{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# One Dimensional Kalman Filters" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "from __future__ import division, print_function\n", "from book_format import load_style, figsize\n", "load_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## One Dimensional Kalman Filters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a 1D Kalman filter. We will do this exactly as we did the discrete Bayes filter - rather than starting with equations we will develop the code step by step based on reasoning about the problem. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking A Dog" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in the *Discrete Bayes Filter* chapter we will be tracking a moving object in a long hallway at work, such as a dog or robot. However, assume that in our latest hackathon someone created an RFID tracker that provides a reasonably accurate position for our dog. Suppose the hallway is 100 meters long. The sensor returns the distance of the dog from the left end of the hallway in meters. So, 23.4 would mean the dog is 23.4 meters from the left end of the hallway.\n", "\n", "Naturally, the sensor is not perfect. A reading of 23.4 could correspond to a real position of 23.7, or 23.0. However, it is very unlikely to correspond to a real position of say 47.6. Testing during the hackathon confirmed this result - the sensor is 'reasonably' accurate, and while it had errors, the errors are small. Furthermore, the errors seemed to be evenly distributed on both sides of the measurement; a true position of 23 m would be equally likely to be measured as 22.9 as 23.1.\n", "\n", "Before we try to implement the filter, let's start by implementing a simulation of the dog's movement and of the sensor. After all, the filter needs to filter data collected from the dog, so we need to understand this movement and sensor behavior to have any hope of filtering it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulating the Sensor Measurement\n", "\n", "Simulating an RFID system is beyond the scope of this book, so we will use a simple model. We said that the sensor is equally likely to give a measurement that is too large as too small. Furthermore, it is more likely to be a small error than a large one. In the *Discrete Bayes* chapter we modelled this error with a probability. But now we know about Gaussians, so let's use them instead. We can model the error in a system with the Gaussian $\\mathcal{N}(\\mu, \\sigma^2)$, where $\\mu$ is the state (such as position or velocity) and $\\sigma^2$ is the variance in that state. So instead of saying our measurement is 22.9, we would say our measurement is 22.9 with a variance of 0.35, or $\\mathcal{N}(22.9, 0.35)$. The variance accounts for the error in the sensor.\n", "\n", "This is a simple model, but it works very well in practice. Many sensors near Gaussian errors, and as you will see the Kalman filter is based on this assumption. Of course, if the sensor errors are not nearly Gaussian your simulations of the filter performance are likely to mislead you.\n", "\n", "In the literature you will often see this charaterized with an equation like:\n", "\n", "$$ z = h(x) + \\epsilon_z$$\n", "\n", "Here $h(x)$ is the **measurement model** - a function which describes how measurements are made from the current system state. In other words, it is the measurement we would get for the state $x$ *if* the sensor was perfect. $\\epsilon_z$ is the error that is in the measurement, and hence $z$ is the actual measurement that results. This is not meant to imply that we can somehow measure or know the exact value of $\\epsilon_z$, it is a mathematical definition that can be restated as\n", "\n", "$$ \\epsilon_z = z - h(x)$$\n", "\n", "The utility of this equation will become apparent later in the book." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulating the Dog's movement\n", "\n", "Let's assume that the dog moves at a constant velocity. We can use Newton's equation to compute the new position based on the old position and velocity like so:\n", "\n", "$$ x = v \\Delta t + x_0$$.\n", "\n", "This is a model of the dog's behavior, and we call it the **system model**. However, clearly it is not perfect. The dog might speed up or slow down due to hills, winds, or whimsy. We could add those things to the model if we knew about them, but there will always be more things that we don't know. this is not due to the tracked object being a living creature. The same holds if we are tracking a missile, aircraft, or paint nozzle on a factory robotic painter. There will always be unpredictable errors in physical systems. We can model this mathematically by saying the dog's actual position is the prediction that comes from our **system model** plus what we call the **process noise**. In the literature this is usually written something like this:\n", "\n", "$$ x = f(x) +\\epsilon$$\n", "\n", "Here $f(x)$ is our system model and $\\epsilon$ is some unknown error between the system model's prediction of position and the actual position. Clearly $\\epsilon$ will change over time, and as with the measurement equation in the last section we are not implying that $\\epsilon$ can be derived analytically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implemention in Python\n", "\n", "We will want our implementation to correctly model the noise both in the movement and the process model. You may recall from the *Gaussians* chapter that we can use `numpy.random.randn()` to generate a random number with a mean of zero and a standard deviation of one. Thus, if we want a random number with a standard deviation of 0.5 we'd multipy the value returned by `randn()` by 0.5. \n", "\n", "Our model assumes that the velocity of our dog is constant, but we acknowledged that things like hills and obstacles make that very unlikely to be true. We can simulate this by adding a randomly generated value to the velocity each time we compute the dog's position.\n", "\n", " noisy_vel = vel + randn()*velocity_std\n", " x = x + noisy_vel*dt\n", " \n", "\n", "To model the sensor we need to take the current position of the dog and then add some noise to it proportional to the Gaussian of the measurement noise. This is simply\n", "\n", " z = x + randn()*measurement_std\n", " \n", "I don't like the bookkeeping required to keep track of the various values for position, velocity, and standard deviations so I will implement the simulation as a class. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from __future__ import print_function, division\n", "import matplotlib.pyplot as plt\n", "from numpy.random import randn\n", "import math\n", "\n", "class DogSimulation(object):\n", " \n", " def __init__(self, x0=0, velocity=1,\n", " measurement_variance=0.0, process_variance=0.0):\n", " \"\"\" x0 - initial position\n", " velocity - (+=right, -=left)\n", " measurement_variance - variance in measurement m^2\n", " process_variance - variance in process (m/s)^2\n", " \"\"\"\n", " self.x = x0\n", " self.velocity = velocity\n", " self.measurement_noise = math.sqrt(measurement_variance)\n", " self.process_noise = math.sqrt(process_variance)\n", "\n", " def move(self, dt=1.0):\n", " '''Compute new position of the dog assuming `dt` seconds have \n", " passed since the last update.'''\n", " # compute new position based on velocity. Add in some\n", " # process noise\n", " velocity = self.velocity + randn() * self.process_noise\n", " self.x += velocity * dt\n", " \n", " def sense_position(self):\n", " # simulate measuring the position with noise\n", " measurement = self.x + randn() * self.measurement_noise\n", " return measurement\n", " \n", " def move_and_sense(self):\n", " self.move()\n", " return self.sense_position()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The constructor `__init()__` initializes the DogSimulation class with an initial position `x0`, velocity `vel`, and the variance in the measurement and noise. The `move()` function has the dog move based on its velocity and the process noise. The `sense_position()` function compute and returns a measurement of the dog's position based on the current position and the sensor noise.\n", "\n", "We need to convert the variances that are passed into `__init__()` into standard deviations because `randn()` is scaled by the standard deviation. Variance is the standard deviation square, so we take the square root of the variance in `__init__()`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Okay, so lets look at the output of the `DogSimulation` class. We will start by setting the variances to 0 to check that the class does what we think it does. Zero variance means there is no noise in the signal or in the system model, so the results should be a straight line." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 " ] }, { "data": { "image/png": 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njo4fP35f56exAoBs5rvvvlNiYqKk9G8pT58+ra+++sqsd+3apWrVqlkZEQBw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\n9vPze6D5AAAAkD243FhNmzZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import book_plots as bp\n", "import numpy as np\n", "\n", "dog = DogSimulation(measurement_variance=0.0)\n", "xs = np.zeros(10)\n", "for i in range(10):\n", " dog.move()\n", " xs[i] = dog.sense_position()\n", " print(\"%.4f\" % xs[i], end=' '),\n", "bp.plot_track(xs, label='position')\n", "bp.show_legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The constructor initialized the dog at position 0 with a velocity of 1 (move 1.0 to the right). So we would expect to see an output of 1..10, and indeed that is what we see.\n", "\n", "Now let's inject some noise in the signal." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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XoFo19j77LN9f1ftXoUIF5s+f71h+6aWXeOSRR9wRoYiDqjWKiIiISOpefBGW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\nBAQEsHz5chreLI//r3/9y77cvYiIiIg4NSVnIo4weTL83//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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def test_sensor(measurement_var, process_var=0.0):\n", " dog = DogSimulation(measurement_variance=measurement_var, \n", " process_variance=process_var)\n", " N = 50\n", " xs = np.zeros(N)\n", " for i in range(N):\n", " dog.move()\n", " xs[i] = dog.sense_position()\n", "\n", " bp.plot_track([0, N-1], [1, N])\n", " bp.plot_measurements(xs, label='Sensor')\n", " bp.set_labels('variance = {}, process variance = {}'.format(\n", " measurement_var, process_var), 'time', 'pos')\n", " plt.ylim([0, N])\n", " bp.show_legend()\n", " plt.show()\n", "\n", "test_sensor(measurement_var=4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "NumPy uses a random number generator to generate the normal distribution samples. The numbers I see as I write this are unlikely to be the ones that you see. If you run the cell above multiple times, you should get a slightly different result each time. I could use `numpy.random.seed(some_value)` to force the results to be the same each time. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a real feel for how normal distributions and Kalman filters work you will probably want to run cells several times, observing what changes, and what stays roughly the same.\n", "\n", "So the output of the sensor should be a wavering dotted red line drawn over a straight black line. The black line shows the actual position of the dog, and the dotted red line is the noisy signal produced by the simulated RFID sensor. Please note that the red dotted line was manually plotted - we do not yet have a filter that recovers that information! \n", "\n", "If you are running this in an interactive IPython Notebook, I strongly urge you to run the script several times in a row. You can do this by putting the cursor in the cell containing the Python code and pressing CTRL+Enter. Each time it runs you should see a different sensor output.\n", "\n", "I also urge you to adjust the noise setting to see the result of various values. However, since you may be reading this in a read only notebook, I will show several examples. The first plot shows the noise set to 100.0, and the second shows noise set to 0.5." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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M4uPj0bJlS+zbt4+ylhFCCDFqlhcvIsPeHmAMoOQs5cfhwzwwq1kT8Pc3dGuM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t9Yv379qF27tnHf398f/5yM8FStCl9/DZMmmf9cUKNLffqor1etyv74HTtUY+dUTa1t5sYNOHXK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\ngAegOQMAA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test_sensor(measurement_var=100.0)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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oKF7cMX9Z0aIA9OvXj8WLFwNgWRa9evVi//79zlX79u3rnN5JJLcoORMRERGR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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test_sensor(measurement_var=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets see the effect of the process noise. My simulation is not meant to exactly model any given physical process. On each call to `sense_position()` I modify the current velocity by randomly generated process noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism in place trying to maintain the same speed. In this case, the control mechanism would be the dog's brain! For an automobile it could be a cruise control or the human driver.\n", "\n", "So let's first look at the plot with some process noise but no measurement noise to obscure the results." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ChfwOSxQCkpwJIYQQQuTE9u3wzDNQty6sWWPpaEQ+2rFjB2PHjtW327Zty44d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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(1234)\n", "test_sensor(measurement_var=0, process_var=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the position wanders slightly from the ideal track. You may have thought that the track would have wandered back and forth the ideal path like the measurement noise did, but recall that we are modifying velocity on each, not the position. So once the track has deviated, it will remain deviated until the random changes in velocity happen to result in the track going back to the original track. \n", "\n", "Finally, let's look at the combination of measurement noise and process noise." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JmYiIiIg81EzTpEGDBuzbtw8Ab29vRo0aRXx8vK1MlSpVsFgscOQIVKkCc+aA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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "test_sensor(measurement_var=1, process_var=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Math with Gaussians" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's say we believe that our dog is at 23 meters, and the variance is 5, or $\\mathcal{N}(23,\\, 5)$. We can represent that in a plot:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9+2RZuRl8/dN7XMu+qnBmQoiKIAW4EKJCFGkLWbp1DkdO/WaI+Xn1ImzQ29Sy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\nXc1o7Wz0OH97VAgvFInqVCRrMjBXk4HEmDRaKpA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import filterpy.stats as stats\n", "with figsize(y=3):\n", " stats.plot_gaussian(mean=23, variance=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how this relates to the bar charts from the Discrete Bayes chapter. In that chapter we drew bars of various heights to depict the probability that the dog was at any given position. In many cases those bars took on a shape very similar to this chart. The differences are that the bars depict the probability of a discrete position, whereas this chart depicts the probability distribution of a continuous range of positions. \n", "\n", "This graph corresponds to a fairly inexact belief. While we believe that the dog is at 23, note that roughly speaking positions 21 to 25 are quite likely as well. Let's assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 as the position. Can we use this additional information to improve our estimate of the dog's position?\n", "\n", "Intuition suggests 'yes'. Consider: if we read the sensor 100 times and each time it returned a value between 21 and 25, all centered around 23, we should be very confident that the dog is somewhere very near 23. Of course, a different physical interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated a normal distribution. But that seems extremely unlikely - I certainly have never seen a dog do that. So the only reasonable assumption is that the dog was mostly standing still at 23.0.\n", "\n", "Let's look at 100 sensor readings in a plot:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Zw3UIpJ7r0KEDOnToILP1eExG+0xnZWWJ/l9DQ0MWS9aKr68vvvnmG4wdOxZe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Xjz5g1yc3Olut7ExARGRkZ4/fo1q3bJgtL0kOrUqYPff/8dixcvRmZmJubNmwddXV2cP3++Utt3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\neqSlpbEdCiFSJyYmB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dog = DogSimulation(x0=23, velocity=0, \n", " measurement_variance=5, process_variance=0.0)\n", "xs = range(100)\n", "ys = []\n", "for _ in xs:\n", " dog.move()\n", " ys.append(dog.sense_position()) \n", "bp.plot_track(xs, ys, label='Dog position')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks like this. So let's proceed and try to solve this mathematically. But how?\n", "\n", "\n", "Recall the discrete Bayes code for adding a measurement to a preexisting belief:\n", "\n", " def update(pos, measure, p_hit, p_miss):\n", " q = array(pos, dtype=float)\n", " for i in range(len(hallway)):\n", " if hallway[i] == measure:\n", " q[i] = pos[i] * p_hit\n", " else:\n", " q[i] = pos[i] * p_miss\n", " normalize(q)\n", " return q\n", " \n", "Note that the algorithm is essentially computing:\n", "\n", " new_belief = prior_belief * measurement * sensor_error\n", " \n", "The measurement term might not be obvious, but recall that measurement in this case was always 1 or 0, and so it was left out for convenience. Here *prior* carries the both the colloquial sense of *previoius*, but also the Bayesian meaning. In Bayesian terms the *prior* is the probability after the prediction and before the measurements have been incorporated.\n", " \n", "If we are implementing this with Gaussians, we might expect it to be implemented as:\n", "\n", " new_gaussian = measurement * old_gaussian\n", " \n", "where measurement is a Gaussian returned from the sensor. But does that make sense? Can we multiply Gaussians? If we multiply a Gaussian with a Gaussian is the result another Gaussian, or something else?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The algebra for this is not extremely hard, but it is messy. It uses Bayes theorem to compute the posterior (new Gaussian) given the prior (old Gaussian) and evidence (the measurement. I've placed the math at the bottom of the chapter if you are interested in the details. Here I will present the results. The subscript $\\mathtt{z}$ stands for the *measurement*.\n", "$$\\begin{aligned}\n", "\\mathcal{N}(\\mu_\\mathtt{posterior}, \\sigma_\\mathtt{posterior}^2) &= \\mathcal{N}(\\mu_\\mathtt{prior}, \\sigma_\\mathtt{prior}^2)\\times \\mathcal{N}(\\mu_\\mathtt{z}, \\sigma_\\mathtt{z}^2) \\\\\n", "&= \\mathcal{N}(\\frac{\\sigma_\\mathtt{prior}^2 \\mu_\\mathtt{z} + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}}{\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2},\\frac{1}{\\frac{1}{\\sigma_\\mathtt{prior}^2} + \\frac{1}{\\sigma_\\mathtt{z}^2}})\n", "\\end{aligned}$$ \n", "\n", "In other words the result of multiplying two Gaussians is a Gaussian is \n", "\n", "$$\\begin{aligned}\n", "\\mu &=\\frac{\\sigma_\\mathtt{prior}^2 \\mu_2 + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}} {\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2}, \\\\\n", "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_\\mathtt{prior}^2} + \\frac{1}{\\sigma_\\mathtt{z}^2}} =\n", "\\frac{\\sigma_\\mathtt{prior}^2\\sigma_\\mathtt{z}^2}{\\sigma_\\mathtt{prior}^2+\\sigma_\\mathtt{z}^2}\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Without doing a deep analysis we can immediately infer some things. First and most importantly the result of multiplying two Gaussians is another Gaussian. The mean is a scaled sum of the prior and the measurement. The variance is a combination of the variances of the variances of the input. We conclude from this that the variances are completely unaffected by the values of the mean!\n", "\n", "Let's examine the result of multiplying $\\mathcal{N}(23,\\, 5)$ with itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance be wider, narrower, or the same?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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xDIM9e/YoGRMRuZukZINe42DvcRj8lMG4/uBpzp4P1RZLMr8e2sDanV8THReZ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\njIkmRatoOZ5xiB2HfufgqT1otZpq21UqNe2DutO/07209jb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import filterpy.stats as stats\n", "\n", "def multiply(mu1, var1, mu2, var2):\n", " if var1 == 0.0:\n", " var1=1.e-80 \n", " if var2 == 0:\n", " var2 = 1e-80\n", " \n", " mean = (var1*mu2 + var2*mu1) / (var1+var2)\n", " variance = 1 / (1/var1 + 1/var2)\n", " return (mean, variance)\n", "\n", "xs = np.arange(16, 30, 0.1)\n", "\n", "mean1, var1 = 23, 5\n", "mean, var = multiply(mean1, var1, mean1, var1)\n", "\n", "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", "plt.plot(xs, ys, label='original')\n", "\n", "ys = [stats.gaussian(x, mean, var) for x in xs]\n", "plt.plot(xs, ys, label='product', ls='--')\n", "bp.show_legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result of the multiplication is taller and narrow than the original Gaussian but the mean is the same. Does this match your intuition of what the result should have been?\n", "\n", "If we think of the Gaussians as two measurements, this makes sense. If I measure twice and get 23 meters each time, I should conclude that the length is close to 23 meters. Thus the mean should be 23. I am more confident with two measurements than with one, so the variance of the result should be smaller. \n", "\n", "\"Measure twice, cut once\" is a useful saying and practice due to this fact! The Gaussian is a mathematical model of this physical fact, so we should expect the math to follow our physical process. \n", "\n", "Now let's multiply two Gaussians (or equivalently, two measurements) that are partially separated. In other words, their means will be different, but their variances will be the same. What do you think the result will be? Think about it, and then look at the graph." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BQKvVMnDgQB4+fGjiqER2NXbsWNRqNX///TedO3emQIECFCpUCD8/P2JjYw31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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = np.arange(16, 30, 0.1)\n", "\n", "mean1, var1 = 23, 5\n", "mean2, var2 = 25, 5\n", "mean, var = multiply(mean1, var1, mean2, var2)\n", "\n", "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", "plt.plot(xs, ys, label='measure 1')\n", "\n", "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", "plt.plot(xs, ys, label='measure 2')\n", "\n", "ys = [stats.gaussian(x, mean, var) for x in xs]\n", "plt.plot(xs, ys, label='product', ls='--')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another beautiful result! If I handed you a measuring tape and asked you to measure the distance from table to a wall, and you got 23 meters, and then a friend make the same measurement and got 25 meters, your best guess must be 24 meters if you trust the skills of your friends equally.\n", "\n", "That is fairly counter-intuitive in more complicated situations, so let's consider it further. Perhaps a more reasonable assumption would be that either you or your coworker made a mistake, and the true distance is either 23 or 25, but certainly not 24. Surely that is possible. However, suppose the two measurements you reported as 24.01 and 23.99. In that case you would agree that in this case the best guess for the correct value is 24? Which interpretation we choose depends on the properties of the sensors we are using.\n", "\n", "This topic is fairly deep, and I will explore it once we have completed our Kalman filter. For now I will merely say that the Kalman filter requires the interpretation that measurements are accurate, with Gaussian noise, and that a large error caused by misreading a measuring tape is not Gaussian noise.\n", "\n", "Dealing with incorrect measurements, such as measuring the distance to the wrong object, is a topic we will need to treat separately. The filter assumes that the data you feed it is correct, just noisy. Engineers that design radar systems probably spend most of their effort on this problem.\n", "\n", "For now I ask that you trust me. The math is correct, so we have no choice but to accept it and use it. We will see how the Kalman filter deals with movements vs error very soon. In the meantime, accept that 24 is the correct answer to this problem.\n", "\n", "One final test of your intuition. What if the two measurements are widely separated? " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BgRg+fDgyMjIqbX/ixAn06tULO3bsQHx8PObMmYOZM2fi+++/l9qkpqZixIgR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\nDidyjcd+jeB/j6gbT13Vs4OGR+LN5f++D2XlkqRfD0nQrdj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = np.arange(0, 60, 0.1)\n", "\n", "mean1, var1 = 10, 5\n", "mean2, var2 = 50, 5\n", "mean, var = multiply(mean1, var1, mean2, var2)\n", "\n", "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", "plt.plot(xs, ys, label='measure 1')\n", "\n", "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", "plt.plot(xs, ys, label='measure 2')\n", "\n", "ys = [stats.gaussian(x, mean, var) for x in xs]\n", "plt.plot(xs, ys, label='product', ls='--')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This result bothered me quite a bit when I first learned it. If my first measurement was 10, and the next one was 50, why would I choose 30 as a result? And why would I be *more* confident? Doesn't it make sense that either one of the measurements is wrong, or that I am measuring a moving object? Shouldn't the result be nearer 50? And, shouldn't the variance be larger, not smaller?\n", "\n", "Well, no. Recall the g-h filter chapter. In that chapter we agreed that if I weighed myself on two scales, and the first read 160 lbs while the second read 170 lbs, and both were equally accurate, the best estimate was 165 lbs. Furthermore I should be a bit more confident about 165 lbs vs 160 lbs or 170 lbs because I know have two readings, both near this estimate, increasing my confidence that neither is wildly wrong. \n", "\n", "Of course, this example is quite exaggerated. The width of the Gaussians is fairly narrow, so this combination of measurements is extremely unlikely. It is hard to eyeball this, but the measurements are well over $3\\sigma$ apart, so the probability of this happening is less than 1%. Still, it can happen, and the math is correct. In practice this is the sort of thing we use to decide if \n", "\n", "Let's look at the math again to convince ourselves that the physical interpretation of the Gaussian equations makes sense. I'm going to switch back to using priors and measurements. The math and reasoning is the same whether you are using a prior and incorporating a measurement, or just trying to compute the mean and variance of two measurements. For Kalman filters we will be doing a lot more of the former than the latter, so let's get used to it.\n", "\n", "$$\n", "\\mu=\\frac{\\sigma_\\mathtt{prior}^2 \\mu_\\mathtt{z} + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}} {\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2}\n", "$$\n", "\n", "If both have the same accuracy, then $\\sigma_\\mathtt{prior}^2 = \\sigma_\\mathtt{z}^2$, and the resulting equation is\n", "\n", "$$\\mu=\\frac{\\sigma_\\mathtt{z}^2(\\mu_\\mathtt{prior} + \\mu_\\mathtt{z})}{2\\sigma_\\mathtt{z}^2}\\\\\n", "= \\frac{1}{2}(\\mu_\\mathtt{prior} + \\mu_\\mathtt{z})$$\n", "\n", "which is the average of the two means. If we look at the extreme cases, assume the first scale is very much more accurate than than the second one. At the limit, we can set \n", "$\\sigma_\\mathtt{prior}^2=0$, yielding\n", "\n", "$$\n", "\\begin{aligned}\n", "\\mu&=\\frac{0*\\mu_\\mathtt{z} + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}} { \\sigma_\\mathtt{z}^2}, \\\\\n", "\\text{or}\\\\\n", "\\mu&=\\mu_\\mathtt{prior}\n", "\\end{aligned}\n", "$$\n", "\n", "Finally, if we set $\\sigma_\\mathtt{prior}^2 = 9\\sigma_\\mathtt{z}^2$, then the resulting equation is\n", "\n", "$$\n", "\\begin{aligned}\n", "\\mu&=\\frac{9 \\sigma_\\mathtt{z}^2 \\mu_2 + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}} {9 \\sigma_\\mathtt{z}^2 + \\sigma_\\mathtt{z}^2} \\\\\n", "\\text{or}\\\\\n", "\\mu&= \\frac{1}{10} \\mu_\\mathtt{prior} + \\frac{9}{10} \\mu_\\mathtt{z}\n", "\\end{aligned}\n", "$$\n", "\n", "This again fits our physical intuition of favoring the second, accurate scale over the first, inaccurate scale." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interactive Example\n", "\n", "Rather than going through a dozen examples, lets use an interactive example. Here you can use sliders to alter the mean and variance of two Gaussians. As you change the values a plot of the two Gaussians along with the product of the two is displayed." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mBw8eZPPmzURFRVGvXj2rFy8iIiIi4kiSDd/jx4+nXbt2dOjQAT8/PyZNmoSX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\nI6+88gqDBw+msbGR2NhYCgsLeeutt9DpdLauvuhmWmuvdnZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.html.widgets import interact, interactive, fixed\n", "import IPython.html.widgets as widgets\n", "\n", "def plot_products(mu_1, mu_2, var_1, var_2):\n", " xs = np.arange(0, 20, min(var_1, var_2)/10)\n", " ys = [stats.gaussian(x, mu_1, var_1) for x in xs]\n", " plt.plot(xs, ys, label='measure 1')\n", "\n", " ys = [stats.gaussian(x, mu_2, var_2) for x in xs]\n", " plt.plot(xs, ys, label='measure 2')\n", "\n", " mean, var = multiply(mu_1, var_1, mu_2, var_2)\n", " ys = [stats.gaussian(x, mean, var) for x in xs]\n", " plt.plot(xs, ys, label='product', ls='--')\n", " plt.ylim(0, 1.5)\n", " plt.legend();\n", " \n", "interact(plot_products,\n", " mu_1=widgets.FloatSliderWidget(value=5, min=0., max=15), \n", " mu_2=widgets.FloatSliderWidget(value=10, min=0., max=15), \n", " var_1=widgets.FloatSliderWidget(value=1, min=.1, max=5.), \n", " var_2=widgets.FloatSliderWidget(value=1, min=.1, max=5.));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementing the Update Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall the discrete Bayes filter uses a NumPy array to encode our belief about the position of our dog at any time. That array stored our belief of our dog's position in the hallway using 10 discrete positions. This was very crude, because with a 100 meter hallway that corresponded to positions 10 meters apart. It would have been trivial to expand the number of positions to say 1,000, and that is what we would do if using it for a real problem. But the problem remains that the distribution is discrete and multimodal - it can express strong belief that the dog is in two positions at the same time.\n", "\n", "Therefore, we will use a single Gaussian to reflect our current belief of the dog's position. In other words, we will use $\\mathtt{pos}_{\\mathtt{dog}} = \\mathcal{N}(\\mu,\\, \\sigma^2)$. Gaussians extend to infinity on both sides of the mean, so the single Gaussian will cover the entire hallway. They are unimodal, and seem to reflect the behavior of real-world sensors - most errors are small and clustered around the mean. Here is the entire implementation of the update function for a Kalman filter:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def update(mean, variance, measurement, measurement_variance):\n", " return multiply(mean, variance, measurement, measurement_variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kalman filters are supposed to be hard! But this is very short and straightforward. All we are doing is multiplying the Gaussian that reflects our belief of where the dog is with the new measurement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perhaps this would be clearer if we used more specific names:\n", "\n", " def update_dog(dog_pos, dog_variance, measurement, measurement_variance):\n", " return multiply(dog_pos, dog_variance, \n", " measurement, measurement_variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is less abstract, which perhaps helps with comprehension, but it is poor coding practice. We are writing a Kalman filter that works for any problem, not just tracking dogs in a hallway, so we don't use variable names with 'dog' in them. Still, the `update_dog()` function should make what we are doing very clear. \n", "\n", "Let's look at an example. We will suppose that our current belief for the dog's position is $\\mathcal{N}(2,\\, 5)$. Don't worry about where that number came from. It may appear that we have a chicken and egg problem, in that how do we know the position before we sense it, but we will resolve that shortly. We will create a `DogSimulation` object initialized to be at position 0.0, and with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that we mistakenly believe the dog is at position 2.0, not 0.0." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time: 0 \tposition = -0.033 \tvariance = 2.500\n", "time: 1 \tposition = -0.969 \tvariance = 1.667\n", "time: 2 \tposition = -0.985 \tvariance = 1.250\n", "time: 3 \tposition = -0.167 \tvariance = 1.000\n", "time: 4 \tposition = 0.024 \tvariance = 0.833\n", "time: 5 \tposition = 0.419 \tvariance = 0.714\n", "time: 6 \tposition = 0.190 \tvariance = 0.625\n", "time: 7 \tposition = 0.109 \tvariance = 0.556\n", "time: 8 \tposition = 0.177 \tvariance = 0.500\n", "time: 9 \tposition = -0.024 \tvariance = 0.455\n", "time: 10 \tposition = -0.042 \tvariance = 0.417\n", "time: 11 \tposition = 0.002 \tvariance = 0.385\n", "time: 12 \tposition = -0.048 \tvariance = 0.357\n", "time: 13 \tposition = -0.054 \tvariance = 0.333\n", "time: 14 \tposition = -0.002 \tvariance = 0.312\n", "time: 15 \tposition = -0.042 \tvariance = 0.294\n", "time: 16 \tposition = -0.195 \tvariance = 0.278\n", "time: 17 \tposition = -0.001 \tvariance = 0.263\n", "time: 18 \tposition = -0.020 \tvariance = 0.250\n", "time: 19 \tposition = -0.077 \tvariance = 0.238\n" ] } ], "source": [ "dog = DogSimulation(velocity=0., measurement_variance=5, process_variance=0.0)\n", "\n", "pos, s = 2, 5\n", "for i in range(20):\n", " dog.move()\n", " pos, s = update(pos, s, dog.sense_position(), 5)\n", " print('time:', i, \n", " '\\tposition =', \"%.3f\" % pos, \n", " '\\tvariance =', \"%.3f\" % s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because of the random numbers I do not know the exact values that you see, but the position should have converged very quickly to almost 0 despite the initial error of believing that the position was 2.0. Furthermore, the variance should have quickly converged from the initial value of 5.0 to 0.238.\n", "\n", "By now the fact that we converged to a position of 0.0 should not be terribly surprising. All we are doing is computing `new_pos = old_pos * measurement` and the measurement is a normal distribution around 0, so we should get very close to 0 after 20 iterations. But the truly amazing part of this code is how the variance became 0.238 despite every measurement having a variance of 5.0. \n", "\n", "If we think about the physical interpretation of this is should be clear that this is what should happen. If you sent 20 people into the hall with a tape measure to physically measure the position of the dog you would be very confident in the result after 20 measurements - more confident than after 1 or 2 measurements. So it makes sense that as we make more measurements the variance gets smaller.\n", "\n", "Mathematically it makes sense as well. Recall the computation for the variance after the multiplication: $\\sigma^2 = 1/(\\frac{1}{{\\sigma}_1^2} + \\frac{1}{{\\sigma}_2^2})$. We take the reciprocals of the sigma from the measurement and prior belief, add them, and take the reciprocal of the result. Think about that for a moment, and you will see that this will always result in smaller numbers as we proceed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementing Predictions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, an extremely dubious assumption. Certainly it is a fairly useless one - who needs a filter to track stationary objects? The discrete Bayes filter used a loop of predict and update functions, and we must do the same to accommodate movement.\n", "\n", "How do we perform the predict function with Gaussians? Recall the discrete Bayes method:\n", "\n", " def predict(pos, move, p_correct, p_under, p_over):\n", " n = len(pos)\n", " result = array(pos, dtype=float)\n", " for i in range(n):\n", " result[i] = \\\n", " pos[(i-move) % n] * p_correct + \\\n", " pos[(i-move-1) % n] * p_over + \\\n", " pos[(i-move+1) % n] * p_under \n", " return result\n", " \n", " \n", "In a nutshell, we shift the probability vector by the amount we believe the animal moved, and adjust the probability. How do we do that with Gaussians?\n", "\n", "It turns out that we add them. Think of the case without Gaussians. I think my dog is at 7.3 meters, and he moves 2.6 meters to right, where is he now? Obviously, 7.3 + 2.6 = 9.9. He is at 9.9 meters. Abstractly, the algorithm is `new_pos = old_pos + dist_moved`. It does not matter if we use floating point numbers or Gaussians for these values, the algorithm must be the same. \n", "\n", "How is addition for Gaussians performed? It turns out to be very simple:\n", "\n", "$$ \\mathcal{N}(\\mu_1, \\sigma_1^2)+\\mathcal{N}(\\mu_2, \\sigma_2^2) = \\mathcal{N}(\\mu_1 +\\mu_2, \\sigma_1^2 + \\sigma_2^2)$$\n", "\n", "In other words\n", "\n", "$$\\mu = \\mu_1 + \\mu_2 \\\\\n", "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n", "$$\n", "\n", "We can make this more readable by changing the subscripts.\n", "\n", "$$\\begin{aligned}\n", "\\mu_\\mathtt{after} &= \\mu_\\mathtt{before} + \\mu_\\mathtt{movement} \\\\\n", "\\sigma^2_\\mathtt{after} &= \\sigma^2_\\mathtt{before}+ \\sigma^2_\\mathtt{movement}\n", "\\end{aligned}$$\n", "\n", "All we do is add the means and the variance separately! Does that make sense? Think of the physical representation of this abstract equation.\n", "${\\mu}_\\mathtt{before}$ is the old position, and ${\\mu}_\\mathtt{movement}$ is how far we moved. Surely it makes sense that our new position is $\\mu_\\mathtt{before} + \\mu_\\mathtt{movement}$.\n", "\n", "What about the variance? It is perhaps harder to form an intuition about this. However, recall that with the `predict()` function for the discrete Bayes filter we always lost information - our confidence after the update was lower than our confidence before the update. We don't really know where the dog is moving, so the confidence should get smaller (variance gets larger). $\\sigma^2_\\mathtt{movement}$ is the amount of uncertainty added to the system due to the imperfect prediction about the movement, and so we would add that to the existing uncertainty. \n", "\n", "I assure you that the equation for Gaussian addition is correct, and derived by basic algebra. Therefore it is reasonable to expect that if we are using Gaussians to model physical events, the results must correctly describe those events.\n", "\n", "Now is a good time to either work through the algebra to convince yourself of the mathematical correctness of the algorithm, or to work through some examples and see that it behaves reasonably. This book will do the latter.\n", "\n", "So, here is our implementation of the predict function:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def predict(pos, variance, movement, movement_variance):\n", " return (pos + movement, variance + movement_variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is left? Just calling these functions. Discrete Bayes did nothing more than loop over the `update()` and `predict()` functions, so let's do the same. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PREDICT: 1.0000 401.0000\tUPDATE: 1.3518 1.9901\tZ: 1.3536\n", "PREDICT: 2.3518 2.9901\tUPDATE: 2.0703 1.1984\tZ: 1.8821\n", "PREDICT: 3.0703 2.1984\tUPDATE: 3.7357 1.0473\tZ: 4.3410\n", "PREDICT: 4.7357 2.0473\tUPDATE: 5.9602 1.0117\tZ: 7.1563\n", "PREDICT: 6.9602 2.0117\tUPDATE: 6.9494 1.0029\tZ: 6.9387\n", "PREDICT: 7.9494 2.0029\tUPDATE: 7.3963 1.0007\tZ: 6.8439\n", "PREDICT: 8.3963 2.0007\tUPDATE: 9.1217 1.0002\tZ: 9.8468\n", "PREDICT: 10.1217 2.0002\tUPDATE: 11.3376 1.0000\tZ: 12.5535\n", "PREDICT: 12.3376 2.0000\tUPDATE: 14.3054 1.0000\tZ: 16.2731\n", "PREDICT: 15.3054 2.0000\tUPDATE: 15.0529 1.0000\tZ: 14.8004\n", "actual final position: 14.8383\n" ] }, { "data": { "image/png": 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uBH//HDu3YRgs+wPGzIOf1zvW16sBQ7vCww29cXMLB8Jz7Nquou8x52nMnBcf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\nOnTg8OHDFlVUf5w4cYL169ezcOFCq0vxeLNnz2bmzJmMGTM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "##### assume dog is always moving 1m to the right\n", "np.random.seed(13)\n", "pos = (0., 400.) # gaussian N(0, 400)\n", "velocity = 1.\n", "# variance in process model and the RFID sensor\n", "process_variance = 1.\n", "sensor_variance = 2.\n", "N = 10\n", "\n", "dog = DogSimulation(pos[0], velocity=velocity, \n", " measurement_variance=sensor_variance, \n", " process_variance=process_variance)\n", "# simulate dog and get measurements\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", "positions = np.zeros(N)\n", "for i, z in enumerate(zs):\n", " pos = predict(pos=pos[0], variance=pos[1], \n", " movement=velocity, movement_variance=process_variance)\n", " print('PREDICT: {: 10.4f} {: 10.4f}'.format(pos[0], pos[1]),end='\\t')\n", "\n", " pos = update(mean=pos[0], variance=pos[1],\n", " measurement=z, measurement_variance=sensor_variance)\n", " positions[i] = pos[0]\n", " print('UPDATE: {: 10.4f} {: 10.4f}\\tZ: {:.4f}'.format(pos[0], pos[1], z))\n", "\n", "print('actual final position: {:10.4f}'.format(dog.x))\n", "bp.plot_filter(positions)\n", "bp.plot_measurements(zs)\n", "bp.show_legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we discuss the code and results, let's try to understand this better with this chart showing one predict update cyle." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KS+np6W6vL1++rPbt2yspKUnPP/+8mjVrprJly8rHx0eTJ0/Wpk2bbBkTCofD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\nbLwzZpjzjRsnvfGG+z5n2Ue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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mkf_internal import show_residual_chart\n", "show_residual_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This chart is very similar to one we already saw in the *g-h Filter* chapter. At each predict step we take our existing estimate and update it based on our system model. We then make a measurement. We know neither the measurement or prediction is perfect, so we choose a value in between the two. This is scaled so that the new estimate is closer to the one we trust more. We then step time forward one step, and what was the new estimate is considered to be the prior estimate, and the process repeats. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's walk through the code and output.\n", "\n", " pos = (0., 400.) # gaussian N(0, 400)\n", "\n", " \n", "Here we set the initial position at 0 m. We set the variance to 400 m$^2$, which is a standard deviation of 20 meters. You can think of this as saying \"I believe with 99% accuracy the position is 0 plus or minus 60 meters\". This is because with Gaussians ~99% of values fall within 3$\\sigma$ of the mean.\n", "\n", " velocity = 1.\n", " \n", "So how do I know the velocity? Magic? Consider it a prediction, or perhaps we have a secondary velocity sensor. If this is a robot then this would be a control input to the robot. In the next chapter we will learn how to handle situations where you don't have a velocity sensor or input, so please accept this simplification for now.\n", "\n", " process_variance = 1.\n", " sensor_variance = 2.\n", " \n", "Here the variance for the predict step is `process_variance` and the variance for the sensor is `sensor_variance`. The meaning of sensor variance should be clear - it is how much variance there is in each sensor reading. The process variance is how much error there is in the prediction model. We are predicting that at each time step the dog moves forward one meter. Dogs rarely do what we expect, and of course things like hills or the whiff of a squirrel will change his progress. If this was a robot responding to digital commands the performance would be better, but not perfect. Perhaps a hand made robot would have a variance of $\\sigma^2=.1$, and an industrial robot might have $\\sigma^2=0.02$. These are not 'magic' numbers; the square root of the express the distance error in meters. It is easy to get a Kalman filter working by just plugging in numbers, but if the numbers do not reflect reality the performance of the filter will be poor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we initialize the simulator and run it with\n", "\n", " dog = DogSimulation(pos[0], velocity=velocity, \n", " measurement_variance=sensor_variance, \n", " process_variance=process_variance)\n", "\n", " # simulate dog and get measurements\n", " zs = [dog.move_and_sense() for _ in range(N)]\n", " \n", "It may seem very 'convenient' to set the simulator to the same position as our guess, and it is. Do not fret. In the next example we will see the effect of a wildly inaccurate guess for the dog's initial position. We move the dog for 10 steps forward and store the measurements in `zs` via a list comprehension.\n", "\n", "It is traditional to call the measurement $z$, and so I follow that convention here. When I was learning this topic I found the standard names very obscure. However, if you wish to read the literature you will have to become used to them, so I will not use a more readable variable name such as `m` or `measure`. It is something you have to memorize if you want to work with Kalman filters. As we continue I will introduce more of the standard naming into the code. The `s` at the end of the name is a plural - I'm saying there are many `z`s in the list.\n", "\n", "The next code allocates an array to store the output of the filtered positions. \n", "\n", " positions = np.zeros(N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we enter our `predict() ... update()` loop.\n", "\n", " for i in range(N):\n", " pos = predict(pos=pos[0], variance=pos[1], \n", " movement=vel, movement_variance=process_variance)\n", "\n", "We call the `predict()` function with the Gaussian for the dog's position, and another Gaussian for its movement. `pos[0], pos[1]` is the mean and variance for the position, and 'vel, process_variance' is the mean and variance for the movement. The first time through the loop we get\n", "\n", " PREDICT: 1.000 401.00\n", "\n", "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 401. Recall we started at 400. The variance got worse, which is always what happens during the prediction step because it involves a loss of information.\n", "\n", "Then we call the update function of our filter and save the result in our `positions` array.\n", "\n", " pos = update(pos[0], pos[1], z, sensor_variance)\n", " positions.append(pos[0])\n", " \n", "For this I get this as the result:\n", "\n", " UPDATE: 1.3518 1.9901\tZ: 1.3536\n", " \n", "What is happening? The dog is actually at 1.0 but the measured position is 1.3536 due to the sensor noise. That is pretty far off from the predicted value of 1. The filter incorporates that measurement into its prediction. This is the first time through the loop and so the variance is 401 m$^2$. A large variance implies that the current prediction is very poor, so the filter estimates the position to be 1.3518 - very close to the measurement. Intuition tells us that the results should get better as we make more measurements, so let's hope that this is true for our filter as well.\n", "\n", "Now look at the variance: 1.9901 m$^2$. It has dropped tremendously from 401 m$^2$. Why? Well, the RFID has a reasonably small variance of 2.0 m$^2$, so we trust it far more than our previous belief.\n", "\n", "Now the software loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 15.0529 vs the actual position of 14.8383. The variance has converged to 1.0 m$^2$. \n", "\n", "Now look at the plot. The noisy measurements are plotted in with a dotted red line, and the filter results are in the solid blue line. Both are quite noisy, but notice how much noisier the measurements (red line) are. This is your first Kalman filter and it seems to work!\n", "\n", "Before we continue I want to point out how few lines of code actually perform the filtering. Most of the code is either initialization, storing of data, simulating the dog movement, and printing results. The code that performs the filtering is the very succinct\n", "\n", " for i in range(N):\n", " pos = predict(pos=pos[0], variance=pos[1], \n", " movement=vel, movement_variance=process_variance)\n", " pos = update(mean=pos[0], variance=pos[1],\n", " measurement=z, measurement_variance=sensor_variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example I only plotted 10 data points so the output from the print statements would not overwhelm us. Now let's look at the filter's performance with more data. This time we will plot both the output of the filter and the variance. The variance is plotted as a lightly shaded yellow area between dotted lines. I've increased the size of the process and sensor variance so they are easier to see on the chart - for a real Kalman filter of course you will not be randomly changing these values." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Variance:\n", "\t4.4502 2.6507 2.2871 2.1955 2.1712\n", "\t2.1647 2.1629 2.1625 2.1623 2.1623\n", "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", "\t2.1623 2.1623 2.1623 2.1623 2.1623\n", "\t2.1623 2.1623 2.1623 2.1623 2.1623\n" ] }, { "data": { "image/png": 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t+MCBY7z//tfMmfMu4M1TT3Vn7NhxNG/evkINCzeSs3vpCSGsKjXhHD9+PMuW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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "process_variance = 2\n", "sensor_variance = 4.5\n", "pos = (0, 400) # gaussian N(0, 100)\n", "N = 25\n", "\n", "dog = DogSimulation(pos[0], velocity=velocity, \n", " measurement_variance=sensor_variance, \n", " process_variance=0.5)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", "positions, variance = [], []\n", "for i, z in enumerate(zs):\n", " pos = predict(pos[0], pos[1], velocity, process_variance) \n", " variance.append(pos[1])\n", " \n", " pos = update(pos[0], pos[1], z, sensor_variance)\n", " positions.append(pos)\n", " \n", "positions = np.array(positions) #convert to ndarray so I can use [:, 0] \n", "bp.plot_measurements(zs)\n", "bp.plot_filter(positions[:, 0], vars=variance)\n", "bp.show_legend()\n", "\n", "print('Variance:')\n", "for i in range(0, len(positions), 5):\n", " print('\\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(\n", " *[v[1] for v in positions[i:i+5]]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see that the variance converges very quickly to roughly 2.1623 in 10 steps. We interpret this as meaning that we become very confident in our position estimate very quickly. The first few measurements are unsure due to our uncertainty in our guess at the initial position, but the filter is able to quickly determine an accurate estimate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Before I go on, I want to emphasize that this code fully implements a 1D Kalman filter. If you have tried to read the literature, you are perhaps surprised, because this looks nothing like the complex, endless pages of math in those books. To be fair, the math gets more complicated in multiple dimensions, but not by much. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters without a lot of effort. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent our beliefs with Gaussians, and our beliefs get better over time because more measurements means more data to work with." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Animating the Tracking" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you are reading this in IPython Notebook you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The top plot shows the output of the filter in green, and the measurements with a dashed red line. The bottom plot shows the Gaussian at each step. \n", "\n", "When the track first starts you can see that the measurements varies quite a bit from the initial prediction. At this point the Gaussian probability is small (the curve is low and wide) so the filter does not trust its prediction. As a result, the filter adjusts its estimate a large amount. As the filter innovates you can see that as the Gaussian becomes taller, indicating greater certainty in the estimate, the filter's output becomes very close to a straight line. At `x=15` and greater you can see that there is a large amount of noise in the measurement, but the filter does not react much to it compared to how much it changed for the firs noisy measurement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Kalman Filter is a g-h Filter\n", "\n", "\n", "Earlier we set $\\sigma_\\mathtt{prior}^2 = 9\\sigma_\\mathtt{z}^2$, to get\n", "\n", "$$\\mu= \\frac{1}{10} \\mu_\\mathtt{prior} + \\frac{9}{10} \\mu_\\mathtt{z}$$\n", "\n", "We can see that we are scaling the prior and the measurement by some factor. Think back to the *The g-h Filter* chapter and this plot:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YunTpAnd3d+Tk5GDlypVo0KABnnnmGQBAQEAATExMMHfuXNy6dQu2trZo2bJl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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import gh_internal\n", "gh_internal.plot_estimate_chart_3()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Kalman filter equation is performing this computation! We have two measurements, or a measurement and a prediction, and the new estimate is chosen as some value between the two. So, as promised, the Kalman filter is a g-h filter. \n", "\n", "I have not made it explicit in this chapter, but the scaling factor is called the **Kalman gain**. In this equation\n", "\n", "$$\\mu= \\frac{1}{10} \\mu_\\mathtt{prior} + \\frac{9}{10} \\mu_\\mathtt{z}$$\n", "\n", "we can set the Kalman gain $K$ to .9, and rewrite the equation as\n", "\n", "$$\\mu = (1-K)\\mu_\\mathtt{prior} + K\\mu_\\mathtt{z}$$\n", "\n", "That is a general equation for the Kalman filter in the one dimensional case. \n", "\n", "How does this differ from the g-h filter? In the g-h filter we chose the constants $g$ and $h$ and didn't vary them. Here the scaling factors are chosen dynamically based on the current variance of the filter and the variance of the measurement. in other words the Kalman gain is determined by a ratio of the variances of the prior and measurement. As the Kalman filter innovates the scaling factors change as we become more (or less) certain about our answer.\n", "\n", "Some algebra will reveal the relationship between the Kalman filter and the g-h filter. If you are curious, I present it in *Kalman Filter Math* chapter.\n", "\n", "At each time step we can show that $g$ equals\n", "\n", "$$g = \\frac{\\sigma^2_\\mathtt{prior}}{\\sigma^2_\\mathtt{z}}$$\n", "\n", "This make intuitive sense. When we perform an update we choose a value somewhere between the measurement and prediction. If the measurement is more accurate we will choose a value nearer it, and vice versa. This computation for $g$ is a ratio of the errors in the prediction and the measurement.\n", "\n", "The equation for $h$ is similar.\n", "\n", "$$h = \\frac{COV (x,\\dot{x})}{\\sigma^2_\\mathtt{z}}$$\n", "\n", "We haven't discussed the covariance (denoted by $COV$), so you may not fully understand this equation. Think of the numerator as the variance between the state and its velocity. Recall that $g$ is used to scale the state, and $h$ is used to scale the velocity of the state, and this equation should seem reasonable. In the next chapter it will become very clear.\n", "\n", "The takeaway point is that *g* and *h* are specified fully by the variance and covariances of the measurement and predictions at time *n*. That is all the Kalman filter is. It is easier to think of the noise in the measurement and the process model, so we don't normally use the g-h formulation, but we could. It's the same thing written differently. The Kalman filter is a g-h filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fixed Gain Filters\n", "\n", "Embedded applications usually have extremely limited processors; many do not have floating point circuitry. These simple equations can impose a heavy burden on the chip. This is less true as technology advances, but do not underestimate the value of spending 10 cents less on a processor for devices that will be manufactured in the millions.\n", "\n", "In the example I ran above the variance of the filter converged to a fixed value. This will always happen if the variance of the measurement is a constant. You can take advantage of this fact by running simulations to determine what the variance converges to. Then you can hard code this value into your filter. So long as you initialize the filter to a good starting guess (I recommend using the first measurement as your initial value the filter will perform very well. \n", "\n", "So for embedded applications it is common to perform many simulations to determine a fixed Kalman gain value, and then hard code this into the application. Besides reducing chip cost this also makes verifying correctness easier. You can scoff at that since it is a tiny difference, but if you are making a medical device, a device that is being sent into space, or a device that will have one million copies made then an error can cost lives, end a scientific mission, or and/or cost millions of dollars. A professional engineer does everything she can, no matter how small, to reduce and eliminate risks." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation in a Class" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For many purposes the code above suffices. However, if you write enough of these filters the functions will become a bit annoying. For example, having to write\n", "\n", " pos = predict(pos[0], pos[1], movement, movement_variance) \n", " \n", "is a bit cumbersome and error prone. Let's investigate how we might implement this in a form that makes our lives easier.\n", "\n", "First, values for the movement error and the measurement errors are typically constant for a given problem, so we only want to specify them once. We can store them in instance variables in the class. Second, it is annoying to have to pass in the state (pos in the code snippet above) and then remember to assign the output of the function back to that state, so the state should also be an instance variable. Our first attempt might look like:\n", "\n", " class KalmanFilter1D:\n", " def __init__(self, initial_state, measurement_variance, movement_variance):\n", " self.state = initial_state\n", " self.measurement_variance = measurement_variance\n", " self.movement_variance = movement_variance\n", "\n", "That works, but I am going to use different naming. The Kalman filter literature uses math, not code, so it uses single letter variables, so I will start exposing you to it now. At first it seems impossibly terse, but as you become familiar with the nomenclature you'll see that the math formulas in the textbooks will have an exact one-to-one correspondence with the code. Unfortunately there is not a lot of meaning behind the naming unless you have training in control theory; you will have to memorize them. If you do not make this effort you will never be able to read the literature.\n", "\n", "So, we use `x` for the state (estimated value of the filter) and `P` for the variance of the state. `R` is the measurement error, and `Q` is the process (prediction) error. This gives us:\n", "\n", " class KalmanFilter1D:\n", " def __init__(self, x0, P, R, Q):\n", " self.x = x0\n", " self.P = P\n", " self.R = R\n", " self.Q = Q\n", " \n", "Now we can implement the `update()` and `predict()` function. In the literature the measurement is usually named either `z` or `y`; I find `y` is too easy to confuse with the y axis of a plot, so I like `z`. I like to think I can hear a `z` in *measurement*, which helps me remember what `z` stands for. So for the update method we might write:\n", "\n", " def update(z):\n", " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n", " self.P = 1 / (1/self.P + 1/self.R)\n", "\n", "Finally, the movement is usually called `u`, and so we will use that. So for the predict function we might write:\n", "\n", " def predict(self, u):\n", " self.x += u\n", " self.P += self.Q\n", " \n", "That give us the following code. Production code would require significant comments and error checking. However, in the next chapter we will develop Kalman filter code that works for any dimension so this class will never be more than a stepping stone for us." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [], "source": [ "class KalmanFilter1D:\n", " def __init__(self, x0, P, R, Q):\n", " self.x = x0\n", " self.P = P\n", " self.R = R\n", " self.Q = Q\n", "\n", " def update(self, z):\n", " self.x = (self.P * z + self.x * self.R) / (self.P + self.R)\n", " self.P = 1. / (1./self.P + 1./self.R)\n", "\n", " def predict(self, u=0.0):\n", " self.x += u\n", " self.P += self.Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Full Description of the Algorithm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the first chapter I stated that the Kalman filter is a form of g-h filter. Recall the diagram we used:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EAmzfvh01NTVYunQpsrOz25w3orMoAbBROTk5OHr0KLfs7OyMxMREm3vamC1g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\n3rwZTz31FEwmE6qqqnDx4sURn7uFvTEA27dvh9lsxiuvvIK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import gh_internal\n", "gh_internal.create_predict_update_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is what we have been doing in this chapter. But also recall this chart from the *g-h Filter* chapter, which displayed how we created a new weight estimate from the prediction of the previous day along with the current day's measurement." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YunTpAnd3d+Tk5GDlypVo0KABnnnmGQBAQEAATExMMHfuXNy6dQu2trZo2bJl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\ngIAAtGzZEiYmJujatSsSEhIaMFrdper/hyqXLl2CmZkZzMz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gh_internal.plot_estimate_chart_3()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the exception of the axis labels of 'day' and 'weight' this is the same as the residual chart I made earlier in this chapter. \n", "\n", "**This is extremely important to understand**: Every filter in this book implements the **same algorithm**, just with different mathematical details. We make a prediction, make a measurement, and then choose the new estimate to be somewhere between those two. The math can become challenging in later chapters, but the idea is easy to understand.\n", "\n", "It is important to see past the details of the equations of a specific filter and understand *what* the equations are calculating and *why*. This is important not only so you can understand the filters in this book, but so that you can understand filters that you will see in other situations. There are a tremendous number of filters that we do not describe - the SVD filter, the unscented particle filter, the H$_\\infty$ filter, the ensemble filter, and so many more. They all use different math to implement the same algorithm. The choice of math affects the quality of results, not the underlying ideas.\n", "\n", "Here it is:\n", "\n", "**Initialization**\n", "\n", " 1. Initialize the state of the filter\n", " 2. Initialize our belief in the state - how accurate do we think it is\n", " \n", "**Predict**\n", "\n", " 1. Use system behavior to predict state at the next time step\n", " 2. Add uncertainty to belief to account for the uncertainty in prediction\n", " \n", "**Update**\n", "\n", " 1. Get a measurement and associated belief about its accuracy\n", " 2. Compute difference (residual) between our estimated state and measurement\n", " 3. Compute scaling factor based on whether the measurement or prediction is more accurate\n", " 4. set state between the prediction and measurement based on scaling factor\n", " 5. update belief in the state based on how certain we are in the measurement\n", "\n", "You will be hard pressed to find a Bayesian filter algorithm that does not fit into this form. Some filters will not include some aspect, such as error in the prediction, and others will have very complicated methods of computation, but this is what they all do. If you go back to the g-h filter chapter and reread it you'll recognize that the very simple thought experiments we did there result in this algorithm." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Modify Variance Values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Modify the values of `movement_variance` and `sensor_variance` and note the effect on the filter and on the variance. Which has a larger effect on the variance convergence?. For example, which results in a smaller variance:\n", "\n", " movement_variance = 40\n", " sensor_variance = 2\n", " \n", "or:\n", "\n", " movement_variance = 2\n", " sensor_variance = 40" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction to Designing a Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far we have developed our filter based on the dog sensors introduced in the Discrete Bayesian filter chapter. We are used to this problem by now, and may feel ill-equipped to implement a Kalman filter for a different problem. To be honest, there is still quite a bit of information missing from this presentation. The next chapter will fill in the gaps. Still, lets get a feel for it by designing and implementing a Kalman filter for a thermometer. The sensor for the thermometer outputs a voltage that corresponds to the temperature that is being measured. We have read the manufacturer's specifications for the sensor, and it tells us that the sensor exhibits white noise with a standard deviation of 0.13.\n", "\n", "We do not have a real sensor to read, so we will simulate the sensor with the following function. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def volt(voltage, temp_variance):\n", " return voltage + (randn() * temp_variance)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We generate white noise with a given variance using the equation `randn() * variance`. The specification gives us the standard deviation of the noise, not the variance, but recall that variance is the square of the standard deviation. Hence we raise 0.13 to the second power." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we need to write the Kalman filter processing loop. As with our previous problem, we need to perform a cycle of predicting and updating. The sensing step probably seems clear - call `volt()` to get the measurement, pass the result into `update()` function, but what about the predict step? We do not have a sensor to detect 'movement' in the voltage, and for any small duration we expect the voltage to remain constant. How shall we handle this?\n", "\n", "As always, we will trust in the math. We have no known movement, so we will set that to zero. However, that means that we are predicting that the temperature will never change. If that is true, then over time we should become extremely confident in our results. Once the filter has enough measurements it will become very confident that it can predict the subsequent temperatures, and this will lead it to ignoring measurements that result due to an actual temperature change. This is called a *smug* filter, and is something you want to avoid. So we will add a bit of error to our prediction step to tell the filter not to discount changes in voltage over time. In the code below I set `process_variance = .05**2`. This is the expected variance in the change of voltage over each time step. I chose this value merely to be able to show how the variance changes through the update and predict steps. For an real sensor you would set this value for the actual amount of change you expect. For example, this would be an extremely small number if it is a thermometer for ambient air temperature in a house, and a high number if this is a thermocouple in a chemical reaction chamber. We will say more about selecting the actual value in the next chapter. \n", "\n", "Let's see what happens. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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3kd2++eYb3nnnLRTlLKoaR7t2TdPNS5xXqKpKsWKFrcsFC7oyb95o7s47n3++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\niIiIiHiUElMRERERERHxqP8H/gKcRrCUNJIAAAAASUVORK5CYII=\n", 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3Jp478QAAAHBz7SLEdwzoLG+vc++1+ramSrV1NS4eEQAAAHDx2kWI9zJ5KZB1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\nB/Xp00cbN2508tJ+WOYOnTT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Variance converges to 0.005\n" ] }, { "data": { "text/plain": [ "array([ 0.1299989 , 0.09503628, 0.08279246, 0.07759846, 0.0752664 ,\n", " 0.07419731, 0.073703 , 0.0734736 , 0.07336696, 0.07331735,\n", " 0.07329426, 0.07328351, 0.07327851, 0.07327618, 0.07327509,\n", " 0.07327459, 0.07327436, 0.07327425, 0.07327419, 0.07327417,\n", " 0.07327416, 0.07327416, 0.07327415, 0.07327415, 0.07327415,\n", " 0.07327415, 0.07327415, 0.07327415, 0.07327415, 0.07327415,\n", " 0.07327415, 0.07327415, 0.07327415, 0.07327415, 0.07327415,\n", " 0.07327415, 0.07327415, 0.07327415, 0.07327415, 0.07327415,\n", " 0.07327415, 0.07327415, 0.07327415, 0.07327415, 0.07327415,\n", " 0.07327415, 0.07327415, 0.07327415, 0.07327415, 0.07327415])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "temp_change = 0\n", "variance = .13**2\n", "process_variance = .05**2\n", "actual_voltage = 16.3\n", "\n", "N = 50\n", "zs = [volt(actual_voltage, variance) for i in range(N)]\n", "ps = []\n", "estimates = []\n", "\n", "kf = KalmanFilter1D(x0=25, # initial state\n", " P=1000, # initial variance \n", " # large says 'who knows?'\n", " R=variance, # sensor noise\n", " Q=process_variance) # error in prediction\n", "\n", "for i in range(N):\n", " kf.predict(temp_change)\n", " kf.update(zs[i])\n", "\n", " # save for latter plotting\n", " estimates.append(kf.x)\n", " ps.append(kf.P)\n", "\n", "# plot the filter output and the variance\n", "bp.plot_measurements(zs)\n", "bp.plot_filter(estimates, vars=np.array(ps))\n", "bp.show_legend()\n", "plt.show()\n", "plt.plot(ps)\n", "plt.title('Variance')\n", "plt.show()\n", "print('Variance converges to {:.3f}'.format(ps[-1]))\n", "np.sqrt(ps)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first plot shows the individual sensor measurements vs the filter output. Despite a lot of noise in the sensor we quickly discover the approximate voltage of the sensor. In the run I just completed at the time of authorship, the last voltage output from the filter is $16.213$, which is quite close to the $16.4$ used by the `volt()` function. On other runs I have gotten larger and smaller results.\n", "\n", "Spec sheets are what they sound like - specifications. Any individual sensor will exhibit different performance based on normal manufacturing variations. Values are often maximums - the spec is a guarantee that the performance will be at least that good. So, our sensor might have standard deviation of 1.8. If you buy an expensive piece of equipment it often comes with a sheet of paper displaying the test results of your specific item; this is usually very trustworthy. On the other hand, if this is a cheap sensor it is likely it received little to no testing prior to being sold. Manufacturers typically test a small subset of their output to verify that a sample falls within the desired performance range. If you have a critical application you will need to read the specification sheet carefully to figure out exactly what they mean by their ranges. Do they guarantee their number is a maximum, or is it, say, the $3\\sigma$ error rate? Is every item tested? Is the variance normal, or some other distribution? Finally, manufacturing is not perfect. Your part might be defective and not match the performance on the sheet.\n", "\n", "For example, I am looking at a data sheet for an airflow sensor. There is a field *Repeatability*, with the value $\\pm 0.50\\%$. Is this a Gaussian? Is there a bias? For example, perhaps the repeatability is nearly 0.0% at low temperatures, and always nearly +0.50 at high temperatures. Data sheets for electrical components often contain a section of \"Typical Performance Characteristics\". These are used to capture information that cannot be easily conveyed in a table. For example, I am looking at a chart showing output voltage vs current for a LM555 timer. There are three curves showing the performance at different temperatures. The response is ideally linear, but all three lines are curved. This clarifies that errors in voltage outputs are probably not Gaussian - in this chip's case higher temperatures leads to lower voltage output, and the voltage output is quite nonlinear if the input current is very high. \n", "\n", "As you might guess, modeling the performance of your sensors is one of the harder parts of creating a Kalman filter that performs well. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Animation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For those reading this in IPython Notebook, here is an animation showing the filter working. The top plot in the animation draws a green line for the predicted next voltage, then a red '+' for the actual measurement, draws a light red line to show the residual, and then draws a blue line to the filter's output. You can see that when the filter starts the corrections made are quite large, but after only a few updates the filter only adjusts its output by a small amount even when the measurement is far from it. \n", "\n", "The lower plot shows the Gaussian belief as the filter innovates. When the filter starts the Gaussian curve is centered over 25, our initial guess for the voltage, and is very wide and short due to our initial uncertainty. But as the filter innovates, the Gaussian quickly moves to about 16.0 and becomes taller, reflecting the growing confidence that the filter has in it's estimate for the voltage. You will also note that the Gaussian's height bounces up and down a little bit. If you watch closely you will see that the Gaussian becomes a bit shorter and more spread out during the prediction step, and becomes taller and narrower as the filter incorporates another measurement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Think of this animation in terms of the g-h filter. At each step the g-h filter makes a prediction, takes a measurement, computes the residual (the difference between the prediction and the measurement), and then selects a point on the residual line based on the scaling factor *g*. The Kalman filter is doing exactly the same thing, except that the scaling factor *g* varies with time. As the filter becomes more confident in its state the scaling factor favors the filter's prediction over the measurement. \n", "\n", "> If this is not clear, I urge you to go back and review the g-h chapter. This is the crux of the algorithms in this book. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise(optional):" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Write a function that runs the Kalman filter many times and record what value the voltage converges to each time. Plot this as a histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?\n", "\n", "> use plt.hist(data, bins=100) to plot the histogram. " ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "variance = 2.13**2\n", "actual_voltage = 16.3\n", "\n", "def VKF():\n", " N = 50\n", " voltage = (14, 1000)\n", " for i in range(N):\n", " Z = volt(actual_voltage, variance)\n", " voltage = update(voltage[0], voltage[1], Z, variance)\n", " return voltage[0]\n", "\n", "vs = []\n", "for i in range(10000):\n", " vs.append(VKF())\n", "plt.hist(vs, bins=100, color='#e24a33');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results do in fact look like a normal distribution. Each voltage is Gaussian, and the **Central Limit Theorem** guarantees that a large number of Gaussians is normally distributed. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Extreme Amounts of Noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I didn't put a lot of noise in the signal, and I also 'correctly guessed' that the dog was at position 0. How does the filter perform in real world conditions? Let's explore and find out. I will start by injecting a lot of noise in the RFID sensor. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition tell about how the filter will perform if the noise is allowed to be anywhere from -300 or 300. In other words, an actual position of 1.0 might be reported as 287.9, or -189.6, or any other number in that range. Think about it before you scroll down." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/5bqS6ysqpfEkRURE4FKup+nKlSswGo0IU55Q7jZ8+ytXriA8PFz1uSRJiIiI\nyFtHIPPUU0+hSZMm+d7eVRQ9P2RlZcG/IPxwAoHg/qR1ayoscr/DI3IFRceOOKmNbj7qXL5M0fDX\nX6f3J06QV9ZRpc4Hxe50LwkIIEGpLTqjR2Ymre+IlSvl35ctoywjx46ReAwKojzinPh4ioS3by8v\nmzePovVJSeqqnzz1oSSRP5rjKm2ixUJCvFUr6hj8+y/Qpg3w669yW6xWEvlnz5KIfuop6riVLUvP\nr80mW1aCg6ktJhOdW0gIUKaM+phRUZTZ5do1GhnYv5+243Abib8/nX9OjuynT0qitI6cixcpMn77\nNvnrX3hBfW7KDobJRM/BTz/R+n5+wEcf6V+XwhTkznAl+pjeEIuH7Nu3z+FnFStWhF9BzGB+QDh3\n7hwqV66MefPm4eWXX9Zdp3Xr1ti2bRsAqOxH3MvPGMPXX3+NOXPm4NSpUyhWrBieffZZTJkyRdWh\nioqKQo0aNfB///d/+OCDD5CQkID33nsPY8eOLcQzFKSnp+Pw4cNF3YyHEmd/SwREgMWCijExOHaf\nX6uGFgsOHDoEpq1SeDfk/r0U9wlR5vvvUW7OHOzLDQzVycrCyZMnUSMnBwd0rlGFK1eQ5e+P64/I\n9VPeJ6UXLoQxLQ0X//Mfu/W8r19HjbQ0JLi4LpUvXEDKlStI0a5ns6GRJGF/Tg6Q+1mVAwdws3Nn\nlDOZcPrQIfhVrQpz06bIyP08YulS+F68iGSFfaTc+fMoA+DMwYPwXbcOpvBw3OzSBWXmzkU5ACar\nFbbsbHBFdfjQIWRnZKAxgMysLBzVtKt2RgZOL1mCrMqV0RhAyoQJOB0cjEbdumH/7t2A0QjJZEID\noxH/nD8PQ2YmGgI4vHMnsitVgiEzExE9eiBNkuBTuzbKbduG07t3wxwaijomEySzGYcSEmDT6aR4\nX7uGegCuT5yIqz17onbu8qzMTGTduIGUc+dg/OwzBB4/jvMffAAwhsZNmiBhzRqYcoscBR4+jBr7\n98MUEQEfACnXriF57VqE7NyJ1BYtUMNmk78ziwWN5s0DAOw/eBDFd+xA6MaNOPvpp3Zt8500CRXs\nlqrJd7e1dG7jr2qGMq9evZr3WenSpWG1WnFTY47XrnNdM1OXMYZr167lrSOQSU1NxY0bN1QvjrOO\n0JgxY1C/fn2ULFkSixYtyntxhg0bhrfffhuPPfYYZsyYgSFDhmDFihVo06YNchQTciRJwqlTp9Cj\nRw+0adM9CAX3AAAgAElEQVQGM2fOVNmNBALBwweTJEjuFBQpYkylShVohNyQmYkId3y+jzI2G5iP\nDyRHFSAZe2Qj5FJODpgiohqydSv8covE2Hx9YXBjsqsxKws2vRFoxpD0zjsqW4rvpUswlS0LZjRC\nYgypTzyBjDp16LPkZBiys+2eY8lsxpW+fZH6xBMwpqfD6/ZtVJg8GaF//gmbry9sfn6qbSRFQNVc\nsqT9OVsssPr7I3LmTKQ1bgzm7Q1IEpi3N6TcKLGkGDXJW5ZrN7EFBOBK//7IrFEDqW3b4tLQobCE\nhualG5SsVjsbWdi6dfC5dAkSH6Wx2WCwWMByr41kNkOy2cAMBhjMZthyLSXG3AQkksLqom2PwWxG\n6fnzUfG//83bR6lFi2DIyqJoOWOQbDZU/ugjBB454vA5yNFOatWDuUlQUBBbsGBB3nubzcbKlCnD\nJk2alLcsKyuLFStWjM2ZM4cxxlhqairz8fFhcXFxeeskJyczg8HANmzYwBhj7OjRo0ySJLZr1668\ndXbu3MkkSWInTpxQtSE1NTXv5YysrCx3T4uN/cHGpOaF9xr7g83ttjhj3rx5TJIku5fBYGCHDx9m\nkiSpvh++/vnz5/OWPf3006xSpUp2++bXe9GiRarlO3bsYJIk5X2fjDFWsWJFJkkSW7NmTYGcl8A9\nPLmnBe4RHx/P4uPji7oZDwaHDjFWp05Rt8I1MTGMHTvGGMDYwYN3v78rV5ipRImCvU927WJs376C\n25+WLVsYmz698Pa/ejVjbdvK78uWZez8ecYkSX/9IUMY+/bbwmvPfYLu35P332esfHnG1q+n9z17\nMrZ0Kf2enc2Yt7frHZ86xZgLzcMYY8xmYyw4mLFbtxhbuZKxGzfUnz/xBGM9ejA2bJh6+ciRjE2b\nRr9XqsTYoEGMvfQSYw0aMNaxIz1TUVH0TD39NGNHjsjrnjpl345Ro+jY9eox9s47jPXqRfeAlxdj\nKSm0TloaY4GB9PuVK7TvvXvpfa1ajFks9vvl2xiNjJnN6s8ef5yxbdsYO3GC9jVgAGO7dzPWuDE9\nb6NG0T6tVsamTmXsrbdou4QEWv/sWXlfmzbRsrp16Wfbtox17Uq/f/ABfRfh4dRuxui8AMZat2Zs\n8GA6X8YYq12bXU9OY9+tsrHRs2zsiddtLjWsU8tKRkYGTp48mdvhsOH8+fM4ePAgwsLCUL58eYwa\nNQqTJk1C9erVUbVqVUycOBHBwcF4KTcpe0hICF599VWMHj0aERERKFGiBN566y3Uq1cP7dq1AwDU\nqFEDHTt2xNChQzFnzhwwxjB06FA8++yzqFq1qusexSPGzJkzUUM5mQG4a3vO8uXLERQUhA4dOqgi\n7jExMYiIiMCWLVswePDgvOXly5fHM888c1fHFAgEDxCRkZQ94X6HlwavWbNgJnd6eTmO/OaXWbPI\na/rDDwW7X86HH1Iau8KavF+8uLpqo81GKd4GD5bzNCuJjFRPcnuUyMmhSZMnTpBPetkyivT27En+\n6KFD9a+Zkqws+k5dVcq9c4eudWgoFcfRYjLRfae9n7lXGyBP94kT5NH286NqlYMHUz7wrl3lIkMA\npWPUy2s+bRr99PGhY9lsVMLe21tOf6nMhsS91SYTXYsjR/RHVCZOpMmdx4/bj4Ll5NDxoqPpudq6\nle7Tjh2pMqlyFP/UKfK4f/EFHXP4cHVKRpOJths5Epg6FVi9mr6D//2P8r43aqQuDmQ0glksuOBX\nAYevVsIGU32kT2a4gC+x+aVAWDz48+H0L1Z8fDzatm0LgKwKY8eOxdixYzFgwADMnTsXo0ePRlZW\nFoYPH46UlBQ0a9YMGzZsQGBgYN4+pk+fDi8vL/Ts2RNZWVlo164dFi1apLJXxMXFYcSIEXjqqacA\nAM899xy+fhTLNLtBbGys3aTOc+fO3dU+T5w4gTt37thN0OVoLUWVtTlVBQLBw02JEurJTfcrPEMD\nF+Z3i16Z7LulenW3S2nnC02ShAKnZUt6cYKCgLFjSbzoCcvnn6f8125UKnzo4EJRWanz3DkSuBkZ\nVADnpZcopV/z5o734U6V3OBgyj7iCJOJJjVqn4uKFYFy5eT3kkTPkK8vTSbt1o0yjWgtF126OG+P\njw89O1Yr/QwOlgW5sq2845yTI2eG0buPeLDQzw9IS6PJncpzO3oUaNKE2m210nM2YYJ6HzEx9Fly\nMr1v1EjdueTt8PGhzk3XrnQNAgKAHj1g/Xkllt1qhL3hE+G3MAhBoTk4Vf47bCneFhfSIuV9rAVQ\nrB3gYV/eqSBv3bq1qoCPHlykO8LHxwczZszAjBkzHK5TvHhx/FREOW7HvSph3KtFcuj7BpvNhrCw\nMCxz4JUM1eQPFRlVBIJHjPXrqdDI/V6wjQvxghLkP/0Er4yMu9+PEh8fyshQWPTo4TwrR0HTuDGw\ndKkoDKRHTg4JR+35KzPI3bwpZzTRg5dld0SzZhQRdjSR+eWXgcmTSbQ2aWKf2vDdd9XvJYmendBQ\n6mwBwBNPOD6+I3x8qHNYqhRFl597To7EGwzUCejUifKZ79lDxZOc1RHw8qIiQW+9RZ2Y7t3lz3Jy\nqMPXrx91HGJjHberWDHn7a5endJ41q6N5PBaOHeQ4cwlYG/lWdjY7HOcnlcBCH4FWJO7fkR/p7tr\nVs2MDrunI2zCO86Pi0LKsiK4P3E06bNKlSrYtGkTmjZtqhrdEAgEjyCSBGzfDjz+uLzs2DFKD3a/\nC3KeMq2gBHlhUNgCNTSU8h7fK7iAyo8g//57EmJPPlk4bStqvvuOhKf2/LOy5LzajipWcgIDnQvy\nY8coAq8nyBcsIDH83nt0jBYtSHA6onx5Kgs/cyYJ+a5dHa/rCm9v6qx16ECWm++/t498m83UOW3X\nDti5kzoAjFFku1w5ui8qVqR1eY0BPz/1iAMgXz+Tif5uKf92ads0ahQwbRqsVoakq8DfR4HLN6lp\nFitgs8VgZ0IM9v/EcFFlDijpNA1KiCETZYOyUbvYDdQwnUTI3j/xfPyXqFQsByjzCTBhEW532O70\nkglB/ggRGBiIFJ2Kab169cI333yDTz75BFOmTFF9ZrVakZ6ejuJ6BQMEAsHDR5069lEkd4uMFCV8\nKNpqlaN8d0thnHNhC/LOnel1r+CC3FFk05ng3L+f7AwPqyA3GMgmwjPNRUaSwMzOJmFps1HhnQED\nHO8jIIDsLVqSk4G4OLqfsrPVFg7O119T9D07m/zVjgJuK1cCO3bQ52XLUpVKSaKy8+vW0TpJSXTM\nFi3ofVYWnVdkpP4+33yTcnK3bUtCWu9ZCgoi7ztARXvq1aNrNm4c/V63LnU4MjPlojy8FL2S118H\n/u//6D7TjA4dOMFw4ARw6BRwIug7XPy5Bq74PY3UNvDI383x9gL6RB5F9ONRuHkuBaV2rkblCcPw\nTPQd+BXzA5b+RQWJri0Eyk0DLP70/TmzE+UiBPkjRGxsLJYvX45Ro0ahSZMmMBgM6NWrF1q2bInh\nw4fj888/R0JCAjp06ABfX1+cOnUKK1euxIQJE9C/v/NhGYFA8JCgV8jlQUhdl5JCbW/cmCr/Ka12\nixfTcL2niQIYw1VHFSjzS0zM/d+5ccaFC1Qo6tQpen83EXJvb7cKptwzrl8nv/Td3OuTJpFN49Vc\nL2y3bnJEd8gQuhbXrpGw5ELb0fWx2UgA6wnyy5dJSOtdw6lTSUzn5JBAzc4m4e8Iq5UK4rzyCtlM\ngoJIBG/eLK+zZw8wYwY9W/7+VGRozBggt75JHvPnU3T9scdogqjBQMv04EV/ADpeWBhw4ABQuzY9\nzyVK0Gjd+fNqQa6JkKcMfgtHv9oM6wGGzWcY0jIAH29g9Xbg+HnFisbmwC1QpNsNMW40ArUrAZER\nQNNaQNOaQGwNoHhwbuXUP/cA8SuANq8DyJ2Dxz3xuQlRPJlcLgT5A4SnVTa167/++uv4999/sWjR\nIsycORMARccByt7SsGFDfPvttxgzZgy8vLxQsWJF9OzZM29ib37aIBAIHjD0BPnVq5SVYOrUommT\nO1itcjaPMmXoHz0fxl+4EChZ0nNBXtCVPwHg4EH7CXIPElevAqdPy++NRrIILF5MQp1bMVJS6Ppf\nuOBYdOdXkJ84QZFc7nEuKCIigDlzKLNIfrlyRR2JVt5zvXrR8/XppyRqFyyg5Y5GELKyKDK9fr39\nZzk5dH35CMSdOyTcS5Wi9evVkz3sWouHFu5Tf0fhc7ZaabuRI4H33wf69qXvatcuinr37aueDArQ\nuQ0cSIKcPzteXkCfPvrHVUbIMzLofa1csXvjBlCiBE7bymDfRX8kPNYX5/5lOL+tCpIS68LrL4bw\n4kBGFnAiGbCUXwuMcX6aWiKCzKhtOIvqIanIqd8EAX5AtgmIkS6g3rKJqLXwE5RuVYuu4een7Xeg\nzFDD4RlYKlWSl/3+u1uT4oUgf0AYMGAABjgY1oqKirKbfKu3vr+/P+Y76qkCGDhwIAYOHOi0HWfP\nnnWnuQKB4EFFT5CnpRVNWzyBCwDGSDgoU+3lV1hbLGAFPTKQmEhRvsLi0iW6BlqxVFD88ov6/fnz\nlDXkmWeoLDkX5G+/TUJ9wwbHKR69vPKXxWbgQGDKFMdeYYAEZmoqCd+33qIS8e5w6ZLn7QHk50Z7\n7ynh4vyzz6hdvFS9coKiEi5SW7e2/4xnA+GdmrVryS/OUytyQe1KkCck0PZanzpP67d0KV1H3nGy\n2ej35GT7tIfHj9NPSbIvM88/r1CBxHbPnpSt59w5irZnZgIBAbDZGC75lMPvAZ3w5bBiSEzqSduu\nzN1HsRZAFoAs4Nxlx6fF8fUB2qb8iRApE0/2jUGV1lVRqZyEkiFAYJNG1HEpWxZ4r6nimqQAH8wF\n/m1Lthyt6OaEhFA0/9o16swB1LnRPt+NGzuedKvgPh+DFAgEAsE9xd/fXry6SnF2P8CHtHnaQ6WQ\n5hPCPOWdd3ChoPN5O8skURD88AMJ5MJCUakRANkaYmLso90rVpCvV6+Dx1m61C1vrR3u+PB376ZO\nyTPPOLZM6OHpfcIYUL48Sq5aRe8XLADGj3e+TenSJOa46A0O1l8vM9Ox75tHyH/9lXzp/D0gPwc5\nOTSy1bgxLU9MJJuLkmHDgDNn7AU5f2+zUYSXY7XK37O2M5VbhTRvvdRUdcrGvn3p+zabgWvXcHn4\nWGws+xw+7boKA8/3QdefG6BCV6BC42QMjZ6DxCT3R+SrlAOii99Be/yNt1pewOga+/FTxQW4+Tuw\n7uZAxF0egldb3kbr0pdRMfAOAv0lCjSULq22BP35J7BlC53b8uW0zJGYbt6cJqUqOyYvvkiTeZWY\nzY5FvQIRIRcIBAKBzO7d9qKkbl3Hk7fuF7jo1otQ3o31pKBtes4EakGQlgbculV4+9cKct4B0ka7\nzWayDTmbEGwyUYTSU/QybejtG5DFlJ69QMvkyUCDBvL77dvp/PQi1ByzGbhwAT5Xr9L7rCz52C1b\nAv/9rzwRUourolMZGY5TWPLMKrxQoJ4gHzGCUhZyUX/sGPDTTxSRv3iR9m8yUecgM5OsLr/+Cnzz\nDYlSwP5+dSTIz55VW4gsFlrvgw+Av/6CxcJwKLgxLm+zYMdXP2Nd6d9w5KUAAI8BFXML9xyxP01/\nX+Dx1K0o0aYxSv3yA1qyA6i/Yz6sNuDGbSDIHwgLAcqFS8CStVToJ7AxFfdJTgb8JLout2/TdXnj\nDTltYno62dsSEshqtHYtbcMtWTzFs7Po9qZN8u9TptD3P26cep2SJdV+fAeICLlAIBAIZLp0oSiR\nkvs5jSBHkihSqCfId+6kSn/5IGLpUhgKspAPF7D5Zc4cEoqO2LHDfXtGflAKcv67wWAfIeci0NmE\n4Jo1gfr1PTs+j9i6ipBz/7TZTHYCnQxjdrz3HlXU5OzcqY4O65ErqvMEuRKzWX3uP/5I9gZOVBTQ\nsKHjfaek2OcN59StS5U+OVpBbrNRusHAQPoODh6UC2cB5AOPiZE7RRs20D4uXqQsPSdO0Ho2m/rZ\n37OHxDegtkUtXUrXKvcesP2+HrseG4zFlrbo8SFDyc5ArOkbdFnZFJ9FvosjXtUcnzeAFnWBTwYD\nl1YDf0zOwZIPTZh+7k10v7MOVSIlVKsgoXkdCXXLm1Dux9zscGazXI1UGZX29SWhbDTKHTPGSJDz\nCHlyMkW2TSb53uXWE60gX75ctufwjv6mTXT/6P2d9PaWO05OEIJcIBAIBDLKstCcB0GQR0XRP771\n62miWIcOFC0DyOeZz4JmZebNg6EgiwNdv06ZKvLL0KHAH38UXHs8xdubhAeg7lw4EuTORgT0fMau\n4J0jV4LcZAKqVKFJpSVK5G/U4P33Sag6IzdK7MOF9vTpsqi32cgfzdMJT5umFuT168vZWPRo2JAi\n2npUrUpRYI5SkA8fru7oZGdT1hMu1AE5FaPJRJHt8HBqn9lMVpOAAJpgabPJHa/BgymV4tatJGSn\nTZOPk5MD+Pnh2AUjXp/KUCruJTwufYd+7COs/AtI03mEvIxAo4hb6HdtIcZe+ASji6/DF17f4Ppv\nwPZvJIwZICEkSKLryecmaO+ljAz5+prNdA1sNvWISLdu1MGoV09enp1N16NqVXkCrK8vfc47Qfx6\najv4K1YAhw7R79osQ0Yj3XPO5jc4QFhWBAKBQCCjJ8hDQmgimrvs2kVpB92IChUoBgPlUG/ThkTv\nxo3ArFlUDGTnznztknl5QXJlLfCEPn1okuHdwDNT6KG1lBQ0kZFy5JD74ePiaJJe+fLyeuXLU4aQ\n6Ghqk574Vi57/nkqHhMe7vz4XJC7yrCSk0OZLg4fBv7+Wy4w4ymuIuu5gtzIO22RkbKQs1qpA5aQ\nQHm2jxwhQcs9/u3akZ3BEQEB1KkYOZJylSvtNFoCA2Uvc/v26s+4CFVGyF9+mSYzzp4tC9StWykn\nvM1G5+DtTc/P6NEU3X/lFTqf8HBc/XIeTixPxLXkKvDZwXD5XF3szIxGXH9+CHvveznvVFT3uoiI\npEOo7n8NQ7aMQqnffgdWDaARribdgaP7gJDX7c+PJ5xYs0a9PCtL7my/8gp95+PGqQsgTZigvhbT\nplEHrVMnSofapAmNCvKMNVFR1LE6c4a+f20nQFmsiQtyXozLy4vuvcuKGadvvEFF1ao5HxUQglwg\nEAgEMnqCPCDAsyqdLVqQEOO5eO8VPJKv9w80P1FuxsCMRueCPD2dIopKMeqMevUc2xDcxZkXunx5\nEqAFxeHDFF3s3p2urdImYTBQFLVPH+Cvv9QVQpcsoajs55+TEKlViywSSpSCfNcu90ZhMjNJ9D77\nrPP1/PxIzJYoQdYKR15sR3Dfu6u0jLn3Rp6tycdH3sZqpfdWqxwJ//df6jAuXEjX9PvvyWb04YeO\nj5GYSB5nZwwb5vgzLsiVEfI7d6hTU78+PR/c9242U3t9feka9O0Lk08AtpfthH+XMdxMexH7fm+L\nDeciqO9X/TngXQCwr+ppgBU1M4/hMa/jGPLTC2i4ZRmkv7YAfy6ncyohUSeiTBkSsCaT47keFy7Q\nz5AQyrE+eTLZdm7fpmWnTlHnhl/vHj3s9zFuHN2nAI0ynTsnf5aTQ7756GjaR3Q0dVj0nlVerCkp\nSRbe/N5njES88jxOnaKRESHIBQKBQOA2WVn22ROWLaMolCfZVvKT1eRuUWZZqV6dBBkg51n2lDff\nhO/ly84F+ebNFP389Vf39umqVLq7+3DE22/L4qUgeP11x551Ly/yG3N/spIyZWiCMED3jt4kzCFD\n5MnCztIFKlFGRJ3Rowe9Jk92z7NvMpFAq1ZNPcrgSpB7eQH9+uHIiBH0vm1bIDaWfrfZ6LuyWKjN\nXLQnJsqCLTNTbWPRw9n9+8YbZMlwNPF0+3bKMuPjQ9FjXujq44+p08I7WFzw5wry/VkV8EXQVJwf\nypBwuisy8qZR9AJcZD9uURcYF7AEzc+vhf+1CyT+q/cAqr8GVChPHuzQUBo5mDCBRq8mTaL71pEg\nt1ppxOvMGeC332jiKUCd4eLFadRp0CDq9Dm6Ftr7i6cqBORn8umnKULubLIx7+AvWUKVjX/4QS5E\ntmkTjSooC5Mpv3snPLQeclbYw3YCwT1C3MuCe8rGjbK/lHPggGfp6QYP1o9QOYJX67tblBHyadPk\n6oT5jZDnCnGngvzGDTnq5g7upOxzhTNBHhhIuZ49hUdGtXAxGxCgny3FUaVOLy951MDR9Y+Ops7M\nTz+RsNLedwAJJR7VTUkhYerJfAB3J9CeP0/pAQ8dovPkgspVlerixSnaza9NYKAcLT1wgGwmyqJV\nkkSdE277caeD5uz+TU7W98dnZ1PKw6wsqqbp40N+6UGD6PNy5agyZi4pt8zYWKE7pvT5HZ29ZyB2\nZWcstbbB7sNQiHE11coD7WOBTs2AAVFH8EmrROz4Ftg2G3iyzCX4VyxDIyRKIZyTQ5lfwsLoGly5\nQpHoihWpg2YwUBGdJUvUB+NZlLiw5fdWaipFyPl1jImhwkt6BASQfQ2g9ZX3UXQ0/Wzb1nXmH95B\nMpmAVq2oEyflRvv79aNzVAYkjhwhS5cLHsoIuY+PD7Kzs+Hn5ycqSwoeaBhjyM7Ohq8bRQUEggKh\nRAn7qnLOUtfpUbOmZ1UUixWjYXtH6eHcITubqkjyCLnS/tCyJcDzRHuCxYLs8uVhcZQnGiAh50nh\nJHcF+Z07NByvV+DH2UhF3bpy/mRP6NULaNSI0tQpee45SpfnqM1ckDtLKxkYqO97P38e+Ogj+f3J\nk+rKlikp1KbVq8nyUqoUfcdxce6dkydkZFDHcNw4KrDj70/LtFaQGzfIB65NbacHr1RpsZAA5NaZ\nrCzPBLlehHzxYhKxjqqdZmRQ1Pn334G0NNiaPoat+xmuplDO7hupQI6Ziuv8sBo4ei4SiPwZiAPg\nZf8c+njZULdsNprZEtDo1m40a+SHmEEdZCGL2uoNoqNp1KhrV7U4zc6m0RODgf5GcMvXjBnk4zYa\nKVe6lxfQuzdts3w5dSqMRrkTwf8eVapE/vrVq11fR39/+Tpq/6fWrk37zs52nBee07YtHYt3dDj7\n99M9rBXkyk6lEx5KQW4wGODr64ucu41CCB5I0nOjbcGuHqoHBF9fXxgKM2+x4OFh40aaKHY3gQg9\nD7az1HV68CiUJ1y/7vk2SuLj6Z9gly7k0Q0JkT+bPZsmsXmKxYIrffvCoogk2uHpCFZgIIlcZ1y9\nStk9li2To/ycX37JX+5uV5Qvrx95bteOBMaXX8rLypShqF+JEo4j5EocRXi9vclWVLw4iRnttVy/\nniYG165NItZgoMi10g5QUPD28Z/+/iTytHMDrl0jgehIkD//PPDJJ3IVzjp1qFBQr17Au++S6MzN\nSAKABJ2eVvnrL5r8uXSpviD/4w+agKkn6BcsoG28vGArVhxHQxthZMX/Ycsb7l4M4pkWwAttgBpR\nQMNfPoPx7Gm6D77bAZw6BNQf7XiCcXg4/S2pWpXsMRzluQcH0/ZZWdTeqlVJxEdHq+9FnoLRaKTO\ndXw8dbCff57ujxo16F5xJMi3b6dI9sSJcoRdWdr+wAH6++PnJ38X//xDoxt6f0tbtaKfmzap5yaU\nK0e+8pgY9eRTN2sgPJSCHCBR7leY5YkF9y2HDx8GADTm1ckEgkeFzp1JULhRFc4heoI8M5MyLbzz\nzt21zxHBwSTy7gZuCzhwgKKa+/bJn335JUXqPBVyVitYQXvhP/3UdeeAV17Uo6v95LkCgad801Kn\nDl23r7+m93yCIbe3GI0kuNeuJUHDheiNG/S9nj4t58JWsmULdaAkiSK8ISH2UcScHDkLSVqa3Mm6\ndo0ime5ac/73P7JcKSdOLllC2/NRmcxMaj8X5FWq0PegfZbS052P/pw7p7b+hIfTq317EnING1LU\nmj9jjiLkCQlyqr8RI+zbkVtqPi9CfuUKEByMpPQA/L7GABbihz2lZmLtqCq4FbYO+Mf5JfKCBfXC\n01ClTgmEFgN6Pgm0bihRdpO5c4ExuSMnLVrQ9Z8zx3nBHF6Mq1QpdW73p5+WBS3PVnLnjlxyns/7\nUApyPz+yfGRkUCaVxx+nEbXnn5fX8fGhyrBXr1LHZ8MGGl0JCyOPN0D3Y2YmpUnk1h2ABP7ff9P5\n8LkOTZvS8Xx9KYWqXqpRk8nel86viXJka/hwGtFwwUMryAUCgeCR4vZt+ieYk1PwgvxuJyG6Iibm\n7qtXcgHgqFJnfoS1xeK6XZ6K/H//BZo1c77O3Yzunj1LwkObTm/vXsqo4UhEOYrUAiSqeOXGsWPp\np8VC4vToUfrs008posgFec+eZH+ZOJEipG3aqPfZuTMJPUmi+6ttW3vrhbK4y+3bZG0CaOQgMVHu\nJOhx/TrdB8WLkzddWdYdoDR+9evLgjwjgyb5cUHuKNf7nTv6lgbemdC7/27epPbUq0frKedjPPOM\n+trYbPTd9ekjZ+WoXNn+eBpBfmPoaHxd9T18/k8NZOX0BS4DCAagmZ5RvypZVYzpt2FOvYPi5Yqh\nV9dgvPrXewiqXpEmiSqZP1/9/Duq1KlF75nLyKCOWloaieYVK+h89+6V89ZzlILc15euiclEglvv\nXq1cma4Hj0a/+y7dX2Fh8j3UoweJY23Emk86HjBA7mxZLHK2IkcTaitVouf/1i258xQQYP+MRUa6\n1XkU4+ACgUDwMMAndt2tVS8gwF6EepLyMD8MGCDnUM4vVqtakP/8s5zvmX/mKQsX4ubTT9PvR4+q\no+6cvn2d55LWwnN3O0NpD/GUjz+mLBRannnGudfdUYQcoOs5cCBlwVCKsfR0smDExtqny7Raye5y\n5ox+p8bHh8rKZ2WR0Pb2tj++MgKZlkbp47Zscc+HP3EiiUlA9nErqV1bHcX09SWBnpFBz1L37vr7\n5ekCOampwObNqNG/PwISE8leoSzYA5DYO3iQfjcY5CgwQEJUm+0jI4NeTmyXpgwTZv8bjU5eX6H+\ntvb5IEwAACAASURBVFcQeeMHfLK7BrJ0LkvJQDOefoxh/Zhb+OeJ+TiyWELCmlAcy+6G3avLYOSL\nEoJKhzjO9qL07NtsVDBp2TL6jmfN0rdtWa30HSmr/h47Rn9LMjPlCbzDhpH9R/tsaQV5Tg7dw0eO\n6N+r771HEfPsbLKvpKfLHThlgZ8zZ+wnL/MsKB99RJaw8+dpOa/S6sgCOGIEZYhRWtqqV5ezC3GU\nHUsnCEEuEAgEDwNccNytIE9Kso/wNWki/1P75RfXkwbbtfMsK8vw4fnLDKKEZ2HggvyDD+QJefkV\n5ID8z/jdd+XKnwD9Az97ljownTq5vz9nlSs57s5/2b7d3sPL26UlI8M+CqnEWYQcAC5dos+VglxZ\nqVNPkAO0jZ6g8fEhW8aXX1KEtG1b/eI93KPLrQSpqWRh0EujqMRkUpeS14owrUjv1IlygsfG0jXc\ns4eWT5miTlmXnk6im+/vzBng7bdhCwiAMTOT9nnxIn1WoQJ1Yvi96Q5mM7X94EGkGYPx+WKGtv9h\niOnF0ORVhhfHMHR/n6GmeR7+s6Ya/jjkh4RzXjBBfmbLeqeiQ4lT6Fv+KP6aBVz9wxtrphrQoUwy\nFbzRXgeAbDXHj8spG5Uonx2rlTrPPH3if/5Dy3bvplEMjsVColtpDeEWlS5dyHICkBh+9VXy3fPs\nKG3aqIsbKTtgkiTfq8oqovza3bhBUf60NPk54mLYaCTLkDbi7e9PIn77duC77+RiUHzfzubkJCY6\n/ozTqZNbhdWEIBcIBIKHgYIS5G+9Rf5QJcqsJYmJ5NN2xsGDrguZFDS+vpQ+jQtypei1WOgzZ0Ps\nDgjdsAE+Fy+S3YBHywGKwFauTNHShQtJIG7b5nqHShHriNhYylSjx6pVNNQPUIdDWdwEoOiedsKh\nzUbtc5YuMCTE3q4A0KTCefNkrzK/hhaLOtqvLDrDj8nX0ztfLpZbtiQBOnQoFRJSMnw4ibN9+8g3\n3KsXiebZs13f58pS8o4EuXZZRARFg5V2i+nT1dU6GzUi4cqtLbli2xoYCIN24iovdMP399//qq7R\nyWSGcT8yDJrM8PpUho+/Z5iyxIBRUdPwFKYhYm43vDsb+OsAcDIZ2HccWLEF+N824IwUaXfK9cvc\nQdx44FyDT7G+zRosXFoLrepLcrY5LmR5p0qS5M53//6UKvTUKcpowzsV/Prx7dets5+gazZTvvrT\np+VlsbGUA155T/DJqbzjwq9RiRI0oTMhgZZt3kypETmtW5Pw523mEfJ336V7ix/XbKbOmtVKglwb\nITca5SJJSnj2le3bqVPBiwFxQa69fy9flvOgu9PRL17crcJhQpALBALBwwD/B+dOcRVn6IkXpSDX\nsxZouXmT0pjdS3jJ73nzyP/LMzMANCHVZstXZ6XkmjXwS0qyL0jTrJlaoKemylFDZ9hslIHBWV70\nevVoqF9pZQBo1KFrV7lD5OfnuODIlSvAa69R54rn7nYW6fvwQ33BvncvMGaMLMjNZsqEUaWKunOh\nLMsOyL+bzfaCJjVVFnyzZtmnWlSybp3s5fXzo+81Pd31d6kUXnqWFb1lHIuFOjANGlCHSzkKUaMG\nWRT4M6AQ7/5nz9L14vMKbDYSb8OG0XP1/vuAJOH4eYYOIxliegGfzAXmrgW+/R8wcT7w/oIAzCg7\nEhv9W8FkdS72igUCk14D4n8ELpk64Z/Rx9CrnQSvXj3UEWYOzyLC7z1lxyMwkISj2UyWHeW9YjBQ\nVPyVV+j74PY4fv+bTOoOEEAR98aNacRtwQJaxgW5UsTyDrTRSJllhgyxb3fFijRKB1C7YmLI+sKr\nZN64Ie/L15eeCZtNbk9sLKVSDA6mtqamqnO3V6pE6/r6yoWGAPnaaJ+bW7fk+QtTplAnUcmff8qV\nWT1ACHKBQCB4GLBYSMi5W8LdEY4EOY8IvfOOOqWXI9ztGDBGvsuCKIBlMJAQ6dVLvfyDDyhalg9B\nzoxGKgykFeTaCKu71UC/+AJYtMh1dcawMHsv+KVL9NNqJcGxf7+9dYNfx9Wrafg9KYkEWGam2lKg\nRemNliRZ9F+7RsflArZ6dfJe806a0UjH6dKFBBiHT3KLiaF7QSmAlJ0Iq5U+0+a+5yiFvr8/rVuh\nguv7XCkQ27WjaK2Sjh1JqHFvtxKrlc7733/tBTmgzoySO5nY//RplPn+e0rZx78DqxUXr9qwZY8J\n82+3wKAq36N95xOo2w/YpDMdQY+60cB3Pc9jd41pmD8GmPchsGwCsPEr4NJq4L1+EhpVl1C6lJds\n0WjalLLjaOHWjzt3aMTo11/VVhre6VKOfEyZQvf2kiU0WhARIT/bXNibzfaCHJD3wa9xYCCJZ2VH\niPurjUb6bvk9rqVtW/ouPvuMBHSfPjRRdtUqOl+AOuMDBlBb+veXhXS3bvTiE78bN1Zn3KlUiaw1\nXl50bYoVo85s2bLUJu3fu6AgWs4YWWCUthyAOox6Ra5cILKsCAQCwcNAqVL2RUzygyNBPniw/N6V\nfxfwzDN7+vTd5U7nKCt1anHHd6yFMVmQay0fXKBeuUICJSeH/hEz5vxc6tWj78pZ5+DGDRJBjRqp\nl3Mha7XKglB7TtHRJNS5LSE1VRaIe/aoU9BxuBVFKaiSkihCzEXVoUO03syZ8jqhobTOa6+R1UE5\nWfG332iS5Jw5FNX+7DOaaAvQsSIjKWOGxUIvPWEMqK0wfn5kH+nUSd9eoyQsTI50lighdxA4EydS\nR23oUBLszz8v+6e5YLRaXQvyXMvKidmzYfHzR8lUX+zzfwpnljD8VW4x1k1sBNTeLG+rmFdrNAKd\nameg/dF5yBz0H1y6ATAbQ8mVc1HxmcZoM7AeKpSWgB0XgOW/oGmntxyfrzZfvR5ckPPOpZeXOuMP\nF+TKkY/hw+l75ZlglFlkuCA/dIiukVaQK1M7AnL+cYDsMQCNOFSoINtYHP3d4NmDlKNGNpucieb6\nddqHtzcdh6c6VHL9Op3bhQv0UpKTQ8Kbn3vLltTp08uiVKECifbvvqNRMe29dfVqvrJGiQi5QCAQ\nPAyULUvi4m5gjP6paQX599+ry8MnJ6sjTEp++ol+8n+st2/be9KVcDHozuQoV/DOhMFAnlSlJ5mL\nkeefd7+yZrt2CN6/n/bZtas8bA7IgnzKFPKQ8/brVU3U4qi6Iuf11/VHIfQEuday8tVXZBcwm0lM\n3L5Npdyfftqx1Sgjg4Qn70g0aECCGZCFRa1ackpDTliYnFFET4D8/jt54bWFgbjw+vhjElU3bzoe\nUVFGyMeMoe9PWfSJc+iQ2ibw7bf6tg1Azv4hSbT/SZNosjK/LypWlCPwOoKc+fjg8ojxSN56HEko\nhelRozFsbWu0m9YGFfsFoHulJXjna2BdsE7nJ5fWDYD9c4HVb17GiAtf4d2+Er4aJWHGWwZ8XOo3\nvFztNIlxwPnoy8KFwNSpDo+jIiiIOjIVKtAkxtKl5fkIgNz5Mpvl3wMD1RlnLBb5u+rWjZ6xDh1o\nREEryHkHli83GKj6pq+v7O/+v/+j74kfz5Egt1qBXbtIKHM2biRBD9B5/Pe/1N7OnfX3UaYMFfMB\n7H3k/J7gnbKXXlIfS4kkUfBj2DAqIKTltdccW8mcICLkAoFAICDMZrKmaDMC7N5N/zBbt6YIVfPm\n+hMYGaOhYqUwunWL7AJ63lB+TIAEVUzM3bVfGSH/8EN1AR4uyHfudN+6YrWC+fpCslgoqn3qlGwF\niIqilIf//EPCs3p1Wp6Z6TrFmd6EQs1xdSeL8XbbbLK41kbnfHwoSm4ykTBPTZWXO+oEaFP5KUdJ\neDsqV1ZHOJXrAvqCnBd7ciTIBw6UhT9A17JhQ/X5Mkbnm5ZGAs9m0xfkJpM8KdAVvMgQT80HkJhr\n1Yo6HqdPw9KsBTak38bemClI/isS1v0MVitw6iKwP/worLeMQJ71vbrTw5W2XEV1n8uoeXEnmqXv\nQZPmxVGNe5DP6xQG+vprWbACJMgdzTlISaHRDC1JSZQiUvkM+PnJeeTzSt5rOHWKRjYcTVY0m2XR\n/N579CpenDpxyqqVAF3jDz5QPw/Z2RRZ1trKmjWjuR485aAWV5lq+KhFaKi9p5sjSTTXZOJE+87a\ns8/SSM7AgY6PoWTkSGpzgwb6n7vTMdcgBLlAIBAICD4RSluRU2kDKVuWholXrbLfnnuUGzWSJ1y5\nyiriTpERd0hLI/HPj6et+vj33ySgtR5WZ1gsSGnbFtkVK1KH4e+/5UqZPj40XL13L0Xq+D9y7XH1\n4Jk3HGE20wS6zp3VIicnhzpDffqQ+ChThrKPKAkNpUjip59SfnT+nTiqCAlQxLN8efLfzp+v7jAM\nHUoFVhxFsJVZVhwRGKiOMnMvr1Zk/vKLWpC/+SZN/nzhBeDtt2mEYto0+04IQN9tRgZlYBkyxLl4\n40WG+ORNANe8w7HoYAw2x3njzPkqOG+bh6yavkC87kk73HWxAIYGMRICfGnS5ctNb6HjoAbU9h2r\naaWgl+QN9HKqly2rfh8Sos70kpFBowXTpjkebTl7lr43V1VhtVSuTKJYm3rz779pROTZZ+07nLdv\nU1YUvQqmJpNsHQLoXMPC7KPpJUtSZ1eZ3YWTnEzecmf3mLP7W4ve6F6PHpRlxV1bmyQ5L/CVj79n\nQpALBALBw8KhQxTJLV06f9s78l8zJi/Pzlb/Q1ZmJbhxg/6hK73srgrhKCfHKdm9m8pf84ieK5Yu\nJUEwdCjtiwtZs5lsJWPGyJ0EDwT5zU6dkBUTQ9dWKbZHjCBhzMVQVhYJaK1YvHmT2qL0n3fu7LzC\np81GfvR9++Qy4wB5nRs3pgjmuXPOI/Fly1IUkpcXdyZYSpWiqCHPA71ggVw0p149Gg1QHqtDB7qe\nrVo5j5BzgoLU4rtCBVn4R0XJqRv1KnU+8wx1On78kdbXq1ppsVB0s1Il8jzHx1Phn7ffRtIVhriN\nQEo60LIeUKcKcOGgFTvD3kDGpopI8v0Ee+rXQmJAdcANGzYn2HYHwSX8cMfshWrlgXZ1z+O59ZMQ\nu/4HGDYq7pPsQGr70qUULZ40yb4svN6ITdWq1LEKD6dXSoo8spCWRpMsp02j70VrZ/ntN/KUO+uU\nMOY46qx3b373HY0Cffutehv+TDiaxNirl/p8s7P1R1oAEvvaiq6AbP/g91p6Oo0ivP++vI6z+/vE\nCRp9czRx3GYDPv9c/V0kJtIzoNfJcEXZsvQ8eYjwkAsEgvuTDRso36/AfSZNUnu9PcWRILfZKA+w\nyUTD4HzyXlKS+p/3zZvqqnWA6wh5RAQJO61IvnlTTnfnDlxcfPstRcD4MU0mui6AHP1yJcjj4uic\nrVYwpeBUCvL0dDmNGt+3XsdjyBB1tpQhQ0jIV6lCUbZ16/TPBVDnYgZIvNavT7/7+lJmE0cMHEid\nBu6FrlqVOk4WizraylFWP6xWTS4i5OtLec25IN+3j8Q1F8/8nDdsoHuDwydsJiTQefJO2+nTtO+A\nAOrM8VR1HTs6r9SpnPBnMlEHicNHAXLbxObPx9/jlqHnRwyVewAffAt8vhjoMhqo1B1oOa0a3vMZ\niQnbo7EgoDuJcR3K+dzGiB7At6Mpu8nCmiuw5tgzuPbFcaReqIkL315B6gYJf/8ooVuLG6jsew0G\naESfnx91wBo0oM5Ut25qQeoodeWVK3IU2cuLoreSROtevy53OL29yUeuLMSVkCDbzByxf7+cncQZ\no0bR9zR3LllKtOlM+TOld08BNFqmzKk/a5Z+8SGARgKU1VM5/Hr98gvZ6XJyKFuREh8fKli2axdV\nBI1XDG3E6w5zyEgSdZaMRvl8Xn3Vdb0FR5Qs6X5xLwUiQi4QTJsGtGihnrAlKHqeeoqGBLVliAX6\nJCZSrl1HE5rcwZkgT08nUVS6tPyPXju8W62aOgsH39aZMPD2puiVViS7mviohdsglFkg+HIu5NwV\n5H36UGSP7xOwF+Tcd81HI0qW1J8Epm0PF7ScgwfV+cwBfUuGljJl9HO9HztGIlwZ2bt4kc6nalX6\nvGtX+86usvrhsWPkpeY8/7zsuX3hBRKKFgtlqjh4kCbDrVlDliEe4WzRgiYO9u5NQmnPHhLpPC3g\n+PGUys5spmtXr559NhNlyXGFd/nk4ds4030SpKVLkZIO2K6Ysb/qVzjuXx2ny1bGLWMorkslgM1w\nGy+bGbE1JfSvdhpRv/2IKos/Q3RkcfVKe/4F3ogFmtWgc9++nSb/5cIcjVjEx1NFzzffJA+zMiLu\n6yvnzI+Pp4qVRqN+3nuA9gGoBTmgtoUYjXQMZxFyo5GE9oEDjn3QAE0SVtpLtHMf+LOkTGvpjOrV\naQLm9u20b3fw9aVRglu36B7x8aEO+7VrctaVkiXpp5cXjQ5cvSoLf1cZnySJrnWDBnJHdOdO+pvq\naGKnM0qVcj5HxAEiQi4Q7NihPylGUPTcbU7tR4njx9WT1PKDzaaeTMbhFhQ+5MttFDYbiTxOaKh9\n1K1ECYreORPBnTrZZ/BwR5AfOEB2AECeCMkF8M8/k59YOUEyK4vEodajq4SLboMB+OcfZPKJplOn\nygVIADlC/sUXJDLr17f33gP2glzZQYmO1r/HFy+WJ2N6yoABwOHD6mUrV8riXSly16yR01nyCPmd\nO/be2JAQGmVYt06uhsgF+ZYtJKy1lTqtVvJ1Hz2qLh7EhVNODk2kNJupc2EwyAVmKlUCXv9/9q47\nPIqq/Z7dzaZXSAggXaSDIEWwoICgKIJYPkRBsaB+Ip+KigURsKCCYgUVEStg+RRBARVRmiIQEAhN\nCIQOCSGE9LK78/vj5OXOzM5uNgXL79vzPHlSdjLlzp255773vOe9F9nFoXh/V3Ms/lXDruIkvPmF\nG7367kTL0YnoX/9TXDEGGDoBuPmtZExLGo3F0X3xR8jZJOM69GyWixGeb9ChOZAYD7RtCgw7Ow33\nxv+EKdqbWHVvKk6V9cIv79hw9wXHcfn66Wj+ysPebatvuwsuYDsfOMBJFgCP3Ofu3Y2VarOzFemO\njSW5FNhsdHUBuM3q1ZywaZo3kTx4kNKRjRsVIe/fX90jgT9CPn06CfEDD3CSEIhVqj4oYs6R2LuX\nBNgqQi5FsMzIz/fviW+G6OzHjeP+ZIIwaZLa5uKLOamz2+lHrn+PBVJNMyKCSev6ybGVg0og+OEH\nYy5EgAgS8iCCsPJdDuKvxz33WOsJg7CGEN7qEPL4eCaDmfdx0UWMuHo8JA3vvsvBvqDAWw+6e7dR\n91yvHgdQf+R68GBvEhgIIR83ThXlEMmKEOBp06gn1hPy4mL2KYmCmTFypCp3DpAsiRXg1q3GwXr/\nflWB8MorvatcahqPo5ddAMZVCH9JYUKw/CWJ7t3L6HRGhvqblYVkQYG65tJSFrwpKSHpF7mERMit\nCrwAjEieOsX2jYjgcSqq1CkkTbbRb19cTEL/7rvwrF2H9W2vx5ykmzHptVxcG/Yymm8ZhzoZ7+GO\npV0x4BGg1fHX8Z+Mm7GiMDAnnthIDcOvAH7/AFj+n12YXfY0Nn1oQ+YiG1I/seGj3r/gzcSP8HDs\nIlxY+wgiUn5h/6lbl2QqNZU72rxZWQPedx+lQGlpfCZcLk5Iyic7mtznbdtI1KUd/flrC265hasN\nmkZrPo/H289envH0dEXIo6LYX/XJvw4HtfZWlWNfeYX9QyaX5vPq358rJHroI//msfLhh/lOSLGo\ndOTxqBwGPaZPV8+OYOdOPq9W0Ce+2mzqeTIHD6Qq7I4dxs8CqYmQleUdmPuTA0JBQh5EEEFC/veE\nlVNGENYQIiU/VwfTp1Mraobcj1OnWJq+qMi7mAxAUrFqlUrUAyovPwGUJ7o/6OU10dGMvgohFzIj\nZOiuu+h77UsOMnkyi4nk5xsiajHr1yMqNZXR/yFD1PYREar4yGuvcfDeskVVGrTZVBEWPSHXk9JO\nnbw193qYo84ANbIzZvDnBQuY6Nm7t3H/I0YYE9j0hFzuQ3Gxmhzs2cPo6w8/eBPyV1+lraPTybYs\nLSX5c7mM0X7ze9TjOX3dms2OohLNMDnKt0fh/TojMHTDQCQP0HD+jE4YvrwnJi1IxNe1B2OvVh8e\nHxTFbtdwfv5aXNoJGHgRMKBrKR7pm4nPnwXWzgLSPgeyv7fhw/E2nHuOzfodLz7ysbFGX/pzzqGe\nWEjcH39wVQWgvrlePU4EV6/mvdUlRrpkEpWfD4wfr/Ypun1/fvybNlXs8CHXUKcOiTDA5zEuzkje\nHQ7KwIYN895HWBhXd2QCaY4eHz1q1HwDipBHRXlHvJ1OtplV7or0X3MypdW7ID+fsiYrhIUxrwNQ\n3vGAt82irN4AlSfkgPE5PXnS+j14BhHUkAcRRJCQ/z0xdqzvbPwgjHjoISZpAUZf582bGdG7++7A\niwb5eh6EkDudJGUhIZRpLFxo3G7VKn4fPVoN3pWxJBMsXGjUxVqhRw9Vgv7uu+nIMnmykQBERZG8\nbNtGiYmvBFMpaJSfz3M9eRJISEDsb7/BHRvrreldv964EgBQ1nLZZYx2Amwrp5P3QRI0PR62UXw8\nMMZP5UVARZ2FULz3HqOnmsbiQfJ8mCPTAKUiiYlM/GzZksv5gDEJVQjymjUk3XPmkJwfOcLIe58+\njBR//DGTUPPz2Q6LF/O6Vq063Z6Z7liElYRAhBPFnhCsDLsYXzW7D9882ARHc4CGteugUb2vkXFN\nEdIKvgaaA1jhvwlqOwthhwelYdG4OP4A+q94AQN+n46G9XsAmySKHAYg2fdOhHyb/+Z2exNywJg7\nEB1NAqtHaCivu7jYEP3OHDoUDR96iBKU889n+2gao8TnnMNIui8/fqkyKX1XP/nTn5ec04AB/Dkv\nT8mABL17+5ZMhIXxeoXMmsmqFXkNDWX/1TTv+gOhoTyvCy/0/j+ZJKSmGiVpH3zg7TfucFAi8sor\nSicvsNuZDKvfJ+D9fpAEYcCYVNmuHV2B/ME8aajo3eMP06dzElxJQh8k5EEEMWcOH77hw//qM/n/\nCV9L4BVBdJWCzEyjBvWfBIkkZmX5j4hWFevWkSDecoux4MbSpdRZVyZHwhchf/VVDrydOqkiOGFh\nqviLQJKs9PvwFyFfv577njPHeKz9+6np9If+/Y0JaXY7B97cXJUwFhtLQn7PPf5XD4SoyjaFhUBC\nArSQENhE26yfIFqRPH1FxY0bSdg++IDnKKXeP/qIEdh69YyTJyusWmWM2m3aRJlH3bpM1BSZgL7I\ni7T7xInAoEG8940a0ZnjwAFFaPSEXK9zN7tmuN28luRkaqGvvPJ0O2huD1bYzsO4qw9jTfZjcNg1\nNN2poX4isK3xRpywJwB1AZTL4Q+eCMHB8K7Ace9LjQ0pRp9Gx3H2ya1o8+/+6NQCaJQMJLw9nc/N\nlCnAsTDgzdpAPTsT9swJw4WFlOGYcwSaN6dNoB4dOzK6nJFBzboe+klQTIw3YQ8NVYmXOvKuhYSw\nrZcsobvItGmqvdPSSPquu46afjP27OEKhcAsgfr8c2VlqO+HzZp5J+iaI9x6CCFv25aR/mnTjJ+b\n/eY7duTqz7hxvJYbbvDevqLVL72kSvYpbkECuY/+kkP79VMTkX/9y6jFB9jGMuEWJyiA7kTPPOP/\nHGsS2dmVD0AgKFkJIgi+CLp0+avP4v8nDh6suSj3VVcZl+YF+fkkKX9nCEkTH+yahth6SdEawW+/\nsdhGZVaA9IT8wAHgp3KriltvVfIJ/QA8a5a6rvvvp33d1KmBE/LcXO92efBB6nYrmsidd57RVUZf\nqdOM8HD/koDSUtVXGzTg+WsaNKcTDnF20O9XCPmePSRmaWmMSsu9Tk/nd9GRC6nr2pWTBH/35Ngx\n/s/55xuPWVpKouZ2syDR7Nn8XBJbAUXGSkrY7g4HCcnKlYzQ9uzJaK2ekOvLoQsxksmGnOeSJdDi\n4vHV/V/hnikahozX0HL6RehdNg1rskmA3R4b0g4BKzeBZLwCNHUfxLj86Vhz3tvIaHwfvrx1F6YU\nvoQRV1FqkhBrM2rT69ZV/s7r1vEc9X7Pv/6qVif0iIxklBRgLsC113JS6Xaz7/XpY9xer/lOTOSE\nQH+/QkNJKG+6ydrL+4orVNsLxLXmq69IrPWQPhwdzQn1rFnefTU7m/kZrVsDK0zLCmatuT+EhzOq\nHhpKqYtVMrUeH33EPI2uXTk5MX9eWOids2BGIJIRaSt/2yYnKylKfLyx3kJJCVfBbOUSJamo+1fg\n1KkgIQ8iiCqhWzejU0QQNQdNqzgK6Atr1yo9LkB9riRa6bFype9l4DONTz8N7MUrJO1MSqPCwrwT\nqFJSKOsIpBDO2LEkjaKLBShleOstSjEk4guQhEqlznffVcvPP/3EAfvcc9U+Dh2im0ajRtbHLSvj\neeqXwgcN4oBbUQl6M2QyYbeThLbUJQBKYtiYMYw0m1FaSoJSVKT2k5gIe1ERbC6X8jIXCCG//npG\nKL//nhFtudcic3C5SGb0+lhxwejRw/o6rriC5AJQpczlHIWQl5bymgYMIFER/Pe/JKBFRSqSO2oU\nJRDlfbUoPA77DrtR1KEryi7uBU9pGX4uboN3F2p4bm1LXH/Zbxj1cyd8vVLDyoJzMKnBU+jRcweS\nF/8b148DZi4AvvgJSMvwUb1Th4ZJHrw5BjixthY+f1rDl5HPYUXjKTioDcKe25bgmewXcT62I0wr\nZST24EHjDqx09ILdu40rK337+i5QI8jKUtvoJyJ6XHKJKkiVnMwIb0iIuieHDnEF5sorGV03R3uL\ni9mHhWSGhRlXMczPo6xG9OnD+1erljchDwnhZKuq3tiCW25htPvxx5lUPHWq93H0aN9eyZ2s2isr\nq+IiOIGskMpx/RHyDz5QE6533jGuoB07pnz5zVH8Pxsvv8zJciURlKwEEYTehSGIymH5cg6gw4eT\nzIWHG0mUrwEvELzwAl++gwfzyxfx1es9/2zcdRcH5YqIo5A0/UDcrh09u2vKScZq0MvPp0TGWzz0\nKgAAIABJREFUqvCIGVOnMlr24INqgiMVFn/+mZG5qChOsMLCSMoBEkS5vhMnGFE8cUIR8j17mMx2\n883Wxy0rI3n97julyU5M5HGtrumVV1i0w8qeUR8h//e/jRpOIeSbN1uTttJSSmUaNFBR41On4KpV\nC6FHjlAe8+GHqhR5ZCTJ/dy5jNbKKo14jOfnU78v5e1XryZhtNmUQ42+uA1A20SZzEifLi3ll0RB\nhwzh/5aWUq4gZEmPNm2A0lJsyq6NLdHXI//7KKxPuRwZx104cquGLTHrgPKcQxs6IjLEhQJXKPCi\n7KAbsBV463EAGA80AuACkOt9KAC4KHcVnv3gQnRuY8feI0DaId6Cvl2ByHBxrMnH9T3dwLtbgZIy\noH4odf/33MOqi6GhJFSHDnEib7OpfuXxMEJsjtCmpXkHUzZt4v/u2mUdaMnLU31H521+GoWFjEAL\nqUtIoORp/HgSzzvvNFoMioRC7zJis3EyK+dvnlSYVw3l9+ho/k/fvt4OPKJ5D/Rdt2EDZX5iiyi4\n7Tb//zd9uvcEQ2DVXg8+yORiX2jb1vpZNaNhQ+rQ/RFyfwXG9HkqZnnSn40+ffxbq/pAMEIeRBAV\nFS4Jwje2bVORv7g45WksCMTuyxf0bhT+/GB9lX/+M1BRFUqBVYS8uLj6jih6CHkVu7SyMh4vNDTw\nyLzNRpL3zjv8PSqK5E/2WVzM6N0VVyi7M4nGapqq1Bkbq3IAKmojkbLoJysREcpez4yJE60jpllZ\nJFtyPPM2Q4YwUdRK+w1wAjh0KCcDDsfpCWZ+hw7I69aNE4svvlDneugQI41lZYyIrV3LqLxcd34+\nNa42GyPkGzfyvPbv5/4LCthu+ohnfr66BnknlZQYbejOP58kqLQU+d17Yfk1k7Btr4bSMg3pRzRM\nnaPhpivXoZPnPZw3+2KMiH8J932UiA/3tsR3eW2xJc142RrsJOMBIjoCGHElMGciMP8FYNcjG7By\n6yXoeZ4dURE2tD/bhsGX2DDoYhsiw3VSCrGkjIlhRFiuT3ywZUIUGUm9O0BJUnw8tcP9+nlPYNLS\nGHl+9FHKVQJBbq5K+LN6P+XmMiFZYLMBt9/OSHlBAe/RyJH+C8aII43s2+EwWuiZJ5rh4ZxEycpJ\nZKR3boa+3375JSew/vDbb97SmEDQsqW35lsQE6MKRAmKi/3LEktLA1vpioxk367qu1xsO/8O+PFH\nSn0qiWCEPIggAiVVfwdomndy2V+Jdev44pk+nb9L1FRgFVEJFN98wwFq0CD/2t+/MkJeWFh1yUrd\nusZqitXBmjUs9JGZSWkPwDZ77z2SwUAJuRRoEURHk4BERChXCX2J9ZkzmcB2++3czulk3+zShcvL\nQMUTXtmXniR368bI81dfGSN6paVsS4lQ7t2r7AonT6Yt3d13K3cTgBrhBQsYfRN3GCtCrnehefNN\nEoS4OBSIFjUzU5H8EycY9c7IYB8Xqcv11zPiC6jCQUePkqR3787COkVFPBe5hief5N8BdW5uN4o1\nJ44e0dAwJ+/0QP3HjWMxo2AkslZGIWdrMyw9OgIuHXc04mxfH8DhAJwODcWlijDHRQP9D36B+iOv\nQS1HAU6VheGnbRE4kgV02/U1rr5QQ5/nBuOsRCDk0YeBP5rSl/sXnT+0PwhJjY5m/xDpwYwZlEUB\nilTv3QvMn68qJTZvzsmP+V2yezdXCBYs8M4v8SWTyM1VEVurFTyrfAdJjJXk18JC68miQJ4hWa2Z\nO5f94JZb+L40HzM8nM+oy8X9FhV5e+Xr++2qVexTV1xhffydO/k8XHed73PUNOtght3u22EkKcnb\nOcTsPmTG1KnekwtfGDu2eoS8CrrtvxOChDyIID7/nAP5PwGffspEIrNF018Fvdd0w4beyVF2e/WK\nK0i1O4kaWRG71FRr14I/CydOVFzqvGVLSh30Wt+anAg2aEBJyMaNKuKotwoLBN99503IJUJeuzY1\np4sXM+omFSklklZYqKLjZlhdZ1YW71uvXkzWffRRo+f48OFMjDJbNcoxhPwtXsxJx6xZKiJ5002U\nFYie9MgR6tw7dybx8UXIBfn5PBePxyhN0Efd9dHP0lK2U2GhsX/eeCOJV4cOXEl68klG0u++G8ff\nnw93Th7WJVyN/XmXwfWphtpxwP6MK2AricexiHGY+2Az5BQCwMVw9CiFAx6UHggFThvmmFyILBAW\nCrRpwqj2+VH7cHHeatS64wa0behCXL0YFA4fCVtqKg4v/BWN6wKhSXcBI/pSpqHHrV8DPXsDhzYA\nzqZ8/8gkWa55+XLe1+uvV+1erx77ZIcO7KMnTyoLyIQEJsG2acPfS0oY1S0o4LMuvtYSXTVHs7du\nZbtee611lFZPyLOzuUKydKki5OnpJP0ygRJY9Y+DB0nIc3J4PnrbQF+Q/YSGUtby889KK24m2+Hh\n7PPDhlGSVVjovU2/fpyoAnzvmp1h9MjKYvv7I7enTnFFp6KKsBMmcMLduDH17atXG/XRFRHyQYP8\n718P/fuxsggJ4bP7D0aQkAfxz8O8eVzaatasZva3fj2XhK++umb2V1107szIY+fO3p9ZlSf+u6Bb\nN+VkIGjdmpHSQJctzZCJR3ExB+s//iAZ009IAoky22xnLpIeiMNBTIyKGAtqMnehQQOSnpQUDtY9\neviuRik4coSERpagL7+cz4GZkAsR3bSJpKlJExWJysvjPW7blnaHIunQQyLkogsGKHV54glG9mNi\nSHZGjWIkUpJFrSKVYhu5dy+ff31Jb4n2mStjyn0vKiLxEX24L2RkUBs+Z46RmPoi5GefTUJSr55R\nz92+PYpLNKxzdsXq+dHILtNQmDwFy/Ivwe7hCQASgNYLADeAN+SfrgQOA4i6ANDNT9y2EPha44gJ\nKUWhywHN7kBiHNAwuhCXXxqOTi3t6NkRSEqwkbzWqQPUGc7VrPeZnBjlLgBc+TinYfl9CQtjJLeg\nwJiM/cILJKADB7JcueQWbNtGrfKCBVyZ2b1bEfJGjfjcXn45I7bbt3Pbn39mpPi77xgRf+89kssG\nDYxEV6K0ci/Nq23/+hdXmbKzVf5K//6UEqWmGgm5x6Nkb3fdxfu3ezf3LZVeBVb9rnt39rcHH+Tn\nRUW8tqeeAp5+2vrG6An5vHnsV2PHcuJstut74w1e944d7OMvvQS8+KJxm1q11MR/wQL/QQC5dn/v\nF7udpHzXLqBFC9/bPf007+Udd3hXYwX4jFQ1T6gmERGhaiD8QxEk5EH88zBrFl9oNUXIN29mJOzv\nQsg3bqT0w4qQn322t4bv74LJk60jpP36kdyY7bUqgs3G+ywynQ4drEnmtdf6r4AnJKq6BFjTKKMZ\nOJAEZ9myqu+rJs7HjBUrlEPFxIkVb//YYyz4Yl5t0RfUmDuXz0XfvoyMybb3309XlPx86q6lr0oE\nT48mTUi+li1j0RzAWAobUEVMJDmsUSNqq81L0FlZ1Hifcw7/Xz8ZEuItk7/PPuOEoUULkiOJok6a\n5D8SJ/elRw9e84YNCN+3j9FUj4erNps2Ke/pFStw8OYx2N66P9YU9MXO8Roiw4C0w8D6HUBp00WA\nyElr3+nzsIHA4QD6dAauugBIiAXOawG0+XYmXH+kwf76q7DbbUBCA2DGHiNhmzSJBLZJE+quZXKc\nk8O+LIiKAj75hORRb6VYrx7fuytXkijHxHCbrVv5t88+I9HX6/bdbvaxEyfUJM/tplxlxAgmSc6e\nzePUrs37JC4mgFqdELJnjpCHhtJD++qr2Q/Dw2nr+Oab3oRcH/WWSVZ6urWUKySEhPuNN5SWvGFD\nfolkpVcvTnCGDWO7WgUbvvpK/f3wYbXaZ7UaK7UVZs0iMfdVa+H776mzB4yuLWbItVtFyH/6ie9q\nqbsxZYqqOOsLoum3qlFw++3+//fPxEUX/dVnUC0ECXkQ/zxUx7nDCv+kSp3VvfYDBxhBuuCCmjmf\nAQNUopWvKIu+WEpl8PTTqrx3376M5oSFedsoViRBsNv5f9W9x3v2cPlV0xhdXrSIE6SqyoeWLKle\nNTgzXC4Sp5AQa792M1q08LYHa92aUUtZhhYSdNllJBJCuKZPp4uAECF/aN2aUVJ91PGHHxjlFnTv\nTr2r6N8zM9lvPB6jr3iDBpQYpKSwb+ij+UKWyspIhKZPZ8RMchGKi3lN/vyJ587lsWWiVE74w/ft\nQ/62vXDfPwbOH1Yi57X3sCzqOuy45Rd84+mBbfunAft979YKkeFAi+QSdNv+XzhvuRknc4GYT95B\n6ZBhKA2NwrWXAgNvaYbsb1bA1bU7ytIP4qxkOxwO04qM3Y4QTxlgL/+7202yGR1tlHs4HCRf6enq\nmW3f3jjxj4nhpMeXYw+gCPn69SR3Yi2pj57KMyHe6zJx0ucT6Cs1vvSS9/HMEfL4eON5iWY4LIyE\nV6wFX36Zqy36fmn1jve1UiLH0/dPgHKNMWMYGIiO5uSlqIjOO3XqeLslNW9OOc6uXRUnt2/cyImE\n9Gdf73iXS7nP+LMSlM+s3gNLl3JyLM++OSgwfTr3L7I0QGnu/VlQVhd5eZwkyArZ/yCChDyIqiEh\nAXj/fW/f4z8DK1eSHEkp6uriTBLylSsZfahsxrUvGUR1XEsA6lrXrKk5DXrnzsZKiVaoKiEXiYDc\nn40buSpiHkAqIuSyTXXvsb5anwzmdnvV2/KllxhRliX+qqK0lO0kCXO1apFU6YtmWKGoyJqcfv89\nB+XFi439zWZTg/HChSQsEyZYE4PiYk7+ZJJmlgFMmcIJVmGhkigMHMifZUVEX0VSjnHOOfwaPZrn\nryfktWqRtJWUkKzJuZaU8Bo6dTLKE3bt4gRrxw5GiqdO5bGOHTvdx/Ye1jD7v7HIWHkulkSPRvGs\ncoIbfgMQDsCUw2yFloU70f3alggNs8HjAaI+eAv3fjkMLdrGAtmFwL3fAmOGcePn7weeug0IK3/+\nHTYkRbuAbmcDSeXPQloao9iyCiIk6cUXlUf5lVdyYiXVCqUt9+3jpG3DBkaTjx/n39esIelatEhF\nyAWPPcYosJ4Yx8ZyRSYzUxUi0r9HJW9AnlV9hFx+rqhwS3w8pYn79/N9v2GD8XOnUxHy995T7jYO\nh7fdodU73td7w2Zj/8zMNP59wQIGBkQiFxXFc/jlF+tnWH+8iuRyJ05wdat+ffZ/X4RcZFn+NNsA\n26RRI+vVVFkBk32Yx5OtW4G331aE/PffVVGjo0d5vWcCHo8qQvY/in+ItUQQfzvk5ARuM3UmoC+y\nUV2cSUK+fTtlAZWFL0J+5ZXGQhiVRSB+1JVBmzYcsP2hqoR8xAjg3nv5swyeVo4dgRDyinTDgUDv\n9CJ95pJLKh4cfSE7u2ZyApYupWxHyPN11ynyK4lsjz/u/X/mJMy336ZGX/886Am5fvIhhPeZZ3if\nzNi715jMZXZAkESyZs1UG5x7LhM8RcoSE0PSaTUB1TtRSFDgpZe43/XrWbRFiMNZZ/EcGzZUiZ4A\no+xScvzUKaTNW4U3jl+CR49eg7EFt+L2sSfRdhjw9qpzMN92GYo13zkQoU6geQPg5ktLMfPQaMx8\nFPhyMnA08kbs2NQG74/OxTvn/oB3O/2AV/8YhRYnNpH41KrFRG1pa7GpFEjUedUqThyaNGF0W1xZ\nZBuPh2TJ41H7WLOGfXbIEL4vQ0JIbsUfWV+pc84ckqEGDXiPZ85UMoZ169iu8k6KjSVBF022EGx9\n9FSeU/lMT8gdDibSSwVTX2jfnueQmsrotFejh6rJWocO/p9Dq3eEv0m6FYE2y6xCQqitX7PGuo/q\n31Xjx/u2EgSUa4s8t77ybQLNg0lK8tagC8TxRNrLvD9zAnbHjmqC0KGDt695TcHhUPUI/kcRjJAH\nUXX8HRI5agITJ1qTipqA6AYrC1+EXG/nVhW0bl2znt1166pI7Fdf8dz0WvzCQuVaUVnoCyuEhDBK\n1qqV0SMY4HJxRaWbJ00KrFqcP/TowagvQCL3yy/eJax94YMPuBT70ktK+yk2cNXFsWMkdlOncrl+\nxgxG8zSNxOeGGxgNNiM5WeVhpKfTneW777wJuej2n32W0bLnn1cE25ycJjBPcp1OJsS1aaMiqjfe\nyDapVYuJdu+8Q1J+6pT6vwEDrAmIEPJBg7wTL0eMoIxCioM0agR0745jJzS8+SWw6BcgIgxo7r4A\nua3mI2eUhsyMuthZbwUgzXQWAD+BQCfKcHZjJ67YOAMtxt+Kwf2jkFzLBrhDgBfeAq5+g7KJvP3U\nnh84QN/2hATguedIqGNjjUnQslqgf/b/+18l0dq8mYRa/OXXr2fbxcYympyVxZ/dbrb38OGcMB49\nSqJz8iQj4g0b8jh6Qi5yH4Cks7CQ/weoqLbcT7vdaI0n/uH9+qkodVgY+5fcO4eDEeeoKD5H+/bx\nfP29y6Kj2T6pqdbEuW1b9gMzUba8YU5jAjDA99bAgbxOsy2flR1geLi3/arIfazeqWZ3ISkYZYXC\nQrrK5OXxmqzaZdMmOjX5sjrUIyqKz5cV5H0dHs73hRS0EvgbH/r2PXM5TNJXqjJW/D9BMEIeRNVw\n5ZU1p0OuCnwRgaqiMvZwlUFV9Ha1aqmKhWYUFFB/W1XceisJ1ZnApk3eZZ2XLaNsp7r2fk4nCc69\n99JvW4+cnIoH5AceUBGh2bOrplO02ZSF47JllVtV2b2bJFlfsl0KpVQXR4+qJEV5Jt95hwROqkJa\nneukSWpw15cS15Npj4fE1+VSsgWxfpPo5u+/k/jrJQjmYzqdHPil4JDNxpUjuW/6wk960uNrEtW8\nOScc/frRZ10gxLG8v2kAtqbbMGishvoDgckfApvTgN+2AZ/sbIyFtQZh5SZg51Hf0e+GcfmYseff\nWNvuNRx9cz9OrK2FkqgB2D7XhmkZT+KehhtJxjdu5MpAeDif0/nzleuLtKnTSZmSVU6DJEoCbCuP\nh9FJ6beTJvG7yFKmTWPk+8YbKbEQO7/zzlMRVqeT59C6tdp3WBhXTPSEXJ+bUrs2J8MyWZRt4uKY\nxCgQqVH79mqyJUm7ACP6DgfPMzKS98rhoJ/4jz8GHhjwpVt+/XW2c/v2FU+2bTYmkwJ8B/7yC68z\nM9O42iCwkgZaEf82beiT7ouQC8mMjVUVXq0wYwbJOECp2NCh3tsUFzO4Ud1EcJl8hIbyZ5E1Cf6q\nImtyXX/V8f8G+N+98iCqh+nTK/ZePlP4z38YFa0p1KunXB7+DrAq6y04fpxV4vQJUZXB5Zf7/uzU\nKaPvcmXxzDPeWsqyMkoKqqKTXrGCg22tWuolvXw5o8x33620kLNnM0pslRgGcNDetInFWAAmDjZp\n4p0cWhk0bMjI6+efk6hWBKvCQDUZIRfN7Pnn83tYmPLFDkSuIyRYEiXlPKdMYRQwJYUESIjKvn2c\nCDRtyrZdtIhRdoH+mNu3s41EduDxkEyL/re4mPv/4gtG85OSOOns18/30v3ixdZ/t9uRVpKIqZv7\nYWWngTgU0QgFYwOTFNk1N65ocBj1CvbDnVeI+tm70HVwK5x1Xhm6XPsOMPRnIMYFuHOUY1BODqPQ\nmkYdc+vW7Je5uSRYCQl8BoSQi3TC4SBhB2idB5A0Cvlu0YLPelQU+9iSJarolhDy48eN78HcXG4z\nZQoL9gBsP4eD0oq+fbkiMnUqAxBff83nKDGR8hl5xkaPNk5yhVgOHmyMztpsfF/oJ0SCpCTe36ee\nUvuVCeiBA5RRmUvD+7wxFlZ7APv3wIHWkWe9xaYZssoA+E6StyLPVoQ8PJySICtP8JEjmWwK8HN/\nOR3PPccVqNq1gUsvtd4mJITj1Ny5vvcTCJo04QTqwgutLWP/qpXvICEPRsiDqCKaNFGZ1382AtEM\nVwY1bT+nR00X8KmJ5EQ9HnmEA+evv1bN8WPOHKP9n3lwrI4rzNixjCwfOcJla4CD7KuvGmUNFekq\n9+2jJCLQ7QNBQgK1lKNGBba9EHJ9v33lFWNhpari2DFGNCXJDSBRKCxUiXW++sxDD1HaIYR81Srq\nuPVEODqahPDkSfWsbNlC6QGgrAb1bao/5oYNJJUvv8zjaBoJo0g0Zs5kNc5//YvXYrcrommOfH7x\nhWEVRtM0FBZr8Hg0/LxBw6DvLsW5hyfj3X3n4o+IliiAIuM2G3BRB2B203lYfNF8TPsPMHcSsOx1\nYMOYrTjmvhLfPleKd59wYHbkq3j2+HMYdPYRhESGoKxWLUYSX3+dkx+Z/N1zDyeMu3fzOkNC+F7M\nzeX1ff45I9gOB6ObP/yg/LQPHFCETfD++4xe699JEskWRERwUpOZaVwpzM1lVHrePDVBczrVvbDZ\nSAwLCtjWMTHK2UIvWQGM7xk5l5gY70DI6tXWk3iRdyQkqImzTEAlsl7ZCHlGhvF9qk8I1uPll/2v\nyOl96n0lyW/Y4H2tfftygmEupDNqlLWMo7BQvRsrmhT37EkC72/FTO5JoKuN331HWZMZ8fFctfBV\nv+HKK6tXzK2qkOsKEvIggvgHoUcPlfVdE6iotHd1cPXVNbuSUNOTkZdeYsQoMtJY1CRQrF5t1G+b\nB4vquMLI4LNnjyIeNhvJoj5SZaX31MNclKii7QNBSYkxaa0iWEXIw8KME4WqorSUqzx6GYmekOvJ\n1dtvK20wQEKWl6cIeWkpvXx//FFtIwO3RCodDq5c3H47Ld+sCHlYmHJYkfvYuDH7msNBj+fiYkaA\nR45US/TZ2fweEQEXHEg/GY7UPRoysjUcOa5h1dxteHhWOC64S0ObmzTE9QWi+wAhFwN9/gN8s68B\nijQjiY+JBC7pBPzyNrDyLRtG1PsdVyTuwQNDbLjxMht6dbah0wWJSHzkLhLZCy9UNolOJzxRUci8\n4QYSwlmzFLk+cIATi+RkTljWruVnV1yhKstGRKhVCmljiZgXFPA+paQYK9LqJz4AnyG91KlpU8rO\nzBHyb7+lZCQ7W3lg6wk5oBKsGzViNF/2f8kllAHNns2cGj2BfO01ZW2ox5IlPP+uXfmzHlbRZHl3\n+Uom9IVWrbhyUq+ekZCLNWdenjFyb9Z5myG2mIDv99NDDynvbUGvXuyvgRQCA9j2cr6BGAdYFSTS\no7ISt4ULrQl5RbjgAqM3/Z8Fm41tHCTkQQTxD8L11weW2BIoarKEuRnNm3NAqynMmuU/W78qkMG3\nKi/CAweoCRWYBytzdT2A+tiKClEAjFJNncqBXTyFxVNc785QUcTbTMireq05Oeq4paXcR2ZmxaWn\nAZKgmBjjoBwfb11IqbJYuJAkWt8u4eGcaH78MWUsr7/Ov0+fbiQaQpKkaE6HDupZmDqVEXyJQuoJ\nufw+YgQnZGZCXqeOsjCTCW+/fjxXQYMGp6VXbnsINkSdh0+nbMDnyzSMnNsQZ/XMxtn31Ma5twD1\nrgYaXANckjkB0za1wm/bgJ37gXwfpkFhoRqG9dOw6UMg56VU/Hzpl+jeTqwELaKV9eoZZVXjxrEt\nnE54wsNx9M47eb0JCUx+XbOGlQtLStju0j9DQtjWdepwIiM2ijExvH6Ari/t2pHkhoVRTrJ6tfp/\nSdqU9iwrUytEHTvyXK++WhVJEiQmUhYhkrcePUjyZs1SHtlRUWpy6HDweS0rY6S/Wzce99Ah3tcH\nH1T7Ma+eaRojqampbBfz+zguzttBRa5N+tNNN1neOy+0bq0SFPXvaYmQFxYacxAqQiARcl/k2LyS\n4A/64MnUqd5WjIEe02p/geCttyqenLhc3qu4ssrzV+D995Xs7n8QQUIeRNWQleXfsuqfhF9+qdkC\nLXrUqmVMhKouKkperAg7dzKBSCDax+qQVD0hNScjRUQwglhYyKjqsWMkhSNHBrb/Awc4qISFcZDP\nzeU1mCPkzzzju21KS2ndJr7CW7ZUzUt35EieR24uddWSxLh7d8X/++yz1Im2amU876qszPgaZMeM\nUROP3r15ftdfz3aT4wqhKCxkZFYG+YsuIsls0UKRnrFjGTEVsjl5MqOhUilQ70ttJuT6c/rqK+7T\n6TRMjDwLv8HvqSV4+E0NCc9ehK7npuCm3cNw41PAe0vDcdwV470/P7BrbvQ55xSW7uqPgkWl+GiC\nHR2a22BL3aL02oBxxUA83PU4epTR18RE4zNht3Ol5j//Uc+LEHJzqfK4ODrrSL2EpCROzGvVAh59\nlO4x117Lto2L4zOkacrxxGbj8W6/XRXxATjJkRWJW29lexYWqr5dq5ZaZVi+nNvWq6ecciIjeX3i\nza5pqvgSoOQ2deoYXY7MkIm3npxu2aIq5q5dy/bTNP4McLKQlUVZjdNprbv2Bav3086dPFf9hB3g\nqtPs2d776NWL20uEvKiIfdMqH8lXfoc+ul4R9AT6kksqXint0YP6f19o0gT48svAji2oyOY2Odl/\nztKfjcaNrasx/48gSMiDqBr69zcuo/6ZeOWVmrVGOnrU+gX+V6C4mNEgPYHQo7rSmokTjWXmRXdc\n3YJDAJfBzc47//oXdZcHD3IZdPPmyh1HisSEhzMaJwlw+smgDHQy+F12mUqAA1TUKSuL3887r2qr\nDDLxcLmYyNWnD38PxEmndWsmy4nuWv6vsvczK4uTHKv+37y5Sva94Qbr5LB9+zgA//EHI7xCGurW\nZfRVXxUTYGRXbAUXLqTMQtpb7uMllzA50KouwSuvQFu0CHvdyZj7vYYn3tZw38sabhyvod7k7uj8\n7zBMmwfkl1r3iVgtH62SixAfA9SOA87DLtza6Ri+fiIXm6fnYWPiIyhaE46SOYeRV3ghlt6fjj4n\nfoA9rJwoFhUZKyDKeUtfad3amIwKkFiKh7PZE1zutTwvTicj3UIIhWRGRjJqrI+oio5bouHSr+Pj\n2bdmz6YEprSUzxLAhFgh2BMnKrISHq5Wmb77jhFugOTe6r28fj2lHTExfKakeqnIt2SCEhpaucnq\n1q3KN3rfPu53/366j3TuzGNJn583j8d86SWOH5VxoLJaaXvzTb67d+0yBgWSkpiTYMb4Ij6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Oo3DgctAs1JkVu20AUkMZH3Qv//+kl4ZRMxIyO52lBczOdM+p5+NeHwYaPzjT9I2/mCBBgCgdvN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "velocity = 1\n", "sensor_variance = 30000\n", "process_variance = 2\n", "pos = (0,500)\n", "N = 1000\n", "dog = DogSimulation(pos[0], velocity, sensor_variance, process_variance)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "ps = []\n", "\n", "for i in range(N):\n", " pos = predict(pos[0], pos[1], velocity, process_variance) \n", " pos = update(pos[0], pos[1], zs[i], sensor_variance)\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", "bp.plot_filter(ps)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example the noise is extreme yet the filter still outputs a nearly straight line! This is an astonishing result! What do you think might be the cause of this performance? \n", "\n", "We get a nearly straight line because our process error is small. A small process error tells the filter to trust the prediction more than the measurement, and the prediction is a straight line, so the filter outputs a straight line. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Incorrect Process Variance\n", "\n", "That last filter looks fantastic! Why wouldn't we set the process variance very low, as it guarantees the result will be straight and smooth?\n", "\n", "The process variance tells the filter how much the system is changing over time. If you lie to the filter by setting this number artificially low the filter will not be able to react to the changes." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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leJzTa7hFRESknHr9dQgMhBdfdM71evSAxYtzrgcHWLMGXnrJOfcSyafLKRbz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\nmw/4sWm/H5sP+LHzt4qkpee9Al03OJn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "velocity = 1\n", "sensor_variance = 20\n", "process_variance = .002\n", "pos = (0,500)\n", "N = 100\n", "dog = DogSimulation(pos[0], velocity, sensor_variance, process_variance*10000)\n", "zs = []\n", "for _ in range(N):\n", " dog.velocity += 0.03\n", " zs.append(dog.move_and_sense())\n", "ps = []\n", "\n", "for i in range(N):\n", " pos = predict(pos[0], pos[1], velocity, process_variance) \n", " pos = update(pos[0], pos[1], zs[i], sensor_variance)\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", "bp.plot_filter(ps)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to see that the filter is not correctly responding to the measurements which are clearly telling the filter that the dog is changing speed. I encourage you to adjust the amount of movement in the dog vs process variance. we will also be studying this topic much more in the following chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Bad Initial Estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Now let's lets look at the results when we make a bad initial estimate of position. To avoid obscuring the results I'll reduce the sensor variance to 30, but set the initial position to 1000m. Can the filter recover from a 1000m initial error?" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wcJytqIqQEEKILM7WVp+JTaOfPUopBk6F75fHtb1VC5aOAUcHM35uRkbCf/+Z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\n/eXixaFkSeuP26SJPgM9erRun/7RR+nPOTpC5crWP6YQQgh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "velocity = 1\n", "sensor_variance = 30\n", "process_variance = 2\n", "pos = (1000, 500)\n", "N = 100\n", "dog = DogSimulation(0, velocity, sensor_variance, process_variance)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "ps = []\n", "\n", "for i in range(N):\n", " pos = predict(pos[0], pos[1], velocity, process_variance) \n", " pos = update(pos[0], pos[1], zs[i], sensor_variance)\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", "bp.plot_filter(ps)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again the answer is yes! Because we are relatively sure about our belief in the sensor ($\\sigma=30$) even after the first step we have changed our belief in the first position from 1000 to somewhere around 60.0 or so. After another 5-10 measurements we have converged to the correct value! So this is how we get around the chicken and egg problem of initial guesses. In practice we would likely assign the first measurement from the sensor as the initial value, but you can see it doesn't matter much if we wildly guess at the initial conditions - the Kalman filter still converges so long as the filter variances are chosen to match the actual process and measurement variances." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Large Noise and Bad Initial Estimate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What about the worst of both worlds, large noise and a bad initial estimate?" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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k1KhRAz/99BMMBoNFBPa7777DDz/8gJ9//hnh4eHw8/NDixYtkJSUlLPNhx9+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\noKC3ilujzznACVmvXsC116pCUfHWtou+W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y9wjNGQosn//U/dh9b7VGjWjBOcWOzYARx9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sensor_variance = 30000\n", "process_variance = 2\n", "pos = (1000, 500)\n", "N = 1000\n", "dog = DogSimulation(0, velocity, sensor_variance, process_variance)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "ps = []\n", "\n", "for i in range(N):\n", " pos = predict(pos[0], pos[1], velocity, process_variance) \n", " pos = update(pos[0], pos[1], zs[i], sensor_variance)\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", "bp.plot_filter(ps)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time the filter does struggle. Notice that the previous example only computed 100 updates, whereas this example uses 1000. By my eye it takes the filter 400 or so iterations to become reasonable accurate, but maybe over 600 before the results are good. Kalman filters are good, but we cannot expect miracles. If we have extremely noisy data and extremely bad initial conditions, this is as good as it gets.\n", "\n", "Finally, let's make the suggest change of making our initial position guess be the first sensor measurement." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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sulo7A5CFIquyUOT7ntGuHe6MHVuiPgl6PW6NGwddkUW/MDAQma1bm22rd3fH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0q3C7MHoNNJ0it0uW+8QUu8pk2l/Zs4PpHdystj1z8xWzFpErOS333HaX1BzjWNWf++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\nZR75qokEmffeU66UWR3grhF81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sABen/hAjBlClxSU+k9b/fWrRTVO3eONKmX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\njOJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sensor_variance = 30000\n", "process_variance = 2\n", "N = 1000\n", "dog = DogSimulation(0, velocity, sensor_variance, process_variance)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", "pos = (zs[0], 500)\n", "ps = []\n", "\n", "for i in range(N):\n", " pos = predict(pos[0], pos[1], velocity, process_variance)\n", " pos = update(pos[0], pos[1], zs[i], sensor_variance)\n", " ps.append(pos[0])\n", "\n", "\n", "bp.plot_measurements(zs, lw=1)\n", "bp.plot_filter(ps)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This simple change significantly improves the results. On some runs it takes 200 iterations or so to settle to a good solution, but other runs it converges very rapidly. This all depends on whether the initial measurement $z$ had a small amount or large amount of noise. A large amount of noise causes the initial estimate to be far from the dog's position.\n", "\n", "200 iterations may seem like a lot, but the amount of noise we are injecting is truly huge. In the real world we use sensors like thermometers, laser range finders, GPS satellites, computer vision, and so on. None have the enormous error as shown here. A reasonable variance for a cheap thermometer might be 4C${^\\circ}^2$, and our code is using 30,000." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Interactive Plots" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implement the Kalman filter using IPython Notebook's animation features to allow you to modify the various constants in real time using sliders. Refer to the section **Interactive Gaussians** in the Gaussian chapter to see how to do this. You will use the `interact()` function to call a calculation and plotting function. Each parameter passed into `interact()` automatically gets a slider created for it. I have built the boilerplate for this; you fill in the required code." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_kalman_filter(start_pos, \n", " sensor_noise, \n", " velocity, \n", " process_noise):\n", " # your code goes here\n", " pass\n", "\n", "interact(plot_kalman_filter,\n", " start_pos=(-10, 10), \n", " sensor_noise=widgets.FloatSliderWidget(value=5, min=0, max=100), \n", " velocity=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n", " process_noise=widgets.FloatSliderWidget(value=5, min=0, max=100.));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One possible solution follows. We have sliders for the start position, the amount of noise in the sensor, the amount we move in each time step, and how much movement error there is. Movement error is perhaps the least clear - it models how much the dog wanders off course at each time step, so we add that into the dog's position at each step. I set the random number generator seed so that each redraw uses the same random numbers, allowing us to compare the graphs as we move the sliders." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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eVPH29sbFxYXy8nKGyz8+IYRo0yordZzLK+J0VkGtYJ1TUNyoczXbLPaxY6oO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\npenTe+0+ee8Srd5cp9K/bFbjybZe+yPCQjRrkk1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.random import seed \n", "def plot_kalman_filter(start_pos, \n", " sensor_noise, \n", " velocity,\n", " process_noise):\n", " N = 20\n", " zs, ps = [], [] \n", " dog = DogSimulation(start_pos, velocity, sensor_noise, process_noise)\n", " zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", " seed(303)\n", " pos = (0., 1000.) # mean and variance\n", "\n", " for i in range(N): \n", " pos = predict(pos[0], pos[1], velocity, process_noise)\n", " pos = update(pos[0], pos[1], zs[i], sensor_noise)\n", " ps.append(pos[0])\n", "\n", " plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", " plt.plot(ps, c='#004080', alpha=0.7, label='filter')\n", " plt.legend(loc='best');\n", "\n", "interact(plot_kalman_filter,\n", " start_pos=(-10, 10), \n", " sensor_noise=widgets.FloatSliderWidget(value=5, min=0., max=100), \n", " velocity=widgets.FloatSliderWidget(value=1, min=-2., max=2.), \n", " process_noise=widgets.FloatSliderWidget(value=.1, min=0, max=100));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise - Nonlinear Systems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our equations are linear:\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{N}(\\mu,\\, \\sigma^2) &= \\mathcal{N}(\\mu,\\, \\sigma^2) + \\mathcal{N}(\\mu_\\mathtt{move},\\, \\sigma^2_\\mathtt{move})\\\\\n", "\\mathcal{N}(\\mu,\\, \\sigma^2) &= \\mathcal{N}(\\mu,\\, \\sigma^2) \\times \\mathcal{N}(\\mu_\\mathtt{z},\\, \\sigma^2_\\mathtt{z})\n", "\\end{aligned}$$\n", "\n", "Do you suppose that this filter works well or poorly with nonlinear systems?\n", "\n", "Implement a Kalman filter that uses the following equation to generate the measurement value for i in range(100):\n", "\n", " Z = math.sin(i/3.) * 2\n", " \n", "Adjust the variance and initial positions to see the effect. What is, for example, the result of a very bad initial guess?" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#enter your code here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5RyNme/LWS3j9MY7FEWkekUiEoSvPMAF4SYsi2Dy2LU18EFbI9a+Qv78/IiIi\nMH/+fAAFfxygjFrhU/0v4cSNcGZ745g2cK8t3654BdG+YWUsGtyM2fY/cx/rj4UqfRzagJ+ZjSEr\nTzPb3Zo6qmRXug6NKmNkZ8kikHEbL+B5pPwWmWi7iM8JMusBZvRqAicVbJIxrFM9tKpfgdnuu/g4\nEpLTWRyRZnkcmYAVhyQLX5cP9YB9iaIsjujXZvdtyjTySc8QLyAVUPUkuflf4GMcvf6C2Q6Y2IGV\nhdmEAHKsEx4eHo7p06cjJCQEPJ44vUIkEuU5y5v7iNBET/IGE3z7AXTT5bsw6eTdD1h6ULKatmeT\nsqhVQsScX9ncK+ijde1SOHdfXBpxzPrz4PLj0aCSZT5Hap+/+RltOh+O1x/FK6yNDXQwoHFJ1n7m\n+fGqVwznb5vg9ZdkZGQJ0Gf+fmwa4kyzMwX0u5+rSCTC8K13kMbPAgCUL2ECj8qGKnsdjG5ph1tP\n3yMpLQsfY77De9YezP+XvQXEmoKfJcCcg4+YNI/6FYujdkn2/gbkZ1L7Sui3LgYCoQg3n33AuFWH\n0Nv1zxqPEImvCekYtlqyLqSrsy0seUky14Eyrwk7OztKR1FBycnJePr06S8/VrGifNcPym0m/Nat\nW4iNjYWTkxN0dXWhq6uLa9euYePGjdDT00NWVtZvj7UuKrkIvyXy5TUkAMC9t3FYdETSje6fKlYY\n1baKXM9RWBwOB9O7VYNTGfEsjFAETN1zHx9jaaGmvER8S8bu4LfM9ojWDrA0U903O31dHuZ612TK\nFt57G4/Ah59ZHpX6O3n3A+6+ET/O53KAmd2rQ1dHddJQflTc1ADTuknapV94+BlXn1IXxb+1+Xw4\nomLE76/G+jqY0b2aSt/gOpQ2w4Bmkqcimy+8QsS3ZBZHpP5EIhHmHHiEVL543UWZ4kYY3Z7dWIAQ\nuc2Ed+7cGfXrSx6pi0Qi9O/fH5UqVcK0adOgq/tz+afcBRB1Xmfg4I334p36pnJbGPHmUzymzQtC\ntkA8+1G9nDXOLu8PEyN9ubz+37pYyRH1hvrjU2wyktOzsercO1xZ1VelchTZ8jcLM4VCEcaM3sH8\n3F2cSmPhiC4q/32tCyA0KgurDt8GAGy48AYje7aCqbFqXK+qKK/r5HNsMtb5SdrSj+3ugr5dmitt\nbH+qbl3g+TcBdl14BADYEPgWw7xbwlCfvRJ66uzGkyjsvX6G2V41ohXae9RhcUQFU6NmLYRFbsOD\n11+RmS1gLawzAAAgAElEQVTE8tNvcHP9QFZqmWuCvZeeIOxtzg05l4ODc7xl+kTIsxhAQfH58p10\nJPJhYmLy2+tAemGmPMjtt9nMzAyOjo7MPycnJxgZGcHc3PynVqI/UkSt8OS0DHSYvo+pOmFtboxT\nC71VJgAHxG2Lj83zYmY/rz1+jy2nVPPxqDrxP30PN55+ACBegLt1fHuVD8Bz+fVzRYliRQAAX+JS\nMGdXMLsDUlMikQjDVp9BUmoGAKC8jTnm9ndjeVQFt8K3BcxNxE9u3n1JxLL9N/M5gvxKZpYAA5ed\nZMqTtqhbXm26Ierq8LBrSifmyc3dl5+x9dQ9lkelnlLSMzFxy0Vme2w3Z1YatRHyI4XeUv+q/uOv\nyLtWuFAoQp9Fx/HivXgVvL4uDyfm94Ct9d+Xk5G3eg6lMElqNfykLZcQ9U3x9dI11Ze4ZEzeKpn9\nnNSjIaqq4CK83zE11scK3xbM9pojd/D0XTSLI1JPh68+l1mI7T+hPavNWArLwswICwa6M9uL9obg\nPTVvKbS1R+8g/IN49tNYXwf+E5Tblv5vVStnjZm9mzDbM7YHUS+BPzD/f9fwOVaczlOiWBHM6tOU\n5RERIqbQIPzKlSsyNcJ/p4ylfGfCF+y5huNSreH9J7RHAxW+653Vt6lMk4YhK09T2cI/NGb9BWb2\ns0KpYpgh9QdMXXg3q8o08REIRRi+mspYFkZyWgZGrTvPbPu0qw23WsqvhPS3fNrVQc0KJQCIK/2M\n3xTI8ojUy7f4FMzdfZXZ9mlRUSUnYvIzsUcjptFbQjIfs3ZcYXlE6uXVhzislKqKs3RIc5VK8aP3\ndtWi7J+HSiSX2RQ3YWpnf0tIQWaW4I9f69TNcMzeGcxsj+nWAL1b1PjLESqWgZ4OAiZ2YL4H50Pf\n4H+Bj/M+iPzkzK1XOBj8jNnePLatWubRcjgcrB/Vmsn9vPb4PfZeepLPUSTXov9C8DWn30BJiyJY\nKlV/W53weFysH9Wa2T5y7QUu3YtgcUTqZdq2y0hOEzdGs7cyhmcje3YH9IcM9HRkOvxuPnUPj9/K\nt4KYphKJRBiz4TyyssUV2FycSqOXR3WWRyWhp6cHPp8PgeDPYx4iPwKBAHw+H3p6eko7p9wWZv4N\nXR0eSlqY4HNsMkQi4FPs9z9qIxweFYteC48x+X9uteyxbGiLvA9SEQ2rlsHIzvWx9qi4ZviYDefR\nol55Jj+Y5C0jMxuj1ktmP3t7VEezOuVYHNHfcSprhTHdGmD5AfEMzoTNF9HOpRLMiqhuhRdVEPFZ\nthb04sHN1fp71qiaLXp5VMeei+Kb8lHrzuHRtqHQ1aEuu3kJC/+MHVJNusZ1cFLrBY0dG1VG8zrl\ncOleBIRCEUavP4+glX3UKrWGDWduv8a5O28AABwOsH5UG5X6nnG5XBgYGCAzMzPPCnK5RCIR7r/+\nwtxcWpsbo4odlTbOz+fYZLz6KFmUW9+hFAz0fg5/ORwODAwMlHqNqEQQDohTUnJztj5EFz4I/56a\ngU4zD+B7TiqCrbUZDszqplZvvAsGNcPJm68Q+TURCcl8jFx7Dof8urM9LLWw9ugdRHxOAACYmxhg\nxTD1uPnKy6w+TbH38lN8jk3G1/gU+O0KxqrhrdgelkqbuPki8yStvkMplZr1+lNLhzTH8ZCXSEnP\nxIv3sVh3NBTjPF3YHpbKEolEGLXuHDMZ086lElwqq3egwuFwsGZEK1QfuAkCoQjBDyNx+OpzdHd1\nYntoKoufmY0xUhMzg9vWRu1KJVkc0a9xOBzo6xc8PUYIHlpPPcBsh6ztj0bVbBUxNI0Qk5iKOr7b\nkZgirkQzt78rWtRXnaZ9KhOhyizOLGTXTKFQhN4LjzHtiA30dHBsrhcsi6pOe/KCKGKoB/8J7Znt\nw1ef4+i1F3kcQQAgOiEV8/dcZ7b9+rqq3c/+V0yM9LFSapHmuqOh9Bg6D8EPI2U64a0Z2UptquLk\npaSFCWb3lSwk89sVjC9xVDP6d/679AS3nn0EAOjqcLFSA27IAcDR3hIjpDrrTth8kWlCRX628uAt\nvJWamFkwqFk+R6iHxtXt4Cl18zV6/XmmCRX52VT/y0wAXt7GHBOlCmGoApUJwm2lyhQuP3iL+aYV\nxLz/XcXJm5JKCNsmtFfJO96CaF6nHAa2kXTIG7b6DFNmkfzarB1XmCcglctYwLej8uq8KpqnmxPc\ncxYVCoQiDF9DizR/RSAQYrTUYsx/m1fTqBJko7o0QOUyFgCA5LRMTNl6meURqaaU9EyZ6khjuzmj\nYmkLFkckX379XFE8p8V61LckLDtwg+URqaYP0UlY8J9kYmZefzfm+6YJlg5pzqRT3Hv1BbsuPMzn\nCO10+/lHBJx9wGyvHdn6l2kobFKZILyHe1Vm1urhm69oPfk/JKdl5Hvc/wIfwW+nZAX8uO7O+FfN\nH0Ev920Bm+ImAIBvCakYt/ECyyNSXU8ivsH/zH1me4VvC43Kl+VwOFg/WrJIM+RJFPZd/nU7XW22\n7cx9PI4QPyUwMtDFYh/Vb8pTGHq6PKwdKVmkuTvwEW7m1MInEov+uy5Tik4dqyPlpWgRA5nSlYv3\n3qDSlb8wUeopQbVyVhjSQXMmZgDArkRRTPRqyGxP9b/MTEQRMaFQhBFrzjLbHRpWRhtn+baclweV\nCcLrOZTCNqlUjNvPP6LD9P1Iz/j147bMLAFGrT2HPouOM/ua1S6LJWpaCUFa0SIG2DSmLbO968Ij\nXAx7m8cR2kkkEmHcxkDmUZxH3XIq+Uv2t6rYWWJsN2dme4r/pd/+Xmij5PQszNguKds2xbsRSkuV\nPdUULeqVR+fGDsz2iLVnIRAIWRyRaon4nIAVB6UX5TZTqeZs8jKwTS3UqigpXTlx88V8jtAuVx9G\n4sAVSZWsdSNbq9XasIKa7N0IpaQm6xZKzfwT8UTFvVdfAIhTlFePaJnPEexQqSuzf+taWCdVkiv4\nYSS6zj74U8nCjzHf4Tp2J9YdC2X2VS5jgf1qthAzLx0aVUYP96rM9si15/6qdKMmOnP7NVOyjcvl\nYOWwliq18l2eZvRuAsui4sepH6K/y9S91XbbLr1GbE4DE1trM0yQmiHSNCuHtWQepz54/RU7z9Nj\n6FzjNwUiQ2pRrqqXpv1TPB5X5qnIoavPEfwwkr0BqRCBQCjTI6CHe1U0zem5oGmMDfWwROqJ36rD\nt/HmUzyLI1IdKemZmLZNkrI3wcvljyruKYPKRawjOtfHYh/JAopzd96g5/wjyM6Z8bl8LwK1fbYw\nC28AoHNjB9zZOEijcr4AYPXwlkxTgfAPcVh9+DbLI1IdWdkCmeYlPu1qq1VnzMIyNdbHPKm264v+\nC6HFeQDex6TgQEgks73Up7la1oYvKPsSRTHZW7KwaHpAUIHS9jTdpXsRMg3a1mrIotzf+aeaLbyl\nJmlGrzvP/I3UZgFnH8ikpS0dollpaT/q2bwaXJzEa18yswSYQA29AABL993AlzhJr4jJ3v+wPKLf\nU7kgHAAme/+DGb0bM9tHrr1A/yUnsOi/62gxaQ9iEsWzXjwuB8uGeuDIHE+1rgX8O9bFimBuP1dm\ne+7uq/gU8/cdRTXBxuN38SqnHbWpsT7mSgWommpgW8mNRio/CzMCglgeEftWn3oBQU460j/VbOHp\npvkl2yZ6NZRZM7J4bwjLI2JXtkAoU4quT4saKt0hWV6WDvWAkYH4hvNxxDdsl1qApo2+p2Zg5g7Z\ntDTpqmuaKLd0Za4TN8K1vqHXh+gkLD94k9leMNAdRQyV13ynsFQyCAeAuf3dZPJg91x8jGnbgpj8\nX2tzY1xe0QcTvBpqbAoCAAzvXF8m8JpA+X+I/56OOVLtqGf2bqIRJQnzo8OTLbe24/xDPHj9hcUR\nsetC6BuEvIgGIG7EsWZEK41+L8hlbKiHRVLl1lYcvKXVi/P8T9/Ds8gYAICxgS4WDdaMUnT5KW1p\niilST0VmbA9CUiGqimmahf9dR3RCKgDx92a8p+ampUmr51AKfVtKUq/GrNfupyLTtgUhPSMbAFCr\nYgn0bVmT5RHlTWWDcA6HgxXDWsCnXe2fPta4ui0e+A/R2FwvaTo/tK7eH/QUVx68Y3FE7JuzKxgJ\nyZK6nyOlaudqOo+65dE2Z/GpSASM2xiolSULs7IFGCtVNah/q5pqW5b0T/TyqI66lW0AABlZAkzx\n186ShYkpfMzaEcxsT/u3MfOUQBuM92yIMjnlfWMS07R2cd67LwlYJZWuuXhwM+YpgTZYNLgZM9v7\nLDIGW0/dY3lE7Ah98YnpLgwAq4a1VPm0NJUNwgFxIL5pbDuZrncTvFxweUUflLTQnjfapjXtZfL/\nRq49h6xs7Vyk+TIqFhuO32W2lw31gL6K1f1UtOW+LZgFyMEPI3HiRng+R2ieLafu4cV7cXMuY30d\njWnEUVDihciSpyL7g57i1jPtK1k4/3/XmEW5dtZmGNvdOZ8jNIuRgS4WD5bkPa8+IukcrE0mb7kk\n0ynXu1k1lkekXCUtTDDtX0ne86wdV5CQrF39RcTV0iQTM50bO6jFRK1KB+GA+I/N7qmdcHF5bzza\nNhTLhmpWHeiCWu7bQuZOd71UZRhtMn5jIJMD3LSGHTr945DPEZrHwbY4fKXq3kq3atcG8d/TMXtn\nMLPdv1kFlChWhL0BsaRxdTt0a+rIbI/dcEGrOue9/hiHtUfvMNtLh3ho9KLc3/FuVpVpTJWZJcCk\nLdqVshjyJAqHrj5ntlcNV/3ZT0UY290FdtbiHPi47+mYt/sayyNSrkPBz3Ejp3eCrg4XS9WkXLXK\nB+GAeEa8eZ1yqF7emu2hsMamuAlm9ZE0npi9U/taV58PfYOzd14DEOcArxquuSUJ8zO7b1MUzVmM\n/OZTvFbdlM3ZFcx0kS1VzAjeje3ZHRCLlvg0h56ueFLizotP2B+kPY2cJm25hKxsce5ro6pl0N3V\nMZ8jNBOHw8Gq4ZIayEeuvcC1R+9ZHJHyCIUijN0gmf30cnNCw6plWBwRewz0dLBsqCTwXHcslCle\noOn4mdkynXJHdq6PCqWKsTiiglOLIJyIje7qDAfb4gDErasnb7mUzxGaIytbIPOoaUDrWqhVUXty\ngH9kYWYkc1M2d/dV5rG8JnvxPkYmHWl0uyrQ08InY7nK2ZhjTNcGzPYU/0tMp0BNFnT/nUxJQm2+\nIQcAZ8fS6CmVgqEtT0X2Xn6CsPDPAAB9XZ5M3Wxt1K2pIxpXtwUgrho0XktKFq4+fBuROYvTLUwN\nMbNPU5ZHVHAUhKsRPV2eTDOj/118jJAnUSyOSHk2nwxjcoBNjPRkWjdrq+Gd6qNiafHdflJqBvyk\nUjQ01TipdCTXmvZwraq9T8dyTe+lXY2cBAKhzOxnb4/qqOdQisURqYZFg5sxjZzuv/6C3YGPWB6R\nYqXxszBVakHyuO4usCtRlMURsY/D4WDVsJbIvR89fesVAu9qdrftb/EpMguS5/RzZZ4SqwMKwtVM\n8zrlZPJAh68+q/HliOKS0mRygGf0agJrLcwB/pGeLg/LpPLeNp8Mw9N30SyOSLHO3XmN86FvAIjT\nkVZr+exnrh8bOS3eG4LPsZqbqrbj/EOZhiwLtaQkYX5src0wUapb7FT/y0hJz2RxRIq1/MBNfMzp\nm2Ftboyp/6puQxZlqlPZBv2kyvKN23hBo2OEmduvIDlNfJ1XsSuOIVLrpdQBBeFqaIVvC5kmDRs0\nPB/YT6okYTkbc4yWevyu7To0qgz3WmUBAAKhCCPXntPIkoXidCTJo9VBbWqjRoUSLI5ItWhLI6fv\nqRmYLvW1Te7RCKUtTVkckWqZ5N0IJS3EExRf41OwZJ9mNnL6FPMdS/bfYLbnD3SHiZE+iyNSLQsG\nuWtFycKw8M/YdvY+s71CqnKYupDbaDds2IAaNWrAzMwMZmZmaNiwIc6ePSuvlydSbK3NMKOXpKPo\nzB1XNHbm69m7aGw6EcZsL9fCkoR54XA4WDOyFXg51QCCH0biwJVnLI9K/jadCMPLKHE6kqmxPuZT\nOpKMHxs57bzwEKEvPrE4IsVYtFe2IcsEL+1oyFJQRX5o5LT8wC1EfUticUSKMW1bELP2oUZ5a/Rv\npdoNWZRNG0oWCoUiDF99FrlzTq0bVECr+hXYHdQfkFsQXqZMGSxduhQPHjzAvXv34O7ujk6dOuHR\nI83OS2PLeM+GMos0pXMkNYW47qckB9itlr1WliTMT9WyVhjVRfJ0YPymQCSnZbA4IvmKS0qD365g\nZntm7yawMtf8DqmF5VG3PNq5VAIgbuTku+oMBBr0GPrdlwSsPKS9DVkKqneLGqiT07jqx6oRmuDa\no/cy+e4rh7UET81mP5VB00sWbj/3AKEvxRMNero8rB3ZWi3TE+V25Xbo0AEtW7ZEuXLlUKFCBcyf\nPx8mJiYIDdXsVAm26OnysGlsW2b7YPAzXMjJl9UUIS+iERgmXlTC5XKwerh2tCX/E379XGGdE5h+\njk3WqDfc2Tu1t0NqYa0Z0Upmcd7mk2H5HKE+xm8KZOrhN6iifQ1ZCorLlS1ZuD/oKYLua0aX5axs\nAYatPsNsd21SBe61y7I4ItWlySUL47+nY4rUzeWkHg3VpiThjxRy+ygQCLB//37w+Xw0adIk/wPI\nH3GtaY/eUt1Eh685i/QMzShPlpUtxOpTL5jtwW1ra3Wd+PyYGuvLvOGuOnwbL97HsDgi+Xj2Llom\nkFzh24LSkfJQzsYcU3tKHkNPDwjCt/gUFkckHydvhOPYddmShNrYkKWgGle3g5ebE7Ptu/oMMjKz\nWRyRfKw+fBvPIsXva8YGulg9ohXLI1JtP5YsHLvhgkasGZoecBlxOb0i7KzNMLVn43yOUF0ckRx/\nIk+ePIGLiwsyMjJgaGiIffv2oW3btjKfk5QkyU97/fq1vE6tteJTMtBtaTCS08VvsIOaV8SQlpVY\nHtXf23stAqtygnBjAx0cm+wK8yK08CYvIpEIPptu4eE7cdvq+hWLY/3g+mr79EAoFMF3y23cj4gH\nANStYIGNPg3U9utRlowsAbxXXsOHWHHd+LZ1SsGvh/rmzKZlZMNz+VV8SxQ/DelQrzRmetZgeVSq\nL/Y7H92WXUUqX/y3wadFJQz2qMjyqP7c18R0dF96FfycpyGj21VBr6blWB6V6nvxMQl914YwudOL\netVG8xrq22Pjx69nWd86cK2qvEX6FStKfofMzMz++vXkOhPu4OCAx48fIzQ0FCNGjECPHj0QFqY5\nj0NVUbEi+hjeWpInvevKW7yPUe+Zr4SUDPhflNygDWpekQLwAuBwOJjYqSpyJwhDX8ci6MlXdgf1\nF07e/cAE4DwuB+PaO1IAXgD6ujxM7FSV2T5z7xPuR6jvY+gtga+YALyosR5Gtq3C8ojUQ3FTAwxr\nVZnZ3hn0BlExqSyO6O+sOPGMCcArlDBBj3/s2R2QmqhS2gxdGtgy28uOP8P3NPV8Yi4UirD02FMm\nAHepbImmTur9hFyuM+E/8vDwQOnSpbFjxw5mn/RMuDzuIoj4wnQZHsAsUmhepxwCl/VS24BlwJIT\n2HH+IQCgYulieLp9GNOam+Rv1NpzWJdTtrKMlSle7BwO45xyVeriS1wyqvTdgKRU8QLTyd6NsPgX\n3fByb/Lr1lWv2rDK0N3vEA5ffQ4AcLK3xAP/IdBVs+6iD15/Qd2h/kz3x91TO6F3i8LPgmvrdSIQ\nCOEyIgB3X4q7SjarXRYXl/dWu78NZ269Qrtp+5jt62v7459qtnkcUXiafI0kpfBRpd8GfIkTT9AN\nblsbWye0Z3lUhRdw5j4GLT8FQLwu7ul2X1QsbaHUMcg7hlXokmKBQAChUHNW56sqLpeDzePaMjmS\nl+5FqG2ZusC7b5kAHBCvfKcAvHDmDnCT6aC4YM/1fI5QPSPXnmMC8PI25pjdV33aEKuKVcNbwjin\nesizyBisOXKH5REVjkAgxJCVp5kA3L1WWfSSWgND8sfjcbFlXDvmb8Pl+++w99ITlkdVOGn8LIxc\nd47Z7t+qptwDcE1nVsQA60e1Ybb9z9zHtUfvWRxR4cV/T8cUqQ6pE70aKj0AVwS5BeFTpkxBSEgI\nIiMj8eTJE0ydOhVXr15Fr1695HUKkodaFUtiRKd6zPbYDReQlMJncUSFl5KeCZ8Vp5jt5tVLMiXX\nSMEVLWKAJVKzxssP3lSrVfHHQ17iyDXJolz/Ce1hqE+l6AqrtKUp/Pq5Mtt+O4OZDoPqYNPJMGYG\nVz+nGpS6zeCqgloVS2JUF0lFoXGbAtWqZvSivdfx7ksiAKCYqSGWSi1AJwXXubEDOjaSpCf5rDgF\nvhot1p0REITYJPE6F1trM0z7V30XY0qTWxD+7ds39OrVCw4ODmjevDnu3buH8+fPw8ODfmGUZd4A\nd5luaTO3X2F5RIUz1f8S3uc0ljAz0sWETk75HEF+p2/LmnB2LA1AXGlm1Dr16KSZlMLH8DWSJl8D\n29SCWy0qQfanRndtACd7SwDiTprq0k/gU8x3TNsmmfWa9m9jVCqj/rNebJnb343pLBqdkCpT3k2V\nhUfFYun+m8z24sHNUNzMiMURqS8Oh4MNo9vAxEicmhj+IQ4L1eQp6b3wz9h8SrK+cPXwlhrTI0Bu\nQfiOHTsQGRkJPp+Pb9++ITAwkAJwJTM11sfq4ZKSTeuPh+Lqw0j2BlQIIU+isOH4XWZ7XAdHWJjQ\nYsw/xeWK33BzJw4v3H2LLWrQuniK/yWm+6u1ubFM2UVSeLo6PGwcI6lQdfjqcwTefcviiApm9Prz\nSE7LBABULmOByd6NWB6RejMx0sfakZK/DVtP38fNpx9YHFH+RCIRhq85y9SGd3YsjYFtarM8KvVW\nytIUiwdLnpIu3heCZ++iWRxR/jIyszF4xSlmMWbLeuU1qmkftZnSMN1dHdGyXnkA4q55vRYeU/lH\nj/zMbAxadlKm/Wzr2qXYHZQGqF2ppEwnzXEbL6h07fDrj99j80nJjcK6Ua1hbmLI4og0Q5MadjL9\nBHxXn8H3VNXtqHrqZrhMOtKWce2oNrwcdPrHAe0bStL7hq46jaxsAYsjytu+y09xOafJEJfLwaax\nbak2vBwM7VAXLk6Sp6Q+KyTrLlTR9IAgPHgtrvKlzp0xf4eCcA3D4XAQMLEDipmKg5ePMd/hs+K0\nSqcizNkVjPCcnGUTIz1sGddOo37J2LTYpzmqlrUCAKRnZKPn/KMq2bSDn5mNwcsl6wE6NKyMbk0d\nWRyRZlk21ANmxuInSxGfE+Cz4pRKviekpGdixFrZRXhNa9qzNyANwuFwsG5ka+Yx/pOIaKw6dJvl\nUf1axOcEmc6YIzvXR80KyqsFrcm4XA78x7eHro44/Lv57IPKdta9EPoGKw7eYraX+jTXuLQ0CsI1\nUClLUwRM7MBsH776HNvPPmBxRL93/9UXLJPK+Vs6xANlrKh0pbwY6Olg74wu0M+pMPPwzVdMDwhi\neVQ/W7DnmsyN2IYxbehGTI6sixXB5nHtmO0DV55h25n7LI7o1yZsCkRUzrqQ4mZGlI4kZ3YlisJP\nqtLQjO1BuPP8I4sj+llGZja85h5mqiPZWZthbn83lkelWZzKWmGKt6Sz7hT/S/ikYou2oxNS0Xfx\ncWa7TYOKGNW1QR5HqCcKwjVUp38cMLRDHWZ71PrzCI+KZXFEP8vKFmDA0hMQ5DwKa1rDDj7t6uRz\nFCmsauWssXSIJJhZcfAWLoapTl7wozdfsXjvDWZ7iU9zZhEZkZ8e7lUxuK0kp3bUuvN4EvGNxRHJ\n2nn+ocy6heVDPWBBi/Dkbkw3Z9SuKO6YmJUtRDe/Q4hJVJ0mPhM3X0RYuLgqjq4OFwdnd4epMa0P\nkrdpvRqjcs6scnJaJgYuOwmBQDVKSguFIvRbchzfEsTXpbW5MXZM7qiREzMUhGuwFb4tUcWuOABx\nrdWe848yi1xUwdL9N/DorTgIMNTXwbaJHSjnT0FGdqmP1g0qMNt9Fx9nyj2xKTYpDV1mH0R2zpt/\no6plMKS95jXLUBVrRrZi0pP4mdnwnHMYKemZLI9K/ERs6MrTzLanqxP6tKTW9Iqgq8PDIb/uKFrE\nAIA4ZbHn/KMqEYAdvvqcaTQGAMuGeKB+FVofpAgGejrYOl7SsOfC3bcyFYnYtO7oHZy784bZ3j21\nM6zMjVkckeJQEK7BjAx0sXdGV6bZzf3XXzBDRVIRHr/9hrm7rzHb8wa4oUKpYiyOSLNxOBzsmNSR\neSP7EpeSsxiWvbzgzCwBus0+iIjPCQAAYwNduhFTMEN9XRyc3Y3JC34ZFYsRUiUh2RCblIYusw4g\nI2eCwMneEgGTOmjkrJeqKGdjjv9N68xsX7oXgdk7g9kbEIC3n+IxcNlJZrtzYweNTD9QJU1q2GHa\nv5K0lKX7b2LPxccsjkicMjlJqoTmeE8XtMgpNqGJKAjXcDUrlJBp3LLswE1cuhfB4ojELcnbTdvL\nzMrXdyiFMV2dWR2TNrAuVgQ7JnVktk/cCMdWlsoWikQijFhzFlelurbtmd4FDrbFWRmPNqliZ4mN\noyXd83ZdeIRdUl1qlUkgEMJ73hGmP4CpsT6OzfNCEUM9VsajTdq5VMKM3pKGJwv2XMepm+GsjCX3\nqUxu1Z6yJYti+yTNTD9QNfMGuMtUzRm07CTuvvzEylhS0zPhPe8IExvUrlgSCwc1Y2UsykJBuBYY\n1aUBWtWXpCL0WXSMtRzA1PRMtJ+2Dx+ixYtATIz0sGNyR/B4dCkqQxvnihjRWaqz6sYLeMnCWoH1\nx0LhL7UwcOEgd42q/arq+raqiT4tJOkew9acZeU6mLE9SGZSYM+0zhrRilpd+PV1RYu6klnG3guP\n4e2neKWPY8KmQNx//QWAJA88N12GKBaXy8GeaV3gaCdu6pWRJUCnmQfwJS5Z6WMZu0Hy98jYQBf7\nZkqe5Gsqiny0AJfLwc7JsqkIfRYdV3qNWIFACO/5R3DvlfjNlsfl4NDs7nDM6ehHlGPpEA+ZsoWd\nZ70Y2BAAACAASURBVB7A1/gUpZ0/8O5bjJHq3NizWTVM6flPHkcQRdgwpg3z5CGNnwXPOYeQnpGl\ntPMfvfZCZkHuzN5N0L5h5TyOIPLG43Hx34wusLUWV6RKSs1A19kHkcZX3nVw8MozmUZtK3xboG5l\nG6Wdn4ifQJ1Y0APmJuIbn8+xyegy66BS29rvufhYZmJm3ajWGleO8FcoCNcSP6YinA99A6+5h5W6\nUHPcxgs4dfMVs71xTFu0lJqhJ8phqK8rU7bwZVQsmo7ZqZQSVeFRsfCcc4hpDlHfoRS2TWxPj51Z\nUMRQDwdmdYNBTiOcJxHRGLD0pFJuzl9GxcqUH2vdoAJmS5XOI8pT3MwIh/26MzOOj95+w7DVZ5Sy\nXuTF+xgMWi7JA+/W1BEjOtdX+HnJzyqUKoYDs7oxa3JuP/8I31XKuQ52nHsg837g5eaEfq1qKvy8\nqoCCcC3SxrmizCKMY9dfKi0QX3vkDtYelax6n9SjIXzaUzlCtlQrZ43dUzuDl/OG++pDHJqM2Yn3\nXxMVds6E5HS0n76Pqf9bqrgJjs/3gqG+rsLOSfJWvbw11oyQtDPfH/QUHabvV2jFlMQUPjrPPMCc\no2zJotgzrQulpLGonkMprBvZmtnedeERlu6/odAA7ObTD2g8ageS08TXQTkbc2ybQDfkbPKoWx4r\nfFsw2zvPP8SaI3cUes71x0IxYOlJZmKmil1xbNaihn08Pz8/P2WeMCND0i7ZwIByvpTNvVZZpPIz\ncfOZuEHDy6hYPIn4hi6Nqyjsj+DJG+Hot0Ryl9u9qWO+v2SfP4vrxNrY0GNJRXEqa4Vq5axw9PoL\nCIUiJCTzcTTkJTq4VGI6rspLRmY2Os86yNT/NdTXQeCy3qhU5u8WYtJ18vdqVyqJ6IRU5mfz5lM8\nLoZFoFMjBxjLeYHk88gYNJ/wP6Yxk6G+Di4u642yJc3lep4f0XWSv9qVSuL9tyQ8fCNuEX7p3jt8\njPmOlvXKQ0fOfxsOX32OjjP2IznnRsxQXwfnFv+LsjaKvQ7yQteIWIMqpWSug4v3IuBoVxxO9lZy\nP9fivSEYvymQ2a5ZoQSCVvaBhanq9geQdwxLUw9ahsPhYOkQD0z0asjsO3EjHJ5zDilkRjws/DO8\n5x9B7oSKi1Np7JraicrQqYjOjavg6Fwv5lF01LckNB2zU66NnV68j4Hz8ACZBXi7pnRCHcr7VAkc\nDgcbxrTBrD5NmH1h4Z/RaOR2pnykPBy99gINhm3Dq5wAHAD8x7dHDWpHrhI4HA42jmmDhk5lmH0B\nZx+g2fjd+CanNSMikQgrD96C55xDTElKy6JGuLKyL70fqAgOh4PNY9vC2bE0AHHjHM85hzFy7Vm5\n5YiLRCJM33YZU/0ldcmdHUvjyqq+sCyqmfXAf4eCcC3E4XCwZEhzTOohG4h395NvIB50/x3aTd3L\nLPIpZ2OOE/N7UPqBimnnUgmnFngzucGfYpPRdMxOPHsX/VevKxKJsOVkGOoM2crMqgCAX7+m6O7q\n9FevTeSLw+FgTn83bB7blrlBfvMpHi4jAnAvZ4b8TwkEQswICELX2QeZFBSjnMoH/3pU/+uxE/kx\n1NfFpRW90Uvq53Lj6QfU8/XHg5zqJX9KIBBi9LrzGL8pkJmUqVi6GG6tH4gGOQEfUQ36ejo4OtcT\nZUsWZfatP3YXDUcE4PXHuDyOzJ9QKMKY9eex8L8QZp9bLXtcXN5bKyviUDqKluJwOGhepxz4mdm4\n8fQDACD8Qxwevf2KLo2r/NXjx++pGRi9/jxGrTuP1JwA3NzEAFdW9oWtddF8jhajR4PKVb5UMTSq\nWgaHrj5HVrYQqfwsHAx+jhrlrFHexrzQ+XlxSWn4d8ExLD94i+mGqa/Lw6rhLTGxRyO55fvRdSJf\ndSvboEZ5a5y4EY5sgfg62Hv5KepVtkF5m8I300pITkc3v0PYfk5Sh7ycjTkuLuuNZnXKyXPoeaLr\npOB0dXjo/I8Dihjq4fL9dxCJxO/puwMfoVJpiz9KS0jjZ8Fr7mHsDpQ0gmlUtQwuLe+DUpam8hz+\nH6NrRJaJkT76tKiBVx/jmLKBX+NTsOP8Q9hbF0W1ctaFfs00fhZ8V53GZqn+FG2dK+L4/B4wNlCP\n3gDyjmEpCNdiHA4HzWqXRUZWNkKeiAPxVx/icOJmOCxMjeBgW7zQaSMXQt+g9ZT/EPQgktlXtIgB\nTi7ogdqVCv7mRm+Iyle2pDma1rDD4avPkZklQFpGFvZceoLDV59DV4cLRztL6OrkX7P18r0ItJi0\nB3dfSmZQnewtcWFZL7RvWFmuC27oOpE/B9vicKtpj2MhL8HPzEZmtgD7gp7ic2wyTAz1YGtlVqCf\n4ZOIb2g2fjdCpa6DlvXK48LSXrAvWbCbcXmh66RwOBwOGlYtg/oONjh16xUysgTIFghx6OpzZAuE\nqOdgA31dnXxfJzktA8euv8Tg5adw5WEks797U0ccm98Dpsb6CvwqCoeukZ8Z6uvC09UJxc2McPn+\nOwiEImRmC3D0+gt8iE5C89rlClTHOzwqFgv2XEOfRcdx6/lHZn/3po44MLs78xRWHcg7huWIlNy3\nOikpifl/MzMzZZ6a/IY4PysIi/aGyOyvXMYCU3v+g57Nq+UbfCWm8DFuwwXs+KHzXsdGlbFpbFuU\ntDAp1JjCwsIAAHXr1i3UceTv3Xn+Ea0m/4fEFL7MfgtTQ/i0q4NhneqhdM7slVAoQlR0El59iMOr\nj3EIC/+M3YGPIP2uMqJzPSwd4qGQNCS6ThTneWQMWk3ewzTWylXa0hRebk7o2awaalUswQTkUd+S\ncP3xe4Q8jcL1x1F4Fhkjc9zUnv9g3gA3Vqqg0HXy515GxaLjjP0yufw6PC4aVCmFZrXLolntcnB2\nLM0EYwnJ6Th5IxxHrr9A4N23TO53rgleLlji46Fy64LoGsnbg9df4DnnMN5INXOqUKoYWtUvj2pl\nrVG1rBWqlrVibqyysgU4cSMcm06EIejBu59er1+rmtg2ob3aVUWSdwxLQTgBIA7El+2/iTm7r/7U\nqMG+RFFM6tEQ/VvXgoGeDlLSM/E1PgXf4lPwNT4FUdFJWH7wFj7HSjpsWZgaYv3oNvByc/qjmU96\nQ2TX+6+JWH7wJnace8ikFOXS4XHRpLodohNT8fpj3E9/ZHMVNzPCjskd0c6l0i8/Lg90nSjWx5jv\n6DzzAFM55UeVyligRjlr3H7x8adgPZexgS52TemErk0dFTnUPNF18ncSktPhPe8ILtx9+8uPGxno\nonE1W4hEQNCDd0wKmjQul4M1I1qpbB1wukbyl5yWAd9VZ/DfpSe//RxbazM42Vvi4Zuv+BL384Le\ncjbmGNvNGcM61lO5G7GCoCCcKFRsUhpWH76NdcdC8T01Q+Zjpsb6yBYI8+2m1r2pI9aPbsN06PwT\n9IaoGhJT+Nh+9gHWHQtFZCFqiLeoWx47p3Qs9BOQwqLrRPGEQhFuPvuAfZef4GDwc8QmpRXoOB0e\nF42r22LdyNZwKiv/8maFQdfJ38sWCLHy4C38d+kJHkd8K/BxNcpbo2uTKujhXhUVS6tuB0S6RgpG\nJBJh5/mHGLH2XIE7q3K5HLR3qQTfDnXhUbe8WgbfuVQ6CF+0aBGOHj2KV69eQV9fH87Ozli0aBGc\nnCSVECgIVw+JKXxsOB6KVYduI+57eoGOsTI3xsbRbeQy40VviKpFIBDi5M1wrDlyB1cfvZf5mJW5\nMSqVtkCl0sVQqYwFalcsiWa1yynljZauE+XKyhbg8v132HvpCY6FvJRp6mNsoAsXpzJoXM0W//y/\nvfsOj6Lq/gD+3U1PCKGEJJRQQgu9haiA9JaAKCK9w0+qCKKoFCkvTV5FihCK8tK7SBGRJiAgiLRQ\npXdIQg2QQOrO74/jZnYhkDa7d2bnfJ6Hx9kQdo5kmL1z77nnVCqKN8oVVrzOeHbxdaKsu4/isfv4\nVfx+7Cp+P371pVKWocGF0aZuObxftxxKFc76hl4R+BrJmodPnuPAmZs4dSUGp67cxamrd3Huxn2r\nVZCAfLnwfy2qoU/LGgj0c4zxnqoH4c2bN0fHjh1Rs2ZNmEwmjB49GgcPHsTZs2eRNy8V4edBuLbE\nP0/C/M1HrdJN3F2d4Z/XCwH5csE/by4E5PNC6SL50bN5VeT3UabIPt8Q1ev0vzfbYv4+KF0kv9Cy\nUnydiPMsIRlb/76Ee7HxqFG2EKqWClC8qYtS+DqxrWvRsdgTeQ0pqSY0q1lSkwMuvkZyLik5FRdu\nPcCZq3eR28sNjWsEZWozv5aoehD+ovj4ePj4+GDjxo1o0aIFAB6Ea1VKqgm37z1BnlzuyO3lZvOW\nsnxDZJnB1wnLDL5OWEb4GmGZofQY1qZ1YZ48eQKTyZQ2C860y9nJiGIB9i0rxhhjjNmDITkZLvfu\nAZIE2HiSialcairgZJ8ZfJvOhLdr1w6XL1/GkSNH0mZOLZ8iLl68aKtTZ1qeXbvwuFYtSFyzXDfc\nbt2C16lTcIqLS/slOTvjYVgYEooXFx0es7Hchw4h32+/weTpieS8efGsfHk8rl1bdFhMLXgQpj+S\nhHJdu8Lr/Hk8L1YMD1q0wIPwcCT7Z70hDdMu92vX4LdqFbyPHsWZlSsB55fnqUuXLp12rOqZ8KFD\nh+LAgQPYv3+/zVMXXsX50SP4r1iBhMBAPGjV6qXf99m/H6W++ALPSpbEla+/5gGYTnj//TeKT578\n0tf9V6zA6bVrkRwQICAqZg9+K1cicNo0GCzmHu63bMmDcJ3xPnwYKXny4LnFB6pZnj/+QOC0aYir\nXBlPQ0LwIDwckovyNe6ZihgMuPfBB/CaOBEe16+jSEQECs+Zgyehobjbti0e16snOkJmK5KE3H//\nDf8VK+Bz4EDal/Pu2YNHjRvb4/zKGzJkiFSoUCHp/PnzL/1ebGxs2i+bio6WpKAgSQIkqWnTl3//\n3j1Jyp+ffh+QJE9PSVq82LYxsUw7fPiwdPjwYdu8+apV8s/d8tfIkbY5H7OZLF0ns2al/3MfNiz9\n7zeZ6BfTvLTrJClJkr78UpIMBkkqV06S4uNf/ubPPrO+PurVk6SEBLvHzOzryMGDUqqTU+bvD8wx\nbNuW/udCz57pfrvSY1jFt7IPHjwYq1evxq5du1CmjO2adLxWfDzQsiVw5Qq9PnIEeDHrJn9+YPJk\nwJyG8uwZ0L070KsX/XnmuEqVAjp0APr2BT7/HPjkE6B/f2D8eNGRMVvq2BEw35PefBOYPh0YORJI\nb7bDZAL69QNGjHj53sE0ye3WLaB2beDrr+ln+s8/wFdfvfyN/27QS/PHH0Dv3nwdOIKkJODHH4GU\nlJd+S3J2RuTu3cDSpXRPMK/gd+9u5yCZXTVuDJQsSccGA9CqFbB7N7BggV1Or2g6ysCBA7Fs2TJs\n2LABPj4+iI6OBgB4e3vDyyv7jVuyJCUFaN9evpEajcDQofShaplobzAAH34IvPEG0K4dcP48fX37\nduD5c8Be8TLbSEgAunYFPvoIeHEpsUYNYOVKMXExcfLlA7ZsAaZMAWbMADw80v++1FS6NyxcSK9d\nXID//Md+cTLF5d2+HcUnTqTJFrMmTYDPPnv5m7dtAyIjgeXLgZkz6WsrVwKDBtHnBdOm5GQacO3b\nByQmAgMHvvQtJg8PoEsX+nXzJrB1K2DR54Q5IKMRGD4cOHEC+PhjmqSz5+mVfLM5c+YgLi4OjRo1\nQqFChdJ+TZ06VcnTvN7MmcCvv8qvZ8+m2a5X7XStXJkG7F260PesWgX4+tonVmYbCQnA++8DP/0E\nhIfTTFZ2nTsHPH2qXGxMrJIlgfnzXz0AB+iB/cED+fX48bxKonHG5GQ4mQfgLi7AN9/QAKtgwZe/\n2dUVCA2llZI+fQBPT2DjRh6Aa93EiTQAB2gFxPLfeHoCA+lhnDm+3r1p7GjnATig8CDcZDIhNTUV\nJpPJ6tfo0aOVPM3rDRxIM+EAPd3065fxn8mVC1iyBDh+HKhTx7bxMdtKSABatwZ++41eP3sG7N2b\nvfe6fh1o2BCoWxeIilIuRmZ7R47QzFd2uLgAa9YAYWHy10aPpjQGpkkPwsPxoFkzoHRp4MABmgE3\nZvDxZzDQJM6RI5TeyLTr6FFgwgT5dbduQO7c2XuvJ09o0i4yUpnYmP3cupVuKpJI6mxvlhNubsCK\nFfRr4sTM/zmDAahUyXZxMdszD8C3bpW/Nno0MGpU1t8rMZFm0aOi6Gbbpg3NkDL1e/QIaN6c8vyz\nm8fr5gb8/DOlLJitWkXXGNMegwHXhw+nwVhWmrE4OwPlytkuLmZ7CQk06E5Npdd16gBTp9LDdlb9\n8w+tkixfTp8Jjx4pGyuznbg4Skdq0IBSjVTC8QbhAM1wdOyoXK1XlT05sVeYNs16AD5mDDBuXPau\nAzc32ktgTmM6eJAe7Jj6jRlDS80LFgDffpv993F3BzZsoJt2jRrArl3yRm6mOSYvL8DbW7k35I2a\n2nDyJM2AApRatGhR9huxGAzA7dt0fOUKDe55ckYbBg6kvX/799ODWFKS6IgAOOogXCnJyZQ7WKkS\nPUUxdfvyS2D9eqqAMWYMMHZszt6vd29g2DD59Rdf8HWgdqdPAxER8uugoJy9n6cn8MsvwM6dtLGT\nMYCuhyZNuJKWFoSGAqdOAY0a0UO5uRJGdgQHyxu2AWDzZqqyxtRt0SJKOTYbP572fqiAtgfhkgSs\nXZv93M+MhIVRCbtz53I+oGO2ZzAA771HAzGlfl4jRgDm5j137gCLFyvzvkx5kgQMGSIvOzdsSBt0\nc8rLC8iTJ+fvw+zDZKLrwFzxSmkLF9Jnw++/0+cDU7+iRanyWWb2iGXkgw+sq+p89RXNrjJ1OnvW\nuhJO9+60gqES2h6Eb9hA5QXLl6eNVEqzrA86fTqVsGHqp2R3O29v2pBXqBA9Sffvr9x7M2WtX08D\nI4CWm2fM4PbjejR/Pv3sK1cGJk1S/v0TE+UUxfnzgatXlT8HU57RqNz9YPJkufRtnz5AzZrKvC9T\n3pw5cmnS4GDabK0i2h2Ep6bKjRYuXQL+/lv5c3TpQvmg5vP17SvPsjH96NqVZtW6ds24ogITp3Jl\n4J136HjAAKBiRdudy2SiKhtMXaKiKC0NoJzP58+VP0ffvsDbb9NxSgqXr9QjZ2faqL1sGTB3Lu0h\nYuo0YwY9NOXKRZO1KusBo90RxZo1wJkzdOzlRfm6SjMY6CnKnDt06BDNfDD1sMdDkdFI/4CZupUq\nBWzaRJtzx42z3Xm2bQOqV6fNPadO2e48LOuGDAEeP6bj0qWpR4TSDAbrgfeSJcDFi8qfh2XP48eU\nMmTrjbMBAUDnzrY9B8s5o5EezK9dU2UFPG0OwlNSaOOd2ZAhQIECtjlX2bLyzEr9+vLMOBMvPp5S\nkcaP5w1STNasGZA3r+3ef8YMSk2TJOpFwNRhyxbrtMS5c21XzaZePdroB9AkkHlCiIn36adAr150\nH1BRKTomWP78oiNIlzYH4T//LM885MmTfuthJQ0fDqxeTSXKgoNtey6WedOmARcuUC3wevXsXzKM\nU5P06euv5dzSX3/NWUdWppyYGKpmA9B+noYNbXu+CRNopv3aNdoQzsS7fFmuXrJjB/DXX2LjYSwD\n2hyEf/ABDYqDg2kAbuvKBe7utAGUN3mpx927wJQp8ut+/ez380lKogeA4GAgNtY+52TqUbky7Q8w\n+/xzrhmtBj170ox0p045qw+fWW++SQNxW666sKyZNk2u292kCdC2rX3Pf/Ik9SdgYmnofqzNQbjR\nSIPi06dtPwvO1GncOLlmd4UKQI8e9jt3q1bUyOfSJeA//7HfeZm1lBQETp0KNxFLzuPHy5ux/v6b\n6gUz8YoXp26Gvr6iI2H29uAB8L//ya/tWT4yPp5WQ6pUoU3h5uZAzP6iooCqVelaUElDntfR5iDc\nzMmJdyXr0fnzwLx58uspU2i3ur307i0ff/891ZFn9vfDD/BftQoV2re3/8NQ0aLAoEFAkSJ0sw8P\nt+/5GWPW5s2Tq+FUqSLn7NuDpydw7x4dJyVRkz8mxrRptCLRuzfQvr3oaDKk7UG4SPfu2aY2OcuY\nkxPQtCkd169v/wHQBx8AdevScUoKMGqUfc/P6O/93051xuRkMaUjR4+mPQk9e2a/DTZzLJLEKWqi\nDBxIg9/ChWmF3J7powaDXDIZoCpq0dH2Oz8jjx5RRTsze66QZxMPwrMqNRX4v/8DAgOBDh24UYMI\npUpRJYSdO6mJkr1z9Q0GOq/Z+vW8C9/eNm9O+ztPzpuXKiLYm7c34OFh//MyWWKi6AiIJAG//UYt\n0jt1Eh2NPvn40OD7yhX6bLa3Zs2AGjXoOCEB+O47+8egd7NmyWmq5cvLfSNUTDuD8JkzKe1AdCk6\nJyf68E9MpBvvrFli49GzRo1o2VGEatXkcpVVq1JlBmY/Fv/u7r/3Hg+G9apBA6BFC2pJLnIz1tWr\nQMuWwJEjNBg/eFBcLHrn6mrf9EQzg8F6VXTRIvU8JOpBXJz15Njw4Zporqf+CAFaYhg9mup1lywJ\n/POP2HgGD5aPFyyQn7yYvkyeTB+2R44AISGio9GPGzeoXCgAyWjE3fffFxwQE+LQIfr3t2ULzXiZ\nc3JFCAqyngG3TE1g+tGqFVC7No1VTp/mPWv2dPMmNVACaIO2iNWQbBDwuJgNM2bIXdB8fKgTmkjN\nmwNlylA+6OPHwOLFlI/G9OWNN0RHoE9Fi9Jm2IgIPLh8GcnmG69oiYnUw6BIEbmtObOdGTPk406d\nAD8/cbEA1EBu5UpKWfz9d6ofX6+e2JiYfRmNwL59XM5YhHLlqIPxL79QmUoRqyHZoP6Z8JQU4Icf\n5Ndjxoj/yzUaqTKC2cyZmqpLqUlJScCTJ6KjYGpRpgwwfTquWXbOFWnrVhp8d+oETJokOhrHd+sW\nsHat/NpydVKUUqWoSZDZtGniYtGLEyeAdevU1TiNB+DiGI3Au+8CrVuLjiTT1D8I37IFuHOHjv39\n7V98/1W6d6eZl+7dafaD/+HZ1k8/AYUKAX37UvkhxtQkOJjqFAPAtm20OYzZTkQETdAANNtctarY\neMzMtakLFwaqV+fJGVubMIGqVZUtS6sPjGmMooPwvXv3olWrVihSpAiMRiMWL16c8ze1bILRsyfg\n4pLz91SCtzdw/TptvqheXXQ0jm/uXNqUO38+LTeplblbG9OX4sUpTQ2ggZfl6h1TXu7ccqfKIUPE\nxmKpbFlKR7h2jfYx8eSM7Vy+TOlf5mPR6UiMZYOig/D4+HhUrlwZM2bMgIeHBwxK3IDmzQN27wY6\ndqTSgGri7i46An04c4Y+2ABKRerVS2w86bl2DfjiCxqMPXokOhomQr9+8vGCBZro1qZZX35JG7EW\nLlRfGbI6dcSnTOqBZYv6Zs2ASpXExpMeSaK9AcOH86qILUiS5v9eFR2Eh4WFYcKECWjTpg2MSpWG\nMRioIcuKFVQZhenP3Lny8XvvAQULiovlVdq0Af77X3lgwJQ3axZw/LjoKF4tPJzywgGq1LFxo9h4\nHJ2XFzXj4EZJ+vNii/rPPhMXy6uYTJQmVb8+8PXXVEWLKev4cSrUMWGCZnt1qD8nnOlbfDywZIn8\nun9/cbG8juUsaEQEp6Uo7fp12nxXvTrNNCYkiI7oZc7OQJ8+1M3155/pgZExpryFC+UW9VWr2rdF\nfWYZjdRPwszyoYEpY+FCSkX66itgxAjR0WSL0DWzIw72ZOh24wZco6PxNDRUdCgO48QffyAwNBR5\ndu9GUuHCOO3trcoZBWNwMCp7e8P56VPg8mVcmDULT2rVEh2Wwyg8axYK/vtg8zglBRdPn7b6fdXc\nS5o3B8LC6PjECbGxsJcIuU4kCYbUVEicoqIYQ+3ayDtuHAKWLUP0++/j4dGjir23ktdIrlq1EPzv\n3riUpUtxsnNnmDiNVRGGxERUWbIkbRB7vlYtPLXDv+/SCpfI5ruCAlzu3kWxyZPh8+efSPL3x6n1\n6zknUCHJfn64MnkynO/fh1t0tGo3Opk8PHD/nXcQsGIFAMBv7VoehCvEkJgI3w0b0l7fU0uFpPSo\n9Pp0BIbEREiurpr5O3aKjYXvli3w3bAB9999FzGdO4sOyWFILi54GB6Oh2Fhqs4JjqtWDQmBgXC/\neRPO8fHIs2sXHoaHiw7LIeTZuxfO/5YtTixUCE9r1BAcUfYIHSmGvKrLYHQ0VRfo1YtKPaldQgKV\nKpQkuEVHI+T2bcoRZtlmno145TWiRmPH0t4FAHm8vRFSpYp6qvlo2eLFcrOuokVRasiQtDxgTV4n\nLHs++gj46y+qhtKuHbUnzyQh18mPP6bVCg/cuhWB332nmQcIPbLZNdK/f1qqRNCffyJo9Ghl31+v\nLLrSuvXpgxA7ZSA8Nn8WKUSdOeELF1J5p6JFgVGjREeTMXd3ql9tNmeOuFiYOKVL08/+wgWqb88D\ncGXMny8fDxjAG/H0KCEBWL4cOHoU6NoV2L9fdEQZ69AByJWLjs+dA/78U2w8TIxu3YCaNYHZs4FV\nq0RH4xiSkoCHD+XXlk2yNEbxEoWRkZGIjIyEyWTC9evXERkZiZtZ2bVqMtEMgvk4OFjJEG2nXz95\nlmPXLuroxvSnXz8ajDPl/Pwz7X4vVQro3Vt0NFkTG0vNvFjO/Por/V0CQIkSQIMGYuPJjFy5qLSu\nGdeO16fChYG//6YJBHNte5Yzrq7AoUO072bWLCoNrFGKDsIPHz6M6tWro3r16khISMCYMWNQvXp1\njMlKa+ldu+Ruc3nyaCeto0gRoGFDOpaktLQElj2G5GTRITC18PcHRo6kFQZfX9HRZI4k0QNZoULU\nyp67vOaMZYWkrl21k9bx4Yfy8dq18oMEy57t29VZGYmJUbkyMHCg6ChyRNFBeP369WEymWAymZCa\nmpp2/L+slOaxnC3o1g3w8FAyRNvq2hUICACGDgVathQdjXZJEsp164aSw4YBO3ZwuT9GtDLw4zRC\nggAAIABJREFUAijW2Fi5jNq8eWLj0bJ79yi9y6xrV3GxZFVICFClCh0HBQE3boiNR8suXqSmPAUL\nAoMGqXpDJmOZpa6c8EePgPXr5deWswha0LEjFYyfOhUoX150NNq1bx88L11C3j17gPffp1rhjGmN\nZe34pUuBuDhxsWjZxYtyS/JatSgtSSsMBuC774ADB4BTp2jmjmWPeTUkNpb6BmjpoZyxV1BXHb28\neWnjzQ8/AJcuARUrio4oa7KwW5+9hnlPAAB06QJ4e4uLJbskCTh4kAZfFSpQZQemL/XqAWXLAufP\nA0+fUm641iYW1KBWLZpB3r2bGqBojTlNkWWfyWSdktSjh7BQciw5mfY4vP02kD+/6GiYYOq7o1Wq\nBMycab38yPTj2TPr1RCtbcQzW7cOqF0bmDuXOmjy0mnWPHhAFTC0/PdmMFhXTVq6VFwsWufkBDRu\nzANavdqzR07lyZcPaNFCaDjZNmcO7R9r3RpYtkx0NNrz00/AZ58BZ86IjkQx6huEM33btClt2f55\nsWKARgvwIywM8PKi43/+ASIjxcajNStW0ExRUJC22z136gT4+ACdO2u2rTJjwv3bdRIA/ZtycxMX\nS044OQF379LxggXanmQQYeZMSvetWNH6mtAwHoTbWnS06Ai0JSoqbfD6sHlz7eb9eXnRbIcZz3pk\njfnv69o1Wr7VKn9/+tBdtoxa2jPGsq5tW6BVK+pEreGa0GjfXi42ceoUpd+yzLl4Edi3j46dnGiT\nrgPgQbgtpKbSE1tICM3k/dtalWXCJ58AMTG4Mn48Hmi9wkyXLvLxihV0XbCMnT9PdXUBanik5jb1\nmcF7RZjZhQvAuHG8NyCrWrYENm6kSRqtro4CtCpmeT/T8iqfvS1aJB+Hh1MlOgegjkH42bP0lOMo\nnJxoqenoUSpRtm6d6Ii0xcsLD5s3R5LW/5E1akQzoQCVWeOUlMxZvlw+btGCckCZ/kycSJVFHGU1\n8e5daj43dix9PkRFiY5Ie3x9tbs6atarl3y8YoVcxpS9WmqqdfqJ5d+hxqljED56NFCmDBAaShUl\nHEG3bvIxb8jSJ2dnygOeMQO4fVvbMzj2IknWqTtaqgnNlPPsGTBlCvDpp9Rx8Nw50RHlnJ8fUL8+\nHUsSsHq10HCYIHXr0nincWPaqOnkJDoi9Tt6lD5DAaBAAe1uzE2H+BKFjx8DmzfT8eHD1CXTEXTq\nBHz+OZVWMu/sLlpUdFTM3j7+WHQE2pKSQilJy5bR0n14uOiIlHfvHpUm02K5PXvZuJHKOgJUF7xs\nWbHxKKVzZyq1CNAs6JAhYuNh9mcwAMePA56eoiPRjtBQ4OpVmg338KA0RQch/lPg55+BxEQ6rlYN\nKFdObDxKKViQnnQBmvWwXGJnjKXPxYW64R06RClq7u6iI1LOhg00g1OwIJVfZK9mWRO6WzftpyCY\nvf++vEfg8GHHSsNUmiTRJJ0j4gF41hUvDowZQ5ObDkT8IHzFCvm4c2dxcdiCeSk9KIiL8r+OJFF3\nwRUruDsmk/n6io5AWdu2Uf+D1FR+KH+d6Ghg+3b5tSN9LuTNa726Y/n/yaz9+SdtvuvUSV49YMzB\niB2ER0UBu3bRscFA5XscSevWdCO5dAno00d0NOoVGQnMm0cftiVLUkoCY47GcjC5di2QlCQuFjXb\ntInS+ADqOlq8uNBwFNevHzBqFDUcGThQdDTqtXgxkJBAnWZXrRIdDWM2ITYn3MkJ+PJLmgEtXpw6\nSTkSLy9qucxez3JWsHFj2tDoiFJS6KHTYACaNBEdDbO3WrWAYsWA69eBR4+A334D3n1XdFTq8+GH\nQJUqlJLy9tuio1Fes2YOU+PYZhIT6UHVTMu1wTMjIYE+H3LlEh0JszOxM+F+flSG6soV639wTD9S\nU2mmw8yRlp4tHTwIBAbSh++oUaKjUZ/ERMdfATEaaWndjFNS0mcwAG+8AcyeDXToIDoaJsK2bXI+\nePHiwFtvCQ3HZo4cAXr2pFK28+aJjkZ9/vyT9gc5cGdR8TnhAN10HS3/k2XOH38Ad+7QcYECjjtD\nHBwMPHxIx3//TZU/mGzpUloJ++QT4PRp0dHYjvkhM29eoFAhsbEwplaWEzMdOjjOxtwXnTxJTWie\nPLH+f2Zk+HDgzTepQtJff4mOxibUMQhn+vXTT/Jx+/aOm4ry4oYsngW1tmwZEBMDTJ8O7NwpOhrb\nqVAB2LGDNh9Ony46GsbUycNDbu/esaPYWGzJslrO0aM8OWPp5k25Tf21a0CJEkLDsRUehNvL5cuU\nehMaCsTFiY5GPaZNo9Jtbds6fmMWyzb2y5Y59BJblty4QSsiAKVsOHoKQuPG3MqeEUkCTpywnoxg\n1M49JgZYvx6oVEl0NLaTJ4/15AzPhsssm1lZdp92MDwIt5f33qNc4MOHgV9+ER2Neri50ea0NWvo\nAcWRtWgB+PjQ8ZUrDru8lmWWZUqbNKGyZEx/tm6lhhx6ERUFVKwIVK1Km1HN/TIY8famz01HTUUx\ns5zpX7GCJ2fMLD8XHHg1RPFBeEREBEqUKAEPDw+EhIRg/+uaUkyaJLcidXSWs3v8tKtP7u5Au3bU\nuvrHH4Hy5UVHpA6O3CuAZU5yMq0UBQXRJrzoaNER2V5AAPDsGR3HxtJDCNOfli2pKoqrKzUr5JVy\n4Px56ioK0ETd+++LjceGFB2Er169GkOGDMGoUaMQGRmJWrVqISwsDDdv3kz/D4wcCZw6pWQI6mU5\nCN+6Vd6kx/RlzhxqPNG7tzwrrmdPnwL58tFsl7s7zXwx/dm5E3jwgI5v3qTKWY7OYLCulmP5MMr0\nw9OTVsejoyk109tbdETi+foCU6cCISGUruPAn5WKDsK/++479OzZE71790bZsmUxc+ZMFCxYEHPm\nzEn/DxQoILd2d3QlS8rpFsnJwM8/i42HieHkJDoCdfH2BvbsobzwNWv09QH06BHwww9AgwY086Nn\nlquD7dvT3gA9sByEb9pEVTKY/tSvT5v3GcmfHxg6lNJ3HTxzQLE7XVJSEo4dO4amTZtafb1p06Y4\ncOBA+n/IkathpMcyr+lVfyd6sXkzDUIYA6g84TvviI7Cvj78kDrp7tmj71nQ589pA56Z5cDU0VWo\nAFSuTMcJCTQTqldRUdRlevVqOU2HMTc30RHYlGKD8Pv37yM1NRX+L+xg9fPzQ/Sr8vv0dLMFKB/4\nyy9pN/yCBaKjEef2baBVK8qJbNOGGvYwpjcv7hPR64asX3+V82BLlwaqVxcbj7116kT7QyZOpBlR\nvVq9mh5COnSgzwXGdEDoNPQRZ2fqGKUnbdoASUlUE1Sn/FesQKAkAUlJeHLjBi6YN2Ck44iDXx+G\n5GQ4PX6MFG5WlSNavE4MAQGo6uUFp/h44OJFnF26FM90uFnXzWiEb7duyLd9Ox7Uq4c7Nrw3qvI6\nqVcPaNiQcsTv3qVfOhT8448wN22/Vq0a7gv6WanyGmGqUbp0aUXfT7GZcF9fXzg5OSEmJsbq6zEx\nMShYsGD6f8jRSw+xdOWzqALwsHlzgZGI43bzJopNmIAqzZuj6DffiA6HCSC5u+ORxcxnvm3bxAUj\nUGLRorg9aBBObdyIqO7dRYdjf87Ouv8sdLt1C7nOnAEAmJyc8KhhQ8ERiWFISkKeP/5A0PDhyK3D\nErbGuDjdrYwrNhPu6uqKGjVqYPv27WhjsZS0Y8cOtG3bNt0/ExISotTpmVZcvAj88w8du7ig+NCh\nKJ7OhhTzbITDXiNeXsDGjQCAfH/+iXxlygC5cwsOyo7276dW9R07AnXrZnsjnuavk0GDKB0DQMC5\ncwjQ6v+Hymn+OnF0Fg+gxubNUU1AwQZVXCMjRgCTJwMA8vn7Ax99JC4WEfr1o0ox7dsDAwdSQQuV\nefz4saLvp+gW9KFDh2LRokVYsGAB/vnnHwwePBjR0dHo16+fkqdhWma50zk8XL87wsuVoyYdADXp\nsNyYpgeLFwPz51NlkJEjRUcjTqNG9GGzYwdw6JDoaBgT498HUQAO3ZglQ5YTlhs26GuDanIydY69\nc4c6ad+5Izoiu1B0EN6uXTtMnz4dEyZMQLVq1XDgwAFs2bIFgYGBSp7GcZw5QxebnjRuDPToQaXo\n9HyzBaz//x28DJOVxERg3Tr5datW4mIRzdkZmDWL/l3oqVIUezVJokoherJrF90TOnSgDsp6VbUq\nEBxMx/HxVLZSL3bskHsFFCkC1K4tNh47UbwYa//+/XH16lUkJCTg8OHDqFOnjtKn0D5Joq5wFStS\nLUy9NCwCgFq1gIULafNR69aioxHLsjrGzp3AvXviYrGnbdvk8pTFiwNvvik0HCYIdwa09ugRrQoF\nBdEKiZ6q5bi7U1fElSupe6RevdjAaflycbHY24tt6nXSK0Af/5dqYzAARYvKr/U0C2rm7k5tevWs\naFF62nd2Bpo310/ddMvrvUMH3W9K063wcJr5mzKFOwgDdD+cPh24do32zZw4IToiJoLlIHz/fn2k\npMTFWadk6miVnAfholj+Q1u1Sl+zHkw2bx61K968GShTRnQ0tpeUBPz2m/xaRzdbZuHmTWDfPhpo\njhxJ+aB65+UFvPee/FrPDZz0rGRJ4NNP6ed/6xa1tXd0MTFAzZp0XL68vF9KB3gQLkrz5kCePHR8\n9SpvytKrChWoRa9euLpShZyICKBbN6BSJdERqUt0NDBzpuOnaqxeLR83agS80ORNtywnZ1auBEwm\ncbEwcb79liYovLxER2IfJUtS5+Br14Aff9TV6igPwkVxc6McODNHT0l5/lx0BEwtChQA+venCik6\nutlmaMAAoHBhYPDgtPKVDsvyfserIbKmTeWH8lu3aLXAUSUnA4sWAQqXfGMaVqwY7ZfTER6Ei9Sx\nI+2EHjeO6gU7qqQkoEQJoFkzGnjx0jNjLytSRJ75dOSH8gsXgGPH6NjNjTdoW3JxAdq1o+PQUCAl\nRWw8trR9O9CzJ62CDB4sOhrGhOBBuEiNGgFnzwKjRwOlSomOxnZ27KCcr+3bga++ApycREfEmPpY\nzghv2wbcvy8uFlu6e1cuwxYeDvj4iI1HbYYNoweVQ4foM8JRLV1K/01MpIcxxnSIB+EiGQz6WI5/\nsRqGTkoPZUlSEjWs6NKFqkUw/SlRQl6KTUmhxhWOqE4dmnw4dAgYNUp0NOpTogRQurToKGzr8WNq\nRmPWtau4WNQuPp42aZ47JzoSZgM8GmK29eyZ9c3WcuMRk/3yC9CyJdWFXbDA8arl3L0LbN3KqUgZ\nsZwNd+TqGAYDpVtUry46EibCTz/RDDgAVKnCG7RfZd48Stfp3Jk6DDuaqVNpf9D+/brdhMyDcGZb\nv/xCT/IALUFXqSI2HrUKD6cuogBVDzl6VGw8Slu2DAgLAwoVAr7/XnQ06tWuHRAQQK3sv/5adDSM\n2YY5FQXgWfDXKV5c/vxctQpITRUajqIkCZg9G5g7F3j7bSrTq0M8CFcTSQJOnxYdhbJiY+Xd/p06\n6SP9Jjs8PKw3qC1ZIi4WpUkSVUEAKM/Zw0NoOKrm7w/cvk2t7GvVEh0NY7YxciSl3uXOzaujr9Oo\nEeDnR8dRUcDu3WLjUdLBg1SeGaByzU2bio1HEB6Eq4EkAZMnU7OWypWpkYWj6NuXbh5btgA9eoiO\nRt26dZOPly+Xl2u17tgx4NQpOvbwkKs/sPTxngkG0OfCkSPA0KFURcSRNGlCs+F37wIFC4qORr2c\nnWkflZkjtbG3/H/54APqoq1DfLdXA4OBnnAvXaIbr+VSnSNwcaFUhMBA0ZGoW4MGVCcVoAH4yZNi\n41GKeRYcoJtt7tzCQmEC9elDlaAuXRIdiTbcukVdBKdNkwesjoaromSsc2f5eN06x+i5kZRk3bCr\nSxdxsQjGg3C16N5dPl682PE25rGMGY1UM/5//6POieY2vlqWmGi9wZBXQ/Tpzh3acDx+PK34RUeL\njkj9AgOpkgxAucBr1oiNh4lRsyatkLdtSw9jzs6iI8q5Y8coVRWg6/ztt8XGI5AD/DQdROvWtDHv\n6VO5Ruybb4qOitmb5cOYIzAYaCPmwoXA5ctA/fqiI9Ke8+eBoCBaUdKq5cvl6gf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sensor_variance = 30\n", "process_variance = 2\n", "pos = (100,500)\n", "\n", "zs, ps = [], []\n", "\n", "for i in range(100):\n", " pos = predict(pos[0], pos[1], velocity, process_variance)\n", "\n", " Z = math.sin(i/3.)*2\n", " zs.append(Z)\n", " \n", " pos = update(pos[0], pos[1], Z, sensor_variance)\n", " ps.append(pos[0])\n", "\n", "plt.plot(zs, c='r', linestyle='dashed', label='input')\n", "plt.plot(ps, c='#004080', label='filter')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we set a bad initial guess of 100. We can see that the filter never 'acquires' the signal. Note now the peak of the filter output always lags the peak of the signal by a small amount, and how the filtered signal does not come very close to capturing the high and low peaks of the input signal.\n", "\n", "If we recall the g-h filter chapter we can understand what is happening here. The structure of the g-h filter requires that the filter output chooses a value part way between the prediction and measurement. A varying signal like this one is always accelerating, whereas our process model assumes constant velocity, so the filter is mathematically guaranteed to always lag the input signal. \n", "\n", "Maybe we didn't adjust things 'quite right'. After all, the output looks like an offset sin wave. Let's test this assumption." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise - Noisy Nonlinear Systems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implement the same system, but add noise to the measurement." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#enter your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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i0tM4bBaGdxG//3dZEWllGYvFKlNenpIiBx0YVlK/8rpbalZTxpX1w2CQ53xS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Uuk/P3JHc9U7FUfXSjkcrIiT0sTb3OqXE4KT5WV9HzxYlX50VOnqPY/MBDo0QN47z3t2/q//wNe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\nOhNh1WOkoEC8XFgy2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sensor_variance = 30\n", "process_variance = 2\n", "pos = (100,500)\n", "\n", "zs, ps = [], []\n", "\n", "for i in range(100):\n", " pos = predict(pos[0], pos[1], velocity, process_variance)\n", "\n", " Z = math.sin(i/3.)*2 + randn()*1.2\n", " zs.append(Z)\n", " \n", " pos = update(pos[0], pos[1], Z, sensor_variance)\n", " ps.append(pos[0])\n", "\n", "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", "p2, = plt.plot(ps, c='#004080', label='filter')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discussion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is terrible! The output is not at all like a sin wave, except in the grossest way. With linear systems we could add extreme amounts of noise to our signal and still extract a very accurate result, but here even modest noise creates a very bad result.\n", "\n", "Very shortly after practitioners began implementing Kalman filters they recognized the poor performance of them for nonlinear systems and began devising ways of dealing with it. Much of the remainder of this book is devoted to this problem and its various solutions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Derivation From Bayes Theorem (Optional)\n", "\n", "\n", "I gave you the equations for the product of two Gaussians but did not derive them for you. They are a direct result of applying Bayes rules to Gaussians, however. You don't need to understand this section to read the rest of the book or to use Kalman filters. You may need to know this if you read the literature, much of which is written in terms of Bayes theorem. It's a bit of neat algebra, so why not read on?\n", "\n", "We can state the problem as: let the prior be $N(\\mu_p, \\sigma_p^2)$, and measurement be $z \\propto N(\\mu_z, \\sigma_z^2)$. What is the posterior x given the measurement z?\n", "\n", "Write the posterior as $P(x|z)$. Now we can use Bayes Theorem to state\n", "\n", "$$P(x|z) = \\frac{P(z|x)P(x)}{P(z)}$$\n", "\n", "$P(z)$ is a normalizing constant, so we can create a proportinality\n", "\n", "$$P(x|z) \\propto P(z|x)P(x)$$\n", "\n", "Now we subtitute in the equations for the Gaussians, which are\n", "\n", "$$P(z|x) = \\frac{1}{\\sqrt{2\\pi\\sigma_z^2}}\\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]$$\n", "\n", "$$P(x) = \\frac{1}{\\sqrt{2\\pi\\sigma_p^2}}\\exp \\Big[-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big]$$\n", "\n", "We can drop the leading terms, as they are constants, giving us\n", "\n", "$$\\begin{aligned}\n", "P(x|z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big]\\\\\n", "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big] \\\\\n", "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z-x)^2-\\sigma_z^2(x-\\mu_z)^2]\\Big]\n", "\\end{aligned}$$\n", "\n", "Now we multiply out the squared terms and group in terms of the posterior $x$.\n", "\n", "$$\\begin{aligned}\n", "P(x|z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z^2 -2xz + x^2) - \\sigma_z^2(x^2 - 2x\\mu_z+\\mu_z^2)]\\Big ] \\\\\n", "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_z + \\sigma_p^2z) + (\\sigma_p^2z^2+\\sigma_z^2\\mu_z^2)]\\Big ]\n", "\\end{aligned}$$\n", "\n", "The last parentheses do not contain the posterior $x$, so it can be treated as a constant and discarded.\n", "\n", "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_z + \\sigma_p^2z)}{\\sigma_z^2\\sigma_p^2}\\Big ]\n", "$$\n", "\n", "Divide numerator and denominator by $\\sigma_p^2+\\sigma_z^2$ to get\n", "\n", "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n", "$$\n", "\n", "Proportionality lets us create or delete constants at will, so we can factor this into\n", "\n", "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n", "$$\n", "\n", "A Gaussian is\n", "\n", "$$N(m,\\, s^2) \\propto \\exp\\Big [-\\frac{1}{2}\\frac{(x - m)^2}{s^2}\\Big ]$$\n", "\n", "So we can see that $P(x|z)$ has a mean of\n", "\n", "$$\\mu_\\mathtt{posterior} =\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2}$$\n", "\n", "and a variance of\n", "$$\\begin{aligned}\n", "\\sigma_\\mathtt{posterior} &=\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2} \\\\\n", "&= \\frac{1}{\\frac{1}{\\sigma_p^2}+\\frac{1}{\\sigma_z^2}}\n", "\\end{aligned}$$\n", "\n", "which are the equations that we have been using." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The one dimensional Kalman filter that we describe in this chapter is a special, restricted case of the more general filter. Most texts do not discuss this form of the Kalman filter at all. However, I think it is a vital stepping stone. We started the book with the g-h filter, then implemented the discrete Bayes filter, and now implemented the one dimensional Kalman filter. I have tried to show you that each of these filters use the same algorithm and reasoning. The mathematics of the Kalman filter that we will learn shortly is fairly sophisticated, and it can be difficult to understand the underlying simplicity of the filter. That sophistication comes with significant benefits: the filters we design in the next chapter will markedly outperform the filters in this chapter.\n", "\n", "This chapter takes time to assimilate. To truly understand it you will probably have to work through this chapter several times. I encourage you to change the various constants in the code and observe the results. Convince yourself that Gaussians are a good representation of a unimodal belief of the position of a dog in a hallway, the position of an aircraft in the sky, or the temperature of a chemical reaction chamber. Then convince yourself that multiplying Gaussians truly does compute a new belief from your prior belief and the new measurement. Finally, convince yourself that if you are measuring movement, that adding the Gaussians together updates your belief. \n", "\n", "Most of all, spend enough time with the **Full Description of the Algorithm** section to ensure you understand the algorithm and how it relates to the g-h filter and discrete Bayes filter. There is just one 'trick' here - selecting a value somewhere between a prediction and a measurement. Each algorithm performs that 'trick' with different math, but all use the same logic.\n", "\n", "If you understand this, you will be able to understand the generalized Kalman filter in the next chapter and the various extensions that have been make on them. If you do not fully understand this, reread this chapter. Try implementing the filter from scratch, just by looking at the equations and reading the text. Change the constants. Maybe try to implement a different tracking problem, like tracking stock prices. Experimentation will build your intuition and understanding of how these marvelous filters work." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }