diff --git a/Multidimensional_Kalman_Filters.ipynb b/Multidimensional_Kalman_Filters.ipynb index fb9d5df..58f67c7 100644 --- a/Multidimensional_Kalman_Filters.ipynb +++ b/Multidimensional_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:93f2aa8528b9bbe96c77fd678d6f33b1dfde74509596240e46ec4c363f0db314" + "signature": "sha256:5a6ba5eb3eb9d457b3a0d8b490f06d44502a5b5a5af5f643466e2ca4eed75e44" }, "nbformat": 3, "nbformat_minor": 0, @@ -26,1221 +26,6 @@ ], "language": "python", "metadata": {}, - "outputs": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

Multidimensional

\n", - "

Kalman Filters

" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Introduction\n", - "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n", - "\n", - "\n", - "###Multivariate Normal Distributions\n", - "\n", - "\n", - "What might a *multivariate normal distribution* look like? In this context, multivariate just means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that $x = 2$ and $y = 7$. Therefore we can see that for $N$ dimensions, we need $N$ means, like so:\n", - "\n", - "$$\n", - "\\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix}\n", - "$$\n", - "\n", - "Therefore for this example we would have\n", - "\n", - "$$\n", - "\\mu = \\begin{bmatrix}2\\\\7\\end{bmatrix} \n", - "$$\n", - "\n", - "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 8, like so. \n", - "\n", - "$$\\sigma^2 = \\begin{bmatrix}10\\\\8\\end{bmatrix}$$ \n", - "\n", - "While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use the following matrix to denote *covariances* with multivariate normal distributions. You might guess, correctly, that *covariance* is short for *correlated variances*." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\Sigma = \\begin{pmatrix}\n", - " \\sigma_1^2 & p\\sigma_1\\sigma_2 & \\cdots & p\\sigma_1\\sigma_n \\\\\n", - " p\\sigma_2\\sigma_1 &\\sigma_2^2 & \\cdots & p\\sigma_2\\sigma_n \\\\\n", - " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", - " p\\sigma_n\\sigma_1 & p\\sigma_n\\sigma_2 & \\cdots & \\sigma_n^2\n", - " \\end{pmatrix}\n", - "$$\n", - "\n", - "If you haven't seen this before it is probably a bit confusing at the moment. Rather than explain the math right now, we will take our usual tactic of building our intuition first with various physical models. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements are a product of the $\\sigma$ corresponding to the $i$th (row) and $j$th (column) state variable multiplied by a constant $p$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, without explanation, here is the full equation for the multivarate normal distribution in $n$ dimensions.\n", - "\n", - "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n", - "\n", - "I urge you to not try to remember this function. We will program it in a Python function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the *univarate normal distribution* except it uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. Here is the *univariate* equation for reference:\n", - "\n", - "$$ \n", - "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 }\n", - "$$\n", - "\n", - "If you are reasonably well-versed in linear algebra this equation should look quite managable; if not, don't worry! If you want to learn the math we will cover it in detail in the next optional chapter. If you choose to skip that chapter the rest of this book should still be managable for you\n", - "\n", - "I have programmed it and saved it in the file *stats.py* with the function name *multivariate_gaussian*. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of numpy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner. If you wish to view the code, I urge you to either load it in an editor, or load it into this worksheet by putting *%load -s multivariate_gaussian stats.py* in the next cell and executing it with ctrl-enter. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - ">As of version 0.14 scipy.stats has implemented the multivariate normal equation with the function **multivariate_normal()**. It is superior to my function in several ways. First, it is implemented in Fortran, and is therefore faster than mine. Second, it implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use **scipy.version.version** to get the version number. I deliberately named my function **multivariate_gaussian()** to ensure it is never confused with the built in version.\n", - "\n", - "> If you intend to use Python for Kalman filters, you will want to read the tutorial for the scipy.stats module, which explains 'freezing' distributions and other very useful features. As of this date, it includes an example of using the multivariate_normal function, which does work a bit differently from my function." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from stats import gaussian, multivariate_gaussian" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n", - "\n", - "First, let's find the probability for our dog being at (2.5, 7.3) if we believe he is at (2,7) with a variance of 8 for $x$ and a variance of 10 for $y$. This function requires us to pass everything in as numpy arrays (we will soon provide a more robust version that works with numpy matrices, numpy arrays, and/or scalars in any combinations. That code contains a lot of boilerplate which obscures the algorithm).\n", - "\n", - "Start by setting $x$ to (2.5,7.3):" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "x = np.array([2.5, 7.3])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 27 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we set the mean of our belief:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mu = np.array([2,7])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 28 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances. I will use the seemingly arbitrary name $P$ for the covariance matrix. The Kalman filters use the name $P$ for this matrix, so I will introduce the terminology now to avoid explaining why I change the name later. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "P = np.array([[8.,0],[0,10.]])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 29 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now just call the function" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print(multivariate_gaussian(x,mu,P))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.0174395374407\n" - ] - } - ], - "prompt_number": 30 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's check the probability for the dog being at exactly (2,7)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from __future__ import print_function\n", - "\n", - "x = np.array([2,7])\n", - "print(\"Probability dog is at (2,7) is %.2f%%\" % (multivariate_gaussian(x,mu,P) * 100.))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Probability dog is at (2,7) is 1.78%\n" - ] - } - ], - "prompt_number": 31 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These numbers are not easy to interpret. Let's plot this in 3D, with the $z$ (up) coordinate being the probability." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib.pylab as pylab\n", - "from matplotlib import cm\n", - "from mpl_toolkits.mplot3d import Axes3D\n", - "import numpy as np\n", - "\n", - "pylab.rcParams['figure.figsize'] = 12,6\n", - "pylab.rcParams['axes.color_cycle'] = '348ABD, 7A68A6, A60628, 467821, CF4457, 188487, E24A33'\n", - "\n", - "P = np.array([[8.,0],[0,10.]])\n", - "mu = np.array([2,7])\n", - "\n", - "xs, ys = np.arange(-8, 13, .5), np.arange(-8, 20, .5)\n", - "xv, yv = np.meshgrid (xs, ys)\n", - "\n", - "zs = np.array([100.* multivariate_gaussian(np.array([x,y]),mu,P) \\\n", - " for x,y in zip(np.ravel(xv), np.ravel(yv))])\n", - "zv = zs.reshape(xv.shape)\n", - "\n", - "ax = plt.figure().add_subplot(111, projection='3d')\n", - "ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n", - "\n", - "ax.set_xlabel('X')\n", - "ax.set_ylabel('Y')\n", - "\n", - "ax.contour(xv, yv, zv, zdir='x', offset=-9, cmap=cm.autumn)\n", - "ax.contour(xv, yv, zv, zdir='y', offset=20, cmap=cm.BuGn)\n", - "plt.xlim((-10,15))\n", - "plt.ylim((-10,20))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 32, - "text": [ - "(-10, 20)" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAFdCAYAAAAkOCRoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngiAIgvBa/h8V+7yxE2a+PQAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 32 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange.\n", - "\n", - "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance or not. So for most of the rest of this book we will display multidimensional Gaussian using contour plots. I will use some helper functions in *gaussian.py* to plot them. If you are interested in linear algebra go ahead and look at the code used to produce these contours, otherwise feel free to ignore it." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import stats\n", - "\n", - "P = np.array([[2,0],[0,2]])\n", - "plt.subplot(131)\n", - "stats.plot_covariance_ellipse(P, x=2, y=7, title='|2 0|\\n|0 2|')\n", - "\n", - "plt.subplot(132)\n", - "P = np.array([[2,0],[0,9]])\n", - "stats.plot_covariance_ellipse(P, x=2, y=7, title='|2 0|\\n|0 9|')\n", - "\n", - "plt.subplot(133)\n", - "P = np.array([[2,1.2],[1.2,2]])\n", - "stats.plot_covariance_ellipse(P, x=2, y=7, title='|2 1.2|\\n|1.2 2|')\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAA1MAAAGpCAYAAABoLmzKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", - "text": [ - "" - ] - } - ], - "prompt_number": 33 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "From a mathematical perspective these display the values that the multivariate gaussian takes for a specific sigma (in this case $\\sigma^2=1$. Think of it as taking a horizontal slice through the 3D surface plot we did above. However, thinking about the physical interpretation of these plots clarifies their meaning.\n", - "\n", - "The first plot uses the mean and covariance matrices of\n", - "$$\n", - "\\begin{align*}\n", - "\\mu &= \\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", - "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&2\\end{bmatrix}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for the $1\\sigma^2$ probability - points where the dog is quite likely to be based on our current knowledge. Of course, the dog might be very far from this point, as Gaussians allow the mean to be any value. For example, the dog could be at (3234.76,189989.62), but that has vanishing low probability of being true. Generally speaking displaying the $1\\sigma^2$ to $2\\sigma^2$ contour captures the most likely values for the distribution. An equivelent way of thinking about this is the circle/ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The second plot uses the mean and covariance matrices of\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", - "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "This time we use a different variance for $x$ (2) vs $y$ (9). The result is an ellipse. When we look at it we can immediately tell that we have a lot more uncertainty in the $y$ value vs the $x$ value. Our belief that the value is (2,7) is the same in both cases, but errors are different. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object, or is closer, than another sensor, and so we end up with different error rates in the different axis." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The third plot uses the mean and covariance matrices of:\n", - "$$\n", - "\\begin{align*}\n", - "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", - "\\sigma^2 &= \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "This is the first contour that has values in the off-diagonal elements of $cov$, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling use the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal. What does this mean in physical terms? Think of trying to park your car in a parking spot. You can not pull up beside the spot and then move sideways into the space because most cars cannot go purely sideways. $x$ and $y$ are not independent. This is a consequence of the steering system in a car. When your tires are turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk straight forward to to the side. If $x$ changes, $y$ must also change in a defined way. \n", - "\n", - "So when we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". I will not prove it here, but a $45^\\circ$ angle denotes complete correlation between $x$ and $y$, whereas $0^\\circ$ and $90^\\circ$ denote no correlation at all. Those who are familiar with this math will be objecting quite strongly, as this is actually quite sloppy language that does not adress all of the mathematical issues. They are right, but for now this is a good first approximation to understanding these ellipses from a physical interpretation point of view. The size of the ellipse shows how much error we have in each axis, and the slant shows how strongly correlated the values are.\n", - "**IS THIS TRUE???**\n", - "\n", - "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. ** wikipedia article 'correlation and dependence' claims multivariate normals are a special case, where the correlation coeff $p$ completely defines the dependence. FIGURE THIS OUT!**" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Unobserved Variables\n", - "\n", - "Let's say we are tracking an aircraft and we get the following data for the $x$ coordinate at time $t$=1,2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import mkf_internal\n", - "mkf_internal.show_position_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF/CAYAAABKRQ+VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", - "text": [ - "" - ] - } - ], - "prompt_number": 34 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It appears that the aircraft is flying in a straight line because we can draw a line between the three points, and we know that aircraft cannot turn on a dime. The most reasonable guess is that $x$=4 at $t$=4. I will depict that with a green arrow." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mkf_internal.show_position_prediction_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF/CAYAAABKRQ+VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 35 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If this is data from a Kalman filter, then each point has both a mean and variance. Let's try to show that by showing the approximate error for each point. Don't worry about why I am using a covariance matrix to depict the variance at this point, it will become clear in a few paragraphs. The intent at this point is to show that while we have $x$=1,2,3 that there is a lot of error associated with each measurement." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mkf_internal.show_x_error_char()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAswAAAF/CAYAAABdZ59cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQgghpAT/H1pjh8jKLMJoAAAAAElFTkSuQmCC\n", - "text": [ - "" - ] - } - ], - "prompt_number": 36 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see that there is a lot of error associated with each value of $x$. We could write a 1D Kalman filter as we did in the last chapter, but suppose this is the output of that filter, and not just raw sensor measurements. Are we out of luck?\n", - "\n", - "Let us think about how we predicted that $x$=4 at $t$=4. In one sense we just drew a straight line between the points and saw where it lay at $t$=4. My constant refrain: what is the physical interpretation of that? What is the difference in $x$ over time? In other words, what is $\\frac{\\partial x}{\\partial t}$? The derivative, or difference in distance over time is *velocity*. \n", - "\n", - "This is the **key point** in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). It does not have any kind of sensor that provides velocity to us. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity an *unobserved variable*. Unobserved means what it sounds like - there is no sensor that is measuring velocity directly. Since the velocity is based on the position, and the position has error, the velocity will have error as well. What happens if we draw the velocity errors over the positions errors?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mkf_internal.show_x_with_unobserved()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAswAAAF/CAYAAABdZ59cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neYSAHwAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 37 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n", - "\n", - "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Cleary the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Kalman Filter Algorithm\n", - "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the **measurement function**. Then we predict the next position by using the current estimate and something called the **state transition function**. In our example above,\n", - "\n", - "$$new\\_position = old\\_position + velocity*time$$ \n", - "\n", - "Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the **residual**. Finally, we use something called the **Kalman gain** to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. \n", - "\n", - "The chart shows a prior estimate of $x=1$ and $\\dot{x}=1$ ($\\dot{x}$ is the shorthand for the derivative of x, which is velocity). Therefore we predict $\\hat{x}=2$. However, the new measurement $x^{'}=1.3$, giving a residual $r=0.7$. Finally, Kalman filter gain $k$ gives us a new estimate of $\\hat{x^{'}}=1.8$.\n", - "\n", - "** CHECK SYMBOLOGY!!!!**" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from mkf_internal import *\n", - "show_residual_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDABAFQEMAEAVAQwAQJUD3H6EnmC5ZoUAAAAASUVORK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 38 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Equations\n", - "\n", - "The brilliance of the Kalman filter is taking the insights of the chapter up to this point and finding mathematical solution. The Kalman filter finds what is called a *least squared fit* to the set of measurements to produce an optimal output. We will not trouble ourselves with the derivation of these equations. It runs to several pages, and offers a lot less insight than the words above, in my opinion. Instead, I will just present the equations and then immediately provide the Python code that implements them. \n", - "> Kalman Filter Predict Step:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "\\hat{x}_{t|t-1} &= F_t\\hat{x}_{t-1} + B u_t \\\\\n", - "P_{t|t-1} &= F_tP_{t-1}F^T_t + Q_t\n", - "\\end{align*}\n", - "$$\n", - "\n", - "> Kalman Filter Update Step:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "\\gamma &= z_t - H_t\\hat{x}_t \\\\\n", - "K_t &= P_t H^T_t (H_t P_t H^T_t + R_t)^{-1} \\\\\n", - "\\\\\n", - "\\hat{x}_t &= \\hat{x}_{t|t-1} + K_t \\gamma \\\\\n", - "P_{t|t} &= (I - K_t H_t)P_{t|t-1} \n", - "\\end{align*}\n", - "\\\\\n", - "$$\n", - "Dash off, wipe the blood out of your eyes, and we'll disuss what this means." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These are nothing more than linear algebra equations that implement the algorithm we used in the last chapter, but using multidimensional Gaussians, and optimizing for a least squares fit. As you should be familiar with, each capital letter denotes a matrix or vector. The subscripts just let us denote from which time step the data comes from; $t$ is now, $t-1$ is the previous step. $A^T$ is the transpose of A, and $A^{-1}$ is the inverse. Finally, the hat denotes an estimate, so $\\hat{x}_t$ is the estimate of $x$ at time $t$.\n", - "\n", - "What do all of the variables mean? What is $P_t$, for example? Don't worry right now. Instead, I am just going to design a Kalman filter, and introduce the names as we go. Then we will just pass them into the Python function that implements the equations above, and we will have our solution.\n", - "\n", - "I will not present all of the Python code for the filter right now, but look at the code for the predict step. Notice how simple it really is. It really isn't much different from the predict step in the previous chapter.\n", - "\n", - " def predict():\n", - " x = F*x + u\n", - " P = F*P*F.T + Q\n", - " \n", - "> *Do not become discouraged when you come across a page of equations like I just gave for the Kalman Filter. They usually turn into very simple code. Take $x = F*x + u$. What does that mean? Clearly we are scaling x by F and then offsetting by u. Once you see that, you can start exploring **why** this is happening. This is really not as obscure as the symbology makes it appear.*" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Tracking a Dog\n", - "\n", - "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of this chapter - that of using *unobserved variables* to improve our estimates. In simple terms, our algorithm is:\n", - "\n", - " 2. predict x using 'x + vel*time'\n", - " 3. get measurement for x\n", - " 4. compute residual as: 'x - predicted x'\n", - " 5. compute new position as 'residual * kalman gain'\n", - " \n", - "That is the entire Kalman filter algorithm. It is both what we described above in words, and it is what the rather obscure Kalman Filter equations do. The Kalman filter equations are just way of expresing this algorithm by using linear algebra.\n", - "\n", - "##### **Step 1:** Design State Transition Function\n", - "\n", - "We know from elementary physics that\n", - "\n", - "$$ x = vt + x_0$$\n", - "\n", - "In our problems we will be running the Kalman filter at fixed time intervals, so $t$ is a constant for us. We will just set it to $1$ and worry about the units later.\n", - "\n", - "We have two variables distance $(x)$ and velocity $(\\dot{x})$ which fully represent the state of our system. We will store them in a 1-dimensional array like so:\n", - "\n", - "$$\\begin{pmatrix}x \\\\ \\dot{x}\\end{pmatrix}$$\n", - "\n", - "Now we have to write a linear equation that performs the $ x = vt + x_0$ assignment with our state array.\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "{\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}}' &=\\begin{pmatrix}1&1 \\\\ 0&1\\end{pmatrix} \\times \\begin{pmatrix}x \\\\ \\dot{x}\\end{pmatrix}, \\mbox{or equivelently} \\\\\n", - "x' &= F \\times x\n", - "\\end{align*}\n", - "$$\n", - "\n", - "If we multiply this equation out, it yields:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "x' &= x + \\dot{x} \\\\\n", - "\\dot{x}' &= \\dot{x}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "You can see that our new $x$ is the old $x$ plus velocity times time, where time equals 1. Velocity is not changed by this equation, so the new $\\dot{x}$ is set to the old $\\dot{x}$.\n", - "\n", - "In the vocabulary of Kalman filters we call this *transforming the state matrix*. We take our state matrix, which for us is $(\\begin{smallmatrix}x \\\\ \\dot{x}\\end{smallmatrix})$,and multipy it by a matrix we will call $F$ to compute the new state. In this case, $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$. \n", - "\n", - "\n", - "You will do this for every Kalman filter you ever design. Your state matrix will change depending on how many state random variables you have, and then you will create $F$ so that it updates your state based on whatever the physics of your problem dictates. $F$ is always a matrix of constants. If this is not fully clear, don't worry, we will do this many times in this book.\n", - "\n", - "I will not keep referring to the Kalman filter equations, but look at the first equation $\\hat{x}_{t|t-1} = F_t\\hat{x}_{t-1} + u_t$. There is an unexplained $u_t$ term in there, but shorn of all the diacritics it should be clear that we just designed $F$ for this equation! \n", - "\n", - "\n", - "##### ** Step 2 **: Design the Measurement Function\n", - "\n", - "Now we need a way to go from our measurement to our state matrix. In our problem we have one sensor for the position. We do not have a sensor for velocity. If we put this in linear algebra terms we get:\n", - "\n", - "$$\n", - "z = \\begin{pmatrix}1&0\\end{pmatrix} \\times \\begin{pmatrix}x \\\\ \\dot{x}\\end{pmatrix}\n", - "$$\n", - "\n", - "In other words, we take one times the sensor's $x$ measurement, and zero times the nonexistent velocity measurement. Simple!\n", - "\n", - "In the nomenclature of Kalman filters the $(\\begin{smallmatrix}1&0\\end{smallmatrix})$ matrix is called $H$. If you scroll up to the Kalman filter equations you will see an $H$ term in the update step.\n", - "\n", - "Believe it or not, we have designed the majority of our Kalman filter!! All that is left is to model the noise in our sensors.\n", - "\n", - "\n", - "##### ** Step 3** Design Noise Matrices\n", - "\n", - "In the last chapter we used a variance of 5 for our position sensor. Let's use the same value here. The Kalman filter calls this the *measurement uncertainty*, and uses the symbol $R$.\n", - "\n", - "$$R = 5$$\n", - "\n", - "That was pretty simple, yes? And we are done. There are more variables in the Kalman filter, and we will have to define them in more complicated problems, but for our problem we have done everything we need to do.\n", - "\n", - "As promised, the Kalman filter equations are already programmed for you. In most circumstances you will never have to write your own Kalman filter equations. We will look at the code later, but for now we will just import the code and use it. I have placed it in *KalmanFilter.py*, so let's start by importing it and creating a filter." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "from KalmanFilter import KalmanFilter\n", - "f = KalmanFilter (dim=2)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 39 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That's it. We import the filter, and create a filter that uses 2 state variables. We specify the number of state variables with the 'dim=2' expression (dim means dimensions).\n", - "\n", - "The Kalman filter class contains a number of variables that you need to set. x is the state, F is the state transition function, and so on. Rather than talk about it, let's just do it!" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f.x = np.matrix([[0], [0]]) # initial state (location and velocity)\n", - "f.F = np.matrix([[1,1],[0,1]]) # state transition matrix\n", - "f.H = np.matrix([[1,0]]) # Measurement function\n", - "f.R = 5 # state uncertainty\n", - "f.P *= 500. # covariance matrix " - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 40 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's look at this line by line. \n", - "\n", - "**1**: We just assign the initial value for our state. Here we just initialize both the position and velocity to zero. \n", - "\n", - "**2**: We set $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$, as in design step 1 above. \n", - "\n", - "**3**: We set $H=(\\begin{smallmatrix}1&0\\end{smallmatrix})$, as in design step 2 above.\n", - "\n", - "**4**: We set $R = 5$ as in step 3.\n", - "\n", - "**5**: Recall in the last chapter we set our initial belief to $\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(0,500)$ to set the initial position to 0 with a very large variance to signify our lack of knowledge about the initial conditions. We implemented in Python with \n", - "\n", - " pos = (0,500)\n", - " \n", - "Multidimensional Kalman filters stores the state variables in $x$ and their *covariance* in $P$. Notionally, this is exactly the same as the one dimension case. We have a mean and variance. For the multidimensional case, we have $$\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(x,P)$$\n", - "\n", - "$P$ is initialized to the identity matrix of size $n\\times n$, so multiplying by 500 assigns a variance of 500 to $x$ and $\\dot{x}$.\n", - "\n", - "> Summary: For our dog tracking problem, in the 1-D case $\\mu$ was the position, and $\\sigma^2$ was the variance. In the 2-D case $x$ is our position and velocity, and $P$ is the *covariance*. It is the same thing, just in higher dimensions!\n", - "\n", - ">| | 1D | 2D and up|\n", - ">|--|----|---|\n", - ">|state|$\\mu$|$x$|\n", - ">|uncertainty|$\\sigma^2$|$P$|\n", - "\n", - "All that is left is to run the code! The *DogSensor* class from the previous chapter has been placed in *DogSensor.py*. There is an extra variable, Q, which we have not discussed yet. For now it is fine to set it to zero." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from DogSensor import DogSensor\n", - "\n", - "def dog_tracking_filter(R,Q=0,cov=1.):\n", - " f = KalmanFilter (dim=2)\n", - " f.x = np.matrix([[0], [0]]) # initial state (location and velocity)\n", - " f.F = np.matrix([[1,1],[0,1]]) # state transition matrix\n", - " f.H = np.matrix([[1,0]]) # Measurement function\n", - " f.R = R # measurement uncertainty\n", - " f.P *= cov # covariance matrix \n", - " f.Q = np.eye(2)*Q\n", - " return f\n", - "\n", - "\n", - "def plot_track(noise, count, R, Q=0, plot_P=True, title='Kalman Filter'):\n", - " dog = DogSensor(velocity=1, noise=noise)\n", - " f = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", - "\n", - " ps = []\n", - " zs = []\n", - " cov = []\n", - " for t in range (count):\n", - " z = dog.sense()\n", - " f.measure (z)\n", - " #print (t,z)\n", - " ps.append (f.x[0,0])\n", - " cov.append(f.P)\n", - " zs.append(z)\n", - " f.predict()\n", - "\n", - " p0, = plt.plot([0,count],[0,count],'g')\n", - " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", - " p2, = plt.plot(range(1,count+1),ps, c='b')\n", - " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", - " plt.title(title)\n", - "\n", - " plt.show()\n", - " if plot_P:\n", - " plt.subplot(121)\n", - " plot_covariance(cov, (0,0))\n", - " plt.subplot(122)\n", - " plot_covariance(cov, (1,1))\n", - " plt.show()\n", - " \n", - "def plot_covariance(P, index=(0,0)):\n", - " ps = []\n", - " for p in P:\n", - " ps.append(p[index[0],index[1]])\n", - " plt.plot(ps)\n", - " \n", - "plot_track (noise=30, R=5, count=100)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAF9CAYAAAAZRJ4tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neZQgi4iIiIicRwmyiIiIiMh5/h/R0w7Zf1YSFwAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAFyCAYAAAD4cmIkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niHje/we3qBc3LqHvegAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 41 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Nobert Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n", - "\n", - "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n", - "\n", - "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, this is just a plot of the diagonals of $P$ over time. $P$ is just a covariance matrix, so the diagonal contains the variance of each state variable. So $P[0,0]$ is the variance of $x$, and $P[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $P=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now we just briefly point out that we quickly converge onto an accurate estimate despite the initial large uncertainty.\n", - "\n", - "You may not be impressed with these charts. After all, in the previous chapter we filtered very noisy signals with much simpler code. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. Though we haven't yet seen it, we can compute very complicated things with this code. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Walking Through the Math\n", - "I promised that you would not have to understand how to derive Kalman filter equations, and that is true. However, I do think it is worth walking through the equations one by one and becoming familiar with the variables. If this is your first time through the material feel free to skip ahead to the next section. However, you will eventually want to work through this material, so why not now? You will need to have passing familarity with these equations to read material written about the Kalman filter, as they all presuppose that you are familiar with the equations.at \n", - "\n", - "I will start with the measurement step, as that is what we started with in the one dimensional Kalman filter case. Our first equation is\n", - "\n", - "$$\n", - "\\gamma = z_t - H_t\\hat{x}_t\n", - "$$\n", - "\n", - "On the right, shorn of the diacritics, we have $H\\times x$. That should be recognizable as the measurement function. We are taking our state $x$ and multiplying it by the measurement function $H$ to get the new state. The variable $z$ is just the measurement; it is typical, but not universal to use $z$ to denote measurements in the literature. Do you remember this chart?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "show_residual_chart()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDABAFQEMAEAVAQwAQJUD3H6EnmC5ZoUAAAAASUVORK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 42 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The blue prediction line is the output of $H \\times x$, and $z$ is the measurement. Therefore, $\\gamma = z - H\\times x$ is how we compute the residual, drawn in red. So $\\gamma$ is the residual.\n", - "\n", - "The next line is the formidable:\n", - "\n", - "$$K_t = P_t H^T_t (H_t P_t H^T_t + R_t)^{-1}$$\n", - "\n", - "Unfortunately it is a fair amount of linear algebra to derive this. But $K$ is just the *Kalman gain* - the ratio of how much measurement vs prediction we should use to create the new estimate. In the graph above we are favoring the prediction more than the measurement, so the new estimate is near the prediction. Other values of $K$ would choose a different point along the residual line. $R$ is our *measurement noise*, and $P$ is our *uncertainty covariance matrix*. \n", - "\n", - "I look at this equation as saying $K=A \\times B^{-1}$ which is just the way we compute a ratio in linear algebra. If these were scalars, we would write $k=a/b$. In other words, the *Kalman gain* equation is doing nothing more than computing the ratio of two values. Those values are some kind of product of our various uncertainties. As you might guess, if we are confident in our measurements and unconfident in our predictions K will favor the measurement, and vice versa. The math looks complicated, but the concept is simple - scale by a ratio.\n", - "\n", - "Without going into the derivation of $K$, I'll say that this equation is the result of finding a value of $K$ that optimizes the *mean-square estimation error*. It does this by finding the minimal values for $P$ along it's diagonal. Recall that the diagonal of $P$ is just the variance for each state variable. So, this equation for $K$ ensures that the Kalman filter output is optimal. To put this in concrete terms, for our dog tracking problem this means that the estimates for both position and velocity will be optimal - a value of $K$ that made the position extremely accurate but the velocity very inaccurate would be rejected in favor of a $K$ that made both position and velocity just somewhat accurate.\n", - "\n", - "\n", - "Our next line is:\n", - " $$ \\hat{x}_t = \\hat{x}_{t|t-1} + K_t \\gamma$$\n", - "\n", - "This just multiplies the residual by the Kalman gain, and adds it to the state variable. In other words, this is the computation of our new estimate.\n", - "\n", - "Finally, we have:\n", - "\n", - "$$P_{t|t} = (I - K_t H_t)P_{t|t-1} $$\n", - "\n", - "$I$ is the identity matrix, and is the way we represent $1$ in multiple dimensions. $H$ is our measurement function, and is a constant. So, simplified, this is simply $P = (1-cK)P$. $K$ is our ratio of how much prediction vs measurement we use. So, if $K$ is large then $(1-cK)$ is small, and P will be made smaller than it was. If $K$ is small, then $(1-cK)$ is large, and P will be made larger than it was. So we adjust the size of our uncertainty by some factor of the *Kalman gain*. \n", - "\n", - "Now we have the measurement steps. The first equation is\n", - "\n", - "$$\\hat{x}_{t|t-1} = F_t\\hat{x}_{t-1} + B_t u_t$$\n", - "\n", - "In simple terms, we have $x' = Fx + Bu$. This is just our state transition equation. $B$ and $u$ are new to us, and they are the control inputs for when you use a Kalman filter to control a system rather than just track it. We will use this in later problems, but for now consider using a Kalman filter to drive a car. We don't want to just track the car, but we will be issuing it direction - go in such and such direction as some speed. $u$ incorporates these instructions into the filter, and $B$ models how those control inputs affect the system.. If we are just passively tracking then we set $u$ to zero. This equation is, for our dog tracking problem, just computing:\n", - "\n", - "$$ x'=(vt)+x$$\n", - "\n", - "The final equation is:\n", - "$$P_{t|t-1} = F_tP_{t-1}F^T_t + Q_t$$\n", - "\n", - "Here we are scaling the covariance matrix with our process matrix, and then adding in the uncertainty with our motion ($Q$). **FIX THIS. THIS IS STUPID EXPLANATION.**" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Adjusting the Filter\n", - "Your results will vary slightly depending on what numbers your random generator creates for the noise componenet of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n", - "\n", - "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the $H$ and $F$ matrices - they develop in an obvious manner based on the physics of the system we are modelling. The art comes in modelling the sensors and selecting appropriate values for the rest of our variables.\n", - "\n", - "Let's look at the effects of the noise parameters $R$ and $Q$.I will only run the filter for twenty steps to ensure we can see see the difference between the measurements and filter output. I will start by holding $R$ to 5 and vary $Q$. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plot_track (noise=30, R=5, Q=10,count=30, plot_P=False, title='R = 5, Q = 10*I')\n", - "plot_track (noise=30, R=5, Q=0.1,count=30, plot_P=False, title='R = 5, Q = 0.1*I')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl4TGf7wPHvbJnJbo3YIvZd7ISgllap3Q9tX+VFW2pp\n9aWqrbaUtiitUvtaSlsqtqqlJVJB7VKlFKWxxU72ZGZyfn8gFbJnJjMnuT/XlUvOzJzz3JNbuPPk\nPs+jURRFQQghhBBCiAJC6+gAhBBCCCGEyEtSAAshhBBCiAJFCmAhhBBCCFGgSAEshBBCCCEKFCmA\nhRBCCCFEgSIFsBBCCCGEKFCkABZCCCGEEAWKFMBCCKej1WpTPooUKUKzZs1Yt26dw2N5+LF9+3ab\nj3PgwAECAwNxdXWlZMmSjB07luTkZJuPk5ndu3fTtWtXypQpg1ar5euvv37iNX/99Rdt2rTBzc2N\nsmXLMnXq1HSv17p16zQf9/f3f+LrqtPpbPY+hBAiI1IACyGc0pdffklkZCRhYWHUrl2bXr16ceDA\nAYfEEhwcTGRkZMpHekVdTt24cYNnnnmGsmXLcvjwYb766itmz57NhAkTbDpOVkRHR1OrVi1mzZoF\ngEajSfV8UlISHTp0wNXVlQMHDjB58mTef//9VIXymjVrOHnyZKrzNm7cyOHDh1OODx8+zNWrV+nd\nuzfNmjUjMjKSq1ev2vGdCSHEv/SODkAIIdLi7e2Nj48PPj4+TJs2jYULF7J3714aN26c57EULlwY\nHx8fu13/m2++IS4ujsWLF+Pp6UmNGjXYv38/c+bMyfMiuGPHjnTs2DHd57ds2cL58+cJCwujZMmS\n1KpVi507dzJr1iz69+8PQKVKlRgxYgRPPfUUd+/e5cUXX8TFxYUpU6akXKdo0aIAmEwmDAaDXb++\nQgjxOJkBFkI4pYe7tJvNZpYsWYJWq6Vp06ZZOjciIgIPDw88PT3T/NizZ0+2YunXrx/FixenadOm\nrFq1KtvvJTOHDh2iatWqeHp6pjzWsGFDbt26xd9//52la3To0CHd9zt06FCbxXrw4EEqVqxIyZIl\nUx5r1aoV4eHhWCwWAOrVq8eOHTsIDw8nPDycZs2asWzZMkqUKGGzOIQQIjdkBlgI4ZSGDBnC8OHD\niY+Pp2rVqoSEhGS5AC5dujS///57us+XKlUqy3F88skntG7dGqPRyIYNG+jXrx9JSUn897//zfI1\nMnP9+nWKFCmS6rGHxzdu3KBChQqZXmPJkiXEx8en+ZyXl1fug3zg+vXrFCtWjPj4eGrUqEHv3r1p\n3bo1VquVW7duUaJECcLDwxk9ejQtWrTg3Llz7N27lyNHjjB58mSZ6RVCOAUpgIUQTmnixIl0796d\n8PBwBgwYwNGjR2nRokWWztXpdFkqGrNi7NixKZ/XrVuXixcvMn36dJsWwBnRarP2i7pHZ2Tzgk6n\nw8/PjxIlSqTM1j90+vRpZs6cSfXq1QkJCWHVqlVs3LiRiIgIKYCFEE5BCmAhhFPy8fGhYsWKVKxY\nkUuXLvH+++/Tt2/fJ2ZK0xIREUGNGjWeuIHroa1bt9K8efMcxVW/fn2+++67HJ2bHh8fH8LDw1M9\ndvv2bQCKFy+epWt06NCBsLCwNJ976aWXmDNnTu6CfMDHx4cbN27g4uJCaGgoAMuXL0en06X09fbu\n3fuJ87p06WKT8YUQwhakABZCOL3BgwczadIkvvzyyyzdFGbLFojHnTx50mazyw81atSINWvWEBUV\nldKucPDgQUqUKIG/v3+WrrF48WISEhLSfM6WLRCNGzfmk08+4cqVKylfx127dlG3bl30+if/SwkJ\nCcn0mun9oCKEEPYiBbAQwukZjUZeffVVZs+ezdtvv42bm1uGr7dVC8SGDRu4fPkyQUFBuLm5sXXr\nVhYtWsTcuXOfeO2yZcsYOHAgS5cuTVkNIav+85//MGHCBAYNGsSECRP4888/mTdvHm+//XaWr5Gb\nov5RsbGxnDlzJuX4n3/+4dixY5QsWZISJUrQoUMHKlSowCuvvMKUKVMIDw9n5cqVLFy4MFvj3Lhx\nA6vVSnx8PImJiVy7dg1FUfD19bXJ+xBCiAwpQgjhZDQajfL111+neuzKlSuKi4uL8uWXX+ZZHFu3\nblVq1aqleHh4KO7u7kq9evWeiOuhWbNmKRqNRtm2bVuOxtq/f7/StGlTxWg0KhqNRunbt69isVhy\nE36OhISEKBqNRtFoNIpWq035fMKECSmvOX36tNK6dWvFZDIppUuXVqZMmZLtccqVK/fEOFqt1pZv\nRQgh0qVRlMfuXkhDdHQ0VatWZdSoUYwaNYrVq1czbtw4NBoN06dPp1OnTnlRqwshhNPq1asX//zz\nj0026xg/fjwzZ85k8+bNBAYG2iA6IYQQj8pSC8THH39Mw4YN0Wg0JCUlMXbsWPbv309CQgKtW7eW\nAlgIUaApisKuXbtstkbw+PHjKVq0KIULF7bJ9YQQQqSWaQF8+vRpbty4QYMGDVAUhQMHDlCzZs2U\nO5PLli1LeHg4AQEBdg9WCCGckUaj4caNGza95ogRI2x6PSGEEP/KdIHJd955h/Hjx6ccR0ZGUrJk\nSebPn8+aNWvw9fWV/duFEEIIIYRqZDgDvGnTJqpUqULZsmWfWOh88ODBAAQHB8sSNkIIIYQQQjUy\nLIAPHDjA2rVr2bBhAzdv3kSr1TJs2LBUM74PZ4Qf9/3331OsWDHbRyyEEEIIIcQjEhISeO6557L8\n+iytAgEwYcIEPD09GTFiBFWrVk25Ca5Nmzap1ox8aMeOHdSvXz/rkQunsmnTJjp37uzoMEQOSO7U\nTfKnXpI7dbNH/jSXLuHZtStRBw9CFrc1Fzlz5MgR2rZtm+XXZ3sjDIPBwOTJk1O2EZ0xY0Z2LyFU\nICIiwtEhiByS3Kmb5E+9JHfqZo/8GXbtQnf+PLqTJ7HWqmXz64ucy3IB/OGHH6Z83rt37zT3ehdC\nCCGEEPcZQkOx1KuHJjra0aGIx8hWyCJN7dq1c3QIIockd+om+VMvyZ262Tx/ioJ+926ifvkFpUwZ\n215b5JoUwCJNVatWdXQIIockd+om+VMvyZ262Tx/Gg1RYWEosiCAU8rzAlhRFK5fv47Vas3roUU2\n3Lt3D29v72yfp9Pp8PHxkaXxHCgsLIygoCBHhyFySPKnXpI7dbNH/qT4dV55XgBfv34dT09P3Nzc\n8npokQ2lSpXK0XlxcXFcv36dEiVK2DgiIYQQQgjbyPM1OaxWqxS/+Zibm5vM7juYzECpm+RPvSR3\n6ib5K1hkUTohhBBCCDu4fVtDv37uJJutmCZPhuRkR4ckHpACWIh8JiwszNEhiFyQ/KmX5E7dbJk/\nzaVLkJRESIieH390Yf8hIy7r1qE7edJmY4jckQLYSbVo0YKyZctStGhRkuUnRiGEEEI1PAYMQL9/\nPzt3Gihf3kpwsAFL8+bo5YckpyEFsI0ULVqUCxcu2Ox6u3fvZu/evTa7nig4pI9N3SR/6iW5Uzdb\n5U9z9y6606cxN2zErl0Gpk6NY+NGF+KbBkkB7ESkALYBRVFS/Wnr6wohhBBCHfRhYVgaNeLUBTdc\nXBTatLFQtmwyu/Tt0O/dK33ATkIK4EfMnDmT+vXrU6ZMGRo2bMj69etTntuzZw/t2rXD39+fJk2a\npMzO9urVi3LlygHQsmVL/Pz8eO+994D7+4o/2sIQFhZGrUf2As9oPCFySvoQ1U3yp16SO3WzVf70\noaGYn3qKkBADrVtb0Gige/ck1u7yRSleHN2JEzYZR+SO7AT3iEKFCrFmzRoqVqzI9u3b6d+/Py1b\ntiQ6OpoXX3yRBQsW8Mwzz3Du3Dlu3boFwJo1a4D7LRC7d+/G398/1+MVKVLEHm9PCCGEEHZmCA0l\ndvFiQj4y0K9fIgDduiXRsqUXdxd9js7X18ERCpACOJV+/fqlfP7MM8/g7e3N6dOn2bdvH23atKF9\n+/YAVKpUiUqVKtllvL/++oumTZvm+tqi4JI+RHWT/KmX5E7dbJK/hASsdeoQW7Em+/frWbQoFoDS\npRWqVrXyc9JTtC9uzv04ItecrgAuMtM2s5+3X7+d7XO+//57Zs+ezeXLl0lOTiY6Ohqz2cyVK1co\nW7asTeLKynhCCCGEUCGTidhFi9gfqqd6dSve3v/ey9Ojh5ngYAPt28v/887A6QrgnBSutnDx4kVG\njhzJxo0badSoEQAVK1ZEURRKly5NeHh4hudrNJonHjMajQBYLBZcXFyIjo7O0ngPGQwG4P7ueVqt\ntGuLrLHHfvYi70j+1Etyp262zN/9/t/UhW6XLklMmuRFfDy4utpkGJELUlU9EBsbi0ajoVixYlgs\nFmbNmsW9e/fQaDT07NmTnTt3snXrVqxWK3///Tf79+9PdX6JEiU4+dgC18WKFcPLy4vDhw8DsHHj\nxkzHe5SPjw9eXl7s2bPHTu9aCCGEELYWEqJ/ogD28VGoV8/Kzz8bHBSVeJQUwA9Uq1aNYcOG0a5d\nO2rUqEFsbGxK24Ofnx8rV65k2rRpVKhQgRdeeOGJzSnGjRvHmDFjqFmzJpMmTQJAp9Px0Ucf8eqr\nr/Lcc89RrFixlJnijMZ7SKfT8dlnnzFkyBD8/PzYsmVLHnwlhNrJDJS6Sf7US3KnbrbK3/XrGiIi\ntDRoYH3iuR49kggOdrHJOCJ3NIqdFpvdsWMH9evXf+LxK1euUKpUKXsMKZyE5FgIIURBtWaNC5s2\nGVi+PPaJ5+7c0VC3rhcRvo1Q9m4Dnc4BEeZPR44coW3btll+vcwAC5HPyFqk6ib5Uy/JnbrlNn/G\nr75Cc+lSmu0PDxUurBAYaGFT1FOyHrCDSQEshBBCCJEbiYm4Tp2K4u6RsgFGenr0MPOdy0uyLbKD\nSQEsRD4jfYjqJvlTL8mduuUmf/qDB7FWqcLJq0Vwc1Pw909/u+Nnn00i7GYNokIyXl1K2JcUwEII\nIYQQufBw++OdO59c/uxxXl7wVIsENu0tAdYnb5QTeUMKYCHyGelDVDfJn3pJ7tQtN/kz7NqFpVWr\nTNsfHur+gpbV2ufRnj2b4zFF7kgBLIQQQgiRQ5p799CdPk10rUYcPKinRYvMd3p7+mkzB3SBXCtS\nLQ8iFGmRAliIfEb6ENVN8qdekjt1y2n+FBcXYr7/nt+OeVCzphUvr8zPcXOD9u3NbNwoawI7ihTA\nQgghhBA55eqKJTAwze2PM9K9u5ngYNkVzlGkABYin5E+RHWT/KmX5E7dcpu/nTvTX/83La1bmzl1\nSsfly5pcjStyRgpgkS1FixblwoULjg5DCCGEcBqRkRquXNFSr17WV3UwGqFjRzPr10sbhCNkWgDf\nunWLRo0aUbduXQICAli9ejUAOp2OevXqUa9ePUaOHGn3QIXjPdw12067ZwsbkT5EdZP8qZfkTt1y\nk79duwy0aGFBr8/eeT06xbB+ZearRgjby7QA9vb2JjQ0lGPHjrFz506GDx+O1WrFzc2No0ePcvTo\nUWbMmJEXsdrVqlWraNOmDTVr1mTgwIG88MILVK9enZMnT5KcnMyUKVOoW7cu1apVY+zYsVgs9//C\n/vPPP3Tt2pUKFSpQrlw5BgwYQFRUVMp1t23bRuPGjfHz86NRo0bs3Lkz5bmAgABCQ0NTjh+fXR02\nbBjvvPMO/fr1w8/Pj4CAAGJiYgDYtGkTzZo1o0KFCvTp04dr166lnNO5c2eqVKnCBx98QJMmTWjT\npg3x8fEA3Llzh8GDB1OtWjXq1avH8uXLU403YsQIOnbsiJ+fHyNGjEh5rlevXpQrVw6Ali1b4ufn\nx3vvvWerL78QQgihPg/W8c1o++OMtKx9k4unE7hwTiaW8lqmBbBer8fNzQ24XzwZjUa7B+UoRqOR\nffv2sXXrVgYNGkTfvn1Zt24dX331Fdu2bWPr1q0cOnSI06dPM3/+fACSkpLo378/f/zxB3/88Qd3\n7txhypQpKdccOXIk7777LhEREQQHB1OyZMmU5zQaDRpNxr0/q1evpm/fvvzzzz+sXLkSvV7P4cOH\neeONN5g9ezZnz56lTp06vPnmmynnNGnShHnz5rFw4UK2b9+OyWTiwIEDAAwZMgQXFxfCw8NZt24d\nU6ZM4dixYynn7tq1i4ULF7J37142bNjAkSNHAFizZg0REREA7N69m4iICD7++ONcfsWFPUgforpJ\n/tRLcqdu2c5fcjJe9eqhXLvBrl1ZW//3cbpSPvT0+pn18+9m+1yRO1nqAY6JiaF27drUqVOHWbNm\nodPpSEhIoEGDBgQFBbF79257x5knypcvj5eXF0WKFKFSpUr4+flx48YNVq5cyVtvvYWvry8eHh4M\nGjSIH3/8EYDKlSvTo0cP3Nzc8PT0pEuXLpw4cSLlmlqtlvPnzxMVFUXZsmWpXr16tmJq0aIFzzzz\nDBqNhlq1amEymfjmm2944YUXqFevHlqtlmHDhrF9+3aSkpJS3oe/vz/FihXD29sbPz8/bt68SWRk\nJDt27GDSpEkYjUb8/f3p3LkzmzdvThmvQ4cOlC5dmjJlylCjRg3OnTtng6+sEEIIkb/o/vwTXFz4\n47ovXl4K5cqlv/1xRno0v0TwJncbRycyk6VuFQ8PD44fP86pU6fo1KkTTz/9NJcvX8bHx4dDhw7R\nvXt3zp49a5PZYdPkybhOnfrE4/FjxpAwdmyWXp/eazPzcDZWr9ej0+nQ6/VYLBYuX77MkCFD0Grv\n/7yQnJyMr68vADdu3GDs2LH89ttvxMXFYTabqVu3bso1ly5dyowZM5g5cyaVK1fmyy+/zFYRXLFi\nxSceu3z5Mnv37mXVqlUpjxmNxpQ2iIex63S6lGOz2cyVK1cAUsVntVrp0aNHyrG3t3fK5y4uLiQm\nJmY5VuEcpA9R3SR/6iW5U7fs5k+fsvtbztofHmrcw4fbO3ScOqWlWrWcFdEi+7LVrl2tWjXKlSvH\nn3/+ScOGDQFo2LAhpUqV4sKFC1StWjXV64cOHYqfnx9wv7CqXbs2FSpUyHCMhLFjs1W8Zvf12aUo\nCqVLl2b27Nkp7/lRH330ETqdjv379+Ph4cH8+fPZsGFDyvONGzdm1apVJCUl8eabb/LJJ5+wYsUK\n4H7R+rCX+NG+4Uc9LLofVaZMGUaPHp3tmw9Lly6NyWTi77//zrT1Ij1ZPe/hr5Ie/oMix3Isx3Is\nx3Kcn46f3bWLxH79WPd5LJ06nQcq5+h6+1z09LJ+y7rgQbzzbqLTvD9nP374eUREBIMOHkTzoDU1\nqzRKJrf0X7lyBaPRSNGiRYmMjKRhw4YcPXoUDw8PXF1duXDhAkFBQZw5cwZXV9eU83bs2EH9+vXT\nvF6pUqWyFWReWLVqFXv27GH27NnUrVuXTZs2sXv3bvbs2UPVqlXZtWsXc+bMoUSJEpw7d46LFy/S\nunVrBg4cSKFChZg2bRoXL17k+eefp3Dhwvz0008oisKaNWvo2LEjRqMxpWCdPXs2AC+++CL16tXj\nrbfe4ptvvuGNN97g8OHD+Pv7A/dvSitVqtQTN5sdPHiQl19+mRUrVlC7dm1u3rxJWFgY3bt3Z9iw\nYQQFBdG8eXO6dOnCsWPHGDZsGC1atOD555+nd+/eVK9enTFjxuDi4sKRI0fw8PCgZs2aT4zXpUsX\nevXqxUsvvZQyds2aNfnss8/o2LFjul9LZ81xQREWFpbyD4VQH8mfeknu1C1b+UtMpFDlylzdf5yq\nTcrxxx93s7QDXHr+eGUhA4+MZP+hWHI4P1XgHTlyhLZt22b59Zn2AEdERNC6dWvq1KnD008/zfTp\n0zl79iz16tUjICCAHj16sHjx4lTFrxo9fkPaw2ONRsOwYcMIDAykY8eO+Pv7079/f27dugXAmDFj\nOHbsGP7+/gwaNIgOHTqkXOdhAVy7dm0qV67MtWvXUhWzb731FqtXr6Zdu3Zcu3YtzdnVtB5r1KgR\nkyZNYvjw4fj7+9O2bVt+//33NGN/3Pz587l58yaNGjWiSpUqTJw4EavVmurcjMYfN24cY8aMoWbN\nmkyaNCnDr6kQQgiRH2nPn8fSqBF7ThSlTh1LropfgJoLXsGcrOOPP3S2CVBkKtMZ4JxS2wywsB3J\nsRBCiILgvfdcKVJEYdSohFxfa+JEE8nJGj78MN4GkRU8Np8BFkIIIYQQTwoJMeTqBrhHde9uJjjY\ngOw1lTekABYin3n0BgGhPpI/9ZLcqVt283flioZr1zQEBGR9++OM1KxpxWSCQ4ekDSIvSAEshBBC\nCJFNu3YZaNXKgs5G9apGAz16JBEc7GKbC+Z3cXGYJk8mp1PmUgALkc/IXejqJvlTL8mdumU3f7Zs\nfwDQXrhAn5jFbNjggtU2k8r5mmH7dvT795PTZTOkABZCCCGEyCLD2rUkJySxa1fuNsB4nOLuTsCK\n9yheLJnfftPb7Lr5lcu6dSQ92MjrwUa42SIFsBD5jPQhqpvkT70kd+qWlfxpLl3CbexYjv9ppEgR\nhTJlbHfHmlK8OEqpUvQM/EfaIDITHY1h1y7MnTqRnAxt2nhm+xJSAAshhBBCZIEhNBRLy5aEhLrY\ndPb3IXNQEL3df2TTJgNm218+33DZuhVzYCBK4cKEhOhz1AUhBbAQ+Yz0Iaqb5E+9JHfqlpX86UND\nMbdqRUiIgTZtbF+hWpo3p+LJnyhXLplff5U2iPQY1q3D3L07APPmmXjttcRsX0MK4McsWrSIypUr\n4+fnx6+//pry+KhRo5g2bVqq144ZMwY/Pz+KFStGaGhoXocqhBBCiLySnIwhNJR7Tdpw9KieZs0s\nNh/C0qwZ+t9+o0e3BGmDyED8pEkkPfccp09rOX5cR48e2W8ClgL4EWazmQ8//JANGzYQERFBy5Yt\nU56bPn06o0ePTvX6qVOnEhERQZkyZdLcdhigc+fOrFixwq5xC/Eo6UNUN8mfeknu1C2z/On+/BPF\n05OwCH/q1rXg4WH7GJTixYn99lu6dklkyxYDidmf2CwQkitUAA8PFiww0b9/IiZT9q8hBfAjrl27\nRkJCAlWrVrXZNdMrjIUQQgihHoqbG/HjxrFzp4HWrW0/+/uQJTCQUmW11KxpZccOg93GUbs7dzQE\nBxsYODBnPyVIAfxAYGAggYGBAJQvXz6lBWL79u34+flRokQJPv744yxf7/PPP8fPz499+/bx9ttv\n4+fnl2qP6jt37jB48GCqVatGvXr1WL58earzhw0bxjvvvEO/fv3w8/MjICCAmJgY27xZka9JH6K6\nSf7US3KnbpnlL7l8eczdutl8/d/09OiRxLp10gaRnhUrXOjQwUyJEjlbiUM6rB/Yt28fFy9epG7d\nuly4cAGt9t+fDSIiIhg2bFi2ZnP/97//8b///Y8uXbrQu3dv+vbtm+r5IUOG4OPjQ3h4OFevXuW5\n556jTp061K1bN+U1q1evZu7cuXz99decOHECvV7SJYQQQjjKpUsabt3SUKeO/Xeq6NzZzIQJrsTG\ngru73YdTFbMZFi408c03OZ8YlBngRyiZbKeX2fNZPS8yMpIdO3YwadIkjEYj/v7+dO7cmc2bN6d6\nXYsWLXjmmWfQaDTUqlULU06aXESBI32I6ib5Uy/JnbplJX8Ptz/W5kH1VKyYQoMGVrZvlzaIh7R/\n/QWKwo8/GihXzkpAQM5/EHG6KcUiRQrb5Dq3b9+xyXVs4fGZ48uXLwOkmu21Wq30eLCjyUMVK1a0\nf3BCCCGEyBJ7LX+WpuTklDaI7t1lUWBNZCSe7dtz788/mTfPixEjEnJ1PacrgJ2pcH1cei0QLi4u\nWNPZuFubxo+JpUuXxmQy8ffff2fYVpHWuUJkRvoQ1U3yp16SO3XLLH9WK4SG6vnoozi7x6IPCcG4\ncCGd5n7Lu++6ERUFXl52H9apuWzciPnZZzn0hzvXrmno0CF3PxRIhZUN6bVAVKpUib1796b5nI+P\nDydPnkz1mK+vL82aNWP8+PHExsZiNpvZv38/J06csHnMQgghhMg5zb17ePTsye/hWooXVyhd2nbb\nH6fHWrs2hj178HY3ExRk5qef5GY4l3XrSOrenfnzTbz6aiI6Xe6uJwXwYx6fke3Rowd+fn788MMP\nzJo1Cz8/P4YPH57qNe+99x6bNm2ibNmyfPDBB6meGzZsGLt27aJmzZp07do15fH58+dz8+ZNGjVq\nRJUqVZg4ceITs8iyhJrICelDVDfJn3pJ7tQtvfzpw8JAUQjZZZ/tj9OiFCtGcpky6H7/Pc9Xg9Dv\n2IFh48Y8Gy8rNJcuoT1zhn+qtGHHDj19++Z+gWSna4FwJD8/P27evJnqseDg4EzPq1mzJr/99lua\nzwUEBKQ5O1y4cGFmz56d7jUzek4IIYQQeUMfGor5qacI+VnP66/nru80O8xBQejDwmg/sD6jRrlx\n+7aGIkXsO/usuXwZ99deA62We23aYJfdPnLAZf16zB07smSFB717J9mkHURmgIXIZ6QPUd0kf+ol\nuVO39PJnCA3lTuO2hIfbZ/vj9FiaN8cQFoaHB7RubWHTJvuvBmFcuZLEwYOxNGuGcdEiu4+XVckl\nS3Kn939ZvtzIK6/YZns8KYCFEEIIIdKguXQJza1b7L5Th/r1LXm6Hq+lWTO0ERGgKHnWBpHw1lv8\nGvQW+7pNwLRw4f0Fd52AuWdPvjvXlEaNLFSsmGyTa0oBLEQ+I32I6ib5Uy/JnbqllT/Dnj1YWrYk\nJDTv+n8fUooVI2rfPtBoaNfOTHi4jshI+90b9M8/WgYM9OC/Azz5z3u1uLx1DxicYw1iRYF580wM\nGWKb2V+QAlgIIYQQIk1JvXoRO2PGg+2P8679IcWDm+FdXeHZZ81s3Gj7WeCoKJgwwZU2bTypUcPK\noUP3aNnSzCdzS9p8rJzatUuPTqfQooXtciAFsBD5jPQhqpvkT70kd+qWZv60Wi7eK8SdOxpq1bL/\n9scZ6dEjieBg2xXAFgssW+ZCkybeXL+uISwsirfeSsDNDT76KJ7gYBeOHcvlWmM28nD215aLY+V5\nAawoSo63FBbOT/IrhBAiPwkJ0fPUU+Y82f44I61aWTh7VsulS7mvAkNC9LRq5cXapYl8P/00s2fH\nUbLkv/8aYci5AAAgAElEQVR3Fy2qMH58PG++6YbFARPfjzpzRsuxYzr+7/+SbHrdPE+nt7c3t2/f\nzuthRR65ffs23t7ejg6jQJM+RHWT/KmX5E7d0sufw9ofHuPiAp06mXN1M9xff2l5/nl3Ro1y450R\nNwi9WZv6ppNpvrZPnyS8vRUWLDDmeLxcURQ8undnwecW+vdPxGSy7eXzfB1gDw8PEhMTuXLlSl4P\nLbLh3r17OSpkjUYjHk6ybqAQQgiRG1Yr/Pqrnk8+sf/2x+nRXLqE9tYtrAEBdO+exIQJrowYkb2b\nwW7f1jB1qom1a114440Evl4WQ5HXhmDu0hlLmzZpj6uB6dPjaN/ek977RlH88zdRihe3xVvKEt2J\nE9w7e4u14YXZuzfK5td3yEYYRYsWdcSwIhtKlSrl6BBEDkkforpJ/tRLcqduqfKXlIT24kUO362C\nr6+Sqj0gr+mPHsW4YgUxq1cTFGThyhUt585ps7QcWFISLFpk5IsvTHTrlsS+fVEUK6bg8v1qdKdP\nEztnTobnV6yYzJAhiYxcMYQfvpxJwqSJtnpbmTKsW8dX/hNpX8aMr6/tv/5yE5wQQgghxCP0hw7h\n/uqrD9ofHLsWrqVZM/T794PFgk4HXbtmviawosBPPxlo3tyLkBADmzZF89ln8RQrpqCNiMB13Dhi\nFyy4v7xEJl5/PYFzhmr8uCwKTWSkrd5WxhQFbfBG5p19lsGDbbf02aMyLIBv3bpFo0aNqFu3LgEB\nAaxevRqA1atXU6VKFapWrcqPP/5ol8CEY0kvm3pJ7tRN8qdekjt1ezR/+pCQ+9sfh+gdXgArRYti\nLVsW3bFjAHTvnvFqEMeP6+je3YOJE1359NM41qyJoVq1f2eLdUePkjBqFNZatbI0vosLfPFVIiM1\nX5I4dV7u3kwW6Y4eZUN8e0qX11G3rn1W38iwAPb29iY0NJRjx46xc+dOhg8fjtlsZuzYsezZs4df\nfvmFkSNH2iUwIYQQQghHMISGcrtRW44f1xMY6Pgb4CxBQej37AGgcWMr0dEaTp5MXcJdu6bh9dfd\n6NXLgy5dkti9O4p27Z6M3dy1K4lDhmRr/KZNrTzdUcNH39ZCc/lyzt9IFukPHmSGYbRNN754XIYF\nsF6vx83NDYC7d+9iNBrZv38/NWvWpHjx4pQtW5ayZcsSHh5utwCFY0gvm3pJ7tRN8qdekjt1S8lf\nVBS6U6cITQykQQMLD8ogh7IEBWF4MEOt1d6fBX7YBhEfD59/bqJ5cy8KFVLYvz+KgQOT0Nv4Lq8P\np0CwoQ9Hgu2/iMG+RkO5pPWjY0f7zb5n+uWJiYkhMDCQc+fOsXLlSiIjIylZsiTz58+nSJEi+Pr6\ncvXqVQICAuwWpBBCCCFEXjDs3o2lYUNC9rg5vP3hIUuzZmjPnk057t49iVdecadaNSsffeRKQICV\nn3+Opnz5zG+My6lChRQmfqFlxBdtCBkSbdddkufPN/LKK4lZLuJvxt3M9hiZXtrDw4Pjx49z6tQp\nOnXqxPjx4wEYPHgwAMHBwWjS2Zpj6NCh+Pn5AffbKWrXrp3yE9bDXhs5ds7juXPnSr5UevxoH5sz\nxCPHkr+CcvzwMWeJR45zlr+Tf/6Jvl49QjYaWLo01mniC3rQchoWFoaigFbbka++MvHaa/upVesW\n5cvbP54ePczMmRPHmDE3+eKLknYZb8OGg2zZ8hRTpyZl+Pp75nusOLyCcHM4t0232dJqC9mhUbKx\nbVfbtm0ZP348U6dOZdOmTQC0bt2aL7/8kjp16qR67Y4dO6hfv362ghHOIywsLOUvm1AXyZ26Sf7U\nS3Knbo/m759/tLRv78nJk/ccvgNceu7e1eDlpWQan37HDjRJSZg7dLDJuBcuaGnXzpMdO6IpV872\nM84ff2wiKkrDlCnxTzx3M+4mP577kQ1nN3D02lHalmtL18pdaVeuHaeOn6Jt27ZZHkef0ZNXrlzB\naDRStGhRIiMjOX36NFWrVuXEiRPcuHGDhIQELl269ETxK9RP/hFXL8mdukn+1Etyp26P5s9Ztj/O\nSKFCmc9fam7exH3ECGIXLrTZuP7+yYwYkcCoUW6sWRNDOk0AORIfD19/bWTLluiUx9IqegfUHsDK\nTitxM+S8QTvDAjgiIoJXX30VAEVRmD59Oj4+PkyePJnmzZsDMGPGjBwPLoQQQgjhbEJCDHa9AStP\nKApuI0eS1Ls3lgc1m60MHZrImjUuBH+bTM8XbfdTQvA7f9CgRgDeJa+z7Ljti95HZasFIjukBULd\n5Fd56iW5UzfJn3pJ7tTtYf4sFqhc2Zt9+6LssgNZXnFZsQLjokVEb98ORqPNr3/so+38Z97T7Dmp\nzdJsdGZu3L1Kt0pQYtAcjpRfkaq9IStF75EjR2zXAiGEEEIIUZAcOaKjTJlkpyx+DZs3o4mKIumF\nFzJ8nfbvv3H96COiN22yS/ELUPfNQLrNW8+EkR35YlnOxni0vcHyvTtW/Wf0f7kR3/i/Y7OZ3vQ4\ncXeLcCSZxVAvyZ26Sf7US3Knbi19fTHOnftg+2OLo8NJl8vatZm+RhMXR/wnn5BcrZr9AvH05P2R\n1/l5u4HfftNl+bSbcTdZdnwZ3dd1p+Hyhuy+tJsBtQfg9cdHvNHxPF0rd7F78QtSAAshhBBCYNi+\nHd2ZMw8KYOfs/7U0a4b+wAEwZxyftVYtknr1sns8pmF9+cL4Nv8bqiMpKf3XpVf0nhx0ksUdFlPT\n3JFDV/3oPq683WN+SApgkaZH10UU6iK5UzfJn3pJ7tQtev16bjR6mpMndTRt6pwzwErhwlj9/dEd\nO+boUO5zd+e50eWpEHeCmTNNqZ7KrOjtUunfmd5FE+4wqNRmTBVK5lno0gMshBBCiIItKYkiJ07w\nvaYNjRpZcHV1dEDpszRvjn7PHqyNGjk6FACSBg5gWsJmguY25Klnr/GHsi5bqzfcu6fh+/0V2ff1\nvTyNW2aARZqkl029JHfqJvlTL8mdeukPHUJTrRo7DxZ22vaHhyxBQRic6LcNN5VYtj4TQ6F2c+nw\n33/49WL6M71pWbHChaefsVCiZaU8jFpmgIUQQghRwLn88APm9u0J+U7PoEEJjg4nQ+annsJaq1aq\nxww//YTuxAkS3norT2JIa3OK90Z244vBgTwT1ZAulTJoCH6ExQILFxpZtizWzhE/SWaARZqkl029\nJHfqJvlTL8mdeiWMHMm3xZsSH6+henXbb+9rU+7uJJcrl3KouXYNt1GjMLdsaddhM+vp7V6tM1/O\nSGD8eFdu3cra9nA//WSgVCmFevWsdo09LTIDLIQQQogCLdnPj4NnNLRubbbp1r52pyi4jxhBYt++\nWJs0sfnls7sNcb16Vrp3T+KDD1yZPTsu0+vPm2dkyBDHzLhLASzSJL1s6iW5UzfJn3pJ7tTt4sVq\ndOni3P2/jzMuWYLm1i0Sxoyx2TWzW/SmYrXyQeBPNH6vG7t362nRIv3VNI4d03EpAp5rH48jylEp\ngIUQQghRoJnNsHu3nunTM5+1dBbav/7CNHky0Vu2gMGQq2vlquh9lKJQ4qO3mNa/DKNGNeDXX6Mw\nmdJ+6fz5RoZ5fo3bRitJvXvnKv6ckB5gkSbpZVMvyZ26Sf7US3KnXocP6yhaNBofH+fb/jg9yb6+\nxC5aRHKlnK2ekJ11erNMrydhzBj+b8frVKtq5Ysv0q5+IyM1bNuq59VLE0h69tkcxZ9bMgMshBBC\niAJHd+gQmExYa9Vi+XIjgYHngRKODivrvLywtGqVrVNsNtObgaSePTFNn85nA3+h+TvP0qNHElWr\npr6xcMkSI73qnMTDsw6xXl42GTe7NIqi2OXHnR07dlC/fn17XFoIIYQQIlc8O3QgYfBgjlTsSa9e\nHhw4cA8H1WJ2lVbR27VyV9qVa2ezovdxhuBgTHPmML3Xr2zY6MKmTTFoH/QcJCRAQIA3OysOxH9Q\nEOaePW0y5pEjR2jbtm2WXy8tEEIIIYQoUHQHDqCJjMTcqRPjx7syenRCvip+7dLekA3mbt3QxMcz\nuOI2EhM1rFzpkvLcDz+4ULdGPDVPBGNu395uMWRGCmCRJullUy/JnbpJ/tRLcqceptmzSXztNXb+\naiIiQkv//omqz5+ji95UtFqiV69Gad2SL76IY+JEV27c0KAo95c+G9ojgoTXXwcPj7yJJw3SAyyE\nEEKIAkN7/jz6vXuJnjWbCZ1def/9+NwuouAwedHTm1NK6dIA1K5t5fnnk3jvPVf69k3CatXQsq8v\nCZpRDo1PeoCFEEIIUWC4jh2L4uHB8iofsWiRkW3bolW1+YUjenpzKzYWmjf3wmCA4cMT6N8/a1sl\nZ0d2e4BlBlgIIYQQBUbC2LEkJGqY9LSJBQtiVVH8OvNMb1a4u8Nnn8UxcqQ7vXrZvvjNCekBFmlS\ney9UQSa5UzfJn3pJ7tRBKVSIBat9qFPHStOm1pTHnS1/TtXTawNPP23h2LF7uDlJyDIDLIQQQogC\n484dDTNnmti8OdrRoTxB7TO96TGsXw96PXTq5OhQUkgPsBBCCCEKjPffdyU2VsPnnzvHtsdq7OnN\nLn1oKG6jR5Pw2mvg6krSCy/YfAzpARZCCCGESENEhJZVq1zYuzfKoXHk15ne9FhatiTZ1xe3998n\n5ptvHB0OID3AIh3O1gslsk5yp26SP/WS3Dkv3W+/od+7l48/NvHKK4mUKPHkL7/tnb/81tObLRoN\nCe++S3Lx4lhatHB0NIDMAAshhBAin3P9+GMOtBnFr78amDbtXp6NW9BmejNiCQwk6tCh+73ATkB6\ngIUQQgiRb+mOHMGt/39pV+EcnbuaGTjQvstwFYSeXmckPcBCCCGEEA+YZs9mc7upXN6j46WXYu0y\nhsz0qo/0AIs0SS+beknu1E3yp16SO+ejjYhAE/Ir7x3oyQcfZLzlcXbzV6B7evOBTGeAL1++TJ8+\nfbh79y5Go5EpU6bQrl07dDodderUAaBVq1bMmDHD7sEKIYQQQmSVy7JlfN1oBu73tDz3nDnX15OZ\n3vwj0x7g69evc+3aNWrXrk1ERATNmjXj0qVLeHp6Eh2d/iLS0gMshBBCCEeKv5tI46BiLFocR5Mm\n1sxPSIP09KqDzXuAfXx88PHxAcDPz4+kpCSSkpxjH2chhBBCiPQs+NqLevWTs138ykxv/petHuBt\n27bRoEEDXFxcSEhIoEGDBgQFBbF79257xSccRHrZ1Etyp26SP/WS3DmX27c1fPWVifffj8/S6zeH\nbJae3gIky6tAREZGMnr0aDZu3Ajc7w328fHh0KFDdO/enbNnz2I0Gu0WqBBCCCFEVk2fbqJr1yQq\nV05O9zWPzvQeunKIZyo8IzO9BUSWCuCEhAR69erF9OnTKV++PEBKW0TDhg0pVaoUFy5coGrVqqnO\nGzp0KH5+fgB4e3tTu3ZtgoKCgH9/UpZj5zx++JizxCPHWT8OCgpyqnjkWPInx3Kc18eRka58910b\n9u2LeuL5zSGb2Xd3Hyc4wdFrRwlwD6B5oeasfPV+0RsWFsaRyCNO9X7k+Mnjh59HREQA8PLLL5Md\nmd4EpygKL774Ii1btuS1114D4M6dO5hMJlxdXblw4QJBQUGcOXMGV1fXlPPkJjghhBBC5DX9vn0M\nmlSdiq18GTMmAZAb2QqC7N4El2kP8J49e1i7di0LFiygXr161K9fn1OnTlGvXj0CAgLo0aMHixcv\nTlX8CvV79CcsoS6SO3WT/KmX5M45nHh/A7tP+tBnwOVs9fRK/goWfWYvCAoKSnPVh1OnTtklICGE\nEEKInIja/ytjjvfFu/ccWq2dJKs3iHRl2gKRU9ICIYQQQgh7e7S9oenHXiy/OYNJW8NoX7GtFL0F\niM3XARZCCCGEcCZp9fS+VrQrky6057N5HnSs1tnRIQonl611gEXBIb1Q6iW5UzfJn3qpLncWi6Mj\nyJabcTcz7Om9u9gfrxIudOhpyNH1VZc/kSsyAyyEEEIUJGYzpqlT0Z05Q+yyZSgKJCZCYqKG+Hjg\n8zkkr9tCXNHSxBcuSVyhksR7+RBbswHxpcqTkKB58HH/nEf/TEjQkJgILi7w2msJ1KiR/hq8WZHV\nHdni4mDCoS4sm38bjSaXXx9RIEgPsBBCCFFAaM+fx/3VV4nz9OH14qv4fpN3SsFqMimYTGA0Kph0\nFozaJEyaBFyVOEzWOIy+3riULnb/+QevNZkU3P84jOuVvzEWdsVYxA1jMXeu6Mry1bryPPOMmXfe\niadUqayXGjlZsuyLL0yEh+tYtizWVl8qoTLSAyyEEEKI1BQFl9WrcR03juP9P+Y/2wZRvZiVkyfv\n4eWloE23IVIPeD34AHiywNT+qUX/RwKaq+fRXrmC9upVdMeOMWDyDD4/3oEWLbwYODCRESMS8PJ6\n4nQg6zO9aZ57U8Ps2Ua2bYvO4hdDCCmARTrCwv7dBU6oi+RO3SR/6uXMuTNs3YppxgyWDQ9jzFdV\neO+9ePr3T7JJu0By9eokVa+e+sHERDz0ej7onsDAgYl8+qkrjRt7M3p0Av37J2Iw5K7ofdS0aSZ6\n9kyiYsXctVs4c/6E7UkBLIQQQuRz0a3a80aTruxaYWLt2hjq1LHad0CjMeXTMmUUZs+O4/hxHe++\nr+OzmVC8y+dcLD2Tdv65W6f377+1rFnjwm+/RdkyelEASA+wEEIIkY+dP69lwAB3/P2TmTkzNt02\nBHt5dKa3eOgBzIYRHAl9mxKF3Zn4USJNmuS8GH+5azw1vf7hzRXVbBixUCObb4UshBBCOEQau5Dm\nhqLAjRsaovN7q+gjy5tt2mSgfXtPXnwxiaVL8674TW/JsgX1JxG8fjF/thnHgD7RvPyyB/37u3Pu\nXPbLkcOHdfy234XhrcPt8A5EfictECJN0gulXpI7dZP8PaAoeNeti1KoEJa6dbEGBGAJCMBauza4\nu6d5SmwsXL6s5dKl+x8PP3/0Tzc3BTc32LIlijJlbPsLUGfIneGHH3D97DNu/hzKh58WZutWA999\nF0P9+nZueSCLPb2VIKpjZ1wnTmTIZ7Xo/fZ4Zt15ifbtPenZM4m33kqgWLHM86IoMOEthQ9Nn2L4\nz1s2id8Z8ifyjhTAQgghnI9Gw71jx9D9+Se6Y8fQHP2d29/s4lIEnJq+mstX9E8Uu3FxGkqXTqZM\nmWRKl77/0bSphTJl/n3MzQ1mzzbSs6cnmzdHZ6nYUoWoKNzGjEF/9CgnP1rOf3sUx9c3mZCQaAoV\nst97zMmNbEqxYsR9+SW6I0coNGYM79bZT9/fvmDaNBNNm3oxdGgiQ4Yk4JZBS/D27QZu/X2XF0Z4\nYnmk31iIrJIeYCGEEE5nyxYD69YZUorcyEgtRYsqlC5tpUwZJaXQffhR1nCVMrM+JLluwP0Z41q1\nwMMj3etPnGhi1y4D69dH4+mZh2/MDnQHDuA+eDCWp55ibctpjBxbhNdfT2Do0ES7bAqRk3V605Wc\njObWLZTixYH7N7VNnOjKwYN63nknnuefT0KnS32KxQItA12ZEvlfWv7+CUrhwjZ6Z0LNZB1gIYQQ\nqnbvnobXX3dj3Lh4KlW6X+CWLJmMi0v652juGbE2C0QfHo7LDz+g+/NPksuWJalLFxLeffeJ148b\nl8CtW1r69fPgu+9iUOskoiYyEo8BA7j38VQ+OPJ/rP/QwIoVMTRubNuWB1stWfYErTal+AWoUCGZ\npUtjOXhQx4cfujJ3rpHx4+Np29aSUsyvWuVCUeUmT7/oTYIUvyKHZAZYpEl6odRLcqdukj+YOtXE\nhQta5syJy/lFzGZ0p06hiYnBEhiY5kusVhgwwB2NBpYsiX1ipjG7HJW7S2cTeXl4Mby8FObOjaVo\nUdv8t27Tmd5s0ty6hfb0X2y625IJE1wpVSqZCRPiqVjRSuPG3ixfHkODgETQ224eT7731E1mgIUQ\nQqiSyzffcKd4JRYubM/WrblcqsFguH/DXDp0J05AzZosXBhLnz4ejB7txuefx9mlZcCefv5Zz4gR\n3gwZksDrrydmsKNb1thtpjebtBcu4DH4Vf4vMJBnVo9n+Q5/+vTxoFixZJo0sdCggRUpYURuyAyw\nEEIIh9Pcu4dXo0a83/0If0f75G72NzNRUXg3a0bcpEmYu3UjOhq6dfOkdWsz48Yl2G/c3DKbwWAA\n7vfBfvqpie++M7JwYSzNmlkyOTl9jpzpzVBsLKYvvsC4bBkJI0Zws+9rLF3pSY8eSTZfwUOon8wA\nCyGEUB3jzJncbN2N+cGlcz/7mxkvL2K+/RaPnj2J8fXFs2lTvv8+huee86RIEYWhQxPtO34O6A4f\nxn3IEGK+/prLhWvyyivuGAywa1cUxYtnvxh0lpneDLm7kzBuHEkvvojru+9SetUqXt+1C1xdHR2Z\nyAdkIwyRprCwMEeHIHJIcqduBTF/mshIjMuWMbPERNq1M1OxYrLdx7TWrk3svHl49O+P9q+/KFZM\nYe3aaObONfHddxncbZcBe+XOOGcOHi++SPy4cey8Xoc2bbxo2dLCDz/EZKv4TW9zipODTrK4w2K6\nVOriPMXvI5IrVCD2u++IWbrUrsVvQfzeK8hkBlgIIYRDmaZN40bPgcz71octW/JumzZLmzbEf/gh\nHn36EL11K2XKlOCHH6Lp2tWTQoUUnn3WnGexpElRME2ahMtPP3Fn+w6mfluJ5cuNzJsXS6tWWWt5\nUMVMbxYl16jh6BBEPiI9wEIIIRzHbMajRw8mNN7A2SsezJ1rx97fdBgXLsTcti3JFSoAcOiQjhde\n8GD58lgCA3PeW5tbpk8/xbBtG3/PX8+rY8tgtcKCBbH4+mb837bT9vQKYUfZ7QGWAlgIIYRDRUVB\ngwbebNkSTaVK9m9/yIqQED2DB7sTHBxDrVr230Y4LcqJU3z9a2U+nVGEfv0SefvthHRX/ZKiVxR0\n2S2ApQdYpEl6odRLcqduBTF/CxeaaNvW7DTFL0Dr1hamTImjTx8Pzp/P2n+Vtszd/v062gxvxOpN\n3vzwQwzvvfdk8avWnl5nVRC/9woy6QEWQgjhMFFRMH++kc2b8673N6u6dzdz9248PXt68NNP0Zm2\nHtjCtWsaJkxwJTTUwPjx8fzf/yWlWps4P/X0CuFI0gIhhBDCYT7/3MTp01rmz8/73t90KQraU6dI\nrl4dgGnTTKxfb+DHH2MoVMg+RbA53sL8xe7MmGGib98kRo2Kx9Pz/nPS3iBE5mQdYCGEEM5NUSA2\nlqhkD+bNM/Ljj841+6u5dg3Pbt2IXbAAS6tWjBqVwK1bGl54wYO1a6Nxs3HNGbI5iXdfiadMtWS2\nbDFTuXIyN+Nusva4zPQKYS/SAyzSJL1Q6iW5U7eCkD/DTz/h8dJLLFpkonVrM1WqOE/vL4Di60vs\nkiW4v/IK2pMn0Wjg44/jKVfOysCB7pjTWR0tu7m7eFFL/xcMjB5kZmKLH5mz4S57EpZIT6+DFITv\nPfEvKYCFEELkHYsF14kTuTHgdebNMzJqlHNuPWxp3py4Tz/Fs08fNJcvo9XCrFn32zRGjHAjORc1\ne3w8TJ1q4qmWHtQ9tISvu73C7D5raLSysRS9QuSRTAvgy5cvExQURK1atWjQoAG//PILAKtXr6ZK\nlSpUrVqVH3/80e6BirwVFBTk6BBEDknu1C2/58/l++9JLlaMeWef5amnnG/291Hmnj1JeOUVPPr0\ngagoDAZYsiSWf/7R8d57rjx+B01muVMU+OknA00CPdge8jebDTUw1BvDF11MDKgzUIpeB8vv33si\ntUx7gA0GA3PnzqV27dpERETQrFkzzp8/z9ixY9m/fz8JCQm0bt2aTp065UW8Qggh1CohAdfJk7k6\ncylzB5ucrvc3LYkjRkByMproaBQvL9zc4NtvY+jUyYPPPzdleQb7wPF7vPEWXLwIdHiDLjXi0Fxv\nysBRO6XYFcIBMp0B9vHxoXbt2gD4+fmRlJTEvn37qFmzJsWLF6ds2bKULVuW8PBwuwcr8o70QqmX\n5E7d8nP+jIsXY6lTh/nHgmjVyuLUs78pNBoSR45EKV065aFChRR++CGGb75xYelSl5THH8/dzbib\nzNu/kjovbqVDB08MlUOYufZX/vp0DpMGrqbq2BlS/DqR/Py9J56UrVUgtm3bRoMGDbh+/TolS5Zk\n/vz5FClSBF9fX65evUpAQIC94hRCCKFylgYNuN38Web2NrJpk/PP/mbE11dh7doYOnf2pHBhhW7d\n7t8Z93DJsvVnNnBweyWUn6fQoNkdNu5Pwr90NwdHLYR4KMsFcGRkJKNHj2bjxo0cPnwYgMGDBwMQ\nHByM5tGVuoXqSS+Ueknu1C0/58/atCkLZxhp1cpC1aoqmP3NRIUKyXz3XQzde7ix//Y2ThWexdHl\nR2mgDCJy9fdUUgrz2bcJNG5c1NGhiizIz9974klZKoATEhLo1asX06dPp3z58ly5coWrV6+mPB8Z\nGUnJkiWfOG/o0KH4+fkB4O3tTe3atVP+gj38VYMcy7Ecy7EcF4zjunWDmDvXxPjxoYSFxTg8nhwf\n796NcuEU5+oa2HB2A3HdjCz+8Hve+MQL/zOBrA828J//nGLCBBd0Ovhz9my8/vmH0lOnOkf8cizH\n+eD44ecREREAvPzyy2RHpjvBKYrCiy++SMuWLXnttdcASEpKolq1aik3wbVp04YzZ86kOk92glO3\nsLCwlL9sQl0kd+qWn/P35ZdGjh/Xs2hRrKNDyZGH7Q2Hw77li08OMeWdVtR+5r+0K9eOX3d407+/\nK/36mXn33QQKF77/X6th2zbcRowgdulSLM2bO/gdiIzk5++9gsDmO8Ht2bOHtWvXcurUKRYsWIBG\no2Hz5s1MnjyZ5g++mWfMmJHziIUQQuR7MTEwZ46JDRvU1fub5jbETw9DW8rM1Hc/ILpTXZINbjz7\nrJlvvw2lTZtmKeca1q3DbexYYlatwtqwoQPfhRDicZnOAOeUzAALIYRwWb0ac/v2zFjmo5rZ3zSL\n3scZ4uEAACAASURBVMpdaVeuXapVG4wLFmBcvJjorVtRChdOdQ2XlStx/fhjYlavxlqrVl6/BSEK\nHJvPAAshhBA5ofvjD1w/+IDbLTs6/exvWkXvgNoDWNlpZbpLlSW++iraixdx79uXmLVrwWS6/0Rs\nLMYVK4hev57kKlXy8F0IIbJKtkIWaXq0yVyoi+RO3fJT/kyTJpHw5pssWV2UoCAL1ao518oPN+Nu\nsuz4Mrqv607D5Q1ztA1x/IQJWJo3RxMb+2/u3N2J3rJFil+VyU/feyJzMgMshBDC5vT79qE7dYpr\nc5YzO9DE+vXOMfubk5neDGm1JLz77pOPy9KgQjg16QEWQghhW4qCZ4cOJA4YwLRr/Th2TM+SJY7r\n/c1qT68QQr2kB1gIIYRD6X7/HWJjudPh/5jT2ERwcN7P/tp8plcIka9ID7BIk/RCqZfkTt3yQ/6s\nAQFEb9/O4mVuNGtmoUaNvOn9tUVPb27kh9wVZJK/gkVmgIUQQthcbLIrc+bYf/ZXZnqFEDkhPcBC\nCJFNxpkzSRwyBFxcHB2K05o1y8iRI3qWLrV976/09AohHic9wEIIYUeaO3dwGz8ea/36WGTb1DTF\nxsLs2bad/ZWZXiGELUkPsEiT9EKpl+TOvnS//w6APjTULtdXbf4e+WXikiVGmjbNfe+vo3t6s0u1\nuROA5K+gkRlgIYTIBl14OEldupDUr5+jQ3EqpmnTSC5enDu9/pur2V+Z6RVC5AXpARZCiGzQHToE\nLi5Y69RxdChOQ3PjBl5NmxK9cyczN1Xh0CE9y5ZlvfdXenqFELklPcBCCGFH1oYNHR2C0zF9/jlJ\nvXoRU7wcX32VtdlfmekVQjiS9ACLNEkvlDpp7tzhyujRjg5D5ILavve0ERG4rF5Nwv/+x9KlRpo0\nSb/3V209vdmlttyJ1CR/BYvMAAuRjyju7lRes4aEXr2wNmni6HBEAWCaMoXEQYOI9fDhq69M/PBD\nTKrnZaZXCOGMpAAWaQqS5Z3UycUF86ef4vbhh0Rv2QIajaMjyt+Sk8FqBYPBZpdU1feeoqAUL07C\n8OEsXWqkcWMLNWtaC2zRq6rciSdI/goWaYEQIp9J6tMHYmMx/Pijo0PJ99yGD8clONjRYTiORkP8\n+PHE6b2YOcuFqt2/z7ftDUKI/EUKYJEm6YVSr7B9+4ifMAHXjz4Cs9nR4eQr7q+8gub69ZRjS6NG\nNl8PWE3few97eluNWsmd4j9xzriuQBe9asqdeJLkr2CRFggh8iFLmzYk+/lh+OUXzB06ODqc/CEq\nCsPWrShz56Y8ZGnZEtdp0+5vAlFA2k0eb29o5duBm78s4ac10TSs28LR4QkhRJZIASzSJL1QKmSx\nQHJySu5ivvkGXF0dHFT+of/jD6zVq4P+3382kytUQNHp0J45Q3KVKjYZxxm/9zLq6f16UWGUQD0N\n67o4OkyHc8bciayT/BUsUgALkU/oDh26f/Pbtm33H5Di16Z0x45hCQhI/aBGg6VVKwyhoSTaqAB2\nFhkVvR6Rt0guW5a4OJg1y8T338dkfkEhhHAi0gMs0iS9UOqjO3sWa8WKkjs70f3+O9bHC2DA3LYt\nmmvXbDaOI/OXlXV63a/fwfOpp9Dcu8fixUYaNrRQu7bVYTE7E/neUzfJX8EiM8BC5BO6M2dIrlTJ\n0WHkW/pjx0gcPvyJx/+/vTuPs7FuHzj+uc8+O7JnKfs2gyFLRhQVxpKEUCGibGmT8jxtT4tEeTyW\nNiVSflqUTAgJIzOyzUxZxxLZhdnPnO3+/TGNyAyznO2ec71fr165xzn3/Z255j6u8z3X9/ra77kH\n+z33+GBE7lHclmWW//0P2+DBpOsimD3bwrJl19/1TQgh/I2iqqrqiROvW7eO6OhoT5xaCFGAkCFD\nsA0ciL1374IfEEALtTxBt38/rptvRjUYeeGFIJ55JofwcF+PqmQKSnr71O9D19pdr9m1QTl9mvD2\n7UnfsoW3P6vNb7/p+fDDLC+OXAghCrZjxw66dOlS5MfLDLAQZYQ+NRVnITPA+oQELLNmkfXZZ14e\nVdmRv8jtj2M65syxcPPNTh5+2ObjURWdOzansMyejW3AANKCqjBvnpm4OJn9FUJok9QAiwJJLZTG\nuFwo2dm46tQpMHbOVq3QHziA4ccffTC4siUxUU+1ai4WLDDjic/P3HnvFaWmt6jJr3LuHKbFi7FO\nmMC8eRa6drVTv77LbWMtC+R1U9skfoFFZoCFKAt0OtJSUgr/e6ORnBdeIOjFF8no1An0eu+NrYxJ\nSDDw2GNWPvrIzPbtelq39q8FYJ7ahlg1m8l67z3OB93IBx+YWbNGZn+FENolNcBCBApVJaxHD3If\nfBDb4MG+Ho1mdewYxjvvZLN5s4EDB/TMnp0N5JWZqOXK4WrUyOtjKmlNb0m8+qqFs2d1/Pe/2W49\nrxBClIbba4CffvppPv30UypVqkTKXzNMer2eqKgoADp16sTMmTNLOFwhhNcoCtkvv0zoww9ju+ce\nCA6cLWpLxeXKWzyoKKSlKRw5oicqyknt2i5uuSWc115TiIhQMf70E4rVSs5LL3llWJ6a6b3mNc8p\nfPyxmZ9+ktlfIYS2XbcGuF+/fsTFxV3xteDgYHbu3MnOnTsl+S2jpBZKu64VO2ebNljHj0fJyfHi\niLRNv20boX+1OfvlFz0tWjgwmaBSJZU77nCwdGneDmj2zp0xbNhQ6utdK37urOktiVmzLNx7r42a\nNaX2tyDyuqltEr/Act0Z4Pbt23PkyBEvDEUI4Q25o0f7egiaYkhKwlWnDgCJiQbatnVc+rthw3J5\n7rlgRo7MxRkdjf7gQZTz51ErVHDb9X0x01uQ06cVFi82sWlTuteuKYQQnlKiLhBWq5VWrVoRExPD\npk2b3D0m4QdkT3Rt0e3bR35LAomde12+BfI/E+COHR3YbLB1qx5MJhzt22Mo5WtiTEyMz2d6L8nI\nwLhqFQDvvGNh4EAb1at7ZNlImSD3nrZJ/AJLibpAHD9+nMqVK7Nt2zb69u1LamoqZrPZ3WMTQhSB\nkpZG+J13cvH33zl1SmHatCAmTrRSq5Z8TO0O+uRkckeOxG6HnTsNtGnzd9cHRYGHHsrlk0/MtG2b\njb1TJ4wbNmDv06fY1/GXmd7LmefPR797N0ciu/PFFya2bJHZXyFE2VCiBLhy5coAtG7dmurVq3Pk\nyBEaNmx41ePGjBlDrVq1AIiIiCAyMvLSO6z8Whs59s/jefPmSbw0cqw7cIC0KlWI37yZEyfuYOVK\nB199FUSPHkeYPr0SISH+NV5NHbdqhf7QITZduMDeRb9Su3Z7IiLUKx4/eLCNFi1C6N07kR6xsbh+\n+63I528U3YgVB1fwybZPSM1O5a46d9He0J5xTcZh1pmJqee7719vtdJt3jwyvv2WZ565yO23n6Ny\n5Rv8Kz5+dpz/NX8ZjxxL/Mrycf6fjx49CsDIkSMpjiK1QTty5Ai9evUiJSWF8+fPExQURFBQEEeO\nHCEmJoYDBw4QFBR0xXOkDZq2xcfHX/plE/7NtGQJxnXryPrgA6ZMCSIr6zBPP12Nl14KJjHRwEsv\nZXPvvfYCd0HW7dmD4nTibNbM+wPXAN3u3YQ8/jgZa9Ywd66Zgwf1zJhxdfuvRx4JoVUrB48+mnvd\nc16vZZm/3Hvm2bMxbNvGnlcWcvvtYWzdms4NN0j5w7X4S+xEyUj8tM3tbdDGjh3LsmXL+PPPP6lZ\nsyajRo1i8eLFmM1m9Ho98+fPvyr5FdonLwLaobtsC+SUFD0TJ9agRg0HH36YxZYtBiZPDuKjj8xM\nnZpDZOSVmzYYkpIwf/wxGatWUWCGHOBcTZqQ8cMPQF79b2ysvcDHDRuWy1NPBTN6dG6BP8bilDf4\nxb2Xk4Nlzhwyv/iCt96y8PDDuZL8FoFfxE6UmMQvsMhGGEJoXMjQodh69ya3bz/q1Ilg27Z0Klb8\n+7Z2OmHRIhNvvBFEbKydKVNy/k5mXC7Cbr8d65NPlqhuNVCoKjRuHMEPP2QUWFutqtCuXTgzZ2bT\nvr0D8O7mFO5mWrAA49q1pLzyGXfdFca2bemUKycJsBDCfxV3BrhEXSBE2Xd5jY3wb2p4OM7Gjfn9\ndx2hobB375VdCPR6GDbMRmJiOiaTSvv24bz/vhmHA9DpyHn5ZYJeeQVsNt98Axpw5IgOvZ5C+98q\nCgwdmst7H6ql7t7gD/eebfBgst9+m2nTLIwalSvJbxH5Q+xEyUn8AoskwEJoXPb//oerSROSk/U0\nb+4o9HHlyqlMnZrDN99ksHKlkU6dwtm40YCjc2dcdepg/vhjL45aW/LbnxVW3rAgZQHfhw1k+UoX\na/fs9E3LMncymdh7oSo//mjk0Uetvh6NEEK4nSTAokBSC6U9ycl5W/ReL3ZNmrj4+utMnnsuhwkT\ngnnooRD2PDoV83vv5dVLiKskJFzZ/7egPr2j2t/HvT1NtD/7LvdtPEe5xUtLdC1/uffefDOIMWOs\nhIf7eiTa4S+xEyUj8QsskgALUUYkJxuIiipaAqso0LOnnS1b0omKctJ5VDST++wiy6r38Ci1Qzl+\nHOX8eSBvBrhh8+tvTjHyYQcLF5pxVbgB08qVPv4OSu633/T8/LOBkSOv39VCCCG0SBJgUSCphdIW\nVYWkJD1RUY5ixS4oCJ5+2sqGDekcOhZEu3YRfPWVEc8sjdWWoOnTsX22gDmbPyf1dytDt7e4bk1v\n27ZO9HrYYLoTw5YtJaqr9od7b+pUC+PHWwkN9fVItMUfYidKTuIXWK7bBk0I4f9OnswrTq1eXeXw\n4eI/v0YN9VLbtGefLbxtWiDI797Q46evGGdxkZn2PA0j0/hhVMp1a3kVJa8l2sdfV6Jb3brod+zA\n2a6dl0ZeOsa4OFSjkW2Vu7Njh4H338/y9ZCEEMJjZAZYFEhqobTBEB8P6emkpBiIjHSiKKWLXfv2\nDtavz6B/fxv33RfKk08G8+efZb8/8D9rercc2UDdUzY+mZxEO+eTxHYuX+SFbAMH2li3zsDJW3pg\n/OmnYo/FJ/ee00nQSy9BUBBvvJG3lba0dy8+ed3UNolfYJEEWAgNCxk9Gt3FiyQlXbsDRHHo9TBs\naC6JCWmYTCrt2l3WNq0MKWghW355w4e1JqLcXIegiBtISDDQrl3Rv/mICJUePex8kjsIw88/e/A7\ncB/jsmWoFSuyxdyJ3bv1PPSQ1P4KIco2SYBFgaQWSgMyM1EuXsRVowbJyfpL5QruiF3wuHFU3L6W\nqVNz+Pbbv9umXbyo7dngayW9l9f06pOScLRoQW4upKQYaN26eNn/sGG5fBzfmPQlxe8E4fV7z+Ui\naPp0cp55hjemBvPUUzmYzd4dQlkhr5vaJvELLJIAC6FR+oMHcdapAzrdXz2A3Veva+/Rg+AXXwSn\n81LbtGbNHHz8sfYyo6ImvVcwGLDfcQdJSXrq1nUSFla8a7Zu7SQoGDZu9f9VZMbly1FDQ9lkuZPD\nh3UMGSIbogghyj7ZClkIjTJ+9RWmFSs4NmMBLVtGcPjwRXTuekurqoTGxmIbPBjbAw8AsHu3jvvu\nC2PnzjS/nyF01zbEs2aZOX5cx5tv5hR7DPPnm9m0ycCCBf69mCzkkUew3tefHrPvZdAgG4MHSwIs\nhNCe4m6FLF0ghNAo/f79OOvV+6v8weG+5BdAUch55RVChw7F1rcvhITQpImLJk2cfPWVyS+TpIKS\n3uGRw1ncc3GJd2LbutVA374l+17798/l1VctnD6tUKWK//aVy3rvPTZsNHL6tI4BA/wvrkII4QlS\nAiEKJLVQ/s9VsyaODh0u7QCXz12xc7ZujaNtWyzz5l362tixVmbPtvhNn+ASlTcUkarmbYBRnAVw\nlwsPh1697Hz2WfGmy71976mKjtffCGbSpBwMMiVSKvK6qW0Sv8AiL3dCaFR+aULSIgN33WX3yDVy\nXngBw2WtvDp3dqDXq6xbZ6BrV9+0hfDETG9BUlN1BAWp3HhjybP9YcNyGTE8iIn9/kCpVcNtY3On\ntWsNpKcr9O3rmd8hIYTwR1IDLITGtWkTzoIFmTRp4vLK9f7v/0wsWWJi2bJMr1wP3FfTWxyffmpi\n40YD77+fXeJzqCrcEWnj1YYL6PDVKDeOzj1UFbp2DWPCBCt9+kgCLITQLqkBFiKApKfDiRM6GjTw\nTvIL0LevjVdeCSIlRe/RneK8NdP7T6alS7HffTcJCdVo27Z035+iwLAHs5n/3yg6qGreF/zIypVG\n7Pa8Ug0hhAgkUgMsCiS1UNrw228GGjd2XlG76enYmUwwerSVOXPc3wrCkzW9ReJwEPzkk6iKwtat\nBtq2LX2Zx72PRfBTbntOJx4r0uM9fu+pKiEPPAC/7eGNNyxMnmx17wLKACavm9om8QssMgMshIb9\ncwGctwwdaqNly3COH1dKVSMLvpvpLYhu/35c1atzNjeCM2cUGjcu/c82LFyhX51tfDYriCfauWGQ\npWSIj0e/bx/f7GuKyQTdu8vsrxAi8Mj7flEg2RPdvxnWrEG3b99fCfCVs5Qei53DgT4hAcjb7vf+\n+228/76lRKfy+UxvIQxJSTijoti61UDr1k70evecd/iAi3yyoT7OIuTTnr73LNOnk/X4k0ydFsrk\nyTn+VpWhafK6qW0Sv8AiCbAQGmR57z30R454dwY4O5vQIUPQHcv7KP/RR3P59FMT6elFe7q/Jr2X\n0ycl4WjevFTtzwrS9IEmVAzL4ccfffuhmz4hAd3RoyzRDyEiQvVZJw8hhPA1SYBFgaQWyr/pUlPJ\nqlmfQ4f0V31M77HYhYdjGzwY87vvAlCrlovbb3ewaFHhtcBaSHovZ0hKwtmiBQkJ7qn/zadWq8ZD\nz1dkwYLr10178t4LeustMsc/wbS3Q3n+eZn9dTd53dQ2iV9gkQRYCK3JyUF3+jS/ZtWhbl0nlpJV\nIZSIdfRoTJ9/jpKWBuRtjPHee2bsl5WRai3pvZytTx8yGrZg92490dHunR29914bW7YYOH7cR1ln\nTg6uG25gkX4YVau6uO02mf0VQgQu6QMshMbodu8mdPhwZj22k19+MTBnTsn71JZE8OjROJs2JXfC\nBAB69Qql36BzELnEq316PWXLFgP//ncQa9dmuP3cTz8dRKVKKs8+a3X7uYvCZsvrGz1vXjbt20sC\nLIQoO6QPsBBlnP7AAZz165OcbKB5c+93gMgdO5bQwYM5/tB9rDj2A2mtzvD06wPpPW2Tz7o3uFNC\ngoE2bTyTHA4bZuP++0N56imrT7Yd/uwzE3XquCT5FUIEPCmBEAWSWij/5apVC9uQIQV2gADPxu5c\n9jnmKzt4elBF2nzWnk1/bOLJwY2oE9KU4WGf+HV5Q1ElJurdWv97uWbNnFSr5mLtWmOhj/FU/KxW\nmD49iOefz/HI+YW8bmqdxC+wyAywEBrjbNkSqx32PqKnWTPPzwAXuA3xwCf59bLyhrQxNubMMdOx\no7ZnFl0u2LrVwMyZnikr0SckMLKJmQULYujWzbv9dxcuNNOsmYPWrb3/qYEQQvgbSYBFgaQfon87\ncEDHjTe6CA29+u/cEbvibk4xcKCNN94IYu9eHY0aeW9bZnfbt09HuXIqVat6ZGkEisPB4JRXef73\nTfzxh0KNGldfx533nmHLFpy1a5NdvjozZ1r4/PNMt51bXE1eN7VN4hdYpARCCA1KSjIQGenembzS\ndG+wWGDEiFzmzvViSwo30v3+O5ZXX3V7/99/ctxyC2GpydzXK4OFC92/lfTllNOnCRk+nL0bzxMb\nG8btt9t9UjMuhBD+6LoJ8NNPP03VqlWJjIy89LWlS5fSoEEDGjZsyIoVKzw6QOEbUgvl3wqr/4Xi\nxc6dLcsefjiX774zcvq09prL6n/5BX1qKomJnlsAB4DZjKNNG0Y22sjixWYcBVzKLfeeqmIeM4H/\nNFhAz393YOjQXGbP9m63kEAkr5vaJvELLNdNgPv160dcXNylY5vNxuTJk9m8eTNr165l4sSJHh2g\nEOJqycn6Es/mubVPb1YWhvXrAbjhBpV+/Wx8+KFnZzY9wbBrF86/doDz1AK4fPbbbiPq0HJq1nSx\nenXhi+FK4+Cry+iY+A4/6buwfn06Q4faZNMLIYS4zHUT4Pbt23PDDTdcOk5MTKRp06ZUqlSJmjVr\nUrNmTZKSkjw6SOF9Ugvlnww//YR++QpSUgyFboFcUOw8tTmFkptLyIgRKKdPA/DYY7ksWGAmK6vY\np/IpfXIyf9Rqy8WLCg0beraG2dG5M8YNGxg2LLfAneFKc+85HDDzuXS6z+zDQ0+E8tXXWQXWGQvP\nkNdNbZP4BZZiL4I7deoU1apV47333qNChQpUrVqVkydP0rx5c0+MTwhxGePatezXNaR8eRfly187\nsSnuQraSUCtUwHbvvZg//BDrlCnUreuiXTsHS5aYGTEi1y3X8DiXC0NSEj/nRNOmjQOdh1dGOJs1\nI2vWLPpE5vKvfwVx9KiOWrVKn3Tv2aNj3LgQymVnsOmlFVQZ38cNoxVCiLKpxC/1o0ePpn///gAo\n8tlamSO1UP5Jl5rKTrVloeUP57LP8a9l//LqNsS5jz2GecEC8qd9x461MneuGadG1lvpDh/GFRFB\nwu7yHl0A9/cFdTjbtiUoWKF/fxsLF5qu+Ovi3nsOB7zzjoXevcN48MFcvvw5TJJfH5HXTW2T+AWW\nYs8AV69enZMnT146zp8RLsiYMWOoVasWABEREURGRl76iCH/F02O/fM4JSXFr8Yjx3nHPQ4eZFeV\nOoSHHyI+/gAxMTGcyz7HzNUz2XxxM4dzD9M8pDkdynVgXJNxdLmti8fH56pbl9P163P2tdeo+frr\ntG3rxGRKY8aMg0yaVM+vfn4Fjr9KFX6eOJG171r573/1Xr3+sGG3cc89YcTErMNgUIv9/IoVb2Pc\nuBCczgu8+eZm7r23lc9/noF8nM9fxiPHEr+yfJz/56NHjwIwcuRIikNRVfW6BWJHjhyhV69epKSk\nYLPZaNSoEYmJiVitVu644w4OHDhw1XPWrVtHdHR0sQYjhLgGm41ytWtzR7s0Bj18jqybll65OUX9\nPnS9bHMKb9InJBAybhzpiYmg1/Ptt0bmzrWwenWG18dSEllZ0LBhOQ4cuEhQkHevHRsbyujRufTu\nXfSNMRwOmD3bzJw5FqZMyZFFbkKIgLdjxw66dOlS5McbrveAsWPHsmzZMs6dO0fNmjWZO3cuU6dO\npUOHDgDMnDmz5KMVws9ZXnuN3MceQ61QwddDIW3vTtQbwojfbmVb+9u509DM7TW9JeVs25as998n\nv4C2Z087L70U9Ne2wv5fC7Fjh4GmTZ1eT34Bhg2zsWCBucgJ8N69ebW+YWEqP/6YQc2a2t14RAgh\nfOW6NcBz5szhxIkT2Gw2jh07Rq9evRgwYAD79+9n//79xMbGemOcwsv++ZFQINInJRE0YwaGH3/0\n2Rgu795w+5r+vNGrA8EmE3ufWF9oTa9PYqcoOKOjyZ+G1OthzJhc5szRxsYYCQmeb39WIJuNXr1s\npKToOXw47+W4sPg5HPDf/5rp1SuMBx7I5euvM6lZ04Xxq68wbNrkzVGLQsjrprZJ/AKL7AQnRCHU\nkBBsPXti9HJyUVjLsvgJe2nR8VPaRBt8PuNbFIMH57Jli4FDh/z/ZcYb/X//ybhqFSHDh2Ox5G0l\nfa2d4fbu1dGtWxg//WRk3boMhg3LK3nQHTxI8OTJuCpW9OLIhRBC+4pUA1wSUgMsygLd7t2EPvAA\n6Tt2ePQ6BbUsK6imd+pUCw4H/OtfVo+Ox11efdVCerrCtGk5vh5KoZxOqFOnHNu3p1Gxovd65ipn\nzxJ+yy2kpaZy4LCJXr3CSE5Ow3RZUwiHA+bMMTN7toXnn8+5lPgCYLcT1r07tv79yR092mvjFkII\nf1TcGmD/n5oRBVLOnyf48cfBM+9fxF9cjRuD2Yxy4YLbz12SzSnytkD2/5rafCNH5vLllybOn/fP\nFVqWadNInfY9Vaq4vJr8AqiVKuGqWRP9jh3Ur++iQQMncXF/7wy3b1/erO/69XmzvsOHX7nQzfLW\nW6jly5M7apRXxy2EEGWBJMAaZYyLw7xoEcrx4x45v9RC/UVRSN+yBbV8ebecrrQ7siUlGa67BbKv\nY6f8+SfGVasAqFpVJTbWzkcf+ef2yIaEBLaca+ib+l/A0akTxo0bARg6NJdPPjGzYUM8s2aZ6dkz\njCFDclm2LPOqjTL0CQmYFy4ka/ZspP2D//D1vSdKR+IXWCQB1ijjmjVkzZ2LWqOGr4cirsNd2xCf\nPauQnY1bdg3zqNxcgh977NKs+ZgxVj780IzV36o2VBV9UhKbz9T3WQJs79QJw4YNQF7njD179Dz1\n1G38+GPBs76Xy5o9G7VKFS+OVgghyg5JgLXIasW4YQP2O+/02CXyG04HIuXcOQBcLhg+PIRjx4p/\nm7gr6c2nT0lh36TPiYpyXnfCz9exU6tXx969e97ucEDjxi6iopx88YXp2k/0Mt2xY2A2k5gU6rsZ\n4PbtUTIzwenEbIZ//zuHsWMNfP311bO+l3O2a4eja1cvjlQUha/vPVE6Er/Act0+wML/GOLjcTZp\ngnrDDb4eSpmjHD9OeOfOpP36KyvXhvLttyZatnQwYULudZ9b0EI2d/Xp1Scns+vQDUTdpo3639wx\nYwgdMADrmDFgNjNunJVJk4IZMsSW3yrY5/RJSRxu0IWc3xTq1fPRrHpoKBnr1186fOABm2/GIYQQ\nAcZP/ikSxaFWqkTOk0969BqBWgtlXrAA2733oprMvPOOhYcftrJ8eeEzl+6e6S2MPjWVXfZmRVoA\n5w+xczZrhrNRI0xffQVAx44OzGaVtWv95z23/tdf2RzRg7ZtHX5VRusP8RMlI7HTNolfYPGff41E\nkTmbN7/6izZb3u4Der33B1RW2GyYP/2UjGXLiI83kJGh8NprOTRtGsGx3zK5+dx2HJ06eXSmJ63+\nTwAAIABJREFUtzC61FR2na/NM1G++ai+JKxjxxL00kvYBg1CURTGjcvbGOOuuzJ9PTQArM8+S/wz\nZtrepJ2fqRBCCPeQPsBlRMjIkdi7dsV2//2+HopmGb/+GvMnn5D57bfce28o/frZGDLExvjxwdxU\n4XeeW9ya2Gkt2XlmV6F9ej1FvaUrtU5s5cjRdO28x1FVdAcP4qpXDwC7HaKjI1i0KJMWLfyjlKNT\npzDeeiubNm38YzyFMc+ahRoRgW3oUF8PRQgh/FJx+wDLDHAZkTt8OMHjx2Pr1w+Mxus/QVzFPH8+\nuaNGsWuXnv379dwee4IFKStIqnSSJcv68rji4PHwbrTp9Zl3d2JzOEg+WoEmUU7tJL8AinIp+YW8\nX8tRo6zMmWPhgw+yfDiwPBkZcOiQ/rpt5XxNv2sXltmzSffhltxCCFHWSA2wRqlqXqP8fI4OHXDV\nqoVpyRK3nD/gaqGcThwdOnCycxueePkUQbfN5dYleTW9E/tHEprWloyY4dx11OT9bYgVhS0P/4/m\nLYu2UMufYzd0aC4//mjgjz98X3S7bZuBqCgHZj9oUaycPIlhzRrgH/HLyiJk1Ciy33hDWh5qgD/f\ne+L6JH6BRRJgjYqPN3DrreF8//3fs705kydjmT49rx5YFNm57HMs2L2I7o1/oeWsB9mzswqTHit/\naSHbvY170u1uO8vM91/atMCr9HqSLt5MZKR/z1QWRXg4DB5s4913Lb4eCgkJBp+1P/sn5cIFgp99\n9qqvB//73ziio7H36+eDUQkhRNklCbCGmL74Ass77wAQF2ekd287jz8ezK5deZ+LO9u1w1W/PqbF\ni0t9rbLeD7Gw7g29Tm/kicdM9I/sccVMb+/edr453BLD5s15DYK9rCg7wOXz99iNHm3ls89MpKX5\nbhZYOXOGrYkG2rb1jzcVrsaNUbKz0f3++6X4GVevxvDjj2RPm+bj0Ymi8vd7T1ybxC+wSAKsIcbl\ny3FVr46qQlyciUmTcnjnnWyGDAm99JFyzosv4qpVy8cj9U/Xa1nWKqgPq74P4pFHru75e/vtdpL3\nBXP0gafw9pZm2dnw++86GjXyj2StJHTHjmH89lsAatRQ6drVzief+GhjDFUluOPtbN+mo00b/5gB\nRlGw33bbpV3hABytWpG1eHHetLkQQgi3kgRYKy7b/W3XLj0Wi0qjRi569rQzZoyV++8PJT0dnJGR\nOIqxCrIwZaUWqjh9eufNszBokI0KFa5ujGKxQNeuDpbVngDB3q0B3r1bT/36TkxFzBf9MnZOJ8FP\nPQWZeS3Qxo7N5f33LT6p1lFOniTJ1pgba6qUL++RJjgl4ujUCeOGDZfip1asiLNpUx+PShSHX957\nosgkfoFFEmCNMGzahKNZM9QKFYiLM9Kzp/1S8/4xY3Jp187Bww+H4vCTCS1fKtbmFDk5AJw/r/D5\n5ybGjCl8drd3b9s1N8XwlORkfZE2wPBnrptuwhETg/mv8pzmzZ3Uq+fkm2+8//M0JCcTX/ke2rXz\nr5+pvVMnDBs3+qTERgghAo0kwBphWrUKe7duAKxYYSI29u+pM0WBqVNzUBSYNCkYd3R21lotVEl3\nZAsZNw7TF1/wwQdmYmPt3Hhj4T+8rl3tbN9u4Px5L9aupqez+/VVxWrV5a+xs44di/ndd8l/lzZ2\nrJXZs81u+X0tDv2uXcTT0W8WwOVTa9Qg57nniGnTxtdDESXkr/eeKBqJX2CRBFgjDAkJ2O++mwMH\ndGRkKERHX5kQGQwwf34mv/yiZ84cP+jr5AWl3YZYOX0aw/r1XOjYjfnzzYwff+3a3uBg6NzZfkXn\nDU/Tp6ayK6cRkZH+layVhPOWW1CrVsW4YgUAXbo4sNsVNm70bjty3a4ktpxt4HcJMIDt4Yfz6m2E\nEEJ4lCTAGpH+00+4GjQgLs5Ijx42dAVELjwcPv88k3nzLHz3nREyMtBv3Vqi6/lrLVRpk97LmRct\nwn7PPSxcVpFbb3VQv/71P3r2dhmEa98h9tjq0bRp0WeA/TV28Ncs8AcfAKDT5c8Cezfh+z23Ki6D\nkZtu8s9SA3+On7g2iZ22SfwCiyTAWmE0gqL8Vf5gL/RhNWqofPZZJk8+GczONWmEPvhg3pZXGubO\npPcShwPzggVkPDiCOXMsTJxYtM4Od91lZ+sWhdxn3yjBd1J8+xLSuancBUJCvHI5j7N3707WRx9d\nOu7f38avv+rZvdt7L0XrB82hTXv1Ug29EEKIwCMJsIacOKFw+LCODh2u/dFt8+ZO/ve/bIb8qykH\nWt+H5f33i30tX9dCeSTpvYxx9WpcNWuyZHdLGjRw0qJF0WZYw8KgQzsrPyy6CPbC34i4S3KKkah6\nxXsD4+vYXZNej1qlyqVDsxmeesrKI4+Eeq0vcGKigXbt/K/8IZ9fx09ck8RO2yR+gUUSYA35/nsT\nd91lx1iEEtRu3ew8/riVe/bOIGfuZyhpaZ4fYCl5Oum9gsNB9oSJzJpV9NnffL3vU/jSeD/6Xbvc\nM5Zr2HX0BqKiy/ZU5YgRuXTsaGfIkBCvtFj2px3ghBBC+IYkwBoSF2e8ZvnDP40encttdyr0N32L\nbvZ7xbqWt2qhvJr0Xsbepw/fOHoSFqbSsWPxkqFu3exsyG2PdV3J6quLY/vN/WjW9YZiPUdrdWyK\nAq+/nkPlyiqjRoXg9GB3srQ0hWPHdH69rbTW4if+JrHTNolfYJEE2M8Z1q+HzEwuXFDYscPAHXcU\n72P3117LwdigFk/MboKa7h+1wL5Kei+nqjBzpoUnnrAWuxY0IkKlXeML/PCdZxdROZ3w2z5zmZ8B\nhrwFcfPmZZGWpvDss0Eea422daueli0dRfoURQghRNklCbA/y8khdNgwFLud1auN3HabvdibkOn1\n8MFiF9tu6sesjysW+XnuroXyh6T3chs3GsjKUujevWR1vL0Gm/hmfxTkXr1tsrscPKijYkUXERHF\nywa1Usem270b49dfXzo2m2HRoky2bjUwY4YHOkOkp/PL/x33n+2PC6GV+ImrSey0TeIXWLzbgFMU\ni2HTJhyRkajly7NiRd7ubyURGgqffWXj7rvDqVXLRd++nl+8BXlJ74qDK/g29Vt2nt5Jl9pdGB45\nnMU9F3s12S3IzJkWHn/cWmA7uaLo3s/AlP/0IsueRoiH2i6npOj9+qP6UlMUgp9/nrQePS71vg0P\nh6VLM+nePYzKlV089JD79ko2bN3K1nX1GP+hfyfAQgghPE9mgP2YadUq7HffTVYWbNxo5O67S564\nVq+u8vnnmUyaFMzWrfrrPr6ktVD+NtN7BVUFl4sdO/Skpurp16/kyVWFCiotW7lY96PnegInJRmK\ntQNcPq3UsbkaN8YZFYXpiy+u+HrVqipffJHJG28EsXKl+2oVXDt+ZXt2E265xb8TYK3ET1xNYqdt\nEr/AIgmwv1JVjKtXY+/WjR9/NNKqlYPy5UtXGNmsmZO5c7MYOjSUI0fcF3q/Tnovo9+2jdB+/Zg5\n08K4cVZMpcxd+/Tx7KYYKck6oqL8O1krLeu4cVjmzAHXlfXU9eq5+PTTTCZMCCYx8fpv2IoiZVMm\nN1fJJDzcLacTQgihYaXKgvR6PS1btqRly5ZMnDjRXWMSgD45GTU4GFf9+sXu/nAtd97p4OmnrQwc\nGMrFi4UvrrpeLZRWkt7LmT/6iF8j+5OYaOCBB0pfu9ujh521aw0ead2lqpAcn03zSn8U+7laqmNz\ndOyIarFcNQsM0KqVk3nzsnjooVD27i39G7aE3yJo187/S0q0FD9xJYmdtkn8AkupaoCDg4PZuXOn\nu8YiLqOGhJDzwgvY7fDDD0ZeeCHHbecee/LfHLn1eR56KJwvv8ws8kyoP9f0Xo/y558YV61ixp3v\nM3Jkrlt2VqtcWSUy0sn69cYSL6YrzLF9VoJcKpWaVXLref2OopD99tsET5qErVcv/rnKs2tXB6+8\nksOAAaGsXJnBjTeW7FMQ5fx5fs5sQfeuQUDZnlUXQghxfVIC4adc9eph79WL+HgDdeq4qF7dfX2h\nlNxc3jQ8T0SEyhNPBBfYciq/FkqLM70FMS1ezKFOD/D9ulAeecR9nRt697Kx/Av39+z6dd2ftAjd\nn9fGo5i0VsfmjI4mY82aq5LffAMH2hg5Mpf+/cOu+anFtajZOcSb76Bte8+2rnMHrcVP/E1ip20S\nv8BSqgTYarXSqlUrYmJi2LRpk7vGJC4TF2ekZ0/3rYQHsE6YQNDXX/Dev/ezd6/+qpZT57LPsers\nKs0nvZc4nZg//ph3DJMYPNhGuXLuS1jvqRzPD9+5sLk3RCQn2GlR7ZR7T+rPrtOMefz4XDp3tjN4\ncAg5Jfgw5JCtJsaIYGrU8P8EWAghhOeVqgTi+PHjVK5cmW3bttG3b19SU1Mxm//uCTVmzBhq1aoF\nQEREBJGRkZdqbPLfaclx4ccuF3z/fSzffpvh1vOrlSpx8I47ML70DJ999jl33RXGheztKJGf8xu/\nsfP0TpqHNKdDuQ4sHpFX3hAfH8+OUzv86udT1GPlzBlSakWz8IeqJCZmu/f8d0XTWN3NezPttLw1\nzW3jT9gJA286Rr7iPD8mJsavfv4lPVacTjrceisYjWzeHE+3bnDmzN2MGhXCyJGr0euLfr5Fiw5R\nt25lFCXYb76/wo7LSvzkWI7lWI49eZz/56NHjwIwcuRIikNRVffsudS2bVsWLlxIw4YNAVi3bh3R\n0dHuOHXA+uUXPePHh5CQkO72cyvnzxPWujUL3h3Lu/uOs33aNGKeeocRPRvStXZXbc3wFsHUqRZO\nntTx3/9mu/3c81suJLlOb/77VTm3nbPpjQrrnv+OqmN7uu2cWmNasgTzRx+RNX8+rpo1gbx9R+6/\nP5Sbb3YxY0Z2kXfxe/zxYJo1c7q1/EUIIYT/2LFjB126dCny40tcAnHhwgVy/vos8siRIxw/fvzS\nbK9wj7g4k9vLH/Jreu/ZMIK3orPJXRPHuO6d+fQjhX3vvkpT5Z5LM75lRWYmzJ9vZsIED7RrAHp3\nz+b7LZWwu2kd3KlTClZLOFUeiy3R88tK7GwDBmDr1Yuwrl0xrlwJ5O0W98knmezYoWfatKLvFpeQ\nYKBtW4enhupWZSV+gUhip20Sv8BiKOkT9+7dy/DhwzGbzej1eubPn09QUJA7xxaQDGvWYFy/nuzX\nXicuzsj772eV+pyFdW/o+tmnBJv+aodQD848l8P994eyenVGqa/pTxYuNBMT46BuXc/Uf1aLjeTm\nhUfYvLk2nTuXPslKSdETFeVE0ZVswVeZodORO348jrZtCRk5EsPmzeS88ALh4SaWLs2kW7cwqlRx\nMWzYtd8knj+vcPKkjiZN/L8FmhBCCO8ocQLcvn179u7d686xCMAUF4ezfn327tVhtSq0aFGyf7RL\n0rJs6FAbhw/refDBED7/PKY034bfyM2FOXMsfP55pseu4WjdmnsrL2P5N3XdkgAnJxuIiip5spZf\nJ1VWONu0IWPDBoLHjiXo5ZfJee01KldW+fLLTHr2DKNSJfWafbK3z0vilrqNMRjct6ucJ5W1+AUS\niZ22SfwCS4kTYOEBLhfGH37AOn48cctMxMbailzjCO7p0/vCCzk8+2wQbdpE8MwzVh56KBejNvKG\nAi1daqJxY2epEsrrMpu5+6vBzOxu5i2ntSSdy66QlKSnTx83t5XQOLV8ebIWL4asvz8RqVPHxeLF\nmQwcGMoNN2QWusnF1uV/0r7B70A9L41WCCGEv5M+wH5En5SEGhqKq27dIu/+5u4+vTodvPVWDs8/\nv4kVK4x06BBOXJyxwF7B/s5y/xD+N0PHxImeqf293M03u6ha1UVCQunfU6ak6GnevOQJe5mtY1MU\nCA294kstWzp599287b337Cn45WzL0Vq0vUs7izrLbPwCgMRO2yR+gUVmgP2IcdUq7HffzbFjOo4d\n09G+fcEfp3tsRzan89LGC3XqpPP115msW2fgxReDmTvXzMsv59C6tTbqKPVJSXy3rSbl6hjo0MHz\nCTBAr152li830qFDycsgLl5UOH8O6lTPBoq+yCuQ3XGHg1dfzWHAgDBWrkynRo2/361Zz6STlNuI\nlr298zsghBBCG2QG2I8YfvkFe7duxMUZ6dbNjuGytyee3pHNuHo1IY88cuk4JiYGRcnbinbjxnTu\nv9/G0KGhjBgRwpEj/v9rY5r/EVPNLzBxYm6xykhKo3dvGytWmHCVYq1dcrKeKMNuzBvWl/gcgVbH\nFjJsGINNXzB6tJX77gvjwoW/A/7rN8doEPwHoRGlrEvxokCLX1kisdM2iV9g8f9MJoBkfvkljvbt\n/9r9ze7VbYjtHTti2LIFfUrKVX+n18ODD9rYujWNRo2cdO0axpQpQVckGv5ESUtjw9fp5IRUpFs3\nN/UmK4L69V2UK6fyyy8lT7aSk/W0dG3DWU/qVYvKOmECQS+9xDPHJnLnHVYGDQq9tFtc4jor7esc\n9+0AhRBC+B1JgP2JTsf+42lsT3IyL/1e725DHByMdcIELG++CRRcCxUSAs88Y+Xnn9OxWhXatg1n\n9mwzuX62t4Dp8895I+RVHn/Kgc6Lv+G6w4e5p9FvLF9uKvE5kncqROf8jOumm0p8jkCrY3NGR5Px\n00/oTp7k7Z9juOmGNEaODMHhgM3Z0dzS/0ZfD7FYAi1+ZYnETtskfoFFEmA/cPlMb+eXZ1ChyQ5G\nRA/xfNL7D7nDhmHYuRP9zp3XfFzlyiozZmTz3XcZ/PyzgbZtw/nqK2OpPvp3p21bXBxW6nDvvd7t\npKBcvMjAnVP47ruSLxpM3qHSovopNN16wwfUiAiyPvkEx5BBfLI1Euu5bJ56Kpite8pxS7+qvh6e\nEEIIP+O2rZD/SbZCvraCFrL1qd+HT6cMYEB/J/fd572P7i9n/vBDjGvWkPl//1fk52zebOCFF4JQ\nFHjllRxuvdW3O249+GAIt93m8P62t04n4XXr0fiG08z7IJfo6OItGMzKggZ1wzh7e19sny/00CDL\nPt2+faRVrU+fvhGcP6+wa5f7txIXQgjhX4q7FbJ0gfCi63VvyMiAcVssfPjBRZ+NMffBB1FOn76i\nI8T1dOjgYM2aDJYtM/LYY8E0a+bkxRdzaNDA+1PC+/bp2LrVwHvvlX4HvWLT63He2p4+uj0sX96I\n6OicYj3911/1NK52HqWtvHEsDVfDhoQBS5dmsm+fdha/CSGE8B4pgfCwoixkC//5F5Tz51m3zkib\nNg7Cw304YLMZ65QpxG/ZctVf6VNS0O3fT0Gf7+t00K+fncTEdNq1cxAbG8bTTwdx5ox3F8rNmmVh\n1Khcgn3U9tURE8N9+mUsX178MoiUFAORnSPInTixVGOQOrY8FSuqpWpJ5ysSP+2S2GmbxC+wSALs\nAcXq3uByEfLooyhpacTFmejZ0393ADNs3kxYv35ENGtG8JgxmJYsQTlx4orHWCwwfnwuiYnpmM1w\n663hTJ9uITvb8+P74w+FVauMjBjhu1V5jo4dabX7MyBvRrc4kpL0REVpL2ETQgghtEZqgN2ksJre\nrrW7XnMBm377dkLGjuXcxgQaNowgISGdKlX8eNs1VUV36BCGjRsxbtiAYdMmMpcuxdmqVYEPP3xY\nx3/+E0RiooHnnsth0CBbqbcKLszkyUGYzfDyy8UrPXArlwvT4sU8l/oIJhNMmVL0DRg6dQrj7bez\nadVKG5uNCCGEEP6iuDXAkgCXQkmT3stZXnsNxW7nu5hXmT49iFWrMjw8ajfLb/1QQL8x/datOKOi\nwGJh2zY9L74YxI4dBqpVc3HjjS5q1Mj7f/5/eccq4eFqsTevuLj4B1pN6s3m7blUrer7NxDbt+sZ\nMyaEhIT0In0vublQp045UlMvEhTk+fEJIYQQZYksgvMwd29DbFy9mpw33yRuqYnYWP8pf4iPjy/a\nrjiFNdq1Wgn+17/Q792Lo1UrOnTuzKpXbyOzVkNOXAzl+HEdf/yh4/hxHUlJBr7//u9jgOrVC0+S\nq1d3XVXj++Gb2dzT5ihVq1Yu5XfuHtHRTrKzFfbu1dG48fUXA+7dq+emm1xuSX6LHDvhlyR+2iWx\n0zaJX2CRBLgI3J305lP++APdiRPkRt/CyuFGVq4s+sflfs9iIeOHHyA9HePmzRg2bCBkzBiCLRaC\n1q+nbt0rk0Ldvn1EtG+PqiikKeU4dqg2Rw/V4vfKrTg06Bk2bzZcSpBPnNARYnFQK3MvNfQnqKU/\nztLcPqz60kffawEUBXr1srF8uYnGja8f16QkPc3rXkT3+zFctWt7YYRCCCFE4JISiEK4o7zhepQT\nJzBs2cKmGwfw9NPBxMdrrPzB3VQ1r6Qi///5f/7HtKiqwrlTTo7vyeL4CT3HTxq44UYD/Qb7V8ur\nhAQ9Tz0VwubN1+9D+8wzQTTc/z3jOu/C+sQTXhidEEIIUXaU+RIIl6vwT91Ly1MzvYVRq1fH3q8f\nK/5lIjbWNxtf+BVFKVLvYUWBStX0VKoWTgsvDKuk2rRxcuGCwoEDOurXv3YZRFKSgUG6LTjrRXpp\ndEIIIUTg0lQbtLNnoGP9HKxn3LezU7FalnmAqkJcnJGePf0rAZZ+iKVjWL+ekCnP0bOnje++M13z\nsU4n7NmjJ/rcWpz16pX62hI7bZP4aZfETtskfoFFUwlwpcpwc9BJlkxIKtV5fJ30Xu633/SoKjRr\nJq2vyhJXrVqYli+ndy8by5cbr/nYAwd0VKnspNzxPbjq1PHSCIUQQojApbkSiGdet/Dgw60YdC4D\nc8WwIj/P2+UNRbVihZHYWHux2355mqyELZ38RLZDlf2cPBnNkSM6brqp4DKI5GQDzeum4VKrgdlc\n6mtL7LRN4qddEjttk/gFFk3NAAM0712dZpVPsWRiynUf608zvYXxx/IH4QaKgr1jR8w/b6JHD/s1\nZ4GTk/U0r5eBrV8/Lw5QCCGECFyaS4ABnvmPkbdXNSf3fNZVf6eFpFe/fTshI0dy5IiOM2d0tGnj\nf9vfSi1U6Tk6dsS4aRO9e+e1QytMcrKeZl1vwDpliluuK7HTNomfdknstE3iF1g0mQC37FeTJpXO\nsGTqaUAbSe/ljKtW4apZkxUrjHTrZvfY1sDCtxwdO2JITCSmg50jR3T88cfVdS6qmpcAR0VJDbgQ\nQgjhLZrtA7wuPoNRj5Sj2Sv3kvTnLx7p0+spYR07kv3WW9z18p08+WQOd97pfzPAwk2ysyE4mHHj\ngmna1Mljj+Ve8ddHjujo1SuMlJQ0Hw1QCCGE0L4y3Qf4nwvZLFV+os7h//D5E7X8PunNpzt2DN2p\nU5ys3YY9e3Tcdpskv2XaX3s29+lj4+23g65KgJOS9ERFye+AEEII4U1+XwJxrfKGhdPq8uPiNhhU\nbSS/AMbVq7HfeSffr7bQpYvDHYv+PUJqodzrttsc7Nun4+TJK8sgPFH+ILHTNomfdknstE3iF1j8\nMgEuak1vmzZO6tVz8fnn195owJ/ot2/HftddxMWZiI21+Xo4wkvMZrj7bjtxcVf+riYnG4iqfhrD\nmjU+GpkQQggRePymBrigPr1FqelNTNQzenQIWxPTMJn9rJluQVSV9DRoFlWe3367SFjRWxkLjfv+\neyPvvmtm+fJMIG8BXKNGEcQ/vojau1aQ/f77Ph6hEEIIoU3FrQEu8Qzw0qVLadCgAQ0bNmTFihUl\nOoc7uje0beuknu4QXz6xs0Rj8DpFYc06E7feapfkN1Ckp6P7/Xduv91OcrKes2fz3qidOqWgqlDj\nXBIuN2yBLIQQQoiiKVECbLPZmDx5Mps3b2bt2rVMnDixyM/1RMuySWP/ZMaX9bFna2NDiRUrTMTG\n+vdYpRbKfYxr1xL03HMEBUHXrg7i4vI2xUhONhAZ6cSQegCnGxNgiZ22Sfy0S2KnbRK/wFKiBDgx\nMZGmTZtSqVIlatasSc2aNUlKSir08Z7u09tmRENuDj3DV8/+WuJzeIvVCuvXG+je3b8TYOE+jpgY\nDFu2gMNBr15/b4qRlKSneXMH+tRUXPXr+3iUQgghROAoURu006dPU61aNd577z0qVKhA1apVOXny\nJM2bN7/icQtSFlxR0zs8cjiLey72SMuySc/mMubf9eg3zYExyH+7u23YYKRZMycVK3qk9NptZE90\n91ErV0atVg19cjJdu0YzYUII588rpKTo6dfXiu7dIzjr1nXb9SR22ibx0y6JnbZJ/AJLqbpAjB49\nmv79+wOgKFcvQPPmjmxtRjWmVvAZvn7uN4+cv7QMmzejnDjBihVGvy9/EO5n79gRQ3w8ISHQubOd\nlSuNeT2AG2RhnTDhUr9gIYQQQnheiaZKq1WrxsmTJy8dnzp1imrVql31OPN3ZnbX2s1udhMREUFk\nZOSld1j5tTZuO968mfvuu8Bb3/ai33RISHDz+Ut5rI4bx65Hx7F69ZM884zV5+O53vG8efM8G68A\nO06pWJHay5djnDCB3r1tvPWWnfPnTdzUxIK12WS3Xu/yOjZ/+f7lWOIXCMf5X/OX8cixxK8sH+f/\n+ejRowCMHDmS4ihRGzSbzUajRo1ITEzEarVyxx13cODAgSse4+mtkAvTu3cogwbZGDTIf3rs6o4e\nJezOO/n+g/1MeSGUn37K8PWQris+Pv7SL5soPeXCBYL+8x+y336b9HRo2LAcrVo5WLEi0+3Xkthp\nm8RPuyR22ibx0zavbIVsMpmYOnUqHTp0AGDmzJklOY1HTJpkZeLEYPr3t2Eo0XfnfsZVq7B37cqK\nlRbNlD/Ii4B7qeXLk/322wCEh8Mdd9ipXdvlkWtJ7LRN4qddEjttk/gFlhKniAMGDGDAgAHuHItb\nxMQ4qFrVxZdfmrj/fv+YBTauWoV12HDi/mVkyRL3z/gJ7Xn55Ry/3QZbCCGEKOv8civk0po0ycqM\nGRYcDl+PBEhPx7BtG9sr3YXJBI0be2bWz90ur7ER7levnouaNT3zuyCx0zaJn3ZJ7LRi/WkTAAAK\ngklEQVRN4hdYymQC3LGjg8qVXXy9yPflBorTSfZbb7HixwhiY+0U0CxDBKrMTCzTpvl6FEIIIUTA\nKZMJsKLAc3cl8Pbz2Tgdvu23q5Yvj23gQOLiTMTG+kdJRlFILZTn6VNTMX73ndvPK7HTNomfdkns\ntE3iF1jKZAIM0GFcEyrq/uSb/xy4/oM97OBBHRcvKrRu7fT1UISP6RMSMH79NQC61FRcbtwCWQgh\nhBBFU2YTYEWv49lHzzD9gyo+nwWOizPSvbsdnYZ+2lIL5RlKZibmjz4CQH/gAE4PbIEssdM2iZ92\nSey0TeIXWDSUkhVfzHO3UIE/WT71oNeuqZw/j3LmzBVf++47bZU/CM9xtGuHISkJsrPRp6bi8kAC\nLIQQQohrK9MJsGLQM3nkCd6aVxGnN6oPMjIIHTAA05Ill7504oTCwYM6YmL8oSVF0UktlIeEhuJs\n2hTD1q3oDhzA6YESCImdtkn8tEtip20Sv8BSphNggJh/tyO8splvlnl4VwyrldAHHsAZGUnu+PEA\nuFwwa5aFu+6yYzJ59vJCO+wdO2KIjyd37FicDRr4ejhCCCFEwCnzCbBiNPD0W2FMnxGMy1MteB0O\nQkaORK1Ykezp00FRSE+HIUNCSE7W88orOR66sOdILZTnODp2xLhxI7aBAyEkxO3nl9hpm8RPuyR2\n2ibxCyxlPgEG6NLFQUiIyrffGt1/cpeL4AkTUGw2subNA72evXt1dO0aTq1aLr75JpPKlX27CE/4\nF0ebNuS8+KKvhyGEEEIELEVVVY9kZ+vWrSM6OtoTpy6RNWsMvPhiMPHx6e7txqCqmBYsyJvNCw7m\nu++MPPlkMC+/nMPgwbLwTQghhBDC03bs2EGXLl2K/PiAmAEG6NrVQXCwyvLlbp4FVhRsw4fjNAfz\n2msWpkwJYunSTEl+hRBCCCH8VMAkwIoCk57KYvrLLrfXAl+8qDBoUCgJCQbWrcugZUvtb3ghtVDa\nJbHTNomfdknstE3iF1gCJgEGuLNzNsHHD/H9nBNuO+fu3Tq6dAmjbl0nX3+dSaVKUu8rhBBCCOHP\nAioBVoIsTB60n2nTS94RwrB2LcoffwDwzTdG+vQJY9IkK2+8kYPRA2vsfEX6IWqXxE7bJH7aJbHT\nNolfYAmoBBjg9tc7YM5J5/v3ThX7uYYNGwh57DHUM3/yyisWXnwxiC+/zGTgQKn3FUIIIYTQioBL\ngJWQYJ69bzfT37QUaxZYv20bISNHcux/i+n3Wgd27Mir923eXPv1vgWRWijtkthpm8RPuyR22ibx\nCywBlwADdHkzBn1WBqvmny3S43W7dxM6ZAiJz3xKp+e60qSJky+/zKRiRan3FUIIIYTQmoDpA/xP\nK98/zdRP6/HThgwUpfDHKefPE96xIwtjF/H0stuZOjWbfv3s3huoEEIIIYS4JukDXETdHqkCCqxc\nee2Va/aw8kzsmMBLazqzbFmmJL9CCCGEEBoXsAmwosAzz1iZNs1CYXPgf/6p0H9AGClnqrFuXQbN\nmpXNet+CSC2UdknstE3ip10SO22T+AWWgE2AAXr0sON0wurVV88CJyfr6dIljObNnSxdmkmFClLv\nK4QQQghRFgRsDXC+774z8vbbFn788e9a4KVLTUyZEsS0adn07SslD0IIIYQQ/kxqgIspNtaO48wF\nfvgsDXuOgxdu286brxn49tsMSX6FEEIIIcqggE+AdTp4vuUK3nxRoX/LMxw4Eca6Hy7SpEkJt4or\nI6QWSrskdtom8dMuiZ22SfwCS8AnwADdZnQg+OIJ2uu38umOGylXxeTrIQkhhBBCCA8J+BrgfIaf\nf8bZtClqRISvhyKEEEIIIYqhuDXABg+ORVMct97q6yEIIYQQQggvKFEJhF6vp2XLlrRs2ZKJEye6\ne0zCD0gtlHZJ7LRN4qddEjttk/gFlhLNAAcHB7Nz5053j0X4kVOnTvl6CKKEJHbaJvHTLomdtkn8\nAossghMFMpvNvh6CKCGJnbZJ/LRLYqdtEr/AUqIE2Gq10qpVK2JiYti0aZO7xySEEEIIIYTHXLME\nYubMmcyfP/+Kr91zzz0cP36cypUrs23bNvr27Utqaqq8cypjjh496ushiBKS2GmbxE+7JHbaJvEL\nLKVug9a2bVsWLlxIw4YNr/h6XFwcFoulVIMTQgghhBDieqxWK7GxsUV+fLET4AsXLmCxWAgKCuLI\nkSPExMRw4MABgoKCij1YIYQQQgghvK3YXSD27t3L8OHDMZvN6PV65s+fL8mvEEIIIYTQDI/tBCeE\nEEIIIYQ/kjZoQgghhBAioEgCLIQQQgghAkqJdoK7np9//pn/+7//A+Chhx6iVatWnriM8ICBAwdS\nu3ZtAJo0acKwYcN8OyBxTQsXLmTTpk2Eh4czY8YMQO4/LSkofnIPasP58+d55513yM7OxmAwMGTI\nEKKiouT+04jC4if3n//LyMjg9ddfx+FwANC3b19uvfXW4t97qpvZ7XZ17Nixalpamnr27Fl13Lhx\n7r6E8KAHH3zQ10MQxbBv3z714MGD6pNPPqmqqtx/WvPP+Kmq3INacfHiRfX3339XVVVVz549q44e\nPVruPw0pKH6qKvefFjgcDtVqtaqqqqrp6enqiBEjSnTvub0E4sCBA9SoUYPw8HAqVqxIxYoVOXLk\niLsvI4QAGjRoQGho6KVjuf+05Z/xE9oRERFBrVq1AKhYsSIOh4P9+/fL/acRBcUvf0ZR+De9Xn9p\n87WsrCyMRiOpqanFvvfcXgKRlpZG+fLlWbNmDaGhoURERHDx4kV3X0Z4iN1u59lnn8VkMjF48GAa\nN27s6yGJYrh48aLcfxon96D27Nq1izp16pCeni73nwblx89gMMj9pxFWq5UpU6Zw+vRpJkyYUKJ/\n+zxSAwxw5513ApCYmOipSwgPePfdd4mIiODgwYNMnz6dWbNmYTQafT0sUUxy/2mX3IPacvHiRRYt\nWsSzzz7LoUOHALn/tOTy+IHcf1phsViYMWMGx48fZ+rUqfTv3x8o3r3n9hKIcuXKceHChUvH+TPC\nQhsiIiIAqFu3LuXLl+fs2bM+HpEojvLly8v9p3FyD2qHzWbj7bff5qGHHqJy5cry75/G/DN+IPef\n1tx4441UqlSJSpUqFfvec/sMcL169fjjjz9IT0/HZrPx559/XlpRKfxbZmYmJpMJk8nEmTNnOH/+\nPBUrVvT1sEQxyP2nbXIPaoeqqsydO5eYmBiaN28OyP2nJQXFT+4/bTh//jxGo5GwsDAuXrzIiRMn\nqF69erHvPY/sBHd5K4qhQ4cSHR3t7ksID9i/fz9z587FaDSi0+kYNGgQLVq08PWwxDV8+OGH/PLL\nL6Snp1OuXDlGjBiBzWaT+08j8uOXkZFBREQEXbp0IT4+Xu5BDdi7dy8vv/wyNWvWBEBRFCZPnsye\nPXvk/tOAguI3YsQI+TdQA/bv38/7778P5L2R6dev31Vt0Ipy78lWyEIIIYQQIqDITnBCCCGEECKg\nSAIshBBCCCECiiTAQgghhBAioEgCLIQQQgghAookwEIIIYQQIqBIAiyEEEIIIQKKJMBCCCGEECKg\nSAIshBBCCCECyv8DkT7gZ1W/o1wAAAAASUVORK5CYII=\n", - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlYlGX3wPHvLDDsuIXlgqi5iwtqbkiK5poWmluZqJVL\nZq/1urSIWZqvlpVJZmqu/TLT1JQssdQS1Awy8S2tXFJMxV1Zh9me3x8krwjCADMMw5zPdXHVzDzP\n/ZzhiB7uOc99qxRFURBCCCGEEMJFqB0dgBBCCCGEEGVJCmAhhBBCCOFSpAAWQgghhBAuRQpgIYQQ\nQgjhUqQAFkIIIYQQLkUKYCGEEEII4VKkABZCCCGEEC5FCmAhhEOp1ercrypVqtCpUye2bNni8Fhu\nfe3cudPm1/npp5/o2LEjnp6e3Hfffbz00ktYLBabX6coJpOJF198kYCAAHx8fBg4cCCXLl0q1hgX\nL17kySefpEmTJmg0GkaPHn3XY9esWcOaNWvyPf/9998X+L0fM2ZMsd+TEEJYQwpgIYTDvf/++6Sk\npBAfH09wcDCDBw/mp59+ckgsmzdvJiUlJferW7duNh3/8uXL9OzZk9q1a/Pzzz/zwQcfsHjxYl5/\n/XWbXscas2bNYvXq1axdu5a9e/dy5swZhg4dWqwxsrKyqFSpEi+//DItW7ZEpVLleV1RFBYsWEBW\nVlbuc5mZmbz99tu5RX/nzp1JSUnhwoULwP/+PCxcuLCU71AIIQomBbAQwuH8/f0JCAigadOmLFiw\nAIvFwv79+x0SS+XKlQkICMj9cnNzs+n4//d//0dmZiYrVqygadOmDBo0iAkTJvDhhx/a9DpFsVgs\nfPTRR0ybNo3evXsTEhLCwoUL+eGHH/j111+tHicoKIjo6GhGjhyJv79/gcf4+PjQrVs39u3bR1xc\nHOHh4fj4+OS+7ubmRkBAANWrVwf+9+fBz8+vdG9SCCHuQgpgIYTD3dqR3Wg0snLlStRqNR06dLDq\n3OTkZHx8fPD19S3wa9++fcWKZeTIkdxzzz106NCBdevWFfu9FCUxMZFGjRrh6+ub+1zbtm25evUq\np06dsmqMPn363PX9Pvvss1aNcerUKa5du0aXLl1yn+vUqRNarZaEhITivalCqFQqxo8fz7p169iy\nZQsxMTGsX7+eCRMmoFbLP0FCCMfQOjoAIYQYP348zz33HFlZWTRq1Ig9e/ZYXQDXrFmTI0eO3PX1\nGjVqWB3H3Llz6datGzqdjq1btzJy5EgMBgOjRo2yeoyiXLp0iSpVquR57tbjy5cvU69evSLHWLly\nZZ6WgttZO2t6q9e3atWqTJkyhS1btvDrr79SpUqVYvcBF0ZRFD7++GNWrlxJREQEiqIwbNgwxowZ\nwzPPPJOvZUIIIcqCFMBCCIebPXs2ERERJCUlMXr0aH755Zc8M5OF0Wg0VhWN1njppZdy/79Vq1ac\nPXuWd955x6YFcGGsnRG97777bHrdgIAA6tSpg1Zrn38Sbty4wZ49e/j8888BWLRoEdHR0SiKIgWw\nEMIh5PMnIYTDBQQEUL9+fQYOHMjs2bOJiori2rVrVp1r6xaI24WEhPDXX3+V+PyCBAQEcPXq1TzP\n3Xqv99xzj1Vj2KIFIiAgAICrV68ybdo0du/ejVqt5tq1a7mv2YJKpWLq1Kl4eHjkPufp6cm0adOk\nBUII4TAyAyyEKFfGjRvHnDlzeP/9961aGcGWLRB3Onr0qM1ml29p164dGzduJDU1NbddISEhgerV\nqxMUFGTVGCtWrECv1xf4mrUtEPXq1aNKlSrs3buXzp07A7Bv3z5MJhMPPPBAnmPNZjNnz57F19eX\nqlWrWjV+QSIjI0t8rhBC2JIUwEKIckWn0zF27FgWL17M9OnT8fLyKvR4W7VAbN26lXPnzhEaGoqX\nlxc7duzg448/ZsmSJfmOXb16NWPGjGHVqlXFLuqeeOIJXn/9dZ566ilef/11jh07xkcffcT06dOt\nHqM0Rf0tarWaCRMm8Pbbb9O6dWvuueceJk+eTNeuXWnWrFmeY8+ePUu9evWIjIxk1apV+cY6fPgw\nAGlpaVy9epXDhw/j4+PD/fffb1UsRqMxz6z4jRs3SElJwcvLS1aCEELYhyKEEA6kUqmUNWvW5Hnu\n/Pnziru7u/L++++XWRw7duxQmjdvrvj4+Cje3t5K69at88V1S3R0tKJSqZTY2NgSXevgwYNKhw4d\nFJ1Op6hUKmXEiBGKyWQqTfglYjKZlBdffFGpVq2a4u3trQwcOFC5dOlSvuP++usvRaVSKaNHjy5w\nHJVKpahUKkWtVuf+f7du3ayOY8+ePQWOcbfrCSFEaakU5Z/1hwpw9epVevfujdFoRFEUXn31VYYM\nGYJGo6FFixYAPPjgg7JYuRDCpQwePJgzZ87YZLOOWbNmsWjRIrZv307Hjh1tEJ0QQoiiFFoAm0wm\nDAYDXl5eXL16lSZNmnDhwgUqVapEWlpaWcYphBDlgqIoBAQEsG7dOh566CGbjBkdHc1DDz1E48aN\nbTKeEEKIwhXaA6zVanOXxbl+/To6na5MghJCiPJKpVJx+fJlm445adIkm44nhBCicEWuQZOenk5w\ncDAtWrQgOjoajUaDXq+nTZs2hIaGEhcXVxZxCiGEEEIIYROFtkDc7vfff+fhhx8mKSmJjIwMAgIC\nSExMJCIighMnTsjssBBCCCGEcApWL4PWuHFj6tSpw7Fjx2jbti2Qs399jRo1OH36NI0aNcpz/Oef\nf061atVsG60QQgghhBB30Ov19OvXz+rjCy2Az58/j06no2rVqqSkpPDHH39Qp04dsrKy8PT05PTp\n05w7d47AwMB851arVo2QkJDivwNRLsTExNC/f39HhyFKQHLn3CR/zkty59wkf87t0KFDxTq+0AI4\nOTmZsWPHAjl3Pr/zzjucOHGC0aNHo9Pp0Gg0rFixAk9Pz5JHLMql5ORkR4cgSkhy59wkf85Lcufc\nJH+updACuEOHDgVuMfr777/bLSAhhBBCCCHsqchVIIRr6tGjh6NDECUkuXNukj/nJblzbpI/1yIF\nsCjQnTc1CuchuXNukj/nJblzbpI/12L1KhC2oigKly5dwmw2l/WlRTHcvHkTf3//Yp+n0WgICAhA\npVLZISphjfj4eEJDQx0dhighyZ/zktw5N8mfaynzAvjSpUv4+vri5eVV1pcWxVCjRo0SnZeZmcml\nS5eoXr26jSMSQgghhLCNMm+BMJvNUvxWYF5eXjK772Ayg+HcJH/OS3Ln3CR/rkV6gIUQQgghhEuR\nAliICiY+Pt7RIYhSkPw5L8mdc5P8uRYpgMupLl26ULt2bapWrYrFYnF0OEIIIYQQFYYUwDZStWpV\nTp8+bbPx4uLi2L9/v83GE65D+ticm+TPeUnunJvkz7VIAWwDiqLk+a+txxVCCCGEELYjBfBtFi1a\nREhICLVq1aJt27Z8+eWXua/t27ePHj16EBQURPv27XNnZwcPHkydOnUACAsLIzAwkFdffRXI2Vf8\n9haG+Ph4mjdvbtX1hCgp6WNzbpI/5yW5c26SP9dS5usAl2eVKlVi48aN1K9fn507dxIZGUlYWBhp\naWk8/vjjLFu2jJ49e3Ly5EmuXr0KwMaNG4GcFoi4uDiCgoJKfb0qVarY4+0JIYQQQgikAM5j5MiR\nuf/fs2dP/P39+eOPPzhw4ADh4eH06tULgPvvv5/777/fLtf7888/6dChQ6nHFq5L+ticm+TPeUnu\nnJvkz7WUuwK4yiLbzH5ee/5asc/5/PPPWbx4MefOncNisZCWlobRaOT8+fPUrl3bJnFZcz0hhBBC\nCGE/5a4ALknhagtnz55l8uTJbNu2jXbt2gFQv359FEWhZs2aJCUlFXq+SqXK95xOpwPAZDLh7u5O\nWlqaVde7xc3NDcjZPU+tlnZtYR3Zz965Sf6cl+TOuUn+XItUVf/IyMhApVJRrVo1TCYT0dHR3Lx5\nE5VKxaBBg9i9ezc7duzAbDZz6tQpDh48mOf86tWrc/To0TzPVatWDT8/P37++WcAtm3bVuT1bhcQ\nEICfnx/79u2z07sWQgghhHA9UgD/o3HjxkycOJEePXrQtGlTMjIyctseAgMD+fTTT1mwYAH16tVj\n+PDh+TanmDFjBtOmTaNZs2bMmTMHAI1GwxtvvMHYsWPp168f1apVy50pLux6t2g0Gt5++23Gjx9P\nYGAg33zzTRl8J4SzkxkM5yb5c16SO+cm+XMtKsVOi83u2rWLkJCQfM+fP3+eGjVq2OOSopyQHAsh\nhHA6BgO4uzs6ClFChw4donv37lYfLzPAQlQwspalc5P8OS/JnROzWPBo2hTV5cuOjkSUESmAhRBC\nCOHa1GquN26M286djo5ElBEpgIWoYKSPzblJ/pyX5M45aQ4dQp2cjP+IEbjFxjo6HFFGpAAWQggh\nhMvyePttNL/8gvGhh3D74QfQ6x0dkigDUgALUcFIH6Jzk/w5L8mdE1IUtImJmNq1I+7YMUzNmqGN\ni3N0VKIMSAEshBBCCJek/usv0OlQ/lm5yDhwIOpz5xwclSgL5W4nOCFE6UgfonOT/DkvyZ3z0SYk\nYPpnN9bQ0FCyJYcuQ2aAhRBCCOGSNImJmNq2dXQYwgGkABaigpE+ROcm+XNekjvnY27RAmN4OCD5\nczVSAItiqVq1KqdPn3Z0GEIIIUSpGZ58EkuTJo4OQziAFMDCard2zbbT7tnCRqQP0blJ/pyX5M65\nSf5cixTA/1i3bh3h4eE0a9aMMWPGMHz4cJo0acLRo0exWCzMnz+fVq1a0bhxY1566SVMJhMAZ86c\n4ZFHHqFevXrUqVOH0aNHk5qamjtubGwsDzzwAIGBgbRr147du3fnvtayZUt++OGH3Md3zq5OnDiR\nl19+mZEjRxIYGEjLli1JT08HICYmhk6dOlGvXj2GDh3KxYsXc8/p378/DRs2ZObMmbRv357w8HCy\nsrIAuH79OuPGjaNx48a0bt2atWvX5rnepEmT6Nu3L4GBgUyaNCn3tcGDB1OnTh0AwsLCCAwM5NVX\nX7XVt18IIYQoNzQ//oj2++8dHYawIymAb6PT6Thw4AA7duzgqaeeYsSIEWzZsoUPPviA2NhYduzY\nQWJiIn/88QdLly4FwGAwEBkZya+//sqvv/7K9evXmT9/fu6YkydP5pVXXiE5OZnNmzdz33335b6m\nUqlQqVSFxrRhwwZGjBjBmTNn+PTTT9Fqtfz888/861//YvHixZw4cYIWLVrwwgsv5J7Tvn17Pvro\nI5YvX87OnTvx8PDgp59+AmD8+PG4u7uTlJTEli1bmD9/PocPH8499/vvv2f58uXs37+frVu3cujQ\nIQA2btxIcnIyAHFxcSQnJ/Pmm2+W8jsu7EH62Jyb5M95Se6c2+35U587h+6ff+dFxSQF8G3q1q2L\nn58fVapU4f777ycwMJDLly/z6aefMnXqVO699158fHx46qmn+OqrrwBo0KABAwcOxMvLC19fXwYM\nGMBvv/2WO6Zareavv/4iNTWV2rVr06SYvUZdunShZ8+eqFQqmjdvjoeHB//3f//H8OHDad26NWq1\nmokTJ7Jz504MBkPu+wgKCqJatWr4+/sTGBjIlStXSElJYdeuXcyZMwedTkdQUBD9+/dn+/btudfr\n06cPNWvWpFatWjRt2pSTJ0/a4DsrhBBCOA9T9+647dsHmZmODkXYSbkrgD3mzaNylSr5vjzmzbP6\n+LsdW5Rbs7FarRaNRoNWq8VkMnHu3DnGjx9P3bp1qVu3LhMnTuTatWsAXL58maeeeopmzZpRt25d\nZs6cmdseAbBq1SoSEhJo2bIlPXv25NixY8WKqX79+vmeO3fuHGvWrMmNp3Xr1uh0utw2iFuxazSa\n3MdGo5Hz588D0KpVq9xz161bx+XLl3PH9vf3z/1/d3d3srOzixWvcDzpY3Nukj/nJblzHqq//8Zj\n7tw8z92eP6VSJUytW+dsjSwqpEI3wrh69Sq9e/fGaDSiKAqvvvoqQ4YMYcOGDcyYMQOVSsU777zD\nww8/bLOA9C+9hP6ll+x2fHEpikLNmjVZvHgxbQtYK/CNN95Ao9Fw8OBBfHx8WLp0KVu3bs19/YEH\nHmDdunUYDAZeeOEF5s6dyyeffALktFzcKpZv7xu+nVqd/3eUWrVqMWXKFCZPnlys91KzZk08PDw4\ndepUka0Xd1PS84QQQojyQvvjj2j++KPQY4y9euG2YwfGPn3KKCpRlgqdAfb39+eHH37g8OHD7N69\nm+eeew6j0chLL73Evn37+O6774pdhDmTW6sdPPHEE8ydO5eUlBQUReHEiRPs2bMHgIyMDHx8fPDy\n8uLMmTOsXr06z/kbNmwgPT09t3D08/PLfb1+/fr8/PPPAGzbts3quIYPH86qVas4cuQIiqJw+fJl\ntmzZki/uO1WvXp1OnToxa9YsMjIyMBqNHDx4ME/Lxt2+B7ePcfToUatjFWVP+hCdm+TPeUnunIc2\nISHfBhh35s/Ypw9uO3eCxVKWoYkyUmgBrNVq8fLyAuDGjRvodDoOHjxIs2bNuOeee6hduza1a9cm\nKSmpTIK1pztvSLv1WKVSMXHiRDp27Ejfvn0JCgoiMjKSq1evAjBt2jQOHz5MUFAQTz31FH369Mkd\nR1EUNm7cSHBwMA0aNODixYt5Vk6YOnUqGzZsoEePHly8eLHA2dWCnmvXrh1z5szhueeeIygoiO7d\nu3PkyJECY7/T0qVLuXLlCu3ataNhw4bMnj0bs9l81+vd+XjGjBlMmzaNZs2aMWfOnEK/p0IIIUR5\ndPsWyHdjqVuXjA8/BFn6s0JSKUUs6pqenk7Hjh05efIkn376KWazmZ07d9KmTRuqVKnC5s2biYyM\npHfv3nnO27VrFyEhIfnGO3/+PDVq1LDtuxDliuRYCCFcl+rmTTQ//YTpoYccHUrBMjOp1LAhN44f\nB09PR0cjbOTQoUN0797d6uOLvAnOx8eH//73vxw6dIipU6ei1+sBGDduHIMHDwakL1QIIYQQOTxf\neQXvZ56B224IL0+0SUmYGzeW4rcCMJqNxP4Vy7M7ny32uYXeBHe7xo0bU6dOHerUqcOFCxdyn09J\nScmztu3tnn32WQIDA4GcfuLg4GDq1atX7CCF87nVS3Xrrlp5XHaPb+9jKw/xyGPJn6s8vvVceYnH\nEY+1e/Zg3rULg78/msREzB06lKv4APbduIHXk08SDHlev3WMo+OTx0U/Pp11mt1Xd/PtxW/xzPIk\n6GYQ5MzJWq3QFojz58+j0+moWrUqKSkptG3blkOHDtGhQwcOHjyIXq8nPDyc48eP5ztXWiBcl+TY\nseLj43P/ohDOR/LnvFw+d2Yzfh07kjl3LkrlyliCglCqVnV0VFZz+fyVc9eyrrHpz018duwzLmVe\nYljjYQxtMpQGlRsAxW+B0Bb2YnJyMmPHjgVybuh65513CAgIYN68eXTu3BmAhQsXlvS9CCHsQP4C\nd26SP+fl8rnTaEjbvBmlVi1HR1IiheYvK0taJhzAaDayO3k3646u44ezP9Czbk+iOkURVisMjVpT\nqrELLYA7dOiQZ3WBW4YMGcKQIUNKdWEhhBBCVCzOWvz+8IMWjQZCQ035X9Tr8W/enJuHD4Ovb9kH\n54KOXjnKZ8c+Y+MfGwnyD2J4k+FE94jGT+dX9MlWKnc7wQkhSuf2fjbhfCR/zkty55zi47U8/bQ3\nY8Zo+de/vLh5844b+z08MLdqhds/6/8L+7iWdY3lScsJXx/OkG1D0Gl0xAyKYcfgHUQ2j7Rp8QvF\nuAlOCCGEEKIi+fVXDWPGeLNiRQZ6fTyxseF06uTHW29l0q+fMfc4Y+/euMXGYhwwwIHRVjz2bHEo\nSpHrAJeU3ATnuiTHQgjhIvR68PDIfagosHChB5995s6GDekE1TaCWg3lZLlUn4gIsubMwdysGWfO\nqOnb15c5czKJiPhfsbtvn5bJk71o3tzM/PmZBAQoqM+exTc8nJu//w4a+xZmrqCgFoeIBhGlmuW1\n+TrArubjjz+mQYMGBAYGsnfv3tzn//3vf7NgwYI8x06bNo3AwECqVavGDz/8UNahCiGEEI5jseAz\ncCDaXbsAMBph8mQvvvzSjaFDDQwY4MPlsFGojx1zcKD/yMpCm5CAuW5drlxR8dhjPkyerM9T/AJ0\n7mxi795UgoIsdOnix/r17phr1cZy771oEhIcFLzzK+sWh6JIAXwbo9HIa6+9xtatW0lOTiYsLCz3\ntXfeeYcpU6bkOf6tt94iOTmZWrVq3XUzkP79+/PJJ5/YNW4hbid9iM5N8ue8XC137qtXozKbMXXt\nSmoqDB/uw4ULar76Ko1//1vP5Ml6eiSv5uzGQ44OFQBNUhLmhg1Jt3gxbJgPjz5q4JlnsnNfvz1/\nnp7w2mtZbNiQzpIlOgYP9uFEz2dQ37YPgijarY0qIrdHErImhISUBKI6RZE0KokZnWbkLmHmCNID\nfJuLFy+i1+tp1KiRzcaUXfKEEEJUNKpz5/D8z39Ii4nhXIqWYcN8aNfOzFtvZaL9p7IYM8aA228n\n6fvRELY8qaZePYtDY9YmJJAZ0oHISB+aNjXzyiv6Is9p2dLMd9+l8cEHHnRePInp0/U8ZclGLdOH\nhSqLVRxKS1L4j44dO9KxY0cA6tatm9sCsXPnTgIDA6levTpvvvmm1eO9++67BAYGcuDAAaZPn05g\nYGCe3pTr168zbtw4GjduTOvWrVm7dm2e8ydOnMjLL7/MyJEjCQwMpGXLlqSnp9vmzYoKzeXXInVy\nkj/n5TK5UxS8pk4l++mn+a+5Gb17+zF4sIF33vlf8XvLk6/dywzmMKC/NydPOrbkUP+UyNjfXkSn\nU3j33cx8bcl3y5+bG7zwgp6vv05j82Z3+vXz5c8/pXy6U3lrcSiKzAD/48CBA5w9e5ZWrVpx+vRp\n1Lf9epecnMzEiROLNZv74osv8uKLLzJgwACGDBnCiBEj8rw+fvx4AgICSEpK4sKFC/Tr148WLVrQ\nqlWr3GM2bNjAkiVLWLNmDb/99hvaO/9mEUIIIcqY21dfoTl9mphR6xgf4cO8eZkMHGgs+GA/P0a3\nOYQx+BcGDGjDl1+m0aCBY2aCX45/hNNB97Hp44x8hbo1Gja0sH17GitX6ujb15dnn81m0iQ9bm62\nj9VZOHIVh9KSX2FuU9SCGCVdMOPO81JSUti1axdz5sxBp9MRFBRE//792b59e57junTpQs+ePVGp\nVDRv3hyP2+60FeJuXK0PsaKR/DkvV8mdsWtXPnzsG5593p+1a9PvXvzeOr53b0bX28PLL2fx6KO+\nHD9e9qVHdLSOb+6NZN0mI15eBR9jTf7Uanj66Wz27EnjwAEt3bv7cvhw+S707OHolaNExUURvCqY\n9xLfI7xOOEdGH2FZr2V0C+xW7otfKIczwFWqVLbJONeuXbfJOLZw58zxuXPnAPLM9prNZgYOHJjn\nuPr169s/OCGEEMJKigJzF93D5s3ufPVVGvffX/RsbvZzzwEwAgNqNTz6qC9btqTRsGHZzAR//rk7\ny5fr+OabNCpXsc2YtWtb2LAhnQ0b3Bk61Ifhww1Mn55VoXdLvpZ1jU1/buKzY59xKfMSwxoPI2ZQ\njENvZCuNclcAl6fC9U53a4Fwd3fHbDYX+Jq6gE75mjVr4uHhwalTpwptqyjoXCGK4jJ9iBWU5M95\nVfTcZWfDpElenD6tITY2jWrViv+p6OOP5xTBERG+bN6cRqNG9i2Cv/1Wy2uvebJ1axo1axYer7X5\n0373HXh5YerUiaFDDXTrZuTll70IC/Nj4cJMOncuYDtlJ1WeWxzctmzBEhSEuXXrEp0vFVYx3K0F\n4v7772f//v0FvhYQEMDRo0fzPHfvvffSqVMnZs2aRUZGBkajkYMHD/Lbb7/ZPGYhhBCitG7cyFk3\nV69XsXVryYrfW4YNMzBzZhYREb78/rv9ypDERA3PPuvN2rXpNi201X//jfvq1bmPAwIUVqzI4PXX\nsxg71pt//9uL1FSbXa7Maffs4VTCjnLd4qC6dAmv6dNRStEaKgXwHe6ckR04cCCBgYF88cUXREdH\nExgYyHP/fJxzy6uvvkpMTAy1a9dm5syZeV6bOHEi33//Pc2aNeORRx7JfX7p0qVcuXKFdu3a0bBh\nQ2bPnp1vFlmWUBMl4Sp9iBWV5M95VdTcnTmjplcvH1q2NLN6dYZNPuYfOtTArFlZDBzoy9Gjti9F\njh9XM2KEDx98kMkDDxT8Ce2drM2fsWdP3L77Lmfnj9v07Wtk//5UzGbo3NmfnTvL3YfshbqWdY2Y\nDa/BiMH4PjkSH6O63K7i4DlzJobHH8fSpEmJx3Cu7NhZYGAgV65cyfPc5s2bizyvWbNm/PjjjwW+\n1rJlywJnhytXrszixYvvOmZhrwkhhBBl4dAhDSOG6HipUjQjZ0fadEvjIUMMqNUKgwb5smlTGk2b\n2maW9sIFFYMH+xAVlUWvXkZUV6+CwYBy3302GV+pUQNLUBDagwcx3dE24e+vsHBhJnv35myn/MUX\nJubOzSrVjLk95WtxCHqIal9+RPjSHcz6OoOs8PLX36uNj0e7fz+pd/nk3epxbBSPEKKcqOh9iBWd\n5M95VbTcff21G5P/5cUy7+fpOb0FhlIWv9r4eCz33ovl/vtzn3vsMSMqVSaDBvnyxRfpNGtm3Wzt\n3dy8mVP8RkYaeOIJAwDun3+O+tQpshYsKPTc4uTP2KsXbjt25CuAbwkLMxEfn8p//uNJSIg/wcEm\nwsJyvtq0MeHubv17soeiNqrIatQTv7AwTN98g7FPH8cGezuDAa8pU8j6z3/Ax6dUQ0kBLIQQQog8\nli3T8f77HmwZ8BHtz/5B+mNvlHpMt127UNzc0L/ySp7nBw26VQT78MUX6TRvXrIiWK+HJ57wJjTU\nxOTJ/9vlTZuQgLF371LFfidjnz54jxlD1uzZd50V9/KC2bOzeOmlLA4e1LJ3rxszZnhy/LiGdu1M\nhIUZCQsz0aKFGU0ZtNQWtorDhQsq9u3WcviwhiNHNDRo4Mmzc1ZT/9MF5aoAVp88ialdO4x9+5Z+\nLBvEI4QfTiS7AAAgAElEQVQoRypqH6KrkPw5r4qQO7MZXn3Vk5UrdexYnESnrVFkvvOOTVofjOHh\nuO3eXeBrAwcamTcvk8ce8+G//y1+NWg2w9ix3lSvrjB3blaecLWJiZjati1yjOLkzxwcTObChVYd\n6+0N4eEmZs3KYteuNI4cuclTT2Vz4YKaiRO9uf9+f0aM8GbpUh1Hj6op4ZYDBTKajcT+FUvk9khC\n1oSQkJLAcw3e5K17j6HdO4eZ44Jp0sSfsDA/VqzQYbHk3KRoNkOn5x9klN9mu/Rol5SlSRMyo6Nt\n8udRZoCFEEIIQWYmjB/vzY0bKnZ8fZNaI55FP20altq1bTK+qX17NH/+ierqVZSqVfO9/uijRtTq\nTAYP9mHDhnRatLBuJlhRYMoUL9LSVKxfn87tK4iqzp8HvR5LvXo2eQ//G1h11/aHolSqpNC3r5G+\nfY1AFhcvqoiP1xIX58bSpToyMlR06WKiS5ecGeKgIEux671bLQ7rE7+nyrWe1Mt8mQfOrSd+kQe7\nDdCypZm2xgOMSd1Dk2//Rc2aSp5rPPKIkalT9axcqWPgQF9atTLx/PPZdOxosmUbuE0YDPDjj9pi\nd0SolJJub1aEXbt2ERISku/58+fPU6NGDXtcUpQTkmMhRLllNufMHsk663lcvqzi8cd9qF/fzPvv\nZ6JzV9B+9x2m8HBs+fm89/DhGB57DOOgQXc9JibGjalTvfj883Ratiy6CJ43z4PYWDe2bk3D746F\nCty2bsV9/XoyPvustKGXmeRkNXFxWuLictomtFolt384NNRIjRoFl21/Jt9k6TeJfLPvMjf+qofm\nQgc0Fm9CWim0bm2iZUszrVubqVXLgueCt3H/4gvStmxBKeLfa70e1q93Z/FiDypVUpg0SU+/fsYy\nadu4G7MZ9u/XsmmTO1995UaDBhbefPMHunfvbvUYZV4Anzt3jho1asgSXxWUoiicP3+emjVrOjoU\nIYTIx2viRNy+/56bBw6Qr1pyUcePqxk61IfHHjPw8st6u87w6ZYvR3P4MJlFrHS0fbsbL76YUwS3\nanX3InjVKnc++MCDb75JIyAgfznjtnUrqrQ0DCNGlDp2R1CUnPzExbmxd6+W+Hgt1aopdOlipG1b\nM2eSFXYduMGv/9Whz9ISUP8snR/Q8XDofbQJUahd+47ZY0XBY+5c3L/6irQvv0SpXt3qWMzmnBsj\nFy3y4Pp1Fc89p2foUEOZ7X6nKPDLLxo2bXLnyy/dqVbNwqBBBgYONFCrlsKhQ4fKdwGcnp5OdnY2\nVQv4+EM4v6tXr6LT6fAp5d2ZouTi4+Mr3N3orkTyZ1+qlBQ8Z85Ec/Ik6V98gVK5ss3GdsbcHTig\nZfRob2bMyGLECIPdr6c6dw5tUpJVNzF9/bUbL7zgxWefpRMSkr8IjolxY/p0L7ZvT6Nu3dIvoeYM\n+bNY4NdfNWz85iqx8dc477afGg3PMyy8AU+Fdcffo5Bf6hQFzzfeQPvdd6Rv2YJSrVqxrq26fh23\nbdvIHhnJjz9qWbRIxy+/aHnmmWzGjMmmcmX7LPV28vMjfH68LZu/zNn04lbRe+fmJsUtgMu8B9jH\nx4fs7GzOnz9f1pcWxXDz5k38/f2LfZ4Uv0KI8ky5914yly7Fc+ZMfB55hPTNm4tdCFQEqanwySc5\nKz0sXZpBt25ls32vUrMmRis/IezbN6cnePhwH9atS6dNm/8Vwfv2afn3v73YuDHdJsVvqaSnl3pJ\nLmvkWcXhnksMe3kYQ5sMpUFl69fqtdx7L+lbt6JUqVLs6ysaDR4LF6JUq0bHfv3o2NHEsWNqPvjA\ngzZt/Bg61MCzz2ZTu3bp83H2rJrNm93YtE7h+skGPPqknuXLzbRqZbbZJxRlPgMshBBCONw/HwW7\nffstabt22bTPtTw7cULNxx/r2LDBna5dTUyblkXjxg4uIIsQG+vGpElerFuXTtu2Zn77TUNEhA/L\nl2fw4INlU7jfjerGDfzatOHmsWPYY3HffBtV1O3J8CbDCasV5pDtiDUHD+ITGUnqnj15NhY5d07F\n0qUefPqpOz16GJk0KbvYy9ldvqxi61Z3Nm1y5/hxNf37G3jy0FTaD6uJccK4Is8v9y0QQgghRHmh\nPnEiz8YMFZHFArt2aVm2zIMjRzSMHJnNqFHZ1KyZ959/z6lTMfbrh6lrV8cEWohvv9UycaI38+Zl\nEhXlxZw5mUREGIs+sQz49uxJ1ssvY+rWzWZjFrRRRUSDiHKxHbHH/Plof/yR9E2b8t1MmpoKq1fr\n+OgjD5o2NfP883q6dLn7yhGpqbB9e07Rm5iooVcvI4MGGeja1YT3ti/wiI7O+QVVW3TDQnELYLkN\nVhSoIqxn6aokd85N8le2bFn8lrfcpabC0qU62rf34803PYmIMJCUdJNXX9XnK36133+PW2wspjZt\nHBRt4R56yMTixRlMnOjNv/6lt0vxW9L8GXv3xi02ttTXv5Z1jeVJywlfH86QbUPQaXTEDIphx+Ad\nRDaPLBfFL4D+3/9GpdejK+BGRj8/eP75bH755SaPPmpg6lQvwsN92bzZDdM/k/VZWbB1qxsjR3oT\nHFyJ7dvdePzxbI4evcnSpZn07GnCXZ+K18yZZC5YYFXxWxKyDrAQQogKze3LL7E0aIC5WTNHh1Im\njh/PaXPYuDGnzSE6OoP27QvpnczIwOuFF3I2vPD1LdNYi+Ohh0z88ccNqxfv0C1ZQvbo0eDhYde4\nDL174zN8eM72vMVsUC2oxSGqU1TpWxxMJjzfeAP9+PFFLnNWbFotGUuX4r5u3V0P0elgxAgDjz9u\nIDY2Z+WI2bM9adPGzK5dWlq1MjNokIHo6Ez8/fM3IujWrcPYqxfmdu1sG/ttpAVCCCFExZWVhX9I\nCGmbNmFp2tS6c7Kzc/4FdyLWtjkUxDMqCtXFi2QuW1YGkeZw27IFzW+/oZ8xwy7jq1JS8OvcmZsn\nTthk17BCKQp+rVuTvm6d1X/G7NriYDTiPX48qhs3SP/kk5w9mcuBgwc1HDumoU8fI9WrF/HnUlFy\nfg6L8ctLuV8FQgghhCgruk8+wdS2rdWFierSJXx79SL900+tL5gdKDUVPvtMx/LlOnx8FMaOzeaT\nTwxW1w2aQ4dw37CB1H377BvoHSx16+I5b57dCmBtQgLmtm3tX/wCqFQYRoxAff58oX9m8qzikHmJ\nYY2HETMoplirOBTJYMD76adRZWeT/umndp/9Lo727c20b2/ljXEqld1jlx5gUaDy1ssmrCe5c26S\nPxsyGPCIjkb/wgtWn6IEBJA1Ywa+gwahOXKkWJcry9wdP65m+nRPWrXy5+BBLR98kMGePWk8/rj1\nxS+AUrkyGR99VOZLwZlbtEB1/Trqs2ftMr42MRFT27bFOqc0+dNPmYKpR498zxvNRmL/iiVyeyQh\na0JISEkgqlMUSaOSmNFphm2L3+xsvEeNAouF9LVry1XxWx7JDLAQQogKyf3zzzE3aIC5mO14xkGD\nyHR3x2fwYNI/+6zY59vLrTaHpUs9+O9/c9oc4uJSrWpzuOuYdetiqVvXhlFaSa3G2LUr2l27MIwa\nZfPhNQkJ6KdNs/m41iqoxSG6R7Rdb2Rz37oV3N3JWL4c3Nzsdp2KQnqAhRBCVEi+PXuS9dprmDp3\nLtH5brGxeE2aRPratZg7dLBxdNZLTYV163R8/LEOX9+cNoeIiOLN9JZH7uvX4/b112SsXWvbgQ0G\nKtWvz43ffivT7a4LanEo7kYVpaIoOb8lOWBNa3VyMh7z5pEZHV3i66tu3kQpwQZct0gPsBBCCAGk\nffkleHqW+Hxjr15kfPQRqsxMG0ZlnbQ02LnTjW3b3Pn+ezd69DCyeHEGDzxQyp2wTCa7LStVXMZu\n3fCcPTunaFPbsCPTaCRz/vwyKX7ttopDSahUDtvQxVKzJuozZ9B98AHZ//pXsc/X7t+P14svkrp/\nv23/LBRCeoBFgaQP0XlJ7pyb5M+GvLxKfROUKTwcU3i4VceWNnepqbBhgzsjRnjTrFklNmzQ0bOn\nkV9+ucmKFUUsZVaUtDS8xo/HY/78UsVoS0r16tw8fNj2BY+3N4bHHy/2acXJ39ErR4mKiyJ4VTDv\nJb5HeJ1wjow+wrJey+gW2M0hu7Q5lEZDxtKleCxejOaXX4p3rtGI15QpZL3ySpkVv1DEDPC5c+cY\nOnQoN27cQKfTMX/+fHr06IFGo6FFixYAPPjggyxcuLBMghVCCCEqkuvXVXzzjRvbtrmxf78bXboY\nGTDAyOLFBa+PWhKaX37B+5lnMHXpUqwbAsuEE/WqWrOKg9uWLVhq1bLr+rUA6pMnwWzG0rChXa9T\nHEqtWmTOn4/32LGk7tkDPj5WnadbsgRLzZoY+/e3c4R5FdoDfOnSJS5evEhwcDDJycl06tSJv//+\nG19fX9LS0godWHqAhRBCiPyuXlWxfXtOe8NPP2np2tXIgAEGevY02vZTe4sF3eLFeERHk/nWWxgf\nfdSGg7uGglochjcZftcWB92iRWjOnMnZVMQeTCZ0S5bg8f77OTkdONA+1ykFr4kTQaMhc9GiIo9V\n/f03fl27krZzJ5Z69Up1XZv2AAcEBBAQEABAYGAgBoMBg8FQqgCFEEIIZ+YWGwvp6RgHDbL6nEuX\nVHz9tRtbt7pz6JCW8HAjTzyRzerV6dZOlBWb7sMPcd++nbRdu7DUrm2fi1RQJV3FwdinDx6PPgoL\nFth8DWL10aN4P/88io8Pad99hyUoyKbj20rmvHlof/rJqmO9oqLIfuaZUhe/JWF1s0VsbCxt2rTB\n3d0dvV5PmzZtCA0NJS4uzp7xCQeRPkTnJblzbpK/0vH6979RJyfb9Rrm2rXxiorKtxXsnblLSVHx\n8cc6Bgzw4YEH/Ni3z40xY7I5duwGq1ZlEBFhtFvxC5A9ZgxpX30lxa+Vvv7+a5YnLSd8fThDtg1B\np9ERMyiGHYN3ENk80qolzCwNGqB4eRV7Demi6KKj8X3kEbKffJL0LVvKbfELgK8vJitnYrNeegl9\nCW6aswWrbgVNSUlhypQpbNu2DcjpDQ4ICCAxMZGIiAhOnDiBzsm2jRRCCFGxaA4eRLtrF5Z58+x6\nHUvTpqR9+SW+AweCwZBnHdu//1bx1VfubNvmxu+/a+jVy8iECdl062Ys+2XLyskWuEVKS0Pz++82\n6ZvVffghlsBAjA8/bNXxt7c47D69mz739yn1Kg7GXr1w27EDc8uWJTq/IOYmTUj9/nuUmjVtNmZ5\nYGnUyGHXLnIdYL1ez0MPPURUVBQ9e/bM93r79u1Zu3Ytje54E7t27eLjjz8mMDAQAH9/f4KDgwkN\nDQX+95uyPJbH8lgey2N5bIvHvT74AGOvXuxu0KBMrhdWsyY+jz7Ksd69+abBk2zc2JETJ9SEhPxN\n584XmDChITpdGb1/RSG0SxeHfv9L+viXDRvo+Mor6I8fB5WqVOP5PPwwP/fqxeXWrQs9/nTWaf7w\n+IONf2ykiqoK3at2Z2qfqfjp/Er9fo4tWULTVatQ/mkDcPT3t6I+vvX/yf984vP0008Xqwe40AJY\nURQef/xxwsLCmDBhAgDXr1/Hw8MDT09PTp8+TWhoKMePH8fzjrUW5SY4IYQQZUXz3//iM2wYN3/+\nuUy3gFUln2V5rx28ZXyR/8zXM2CAscwXNnD//HPcP/2U9K1bbd53WiYUBb82bUj/v//D0rRpyccx\nmahUt+5dN8Aos40qTCY0hw9jLuZWzBWawQDu7na9RHFvgiu0B3jfvn1s2rSJZcuW0bp1a0JCQvj9\n999p3bo1LVu2ZODAgaxYsSJf8Suc3+2/YQnnIrlzbpK/kvF49130EyaUafF744aKJ15pzPoaL/Dt\nrgyqV99TtsXvrbV933uPrP/8xzmLXwCVCmN4OG67dpVqGM1vv2GpVStP8Ws0G4n9K5bI7ZGErAkh\nISWBqE5RJI1KYkanGXmKX5v97Gm1JSt+09LwnDIF988+s00c5YT6+HH8wsIgPd3RoeShLezF0NDQ\nAld9+P333+0WkBBCCFEsmZmoz50jOzq6zC75888annrKmz59jKxcmYW7O5w9m/cYt6+/BqMRU7t2\nKDVq2PT6uWv7hoaSumsXeHvbdPyyZgoPR7d8OdmTJpV4DG1iIqZ/+ohLuoqDo2i/+w6vF1/E9OCD\nGPv2dXQ4NmVp0ABTu3Z4vfQSxvBwNMeOoX/1VUeHVXQPcElJC4QQQoiKRlFg6VId777rwbvvZvLw\nw8a7Huu+fj1uW7eiTUwEnQ5T27aY2rXDMHgwyj9LjJaE+tgxfB95pGKt7ZuWRqVmzbhx7FiJi3nt\n06OJr6fllXon7dviYEOq69fxnDED7b59ZL73HqZu3Rwdkn2kp+PXrRvqS5dI27ABc/v2Nr+ETdcB\nFkIIIUSOmzdVTJrkxd9/q9m5M42gIEuhxxuGDcMwbBgoCurTp9EmJKBJTESl11OamSdL48ak7tuH\ncs89pRilnPH1JWvqVFQZGSjFKIBvX8XhSNM9hNXtTlSb0q3iUJa8nn0WS506pMbHW71zmlPy8SFj\n5Uq0e/fapfgtCZkBFgWKj4/PveNSOBfJnXOT/JVPv/yiYcwYb3r1MvL661kUtPJnqXJnseDXqRPm\n++/H1K4d5rZtMbVq5fStDfZSUItDRIOIUrU42ONnT3XzJoq//90PyM6mwD9MothkBlgIIYSwEUWB\n5ct1LFjgwdtvZ/LII3dveSgVlYq0L75A+9NPaBMTcZ81C82xY5ibNSNtxw7nvcHNhgpaxSFmUEy5\nbXFQ/f03ft27c/PYMVDfZc0BKX4dRmaAhRBCOCdFsWthmJoKkyZ5k5ysZuXKDOrWLbzlweb0etSn\nTpVuaTAnd3uLww9nf6Bn3Z4MbzLcaVoc/Dp2JGPRIiz33Qfe3iiVKzs6pArLpsugCSGEEOWR6to1\nfB98MOcjZDtIStLQrZsf1atb+OabtLIvfgE8PFy2+D165ShRcVEErwrmvcT3CK8TzpHRR1jWaxnd\nArs5RfELYOjTB8/XXsOvWze0P/7o6HDEbaQAFgWStUidl+TOuUn+rKNbuhRzq1Y2/whZUWDFCh2D\nB/swY0YWb72VZfXSwpK70rmWdY3lScsJXx/OkG1D0Gl0xAyKYcfgHUQ2j7x7f6/FAllZpb6+PfJn\neOwx8PEhLSYGY58+Nh9flJz0AAshhHAuqanoVq4kLTbW1sMyebI3J0+q+eabNOrXd8Csr4u5s8Wh\nT+0ebN/ghvtniWh01v3moTl6FO9x40jdt8/O0RafpWlT0jdscHQYogAyAywKJHehOy/JnXOT/BVN\nt3o1pq5dsdSrZ7MxjxzREB7uR+XKCrGxJSt+JXfWu1uLw5J+HxNwLRv3Xw5bPZYmISFnxYxSkvy5\nFpkBFkII4TyysvBYsoS0TZtsMpyiwOrV7syd68m8eZkMGmSnVR6E1as43NoW2dyhg1XjahMSMD3w\ngD1CFhWYzACLAkkvm/OS3Dk3yV/h1Bcvkj18uE1uDktLg2ee8WblSh3ffJNW6uJXcpef0Wwk9q9Y\nIrdHErImhISUBKI6RZE0KokZnWYUuISZKTwctz17rL6GNjHRJgWw5M+1yAywEEIIp2EJCkI/c2ap\nx/n1Vw2jR3sTGmpi5840PD1tEJzIVdBGFdE9oq3aqML0wANojh9HdfUqStWqhR6runYN9cWLWBo1\nslXowkVIASwKJL1Qzkty59wkf/alKLB2rTtz5ngyd24WgwcbbDa2q+fOZhtVuLtj7NwZ7fffYxw0\nqNBD1WfOYOzRAzSlXxbN1fPnaqQAFkII4TLefdeDzZvd2b49jYYNZZWH0ipoo4qoTlGl3qgic9Ei\nlEqVijzO3Lo1GStWlPg6wnVJD7AokPRCOS/JnXOT/NlPcrKaJUt0bNhgn+LXlXJn740qlGrVQFu2\nc3SulD8hM8BCCCHKO0XJuWPNr+j+0cJERXkyblw2NWsqNgrMtdisxUGIckClKIpd/ibYtWsXISEh\n9hhaCCGEC3HbsQPd4sWkx8SUeIy4OC2TJnlx4ECq3PBWDAW1OAxvMrzULQ5C2NqhQ4fo3r271cfL\nDLAQQojyS1HweOcd9M89V+IhTCZ4+WVP3ngjS4pfK5VmFQchnIH0AIsCSS+U85LcOTfJX17avXtR\npaZi7N+/xGOsWaOjShWF/v3tu8mFs+fuWtY1lictJ3x9OEO2DUGn0REzKIYdg3cQ2TzSIcWv6tw5\n0OsLfE174ACqq1dtdi1nz58oHpkBFkIIUW55vPsu+smTQV2y+Zrr11W89ZYHmzeno1LZOLgKwF6r\nONiK9/jx6J9/HtNDD+V7zWvyZDJWrMBcxFrBQhREeoCFEEKUS5qffsJ77FhSExLAza1EY0yf7onF\nAm+/nWXj6JxbQS0OEQ0iyl2Lg8d776G6eJGsefPyPK+6fh3/li25cepUma8WIcon6QEWQghRISg+\nPmS+/XaJi9+jR9Vs2eLOjz+m2jgy5+SMqzgYw8PxfuYZ7vz1RZOYiKl1ayl+RYlJD7AokPRCOS/J\nnXOT/P2PpWnTAj/6toaiwCuveDF1qp4qVcpm2bPymDuj2UjsX7FEbo8kZE0ICSkJRHWKImlUEjM6\nzSjXxS+AOTgY1c2bqJOT8zyvTUzE1K6dTa9VHvMn7Ed+dRJCCFHhbN/uxqVLakaPznZ0KA5RYVZx\nUKsxdu2KdvduDKNG5T6tTUgge+xYx8UlnJ4UwKJAsie685LcOTfJX+np9TmbXixcmFmmn5A7OnfO\n2OJgDePAgaguX87znKl9e5vPADs6f6JsSQEshBCiQvnwQw+Cg808+KDJ0aHYXXlfxcEWjL165XtO\nP326AyIRFYn0AIsCSS+U85LcOTfJH2As+Xq958+r+PBDHW+8UfarPpRl7o5eOUpUXBTBq4J5L/E9\nwuuEc2T0EZb1Wka3wG4VpvgtS/Kz51pkBlgIIUS54hMRQdaMGZg7dCj2ua+/7smoUdkEBVnsEJlj\nVdQWByEcQdYBFkIIUX5kZFCpcWNu/P47eHsX69SDBzWMGePDwYM38fGxU3xlrKAWh+FNhleoFgch\nbEHWARZCCOG0tAcOYGrZstjFr8WSs+zZrFlZFaL4rTCrOAhRTkkPsCiQ9EI5L8mdc3P1/Lnt3Ysp\nLKzY561b545WC489ZrBDVNYpbe6uZV1jedJywteHM2TbEHQaHTGDYtgxeAeRzSNdvvh1+/JLdAsX\n4r5mjV3Gd/WfPVcjM8BCCCHKDe3evWTese1tUVJT4c03PVm3Lh2Vyk6B2YkrrOJgK+qrV/F8802y\nn3vO0aGICkAKYFEgWQ/ReUnunJtL50+vB7MZczHvH1mwwJMePYy0bm22U2DWKU7upMWh+Izh4XiZ\nzTZf//cWl/7Zc0GFtkCcO3eO0NBQmjdvTps2bfjuu+8A2LBhAw0bNqRRo0Z89dVXZRKoEEKICs7D\ng7S4OHB3t/qUEyfUrFvnzowZZb/sWXFJi0PpWOrWxTBoEKYSrA4ixJ0KXQXi0qVLXLx4keDgYJKT\nk+nUqRN//fUXjRo14uDBg+j1erp168aJEyfynSurQDi3+Ph4+W3YSUnunJvkr3iGDfOmc2cTkyY5\nfsvjgnInqzg4D/nZc242XQUiICCAgIAAAAIDAzEYDBw4cIBmzZpxzz33AFC7dm2SkpJo2bJlKcIW\nQgghiufbb7WcPKlh7doMR4eSj7Q4CFG+Wd0DHBsbS5s2bbh06RL33XcfS5cupUqVKtx7771cuHBB\nCuAKRn4Ldl6SO+cm+bOOwQCvvurFm29mFqdjwq6atmnK8qTlslGFk5KfPddiVQGckpLClClT2LZt\nGz///DMA48aNA2Dz5s2onO22WyGEEE5t+XIdQUEWevY0OTQOWcVBCOdUZAGs1+sZPHgw77zzDnXr\n1uX8+fNcuHAh9/WUlBTuu+++As999tlnCQwMBMDf35/g4ODc37Burbcnj8vn4yVLlki+nPTx7WtZ\nlod45LHkz5rHAYmJNHriCZR77iny+JiYn3j77a7s3JnpsHhPZ53mD48/2PjHRqqoqtC9aneWNllK\nrwd7ER8fz4HkA+Xq+yuPi35867nyEo88Ljpf8fHxJCcnA/D0009THIXeBKcoCo8//jhhYWFMmDAB\nAIPBQOPGjXNvggsPD+f48eP5zpWb4JxbfLzcDOCsJHfOzSXzpyj4N29O2rZtWOrXL/Lw55/3ws9P\nYc6csl354VrWNTb9uSlPi8PQJkNzWxxcMncViOTPuRX3JrhCC+D4+HjCw8Np1qxZzsEqFdu3bycu\nLo4ZM2YA8N5779GvX79850oBLIQQwhrqP//Ed9Agbh45QlE7WRw+rGHYMB9++ukmfmVwP5ms4iCE\nc7DpKhChoaEYDPm3lRwyZAhDhgwpfnRCCCHEHdzi4jCGhRVZ/CoKvPyyF6+8kmX34ldWcRCiYit0\nIwzhum7vsRHORXLn3Fwxf9offsAUFlbkcZs2uaHXwxNP5J+YsYXSblThirmrSCR/rqXQGWAhhBDC\nrsxmtPv2kTl/fqGHZWTArFlefPxxOhobdh7IKg5CuKZCe4BLQ3qAhRBCFCkzE93//R/ZY8cWetib\nb3pw+rSG5ctts+lFQS0OEQ0ipMVBCCdl0x5gIYQQwq68vIosfs+cUbNypY69e1NLdamCVnGQjSqE\ncE3SAywKJL1Qzkty59wkf/nNnOnJhAnZ1KxZ/A8sjWYjsX/FErk9kpA1ISSkJBDVKYqkUUnM6DTD\npsWv5M65Sf5ci8wACyGEKLfi4rQkJWn46KPitT7IKg5CiMJID7AQQohyyWSCBx/0Y/r0LAYMMBZ5\nfFEbVQghKi7pARZCCFEhrFmjo1o1C/373734lVUchBAlIT3AokDSC+W8JHfOzZXy5zVxIurjxwt8\n7fp1FfPnezB3blaB+2McvXKUqLgoglcF817ie4TXCefI6CMs67WMboHdHFL8ulLuKiLJn2uRGWAh\nhJVhv00AACAASURBVBBlLz0d923byHz77QJfnjvXg0ceMdCsmTn3OVnFQQhhK1IAiwKFhoY6OgRR\nQpI75+Yq+dMeOICpVSvw8sr32ubNbuzc6caePWlO1eLgKrmrqCR/rkUKYCGEEGXO7S7bHx8+rGH6\ndC8WrDjCe799LKs4CCHsQnqARYGkF8p5Se6cm6vkTxsXh/GOAviPMzeJGAa+A6fx6ol+6DQ6YgbF\nsGPwDiKbR5b74tdVcldRSf5ci8wACyGEKFOqGzfQnD6NOSQkt8Xhk6QNxM6aTsPQBOZM7ERYrZfK\nXYuDEKLikHWAhRBClLk/T/zIJxe2s/GPjdTxC0K1bSWVlbp8+kk2avlsUghRTMVdB1j+mhFCCFEm\nrmVdY3nScsLXhzNw79O5LQ4R1/aQfroRy5dK8SuEKBvyV40okPRCOS/JnXOraPkzmo3E/hVL5PZI\nQtaEkJCSQFSnKJJGJTGj0wzO/tKEhQs9WLcuAx8fR0dbOhUtd65G8udapAdYCCGEzR29cpTPjn1W\n6CoOJ0+qmTDBm5UrMwgMtDgwWiGEq5EeYCGEEDZR0EYVQ5sMLXCjitRUeOghPyZM0DNqlMEB0Qoh\nKpLi9gDLDLAQQogSK+5GFerTpzHeV4tnnqlEWJhRil8hhENID7AokPRCOS/JnXNzlvwdvXKUqLgo\nglcF817ie4TXCefI6CMs67WMboHdCl7CTFHw7duXOdPNZGXB3LlZZR+4HTlL7kTBJH+uRWaAhRBC\nWKWgFoeYQTEFtjgURP3nn3xqeIwvf7iH775Lw83NzgELIcRdSA+wEEKIuyqoxWF4k+F3bXEozK8z\nYxi4/FG+3KXQtKnc9CaEsB3pARZCCFFq1qziUBwXLqgY/nFfPhhzgKZNH7BxtEIIUTzSAywKJL1Q\nzkty59wcmb/bN6oYsm1I7kYVOwbvILJ5ZImLX70ennzSm3F8RK/nats46vJDfvacm+TPtcgMsBBC\nuLDiruJQXIoCL7zgRWCAnqmNfyfrvvtsELUQQpSO9AALIURFYTajunwZ9cWLqFNSUF24gDolhZ8q\nP8TVhu3p2tWESpVzaEEtDhENIko8y3s30dE6Nm1yZ/v2NLy9bTq0EELkkh5gIYQoI+pTp9AeOIDi\n4/O/L19flGrVUAICbHchiwXVlSs5RW1KCkpAAOZWrfIdplu8GI/Fi7Hcey9K9eoc925B1LGRHLja\niMrVtRjNFlo9+h1/1HyNK4bzxV7Fobi+/VbLkiUe7NyZKsWvEKJckQJYFCg+Pp7Q0FBHhyFKQHJX\ndlRXr6Ldvx9VWhqq9PTcL2O3bmS9+Wa+491iY/F49928BbOPD6b27TEOHAjkzZ/bli14zZiB6soV\nFH//3MLWEBFRYAGcPWkS2c8/z5UrKhYs8OCLL9wZNz6TAX1j+OLUJ+zeo+Hm9tcxXdrLc+MtjGlu\nwM+2E765/vxTzcSJ3qxdm06tWnb5oLHckZ895yb5cy1SAAshRAmZ27Ujs107q483tW1L5uuv5ymW\nVenpKL6+BR/ftSupsbE5s8nu7kWOn5ml4qOPPPjwQx3h/VJ4dOEiVqSsIui3nBaHD+bmtDgcOWLk\ngw90tG7tyRNPGBg3Tk/NmrYrUm/cUDFihA8zZ2bRoYPZZuMKIYStSA+wEEI4ObMZPvvMnTfn6gho\ndAJTt2nc9PmZYY2HMbTJ0Lu2OJw9q2bJEh3r17vTu7eR557Tl3p9XpMJhg3zoUEDM//5T8Xa6U0I\nUX4VtwdYlkETQggrecyejfrMGUeHkUtR4JsdKlp3UDFr8WnSInrSaHwUcx4dRdKoJGZ0mpGv+NXG\nxaE+ehSA2rUtzJ2bxaFDqTRoYOGxx3wZPNiHvXu1lHRqZNYsT8xmmD37f8Wv7v33+f/27jwuqnr9\nA/hn9hlWLfcFLRWlREMTFchUUspcIvcNNSlLs2teTX+JlllmXbesTHHX0jKXyixwywVF3BLtumfu\nSyrKOvuc3x9cSHSAmWGGmcN83q/XfV0Pc+bMg48nH74+5/lKbt1y+PskInI2FsBkFechihdz5xrS\nM2eg+vprWJz5cJsVtuZvw2+X0Kz934gbcxOamA+RkLgVJ6YsQ2JMIjoEdSh2hJn07Fn4TJqE+yvc\nSpUEvP22Dr//nonu3Q0YP94HHTv6Y/16BUwm22NfvVqJpCQFli7NhbygwS47G5qZMyF4wVNwvPfE\njfnzLqUWwOPGjUONGjUQGhpa+DWZTIawsDCEhYVhzJgxLg2QiMgTqBcuhH7oUECjcVsMGdoMzPh1\nLR7vnIbXhlVDyLPp2L0nE2kfTsLQUNs2qjAMHgzptWuQb9/+0GsqFTB4sAGpqVmYMEGHpUtVePrp\nACxcqEJOTsnXPXBAhvff1+Cbb3JQufI/xbU8NRWmsDDAx8fu75eIyFVK7QFOTU2FUqnE0KFDcfz4\ncQCAv78/srOzS7wwe4CJqKKQ3LmDgKefRlZamnPHm9mgYKOK5Wmb8Ns3EUB6HF6Ou4wZE6ohwN+x\njSoUmzdDM306snbvBmQlX+PQIRk+/1yNffvkGDpUj1df1aNataJ/bVy9KkHnzgGYPTsPMTHGIq9p\nJk2CULkydOPGORQrEZEtnN4D3LZtWzz66KNlCoqISMxUy5fD2LVruRa/J26fwOQ9k9E0sRXGf3gb\nKf+3CH0bxeHYITPmf1jT4eIXAIxdusASGAjlmjWlnvv002asWJGL5ORs3L0rQZs2ARgzxgdnz+b/\n9aHVAoMH++G113QPFb9Afs+xsV07h2MlInIFh3qAdTodWrZsiaioKOzZs8fZMZEHYC+UeDF3TiYI\nUPzyC3RvvOHyj8rQZmDihono+G1H9P6hH87tjIT0izN4yvgadmwx4rPZpodWXx0ikUD7wQdQrVwJ\nW592e/xxC2bO1OLAgSzUqGHBiy/6Y9AgX8TH+6JhQzPeekv/8Mfcvg3ZxYswe8m/BvLeEzfmz7s4\nNAf46tWrqFatGg4dOoTY2FicO3cOKpXqofNGjhyJoKAgAEBgYCBCQ0MLh0wX/EHjsWceF7S7eEo8\nPOax244lEiRNmQIhIwMFI/KdeX2j2YjPf/0c2zO244+8PxDm0wKh18bh3tquuFvNF8uX5sFo3IWb\nN4FGjZz8/W3eDEgkdr2/ShUBUVHb0KqVDBcutMfBgzL07r0Ne/daHj4/LAw533yDlP373Ze/cjwu\n4Cnx8Jj5q8jHBb++dOkSACA+Ph72sGkO8IULF9CtW7fCouh+rVu3xsqVK9G4ceMiX2cPMBFR8U7c\nPoHVJ1dj3el1qB+Yv1FFY0MffDKtKq5eleK997To0sUIicTdkRIReT57e4Dl9n5ARkYGNBoNNBoN\nLly4gKtXrxau8hIRUfEytBlYf2Y91pxcg7/z/ka/Jv2wqecmNKzUCCtWKBE3XYOJE7UYPNgAhcLd\n0RIRVVylFsCjRo3Cxo0bcefOHdStWxevvfYavvnmG6hUKshkMixZsgQaN44FItdISeGe6GLF3HkW\no9mI7Re3Y/XJ1dh1eRdiHovB5IjJaFenHWRSGXQ64K23fHD4sBy//pqN69d3Q6Fg/sSI9564MX/e\npdQC+Msvv8SXX35Z5GuTJ092WUBERBWBtRaHL577osis3itXJBgyxA/16lmwZUsW/PyA69fdFLDZ\nXOpINCKiisKmHmBHsAeYiMRMPWcOjO3awdyypc3vsdbi0Dek70PbEQPAnj1yvPaaL0aO1OHNN/Vu\n7/X1i42F7p13YGrb1jkXFAS4/ZsiIq/h8h5gIqKKTpKRAdW8edAPGFDquaW1ODxIEIAvv1Thyy/V\nWLgwF+3amVzxLdjN0L8/NFOmIHvLlrIXroKAgFatkL15M4Tq1Z0TIBGREzk0B5gqvgfHwpB4MHdl\np1q+HMYXXyyxeDtx+wQS9iQgdFko5h6ei+h60Tg+7DgSYxLRIaiD1eI3NxeIj/fFhg1KbN2aZbX4\ndVf+DL16ASYTFD/8UOZrSU+fBozGct81z91474kb8+dduAJMRHQ/vR6qxYuRvW7dQy8VN8XBWovD\ng86fl2LwYD+EhZnwyy/ZUKtdEXwZSKXQTp0KnzFjYOzSBbAy291Wit27YWrXji0QROSxWACTVXwS\nVryYu7JRbtwIc5MmsDzxBAD7Wxys2bJFjtGjfTFxohZDhxpKrAvdmT9Tu3awNGoE1bJl0L/+usPX\nke/eDcNLLzkxMnHgvSduzJ93YQFMRHQfxbZt0L3xhk1THEpjsQAzZ6qxYoUKq1blIDzc7MLInSNv\n6lRI/7ezkkPMZsj37kXerFnOC4qIyMnYA0xWsRdKvJg7x2VoMzD3zXC0uz0dfX7qA7VMjU09NyGp\ndxKGNB1iV/GbmSnBwIG+2LlTjh07smwuft2dP0uTJjB17uzw+6UXLsDSqJFXPvzm7txR2TB/3oUr\nwETk1ay2OEROsavF4UEnT0oRF+eHjh2NmDZNC6XSyUF7MEuDBshOTnZ3GEREJeIcYCLyStZaHGIb\nxdq1ymvNDz8oMH68D6ZN06JfP4OToiUiopJwDjARUTHKMsWhNCYTMG2aBj/+qMD69Tlo1szz+32J\niLwVe4DJKvZCiRdzV5TRbETS+STEbY5D2IowHLxxEJMjJiN9aDoSIhKcUvzeuSNB795+OH5chh07\nsstU/HpU/vR6KNesyd+9g0rlUbkjuzF/3oUrwERUIdkzxUG1ZAksNWvmz7+109GjMgwZ4ouePQ2Y\nNEkHmWNtw55JKoV67lxYqlSBqVMnd0dDROQ07AEmogrDWotD35C+Ja/yGgwIDAtDztq1MD/5pF2f\nt3q1Eu+/r8HMmXno3t1Yxug9k+KXX6D58ENk7dmD0qp7+datMEVFARpNOUVHRJSPPcBE5FXKulGF\ncuNGmIOD7Sp+DQZg0iQNdu1S4KefstGkiaUs34JHM77wAlRffgnl6tUwDB5c/IlZWfB75RXcO3Om\n/IIjInIQe4DJKvZCiZe35O7E7RNI2JOA0GWhmHt4LqLrReP4sONIjElEh6AOto0wEwSo5s+HbuRI\nmz83M1OC7t39cf26FNu2ZTm9+PW4/Ekk0H7wATQzZgC5ucWepkhNhalFC69e/fW43JFdmD/vwhVg\nIhINZ09xkKekQKLTwWTjP5sZjcDQob4IDTXhk0+0kHrJEoK5ZUuY2rSBcvNmGPr0sXqOfNcumNq1\nK+fIiIgcwx5gIvJo1loc+of0L9NGFQXU06fDUqsWDEOHlnquIABvv+2D69el+OabHMi9bflApwPU\n6mJf9o+KQt6cOTC3alWOQRER5WMPMDlOEAC9vsS/5IjKiz1THByle/ddm0d8ffGFCkeOyLB5c7b3\nFb9Aif9dkNy6BdnlyzCHhZVjQEREjvOSf8AjW8jS0uDfvTsA4MjatZBeuuTmiMgRYu5jy9BmYFH6\nInT8tiP6/NQHapkam3puQlLvJAxpOsSpxW8hiaTUU37+WYEFC9RYvToH/v7OD+F+osyfwQDtlCnw\nzp8M/iHK3FEh5s+7ePd/ragI9eLFMLz8MgCgdkoK1Pv3I2/2bDdHRRVdWac4uNrvv8vw9ts++P77\nHNSpww0hrBFq14Z++HB3h0FEZDP2ABMAQHLjBgIiIpB59CgQEADJtWsIiIpC5rFjgJ+fu8OjCsha\ni0Nso1jXrPI66MoVCWJiAvDpp3l48cWKOefXYRYLvOYpQCLyeOwBJoeoVqzIX/0NyC8+hFq18p/6\n/vFHGAYOdHN0VFE4e4qDK2VlAf36+eGNN3Qsfh8gO34cmnffRc5PP9nUQkJE5Gn44zsBBgNUK1YU\n+SfMlJQUGAYPhmrVKjcGRo7wtD42o9mIpPNJiNsch7AVYTh44yAmR0xG+tB0JEQklHvxq9iwAarF\ni0s8x2QC4uP9EB5uxqhR+nKKLJ+n5c8a85NPQpKTA8UPP7g7FI8ihtxR8Zg/78ICmCDJyIC+f39Y\nQkKKfN3YqROkly9DevKkmyIjMXPKRhXOJghQf/YZzPXqlXQK3n1XA5MJ+OSTPC5wWiOV5m+OMW1a\n/uQYIiKRYQ8wlUj+228wh4RAqFHD3aGQCFhrcegb0tdjWhzkKSnw+fe/kZWaWmz/6sKFKqxYoUJS\nUlZBRxAVw69vXyi2bsXdS5f4rAARuRV7gMmpTB06uDsE8nCePsXhfqr586F7441ii9/kZAU++0yN\npKRsFr820CYkQHrqFItfIhIdtkCQVeyFEq/yyp1HtjiUQHruHOSHDsHQt6/V148dk+HNN32wcmUO\ngoIs5RzdP8R075lDQ5GVnu7uMDyGmHJHD2P+vAtXgInIZmKa4vAg+YED+Q96ajQPvXbtmgQDBvjh\nP//Jw9NPm90QHRERlSf2AHszk8nrd26i0llrcegf0t8jWxwckZMDdO3qjx49jHj7bZ27wyEiIgew\nB5hsYzYjIDISOevWwVK3bunnCwIkN25AqFnT9bGRR7C2UcUXz33hURtVlJXZDIwY4YumTc0YM4bF\nLxGRt2APsJdSbNkCISCg2OL3wV4o6fnzCIiOzl81Jo9Wlj62DG0GFqUvQsdvO6LPT32glqmxqecm\nJPVOwpCmQypU8QsAU6ZokJMjwezZnjPujH2I4sXciRvz5124AuylVImJ0L/6qs3nWxo0gCUoCIot\nW2Ds0sWFkVF5E9MUB2daulSJbdsUSE7OhlLp7miIiKg8lboCPG7cONSoUQOhoaGFX1u7di2Cg4PR\nuHFj/Pzzzy4NkJxPevo0ZCdPwtCjR7HnREVFPfQ1fVwclNwZzuNZy501Ypvi4Ezbtsnx6acafPtt\nDipVcsljEA6zNX/keZg7cWP+vEupBXDPnj2xefPmwmODwYCJEydi79692LZtG8aMGePSAMn5VEuX\nQj94MKBS2fU+Q48ekKelQXL1qosiI1fzthYH+d690CQkFPnaiRNSjBzpi+XLc/DYY+4bd0ZERO5T\nagHctm1bPProo4XHaWlpePLJJ1G1alXUrVsXdevWRTrnQIqLRAL90KElnmK1F8rXF8bYWKjWrHFN\nXOQUD+bOaDYi6XwS4jbHIWxFGA7eOIjJEZORPjQdCREJohhh5ijVl1/C3LBh4fHNmxL07++H6dPz\n0KaNZ447Yx+ieDF34sb8eRe7e4Bv3LiBmjVrYuHChXjkkUdQo0YNXL9+Hc2bN3dFfOQC2hkzHH6v\nbvhwyPkDjyh4wxSHkkhPnID80CHkLl4MAMjLAwYO9MOAAQb06mV0c3RERORODj8EN2LECADAhg0b\nIPGUx6fJaYrrhbI88QQMTzxRztGQrTK0GTjpfxJTvp0iuo0qnEX2++9Qz5sH+c6d0L73HuDjA4sF\neOMNXzRsaMY773j2uDP2IYoXcyduzJ93sbsArlWrFq5fv154XLAibM3IkSMRFBQEAAgMDERoaGjh\nH7CCf2rgMY+9+jgyEpBIynQ9o9mIz3/9HNsztuOPvD8Q81gMYgNi0ax2Mzwb8axnfb/lcCy9ehWn\nq1fHlQUL0CYmBgAwYsRt/PmnBdu3SyGReFa8POYxj3nMY/uPC3596dIlAEB8fDzsYdNOcBcuXEC3\nbt1w/PhxGAwGNGnSBGlpadDpdOjYsSPOnj370Hu4E5y4paSkFP5hI+eQ3LsHoVKlwmPpxYvwffVV\nZP/4o9XteUtjrcUhtlEsjh08xtzdZ+VKJebNUyM5ORuPPupZEx+s4b0nXsyduDF/4mbvTnClPgQ3\natQoRERE4PTp06hbty6Sk5MxY8YMREZGIjo6GnPnzi1TwFROXLPjNdlIlp6OgLZtIT1/vvBrlqAg\nWOrWhWbqVJuv421THKwymaDYtAm+cXGAruR2hl275PjoIw3WrMkRRfFLRETlw6YVYEdwBdizaKZO\nhblePRhKmf5gF7MZkErhMVtoeShZWhr84uKQN2sWjF27FnlNcu8e/Nu1Q97s2TA995zV91vbqKJ/\nSP8Kv1HFgyQ3b0K1ciVUK1bAUrcudPHxMHbvDigUD51rNAI7digwerQPli7NRVSUyQ0RExFRebF3\nBVjuwljIU+TlQfn118jessWpl/Xr1QvaCRNgbtPGqdetSOS7dsH31VeR+9VXMFm5MYVKlZA3fz58\nR4xA1q5dEKpUKXzN26c43E81bx7Uc+bA2KMHcr79FuamTR86x2DIX/H98Uclfv1VgQYNLJg7N4/F\nLxERPaTUFggSP+WGDTC1bAnLY4/Z/J77m8yLY4yOhmrlyrKEVqHJt27NL36XL7da/BYwRUXB0Ls3\nfMaNc0qLgy25Extj167IOnoUeXPnFil+DQZg61Y5Ro3yQUhIIGbO1OCJJ8zYtSsLW7Zko0sX8Y07\nq4j58xbMnbgxf96FK8AVnSBAtWgRtJMnO/3Shn79EPD005BkZkIIDHT69cXOEhSEnDVrYG7ZssTz\njGYjtvR/Grt2pePrFWGIeSwGkyMme12LAwBI7tyBcN/GOwUsjz9e+OuCld4fflAiKUmBhg0t6NHD\ngP/7Py3q1GGfLxERlY49wBWcbP9++L75JrIOHMjv13Uy32HDYIqKgn74cKdfu6IrboqD17U4mM1Q\nbNkC1eLFkP75J7IOHnyor9dgAHbu/Ke9ITg4v+jt1s3AopeIiNgDTEVJr16F7q23XFL8AoA+Lg6a\nqVNZANsoQ5uB9WfWY83JNV67UUUhQYAiORmayZMhVKoEfXw8DD16FBa/BUVvwUpvcLAFL71kwLvv\nalG7NoteIiJyHAvgCs7Ys6dD77N1HqLp2Wfze4uzsoAAL1u5tJG1KQ6ubHEQyyxL9Zw5UH73HfI+\n/rhwAoZeD+xMVuDHHxVISlKgceP8ld5Jk7yn6BVL/uhhzJ24MX/ehQUwFSEIwNKlKmRmVseTT0pQ\nuXIpRYdUitxly8onOE8lCFBPmwbLY4/BMHhw4ZfLOsVBkpEB4ZFHXBW12+mHDYNu9GjoLQrsTFbg\nhx/yi96QEDN69DAiIUGLWrW8o+glIqLyxR5gKiI1VY74eF8EB5tx+LAcdepY0KaNCW3amNC2rQl1\n6lg49vd+Fgs0EydCfvAgctatwx0fyUMtDn1D+trd4iA7dgy+gwcje/fuCveAoU4HHDkix969cuzb\nJ8fhw3I0bWpCjx5GdOtmYNFLRER2s7cHmAUwFREX54tnnzVh+HA9TCbgjz9kSE2VY//+/P8pFEDb\ntqbCojgkxOyq9mLPZzLB51//guTPP/HTp69hxeUfnLpRhc+//w3k5CBv4UInBl3+9DsP4MD1+tjz\nVxBSU+U4elSO4GAzIiJMiIjI/8GqUiUWvURE5DgWwOSwixeliI72x9GjmTh69OFeKEEAzp+XYv9+\nOVJT5UhLk+P2bQnCw81o29aINm1MeOopM9RqN30D5clggHlYf9y6dhZdeutRrepjdk1x2LZNjqws\nCRo3tqBBg2J+z/LyENChA7TvvGNXL7e7+9iys4EDB+TYl6xD6sY7OJYRhKbBOrR93gcREUa0bm1i\nu3gJ3J0/chxzJ27Mn7hxCgRBduwY1DNnItfOTSoWLVJh4EAD/Pysvy6RAA0aWNCggQEDBxoAADdv\nSpCWlr86/O67PjhzRoZmzf5ZIW7d2ozAwIqzulcwxWH7vhUYnHEBx9+Lx3fNB9rc4pCZKcGECRoc\nPixHSIgZp0/LcOmSFLVrWxAcbEZwsAWNG5sRHGxGo0Y+kCUmwq93b2SHh8NSt66LvzvHZGZKsH//\nPy0Np05KEVblEtrfWoeErv5o/uGL8K3mC0Dr7lCJiIgAcAW4QvIZPRqWxx+H7u23bX5Pdjbw1FOB\n2LUry+G5qoqkJOQdOImUZ8Zj//78FeIjR+QICjIXtk288IIRPj4OXd5trE1xcKTFISVFjpEjfdC5\nsxFTp2rh6/u/6xvzV9bPnJHh9GkZzpzJ//W5czIEBgoI0fyFEPlZPD7iGTRunF8oV6nivh8qMjIk\n2Lcvv+BNTZXj/HkZWrTIb2eIbKNHhwntoWhUF9oPPoClfn23xUlERN6DLRBeTpKRgYCWLZF18CCE\nKlVsfl9iogqpqXIsW5br8GdL//oL/p07I/OPPwCVCkB+cXfsmAz798uxZYsCZjOwdm2OKIpgZ21U\nodcDH32kwbp1Snz2WS46dTLZ9D6LBbh8WYozJ4HTJwSc/kuDM2fyC2SZDAgONhcWxPm/NqN2bcHq\nQ4omU/7DZ3q95KH/1+sBrVZi9bX7z8nIkCItTY7Ll6UIDzchMtKEiAgjwsLMUCr/+SzJlSsQ6tSx\n6/eIiIioLFgAeznVvHmQnTqFvPnzbX6PxQK0ahWA+fNz0bq1GYDjvVB+sbHQDx4M48svW/2cUaN8\ncOOGFGvW5Hhkr7C1jSocmeJQ4MQJKUaM8EX9+hbMmZPnlJVbQQD+/lvyv9Xif1aMT5+WITdXAj+/\nPEilGuj1gE6XX8RaLIBGA6hUAtRqQK0WoFI9+P/WX1OpBGg0gJ+fgJYtTWje3Aw5m6dchn2I4sXc\niRvzJ27sAfZmZjNUS5Ygd/lyu96WnKxA5coCwsPNZQ5BP2gQVKtWWS2ApVLg88/zMGKEL4YM8cOq\nVTlFVg7dpbSNKiTXrkG5fjH08fE2X9NiAb76SoW5c9V4/30tBgwwOG18nEQCVK8uoHp1E9q1K7qa\nfO+eBMnJRxAZ2QJq9T8Fr1wO546vM5uh+PVXGF980ckXJiIicj2uAFcg0gsXoPngA+QuXWrX+3r0\n8ENcnB49exrLHoRej8CmTZG9dWux/Z9GIzB8eH4D7JIluQU735Y7W1ocpBcv5q9qDx0K/Vtv2XTd\nK1ckGDXKFwaDBF99lYv69S2u+hbcQr5vHzQTJ0IICEDO6tXcAZCIiNzO3hVgb53gWiFZ6te3u/j9\n44/8h626d3dC8QsAKhUM/ftDvn9/sacoFMDixbkwGIDXX/eFuewLzzbL0GZgUfoidPy2I/r81Adq\nmRqbem5CUu8kDGk6pGh/b24u/Lp1g37UKJuL33XrFOjYMQDPPmvCzz9nu6b4zcuD7Phx51+3PkOw\ncwAAIABJREFUFJIrV+D7yivwef116N5+GzmbNrH4JSIiUWIB7OUWLFAhPl7/0CpsSkqKw9fUTp0K\nQ79+JZ6jVALLl+ciI0OC0aN9YHHhIqnRbETS+STEbY5D2IowHLxxEJMjJiN9aDoSIhKK7e9Vfv89\nzM2aQT98eKmfce+eBPHxvvjPfzRYuzYHY8fqIHN8D4wSyf74A359+kDy999WXy9L7ooj37cPAe3a\nwRwcjKz9+2GMjWXrg4u4In9UPpg7cWP+vAt7gL3YrVsSbN6swOHDWc69sI2FkVoNfPNNDvr08cPb\nb/tgzpw8p+4qZ63F4YvnvrBtioMgQLV4MbQffljqqbt2yfHmm7548UUDfvst1+UTLszh4dAPHAjf\n0aOR8+235VKImsLCkJWWBqFqVZd/FhERkauxB9iLffqpGtevSzFnTp5b48jOBnr18sdTT5kwY4a2\nTPXcHe2d/CkOJ9bglvaW41MctFqov/gCunHjii0wdTpg2jQNfvhBiXnzchEdbdt4M6cwGuH//PMw\nDBhg0wq1rSS3b0Pw9y8cY0dERCQG7AEmm+j1wLJlKowYoXN3KPD3B77/PhuHDskxZYoG9v5Idn+L\nQ4sVLXDoxiFMiZxSaotDiTQa6MaPL7b4/eMPGTp2DMDVq1Ls2ZNVvsUvACgUyF24EOoZMyA9fbrM\nl5MdPQqfUaMQ0KoVZOnpTgiQiIjIc7EAFjtBgF/v3pDcuGHX2zZuVOKJJ8xo0sR6821590IFBADr\n1uVg1y45pk+3bUDwidsnkLAnAaHLQjH38FxE14vG8WHHkRiTiA5BHezapc1WZjMwb54KsbF+eOst\nHZYty8Ujj7hnVzZLw4bQTpoE5Y8/Fvm6zbkzGKBYvx7+MTHwHTIE5saNkXX4MMzh4S6IlmzFPkTx\nYu7EjfnzLuwBLiAIonyoR75zJyTXr0OoXt3m9whC/ozahAStCyMDoNVC8/770H78MWxp7q1cWcCG\nDTno1s0fKhUwbtzDq9PWWhw29dzk8EYV9rh8WYo33vCBIADbt2cjKMj9480MQ4Y4/OdWsWMHVCtX\nQjd6NIzPPw/ubkFERN6CPcAAzJevY1bUdow+1geaQA/YmcEOvgMHwtipEwxDh9r8nr175Rg71gep\nqVlOfejsIYIA//btoX3/fZg6dLD5bTdvStCtmz8GD9Zj9Gi91Y0q+of0L9yowtUEAfjuOyUmT9Zg\n9GgdRo3Su2zCAxEREdmPO8E5YFG/NMzIHo3m+3MQE+OkebjlQHrpEuRpachNTLTrfQsWqPD66zrX\nFr8AIJHAEBcH1apVdhXA1asL2LgxGzFdVNh6ZSvONBpt/xQHR2Vn5zcl/09GhgRjx/rgzBkZNmzI\nQWhoOQ4tdga9HsqNG2F8/nkIlSq5OxoiIiKP4PU9wFeW78as0z3wypBcJCe7aUsyB6mWLs2ft+vr\na/N7LlyQYv9+Ofr0MZR4nrN6oQy9ekG+Ywckt2/bdP4d7R0kpidi0O72MA1uj2M/PodXDPutb1Th\nAv4vvwx5SgoyMiSYO1eFqKgA1KplwY4dWaIpflNSUiC5dg3qjz5CYLNmUH7/PSQZGe4Oi2zEPkTx\nYu7EjfnzLl5dAAuZWfj3/wXiX4Nv4LU3TNiyRWH3BAJ3kp04Af0rr9j1nsREFQYNMthTM5eJEBgI\nY5cuUH73XbHnFDfF4b9jN2PHLzKsnF8Pa9a4vjVFduQI/rj6CEat7YSWLQNw9qwM336bg+nTtVDb\n9lye20lPnULExIkIiIyEJDMT2Zs2IWf9elgef9zdoREREXkMr+4B/qHnRsw9Go2tpwIglwMtWwZg\n5cpcNG0qjpU+e2VlAWFhgdi1Kwt16pRfpS9PTYVm0iRk79hR5OvWNqqIbRT70CrvmTNSvPSSP6ZN\ny0PPns5vUTGbgaQkBRb/+yLOaOti2GgFhgzRo2pVEf009D/SM2cgT0mBoVcvblNMRERegz3ANrpz\nR4KJh/thzYq7hdsAd+5sRHKyosIWwKtXq9C+valci18AMLVpg+wffgDg2BSH4GAL1q3Lxssv+0Ol\nykPXrs4pgu/dk+Drr5VYvFiF6o8Y8K/s2eh0+F0oajzilOu7gyU4GIbgYHeHQURE5NG8tgVi8mQN\nXh4gRdiz/+xb+8LjJ7D1e/fuiuYqZnN++8Prr9u28YUze6GMFhOSbu8r00YVTzxhwXff5eDf//bB\nli1l+7nt9Gkpxo3TICwsAMePy7BkSS52dZ2OXi/rRV38FmAfm7gxf+LF3Ikb8+ddvHIFeOdOOfbu\nlWPv3qwiX38m4CiGnG+M27eNqFJFfP/8XZLkZAUefVRAq1blt7ptrcWhLFMcmjc3Y/XqHPTv74eF\nC3PRoYPtu69ZLMC2bXIsXKjGf/8rw5AheqSmZqFGjfw8W44/AmNMjENxERERkbh4XQ9wXh4QFRWA\nTz7JQ6dORQsoyZUrGPb0JXSe8yz69RfPODRbdOvmh6FD9S7pob2ftRaHviF9nbpRxf79MsTF+WHZ\nslxERpZcBGdlAWvWqLBokQr+/gJGjNAjNtYAlcpp4RAREZGbsQe4FP/5jwZhYeaHil8AEOrUQRfN\ncvz6QwT69XdDcDaS79gBS+3asDRubNP5x47J8NdfMnTv7pri19pGFVMip7hso4o2bcxYsiQXw4b5\nYtWqHLRu/fCq9vnzUiQmqrB2rRLt25vwxRe5aN3aLMbN/oiIiMjJHO4BlslkCAsLQ1hYGMaMGePM\nmFzm1Gc78c1SAR9/XHyfb+e2d/Fbig+MHrwArJ4zB9IrV2w+f+FCFV59VVf4sJ8tbOmFOnH7BBL2\nJCB0WSjmHp6L6HrROD7sOBJjEtEhqIPV4ld67hzU06fbHkgxnnnGhK++ysXgwX44ciT/cwQB2LFD\njn79fPH88/7w9RWwe3cWli7NRZs23lP8so9N3Jg/8WLuxI358y4OrwD7+Pjg999/d2YsLmX5+w7+\n9VF9vPevv1CtWs1iz6varhEaHLyGtLQqiIqyvce03Oj1kB89ClOrVjadfvOmBL/8osCHH2qd8vGO\nTHG4n6VGDai++QbGjh1hbtOmTLFER5swb14e+vf3w+uv6/Hdd0rI5fltDsuW5UKjKdPliYiIqIJy\nuAfY398f2dnZxb7uaT3AS5/bhJ9utMbG49VKXAmUXrqEGdOVyK76GKZNc07R6EyytDT4TJiA7J07\nbTp/xgw1bt2SYtYsx6dbWGtx6B/S3+EWB8X69VB//jmyt28HZGVvkfjlFwV+/FGBwYMNiIw02b7S\nazAAcjlcvyc0ERERuZK9PcAO/82v0+nQsmVLREVFYc+ePY5eplxc+/4APj7aFTNXB5RaHFmCgtBp\nRG1s2eKZ2yLL09JgsnHlVKcDli9X4bXXbBt99iBHWhxsYXz5ZQi+vlCuWuXQ+x/UpYsRCxfmISrK\njuIX+VtJa9591ykxEBERkXg4XABfvXoVhw8fxty5czFgwADo9XpnxuU0Qp4W77ytwMieV9CwmW37\n2TZvbkZmpgTnz3veyqA8NdXmAnjDBiVCQ81o3Nhi8/XvaO8gMT0RrRa1Qp+f+kAtU2NTz01I6p2E\nIU2HODzCrAiJBNoZM6D5+GNI7t4t+/UcYbFAtXgxDC+95J7PdyH2sYkb8ydezJ24MX/exeEe4GrV\nqgEAnn76adSqVQsXLlxA4wemEowcORJBQUEAgMDAQISGhiIqKgrAP3/QXH1860wYLvg8ieH9DiIl\n5aJN75dKgWbNrmDBgix8+mntco23tOMOPXvCFBVV6vl79qRg1qx2+PRTS6nXN5qN+PzXz7E9Yzv+\nyPsDMY/FoJ2hHbo3645nI551yfezKzMTwdHRqPnnnzA//XS5/36e/vxzhACwtG5dLp/HYx7zuOIf\nF/CUeHjM/FXk44JfX7p0CQAQHx8PezjUA3z37l2o1WpoNBpcuHABUVFROHv2LDT3PXXkCT3A9+5J\nEBERgOXLcxAebt8GED//rMDSpSps2JDjouhca88eOcaP90FqalaxbQHWNqqIbRTrnFVeD+fXty8M\n3brBMGiQu0MhIiKiMiqXOcCnTp3CsGHDoFKpIJPJsGTJkiLFr6eYMkWDrl0Ndhe/APDss0aMHOmL\n7GzA398FwbnYggX52x4/WPyWdYpDRSA9fx6yI0dgWL7c3aEQERGRGzjU5Nq2bVucOnUK6enpOHLk\nCGI8cAvZlBQ5duxQICHBsUkO1d8djVYh97Bzp2c+DFeS8+elOHBAjj59DADypzgknU9C3OY4tFjR\nAoduHMKUyClIH5qOhIgEq8Xvg/8kVJFI7tyBbsIEVNQ5aRU5d96A+RMv5k7cmD/v4tAKsKfT6YCx\nY33w6ad5CCjDv+a/UPN3bNkSiW7dPHhXDCsSE1WIi9PjQt4JrD5ctMXhi+e+8IoWh5KYW7WC2cY5\nykRERFTxODwHuDTu7AH+JPYPnFC3wIo1BoevoVy1CheTzqLD4c9w4kSmaEbFXrh5F5HhNVF/Qg9k\nqv+Lfk36oW9IX89vcTAYIDtypMybYxAREZH3KZceYE92dkEKlqREYtfBHABKh69jCg9H49mzERg4\nF+npMoSF2d9H7EyKzZshPX8e+tGjH3rt/o0qtq5pimqhL+LDrq87vFGFO0hu34bfwIHI3r4dlvr1\n3R0OERERVWAiWde0jeVeFsa8VxOTRlxBzfqOF78AYGnUCJKsLMRE3kNysvv7gBXbt+fvWnafBzeq\n6FDnOVQ9Pg1LpzYr00YVQPn3Qgm1akE/ahQ0CQnl+rkVEfvYxI35Ey/mTtyYP+9SoQrgrwelAJX8\nMfiDumW/mFQKU6tW6FLjkEfsCidPTYWpbdvCjSo6rOnw0EYVVS8PR80aQMuW7l2tdpRu5EjITp6E\nfPt213yAWZy/L0RERORcFaYH+MYvx9BucFNs+jUPjcP9nHJNyZ07MPhWQnDII0hNzUKNGi75rSqV\n6dZNVGrRAr2+7IDfru1BzGMx6B/S/6EWhxdf9EN8vB6xseJ6aO9+iqQkaN57D1l79gDKsq3i309y\n9Sr8X34ZWfv2ATJxtIUQERGRbeztAa4wK8ATPq6J+K4XnVb8AoDw6KNQqGXo0MGErVvLfxW4oMXh\n39Pb4EiQAh0e74Tjw44jMSbxoRaHo0dluHRJJrqJFQ8yxsTAUq8elD/+6NTrqpYvh/HZZ1n8EhER\nUcUogH/+WYFThgZ4a+FjLrl+TIyx3Apgay0Onyi7odlLozCk6ZBiR5gtXKjCq6/qHmwTdpjbeqEk\nEuQsXgxDr17Ou6ZeD9WqVdDbuU2iWLGPTdyYP/Fi7sSN+fMuop8CkZUFTJjgg0WLcqFWu+YzoqON\neOcdH+j1gErl/OvfP8Vh1+VdiHksBlMip/zT4tA8F3qTqdj337ghQXKyAh9/7NimHx6nLMObrVD+\n9BPMISGwBAc79bpEREQkTqIvgD/4QINOnYyIiCi+QCyrKlUENGlixt69cnTs6LzPOXH7BFaftGGj\nCl9flNR9vHSpCj17GlCpkvN6lKOiopx2LXdTJSZCN3asu8MoNxUpd96I+RMv5k7cmD/vIuoCeP9+\nGX79VYl9+7Jc9yGCAMndu+jcWY0tWxRlLoDvaO9g/Zn1WHNiDW5pb6Ffk37Y1HOTwxtV6HTAihUq\n/PxzdpniqrBycmBu0ADGzp3dHQkRERF5CNH2ABuu3cHbrwEffZSHwEDXTWeQXLuGgDZtENPZgC1b\nFHBkZobRbETS+STEbY5DixUtcOjGIUyJnIL0oelIiEgo0y5t69Yp8dRTZjRqZHH4GtZ4VC+UsQwP\n9vn5IW/BAq96+M2jckd2Y/7Ei7kTN+bPu4h2BfjLfr+jgawJevSo49LPEWrXBpRKhPqcg8EQhrNn\npQgOtq3YtLnFwdHYBGDBAhWmTasgvb9WSDIy4N+5M7K3b4cQGOjucIiIiKgCEGUBfP7rQ5h/Ihq/\n7dNBInH955nCw6E4eACdOzdFcrICwcH6Ys91aouD2QxJTk6xhd+ePXKYzRK0b+/8/mdP6YUSHnkE\npmeegXrGDGg//tjd4YiCp+SOHMP8iRdzJ27Mn3cRXQuEJScPY8YH4p24i6gTrCmXzzS1bg35gQOI\niTFa3RXOVS0OsuPH4f/CC8W+/tVXKrz+evn8EOBO2kmToFy3DtKTJ90dChEREVUAoiuAvx2WAr1P\nJbzyn/rl9pmm8HDIDhzAM88YkZ4uR2ZmfsVZsFFF6LJQzD08F9H1oovdqMIR8tRUmNq0sfrauXNS\nHD4sR58+hjJ9RnE8qRdKqFIFuvHj4fN//webm7Bds8GhKHhS7sh+zJ94MXfixvx5F1EVwDcu6PH+\nzk6YvUxRrs80mZs2Bfz84KMwomV4Ht5duqvIRhWbem5CUu+kEjeqcIR8//5iC+AZMzR47TU9NOWz\nCO52+ldegfTWLSg2bbLpfN/+/SE7fNjFUREREZEYSQTBNUtl27dvR4sWLZx6zcuXpdizW4YBA8t3\nu9/7N6rY+n0jVL/bA3M+v/PPRhWuIAgIbNIE2du2wVK3bpGXjh6VYcAAPxw8mAlfX9d8vCeSHT0K\nQaOBpXHjEs+TnjwJ/549kXn0KKBUllN0RERE5C5HjhxBdHS0zeeL6iG4unUtGDDQueO+SmJtisPE\nhF7o/nwttKudCZkL18+l588DCgUsdR6ecvHBBxqMH6/1quIXAMxPPWXTeaolS6CPi2PxS0RERFaJ\nqgWiPNzR3kFiemKxLQ5PNPRFjRoWHDrk2h4M6Y0bMPTogQefcPvtNzkuX5Zi0CDX9P4WEG0vVFYW\nlBs2QD90qLsjcRvR5o4AMH9ixtyJG/PnXUS1Auwq97c47Lq8CzGPxWBK5JRiWxw6dzZi61YFWrc2\nuywmU2QkTJGRRb5mseSv/iYkaKF4eBgFAVCtXg1Tx44QatRwdyhERETkoby6AHZ0o4rOnY0YP94H\nCQm6coo038aN+Q//de/u+h5osc5DlNy6Bd1rr7k7DLcSa+4oH/MnXsyduDF/3sXrCuCybFQhPXEC\nEp0OrVq1wPXrUly5IkGdOuUzbstgAD76SIPPPsur8HN/baLVQvPhh9C+/z7uXw7XTZ7svpiIiIhI\nFLyiB9hZG1XIDx+GauFCyGRAdHR+G0R5WbFChQYNLHjmGefv+maNx/dCqdWQnTwJ1eLF7o7E43h8\n7qhEzJ94MXfixvx5lwq9Auxoi0NxTK1bQz17NoD8Nojvv1di2DDXPowGANnZwKxZaqxbl+PyzxIN\niQR5H38M/65dYejZE0K1au6OiIiIiERCVHOAbWGtxaFvSF+HtyMuwmJBYKNGyNq7F3fVNdGsWSBO\nnboHH5+yX/p+yu+/h6FLFxTMOfvkEzX++kuKBQvynPtBFYAmIQGSzEzkff65u0MhIiIiN6nQc4CL\nY+8UB4dJpTC1agX5gQOo1L07mjUzISVFjs6dndiWkJ0Nn7FjYejeHQDw998SLFqkwo4d2c77jApE\n+847CGzTBrLDh2Fu2dLd4RAREZEIiLoH+MTtE0jYk4DQZaGYe3guoutF4/iw40iMSUSHoA4u2aXN\nHB4O+YEDAPLbILZscW4fsPzgQZiaNQNUKgD5rQ99+hgQFFR+G4AAIuqFCgiA9t13odiyxd2ReAzR\n5I6sYv7Ei7kTN+bPu4huBbgsUxycwfDCC5CdOQMgvwDu3dsf//mP1mmTGeSpqTC1bQsA+OsvKdav\nVyItLcs5F6+gDIMGuTsEIiIiEhFR9ABba3HoH9Lf+S0OdhIEoEWLAHz9dS6efNI5m2L4de8O3Vtv\nwfTcc4iP90WTJmaMG1e+84aJiIiIxKRC9QA7e4qDs0kk/7RBOKUANhgg//13mMLDcfSoDPv2yfHZ\nZ7llvy4RERERFfK4HuA72jtITE9EhzUd0OenPlDL1NjUcxOSeidhSNMhHlP8Fujc2YjkZCf1Aet0\n0L73HhAQgKlTNRg/XlswCKLcsRdKvJg7cWP+xIu5Ezfmz7t4xApwuU1xcIHISBOGDZPhzh0JHn20\njN0kAQHQx8fjt9/kuHJFikGDXD9jmIiIiMjbONwDvHbtWiQkJEAikWDWrFno2rVrkddt6QG21uIQ\n2yjW41Z5SzNokC+6dzeiT5+yF6wWCxAd7Y8xY3To0cPohOiIiIiIKrZy6QE2GAyYOHEi0tLSoNPp\n0KFDh4cK4OK4e4qDs2gmTYL+1VdhqV+/sA3CGQXwxo0KyGRA9+4sfomIiIhcwaEe4LS0NDz55JOo\nWrUq6tati7p16yI9Pb3Y841mI5LOJyFucxxarGiBQzcOYUrkFKQPTUdCRILoil8AkN64AXlqKgCg\nUycjfvtNDmMZa1aDAfjoIw3ee895Y9UcxV4o8WLuxI35Ey/mTtyYP+/i0ArwzZs3UbNmTSxcuBCP\nPPIIatSogevXr6N58+ZFzvP0KQ5lYfrfhhiG/v1Rs6aAevUsOHBAjshIx3eFW7FChQYNLHjmGSfu\nLEdERERERZTpIbgRI0YAADZs2ACJlSXLPj/1EW2LQ2lM4eFQrVxZeNypU/44NEcLYOP7szBr1WSs\n+1HrrBDLJCoqyt0hkIOYO3Fj/sSLuRM35s+7OFQA16xZE9evXy88vnHjBmrWrPnQeVGHoiD/W471\nu9cjMDAQoaGhhX/ACv6pQazHuzMz8fyFC5BkZkIIDESNGofw2WdPYepUOHS9zxYHolnTC2jatJpH\nfH885jGPecxjHvOYx556XPDrS5cuAQDi4+NhD4emQBgMBjRp0qTwIbiOHTvi7NmzRc5x5k5wnsqv\ne3fo/vUvmKKjYbEAISGBSE7ORv36Fruucyv9BiI6VsP2IzIE1XPJxnx2S0lJKfzDRuLC3Ikb8yde\nzJ24MX/iZu8UCIceglMqlZgxYwYiIyMRHR2NuXPnOnIZ0cubMwem8HAAgFQKPPdcfhuEvWZ/YMGA\n+ikeU/wSERERVWQOzwEujTesAD/op58UWLFChfXrc2x+z19/SdE5QoojYxfBf/wwF0ZHREREVDGV\nywowWde+vREHD8qRY3v9i48+0uAt/6Wo9NxTrguMiIiIiAqxAHaigACgZUsTdu2yrQ3i6FEZ9u2T\nI35TR5hDQ10cnX3ubzIncWHuxI35Ey/mTtyYP+/CAtjJCnaFs8XUqRqMH6+FpnEdQC53cWRERERE\nBLAAdg6zufCXnTsbsW2bApZSBkH89pscV65IMWhQ2bdPdgU+CStezJ24MX/ixdyJG/PnXVgAl5H0\n0iUEtGlTeNyggQV+fgKOHZMV+x6LBfjgAw0SErRQ2D80goiIiIjKgAVwGVnq1IEkIwOS+zYGKdgV\nrjgbNyogkwHduxvLI0SHsBdKvJg7cWP+xIu5Ezfmz7uwAC4rqRSmVq0gP3iw8EsxMcUXwAZD/uSH\n997TQqLNK9I+QURERESuxwLYCcytW0N+4EDhcZs2Jpw7J8XNm5KHzl2xQoUGDSx45hkT1PPnQ/Ph\nh+UZqs3YCyVezJ24MX/ixdyJG/PnXVgAO4EpPLxIAaxUAu3bm7BtW9FV4OxsYNYsNd57TwsAkKem\nwtSqVbnGSkREROTtWAA7gSksDJLbt4u0M8TEPDwO7csv1Wjf3oimTc2AyQT5oUMwtW5d3uHahL1Q\n4sXciRvzJ17Mnbgxf96FBbAz+Pgg68gRQPbP5IfnnjNi9245DP+bcvb33xIsWqTCu+/qAACy//4X\nlpo1ITz6qDsiJiIiIvJaLIBdpGpVAY0aWbBvX/4GFzNnqtG3rwFBQfkDguWpqTC1bevOEEvEXijx\nYu7EjfkTL+ZO3Jg/78Ltx1yooA2iXj0LNmxQIi0tq/A1SWYmjO3auTE6IiIiIu/EFWAX6tw5fxza\nhx9q8Prrejz6qFD4mm7CBBhjY90YXcnYCyVezJ24MX/ixdyJG/PnXVgAu1BoqBk6nQT79snxxhs6\nd4dDRERERAAkgiAIpZ9mv+3bt6NFixauuLTHkl6+DOj1sDRsWPi1mTPVqF/fjF69PHfXNyIiIiIx\nO3LkCKKjo20+nz3ATqT45RfITp1C3pw5hV8bN44rv0RERESehC0QTvTghhhixl4o8WLuxI35Ey/m\nTtyYP+/CAtiJzE2bQnr5MiSZmcWeI7l7F4rk5HKMioiIiIjuxwLYmRQKmJ56CrJDh4o9Rb57N5TL\nlpVjUI7hPETxYu7EjfkTL+ZO3Jg/78IC2MlM4eGQp6UV+7p8/36Y2rQpx4iIiIiI6H4sgJ3M2Lkz\nLHXrFvu6WApg9kKJF3MnbsyfeDF34sb8eRdOgXAyc3g4zOHh1l/Mzobs3DmYw8LKNygiIiIiKsQV\n4HIkP3gQpmbNAJXK3aGUir1Q4sXciRvzJ17Mnbgxf96FBXA5EqpWhf6NN9wdBhEREZFXYwFcjsyh\noTB27eruMGzCXijxYu7EjfkTL+ZO3Jg/78ICmIiIiIi8ikQQBMEVF96+fTtatGjhikuLgnrmTOgH\nD4ZQvbq7QyEiIiKq0I4cOYLo6Gibz+cKsIvIDh0qcR4wEREREbkHC2AXMbduLeoCmL1Q4sXciRvz\nJ17Mnbgxf96FBbCLmMLDIT9wIP/AYoHvsGGATufeoIiIiIiIPcAuk5eHSsHBuHf2LKQXL8JvwABk\nHTni7qiIiIiIKhx7e4C5E5yr+PjA3KQJZOnpkJ06JYrtj4mIiIi8gUMtEDKZDGFhYQgLC8OYMWOc\nHVOFkffxx7A0aAD5/v2iK4DZCyVezJ24MX/ixdyJG/PnXRxaAfbx8cHvv//u7FgqHHOrVgAAeWoq\ndGPHujka+9y4ccPdIZCDmDtxY/7Ei7kTN+bPu/AhOBeTXLkCiVYLS6NG7g7FLiqVyt0hkIOYO3Fj\n/sSLuRM35s+7OFQA63Q6tGzZElFRUdizZ4+zY6pQhOrVkf3LL4BE4u5QiIiIiAiltEDMnTsXS5Ys\nKfK1l156CVevXkW1atVw6NAhxMbG4ty5c/zJqTgKBSwNG7o7CrtdunTJ3SGQg5g7cWOhnmp1AAAE\nQ0lEQVT+xIu5Ezfmz7uUeQxa69atsXLlSjRu3LjI1zdv3gy1Wl2m4IiIiIiISqPT6fDiiy/afL7d\nBfDdu3ehVquh0Whw4cIFREVF4ezZs9BoNHYHS0RERERU3uyeAnHq1CkMGzYMKpUKMpkMS5YsYfFL\nRERERKLhsp3giIiIiIg8EcegEREREZFXYQFMRERERF7FoZ3gSrNv3z589913AIC4uDi0bNnSFR9D\nLtC3b1/Uq1cPAPDEE09g6NCh7g2ISrRy5Urs2bMHAQEBmDVrFgDef2JiLX+8B8UhIyMDc+bMQV5e\nHuRyOQYOHIhmzZrx/hOJ4vLH+8/zZWdnY/r06TCZTACA2NhYRERE2H/vCU5mNBqFUaNGCZmZmcKt\nW7eEN99809kfQS40ePBgd4dAdjh9+rTw559/CmPHjhUEgfef2DyYP0HgPSgW9+7dEy5evCgIgiDc\nunVLGDFiBO8/EbGWP0Hg/ScGJpNJ0Ol0giAIQlZWljB8+HCH7j2nt0CcPXsWderUQUBAAKpUqYIq\nVargwoULzv4YIgIQHBwMPz+/wmPef+LyYP5IPAIDAxEUFAQAqFKlCkwmE86cOcP7TySs5a9gRZE8\nm0wmK9x8LTc3FwqFAufOnbP73nN6C0RmZiYqV66MrVu3ws/PD4GBgbh3756zP4ZcxGg0YsKECVAq\nlRgwYABCQkLcHRLZ4d69e7z/RI73oPgcPXoUjz/+OLKysnj/iVBB/uRyOe8/kdDpdJg0aRJu3ryJ\nt956y6G/+1zSAwwAnTp1AgCkpaW56iPIBRYsWIDAwED8+eefmDlzJubNmweFQuHusMhOvP/Ei/eg\nuNy7dw+rVq3ChAkTcP78eQC8/8Tk/vwBvP/EQq1WY9asWbh69SpmzJiB3r17A7Dv3nN6C0SlSpVw\n9+7dwuOCFWESh8DAQABAgwYNULlyZdy6dcvNEZE9KleuzPtP5HgPiofBYMDs2bMRFxeHatWq8e8/\nkXkwfwDvP7GpXbs2qlatiqpVq9p97zl9Bbhhw4a4cuUKsrKyYDAYcOfOncInKsmz5eTkQKlUQqlU\n4u+//0ZGRgaqVKni7rDIDrz/xI33oHgIgoD58+cjKioKzZs3B8D7T0ys5Y/3nzhkZGRAoVDA398f\n9+7dw7Vr11CrVi277z2X7AR3/yiKIUOGoEWLFs7+CHKBM2fOYP78+VAoFJBKpejfvz+eeuopd4dF\nJVi8eDEOHjyIrKwsVKpUCcOHD4fBYOD9JxIF+cvOzkZgYCCio6ORkpLCe1AETp06halTp6Ju3boA\nAIlEgokTJ+LkyZO8/0TAWv6GDx/OvwNF4MyZM0hMTASQ/4NMz549HxqDZsu9x62QiYiIiMircCc4\nIiIiIvIqLICJiIiIyKuwACYiIiIir8ICmIiIiIi8CgtgIiIiIvIqLICJiIiIyKuwACYiIiIir8IC\nmIiIiIi8yv8DzR/6WuvQ2d0AAAAASUVORK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 43 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n", - "\n", - "In the Kalman filter $R$ is the *measurement noise* and $Q$ is the *process uncertainty*. $R$ is the same in both plots, so ignore it for the moment. Why does $Q$ affect the plots this way?\n", - "\n", - "Let's understand the term *process uncertainty*. Consider the problem of tracking a ball. We can accurately model its behavior in statid air with math, but if there is any wind our model will diverge from reality. \n", - "\n", - "In the first case we set $Q=100$, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\". So the filter will be computing velocity ($\\dot{x}), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n", - "\n", - "In the second case we set $Q=0.1$, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our velocity prediction. \n", - "\n", - "Now let's leave $Q=0.1$, but bump $R$ up to $1000$. This is telling the filter that the measurement noise is very large. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plot_track (noise=30, R=1000, Q=0.1,count=50, plot_P=False, title='R = 1000, Q = 0.1')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF9CAYAAAAHja6eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 44 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The filter output should be much closer to the green line, especially after 10-20 cycles. If you are running this in Ipython Notebook, I strongly urge you to run this many times in a row (click inside the code box, and press CTRL-Enter). Most times the filter tracks almost exactly with the actual position, randomly going slightly above and below the green line, but sometimes it stays well over or under the green line for a long time. What is happening in the latter case?\n", - "\n", - "The filter is strongly preferring the motion update to the measurement, so if the prediction is off it takes a lot of measurements to correct it. It will eventually correct because the velocity is a hidden variable - it is computed from the measurements, but it will take awhile **I DON\"T LIKE THIS. I am not sure I have R and Q right**\n", - "\n", - "To some extent you can get similar looking output by varying either $R$ or $Q$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary $R$ and/or $Q$ based on your knowledge of the system you are filtering." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### A Detailed Examination of the Covariance Matrix\n", - "\n", - "So far I have not given a lot of coverage of the covariance matrix. It is time to look at it more closely. Recall this table comparing the one dimensional and multidimensional Kalman filter.\n", - "\n", - "| | 1D | 2+D|\n", - "|--|----|---|\n", - "|state|$\\mu$|$x$|\n", - "|uncertainty|$\\sigma^2$|$P$|\n", - "\n", - "This should remind you that $P$, the covariance matrix is nothing more than the variance of our state - such as the position of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9\\times 9$ covariance matrix, or even larger.\n", - "\n", - "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n", - "\n", - "$$\n", - "P = \\begin{pmatrix}\n", - " {{\\sigma}_{1}}^2 & p{\\sigma}_{1}{\\sigma}_{2} & \\cdots & p{\\sigma}_{1}{\\sigma}_{n} \\\\\n", - " p{\\sigma}_{2}{\\sigma}_{1} &{{\\sigma}_{2}}^2 & \\cdots & p{\\sigma}_{2}{\\sigma}_{n} \\\\\n", - " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", - " p{\\sigma}_{n}{\\sigma}_{1} & p{\\sigma}_{n}{\\sigma}_{2} & \\cdots & {{\\sigma}_{n}}^2\n", - " \\end{pmatrix}\n", - "$$\n", - "\n", - "(I have subtituted $P$ for $\\Sigma$ because of the nomenclature used by the Kalman filter literature).\n", - "\n", - "The diagonal contains the variance of each of our state variables. So, if our state variables are\n", - "\n", - "$$\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}$$\n", - "\n", - "and the covariance matrix happens to be\n", - "$$\\begin{pmatrix}2&0\\\\0&6\\end{pmatrix}$$\n", - "\n", - "we know that the variance of $x$ is 2, and the variance of $\\dot{x}$ is 6. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "P = np.array([[2,0],[0,6]])\n", - "e = stats.sigma_ellipse (P, 0, 0)\n", - "stats.plot_sigma_ellipse(e, '|2 0|\\n|0 6|')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAGNCAYAAAActsnoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl4VFW67/FfVaoykYExImAYHICWgICgYmQQQU4LOCuN\nVxsFbUHsg4pDD6jYfWg9NrQ+aoPIsR1arkA7AioIigoitkYBJ67KEAaDGiDzVKm6f+RAt1pAUqmq\nvdau7+d5eGSHUHn1Z+39ZuXda3tCoVBIAAAAgIt5nS4AAAAAiDWaXgAAALgeTS8AAABcj6YXAAAA\nrkfTCwAAANej6QUAAIDr0fQCQJSsWbNGXq8Zp9WhQ4dq5syZTpcBAMYw4+wMAC524MAB3XDDDTrx\nxBOVnp6uzp07a+rUqTpw4ECTXicQCOjmm29WTk6OMjIydNFFF+nbb78N+7kej0cejyca5QOAK9D0\nAkCM7d27V3v37tUDDzygTz/9VI8//riWLl2qyy+/vEmvc/fdd+uJJ57QU089pbfffls7duxo8msA\nQKLyOV0AALhd9+7d9Y9//OPQcdeuXXXTTTfplltuUVlZmTIzM4/6GsFgUPPmzdNtt92mUaNGSZIe\neOABDRkyRJ988ol69eoVs/oBwA1Y6QUAB+zfv1/p6elKSUlp1Odv3bpV+/bt01lnnXXoY4MGDZLP\n59M///nPWJUJAK5B0wsAcbZz50499NBDuvnmm5WcnNyov3NwdrdNmzaaPn26jj/+eNXW1qp169aH\nnesFAPwLTS8AxNGBAwc0ZswYDR48WHfffXdEr5GTk6POnTvL52NCDQAai6YXAOKkpKREI0eOVMeO\nHbVkyZIm7a6Qk5MjSSouLtZtt92mN954Q16vV/v27Tv0ZwCAw6PpBYA4KC0t1bnnnqucnBy9+OKL\n8vv9Tfr73bp1U+vWrfX2228f+ti6desUCAQ0cODAaJcLAK7Dz8YAIMbKyso0cuRI+f1+zZ07V8XF\nxYf+LCcnp1EPtPB6vZo8ebLuv/9+9e3bV+3atdO0adM0dOhQnXzyybEsHwBcgaYXAGLsww8/1Pvv\nvy+Px6POnTsf+rjH49G2bduUm5vbqNe5++67VVlZqSuvvFJVVVU699xzNW/evFiVDQCuQtMLADE2\ndOhQBYPBZr9OUlKSZs+erdmzZ0ehKgBILMz0AoALhUIhhUIhp8sAAGPQ9AJAFDVlR4ZY8ng8xtQC\nACbwhFgKAAAAgMux0gsAAADXo+kFgChZs2ZNo7Yfi4ehQ4dq5syZTpcBAMYw4+wMAC5XVFSkCy+8\nUBkZGcrJydGtt94a0Y4OzzzzjHr37q20tDS1b99ed9xxR9jPY6YXAH6ILcsAIA4uvfRS1dTU6J13\n3lFRUZHGjx+vjIwM3XXXXY1+jWeeeUYTJ07UrFmzNHr0aAUCAe3cuTOGVQOAe9D0AkCMbdy4UevW\nrdO7776rvn37SpJuvvlmPfzww01qeu+8807ddNNNuvnmmw997Gc/+1nU6wUAN2K8AQBi7J///Kf8\nfr9OP/30Qx8bMmSIvvvuO23btq1Rr1FYWHjo6W2DBg3SscceqxEjRujjjz+OVdkA4Co0vQAQY99+\n+61at24tSRowYIDGjRunnJycQ3/WGLt375YkzZo1S1OnTtXy5cvVrl07jRgxQiUlJbEpHABchKYX\nAOLg4Jboubm56tixY5P//sGb3q644gqNHz9e/fr10/z581VSUqLly5dHtVYAcCNmegEgxnJycrR/\n/35J0nPPPSdJevvttw/9WWO0bdtWknTSSScd+lhGRobatm2rPXv2RLNcAHAlVnoBIMYGDBiguro6\nrV+//tDH1qxZo3bt2qlr166Neo3jjz9eWVlZ2rp166GPVVZWqri4WJ06dYp6zQDgNqz0AkCM9enT\nR2eeeaZ+/etf69FHH1VRUZH+8pe/6Kabbmr0a/h8Pk2cOFFz587Vaaedpu7du+v+++9Xy5Yt9fOf\n/zyG1QOAO9D0AkAcLFmyRJMnT9bgwYOVlpamSZMmacaMGU16jT/96U8KBAKaNGmSqqqq1K9fP732\n2mvKysqKUdUA4B4RNb3FxcUaNWqU6urqFAqF9Lvf/U6XXXZZtGsDANdo3769XnjhhWa9RnJysh58\n8EE9+OCDUaoKABJHRE1vdna23nrrLaWnp6u4uFg9e/bUJZdcYswz5wEg0YVCoUM7RgAAImx6fT6f\nfL6Gv7p//36lpKREtSgAsJXH43G6BEkNdZhSCwCYwBOKcCmgvLxcZ5xxhr7++mstXLhQF1xwQbRr\nAwAAAKIi4qb3oC+++EKjR4/Wxo0b1aJFi2jVBQAAAERNs3dv6NGjhzp37qzPP/9cp5566qGPL1q0\n6NBm6gAAAECsVFdX67zzzjvi50TU9O7Zs0cpKSlq06aNioqKtGXLlp9ssN62bVv169cvkpeHAZYu\nXaoxY8Y4XQYiQHZ2Iz97kZ3dyM9uBQUFR/2ciJrewsJCXXfddZIa7hCePXu22rRpE8lLwVCFhYVO\nl4AIkZ3dyM9eZGc38nO/iJre008/XZs2bYp2LQAAAEBMsLEuwjrnnHOcLgERIju7kZ+9yM5u5Od+\nNL0Iq3v37k6XgAiRnd3Iz15kZzfycz+aXoS1du1ap0tAhMjObuRnL7KzG/m5H00vAAAAXK/ZD6c4\nnNWrV7NlGQAAAGKuoKBAw4cPP+LnsNILAAAA16PpRVjMNtmL7OxGfvYiO7uRn/vR9AIAAMD1mOkF\nAACA1ZjpBQAAAETTi8NgtsleZGc38rMX2dmN/NyPphcAAACux0wvAAAArMZMLwAAACCaXhwGs032\nIju7kZ+9yM5u5Od+NL0AAABwPWZ6AQAAYDVmegEAAADR9OIwmG2yF9nZjfzsRXZ2Iz/3o+kFAACA\n6zHTCwAAAKsx0wsAAACIpheHwWyTvcjObuRnL7KzG/m5H00vAAAAXI+ZXgAAAFiNmV4AAABAks/p\nAmCmtWvXKj8/3+kyEAGyM1cwKG3d6tWnnyapqMir77/3qLi44Z/793vk8UgVFft17LEtlZwspaWF\n1KFDUF27Nvzq0qVe7duH5PE4/W+CcHjv2Y383I+mFwBipLjYo9Wr/SooSNKmTUn65BOfWrcOqlev\nenXoEFTbtiH16hVQmzYhtW4dUigkffTRNp1wwsmqqZGqqjzatcurd97x6amnkrRtm1eVlR717x/Q\nmWc2/OrfP6CUFKf/TQHAfMz0AkAUffmlV6++6tdrr/n16ac+DRlSpwEDAurTp155efVq1ap5p9yS\nEo82bEjSunV+rVvn05YtSerfP6Dzz6/VBRfUNfv1AcBGjZnpZaUXAJqptFRavDhFjz+eopISj0aN\nqtNNN1XrrLMCSk2N7tfKzg5p5MiARo4MHPraa9f69Y9/JGvmzDQNHhzQZZfVasSIOlaAAeDfcCMb\nwmK/QnuRXfx88YVXt96aplNOyda6dT7df3+lPvmkRLNnV2rEiMga3qbml5Ul/fzndXr88Qpt2lSi\nESPqNH9+inr1ytZ996Vq/34GgOOF957dyM/9aHoBoIk2bUrSpZdm6MILM9WqVUhr15bqb3+r0Jln\nBhy9ySwrS7ryylq9/HK5Xn21TLt2eXXqqVm666407d1L8wsgsTHTCwCNtH27V7Nmpeqdd/yaPr1a\nV15Zo+Rkp6s6sl27PHrooVQtWZKsyy6r1e23VzP3C8B12KcXAKKguNijO+5I0znnZOrEE4P65z9L\nNHGi+Q2vJHXqFNJ991XpvfdKVV8vnXFGlp5+OlnBoNOVAUB80fQiLGab7EV20fXii37l52cpFJLW\nry/VrbdWKyMjdl8vVvnl5IR0//1VWrSoXE8/naJzz83Uxx8nxeRrJSree3YjP/dj9wYACOO77zy6\n9dZ0ff55kp56qlwDBtQ7XVJU9OlTr9deK9P//b/JGjcuQxddVKu77qpipwcArsdKL8LiqTT2Irvm\nCYWk557z66yzstS1a1BvvVUa14Y3Hvl5vdIVV9Rq/fpS7d7t1YgRmdqyhctBc/Hesxv5uR8rvQDw\nv6qrpdtuS9eGDT4980y5+vd3x+ru4bRqFdITT1ToySeTNXp0pmbMqNKVV9bymGMArsS39giL2SZ7\nkV1kdu3yaPToTJWWerRqValjDW+88/N4pAkTarV0aZnmz0/RNde0UGlpXEtwDd57diM/96PpBZDw\n1q71acSILI0dW6u//a1CmZlOVxR/PXoEtWpVmbKzQzrvvEzt2sVyLwB3YZ9eAAlt/vwUzZmTqnnz\nKjR0aMDpchwXCkkPP5yiefNStXBhufr0cfeIBwB3aMw+vcz0AkhIoZA0a1aqXn45WStXlik3l41r\npYZxhxtvrFGXLkFdckmGHnqoUqNG1TldFgA0G+MNCIvZJnuR3dEFg9Ktt6Zp9Wq/li83q+E1Jb8x\nY+r07LPluvnmdC1YwH5mjWFKdogM+bkfK70AEkptrTRlSgvt3evRiy+WKSvL6YrM1b9/w56+55+f\noUBAuv76GqdLAoCIMdMLIGFUV0tXXZUhvz+kBQsqlJbmdEV22LnTq7FjM/SrX9XQ+AIwEjO9APC/\nAgFp4sQWysgIaf78Cvk4+zXacccF9fLL5Ro7tuH5yzS+AGzETC/CYrbJXmT3U8GgdOON6aqr82je\nPLMbXlPzO9j4PvpoiubNY8Y3HFOzQ+OQn/tF3PTu3r1b+fn56tWrl/r3769Vq1ZFsy4AiIpQSPrt\nb9O0fXuSnniiXMnJTldkr4ON79y5KVq8mP+QAOwS8Uzvt99+q7179yovL0+FhYUaNGiQdu3adejP\nmekFYIL77kvV8uV+LV1aruzsmNzCkHA+/9yr88/P1N/+VqEzz2RvYwDOa8xMb8QrvTk5OcrLy5Mk\n5ebmqra2VnV17OUIwBxPPJGsJUuS9Y9/0PBGU8+eQT32WIWuuaaFtmxhSg6AHaJytlqxYoX69+8v\nv98fjZeDAZhtshfZNVi/3qc//SlNixaVKyfHnobXlvyGDAnorruqNG5chr79lkcWS/Zkh/DIz/2a\nfTtHUVGRpk+frpdffjka9QBAs+3a5dHEiS30yCMVOv54cx484Tbjx9dqxw6vxo/P0NKlZWwBB8Bo\nzdqnt7q6WiNGjNCMGTM0cuTIH/zZ6tWrtWDBAuXm5kqSsrOzlZeXp/z8fEn/+o6KY4455jiax1VV\n0uDBHp111h7NmXOs4/W4/TgUki64oFKpqQEtWpTleD0cc8xxYhwf/H1hYaEkadKkSUed6Y246Q2F\nQho/frwGDx6syZMn/+TPuZENQLyFQtL116crGPRo/vwKefipe1yUlUnnnJOladOq9Ytf1DpdDoAE\nFNMb2datW6fnnntO8+fPV9++fdW3b18VFRVF+nIwzL9/JwW7JHJ28+enaMuWJD34oL0Nr435ZWZK\nf/tbue68M02ffZa4N7bZmB3+hfzczxfpX8zPz1dtLd/RAzDDp58m6c9/TtXKlWVKT3e6msTzs58F\ndc89Vbr66gytXl2qjAynKwKAH2rWTO+RMN4AIF6qqhp+vD51Kj9ed9qNN6arpkZ69NFKa1fbAdgn\npuMNAGCKmTPT1L17vcaNo+F12n33VeqTT3xasoQntgEwC00vwmK2yV6Jlt3rr/u0fHmy5sxxx8qi\n7fmlp0t//WuFfv/7NBUVuSCQJrA9u0RHfu5H0wvAWt9959F//mcLzZ1boZYt7XkAhdudckq9fvnL\nGt1yS7piM0AHAE3HTC8Aa113XbqOOSakP/yhyulS8CM1NdLZZzdsY3bppYydAIitxsz0Rrx7AwA4\n6Y03fHr/fZ/WrSt1uhSEkZIiPfJIhS6/PENnnVWn9u1Z8gXgLMYbEBazTfZKhOyqqqRbb03X/fdX\nqkULp6uJLjfld8op9brqqhpNn54Ye8i5KbtERH7uR9MLwDpz5qSqT596jRgRcLoUHMX06dX68ssk\nrVzJDxYBOIuZXgBW+fxzr8aOzdQ775TyI3NLrFrl0x13pGvdulKlpDhdDQA3Yp9eAK4SCkm33JKu\n3/ymiobXIuecE1D37vWaO5eOF4BzaHoRFrNN9nJzdi++6FdlpUcTJrh3NwC35vfHP1bp4YdTtWeP\ne/fudWt2iYL83I+mF4AVamqkP/whTffcUyUvZy7rdO0a1IQJNZo5M83pUgAkKGZ6AVhh7twUrVnj\n16JF5U6XggiVl0unn56tBQvKdfrp9U6XA8BFmOkF4AolJR795S+puvvuSqdLQTNkZEgzZlRp5kye\n1AYg/mh6ERazTfZyY3Zz5qTqP/6jTj17Bp0uJebcmN+/u+SSWu3f79GqVe7bwszt2bkd+bkfTS8A\no+3c6dXf/56s3/yGRw27QVKS9JvfVGnWrDRWewHEFU0vwsrPz3e6BETIbdn9+c+puuaamoTZosxt\n+YUzZkydQiFp+XK/06VEVSJk52bk5340vQCMtWuXR8uW+TV5co3TpSCKvF7pt79tWO2t5342AHFC\n04uwmG2yl5uye+ihVF15Za1at06MVV7JXfkdyYgRAWVkhPTCC+5Z7U2U7NyK/NyPpheAkfbu9WjJ\nkmRNmVLtdCmIAY+nYbX3v/87TUH3358IwAA0vQiL2SZ7uSW7Rx5J1WWX1SonJ3FWeSX35NcYQ4YE\nlJkZ0muvuWO1N5GycyPycz+aXgDGKS726O9/T9aNN7LK62YejzR1arUeeijV6VIAJACaXoTFbJO9\n3JDdvHkpOv/8OnXsmFirvJI78muKMWPq9M03Hr3/fpLTpTRbomXnNuTnfjS9AIxSVSU9+WSKpk5l\nlTcR+HzS5Mk1euQRVnsBxJYnFIrN9uCrV69Wv379YvHSAFzsmWeS9dJLyVq8uNzpUhAn5eVS377Z\nWrmyTF27clcbgKYrKCjQ8OHDj/g5rPQCMEYoJD32WIquvZZV3kSSkSH98pc1mjs3xelSALgYTS/C\nYrbJXjZnt2FDksrLPRo+POB0KY6xOb/mmDSpRkuWJKu01OlKIpeo2bkF+bkfTS8AYzz2WKomTqyR\nlzNTwmnfPqShQwNasoTVXgCxwUwvACN8841HgwZlaePGEmVlOV0NnPDmmz7ddVea3nqrTB6P09UA\nsAkzvQCs8eSTKbr44loa3gQ2ZEhAZWUeffSR/duXATAPTS/CYrbJXjZmFwxKCxcma8KEWqdLcZyN\n+UWL1ytddVWtnnzSzhGHRM7ODcjP/Wh6AThu7VqfWrYMqVeveqdLgcPGj6/Ryy/7VVbmdCUA3Iam\nF2HxDHJ72Zjds88ma9w4VnklO/OLpmOOCemsswJ67rlkp0tpskTPznbk5340vQAcVV4uvfKKX5dc\nQtOLBldeWaO//93OEQcA5qLpRVjMNtnLtuyWLk3WGWcElJMTk41krGNbfrEwbFhAO3d6tW2bXZco\nsrMb+bmfXWcUAK7DaAN+zOeTxo6t1fPP2zfiAMBc7NMLwDE7d3o1bFimPv20RCn8NBv/5r33knTL\nLS20bp3Fj2gDEDfs0wvAaC+84NeYMXU0vPiJgQPrVVLi0WefcZkCEB2cTRAWs032sim7pUuTNXYs\now3/zqb8YsnrlS66qFYvvGDPiAPZ2Y383I+mF4Ajdu/2aOtWr/LzA06XAkNddFHDXG9shvAAJBqa\nXoTFfoX2siW7V15J1rnn1snvd7oSs9iSXzz06VMvj0fWPJaY7OxGfu5H0wvAEUuX+jV6dJ3TZcBg\nHk/DLg6vvsp3RgCaj6YXYTHbZC8bsvv+e482bvRp2DCa3h+zIb94GjmyTq+9ZkfTS3Z2Iz/3o+kF\nEHevvurX2WfXKS3N6UpgugED6vXNN17t2uVxuhQAlqPpRVjMNtnLhuyWLUvW6NHs2hCODfnFU1KS\nNGJEnVauNH+1l+zsRn7uR9MLIK6qq6X1630aPpxdG9A4I0fWacUKe7YuA2Amml6ExWyTvUzPbsMG\nn3r0qFfLluxDFY7p+Tnh7LMDWr/ep4oKpys5MrKzG/m5X8RN7/Tp09W+fXvl5eVFsx4ALvfGGw3z\nvEBjZWeH1LdvQG+/bf6IAwBzRdz0XnzxxVq+fHk0a4FBmG2yl+nZvfkmuzYcien5OWXkSPPnesnO\nbuTnfhE3vWeccYbatGkTzVoAuNzevR7t3OlV//71TpcCywwdGtA77/icLgOAxZjpRVjMNtnL5OzW\nrPHrrLMC8tG7HJbJ+TmpZ896lZR4tHu3uVuXkZ3dyM/9aHoBxM2bb/qY50VEvF5p0KCA1q0ze8QB\ngLliut4yZcoU5ebmSpKys7OVl5d3aGbm4HdUHJt5fPBjptTDceOP8/Pzjarn4HEoJL311nn6zW+q\njajH1GNT8zPjeLjeecenDh3eMKQejjnm2Knjg78vLCyUJE2aNElH4wmFQhHvG7R9+3aNGTNGmzdv\n/smfrV69Wv369Yv0pQG4zNatXo0dm6lPPilxuhRY6vPPvRo/PkMffVTqdCkADFNQUKDhw4cf8XMi\nHm+44YYbNGjQIG3ZskXHHXecli1bFulLwUD//p0U7GJqdu+959NppwWcLsN4puZngh49gqqsbLgZ\n0kRkZzfyc7+IzxyPPPKI9uzZo9raWu3cuVOjR4+OZl0AXGbDBppeNI/HI515ZkBr1/qcLgWAhcz8\ndhmOOzg7A/uYmh1Nb+OYmp8p8vPrjG16yc5u5Od+NL0AYm7/fo/27PHq5JPZnxfNM2BAvQoKzGx6\nAZiNphdhMdtkLxOze/99n/r3Z3/exjAxP5P06FGvXbu8KjXwXjaysxv5uR9NL4CY4yY2RIvfL518\ncr02buQ7KABNQ9OLsJhtspeJ2b3/fpIGDqTpbQwT8zNNv34BFRQkOV3GT5Cd3cjP/Wh6AcRUMCht\n3uxT377M8yI6+vcP6MMPWekF0DQ0vQiL2SZ7mZbd9u1etWwZVKtWET8HJ6GYlp+J+vat10cfmdf0\nkp3dyM/9aHoBxNSmTUnKy2OVF9HTtWtQFRVSUZHH6VIAWISmF2Ex22Qv07LbvJmmtylMy89EHo/U\nr595q71kZzfycz+aXgAxtXmzT7170/Qiunr1qtdnn5l3MxsAc9H0Iixmm+xlWnas9DaNafmZqkeP\nen3+uVlNL9nZjfzcj6YXQMzs3etRTY3UqVPQ6VLgMj171uuLL7iEAWg8zhgIi9kme5mU3SefNKzy\nerjfqNFMys9kJ55Yr61bk1RX53Ql/0J2diM/96PpBRAzW7YkqUcPRhsQfenpUocOQW3dymUMQONw\ntkBYzDbZy6Tsvv46SSecwGhDU5iUn+l69KjXF1+YM9dLdnYjP/ej6QUQM1995dXxx7PSi9jo2dO8\nm9kAmIumF2Ex22Qvk7L76itWepvKpPxMZ9pKL9nZjfzcj6YXQEyUl0v793vYuQExc+KJQX31FZcx\nAI3D2QJhMdtkL1Oy27YtSV27BuXlLNMkpuRng86dgyosTFIo5HQlDcjObuTnflyOAMTEl18yz4vY\nys4OKSkppH372BMPwNHR9CIsZpvsZUp2X3+dpBNPpOltKlPys0WXLkFt327GpYzs7EZ+7mfGmQKA\n62zb5lWXLszzIrZyc4PasYNLGYCj40yBsJhtspcp2e3Z4+UmtgiYkp8tGuZ6zbiUkZ3dyM/9zDhT\nAHCd3bu96tiRphex1aVLvbZvN2fbMgDmoulFWMw22cuE7EKhhpXeDh1oepvKhPxsYtJ4A9nZjfzc\nz4wzBQBX2b/fo+TkkDIynK4Ebpeba854AwCzcaZAWMw22cuE7BpWeQ3ZPNUyJuRnk/btg/r2WzMu\nZWRnN/JzPzPOFABcZc8eD/O8iIvMTCkYbHgCIAAcCU0vwmK2yV4mZMdNbJEzIT+beDxSTk5Q333n\n/OWM7OxGfu7n/FkCgOtwExviqV27kPbu5alsAI6MphdhMdtkLxOy++47r9q1o+mNhAn52eaYY8xY\n6SU7u5Gf+zl/lgDgOvv2edSqFTeyIT5yckLG3MwGwFycJRAWs032MiG7/fs9at2apjcSJuRnm5yc\noBHjDWRnN/JzP5peAFG3b5+XphdxY8qNbADMxlkCYTHbZC8Tstu/36OWLZnpjYQJ+dmmdeuQioud\nX+klO7uRn/vR9AKIqlCoYaaXlV7ES1ZWSGVlzje9AMxG04uwmG2yl9PZVVZKSUlSWpqjZVjL6fxs\nlJlpRtNLdnYjP/ej6QUQVfv3s3MD4suUpheA2Wh6ERazTfZyOrsDB7zKzqbpjZTT+dkoMzOk8nLn\nm16ysxv5uR9NL4CoqqyU0tNpehE/rPQCaAyaXoTFbJO9nM6uqspD09sMTudnoxYtGr7Zqq93tg6y\nsxv5uR9NL4Coqq72KDXV6SqQSLzehsa3osLpSgCYjKYXYTHbZC+ns6uslNLSWOmNlNP52SozM6TS\nUmdHHMjObuTnfjS9AKKqutpD04u4S0kJqaaGuV4Ah0fTi7CYbbKX09lVVbFHb3M4nZ+tfD4pEHC2\nBrKzG/m5H00vgKiqqvIoNZWVXsRXQ9PLSi+Aw6PpRVjMNtnL6ezYvaF5nM7PVn5/SHV1ztZAdnYj\nP/eLuOldvHixTjrpJHXv3l3Lli2LZk0ALBYINKy6AfFkwngDALNFdGmqra3VHXfcoQ0bNqi6ulrD\nhg3T6NGjo10bHMRsk73Izm7kFxkTml6ysxv5uV9EK70bNmzQySefrHbt2um4447Tcccdp40bN0a7\nNgBIOGvXskweiYbxBmZ6ARxeRE3v3r17deyxx+rRRx/VkiVL1L59e33zzTfRrg0OYrbJXmRnt4UL\n9zhdgpXKyjyqqGCfXkSO/NyvWUsKv/rVryRJzz//vDyen55spkyZotzcXElSdna28vLyDv344OD/\nXBybebx582aj6uHYruPCwkKtXfv/jKnHhuPNm9uopKSvnn22u6Qtyssr1uTJPY2pz/TjTZvG6N13\nfRo1qs6xeg4y4b8Hx+Tn9uODvy8sLJQkTZo0SUfjCYVCTb7Net26dbr33nu1dOlSSdKwYcP04IMP\nqnfv3oc+Z/Xq1erXr19TXxqA5e69t+EZxHfcUe1wJXa6995U/ttF4MILM/Sf/1mtoUMDTpcCwAEF\nBQUaPnxcNGojAAAcTklEQVT4ET/HF8kLDxgwQJ9++qm+++47VVdXa9euXT9oeAEAiKe6OnYNAXBk\nEc30Jicn695779WZZ56p4cOH64EHHoh2XXDYj3/cA3uQnd2ysz9yugQr1dV55PM5uz807z27kZ/7\nRfx98WWXXabLLrssmrUAcImmD03hoLy8YqdLsFJ9veT3O10FAJPxRDaEdXBgHPZxOrvkZDn+ZCyb\nOZ2frUwYbyA7u5Gf+9H0AoiqtLSQKivZLxXxVVfnkd/PjxgAHB5NL8JitsleTmeXlhZSdTVNb6Sc\nzs9WJjz+muzsRn7uR9MLIKrS0qSqKqerQKIxoekFYDaaXoTFbJO9nM4uNTWkqipWeiPldH62qq72\nKCXF2fEGsrMb+bkfTS+AqEpPp+lF/JWVeZSVxUwvgMOj6UVYzDbZy+nsUlOlah4oFjGn87NRfX3D\nSE2LFs7WQXZ2Iz/3o+kFEFVpaaz0Ir7Kyz3KyAjJyxUNwBFwikBYzDbZy+ns0tNDqqig6Y2U0/nZ\nqKxMysx0ugqysx35uR9NL4CoatkypAMHaHoRP6WlHmVmMs8L4MhoehEWs032cjq71q1D2rfPw6OI\nI+R0fjYqKzOj6SU7u5Gf+9H0Aoiq1FTJ75fKy52uBInClKYXgNloehEWs032MiG7Vq1COnCA00sk\nTMjPNqaMN5Cd3cjP/bgqAYi61q2D2rePuV7ER3GxV23bBp0uA4DhaHoRFrNN9jIhu4NzvWg6E/Kz\nzbffepST4/xKL9nZjfzcj6YXQNS1akXTi/jZu9ernBxWegEcGU0vwmK2yV4mZNe6dVD793N6iYQJ\n+dnGlJVesrMb+bkfVyUAUdeuXUh797LSi/j47jtWegEcHU0vwmK2yV4mZNexY1B79nB6iYQJ+dlm\n716vjjnG+aaX7OxGfu7HVQlA1HXoQNOL+AgGpe++86htW+fHGwCYjasSwmK2yV4mZMdKb+RMyM8m\nBw54lJ4eUmqq05WQne3Iz/24KgGIug4dgtq928ujiBFz33zj1THH8D8agKOj6UVYzDbZy4TsMjMl\nny+kkhJuZmsqE/KzyY4dXnXu7Pw8r0R2tiM/96PpBRATHTqEtHs3pxjE1o4dXnXpUu90GQAswBUJ\nYTHbZC9TsuvYMajdu1npbSpT8rPFjh1e5eaasdJLdnYjP/ej6QUQEx07BrVrF6cYxFbDSq8ZTS8A\ns3FFQljMNtnLlOy6davX118nOV2GdUzJzxY7diQx04uoID/3o+kFEBMnnBDU119zikHshELSzp1e\n5eYy0wvg6LgiISxmm+xlSnbHH1+vr75ipbepTMnPBt9/71FKSkhZWU5X0oDs7EZ+7kfTCyAmunRp\nmOmtrXW6ErjV9u3mbFcGwHw0vQiL2SZ7mZJdSkrDzWw7dnCaaQpT8rPBli1JOukkc0YbyM5u5Od+\nXI0AxMzxxwcZcUDMfPFFknr0MKfpBWA2ml6ExWyTvUzKrmGul9NMU5iUn+k+/zxJPXqYM95AdnYj\nP/fjagQgZk48kZvZEDtffJGknj1Z6QXQODS9CIvZJnuZlF2PHkF99hlNb1OYlJ/JSko8KivzqFMn\nc1Z6yc5u5Od+NL0AYqZXr4A+/zxJ9SzGIco+/9yrk06ql5erGIBG4nSBsJhtspdJ2WVlSTk5QeZ6\nm8Ck/Exm4k1sZGc38nM/rkQAYiovr16ffMKIA6LLxKYXgNloehEWs032Mi27vLx6bdrkc7oMa5iW\nn6k2bUpSr15mNb1kZzfycz+aXgAx1bt3QJs3s9KL6AkEpM2bferXL+B0KQAsQtOLsJhtspdp2fXq\nVa/Nm5MUCjldiR1My89EW7YkqUOHoLKynK7kh8jObuTnfjS9AGLq2GND8nikb77xOF0KXOLDD5NY\n5QXQZDS9CIvZJnuZlp3HI/XpU6+CAuZ6G8O0/ExUUOBTv35mzfNKZGc78nM/ml4AMXfaaQFt2EDT\ni+goKGClF0DT0fQiLGab7GVidjS9jWdifiaprJS2bjVv5waJ7GxHfu5H0wsg5vr1C+izz5JUVeV0\nJbDdpk0N+/OmpDhdCQDb0PQiLGab7GVidi1aSD161Ovjj1ntPRoT8zPJ++/71L+/maMNZGc38nO/\niJre6dOnq3379srLy4t2PQBcauDAgN57j6YXzbN2rV/5+WY2vQDMFlHTe/HFF2v58uXRrgUGYbbJ\nXqZm1zDXy0MqjsbU/ExQVydt2ODTmWea2fSSnd3Iz/0ianrPOOMMtWnTJtq1AHCx004L6P33fQoG\nna4Etvr44yTl5tardWuedAKg6ZjpRVjMNtnL1Ozatw+pdeuQPvuM1d4jMTU/E5g+2kB2diM/9zvi\ngN0DDzyg//mf//nBxy688ELdc889jXrxKVOmKDc3V5KUnZ2tvLy8Qz8+OPg/F8dmHm/evNmoejh2\nx/GwYSP0xhs+HTjwlhH1cGzX8dq1ozRxYo0x9fz4+CBT6uGY/Nx8fPD3hYWFkqRJkybpaDyhUCii\nnxNt375dY8aMOdQc/djq1avVr1+/SF4agEu98opfjz2WohdeKHe6FFimtlY64YSW2rSpRC1bMt4A\n4IcKCgo0fPjwI34O4w0A4iY/v04ffuhTZaXTlcA2BQVJ6tatnoYXQMQianpvuOEGDRo0SFu2bNFx\nxx2nZcuWRbsuOOzHP+6BPUzOLitLyssL6N13fU6XYiyT83PSm2/6NXhwwOkyjojs7EZ+7hdR0/vI\nI49oz549qq2t1c6dOzV69Oho1wXApYYNC+iNN/xOlwHLrFzp16hRdU6XAcBijDcgrIMD47CP6dmd\nfXad3nyTpvdwTM/PCXv2eLRjh1cDB5q90kt2diM/96PpBRBXffrU69tvPdq1y+N0KbDEypV+DR8e\nkI+pGADNQNOLsJhtspfp2SUlScOH12nlSlZ7wzE9PyesXOnXuefWOl3GUZGd3cjP/Wh6AcTd6NF1\nWro02ekyYIGqKmnt2oaVXgBoDppehMVsk71syG748DoVFPi0fz8jDj9mQ37xtHatT717B9Sqlflb\nlZGd3cjP/Wh6AcRdixbSkCF1eu01RhxwZK+9lqyRI9m1AUDz0fQiLGab7GVLdg0jDjS9P2ZLfvEQ\nCEjLlvk1erQdTS/Z2Y383I+mF4Ajzj23TmvX+lVW5nQlMNU77/jUqVNQ3boFnS4FgAvQ9CIsZpvs\nZUt22dkhnXZaQKtWsdr772zJLx6efz5ZF11k/q4NB5Gd3cjP/Wh6AThm9OhavfQSuzjgp2pqpFde\n8euCC+xpegGYjaYXYTHbZC+bshs7tk5r1vh04AC7OBxkU36x9MYbfvXsWa+OHc3fteEgsrMb+bkf\nTS8Ax7RqFdLQoQG9+CIjDvgh20YbAJjPEwqFYvJt9OrVq9WvX79YvDQAF1mxwq85c1K1YgV3tKFB\nRYV08snZ+uCDUrVta89KLwDnFBQUaPjw4Uf8HFZ6ATjq7LPrtGOHV199xekIDZYvT9bAgfU0vACi\niqsMwmK2yV62Zef3SxdfXKtFi7ihTbIvv1h48slkXXlljdNlNBnZ2Y383I+mF4DjfvGLhqY3yHas\nCW/LFq+2bk3SqFF2PJACgD1oehEW+xXay8bsevWqV8uWIb3zjs/pUhxnY37R9NRTKRo/vkZ+C+9t\nTPTsbEd+7kfTC8AIV11Vq8cfT3G6DDioulpavDhZ/+f/sGsDgOij6UVYzDbZy9bsLr+8Ru+849Ou\nXYm9Z6+t+UXD8uV+9epVr65d7ZxzSeTs3ID83I+mF4ARMjOlyy6r1RNPsNqbqJ58MkW//KV9N7AB\nsAP79AIwxldfeXXeeZnauLFEqalOV4N4+uILry64IFObNpUomY08ADQR+/QCsMoJJwSVl1evF16g\n60k0jzySqokTa2h4AcQMTS/CYrbJXrZnd9111XrssRTF5mdQ5rM9v0gUFXm0bJlf11xj92hDImbn\nJuTnfjS9AIxyzjkBlZR49P77SU6XgjhZsCBFl1xSqzZtEvQ7HQBxwUwvAOMsWJCiN97waeHCCqdL\nQYyVl0t9+2ZrxYoydetm564NAJzHTC8AK11xRY0+/tinzZtZ7XW7Z55J0aBBARpeADFH04uwmG2y\nlxuyS0uTpkyp1pw5ibeFgxvya6xAQJo7N0VTp1Y7XUpUJFJ2bkR+7kfTC8BIEybUaN06n7Zs4TTl\nVs89l6yOHYMaMKDe6VIAJABmegEYa/bsVH31lVdz51Y6XQqirK5OOu20LD30UKXOPDPgdDkALMdM\nLwCrXXtttV5/3a9t2zhVuc0zzySrc+cgDS+AuOFKgrCYbbKXm7LLypKuuaZGs2cnzmyvm/I7nOpq\n6c9/TtPvflfldClRlQjZuRn5uR9NLwCjTZ3asNr72WecrtziySdT1Lt3QKeeyiwvgPhhpheA8R59\nNEWrVvm1ZEm506WgmSoqpFNPzdbixeXKy6PpBRAdzPQCcIWrr67Rtm1erVnjc7oUNNP8+ak6/fQA\nDS+AuKPpRVjMNtnLjdklJ0szZlTprrvSFHT5MwzcmN9B33zj0SOPpGjGDHfN8h7k5uwSAfm5H00v\nACuMHVun1FRp8eJkp0tBhGbOTNMvf1nD09cAOIKZXgDW2LAhSZMmZei990rUooXT1aAp3nvvX9ll\nZDhdDQC3YaYXgKucdlq9Bg2q0/33pzldCpqgvl76zW/SNXNmJQ0vAMfQ9CIsZpvs5fbs/vjHKi1c\nmKxPP01yupSYcGN+Tz+drLS0kC66qM7pUmLKjdklEvJzP5peAFZp1y6k3/++StOmpbv+pjY32LfP\no3vvTdN991XJ43G6GgCJjJleANYJBqXRozN08cV1mjixxulycATXXttC7doFNWuWO3dsAGCGxsz0\nsuklAOt4vdKcOZUaMyZTP/95rY49Nibfu6OZli3z6+OPk/TWWxVOlwIAjDcgPGab7JUo2fXoEdSE\nCTW6/fZ0xebnVc5wS3779nl0223peuihCqWnO11NfLglu0RFfu5H0wvAWrfcUq2tW71auJC9e01z\n++3puuCCWp1+Ok9eA2AGZnoBWO2zz7w6//xMrVhRxkMPDLFsmV8zZ6bprbdKE2aVF4Cz2KcXgOv9\n7GdB3Xprta67roXq3L0jlhW++cajW29NrLEGAHZoctO7e/du5efnq1evXurfv79WrVoVi7rgMGab\n7JWI2V17bY1atQrpv/871elSms3m/AKBht0arr66JiHHGmzODuSXCJq8e4Pf79fcuXOVl5enwsJC\nDRo0SLt27YpFbQDQKB6P9PDDFRo6NEvDhgU0aFDA6ZIS0p/+lKqUFGn69GqnSwGAn2j2TG9OTo52\n794tv9//g48z0wsg3l5/3adp01po1apStjGLs9df9+mmm1pozZpStW3Lf3sA8RXzmd4VK1aof//+\nP2l4AcAJI0YEdM01NbryygxVs9gYN7t2eTR1agstWFBOwwvAWEdseh944AHl5eX94Nedd94pSSoq\nKtL06dP117/+NS6FIr6YbbJXomd3883VOu64oG65xc79e23Lr6pKmjAhQzfcUJ2Qc7z/zrbs8EPk\n535HnOmdNm2apk2b9pOPV1dX69JLL9Xs2bPVtWvXw/79KVOmKDc3V5KUnZ2tvLw85efnS/rX/1wc\nm3m8efNmo+rhmOPGHns80hVXrNJtt52pRx9N0fXX1xhVn5uOBw3K1/XXt1BGRpFOOeUjSWbVF+/j\ng0yph2Pyc/Pxwd8XFhZKkiZNmqSjafJMbygU0vjx4zV48GBNnjz5sJ/HTC8AJ+3Y4dW552bq0Ucr\nNGRIwOlyXGnGjDQVFCTp+efLlZLidDUAEllMZnrXrVun5557TvPnz1ffvn3Vt29fFRUVRVwkAMRC\n585BLVhQoWuvbaFNm5KcLsd1FixI0cqVfv397xU0vACs0OSmNz8/X7W1tfroo48O/Wrfvn0saoOD\nfvzjHtiD7P4lPz+g2bMrdfnlGfrySzuexWNDfitW+DV7dqoWLSpXq1YWDk7HiA3Z4fDIz/18ThcA\nALE0ZkydSkqqdPHFGXrllTJ16kST1hzr1/s0dWq6Fi4sV5cuPPYZgD2avU/v4TDTC8AkDz+coqef\nTtHy5WVsqxWh9et9uuqqFpo/v0LDhjEnDcAcMd+nFwBsMXVqjcaOrdUll2SouNjjdDnWoeEFYDua\nXoTFbJO9yO7wfvvbap19dp3OOy9Tu3eb2fiamB8Nb+OYmB0aj/zcj6YXQMLweKQ776zW+PE1+vnP\nM/X115wCj+btt2l4AbgDM70AEtJTTyXr3nvTtGhRufLyEvtJYoezcGGyZs5M0//8T4Xy82l4AZir\nMTO97N4AICFddVWtWrYM6eKLM/TYYzzA4t8Fg9Kf/pSq555L1tKlZTrpJHZpAGA/fraHsJhtshfZ\nNd7YsXV6/PEKXX99Cz30UIpi83OvpnE6v+pq6brrWujtt/1auZKGtymczg7NQ37uR9MLIKHl5wf0\n+uulevHFZE2c2ELl5U5X5JydO70aOzZTwaD04ots7QbAXWh6EVZ+fr7TJSBCZNd0nTqFtHx5mdLT\nQxo5MsvRG9ycyu+ll/waPjxTo0fXasGCCqWlOVKG1Xjv2Y383I+mFwAkpaZKDz1UqWuvrdaoUZl6\n8slkI8YdYq2yUpo2LV333JOmZ58t169/XSMvVwYALsSpDWEx22QvsoucxyNdfXWtXnqpTE89laKL\nLspQYWF8T5PxzO/jj5N09tlZqq6W3nyzVP36sYtFc/Desxv5uR9NLwD8yM9+FtSKFWUaMqROZ5+d\nqccfT1bQRfdzHTjg0a23pmncuAzdfHO15s2rVFaW01UBQGyxTy8AHMGWLV5NndpCXq80c2alTj/d\n3tXQYLBh790//jFNo0fX6ne/q1arVgkwwwHA9dinFwCaqXv3oF57rUz/+EeyfvWrFjr55HrNmFGl\nnj3tWfoNhaS1a336wx/SFApJzz5brlNOsbd5B4BIMN6AsJhtshfZRV9SknT55bXasKFU+fkBnX9+\npqZOTde2bdE/hUYzv1BIWrHCr3PPzdQtt6TrmmtqtGJFGQ1vjPDesxv5uR9NLwA0UmqqNGVKjT74\noETHHhvUyJGZuuyyDL3+us+omd+aGum55/waPDhT//VfqZo8uVrr15dq3LhadmYAkLCY6QWACFVV\nSS+8kKzHHktRaalHV19do4suqlWHDvGfkw2FpPffT9LixSl66SW/evas1403VmvEiIA8nriXAwBx\nxUwvAMRQWpo0fnytfvGLWn3wQZKeeCJF+flZ6to1qFGj6vQf/1Gnk0+uj1nTWV0tffihT2vW+PT8\n88ny+RrGMN58s0zHHWfQ0jMAGICmF2GtXbuWp9NYiuziz+ORBgyo14ABlaqrk957z6dXX/Xryitb\nKBDwaODAgHr3Dqh373r17l2vNm0OvxJ8uPyCQWnPHo+++ipJ773n07vv+vTRRz51716v/PyAFiyo\n0CmnxK7BxtHx3rMb+bkfTS8ARJHfL511VkBnnRXQf/1Xlb780quPPvJp06YkzZnj1+bNSWrRQurQ\nIai2bYNq0yaktm1Dat06qFBI+vLLE7VmTapqajyqrpZ27vRq27YkFRZ61apVSF271mvgwHr9+tfV\nOu20gDIznf43BgA7MNMLAHEUDEq7dnlVVOTR99979f33HhUXe7Vvn0der5ScHFJKSsM/U1Oljh2D\n6tq1Xl26BJWe7nT1AGAmZnoBwDBer5SbG1RuriSxdRgAxAub1yAs9iu0F9nZjfzsRXZ2Iz/3o+kF\nAACA6zHTCwAAAKs1ZqaXlV4AAAC4Hk0vwmK2yV5kZzfysxfZ2Y383I+mFwAAAK7HTC8AAACsxkwv\nAAAAIJpeHAazTfYiO7uRn73Izm7k5340vQAAAHA9ZnoBAABgNWZ6AQAAANH04jCYbbIX2dmN/OxF\ndnYjP/ej6QUAAIDrMdMLAAAAqzHTCwAAAIimF4fBbJO9yM5u5GcvsrMb+bkfTS8AAABcj5leAAAA\nWI2ZXgAAAEA0vTgMZpvsRXZ2Iz97kZ3dyM/9aHoBAADgesz0AgAAwGrM9AIAAACKoOktLi7WgAED\ndMopp6hPnz5avHhxLOqCw5htshfZ2Y387EV2diM/9/M19S9kZ2frrbfeUnp6uoqLi9WzZ09dcskl\n8npZNHaToqIip0tAhMjObuRnL7KzG/m5X5ObXp/PJ5+v4a/t379fKSkpUS8KziNXe5Gd3cjPXmRn\nN/JzvyY3vZJUXl6uM844Q19//bUWLlzIKi8AAACMdsRu9YEHHlBeXt4Pft15553KyMjQ5s2bVVBQ\noOnTp6uioiJe9SJOCgsLnS4BESI7u5GfvcjObuTnfs3esmz48OG67777dOqpp/7g48uXL1dqamqz\nigMAAACOprq6Wuedd94RP6fJTe+ePXuUkpKiNm3aqKioSKeeeqo2btyoNm3aNKtYAAAAIFaaPNNb\nWFio6667TpIUCoU0e/ZsGl4AAAAYLWZPZAMAAABMwbYLAAAAcD2aXgAAALheRPv0NtaXX36pRx99\nVPX19crNzdVNN90Uyy+HKKuqqtK0adM0evRojRkzxuly0Ej79u3TX/7yF1VWVsrn8+mKK65Q7969\nnS4LjfDuu+9q0aJFkqSrrrpK/fv3d7giNAbvOXfgmmenpvSaMWt6g8GgHn74YU2ZMkXdu3dXWVlZ\nrL4UYuT5559Xt27d5PF4nC4FTZCUlKRrr71Wubm5+v777/X73/9e8+bNc7osHEUgENDChQs1a9Ys\n1dbWaubMmTS9luA95w5c8+zT1F4zZk3v1q1blZWVpe7du0uSMjMzY/WlEAN79uxRaWmpunXrJu51\ntEt2drays7MlSW3btlUgEFAgEDj0+HCY6csvv1SnTp2UlZUlqSG77du3q0uXLs4WhqPiPWc/rnl2\namqvGbOZ3u+//17p6emaNWuWbr/9dq1cuTJWXwoxsHDhQl166aVOl4Fm+vjjj9WtWzcuvhYoKSlR\nq1at9Prrr2v9+vXKzs7WgQMHnC4LTcR7zk5c8+zU1F4zKu/K5cuX64033vjBx2pqalReXq7Zs2cr\nPT1dd9xxh0455RTl5ORE40siSsJl5/f7lZeXp7Zt2/Idr+HC5Tdw4EBdfvnlOnDggJ5++mndfvvt\nDlWHSIwYMUKStGHDBocrQVPxnrPTBx98oGOPPZZrnoXq6uq0ZcuWRveaUWl6zzvvvJ88+m3z5s1a\ntGjRoQdXdOvWTbt376bpNUy47J599lm9++67+uCDD1RaWiqv16tWrVopPz/foSpxOOHyk6Ta2lrN\nmTNHV111Fe85S7Rs2VL79+8/dHxw5Rd24D1nr6+++kobNmzgmmehli1bqlOnTo3uNWP285fjjz9e\n33//vcrLy5WamqrCwkIdc8wxsfpyiKJx48Zp3LhxkqQlS5YoLS2NN79FQqGQ/vrXvyo/P199+vRx\nuhw00gknnKBdu3aptLRUtbW1Ki4uVufOnZ0uC43Ae85uXPPs1dReM2ZNb3p6uiZMmKB77rlH9fX1\nys/PV4cOHWL15QD8ry1btmjDhg3as2ePVq1aJUn67W9/q5YtWzpcGY7E5/Np/PjxmjFjhiRpwoQJ\nzhaERuM9Bzijqb0mjyEGAACA6/FENgAAALgeTS8AAABcj6YXAAAArkfTCwAAANej6QUAAIDr0fQC\nAADA9Wh6AQAA4Ho0vQAAAHC9/w8SA8Mh7xQ32gAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 45 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "P = np.array([[2,2.4],[2.4,6]])\n", - "e = stats.sigma_ellipse (P, 0, 0)\n", - "stats.plot_sigma_ellipse(e, '|2.0 2.4|\\n|2.4 6.0|')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAGNCAYAAAActsnoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nR9MLAAAAx/t/RnocGkqbtNEAAAAASUVORK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 46 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, not independent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n", - "\n", - "$$\n", - "P = \\begin{pmatrix}\n", - " \\sigma_1^2 & p\\sigma_1\\sigma_2 \\\\\n", - " p\\sigma_2\\sigma_1 &\\sigma_2^2 \n", - " \\end{pmatrix}\n", - "$$\n", - "\n", - "Look at the computation for the off diagonal elements. \n", - "\n", - "$$\\begin{align*}\n", - "P_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", - "P_{1,0}&=p\\sigma_2\\sigma_1.\n", - "\\end{align*}$$\n", - "\n", - "If we re-arrange terms we get\n", - "$$\\begin{align*}\n", - "P_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", - "P_{1,0}&=p\\sigma_1\\sigma_1 \\mbox{, yielding} \\\\\n", - "P_{0,1}&=P_{1,0}\n", - "\\end{align*}$$\n", - "\n", - "In general, we can state that $P_{i,j}=P_{j,i}$.\n", - "\n", - "So for my example I multiplied the diagonals, 2 and 6, to get 12, and then scaled that with the arbitrarily chosen $p=.2$ to get 2.4.\n", - "\n", - "Let's get back to concrete terms. Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def plot_track(noise, count, R, Q=0, plot_P=True, title='Kalman Filter'):\n", - " dog = DogSensor(velocity=1, noise=noise)\n", - " f = dog_tracking_filter(R=R, Q=Q, cov=20.)\n", - "\n", - " ps = []\n", - " zs = []\n", - " cov = []\n", - " for t in range (count):\n", - " z = dog.sense()\n", - " f.measure (z)\n", - " ps.append (f.x[0,0])\n", - " cov.append(f.P)\n", - " zs.append(z)\n", - " f.predict()\n", - "\n", - " p0, = plt.plot([0,count],[0,count],'g')\n", - " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", - " p2, = plt.plot(range(1,count+1),ps, c='b')\n", - " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", - " plt.title(title)\n", - "\n", - " for i,p in enumerate(cov):\n", - " e = stats.sigma_ellipse (p, i+1, ps[i])\n", - " stats.plot_sigma_ellipse(e, axis_equal=False)\n", - " if i == len(cov)-1:\n", - " s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n", - " plt.text (30,1,s,fontsize=18)\n", - " s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n", - " plt.text (30,-4,s,fontsize=18)\n", - " plt.xlim((0,40))\n", - " plt.ylim((0,40))\n", - " plt.axis('equal')\n", - " \n", - " plt.show()\n", - "\n", - "\n", - "plot_track (noise=5, R=5, Q=5, count=20, title='R = 5')\n", - "plot_track (noise=5, R=.5, Q=5, count=20, title='R = 0.5')" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF9CAYAAAAHja6eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIgAsDAmIiIiIgLAwpiIiIiICADw/5SsbYw+YWCiAAAAAElFTkSuQmCC\n", - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZN3TeDfbWwAAAABJRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 47 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $P=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slighly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n", - "\n", - "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n", - "\n", - "The first plot, with $R=5$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85, and the variance for velocity is 3.0. \n", - "\n", - "In contrast, the second plot, with $R=0.5$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $R$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. \n", - "\n", - "** EXPLAIN WHY SECOND PLOT ELLIPSE IS TALLER THAN WIDE!!!**\n", - "\n", - "Keep looking at these plots until you grasp how the covariance matrix $P$ has a real, physical interpretation. When you start dealing with a, say, $9\\times 9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9\\times 9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intution and understanding in this simple, 2-D case. \n", - "\n", - "> **sidebar**: when plotting covariance ellipses, make sure to always use *plt.axis('equal')* in your code. If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall.\n", - "\n", - "** I am confused. formula for P suggests correlation is pre-ordained. why would correlation between, say x'' and Z be the same as the correlation between x' and y''? Sure, # will be different, but p is the same for both. I confused.**\n", - "\n", - "** Question: why can't I effect the velocity variance directly? Is it just because it is unobserved **\n", - "\n", - "** question: why are Q and R scalar? Are they always scalar? ** - So no. I think I am 'getting lucky' with them being scalars. \n", - "\n", - "** I seem to be conflating Q with motion, but Q is the 'process noise'. I still don't have a handle on that at all!!!!**\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "from IPython.core.display import HTML\n", - "def css_styling():\n", - " styles = open(\"./styles/custom2.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, "outputs": [ { "html": [ @@ -1451,13 +236,1218 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 48, + "prompt_number": 1, "text": [ - "" + "" ] } ], - "prompt_number": 48 + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "

Multidimensional

\n", + "

Kalman Filters

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Introduction\n", + "The techniques in the last chapter are very powerful, but they only work in one dimension. The gaussians represent a mean and variance that are scalars - real numbers. They provide no way to represent multidimensional data, such as the position of a dog in a field. You may retort that you could use two Kalman filters for that case, one tracks the x coordinate and the other tracks the y coordinate. That does work in some cases, but put that thought aside, because soon you will see some enormous benefits to implementing the multidimensional case.\n", + "\n", + "\n", + "###Multivariate Normal Distributions\n", + "\n", + "\n", + "What might a *multivariate normal distribution* look like? In this context, multivariate just means multiple variables. Our goal is to be able to represent a normal distribution across multiple dimensions. Consider the 2 dimensional case. Let's say we believe that $x = 2$ and $y = 7$. Therefore we can see that for $N$ dimensions, we need $N$ means, like so:\n", + "\n", + "$$\n", + "\\mu = \\begin{bmatrix}{\\mu}_1\\\\{\\mu}_2\\\\ \\vdots \\\\{\\mu}_n\\end{bmatrix}\n", + "$$\n", + "\n", + "Therefore for this example we would have\n", + "\n", + "$$\n", + "\\mu = \\begin{bmatrix}2\\\\7\\end{bmatrix} \n", + "$$\n", + "\n", + "The next step is representing our variances. At first blush we might think we would also need N variances for N dimensions. We might want to say the variance for x is 10 and the variance for y is 8, like so. \n", + "\n", + "$$\\sigma^2 = \\begin{bmatrix}10\\\\8\\end{bmatrix}$$ \n", + "\n", + "While this is possible, it does not consider the more general case. For example, suppose we were tracking house prices vs total $m^2$ of the floor plan. These numbers are *correlated*. It is not an exact correlation, but in general houses in the same neighborhood are more expensive if they have a larger floor plan. We want a way to express not only what we think the variance is in the price and the $m^2$, but also the degree to which they are correlated. It turns out that we use the following matrix to denote *covariances* with multivariate normal distributions. You might guess, correctly, that *covariance* is short for *correlated variances*." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\Sigma = \\begin{pmatrix}\n", + " \\sigma_1^2 & p\\sigma_1\\sigma_2 & \\cdots & p\\sigma_1\\sigma_n \\\\\n", + " p\\sigma_2\\sigma_1 &\\sigma_2^2 & \\cdots & p\\sigma_2\\sigma_n \\\\\n", + " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + " p\\sigma_n\\sigma_1 & p\\sigma_n\\sigma_2 & \\cdots & \\sigma_n^2\n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "If you haven't seen this before it is probably a bit confusing at the moment. Rather than explain the math right now, we will take our usual tactic of building our intuition first with various physical models. At this point, note that the diagonal contains the variance for each state variable, and that all off-diagonal elements are a product of the $\\sigma$ corresponding to the $i$th (row) and $j$th (column) state variable multiplied by a constant $p$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, without explanation, here is the full equation for the multivarate normal distribution in $n$ dimensions.\n", + "\n", + "$$\\mathcal{N}(\\mu,\\,\\Sigma) = (2\\pi)^{-\\frac{n}{2}}|\\Sigma|^{-\\frac{1}{2}}\\, e^{ -\\frac{1}{2}(\\mathbf{x}-\\mu)'\\Sigma^{-1}(\\mathbf{x}-\\mu) }$$\n", + "\n", + "I urge you to not try to remember this function. We will program it in a Python function and then call it when we need to compute a specific value. However, if you look at it briefly you will note that it looks quite similar to the *univarate normal distribution* except it uses matrices instead of scalar values, and the root of $\\pi$ is scaled by $n$. Here is the *univariate* equation for reference:\n", + "\n", + "$$ \n", + "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{{-\\frac{1}{2}}{(x-\\mu)^2}/\\sigma^2 }\n", + "$$\n", + "\n", + "If you are reasonably well-versed in linear algebra this equation should look quite managable; if not, don't worry! If you want to learn the math we will cover it in detail in the next optional chapter. If you choose to skip that chapter the rest of this book should still be managable for you\n", + "\n", + "I have programmed it and saved it in the file *stats.py* with the function name *multivariate_gaussian*. I am not showing the code here because I have taken advantage of the linear algebra solving apparatus of numpy to efficiently compute a solution - the code does not correspond to the equation in a one to one manner. If you wish to view the code, I urge you to either load it in an editor, or load it into this worksheet by putting *%load -s multivariate_gaussian stats.py* in the next cell and executing it with ctrl-enter. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ">As of version 0.14 scipy.stats has implemented the multivariate normal equation with the function **multivariate_normal()**. It is superior to my function in several ways. First, it is implemented in Fortran, and is therefore faster than mine. Second, it implements a 'frozen' form where you set the mean and covariance once, and then calculate the probability for any number of values for x over any arbitrary number of calls. This is much more efficient then recomputing everything in each call. So, if you have version 0.14 or later you may want to substitute my function for the built in version. Use **scipy.version.version** to get the version number. I deliberately named my function **multivariate_gaussian()** to ensure it is never confused with the built in version.\n", + "\n", + "> If you intend to use Python for Kalman filters, you will want to read the tutorial for the scipy.stats module, which explains 'freezing' distributions and other very useful features. As of this date, it includes an example of using the multivariate_normal function, which does work a bit differently from my function." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from stats import gaussian, multivariate_gaussian" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's use it to compute a few values just to make sure we know how to call and use the function, and then move on to more interesting things.\n", + "\n", + "First, let's find the probability for our dog being at (2.5, 7.3) if we believe he is at (2,7) with a variance of 8 for $x$ and a variance of 10 for $y$. This function requires us to pass everything in as numpy arrays (we will soon provide a more robust version that works with numpy matrices, numpy arrays, and/or scalars in any combinations. That code contains a lot of boilerplate which obscures the algorithm).\n", + "\n", + "Start by setting $x$ to (2.5,7.3):" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "x = np.array([2.5, 7.3])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we set the mean of our belief:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mu = np.array([2,7])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we have to define our covariance matrix. In the problem statement we did not mention any correlation between $x$ and $y$, and we will assume there is none. This makes sense; a dog can choose to independently wander in either the $x$ direction or $y$ direction without affecting the other. If there is no correlation between the values you just fill in the diagonal of the covariance matrix with the variances. I will use the seemingly arbitrary name $P$ for the covariance matrix. The Kalman filters use the name $P$ for this matrix, so I will introduce the terminology now to avoid explaining why I change the name later. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "P = np.array([[8.,0],[0,10.]])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now just call the function" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print(multivariate_gaussian(x,mu,P))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0174395374407\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check the probability for the dog being at exactly (2,7)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import print_function\n", + "\n", + "x = np.array([2,7])\n", + "print(\"Probability dog is at (2,7) is %.2f%%\" % (multivariate_gaussian(x,mu,P) * 100.))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Probability dog is at (2,7) is 1.78%\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These numbers are not easy to interpret. Let's plot this in 3D, with the $z$ (up) coordinate being the probability." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.pylab as pylab\n", + "from matplotlib import cm\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "import numpy as np\n", + "\n", + "pylab.rcParams['figure.figsize'] = 12,6\n", + "pylab.rcParams['axes.color_cycle'] = '348ABD, 7A68A6, A60628, 467821, CF4457, 188487, E24A33'\n", + "\n", + "P = np.array([[8.,0],[0,10.]])\n", + "mu = np.array([2,7])\n", + "\n", + "xs, ys = np.arange(-8, 13, .5), np.arange(-8, 20, .5)\n", + "xv, yv = np.meshgrid (xs, ys)\n", + "\n", + "zs = np.array([100.* multivariate_gaussian(np.array([x,y]),mu,P) \\\n", + " for x,y in zip(np.ravel(xv), np.ravel(yv))])\n", + "zv = zs.reshape(xv.shape)\n", + "\n", + "ax = plt.figure().add_subplot(111, projection='3d')\n", + "ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n", + "\n", + "ax.set_xlabel('X')\n", + "ax.set_ylabel('Y')\n", + "\n", + "ax.contour(xv, yv, zv, zdir='x', offset=-9, cmap=cm.autumn)\n", + "ax.contour(xv, yv, zv, zdir='y', offset=20, cmap=cm.BuGn)\n", + "plt.xlim((-10,15))\n", + "plt.ylim((-10,20))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 8, + "text": [ + "(-10, 20)" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAqsAAAFdCAYAAAAkOCRoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngiAIgvBa/h8V+7yxE2a+PQAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result is clearly a 3D bell shaped curve. We can see that the gaussian is centered around (2,7), and that the probability quickly drops away in all directions. On the sides of the plot I have drawn the Gaussians for $x$ in greens and for $y$ in orange.\n", + "\n", + "As beautiful as this is, it is perhaps a bit hard to get useful information. For example, it is not easy to tell if $x$ and $y$ both have the same variance or not. So for most of the rest of this book we will display multidimensional Gaussian using contour plots. I will use some helper functions in *gaussian.py* to plot them. If you are interested in linear algebra go ahead and look at the code used to produce these contours, otherwise feel free to ignore it." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import stats\n", + "\n", + "P = np.array([[2,0],[0,2]])\n", + "plt.subplot(131)\n", + "stats.plot_covariance_ellipse(P, x=2, y=7, title='|2 0|\\n|0 2|')\n", + "\n", + "plt.subplot(132)\n", + "P = np.array([[2,0],[0,9]])\n", + "stats.plot_covariance_ellipse(P, x=2, y=7, title='|2 0|\\n|0 9|')\n", + "\n", + "plt.subplot(133)\n", + "P = np.array([[2,1.2],[1.2,2]])\n", + "stats.plot_covariance_ellipse(P, x=2, y=7, title='|2 1.2|\\n|1.2 2|')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAA1MAAAGpCAYAAABoLmzKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From a mathematical perspective these display the values that the multivariate gaussian takes for a specific sigma (in this case $\\sigma^2=1$. Think of it as taking a horizontal slice through the 3D surface plot we did above. However, thinking about the physical interpretation of these plots clarifies their meaning.\n", + "\n", + "The first plot uses the mean and covariance matrices of\n", + "$$\n", + "\\begin{align*}\n", + "\\mu &= \\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", + "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&2\\end{bmatrix}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "Let this be our current belief about the position of our dog in a field. In other words, we believe that he is positioned at (2,7) with a variance of $\\sigma^2=2$ for both x and y. The contour plot shows where we believe the dog is located with the '+' in the center of the ellipse. The ellipse shows the boundary for the $1\\sigma^2$ probability - points where the dog is quite likely to be based on our current knowledge. Of course, the dog might be very far from this point, as Gaussians allow the mean to be any value. For example, the dog could be at (3234.76,189989.62), but that has vanishing low probability of being true. Generally speaking displaying the $1\\sigma^2$ to $2\\sigma^2$ contour captures the most likely values for the distribution. An equivelent way of thinking about this is the circle/ellipse shows us the amount of error in our belief. A tiny circle would indicate that we have a very small error, and a very large circle indicates a lot of error in our belief. We will use this throughout the rest of the book to display and evaluate the accuracy of our filters at any point in time. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second plot uses the mean and covariance matrices of\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", + "\\sigma^2 &= \\begin{bmatrix}2&0\\\\0&9\\end{bmatrix}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "This time we use a different variance for $x$ (2) vs $y$ (9). The result is an ellipse. When we look at it we can immediately tell that we have a lot more uncertainty in the $y$ value vs the $x$ value. Our belief that the value is (2,7) is the same in both cases, but errors are different. This sort of thing happens naturally as we track objects in the world - one sensor has a better view of the object, or is closer, than another sensor, and so we end up with different error rates in the different axis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third plot uses the mean and covariance matrices of:\n", + "$$\n", + "\\begin{align*}\n", + "\\mu &=\\begin{bmatrix}2\\\\7\\end{bmatrix} \\\\\n", + "\\sigma^2 &= \\begin{bmatrix}2&1.2\\\\1.2&2\\end{bmatrix}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "This is the first contour that has values in the off-diagonal elements of $cov$, and this is the first contour plot with a slanted ellipse. This is not a coincidence. The two facts are telling use the same thing. A slanted ellipse tells us that the $x$ and $y$ values are somehow **correlated**. We denote that in the covariance matrix with values off the diagonal. What does this mean in physical terms? Think of trying to park your car in a parking spot. You can not pull up beside the spot and then move sideways into the space because most cars cannot go purely sideways. $x$ and $y$ are not independent. This is a consequence of the steering system in a car. When your tires are turned the car rotates around its rear axle while moving forward. Or think of a horse attached to a pivoting exercise bar in a corral. The horse can only walk in circles, he cannot vary $x$ and $y$ independently, which means he cannot walk straight forward to to the side. If $x$ changes, $y$ must also change in a defined way. \n", + "\n", + "So when we see this ellipse we know that $x$ and $y$ are correlated, and that the correlation is \"strong\". I will not prove it here, but a $45^\\circ$ angle denotes complete correlation between $x$ and $y$, whereas $0^\\circ$ and $90^\\circ$ denote no correlation at all. Those who are familiar with this math will be objecting quite strongly, as this is actually quite sloppy language that does not adress all of the mathematical issues. They are right, but for now this is a good first approximation to understanding these ellipses from a physical interpretation point of view. The size of the ellipse shows how much error we have in each axis, and the slant shows how strongly correlated the values are.\n", + "\n", + "A word about **correlation** and **independence**. If variables are **independent** they can vary separately. If you walk in an open field, you can move in the $x$ direction (east-west), the $y$ direction(north-south), or any combination thereof. Independent variables are always also **uncorrelated**. Except in special cases, the reverse does not hold true. Variables can be uncorrelated, but dependent. For example, consider the pair$(x,y)$ where $y=x^2$. Correlation is a linear measurement, so $x$ and $y$ are uncorrelated. However, they are obviously dependent on each other. \n", + "\n", + "** wikipedia article 'correlation and dependence' claims multivariate normals are a special case, where the correlation coeff $p$ completely defines the dependence. FIGURE THIS OUT!**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Unobserved Variables\n", + "\n", + "Let's say we are tracking an aircraft and we get the following data for the $x$ coordinate at time $t$=1,2, and 3 seconds. What does your intuition tell you the value of $x$ will be at time $t$=4 seconds?\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import mkf_internal\n", + "mkf_internal.show_position_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF/CAYAAABKRQ+VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAHChJREFUeJzt3X+s1nWhB/D3OZzjQSIOivkDJ+aPKf5A48eWIiqKel3L\n25y75bRc3eEtcWpNbU1tq0V1uQ6dc2qh7U5cZia5LLvThjW1siGUYkO5rewQBIQIyiE4HM5z//BC\nkRy+J4TzfL74em1sfM/zcJ6P7M3xzXPez0NLo9FoBAAA3uVam30AAAAogWIMAABRjAEAIIliDAAA\nSRRjAABIohgDAECSpK3ZB9jmueeeS3d3d7OPAQDAPmzkyJGZOHHiTm8rphh3d3dnwoQJzT4GvM0P\nf/jDXHTRRc0+BuyUfFIq2aRUixYt6vc2Uwqo0NXV1ewjQL/kk1LJJnWkGAMAQBRjqHTeeec1+wjQ\nL/mkVLJJHSnGUOH4449v9hGgX/JJqWSTOlKMocKzzz7b7CNAv+STUskmdaQYAwBAFGOoNGXKlGYf\nAfoln5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUom\nn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RK\nNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkj\nxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgA\nAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIY\nQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7\nOUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUom\nn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RK\nNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkj\nxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgA\nAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIYQyU7OUomn5RKNqkjxRgAAKIY\nQyU7OUomn5Ri69Zk6dLWPPjgfpkxY1iuuqojDz/cnt/9rjV9fc0+HQxM22A8yGuvvZYLL7wwW7Zs\nSaPRyM0335yPfvSjg/HQAMBetnFj8qMftee6696TzZtbtn/8u99N9t+/kbvv7s6FF25JR0cTDwkD\n0NJoNBp7+0F6e3vT09OTYcOG5bXXXssJJ5yQlStXprX1b09Yz58/PxMmTNjbRwEA9rD/+Z+2XH75\n8CQtO729paWRRx7ZkHPO6R3cg8FOLFq0KNOmTdvpbYMypWhra8uwYcOSJK+//no6/JURAPYJq1a1\n5AtfGJb+SnGSNBotufnm/bN2bf/3gRIM2sZ4w4YNGTduXE455ZTceeedOzxbDCWz4aRk8kmzLV06\nJMuWDam838svt2XpUv/vp2yDltDhw4dn8eLFWbRoUW644YZ0d3cP1kMDAHvJP/Ms8Ouve8aYsg3K\ni+/+3tixY3PkkUdmyZIlmTRp0g63zZgxI2PGjEmSdHZ2Zty4cdvfB3HbsyKuXQ/29ZQpU4o6j2vX\n8um6pOstWzYkGZ6B2G+/5p/X9bvvevHixVm/fn2SpKurK9OnT09/BuXFdytWrEhHR0dGjRqVlStX\nZtKkSXnhhRcyatSo7ffx4jsAqJ9XXmnN1Kkjdng3ip0ZPryRn/3sjRx9tPduo7ma/uK7rq6unHPO\nOTnllFNy/vnnZ/bs2TuUYijZtr99Qonkk2Y75pi+TJ++ufJ+11yzKUcdpRRTtrbBeJDTTjstL774\n4mA8FAAwiNrakv/4j0154YUhefbZ9p3e54ILenL55ZvTYmJM4bw8FCps2ylBieSTEhxxRCP33NOd\nb3xjQ449tnf7x8eO7c29927I7bdvzOjRe325Ce/YoDxjDADs2w4/vJGPfnRLzj23N6+91pKWluSg\ngxo58ECFmPrwjDFUsOGkZPJJaQ46qJHjj+/L6tVPK8XUjmIMAABRjKGSDSclk09KJZvUkWIMAABR\njKGSDSclk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGS\nnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwl\nk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09K\nJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvU\nkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIM\nAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABR\njKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGS\nnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwl\nk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09K\nJZvUkWIMAABRjKGSnRwlk09KJZvUkWIMAABRjKGSnRwlk09KJZvU0YCLcU9PT1588cU8/fTTSZLu\n7u5s3Lhxrx0MAAAGU9tA7rR06dLMnj07I0aMyMqVK3PWWWflpZdeyrPPPpvrr79+b58RmspOjpLJ\nJ6WSTepoQM8Yf+tb38pnPvOZ3HrrrWlre6tLn3rqqVmyZMlePRwAAAyWARXj1atX5wMf+MAOH2tv\nb09fX99eORSUxE6OksknpZJN6mhAxfjII4/MU089tcPHFixYkKOOOmqvHAoAAAZbS6PRaFTdqaur\nKzNnzswBBxyQZcuW5aSTTsqyZcty0003ZcyYMXvkIPPnz8+ECRP2yOcCAICdWbRoUaZNm7bT2wb0\n4rsxY8bkjjvuyMKFC/Paa6/loIMOyoQJE7L//vvv0YMCMDCrV7dk8+aWtLc3csghjbS0NPtEAPU3\n4Ldra29vz4knnpgzzjgjxx9/fLq7u7NmzZq9eTYogp0cJVm6tDVz5uyXadNGZPz4EZkyZURuvXVo\nFi8ekurv/8Hg8bWTOhrQM8Zz5szJM888k+HDh6e1dccufdddd1X++uXLl+djH/tY1q1bl46Ojsya\nNSvnnXfe7p0Y4F3q178ekn/7t+FZu/ZvX4fXrm3Jf/7n/rn99qH59rc35Jxzej17DLCbBlSMn3/+\n+Xzzm9/MsGHDdutB2tvbc88992TcuHHp6urK5MmT86c//Wm3PhcMNu/FSQlefbU1H/vYjqX4723e\n3JLLLx+eJ598I+PGeccgms/XTupoQMX43HPPzVe/+tUcdthhb3vGeMaMGZW//uCDD87BBx+c5K29\nck9PT7Zs2ZL29vbdODLAu89vfjMka9bsev22eXNLnnxyv4wbt2mQTgWwbxnQxvipp57KSSedlBNP\nPPFtP/5ZTzzxRCZOnKgUUxt2cjRbb2/y3/+934Due999HVm1ypaC5vO1kzoa0DPGRx11VE4++eQc\ncsghOzxj3PJPDtlWrlyZG264IY899thOb58xY8b2t3/r7OzMuHHjtn8rZtsfMNeuXbt+t10vXvxK\n1q2blIFYv74lXV1/zv/+7++KOb/rd+f1NqWcx/W793rx4sVZv359krfegnj69Onpz4Dex/jqq6/u\n97aBvPguSTZt2pTzzz8/X/ziF3PBBRe87XbvYwywc319yb//+3vy2GPVzxofffTWPPnkGznwwEE4\nGEANveP3MR5o+e1Po9HIpz71qVx22WU7LcUA9K+1Nbniis0DKsbXXbdJKQbYTQN+H+Odufvuuwd0\nv5///OeZN29e5syZk/Hjx2f8+PFZuXLlO3loGDT/+G1BaIYTT9ya8eN7d3mfQw7py+mn7/o+MFh8\n7aSO3lExfu655wZ0vylTpqSnpye//vWvt/849NBD38lDA7yrHHpoI3PmdGfChC07vf3ww7fm4Yff\nzLHHeqs2gN3V75Ri3rx5ueSSS5IkDz30UFpaWrJtjrzt5729nplg37dtwA/Ndswxffn2t7uzZMmQ\nPPjgfvnDH4bkfe/ryyc+sTknn7w1Rxzhn76jHL52Ukf9FuO1a9du//kPfvCDnHnmmTvc3mg0MoDX\n7QGwBx1ySCOHHNKbqVN7s2lT0tER/9IdwB7SbzG+8sort/+8vb19p/+Qx69+9au9cyooyLPPPuuZ\nD4o0dKh8Ui7ZpI4GtDG+7rrrdvrx4447bo8eBgAAmmWX72N8/fXXZ/bs2YNyEO9jDADA3rar9zHe\n5TPGf/nLX/bKgQAAoDS7LMaNRiOrVq3a5Q/Y13kvTkomn5RKNqmjXf7Ldz09Pbn22mt3+Qm++93v\n7tEDAQBAM+yyGHd0dGTu3LmDdRYokldVUzL5pFSySR29o3/5DgAA9hW7LMZjx44drHNAsezkKJl8\nUirZpI52WYxvuummwToHAAA0lSkFVLCTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIox\nVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKT\no2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2Ty\nSalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalk\nkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpS\njAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEA\nIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIox\nVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKT\no2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2Ty\nSalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalkkzpSjAEAIIoxVLKTo2TySalk\nkzpqa/YBoFR//GNrli1rydatLRk1qi/HHNOX/fdv9qkAgL1l0J4xvuGGG3LooYdm3Lhxg/WQsFuW\nLWvJbbd15Oyz35t//dcRufji9+bss0fkqquG5YUXfJOFsthxUirZpI4G7f/yl1xySR5//PHBejjY\nLX/6U0tmzHhPZs4cljfe+Nsfj0ajJY891pEPf3hEnn9+SBNPCADsLYNWjE8//fSMGjVqsB4OdsuP\nf9yen/+8vd/bu7tb8ulPD8vq1S2DeCronx0npZJN6sj3heH/LV/ekttuqx4R/+EPbXn5Zc8aA8C+\nRjGG/7diRWtWrx7YH4klSxRjymDHSalkkzoq6l0pZsyYkTFjxiRJOjs7M27cuO3fitn2B8y16711\nvXHjqUlGZCA2buzJL3/5y5x++unFnN+1a9euS7reppTzuH73Xi9evDjr169PknR1dWX69OnpT0uj\n0Wj0e+se9uqrr+aiiy7K4sWL33bb/PnzM2HChME6CrzN73/fmrPPHpHu7ur98He+82b+5V96B+FU\nAMCetGjRokybNm2ntw3alOLqq6/O5MmT88orr+SII47Ij370o8F6aBiQ97+/L1deuanyfgce2JcT\nTtg6CCcCAAbToBXju+66KytWrEhPT0+WLVuWD3/4w4P10DAgra3JpZf2ZPToXZXeRu64Y2PGjBm0\nb7TALv3jt62hFLJJHXnxHfyd447ryyOPbMjUqVuS7Fh+R4/uy4MPbsi0aVuaczgAYK9qa/YBoDRj\nx/Zl7twNWbp0SH7/+9b09iYHH9zICSdszWGHeaaYsmx7gQmURjapI8UYdmL48GTChK2ZMMGWGADe\nLUwpoIKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGM\noZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKd\nHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWT\nT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0ol\nm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SR\nYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwA\nAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGM\noZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKd\nHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWT\nT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0ol\nm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SR\nYgwAAFGMoZKdHCWTT0olm9SRYgwAAFGMoZKdHCWTT0olm9SRYgwVVq5c2ewjQL/kk1LJJnWkGEOF\njo6OZh8B+iWflEo2qSPFGAAAohhDpa6urmYfAfoln5RKNqmjlkaj0Wj2IZJk4cKFWbduXbOPAQDA\nPmzkyJGZOHHiTm8rphgDAEAzmVIAAEAUYwAASKIYAwBAEsUYAACSJG3NPgCUau7cuXnmmWcyYsSI\nzJ49u9nHge3Wrl2b22+/PRs3bkxbW1suv/zynHLKKc0+FiRJ3nzzzXzta19Lb29vkuTiiy/O5MmT\nm3wqGBjvSgH9WLp0adra2nLXXXcpxhRl/fr1Wb9+fcaMGZM1a9bklltuyTe+8Y1mHwuSJFu3bk1v\nb286Ojry5ptv5nOf+1zmzJmT1lbfpKZ8njGGfhx33HFZvXp1s48Bb9PZ2ZnOzs4kyUEHHZTe3t70\n9vamrc2XdJpvyJAhGTJkSJKku7s77e3tTT4RDJyvogA19pvf/CZHH320UkxRNm3alJtvvjmrVq3K\ntdde69liakNSAWpq3bp1eeCBBzJ9+vRmHwV2MHTo0MyePTuzZs3KAw88kE2bNjX7SDAgijFADfX0\n9OS2227LFVdckYMPPrjZx4GdOvzww/O+970vy5cvb/ZRYEAUY4CaaTQaufvuuzNlypSceuqpzT4O\n7GDt2rV58803k7z1XY0VK1b4yxu14V0poB/33XdfFixYkDfeeCMjR47M9OnTM3HixGYfC/Lyyy/n\ny1/+co444ojtH7vpppsycuTIJp4K3rJ06dLMmTMnyVt/ibvkkku8XRu1oRgDAEBMKQAAIIliDAAA\nSRRjAABIohgDAEASxRgAAJIoxgAAkEQxBqiFNWvW5IorrsjuvMPmvffem3nz5u2FUwHsW7yPMcAe\ndPXVV2f9+vVpbW3NsGHDMnny5Hz84x9Pa+veex7i4YcfzqpVq3LNNdfstccAeDdoa/YBAPY1X/jC\nF3LyySdnxYoV+dKXvpTDDjss559/frOPBUAFxRhgLxk9enTGjh2bZcuWZePGjbnvvvvywgsvZNiw\nYbn44otz7rnnbr/v97///TzxxBPZtGlTRo8enRtvvDEHHnhgkuSWW27JH//4x/T09OQ73/nO9mef\nlyxZkq9//evp7e1No9HIggUL0tLSkjvvvDMjRozIwoULc8cdd2TLli35yEc+kksvvXSH8z3yyCOZ\nP39+tm7dmsmTJ+cTn/hEhgwZktWrV+eaa67JFVdckUcffTRDhw7NZz/72Rx77LGD95sH0AQ2xgB7\n2LaFWldXV5YsWZKjjjoqDz30UDZt2pR77rknN954Yx544IG8+uqrSZIVK1bk0UcfzcyZM3P//fdn\n+vTpaW9v3/75Zs6cmdtuu+1tj3PCCSdk7ty5ufjii3PGGWdk7ty5uf/++zNixIgkycSJEzN37tyc\neeaZaWlp2eHXPvfcc/nZz362/XO/8soreeKJJ3a4z1//+tfMmTMnkyZNyve+9709+VsEUCTPGAPs\nYbfeemuGDBmS4cOH57zzzsvUqVPzyCOPZMaMGdlvv/0yZsyYTJw4MQsWLMj73//+JElfX1+WL1+e\nAw44IMccc8zbPueuXg7SaDQqX5T3j7c///zzOeusszJq1KgkyQUXXJCnn346H/rQh7bf54ILLkhr\na2vGjx+fRYsWDfQ/H6C2FGOAPezzn/98Tj755B0+tm7duowcOXL79ciRI7Nu3bokb00urrzyysyb\nNy+33357Tj311Fx11VXZf//999oZ33jjjRx33HHbrzs7O7efZ5vhw4cnSdra2rJly5a9dhaAUphS\nAAyCzs7OvP7669uv/7EoT506NV/5yldy55135s9//nN++tOfDvhzD+QdL/5xSjFixIgdivC6devS\n2dk54McE2BcpxgCDYNKkSXn88cfT09OTrq6uLFy4MBMnTkySrFq1Ki+99FJ6e3vT2tqaRqORYcOG\nDfhzjxw5MitWrEhfX99Ob9/Z1GLSpEl5+umns2bNmmzYsCE/+clPMmnSpN3/DwTYB5hSAAyCSy+9\nNPfee2+uuuqqDB06NJdddlmOPvroJElvb28efPDBLF++PG1tbfngBz+Ys846K0ny29/+NrNmzdpe\nbD/5yU+mpaUls2bNyqGHHpokmTx5cn7xi1/k05/+dNra2vJf//Vfee9735uZM2dm6dKl2bJlS1pa\nWvLjH/84p512WmbMmJHTTjstXV1dueWWW7J169acfvrpufDCC5vzmwNQCP/ABwAAxJQCAACSKMYA\nAJBEMQYAgCSKMQAAJFGMAQAgiWIMAABJFGMAAEiiGAMAQBLFGAAAkiT/B4ZknI+5JOVEAAAAAElF\nTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears that the aircraft is flying in a straight line because we can draw a line between the three points, and we know that aircraft cannot turn on a dime. The most reasonable guess is that $x$=4 at $t$=4. I will depict that with a green arrow." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mkf_internal.show_position_prediction_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF/CAYAAABKRQ+VAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If this is data from a Kalman filter, then each point has both a mean and variance. Let's try to show that by showing the approximate error for each point. Don't worry about why I am using a covariance matrix to depict the variance at this point, it will become clear in a few paragraphs. The intent at this point is to show that while we have $x$=1,2,3 that there is a lot of error associated with each measurement." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mkf_internal.show_x_error_char()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAswAAAF/CAYAAABdZ59cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQgghpAT/H1pjh8jKLMJoAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that there is a lot of error associated with each value of $x$. We could write a 1D Kalman filter as we did in the last chapter, but suppose this is the output of that filter, and not just raw sensor measurements. Are we out of luck?\n", + "\n", + "Let us think about how we predicted that $x$=4 at $t$=4. In one sense we just drew a straight line between the points and saw where it lay at $t$=4. My constant refrain: what is the physical interpretation of that? What is the difference in $x$ over time? In other words, what is $\\frac{\\partial x}{\\partial t}$? The derivative, or difference in distance over time is *velocity*. \n", + "\n", + "This is the **key point** in Kalman filters, so read carefully! Our sensor is only detecting the position of the aircraft (how doesn't matter). It does not have any kind of sensor that provides velocity to us. But based on the position estimates we can compute velocity. In Kalman filters we would call the velocity an *unobserved variable*. Unobserved means what it sounds like - there is no sensor that is measuring velocity directly. Since the velocity is based on the position, and the position has error, the velocity will have error as well. What happens if we draw the velocity errors over the positions errors?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mkf_internal.show_x_with_unobserved()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAswAAAF/CAYAAABdZ59cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neYSAHwAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Think about what this plot means. We have a lot of error in our position estimates. We therefore have a lot of error in our velocity estimates. But look at the intersections between the velocity and the positions. Take the intersection at $t$=2. The intersection between the velocity and the position is where our aircraft is most likely to be, which I have roughly depicted with a red ellipse ('roughly' because I set the size via eyeball, not via math). The size of the error is much smaller than the error of the positions, despite the fact that velocity was derived from position. \n", + "\n", + "What makes this possible? Imagine for a moment that we superimposed the velocity from a *different* airplane over the position graph. Cleary the two are not related, and there is no way that combining the two could possibly yield any additional information. In contrast, the velocity of the this airplane tells us something very important - the direction and speed of travel. So long as the aircraft does not alter its velocity the velocity allows us to predict where the next position is. After a relatively small amount of error in velocity the probability that it is a good match with the position is very small. Think about it - if you suddenly change direction your position is also going to change a lot. If the position measurement is not in the direction of the assumed velocity change it is very unlikely to be true. The two are correlated, so if the velocity changes so must the position, and in a predictable way. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Kalman Filter Algorithm\n", + "So in general terms we can show how a multidimensional Kalman filter works. In the example above, we compute velocity from the previous position measurements using something called the **measurement function**. Then we predict the next position by using the current estimate and something called the **state transition function**. In our example above,\n", + "\n", + "$$new\\_position = old\\_position + velocity*time$$ \n", + "\n", + "Next, we take the measurement from the sensor, and compare it to the prediction we just made. In a world with perfect sensors and perfect airplanes the prediction will always match the measured value. In the real world they will always be at least slightly different. We call the difference between the two the **residual**. Finally, we use something called the **Kalman gain** to update our estimate to be somewhere between the measured position and the predicted position. I will not describe how the gain is set, but suppose we had perfect confidence in our measurement - no error is possible. Then, clearly, we would set the gain so that 100% of the position came from the measurement, and 0% from the prediction. At the other extreme, if he have no confidence at all in the sensor (maybe it reported a hardware fault), we would set the gain so that 100% of the position came from the prediction, and 0% from the measurement. In normal cases, we will take a ratio of the two: maybe 53% of the measurement, and 47% of the prediction. The gain is updated on every cycle based on the variance of the variables (in a way yet to be explained). It should be clear that if the variance of the measurement is low, and the variance of the prediction is high we will favor the measurement, and vice versa. \n", + "\n", + "The chart shows a prior estimate of $x=1$ and $\\dot{x}=1$ ($\\dot{x}$ is the shorthand for the derivative of x, which is velocity). Therefore we predict $\\hat{x}=2$. However, the new measurement $x^{'}=1.3$, giving a residual $r=0.7$. Finally, Kalman filter gain $k$ gives us a new estimate of $\\hat{x^{'}}=1.8$.\n", + "\n", + "** CHECK SYMBOLOGY!!!!**" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from mkf_internal import *\n", + "show_residual_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Equations\n", + "\n", + "The brilliance of the Kalman filter is taking the insights of the chapter up to this point and finding mathematical solution. The Kalman filter finds what is called a *least squared fit* to the set of measurements to produce an optimal output. We will not trouble ourselves with the derivation of these equations. It runs to several pages, and offers a lot less insight than the words above, in my opinion. Instead, I will just present the equations and then immediately provide the Python code that implements them. \n", + "> Kalman Filter Predict Step:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "\\hat{x}_{t|t-1} &= F_t\\hat{x}_{t-1} + B u_t \\\\\n", + "P_{t|t-1} &= F_tP_{t-1}F^T_t + Q_t\n", + "\\end{align*}\n", + "$$\n", + "\n", + "> Kalman Filter Update Step:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "\\gamma &= z_t - H_t\\hat{x}_t \\\\\n", + "K_t &= P_t H^T_t (H_t P_t H^T_t + R_t)^{-1} \\\\\n", + "\\\\\n", + "\\hat{x}_t &= \\hat{x}_{t|t-1} + K_t \\gamma \\\\\n", + "P_{t|t} &= (I - K_t H_t)P_{t|t-1} \n", + "\\end{align*}\n", + "\\\\\n", + "$$\n", + "Dash off, wipe the blood out of your eyes, and we'll disuss what this means." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are nothing more than linear algebra equations that implement the algorithm we used in the last chapter, but using multidimensional Gaussians, and optimizing for a least squares fit. As you should be familiar with, each capital letter denotes a matrix or vector. The subscripts just let us denote from which time step the data comes from; $t$ is now, $t-1$ is the previous step. $A^T$ is the transpose of A, and $A^{-1}$ is the inverse. Finally, the hat denotes an estimate, so $\\hat{x}_t$ is the estimate of $x$ at time $t$.\n", + "\n", + "What do all of the variables mean? What is $P_t$, for example? Don't worry right now. Instead, I am just going to design a Kalman filter, and introduce the names as we go. Then we will just pass them into the Python function that implements the equations above, and we will have our solution.\n", + "\n", + "I will not present all of the Python code for the filter right now, but look at the code for the predict step. Notice how simple it really is. It really isn't much different from the predict step in the previous chapter.\n", + "\n", + " def predict():\n", + " x = F*x + u\n", + " P = F*P*F.T + Q\n", + " \n", + "> *Do not become discouraged when you come across a page of equations like I just gave for the Kalman Filter. They usually turn into very simple code. Take $x = F*x + u$. What does that mean? Clearly we are scaling x by F and then offsetting by u. Once you see that, you can start exploring **why** this is happening. This is really not as obscure as the symbology makes it appear.*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Tracking a Dog\n", + "\n", + "Let's go back to our tried and true problem of tracking our dog. This time we will include the fundamental insight of this chapter - that of using *unobserved variables* to improve our estimates. In simple terms, our algorithm is:\n", + "\n", + " 2. predict x using 'x + vel*time'\n", + " 3. get measurement for x\n", + " 4. compute residual as: 'x - predicted x'\n", + " 5. compute new position as 'residual * kalman gain'\n", + " \n", + "That is the entire Kalman filter algorithm. It is both what we described above in words, and it is what the rather obscure Kalman Filter equations do. The Kalman filter equations are just way of expresing this algorithm by using linear algebra.\n", + "\n", + "##### **Step 1:** Design State Transition Function\n", + "\n", + "We know from elementary physics that\n", + "\n", + "$$ x = vt + x_0$$\n", + "\n", + "In our problems we will be running the Kalman filter at fixed time intervals, so $t$ is a constant for us. We will just set it to $1$ and worry about the units later.\n", + "\n", + "We have two variables distance $(x)$ and velocity $(\\dot{x})$ which fully represent the state of our system. We will store them in a 1-dimensional array like so:\n", + "\n", + "$$\\begin{pmatrix}x \\\\ \\dot{x}\\end{pmatrix}$$\n", + "\n", + "Now we have to write a linear equation that performs the $ x = vt + x_0$ assignment with our state array.\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "{\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}}' &=\\begin{pmatrix}1&1 \\\\ 0&1\\end{pmatrix} \\times \\begin{pmatrix}x \\\\ \\dot{x}\\end{pmatrix}, \\mbox{or equivelently} \\\\\n", + "x' &= F \\times x\n", + "\\end{align*}\n", + "$$\n", + "\n", + "If we multiply this equation out, it yields:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "x' &= x + \\dot{x} \\\\\n", + "\\dot{x}' &= \\dot{x}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "You can see that our new $x$ is the old $x$ plus velocity times time, where time equals 1. Velocity is not changed by this equation, so the new $\\dot{x}$ is set to the old $\\dot{x}$.\n", + "\n", + "In the vocabulary of Kalman filters we call this *transforming the state matrix*. We take our state matrix, which for us is $(\\begin{smallmatrix}x \\\\ \\dot{x}\\end{smallmatrix})$,and multipy it by a matrix we will call $F$ to compute the new state. In this case, $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$. \n", + "\n", + "\n", + "You will do this for every Kalman filter you ever design. Your state matrix will change depending on how many state random variables you have, and then you will create $F$ so that it updates your state based on whatever the physics of your problem dictates. $F$ is always a matrix of constants. If this is not fully clear, don't worry, we will do this many times in this book.\n", + "\n", + "I will not keep referring to the Kalman filter equations, but look at the first equation $\\hat{x}_{t|t-1} = F_t\\hat{x}_{t-1} + u_t$. There is an unexplained $u_t$ term in there, but shorn of all the diacritics it should be clear that we just designed $F$ for this equation! \n", + "\n", + "\n", + "##### ** Step 2 **: Design the Measurement Function\n", + "\n", + "Now we need a way to go from our measurement to our state matrix. In our problem we have one sensor for the position. We do not have a sensor for velocity. If we put this in linear algebra terms we get:\n", + "\n", + "$$\n", + "z = \\begin{pmatrix}1&0\\end{pmatrix} \\times \\begin{pmatrix}x \\\\ \\dot{x}\\end{pmatrix}\n", + "$$\n", + "\n", + "In other words, we take one times the sensor's $x$ measurement, and zero times the nonexistent velocity measurement. Simple!\n", + "\n", + "In the nomenclature of Kalman filters the $(\\begin{smallmatrix}1&0\\end{smallmatrix})$ matrix is called $H$. If you scroll up to the Kalman filter equations you will see an $H$ term in the update step.\n", + "\n", + "Believe it or not, we have designed the majority of our Kalman filter!! All that is left is to model the noise in our sensors.\n", + "\n", + "\n", + "##### ** Step 3** Design Noise Matrices\n", + "\n", + "In the last chapter we used a variance of 5 for our position sensor. Let's use the same value here. The Kalman filter calls this the *measurement uncertainty*, and uses the symbol $R$.\n", + "\n", + "$$R = 5$$\n", + "\n", + "That was pretty simple, yes? And we are done. There are more variables in the Kalman filter, and we will have to define them in more complicated problems, but for our problem we have done everything we need to do.\n", + "\n", + "As promised, the Kalman filter equations are already programmed for you. In most circumstances you will never have to write your own Kalman filter equations. We will look at the code later, but for now we will just import the code and use it. I have placed it in *KalmanFilter.py*, so let's start by importing it and creating a filter." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "from KalmanFilter import KalmanFilter\n", + "f = KalmanFilter (dim=2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's it. We import the filter, and create a filter that uses 2 state variables. We specify the number of state variables with the 'dim=2' expression (dim means dimensions).\n", + "\n", + "The Kalman filter class contains a number of variables that you need to set. x is the state, F is the state transition function, and so on. Rather than talk about it, let's just do it!" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f.x = np.matrix([[0], [0]]) # initial state (location and velocity)\n", + "f.F = np.matrix([[1,1],[0,1]]) # state transition matrix\n", + "f.H = np.matrix([[1,0]]) # Measurement function\n", + "f.R = 5 # state uncertainty\n", + "f.P *= 500. # covariance matrix " + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at this line by line. \n", + "\n", + "**1**: We just assign the initial value for our state. Here we just initialize both the position and velocity to zero. \n", + "\n", + "**2**: We set $F=(\\begin{smallmatrix}1&1\\\\0&1\\end{smallmatrix})$, as in design step 1 above. \n", + "\n", + "**3**: We set $H=(\\begin{smallmatrix}1&0\\end{smallmatrix})$, as in design step 2 above.\n", + "\n", + "**4**: We set $R = 5$ as in step 3.\n", + "\n", + "**5**: Recall in the last chapter we set our initial belief to $\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(0,500)$ to set the initial position to 0 with a very large variance to signify our lack of knowledge about the initial conditions. We implemented in Python with \n", + "\n", + " pos = (0,500)\n", + " \n", + "Multidimensional Kalman filters stores the state variables in $x$ and their *covariance* in $P$. Notionally, this is exactly the same as the one dimension case. We have a mean and variance. For the multidimensional case, we have $$\\mathcal{N}(\\mu,\\sigma^2)=\\mathcal{N}(x,P)$$\n", + "\n", + "$P$ is initialized to the identity matrix of size $n\\times n$, so multiplying by 500 assigns a variance of 500 to $x$ and $\\dot{x}$.\n", + "\n", + "> Summary: For our dog tracking problem, in the 1-D case $\\mu$ was the position, and $\\sigma^2$ was the variance. In the 2-D case $x$ is our position and velocity, and $P$ is the *covariance*. It is the same thing, just in higher dimensions!\n", + "\n", + ">| | 1D | 2D and up|\n", + ">|--|----|---|\n", + ">|state|$\\mu$|$x$|\n", + ">|uncertainty|$\\sigma^2$|$P$|\n", + "\n", + "All that is left is to run the code! The *DogSensor* class from the previous chapter has been placed in *DogSensor.py*. There is an extra variable, Q, which we have not discussed yet. For now it is fine to set it to zero." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from DogSensor import DogSensor\n", + "\n", + "def dog_tracking_filter(R,Q=0,cov=1.):\n", + " f = KalmanFilter (dim=2)\n", + " f.x = np.matrix([[0], [0]]) # initial state (location and velocity)\n", + " f.F = np.matrix([[1,1],[0,1]]) # state transition matrix\n", + " f.H = np.matrix([[1,0]]) # Measurement function\n", + " f.R = R # measurement uncertainty\n", + " f.P *= cov # covariance matrix \n", + " f.Q = np.eye(2)*Q\n", + " return f\n", + "\n", + "\n", + "def plot_track(noise, count, R, Q=0, plot_P=True, title='Kalman Filter'):\n", + " dog = DogSensor(velocity=1, noise=noise)\n", + " f = dog_tracking_filter(R=R, Q=Q, cov=500.)\n", + "\n", + " ps = []\n", + " zs = []\n", + " cov = []\n", + " for t in range (count):\n", + " z = dog.sense()\n", + " f.measure (z)\n", + " #print (t,z)\n", + " ps.append (f.x[0,0])\n", + " cov.append(f.P)\n", + " zs.append(z)\n", + " f.predict()\n", + "\n", + " p0, = plt.plot([0,count],[0,count],'g')\n", + " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", + " p2, = plt.plot(range(1,count+1),ps, c='b')\n", + " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", + " plt.title(title)\n", + "\n", + " plt.show()\n", + " if plot_P:\n", + " plt.subplot(121)\n", + " plot_covariance(cov, (0,0))\n", + " plt.subplot(122)\n", + " plot_covariance(cov, (1,1))\n", + " plt.show()\n", + " \n", + "def plot_covariance(P, index=(0,0)):\n", + " ps = []\n", + " for p in P:\n", + " ps.append(p[index[0],index[1]])\n", + " plt.plot(ps)\n", + " \n", + "plot_track (noise=30, R=5, count=100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAF9CAYAAAAZRJ4tAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nInIRJcgiIiIiIhf5fwarySjTK0xeAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAFyCAYAAAD4cmIkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niHje/we3qBc3LqHvegAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Nobert Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n", + "\n", + "The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n", + "\n", + "The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, this is just a plot of the diagonals of $P$ over time. $P$ is just a covariance matrix, so the diagonal contains the variance of each state variable. So $P[0,0]$ is the variance of $x$, and $P[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $P=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now we just briefly point out that we quickly converge onto an accurate estimate despite the initial large uncertainty.\n", + "\n", + "You may not be impressed with these charts. After all, in the previous chapter we filtered very noisy signals with much simpler code. However, realize that right now we are working with a very simple example - an object moving through 1-D space and one sensor. That is about the limit of what we can compute with the code in the last chapter. Though we haven't yet seen it, we can compute very complicated things with this code. Perhaps we want to track 100 dimensions in financial models. Or we have an aircraft with a GPS, INS, TACAN, radar altimeter, baro altimeter, and airspeed indicator, and we want to integrate all those sensors into a model that predicts position, velocity, and accelerations in 3D (which requires 9 state variables). We can do that with the code in this chapter." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Walking Through the Math (Optional)\n", + "I promised that you would not have to understand how to derive Kalman filter equations, and that is true. However, I do think it is worth walking through the equations one by one and becoming familiar with the variables. If this is your first time through the material feel free to skip ahead to the next section. However, you will eventually want to work through this material, so why not now? You will need to have passing familarity with these equations to read material written about the Kalman filter, as they all presuppose that you are familiar with the equations.at \n", + "\n", + "I will start with the measurement step, as that is what we started with in the one dimensional Kalman filter case. Our first equation is\n", + "\n", + "$$\n", + "\\gamma = z_t - H_t\\hat{x}_t\n", + "$$\n", + "\n", + "On the right, shorn of the diacritics, we have $H\\times x$. That should be recognizable as the measurement function. We are taking our state $x$ and multiplying it by the measurement function $H$ to get the new state. The variable $z$ is just the measurement; it is typical, but not universal to use $z$ to denote measurements in the literature. Do you remember this chart?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "show_residual_chart()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The blue prediction line is the output of $H \\times x$, and $z$ is the measurement. Therefore, $\\gamma = z - H\\times x$ is how we compute the residual, drawn in red. So $\\gamma$ is the residual.\n", + "\n", + "The next line is the formidable:\n", + "\n", + "$$K_t = P_t H^T_t (H_t P_t H^T_t + R_t)^{-1}$$\n", + "\n", + "Unfortunately it is a fair amount of linear algebra to derive this. But $K$ is just the *Kalman gain* - the ratio of how much measurement vs prediction we should use to create the new estimate. $R$ is our *measurement noise*, and $P$ is our *uncertainty covariance matrix*.\n", + "\n", + "So let's work through this expression by expression. Start with $H_t P_t H^T_t$. The linear equation $ABA^T$ changes the basis of B to A. So $H_t P_t H^T_t$ is taking our covariance $P$ and putting it in measurement ($H$) space. Then, once in measurement space, we can add the measurement noise to it. Hence, the uncertainty in measurement space for the measurement is:\n", + "\n", + "$$(H_t P_t H^T_t + R_t)^{-1}$$\n", + "\n", + "Taking the inverse is linear algebra's way of doing $\\frac{1}{x}$. So the full expession is can be seen to be computing:\n", + "\n", + "$$ \n", + "gain_{measurement\\,space} = \\frac{uncertainty_{prediction}}{uncertainty_{measurement}}\n", + "$$\n", + "\n", + "\n", + "In other words, the *Kalman gain* equation is doing nothing more than computing the ratio. If we are confident in our measurements and unconfident in our predictions K will favor the measurement, and vice versa. The math is complicated because we are doing this in multiple dimensions via matrices, but the concept is simple - scale by a ratio.\n", + "\n", + "Without going into the derivation of $K$, I'll say that this equation is the result of finding a value of $K$ that optimizes the *mean-square estimation error*. It does this by finding the minimal values for $P$ along it's diagonal. Recall that the diagonal of $P$ is just the variance for each state variable. So, this equation for $K$ ensures that the Kalman filter output is optimal. To put this in concrete terms, for our dog tracking problem this means that the estimates for both position and velocity will be optimal - a value of $K$ that made the position extremely accurate but the velocity very inaccurate would be rejected in favor of a $K$ that made both position and velocity just somewhat accurate.\n", + "\n", + "\n", + "Our next line is:\n", + " $$ \\hat{x}_t = \\hat{x}_{t|t-1} + K_t \\gamma$$\n", + "\n", + "This just multiplies the residual by the Kalman gain, and adds it to the state variable. In other words, this is the computation of our new estimate.\n", + "\n", + "Finally, we have:\n", + "\n", + "$$P_{t|t} = (I - K_t H_t)P_{t|t-1} $$\n", + "\n", + "$I$ is the identity matrix, and is the way we represent $1$ in multiple dimensions. $H$ is our measurement function, and is a constant. So, simplified, this is simply $P = (1-cK)P$. $K$ is our ratio of how much prediction vs measurement we use. So, if $K$ is large then $(1-cK)$ is small, and P will be made smaller than it was. If $K$ is small, then $(1-cK)$ is large, and P will be made larger than it was. So we adjust the size of our uncertainty by some factor of the *Kalman gain*. \n", + "\n", + "Now we have the measurement steps. The first equation is\n", + "\n", + "$$\\hat{x}_{t|t-1} = F_t\\hat{x}_{t-1} + B_t u_t$$\n", + "\n", + "In simple terms, we have $x' = Fx + Bu$. This is just our state transition equation. $B$ and $u$ are new to us, and they are the control inputs for when you use a Kalman filter to control a system rather than just track it. We will use this in later problems, but for now consider using a Kalman filter to drive a car. We don't want to just track the car, but we will be issuing it direction - go in such and such direction as some speed. $u$ incorporates these instructions into the filter, and $B$ models how those control inputs affect the system.. If we are just passively tracking then we set $u$ to zero. This equation is, for our dog tracking problem, just computing:\n", + "\n", + "$$ x'=(vt)+x$$\n", + "\n", + "The final equation is:\n", + "$$P_{t|t-1} = F_tP_{t-1}F^T_t + Q_t$$\n", + "\n", + "Here we are scaling the covariance matrix with our process matrix, and then adding in the uncertainty with our motion ($Q$). **FIX THIS. THIS IS STUPID EXPLANATION.**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Adjusting the Filter\n", + "Your results will vary slightly depending on what numbers your random generator creates for the noise componenet of the noise, but the filter in the last section should track the actual position quite well. Typically as the filter starts up the first several predictions are quite bad, and varies a lot. But as the filter builds its state the estimates become much better. \n", + "\n", + "Let's start varying our parameters to see the effect of various changes. This is a *very normal* thing to be doing with Kalman filters. It is difficult, and often impossible to exactly model our sensors. An imperfect model means imperfect output from our filter. Engineers spend a lot of time tuning Kalman filters so that they perform well with real world sensors. We will spend time now to learn the effect of these changes. As you learn the effect of each change you will develop an intuition for how to design a Kalman filter. As I wrote earlier, designing a Kalman filter is as much art as science. The science is, roughly, designing the $H$ and $F$ matrices - they develop in an obvious manner based on the physics of the system we are modelling. The art comes in modelling the sensors and selecting appropriate values for the rest of our variables.\n", + "\n", + "Let's look at the effects of the noise parameters $R$ and $Q$.I will only run the filter for twenty steps to ensure we can see see the difference between the measurements and filter output. I will start by holding $R$ to 5 and vary $Q$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_track (noise=30, R=5, Q=10,count=30, plot_P=False, title='R = 5, Q = 10*I')\n", + "plot_track (noise=30, R=5, Q=0.1,count=30, plot_P=False, title='R = 5, Q = 0.1*I')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsAAAAF9CAYAAAAKk97ZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n", + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF9CAYAAAAHja6eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filter in the first plot should follow the noisy measurement almost exactly. In the second plot the filter should vary from the measurement quite a bit, and be much closer to a straight line than in the first graph. \n", + "\n", + "In the Kalman filter $R$ is the *measurement noise* and $Q$ is the *process uncertainty*. $R$ is the same in both plots, so ignore it for the moment. Why does $Q$ affect the plots this way?\n", + "\n", + "Let's understand the term *process uncertainty*. Consider the problem of tracking a ball. We can accurately model its behavior in statid air with math, but if there is any wind our model will diverge from reality. \n", + "\n", + "In the first case we set $Q=100$, which is quite large. In physical terms this is telling the filter \"I don't trust my motion prediction step\". So the filter will be computing velocity ($\\dot{x}), but then mostly ignoring it because we are telling the filter that the computation is extremely suspect. Therefore the filter has nothing to use but the measurements, and thus it follows the measurements closely. \n", + "\n", + "In the second case we set $Q=0.1$, which is quite small. In physical terms we are telling the filter \"trust the motion computation, it is really good!\". So the filter ends up ignoring some of the measurement as it jumps up and down, because the variation in the measurement does not match our velocity prediction. \n", + "\n", + "Now let's leave $Q=0.1$, but bump $R$ up to $1000$. This is telling the filter that the measurement noise is very large. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_track (noise=30, R=1000, Q=0.1,count=50, plot_P=False, title='R = 1000, Q = 0.1')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF9CAYAAAAHja6eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", + "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The filter output should be much closer to the green line, especially after 10-20 cycles. If you are running this in Ipython Notebook, I strongly urge you to run this many times in a row (click inside the code box, and press CTRL-Enter). Most times the filter tracks almost exactly with the actual position, randomly going slightly above and below the green line, but sometimes it stays well over or under the green line for a long time. What is happening in the latter case?\n", + "\n", + "The filter is strongly preferring the motion update to the measurement, so if the prediction is off it takes a lot of measurements to correct it. It will eventually correct because the velocity is a hidden variable - it is computed from the measurements, but it will take awhile **I DON\"T LIKE THIS. I am not sure I have R and Q right**\n", + "\n", + "To some extent you can get similar looking output by varying either $R$ or $Q$, but I urge you to not 'magically' alter these until you get output that you like. Always think about the physical implications of these assignments, and vary $R$ and/or $Q$ based on your knowledge of the system you are filtering." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A Detailed Examination of the Covariance Matrix\n", + "\n", + "So far I have not given a lot of coverage of the covariance matrix. It is time to look at it more closely. Recall this table comparing the one dimensional and multidimensional Kalman filter.\n", + "\n", + "| | 1D | 2+D|\n", + "|--|----|---|\n", + "|state|$\\mu$|$x$|\n", + "|uncertainty|$\\sigma^2$|$P$|\n", + "\n", + "This should remind you that $P$, the covariance matrix is nothing more than the variance of our state - such as the position of our dog. It has many elements in it, but don't be daunted; we will learn how to interpret a very large $9\\times 9$ covariance matrix, or even larger.\n", + "\n", + "Recall the beginning of the chapter, where we provided the equation for the covariance matrix. It read:\n", + "\n", + "$$\n", + "P = \\begin{pmatrix}\n", + " {{\\sigma}_{1}}^2 & p{\\sigma}_{1}{\\sigma}_{2} & \\cdots & p{\\sigma}_{1}{\\sigma}_{n} \\\\\n", + " p{\\sigma}_{2}{\\sigma}_{1} &{{\\sigma}_{2}}^2 & \\cdots & p{\\sigma}_{2}{\\sigma}_{n} \\\\\n", + " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + " p{\\sigma}_{n}{\\sigma}_{1} & p{\\sigma}_{n}{\\sigma}_{2} & \\cdots & {{\\sigma}_{n}}^2\n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "(I have subtituted $P$ for $\\Sigma$ because of the nomenclature used by the Kalman filter literature).\n", + "\n", + "The diagonal contains the variance of each of our state variables. So, if our state variables are\n", + "\n", + "$$\\begin{pmatrix}x\\\\\\dot{x}\\end{pmatrix}$$\n", + "\n", + "and the covariance matrix happens to be\n", + "$$\\begin{pmatrix}2&0\\\\0&6\\end{pmatrix}$$\n", + "\n", + "we know that the variance of $x$ is 2, and the variance of $\\dot{x}$ is 6. The off diagonal elements are all 0, so we also know that $x$ and $\\dot{x}$ are not correlated. Recall the ellipses that we drew of the covariance matrices. Let's look at the ellipse for the matrix." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "P = np.array([[2,0],[0,6]])\n", + "e = stats.sigma_ellipse (P, 0, 0)\n", + "stats.plot_sigma_ellipse(e, '|2 0|\\n|0 6|')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAGNCAYAAAActsnoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAADA9Wh6AQAA4Ho0vQAAAHC9/w8SA8Mh7xQ32gAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course it is unlikely that the position and velocity of an object remain uncorrelated for long. Let's look at a more typical covariance matrix" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "P = np.array([[2,2.4],[2.4,6]])\n", + "e = stats.sigma_ellipse (P, 0, 0)\n", + "stats.plot_sigma_ellipse(e, '|2.0 2.4|\\n|2.4 6.0|')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAr0AAAGNCAYAAAActsnoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nR9MLAAAAx/t/RnocGkqbtNEAAAAASUVORK5CYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here the ellipse is slanted, signifying that $x$ and $\\dot{x}$ are correlated (and, of course, not independent - all correlated variables are dependent). You may or may not have noticed that the off diagonal elements were set to the same value, 2.4. This was not an accident. Let's look at the equation for the covariance for the case where the number of dimensions is two.\n", + "\n", + "$$\n", + "P = \\begin{pmatrix}\n", + " \\sigma_1^2 & p\\sigma_1\\sigma_2 \\\\\n", + " p\\sigma_2\\sigma_1 &\\sigma_2^2 \n", + " \\end{pmatrix}\n", + "$$\n", + "\n", + "Look at the computation for the off diagonal elements. \n", + "\n", + "$$\\begin{align*}\n", + "P_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", + "P_{1,0}&=p\\sigma_2\\sigma_1.\n", + "\\end{align*}$$\n", + "\n", + "If we re-arrange terms we get\n", + "$$\\begin{align*}\n", + "P_{0,1}&=p\\sigma_1\\sigma_2 \\\\\n", + "P_{1,0}&=p\\sigma_1\\sigma_1 \\mbox{, yielding} \\\\\n", + "P_{0,1}&=P_{1,0}\n", + "\\end{align*}$$\n", + "\n", + "In general, we can state that $P_{i,j}=P_{j,i}$.\n", + "\n", + "So for my example I multiplied the diagonals, 2 and 6, to get 12, and then scaled that with the arbitrarily chosen $p=.2$ to get 2.4.\n", + "\n", + "Let's get back to concrete terms. Lets do another Kalman filter for our dog, and this time plot the covariance ellipses on the same plot as the position." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_track(noise, count, R, Q=0, plot_P=True, title='Kalman Filter'):\n", + " dog = DogSensor(velocity=1, noise=noise)\n", + " f = dog_tracking_filter(R=R, Q=Q, cov=20.)\n", + "\n", + " ps = []\n", + " zs = []\n", + " cov = []\n", + " for t in range (count):\n", + " z = dog.sense()\n", + " f.measure (z)\n", + " ps.append (f.x[0,0])\n", + " cov.append(f.P)\n", + " zs.append(z)\n", + " f.predict()\n", + "\n", + " p0, = plt.plot([0,count],[0,count],'g')\n", + " p1, = plt.plot(range(1,count+1),zs,c='r', linestyle='dashed')\n", + " p2, = plt.plot(range(1,count+1),ps, c='b')\n", + " plt.legend([p0,p1,p2], ['actual','measurement', 'filter'], 2)\n", + " plt.title(title)\n", + "\n", + " for i,p in enumerate(cov):\n", + " e = stats.sigma_ellipse (p, i+1, ps[i])\n", + " stats.plot_sigma_ellipse(e, axis_equal=False)\n", + " if i == len(cov)-1:\n", + " s = ('$\\sigma^2_{pos} = %.2f$' % p[0,0])\n", + " plt.text (30,1,s,fontsize=18)\n", + " s = ('$\\sigma^2_{vel} = %.2f$' % p[1,1])\n", + " plt.text (30,-4,s,fontsize=18)\n", + " plt.xlim((0,40))\n", + " plt.ylim((0,40))\n", + " plt.axis('equal')\n", + " \n", + " plt.show()\n", + "\n", + "\n", + "plot_track (noise=5, R=5, Q=5, count=20, title='R = 5')\n", + "plot_track (noise=5, R=.5, Q=5, count=20, title='R = 0.5')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAroAAAF9CAYAAADr+MuIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n", + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAsYAAAF9CAYAAAAHja6eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAwAAAJKkvwDSTkrxa+uaKgAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The output on these is a bit messy, but you should be able to see what is happening. In both plots we are drawing the covariance matrix for each point. We start with the covariance $P=(\\begin{smallmatrix}50&0\\\\0&50\\end{smallmatrix})$, which signifies a lot of uncertainty about our initial belief. After we receive the first measurement the Kalman filter updates this belief, and so the variance is no longer as large. In the top plot the first ellipse (the one on the far left) should be a slighly squashed ellipse. As the filter continues processing the measurements the covariance ellipse quickly shifts shape until it settles down to being a long, narrow ellipse tilted in the direction of movement.\n", + "\n", + "Think about what this means physically. The x-axis of the ellipse denotes our uncertainty in position, and the y-axis our uncertainty in velocity. So, an ellipse that is taller than it is wide signifies that we are more uncertain about the velocity than the position. Conversely, a wide, narrow ellipse shows high uncertainty in position and low uncertainty in velocity. Finally, the amount of tilt shows the amount of correlation between the two variables. \n", + "\n", + "The first plot, with $R=5$, finishes up with an ellipse that is wider than it is tall. If that is not clear I have printed out the variances for the last ellipse in the lower right hand corner. The variance for position is 3.85, and the variance for velocity is 3.0. \n", + "\n", + "In contrast, the second plot, with $R=0.5$, has a final ellipse that is taller than wide. The ellipses in the second plot are all much smaller than the ellipses in the first plot. This stands to reason because a small $R$ implies a small amount of noise in our measurements. Small noise means accurate predictions, and thus a strong belief in our position. \n", + "\n", + "** EXPLAIN WHY SECOND PLOT ELLIPSE IS TALLER THAN WIDE!!!**\n", + "\n", + "Keep looking at these plots until you grasp how the covariance matrix $P$ has a real, physical interpretation. When you start dealing with a, say, $9\\times 9$ matrix it may seem overwhelming - there are 81 numbers to interpret. Just break it down - the diagonal contains the variance for each state variable, and all off diagonal elements are the product of two variances and a scaling factor $p$. You will not be able to plot a $9\\times 9$ matrix on the screen because it would require living in 10-D space, so you have to develop your intution and understanding in this simple, 2-D case. \n", + "\n", + "> **sidebar**: when plotting covariance ellipses, make sure to always use *plt.axis('equal')* in your code. If the axis use different scales the ellipses will be drawn distorted. For example, the ellipse may be drawn as being taller than it is wide, but it may actually be wider than tall.\n", + "\n" + ] } ], "metadata": {} diff --git a/mkf_internal.py b/mkf_internal.py index ac2837f..c1e5483 100644 --- a/mkf_internal.py +++ b/mkf_internal.py @@ -18,23 +18,24 @@ def show_residual_chart(): ax = plt.axes() ax.annotate('', xy=(2,2), xytext=(1,1), arrowprops=dict(arrowstyle='->', ec='b',shrinkA=3, shrinkB=4)) - ax.annotate('prediction', xy=(1.7,2), color='b') + ax.annotate('prediction', xy=(2.04,2.), color='b') ax.annotate('measurement', xy=(2.05, 1.28)) ax.annotate('prior measurement', xy=(1, 0.9)) ax.annotate('residual', xy=(2.04,1.6), color='r') - ax.annotate('new estimate', xy=(2,1.8),xytext=(2.15,1.9), - arrowprops=dict(arrowstyle='->', shrinkA=3, shrinkB=4)) + ax.annotate('new estimate', xy=(2,1.8),xytext=(2.1,1.8), + arrowprops=dict(arrowstyle='->', ec="k", shrinkA=3, shrinkB=4)) ax.annotate('', xy=(2,2), xytext=(2,1.3), - arrowprops=dict(arrowstyle="<->", + arrowprops=dict(arrowstyle="-", ec="r", shrinkA=5, shrinkB=5)) plt.title("Kalman Filter Prediction Update Step") plt.show() + def show_position_chart(): """ Displays 3 measurements at t=1,2,3, with x=1,2,3""" - plt.scatter ([1,2,3],[1,2,3]) + plt.scatter ([1,2,3], [1,2,3], s=128) plt.xlim([0,4]); plt.ylim([0,4]) @@ -48,7 +49,7 @@ def show_position_chart(): def show_position_prediction_chart(): """ displays 3 measurements, with the next position predicted""" - plt.scatter ([1,2,3],[1,2,3],s=128) + plt.scatter ([1,2,3], [1,2,3], s=128) plt.xlim([0,5]) plt.ylim([0,5])