{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multivariate Gaussians\n", "\n", "Modeling Uncertainty in Multiple Dimensions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "import book_format\n", "book_format.set_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The techniques in the last chapter are very powerful, but they only work with one variable or dimension. They provide no way to represent multidimensional data, such as the position and velocity of a dog in a field. Position and velocity are related to each other, and as we learned in the g-h chapter we should never throw away information. In this chapter we learn how to describe this relationship probabilistically. Through this key insight we will achieve markedly better filter performance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distributions\n", "\n", "We've been using Gaussians for a scalar random variable, expressed as $\\mathcal{N}(\\mu, \\sigma^2)$. A more formal term for this is *univariate normal*, where univariate means 'one variable'. The probability distribution of the Gaussian is known as the *univariate normal distribution*.\n", "\n", "What might a *multivariate normal distribution* be? *Multivariate* means multiple variables. Our goal is to be able to represent a normal distribution with multiple dimensions. I don't necessarily mean spatial dimensions - if we track the position, velocity, and acceleration of an aircraft in (x, y, z) that gives us a nine dimensional problem. Consider a two dimensional case. It might be the *x* and *y* coordinates of a robot, it might be the position and velocity of a dog on the x-axis, or milk production and feed rate at a dairy. It doesn't really matter. We can see that for $N$ dimensions, we need $N$ means, which we will arrange in a column matrix (vector) like so:\n", "\n", "$$\n", "\\mu = \\begin{bmatrix}\\mu_1\\\\\\mu_2\\\\ \\vdots \\\\\\mu_n\\end{bmatrix}\n", "$$\n", "\n", "Let's say we believe that $x = 2$ and $y = 17$. We would have\n", "\n", "$$\n", "\\mu = \\begin{bmatrix}2\\\\17\\end{bmatrix} \n", "$$\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 4, like so. \n", "\n", "$$\\sigma^2 = \\begin{bmatrix}10\\\\4\\end{bmatrix}$$ \n", "\n", "This is incomplete because it does not consider the more general case. In the **Gaussians** chapter we computed the variance in the heights of students. That is a measure of how the heights vary relative to each other. If all students are the same height, then the variance is 0, and if their heights are wildly different, then the variance will be large. \n", "\n", "There is also a relationship between height and weight. In general, a taller person weighs more than a shorter person. Height and weight are *correlated*. We want a way to express not only what we think the variance is in the height and the weight, but also the degree to which they are correlated. In other words, we want to know how weight varies compared to the heights. We call that the *covariance*. \n", "\n", "Before we can understand multivariate normal distributions we need to understand the mathematics behind correlations and covariances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlation and Covariance\n", "\n", "*Covariance* describes how much two variables vary together. Covariance is short for *correlated variances*. In other words, *variance* is a measure for how a population vary amongst themselves, and *covariance* is a measure for how much two variables change in relation to each other. For example, as height increases weight also generally increases. These variables are *correlated*. They are *positively correlated* because as one variable gets larger so does the other. As the outdoor temperature decreases home heating bills increase. These are *inversely correlated* or *negatively correlated* because as one variable gets larger the other variable lowers. The price of tea and the number of tail wags my dog makes have no relation to each other, and we say they are *uncorrelated* or *independent*- each can change independent of the other.\n", "\n", "Correlation allows prediction. If you are significantly taller than me I can predict that you also weigh more than me. As winter comes I predict that I will be spending more to heat my house. If my dog wags his tail more I don't conclude that tea prices will be changing.\n", "\n", "For example, here is a plot of height and weight of students on the school's track team. If a student is 68 inches tall I can predict they weigh roughly 160 pounds. Since the correlation is not perfect neither is my prediction. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.gaussian_internal import plot_correlated_data\n", "\n", "height = [60, 62, 63, 65, 65.1, 68, 69, 70, 72, 74]\n", "weight = [95, 120, 127, 119, 151, 143, 173, 171, 180, 210]\n", "plot_correlated_data(height, weight, 'Height (in)', 'Weight (lbs)', False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this book we only consider *linear correlation*. We assume that the relationship between variables is linear. That is, a straight line is a good fit for the data. I've fit a straight line through the data in the above chart. The concept of *nonlinear correlation* exists, but we will not be using it.\n", "\n", "The equation for the covariance between $X$ and $Y$ is\n", "\n", "$$ COV(X, Y) = \\sigma_{xy} = \\mathbb E\\big[(X-\\mu_x)(Y-\\mu_y)\\big]$$\n", "\n", "Where $\\mathbb E[X]$ is the *expected value* of X, defined as\n", "\n", "$$\\mathbb E[X] = \\begin{cases} \\sum_{i=1}^n p_ix_i & \\mbox{discrete}\\\\ \\int_{-\\infty}^\\infty f(x)\\, x dx & \\mbox{continuous}\\end{cases}$$\n", "\n", "We assume each data point is equally likely, so the probability of each is $\\frac{1}{N}$, giving\n", "\n", "$$\\mathbb E[X] = \\frac{1}{N}\\sum_{i=1}^n x_i$$\n", "\n", "for the discrete case we will be considering.\n", "\n", "Compare the covariance equation to the equation for the variance. As you can see they are very similar:\n", "\n", "$$\\begin{aligned}VAR(X) = \\sigma_x^2 &= \\mathbb E[(X - \\mu)^2]\\\\\n", "COV(X, Y) = \\sigma_{xy} &= \\mathbb E\\big[(X-\\mu_x)(Y-\\mu_y)\\big]\\end{aligned}$$\n", "\n", "In particular, if you compute $COV(X, X)$ you get the equation for $VAR(X)$, which supports my statement that the variance computes how a random variable varies amongst itself." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use a *covariance matrix* to denote covariances of a multivariate normal distribution, and it looks like this:\n", "$$\n", "\\Sigma = \\begin{bmatrix}\n", " \\sigma_1^2 & \\sigma_{12} & \\cdots & \\sigma_{1n} \\\\\n", " \\sigma_{21} &\\sigma_2^2 & \\cdots & \\sigma_{2n} \\\\\n", " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", " \\sigma_{n1} & \\sigma_{n2} & \\cdots & \\sigma_n^2\n", " \\end{bmatrix}\n", "$$\n", "\n", "The diagonal contains the variance for each variable, and the off-diagonal elements contain the covariance between the $i^{th}$ and $j^{th}$ variables. So $\\sigma_3^2$ is the variance of the third variable, and $\\sigma_{13}$ is the covariance between the first and third variables.\n", "\n", "A covariance of 0 indicates no correlation. If the variance for $x$ is 10, the variance for $y$ is 4, and there is no linear correlation between $x$ and $y$, then we would write\n", "\n", "$$\\Sigma = \\begin{bmatrix}10&0\\\\0&4\\end{bmatrix}$$\n", "\n", "If there was a small amount of positive correlation between $x$ and $y$ we might have\n", "\n", "$$\\Sigma = \\begin{bmatrix}10&1.2\\\\1.2&4\\end{bmatrix}$$\n", "\n", "where 1.2 is the covariance between $x$ and $y$. I say the correlation is \"small\" because the covariance of 1.2 is small relative to the variances of 10. \n", "\n", "If there was a large amount of negative correlation between between $x$ and $y$ we might have\n", "$$\\Sigma = \\begin{bmatrix}10&-9.7\\\\-9.7&4\\end{bmatrix}$$\n", "\n", "The covariance matrix is symmetric. After all, the covariance between $x$ and $y$ is always equal to the covariance between $y$ and $x$. That is, $\\sigma_{xy}=\\sigma_{yx}$ for any $x$ and $y$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I fear I might be losing you, so let's work an example. In the **Gaussians** chapter we had a class of students with heights H=[1.8, 2.0, 1.7, 1.9, 1.6] meters. We computed:\n", "\n", "$$\\begin{aligned}\n", "\\mathit{VAR}(H) &= E[(H - \\mu_H)^2] \\\\\n", "&= \\frac{1}{N}\\sum_{i=1}^n (H_i - \\mu_H)^2 \\\\\n", "&= \\frac{1}{5}\\left[(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2\\right] \\\\\n", "&= 0.02\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Easy, right? If we weigh the students we might find their weights to be W = [70.1, 91.2, 59.5, 93.2, 53.5]. Can we use the covariance equation to create the covariance matrix? Sure. It will look like:\n", "\n", "$$\\Sigma = \\begin{bmatrix}\\sigma_H^2 & \\sigma_{H,W} \\\\\n", "\\sigma_{W,H} & \\sigma_{W}^2\\end{bmatrix}$$\n", "\n", "We just computed the variance of the height, and it will go in the upper left hand corner of the matrix. The lower right corner contains the variance in weights. Using the same equation we get:\n", "\n", "$$\\begin{aligned}\n", "\\mu_W &= \\frac{1}{5}(70.1 + 91.2 + 59.5 + 93.2 + 53.5) = 73.5 \\\\\n", "\\sigma_W^2 &= \\frac{1}{5}\\left[(70.1-73.5)^2 + (91.2-73.5)^2 + (59.5-73.5)^2 + (93.2-73.5)^2 + (53.5-73.5)^2\\right] \\\\\n", "&= 261.8\n", "\\end{aligned}$$\n", "\n", "Now the covariances. Using the formula above, we compute:\n", "\n", "$$\\begin{aligned}\n", "\\sigma_{H,W} &= \\mathbb E\\big[(H-\\mu_H)(W-\\mu_W)\\big] \\\\\n", "&= \\frac{1}{N}\\sum_{i=1}^n (H_i-\\mu_H)(W_i-\\mu_W) \\\\\n", "&= \\frac{1}{5}[(1.8-1.8)(70.1-73.5) + (2-1.8)(91.2-73.5) + (1.7-1.8)(59.5-73.5)\\, +\\\\\n", "&\\, \\, \\, \\, \\, (1.9-1.8)(93.2-73.5) + (1.6-1.8)(53.5-73.5)] \\\\\n", "&= 2.18\n", "\\end{aligned}$$\n", "\n", "That was tedious, but easy enough. We will never do that again because, of course, NumPy will compute it for you. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.025, 2.727],\n", " [ 2.727, 327.235]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "\n", "W = [70.1, 91.2, 59.5, 93.2, 53.5]\n", "H = [1.8, 2.0, 1.7, 1.9, 1.6]\n", "np.cov(H, W)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That doesn't agree with our calculation! What went wrong? Nothing. NumPy applies a correction for small sample sizes; it uses $\\frac{1}{N-1}$ as the normalization term instead of $\\frac{1}{N}$.\n", "\n", "This is a bit beyond the scope of this book. Briefly, suppose the actual class size is 200 students, and we took a sample of 5 students to perform this computation because we couldn't afford to measure and weigh all 200 students. It is nearly certain that there will be some error in our estimator because the sample is unlikely to perfectly represent the class. As our sample size approaches 200 the error will approach 0. We say there is no *bias* in the latter, and that we have an *unbiased estimator*. In contrast, when we take a small sample there is bias (error is nonzero), and we have a *biased estimator*.\n", "\n", "If the error is zero it makes sense to divide by $N$. I will not prove why, but for biased estimators we use $\\frac{1}{N-1}$ to correct for the small sample size. NumPy does this by default because in practice we are almost always working from data samples from a larger collection. If you want the unbiased estimator, which we computed above, use `bias=1` in the call to `np.cov'." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.02 , 2.182],\n", " [ 2.182, 261.788]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.cov(H, W, bias=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This agrees with our computation. We will not use `bias=1` again in this book since we are using *random variables* which are sampling from the infinite set of positions of the objects we are tracking. Here we are computing the variance and covariance for the entire population, so `bias=1` is correct.\n", "\n", "What does this matrix tell us? It tells us the variance in heights is 0.02 $m^2$ and the variance in weights is 261.788 $kg^2$. Furthermore, it tells us the weights and heights are positively correlated - as heights increase so do the weights.\n", "\n", "Let's create perfectly correlated data. By this I mean that the data perfectly fits on a line - there is no variance from the line." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[6.956, 6.956],\n", " [6.956, 6.956]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = np.linspace(1, 10, 100)\n", "Y = np.linspace(1, 10, 100)\n", "np.cov(X, Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the covariance matrix that the covariance is equal to the variance in x and in y. \n", "\n", "Now let's add some noise to one of the variables so that they are no longer perfectly correlated. I will make $Y$ negative to create a negative correlation." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[ 6.956 -3.084]\n", " [-3.084 1.387]]\n" ] } ], "source": [ "X = np.linspace(1, 10, 100)\n", "Y = -(np.linspace(1, 5, 100) + np.sin(X)*.2)\n", "plot_correlated_data(X, Y)\n", "print(np.cov(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data no longer forms a straight line. The covariance is $\\sigma_{xy}=-3.08$. It is not close to zero compared to the magnitudes of $\\sigma_x^2$ and $\\sigma_y^2$, and so we know there is still a high degree of correlation. We can verify this by looking at the chart. The data forms nearly a straight line.\n", "\n", "Now I will add random noise to a straight line." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[10.295 2.875]\n", " [ 2.875 2.299]]\n" ] } ], "source": [ "from numpy.random import randn\n", "X = np.linspace(1, 10, 1000) + randn(1000)*2\n", "Y = np.linspace(1, 5, 1000) + randn(1000)\n", "plot_correlated_data(X, Y)\n", "print(np.cov(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the covariance is smaller in relation to the variances, reflecting the lower correlation between $X$ and $Y$. We can still fit a straight line through this data, but there is much greater variation in the data.\n", "\n", "Finally, here is the covariance between completely random data." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[[1.003 0.003]\n", " [0.003 1.001]]\n" ] } ], "source": [ "X = randn(100000)\n", "Y = randn(100000)\n", "plot_correlated_data(X, Y)\n", "print(np.cov(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the covariances are very near zero. As you can see with the plot, there is no clear way to draw a line to fit the data. A vertical line would be as unconvincing as the horizontal line I've shown." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distribution Equation\n", "\n", "Recall the equation for the normal distribution from the **Gaussians** chapter:\n", "\n", "$$ \n", "f(x, \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp \\Big [{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 \\Big ]\n", "$$\n", "\n", "\n", "Here is the multivariate normal distribution in $n$ dimensions.\n", "\n", "$$\n", "f(\\mathbf{x},\\, \\mu,\\,\\Sigma) = \\frac{1}{\\sqrt{(2\\pi)^n|\\Sigma|}}\\, \\exp \\Big [{ -\\frac{1}{2}(\\mathbf{x}-\\mu)^\\mathsf{T}\\Sigma^{-1}(\\mathbf{x}-\\mu) \\Big ]}\n", "$$\n", "\n", "The multivariate version merely replaces the scalars of the univariate equations with matrices. If you are reasonably well-versed in linear algebra this equation should look quite manageable. If not, don't worry, both FilterPy and SciPy provide functions to compute it for you. Let's ignore the computation for a moment and plot it to see what it looks like." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.mkf_internal as mkf_internal\n", "\n", "mean = [2., 17.]\n", "cov = [[10., 0.], \n", " [0., 4.]]\n", "\n", "mkf_internal.plot_3d_covariance(mean, cov)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a plot of multivariate Gaussian with a mean of $\\mu=[\\begin{smallmatrix}2\\\\17\\end{smallmatrix}]$ and a covariance of $\\Sigma=[\\begin{smallmatrix}10&0\\\\0&4\\end{smallmatrix}]$. The three dimensional shape shows the probability density for any value of $(X, Y)$ in the z-axis. I have projected the variance for x and y onto the walls of the chart - you can see that they take on the Gaussian bell curve shape. The curve for $X$ is wider than the curve for $Y$, which is explained by $\\sigma_x^2=10$ and $\\sigma_y^2=4$. The highest point of the 3D surface is at the the means for $X$ and $Y$. \n", "\n", "All multivariate Gaussians have this shape. If we think of this as the Gaussian for the position of a dog, the z-value at each point of ($X, Y$) is the probability density of the dog being at that position. Strictly speaking this is the *joint probability density function*, which I will define soon. So, the dog has the highest probability of being near (2, 17), a modest probability of being near (5, 14), and a very low probability of being near (10, 10). As with the univariate case this is a *probability density*, not a *probability*. Continuous distributions have an infinite range, and so the probability of being exactly at (2, 17), or any other point, is 0%. We can compute the probability of being within a given range by computing the volume under the surface with an integral." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FilterPy [2] implements the equation with the function `multivariate_gaussian()` in the `filterpy.stats.` module. SciPy's `stats` module implements the multivariate normal equation with `multivariate_normal()`. It implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability density for any number of values for x over any arbitrary number of calls. I named my function `multivariate_gaussian()` to ensure it is never confused with the SciPy version.\n", "\n", "> The tutorial[1] for the `scipy.stats` module explains 'freezing' distributions and other very useful features." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "from filterpy.stats import gaussian, multivariate_gaussian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll demonstrate using it, and then move on to more interesting things.\n", "\n", "First, let's find the probability density 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 3 for $y$.\n", "\n", "Start by setting $x$ to (2.5, 7.3). You can use a tuple, list, or NumPy array." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "x = [2.5, 7.3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we set the mean of our belief:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "mu = [2.0, 7.0]" ] }, { "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. I will use the variable name `P`. Kalman filters use the name $\\textbf{P}$ for the covariance matrix, and we need to become familiar with the conventions." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "P = [[8., 0.], \n", " [0., 3.]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now call the function" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0315" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%precision 4\n", "multivariate_gaussian(x, mu, P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get the same result from the `scipy.stats` module." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0315\n" ] } ], "source": [ "import scipy\n", "from scipy.stats import multivariate_normal\n", "print(f'{multivariate_normal(mu, P).pdf(x):.4f}')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's time to define some terms. The *joint probability*, denoted $P(x,y)$, is the probability of both $x$ and $y$ happening. For example, if you roll two die $P(2,5)$ is the probability of the first die rolling a 2 and the second die rolling a 5. Assuming the die are six sided and fair, the probability $P(2,5) = \\frac{1}{6}\\times \\frac{1}{6}=\\frac{1}{36}$. The 3D chart above shows the *joint probability density function*.\n", "\n", "The *marginal probability* is the probability of an event happening without regard of any other event. In the chart above the Gaussian curve drawn to the left is the marginal for $Y$. This is the probability for the dog being at any position in $Y$ disregarding the value for $X$. Earlier I wrote \"I have projected the variance for x and y onto the walls of the chart\"; these are the marginal probabilities for $x$ and $y$. Another computational benefit of Gaussians is that the marginal of a multivariate Gaussian is another Gaussian!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at this in a slightly different way. Instead of plotting a surface showing the probability distribution I will generate 1,000 points with the distribution of $[\\begin{smallmatrix}8&0\\\\0&3\\end{smallmatrix}]$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_3d_sampled_covariance(mu, P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can think of the sampled points as being possible locations for our dog given those particular mean and covariances. The contours on the side show the marginal probability for $X$ and $Y$. We can see that he is far more likely to be at (2, 7) where there are many points, than at (-5, 5) where there are few." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As beautiful as these plots are, it is hard to get useful information from them. For example, it is not easy to tell if $X$ and $Y$ both have the same variance, and how much they are correlated. In most of the book I'll display Gaussians as contour plots.\n", "\n", "The contour plots display the range of values that the multivariate Gaussian takes for a specific standard deviation. This is like taking a horizontal slice out of the 3D plot.\n", "\n", "These plots show the shape of the slice for 3 standard deviations." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_3_covariances()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For those of you viewing this online or in Juptyer Notebook on your computer, here is an animation of varying the covariance while holding the variance constant.\n", "\n", "\n", "\n", "(source: http://git.io/vqxLS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These plots look like circles and ellipses. Indeed, it turns out that any slice through the multivariate Gaussian is an ellipse. Hence, in statistics we do not call these 'contour plots', but either *error ellipses* or *confidence ellipses*; the terms are interchangable.\n", "\n", "This code uses the function `plot_covariance_ellipse()` from `filterpy.stats`. By default the function displays one standard deviation, but you can use either the `variance` or `std` parameter to control what is displayed. For example, `variance=3**2` or `std=3` would display the 3rd standard deviation, and `variance=[1,4,9]` or `std=[1,2,3]` would display the 1st, 2nd, and 3rd standard deviations. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "import matplotlib.pyplot as plt\n", "\n", "P = [[2, 0], [0, 6]]\n", "plot_covariance_ellipse((2, 7), P, fc='g', alpha=0.2, \n", " std=[1, 2, 3],\n", " title='|2 0|\\n|0 6|')\n", "plt.gca().grid(b=False);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solid colors may suggest to you that the probability distribution is constant between the standard deviations. This is not true, as you can tell from the 3D plot of the Gaussian. Here is a 2D shaded representation of the probability distribution for the covariance ($\\begin{smallmatrix}2&1.2\\\\1.2&1.3\\end{smallmatrix})$. Darker gray corresponds to higher probability density." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.nonlinear_plots import plot_cov_ellipse_colormap\n", "plot_cov_ellipse_colormap(cov=[[2, 1.2], [1.2, 1.3]]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thinking about the physical interpretation of these plots clarifies their meaning. The mean and covariance of the first plot is\n", "\n", "$$\n", "\\mathbf{\\mu} =\\begin{bmatrix}2\\\\7\\end{bmatrix},\\, \\,\n", "\\Sigma = \\begin{bmatrix}2&0\\\\0&2 \\end{bmatrix}\n", "$$ " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [2, 7]\n", "P = [[2, 0], [0, 2]]\n", "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", " title='|2 0|\\n|0 2|')\n", "plt.gca().grid(b=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Bayesian way of thinking about this is that the 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. The shape of the ellipse shows us the geometric relationship of the errors in $X$ and $Y$. Here we have a circle so errors in $X$ and $Y$ are equally likely." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean and covariance of the second plot are\n", "\n", "$$\n", "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n", "\\Sigma = \\begin{bmatrix}2&0\\\\0&6\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [2, 7]\n", "P = [[2, 0], [0, 6]]\n", "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", " title='|2 0|\\n|0 6|')\n", "plt.gca().grid(b=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time we use a different variance for $X$ ($\\sigma_x^2=2$) vs $Y$ ($\\sigma^2_y=6$). The result is a tall and narrow ellipse. We can see that a lot more uncertainty in $Y$ vs $X$. In both cases we believe the dog is at (2, 7), but the uncertainties are different." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The third plot shows the mean and covariance\n", "\n", "$$\n", "\\mu =\\begin{bmatrix}2\\\\7\\end{bmatrix}, \\, \\, \\, \n", "\\Sigma = \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = [2, 7]\n", "P = [[2, 1.2], [1.2, 2]]\n", "plot_covariance_ellipse(x, P, fc='g', alpha=0.2, \n", " title='|2 1.2|\\n|1.2 2|')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the first contour that has values in the off-diagonal elements of the covariance, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling us the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow correlated. The off-diagonal elements in the covariance matrix are non-zero, indicating that a correlation exists.\n", "\n", "Recall the plot for height versus weight. It formed a slanted grouping of points. We can use NumPy's `cov()` function to compute the covariance of two or more variables by placing them into a 2D array. Let's do that, then plot the $2\\sigma$ covariance ellipse on top of the data. We will need to use `bias=1` because the data represents the entire population; it is not a sample." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 18.5249, 135.701 ],\n", " [ 135.701 , 1092.29 ]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cov_hw = np.cov(np.vstack((height, weight)), bias=1)\n", "cov_hw" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(height, weight, s=120, marker='s')\n", "plt.title('Track Team Height vs. Weight')\n", "plt.xlabel('Height (in)'); plt.ylabel('Weight (lbs)')\n", "plot_covariance_ellipse((np.mean(height), np.mean(weight)), cov_hw, fc='g', \n", " alpha=0.2, axis_equal=False, std=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should help you form a strong intuition on the meaning and use of covariances. The covariance ellipse shows you how the data is 'scattered' in relation to each other. A narrow ellipse like this tells you that the data is very correlated. There is only a narrow range of weights for any given height. The ellipse leans towards the right, telling us there is a positive correlation - as x increases y also increases. If the ellipse leaned towards the left then the correlation would be negative - as x increases y decreases. We can see this in the following plot:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "max_temp = [200, 250, 300, 400, 450, 500]\n", "lifespan = [10, 9.7, 5, 5.4, 4.3, 0.3]\n", "\n", "plt.scatter(max_temp, lifespan, s=80)\n", "cov = np.cov(np.vstack((max_temp, lifespan)))\n", "plot_covariance_ellipse((np.mean(max_temp), np.mean(lifespan)), cov, fc='g', \n", " alpha=0.2, axis_equal=False, std=2)\n", "plt.title('Engine Temperature vs Lifespan')\n", "plt.xlabel('Temperature (C)'); plt.ylabel('Years');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The relationships between variances and covariances can be hard to puzzle out by inspection, so here is an interactive plot. (If you are reading this in a static form instructions to run this online are here: https://git.io/vza7b)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1a640a6a137140e3863e9657146fad7a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=5.0, continuous_update=False, description='var_x', max=20.0), FloatSli…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ipywidgets import interact\n", "from kf_book.book_plots import figsize, FloatSlider\n", "\n", "fig = None\n", "def plot_covariance(var_x, var_y, cov_xy):\n", " global fig\n", " if fig: plt.close(fig)\n", " fig = plt.figure(figsize=(4,4))\n", " P1 = [[var_x, cov_xy], [cov_xy, var_y]]\n", "\n", " plot_covariance_ellipse((10, 10), P1, axis_equal=False,\n", " show_semiaxis=True)\n", "\n", " plt.xlim(4, 16)\n", " plt.gca().set_aspect('equal')\n", " plt.ylim(4, 16)\n", "\n", " \n", "with figsize(y=6):\n", " interact (plot_covariance, \n", " var_x=FloatSlider(5, min=0, max=20), \n", " var_y=FloatSlider(5, min=0, max=20), \n", " cov_xy=FloatSlider(1.5, min=0, max=50, step=.2));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pearson's Correlation Coefficient\n", "\n", "We will not be using this coefficient in this book, but you may see it elsewhere. You can safely skip this section if uninterested.\n", "\n", "The correlation between two variables can be given a numerical value with *Pearson's Correlation Coefficient*. It is defined as\n", "\n", "$$\\rho_{xy} = \\frac{COV(X, Y)}{\\sigma_x \\sigma_y}$$\n", "\n", "This value can range in value from -1 to 1. If the covariance is 0 than $\\rho=0$. A value greater than 0 indicates that the relationship is a positive correlation, and a negative value indicates that there is a negative correlation. Values near -1 or 1 indicate a very strong correlation, and values near 0 indicate a very weak correlation.\n", "\n", "Correlation and covariance are very closely related. Covariance has units associated with it, and correlation is a unitless ratio. For example, for our dog $\\sigma_{xy}$ has units of meters squared.\n", "\n", "We can use `scipy.stats.pearsonr` function to compute the Pearson coefficient. It returns a tuple of the Pearson coefficient and of the 2 tailed p-value. The latter is not used in this book. Here we compute $\\rho$ for height vs weight of student athletes:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9539731096080194" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import pearsonr\n", "pearsonr(height, weight)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we compute the correlation between engine temperature and lifespan." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.9178223453527254" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pearsonr(max_temp, lifespan)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Correlations to Improve Estimates\n", "\n", "Suppose we believe our dog is at position (5, 10) with some given covariance. If the standard deviation in x and y is each 2 meters, but they are strongly correlated, the covariance contour would look something like this." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = [[4, 3.9], [3.9, 4]]\n", "\n", "plot_covariance_ellipse((5, 10), P, ec='k', std=[1, 2, 3])\n", "plt.xlabel('X')\n", "plt.ylabel('Y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose I were to tell you that we know that $x=7.5$. What can we infer about the value for $y$? The position is extremely likely to lie within the 3$\\sigma$ covariance ellipse. We can infer the position in *y* based on the covariance matrix because there is a correlation between *x* and *y*. I've illustrated the likely range of values for y as a blue filled circle." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_correlation_covariance()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The circle not mathematically correct, but it gets the idea across. We will tackle the mathematics in the next section. For now recognize that we can predict that $y$ is likely near 12. A value of $y=-10$ is extremely improbable.\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 $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, $y$ is dependent on $x$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiplying Multidimensional Gaussians" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the previous chapter we incorporated an uncertain measurement with an uncertain estimate by multiplying their Gaussians together. The result was another Gaussian with a smaller variance. If two pieces of uncertain information corroborate each other we should be more certain in our conclusion. The graphs look like this:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.plot_gaussian_multiply()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The combination of measurements 1 and 2 yields more certainty, so the new Gaussian is taller and narrower - the variance became smaller. The same happens in multiple dimensions with multivariate Gaussians.\n", "\n", "Here are the equations for multiplying multivariate Gaussians. The capital sigma ($\\Sigma$) indicates that these are matrices, not scalars. Specifically, they are covariance matrices:\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\Sigma_2(\\Sigma_1 + \\Sigma_2)^{-1}\\mu_1 + \\Sigma_1(\\Sigma_1 + \\Sigma_2)^{-1}\\mu_2 \\\\\n", "\\Sigma &= \\Sigma_1(\\Sigma_1+\\Sigma_2)^{-1}\\Sigma_2\n", "\\end{aligned}$$\n", "\n", "\n", "They are generated by plugging the multivariate Gaussians for the prior and the estimate into Bayes Theorem. I gave you the algebra for the univariate case in the **Gaussians** chapter. \n", "\n", "You will not need to remember these equations as they are computed by Kalman filter equations that will be presented shortly. This computation is also available in FilterPy using the `multivariate_multiply()` method, which you can import from `filterpy.stats`. \n", "\n", "To give you some intuition about this, recall the equations for multiplying univariate Gaussians:\n", "\n", "$$\\begin{aligned}\n", "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", "\\sigma^2 &= \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n", "\\end{aligned}$$\n", "\n", "This looks similar to the equations for the multivariate equations. This will be more obvious if you recognize that matrix inversion, denoted by the -1 power, is *like* a reciprocal since $AA^{-1} =I$. I will rewrite the inversions as divisions - this is not a mathematically correct thing to do as division for matrices is not defined, but it does help us compare the equations.\n", "\n", "$$\\begin{aligned}\n", "\\mu &\\approx \\frac{\\Sigma_2\\mu_1 + \\Sigma_1\\mu_2}{\\Sigma_1 + \\Sigma_2} \\\\ \\\\\n", "\\Sigma &\\approx \\frac{\\Sigma_1\\Sigma_2}{(\\Sigma_1+\\Sigma_2)}\n", "\\end{aligned}$$\n", "\n", "In this form the relationship between the univariate and multivariate equations is clear.\n", "\n", "Now let's explore multivariate Gaussians in terms of a concrete example. Suppose that we are tracking an aircraft with two radar systems. I will ignore altitude so I can use two dimensional plots. Radar provides the range and bearing to a target. We start out being uncertain about the position of the aircraft, so the covariance, which is our uncertainty about the position, might look like this. In the language of Bayesian statistics this is our *prior*. " ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P0 = [[6, 0], [0, 6]]\n", "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose that there is a radar to the lower left of the aircraft. Further suppose that the radar's bearing measurement is accurate, but the range measurement is inaccurate. The covariance for the error in the measurement might look like this (plotted in green on top of the yellow prior):" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P1 = [[2, 1.9], [1.9, 2]]\n", "plot_covariance_ellipse((10, 10), P0, fc='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P1, fc='g', alpha=0.9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall that Bayesian statistics calls this the *evidence*. The ellipse points towards the radar. It is very long because the range measurement is inaccurate, and the aircraft could be within a considerable distance of the measured range. It is very narrow because the bearing estimate is very accurate and thus the aircraft must be very close to the bearing estimate.\n", "\n", "We want to find the *posterior* - the mean and covariance that results from incorporating the evidence into the prior. As in every other chapter we combine evidence by multiplying them together. " ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import multivariate_multiply\n", "\n", "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n", "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.9)\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I have plotted the original estimate (prior) in a very transparent yellow, the radar reading in green (evidence), and the finale estimate (posterior) in blue.\n", "\n", "The posterior retained the same shape and position as the radar measurement, but is smaller. We've seen this with one dimensional Gaussians. Multiplying two Gaussians makes the variance smaller because we are incorporating more information, hence we are less uncertain. Another point to recognize is that the covariance shape reflects the physical layout of the aircraft and the radar system. The importance of this will become clear in the next step.\n", "\n", "Now let's say we get a measurement from a second radar, this one to the lower right. The posterior from the last step becomes our new prior, which I plot in yellow. The new measurement is plotted in green." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P3 = [[2, -1.9], [-1.9, 2.2]]\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We incorporate this information by multiplying the Gaussians:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The only likely place for the aircraft is where the two ellipses intersect. The intersection, formed by multiplying the prior and measurement, is a new Gaussian. The shapes reflects the geometry of the problem. This allows us to *triangulate* on the aircraft, resulting in a very accurate estimate. We didn't explicitly write any code to perform triangulation; it was a natural outcome of multiplying the Gaussians of each measurement together.\n", "\n", "Think back to the **g-h Filter** chapter where we displayed the error bars of two weighings on a scale. The estimate must fall somewhere within the region where the error bars overlap. Here the estimate must fall between 161 to 163 pounds." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.book_plots as book_plots\n", "book_plots.plot_errorbars([(160, 8, 'A'), (170, 8, 'B')], xlims=(150, 180))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's consider a different layout. Suppose the first radar is directly to the left of the aircraft. I can model the measurement error with\n", "$$\\Sigma = \\begin{bmatrix}2&0\\\\0&0.2\\end{bmatrix}$$\n", "\n", "Here we see the result of multiplying the prior with the measurement." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P1 = [[2, 0], [0, .2]]\n", "P2 = multivariate_multiply((10, 10), P0, (10, 10), P1)[1]\n", "plot_covariance_ellipse((10, 10), P0, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P1, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can incorporate the measurement from the second radar system, which we will leave in the same position as before." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P3 = [[2, -1.9], [-1.9, 2.2]]\n", "P4 = multivariate_multiply((10, 10), P2, (10, 10), P3)[1]\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10, 10), P3, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse((10, 10), P4, ec='k', fc='b')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our estimate is not as accurate as the previous example. The two radar stations are no longer orthogonal to each other relative to the aircraft's position so the triangulation is not optimal.\n", "\n", "For a final example, imagine taking two measurements from the same radar a short time apart. The covariance ellipses will nearly overlap, leaving a very large error in our new estimate:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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Gb+9eTNPAtrNHBmzbxnGybbHt7HYNw8A0jcHb7O++aZqYpg+Px4NheDFNLz6fH9P0YhiewR0ED5Bdsuu9w3YaDMPIjS32+/34/f7cuWDBYBC/338s5RcRmbKOOvyfd955h+1BguwP8rp161i3bt1hX7Nx48Zhj++++27uvvvuo22KiMikl06nc+H+4KCfSCSGDbWx7RSOYw320KcPuj90mxmxbY9naLiNmetNN00fjuMllbJIJm0sKzN4P0UymSKRSDEwkCCRSBKPDwzeTxGPJxgYSJBOZ3ccWlpa2b59fy6Qj/bvwoH2D+2cMLiD4OSWoR0HcPD5fAQCfvz+7G0g4CcYDBAM+nOhPhQKEwpFCIUKCAbDhMMRAoEIHk8A0/QPG2o09J6h26HF4/G49F9TRGTic2W2HxERGSmVShGPx3PLwMAAqVQq97xtW9h2EsdJDYb9ods0B/fQ+3xe/H7vYM93GL/fi9frxefzkkqliMUG6Ovrp7e3j56ePnp6ooO32fuHu2BMxrZJ2xnSdpq0kyFjZ4Y9TtvZdRnbpjfRS2/XAAAOzmDrBkM9ZBM/gGEMDgDK9v5nBwgZufUGBoYBpuHB63jwpr144x48ponH8ODBxMTEcMDExLazRxgOLNnZ5AoKwhQUhCksLKKoqITCwiKKi8soKiqluLicoqKSwSFK4Pf7CYfDuSUUCulIgYjkDYV/EREXZEN4bFjQT6fTANh2GttO5JahkD8U8A3DIBDwDQ5jKSQYDOR6w71eD9FoP+3tXbS0tNPW1klbWxdtbV10dfWSyaRzbbAdh1TGyi3JTIpUxsKyLazBUJ8N/Nlwf7ijuh6fidfvwRv04vF7MEywAzZ2kZ0dwpNN7xjG4Am/B93igGMP9fQPPnYcnNwQIQfHdshYSdLJDJlEmnQqw2hNMQDT9OAzPXgMD96hWzxE+2PZnYY2Dx4nu9Mw7PQFIBIpoKysnIqKaZSXV1JeXk1FxTRKSkoIBoPDdggKCgo0XaGITEkK/yIiYyCRSNDX10csFiMWi+V69G07hW0nDwn72YDu8ZiEQgGCwTDBYEluqIvfnw2dXV297NvXQnNzG62tnbS1ddLe3p3btuNAIpNkwEqSSCdIZFIk0ylStkUqnQ35B2doj88kUODHF/LiDXoJ+EN4A57BxYsn4BkM+YO3AQ8evxfTM/zEWttxaGlpobq6Ohv8x5jjOGQsm3Qynd0hSGZIJzOkU4O3yfSBdckM8USCVCxFKp4eth2PYeIzfXgNDz7Di7evl9a+Vjx7PPhNPx7DBExM00tJSSnl5dmdgsrKaqqqqpgxYwalpaUUFBRQUFBAMBgc8+8qInK8KfyLiLwP8Xh8WNgfOgE3G/DjZDID2HY8Nxbf5/MSiQQJhYoJhYKEw0ECgexQE9u2aWnpoL6+kf37W2hsbGX//lYSiQQAqUyaASvBQDrBQDpJIp3M3maSud5602MSLPYTKPNTEAnhjxThL/ATiPjwF/jxR3x4/ZNjrLthGNmdD78HCt/99UPsjE0qbpGKWST7rewOQf+B+7G+ONZAdgfBcRw8hge/4cNv+GhtaSXQuhO/GSDo8WMYPjwePxUVlVRXT6e6upoZM2Ywb948pk2bRmFhIaFQyKUKiIi4R+FfROQ9yGQy9PX10dvbS29vL5Zl4Tj2YMgfwLb7yWQGAAfTNAiHQxQUlBIOhwiHg/h8B35ue3tjvPHGTnbv3seePY00NbWTyaRzPfn9qQH6rQFiVpz+VBzLzgZWwzAIFvkJlgUoLS4kVDKNYHGAUEkAf8SX91Nfmh6TYGGAYOHIq78PSSfTDPQmSfQks7e9SQZ6kvT2RsmkbGzHBgf8hp+A4aM13sju/dsJeyOYpg/D8FJaWkFNTQ1z585l2bJlLFq0iOLiYl2nQEQmBYV/EZHDSCaTubDf19eXHY6SSWLbMTKZWC7sezwmkUiYwsJpRCJhwuFgLog7jkNnZw+7djWwc+c+du/eR0dHFwAD6SR9yf5syLeygT9jZ48U+CM+CqrCVFdUECkPES4LEij0Y3oUMI+FN+ClsNJLYWVk2HrHcbDiaQZ6E/R3DGSXzgHaO7rIpLIzFPnwEvIEaYnvo6H1bV5/Ywt//vMfCQbDzJgxg0WLFrF8+XJOOOEEwuHwOH1DEZEjU/gXETlIIpGgq6uL7u7u3HSbmUz/YNiP4TgWpmlQUBChuLiKSCREKDR8LHg0GmP79l1s376bXbsaiEZjOA7ErQGiqX6iyT6iyX5SdnbWnVBxgEhViLKKKiIVISIVIXwhnWx6PBmGgT/iwx/xUVx7YKyRnbaJdyWIdcTp7xygr62fzvZuWvrbwYGwJ0jEG6Gldx9vvf0mf/7zn/F6vcyePZvly5dz5plnMm/evLw/KiMiE4fCv4jkPcuy6OzspKuri4GBARwnQybTRzqdDfzg4Pf7KCkpoKiogMLC8LAhHo7jsG9fC2+8sZM339zJvn3N2LZDzIrTm4wRTfbRl+onbWeyOw6VYSpryiiqKaCwKow3oJ/iicr0mhRUhimoPNCT79gO/Z0D9DbF6N4fpbcpSlusAxwIeYIU+AroeKOFHe/s4JFHHqGsrIyVK1dy+umns3z5cgKBww9LEhFxm/7FEZG8ZNs2PT09dHZ2Eo1GB8fvx0ino7nAX1AQoqiogqKighG9+6mUxVtv7eb1199h+/ZdRKMx0naGnkQf3YleuhNRLDuNx2dSWBWhtqaSopoIhZURTO/kGrqTsWxS/SlScQsn45DJ2ETb+/H198DgVJ2O7WTn7jcPLGbuPni8HvwFPvxhH4Y5uXvBDdOgYFqYgmlhpq+oxHEcBnqSdO+P0t04uDMQ7cAACnwFFA+U0dTexN/+9jdCoRAnnHACH/jAB1ixYgXl5eXj/XVEJM8o/ItIXrEsi7a2Njo6Okin06TTcTKZXtLpKGATiYQoLa2kpKRo2Em6kL0a744de3jllTd47bW3sxftshJ0J6J0J3qJJvtxcIiUhahaVE7prCIKKyMTKuwmYykGepIkYymSfSmSsRSpmEWiL0Uqljrk1iIZS+VmyBkLhgn+iJ9AgY9AoZ9Agf/Abe6+b9i6UFlwQs9UZBgG4dIg4dIg05dXAtDfm6B9Zxede7ppatrH/v4Ggp4gxf5SWv+7lRdefIFIOMKSJUs488wzOeWUUygqKhrnbyIi+UDhX0TyQn9/P21tbXR3d2PbadLpHiyrG8exCAR8VFSUUVZWnJt+c4jjODQ0NPPCC6/xyitvEo8PELcSdMS7aR/oJpFOYnpMSmYUMrduBqV1RQQKx/dqselkhmhLjGhTjGhzjN6m7BJtipHsS737Blzk2GR3OvpS0Nz/3t5kQMG0MEU1BRTXFlBUe+A2Uh4ecR2CiSBSHCRySi2zT6klmUzTUd9FR30P3fvbaettxmP6Ke4robmnmde2vUZBpCB3jsCyZcvGu/kiMoUp/IvIlOU4Dt3d3XR3dxOLxbDtFJbVRTrdi2E4lJQUUlFRS0HByJlZ+vsHeO65rTz//Gu0tXWQTFu0x7toH+gibiXwBjyUzy9h7twZFNcWHPehPHbGIdbeT3Qo2DfHcvf7OwbG4BM8QDlQNriUA8Vk/9nwDj5/6OIAmUOW9OBtEug6aOkEet9bUxyItcWJtcVperVteCt9JoXVkewOQc3BOwaFhIonxtj6QMDL9MWV1C6uJJWy6GmJ0rG7h969vXT1dLAnVk+Jv5Tmrma2bNlCYWEhHo+HZcuWMX/+/PFuvohMMQr/IjIl9fT0sG/fPurr64Ek6XQ3mUwfXq+H6uoyKipKRwzrAWhp6eCZZ17khRdeI5Wy6Ej00B7vpDfRh+ExKZ9TzKz5tZTMLDyu025mrAwdu3pofbODljc7advRiRU/2uE4M4AFwEyGh/qDb4fuFwJu96ingR6yOwJdB90efL8DqAd2ANERW8hYNj37+ujZ1zfiuYLKMFVLy6leUkHV0nKKagrGddYdAwj4fVTVlVMxo5REIkVPS5Tu+l566rvo7GzH3xOkIliBJ+HhzjvvZNGiRVxwwQWsWLFC1xEQkTGh8C8iU0osFqOxsZGenh5SqT4SiXoMI00oFGDatBpKS4tGhCjHcXjrrd1s3Pgib721i1QmTUusnZb+Diw7TVFNAfMW1VE+t+S4jT23BtK0vd1F65sdtG7vpP2d7Hzz764EWAQsPOh2ITAfiBz+bePCC1QMLu/GAdqBtw9ZdgA7gZHDmYaOFuzauA+AUEmAqiXlVC2poGpJOaWzisdtyJDHNImEg4TnBCmvLSF+8gDR5n56dsdo3ttEf1+c/n39dA90884771BeXs4//MM/cPbZZ+vKwiJyTBT+RWRKSCQSudCfySRIJJowzXaCwXnMmDGToqKCEe+xbZsXX3ydp556jtbWDmKpAZpibXQO9GB4oXJZOTUnTDsuw0cSfUla3+ykdXsnrW920Fnfm51B57AqgbOAJRwI+AvJ9tpPvDHwx84g+50rgXMOeS4DNDB8p+A14Hmyw42yBnqS7HmuiT3PNQHgC3upXFRO9dJyqpZWUDGvFI/v+PauGwYEg36CQT8FkQgl0wtJnJxi72tN9LfEeHn/yxQFipgVnUXHf3bw2GOPcc455/CP//iPOkFYRN4XhX8RmdRs26a5uZmWlhZsO0Uq1U4mE8Xn81BdXc7ChbPxeof/1DmOwxtv7OSPf3ya5uZ2uhK9NMXaiCZjBAv9zDqjhsrF5XgD7vbyJ6JJ9v69ifpnG2l5ox3niB37s4FVwAcHl4VMzZD/fniAOYPLxQetTwIvAv81uPw3Bw8dsuJpGre00rilFcheVXnW6TXMPmsGtcunHffzOPx+L35/IQOBJKVzw5ScXEp/a5quHb1sa9rGrs5dzCydSf+GfjZv3szq1atZvXo1wWDw3TcuIjJI4V9EJq3+/n727NnDwMAAltWOZXXh83mYPr2GoqIInZ1NI96ze/d+/vjHv7F79z56EjH2RhuJpeIU1RSwePkcymYXuzo1ZzKWygX+5m3tR+jdX0Y25A8F/hmutWnqCpA9SnAOsJbsEYLXyO4IbBq8PXACcarf4p2/NfDO3xrwF/iY9YFa5pw1nZoTpx3X8zsCAT8FBSEKCsJ4vUkKa6eRik6jc0cfO+t3sr93P3UldQz8cYBnnnmGyy67jA9+8IMjdnJFREajXwoRmXQcx8n19qfTA6RSTThOipqaCioryzBNk3R6+Mmw7e1d/OEPf2Pbth3EUgPsjTbRk4hSWBXhhNMXUFw7cljQWLEzDo1bW9n59F4aXmzBTo/WxT8XuAI4l2xY1cWfxp4HWDm4fIHseQTvkN0JeAr4IxADIBWzeOdve3nnb3sJlQaZ98EZLLhgFiUzjtNQG8MgGAoQDAUYGEgCCWpPK6FqxTTatnWwc/dOGvsamd0/m9/85jc8+eSTfPSjH+WUU04Z15OaRWTiU/gXkUklmUyya9cu4vE4ltWBZXUSDgeoq5s94iq8kN1R2LjxBf74x6eJJeI0RJvoiHcTLA6weNUcyuYUuxaWrIFsT/Kbf9lFX8toc9rPBq4aXE5Gw3iON4MD50r8P8AA8Djwn8BjQPa/2UB3gtcf28nrj+1k+kmVLP3QfKafVHlcQrZpGETCQQJ+H32xfhx/gtrTKpi2ZBptr7WxY/8O9kf3M2dgDr/4xS944YUX+PSnP63zAUTksBT+RWTSiMVi7Nq1i2Syn1SqMdfbX1VVPmoQi0b7ueeeh6iv309zfzt7e5vwhj3MO3cmlYvKXRve09fWz/a/7Obtp/aMMh3nNOB/AGuAU1Hgn0hCwEcGlzjwV+BB4E9kpyWFxq1tNG5to3hGIUsvm8f8c+tcPzcEwOv1UFJcRHwgwcBAAm/Yy8yzpzPQnaT7jW7eaHqDinAFqVdS7Ny5kzVr1ugogIiMSuFfRCaF7u5u6uvrsawYyeR+gkEvs2bNJhwevbd/8+aX+e1vNxApLmR37z56kzFqlk9j1gdq8PjcCWsDvUle/X/f4q0n6nEyh47lXw38C3AJ4HPl82UshYGPDy4dwAPAj8lecwB69/fx3P/Zyqv/71us/OQS5p9f5/p5AYYBkXAQv99HrK+fdCZGsDTC9FXTqWyvZO+ze3m56WXmJ+bzi1/8gpdffpk1a9ZQWFjoartEZHJR+BeRCa+lpYXGxkbS6V6SyWYKC8PMmTMdj2dkiE+lLB544A9s3bqd1ngXfakm/AVeTrh4PsW17oQga8Di9T/u5PU/7CSdOLinPwBcA9wEnODKZ8vxUAF8kex5Ao8B68meMAzxrgT//bMtvP7YO5zyP5ZR94Ea13vbfV4PxSWFRKP9pNN94ETwVvhY+rGlND7fyPad2+mId2C9aLFr1y7+5V/+hbq6OlfbJCKThy4XKCIT2lDwT6U6SCabKCsrYt68maMG/2g0xo9//CBbtm7nrc56mpMdTFtSyklXLXYt+O99vomH/2UDW3/31kHBPwx8HdgH/AIF/6nCA3wUeAZ4iewJ2lm9jTH+9oPn+b/f3nyY8zvGlmkYFBcV4Pf7yNj92HaSZDrJ7HNns+SiJfTYPbzc/DL72/bz7//+77z22muut0lEJgeFfxGZsLq7u3PB37LaqamZxqxZtaP2rLa2drB+/a/YWd/A6x3vELVj1J1bzdwPznRlmE+yL8UzP3yJv/3geQZ6hi4k5QU+B+wCvkt2fL9MTacAjwKbyV5sLavljQ4e/V9Psf3/7n6Xi7QdO8OAosIIoVAQ2x7AtpP0x/opnl3MKZ86heC0IK+2vkpjdyM//elP2bhxo6vtEZHJQeFfRCakeDzOnj17SKd7c8G/urpi1Nfu3r2fu+/+FftaWnitbQeWz2LZFQsorA270rbGV9t45OYn2b1p30FrPwS8CfwEqHblc2UiOpvsDsCjZGdvgnQiw99/8SqP/+t/E+9OuN6CSDhIKBgY3AGw6Iv24Ql4OPGKE6mYX8H29u3s793Pb37zGx5++GEcx92dEhGZ2BT+RWTCsSyLnTt3Yln9JJPNlJUVHzb4t7V18vOf/46Wng5ea38bb6mH5R9bSKQ85ErbdmyoZ8N3nz2ot78E+DXZseALXPlMmegMskOAXgP+Obe2eVs7f177DD37ood745iJREKDQ4BiZGyL3mgveGDR6kXMPGUmu7p3satrF0888QQbNmxwvT0iMnEp/IvIhLNv3z6SyQGSyf0UFASpq6sZ9XX9/QP8n//zn3RGe3irczeFtWFO+PACAhH/mLfJsR1eevANnr1360HDOS4GXid7Uq+mVJRC4GfAE8B0AGLtcf78tU00b2t3/9MLIni9HjKZfjLpNP39/RiGwewzZrPg3AU09jXS0NvA73//e7Zu3ep6e0RkYlL4F5EJpb+/n+7ublKpNjwehzlzZow6xj+dTvMf//Ewza1tbO/cRaDEz6KL5uD1uzON5/P3vca2R94+aM0XgT8zFPJEDlgNvED2SsKQils88d3/dn0HwDCgsDCCYTjYdoJEIkE6kz0JveaEGmZ9YBZ7e/bSFmvjl7/8JQ0NDa62R0QmJoV/EZlQ9u/fTyaTIJPppaZmGl7v6DMSP/roU7z9zh7e6tyN7bNZfIl7wf/Nv+xi+192Dz4ygR8Bd5Gd/UVkNLVkpwO9FAA77fC3f3+e3qY+Vz/VY5qEQgFsJwmOTX//gZmH6k6tY9qCaezo3EFnXyc/+clPGBgYcLU9IjLxKPyLyITR09NDLBbDsloJBv2Ul5eM+rrm5nY2b36Zvb1NxDIDLP7HuQQLA660qXFLKy/cd/A0ib8A/j+ufJZMNQXAHxjaAUjFLDZ87zmSfSlXPzUUDGKaJhl7gFQqhWVZABiGwcJ/WEhBVQFvtr9JZ1cnf/3rX11ti4hMPAr/IjJhdHZ2kk7HyWTi1NRUHvZiSX/4w1PErQTN/e3MPKWKwqqIK+1JJ9Ns/ukrOPbQmq8AN7jyWTJVeYHfAssB6Gvp5+WH3nT1Ew0DwuEgjmPhOBkSyQMzDplek8WrF2Nhsb9vP0899RSdnZ2utkdEJhaFfxGZEBzHoa+vD9vux+v1UFxcMOrrduyoZ/v2XeztbcIf9lJ7YqVrbXr9jzuJdw0Fp4uA2137LJnKCoE/kj0SAG8/ucf1GYACfj8G4DhpUqnhRxqCRUFqT6xlf3Q/8WScRx991NW2iMjEctThf9OmTVx++eXU1mYvtHPoj4bjOKxbt47a2lpCoRDnnXceb7zxxrtu9+GHH2bp0qUEAgGWLl3KI488crRNE5FJrL+/n0wmQyYTGzxpcfRe/7/+dRPRZD+dAz3MOr0W0+tOH0aiN3nQCb4eYD3qL5H3bxbwVeDAzFFuMgzw+Xw4joVt27kTf4fUnVKH6TfZ07OHF154gZaWFlfbIyITx1H/S9bf38+KFSu45557Rn3+Bz/4AXfddRf33HMPL774ItXV1axevZq+vsOf5PTcc8/xyU9+kmuuuYZXX32Va665hquuuornn3/+aJsnIpNUNBrFttPYdoLCwtGH8cRicfbsaaS1v4NwSZCKBaWutafhxWbSiczgoxuBJa59luSLL5I9ERj2v9JKst/dsf8+vxfHyYZ+K2UNe84b8DLjpBm09bdhOzbbtm1ztS0iMnEcdfi/5JJL+O53v8vHPvaxEc85jsP69ev5+te/zsc+9jFOOOEEfvWrXxGPx3nooYcOu83169ezevVq1q5dy+LFi1m7di0XXHAB69evP9rmicgklUqlsO1sGIpERr9A144d9TiOQ0+yj9JZRYc9OjAWGl9tO+jRda59juSTMPAJINv77/bUn0MzZTlOhoydGfF8+ZxybMemN9HLm2+6ex6CiEwco8+h9z7V19fT0tLCRRddlFsXCAQ499xzefbZZ/nsZz876vuee+45vvjFLw5bd/HFFx8x/CeTSZLJZO5xNJodP2lZVm5mAxkbQ/VUXceeantAIpEgnU6RyWRwHId0Oj3iNW++uZO+ZJxUxqJ4ZiG244yypSzbtg/cmkfXz+E4Ds2vDYX/EuC0o3q/yOFdBPwQyO5g1p1eO+IVx/K3O4zj4NgOjmGTyWRy2x0SKA7gj/jpjHeyY8cO4vE4Pp/v/X/eJKDfXPeotu4Z65qOafgfGjNYVVU1bH1VVRV79+494vtGe8+RxiDecccd3HbbbSPWP/3004TD4aNptrxHuiS8e1RbaG5upr+/E9PsoKenFa935Bz6Gzc+y56ORgYyA/TTx0BL/yhbGq6tre1dX3OojGWTjA392J7IGP9USl47OXevu7n3iP/OvZ+/3YPZGZu+WBycfnz+IKHQyCNqdthm7969ePu83H///Uyfnh8XrdNvrntU27EXj8fHdHuu/It26KF4x3He9fD80b5n7dq13HLLLbnH0WiUmTNncv7551NeXv4+Wi2HY1kWGzZsYPXq1VO+V+h4U20P2LNnD+3t+0kmG1i8eA7B4Mh5+//yl5doT0dJeRxqp4/sMT2Ybdu0tbVRWVmJeZS9p6n4wb0s/qN6r8iRHfi79nl8VFdXj3jFsfztHsyy0gQCMTyeQkLhCAWRkTNoGe0GjZ2N1E2v47TTTuOkk0563583Geg31z2qrXvGejreMQ3/Qz9iLS0t1NTU5Na3tbWN6Nk/9H2H9n6823sCgQCBwMhw4PP59EfnEtXWPaotFBQU0NsbIZ32kkxaFBSMPOk3nc7g4ODxmpjvNt5/MDSZ5nt47SH8wYN/Gt0dly355kBvvi/oHf1v8xj+dg9mZ2wM08D0ePH5fKPuSHh9XhzHwTRNHMfJm98h/ea6R7Ude2NdzzGdt27OnDlUV1cPO+STSqV45plnOOussw77vjPPPHPEYaInnnjiiO8RkamlqKgIw/BgmkGi0dior/F6PRiYOJnDj/UfC6bHpGx28eCj14AOVz9P8snfcvcq5pW4+kkpy8Iwsjuyft/oR7DsjJ07yq7AJpIfjrrnPxaLsXPnztzj+vp6tm7dSllZGXV1ddx8883cfvvtLFiwgAULFnD77bcTDodZs2ZN7j3XXnst06dP54477gDgpptuYtWqVdx5551cccUV/OEPf+DJJ59k8+bNY/AVRWQyCIfDeDwePJ4IfX1dow79C4UC+EwvqbiFYzsYpnuz/dSuqKRrTy/gAI8D/8O1z5J88tfcvdoV7l2gznGyw35MM4TH9ODxjDyHBiAZS+Izs6E/GAy61h4RmTiOuuf/pZdeYuXKlaxcuRKAW265hZUrV/Ktb30LgC9/+cvcfPPNfO5zn+PUU0+lsbGRJ554gsLCwtw2GhoaaG5uzj0+66yz+O1vf8t9993HiSeeyP3338/vfvc7Tj/99GP9fiIySRiGQVFRER5PIZmMTU/PyGuDzJpVS1GggHQqQ6x9bE+AOtT0lQcPO/w+MHKqRJGj8yrwJwCCRX7K55S49knJwav6GoYPn//wPfo9+3soCZZgmiazZs1yrT0iMnEcdc//eeedh3OE6fUMw2DdunWsW7fusK/ZuHHjiHVXXnklV1555dE2R0SmkPLycrq7u/F4CmhubqOkpHBY7/+SJfPYuvUtvKaHnn1RCqtGvxjYWKhZVkHF/FI6dnYDrwP3kb3Yl8j74QBfGryFEz6y0LUjV44D8XgCw/BjGOZhe/QTfQni3XFmT5vNnDlzNFOeSJ7QtepFZMIoLi6msLAQn6+SZDJNe3vXsOcXLZqDYUBxoJDuhqirbTFMg9OuO+GgNV8Bdh7u5SLv4ufAkwAUVIZZcslc1z5pYCCBbdt4zCABfwCfd/Se/+693RgYlARLWLp0qWvtEZGJReFfRCaUGTNm4PEE8HpLaGnpwLIOXOyrrKyYqqoKpoVL6WuL07Pf3R2A6qUVzD5zaErRLuBDQLernylT0ZPA53OPTrv2BLz+0cfgH6tMxmZgIIFpBjEMD5FRZs2C7Im++7bsoyxUhtf0csIJJ4z6OhGZehT+RWRCCYfDlJeX4/NVYNsedu/eN+zKpKtXn015qIQif4Q9zzXh2O7O/HP2/zyZkhlD5yztAD4KuLvTIVPJS8CVDJ0zsuzy+cw+050LadmOQ7QvhoOJaQYIhoJ4zNF3Mpq2NZGMJplTOofFixdrvL9IHlH4F5EJZ8aMGQSDYQKBGcTjSfbsaco9d+qpy5gxo5rZJTOIdw7Q9nbXEbZ07PwRHxd+7UwCRUNTJT4DfBDY7+rnylTwGHAu0AvAzNOqOfUad3rYHaCvr59MxsHrKcDr8REJj97rbyUsGl5qoLqgmog/wpVXXvmuF+IUkalD4V9EJhyv18v8+fPx+yMEAjPo7e2jqSl7cSTDMPjIRy6k0B+mIlzK3r83kehLutqewqoIq9eeib9gaOz0a8DpwCuufq5MVg7wQ+AjQHZWqqql5Zx702mYHndCdn//AJaVxmNGMD1eioqLRg30juOw85mdYMHsktmcfvrpzJw505U2icjEpPAvIhNSKBRi7ty5eL0F+P2VtLZ20tjYCsCCBbM48cRFzCmZiSftYftfd5NOujsV57SFZXzo9nMPmmGoCTgD+C5gufrZMpk0ApcBNzM0s8/cD87g4m+djS901BPsvSsHiMXiJBJJTDOMafqyU+YeZrhPw4sNdOzsYGH5QgrCBXzkIx8Z8zaJyMSm8C8iE1ZRURF1dXX4fOX4/VW0tXVRX78f27b51Kc+RG1VJUvL55HqsXj7yT2uj/8vnl7Ih+44l2kLSwfXWMA3gTOBN1z9bJnoHODXwDIOvpDXiR9fxKqbTsXjG/sTfG3HIRqNkUim8JhhTNNPQWHBYWf3advRxt4X9zK7ZDbTItO48cYbKS0tHfW1IjJ1KfyLyIQ2bdo0Zs2ahd9fTiAwg56eGDt3NuD3e/nsZ6+ivLiERWVz6dnXx+7/2uf6DkCwOMAl//pBTvzYQozcL+jLwErgJqDd1c+Xieh54HzgOobG94dKg1y49gxOWbPUlfH0Gdsm2hvDsjJ4zAJMM0BRYRHBwOhz+vfs7+Htp9+muqCamcUzufLKKznxxBPHvF0iMvEp/IvIhFdRUTF4DkAxweBs4nGLHTv2EAoFueGGj1MWLmZ+aR2t27vYsWEPGct+940eA4/Pwyn/YxmX3X4uxbmZgCzgR8Bc4F+BmKttkIlgB9mZfM4geyJ41rxVM/no3Rcw89QaVz41ZaXp7Y2Rzjh4PAV4PH6KS4oJBAKjvr71rVZe/+PrlPhLmF82nw9+8INccMEFrrRNRCY+hX8RmRSKiopYvHgxwWAhweBsMhkv77yzl3A4yJo1l1FdWMHi8rn07Inyxh/fwRpwfxz+tAVlfPjfzuekTyzGGxga1hEDvg3MI7sT0OZ6O+R4ewn4NNkhPg/n1hbVRLjgq2ew6qZTCRT6D/fm9812HGL9A0SjMRzHxOspxOv1U1JSMupQH8dx2PviXnY8tYPKcCXLpi3jpBUn8alPfUqz+4jkMYV/EZk0QqEQixcvpqiolGBwNn5/JW1t3RQUhLnmmiuoKZnGCdMWkuy02PbIOyR7U663yev3sPLqJXz8Jxex+OI5GOZQqGojuxNQB9xAdoYgmbzSZIP+OcBpwP+Xobn7QyUBzvzsSXx0/YXUneZeb39PT1/uxF6PpwC/P0BJSQkez8jzCeyMzdt/e5uGFxqYXTKbheULOffcc/mf//N/jvp6EckfYz/1gIiIi/x+PwsXLqStrY3GRgPTLCCVasYwDD75yUt45JEn8Zoe3uzYxe7HG/FbIWpPmOZ6T2e4NMiZ/3QSSz80jy2/fYs9z+3HsQGSwH2DyyrgerJDRQoPuy2ZSHaRPZH3fqBh2DOBQj/LPjSfpR+ahy/ozj+ntuMQjydIJJIYhhevpwDD9BCJRAgFQ6O+J9YeY8dTOxjoGmBRxSIqI5V8/OMfZ/Xq1erxFxGFfxGZfAzDoKqqiuLiYvbs2UMs5seyOrGsDi655IM8/vhmTEy2DWxnz3830l3fy/zz6wgWjj4meiwV1xZy3i2nEWtbxva/7uLtJ/eSig8NQdo0uPwL8GHgKuAfgdFDnIyXRuD/B/wn8OyIZ0tmFLL0Q/OYt6ruoOFeY8sZDP3JZArHAdMMYZoB/L7sjD6jTeVpZ2z2vbKPhhcbiPgirKxeSUmkhBtuuIGTTz7ZlXaKyOSj8C8ik1YwGGTRokW0trbS1GTi9Zbg9XZw2WXns3nzizTtb6KorIT6tn1s/c+3mH3mdKqWlB+X3s+CyjCnXbeck65aws6NDWz/yy56m4ZOAo4Dvx1cCsjuCHyC7I7A6LO1iNuayA7r+U9g84hnDRNqV1Sx7EPzqF1R6drfkAMkEklifXH8vhAeTxCPJ4hhmkfs7e/v7GfHUzvob++nrriOuuI6Zs6cyfXXX6+LeInIMAr/IjKpGYZBdXU1ZWVlNDU10dnpxecr4x/+oZBEIkZTUw9LiufRlGhj16Z9tL/dxawzaimqLjgu7fOFvCy5ZC6L/3EO7e90s/PpBvY8u59kbOhoQAx4aHAJAB8gOzzog8BZaHiQW/YC/3XQsn3UV5XMLGTeuXXMWzWTSLl7R2gcIJlMMRBPkE5nsB0PHm8RHtNLMBgkHA5jmiNP07MGLBpebqB5WzMhT4iVNSspChZxySWXcOmll+L16p95ERlOvwoiMiX4/X5mz55NVVUVjY2N2LbJtGlL+Id/mMmmTZtJvJ6isDBCc2c72x59h7LZxcw6vZZw6fHpaTcMg8qFZVQuLOOM/+dEmre1U/9sI3tfaCKV2xFIciCMQnZOhpVkdwSGlmnHpb1TiwO8RbaumwZvGw776uIZhcw5azpzzppOycwiV1tmOw6JRJJEIoVt2xiGD48nDE6CQCBIYUHhqCfoZqwMja82sn/LfkjDrKJZTC+azvTa6XzmM59h1qxZrrZbRCYvhX8RmVJCoRDz58+nvLycl156ieLi+Xz4w7NZtGgrTz31FB7LQ9w7QGtDJ1v3bqdyUTkzT60mUDD2UzMejuk1mb6yiukrqzjzn06ieVsbe55rouWNDvpa+w96pU32AmIvA+sH1y0muxOwiuyRgdlo4rZDDZC94vLBPfsdh3214TGomFtC7YpK5pw9g5KZha4PDUtnbBIDg2P6AdPwZ4f3GCZej5dIQYSiwqIRvf12xqZ1eyt7X9xLeiBNbWEtM4tmEg6GWb16NZdeeik+3+hX+BURAYV/EZmiCgoKmDFjBvPnz6e7u5ulS89g4cKT2bLlv9m0aRNBO0jU7qP9rW7a3+mmclEZNcunHbcjAUM8PpMZJ1cz4+RqAPo7B2jd3knr9g5a3+ykuyF6yDveGlx+Mfg4CMwHFh6yLALKgak6u0uGbO/922QvtvX2QUsD2d7+0Xn8HioXlVG1pJyqJeVMW1jm2mw9B3OAVNIikUxiWWnAxDSDeIwAGAYBf4BQOITH9NAb7R323oyVoXV7K42vNZLoTVAZqWRW7SzC/jDnnHMOl112GSUlJa5/BxGZ/BT+RWRKKyoqory8nEQiQVtbG37/BaxYcTbPP7+RZ5/dTOFAAZ2pblpe76D59XbKZhVTe+I0ime43/s7mkh5iLnnzGDuOTMASPalaH2rM7tD8GYHHbt7cDIHB9sE8PrgcqhSRu4ULARmACVM/H8CEmR77OsZHu7fBnYC7+06Dv6Ij6rF5VQtLadqaQXlc0rw+I7f0RIrnSGZTA3O3ONg4MVjhjFMP6ZhEgwGCYaCuRl8bPvAFaoT0QRN25poebOFTCpDRbiCpTVLifgjnHzyyXzkIx+hqqrquH0XEZn8Jvovv4jImAgGg9TV1TF9+nTa29spKCjg1FM/yObNz/Dyy88zLRmjJ9VL554e2uu7KSgPM31FJdMWlB3XoHioQKGfutNqchePshJp2t/ppvXNDrrqe+ltjtHXEsNOj9bT3Q08P7iMpgQoG1zKR7l/6Lpisv9seAHPIYtJtm/bJtsrP7SkB2+TQNdBS+co9w9dN3B0xQL8YR9FtQUU1xYwbWG2d7+0ruigi68dH+lMhmTSIpVMkbFtsr38AUzTj2GYeDweQqEQwUBwxE6m4zjE2+Nsf3M7XfVdeAwPNQU11E6rJeANsGTJEj784Q8zd+7c4/qdRGRqUPgXkbzi8Xiorq6mqqqKaDRKbW0tq1adz5YtW3jxxeco6+4gZvXS3tXF9id3s3PzPioXlFK9dBqFleFxv0iSL+ildvk0apcfOPHXztjE2uNEm2L0NsWINsdy9/s7jhSgewaX3e42eoyZXpOimkg25NcU5MJ+UW0hwSL/uPw3cgDLSmOlLFKWRSZjAwam4cNj+jFML8bg0J5AMIDP58M4ZEhWKp6i7e02Wre30trQyrSSacwvnU9lQSUBX4DTTz+dCy64gOnTpx/37yciU4fCv4jkJcMwKC4upri4mFmzZrFw4UIuuOACXn75ZV544XkaGupJpPvpTHbQuq2T/a+1Ei4JUrmonOolFYSLJ858/KbHpKi6gKLqAmYcci2ndDJNtKWf6OBOQW9TjIGeJKlYimQsRbIvRbLfOtIQ+ePK9BoECvwECv3Z2wI/kYrQgaA/vYBIeRjTM/7nMtiOQyplkUpZWFYax3EAE9Pw5gI/ZGeiCgQCBPyBETsmGStD555O2na00d3QjYFBWbCMumAdS6qXUFpaynnnnceqVasoLNS0ryJy7BT+RSTveTweKioqqKioYN68eVx44YW8/vrrbNq0ie3btzPdShBN9dDV38ne55uo/3sjhZVhpi0oZdq8MiKlYcb5gMBheQNeymYVUzar+LCvcWyHVNzK7gjEUiRjB90/aJ3Vb2HbDnbGJplI4vP6wAHbdnBsBwMwTGPUxeM1CRT68Bf4CRb68Q8G+2zI9+XuewOecT+6cjiOA1Y6TTqdJpXK3gIYeDHMAKbpwzCy4/Z9Pl8u8B86Y0/GytCzv4f2d9rprO8kk85QFChiful8pkWmYWKSKkpx/fXXc8YZZ2iufhEZU/pFERE5iM/no6qqiqqqKs4991xaW1t59tlnee6559izZw+2k6En2Ul3Txd7nm1i9383EizxU1pXRNnsEkqnF+HzezEnaIAdjWEauV7298J2HFpaWqiurp5U3/No2Y5D2spgpdNY1oGwDwaGMXjSruEDw8A0TPx+P36/H5/fh2kMD/yJaIKuPV107e2ip7EHO2NT4C+grqCOaZFpBL1BSktLOeOMMzj11FN5+eWXOf300xX8RWTM6VdFROQwvF4v06dP5xOf+ARXXnkle/fuZfPmzbzwwgvs378f27HpTfXQm+im4/Uoza914PGbFNZGBncGiglGAni9Xjwec8pOujkVOEAmkyGdHlysNOlMZvBZE8PwYpphDMOT6933er25wO/1eoeN4bczNtGWKF17u+ja00W8O45pmBQHiplTNIeyUBkhX4hIJMIpp5zCaaedxoIFCzAMA8uyRjZQRGSMKPyLiLwHhmEwe/ZsZs+ezac//Wn27NnD3//+d7Zu3cru3btJp9PE03F6U930NvayZ28ze/6riVCZn0hlmILKEIU1hYQKA3i9HrweDx6PZ8IOF5rKHCc7G08mnSE9GPgz6fRBpz0MjdsPYBheGOzF93q8eH1efD4fPp8vNzUnZMN+X1sfvc299Db1Em2Okk6l8Xv8lIXKmD1tNqXBUjymh9LSUpYvX86KFStYsmTJqFfwFRFxi8K/iMj7MLQjcPXVV9PX18err77KSy+9xLZt2+jr6yORStBr9RLr76PvnT463ooCLQSKfEQqg0QqQ0Qqw4SLg3g8HjxeE9M08Xo8mB5zSg+nOV5sxyGTsclkMtgZO3f/QI8+GHjA8GCYIUw8GKaHoQujeb0Hgr7P6xs2dj9jZehu7M4G/aYo0dYodsbGY3oo8hcxIzyD0rJSCvwFmKbJ3LlzWb58OcuXL2f69OkT9rwGEZn6FP5FRI5RYWEh55xzDueccw6ZTIZdu3bx6quv8sorr7B///7sUYFUnGgySiwVI7YnRveuThynA1/YQ6g8QKjUT6gsQKgsgDfkze4QmCYeT3ZOeNNj4jFN7RgcwnayJyBn7ENCvm0Pu1hWduiOiYEX0wwMG74D2ZO+vV5vbvF5fbmAnrEyxFpjxDpixNqzt/0d/TiOg8/0URzMDuUpChRR4C/AMAwKCwtZtGgRJ554IsuWLaOgoOA4V0ZEZHQK/yIiY8jj8bBw4UIWLlzIJz7xCfr7+9m5cyc7d+5kx44d7N69m1QqRSKVoCfRQzQRJd4ap6sxTtqJAg7egEmwLEiwNEC41E+wzI+/wDvsQlUeM3ukwBzaITCNA4+NwVl2jENnkp8cHLIXunJsJxfubcfO3toO9mCwzwwL9wAGBma2J9/w4jGH7psM9eYbGHi8w4O+15Odg99xHKwBi/6Wfvo7+nNBf6BnAMdxMA2TsC9Mgb+AmtIaioPFhLwhDMOgvLycBQsWMH/+fBYsWEBVVZV690VkQlL4FxFxUSQSYcWKFaxYsQKAZDJJfX0977zzDjt37mT37t0MDAzkjg7EkjH6kn3EOmNEW+N02D1AdkYef6EvOzVmkY9AkT/7uMiHJ2BgGKNP1G8Y2Z0Ac/DWMA+9b4IBpmEO7jDk3nng/xpDa7J3bMfOBnPbzo2Hd4ZGzDsHXzIge89xGAzydjbUHxTsh+47zkGPncNddMAcDPJDJ+Ca2TYZ5mDoPxC2s0OovJiekbe2ZTPQO0CsO8ZA7wADPdkl3hMnnczO6OMxPRT4Cij1lzKzbCYRf4SwL5ytk2FQU1OTC/oLFiygtLT0Pf09iIiMN4V/EZHjKBAIsHjxYhYvXgxke7jb2trYt28fDQ0NNDQ0sG/fPmKxGI7jkEglskcHUnHiVpx4R5y+lgE6Mj25kOzxeQgUBfAX+PFFvPjDXnxhH96wF3/EgzfowTYGA3rGAccG7MFofmjv+btzbIdoXz9+f3TY0Yj3bmjmo6HAPhTiD+yoZPc4BtcdEuyBA0c5BhePmT2B2jRNyECqP0WyJ0k8Fs/ejyVJ9CUY6BkgGUvmtuMzfYR8IcK+MOWhckJFISK+CEFvEMMwcjM+zZw5k5kzZ1JXV8f06dMJBALv43uLiIw/hX8RkXFkGEbuugKnnnoqkN0h6Onpye0Q7N+/n9bWVtra2nJzzduOzYA1QH+yn36rn3gqzkD7APGWAXoyKTL24EmtDjiGgy/owxfx4Qv78IV8eAIePP7s4vV78fhNTL+RW2d6jMMOW7ENG5wYpicyYj77Q77cgbujBPhhL+XAkYiDj0o4joOTdrAtGyc1OATIyl5kLJ1Mk06msQYskv1DVy1Okklnhm3X7/Hj9/gJeoMU+YoIVYQIebOLz+PLvbasrIyqqipqampyQb+mpkaz8YjIlKLwLyIywRiGQWlpKaWlpZx44om59Y7j0NXVRVtbG62trcOWzs7OYcNlrIxFKpMimUmSTCdJZVIk0gkSPQlSnSkSmQSWbeV2EobeO3RrmAbegPeQHQQPnoAHDOjpiWG0Dk53aZI7AmCa5mCH/mDQH2rSQSN5cmciOGA4B06qHQrz6USadCp7P2MdCPIHMw0Tr+nNLQFPgAJvAYHCAH6Pn4A3QMCTvX/wTkwkEsntbB28TJs2Db//vV3kTERkMnMl/Pf19fHNb36TRx55hLa2NlauXMkPf/hDTjvttFFfv3HjRs4///wR67dv3547NC4iku+GTiwtLy9nyZIlw56zLIvu7m66u7vp6enJ3T/4cTQaHbFNx3FI2+kjLlbayobxwce2bZPqTTHQM4CBgTP4P9n/HRy3P5j2DQ4cQciegGwMWz90axomPtNH0AxmA73Hi7fAOyzgez1evEb2/sFz7A8JBAK5nabS0lJKSkqGPS4tLSUSiYz1fxYRkUnFlfB/44038vrrr/PAAw9QW1vLgw8+yIUXXsibb77J9OnTD/u+HTt2UFRUlHs8bdo0N5onIjLl+Hw+KisrqaysPOxr0uk0vb29RKNR4vH4iKW/v5+BgYHc/aH1AwMDw7Zj2zYNVgN1NXXD5r4fy+8SiUQIhUKEw2EikQjhcPiwS0FBAaWlpQSDwTFvi4jIVDPm4X9gYICHH36YP/zhD6xatQqAdevW8eijj/Kzn/2M7373u4d9b2VlJSUlJWPdJBERIXvRqqEjB0fDtm0SiURuZyCRSPC3v/2NVatW4fV6c1NvHrpAtrf/0JNzD16Gng8EArmQ7/VqRKqIiFvG/Bc2nU6TyWRG9MCEQiE2b958xPeuXLmSRCLB0qVL+cY3vjHqUKAhyWSSZPLAjA1Dh7Mty8KyrGP4BnKooXqqrmNPtXWPaju2fD4fxcXFFBcXY1kWNTU1zJ49G5/P9+5vPgqO4+T9fzP97bpHtXWPauuesa6p4Rx+QuX37ayzzsLv9/PQQw9RVVXFb37zG6699loWLFjAjh07Rrx+x44dbNq0iVNOOYVkMskDDzzAvffey8aNG3NHDw61bt06brvtthHrH3roIcLh8Fh/JRERERGR4y4ej7NmzRp6e3uHDY9/v1wJ/7t27eKGG25g06ZNeDweTj75ZBYuXMgrr7zCm2+++Z62cfnll2MYBo899tioz4/W8z9z5kyam5uP+pC2HJllWWzYsIHVq1ePeS9fvlNt3aPauke1dZfq6x7V1j2qrXs6OzupqakZs/DvysDKefPm8cwzz9Df3080GqWmpoZPfvKTzJkz5z1v44wzzuDBBx887POBQGDUi6z4fD790blEtXWPause1dY9qq27VF/3qLbuUW3H3ljXc+ynaThIJBKhpqaG7u5uHn/8ca644or3/N4tW7ZQU1PjYutERERERPKLKz3/jz/+OI7jsGjRInbu3Mmtt97KokWL+MxnPgPA2rVraWxs5Ne//jUA69evZ/bs2SxbtoxUKsWDDz7Iww8/zMMPP+xG80RERERE8pIr4b+3t5e1a9eyf/9+ysrK+PjHP873vve93GGL5uZmGhoacq9PpVJ86UtforGxkVAoxLJly/jzn//MpZde6kbzRERERETykivh/6qrruKqq6467PP333//sMdf/vKX+fKXv+xGU0REREREZJCrY/5FRERERGTiUPgXEREREckTCv8iIiIiInlC4V9EREREJE8o/IuIiIiI5AmFfxERERGRPKHwLyIiIiKSJxT+RURERETyhMK/iIiIiEieUPgXEREREckTCv8iIiIiInlC4V9EREREJE8o/IuIiIiI5AmFfxERERGRPKHwLyIiIiKSJxT+RURERETyhMK/iIiIiEieUPgXEREREckTCv8iIiIiInlC4V9EREREJE8o/IuIiIiI5AmFfxERERGRPKHwLyIiIiKSJxT+RURERETyhMK/iIiIiEieUPgXEREREckTCv8iIiIiInlC4V9EREREJE8o/IuIiIiI5AmFfxERERGRPKHwLyIiIiKSJxT+RURERETyhCvhv6+vj5tvvplZs2YRCoU466yzePHFF4/4nmeeeYZTTjmFYDDI3Llzuffee91omoiIiIhI3nIl/N94441s2LCBBx54gG3btnHRRRdx4YUX0tjYOOrr6+vrufTSS/ngBz/Ili1b+NrXvsYXvvAFHn74YTeaJyIiIiKSl8Y8/A8MDPDwww/zgx/8gFWrVjF//nzWrVvHnDlz+NnPfjbqe+69917q6upYv349S5Ys4cYbb+SGG27g3//938e6eSIiIiIiecs71htMp9NkMhmCweCw9aFQiM2bN4/6nueee46LLrpo2LqLL76YX/7yl1iWhc/nG/GeZDJJMpnMPY5GowBYloVlWcf6NeQgQ/VUXceeause1dY9qq27VF/3qLbuUW3dM9Y1NRzHccZ0i8BZZ52F3+/noYceoqqqit/85jdce+21LFiwgB07dox4/cKFC7n++uv52te+llv37LPPcvbZZ9PU1ERNTc2I96xbt47bbrttxPqHHnqIcDg8tl9IRERERGQcxONx1qxZQ29vL0VFRce8vTHv+Qd44IEHuOGGG5g+fToej4eTTz6ZNWvW8Morrxz2PYZhDHs8tE9y6Poha9eu5ZZbbsk9jkajzJw5k/PPP5/y8vIx+BYyxLIsNmzYwOrVq0c9CiPvn2rrHtXWPaqtu1Rf96i27lFt3dPZ2Tmm23Ml/M+bN49nnnmG/v5+otEoNTU1fPKTn2TOnDmjvr66upqWlpZh69ra2vB6vYcN8oFAgEAgMGK9z+fTH51LVFv3qLbuUW3do9q6S/V1j2rrHtV27I11PV2d5z8SiVBTU0N3dzePP/44V1xxxaivO/PMM9mwYcOwdU888QSnnnqq/oBERERERMaIK+H/8ccf5//+3/9LfX09GzZs4Pzzz2fRokV85jOfAbJDdq699trc6//5n/+ZvXv3csstt7B9+3b+4z/+g1/+8pd86UtfcqN5IiIiIiJ5yZXw39vby+c//3kWL17MtddeyznnnMMTTzyR68Vvbm6moaEh9/o5c+bwl7/8hY0bN3LSSSfxne98hx/96Ed8/OMfd6N5IiIiIiJ5yZUx/1dddRVXXXXVYZ+///77R6w799xzj3hCsIiIiIiIHBtXx/yLiIiIiMjEofAvIiIiIpInFP5FRERERPKEwr+IiIiISJ5Q+BcRERERyRMK/yIiIiIieULhX0REREQkTyj8i4iIiIjkCYV/EREREZE8ofAvIiIiIpInFP5FRERERPKEwr+IiIiISJ5Q+BcRERERyRMK/yIiIiIieULhX0REREQkTyj8i4iIiIjkCYV/EREREZE8ofAvIiIiIpInFP5FRERERPKEwr+IiIiISJ5Q+BcRERERyRMK/yIiIiIieULhX0REREQkTyj8i4iIiIjkCYV/EREREZE8ofAvIiIiIpInFP5FRERERPKEwr+IiIiISJ5Q+BcRERERyRMK/yIiIiIieULhX0REREQkTyj8i4iIiIjkCYV/EREREZE8MebhP51O841vfIM5c+YQCoWYO3cu//qv/4pt24d9z8aNGzEMY8Ty1ltvjXXzRERERETylnesN3jnnXdy77338qtf/Yply5bx0ksv8ZnPfIbi4mJuuummI753x44dFBUV5R5PmzZtrJsnIiIiIpK3xjz8P/fcc1xxxRVcdtllAMyePZvf/OY3vPTSS+/63srKSkpKSsa6SSIiIiIiggvh/5xzzuHee+/l7bffZuHChbz66qts3ryZ9evXv+t7V65cSSKRYOnSpXzjG9/g/PPPP+xrk8kkyWQy9zgajQJgWRaWZR3z95ADhuqpuo491dY9qq17VFt3qb7uUW3do9q6Z6xrajiO44zlBh3H4Wtf+xp33nknHo+HTCbD9773PdauXXvY9+zYsYNNmzZxyimnkEwmeeCBB7j33nvZuHEjq1atGvU969at47bbbhux/qGHHiIcDo/Z9xERERERGS/xeJw1a9bQ29s7bHj8+zXm4f+3v/0tt956K//2b//GsmXL2Lp1KzfffDN33XUX11133XvezuWXX45hGDz22GOjPj9az//MmTNpbm6mvLz8mL+HHGBZFhs2bGD16tX4fL7xbs6Uotq6R7V1j2rrLtXXPaqte1Rb93R2dlJTUzNm4X/Mh/3ceuutfPWrX+Xqq68GYPny5ezdu5c77rjjqML/GWecwYMPPnjY5wOBAIFAYMR6n8+nPzqXqLbuUW3do9q6R7V1l+rrHtXWPart2Bvreo75VJ/xeBzTHL5Zj8dzxKk+R7NlyxZqamrGsmkiIiIiInltzHv+L7/8cr73ve9RV1fHsmXL2LJlC3fddRc33HBD7jVr166lsbGRX//61wCsX7+e2bNns2zZMlKpFA8++CAPP/wwDz/88Fg3T0REREQkb415+P/xj3/MN7/5TT73uc/R1tZGbW0tn/3sZ/nWt76Ve01zczMNDQ25x6lUii996Us0NjYSCoVYtmwZf/7zn7n00kvHunkiIiIiInlrzMN/YWEh69evP+LUnvfff/+wx1/+8pf58pe/PNZNERERERGRg4z5mH8REREREZmYFP5FRERERPKEwr+IiIiISJ5Q+BcRERERyRMK/yIiIiIieULhX0REREQkTyj8i4iIiIjkCYV/EREREZE8ofAvIiIiIpInFP5FRERERPKEwr+IiIiISJ5Q+BcRERERyRMK/yIiIiIieULhX0REREQkTyj8i4iIiIjkCYV/EREREZE84R3vBowVx3EA6Ovrw+fzjXNrphbLsojH40SjUdV2jKm27lFt3aPaukv1dY9q6x7V1j19fX3Agax7rKZM+O/s7ARgzpw549wSEREREZGx1dnZSXFx8TFvZ8qE/7KyMgAaGhrGpDByQDQaZebMmezbt4+ioqLxbs6Uotq6R7V1j2rrLtXXPaqte1Rb9/T29lJXV5fLusdqyoR/08yevlBcXKw/OpcUFRWpti5Rbd2j2rpHtXWX6use1dY9qq17hrLuMW9nTLYiIiIiIiITnsK/iIiIiEiemDLhPxAI8O1vf5tAIDDeTZlyVFv3qLbuUW3do9q6S/V1j2rrHtXWPWNdW8MZq3mDRERERERkQpsyPf8iIiIiInJkCv8iIiIiInlC4V9EREREJE8o/IuIiIiI5AmFfxERERGRPDHpw39jYyOf/vSnKS8vJxwOc9JJJ/Hyyy+Pd7OmhNmzZ2MYxojl85///Hg3bdJLp9N84xvfYM6cOYRCIebOncu//uu/Ytv2eDdtSujr6+Pmm29m1qxZhEIhzjrrLF588cXxbtaks2nTJi6//HJqa2sxDINHH3102POO47Bu3Tpqa2sJhUKcd955vPHGG+PT2Enm3Wr7+9//nosvvpiKigoMw2Dr1q3j0s7J6kj1tSyLr3zlKyxfvpxIJEJtbS3XXnstTU1N49fgSeTd/nbXrVvH4sWLiUQilJaWcuGFF/L888+PT2MnmXer7cE++9nPYhgG69evP+rPmdThv7u7m7PPPhufz8df//pX3nzzTf73//7flJSUjHfTpoQXX3yR5ubm3LJhwwYAPvGJT4xzyya/O++8k3vvvZd77rmH7du384Mf/IB/+7d/48c//vF4N21KuPHGG9mwYQMPPPAA27Zt46KLLuLCCy+ksbFxvJs2qfT397NixQruueeeUZ//wQ9+wF133cU999zDiy++SHV1NatXr6avr+84t3Tyebfa9vf3c/bZZ/P973//OLdsajhSfePxOK+88grf/OY3eeWVV/j973/P22+/zYc//OFxaOnk825/uwsXLuSee+5h27ZtbN68mdmzZ3PRRRfR3t5+nFs6+bxbbYc8+uijPP/889TW1r6/D3Imsa985SvOOeecM97NyBs33XSTM2/ePMe27fFuyqR32WWXOTfccMOwdR/72MecT3/60+PUoqkjHo87Ho/H+dOf/jRs/YoVK5yvf/3r49SqyQ9wHnnkkdxj27ad6upq5/vf/35uXSKRcIqLi5177713HFo4eR1a24PV19c7gLNly5bj2qap5Ej1HfLCCy84gLN3797j06gp4r3Utre31wGcJ5988vg0aoo4XG3379/vTJ8+3Xn99dedWbNmOXffffdRb3tS9/w/9thjnHrqqXziE5+gsrKSlStX8otf/GK8mzUlpVIpHnzwQW644QYMwxjv5kx655xzDk899RRvv/02AK+++iqbN2/m0ksvHeeWTX7pdJpMJkMwGBy2PhQKsXnz5nFq1dRTX19PS0sLF110UW5dIBDg3HPP5dlnnx3Hlokcvd7eXgzD0MiBMZZKpfj5z39OcXExK1asGO/mTHq2bXPNNddw6623smzZsve9nUkd/nfv3s3PfvYzFixYwOOPP84///M/84UvfIFf//rX4920KefRRx+lp6eH66+/frybMiV85Stf4VOf+hSLFy/G5/OxcuVKbr75Zj71qU+Nd9MmvcLCQs4880y+853v0NTURCaT4cEHH+T555+nubl5vJs3ZbS0tABQVVU1bH1VVVXuOZHJIJFI8NWvfpU1a9ZQVFQ03s2ZEv70pz9RUFBAMBjk7rvvZsOGDVRUVIx3sya9O++8E6/Xyxe+8IVj2o53jNozLmzb5tRTT+X2228HYOXKlbzxxhv87Gc/49prrx3n1k0tv/zlL7nkkkve//gyGeZ3v/sdDz74IA899BDLli1j69at3HzzzdTW1nLdddeNd/MmvQceeIAbbriB6dOn4/F4OPnkk1mzZg2vvPLKeDdtyjn0SKDjODo6KJOGZVlcffXV2LbNT3/60/FuzpRx/vnns3XrVjo6OvjFL37BVVddxfPPP09lZeV4N23Sevnll/nhD3/IK6+8csy/sZO657+mpoalS5cOW7dkyRIaGhrGqUVT0969e3nyySe58cYbx7spU8att97KV7/6Va6++mqWL1/ONddcwxe/+EXuuOOO8W7alDBv3jyeeeYZYrEY+/bt44UXXsCyLObMmTPeTZsyqqurAUb08re1tY04GiAyEVmWxVVXXUV9fT0bNmxQr/8YikQizJ8/nzPOOINf/vKXeL1efvnLX453sya1//qv/6KtrY26ujq8Xi9er5e9e/fyv/7X/2L27NlHta1JHf7PPvtsduzYMWzd22+/zaxZs8apRVPTfffdR2VlJZdddtl4N2XKiMfjmObw//fzeDya6nOMRSIRampq6O7u5vHHH+eKK64Y7yZNGXPmzKG6ujo3Cxhkx/c+88wznHXWWePYMpF3NxT833nnHZ588knKy8vHu0lTmuM4JJPJ8W7GpHbNNdfw2muvsXXr1txSW1vLrbfeyuOPP35U25rUw36++MUvctZZZ3H77bdz1VVX8cILL/Dzn/+cn//85+PdtCnDtm3uu+8+rrvuOrzeSf3nMqFcfvnlfO9736Ouro5ly5axZcsW7rrrLm644YbxbtqU8Pjjj+M4DosWLWLnzp3ceuutLFq0iM985jPj3bRJJRaLsXPnztzj+vp6tm7dSllZGXV1ddx8883cfvvtLFiwgAULFnD77bcTDodZs2bNOLZ6cni32nZ1ddHQ0JCbe36oo6u6ujp31EUO70j1ra2t5corr+SVV17hT3/6E5lMJncEq6ysDL/fP17NnhSOVNvy8nK+973v8eEPf5iamho6Ozv56U9/yv79+zVN+Hvwbr8Lh+6k+nw+qqurWbRo0dF90DHORDTu/vjHPzonnHCCEwgEnMWLFzs///nPx7tJU8rjjz/uAM6OHTvGuylTSjQadW666Sanrq7OCQaDzty5c52vf/3rTjKZHO+mTQm/+93vnLlz5zp+v9+prq52Pv/5zzs9PT3j3axJ5+mnn3aAEct1113nOE52us9vf/vbTnV1tRMIBJxVq1Y527ZtG99GTxLvVtv77rtv1Oe//e1vj2u7J4sj1Xdo+tTRlqeffnq8mz7hHam2AwMDzkc/+lGntrbW8fv9Tk1NjfPhD3/YeeGFF8a72ZPCu/0uHOr9TvVpOI7jHN3ugoiIiIiITEaTesy/iIiIiIi8dwr/IiIiIiJ5QuFfRERERCRPKPyLiIiIiOQJhX8RERERkTyh8C8iIiIikicU/kVERERE8oTCv4iIiIhInlD4FxERERHJEwr/IiIiIiJ5QuFfRERERCRP/P8BzLjLUuP3/44AAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P5 = multivariate_multiply((10,10), P2, (10.1, 9.97), P2)\n", "plot_covariance_ellipse((10, 10), P2, ec='k', fc='y', alpha=0.2)\n", "plot_covariance_ellipse((10.1, 9.97), P2, ec='k', fc='g', alpha=0.6)\n", "plot_covariance_ellipse(P5[0], P5[1], ec='k', fc='b')\n", "plt.xlim(6, 14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hidden Variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can already see why a multivariate Kalman filter can perform better than a univariate one. Correlations between variables can significantly improve our estimates. We can take this much further. **This section contains the key insight to this chapter, so read carefully**.\n", "\n", "Let's say we are tracking an aircraft and we get the following data for the $x$ and $y$ coordinates 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", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_position_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that the aircraft is flying in a straight line and we know that aircraft cannot turn on a dime. The most reasonable guess is that at $t$=4 the aircraft is at (4,4). I will depict that with a green arrow." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_position_prediction_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You made this inference because you *inferred* a constant velocity for the airplane. The reasonable\n", "assumption is that the aircraft is moving one unit each in *x* and *y* per time step.\n", "\n", "Think back to the **g-h Filter** chapter when we were trying to improve the weight predictions of a noisy scale. We incorporated *weight gain* into the equations because it allowed us to make a better prediction of the weight the next day. The g-h filter uses the $g$ parameter to scale the amount of significance given to the current weight measurement, and the $h$ parameter scaled the amount of significance given to the weight gain.\n", "\n", "We are going to do the same thing with our Kalman filter. After all, the Kalman filter is a form of a g-h filter. In this case we are tracking an airplane, so instead of weight and weight gain we need to track position and velocity. Weight gain is the *derivative* of weight, and of course velocity is the derivative of position. It's impossible to plot and understand the 4D chart that would be needed to plot *x* and *y* and their respective velocities so let's do it for $x$, knowing that the math generalizes to more dimensions.\n", "\n", "At time 1 we might be fairly certain about the position (x=0) but have no idea about the velocity. We can plot that with a covariance matrix like this. The narrower width expresses our relative certainty about position, and the tall height expresses our lack of knowledge about velocity." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, position and velocity are correlated. If the velocity is 5 m/s, then in 1 second the position will be 5 m. If the velocity is -10 m/s then in 1 second the position will be -10 m. Let's visualize this with a velocity covariance drawn on the diagonal. " ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this point the velocity covariance doesn't help us. We can't predict a new position because we have no idea what the velocity is. But after one second we get a position update of x=5." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It won't be clear until the next chapter how I calculate what I'm about to say. Ignore the calculation, and think about what this implies. We have no easy way to say where the object really is because we are so uncertain about the velocity. Hence the ellipse stretches very far in the x-axis. Our uncertainty in velocity of course means it is also very spread in the y-axis. But as I said in the last paragraph, position is correlated to velocity. If the velocity is 5 m/s the next position would be 5, and if the velocity is 10 the next position would be 10. They are very correlated, so the ellipse must be very narrow. \n", "\n", "This superposition of the two covariances is where the magic happens. The only reasonable estimate at time t=1 (where position=5) is roughly the intersection between the velocity covariance and measurement covariance! More exactly, we can use the math from the last section and multiply the two covariances together. From a Bayesian point of view we multiply the prior with the probability of the evidence (the *likelihood*) to get the posterior. If we multiply the position covariance with the velocity covariance using the Bayesian equations we get this result:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mkf_internal.show_x_error_chart(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The new covariance (the posterior) lies at the intersection of the position covariance and the velocity covariance. It is slightly tilted, showing that there is some correlation between the position and velocity. Far more importantly, it is much smaller than either the position or velocity covariances. In the previous chapter our variance would get smaller each time we performed an `update()` because the previous estimate was multiplied by the new measurement. The same happens here. However, here the improvement is markedly better. This is because we are using two different pieces of information which are nevertheless correlated. Knowing the velocity approximately and their correlation and the position approximately allows us to make a very accurate estimate. It is not easy to see in this diagram, but the uncertainty in position has become smaller. We know this because the new covariance doesn't reach as far in the x-axis as the measurement covariance at t=1. So we are not just more certain about velocity, but we are also more certain about the position than we would be if we only used position measurement without considering the velocity!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a key point, so read carefully! The radar is only detecting the position of the aircraft. This is called an *observed variable*. Based on the position estimates we can compute velocity. We call the velocity a *hidden variable*. Hidden means what it sounds like - there is no sensor that is measuring velocity, thus its value is hidden from us. We are able to use the correlation between position and velocity to infer its value very accurately.\n", "\n", "To round out the terminology there are also *unobserved variables*. For example, the aircraft's state includes things such as as heading, engine RPM, weight, color, the first name of the pilot, and so on. We cannot sense these directly using the position sensor so they are not *observed*. There is no way to *infer* them from the sensor measurements and correlations (red planes don't go faster than white planes), so they are not *hidden*. Instead, they are *unobservable*. If you include an unobserved variable in your filter state the estimate for that variable will be nonsense." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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 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 measurement of the position is not in the direction of the 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. \n", "\n", "It is important to understand that we are taking advantage of the fact that velocity and position are correlated. We get a rough estimate of velocity from the distance and time between two measurements, and use Bayes theorem to produce very accurate estimates after only a few observations. Please reread this section if you have any doubts. If you do not understand this you will quickly find it impossible to reason about what you will learn in the following chapters.\n", "\n", "The effect of including velocity appears to me minor if only care about the position. But this is only after one update. In the next chapter we will see what a dramatic increase in certainty we have after multiple updates. The measurment variance will be large, but the estimated position variance will be small. Each time you intersect the velocity covariance with position it gets narrower on the x-axis, hence the variance is also smaller each time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Higher Dimensions\n", "\n", "So far I have shown you two dimensional Gaussians, but the math does not limit you to two dimensions. In later chapters we will be working in 9, or even 12 dimensions. If you work in areas such as weather prediction, you can end up with thousands of dimensions.\n", "\n", "What do these higher dimensions 'look like? Well, a two dimensional Gaussian can be represented by an error ellipse, so it stands to reason a three dimensional Gaussian could be represented by a 3D error ellipsoid. We won't delve into the math here, but this turns out to be true. `FilterPy` provides a function to plot this ellipse.\n", "\n", "First, let's make some noisy data with a given covariance, just so we can plot it inside the ellipsoid." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "from filterpy.stats import plot_3d_covariance\n", "\n", "mu = [0.3, 5., 10.]\n", "C = np.array([[1.0, .03, .2],\n", " [.03, 4.0, .0],\n", " [.2, .0, 16.1]])\n", "\n", "sample = np.random.multivariate_normal(mu, C, size=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we plot the ellipsoid with the `FilterPy` function `plot_3d_covariance`, and then scatter plot the samples." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plot_3d_covariance(mu, C, alpha=.4, std=3, limit_xyz=True)\n", "ax.scatter(sample[:, 0], sample[:, 1], zs=sample[:, 2],);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Theory states that roughly 99% of a distribution will fall within 3 standard deviations, and this appears to be the case.\n", "\n", "Nine dimensions? I haven't quite figured out how to plot a 9D ellipsoid on a 2D screen, so there will be no graphs. The concept is the same; the standard deviation error of the distribution can be described by a 9D ellipsoid." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "We have taken advantage of the geometry and correlations of the system to produce a very accurate estimate. The math does not care whether we are working with two positions, or a position and a correlated velocity, or if these are spatial dimensions. If floor space is correlated to house price you can write a Kalman filter to track house prices. If age is correlated to disease incidence you can write a Kalman filter to track diseases. If the zombie population is inversely correlated with the number of shotguns then you can write a Kalman filter to track zombie populations. I showed you this in terms of geometry and talked about *triangulation*. That was just to build your intuition. You can write a Kalman filter for state variables that have no geometric representation, such as filters for stock prices or milk production of cows (I received an email from someone tracking milk production!) Get used to thinking of these as Gaussians with correlations. If we can express our uncertainties as a multidimensional Gaussian we can then multiply the prior with the likelihood and get a much more accurate result. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [1] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\n", "\n", "- [2] `FilterPy` library. Roger Labbe.\n", "https://github.com/rlabbe/filterpy" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "085fcd724d9847049501c96196f0fde6": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.2.0", "model_name": "LayoutModel", "state": { "_model_module": "@jupyter-widgets/base", "_model_module_version": "1.2.0", "_model_name": "LayoutModel", "_view_count": null, "_view_module": "@jupyter-widgets/base", "_view_module_version": "1.2.0", "_view_name": "LayoutView", "align_content": null, "align_items": null, "align_self": null, "border": null, "bottom": null, "display": null, "flex": 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