", + "\n", + " h2_element.html(h1_number + \".\" + h2_number + \". \" + h2_html);\n", + " \n", + " }\n", + " \n", + " }\n", + " \n", + "}\n", + "\n", + "number_sections();\n", + "\n", + "// $([IPython.evnts]).on('create.Cell', number_sections);\n", + "\n", + "$([IPython.events]).on('selected_cell_type_changed.Notebook', number_sections);\n", + "\n" + ], + "metadata": {}, + "output_type": "display_data" + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n", + "\n", + "In this chapter I am purposefully glossing over many aspects of the mathematics behind Kalman filters. If you are familiar with the topic you will read statements that you disagree with because they contain simplifications that do not necessarily hold in more general cases. If you are not familiar with the topic, expect some paragraphs to be somewhat 'magical' - it will not be clear how I derived a certaina result. I prefer that you develop an intuition for how these filters work through several worked examples. If I started by presenting a rigorous mathematical formulation you would be left scratching your head about what all these terms mean and how you might apply them to your problem. In later chapters I will provide a more rigorous mathematical foundation, and at that time I will have to either correct approximations that I made in this chapter or provide additional information that I did not cover here. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Multivariate Normal Distributions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What might a *multivariate normal distribution* look like? In this context, multivariate just means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that $x = 2$ and $y = 7$. Therefore we can see that for $N$ dimensions, we need $N$ means, like so:\n", + "\n", + "$$\n", + "\\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix}\n", + "$$\n", + "\n", + "Therefore for this example we would have\n", + "\n", + "$$\n", + "\\mu = \\begin{bmatrix}2\\\\7\\end{bmatrix} \n", + "$$\n", + "\n", + "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 8, like so. \n", + "\n", + "$$\\sigma^2 = \\begin{bmatrix}10\\\\8\\end{bmatrix}$$ \n", + "\n", + "While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use the following matrix to denote *covariances* with multivariate normal distributions. You might guess, correctly, that *covariance* is short for *correlated variances*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\Sigma = \\begin{pmatrix}\n", + " \\sigma_1^2 & p\\sigma_1\\sigma_2 & \\cdots & p\\sigma_1\\sigma_n \\\\\n", + " p\\sigma_2\\sigma_1 &\\sigma_2^2 & \\cdots & p\\sigma_2\\sigma_n \\\\\n", + " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + " p\\sigma_n\\sigma_1 & p\\sigma_n\\sigma_2 & \\cdots & \\sigma_n^2\n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "If you haven't seen this before it is probably a bit confusing at the moment. Rather than explain the math right now, we will take our usual tactic of building our intuition first with various physical models. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements are a product of the $\\sigma$ corresponding to the $i$th (row) and $j$th (column) state variable multiplied by a constant $p$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, without explanation, here is the full equation for the multivarate normal distribution in $n$ dimensions.\n", + "\n", + "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n", + "\n", + "I urge you to not try to remember this function. We will program it in a Python function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the *univarate normal distribution* except it uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. Here is the *univariate* equation for reference:\n", + "\n", + "$$ \n", + "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 }\n", + "$$\n", + "\n", + "If you are reasonably well-versed in linear algebra this equation should look quite managable; if not, don't worry! If you want to learn the math we will cover it in detail in the next optional chapter. If you choose to skip that chapter the rest of this book should still be managable for you\n", + "\n", + "I have programmed it and saved it in the file *stats.py* with the function name *multivariate_gaussian*. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of numpy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner. If you wish to view the code, I urge you to either load it in an editor, or load it into this worksheet by putting $\\verb,%load -s multivariate_gaussian stats.py,$ in the next cell and executing it with ctrl-enter. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ">As of version 0.14 scipy.stats has implemented the multivariate normal equation with the function $\\verb,multivariate_normal(),$. It is superior to my function in several ways. First, it is implemented in Fortran, and is therefore faster than mine. Second, it implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use $\\verb,scipy.version.version,$ to get the version number. I deliberately named my function $\\verb,multivariate_gaussian(),$ to ensure it is never confused with the built in version.\n", + "\n", + "> If you intend to use Python for Kalman filters, you will want to read the tutorial for the $\\verb,scipy.stats,$ module, which explains 'freezing' distributions and other very useful features. As of this date, it includes an example of using the multivariate_normal function, which does work a bit differently from my function." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from stats import gaussian, multivariate_gaussian" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n", + "\n", + "First, let's find the probability for our dog being at (2.5, 7.3) if we believe he is at (2,7) with a variance of 8 for $x$ and a variance of 10 for $y$. This function requires us to pass everything in as numpy arrays (we will soon provide a more robust version that works with numpy matrices, numpy arrays, and/or scalars in any combinations. That code contains a lot of boilerplate which obscures the algorithm).\n", + "\n", + "Start by setting $x$ to (2.5,7.3):" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "x = np.array([2.5, 7.3])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we set the mean of our belief:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mu = np.array([2,7])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances. I will use the seemingly arbitrary name $\\textbf{P}$ for the covariance matrix. The Kalman filters use the name $\\textbf{P}$ for this matrix, so I will introduce the terminology now to avoid explaining why I change the name later. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "P = np.array([[8.,0],[0,10.]])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now just call the function" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print(multivariate_gaussian(x,mu,P))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0174395374407\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check the probability for the dog being at exactly (2,7)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import print_function\n", + "\n", + "x = np.array([2,7])\n", + "print(\"Probability dog is at (2,7) is %.2f%%\" % (multivariate_gaussian(x,mu,P) * 100.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Probability dog is at (2,7) is 1.78%\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These numbers are not easy to interpret. Let's plot this in 3D, with the $z$ (up) coordinate being the probability." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib.pylab as pylab\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "import numpy as np\n", + "\n", + "pylab.rcParams['axes.color_cycle'] = '348ABD, 7A68A6, A60628, 467821, CF4457, 188487, E24A33'\n", + "\n", + "P = np.array([[8.,0],[0,4.]])\n", + "mu = np.array([2,7])\n", + "\n", + "xs, ys = np.arange(-8, 13, .5), np.arange(-8, 20, .5)\n", + "xv, yv = np.meshgrid (xs, ys)\n", + "\n", + "zs = np.array([100.* multivariate_gaussian(np.array([x,y]),mu,P) \\\n", + " for x,y in zip(np.ravel(xv), np.ravel(yv))])\n", + "zv = zs.reshape(xv.shape)\n", + "\n", + "ax = plt.figure().add_subplot(111, projection='3d')\n", + "ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n", + "\n", + "ax.set_xlabel('X')\n", + "ax.set_ylabel('Y')\n", + "\n", + "ax.contour(xv, yv, zv, zdir='x', offset=-9, cmap=cm.autumn)\n", + "ax.contour(xv, yv, zv, zdir='y', offset=20, cmap=cm.BuGn)\n", + "plt.xlim((-10,15))\n", + "plt.ylim((-10,20))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 8, + "text": [ + "(-10, 20)" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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ZvabmLeoS47hs1pl4ysUiAeVYZWvZV5amuZM49QEFV5UGiVWP8IMwsymlLenT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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange.\n", + "\n", + "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance or not. So for most of the rest of this book we will display multidimensional Gaussian using contour plots. I will use some helper functions in $\\verb,gaussian.py,$ to plot them. If you are interested in linear algebra go ahead and look at the code used to produce these contours, otherwise feel free to ignore it." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import stats\n", + "\n", + "P = np.array([[2,0],[0,2]])\n", + "plt.subplot(131)\n", + "stats.plot_covariance_ellipse((2,7), cov=P, title='|2 0|\\n|0 2|')\n", + "\n", + "plt.subplot(132)\n", + "P = np.array([[2,0],[0,9]])\n", + "stats.plot_covariance_ellipse((2,7), P, title='|2 0|\\n|0 9|')\n", + "\n", + "plt.subplot(133)\n", + "P = np.array([[2,1.2],[1.2,2]])\n", + "stats.plot_covariance_ellipse((2,7), P, title='|2 1.2|\\n|1.2 2|')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ssQj06eNEp04u0V1RDa6ZIqJg8ifn8M4UEanKyJEjcebMGVgsFkydOlV0d1Rr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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From a mathematical perspective these display the values that the multivariate gaussian takes for a specific sigma (in this case $\\sigma^2=1$. Think of it as taking a horizontal slice through the 3D surface plot we did above. However, thinking about the physical interpretation of these plots clarifies their meaning.\n", + "\n", + "The first plot uses the mean and covariance matrices of\n", + "$$\n", + "\\begin{aligned}\n", + "\\mathbf{\\mu} &= \\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", + "\\mathbf{\\sigma}^2 &= \\begin{bmatrix}2&0\\\\0&2\\end{bmatrix}\n", + "\\end{aligned}\n", + "$$ \n", + "\n", + "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for the $1\\sigma^2$ probability - points where the dog is quite likely to be based on our current knowledge. Of course, the dog might be very far from this point, as Gaussians allow the mean to be any value. For example, the dog could be at (3234.76,189989.62), but that has vanishing low probability of being true. Generally speaking displaying the $1\\sigma^2$ to $2\\sigma^2$ contour captures the most likely values for the distribution. An equivelent way of thinking about this is the circle/ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second plot uses the mean and covariance matrices of\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", + "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "This time we use a different variance for $x$ (2) vs $y$ (9). The result is an ellipse. When we look at it we can immediately tell that we have a lot more uncertainty in the $y$ value vs the $x$ value. Our belief that the value is (2,7) is the same in both cases, but errors are different. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object, or is closer, than another sensor, and so we end up with different error rates in the different axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third plot uses the mean and covariance matrices of:\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", + "\\sigma^2 &= \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "This is the first contour that has values in the off-diagonal elements of $cov$, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling use the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal. What does this mean in physical terms? Think of trying to park your car in a parking spot. You can not pull up beside the spot and then move sideways into the space because most cars cannot go purely sideways. $x$ and $y$ are not independent. This is a consequence of the steering system in a car. When your tires are turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk straight forward to to the side. If $x$ changes, $y$ must also change in a defined way. \n", + "\n", + "So when we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". The size of the ellipse shows how much error we have in each axis, and the slant shows how strongly correlated the values are.\n", + "\n", + "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Unobserved Variables" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's say we are tracking an aircraft and we get the following data for the $x$ coordinate at time $t$=1,2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import mkf_internal\n", + "mkf_internal.show_position_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears that the aircraft is flying in a straight line because we can draw a line between the three points, and we know that aircraft cannot turn on a dime. The most reasonable guess is that $x$=4 at $t$=4. I will depict that with a green arrow." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mkf_internal.show_position_prediction_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If this is data from a Kalman filter, then each point has both a mean and variance. Let's try to show that by showing the approximate error for each point. Don't worry about why I am using a covariance matrix to depict the variance at this point, it will become clear in a few paragraphs. The intent at this point is to show that while we have $x$=1,2,3 that there is a lot of error associated with each measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mkf_internal.show_x_error_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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gl2/Yib3iYuC008LYsMHaxlu97+MJUZnGUjby8ssvY9myZbj55puhqvqXnHDC\nCdizZ08qn40ccOCAimnTolAt/GWsXx/AOeeExxwlZ2bWrChycjQ0NZn/gOpqjQkzZRWrnfaOHSpU\nVcNxx1k/UcPnA845J4x168w7bUUBKis5YKXs0d5uLfbCYaChwY9zzzWeKBJZvDiEtWutdZZVVbzt\nLxNZ+o0cPXoUJ5xwwpiP+Xw+RKO8icZr2tsVVFVZ2we6dq1fepScUS0XACxaFMbateaddnGxhmgU\nlpaxiNxuYEC/YbOszDz+1q0LYNGisPByIXHshbBunfVOmwkzZQurg9UtW3yoqYkKV2En2u8BjL1M\nZek3Mm3aNGzevHnMxxobG1FZWZmShyLn7N9vrdGILQkvXmx/Z8LixdY6bc5yUTZpb1dRWWnths21\na/0Jxd6SJWFbJVGso6RsoSfM1garixfbm10GgJNPjuDIEQX795sHOGMvM1n6jVxyySV4/fXX8dhj\njyEUCuHpp5/Gq6++iosuuijVz0dpZmdJ2OfTpPfdG9VyAcC554bx1lsBjFjYr8SGg7KF1dgLh4E3\n35QvCYtib8aMKPLyNDQ2msdUVZVmqd6ZyO16evRJoOJi84RZX1kVD1ZFsaeqeknU+vXms8zs9zKT\npbW5iooK3HbbbWhqakJPTw9KSkowZ84c5ORYv72G3KGtzdpO4bVr5UvCMmVlGo47LoLNm/1jrhQ1\nwqUpyhZtbfoMs5nNm/Wj56ZMSewI/djS8Lx58ruyKyuj+Ogjxh55X6x+2aw/6+sD3n/fj7POsj/D\nDOglUWvX+nH11fLZospKJsyZyPJvxOfzYdasWViwYAFqa2sxODiIo0ePpvLZyAFWZ7nWrTNfEhbV\ncgF6WYaV85g50qZskcwlYbPYs7Lxj7FH2cJqv7dhgx+nnhpGfr74c2SxZ7Ukqrqax8plIkszzC++\n+CLee+895ObmHjslI+Zf//VfU/Jg5AwrO4VDIX1J+Kc/TfzMqUWLwvjBD/LwrW/Jz/KurNTw4YcW\nrgUkcrn2dgXHH29ldcePO+5I/Az8c84J45ZbCjAyAgQlxzJzdYeyhdXVndjKaqJmzIgiP18viZo3\nT/zzpk3TLy+JRGDpVlxKD0sJc1NTE+68807k5uam+nnIYW1tKqqr5Q3H1q36LmGzJWFRLRcAfPrT\nYTQ2+tDXBxQWir9HVVUUr71m49w6Ipdqa1NNj6oaGADee8+8lEkWe2VlGo4/PoItW3z4zGfEV2pz\nhpmyhdVIZauBAAAgAElEQVQZ5jfe8OMnP5FPFMliD9Ani9avl5dEBYN6nB46pKCyMrHSK0o+S5nI\naaedhqeffhrl5eVQRhX5KIqCK664ImUPR+kVDgOHDyuYNk0eoB984MMpp4g7Wityc4Hjj4+gsdGH\nM86Qd9qc5aJsYGWWq7nZh9mzI9IlYSs+9akIPvjAL02Yp07V0NmpmM5EE7lde7uK+fPlg9CREeCj\nj3yYP39ifd+nPhXGpk3mqVesjrmycmI/j5LHUiayefNmzJo1CzNnzsSsWbOO/TNz5swUPx6l06FD\n+hmwAZPyxsZGH+rqzINYVssFAHV1esIsw1kuyhZWZrnSGXs+n35F78GDjD/yNv2GTflE0c6dKmpq\nojBbaLcSe01N5nUW7Psyj6UZ5qqqKsyePRtlZWVxM8zkHVaXpbZt8+HCC+2fATteXV0E27bJG47y\ncg29vQqGhmDaUBG51cgI0NVlfiX9tm0+zJs38RmnefMi+NOfzKeN9RvHFNTUTPhHEmUsK6s7yYq9\nuroImpt9iEYhvVGXCXPmsZQwHzp0CC+++KLhe9z05x1WEmZNsz7LZVbLVVcXweuvy6ezVRWoqNDL\nMmbN4s2S5E0HDqiYOlUz3eDT2OjDueeaD1atxF5jowpNg/QorU86bS4Lk3clc3XHLPaKi4HS0ij2\n7pX3aUyYM4+lhJlJcXawckLGwYMKFAWmM2FWzJtnPsMMfFLHzISZvEpfEjb/+25sTM4sV3m5hrw8\nYP9+BdOni2OZewjI64aGgP5+BeXl5qs7y5dbuG3LgljfJ0+YNWzbxlX8TDKhlvCFF15I1nNQBmhv\nV1FRIW80YqNsK9U4ZrVcFRXasY2GMpWVvHGMvE2PPXnC3NmpoL9fQXW1+WDVLPYAYO5c8zpmXqBA\nXqev7kSl5RFA8vYPAEBdXZSx50IT+m188MEHyXoOygBHjiiYPDk9dVyAvhRsZZZ58uQoOjrYcJB3\ndXSomDLF2pJwsraOzJtnnjBPnqyflEHkVUeOKKZHpPb2AkeOqJg5MzmrnFb6vfJy9nuZRliSsWbN\nGixZsgQA8Prrrxt+TiTCujYv6ew0X5ZqbPTh9NOtHdxuVssFfLJbX3YYfFmZho4OdtrkXR0d+gk1\nMlZnuADrsffmm/KqPHba5HWdneax19Tkw4knRixdImI19h5+WL6Lvbycg9VMI2wJe3t7j/37G2+8\nge7u7rh/yFs6O1WUlZnPciVrhhmwNtIuK9PQ1cWGg7yrq8u8007m6g5gLfZKS9lpk7dZ6fe2bbM+\nWLXihBMi2LtXxbD47hKUlur9ntk12pQ+woT5sssuO/bvPp8PV155Zdw/Pt7Z6ClmI+1oFNi+3Ye5\nc601HNZqucyXhcvKOMtF3tbRoVpa3bHaaVuJvTlzIti504ewZMGIs1zkdcle3bESezk5QG1tFDt3\nivu+YBDIywN6ehh/mcJSFvLFL37R8OM1PJzTUzo65CUZe/boI/Hi4uT9zLq66LEzKUXYaZPX6Z22\nOAj04xzVpM5yFRToRzbu2iXuBsrLNQ5WydOsliImc3UHsFPHzL4vU0hbwp/97GcAgLlz5xq+f8MN\nNyT/icgR4bA+kp00Sdxw2BllA9ZquUpKNBQXa2htNeu02WiQd5l12vv3K8jLg2nHHmMl9gDzFZ7i\nYg2Dg/rFKkRepK/uJOcMZsBu7MkHo9y/k1mkv62urq50PQc57OhRBcXF8osTkl1DGWM20i4ri6Kz\nk7Nc5F0dHap0WdjuYNUqs9s2FYV1zORtZqWIhw4piERgeuSqXVb377Dvyxymv4nOzk7pP+QNVpel\n6uqsH6tjpZYLMJ/l0hsNbn4g79I3/Yljy27CnKzYAz6JPyIvMkuY7R7nmMzYKy+PMvYyiPRMoVAo\nhJ/85CfSb3D//fcn9YHIGVaO1tm2zYc77hhK+s+eNy+C114TX5Gdlwf4fEB/P1BYmPQfT+SogQEg\nEtFrikW2bfPhnHOsHedox7x5ETzwgJVOWwXAmzbJe/TVHfHfdqpWVmfO1OOqpwfCfUEsycgs0oQ5\nEAjgnnvuSdezkIPM6riGh4GWFhXHH5/cGmZAH2k/8oj8TMpYWUZhITtt8pbYYFU2g9XY6MONN0rO\noBrHauwdd1wU+/erGBzUB6ZG2GmTl5mtrjY2+nDqqdYHq1ZjT1WBE0+MoKnJhzPPNO5XueE9s7A4\nhgCYH62zc6cPtbVR5OQk/2efeGIEu3er0o1F3PhHXtXZKR+shsN6/M2Zk/xZrkAAOO64CJqbxbPM\n7LTJq6JR8zPQU7V/ADDfQ8AjVTOL9DcxY8aMdD0HOcysJGPXLnuzy4D1Wq7cXGDqVH2mS4SzXORV\nZoPV9nYVpaWatGRjPKuxBwCzZ0exe7cs9thpkzf19CjIz9cQEFcEYvduFccdl/y9O4C+wrNnj/n+\nHcoM0lbw+uuvT9dzkMPMZrlaW1XU1KSuHKKmJmpytFwUXV3stMl7zAarTsceO23yKrNyjL4+YHBQ\nweTJqdlxXlsbMT1SlbGXOZiBEADzWa6WFvudttVaLkC/9ailhTPMlH3MBqstLSpqa+2t7tiNPXba\nlI06OhSUlsoHq9OnRy2fkAHYi73p0836Pa7uZBL+JgiA+Ui7tVVFbW1qZ7mYMFM2sjJYTWXs6YNV\nWQ0zO23yJn2w6ly/x8Gqu7AVJAD6KRmlpWazXPYaDju1XDU1UezbZ9Zw8M+VvMesJKOlRZ/lssNu\n7MkGq7y4hLyqo0MxKUX02V5ZtRN706Zp6O5WMDho/H5pqYauLgVRHg6VEZiBEAB9p7BspN3S4kvD\nLJd8aYqdNnmRlf0DqV3d0esoRRcDcZaLvMrKYNVuOZQdqqqXZYhmmQMBoKBAQ08P4y8TMGEmALGR\ntnHD0d2t37JXUmJv40Mya5jZaZNXmZVkJJIw24m94mIgGBTHF0syyKvMShFTvXcHkCfMAI9UzSRs\nBQnhMNDbqwgT4tgo287GB7uqqqI4dEhFWHA+PGuYyatknXYkArS1qaiuTu2arKwso6hIv7ho2Pq9\nKUSuYFaKmOoTagDzOmb2fZmDCTOhq0vBpEkafIJ9P4luOrJTyxUIAFOmaGhrM/6TjN30R+Q1sls2\n29v12edc+UWYcezEHiBf4VEUHi1H3pSKze7JjD1g9NX05DT+FsjxXfoxtbURYcMRG2WL6iyJ3Kqz\nU3y0VSKbjhJhbeMfuwvyFlkp4sCAvvI6dWpqOx2zU2o4w5w52AISurpU0xpKu7v0Afu1XLILFHJz\ngZwc/SB5Iq8YGND/Nz/f+P1El4QTiT35KTXcdEve09mpoqzMOL727dNLoVSbWZL92JNfXsLVnczB\nhJlMj9ZJRw0lAFRXR4UlGQDLMsh7Yrv0RfsD2tqUDIk9znKR98hKMtLX74lLEQEeqZpJ+Fsg05KM\ntjYVlZWprWEGgMpKecPBTpu8Rla/DKQz9uQJM0+pIa+JRvX9O6JyqHTF3rRpURw6pCAiOL1Ov+2P\nsZcJmDDTx8tS8oS5ujr1xcNVVVG0tYkbBibM5DVWBqtVVamf5dJjj1f0Uvbo7lZQWKjB7zd+P12x\nFwzqewQOHTLu21iSkTnYAtLHnbZxwxCJAIcPK5g2LfV1lGadNncLk9eYXZzQ3p5Yp2039qZN0zvl\nUMj4fQ5WyWtkG/6AWMJsf6LIbuwBet/X3m7ct+nnMLPfywT8LZD0lr9Dh/Qlq2Aw9c8hazQAjrTJ\ne8xu+UvXLJffD0yerOHgQdHlJfoVvUReYT5YVdISe4C8JIq33GYOJswkHWkn0mEfOqTg+9/PxW23\ntWNoyPrXTZ6sXwEq+hrWUZLXyEoyRkb0Tn3aNOuzXMPDwCOP5OBrXzssTH5Fqqqi2L9f3Glzlou8\nJNmDVU0DnnsuiK9+tQMffig+Js6IbHWV/V7mYAtI6OgQH61jt9HYvVvFBRcUobNTRWNjGS6/vAg9\nPda+VlX1DRAHDrDTpuwg26V/8KCKyZPFFwqN19sLLFtWiLfe8qOvL4Dzzy/Czp3W40U2y8VOm7wm\nmZvdNQ34l3/Jx89/noNgMIplywqxerWgONpAVZV4w3tpqYajR8WbAil9mH2QdGnKbg3lN7+Zj+uv\nH8ZDDw3g1VdzUFsbwU9/av2aMlnDwTpK8hr5YNXekvAjj+SiokLDb3/bj2eemYQVK4Zx552CA54N\nyEqiGHvkNbKEeWhIv7Rk8mRrqzuvvhrApk1+rFzZi8cfn4L/9//6ceutBRgctPYseuwZx5ffDxQW\naujuZvw5jQkzmZZkVFZaazTefNOPHTtU3HTTMAB9xvjeewfx9NM5wsZgPNlJGZzlIq+RDVbtrO4c\nPKjgqady8J3vDB67aOFrXxvG3r0q1q2zNtMlWxbmGejkNbKSjPZ2FRUV1i4tiUSA++/Pw333DaCw\nUP/YOeeEsXBhGE8+mWPpWawc68gBq/PYAma5UAjo71dQUiLqtK3NcmkacN99efj3fx86tkGwoaEB\n1dUali8fwYMP5ll6HnktFztt8hazixOsJsw//nEu/umfRo7dCtjQ0IBAAPjWtwbx3e/mWbpSXnZ5\nSVGRXlNtZ08CUSZL1mD1+eeDKC+P4rOfDQP45Bzmu+8exM9+loujR80TXfNjHTlZlAmYfWS52MHt\nopG01ZKMTZt86O5W8IUvjMS9d9ttQ/jjH4OWapnls1xsNMhbZCUZVmOvrw/43e9ycPvt8dnssmUh\nDAwo2LjRfJZZVg6lKFzhIW+RDVb1EzKsraw+/ngO7rprKO62zjlzoli6NITnnjM/YqqyUi+HEg1s\nOVmUGfgbyHIdHeKbjgDg0CEVU6aYd9qrVgVw4YWhMYl37DzK0lINZ5wRxvr1AdPvM3VqFIcOyRNm\nK7NlRJlO0+SzXIcOKZg61fyPvaEhgIULw2PqLWOxp6rARReNWNqANHVqFIcPixPi0lKeB0veoQ9W\nxRturfR7bW0K2ttVnHVW+NjHRp/DfPHFIaxebd7vFRTotcq9vcbvl5VpOHKEg1WnsfXLcj094nIM\nQE+orWx8WLUqgPPOE9x6AOC880JYtcq84ZDNIgeDeqNidSMFUSYbGdGv580X7MuTzT6PtmqVH0uX\nymIvbDn2ZHWSJSVR9Pay0yZv0Ps+4/iSzT6Ptnp1AIsXh4Un2SxaFMbf/ua31GeVl4tPgSou1hh7\nGYAJc5br71dQUGDcMEQi+vWhkybJG47OTgXNzT58+tPhMR+P1XIBwNKlIaxa5TedHTZb9i0o0NDX\nx4aD3E8We4D8QqHR9MGqOPbOOCOMXbtU6ewxAJSUaOjvF9/2V1AA9PebPg6RK/T16X/TRszOaI5Z\ntSoQN1gdHXslJRpOOimCDRvMV3hkk0WFhXpskrOYMGe5vj4FRUXGnXJ3t/6e3yTW16714+yzQ8iR\nbAieMycKTVOwY4f8T87srGU2HOQVfX0KCgvlqztmCfOuXSqGhhTMmyc+pDUQ0Hftr10rn2VWVb3s\nQnSjX2EhZ7nIO/r7xfFndkYzAITDwLp18tUdQF9dtVKWYZYwc6LIeY4nzH19faivr8dTTz3l9KNk\nJdksl5UOGzCe4QLG1nIpirWyDLM65YICJszkDbIZLkCf5TIryYjNcI3fcDQ69oBY7Fmb5RKVZTD2\nyEtkfZ+VkowtW3yoro7GHbtqHHvmCbOsJIOrO5nB8YT5iSeewPz586GMb/EpLcwSZrNRtqYBa9bE\nL0sZ0csy5A1Hfj7g84kbh4ICPdEgcjtZ7A0O6kc+xs51FTGrX45ZujSM1asDiJqsMst243N1h7wi\nFNJniEWrolb2D+iD1fiJovE+9akIOjoU7Nsnjx0OVjOfownzrl270NnZifnz50Pj0QeO6OsTd8pW\n6ri2bfMhL0/D7Nnxnze6lgvQN0C8/bb5BojSUk3aaXNpirxAVg4VOz1DNo8wPAxs2KBvOhpvfOzV\n1kZRWqrh/ffl92zLOm3GHnlFrBxDFF+y02tiVq823ug+PvZUFViyxHyySLZ/h7GXGRxNmB9++GHc\ncsstTj5C1jNblpIdOQcAb73lR329+Sgb0DdAnHhiBFu3yjttfZaLI23yNlnsdXWZz3C9954Ps2dH\nTDv2mPr6MN56S16WIauj1JeFGXvkfrJyKE3TN9zK4mpwEPjww/iN7iL19WHTs9Blt2lys3tmcCxh\nXr16NWbOnInKykrOLjuor29idVyNjT6cdJLxhqPxtVwAMG9eBI2NE5vlYqdNXjDR/QN2Y++kk8Km\nsScrydAHq9IvJ3IFWez19CjIy8OxG2uN7Njhw6xZUcOSDuPYm1i/x4mizGC+CyRF3nvvPfz1r3/F\nqlWr0NXVBVVVMXXqVFxyySVjPu+mm25CbW0tAKCkpAQLFiw49gcZW/rg68Rf79p1MubOnWz4/tat\nbSguHgFQKfz6jRvPxrJlAcs/Lzd3FrZtO176+eXlF6CzUzV8v7t7Pvr6pmXMfz++5utEX2/d+hF6\ne4sBlMS939GhIBo9jIaGzcKvX7XqICZPHgRQZennhcPv4m9/m4cY4/iajeHh4wzfb2vbjl27ygEU\nZsR/P77m60Rf9/Up0LReNDQ0xL1fVXUuysuj0q/fts2HKVPa0dDwd0s/b+7cCJqaFKxb9yYWLTrb\n8PPb2t7D7t1zEJvHHP1+YSFw+PCA4fPy9cRex/69paUFALBixQqIKM3NzY5P7z766KMoKCjADTfc\nMObjra2tWLhwoUNPlR2+8pUCXHzxCK68Mr4W6+ab8/HpT4dx7bXx110D+tLVrFkl2Ly5x3A2bHRw\nx6xb58eDD+Zi5Urxzr277srDzJlRfO1rw3Hvffe7uSgq0q/bJnKzRx7JwZEjKr773fii/l/8IgdN\nTSp+/GNxwf/llxfilluGDE+oMYq9o0cVnHxyCfbsOTrmRs7RnnsuiPXr/Xj88YG49156KYD//u8g\nfv1rTjOTu61f78dDD+XipZfi+6F33vHh3/89H6+/Lrh2D8C99+ahpEQzvI7eKPYAYOHCYvzud304\n4QTjUqtt21R89auFeOutnrj39u5Vcdllhdi6Nf49Sq4tW7agpqbG8D3HT8kgZ+mbH4zfMyvJ2L9f\nX7qycvRczLx5EWzb5pNeYKJfwSuro7T844gylqwcyuzKekDfcCs7f3m8SZM0FBdraG0VN/v6srCs\nJIPLwuR+8r074iuzY+zGHvBJ3yci2/TH2MsMGZEw33zzzXGzy5Qe/f0waTjEG48aG32YO1fcaBiN\nsqdM0S9CaW8XB395ufjyBG5+IK+Qb/qTD1YPHVIQDgMVFcafYxR7AFBXJ++09Y1H3D9A3qYPVo3f\n0yeKzE+Hqquzvn8AsBJ7er9nNJnEhDkzZETCTM6R3TZmdrROY6P9UTZgvvFPdtsfj9chr5DFXkeH\nKk2YY7Fn9/h6s9iTH23FM9DJG/r7kfAtf0ePKujtVVBTY3519mh1dfLYCwSAvDx90+F4ubn6udGi\na+spPZgwZ7mJ7NSXjbKBsUX1o82dy6UpIvOrecUdcqKxZzbLVV7OkgzyvomcDtXY6MOcORHhPgBZ\n7Fk5pcaoHFFRGH+ZgAlzlhMlzOGwPtKdNCk1M8xNTfKlKR4rR16nl0MZv+fU6k5xsYbBQWDEYJ8v\nO2zyCvlEkVkpoppQ7B1/fBT796vSi7vkR8txhcdpTJiznGhZ+OhRBSUlGnyCvjUcBnbu1EfaIqJa\nLrPND/ID3NlokDeYddoTWd0Rxd6JJ0awe7dqmBAD+kyWftNmfKfNhJm8wmyGWTZYNdvwJ4q9QAA4\n7rgImpvNVld5NX2mYsKcxTQNGBgwnuUyW5batUtFRUVUOEMmM2dOBDt2+BARtDmx28aMNj+w0SCv\nkNUw6zeNGc9yRaPA9u0+1NXZq6EE9FrImpoodu6Un5RhlDDn5+vXcYfjT7EjcpX+fvm19GYlGbLB\nqoxZWYbsllvu33EeE+YsNjAA5OTAcBbZbJTd1GTeaIhquYqKgMmTo9izx/jPLy9PH40bzSRzlou8\nQjTDPDAARCLico19+1QUF2soKRHHpyj2AH0PgXmnHR+biqInzQPxRzQTuYqsHMqsJMOs75PFXl1d\n1GTDO2/7y2RMmLPYROq49uxRMXOm/RmumFmzoti7VzbLZdxp81g58grRsnBssCo6AWPPHhWzZiU2\nwwXosdfSkvgeAsYfuV2im/66uxWEQgomT07svreZMyMm/R43vGcyJsxZTH6slXyGubVVRW2tPGEW\n1XIB+rJwS4vZBQrxjQNLMsgr+voUFBXFf9zs/POWlonFXm1txDT2uCxMXiY6oSYa1cuhRJcGtbaq\nqKmJSo9zlMde1OTiINmRqmDsOYwJcxaT33Ykr+NqafGZdtoy5g2HccKcnw8MDuoNG5FbaZq+LJyf\nHx9jZsc5trSots+AHc1ssKofbcWj5ci7RDPM3d36xwMB46/TB6uJr+7U1prFntkMc8I/mpKACXMW\nkx9rJZ/l0meYE6thBswT5vLyKLq64t9XVb3GmQ0HudnQkF6nb9Qxm+0f2LfPfIbZLPb27eOyMGUv\nWTmUbLBqZWVVFnuTJ2sYHFSEJz2ZJcycYXYWE+YsJqvjks1yaZrecEyfPtFZLm5+oOwkX91RpVfz\nTnSGefp0fbBqdAoNYNZpg7FHrqeXZMR/3KwUsaVlYv2eonwSf0ZkJRns95zHhDmLJXotdmengkBA\nQ3Gx/PvLa5gjJjPM8jpKNhzkZhPZPzDRGuaCAj2GDh0yjiFZSYZewyz90UQZT3Q1ttlgdaJ7dwD5\n6ir3D2Q2JsxZTH41r4rSUuOGYaIzXABQWanPIA8PG7+vzzCLR9psOMjN9Blm4/dkg9VwGDh4UEVV\n1cTiT1ZLKbq4BGDskftpmnh11cpgdaJ9nx57xqurpaUauroUwz06nChyHhPmLCZbFu7tVYTnvLa1\nWVuWktVy+XzAtGlRHDhg/CdYXKyht5clGeRNfX2Qxl5xsfF7Bw7oR1qJNiXFyGIPAKqqomhrY+xR\n9hkZ0UsjgsH492SxB1jr+8xir7o6irY24xgKBPTLhYzOOtfLoaTfmlKMCXMWk80w60tWxl/X1jbx\nGS4AqKrShJ22bEdwYSEbDnI3eeyJB7LJiz1xwixLijnLRW6XaOwNDQE9PYmfwRwjiz1AHH+MPecx\nYc5i+iyX6D2zTtu80TCr5aqsFI+0ZZ02l4XJ7WQ1zL29E0+YzWJP1mkXFkI4w8w6SnI7WVIsOznq\nwAEV06ZFoZpkTROJPUDcv7Hfcx4T5iwmbzjEHXpbm4LKyuTMcu3fL9tcxISZvCnx2FOTFnuyGeaB\nARieosFlYXK73l75RJEs9qxMFJnRJ4rEqZdoJpn9nvOYMGcxUeMwMqL/r1GNF2B9lstKHWV7u/2N\nfVyaIrczWxaeaDmUeeyJy6H8fj32Bwfj32PskdslWpLR3q4kJfZiCbPoWEeWZGQuJsxZTFR2IWs0\ngOTVUcpG2rLGgQ0HuZ2sHEpfFhbPclVXJ2uGWRxDok6bs1zkdrKEWVaKuH9/clZ3CguBnBz9NAwj\nBQUwPLqRV2M7jwlzFhM1HLJlKU0D2tutNRwTraMULf3qDQobDnIv2aA0GcvCZrFXURHFwYOq8Ip5\nUUkUE2ZyO1lSbFYOlYz9A4B8hUcWeyyHchYT5iwm2uAgm/06elRBMKgJ37ejqkoTHiuXn683GsZ1\nlGw4yN3MOm3RewcOKKiomPgsV24uUFRk/zZNHitHbpfoYPXAATUpsQfoq6vt7Yw9t2HCnMVEo2lZ\ng9LRYf1YHbNarrKyqPCChGBQP6vZ6GITlmSQ24liLxTSLyfJzTX+OrObyGLMYg8wu37eeFm4qIix\nR+4mOzJVdkpGZ6e1vs9K7JWXR9HZaa8cMSdH/9/YHiNKPybMWUw0yzWRa3vtyM/XSzyMDmkH5CNt\n0bFXRG5gtn9AMfjzHhrSB5BFRcl5BrNO23hZ2DiRJnKLRFd3OjpUlJcnp++TD1Z5QlSmYsKcxUSN\ng6yOy+oMF2Bey6UoesMhmmWW13Kx0SD3Ep2EISuH6uxUUF5unEyPZ6WOsrycJRmUfWQJs2yySL+y\nPjk1zOXlsn5Pvn+H8eccJsxZLNGSjGTNMAP6LFdHh+hoOeOGgyUZ5Hb6srD9waqVDtsq2SyXKMYY\ne+R2iRwrp2mxhDk5fZ+835OfEMUVHucwYc5S0aheCpGfH/+elVkuKyZeR2k8w6wfr2PpEYgyUl+f\ngvx8e+VQyY698vIourrslWTk5Og11qGQpccgyjiiGeZIRC97ysuL/5reXv1vP1ZHLGO13xPNMLMk\nI3MxYc5Sw8N68Btd8ylbskrFLJfoPErRbFZurobhYTYa5F5DQwry8uyv7pSWJm91p7RUvunPKPYU\nRU8ohoaS9hhEaTU8bJwUxzb8GfWJqej3EkmY8/LY9zmJCXOWCoWAQMD4PdmSlZ2SDGu1XOKlKdEs\nVzDIncLkbqGQ8U2asoRZ3z+QzNiTd9qiOspAQEMoxE6b3GlkREEgYH+ze3JjT97viUoyAgH2fU5i\nwpylRkb085SNyDtt6w2HFWYlGUYNBztscjtR/MmOvNIHq8mb5dI3/dkbrAIcsJK7JTZYTe7eHbPN\n7qKEORhk3+ckJsxZamTEuNEAzOoorZ+SYa2OUjbLZbwszFE2uZ1ohUdeDpXs/QPic9Bly8IcsJKb\n6TPM8R83P1Iuef1erBTR+GIu8R4dDladxYQ5S4VCxstSgNlO/eTWUZaVmS1NxX88GNQwMsIOm9xL\nNGA1S5jTNcsl26nPTpvcbGQEhn2fWSliMvu9YFDfQ9TbG/8eSzIyFxPmLKU3GsbvyW47SnYtl1mn\nbXRBSSDAXfrkbqGQAr/fbqdtfePRRM9hlt3o5/ez0yb3EpVk6INV46+xs7pjJfYAcR2zbLDK1R1n\nMWHOUrJNf7Jjd7q7FUyalMxzmO3PcnGGi9wu0RnmZO4fKC7WMDCgGA4+5cvC7LTJvcSb/mCy4TZ5\n+ywKuJkAACAASURBVAcA8YBVXg7Fvs9JTJizVCKb/rq7FRQXa/D7rf0Mq3WUdg9w9/n0460iEWvP\nQZRJNC1WEhX/nlk5VDJrmFVVP1rO6FhHlmSQV4XD9jf92TkdykrsAeIjVfPz9aPvjPq3YBAcrDqI\nCXOWkpVkiDb9WS3H2LdPwec/X4gHH1xoesFIrCTDaPNDURF36pP3hEKA368ZnvcqK4eychbswABw\n4435uPvuf0Brq3nzLjqlRr4szE6b3Eu2ujORwaqmAd//fi5uu+0cbNzoM30OUUmGouhJs9H+nUBA\nY7/nICbMWSoUEs8wi5aFrW58+MY3CnD66WFMmjQFDz5ocEL8KPn5+kyXUeMguhobYB0zuVciJ9QM\nDup/76JkOuahh3IxOKjg/PMLcMst+YYD0dH0kzLiuwH5sXLstMm9RBveJ7p/4JVXAli5Mojbbw/g\nq18txMCA/DlkFwfJ7iBgv+ccJsxZSrTxARCfBWuljmvDBj/27FFx111DeOCBAfzmN0EcPCifjdJn\nme1tfuBJGeRW4bD8hBqjwWpshkuR/MkfOaLgV7/KwQMPDOCb3xxCW5uKN96Q10/J6ijlM8zSb0uU\nsUQD1omcw6zPLufh/vsHcPXVIzjzzDB+8Qv5PdqJ7d/h/gEnMWHOUqJNf5om77TNZphfeimA664b\nRiAA7Nr1Bs47L4y//EVQ+/Ex0Xmw8gPcWZJB7mQ2w2wUe11dKkpL5YPVv/41gHPOCWP6dA0bNzbg\nuuuG8dJLgh/0sdJS4067oEAv74ga/Eh22uRmok1/ookiTQO6uuQJc2OjipER4LzzwmhoaMCKFcN4\n+WV57IlWdwBx38dNf85iwpylRJv+hob0Y6OMkuneXn3Tn8yqVQGcd1742Ovzzgth1Sp5wlxcbHx8\nHC9PIC9KZP+A1dj77Gc/mfrVY88vLcsQxZ6qyuoo2WmTe8mPlTMuh/L7xYNcAHj9dT32YitAZ5wR\nxo4dPmHJBSCOPUDc97Ekw1lMmLOUqNOWLUvJarwAYPduFf39Ck46Sd/eW19fjyVLQli/3o9wWPhl\nwuUn7tQnL5LtH9BjLP7j+pFX4u8ZiQDr1vmxZInem9bX12Pu3ChCIQUffSRu5mUxJjvWkZ02uZXd\nkgxZnxizZk0AS5fqnVx9fT2CQeCcc0JYu1ZcEiXboyO+5ZaliE5iwpylRJ22WcIsazjWrPFj6dLQ\nmDrLadM01NZGsXmzeNewqOEoLIT0PEp22uRG5pcG2e+0333Xh6lTNVRXf/I5iqLPMq9eLV7hSSxh\nZqdN7iXa9CeaYTaLvYEBYPNmP+rrx3ZIS5dOLPaMTpjiYNVZTJizlHiGWV+KNWI2y/Xuu36cdton\nU8mx8yhPOy2CrVvFI+3CQuOlqfx8TbjTmJ02uZVshnlgQEF+vvXOPGbrVh9OP90o9sLYulU8WJWd\nhqHHH+soyVtEM8wDA8YxJjtuDgAaG32YNSuCoiL99eh+7913ZTPM9mOP/Z6zmDBnKVEdVyikICcn\nsZKMxkYf5s2LP2193rwIGhtlM8zGI22/X990ZHSAO6/nJbcSddiaFttbEP9ef7+CoqLkx15hoXhZ\nOCfHOMa46Y/cKhIBIhEFPoOQENc2yyeKRLF34okR7N6tCvsp2ab2nBzjmWQOVp3FhDlLiTb9jYxA\neJOfbJYrGgWam32YO/eTbfX19fUAgLq6CLZts58wK4p4CYqdNrmVaHUnHAZ8PtGFJvIZ5m3bfKir\n+6TTjsXe3LkRbN/uE96KKVsW9vvZaZO36Emx8fGMiRw3B4hjLy8PmD49ip07xTfZyja1G80ksyTD\nWUyYs5So0zbbkCRqOFpbVRQXa5g0Kf79ujp9lku0W1820hZ1ztz0R24lijHZcXOyGwA1TTzLVVQE\nTJ4cxZ499q6fB8TLv+y0ya1kMTYyosDvt3ehCaDH3uiEebRY32dEtroj6ve46c9ZTJizVCKdtmyG\nedu2+A47VstVVqahsFDDvn2iMydlm/uMZ5IDAUhP3iDKVLLBquhCE1nstbcrCASAKVM+eT8We4Be\nliFa4ZHPcrHTJm+RXRokO27OTsI8PvZECXNssGo0kSRaQeVg1VlMmLOUuNOW7+CPbWwYr7lZxZw5\ngnVfAHPmRNDUJJvlMv460UwyNz+QW4kGq7LbN2WddnOzTxp7c+dG0NQkmuWSX4EdDrPTJu8wm2G2\ne3JUV5eCgQFlzOk0o8liL3bfwdBQ/HuiU6A4WHUWE+YsJdv0l0hJxt69+k7h0WK1XAAwc2YULS3y\nkbYR2QwzSzLIjUSDVflxc7LYUzFz5tgr+UbH3owZUbS02LtRDJCVQ7HTJneSreKIJotk5VB67EXG\n1ETH93v2z0EX793hYNVJTJizlOh6ULNbyESddku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+ "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that there is a lot of error associated with each value of $x$. We could write a 1D Kalman filter as we did in the last chapter, but suppose this is the output of that filter, and not just raw sensor measurements. Are we out of luck?\n", + "\n", + "Let us think about how we predicted that $x$=4 at $t$=4. In one sense we just drew a straight line between the points and saw where it lay at $t$=4. My constant refrain: what is the physical interpretation of that? What is the difference in $x$ over time? In other words, what is $\\frac{\\partial x}{\\partial t}$? The derivative, or difference in distance over time is *velocity*. \n", + "\n", + "This is the **key point** in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). It does not have any kind of sensor that provides velocity to us. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity an *unobserved variable*. Unobserved means what it sounds like - there is no sensor that is measuring velocity directly. Since the velocity is based on the position, and the position has error, the velocity will have error as well. What happens if we draw the velocity errors over the positions errors?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mkf_internal.show_x_with_unobserved()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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3wj1Fabzs3h35Hrf+RJ8oE2aKvbHOfrDYQFbGqCQKYnbQ1+vDA1jFo/Ejbuai668HxM0c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042/+i5bUTfE8+AYXyXuE/XJ9qVh/l0zmlgYKErW4QMPTW5rxTmrs5h3NAZ6E8YhNlAr9Ef/mMt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\nYLPZ0NjYiKKiIvT39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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n", + "\n", + "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Clearly the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Kalman Filter Algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the *measurement function*. Then we predict the next position by using the current estimate and something called the *state transition function*. In our example above,\n", + "\n", + "$$new\\_position = old\\_position + velocity*time$$ \n", + "\n", + "Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the *residual*. Finally, we use something called the *Kalman gain* to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. \n", + "\n", + "The chart shows a prior estimate of $x=1$ and $\\dot{x}=1$ ($\\dot{x}$ is the shorthand for the derivative of x, which is velocity). Therefore we predict $\\hat{x}=2$. However, the new measurement $x^{'}=1.3$, giving a residual $r=0.7$. Finally, Kalman filter gain $k$ gives us a new estimate of $\\hat{x^{'}}=1.8$.\n", + "\n", + "** CHECK SYMBOLOGY!!!!**" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from mkf_internal import *\n", + "show_residual_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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DD376/PPP1bBhngYN6iGbrfT2kJAwxcR01zfflL48t2hRpJCQkot+vMzM+rLb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\nLrmEygMAAIC34ZPgXEhJSXEsq6N6yNI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+ "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "The Equations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The brilliance of the Kalman filter is taking the insights of the chapter up to this point and finding an optimal mathematical solution. The Kalman filter finds what is called a *least squared fit* to the set of measurements to produce an optimal output. We will not trouble ourselves with the derivation of these equations. It runs to several pages, and offers a lot less insight than the words above, in my opinion. Furthermore, to create a Kalman filter for your application you will not be manipulating these equations, but only specifing a number of parameters that are used by them. It would be going too far to say that you will never need to understand these equations; but to start we can pass them by and I will present the code that implements them. So, first, let's see the equations. \n", + "> Kalman Filter Predict Step:\n", + "\n", + "> $$\n", + "\\begin{aligned}\n", + "\\hat{\\mathbf{x}}_{t|t-1} &= \\mathbf{\\Phi_t}\\hat{\\mathbf{x}}_{t-1} + \\mathbf{B u}_t\\;\\;\\;&(1) \\\\\n", + "\\mathbf{P}_{t|t-1} &= \\mathbf{\\Phi_tP}_{t-1}\\mathbf{\\Phi}^T_t + \\mathbf{Q}_t\\;\\;\\;&(2)\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "> Kalman Filter Update Step:\n", + "\n", + ">$$\n", + "\\begin{aligned}\n", + "\\mathbf{\\gamma} &= \\mathbf{z}_t - \\mathbf{H}_t\\hat{\\mathbf{x}}_t\\;\\;\\;&(3) \\\\\n", + "\\mathbf{K}_t &= \\mathbf{P}_t \\mathbf{H}^T_t (\\mathbf{H}_t \\mathbf{P}_t \\mathbf{H}^T_t + \\mathbf{R}_t)^{-1}\\;\\;\\;(4) \\\\\n", + "\\\\\n", + "\\hat{\\mathbf{x}}_t &= \\hat{\\mathbf{x}}_{t|t-1} + \\mathbf{K}_t \\gamma \\;\\;\\;&(5) \\\\\n", + "\\mathbf{P}_{t|t} &= (\\mathbf{I} - \\mathbf{K}_t \\mathbf{H}_t)\\mathbf{P}_{t|t-1} \\;\\;\\;&(6)\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Dash off, wipe the blood out of your eyes, and we'll disuss what this means. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are nothing more than linear algebra equations that implement the algorithm we used in the last chapter, but using multidimensional Gaussians instead of univariate Gaussians, and optimized for a least squares fit. Each capital letter denotes a matrix or vector. The subscripts indicate which time step the data comes from; $t$ is now, $t-1$ is the previous step. $A^T$ is the transpose of A, and $A^{-1}$ is the inverse. Finally, the hat denotes an estimate, so $\\hat{x}_t$ is the estimate of $x$ at time $t$." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Kalman Equations Expressed as an Algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Different texts use different notation and variable names for the Kalman filter. Later we will expose you to these different forms to prepare you for reading the original literature. However, I find much of the notation very dense, and unnecessary for writing code. The subscripts indicate the time step, but we know the left hand side is for this time step, and the right hand side is for the previous step. For most of this book I'm going to use the following simplified equations, which express an algorithm.\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\text{Predict Step}\\\\\n", + "\\mathbf{x}' &= \\mathbf{F x} + \\mathbf{B u}\\;\\;\\;&(1) \\\\\n", + "\\mathbf{P} &= \\mathbf{FP{F}}^T + \\mathbf{Q}\\;\\;\\;&(2) \\\\\n", + "\\\\\n", + "\\text{Update Step}\\\\\n", + "\\mathbf{\\gamma} &= \\mathbf{z} - \\mathbf{H x} \\;\\;\\;&(3)\\\\\n", + "\\mathbf{K}&= \\mathbf{PH}^T (\\mathbf{HPH}^T + \\mathbf{R})^{-1}\\;\\;\\;&(4) \\\\\n", + "\\mathbf{x}&=\\mathbf{x}' +\\mathbf{K\\gamma} \\;\\;\\;&(5)\\\\\n", + "\\mathbf{P}&= (\\mathbf{I}-\\mathbf{KH})\\mathbf{P}\\;\\;\\;&(6)\n", + "\\end{aligned}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is an algorithm, so $=$ denotes assignment, not equality. For example, equation (6) has P on both sides of the $=$. This equation updates the value of P by the computation on the right hand side. \n", + "\n", + "Here, a $'$ means estimate, so $\\mathbf{x}'$ is the estimate of the state $\\mathbf{x}$. Many texts use $\\hat{\\mathbf{x}}$ or $\\mathbf{x}^*$ to express this. I find these choices unfortunate because we will often want to express these in matrix form. The notation of a hat over a matrix is clumsy at best, and an asterisk followin a matrix normally means the *complex congugate* of the matrix, which is *not* what is intended. So I use $'$. \n", + "\n", + "What do all of the variables mean? What is $\\mathbf{P}$, for example? Don't worry right now. Instead, I am just going to design a Kalman filter, and introduce the names as we go. Then we will just pass them into Python function that implement the equations above, and we will have our solution. Later sections will then delve into more detail about each step and equation. I think learning by example and practice is far easier than trying to memorize a dozen abstract facts at once. \n", + "\n", + "Look at the code below for the predict step (which we will present a bit later). \n", + "\n", + " def predict():\n", + " x = F*x + B*u # equation (1)\n", + " P = F*P*F.T + Q # equation (2)\n", + " \n", + "Notice how simple it really is. It really isn't much different from the predict step in the previous chapter, and it is a nearly exact transliteration of the equations above. As you become familiar with this notation you will find yourself able to read textbooks and paper and implement the equations without much difficulty. \n", + " \n", + "> Later, if you become interested in the details of numerical computation you may change the implementation to be faster or more numerically stable than this written form, but for most of this book our code will follow the Kalman filter equations almost exactly. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking a Dog" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of this chapter - that of using *unobserved variables* to improve our estimates. In simple terms, our algorithm is:\n", + "\n", + " 1. predict the next value for x with \"x + vel*time\"\n", + " 2. get measurement for x\n", + " 3. compute residual as: \"x - x_prediction\"\n", + " 4. compute kalman gain based on noise levels\n", + " 5. compute new position as \"residual * kalman gain\"\n", + " \n", + "That is the entire Kalman filter algorithm. It is both what we described above in words, and it is what the rather obscure Kalman Filter equations do. The Kalman filter equations just express this algorithm by using linear algebra. \n", + "\n", + "As I mentioned above, there is actually very little programming involved in creating a Kalman filter. We will just be defining several matrices and parameters that get passed into the Kalman filter algorithm code. Rather than try to explain each of the steps ahead of time, which can be a bit abstract and hard to follow, let's just do it for our by now well known dog tracking problem. Naturally this one example will not cover every use case of the Kalman filter, but we will learn by starting with a simple problem and then slowly start addressing more complicated situations.\n", + "\n", + "\n", + "##### **Step 1:** Choose the State Variables\n", + "\n", + "*State variables* are the variables that the Kalman filter estimates. They include the *observed variables* - the data that is directly measured by a sensor, and the *unobserved variables*, which we can infer from the observed variables.\n", + "\n", + "For our dog tracking problem, our observed state variable is position, and the unobserved variable is velocity. \n", + "\n", + "The Kalman filter is implemented using linear algebra. We use an $n\\times 1$ matrix to store $n$ state variables. For the dog tracking problem, we use $x$ to denote position, and the first derivative of $x$, $\\dot{x}$, for velocity. The Kalman filter equations use $\\mathbf{x}$ for the state, so we define $\\mathbf{x}$ as:\n", + "\n", + "$$\\mathbf{x} =\\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 2:** Design State Transition Function\n", + "\n", + "\n", + "The next step in designing a Kalman filter is designing what is called the *State Transition Function.* This is a set of equations that mathematically describe the behavior of the system we are filtering. So, for the dog tracking problem we are tracking a moving object, so we just need the Newtonian equations for motion. In other words, these are the equations that we use to predict the next state from the current state. \n", + "\n", + "We know from elementary physics how to compute a new position given a previous position, velocity, and time, like so:\n", + "\n", + "$$ x' = {velocity}*{time} + x_{previous}$$\n", + "\n", + "In more formal mathematics we would write:\n", + "\n", + "$$x' = \\dot{x}(\\Delta t) + x$$\n", + "\n", + "where $\\dot{x}$ is velocity, and $\\Delta t$ is the amount of time between $t-1$ and $t$. In our problems we will be running the Kalman filter at fixed time intervals, so $\\Delta t$ is a constant for us. We will just set it to $1$ and worry about the units later.\n", + "\n", + "As in step one we must express this in the form of matrices so that our linear algebra software and solve the equations for us. The Kalman filter equations require that we write it in the form:\n", + "\n", + "$$ \\mathbf{x}' = \\mathbf{Fx}$$\n", + "\n", + "where as in step 1 $\\mathbf{x}$ is the matrix containing the state variables, and $\\mathbf{F}$ is the matrix that when multiplied by $\\mathbf{x}$ yields our equations. Note that this is just part of the Kalman filter equation (1) above. We will deal with the second half of equation (1) in the next step.\n", + "\n", + "Since $\\mathbf{x}$ is a $2{\\times}1$ matrix $\\mathbf{F}$ must be a $2{\\times}2$ matrix to yield another $2{\\times}1$ matrix as a result. The first row of the F is easy to derive:\n", + "\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}' &=\\begin{bmatrix}1&\\Delta t \\\\ ?&?\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "When we multiply the first row of $\\mathbf{F}$ that out we get:\n", + "$$ \n", + "\\begin{aligned}\n", + "x' &= 1 \\times x + \\Delta t * \\dot{x} \\mbox{, or} \\\\\n", + "x' &= \\dot{x}(\\Delta t) + x\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Now we have to account for the second row. I've let it somewhat unstated up to now, but we are assuming constant velocity for this problem. Naturally this assumption is not true; if our dog moves it must accelerate and deaccelerate. If you cast your mind back to the $g-h Filter$ chapter we explored the effect of assuming constant velocity. So long as the acceleration is small compared to $\\Delta t$ the filter will still perform well. \n", + "\n", + "Therefore we will assume that\n", + "\n", + "$$\\dot{x}' = \\dot{x}$$\n", + "\n", + "which gives us the second row of $\\mathbf{F}$ as follows, once we set $\\Delta t = 1$:\n", + "\n", + "\n", + "$$\n", + "{\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}}' =\\begin{bmatrix}1&1 \\\\ 0&1\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", + "$$\n", + "\n", + "Which, when multiplied out, yields our desired equations:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "x' &= x + \\dot{x} \\\\\n", + "\\dot{x}' &= \\dot{x}\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "In the vocabulary of Kalman filters we call this *transforming the state matrix*. We take our state matrix, which for us is $(\\begin{smallmatrix}x \\\\ \\dot{x}\\end{smallmatrix})$,and multipy it by a matrix we will call $F$ to compute the new state. In this case, $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$. \n", + "\n", + "\n", + "You will do this for every Kalman filter you ever design. Your state matrix will change depending on how many state random variables you have, and then you will create $F$ so that it updates your state based on whatever the physics of your problem dictates. $F$ is always a matrix of constants. If this is not fully clear, don't worry, we will do this many times in this book.\n", + "\n", + "Refer back to the first Kalman filter equation $\\hat{\\mathbf{x}}_{t|t-1} = \\mathbf{F_t}\\hat{\\mathbf{x}}_{t-1} + \\mathbf{B u}_t$. There is an unexplained $\\mathbf{B u}_t$ term in there, but shorn of all the diacritics it should be clear that we just designed $F$ for this equation!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 3**: Design the Motion Function\n", + "\n", + "The Kalman filter does not just filter data, it allows us to incorporate control inputs for systems like robots and airplanes. Consider the state transition function we wrote for the dog:\n", + "\n", + "$$x_t = \\dot{x}(\\Delta t) + x_{t-1}$$\n", + "\n", + "Suppose that instead of passively tracking our dog we were actively controlling a robot. At each time step we would send control signals to the robot based on our current position vs desired position. Kalman filter equations incorporate that knowledge into the filter equations, creating a predicted position based both on current velocity *and* control inputs to the drive motors. \n", + "\n", + "We will cover this use case later, but for now passive tracking applications we set those terms to 0. In step 2 there was the unexplained term $\\mathbf{Bu}$ in equation (1):\n", + "\n", + "$$\\mathbf{x}' = \\mathbf{Fx} + \\mathbf{Bu}$$.\n", + "\n", + "Here $\\mathbf{u}$ is the control input, and $\\mathbf{B}$ is its transfer function. For example, $\\mathbf{u}$ might be a voltage controlling how fast the wheel's motor turns, and multiplying by $\\mathbf{B}$ yields $\\begin{smallmatrix}x\\\\\\dot{x}\\end{smallmatrix}$. Since we do not need these terms we will set them both to zero and not concern ourselves with them for now.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 4**: Design the Measurement Function\n", + "\n", + "Now we need a way to compute the state variables to our measurements. In our problem we have one sensor for the position, and it outputs position directly. We do not have a sensor for velocity. If we put this in linear algebra terms we get:\n", + "\n", + "$$\n", + "z = \\begin{bmatrix}1&0\\end{bmatrix} \\times \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}\n", + "$$\n", + "\n", + "In other words, the measurement sensor provides one times the sensor's measurement of $x$, and zero times the nonexistent velocity measurement. This is simple, because the problem is simple! A slightly more complicated problem might use a temperature sensor might, for example, output a voltage, and we would need to provide an equation to convert from voltage to temperature. \n", + "\n", + "In the nomenclature of Kalman filters the $[1\\space\\space0]$ matrix is called $H$. If you scroll up to the Kalman filter equations you will see an $H$ term in the update step.\n", + "\n", + "$$\\mathbf{\\gamma} = \\mathbf{z} - \\mathbf{H x}\\tag{3}$$\n", + "\n", + "Believe it or not, we have designed the majority of our Kalman filter!! All that is left is to model the noise in our sensors." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 5**: Design the Measurement Noise Matrix\n", + "\n", + "The *measurement noise* is a matrix that models the noise in our sensors as a covariance matrix. This can be admittedly a very difficult thing to do in practice. A complicated system may have many sensors, the correlation between them might not be clear, and usually their noise is not a pure Gaussian. For example, a sensor might be biased to already read high if the temperature is high, and so the noise is not distributed equally on both sides of the mean. Later we will address this topic in detail. For now I just want you to get used to the idea of the measurement noise matrix so we will keep it deliberately simple.\n", + "\n", + "In the last chapter we used a variance of 5 for our position sensor. Let's use the same value here. The Kalman filter equations uses the symbol $R$ for this matrix.\n", + "\n", + "$$R = 5$$\n", + "\n", + "In general the matrix will have dimension $m{\\times}m$, where $m$ is the number of sensors. It is $m{\\times}m$ because it is a covariance matrix, as there may be correlations between the sensors. We have only 1 sensor here so we write:\n", + "\n", + "$$R = \\begin{bmatrix}5\\end{bmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 6**: Design the Process Noise Matrix\n", + "\n", + "What is *process noise*? Consider the motion of a thrown ball. In a vacuum and with constant gravitational force it moves in a parabola. However, if you throw the ball on the surface of the earth you will also need to model factors like rotation and air drag. However, even when you have done all of that there is usually things you cannot account for. For example, consider wind. On a windy day the ball's trajectory will differ from the computed trajectory, perhaps by a significant amount. Without wind sensors, we may have no way to model the wind. Wind can come from any direction, so it is likely to have a near Gaussian distribution. The Kalman filter models this as *process noise*, and calls it $\\small\\mathbf{Q}$.\n", + "\n", + "Astute readers will realize that we can inspect the ball's path and extract wind as an unobserved state variable, but the point to grasp here is there will always be some unmodelled noise in our process, and the Kalman filter gives us a way to model it.\n", + "\n", + "Designing the process noise matrix can be quite demanding. For our first example, we will set it to 0, like so: $\\small\\mathbf{Q}=0$. It is unlikely that you would do that for a real filter.\n", + "\n", + "> Some books and papers use $\\small\\mathbf{R}$ for measurement noise and $\\small\\mathbf{Q}$ for the process noise. Others do the opposite, using $\\small\\mathbf{Q}$ for measurement noise and $\\small\\mathbf{R}$ for the process noise! Read carefully, and make sure you don't get confused. I use the following mnemonic. Radars are used to measure positions, and they have measurement error. So, for me, $\\small\\mathbf{R}$ is the **R**adar's measurement noise. I've read a lot of Kalman filter literature in the context of radar tracking, so it makes sense to me. I don't have a good one for $\\small\\mathbf{Q}$, other than to note that it alphabetically follows the p in **P**rocess." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### **Step 7**: Design Initial Conditions\n", + "\n", + "Finally, we need to specify the initial conditions for the state variables and their associated covariance matrix. If you have a rough idea of the values you can use that as your initial settings, or, you could always read the sensors for the first time, and calculate a initial value. The Kalman filter will converge and find the solution even if your initial conditions are far off, but the more accurate they are the faster and better the output will be. \n", + "\n", + "The covariance matrix ($\\small{\\mathbf{P}}$) is a $n{\\times}n$ matrix that specifies the variances and covariances of each state variable. This is a complicated topic, and I'd rather demostrate the matrix rather than talk about it abstractly here. For now, recognize that the Kalman filter will be calculating the covariance matrix at each step, just like the 1-D filter computed the variance of the mean at each step. So as with those examples we can make an initial guess and trust that $\\small{\\mathbf{P}}$ will converge to a smaller value as the filter progresses. I find this description somewhat unsatisfactory for several reasons, but until you've seen some examples it is hard to talk about in an understandable way." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implementing the Kalman Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As promised, the Kalman filter equations are already programmed for you. In many circumstances you will never have to write your own Kalman filter equations. We will look at the code later, but for now we will just import the code and use it. I have placed it in *KalmanFilter.py*, so let's start by importing it and creating a filter." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "from KalmanFilter import KalmanFilter\n", + "dog_filter = KalmanFilter (dim_x=2, dim_z=2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's it. We import the filter, and create a filter that uses 2 state variables. We specify the number of state variables with the 'dim=2' expression (dim means dimensions).\n", + "\n", + "The Kalman filter class contains a number of variables that you need to set. x is the state, F is the state transition function, and so on. Rather than talk about it, let's just do it!" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog_filter.x = np.matrix([[0], [0]]) # initial state (location and velocity)\n", + "dog_filter.F = np.matrix([[1,1], [0,1]]) # state transition matrix\n", + "dog_filter.H = np.matrix([[1,0]]) # Measurement function\n", + "dog_filter.R = 5 # measurement noise\n", + "dog_filter.Q = 0 # process noise\n", + "dog_filter.P *= 500. # covariance matrix \n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at this line by line. \n", + "\n", + "**1**: We just assign the initial value for our state. Here we just initialize both the position and velocity to zero. \n", + "\n", + "**2**: We set $\\textbf{F}=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$, as in design step 2 above. \n", + "\n", + "**3**: We set $\\textbf{H}=(\\begin{smallmatrix}1&0\\end{smallmatrix})$, as in design step 3 above.\n", + "\n", + "**4**: We set $\\textbf{R} = 5$ and $\\mathbf{Q}=0$ as in steps 5 and 6.\n", + "\n", + "**5**: Recall in the last chapter we set our initial belief to $\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(0,500)$ to signify our lack of knowledge about the initial conditions. We implemented this in Python with a list that contained both $\\mu$ and $\\sigma^2$ in the variable $pos$:\n", + "\n", + " pos = (0,500)\n", + " \n", + "Multidimensional Kalman filters stores the state variables in $\\mathbf{x}$ and their *covariance* in $\\mathbf{P}$. These are $\\verb,f.x,$ and $\\verb,f.P,$ in the code above. Notionally, this is similar as the one dimension case, but instead of having a mean and variance we have a mean and covariance. For the multidimensional case, we have\n", + "\n", + "$$\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(\\mathbf{x},\\mathbf{P})$$\n", + "\n", + "$\\mathbf{P}$ is initialized to the identity matrix of size $n{\\times}n$, so multiplying by 500 assigns a variance of 500 to $x$ and $\\dot{x}$. So $\\verb,f.P,$ contains\n", + "\n", + "$$\\begin{bmatrix} 500&0\\\\0&500\\end{bmatrix}$$\n", + "\n", + "This will become much clearer once we look at the covariance matrix in detail in later sessions. For now recognize that each diagonal element $e_{ii}$ is the variance for the $ith$ state variable. \n", + "\n", + "> Summary: For our dog tracking problem, in the 1-D case $\\mu$ was the position, and $\\sigma^2$ was the variance. In the 2-D case $\\mathbf{x}$ is our position and velocity, and $\\mathbf{P}$ is the *covariance* of the position and velocity. It is the same thing, just in higher dimensions!\n", + "\n", + "\n", + "All that is left is to run the code! The $\\tt DogSensor$ class from the previous chapter has been placed in $\\verb,DogSensor.py,$." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from DogSensor import DogSensor\n", + "\n", + "def dog_tracking_filter(R,Q=0,cov=1.):\n", + " dog_filter = KalmanFilter (dim_x=2, dim_z=2)\n", + " dog_filter.x = np.matrix([[0], \n", + " [0]]) # initial state (location and velocity)\n", + " dog_filter.F = np.matrix([[1,1],\n", + " [0,1]]) # state transition matrix\n", + " dog_filter.H = np.matrix([[1,0]]) # Measurement function\n", + " dog_filter.R = R # measurement uncertainty\n", + " dog_filter.P *= cov # covariance matrix \n", + " if np.isscalar(Q):\n", + " dog_filter.Q = np.matrix([[0,0],\n", + " [0,Q]])\n", + " else:\n", + " dog_filter.Q = Q\n", + " return dog_filter\n", + "\n", + "\n", + "def filter_dog(noise=0, count=0, R=0, Q=0, data=None):\n", + " \"\"\" Kalman filter 'count' readings from the DogSensor.\n", + " 'noise' is the noise scaling factor for the DogSensor.\n", + " 'data' provides the measurements. If set, noise will\n", + " be ignored and data will not be generated for you.\n", + " \n", + " returns a tuple of (positions, measurements, covariance)\n", + " \"\"\"\n", + " if data is None: \n", + " dog = DogSensor(velocity=1, noise=noise)\n", + " zs = [dog.sense() for t in range(count)]\n", + " else:\n", + " zs = data\n", + "\n", + " dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", + "\n", + " pos = [None] * count\n", + " cov = [None] * count\n", + " \n", + " for t in range(count):\n", + " z = zs[t]\n", + " pos[t] = dog_filter.x[0,0]\n", + " cov[t] = dog_filter.P\n", + " \n", + " # perform the kalman filter steps\n", + " dog_filter.update (z)\n", + " dog_filter.predict()\n", + " \n", + " return (pos, zs, cov)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the complete code for the filter, and most of it is just boilerplate. The first function $\\verb,dog_tracking_filter(),$ is a helper function that creates a $\\verb,KalmanFilter,$ object with specified $\\mathbf{R}$, $\\mathbf{Q}$ and $\\mathbf{P}$ matrices. We've shown this code already, so I will not discuss it more here. \n", + "\n", + "The function $\\verb,filter_dog(),$ implements the filter itself. Lets work through it line by line. The first line creates the simulation of the DogSensor, as we have seen in the previous chapter.\n", + "\n", + " dog = DogSensor(velocity=1, noise=noise)\n", + "\n", + "The next line uses our helper function to create a Kalman filter.\n", + "\n", + " dog_filter = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", + " \n", + "We will want to plot the filtered position, the measurements, and the covariance, so we will need to store them in lists. The next three lines initialize empty lists of length *count* in a pythonic way.\n", + "\n", + " pos = [None] * count\n", + " zs = [None] * count\n", + " cov = [None] * count\n", + " \n", + "Finally we get to the filter. All we need to do is perform the update and predict steps of the Kalman filter for each measurement. The $\\verb,KalmanFilter,$ class provides the two functions $\\verb,update(),$ and $\\verb,predict(),$ for this purpose. $\\verb,update(),$ performs the measurement update step of the Kalman filter, and so it takes a variable containing the sensor measurement. \n", + "\n", + "Absent the bookkeeping work of storing the filter's data, the for loop reads:\n", + "\n", + " for t in range (count):\n", + " z = dog.sense()\n", + " dog_filter.update (z)\n", + " dog_filter.predict()\n", + " \n", + "It really cannot get much simpler than that. As we tackle more complicated problems this code will remain largely the same; all of the work goes into setting up the $\\verb,KalmanFilter,$ variables; executing the filter is trivial.\n", + "\n", + "Now let's look at the result. Here is some code that calls $\\verb,filter_track(),$ and then plots the result. It is fairly uninteresting code, so I will not walk through it." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_track(noise=None, count=0, R=0, Q=0, data=None, plot_P=True, title='Kalman Filter'):\n", + " \n", + " ps, zs, cov = filter_dog(noise=noise, data=data, count=count, R=R, Q=Q)\n", + " \n", + " p0, = plt.plot([0,count],[0,count],'g')\n", + " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", + " p2, = plt.plot(range(1,count+1),ps, c='b')\n", + " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", + " plt.ylim((0-10,count+10))\n", + " plt.title(title)\n", + " plt.show()\n", + " \n", + " if plot_P:\n", + " plt.subplot(121)\n", + " plot_covariance(cov, (0,0))\n", + " plt.subplot(122)\n", + " plot_covariance(cov, (1,1))\n", + " plt.show()\n", + " \n", + "def plot_covariance(P, index=(0,0)):\n", + " ps = []\n", + " for p in P:\n", + " ps.append(p[index[0],index[1]])\n", + " plt.plot(ps)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, call it. We will start by filtering 100 measurements with a noise factor of 30, $\\mathbf{R}=5$ and $\\mathbf{Q}=0$." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_track (noise=30, R=5, Q=0, count=100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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t2zl37hwNGzbk9OnTqO+YRXr27FlCQkKy1Rv81ltv8dZbb/H000/To0cPXnzx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+ "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Nobert Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n", + "\n", + "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n", + "\n", + "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that.\n", + "\n", + "In the previous chapter we filtered very noisy signals with much simpler code than the code above. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. In contrast, we can implement very complicated, multidimensional filter with this code merely by altering are assignments to the filter's variables. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Walking Through the KalmanFilter Code (Optional)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "import scipy.linalg as linalg\n", + "\n", + "class KalmanFilter:\n", + "\n", + " def __init__(self, dim_x, dim_z):\n", + " \"\"\" Create a Kalman filter of dimension 'dim'\"\"\"\n", + " \n", + " self.x = 0 # state\n", + " self.P = np.matrix(np.eye(dim_x)) # uncertainty covariance\n", + " self.Q = np.matrix(np.eye(dim_x)) # process uncertainty\n", + " self.u = np.matrix(np.zeros((dim_x,1))) # motion vector\n", + " self.B = 0\n", + " self.F = 0 # state transition matrix\n", + " self.H = 0 # Measurement function (maps state to measurements)\n", + " self.R = np.matrix(np.eye(dim_z)) # state uncertainty\n", + " self.I = np.matrix(np.eye(dim_x))\n", + "\n", + "\n", + " def update(self, Z):\n", + " \"\"\"\n", + " Add a new measurement to the kalman filter.\n", + " \"\"\"\n", + "\n", + " # measurement update\n", + " y = Z - (self.H * self.x) # error (residual) between measurement \n", + " # and prediction\n", + " S = (self.H * self.P * self.H.T) + self.R # project system uncertainty into \n", + " # measurment space + measurement noise(R)\n", + "\n", + "\n", + " K = self.P * self.H.T * linalg.inv(S) # map system uncertainty into kalman gain\n", + "\n", + " self.x = self.x + (K*y) # predict new x with residual scaled \n", + " #by the kalman gain\n", + " self.P = (self.I - (K*self.H))*self.P # and compute the new covariance\n", + "\n", + " def predict(self):\n", + " # prediction\n", + " self.x = (self.F*self.x) + self.u\n", + " self.P = self.F * self.P * self.F.T + self.Q" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Adjusting the Filter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Your results will vary slightly depending on what numbers your random generator creates for the noise componenet of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n", + "\n", + "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the ${\\mathbf{H}}$ and ${\\mathbf{F}}$ matrices - they develop in an obvious manner based on the physics of the system we are modelling. The art comes in modelling the sensors and selecting appropriate values for the rest of our variables.\n", + "\n", + "Let's look at the effects of the noise parameters ${\\mathbf{R}}$ and ${\\mathbf{Q}}$. I will only run the filter for twenty steps to ensure we can see see the difference between the measurements and filter output. I will start by holding ${\\mathbf{R}}$ to 5 and vary ${\\mathbf{Q}}$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dog = DogSensor(velocity=1, noise=30)\n", + "zs = [dog.sense() for t in range(30)]\n", + "\n", + "plot_track (data=zs, R=5, Q=10,count=30, plot_P=False, title='R = 5, Q = 10')\n", + "plot_track (data=zs, R=5, Q=.02,count=30, plot_P=False, title='R = 5, Q = 0.02')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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VwTEbe44QYjsHD0px/TqLffukGDdOY+vpEGITFRXA6tVyJCWV2uT6cXFarFol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\nttsw5OSMq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M1cYldB2hunWLkFq1uPf332DHqmTXrqmYO8+HRi/tYUvchnQtEjGRMTQOb5yt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\nRoQjKkrEvHnZ/ChUFBHZqBEMixe79WrMhx+GYPd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dv5P6Rht3kx87BlOfPt4/cHY21EuW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+ "text": [ + "" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n", + "\n", + "In the Kalman filter ${\\mathbf{R}}$ is the *measurement noise* and ${\\mathbf{Q}}$ is the *process uncertainty*. ${\\mathbf{R}}$ is the same in both plots, so ignore it for the moment. Why does ${\\mathbf{Q}}$ affect the plots this way?\n", + "\n", + "Let's remind ourselves of what the term *process uncertainty* means. Consider the problem of tracking a ball. We can accurately model its behavior in statid air with math, but if there is any wind our model will diverge from reality. \n", + "\n", + "In the first case we set ${\\mathbf{Q}}=10$, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\". Strictly speaking, we are telling the filter there is a lot of external noise that we are not modeling with $\\small{\\mathbf{F}}$, but the upshot of that is to not trust the motion prediction step. So the filter will be computing velocity ($\\dot{x}$), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n", + "\n", + "In the second case we set ${\\mathbf{Q}}=0.02$, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". Again, more strictly this actually says there is very small amounts of process noise, so the motion computation will be accurate. So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our trustworthy velocity prediction.\n", + "\n", + "**AUTHOR'S NOTE: move covariance matrix coverage here, then do R, then Q. Order as below is confusing.**" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Designing $\\textbf{Q}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But what does \"quite large\" and \"quite small\" mean, and what should $\\textbf{Q}$ contain? The numbers in the $\\textbf{Q}$ matrix are not arbitrary, but the variances of the process noise. This means that they have the same units as the rest of the system. So, suppose the noise of our sensor has a standard deviation of $0.5m$, and the rest of our system is specified in meters as well. Variance is the standard deviation squared, so if $\\sigma=0.5$, then $\\sigma^2 = 0.25$.\n", + "\n", + "If we have $m$ state variables then $\\textbf{Q}$ will be an $m{\\times}m$ matrix. $\\textbf{Q}$ is a covariance matrix for the state variables, so it will contain the variances and covariances for the process noise for each state variable. \n", + "\n", + "Let's make this concrete. Assume our state variables are $x=\\begin{bmatrix}x&\\dot{x}\\end{bmatrix}^T$. (**note**: it is customary to use this transpose form of writing an matrix in text. It is how we denote that $x$ is a column matrix without taking up a lot of line space). Then $\\textbf{Q}$ will contain:\n", + "\n", + "$$Q = \\begin{bmatrix}\n", + "\\sigma_x^2 & p\\sigma_x\\sigma_{\\dot{x}} \\\\\n", + "p\\sigma_x\\sigma_{\\dot{x}}& \\sigma_{\\dot{x}}^2\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "But again, what does this *mean*? This is a one dimensional problem, where our variables are $x$ and $\\dot{x}$. Assume we are tracking a person walking in 1D, so $x$ is their position, and $\\dot{x}$ is their velocity. We have no state variable for $\\ddot{x}$, so we are assuming aceleration is zero, and thus their velocity is constant. No one walks with constant velocity, even if they are trying to do so. The *process noise* specifies how much variance there is in each state variable due to the changes in velocity that inevitably happen.\n", + "\n", + "You will very typically see Q expressed in this form (indeed, this is what the code immediately above does):\n", + "\n", + "$$\\begin{bmatrix}\n", + "0&0 \\\\\n", + "0&0.1\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Why all zeros but in the last row and column. This is a useful approximation that we can use for $\\textbf{Q}$ under certain circumstances. Think about the person. As they accelerate, that will also alter their velocity, and eventually their position. But if the acceleration is small compared to our time sample rate, then the changes to distance will small. This follows from the Newtonian equations:\n", + "$$\n", + "\\begin{aligned}\n", + "v&=a\\Delta t \\\\\n", + "d&=\\frac{a}{2}{\\Delta t}^2\n", + "\\end{aligned}\n", + "$$\n", + "If t is small and a is small than the contribution of $\\frac{a}{2}{\\Delta t}^2$ will be extremely small. In this case it is safe to set all of the terms in $\\mathbf{Q}$ to 0 except the variance for the last term. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On the other hand, let's suppose this is not the case. How should Q be designed? Our design of the system is:\n", + "\n", + "$$ X_{n+1} = \\Phi X_n + U_n$$\n", + "\n", + "where $\\Phi X_n$ is our state transition, which computes $\\mathbf{x}$ at time $n+1$ using Newtonan equations, and $U_n$ is the white noise associated with the process. For a walking human, based on the equations above we get\n", + "\n", + "$$U_n = \\begin{bmatrix}\\frac{a{\\Delta t}^2}{2} \\\\ \\Delta t\\end{bmatrix}$$\n", + "\n", + "So white noise has the variance $U_n$ and a mean of 0, which we notate as $w \\sim \\mathcal{N}(0,Q)$. \n", + "\n", + "Finding an analytic value for $\\textbf{Q}$ in a simple problem like this is not difficult, but it quickly becomes difficult to impossible as the number of state variables increase. So in this chapter we will use the simplification that only the variance of the last term is important. In the Kalman filter math chapter we will discuss finding an analytic solution ofr $\\textbf{Q}$, and then present C. F. van Loan's extremely useful numerical technique for finding $\\textbf{Q}$, which is what you will typically use in practice. \n", + "\n", + "**author's note: text needs to move to kalman math chapter. leaving here for now **" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Designing R" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's leave ${\\mathbf{Q}}=0.1$, but bump ${\\mathbf{R}}$ up to $1000$. This is telling the filter that the measurement noise is very large. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_track (data=zs, R=1000, Q=0.1,count=30, plot_P=False, title='R = 1000, Q = 0.1')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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sMTGEfPut/edb4OOPQ5k1K4QXXsjkxx9DGDkynEceMdGy43lullvKxrNrs7VI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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filter output should be much closer to the green line, especially after 10-20 cycles. If you are running this in Ipython Notebook, I strongly urge you to run this many times in a row (click inside the code box, and press CTRL-Enter). Most times the filter tracks almost exactly with the actual position, randomly going slightly above and below the green line, but sometimes it stays well over or under the green line for a long time. What is happening in the latter case?\n", + "\n", + "The filter is strongly preferring the motion update to the measurement, so if the prediction is off it takes a lot of measurements to correct it. It will eventually correct because the velocity is a hidden variable - it is computed from the measurements, but it will take awhile.\n", + "\n", + "To some extent you can get similar looking output by varying either ${\\mathbf{R}}$ or ${\\mathbf{Q}}$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary ${\\mathbf{R}}$ and/or ${\\mathbf{Q}}$ based on your knowledge of the system you are filtering." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "A Detailed Examination of the Covariance Matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far I have not given a lot of coverage of the covariance matrix. $\\mathbf{P}$, the covariance matrix is nothing more than the variance of our state - such as the position of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9{\\times}9$ covariance matrix, or even larger.\n", + "\n", + "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n", + "\n", + "$$\n", + "\\mathbf{P} = \\begin{pmatrix}\n", + " {{\\sigma}_{1}}^2 & p{\\sigma}_{1}{\\sigma}_{2} & \\cdots & p{\\sigma}_{1}{\\sigma}_{n} \\\\\n", + " p{\\sigma}_{2}{\\sigma}_{1} &{{\\sigma}_{2}}^2 & \\cdots & p{\\sigma}_{2}{\\sigma}_{n} \\\\\n", + " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + " p{\\sigma}_{n}{\\sigma}_{1} & p{\\sigma}_{n}{\\sigma}_{2} & \\cdots & {{\\sigma}_{n}}^2\n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "(I have subtituted $\\mathbf{P}$ for $\\Sigma$ because of the nomenclature used by the Kalman filter literature).\n", + "\n", + "The diagonal contains the variance of each of our state variables. So, if our state variables are\n", + "\n", + "$$\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}$$\n", + "\n", + "and the covariance matrix happens to be\n", + "$$\\begin{pmatrix}2&0\\\\0&6\\end{pmatrix}$$\n", + "\n", + "we know that the variance of $x$ is 2, and the variance of $\\dot{x}$ is 6. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "P = np.array([[2,0],[0,6]])\n", + "stats.plot_covariance_ellipse ((0,0), P, title='|2 0|\\n|0 6|')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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0onkcfXRMO3dyOQNweJwlEBezTeayQ3aVlS7l5rJdWSLskJ9pcnNjqqy0ugqy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\nSLW1Li1Z4rW6FDSTxx7za/j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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "P = np.array([[2,2.4],[2.4,6]])\n", + "stats.plot_covariance_ellipse ((0,0), P, title ='|2.0 2.4|\\n|2.4 6.0|')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Vr15AX35ZoL59rWt4D2vbtloTJpRq2LAklZZaW8uJcO+Zjfycj5VeAIhy69a59fvfJykQ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\nRn7Ox5ZlAKLSvn0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+ "text": [ + "" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, dependent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n", + "\n", + "$$\n", + "\\mathbf{P} = \\begin{pmatrix}\n", + " \\sigma_1^2 & p\\sigma_1\\sigma_2 \\\\\n", + " p\\sigma_2\\sigma_1 &\\sigma_2^2 \n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "Look at the computation for the off diagonal elements. \n", + "\n", + "$$\\begin{aligned}\n", + "\\mathbf{P}_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", + "\\mathbf{P}_{1,0}&=p\\sigma_2\\sigma_1.\n", + "\\end{aligned}$$\n", + "\n", + "If we re-arrange terms we get\n", + "$$\\begin{aligned}\n", + "\\mathbf{P}_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", + "\\mathbf{P}_{1,0}&=p\\sigma_1\\sigma_1 \\mbox{, yielding} \\\\\n", + "\\mathbf{P}_{0,1}&=P_{1,0}\n", + "\\end{aligned}$$\n", + "\n", + "In general, we can state that $\\small\\mathbf{P}_{i,j}=\\small\\mathbf{P}_{j,i}$.\n", + "\n", + "So for my example I multiplied the diagonals, 2 and 6, to get 12, and then scaled that with the arbitrarily chosen $p=.2$ to get 2.4.\n", + "\n", + "Let's get back to concrete terms. Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_track(noise, count, R, Q=0, plot_P=True, title='Kalman Filter'):\n", + " dog = DogSensor(velocity=1, noise=noise)\n", + " f = dog_tracking_filter(R=R, Q=Q, cov=20.)\n", + "\n", + " ps = []\n", + " zs = []\n", + " cov = []\n", + " for t in range (count):\n", + " z = dog.sense()\n", + " f.update (z)\n", + " ps.append (f.x[0,0])\n", + " cov.append(f.P)\n", + " zs.append(z)\n", + " f.predict()\n", + "\n", + " p0, = plt.plot([0,count],[0,count],'g')\n", + " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", + " p2, = plt.plot(range(1,count+1),ps, c='b')\n", + " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", + " plt.title(title)\n", + "\n", + " for i,p in enumerate(cov):\n", + " stats.plot_covariance_ellipse ((i+1, ps[i]), cov=p)\n", + "\n", + " if i == len(cov)-1:\n", + " s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n", + " plt.text (30,1,s,fontsize=18)\n", + " s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n", + " plt.text (30,-4,s,fontsize=18)\n", + " plt.xlim((0,40))\n", + " plt.ylim((0,40))\n", + " plt.axis('equal')\n", + " \n", + " plt.show()\n", + "\n", + "\n", + "plot_track (noise=5, R=5, Q=5, count=20, title='R = 5')\n", + "plot_track (noise=5, R=.5, Q=5, count=20, title='R = 0.5')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Oli09ad3ayrJl8RQtqrBpkwvNmlkxm2/vFxWl4eWX3Zk714heDytWxFOvnh2N\nBsaOTebmTS0Xdl3m7S0dSE7W4O6uEB2t5fvv49FooE8f99sTVmQwSbGiZN5D/PffWo4e1dGtm/QX\nC1HQ5ajHODIykhs3blCxYkUuX75M9+7d2bp1K23atGHFihVYLBZ69erFli1b0h0rPcZCCCHA2brw\n/PNmpk5NTLOAx5AhbtSoYadvX+cI7ZEjOnr1cqdDBytvvplMs2ae/PtvTJpzbd6sZ+xYNyIjNfTp\nY2HChNsP0Fmt0KGDB336WAgKyri4PX5cR48e7hw6FJuubh40yI3SpR2MHp3xQ3lCiLzrkfQY+/j4\nULFiRQBKlCiB1Wrl0KFDVKhQAW9vb4oXL06xYsU4depUTk4vhBCigDtxQssLL5j5+OPEdKvahYbq\nqFXL2QO8d6+zeB4/PolJk5KIi9NkuAR0y5Y2LBYIDLTTokXa/mEXF/jww0SmTHElOZPadu1aFzp1\nsqYrii9e1PLLLy707y9tFEI8Dh64x3jXrl1UqVKFyMhIChcuzLJly/jll18oXLgw165dU+MaRRak\nF0k9kqW6JE91FaQ8z5zR8txzHkyenEiXLmmL4oQEOH9eR5Uqdvbv19Grl5mvv06ga1fnflFRWry9\nM/6LTotFg6+vI8MH6+rXt1Ozpo3vvjOiKEqaPG02WLbMyPPPpx9NnjLFRJ8+lixXw3vcFaR7My+Q\nPHPXAxXG169fZ9q0aYwfPz51W/fu3Wnbti0AmswWmxdCCPFYSkyE3r3dGTkyiW7d0j/odvSojoAA\nO4cP63j5ZTOzZiXwzDO3C92oKA0+Po50x4WG6jAY4N9/dZl+dq9eFtZsvU7HVR2JtcWmbt+40YXS\npe3UqJF2YY+9e3Xs3OnCsGHSQiHE4yLHC3xYLBaGDh3K6NGjKV26NNeuXeP69eup71+/fp3ChQtn\neOzAgQPx8/MDwMvLi2rVqqWuDX7rNyV5nb3Xt7bllevJz68bN26cp64nv7+WPCXPu1/v2hXCl1/W\npEoVN159NSXD/X/++UnKlAng5ZfNvPnmn5hM14Db74eGlsJsrpzu/IsXG3n66b9Zs6Y8sbHg6Zn+\n86OsazlQdSKjigfR7n/tCAkJQVFg1qy2BAcnp9nfZoPgYIWePQ/i4eGfJ/KT1/JaXt/79a0/h4WF\nAdCvXz/uR44evlMUhREjRlCnTh169OgBQEpKCm3btk19+K53795s3rw53bHy8J0QQjyevv/ewKxZ\nJrZsiU1KV/cMAAAgAElEQVQz48SdJk82sXixkSFDknnzzfR9vWvXurBmjYGFCxNStyXvPkzlHo0J\n2R3P8897MG9eAlWqpB39vRJ/hU6rO2Hd/yqfdB5Cy5Y2AHbu1DNypBu7d8eiu2Owed48Ixs3urB2\nbXxGk1gIIfKJR/Lw3YEDB9i8eTPLly+nS5cudO3alZs3bzJixAiCgoLo06cP77zzTk5OLe7Tnb8h\niQcjWapL8lRXfs/zzBktH37oyoIF8ZjNzr7erVv1TJliols3M5Ure1G/viezZpmwWCAgwI6SwbCN\nh4dCbGzaSvWXcaHU97tMiRIKxYo5uHo17fu3iuKelXvyXNHhHDyoTx0tnjbNxNChyWmK4nPntEyb\nZuLjjxOlKM6G/H5v5jWSZ+7S5+SgOnXqcOzYsXTb27VrR7t27R74ooQQQhQcigJjxrgxZEgy/v4O\nFi828MUXJgoVUmje3Er//haqVLGzdq0LH33kyrPPWhk3zg2zWeGrrxKoUOF2T3GxYgoREXeM6djt\nLDxWn36fO7d5eirExd2uZu8siofVGcY3hxWOH3dWwWvWuBATo+HFF28/dJeU5JzzeOTIZCpVSt/L\nLIQo2HJUGIu841ZvjXhwkqW6JE915ec8f/7ZhYsXtTz5pIM6dTzx93fw5ZeJ/O9/ttR9IiM1zJhh\nokoVO927p/D004l8952RLl08WLUqjoAAZ5FaqpSD8HAtVqtzGrbzP/3NKSrS6iVnsevmppCY6CyM\n7y6KAXx9Hdy4oadmzcY0aODG/Pnx6O/4STh2rBvlyjl4/XWZni278vO9mRdJnrlLCmMhhBAPTWIi\njB3rSkCAnQkTXJk9O5FGjWzp9vvwQ1eeey6Fv//WoSig1ULfvhY8PRW6dfNg48Y4/P0deHkp+Pvb\nOXBAR4MGdpbMsxNUJRSDoS4A8fEazGYlw6IYwGxWSEjQ8OmnrjRpYqVBg9u9yMuWGdizR89vv6Vf\n5EMI8Xh44HmMRe6SXiT1SJbqkjzVlV/znDzZlbg4DYUKKezYEZthUXzggI7Nm10YMyYZd3eF+Pjb\nVekLL6TwxhvJvP++a+q2Zs1sbN/ugs0GS/+sxMs9b4/uRkZqwONyhkUxgE4HsbHw3Xdaxo9PSt2+\naZML48e78t138Xh4qJlAwZdf7828SvLMXVIYCyGEeCiOHtUyZ46R116zMGdOYoYFp90Oo0a58f77\nSXh5Kfj6KkRGpv3R9MYbFo4c0bF3r7NdolkzK7/95sLWrS6ULmqh3EvVU/eNSLzKu2faZVgUA1y+\nrOH0aT29e5+gWDHn032bN+sZMsSNH36Ip3Jl6SsW4nGWo+naHoRM1yaEEAXfhQtamjXzoFw5B1u3\nxmW636pVLnz9tYlff41Dq4VPPjGRnAzvvZd2UY0ffjDw448G1q6Nx2qF//3PE29vBz16pNCrl/Ph\nuSvxV6j2eReGNQ3i3ebpi2JFgRYtPIiPh71749BoYMsWPcHB7ixdGk+dOvZ0xwgh8rdHMl2bEEII\nkZmLF7V06uScqHj69MRM93M44PPPXRk1Kgntfz+Nata08eef6R9/6do1hdBQPbGxzofuBg9O5sAB\nPZ073y6K26/shO7wq4xpnL4oBli40EB4uJZ27Zwr7n39tZFBg9xZvFiKYiGEkxTG+Zz0IqlHslSX\n5Kmu/JJnfDy88IKZhg1t1KxpT7fQxp02b3bBxUWhRYvbfccNG9o4eFBPQkLafU0mqF3bxh9/uAAQ\nHe3sW543z5T6oF1jt1eonfR2mlkmbtm5U8/kya40aWLD01OhY8ckli418OuvcdSrJ0Xxg8gv92Z+\nIXnmLimMhRBCqEJRYMQIN2rXtnHpkpZ+/bKe8uzrr40EB1vSzABhNkP16jb27k1f3TZvbmX7dj2K\nAkuWGPniiwR+2HiDJt90pmflnpS9NIrAwPRFbkiInr593Zk7N4G//tIxa5YJX99kNm+Oo0wZ6SkW\nQtwmhXE+J/MdqkeyVJfkqa78kOfChQaOH9cxcmQSx47paNHCmum+J05o+ecfXWorxJ3atbPy/ffG\ndNvr1LFz9KiO/fudD+EFNr2Io9fTaA+/yqGZ49i5U0+tWmlnvdi9W0/v3u506ZJCcLA74eFa5s+P\nZ8GCJzCZHvALFkD+uDfzE8kzd0lhLIQQ4oEdOaJjyhRXFixIYOtWA61aWbMsPFeuNPDiiykYDGm3\nh4ToefVVC3/+qefAAV2a94oXd3D1qpbFi428VPJnPpv8LL2r9+TgjDepVs3Orl16pk515aWXzAwc\n6Ea7dmY6dTJjtWqIjNTy4YeJVKjgoFkzaZ0QQmRMCuN8TnqR1CNZqkvyVJeaeVqtzrmDv/7aSL9+\n7rz0kpngYDfee8+VzZv12NJPNZwlux2GDnXjww+TKF/ewbp1LnTqlPlosaLAunWGdKPF0dEaxo1z\n5f/+z0SbNimMGuVKyh27+Po6uH5dy5q1etocH0iDqu0ZVmcY7u7OKdz8/R3MmpVA794Wbt7UcPKk\njrlzE7hw4SbffptAfLwmdURZ7k/1SJbqkjxzl6x8J4QQj4nERFi40MjMmSa8vR3UrWvn2WeteHsr\nREZqiIjQMm2aK2PHavjggyQ6dMi8uL3TokUG3N0VXnophevXNRw5ouOZZ9Ifqz15Epdt2zhWth0O\nR3Vq1Lg9crtrl56333bjn390eHgoRERoCQvTUqpUIWrVslO9uo1KlewkWOMwl95LrYgbVA76OPX4\nW4W22azwzjsm3N0V9u6NpWjR2zOS7tzpQvPm2fuahBCPJ5nHWAghCji7HebONfLllybq1bMxYkRy\nmqL0bjt36hk0yI2hQy307Zv1A3SRkRoaNvRkzZp4qlSxs369C0uXGli2LCHdvq7vv49+504Sz0Sw\nuvE0Ov/QMfW9b781sGiRkRYtrLz7rnMO4+Rk6N7dTEoKPPOMje1/pLD7xEWeNq5hhmk/Zz9fSuPG\nNhQFKlf2pFIlB8eP6xgxIpl+/SypU8CB85eCSpUKERoag4/PI/2xJ4TIRfc7j7GMGAshRAF28aKW\nAQPc0Gph9eq4bK3s1rSpjQ0b4unc2YzDAa+/nnlxPGmSK926paROy3bwoJ5atTIuunVHjpD07rs0\neK8L04fEpG4/cULLRx+58ssvcVy9dLtoNZngxx/jGT/ela8WReLo9TQG/Wu8d/YMrh2aEBenYeJE\nE7/95sKNG1qefdbC99/H4+6e/rO3bnWhVi2bFMVCiCxJj3E+J71I6pEs1SV5qisneW7bpqdlSw9a\ntbKybt39LXf85JMO1q+PZ+pUE+fOZfyj4p9/tPz0kwtjx95epS40VEdgYAZNyoqC7vBhbvrX4MJF\nPdXrOB+sS0yE114zM3FiEuX9bbQbWgO3gQPRh4SAw4HRCEPfPUuhYc0JSOqFYd8Y/MN2Ery6Ld98\nY8TFBUqUcDB4cDLBwZYMi2JI39Ms96d6JEt1SZ65S0aMhRCiAFqzxoWxY92YPz+Bxo3v82m6//j5\nOXjjDQuTJ7syf3761ogvvjDRr58FLy/nKKzDAYcOZTJinJyMJTiYg5eKU7WqHRfnOh28844bNWva\n6N49BdASt2ULhhUrcB0zBk1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NM7JxYxy9gmMIKd+S1wJ78P0b4/n335g07RjDh7tRsaI9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\nAnuMiYiIi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wzTd6t9fduFGP0Xi2EnaVfb9+ZvbulRndpiCffXX5av5S6AohhGjWLrrISn6+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\nLR79/W0MGmTmxx915OUp7N+v4fgJDVd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3dE91+vzRzP3kTrwVn29Wc+/1zgvPyouL0xIZ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+ "text": [ + "" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $\\mathbf{P}=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slighly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n", + "\n", + "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n", + "\n", + "The first plot, with $\\mathbf{R}=5$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85, and the variance for velocity is 3.0. \n", + "\n", + "In contrast, the second plot, with $\\mathbf{R}=0.5$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $\\small\\mathbf{R}$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Question: Explain Ellipse Differences" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Why are the ellipses for $\\mathbf{R}=5$ shorter, and more tilted than the ellipses for $\\mathbf{R}=0.5$. Hint: think about this in the context of what these ellipses mean physically, not in terms of the math. If you aren't sure about the answer,change $\\mathbf{R}$ to truly large and small numbers such as 100 and 0.1, observe the changes, and think about what this means. " + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The $x$ axis is for position, and $y$ is velocity. An ellipse that is vertical, or nearly so, says there is no correlation between position and velocity, and an ellipse that is diagnal says that there is a lot of correlation. Phrased that way, it sounds unlikely - either they are correlated or not. But this is a measure of the *output of the filter*, not a description of the actual, physical world. When $\\mathbf{R}$ is very large we are telling the filter that there is a lot of noise in the measurements. In that case the Kalman gain $\\mathbf{K}$ is set to favor the prediction over the measurement, and the prediction comes from the velocity state variable. So, there is a large correlation between $x$ and $\\dot{x}$. Conversely, if $\\mathbf{R}$ is small, we are telling the filter that the measurement is very trustworthy, and $\\mathbf{K}$ is set to favor the measurement over the prediction. Why would the filter want to use the prediction if the measurement is nearly perfect? If the filter is not using much from the prediction there will be very little correlation reported. \n", + "\n", + "**This is a critical point to understand!**. The Kalman filter is just a mathematical model for a real world system. A report of little correlation *does not mean* there is no correlation in the physical system, just that there was no correlation in the mathematical model. It's just a report of how much measurement vs prediction was incorporated into the model. \n", + "\n", + "Let's bring that point home with a truly large measurement error. We will set $\\mathbf{R}=500$. Think about what the plot will look like before scrolling down. To emphasize the issue, I will set the amount of noise injected into the measurements to 0, so the measurement will exactly equal the actual position. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_track (noise=0, R=500, Q=5, count=7, title='R = 500')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ysrKYO3cu7du391axhSjxsrNh40Yzq1ZZWLnSzNGjKnfd5SQhwcWwYdnUrCmT\nrBQX2dnw++9GgLs62B09auL4cRPh4TrVq7uJitKIjtbo3dvhaVUKDZWgX9SEh+vcd5+T++5zAjbO\nnFFITDSTmGhhyhQ/zp9XuOsuFx07OunTx0FIiLdLnDddhwMHVGrW1LxdFCFECSEtfH/gdDqJiopi\n6dKl1KtX75YfFxcXx4QJEzzh8Go9e/bkgQceYODAgflZVJ/l63/jglYcxjAVFZpmzKS5cqUR8jZv\nNlOlSio9ewbQoYOTpk3dPj/hRXGTn5//tDRytc4dPmwEuiNHVM6eVahaVSMqSqN6dbcnzEVFualW\nTSMgIF+KUKSU5O+elBSFdessLFpknOzp3t3JwIF2WrZ0F9pJnlut/5QUhfbtQzh48FIhlKrkkBY+\nIfImLXx/cPr0abKzs6ldu3a+PaciTQpC5JvkZOXyODwLq1ebCQ3VSUhwMniwnSlTMti5c12J/dFb\nVJ0/r7Bvn8r+/Sb271cv76tkZipERbkvBzmNJk1c9OljBLuICM3nJ/EQhadyZZ1+/Rz06+fg7FmF\nWbOsDB8ehKLAwIF2+vd3EB7uGy27K1ZYaN1aBvAJIQqPtPBdpXXr1pw4cYKsrCyCgoIAmD59OtnZ\n2Tz22GPY7XaGDRvGyJEjr3ns9Vr4PvzwQz766CNsNhsWiwWz2UzNmjVZvnw5AKmpqbz88susXr2a\ngIAAnnvuOQYNGuR5/JAhQwgJCSE5OZlVq1YRFhbGunXrCA4OLuCa+HN8+W8sip70dFi3zphoZeVK\nC+fOKbRr57o8Fs9FZKR0iyoKdN0YU3kl0F0Jdw6HsRh17dpuatd2U6eOcVm5si5dcMUd03Wji/fU\nqVYWL7bQs6eTESOyqVrVu98Z/foF07+/nb59nV4tR3EjLXxC5E3Oj15lw4YNHD9+nLi4OI4ePYrp\nqhHgx44dY8iQIbfVWvf888/z/PPPc9999/HAAw/w0EMP5br9qaeeonz58uzYsYOTJ0/SvXt3GjZs\nSFxcnOc+3377LZMmTeLrr79m9+7dmOWUtijmXC7YulX1zKa5a5eZJk1cJCS4+OSTTBo2LNqz8xV3\nug5nzhjB7upwt2+fiqZxOcwZ4a57dye1a7upWFGCnch/igKtW7to3dpFaqrCf//rR0JCKfr1c/D8\n89lemZX34kWFX34x89VXGYX+2kKIkkvSwx/o+o3/A7jZ7bf6uFOnTrF8+XKSkpLw8/MjKiqKnj17\nsnDhwlzfT7jUAAAgAElEQVSBr23btnTp0gWABg0a3NFri8JVksfR3KnUVIXly80sWWJh+XILlSpp\nJCS4eP75bFq3dnG5wf2WSP0XDl2H06cVT/fLnGC3e7eO2WymTh23p9Xuvvsc1Knjpnx5CXYFST77\neQsL0xk5MpsnnrAzbpw/rVuH8Oyz2Tz9tD3fTiDdSv3/739WOnZ04uMddYQQxYxPBr4yZcL+9HNc\nuJCaDyXJP39sGUxOTgbIFe7cbjd9+vTJdb+YmJiCL5wQhUzXYd8+E0uWWFiyxMKuXWbatHHSpYuT\n11+3ERHhG2NthEHTICnJxM6dKrt2mS9fGr+Sc7pf1q/vpk8fBxcvrqdHjxYS7IRPKldOZ8wYG088\nYWfo0EAWLbIycWIm0dEF380zOxsmTPBnxgxp3RNCFC6fDHy+FtaulleXTqvVitt9/fV0TNdZHCgi\nIgJ/f38OHz58w26i13us8G1yhv36srMhMdHsCXmaBl27Onn22WzatHHl26yKUv9/jsMB+/ap7Nhh\nhLqdO83s2aNSpoxGw4ZuYmPdPPVUNrGxeXXFbOGNYgvks387oqI05s/PYPJkP7p0KcXbb9vo39/x\np57zZvU/c6aV2FgXcXGy9p4QonD5ZODzZXl16axRowbr16+nQ4cO19xWvnx59uzZk+u6ihUrEh8f\nzxtvvMGIESOwWq1s3bqV4OBg6tevXyBlF6KwnTypeAJeYqKFevXcdO3qYObMDOrWlTXxvC093VjW\nYufOK612hw6pVKum0bChi9hYNz172oiNdVO6tLS6iuLFZIK//91Ohw5O+vcP5tQpheHD7QXyvZSd\nDePGBcjYPSGEV0jz0XX8scWtT58+REZGMmfOHD7++GMiIyMZOnRorvuMHDmSBQsWULVqVV577bVc\ntw0ZMoRVq1ZRv3597r//fs/1kydP5ty5czRv3pxatWrx1ltvXdNKKEs6FD2JiYneLoLXaBps2aIy\nZow/CQmluOuuENautdCrl5Nt2y6xeHE6zz5rp169ggt7Jbn+b+TsWWOc5Ecf+fHoo0E0bx5C3bql\nGTUqkH37VJo1c/Hhh1kcOnSR9evT+OSTLIYMsdO2reu2wp7Uv/dI3d+ZOnU0Fi9OZ84cKyNHBqDd\nYe/OG9X/Bx/406SJi2bNpHVPCFH4pIXvDyIjIzl37lyu67777rubPq5+/fps3Ljxurc1atSI9evX\nX3N9WFgYEydOzPM5b3SbEL4iLQ1WrbLw888Wli2zUKaMTpcuTsaMsdGihUvWSvOCU6cUtmwxs327\n0Wq3a5eZrCw8XTLvucfJiy/aqFlT1rITAqBSJZ2FCzPo2zeYDz/05x//yM635969W+Xrr/1YsyYt\n355TCCFuh6zDJ/Kd/I2Lv8OHTfz8s9FVc8sWMy1auOjSxZh0JSpK1sUrTDYb7NihsnmzmS1bzGze\nbMZmgyZN3MTFuWjY0E3Dhm6qVpUutELczMmTCp06hTB+fCadOv35xdFdLujatRSPPGJn4MA/N0ZQ\n3JiswydE3uTcrhDipnTdWBtvwQIrixZZyMhQ6NzZyWOP2Zk2LUOmGC8kum7MlmmEOyPkHTyoUqeO\nm6ZNXXTr5uTVV21Ury7hTog7UamSzuefZ/LII0GsWpVGpUp/7pz4+PH+lCql89BDEvaEEN4jgU+I\nfFZc1sJyu2HjRjMLFlj48UcrQUE6PXs6mDw5k0aN3PjqBLLFpf4BLlxQ2LJF9bTcbd2qUqqUTrNm\nRsDr1y+Lhg3d+Pt7u6RXFKf6L2qk7vNH69YuHnjAwYcf+vP++7Zbftwf63/JEjNffunH0qVpcgJG\nCOFVEviEEB4OB6xda2bBAiuLF1uoWFGjZ08nc+akU6eOdNUsSA6HMdbHCHfG5enTJho3dtGsmYtH\nH7UzcaKLChVktkwhCtrw4dm0aBHCsGF2qla9/e++gwdNDB0axLRpGVSuLP9mhRDeJWP4RL6Tv3HR\nYrPBypUWFiwwJl6pUUOjZ08HPXo4qV5dQl5B0HU4ccLE5s1Xxt799puxHEKzZi6aNjVCXu3aGqrq\n7dIKUTK9+WYANhv861+33soHxkRWnTuHMGRINoMGSVfOwiJj+ITIm1da+DRNkwXFiyld1/Ncq1D4\njvR0WLrUwoIFVlauNNOokZsePYzxX3I2Ov9pGuzdq7J+vZkNG8xs3GhG07gc7Ny88oqNuDgXISHe\nLqkQIsdf/mKnX79SjB1ru+UumZoGTz4ZRLt2Tgl7QgifUeiBr2zZsiQnJxMRESGhrxi6cOECoaGh\n3i6GV/nqOJrUVIWffjJa8hITLbRq5aJHDwfvv59F2bLFJ+T5Qv07ncbMmTkBb9MmM+HhOq1auejc\n2clrr9moVq14TqziC/VfUknd56/atTV0HY4cMREdffPeDomJiaxe3Yn0dIUxY26vVVAIIQrSHQe+\n//znPyxevBiAe++995qFyPNitVqpUKECp06dutOXFrfg0qVLXglefn5+BMuUjT7j9GmFRYuMlrwt\nW8y0b++kd28nkyZlERpafEKet2VlwZYtRrjbsMHoolmtmpv4eGPyh3HjsqhYUepbiKJEUYxW+G3b\n1FsKfD/8UJ1ly6wsWZKOxVIIBRRCiFt0R4Hv+PHj/PDDD/z888+43W7uvfdeevfuTURExC093mq1\nyhivAib16z3ePsN+4oTCggVWFiywsHevSufOTh55xFg+ISjIq0UrFIVR/2lpsGmTmfXrLWzYYIy/\nq1vXCHhPPWWnZctMSpcumQHP25//kkzqPv+Fh+ukpd24KV7X4cMP/Vm5si4LFqRTrlzJ/LcvhPBd\ndxT4goODMZvNZGdno2kaFouFUqVK5XfZhBC36OxZhR9+sDJnjpVDh0zce6+TZ5/Npn17F35+3i5d\n0XfmjOJpvduwwczhwypNmrho1crFP/9po1kzV4kI0yL/uN1Gy7DTqeBwXLm8et/pVHA6/3gdOBxX\nbjebdfz9wd9fJyDAuLx6/8qlsW+WublvS1CQTkZG3oFP1+Gtt/z56ScrP/6YLi35QgifdEdf/WFh\nYQwaNIiEhAQ0TeOll14iRGYb8CkylsN7Cqvu09Nh0SIj5P36q0rXrk5eeMFGQoKrRHcnyo/6P37c\nxPr1ZtavNyZYOX1aoWVLN/HxTt5/P4u4ODdWaz4VuJgpSd89um6EtgsXTJw/r3DhgrGdP28iNVXh\n0iWFtDTj8tIlhYsXc/ZNZGZCQABYrTpWK1gsOZfGdRZL7v0rl1ffruNyKWRng82mkJKSSmBgGWw2\n47rsbAWbzbjM2VcU8PeHwECd8uU1IiI0KlfWqVxZu2aTkxhGWLbZrh/4NA1eeSWATZvMLFiQzt69\na6lYsWR89oUQRcsdBb4TJ04wa9YsVqxYgdPpZMCAASQkJFCuXLn8Lp8Q4ip2OyxfbmHOHCvLl1u4\n6y4n/fvbmTLFKT/O/oSUFIU1ayysXWtm7VozdrtC69YuWrd28dhjdurVc8vyCCWIrsPFiwopKSZS\nUhSSk00kJ5suHxvh7vx5ExcuKJhMUKaMTni4Rpkyume/dGmdyEiN0FD9ultwsJ7vn6nExF9uGrad\nTmMplqwshdOnr7wn49+A+apjE1arnisMRkZqNGrkokkTN2XKlIyWrORkE/Hxrmuud7th+PBADh1S\n+eGHdJlhVwjh0+4o8O3cuZPY2FjP5Bz16tVjz549tG/fPtf9nn76aSIjIwEIDQ0lNjbW859RYmIi\ngBwX0HHOdb5SnpJ03KZNm3x9PrcbJk/ey5o1Efz6a1Xq1XPTqNEeJk06SbduLb3+fn3t+Fbqf/Hi\nTezaFc7Zs7GsWWPh1Ck3sbHn6N27NMOHZ3P69BoUxTfeT1E7zu/Pf34f6zosXvwLZ8/6U6FCU1JS\nFDZtSuHcOX/c7ookJ5s4fhwsFo2qVU1UrqxhNqcQHp5Nq1ZVqFRJIzl5KyEhDrp2bUZg4K2/fmys\n99+/xQKbNl05btTITWJiIrVr576/rkP9+m1JSTGxdOlezp8PIC2tFh9/7M/mzVC6tJ277rLQpIkb\ns3kL0dFpdOwY7/X3l9/Hhw6pxMVtJjHxguf2VavWMW5cY0ymYObOTWfbNt8pb0k6ztk/duwYAI89\n9hhCiOu7o4XXd+3axahRo5g9ezaapnH//fczadIkoqOjPffJa+F1IcTN6boxrf+cOVbmzbNSrpxG\n374Oevd2UKVKyTiznp8yM2HjRjNr1lhYs8ZMUpJKixYu2rVz0r69i9hYN7JKTPGg63DunEJSkonD\nh1UOHzZx/PiVVquTJ00EBOS0WuXuymh0b9SoVElDhqXnze2GAwdMbN1qzEi7davKwYMqtWu7adLE\nRdOmbu66y0Vk5M1ntvRlug4xMaFs3JhG+fLG9252Njz6aBCaBlOmZOLv7+VCCg9ZeF2IvJnv5EGx\nsbF07tyZ3r17A/DAAw/kCnvC+65u3ROF68/UfVKSiTlzrMyda8Xthr59HXz3XTq1axftH06FKTEx\nkVat2rBli8rq1UbA27HDTGysi3btXIwZY6NpU5eMwSsghfHdo+tw4YIR6o4cUXOFu6QkFVXViY7W\niIlxEx2t0aGDyxPqKlUqvmPTCut7X1Whbl2NunUdPPigsbh4Vhbs2qWyZYuZZcssvPZaANWrGyeq\nevVyUKFC0TtRtW2bStmyumfWzcxMeOihYEqX1pk8OfOa7xD5f1cI4avuKPABDB069JbX3hNC5O3k\nSYV584yQl5xsondvB5MmZdKkibtYLsxdEHTdCMurVlmYO7c5e/eGUrWqRkKCi+HDs2nd2oUsD1n0\nXLx4paXOuLyyb7S+aERHa0RHu+nSxUl0tJuYGI2wsKIXLoq6wEBo2dJNy5ZuwI7TCatWmZk718rY\nsSE0buymb18HPXs6i8waoPPnW7n/fgeKYiy+/vDDQTRq5Oajj7JkTK8Qoki5oy6dt0K6dAqRt0uX\nFObPtzB3rpWdO1W6dXPyf//noE0bl0ybfovOn1dYvdrMqlUWVq0y43YrJCQ4SUhw0b6909MFS/g2\nTTNmRd2zR2XvXpWDB41WusOHTTgcCtHR7lytdTmhLjxclxMiRURWFixZYuG776ysXm2hVy8Hw4Zl\nExPjuz0XdB2aNg1hypRMUlJMDBsWyIgR2QwebJfPnY+SLp1C5E1+WgpRSNxuWL3azIwZfixbZqF9\neyePPmqnc2cnAQHeLp3vy842FjvPCXhJSSrx8UbAe/rpbGrX1uSHmI87f15hzx7Vs+3dq7Jvn0qp\nUjr16rmpW9cY+zVokIPoaDfly0uoKw4CA6FXLye9ejk5f17h00/9uOeeUrRt6+L557Np0MDt7SJe\nY80aM2Yz/PCDhW+/9WP69AxatPC9cgohxK2QFr5iSsYSeM8f6/73303MnGnlm2+shIfrPPSQg759\nHZQuLS1QN3P8uImlS80sXWph3ToLdeq4SUhw0qGDK89xePLZ967ExESaNGnD/v1qrnC3b5+KzWaM\n/apXz+3Z6tRxSxfMfFKUPvvp6fD1135MnOhP9+4OXn0126e6enbpEkx6uokKFTQ++yzTM47vRopS\n/RdH0sInRN6khU+IAmCzwcKFFqZP92P3bpW+fR3MmJFJbKycIb4Rp9NoxVu61MLSpRbOnlXo1Mno\n7vrf/2ZJMPAxLhccPmxi794rLXZbtnQgNTWImJgroS4hwUndum4iIqTFThhKlYKhQ+089JCD0aMD\niI8P4a23sujd2+n1z8gXX1jZts3M0KHZjBqVLeP1hBBFnrTwCZFPdB22b1eZMcNYSqFxYzcPPmin\nWzcnfn7eLp3vOnVKYflyC0uWWFi92kxMjEanTk46d3bSuLEseO4rsrPht99Utm83s22byu7dxlT8\nFSpo1K3r9nTJrFfPGGNnsXi7xKIo2bRJZdiwINq2dTJ2rM0rnx9dh88+8+PVVwN4+GE7771nK/xC\niDsmLXxC5E0CnxB/0vnzCrNnW5kxw0pGhsKDDzro398u6+Xlwe2GLVtUli61sGyZhaNHTSQkuOjS\nxcndd8tkK77A4YA9e1S2b1fZts3M9u0qhw6p1KjhJi7OTePGLho0MLpjyuynIr+kpcFjjwXjdMJX\nX2UWarf3zEx47rlANmwwU6qUzpo16TKBVhEjgU+IvMnXWTElYwkKltsNK1eamT7dj1WrzNxzj5Mx\nY2zcdZeL9esTqVJF6v5qFy4orFhhdNVcvtxCxYoanTu7eOcdG82bu/L1bL589m+P0wn79qls26ay\nY4cR7vbtU6lePSfcuRk40E79+u5bmlxI6t97inrdh4TAN99kMGpUAD17BrNoUTqlShX86x46ZGLQ\noGBq13aTna0wY0bmHYW9ol7/QojiSwKfELfhyBFjApaZM/2oVEnjoYfsTJiQSUiIt0vmW3TdWIR5\nyRJjLN7evSpt2xrdNF991Satn17icsGBAya2bzd7Wu/27lWpUkWjcWMXcXFuHnjAToMG7mK7OLnw\nbaoKY8bYeP75QB57LJgZMzIKrKVN12HaNCtvvRXAyJE21qyx8NBDDho2lLHWQojiRbp0CnETWVmw\nYIHRZXPfPpV+/Rw8+KCdevV8dw0pb0hLg1WrLJ5WvOBg3TMWLz7eJeMYC5mmGS0XOWPutm8389tv\nKpUqacTFGeEuLs5NbKyrUFpRhLgdTic88EAwDRq4eeut/B9Ld+yYieHDA7l4UeE//8li1y6VDz/0\nZ/XqNFkmp4iSLp1C5E1a+ITIw549Jr74wp958yy0aOHi8cftdO3qvO5SACXViRMKCxdaWbzYwtat\nZlq0cNG5s5PnnssmOloCcWHKzIQtW8z88ouZTZvMbN6sUrq0TuPGbuLiXHTrZqNRI5e0RosiwWKB\nL7/MpGXLEAYMyL8TbJoGX33lx9ix/gwZYueZZ7LZtUvl1VcDmD8/XcKeEKJYksBXTMlYgjvjdMKP\nP1r44gs/jhxRefhhO4mJaVSufOsN4cW57nUd9u0zsXChlYULLRw/bqJrVydPPGGnffsMn+gGWJzr\n/2onTij88ovZsx04oNKggZsWLVw88oidiRNdXpkAp6TUvy8qbnUfFqbz3HPZvPFGIN9+m/Gnn+/I\nEaNVz2ZT+PHHdOrU0ThzRmHQoGDGjcuibt0/FyqLW/0LIYoPCXxCYCwN8PXXfkyd6kd0tJvHHrPT\nvbtTppbHOCO+ebPqCXl2u0L37g5Gj7bRurVLZrIrBC4X7N6tsmmT0Xr3yy9m7HZo0cJFixYuxozJ\nIi7Ojb+/t0sqRP4aPNjOp5/6sXmzSrNmdza2TtPg00/9+Pe//Xn22Wz+/nc7qmrMRvvII0H89a92\nevRw5nPJhRDCd8gYPlFi6bqx9tNnn/mzcqWZ3r2dDB6cLWPzMH4IrV1r9nTXDAvT6d7dQffuTho1\ncnt9YeTi7tIlhV9/NQLer7+a2brVTESERsuWRsBr2dJFdLQmfwdRIrz7rj8XLyqMHXv7Y/kOHTLx\nzDNBKIrOhAlZ1Khx5fv9xRcDSE42MX16JiZTfpZYeIOM4RMib3JuXpQ4mZkwe7aVL77ww25XGDzY\nzrhxMtNmejosW2Zh0SIry5aZqVVLo3t3Bz/+mE1MjITggqLrcPSoydNyt2mTmePHTcTFGeFuyJBs\nmjd3F+qaZEL4knvvdfL440HArQc+txsmTvRjwgR/Xnwxm8cft+cKdVOmWFmzxsLSpWkS9oQQxZ4E\nvmJKxhJcKynJxBdf+PHtt1ZatXIxerSN9u1d+f6ffVGq+7NnFRYvtrBokYX1643JaXr0cPDWW1lU\nrFg0A4Yv1v/plAOMO/AF77Qbg0lR2bvXRGKihcREI+SpKp6Wu4EDjWURimp3Yl+s/5KiuNZ9gwZu\nTpwwkZEBwcE3v/++fSaGDg0iKEhn2bJ0oqJyn7CaMsXK++8H8MMP6fl6oq+41r8QouiTwCeKNbcb\nli618PnnfuzcqfLQQ3ZWrkynatWS22L1++8mfvzRCHm7d6t06OCiXz8Hn34qrZwF4cyhHVi6dSHs\n/r/y2NchrFtnJjhYp00bFz16OHnnHRtVqkj3TCHyYjJBeLjGhQsmgoPz/u52OOA///Hnv//1Y+RI\nGw8/7LjmhN4nn/gxaZIfCxaky0zCQogSQ8bwiWLpwgWF6dOtfPmlH2XL6jz2mJ1evRwlclILXTcm\n/PjxRwsLF1o4fdrEPfc46dHDQbt2rhJZJwVJ143ZANeuNbNl5W+MWtuWWeUT2N9kAW3auGjb1ikL\nzwtxmzp2LMW//51FkybXTtyi6/DzzxZGjQqgRg03779vu+5JvY8+8mPaND++/z6jRJ/0K65kDJ8Q\neZMWPlGsbN+u8tlnfixaZKFbNydffpl53R8IJcGePSbmzbMyb54Vlwu6d3fy3ns2WrRwoareLl3x\ncuyYEfASE82sXWtB16Fzi194fV079nRtyzMT/4eiZHm7mOImbDa4eFEhLU3B7QZdV9A0Y5ZHXeea\nfV3PfR8/P50yZXTCwnRCQ3WZwTYfqaqxbM4f7d1rYuTIQJKTTfzrX1l06uS65j66DmPH+vPDD1Z+\n/DGdSpXkhIsQomSR/46KqZI0lkDXYdkyMxMm+PP77yYGD7YzerSN8HDv/Kfuzbo/dOhKyEtLU+jd\n2+iq2bhxyZlZszDqPzlZITHR4gl5Npviab174YVsQtiGpXsXku5rQ9sP5hRoWXyNL3z3pKXB6dMm\nUlMVLl5UuHjRdPlSITVV4dKlnH3j+kuXjOt13Vj7LSRER1XBZNJRFKNLYc6mKHiuMy51z352du7X\nCAoywl9YmE7p0jn7mue66GiNevXcVK2aP116faHuC0pKiomIiCutcqmpCv/6lz/ffWflH//I5tFH\n7dcd96rr8PrrAaxcaebHH9MpV67g/l8ozvUvhCjaJPCJIsvphLlzrXz8sT+qqjNsWDa9ejlL3Fn1\nY8dMzJtnYd48K6dPm7jvPgcffphJixZumX0un5w+rXha7xITzVy8qHDXXS7atnUxdGg2tWtf+cF+\nMuMkj371N14a0Jm2b0z3bsGLocxM4zN/4oSJlJQrW3LylX1dh4oVNUqXzglaxn5oqE6VKhqxsbrn\nttKlr9wvIIB8OzGiaZCWZoS/nC0nZKamKhw7ZmLFCgt796qkpyvUreumXj1jy9kvU0ZaosAYm3fu\nnELFijouF3z1lR/vv+/P/fc72LgxLc+Te5oGL70UwNatZubPzyAsTOpTCFEyyRg+UeSkp8O0aX5M\nmuRPTIybYcOy6dDBVWJasABSUhR++MHKd99ZOXrURI8eTvr0cRAfL90180N6OiQmWlixwsyaNRbO\nnFGIjzcCXtu2LurWvX6YPplxkvu/u58BdQfwXPPnCr/gxYDDYYyBPHbMxLFj6uVLE8ePG5eZmQpV\nqmhUqaIREaFRuXLuLSLCaKErSt8HqakKe/eq7NlzZdu7VyUoSKdePTcJCU66d3dSvXrJHHf2228q\nf/tbEO+9l8XIkYGUL68xZkzWDddMdbvh2WcDOXhQ5dtv83c2TuGbZAyfEHkrYW0hoig7c0bhs8/8\nmDLFj7ZtXUydmkHjxiVnfN7Zswrz51uZN8/Cnj0q997r5KWXjKUliuoU/r5C04wflStWmFm+3MKO\nHWaaNHHRsaOTyZMziY113zRIS9i7PenpcPCgyoEDKgcOmDhwQOXgQZXjx42ue9WqaURGakRGumnU\nyHV5X6NcuaIV5m5FWJhOfLyL+Pgr4890HU6cMLFzp8qyZRbuvdef8HCdbt0cdO/upFGjktNNe9Ys\nYxzyCy8E8tZbNrp1c97wvdtsMHRoEOfOKcyZk35LSzkIIURxJi18xVRxGkuQlGRi4kR/vv/eQt++\nDp5+2u7TZ7rzs+5TUxUWLDC6a27bptKli5PevZ107OjEzy9fXqLYudX6P3tWYdUqC8uXm1m50kJI\niM7ddxt1e9ddLoKCbv01JexdcXX967rRFS8n1O3fnxPwVC5eVIiJcVOrlkatWm7PFh2tyWf7OjQN\nNm9WWbTIysKFFrKzFfr3t/Poo3bPJCTF6XsfjLGYH3wQwKRJfjzwgIMPPsi66Wfj999NPPxwEDVq\naHz8cSYBAYVTVih+9V/USAufEHmTFj7hs7ZsUZkwwZ/168387W92Nm1KK9AB974iLQ0WLza6a27c\naCYhwckjj9iZMcNJYKC3S1d0OZ3w669mli83s2KFhcOHVdq1MwLeP/+ZTbVqd3YS4eyhHSx6sy8D\nnnm6RIe9s2cVdu5UWbw4mtmzAz0hT9fJFeruvttJrVoaVatqMsb0NphM0KKFmxYtbLz+uo29e01M\nmeJHfHwInTs7efppu7eLmG/cbpg508qYMQHExxsnt/7975uHvRUrzPz970E8+2w2Tz1lLzEtoEII\ncTPSwid8Ss6Mmx9/7M/RoyaeftrOQw/Zi32XnMxMYx2p77+3snq1hbvuMsbkde3qpFQpb5eu6Pr9\nd5Onm2ZiopnoaI2OHZ107OiiefM/3xX27KEdmLt3IalHG5p9MDd/Cl0EnDypsHOnme3bVXbuVNmx\nw0xmJjRsaEw4YoQ7I+QVxy6YvuTSJYVp06xMmuRPmzZOXnvNRkRE0TwxpuuwcqWZ0aMD8PeHsWOz\n+PFHCxkZCu++a8vzcZoG48b588UXfnz+eWaurrGi5JAWPiHyJoFP+ASnE777zsrHH/uhKDBsmLFQ\nenEem6ZpkJhoZtYsK4sWWWjWzE2fPsb4nNDQovmDzdsyM2HdOiPgrVhhIT1doUMHI+AlJDjztYW4\nJIQ9XTeWoNixw8yOHUaw27lTxemERo2MsXXGpZtq1fJnaQFxZzIyYPx4f7780o8hQ+wMH55dpCZw\n2rhR5Z13Ajh92sQ//2mjVy8nmZkQFxfK0qXpeXbjT0uDp58O4swZE1OmZFC5snx3llQS+ITIm3Tp\nLKaKyliCrCz4+ms//vtff6Kj3bz5po2OHYv2jJs3q/tDh0zMmmXlf//zo0wZjf79Hbzxho3y5eWH\nyt6ZdZcAACAASURBVO3SddizR/V009y61Uz16ufp3Vvliy8yadCgYJamKI5hT9eN5Q5yWu22bzfC\nnaoa4a5hQxeDBtlp1MhFRETerXZF5bunuAkOhvbtl/HQQ+0YPjyQtWuD+eyzTMqW9e3vlV27VN55\nx589e1Reeimbv/zF4VlaZ/p0P9q0ceUZ9vbuNfHww8G0b+/kyy8zsVoLseDXIZ99IYSvksAnvMJm\nM9ZS+vhjf5o3d/H11xk0aVJ8Z9y8eFFh3jwL33zjx/HjJv7v/xzMmpVB/frF9z0XlMxMWL3awk8/\nWVi2zEJAgE7Hjk6efNJOmzYZ7NixoUB/dJ3MOMmJx3qgFPGwd+6cwq+/mvnlFzPbtqns2KESGAhx\ncS4aNnTzxBN2GjZ0eSYEEUVDtWoac+ZkMGaMPx07lmL69EwaNvS975mDB02MHRvAhg1mnnsum6+/\nzsw1Ri81VWHcOH/mzMm47uPnzbMwYkQgo0fbGDDAUUilFkKIokm6dIpCZbMZLXoTJvjTtKmLESOy\niY31vR8j+cHphBUrLHzzjZVVq8x07OhiwAA7HTq4Stzi8H/WiRMKP/9s5eefLWzcaCyZ0LWrky5d\nnMTEFN6MrTmzcQ6q/n8MbTvith6bmGimTRvvjC3SdeMH9qZNZjZtMkLemTMKzZq5adHCRZMmRsiT\nVubiZd48C6+8Esj8+enUrOkbMxsfP27ivff8+eknC0OGZPP44/brzoj7wguBmM36NWP3XC4YPTqA\n+fMtTJ3qm2FWeId06RQib3f8s3PHjh2MGjUKt9tNrVq1+Oijj/KzXKKYyc6GqVP9GD/en7g4F7Nm\nZRTb/6h37VL55hsrc+daqV5do39/Ox99lEXp0vJj+lZpmjFL65IlRkveyZMmOnd28te/2vn88wyv\nLKJ89dILQ+9gNs6FCy2FFvhsNti+3cymTf/P3nmHN1X+ffhOck5GBygIIvjDhaCAyhZky5CNMhSo\nrDKUPRxsEWSJyN5boECRFiij7BYoew8REFFZhQICTdKsk5z3j/MWRSh0pG3anvu6etHQJOfkyZOT\n5/N8x0fHwYMChw8LBATIvPuuxLvvSnTr5uCNN57uLaiStfnoIxcJCTZatAhg0yZzpjZzuXpVw8SJ\nJtatEwkOdnDkSHyStcrHj+vYtEnkwIH4h/7/5k0NXbv6I4qwc6eZPHnUa6qKiopKckiV4PN4PHz9\n9deMHTuWMmXKcPfuXW+fl0oa8ZVaArsdli41MHmykXfekQgJsVCqVPYTejdvavj5Zz2hoXpu3XLS\nrp3Mpk3mDI0+ZXUsFoiK+idVM29emQ8+cPHDDwmUL598cZIecz8tPnsxMQILF+pZu9ZArlxK7VuV\nKpJXxV9cnOah6N3ZszreeEOJ3n3yiZOJExMyLDXTV649OZHHjX1QkJMbN7T06OHPmjWWDK+PvnZN\nSc1cs0ZP+/YODh2KJ2/epOei3Q79+vkxbJjtgSCUZQgPV6KVHTo4+Ppr32xIo859FRUVXyVVgu/M\nmTPkyZPnQcrms88+69WTUsn6uFywYoWeH34wUby4m2XLLJQunb2Ent0OmzaJhIYaOHRIR4MGLsaO\nteHxRFOtmvqlnxxiYzVs2SKyaZPiOViunES9ei6++srOyy/7hli+efVXPtzejtYl2qTKZ69YMTf7\n94sEBTkYNMie5vPxeODcOS2HDini7uBBgb//1lC+vJt335X45hsbpUunzDheJXvTp4+d9esDWbVK\nzyefZEy92/XrGiZPNhIWpqdtWycHD8Ynq4HMsGEmChf2PKjLu3VLw5dfKr6OK1Zk71pvFRUVlfQi\nVTV8W7ZsISwsDI/Hw507d2jZsiVt2rR56D5qDV/OxONR6kbGjjXx4osehgyxUb589vmClmU4eFBH\naKiBiAiRt99207q1k4YNneoCOxnIstJZLzJST2SkyKVLWmrXdlGvnovatV2Zkqr5JBK7ccb0aUHj\n7jNS/HhZhrZt/SlWzI0owsCBKRd8sqx0dt2zR2DXLpG9ewVy51bSMytUUFI0ixVTTcxVnszx4zpa\ntw7g2LH7+Pml33FiYxWh9/PPej791EmvXvZk26GEh4uMGmUiOjqeXLlg3TqRAQP8aN3ayYABNozG\n9DtvlayPWsOnopI0qYrwORwOjh07xoYNGwgICKB58+ZUrVpV/aDlYGQZNm8WGT3aiMkEP/6YQPXq\n2cf89uZNDSEhBpYv16PTQevWDnbvzroGxxmJJMH+/QKRkSKRkSIeD9Sv72LYMBvvvZd28/P04t/W\nC6kRe6BEuf/6S8uCBVYOH07+5fbaNQ27d4sPRJ5GA9Wru6hf38WYMQnqvFNJMaVLuylVSmLNGj1B\nQd6P8v3xh5YZMwysWaOnTRsnBw7Ep6gJ0MWLWgYM8GP1aguSpKFTJz/OnNGxdKklW20aqqioqGQG\nqRJ8+fLlo0iRIhQoUACAkiVLcunSpUcEX/fu3SlcuDAAuXPn5q233nqQ3x4TEwOg3k6n27Nmzcqw\n8d61S2DAAAmHw8OYMXbq1XOxd28MMTG+Mx6pue3xgCTVYPFiA1FRULlyLLNnP0vZsm727o3hjz+g\nUKFHH5/4e2aff2be3rFjP0eP5ufSpbfYtk0kb954KlS4xtKlBSlRQhk/AFH0/vG9Mf5bVy+m3OCv\n+b1xVcr9GJaq84mLM/Htt++zZo2Fw4cTz+nx99+06RCnT+clLu4tdu8WiItz89Zbt2nePDdffGHn\n+vXd/1/75xvvb3qPv3o7dbcT/y+pv7duXZPFiw289NJOrx3/+HEdw4ebOXXqObp08bB/fzwXLuzh\nwgXInz+514t9fPVVFQYNsnHtmpbmzfVUq3aF6Og8mEy+M75pHX/1tvfHOyYmhsuXLwPQuXNnVFRU\nHk+qUjrNZjMNGzZk/fr1mEwmmjdvztSpU3nllVce3EdN6cxcYmLSv3j81Ckd33xj4upVLYMG2fjo\nI1e2SCu7eVPD8uUGlizRkyuXTIcODpo3dyY73TAjxt4XsVhg61aRiAg9UVEiZcpINGrkol49Z4ZG\npNI6/t4wVfd44KOPAqhZ00Xfvo5H/m42w4EDSvRuzx6BP//UUbGiRLVqLqpVkyhRIn0M4zOCnDr/\nfYGnjb3VCkWKPMPly/fSFFmXZdi5U2DaNCO//66je3c7bds6CAhI3XP17evH3bsaTCaZo0cFpk+3\nUrFi1ovqqXM/c1FTOlVUkibVPnybN29m9uzZSJJE48aN+eyzzx76uyr4si9xcRpGjzaxZYvIgAE2\nPv3U6bNpecnF44FduwR++snArl0CjRu76NDBQenS7gzvapeViI+HLVv0RESI7N4t8u67Eo0bO2nQ\nwPXETny+Sqwllg5LGjH4TgmqD1uS6ueZM0dJbdu40YxOBw4HHD4ssHu3wO7dIr/8oqN0aYmqVRWR\nV6aMO0t/htxuxQrCZtMgyxAQIGMyoX52fJAyZXIRGmpJlS+fy6XU1U2dasTjgd69HXz0Ueqv/7IM\no0cbWb1aj9OpoUkTJ998Y0vXGkOV7Isq+FRUkkZI7QPr1atHvXr1vHkuKj6O06ksZKdMMdKqldJ1\nLSkfpaxCXJyG5cv1LFliICBAieZNnWr1ueYhvsTduxoiI0UiIkT27ROpUsVFkyYupk3L2l6DD6wX\nyn9K9VR040zkwgUtP/xgZM4cK7NnG9ixQ+TIEYGiRd1Uq+Zi4EAbFSpIPreo9Xjg9m0N169r//Wj\n3I6P12CzaUhI0DwQdv/+3ekEkwlMJsV2wmJR/s/fXxF/AQEygYEy/v7yg9v58skUK+amWDE3b7zh\nVj9zGUSRIh4uXtSlSPBZrbBsmYGZMw289JKHYcNs1K4tpVnQf/edkUWLDAQGysybZ6VyZSltT6ii\noqKi8lhSLfhUfBtvppbIMmzZIjJ0qIkiRdxERppTtTvsK3g8sHu3Es2LjhZo1MjF3LlWypb1TjQv\nO6b13LmjYeNGJV3z0CGBGjVctGjhZO5c3xPHqRn/tPjsJZKQoMyrPn2Udq19+vhTp46LTp0cLFpk\nzfTNEbsdfv9dx6VL2kdE3bVrWm7c0BIYKFOokIeCBRN/ZKpXl3jmGRmTSfnx8+OR3w2Gf6J5ieMv\nSWC1ajCbFQFotWqwWP75uXFDw4EDAosXG7hwQUeuXA8LwGLF3JQp40avz9Rhy1IkZ+7nzevh3r3k\nXehu3dIwb56BRYsMVK4ssXChcp1MK7IMXbr4ExEh8vHHTsaNS0hVOqivkR2v/SoqKtkDVfCpPJFf\nf9UyZIgf165pGTcugdq1s+4O7K1bGlas0PPTTwZMJpkOHZxMmeJ7gsVXiIv7R+QdOybw/vsugoIc\nLF5syRaLs0TSIvb++EPLtm0i27aJHDwokCePh1y5ZBYvtlC8uCdTUhotFjh3TseFC8rP+fNaLlzQ\ncf26lsKFPRQp4n4g6kqWdD8Qdy+84PFq23tBgNy5ZXLnBniy2PV44No1LefOaTl3Tsfhw8qGzJ9/\naqlbV4kg16zpwmTy3vnlVGw2DUbjk9+PxI6b4eF6PvzQxebNZl57zTubfGfPavn00wCuX9eycKGF\nRo2y7neKioqKSlYh1TV8T0Ot4cva3L2rYdw4I+Hher780k5wsCNL1hh5PBATo0QRdu4UaNhQqc0r\nV06tzXscsbEaNmxQavLOnNFRp46y2H7/fZfPpSB6g1sXT7JtaDNu9u9Bvwr9n3p/ux327RPYvl1k\n+3YRs1lDrVou6tRRahaDg/2JiorPkCY1Ho+yMD97Vscvv+ge/HvjhpYiRZQoWdGiHooWdVO0qJtX\nX/Vkuc/wjRsaNm5U5uPJkzpq1VJqROvUcam+l6mkVSt/OnZ08sEHrkf+duKEjqlTjezZI9Chg4Mu\nXRwpslZ4Evfvaxg71khIiAGDQWbHjnheeinrpoCr+B5qDZ+KStKoET6Vh5AkWLzYwPjxRpo0UbyU\nsmLzjdu3/6nNMxigQwcHkyYlZHpanS9y9aqG9ev1REToOX9eS716Lnr0cFCjhitbGx0nduMs2qgK\nbZ4g9q5c0bJ9u8C2bSIxMSLFi7upU8fF/PlWSpZUumna7VCzZi5Gj04/b8ZbtzQcOSJw+LASATt5\nUuDZZz2UKOGmRAk3H37oZMgQN6+95kHIJlf2AgVkOnVy0KmTg1u3NGzaJLJ0qYE+ffxp1kwx4y5Q\nQP1Mp4SrV7Xkz/9PtO5xHTenTLESGOid43k8sGyZnjFjTLz6qpvcuT1ERlr43//U901FRUUlo1Aj\nfNmU1NQSREcLDB7sR/78HsaMSaB48axXp3f6tI7Zsw1s3CjSsKGLdu0cVKiQsdG8rFDHcf26hjVr\n9Kxdq+ePP7TUr++iSRMn1atLWb5mKjnj/yTrBacTDh5UBN727SK3bytRvNq1XdSsKZEnz6OXzGHD\nTFy5omXRIqtX5prLBb/8ontI4P39t4ayZd2ULy9RvrxE2bJun2ySkxHz/84dDZMnG1m+XE/nzg56\n9rR7TaBkZZ429gkJ8Prrz3Dp0j0cDggNNTB/vgFRlOnVy0GzZt7tuHzkiI6BA/0QBKhWzcWKFQbW\nrzfz8stZ77slOWSFa392Ro3wqagkTTbZB1ZJC5cuaRk2zMSvv+r47jsbDRq4slS6o9sNmzeLzJlj\n4PffdXTu7ODo0awZmUxP7t/XEBEhsnq1ntOndTRs6GLQIBtVq0pZLtUvLTxO7N29q2HLFpFNm0R2\n7xYoUsRD7doupk2zUqqUG50u6efbt08gLEzPnj3xqf7cxMVpOHxYeCDwTp0SePFFD+XKSVSpItGv\nn52iRT1Z1pvP2+TNK/Pddza6dHEwerSRChVyM3iwYhGTla5dGc3p0zpeesnN0KEmwsL0VK8uMWlS\nApUqpb3j5r+Ji9MwcqSJnTtFhg+34XDA99+biIjIvmJPRUVFxZdRI3w5GKcTJk0yMm+egV697Hz+\nuQODIbPPKvnEx0NIiIG5cw3kzSvTrZudJk1cOUq8PA27XemwGhamZ9cu8UF3zTp1sne6ZlLEWmK5\n1PRdDKXK80L/cDZt0rNpk8ixYwLVqrlo0ECJ5OXLl7zLotkM1arlYuxYG/XqPVoTleR5xGrYtUtk\n1y6BAwcE7t17NHqnph8nn5MndfTu7cdrr3mYPFltxPRfJAk2bRIZPtzErVtaevSw0769g4IFvTvH\nXC6YP9/AxImKdc+XX9qYMsXI2rX6VHv/qagkFzXCp6KSNGqEL4dy8qSOnj39KFTIw65dGdNkwltc\nuqRl7lwDq1bpqVlTYu5cK+XLp71VeHbB7YY9ewR+/llPZKTIO++4adHCybRpObuGMdYSS/2VTXmj\nfj9ub/6GP6opHSA7dXIQEmJJVVOaYcP8qFpVeqrYM5th3z6RqCiBXbtEbt7UULWqRI0aLvr2tfP6\n62r0Li28846bLVvMDB7sx/vvK8bi3uoqmZWJi9OwZIliq/DSS24cDg2rVpl57z3vXy937xYYONCP\nAgU8bNhgplAhD926+fP33xq2bTOrGRcqKioqmYgq+LIpSdUSOBwwYYKRJUsMjBxp4+OPs0YKlCwr\n3TZnzzZw6JBA27YOdu+O58UXfW8RkRl1HLIMx4/rWL1az5o1egoW9NC8uZNhw3JeU4t/j7/Ho4xL\n6KZb/KT5COOvHSlcqD/dhtl47720pbJu3SoQHS2we3f8I39zueDoUd2DKN6ZMwJlykhUry4xc6aV\nt99+cppoViaz6piMRpg4MYHFi/V8+GEgERFmXnklZ4m+mJgYKleuwqFDOhYsMLBtm0jTpi5CQy14\nPNC+vT+VKnlX7F29qmHoUD9OnNAxapSNhg1dXLumoWHDQEqWdDN/vjVLZY6kBbWGT0VFxVdRBV8O\n4uhRHT17+lOkiJtdu+KzhBCw22H1aj1z5hhwuTR8/rmduXOtakv2/+fiRS2rV+sJC9Mjy9CihZOI\nCHOOTp2SJA3R0QIbN4ps2qTHmO8a95rWp+2rrRk/uBtarS3Nx/j7bw39+vk/MJ6XZbhwQcuuXSLR\n0QL79gm89JKH6tUlvvzSTsWKUra0tfBFOnRwAtC0aQCbNpl9clMoPUhIgK1b/8fQoYGYzRo6dXIw\nfrztQWOfgQNNtGjhvQ2+e/c0TJliZMkSPV27Opg1y4rJpHzPtGsXwGef2enVy5ElNhRVVFRUsjtq\nDV8OwGaDceNMhIbqGT06gWbNfL8py40bGhYuNPDTTwbeecfN55/bqVnTu40Fsio3bmgID1dE3vXr\nWj76yEmLFk5Kl8653oJWK0RFiWzcKLJ1q8grr3ho1MhJ5TI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6f15Lv35+SJKGiAgzb76Z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BwwYYKO+fP9Et1V19dQasjSFmX+FRQUfBVF8HmImzcFGjXKQIMGdgYNssYtFOrXd7B+vdxeftq0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+ "text": [ + "" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I hope the result was what you were expecting. The ellipse quickly became very wide and not very tall. It did this because the Kalman filter mostly used the prediction vs the measurement to produce the filtered result. We can also see how the filter output is slow to acquire the track. The Kalman filter assumes that the measurements are extremely noisy, and so it is very slow to update its estimate for $\\dot{x}$. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep looking at these plots until you grasp how to interpret the covariance matrix $\\mathbf{P}$. When you start dealing with a, say, $9{\\times}9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9{\\times}9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intution and understanding in this simple, 2-D case. \n", + "\n", + "> **sidebar**: when plotting covariance ellipses, make sure to always use *plt.axis('equal')* in your code. If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall." + ] + } + ], + "metadata": {} + } + ] } \ No newline at end of file