From 0a41e78aebaa3f6b5399c485bfb25e7b5d42a31a Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sun, 17 Jan 2016 20:16:27 -0800 Subject: [PATCH] Added likelihood and orthogonal projections Added the likelihood equations/form from the discrete bayes chapter to better tie in that form of reasoning. then I converted the 1d equations to the orthogonal projection form to show how the Kalman gain is computed and where the residual comes from computationally. This should make the full KF equations much more approachable. --- 04-One-Dimensional-Kalman-Filters.ipynb | 1487 +++++++++++------------ code/kf_internal.py | 4 +- code/mkf_internal.py | 4 +- 3 files changed, 690 insertions(+), 805 deletions(-) diff --git a/04-One-Dimensional-Kalman-Filters.ipynb b/04-One-Dimensional-Kalman-Filters.ipynb index e58e640..b96705e 100644 --- a/04-One-Dimensional-Kalman-Filters.ipynb +++ b/04-One-Dimensional-Kalman-Filters.ipynb @@ -28,7 +28,7 @@ "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n", "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n", "@import url('http://fonts.googleapis.com/css?family=Arimo');\n", - "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n", + "@import url('http://fonts.googleapis.com/css?family=Fira+sans');\n", "\n", ".CodeMirror pre {\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", @@ -42,7 +42,7 @@ " background: transparent;\n", " color: #000000;\n", " font-weight: 600;\n", - " font-size: 11pt;\n", + " font-size: 12pt;\n", " font-style: bold;\n", " font-family: 'Source Code Pro', Consolas, monocco, monospace;\n", " }\n", @@ -123,11 +123,10 @@ " white-space: nowrap;\n", " }\n", " div.text_cell_render{\n", - " font-family: 'Fira sans', verdana,arial,sans-serif;\n", + " /*font-family: 'Vollkorn', verdana,arial,sans-serif;*/\n", " line-height: 150%;\n", - " font-size: 110%;\n", - " font-weight: 400;\n", - " text-align:justify;\n", + " font-size: 130%;\n", + " text-align: justify;\n", " text-justify:inter-word;\n", " }\n", " div.output_subarea.output_text.output_pyout {\n", @@ -279,89 +278,116 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## One Dimensional Kalman Filters" + "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a 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. \n", + "\n", + "\"One dimensional\" means that the filter only tracks one variable, such as position on the x-axis. In subsequent chapters we will learn a more general form of the filter that can track many variables simultaneously, such as position, velocity, and accelerations in x, y, and z. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now that we understand the discrete Bayes filter and Gaussians we are prepared to implement a 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. \"One dimensional\" just means that the filter only tracks one variable, such as position on the x-axis. In the subsequent chapters we will learn a more general form that can track many variables simultaneously, such as position, velocity, and accelerations in x, y, z. " + "## Tracking A Dog\n", + "\n", + "As in the **Discrete Bayes Filter** chapter we will be tracking a moving object in a long hallway at work, such as a dog. Assume that in our latest hackathon someone created an RFID tracker that provides a reasonably accurate position of the dog. 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", + "The sensor is not perfect. A reading of 23.4 could correspond to the dog being at 23.7, or 23.0. However, it is very unlikely to correspond to a position of 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 true position; a position of 23 m would equally likely be measured as 22.9 or 23.1." ] }, { "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. 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", + "### Simulating the Sensor\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", + "Accurately simulating an RFID tracking sensor 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 understand Gaussians so let's use them instead. \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", + "We can model the error in a system with a Gaussian. Instead of saying our measurement is 23, we would say our measurement is 23 with a variance of 0.35, or $\\mathcal{N}(23, 0.35)$. The variance accounts for the error in the sensor, and has physical meaning. The standard deviation $\\sigma$ is the square root of the variance. The 68-95-99.7 rule says that 68%, 95%, and 99.7% fall within $\\pm1\\sigma$, $\\pm2\\sigma$, and $\\pm3\\sigma$. $\\mathcal{N}(23, 0.35)$, 68% of the measurements will fall between 22.41 and 23.59 meters, and 99.7% will fall between 21.2 and 24.8.\n", "\n", - "Accurately simulating an RFID tracker 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 understand 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", + "This is a simple model, but it works well in practice. Error distributions of many sensors approximate a normal distribution. Of course, if the sensor errors are not well modelled by Gaussians the simulation will be poor.\n", "\n", - "This is a simple model, but it works very well in practice. Error distributions of many sensors approximate a normal distribution. Of course, if the sensor errors are not well modelled by Gaussians 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", + "We can describe the measurement with this equation:\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, $h(x)$ 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", + "Here $h(x)$ is the *measurement model* - a function which describes how measurements are made from the current system state. In other words, $h(x)$ is the measurement we would get for the state $x$ *if* the sensor was perfect. $\\epsilon_z$ is the measurement error, and hence $z$ is the measurement given by the sensor. This does not imply that we know the value of $\\epsilon_z$, it is merely 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. For now recognize that we will be modelling $\\epsilon_z$ with a Gaussian. If $\\epsilon_z$ is close to being Gaussian our model will be accurate, and if it is not our model may not work well." + "The utility of this equation will become apparent later. For now recognize that we model $\\epsilon_z$ with a Gaussian. If $\\epsilon_z$ is nearly Gaussian our Gaussian model will be accurate, and if not our model may not work well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Simulating the Dog's movement\n", + "### Modeling 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 current velocity and previous position like so:\n", + "We can use Newton's equation of motion to compute the current position based on the current velocity and previous position:\n", "\n", "$$ x_k = v_k \\Delta t + x_{k-1}$$.\n", "\n", - "This is a model of the dog's behavior, and we call it the *system model* or *process 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 process model plus what we call the *process noise*. In the literature this is usually written something like this:\n", + "This model of the dog's behavior is called the *process model*. 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 true if we are tracking dog, a missile, or the nozzle of a water jet cutter. We model this by saying the system's state is the prediction that comes from the process model plus what we call the *process noise*. We describe the process model with this equation:\n", "\n", "$$ x = f(x) +\\epsilon$$\n", "\n", - "Here $f(x)$ is our process model and $\\epsilon$ is some unknown error between the process 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." + "Here $f(x)$ is the process model, and $\\epsilon$ is the unknown error in the model. \n", + "\n", + "An example. The dog's process model is $f(x_k) = v_k \\Delta t + x_{k-1}$. If $v_k = 0.3$ m/s, $\\Delta t = 1$ second, and $x_{k_1} = 10$ m then we predict that in one second the dog's new position is\n", + "\n", + "$$\\begin{aligned}f(x) &= v_k \\Delta t + x_{k-1} \\\\ \n", + "&= 0.3\\times 1 + 10 \\\\ &= 10.3\\end{aligned}$$\n", + "\n", + "But the dog may have sped up, and his true position is 10.37 m. Therefore $\\epsilon=0.07$ m. Again, this does not imply that we *know* the values of $x$ or $\\epsilon$. If we did know these values than we would not need a filter!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Implemention in Python\n", + "### Implementation\n", "\n", - "We will want our implementation to correctly model the noise both in the measurement 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", + "`numpy.random.randn()` generates a random number with a mean of zero and a standard deviation of one. To draw a random number from $\\mathcal N(3, 0.5)$ we'd write:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4.1484130063403395" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from math import sqrt\n", + "from numpy.random import randn\n", "\n", - "Our model assumes that the velocity of our dog is constant, but 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", + "(randn() * sqrt(0.5)) + 3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can simulate slight changes in velocity by adding a randomly generated value to the velocity each time we compute the dog's position. \n", "\n", "```python\n", "noisy_vel = vel + randn()*velocity_std\n", - "x = x + noisy_vel*dt\n", + "x += noisy_vel*dt\n", "```\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", + "To model the position sensor we need to take the current position of the dog and then add noise proportional to the Gaussian of the measurement noise. This is simply\n", "\n", "```python\n", "z = x + randn()*measurement_std\n", @@ -372,42 +398,36 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "import math\n", "import matplotlib.pyplot as plt\n", - "from numpy.random import randn\n", "\n", "class DogSimulation(object): \n", " def __init__(self, x0=0, velocity=1,\n", " measurement_var=0.0, \n", " process_var=0.0):\n", - " \"\"\" x0 : \n", - " initial position\n", - " velocity:\n", - " (+=right, -=left)\n", - " measurement_var:\n", - " variance in measurement m^2\n", - " process_var:\n", - " variance in process (m/s)^2\n", + " \"\"\" x0 : initial position\n", + " velocity: (+=right, -=left)\n", + " measurement_var: variance in measurement m^2\n", + " process_var: variance in process (m/s)^2\n", " \"\"\"\n", " self.x = x0\n", " self.velocity = velocity\n", - " self.meas_noise = math.sqrt(measurement_var)\n", - " self.process_noise = math.sqrt(process_var)\n", + " self.meas_std = sqrt(measurement_var)\n", + " self.process_std = sqrt(process_var)\n", "\n", " def move(self, dt=1.0):\n", " \"\"\"Compute new position of the dog in dt seconds.\"\"\"\n", - " dx = self.velocity + randn()*self.process_noise\n", + " dx = self.velocity + randn()*self.process_std\n", " self.x += dx * dt\n", " \n", " def sense_position(self):\n", " \"\"\" Returns measurement of new position in meters.\"\"\"\n", - " measurement = self.x + randn()*self.meas_noise\n", + " measurement = self.x + randn()*self.meas_std\n", " return measurement\n", " \n", " def move_and_sense(self):\n", @@ -420,21 +440,19 @@ "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()` method moves the dog based on its velocity and the process noise. The `sense_position()` method computes and returns a measurement of the dog's position based on the current position and the sensor noise. `move_and_sense()` first performs `move()`, then `sense_position()`.\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 square of rhe standard deviation, so we take the square root of the variance." + "The constructor `__init()__` initializes the class with an initial position, velocity, and the variances of the measurement and process. It takes the square roots of the variances to convert them into standard deviations. The `move()` method moves the dog based on its velocity and the process noise. The `sense_position()` method computes and returns a measurement of the dog's position based on the current position and the sensor noise. `move_and_sense()` first performs `move()`, then `sense_position()`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now let's look at the output of the `DogSimulation` class. We will start by setting the variances to zero. Zero variance means there is no noise in the signal or in the process model, so the results should be a straight line. I use code from `book_plots` to plot the tracks without a lot of superflous code distracting you from the core ideas." + "Let's test the class. We will start by setting the variances to zero. That means there is no noise in the sensor or in the process model, so the results should be a straight line. I use code from `book_plots` to plot the tracks without a lot of superfluous code to distract you." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -448,9 +466,9 @@ }, { "data": { - "image/png": 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KqlSpkpxOp/bv3+9yjtPp1MGDB1W5cmWX98PDw/Xcc8/pm2++0Y8//qiLFy9q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\ne7YaNGigWrVqWZ2K21q8eLEWLVqkxYs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pMHToUNy7d0+8vmTJEri6uuo8JxGRvmHDRURERC+5efMm7ty5I+oZM2bg999/F3W/fv3w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\nd++OLl26iNrDwwNNmzbVaUY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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -477,23 +495,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The constructor initialized the dog at position 0 with a velocity of 1 m/s (move 1.0 m to the right). So we would expect to see an output of 1..10, and indeed that is what we see.\n", + "The constructor initialized the dog at position 0 with a velocity of 1 m/s (move 1.0 m to the right). So we would expect to see an output of 1, 2, 3, .. 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, + "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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S0rBs2bJij6OrqytTVvRhXSKRCGVpaWngOA6mpqaljuf169cAgOPHj+P48eNy63AcJxVM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\nRCSb+X+1fahPdD6GigAAAABJRU5ErkJggg==\n", 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S0tPTER4eXux2dHV1ZcqKTtYlEolQlp6eDo7jYGZmVup4Xr16BQA4ceIETpw4IbcOx3FS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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -506,11 +524,13 @@ " dog = DogSimulation(0., 1., measurement_var, process_var)\n", " N = 50\n", " xs = np.zeros(N)\n", + " dog_pos = np.zeros(N)\n", " for i in range(N):\n", " dog.move()\n", " xs[i] = dog.sense_position()\n", + " dog_pos[i] = dog.x\n", " \n", - " plot_dog_track(xs, measurement_var, process_var)\n", + " plot_dog_track(xs, dog_pos, measurement_var, process_var)\n", "test_sensor(measurement_var=4.0)" ] }, @@ -518,27 +538,25 @@ "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", + "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 multiple times you should get slightly different results each time. I could use `numpy.random.seed()` to force the results to be the same. This would simplify my explanations in some cases, but would ruin the interactive nature of this chapter. To get a 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. Try it now.\n", "\n", - "The dotted line (labeled 'track') shows the actual position of the dog, and the circles (labeled 'sensor') depict the noisy signal produced by the simulated RFID sensor. Please note that the track was manually plotted - we do not yet have a filter that recovers that information from the sensor measurements! \n", - "\n", - "If you are running this in an interactive Jupyter 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", + "The dotted line (labeled 'track') shows the actual position of the dog, and the circles (labeled 'sensor') depict the noisy signal produced by the simulated RFID sensor. \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 static format 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, + "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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TAQC6d+9ebkkaIZVF1Dtqf/zxx0fb+Pr60mCthBBCaqWhQ4fC1tYWUVFR0NDQ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\nAAAAAElFTkSuQmCC\n", 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3bl08ePAAVlZWyM7Oxrt379CkSRMYGBjIOjxCiBRFRUXByMgIzZs3BwCcPn0a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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -551,7 +569,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "collapsed": false, "scrolled": true @@ -559,9 +577,9 @@ "outputs": [ { "data": { - "image/png": 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8GXfv3s3Xdvfu3UNUVBQePXoEAOjYsSP2798PIHtuybFjx+L169dK/9atWzNJ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+ "image/png": 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RFBYWyt3O3w/yPiQ3NxcdO3bEkydP0LlzZ4wePRq6uroQi8XIycnB6tWrK9yOjo6OTFn5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\nQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -576,23 +594,23 @@ "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 normal 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", + "Now lets see the effect of the process noise. On each call to `sense_position()` I modify the current velocity with random noise. However, I strive to keep the velocity close to the initial value, as I am assuming that there is a control mechanism trying to maintain the same speed. In this case, the control mechanism is 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." + "First we observe the results of having process noise but no measurement noise." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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wMzNDbGwshEKhjCMl5PPVqGfUCCGEEEK+xKtXr7B7924EBwfj2bNn5bbV1tbG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pFClShEmTJqGU4tChQ1y4cIEyZcqwYMECI7dECCFegQWvhRBCCCHywuDBg5k5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\ntm1mhyQFbMuWLYbFYjGsVqvD4/nnn7f3mThxouHv72+ULl3aiIqKMhI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -608,23 +626,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can see that the position wanders 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", + "We can see that the track wanders. You may have thought that the measurements would wander back and forth over the ideal path, but recall that we are modifying velocity on each time step, 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. Depending on the random number generation the sensor reading may lie on top of the track, or wander away from it. Try running it several times to observe the various possibilities. " ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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OacdDhgyhSZMmGBsbM2zYMAD+97//UbduXa5evUqDBg3w8/MrsOyLFy8yaNAg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QoTRs2JCGDRvSu3dvWflTCJHtclygJoQQQghx584dmjZtypEjR/S0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\nRERERJ46dn9GTZ4+d58hgzvDEUeOHIlhGAC0atVKC0qLiIiIiDwm9ah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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -639,19 +657,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Math with Gaussians" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can express our belief in the dog's position with a Gaussian. Say we believe that our dog is at 23 meters, and the variance in that belief is 5 m$^2$, or $\\mathcal{N}(23,\\, 5)$. We can represent that in a plot:" + "## Math with Gaussians\n", + "\n", + "We can express our belief in the dog's position with a Gaussian. Say we believe that our dog is at 23 meters, and the variance in that belief is 5 m$^2$, or $\\mathcal{N}(23,\\, 5)$. A plot of the pdf illustrates this:" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -660,7 +673,7 @@ "data": { "image/png": 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m3YcUlxQpmJkQoqZIIS6EqFE517P4csVbZORcAECFimcGvMpjjwxRODMh6h4j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\nxTMzM3FwcKhwHwcHhwrbq1QqHBwcUKv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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -678,27 +691,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This chart depicts our belief, in other words our uncertainty about the dog's position. 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", + "This plot depicts our uncertainty about the dog's position. It corresponds to a fairly inexact belief. While we believe that it is most likely that the dog is at 23 m, any position from 21 m to 25 m are quite likely as well. Assume for the moment our dog is standing still, and we query the sensor again. This time it returns 23.2 m as the position. Can we use this additional information to improve our estimate of the dog's position?\n", "\n", - "This graph corresponds to a fairly inexact belief. While we believe that the dog is at 23 m, note that roughly speaking positions 21 m to 25 m 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 m as the position. Can we use this additional information to improve our estimate of the dog's position?\n", - "\n", - "Intuition suggests we can. 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 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, where we assume the dog stands still at 23 m." + "Intuition suggests we can. 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 near 23. Of course, a different interpretation is possible. Perhaps our dog was randomly wandering back and forth in a way that exactly emulated random draws from a normal distribution. But that seems extremely unlikely - I've never seen a dog do that. Let's look at 100 sensor readings in a plot, assuming the dog stands still:" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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Dh3Bzc8PXX3+N+fPnKzAyUpds3LhR7mNSIv6JjIwMJCQkwMjICE2aNAHwYQHX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\nhfT09GrH6OHhgRUrViA2NrbafQAfrv5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HivV+qkhPnjzBs2fPYGVlJdYmbJJszpSQkICc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\nERERieD/ADW5fkQed7stAAAAAElFTkSuQmCC\n", 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pLdWRlZWFn58f5s+fj5UrV0JJSQkrV64U6PADwIkTJ6Cvr4/Tp0/D29sbHTp0wMqVK7Fx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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -720,80 +729,66 @@ "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", + "Eyeballing this confirms our intuition - no dog moves like this. However, noisy sensor data certainly looks this way. So let's proceed and try to solve this mathematically. But how?\n", "\n", - "\n", - "Recall the code for adding a measurement to a preexisting belief from the **Discrete Bayes** chapter:\n", + "For the discrete Bayes filter we used this function to incorporate a measurement into a pre-existing belief:\n", "\n", "```python\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", + "def update(likelihood, prior):\n", + " posterior = prior * likelihood\n", + " return normalize(posterior)\n", "```\n", - " \n", - "The algorithm is computing:\n", + " \n", + "Recalls that in Bayesian terms the *prior* is the probability before taking *evidence* (measurements) into account, the *likelihood* describes how likely the measurement is given the state of the system, and the *posterior* is the belief in the state after incorporating the measurements. \n", "\n", - "```python\n", - "new_belief = prior_belief * measurement * sensor_error\n", - "```\n", - " \n", - "The `measurement * sensor_error` 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 *previous*, 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", + "If we are now implementing this with Gaussians, we might expect it to be implemented as:\n", "\n", "```python\n", "new_gaussian = measurement * old_gaussian\n", "```\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 the likelihood (the probability for 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", + "which equates to:\n", + "\n", + " ```python\n", + "posterior = measurement * prior\n", + "``` \n", + "\n", + "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?\n", + "\n", + "The algebra for this is not hard, but it is messy. It uses Bayes theorem to compute the posterior given the prior and the likelihood. I've placed the math at the bottom of the chapter if you are interested in the details. Here I will present the results. These give the mean and variance of multiplying two Gaussians:\n", "\n", "$$\\begin{aligned}\n", - "\\mu &=\\frac{\\sigma_\\mathtt{prior}^2 \\mu_z + \\sigma_\\mathtt{z}^2 \\mu_\\mathtt{prior}} {\\sigma_\\mathtt{prior}^2 + \\sigma_\\mathtt{z}^2}, \\\\\n", - "\\sigma^2 &= \\frac{1}{\\frac{1}{\\sigma_\\mathtt{prior}^2} + \\frac{1}{\\sigma_\\mathtt{z}^2}} =\n", - "\\frac{\\sigma_\\mathtt{prior}^2\\sigma_\\mathtt{z}^2}{\\sigma_\\mathtt{prior}^2+\\sigma_\\mathtt{z}^2}\n", - "\\end{aligned}$$" - ] - }, - { - "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", + "\\mu &=\\frac{\\sigma_1^2 \\mu_2 + \\sigma_2^2 \\mu_1} {\\sigma_1^2 + \\sigma_2^2}, \\\\\n", + "\\sigma_1^2 &= \\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2}\n", + "\\end{aligned}$$\n", "\n", - "Let's examine the result of multiplying $\\mathcal{N}(23,\\, 5)$ with itself. This corresponds to getting 23.0 as the sensor value twice in a row. But before you look at the result, what do you think the result will look like? What should the new mean be? Will the variance be wider, narrower, or the same?" + "We can immediately infer several things. First, the result of multiplying two Gaussians is another Gaussian. If one Gaussian is the likelihood, and the second is then, prior, then the mean is a scaled sum of the prior and the measurement. The variance is a combination of the variances of the prior and measurement. Finally, the variances are completely unaffected by the values of the mean!\n", + "\n", + "We put this in Bayesian terms by letting $\\mathcal N(\\mu_1, \\sigma_1^2)$ be the prior and $\\mathcal N(\\mu_2, \\sigma_2^2)$ be the measurement. In this text a bar over a variable indicates that it is a prior. Hence $\\mathcal{N}(\\bar\\mu, \\bar\\sigma^2)$ is the prior, and $\\mathcal{N}(\\mu, \\sigma^2)$ is the posterior. Typical filtering texts might use $x_{k+1}^-$ for the prior, and $x_k^+$ for the posterior. I've simplified the traditional notation to keep the equations uncluttered. I use the subscript $z$ for measurements.\n", + "\n", + "$$\\begin{aligned}\n", + "\\mathcal N(\\mu, \\sigma^2) &= prior \\cdot likelihood\\\\\n", + "&=\\mathcal{N}(\\bar\\mu, \\bar\\sigma^2)\\cdot \\mathcal{N}(\\mu_z, \\sigma_z^2) \\\\\n", + "\\\\\n", + "&= \\mathcal N(\\frac{\\bar\\sigma^2 \\mu_z + \\sigma_z^2 \\bar\\mu}{\\bar\\sigma^2 + \\sigma_z^2},\\frac{\\bar\\sigma^2\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2})\n", + "\\end{aligned}$$\n", + "\n", + "Let's plot the pdf of $\\mathcal{N}(23,\\, 5) \\cdot \\mathcal{N}(23,\\, 5)$. Can you determine its shape without looking? What should the new mean be? Will the curve be wider, narrower, or the same as $\\mathcal{N}(23,\\, 5)$?" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "outputs": [ { "data": { - "image/png": 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0/lGldG0aVG1JjcAGuLtlzQxPuYFHvoI0qtaaRtVac+FyDFv3r2Hj7mWc+euU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\nhBDCDEhyJoQQQgghhBBm4P8DoeqRNYMfLNwAAAAASUVORK5CYII=\n", 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bti0tWrRg5syZ1jJ/f3/69evHhAkTCvVCjzzyCDk5Ofzwww8AvPzyyyxevJgDBw5Y6/z7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\nKMJuMk6IdLbyavhqO9x2lXXiEkKI3sDZ0XLi+e8E43NVLfz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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -804,24 +799,19 @@ "import filterpy.stats as stats\n", "\n", "def multiply(mu1, var1, mu2, var2):\n", - " # avoid division by zero\n", - " if var1 == 0.0: var1 = 1.e-80\n", - " if var2 == 0.0: var2 = 1.e-80\n", - "\n", " mean = (var1*mu2 + var2*mu1) / (var1 + var2)\n", - " variance = 1 / (1/var1 + 1/var2)\n", + " variance = (var1 * var2) / (var1 + 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", + "xs = np.arange(16, 30, 0.1)\n", "ys = [stats.gaussian(x, mean1, var1) for x in xs]\n", - "plt.plot(xs, ys, label='original')\n", + "plt.plot(xs, ys, label='$\\mathcal{N}(23,5)$')\n", "\n", "ys = [stats.gaussian(x, mean, var) for x in xs]\n", - "plt.plot(xs, ys, label='product', ls='--')\n", + "plt.plot(xs, ys, label='$\\mathcal{N}(23,5) \\cdot \\mathcal{N}(23,5)$', ls='--')\n", "bp.show_legend();" ] }, @@ -829,27 +819,27 @@ "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", + "The result of the multiplication is taller and narrow than the original Gaussian but the mean is unchanged. Does this match your intuition?\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", + "Think of the Gaussians as two measurements. 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", + "\"Measure twice, cut once\" is a well known saying. Gaussian multiplication is a mathematical model of this physical fact. \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." + "Now let's plot the pdf of $\\mathcal{N}(23,\\, 5) \\cdot \\mathcal{N}(25,\\, 5)$. What do you think the result will be? Think about it, and then look at the graph." ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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udjBt0KABtWrVIjg4WF/m4eFBp06dmDhxYq4u1KVLF7RaLevXrwdgxIgRbNy4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P0q1bN8aMGUP//v11R9BNTEx0R819fHxYuXIlEydOZNSoUZw8eZKNGzfqTnsI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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -864,10 +854,10 @@ "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", + "plt.plot(xs, ys, label='$\\mathcal{N}(23,\\, 5)$')\n", "\n", "ys = [stats.gaussian(x, mean2, var2) for x in xs]\n", - "plt.plot(xs, ys, label='measure 2')\n", + "plt.plot(xs, ys, label='$\\mathcal{N}(25,\\, 5)$')\n", "\n", "ys = [stats.gaussian(x, mean, var) for x in xs]\n", "plt.plot(xs, ys, label='product', ls='--')\n", @@ -878,96 +868,13 @@ "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", + "If you ask two people to measure the distance of a table from a wall, and one gets 23 meters, and the other got 25 meters, your best guess must be 24 meters if you trust the skills of both 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", + "Recall the g-h filter 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", - "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", + "This becomes counter-intuitive in more complicated situations, so let's consider it further. Perhaps a more reasonable assumption would be that one person 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 were 24.01 and 23.99. In that case you would agree that the best estimate for the distance is 24.\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 much of their effort on the problem of incorrect measurements; it is a deep and difficult topic which we will ignore for now.\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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+PdasWYPExERMmzYNaWlpCA0NBQDMmTMH/fr1E+sfPHgQAwcOxKRJkzBy5Ehk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\nRU5ErkJggg==\n", - "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. 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 extraordinarily unlikely. It is hard to eyeball this, but the measurements are well over $3\\sigma$ apart, so the probability of this happening is much less than 1%. Still, it can happen, and the math is correct. \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_\\mathtt{z} + \\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." + "This topic is fairly deep. The Kalman filter assumes that no measurement is in error. Large deviations are assume to be due to noise, not error. If the measurement is in error you must not pass it to the filter. Engineers that design radar systems spend much of their effort on the problem of incorrect measurements; it is a difficult topic which we will ignore for now. " ] }, { @@ -976,7 +883,7 @@ "source": [ "### Interactive Example\n", "\n", - "Rather than going through a dozen examples, lets use interactive code. 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." + "This interactive code provides sliders to alter the mean and variance of two Gaussians that are being multiplied together. As you move the sliders the plot is redrawn. Place your cursor inside the code cell and press CTRL+Enter to execute it." ] }, { @@ -989,9 +896,9 @@ "outputs": [ { "data": { - "image/png": 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mb0JERETEZDKROXNmR5chkmIpivljx44lNDSU0NBQAgICmDBhAvny5WPKlCn3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\ndCCJuBBCCCGEEDqQRFwIIYQQQggd/D93JzDZSaoKLwAAAABJRU5ErkJggg==\n", 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O5OXlabZ5eXkBkJiYWOnxiYmJXLp0SWuYh42NDV5eXpUOddEHXet3cHDAwcGBuLg4g8aj\nU5IdFhbGY489hoeHByYmJnz11VeVHhMXF8eAAQOwsbHB09OTpUuXPnCwQgghhBANUVFREZMmTeLM\nmTOcPn1aa19ycjI+Pj6a5xcuXMDJyQlzc/Mq1WFjY0NycjLvvfee1rkArfNXJDExEZVKhb29vdZ2\ne3t7Ll26VKVYqqMq9ffu3Ztdu3YZNB6dxmTfuXOHzp07M3HiRJ5//vlKy+fk5DBkyBAGDBhAdHQ0\n8fHxTJo0iUaNGvHqq68+cNBCCCGEEFW1eIPC259XXq46Fk6BxVNVBjl3VlYW7u7uBAUFYWdnxzff\nfMM777yj2R8SEkJQUJDm+dWrV3F1ddVL3V9//TVNmzZlypQplZa9desWALa2tlrbbW1tNfsMqSr1\nd+3alc2bNxs0Hp16socPH86yZct44oknUKkqb0CbN28mLy+PL7/8kvbt2/PEE08wd+5cPvroowcO\nWAghhBCiIQkLC2PIkCFYWloyZswYvv32W6390dHRBAQEaJ5nZGSU6c2tjsuXL7N27Vo2btyo002P\npqamWn/eU1xcTHFx8QPHo8/6HR0dNb30hmKQMdlHjhzhoYcewsLCQrNt2LBhpKSk1MjlAiGEEEKI\n+uLgwYOaua6nTp3KxYsXCQkJAdTjqP/eAVpSUoKJyYOleEVFRUyePJn169czfPhwnY5xcXEBoLS0\nVGt7bm4ujRs3fqB49F2/o6Mj2dnZBo3HIFP4paWl4enpqbXN1dUVRVFIS0vTDKL/u6ioKEOEU2fJ\n+yF0Ie1E6ELaidBFXWsnXl5eWFlZ6Vx+8VQVi6caMCADyc7OxtLSEoDAwEB8fX355JNPCAoKIjIy\nUqsXG8DZ2fmBh2e8+uqrvP766wwbNgyApKSkSsdlt2zZEih7E2ZmZiatWrV6oHh0UZX6S0pKtDqD\nK5KTk1PhDZJt2rS577Eyu4gQQgghRC0VERFBYGCg1rYZM2YQEhLCiRMnOHDgQJkVHd3c3MjMzKx2\nnatWreKRRx7RJNjFxcVs2bKl0uO8vb3x8fHRmt86IyODlJQUBg0aVO14dFWV+m/duqXp+TYUg/Rk\nN2vWjPT0dK1t6enpqFQqrV8Wf/f3X2IN1b2eBHk/xP1IOxG6kHYidFFX20l+fr6xQzCYvLw8rK2t\n2bJli9ZsHwDTpk3j3XffZe7cubi7u+Pr66u1v127dqSmplJaWlrusJGSkpIK6/3pp5/45ZdfGDJk\nCCdPngTg2rVr9OrVC1Av7vLee+9x9OjRcm+unDRpEl999RXjxo0D4PPPP6d379707dsXgA0bNrBk\nyRJiYmJwdHSsMI6KYnzQ+u/JyMjA3d29wvrvsbOzq/D/RWXDTQySZPfu3Zs33niDwsJCTVf87t27\ncXd3r3CoiBBCCCGEgG3btvHyyy/Tt29f2rZtW2a2DGtraxYsWMDMmTMZP358meNVKhU9e/YkJiYG\nPz8/zfadO3fy+eefEx4eDoC/vz8dOnRgzZo12NnZkZmZyYQJE8jLy2P//v1a57w3u5yiKBQUFJQZ\n93zP3LlzefPNN5k1axZOTk4kJCSwdetWzf57xx85coQRI0aUOb6yGB+0/nuioqLo0aNHuefQF5Wi\nKEplhXJzc0lMTERRFAIDA5k3bx6PPvoojo6OeHp6Mm/ePCIjIzVLWN6+fZt27doxYMAA3nrrLRIS\nEpg8eTJLlixh9uzZWuf+66+AmhgUXxfU1R4FUbOknQhdSDsRuqir7SQ/P79KY7Lriv379zNt2jRc\nXV3Zu3cv1tbWZcqUlpayZMkSJk+ejLe3d5n9ISEhhIWFaU31V1vk5OSwd+9eRo8ebbQYBg4cyGef\nfVbpWPH7tbHKclidxmRHRUXRvXt3/P39yc/PZ9GiRfj5+bFo0SJAfaNjcnKypry9vT179uwhJSWF\nHj16MGvWLF577bUyCbYQQgghhND28MMPk5SURERERLkJNoCJiQlLliwpN8EGCAoK4uTJk1qrN9YW\nBw8erPJqlPp0+fJlHB0dDX4zpk7DRfr3719htzxQ7nr2HTt25MCBA9UOTAghhBBCVN/ixYtZsmQJ\n//73v40dikZRURGxsbGMHDnSaDGsWrWK+fPnG7wemV1ECCGEEKIe8vf3JyAggN27dxs7FI0rV64w\nffp0o9V/7NgxzMzM6Natm8HrMsiNj0IIIYQQwviefPJJY4egpSbmy76fffv21VjPviTZQgghhBCi\nQXjjjTdqrC4ZLiKEEEIIIYSeSZIthBBCCCGEnkmSLYQQQgghhJ5Jki2EEEIIIYSeSZIthBBCCCGE\nnkmSLYQQQgghhJ5Jki2EEEIIIYSeSZIthBBCCCGEnkmSLYQQQgghhJ5Jki2EEEIIIcoYMGAAAwcO\nNHYYdZbOSfaaNWto1aoV1tbWBAQEEB4eft/yv/32G3369MHe3h4XFxdGjx7N+fPnHzhgIYQQQghh\neCqVyqDn37VrF0uWLDFoHcakU5L93XffMXv2bObPn09MTAx9+vRh+PDhXL16tdzyFy9eZPTo0fTv\n35+YmBj27t1Lfn4+jzzyiF6DF0IIIYQQddPOnTt5++23jR2GweiUZK9YsYIpU6YwZcoUfH19+fjj\nj3Fzc2Pt2rXllo+Ojqa4uJh3332XVq1a0aVLF9544w2SkpLIzMzU6wsQQgghhBB/ysvLM3YIOlEU\nxdghGFSlSXZRURHR0dEMGTJEa/vQoUOJiIgo95gePXpgbm7OZ599RmlpKTk5OXzxxRf07NkTR0dH\n/UQuhBC1WElJibFDEELUYYsXL8bExIT4+HieeeYZHBwccHR0JDg4mNzcXE05b29vRowYwb59++jV\nqxfW1tZ8+OGHmv3r1q2jc+fOWFtb4+bmRnBwMLdu3SpT3/r162ndujU2Njb06tWr3GHBX3zxBSYm\nJly+fFlr+8GDBzExMeH333/X2h4VFcWjjz6Kk5MTtra2dO7cmX//+98ATJ48mTVr1gBgYmKCiYkJ\npqamZc5dl5lVVuDGjRuUlJTg6uqqtd3V1ZW9e/eWe0yLFi3YvXs3Y8eOZcaMGZSWluLn58euXbvu\nW1dUVFQVQq//5P0QupB2Ujvk5eVx5swZYmNjiY2NJSUlhccff5xnnnnG2KEB0k6EbupaO/Hy8sLK\nysrYYRjEvfHQTz/9NB4eHrz33nvExMSwfv16rl69yo4dOzTlzp8/z9ixY3nhhReYNm0aLVq0AGDZ\nsmUsXLiQwYMHExwcTFJSEp988gnHjh3j6NGjmJubA7BhwwaCg4Pp27cvs2fP5tKlSzz22GM0adJE\nc657dVU0Tvvv2/fu3cvIkSNxdXXllVdewc3NjYSEBH755RfeeOMNXnzxRVJSUggNDeXrr7/W9Gq7\nuLjo9418QDk5OcTFxZW7r02bNvc9ttIkuzrS09OZOnUqEydOZPz48eTk5LBw4ULGjh3L/v37DVGl\nEEIYzSeffEJ4eHiZ3msfH59yy9++fRs7OzuD31QkhKj7PD09NQk1QLNmzVi2bBn79u3TzPxx4cIF\nfv75Z617327cuMGyZcsYMmQIISEhms+brl27MnnyZP73v/8xY8YMiouLeeutt/Dz82Pfvn2YmalT\nw44dOzJlyhStJFtXiqIwffp0mjZtSmxsLI0bNy5TplevXrRt25bQ0FDGjx9f5TrqgkqTbGdnZ0xN\nTUlPT9fanp6eTrNmzco9ZvXq1TRq1EhzSQBg06ZNeHp6EhERQZ8+fco9LiAgoCqx11v3ehLk/RD3\nI+2k9vDw8Ch3eMiECROwt7cvs/25557D3NycFStW4ODgYNDYpJ0IXdTVdpKfn1+l8itXrmTVqlVl\ntr/yyivMnj37gcvrm0qlYubMmVrbXn75ZZYuXcqOHTs0SbaHh0eZySVCQ0MpKirilVde0fpBP2HC\nBN544w1+/fVXZsyYQWRkJNevX2fJkiWaBPteuTlz5lQr7uPHj5OcnMx//vOfchPsusTOzq7C/xfZ\n2dn3PbbSMdnm5ub4+/uzZ88ere179uwhMDCw3GPu3r2LqampdkUm6qpKS0srq1IIIeqUhx56CIB2\n7drxwgsv8NVXX3Hq1KlyE+y8vDwiIyM5cOAAo0aN4syZMzUdrhCiDmndurXWcycnJ5o0acLFixc1\n21q1alXmuEuXLgHQtm1bre0mJia0adNGc/zly5dRqVRl6jE1NaVly5bVijkpKQmVSkXHjh2rdXx9\nodPsInPmzOGLL75gw4YNnD17lldeeYXU1FSCg4MBmDdvHoMHD9aUf+SRRzh+/DhLly4lMTGR48eP\nM3nyZFq0aIG/v79hXokQQhjYtWvXyt3ev39/jh49yq5du3jzzTd56KGHaNSoUbllz549S2FhIQBX\nrlxhzJgxbNu2zWAxCyHqP2tr6xqpp6IhbnKjd/l0SrLHjRvHypUreeedd+jevTsRERHs2rULDw8P\nANLS0khOTtaUf/jhh/nmm2/Yvn07fn5+jBgxAisrK0JCQmqsIQghhL4UFxfz3nvvMWjQIE6ePFlm\nv5WVFU2bNtXpXN27d2fdunWaJDw/P59XX32VTz/9VK8xCyHKmj17NsnJyWUeFQ39qGp5Q/j7Qn43\nb97k1q1blfYye3l5oSgKCQkJWtsVReH8+fN4e3trlft7PSUlJVq5HUCTJk0AyMrK0tr+1151UN+P\noihKhTcM3lPf70vRecXH4OBgLly4oLnU+dehIhs3biQpKUmr/Lhx44iKiuL27dukpaWxbds22rVr\np7/IhRCiBty8eZOJEyeyfv16CgoK+Oc//8nNmzcf6JzDhg1j27ZtmhsjGzVqpHU1UAghQJ0Qf/LJ\nJ1rbVq1ahUqlqnSBvyFDhmBhYcHHH3+sNR/15s2bSU9P59FHHwXU4/BdXFz43//+R3Fxsabcl19+\nWSaZvpc8/3WqvtLSUtavX69Vzs/Pj1atWrFq1apypwu8x9bWFqh8bHNdZZDZRYQQoj44e/YsU6dO\nJSUlRbOtXbt2mmmvHoSPjw8//fQTr7/+Oo8//niFM5EIIRq2a9euMWLECEaOHElMTAyfffYZQUFB\nmpseK+Lk5MSCBQtYuHAhQ4cOZfTo0SQlJbF69Wq6d+/O1KlTATAzM2PZsmUEBwczYMAAnn76aS5e\nvMjGjRvLfC516NCBXr168cYbb3Dz5k0cHR3ZsmVLmfvtVCoV69atY+TIkXTr1o0pU6bg7u7O+fPn\nOXz4MGFhYYA6wVcUhZdeeonhw4djZmbGqFGj6s2oB0myhRCiHLdv32by5MmkpaVpts2ePZtZs2Zp\nbuR+UHZ2dqxZs6beXzIVQlSPSqXi22+/ZdmyZbz11luoVCqmT5/O8uXLtcpU9Bny1ltv4eLiwn//\n+1/+9a9/4eDgwJQpU3j33Xe1OgteeOEFSktL+fDDD3n99dfp3LkzP//8MwsWLChz7m+++YYXX3yR\n999/HwcHB6ZNm8aAAQPKLFo4ePBgDh48yJIlS1ixYgUlJSW0atWKCRMmaMo88cQTvPrqq3z77bds\n2bIFRVFITk6u1rSBtZFKMfKaln+9RFDXp3nRl7o6lZKoWdJODG/z5s0sXrwYa2trVq5cyaBBg4wd\nUpVJOxG6qKvtJD8/v94uRrNkyRLefvttUlNTdb7nQ+jf/dpYZTms9GQLIUQFnnvuOXx8fCgpKaFv\n3741WveOHTs4cOAAH374ofR0CyFEHSRJthBC3Efv3r1rtD5FUfjoo480Nzt5eXkxa9asGo1BCCHE\ng9PPwEIhhBB6oVKptC5BfvTRR/z2229GjEgIIUR1SJIthBBAYmIi586dM3YYACxYsECrB33OnDnE\nx8cbMSIhRE1btGgRJSUlMh67DpMkWwjR4GVlZTFt2jTGjBlDaGioscPB3Nyc1atX4+XlBcDdu3d5\n5ZVXZFU1IYSoQyTJFkI0aMXFxcycOZNLly5x584dZs+efd/FE2pKkyZNWL9+PY0aNcLd3Z0VK1Zg\nampq7LCEEELoSG58FEI0aCtWrODQoUOa5x9++KFm6WBja9u2Lf/73//w8fHBxcXF2OEIIYSoAkmy\nhRANVmxsLOvWrdM8nz17NsOHDzdiRGX16tXL2CEIUaspiiLTXAqDeNClZGS4iBCiwYqLi9N8Offq\n1UumyhPv43cDAAAgAElEQVSijrGwsCA/P1/uVxB6pygK+fn5WFhYVPsc0pMthGiwnn32Wbp27cri\nxYt5//339bZcek24du0azZs3N3YYQhiViYkJVlZWFBYWUlRUZOxw6r2cnBwA7OzsjBxJzbC0tHyg\n7wWdk+w1a9awfPlyUlNT6dixIytXrqx0BbSVK1fy6aefkpycjJOTExMnTuTdd9+tdrBCCKFvnTp1\n4ocffqgzl5vv3r3L8uXL2bRpE9999x1+fn7GDkkIo1KpVFhaWho7jAYhLi4OgICAACNHUjfolJ5/\n9913zJ49m/nz5xMTE0OfPn0YPnw4V69erfCYOXPmsG7dOj788EPOnj3Lzp076devn94CF0IIfakr\nCTbAkiVL2LhxI8XFxbz++usUFBQYOyQhhBDl0CnJXrFiBVOmTGHKlCn4+vry8ccf4+bmxtq1a8st\nn5CQwCeffMLPP//MyJEj8fb2pmvXrgQFBek1eCGEaGhmzZqFra0tAElJSaxcudLIEQkhhChPpUl2\nUVER0dHRDBkyRGv70KFDiYiIKPeYn3/+GR8fH3bu3ImPjw8tW7Zk0qRJZGRk6CdqIYSohvj4eA4c\nOGDsMB6Ih4cHb775pub5+vXriYmJMWJEQgghylPpmOwbN25QUlKCq6ur1nZXV1f27t1b7jEXLlzg\n4sWLfPfdd3z11VcA/L//9/8YNWoUhw8frrCuqKioqsRe78n7IXQh7UQ3xcXFzJs3j4sXL/Lwww8z\nceJETY9wXdOmTRs6depEXFwcpaWlzJ8/n8WLF9/3GGknQhfSToQupJ2otWnT5r77DXIrfWlpKYWF\nhWzevJnAwEACAwPZtGkTR48eJTIy0hBVCiHEfW3fvp2LFy8CEB4eTlZWlnEDegAqlYrg4GAsLS3p\n27cvc+bMMXZIQggh/qbSnmxnZ2dMTU1JT0/X2p6enk6zZs3KPcbNzQ0zMzN8fHw029q0aYOpqSmX\nL1+mR48e5R4nd6uq3fuFKO+HuB9pJ7pLSEjgxx9/1Dx/7bXXeOyxx4wYkX5069at0mn8pJ0IXUg7\nEbqQdqItOzv7vvsr7ck2NzfH39+fPXv2aG3fs2cPgYGB5R4TGBhIcXExycnJmm1JSUmUlJTg5eWl\nS9xCCKEXiqIwf/58zRy63bt3Z8qUKUaOSj9knmwhhKi9dBouMmfOHL744gs2bNjA2bNneeWVV0hN\nTSU4OBiAefPmMXjwYE35wYMH4+fnx5QpU4iJieHEiRNMnTqV3r17y68fIUSNunbtGpcuXQLAzMyM\n999/H1NTUyNHJYQQor7TaTGacePGkZmZyTvvvENqaiqdOnVi165deHh4AJCWlqbVa61SqdixYwcv\nv/wy/fv3x9ramqFDh/Kf//zHMK9CCCEq4OHhwd69e1m5ciXW1taV3qhS15WWllJQUIC1tbWxQxFC\niAZN5xUfg4ODNT3Xf7dx48Yy21xdXfnuu++qH5kQQuiJnZ0dCxYsMHYYBnfmzBkWLlyIj48P77//\nvrHDEUKIBs0gs4sIIYSoWYmJiTz66KNER0fz/fffc/z4cWOHJIQQDZok2UIIUQ+0bt2aQYMGaZ4v\nWLCA4uJiI0YkhBANmyTZQoh6Jz4+XjObSEOycOFCrKysAPXQkc2bNxs5IiGEaLgkyRZC1Cu3bt3i\nmWeeYeTIkRw5csTY4dQoDw8PXnrpJc3zjz76qE4vuiOEEHWZJNlCiHrlgw8+ICsri3PnzvHaa681\nuB7tF154AW9vb+zs7PjXv/6FnZ2dsUMSQogGSefZRYQQorY7ceKE1qxGCxcuxNzc3IgR1TxLS0tW\nr16Ni4sLLi4umhXahBBC1CxJsoUQ9UJJSQkLFy5EURQABg4cyJAhQ4wclXF06NDB2CEIIUSDJ8NF\nhBD1wu7du4mLiwPUvbmLFi0yckRCCCEaMkmyhRD1QlBQECtXrsTFxYUZM2bQokULY4ckhBCiAZPh\nIkKIekGlUvHYY48xcOBALCwsjB1OrVJaWsr3339PXFwcb7/9trHDEUKIBkGSbCFEvSKzaWgrKCjg\n7bff5ty5c4C6x79Pnz5GjkoIIeo/GS4ihBD1mKWlJS4uLprnixYtorCw0IgRCSFEwyBJthCizpJk\nUTfPP/88jRo1AiAxMZGNGzcaOSIhhKj/dE6y16xZQ6tWrbC2tiYgIIDw8HCdjjt//jx2dnbY29tX\nO0ghhPi7jIwM+vfvz/r16xvcgjNV5ejoyOzZszXPP/74Y1JTU40YkRBC1H86Jdnfffcds2fPZv78\n+cTExNCnTx+GDx/O1atX73tcUVER48ePZ8CAAfqIVQghNN577z3S0tJ47733mDlzprHDqfUmTpyI\nr68vAN7e3uTk5Bg5IiGEqN90SrJXrFjBlClTmDJlCr6+vnz88ce4ubmxdu3a+x73+uuv07VrV558\n8km9BCuEEABHjx7lp59+0jx/7rnnjBhN3WBmZsayZctYvHgxP//8M23btjV2SEIIUa9VOrtIUVER\n0dHRvPbaa1rbhw4dSkRERIXH/frrr+zcuZMTJ07www8/PHikol5TFIW8glzu5GVTWFxAUXGh9qOk\nkNLSEsxMLTA3Uz8szCwwN7PEzNQcKwsb7G0dMDNtWEtoN0RFRUUsXLhQ83zEiBE89NBDRoyo7ggI\nCCAgIMDYYQgjKCpWSLsJt3Mhr+Avj0L1n2cTnDAxUbiYo2BtyZ8PC/WfTZuAg516qkwhhG4qTbJv\n3LhBSUkJrq6uWttdXV3Zu3dvucekpKQwffp0tm/fjo2Njc7BREVF6Vy2IahP74eiKNwpyCLrbga3\n8zK5W5hDXmHOH3/e4W5hDiWlxQ9cj5W5DdYWdthY2GFt0QgbCztsLRvjYONMY2sXLMws9fBqapf6\n1E508csvv2imo7O0tGTUqFEN7j2oDnmP6re7BSYkp1lxIdWa1FsW3Mg2JyPbnIxs9d9v5ZqhKPdL\nkL0rrcPSvBRn+yKcGxfi0rgIZ/simjoU0cIln1Zuebg7FmIi0yk0CPJ5otamTZv77jfIPNkTJkxg\nxowZmh4TRVEMUY2opfKL7nIjJ4Wsu9fJuptB9t0bZOfdoLjU8Den5RfdJb/oLrdy08vdb2Nhj4ON\nyx8PZ5rYNqOJbVNMVPLNUFd069aN6OhoTp8+zdixY3FycjJ2SELUmJJSSEq15tw1ay6kWpOcZs2F\nNCtSMw3fgVBQZMK1m5Zcu1l+XZbmpbR0zaOlWz6tmuXh45ZHhxZ3cbR78A4UIeoilVJJBlxUVISN\njQ1btmxhzJgxmu0zZ87k9OnT7N+/v8wxJiYmmJmZaZJrRVEoLS3FzMyMNWvWMG3aNE3Z7Oxszd8b\nN278wC+oPrj3C7EuXNYtVUpJz7xGcmo8ySlnSU49y/WslGqdy8LMEjtbByzNrDRDQszNLNV/mppj\nYmJKUcmfQ0iKi4soLFEPLcnLzyXnbhYKVf9BZ2FuhbdrG1q6t6elWzu83dpiY9moWq+hJtWldqJv\niqKwe/duHn74YVndsRKVtZPMzEy+//57XnzxRRkKUAtl31E4ehoOnYLDp+DIabiTV/XzqFTqIR+O\n9mBlgfaQEEu4k3OT0lKwsXXSDCHJK4D8QsjNg7RM9Z/V0doD+nSCPl2gT2fo4A0mJtLW6qKG/L1T\nnspy2Ep7ss3NzfH392fPnj1aSfaePXsYO3ZsucfExcVpPd+2bRvvvvsukZGRuLu76xy8qH0UReH6\nrWucuXSchMuxJKeeJa8gV6djG1k3ppmTJ82aeNDEvimNbZvQ2NYRh0ZO2Ns6YmVh/UBf8iWlJeTc\nzSL7TibZuZlk37lJdm4mGVmppGVe4fqtlHKHpBQW5XPu6inOXT0FgAoVzZw88WnekfZe3Wnr0RlL\nC+tqxyX0T6VSMWzYMGOHUef98ssvLF68mMzMTFxcXLQ+44Vx5OYpHDgBIUfg9xiIuwC6XAw2M4W2\nntChJbTxhOYu4O7858PVEczNKv58jYq6CEBAgHOFZXJyFa7dgJS/PC6nQfxFOHMR0jPLPy7xqvrx\nVYj6eeNG0KujwuAeEPQPdczyA0/URzoNF5kzZw7PP/88PXr0IDAwkLVr15KamkpwcDAA8+bNIzIy\nktDQUAA6dOigdXxkZCQmJia0b99ez+GLmpBXcJdzV04Sf+k4Zy+dIDMn477lTU3N8HTxwaNpK9wc\nPdWJtWML7GwMe6XC1MQUh0ZOODQqf/hASUkx1/9IuNNuXib15mUupZ3j1p0bWuUUFFL/2B9+chem\nJmb4uLenvbcf7b264+bkJV8Iol6IjY0lM1OdGS1dupR+/fpprQ4pDE9RFM4kQ8hR+O0I/B4LhZWM\nrHN3hl4doWMr6NhS/WjjCRbmhv1csrNV0c4W2nmVv/9GlsKZi3A6GU5fgJjzEJ0ABX9bMyr7Dvx2\nVP147RPwaArD/qEQ9A8YFAAOdvL5KuoHnZLscePGkZmZyTvvvENqaiqdOnVi165deHh4AJCWlkZy\ncrJBAxU161ZOBrGJRziZdIQLqWcpLS2psKyddWNaurejpZt6uIVn01aYm9W+S/impma4OXni5uQJ\nbfpott/KySA5NYHk1LMkp5zlasYFSpVSzf6S0mJNT/f28C9pbOtIx5b+dG3dh7YenTE1NcitDUIY\n3Jw5c9i9ezdXrlwhOzubRYsWsWbNGmOHVe8VF6t7q388AL9GwNXrFZc1NYWuraF3Jwjsoh524ela\nO3t+nR1U9OsG/br9ua2gUOHEOYiIg4iT6mEvf+/xvnodNvyifpiaQu+OCqP7w5gB4NWs9r1OIXRV\n6ZhsQ5Mx2WUZa8zTzex0YhIPE5MYwaW0cxWWs7KwwdezC+29/Wjj0Rnnxs1q5Qd+dRUU5XMp7Rxn\nL8UQf+k4125crLCsjWUjOrfqSbc2fWjr2RVzs5qbQrChjI3bv38/mzdvZunSpTLcrBoqayeHDh3S\nmmd87dq1BAUF1UhsDUlhkcLeKHVivT0MbmZXXLZTKxj2DxjaU51cN7Ix/OdrTX2eKIpCcgrsP67u\nyd4Tqe7ZrkiP9vDEAHXC3dqj/nzP1FUN5XtHVw88JlvUb5m3rxOdEMaJxENcvX6hwnIeTVvRwUs9\nXMK7mW+97r21NLeirWcX2np2YVTf58m+k8nZyyeIv3SCs5diuFvw5zfC3YI7HI3fx9H4fVhZ2NCp\nZQ+6tw2kg5dfvX6PakpOTg7z588nJSWFY8eOsXbtWvr27WvssOqVwMBAxo0bx/fff49KpeLcuXOS\nZOtJcbHC7mPw/V7YHl5xMulgB0N6/JlYezStv8mkSqWiVXNo1RymPqp+j46eUY9B/+0oRJ3VLh8Z\nr37MWwvd2iiMeRieGQIt3evveyTqD8kCGqC8glxizkcQefYAiddOl1vGRGVCW88udG3dm86temJv\n26SGo6w9Gjdy5B8dBvGPDoMoLS0hOTWB2KQjxJ6P0BrPnV94l6iEg0QlHKSRdWP82valR7sBtHBt\nXa96+mvSBx98QEqKerYaCwsLua/DQN58802uXbvGnDlz8PPzM3Y4dZqiqIdHbAqBb/fA9Vvll2vu\n8mcPbZ9OYHafmxLrMzMzFYFd1ENhlk6H67cUfgmHrQcgNAqK/nKvesx59WPBeujbReG5IBj7MDSx\nb5jvnaj9ZLhILWSIyzElJcWcvRzDsfj9xF2IpKiksEwZUxMz2rXo9kdi3QNba3u91V8fKYrC5fTz\nxCRGEJN4mJvZ5c/N3bRJc3q0G0CPdv1xtG+qt/rr+2W7Y8eO8dRTT2mer1q1ilGjRhkxorqpvreT\n2uJKusLXu2FziHqmjfJ4NYMxD6sT6390qF3T2NXGdnLrtsIvh+DH/bA7suwNlAAW5jCqLzw3DIJ6\nGf7mz4auNrYTY5LhIg3c9VvXOHx6D8fO7Ccnr+wgQJXKBN8WXQnw7UfnVj2xtrQ1QpR1k0qlwqtZ\nW7yatWVU4ESuZiRz/FwYUQm/k33npqbc9VvX+PXw1/x6+GvaenSmd6chdPHpVStvDq0t8vPzmTt3\nrub5oEGDePTRR40YkRBlFRQqbA9T37AXGlX+VHtuTjB+KIwfDH6+tfOGxdqqib2K54fD88Phdq7C\njkPwzW747RiU/HEvfmER/N9+9cPZASYEKUx7FNp7y/ssjE+S7HqosKiAmMQIDp8OJamC4SDNnb3p\n0X4A/r79aGzrWMMR1j8qlQrPpq3wbNqKR/s8x/mrcUSePUBs4mEKivI15e7NUmJjZUePdv3p3XEI\n7s4VzIfVgKlUKkaNGsWaNWuwtrZm6dKlkpyIWuNMssKGHeohITeyyu63sYIn+qt7VwcFgKmptN0H\nZW+r4pmh8MxQSM9U2BKqvmoQnfBnmRtZsGKL+hHYRWHqSBg7EGyt5f0XxiHDRWqh6l6OuZaRTETc\nHqLOHiCv8G6Z/Y1tHQlo148e7Qbg7uytj1BFJQqK8jmVdJTIswc5ezkG5S9TA97j1awtvTsOwb9t\n3yotetMQLtvFx8dz5coVhg4dauxQ6qwHaSd79+7F1taWXr166TusOuduvsL3e+GzXyDiVNn9KhUM\nDoDnguDxfjUzI4g+1dXPkzPJCptC4Ovd5U+FaGcD44fAC6PAv13d+jepjepqOzGUynJYSbJroao0\n4sLiAmLORxB+MoSLaQll9puoTOjUqge9Ow6hnVd3TE1M9R6v0M2tnBsci9/H4dOhZN4u+21gZWFD\nj3YD6NslCDenFpWeTz7shC6q004KCwv54IMP2LBhA02bNuXXX3/F2bnilQDrs/iLCuu2wVe7yp8d\nxNMVpoyEySOgRR2e07muf56UlCjsiVQP3dkeBsXlLO3Qoz28OBqeHgw2VnX338qY6no70TcZk11P\nXb+VwqFTIRyN38/d/Jwy+50bN6N3xyH07PCwDAepJZrYOTOs5ziG9HiS81dOERG3m5NJRzVLvecX\n3iXs5E7CTu7Ex70DfbsE0cWnd43OvS0EqL84tm3bBsD169eZM2cOX3zxBSYmJkaOrGYUFils+x3W\n/QQHTpTdb2YKjz2knoJuSA8ZDlIbmJqqCOqlvvkxPVPhq13qhPvclT/L3JsO8F+fwPNBCsGPQzsv\n+bcThiNJdh1SUlpC3IVIwk/uIuFKbJn9piZmdGvdmz6dh+LTvCMmqobxhVjXmPxxs6lvi67cybvN\nsfj9RMTt5vqta5oySSlnSEo5QyPrxvTqMIjALsNwsnc1YtSGl5+fj5WVlbHDEICLiwv/+c9/mDRp\nEgBhYWF8+umn/POf/zRuYAZ2OU1h/c/q5OzvqxIC+DSH6Y/BxBHQtIkkZ7WVq6OK156Ffz2jEB4L\n//sZftj/5+wkWTnw8Q/qx8N+6mR7dD8wb6DTKArDkeEitdDfL8fczs3i8OndHDr1G1l/mbXiHid7\nV/p0HkavDgOxs3Go0ViFfiiKwvmrpwg/FcLJpKNllrFXoaJjywD6dhlOO69umKhM6tVlu9jYWKZN\nm8Y777wj46/17EHayQcffMDatWsBMDU1ZcuWLfWivf2VoqhXYlyzFX4Oh9K/3TZhagqjAiH4cfVN\njLVp2j19qk+fJ+W5kaXwxU74dBskXSu7390ZXngMpo8CN+f6+W+sD/W9nVSVjMmug6KiolAUBafm\njQiL3UlM4mHNkIJ7VCoTddLVeRjtvLpLr3U9kp2byZHToUSc2q212M09Lo3dCOwShGWhI5Zm1nX+\nw+727duMHDmSK1fU13UXLlzI5MmTjRxV/fEgX4rFxcWMHz+eqKgo3Nzc+OSTT+rNYjXZdxS+3AVr\nt0LC5bL77yVd0x6F5i71P+lqKMlTaan6R9W6n+DnQ39OBXiPmal6ZpgZY+ChrjLl4t81lHaiKxmT\nXccUFOVzLu04CWnR3Ioou7iJnXVjencaSp9OQ3G0dzFChMLQGts6qsduB4zh9MVowk7u4uylPweG\nZmSnsi1sI6YmZrR07oRrC0c8m7YyYsTVpygKb7zxhibBtrOzY+DAgUaOStxjZmbGqlWr+PDDD1m4\ncCFNmtT9lV9PJSms/lE9G0VuXtn9gwLgn4+rFzhpqKsw1mcmJiqG9IQhPeFahsL/fob12yHtj4vE\nxSXw/T71o1MrmPGEwnPD6t5sMaJ2kJ7sWuL6rRTCT+7i6Jm95U6/19KtHQ91GU7X1n3kRrgG6Pqt\nFMJPhajbR0Fumf3ebr706zKizrWPzZs3s2DBAs3z//73v4wcOdKIEdU/0vMERcUKWw+oh4SElb2d\nBXtb9YInM55ouDfCNeR2Ulik8NNBaR+6aMjtpDx6Gy6yZs0ali9fTmpqKh07dmTlypX07du33LIH\nDx5kxYoVHDt2jOzsbFq3bs3s2bPLvQTckJPs0tISdU9l7E7OXo4ps9/czIIA3/481HU4Hi51s6dS\n6FdBUT7RCWGEndzJtYzkMvvvXekI7DyUJna1+0pHVlYWffv2JTdX/aPh2WefZdmyZUaOqv5pyF+K\n1zIU1m9X3/iWVvZ2lj96KpGeShp2O/krXa50zHgCHg1smFc6pJ1o00uS/d133zFhwgTWrVtHYGAg\nq1evZuPGjcTHx+Ph4VGm/HvvvUdeXh7Dhw/Hzc2NkJAQZs2axaZNm3j66aerFGB9lHM3iyOn93Lo\nVAiZORll9ttZNcG3WQBPDpuIjVUjI0QoajtFUdi1fxsJqVFczkwod8x+51Y96ds5iLYtutTaMfvH\njx9n1qxZ2Nvbs23bNiwtLY0dUr1jqC9FRVG4c+cOdnZ2ej3vg1IUhQPHYe1P8NPvMuZWV5I8aats\nzL6nq3qBm2mPQjOnhtOGpJ1o00uS3atXL7p168a6des029q2bcvYsWN55513dArkqaeeorS0lB9+\n+KFKAdYXiqJwIeUM4SdDyr+RERUdWvrzUJcR5GaUoFKppBGL+7r3Yde2fWsOn95N+KnfyC5n9hkX\nB3cCOw/lH+0HYmttX9NhViorK4ucnBw8PT2NHUq9ZIgvxeLiYt566y1Onz7Nli1baNTI+J0BWTnq\npOjTbXD2Utn9bk4wfTS88Ci4N4AbGatKkqfyVTb7zL0fbcGPQ//u9f9Hm7QTbQ9842NRURHR0dG8\n9tprWtuHDh1KRESEzoHcvn27QX6J5hXcJfLsAQ6dCiH1Ztmfw7ZWdvTqOJi+nYNwaqyeBznqRlRN\nhynqMHtbB4b1HMfggDHEXThGWOxOzl39c93njKwUtoV9wY6Ir/Fr25e+XYbj5dqm1nwZODg44OAg\nU0/WFYqi8NJLL7F7924AgoOD+fzzz7GwsDBKPFHxCmu3wZY9kFdQdn+/burL+4/3l3mQRdWpVCoG\n94DBPdTzqH+6HT77GTKy1Pv/eqNke294cbTC80HgYCdtTejQk52amkrz5s35/ffftcZgL126lG++\n+Yb4+PhKK9mxYwdjxowhIiICf39/rX1//RVw/vz5qsZfKymKws07qZxPP0FyRhzFpUVlyjjbNce3\nmR9eTh0wM607N6qJuiHrbgbn0o6TdP0kRSVlMw9H22a0ce1OS5eOWJjJAjCiavbu3at1ZTMwMJCX\nX365xlaEzM03Yc9xR36KcCb+im2Z/baWJQzvcZMnAjNo7Z5fIzGJhqOwWMW+mCb8GO5CbHLZqzhW\nFiUM6X6L0X1u0Mkrl1rSnyEMoE2bNpq/G2UKv0OHDvHss8/y3//+t0yCXd8UFudzISOO8+knuJVb\ndvo9MxNzWrp0om0zf5waNTNChKKhcLBxoWerYXT3epiLGadJSIsmMzdNsz8zN42jF3YRfTEUL+cO\ntHXtjrNdc4P2bn/77bc4OjoybNgwg9UhasagQYPIyspiy5YtgPpz3sHBgYkTJxqsDSkKxF+24afD\nzuyOdiSv0LRMmTbN7zImMINh/pnYWpWWcxYhHpyFmUJQQCZBAZkkpljxY7gLu6KcuFugbpP5hab8\nctSZX4464+OWx+jeGQzvkYm9TUklZxb1TaVJtrOzM6ampqSnayeN6enpNGt2/0QxPDycRx55hGXL\nljF9+vRKg6mLY3wURSE5NYHDcbs5fj6couLCMmXcnFoQ2DmIHu36Y21Zttfl72TMk9CFru2kN31Q\nlGlcTj9P+KnfOJ4QRlGJup0WlxaRdD2WpOuxuDm1oE+noQS064+tlX5vZvviiy/YunUrANbW1rz6\n6qu1ZrhKfWeozxN/f3/Mzc3ZtGkTAMnJyXTo0AFb28o/46oiK0fh693qS/SxiWX3W1rAuIHqMbG9\nOtqgUnkD3nqNoSGQ753qCQCeHgU5uep2um4bnPxLO01KteY/W1uwekcLnnwYpo2q2zfcSjvR9tfR\nGOWpNMk2NzfH39+fPXv2MGbMGM32PXv2MHbs2AqP+/333xk5ciRLly5l1qxZVQi5bsi6c5PI+AMc\njd/H9Vtl12g1N7Wge9tA+nQaSku3dnX2P5SoH1QqFV7N2uLVrC2PPzSZqISDRJzaTcrNP+8QS715\nmR8Pfsb28C/p3Kon/+gwEN8W3TA1KdtjWBU7duzg7bff1jw/ffo0JSUlmJnJWlh1mUqlYtGiRWRk\nZHD79m3WrVuntwS7pER9s9mXu+Cng5Bftu+CDt7qhGVCEDg1ls9XYVx2tiqCH1ePyT56Gv73C3wX\nCnf/GK2UXwibf1M/WnvAxBHqsduertJ26zOdZhf5/vvvef7551m9ejWBgYGsXbuWjRs3cubMGTw8\nPJg3bx6RkZGEhoYCcODAAUaOHMlLL73EnDlzNOcxNTXF2dlZ69x1aXaRouJCTl04xtEz+zh7OQZF\nKXs50t3Z+4/ewH7YWFbvjnv5pSh08aDtRFEULqWfJ+LUbxw/F05hcdmx241tHenRbgA9OzxMM8eq\n37gcERHB5MmTKSxUZ0l+fn5s3rwZa2vrasUsqs7QnycFBep2o4/pF89dVs8QsikErl4vu9/aUt1r\n/cJj0LtT3e0NrI3ke0f/bucqfLNbPU/7iXNl96tUMDgAJo6A0f3Axqr2t2dpJ9r0sqz6uHHjyMzM\n5ASx6QsAABpjSURBVJ133iE1NZVOnTqxa9cuzRzZaWlpJCf/uTDGl19+SV5eHsuXL2f58uWa7V5e\nXly4cKHaL8YYSpVSklPOEpXwO8fPhZW72p6luRXd2/YlsNNQWtSiWRuEuB+VSoV3s7Z4N2vL4/2m\nEp3wO4dP7+HK9SRNmezcTEKjtxIavRWvZm3p2W4A3doEYmdT+Q9iRVH497//rUmwW7duzWeffSYJ\ndj3zoMn1zWyF/9uvTqwjTpVfplsbmPooPDtUZm0QdYf9H73bwY9D9Fn1Eu5bQuH2H2mEosCeSPXD\n3hbGDVJ4dqh6OImJibTz+kCWVS+Hoiik3Lj4R2Idzq1yFowBaOvRmZ4dBtK1dW8szfU3Q4P8UhS6\nMFQ7SblxkWPx+4mMP0BOXtnxZiYqE9q16Iaf70N08emFlUXFSfPVq1d5/PHHMTU15ccff6R58+Z6\njVVUzlifJ7m5uWzfvp3x48eX6Xi4c1fh53B1whFyRD0N2t85O6iT6onDoVtbSTgMTb53asbdfIVt\nv8OXOyE0Sp1o/51HU3hqEIwfAt3b1q4rNtJOtOltWXVDqU1JdkZWKsfPhROd8DtpmVfKLePU2JV/\ntB9Ij/YDcLJ3NUgc0oiFLgzdTkpKiom/dIKj8fuIuxBZZgElUN970LFVAAG+/Wjv5Y+5WdnpKOPi\n4rCzs8PLy8sgcYr7M8bnSUlJCS+++CJ79+7lySefVC9apjJn9zH4dg9sD/tzrOpfmZnCyED15fPh\nvcDCvPYkF/WdfO/UvCvpCptC1PcenC8/5cC3hTrZHj8E2nga//+DtBNtkmRXIi3zCrGJh4lJPMy1\njORyy9hY2dGtdW8C2vXHx72DwX9VSiMWuqjJdpKbd5voc+EcTwjjQmr5c+NbWljTyTuALq1708Hb\nT69Xd0T1GePz5KuvvmLRokWa543d+nDZZg1ZeeWvONqrIzw9BJ4eDE2bGD+RaIjke8d4FEUh4hR8\nvRv+bz/cyCq/XJfW6kWVxgyAji2N08Mt7USbXsZk1yeKonA14wKxiUeITTxM+q2r5ZazMLOkc6ue\n+Pv2o51XN1kwRjRottb29Os6gn5dR3DzdjrHE8KJPhdGyo2LAOTdKeJcXBr5BXeJPheGuakF7b27\n07V1bzq2DKj2TcCi7rmdq6ByeQqnVqe4eeH/AMhOjcDabBw5jhsoMVMPGergDeOHwvjB0Kq5JNai\n4VKpVAR2gcAusGq2Qmik+orPT79Dbt6f5U4mqh9LNkBbT3i8v8KYAeDfrnYNKRF/ahBJdmFxAeev\nnOL0xWjOJEeRWcEYa1NTM9q16EaAbz86teopPXFClMPJ3pUhPcYwpMcYUm5cYttvW1i9YSN3cwpQ\nAN9ezSgqKeRk0lFOJh3F1MSM1s070qGlPx29/WnaRMZl1zdJVxV+PQw7I+DACSgssgDlfRrbtcAh\n5yMALIrP4cEGnnpuIc8Mgc4+khgI8XfmZiqG9/7/7d17eFTlncDx75nJbXK/ZzJJyI17AiwGVAi2\naAErij7bBUTZbUFb3SqPD9iC5dFgbUuhz9OCiwZ6sdsiLAvW7VYL4oIgSptYIRQwF5JCyAWSyYXc\nIclMZs7+cYYhQyYkashM4Pd5nvc5Z968Z+YXOJn5zXve877wwAxt/Pbev2oJ9/t/g+5eU1mWVcPP\ndmolKQ7mz1B5cCbclzUyZim5XdyySXZTWwNFFccpPl9A2YXTbheJAa3HemJKFlNG383ElGkY/AOH\nOVIhRqauri7efOO/eeONN7DZtDvXzh1r5I4ZGVxWLznb2ew9lFaforT6FP/78X8SExbvSLinkZ6Q\n4XYct/BuFqvKX07DvjwtsS6tctNIUWgNWUFMXCK28z9gYmYWb+/5Af7+kgAIMRiBAQqLvwaLv6Yt\ndrP/E/jjEdiX79rDXV0Hv/qTVvz94N47VObPgAdnQqpJ/t486ZZJsq90d3D2QhFl1acpqz7d742L\nAAa/QDLSpjMlfQYTkqfi5/vl53cV4nbS2NjIwoULqay8tphNSEgIW7duZdasWdQ1X+TU2XxOn/2E\nqnrXZfoaWmv56ORePjq5Fz/fAEYnZDA2aTLjkiYTH52MTtEN968jBqCqKkXn4dBxOHxc661uv9J/\n+6ljr40dnZDyzxQUjGL06NFDMpe2ELejkKBrCXdnt8rBT7WFmt75C7S0X2vXbdFm7Hn/E3huM4wb\npXLfNG0+7tlTISJUku7hNGKTbEtPN+drzjiT6qr6c24Xh7kqLiKRjNQsJqZMI800XsZYC/ElREVF\nkZaW5kyy7777bjZs2EBKSgoAcREJzJu+kHnTF9Lc3khxRQFFFQWUVZ1yWfTGYu2iuKKA4ooCAIIN\nYYxJzGRs0mTGJk0mOswoQwo8QFVVKs2OpLpAK3V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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -999,63 +906,88 @@ } ], "source": [ - "from IPython.html.widgets import interact, interactive, fixed\n", - "from IPython.html.widgets import FloatSlider\n", + "from IPython.html.widgets import interact\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", + " xs = np.arange(5, 15, .1)\n", + " ys = stats.norm.pdf(xs, mu_1, var_1)\n", + " plt.plot(xs, ys, \n", + " label='$\\mathcal{N}'+'({:.1f},{:.1f})$'.format(mu_1, var_1))\n", "\n", - " ys = [stats.gaussian(x, mu_2, var_2) for x in xs]\n", - " plt.plot(xs, ys, label='measure 2')\n", + " ys = stats.norm.pdf(xs, mu_2, var_2)\n", + " plt.plot(xs, ys, \n", + " label='$\\mathcal{N}'+'({:.1f},{:.1f})$'.format(mu_2, var_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", + " ys = stats.norm.pdf(xs, mean, var)\n", " plt.plot(xs, ys, label='product', ls='--')\n", - " plt.ylim(0, 1.5)\n", + " plt.xlim(5, 15);plt.ylim(0, 1.5)\n", " plt.legend();\n", " \n", "interact(plot_products,\n", - " mu_1=FloatSlider(value=5, min=0., max=15), \n", - " mu_2=FloatSlider(value=10, min=0., max=15), \n", - " var_1=FloatSlider(value=1, min=.1, max=5.), \n", - " var_2=FloatSlider(value=1, min=.1, max=5.));" + " mu_1=(5, 10., .5), mu_2=(10, 15, .5), \n", + " var_1=(.1, 2, .1), var_2=(.1, 2, .1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Implementing the Update Step" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "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", + "## Implementing the Update Step\n", "\n", - "In this chapter we use a Gaussian to reflect our 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:" + "The discrete Bayes filter encodes our belief about the position of our dog in an NumPy array. That array stored the belief 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 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 once.\n", + "\n", + "In this chapter we use a Gaussian to reflect our 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. Earlier we concluded that the computation of the posterior should be\n", + "\n", + "```python\n", + "posterior = measurement * prior\n", + "```\n", + "\n", + "We know how to multiply Gaussians. Here is the entire implementation of the update function for a Kalman filter:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { - "collapsed": false + "collapsed": true }, "outputs": [], "source": [ - "def update(mean, var, measurement, measurement_var):\n", - " return multiply(mean, var, measurement, measurement_var)" + "def update(prior, measurement):\n", + " \"\"\" prior and measurements are Gaussian tuples (mu, var)\"\"\"\n", + " \n", + " return multiply(prior[0], prior[1],\n", + " measurement[0], measurement[1])" ] }, { "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." + "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. We represent the Gaussian in a tuple `(mu, var)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1.2, 0.3333333333333333)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "update(prior=(1, 1.), measurement=(1.3, .5))" ] }, { @@ -1077,63 +1009,64 @@ "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 won'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 as I'll answer that shortly. We will create a `DogSimulation` object initialized to be at position 0.0 with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that the belief $\\mathcal{N}(2,\\, 5)$ means that we mistakenly believe the dog is at position 2.0, not 0.0." + "Let's look at an example. Let our initial belief for the dog's position be $\\mathcal{N}(2,\\, 3^2)$. Don't worry about where that number came from as I'll answer that shortly. We will create a `DogSimulation` object initialized to be at position 0.0 with no velocity, and modest noise. This corresponds to the dog standing still at the far left side of the hallway. Note that the belief $\\mathcal{N}(2,\\, 9)$ means that we mistakenly believe the dog is at position 2.0, not 0.0." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "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" + "time: 0 \tposition: -0.664 m \tstd: 1.664 m\n", + "time: 1 \tposition: -1.431 m \tstd: 1.279 m\n", + "time: 2 \tposition: -1.285 m \tstd: 1.078 m\n", + "time: 3 \tposition: -0.371 m \tstd: 0.949 m\n", + "time: 4 \tposition: -0.142 m \tstd: 0.857 m\n", + "time: 5 \tposition: 0.267 m \tstd: 0.788 m\n", + "time: 6 \tposition: 0.061 m \tstd: 0.733 m\n", + "time: 7 \tposition: -0.003 m \tstd: 0.688 m\n", + "time: 8 \tposition: 0.072 m \tstd: 0.651 m\n", + "time: 9 \tposition: -0.109 m \tstd: 0.619 m\n", + "time: 10 \tposition: -0.118 m \tstd: 0.591 m\n", + "time: 11 \tposition: -0.071 m \tstd: 0.567 m\n", + "time: 12 \tposition: -0.112 m \tstd: 0.545 m\n", + "time: 13 \tposition: -0.112 m \tstd: 0.526 m\n", + "time: 14 \tposition: -0.060 m \tstd: 0.509 m\n", + "time: 15 \tposition: -0.094 m \tstd: 0.493 m\n", + "time: 16 \tposition: -0.231 m \tstd: 0.479 m\n", + "time: 17 \tposition: -0.050 m \tstd: 0.466 m\n", + "time: 18 \tposition: -0.065 m \tstd: 0.454 m\n", + "time: 19 \tposition: -0.115 m \tstd: 0.442 m\n" ] } ], "source": [ - "dog = DogSimulation(velocity=0., measurement_var=5, process_var=0.0)\n", - "pos, var = 2, 5\n", + "dog = DogSimulation(velocity=0., measurement_var=4, process_var=0.0)\n", + "pos = (2, 9) # Gaussian N(2, 9)\n", "for i in range(20):\n", " dog.move()\n", - " pos, var = update(pos, var, dog.sense_position(), 5)\n", + " pos = update(pos, (dog.sense_position(), 4))\n", " print('time:', \"%2d\" % i, \n", - " '\\tposition:', \"%.3f\" % pos, \n", - " '\\tvariance:', \"%.3f\" % var)" + " '\\tposition:', \"%.3f m\" % pos[0], \n", + " '\\tstd:', \"%.3f m\" % sqrt(pos[1]))" ] }, { "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 to near 0 m despite the initial error of believing that the position was 2.0 m. Furthermore, the variance should have converged from the initial value of 5.0 to 0.238.\n", + "Because of the random numbers I do not know the exact values that you see, but the position should have converged to near 0 m despite the initial error of believing that the position was 2.0 m. Furthermore, the standard deviation should have converged from the initial value of 3.0 m ($3^2 = 9$) to 0.442 m.\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", + "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 standard deviation became 0.442 m despite every measurement having a std of 2.0 m.\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", + "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 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." ] @@ -1142,14 +1075,125 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Implementing Predictions" + "## Kalman Gain\n", + "\n", + "Lets examine the math to better understand what is happening. The posterior mean is:\n", + "\n", + "$$\n", + "\\mu=\\frac{\\bar\\sigma^2\\, \\mu_z + \\sigma_z^2 \\, \\bar\\mu} {\\bar\\sigma^2 + \\sigma_z^2}\n", + "$$\n", + "\n", + "We can rewrite this as:\n", + "\n", + "$$\\mu = \\left( \\frac{\\bar\\sigma^2}{\\bar\\sigma^2 + \\sigma_z^2}\\right) \\mu_z + \\left(\\frac{\\sigma_z^2}{\\bar\\sigma^2 + \\sigma_z^2}\\right)\\bar\\mu$$\n", + "\n", + "In this form it is easy to see that we are scaling the meaurement and the prior by weights: \n", + "\n", + "$$\\mu = w_1 \\mu_z + w_2 \\bar\\mu$$\n", + "\n", + "\n", + "The weights sum to one because the denominator is a normalization term. We introduce a new term, $K$, giving us:\n", + "\n", + "$$\\begin{aligned}\n", + "\\mu &= K \\mu_z + (1-K) \\bar\\mu\\\\\n", + "&= \\bar\\mu + K(\\mu_z - \\bar\\mu)\n", + "\\end{aligned}$$\n", + "\n", + "\n", + "$K$ is the *Kalman gain*. It's the crux of the Kalman filter. It is a scaling term that chooses a value partway between $\\mu_z$ and $\\bar\\mu$.\n", + "\n", + "Let's work a few example. If the measurement is nine times more accurate than the prior, then $\\bar\\sigma^2 = 9\\sigma_z^2$, and\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\mu&=\\frac{9 \\sigma_z^2 \\mu_z + \\sigma_z^2\\, \\bar\\mu} {9 \\sigma_z^2 + \\sigma_\\mathtt{z}^2} \\\\\n", + "&= \\left(\\frac{9}{10}\\right) \\mu_z + \\left(\\frac{1}{10}\\right) \\bar\\mu\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Hence $K = \\frac 9 {10}$, and to form the posterior we take nine tenths of the measurement and one tenth of the prior.\n", + "\n", + "If the measurement and prior are equally accurate, then $\\bar\\sigma^2 = \\sigma_z^2$ and\n", + "\n", + "$$\\mu=\\frac{\\sigma_z^2\\, (\\bar\\mu + \\mu_z)}{2\\sigma_\\mathtt{z}^2}\\\\\n", + "= \\left(\\frac{1}{2}\\right)\\bar\\mu + \\left(\\frac{1}{2}\\right)\\mu_z$$\n", + "\n", + "which is the average of the two means. It makes intuitive sense to take the average of two equally accurate values.\n", + "\n", + "We can understand this by looking at this chart:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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++eYbnWNW5Y1XRKdOneDk5ISdO3dq5ETn5+dj9erVUCqVZc6qF3fy5EkYGxuj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\nEEIIB5DEWgghhBBCCAf4P7wHyjrjStCIAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mkf_internal import show_residual_chart\n", + "show_residual_chart()" ] }, { "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. The discrete Bayes filter used a loop of predict and update functions, and we must do the same to accommodate movement.\n", + "The Kalman gain $K$ is a scale factor that chooses a value along the residual.\n", + "\n", + "This leads to an alternative but equivalent implementation for `update`:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def update(prior, measurement):\n", + " x, P = prior # mean and variance of prior\n", + " z, R = measurement # measurement and measurement noise\n", + " \n", + " y = z - x # residual\n", + " K = P / (P + R) # Kalman gain\n", + "\n", + " x = x + K*y\n", + " P = (P * R) / (P + R)\n", + " return x, P # posterior mean and variance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Why have I written it in this form, and why have I chosen these terrible variable names? A few related reasons. This is the form that the Kalman filter that is presented in most books and papers. My derivation of the filter from Bayesian principles is not unknown, but it is not used nearly as often as this form. The equations for the multivariate Kalman filter look almost exactly like these equation. So, you need to learn and understand them. \n", + "\n", + "This also a powerful way to think about the filter. It emphasizes taking the residual ($y = \\mu_z - \\bar\\mu$), finding the Kalman gain, and computing the posterior by adding $Ky$ to the prior. The Bayesian aspect is obscured in this form, as is the fact that this is multiplying the likelihood by the prior. Both viewpoints are equivalent because the math is identical. I chose the Bayesian approach because I think it give a much more intuitive yet deep understanding of the probabilistic reasoning. This form gives a deep understanding of what is known as the *orthogonal projection* approach. Dr. Kalman used that derivation, not Bayesian reasoning, when he invented this filter. You will understand more of what I mean in the next few chapters.\n", + "\n", + "Where do `P` and `R` come from? You will see them used in the rest of this book. $R$ is nearly universally used to express the measurement noise, and $P$ is the variance of the system. In the remainder of the book these are *covariances*, not variances, and we will learn about those in the next chapter. Every book and paper you read will use these variable names." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Implementing Predictions\n", + "\n", + "That is a beautiful result, but it is not yet a filter. We assumed that the dog was sitting still, a dubious assumption. 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", @@ -1165,11 +1209,11 @@ " return result\n", "```\n", "\n", - "In a nutshell, we shift the probability array by the amount we believe the dog moved, and adjust the probability. How do we do that with Gaussians?\n", + "In a nutshell, we shift the probability array by the amount we believe the dog moved, and added the probability of the movement. 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. 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", + "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 the right, where is he now? Obviously, 7.3 + 2.6 = 9.9. I think he is at 9.9 meters. 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", + "How is addition for Gaussians performed? It's 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)$$\n", "\n", @@ -1179,50 +1223,74 @@ "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n", "$$\n", "\n", - "We can make this more meaningful by changing the subscripts.\n", + "We can make this Bayesian by changing the notation:\n", "\n", "$$\\begin{aligned}\n", - "\\mu_\\mathtt{after} &= \\mu_\\mathtt{before} + \\mu_\\mathtt{movement} \\\\\n", - "\\sigma^2_\\mathtt{after} &= \\sigma^2_\\mathtt{before}+ \\sigma^2_\\mathtt{movement}\n", + "\\bar\\mu &= \\mu + \\mu_\\mathtt{movement} \\\\\n", + "\\bar\\sigma^2 &= \\sigma^2 + \\sigma^2_\\mathtt{movement}\n", "\\end{aligned}$$\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", + "$\\mu$ is the old position, and ${\\mu}_\\mathtt{movement}$ is how far we moved. Surely it makes sense that our new position is $\\mu + \\mu_\\mathtt{movement}$.\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", + "Where does $\\mathcal{N}(\\mu_\\mathtt{movement}, \\sigma^2_\\mathtt{movement})$ come from? It is computed from the process model. If we think the dog is moving 1 m/s to the right, over 1 second, then $\\mu_\\mathtt{movement} = 1\\cdot1=1$. If we think the standard deviation of the error in our prediction is 0.2 m, then $\\sigma^2_\\mathtt{movement}=0.2^2 = 0.04$.\n", "\n", - "So, here is our implementation of the predict function:" + "\n", + "The equation for Gaussian addition is derived by basic algebra. I assure you it is correct. 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", + "Here is our implementation of the predict function, where `pos` and `movements` are Gaussian tuples:" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "def predict(pos, variance, movement, movement_variance):\n", - " return (pos + movement, variance + movement_variance)" + "def predict(pos, movement):\n", + " return (pos[0] + movement[0], pos[1] + movement[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1.5, 0.14)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "predict(pos=(1.3, 0.1), movement=(0.2, 0.04))" ] }, { "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. " + "What is left? Just calling these functions. The discrete Bayes filter did nothing more than loop over the `update()` and `predict()` functions, and we do the same. " ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 22, "metadata": { "collapsed": false, - "scrolled": false + "scrolled": true }, "outputs": [ { @@ -1244,30 +1312,23 @@ "final estimate: 15.053\n", "actual final position: 14.838\n" ] - }, - { - "data": { - "image/png": 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3vwEQExPj/O/x+eefM2zYMO6++27i4uLYtGkT27Zto3Hjxjf9/mXI5LH4+Hjn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\noUIFQnM4PP223/Dxf2HOSjibzsKqJcO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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ "import kf_internal\n", "\n", "np.random.seed(13)\n", - "pos = (0., 400.) # Gaussian N(0, 400)\n", - "velocity = 1.\n", "\n", "# variance in process model and the RFID sensor\n", "process_var = 1.\n", "sensor_var = 2.\n", "\n", - "dog = DogSimulation(pos[0], velocity, sensor_var, process_var)\n", + "pos = (0., 400.) # Gaussian N(0, 400)\n", + "process = (1, process_var) # N(velocity, var)\n", + " \n", + "dog = DogSimulation(x0=pos[0], velocity=process[0], \n", + " measurement_var=sensor_var,\n", + " process_var=process[1])\n", "\n", "# simulate dog and get measurements\n", "N = 10\n", @@ -1275,17 +1336,38 @@ "\n", "positions, predictions = [], []\n", "print('PREDICT: x var\\t UPDATE: x var z')\n", - "for i, z in enumerate(zs):\n", - " pred_pos = predict(pos[0], pos[1], velocity, process_var)\n", - " predictions.append(pred_pos[0])\n", "\n", - " pos = update(pred_pos[0], pred_pos[1], z, sensor_var)\n", + "for i, z in enumerate(zs):\n", + " prior = predict(pos, process)\n", + " pos = update(prior, measurement=(z, sensor_var))\n", + "\n", + " predictions.append(prior[0])\n", " positions.append(pos[0])\n", - " \n", - " kf_internal.print_gh(pred_pos, pos, z)\n", + " kf_internal.print_gh(prior, pos, z)\n", "print()\n", "print('final estimate: {:10.3f}'.format(pos[0]))\n", - "print('actual final position: {:10.3f}'.format(dog.x))\n", + "print('actual final position: {:10.3f}'.format(dog.x))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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oET4+PnTv3p3z58/bHo0aNSI4OJg1a9bYynp6egLWn82XLl3i/PnzREdHY7FY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\nzz1oYngvE+2bmUodKHMZnp4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IrOVn7Yns3Nr69aZ6+bb9SEmF9+dBVhYA1S9/8y+/wIsv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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ "bp.plot_filter(positions)\n", "bp.plot_measurements(zs)\n", "bp.plot_predictions(predictions)\n", @@ -1301,16 +1383,16 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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AWEf5+/tj+/btJrd/8803Fj9YiCPWREREVGMCAwMhhICjoyPCw8PN2qdt27Zo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\nYA4YMACXLl3Czp07kZaWhpSUFKxZswY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++eYbnWNW5Y1XRKdOneDk5ISdO3dq5ETn5+dj9erVUCqVZc6qF3fy5EkYGxuj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\nA5s3yyXn+vYt+3x/f+D2bWDtWt3H795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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1318,7 +1400,6 @@ } ], "source": [ - "from mkf_internal import show_residual_chart\n", "show_residual_chart()" ] }, @@ -1326,96 +1407,90 @@ "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 process model. We then make a measurement. The difference between the measurement and the prediction is called the *residual*. 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. That scaling depends on the variance of the measurement vs the variance of the process model. 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", + "At each predict step we take our existing estimate and update it based on our process model, giving the prior. We then take a measurement. The difference between the measurement and the prior is the *residual*. We know neither the measurement or prior is perfect, so we choose a value between the two. This is scaled so that the new estimate is closer to the one we trust more. That scaling depends on the variance of the measurement vs. the variance of the process model. We then step forward in time and the process repeats. The plotted output shows the prediction and measurement for each epoch; the filter's estimate always lies between the two.\n", "\n", - "```python\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", - "```python\n", - "velocity = 1.\n", - "```\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 subsequent chapters 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", + "Now let's walk through the code.\n", "\n", "```python\n", "process_var = 1.\n", "sensor_var = 2.\n", "```\n", - " \n", - "Here the variance for the predict step is `process_var` and the variance for the sensor is `sensor_var`. 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", + "These are the variances for the process model and sensor. The meaning of sensor variance should be clear - it is how much variance there is in each measurement. 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 hobbyist 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 variance is 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.\n", + "\n", "\n", "```python\n", - "dog = DogSimulation(pos[0], velocity, sensor_var, process_var)\n", - "zs = [dog.move_and_sense() for _ in range(N)]\n", + "pos = (0., 400.) # Gaussian N(0, 400)\n", + "```\n", + "\n", + "This is the dog's initial position expressed as a Gaussian. The position is 0 meters, and 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", + "```python\n", + "process = (1, process_var) # N(velocity, var)\n", + "```\n", + "\n", + "This is the process model. I set the velocity to one, and the variance to `process_var`.\n", + "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 subsequent chapters 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", + "Next we initialize the simulator\n", + "\n", + "```python\n", + "dog = DogSimulation(x0=pos[0], velocity=process[0], \n", + " measurement_var=sensor_var,\n", + " process_var=process[1])\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", + "It may seem overly 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. \n", "\n", - "It is traditional to label the measurement $z$, and so I follow that convention here. When I was learning this topic I found the standard variable 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. This is a common convention with mathematical Python code.\n", + "We move the dog for 10 steps forward and store the measurements in `zs` via a list comprehension.\n", + "\n", + "```python\n", + "zs = [dog.move_and_sense() for _ in range(N)]\n", + "```\n", + "\n", + "It is traditional to name the measurement $z$, and so I follow that convention here. When I was learning this topic I found the standard variable 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`. You just have to memorize the notation you want to work with Kalman filters. As we continue I will introduce more of the standard variable names. The `s` at the end of the name is a plural - I'm saying there are many `z`s in the list. This is a common convention with mathematical Python code.\n", "\n", "The next line allocates an array to store the output of the filtered positions. \n", "\n", "```python\n", "positions = np.zeros(N)\n", - "```" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "```\n", + "\n", "Now we enter our `predict() ... update()` loop.\n", "\n", "```python\n", - "for i in range(N):\n", - " pred_pos = predict(pos[0], pos[1], vel, process_var)\n", - " pos = update(pred_pos[0], pred_pos[1], z, sensor_var)\n", - " positions.append(pos[0])\n", + "for i, z in enumerate(zs):\n", + " prior = predict(pos, process)\n", + " pos = update(prior, measurement=(z, sensor_var)))\n", "```\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_var' is the mean and variance for the movement. \n", + "We call the `predict()` function with the Gaussian for the dog's position, and another Gaussian describing his movement. This computes the prior. The prior and the measurement Gaussian is then passed into `update()` to generate the new posterior, which I store in `pos`.\n", "\n", - "The first time through the loop I get `pred_pos = (1.0, 401.0)`, as can be seen in the printed table.\n", + "The first time through the loop `prior` is `(1.0, 401.0)`, as can be seen in the printed table.\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", + "What is this saying? After the prediction, we believe that we are at 1.0, and the variance is now 401, up from 400. The variance got worse, which is what always happens during the prediction step because it involves a loss of information.\n", "\n", - "Then we call the update function of our filter, using `pred_pos` as the current position and save the result in our `positions` array.\n", + "Then we call the update function using `prior` as the current position.\n", "\n", "For this I get this as the result: `pos = (1.352, 1.990), z = 1.354`.\n", "\n", - "What is happening? The dog is actually at 1.0 but the measured position is 1.354 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 1.352 - 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", + "What is happening? The dog is actually at 1.0 but the measured position is 1.354 due to sensor noise. That is pretty far from the predicted value of 1. The variance of the prior is 401 m$^2$. A large variance implies that confidence is very low, so the filter estimates the position to be 1.352 - 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: 1.99 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. However, the previous belief does contain a bit of useful information, so our variance is now slightly smaller than 2.0, which is the variance of the measurement alone.\n", + "Now look at the variance: 1.99 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 the prior. However, the previous belief does contain a bit of useful information, so our variance is now slightly smaller than 2.0.\n", "\n", "Now the software loops, calling `predict()` and `update()` in turn. By the end the final estimated position is 15.053 vs the actual position of 14.838. 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", + "Now look at the plot. The noisy measurements are plotted with black circles, and the filter results are drawn with a solid blue line. Both are quite noisy, but notice how much noisier the measurements are. I plotted the prediction (prior) with red triangles. The estimate always lies between the prior and the measurement. 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", + "The filtering is implemented in only a few lines of code. 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", "```python\n", "for i in range(N):\n", " pos = predict(pos[0], pos[1], vel, process_var)\n", " pos = update(pos[0], pos[1], z, sensor_var)\n", "```\n", - "If we didn't use pre-written functions the the code would be:\n", + "\n", + "If we didn't use the `predict` and `update` functions the code might be:\n", "\n", "```python\n", "for i in range(N):\n", @@ -1425,22 +1500,17 @@ "\n", " # update\n", " pos = (var*vel + process_var*pos) / (var + process_var)\n", - " var = 1 / (1/var + 1/process_var)\n", + " var = (var * process_var) / (var + process_var)\n", "``` \n", "\n", - "Just 4 lines of very simple math implements the entire filter!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "Just 5 lines of very simple math implements the entire filter!\n", + "\n", "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": 20, + "execution_count": 25, "metadata": { "collapsed": false }, @@ -1459,9 +1529,9 @@ }, { "data": { - "image/png": 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fej+orVu3MXPmzBzrGjZsSO/e4Sh3rDR0Z6ZslbOXPDkT68XpWG+i4zxxdTHT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UrFkdd3f7M8Jzz73FiBHPEhoaCCg8+GBfFiz4mBo1ouCH2XzfsD0d6jxIbS0C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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1472,17 +1542,18 @@ "process_var = 2\n", "sensor_var = 4.5\n", "pos = (0, 400) # gaussian N(0, 400)\n", + "process = (1, process_var)\n", "N = 25\n", "\n", - "dog = DogSimulation(pos[0], velocity, sensor_var, process_var)\n", + "dog = DogSimulation(pos[0], process[1], sensor_var, process_var)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", "positions, predictions = np.zeros((N, 2)), np.zeros((N, 2))\n", "for i, z in enumerate(zs):\n", - " pos = predict(pos[0], pos[1], velocity, process_var) \n", - " predictions[i] = pos\n", + " prior = predict(pos, process) \n", + " predictions[i] = prior\n", " \n", - " pos = update(pos[0], pos[1], z, sensor_var)\n", + " pos = update(prior, (z, sensor_var))\n", " positions[i] = pos\n", "\n", "bp.plot_measurements(zs)\n", @@ -1496,14 +1567,9 @@ "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 one dimensional Kalman filter. \"One dimensional\" just refers to the fact we are tracking one variable. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the 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 we have more data to work with." + "Here we can see that the variance converges to 2.163 in 9 steps. This means that we have become very confident in our position estimate. It is equal to $1.47\\sigma$ meters. Contrast this to the sensor's $2.12\\sigma$ meters. The first few measurements are unsure due to our uncertainty of the initial position, but the filter quicly converges to an accurate estimate.\n", + "\n", + "This code fully implements a Kalman filter. If you have tried to read the literature you are perhaps surprised, because this looks nothing like the endless pages of math in those books. So long as we worry about *using* the equations rather than *deriving* them we can create Kalman filters the topic is approachable. Moreover, I hope you'll agree that you have a decent intuitive grasp of what is happening. We represent beliefs with Gaussians, and they get better over time because more measurements means we have more data to work with." ] }, { @@ -1531,98 +1597,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Tracking Animation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "### KF Animation\n", + "\n", "If you are reading this in a browser you will be able to see an animation of the filter tracking the dog directly below this sentence.\n", - "" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "\n", + "\n", "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 **g-h Filter** chapter and this plot:" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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TsX//fkybNg2RkZHw9fWFra0tkpKScODAAdSuXRsHDhxQl+/Tpw+USiUuXryI\nV199Vb3ew8MDDRo0wPnz59G9e3dYWVnp9dgPHjyAk5MTBg0ahI4dO6J+/fr4888/sWLFCtStWxcD\nBw4EIL2YU6lUYt68eUhNTYWVlRWaNm0KLy+vSl2re/fulXsew4YNQ0hICPz9/fHyyy8jPT0dmzdv\nhrm5udZ9l1XHisajOKVSiZdffhnbt29HXl4ezMzMAAArV67EpEmT1C8stbS0VN9t37Fjh8ad/GHD\nhuHMmTPo378/xo4dW+IYWVlZiImJKfMJQmXZ2tpizpw5OHHihNaED5CeAoWGhsLW1lbvx6fqo3MC\ncO/ePRw9ehTnz5/HvXv3oFAo4OjoCA8PD/To0QOOjo6GrCc9ZdjIkQ/GQh4YB/nQRyzK6mZSdJup\nqSl27dqF5cuXY+PGjQgNDQUgDX718vJCcHCwxmfr1KmDDh06ID4+Hn379tXY5uvri82bN5dYX5qK\nHNvS0hLvv/8+Dhw4gAMHDiAzMxNOTk4YMmQIPvroI3VXFRcXF6xbtw4LFizAxIkTkZeXh+DgYHUC\noO26lHatFAqF1sG4xT8zbdo0AMCaNWvw3nvvoUGDBhg5ciReffVVtGrVqsT+y6pjReOhzYQJE7Bh\nwwb8+uuveOmllwAAPXr0wOjRo7Flyxa0b98eK1euxLRp0+Dq6oqmTZtizJgxGvs4dOgQXnnlFa37\n//HHH/Hw4UOMHz++3LpUlEKhgJeXF/bs2YPQ0NAS3aj8/f0xa9YsdO3a1ehvdKaqUYgyUu/c3Fxs\n2rQJ69atw5EjR0rN0hUKBbp3747XXnsNgYGBsLCwMFiFq6poRmtnZ2fEmhAREdHTKCAgANnZ2YiO\njq7wZ3Nzc+Hu7o6//voL9+7dK3GDtVOnTnBzc8PWrVv1Vd0ShBDIyMjAsWPHEBAQAECabfHvv/+G\nra0tG/9Gos82bKljAFasWIFmzZphwoQJqFOnDhYvXozDhw/j5s2bePjwIbKzs/HPP//g8OHD+Oqr\nr+Dg4ICJEyfCzc0NK1eurFKliIiIiJ5UX3zxBY4dO4aIiIgKf/bs2bNo164dAGmAc1Hbt2/H+fPn\nsWDBAr3UszQKhQJ2dnYaXbdMTU1hZ2fHxv9TotQnAC4uLvjggw/w2muv6ZxlpKenY82aNVi8eDGS\nkpL0WlF94RMAeWB/Z/lgLOSBcZAPxkIeamoc0tLSMG7cOPj7+6N///5GnW0nNTUVdevWBSC9f6E6\nB3dTSfpt2Bk0AAAgAElEQVRsw5aaABQdvFJRVfmsoTEBICIiIiofEwB5qZYuQFVpwMu18U9ERERE\nVNPp/B6AO3fuID4+XmPdxYsXMX78eIwYMQLbtm3Te+WIiIiIiEi/dJ4GdNKkSUhOTsahQ4cASI+F\nevXqhbS0NNSuXRs//vgjtm/fzrfvkk5qat9OOWIs5IFxkA/GQh4YByLDKXMa0KIaNWqESZMmISQk\nBACwZMkSfPjhh4iPj0fLli3Rt29fKBSKSk15VZ04BoCIiIiofBwDIC/VMgaguJSUFDg5OamXd+7c\niV69eqFNmzYwMzPDyJEjkZCQUKXKEBERERGRYemcADg4OODWrVsAgOzsbBw5cgQDBgxQb1coFMjJ\nydF/DYmIiIiISG90HgPg7e2N5cuXw8PDA3v27MGjR48waNAg9fZLly6hUaNGBqkkPX3Yt1M+GAt5\nYBzkg7GQB8aByHB0HgNw9epVDBgwANeuXQMAfPjhh/j8888BAAUFBWjSpAmef/55rFq1ynC11QOO\nASAiIiIqH8cAyIs+27A6PwFwc3PDpUuXcP78edja2sLV1VW9LTs7G8uWLUP79u2rVBkiIiIiIjIs\nnZ8APC34BICIiIiofHwCIC9GeQIAAPn5+QgLC8Ovv/6K69evAwBcXV3x4osvIigoCKamFdod1WDs\n2ykfjIU8MA7ywVjIA+NAZDg6zwKUnJyMLl264I033kBUVBQUCgUUCgWioqLwxhtvwNPTE3fu3Klw\nBWJiYjB48GA4OztDqVQiLCysRJnExEQMHToU9vb2sLKygqenJy5dugQAuH//Pt599114eHjA0tIS\njRs3xsSJE5mlypynpye/1GWCsZAHxkE+GAt5YByIDEfnBOCdd97B+fPnsWbNGty9exdxcXGIi4vD\n3bt38e233+LChQt49913K1yBzMxMtG3bFkuWLIGlpWWJ7devX4e3tzfc3NwQFRWFhIQEzJ07F9bW\n1gCAmzdv4ubNm1i0aBHOnTuHTZs24dChQxg9enSF60JERERE9LTTeQyAra0txo8fr575p7gPP/wQ\nq1evRkZGRqUrY2Njg2XLliEoKEi9LjAwEEqlEhs3btR5P7t378bAgQORlpamThRUOAaAiIiIqHwc\nAyAvRnkTsIWFBZo0aVLq9qZNm6JWrVpVqkxxQgjs3LkTrVq1QkBAAOrXrw8vLy9s2bKlzM+lp6fD\nwsJC6xMFkofY2Fh1/04yLsZCHhgH+WAs5IFxIDIcnROAESNGYPPmzcjLyyuxLTc3F5s3b8aIESP0\nWrnk5GRkZmZi/vz58Pf3R0REBEaNGoXAwEDs3r1b62fS0tLwySefYNy4cVAqdTu94l8wXDb8ctG+\nnXKoT01eBjQH2Rm7PjV1WfU3IZf61ORlfj/JY1lb/3851a8mLMfHx8uqPjV9WZ9Knbbn5MmTGsv/\n+c9/EBMTgy5duuCtt95C8+bNAQCXL1/GypUrAQDDhg3Ta+UKCwsBAEOGDMHkyZMBAO3atUNsbCyW\nLl2KgIAAjfJZWVkYOHAgXFxcsGDBAr3WhYiIiIjoaVDqGAClUgmFQqGxrmhR1bbi6woKCipdmeJj\nAPLy8mBlZYXQ0FCEhISoy82dOxfh4eE4e/asel1WVhYCAgKgVCqxa9euUrv/cAwAERERUfk4BkBe\nquU9AOvWravSjvXBzMwMXbp0UU/5qZKYmKgxHiEzMxMBAQFQKBRlNv5JPop2eyDjYizkgXGQD8ZC\nHhgHIsMpNQEIDg6ulgpkZWXhypUrEEKgsLAQSUlJOH36NBwcHODi4oJp06ZhxIgR8Pb2hq+vLyIj\nIxEeHo7t27cDkBr//fv3R2ZmJn755Rc8ePAADx48AAA4ODjAzMysWs6DKoZf6PLBWMgD4yAfjIU8\nMA5EhqPzNKCGEh0dDR8fnxLdjYKDg7F27VoAQFhYGObNm4cbN27A3d0dISEhGD58uPrzvr6+Gp8V\nQkChUODgwYPo1auXxjZ2ASIiIiIqH7sAyYs+27ClJgBz5syp+M4UCsycObNKFTI0JgBERERE5WMC\nIC/VkgDoOoWmxs6qOAi4OjABkAf27ZQPxkIeGAf5YCzkgXEwPiYA8lItCcDTigkAERERUfmYAMiL\nUd4ETERERERETz4mAERERERENUipCUDv3r2xb9++Cu9w79696N27d5UqRU+/2NhYg77imnTHWMgD\n4yAfjIU8MA5EhlPqewDatWuHQYMGoWHDhhg+fDj69esHT09P1KlTR6Pc/fv3ERcXh/3792Pr1q24\ndesWxo0bZ/CK05ONg7rkg7GQB8ZBPhgLeWAciAynzEHA169fx9dff41Nmzbh3r17UCgUsLOzg729\nPYQQuH//PjIyMiCEQL169fDKK6/g3XffRePGjavzHCqEg4CJiIiIysdBwPJS7bMA5efnIyYmBseO\nHcPFixeRkpICAHB0dISHhweee+45dO/eHaampT5QkA0mAERERETlYwIgL5wGtAqYAMgD53eWD8ZC\nHhgH+WAs5IFxMD4mAPLCBKAKmAAQERERlY8JgLzwPQBERERERFQpTACIiIiIiGoQJgBkFJzfWT4Y\nC3lgHOSDsZAHxoHIcDgGgIiIiIhK4BgAeeEYACIiIiIiqhSdEwATExN8//33pW4PDw+HiYlJhSsQ\nExODwYMHw9nZGUqlEmFhYSXKJCYmYujQobC3t4eVlRU8PT1x6dIl9fbVq1fD19cX9vb2UCqVSEpK\nqnA9iIiIiIhqAp0TgPJ6ChUWFkKhUFS4ApmZmWjbti2WLFkCS0vLEtuvX78Ob29vuLm5ISoqCgkJ\nCZg7dy6sra3VZbKzs+Hn54fZs2dXqg5U/di3Uz4YC3lgHOSDsZAHxoHIcCr06t6yGtcnTpyAvb19\nhSsQEBCAgIAAAEBwcHCJ7TNmzICfnx8WLlyoXufq6qpRZvLkyQCAuLi4Ch+fjIMvdpEPxkIeGAf5\nYCzkgXEgMpwynwB8/fXXaNasGZo1awYAeO+999TLRX8cHBzwv//9Dy+++KJeKyeEwM6dO9GqVSsE\nBASgfv368PLywpYtW/R6HCIiIiKimqLMBKB+/fpo3bo1WrduDQBo1KiReln106ZNG/Ud+uXLl+u1\ncsnJycjMzMT8+fPh7++PiIgIjBo1CoGBgdi9e7fejlP8ESOXucxlLnOZy1zmck1fjo+Pl1V9avqy\nPpXZBWjUqFEYNWoUAMDHxwcff/wx+vbta7DKFFdYWAgAGDJkiLqbT7t27RAbG4ulS5equw7Rk0f1\nHzUf8cpDbGwsY2Fkhvyip4rh95M88G+CyHBk9R4AGxsbLFu2DEFBQQCAvLw8WFlZITQ0FCEhIepy\nc+fORXh4OM6ePavx+bi4OHh5eeHatWto3Lix1mPwPQBERERE5eN7AORFn23YCg0CBoDz58/jzz//\nxP3797XODKRqvOuDmZkZunTpojHlJyBNC9qkSRO9HYeIiIiIqKbQOQG4evUqxowZg5MnT5Y6JahC\noahwApCVlYUrV65ACIHCwkIkJSXh9OnTcHBwgIuLC6ZNm4YRI0bA29sbvr6+iIyMRHh4OLZv367e\nx507d3D79m1cunQJQggkJCTg/v37aNy4caVmJiIiIiIielrp3AWoX79+OH78OD777DP07Nmz1IZ1\nRe/MR0dHw8fHp8QUo8HBwVi7di0AICwsDPPmzcONGzfg7u6OkJAQDB8+XF129uzZWt8BsG7duhIJ\nCbsAyQP72MoHYyEPjIN8MBbywDgYH7sAyYs+27A6JwC1a9dGSEgIZs6cWaUDGhsTACIiIqLyMQGQ\nF322YXV+E7CjoyMbzERERERETzidE4AJEybgu+++Q0FBgSHrQ0REREREBlTqIODib9t1c3NDfn4+\n2rVrh+DgYLi4uMDExKTE54r2zScqDft2ygdjIQ+Mg3wwFvLAOBAZTqljAJRKJRQKhXrGn6L/LnVn\nCoXsnxBwDAARERFR+TgGQF6q5T0ABw8erNKOiYiIiIhIfkpNAHr37l2d9SAiIiIiomqg8yBgIn2K\njY1V9+8k42Is5IFxkA/GQh4YByLD0fk9AL6+vmXvSKFArVq14OzsDB8fHwwbNgympjq/aLjacAwA\nERERUfk4BkBeqmUMQHGFhYX4559/cPXqVdjb28PV1RUAcP36ddy/fx/NmzeHnZ0dTpw4gdWrV+P/\n/u//EBERAUdHxypVkIiIiIiI9EfnLkCffvopUlNTsWHDBiQnJyMuLg5xcXFITk7GunXrkJqaisWL\nF+Pu3btYu3YtEhISMH36dEPWnYiIiIiIKkjnLkDdunVDr169sHDhQq3bp06dikOHDuHEiRMAgPHj\nx2Pnzp24efOm/mqrB+wCJA+c31k+GAt5YBzkg7GQB8bB+NgFSF6M0gXozJkzeOWVV0rd3qRJE5w9\ne1a93LlzZ2zYsKFKlaOnF7/Q5YOxkAfGQT4YC3lgHIgMR+cuQE5OTti6davWF30VFBRgy5YtaNCg\ngXpdSkoKHBwc9FNLIiIiIiLSC52fAHzwwQd455130K1bN7z55ptwc3MDAFy5cgWrV69GfHw8lixZ\noi6/detWeHl56b/GRERERERUaTonAJMmTYJSqcQnn3yCt956CwqFAgAghEDdunWxZMkSTJo0CQDw\n6NEjfPXVV+qZgoiKY99O+WAs5IFxkA/GQh4YByLD0XkQsEpeXh5iY2Px119/AZD6/nt6esLMzKxS\nFYiJicGiRYsQFxeHmzdvYv369QgKCtIok5iYiOnTpyMyMhK5ubnw8PDApk2b0LJlSwBAbm4uPvzw\nQ/zwww94+PAh+vbti+XLl6NRo0YljsdBwERERETl4yBgedFnG7bCbwI2MzND9+7dMXLkSIwcORLd\nu3evdOMfADIzM9G2bVssWbIElpaWJbZfv34d3t7ecHNzQ1RUFBISEjB37lxYW1ury0yePBnbtm1D\neHg4Dh8+jIyMDLz44ouoYG5DRERERPTUK/UJQFJSEgCgcePGGsvlUZWvDBsbGyxbtkzjCUBgYCCU\nSiU2btyo9TMZGRmoV68eNmzYgJEjRwIAbty4gSZNmmDPnj3o37+/Rnk+ASAiIiIqH58AyEu1TAPq\n6uoKhUKBhw8fwtzcXL1cHm2zBFWWEAI7d+7E9OnTERAQgLi4OLi6umLKlCkYPnw4ACAuLg75+fka\nDX1nZ2d4eHjg6NGjJRIAkgf27ZQPxkIeGAf5YCzkgXEgMpxSuwCtXbsWa9euVXfvUS2X96NPycnJ\nyMzMxPz58+Hv74+IiAiMGjUKgYGB2L17NwDg9u3bMDExUWeoKs888wxu376t03FUXzJcrr5lT09P\n9Ze6HOpTk5cBzf/BGrs+NXVZ9Tchl/rU5GV+P8ljWVvDX071qwnL8fHxsqpPTV/Wp1KfALz66qtl\nLleHwsJCAMCQIUMwefJkAEC7du0QGxuLpUuXIiAgoNrrRERERET0JKvwLEAAkJOTg5SUFNSrVw/m\n5uZ6q0zxMQB5eXmwsrJCaGgoQkJC1OXmzp2L8PBwnD17FgcPHkS/fv2QnJys8RSgTZs2+M9//oNZ\ns2ZpHINjAIiIiIjKxzEA8mK0WYAOHToEb29v2NjYoHHjxjh8+DAA4N69e+jbty/27dtXpcoUZ2Zm\nhi5duuDSpUsa6xMTE9GkSRMAQOfOnWFqaor9+/ert9+4cQMXLlzAc889p9f6kP7ExsYa9NEW6Y6x\nkAfGQT4YC3lgHIgMR+cXgUVFRWHAgAFo0aIF3n77bXz99dfqbY6OjgCAb7/9FgMGDKhQBbKysnDl\nyhUIIVBYWIikpCScPn0aDg4OcHFxwbRp0zBixAh4e3vD19cXkZGRCA8Px/bt2wEAtra2eP311zFt\n2jTUq1cPDg4O+PDDD9GhQwf07du3QnWh6sNBXfLBWMgD4yAfjIU8MA5EhqNzF6CePXsiNzcXR44c\nQVpaGurXr4+IiAj4+voCAObMmYN169bh2rVrFapAdHQ0fHx8SswwFBwcrB5UHBYWhnnz5uHGjRtw\nd3dHSEiIehYgQOoqNGXKFHz//fd4+PAh+vXrh2XLlvFFYERERESVxC5A8lIt04AWFxcXh4ULF8LU\n1FTrdKANGzbUedadonr37q0e7FuaoKCgEm8HLsrMzAxff/21xlMJIiIiIiIqSecxAObm5sjLyyt1\n+40bN2Bra6uXStHTj3075YOxkAfGQT4YC3lgHIgMR+cuQM8//zzS0tJw9OhR9QxAqi5AmZmZaNWq\nFbp3747w8HBD17lK2AWIiIiIqHzsAiQvRpkFaPbs2YiPj4efnx927twJAPj999+xYsUKdOrUCamp\nqZg5c2aVKkNERERERIZVofcAREdH46233ioxLWfz5s2xZs0a9OzZU+8V1Dc+ASAiIiIqH58AyItR\nBgED0oDdCxcu4PTp00hMTERhYSHc3NzQuXNnrQODiUqj6tfJad6Mj7GQB8ZBPhgLeWAciAynUm8C\nfpLxCQARERFR+fgEQF6M8gSgadOm6N27N3r27ImePXuiRYsWVTowERERERFVP50TAG9vb0RHRyMs\nLAwKhQL169eHt7c3evXqhV69eqF9+/aGrCcREREREemBzgnAxo0bAUjz/R86dAgxMTE4fPgwfv75\nZwCAra0tvL291TMEEZWFfTvlg7GQB8ZBPhgLeWAciAynSmMA7t+/j+3bt2PBggW4dOkSFAoFCgoK\n9Fk/veMYACIiIqLycQyAvBhtFqA7d+7g0KFD6p+EhASYmpqic+fO+O9///tETANKRERERFST6ZwA\ntGzZEleuXIGVlRW6deuGYcOG4euvv0a3bt1Qq1YtQ9aRiIiIiIj0ROcE4PLly1AqlejTpw98fX3R\nq1cvdOzYkfP/U6Wwb6d8MBbywDjIB2MhD4yD8VlYWMDExAQFBQWwtrY2dnVIj3QeA5CYmKge/Hvo\n0CH89ddfsLW1RY8ePdQzAXl5ecHUtEK9iqodxwAQERER6eaTTz7B6tWrMXv2bIwbN87Y1anR9NmG\nrfQg4KKzAUVERODPP/9E7dq1kZmZWaUKGRoTACIiIiLdCSHY40MG9NmGVVbmQw8ePMDZs2dx9uxZ\nnD59GklJSRBCIDc3t8L7iomJweDBg+Hs7AylUomwsDCN7WPHjoVSqdT46dGjh0aZP//8Ey+//DLq\n168POzs7jBw5EsnJyZU5NSIiIqIaTQiBvPR0PDxyBDnh4Xi0ZQseHjmCvPR0VGHySJIRnROAbdu2\n4f3330fnzp3h4OCAF154AUuWLEHt2rUxffp07N+/H2lpaRWuQGZmJtq2bYslS5bA0tJSa5n+/fvj\nzp07uH37Nm7fvo1du3apt2VnZ2PAgAEAgKioKBw9ehSPHj3CwIEDK1wXqj6xsbHq/p1kXIyFPDAO\n8sFYyAPjYBxCCOScOAHF8OGo5e2NWiNHSj/e3lCMGIGckyeZBDwFdO4CpFQqYW9vj+eeew49e/ZE\nz5494enpqdc+/zY2Nli2bBmCgoLU68aOHYuUlBTs2LFD62f279+PgIAApKamwtbWFgCQkZEBe3t7\n7N+/H76+vhrl2QWIiIiIapTCQiA4GPj1V8DHB5g8GejVCyjWrUfV+K/l7w9FkfaSRhk7O+Ts2YNa\nXbuyW1A1M0oXoDNnzqgb4lOnTkW3bt2qbcDv4cOH8cwzz6Bly5YYN24c7t69q9726NEjKBQKWFhY\nqNdZWFhAqVTi8OHD1VI/IiIiItl6+BD47jsgLQ3Ytg3o0wfo2BFYvx7IyVEXy8/IgNmsWaU2/gFA\nkZ4Os9BQ5GdkGL7eZDA6JwBt2rQxZD1KFRAQgLCwMERGRuLLL7/EyZMn0bdvX+Tl5QEAunXrBmtr\na0yZMgXZ2dnIysrClClTUFhYiFu3bhmlzkRERERGJQSQlQXcvg3cuAGMHq25/fRpYOxYoG5dYNgw\nICcH+efOwWTfvnJ3bbJ3L/ITEgxUcaoOlRoEXJ2GDx+OF198Ea1bt8YLL7yA3bt34+LFi/jtt98A\nAI6Ojti6dSv27NkDGxsb2NvbIyMjAx07doRSqdvpFe9jyGXDLxft2ymH+tT05aLr5FCfmrhc/O/C\n2PWpycv8fpLHco38ezh1Srojn5wMXL2KhE2bgOhoqevO99/jekgI8PnnwMyZwHvv4d6gQcB//gP4\n+QHdu+OhmxvQuDFgbw+YmgLW1oCTE/Dss8D330Or7Gzgp5+A11/Hw8RE6NKpRwFA8fffxr9eNWxZ\nn+Q9ab8WTk5OcHZ2xuXLl9Xr+vXrh8uXLyM1NRWmpqawtbWFk5MTmjVrZsSaUln4Yhd5YTyMTxUD\nQ37hk2749yAPnp6eT87fQ24u8OABzP/5BzAzAx48ADIyYP/HH0B8PJCRATx4AOfLlwFLS2k5IwMt\nb92S+uf/W75TejpQUKDebetih3EttuxYbLl2Vc6BL/qqUSr9HgBD0DYIuLi7d+/C2dkZa9aswZgx\nY7SWiYyMxIABA3DhwgW4u7trbOMgYCIiIkJ+vrrhXeJ3Rdc9emTss9GuVi3A1hawsQGsrKQnC7dv\nlywTFAR88w0eHjsmzfZTzm4FgJwjR1C72LTsZFj6bMMa/QlAVlYWrly5AiEECgsLkZSUhNOnT8PB\nwQEODg4IDQ3F0KFD4eTkhGvXriEkJAQNGjTASy+9pN7H+vXr8eyzz6J+/fo4evQo3nvvPXzwwQcl\nGv9ERET0BCsoADIzK99QL/r74UNjn412ZmZSo13VcC/+74qsMzN7vN9XXpEGAquYmABvvQWEhgKO\n0rME0zZtUDBgAEzLGQdQ4OcH09bFn0/Qk8ToTwCio6Ph4+NTYiqp4OBgLF++HEOGDMEff/yBtLQ0\nODk5wdfXF3PmzEGjRo3UZadPn47169fj/v37cHV1xYQJEzB58mStx+MTAHlQPdblo3bjYyzkgXGQ\nD8ZCz1SDUSvYYM/45x+YZGXBqrDwcbmsLGOfjXYmJvppsNvaAkVmNdSroUOBn3+W/u3vD3zxBdCq\nlUYRIQRyTp5ELT+/UmcCKqxTB4927+Y0oEagzzas0ROA6sYEgIiIqBxCSHfI9dE95sEDaX9yo1BU\nraFedFutWiXm1JedtDRp2s/27aV3AZRC9S4As9BQmOzdq+4OJAAU+Psjb9YsNv6NhAlAFTABICKi\np5IQUl90fXSPefBAYzCqrFhb6+duu5WV/BvtRiKEQH5GBvITEqD4+29pnYsLTFu3hqmtLRv/RvJU\njQEgIiKq0f6dQUYvd9v/fUeO7Fha6qd7jLU1oOMU31R5CoUCZnZ2MOMg36cWEwAyCvaxlQ/GQh4Y\nB/nQKRaqGWQqc2e9+DY5zyCjj+4x1tbSnPQVpI6Dh4e+z+zp4uoKNGsGREY+XhcdLXXzWb9emuGn\nCjT+HvS43yo7d056m/GePUDfvsatyxOICQAZBRs58sFYyAPjUA0KC6UZZMppsHuq1i1eXHo5uc8g\nU9W77TY2gLm5UU+FfxM6Kq07TmW76Zw+Dfzyi/SW4MaNS8ZBLt1/PvgA6NlTv43/KVOAadOA+vX1\nt0+ZYgJARETyVXQGmap2j8nMNPbZaFd8BpnK3nU35Awy9GTp3VtKUotOA6qrP/4AZs+W7vQ3bqy/\n/erTsWNARASwY4d+9zt9OvD668CWLUZPgA2NCQAREemXagYZfXSPkfMMMlVpqBddV7u2fO6qkuEV\nFkrdvmpX6b295atsA1aIsv97lEPDePlyoF49ICBAv/utWxcIDgZmzAA+/1y/+5YZJgBkFOzvLB+M\nhTzIIg6PHlV99pgnYQaZchrnN9LTUWBlhSZt2pReztKSg1ENTBZ/E9ps2CB1j9m/H4iJkfrD374N\ntGwJhIQAI0ZoL3v0qLT899/A6tVSH/rcXGDRIuD774GrV6VxFz17AnPmAB06aB73xg2p28u+fVIj\nvU8f4KuvtNextL76eXnSZzZvBhITpTv57u7Aq68CkyZJd/5nz5YSgD59AEjTf6a8+CIcd+wofb8p\nKcAnnwA7dwJ37gDPPAMMGiSdh4NDyetx4AAQFwesWCGdV5MmUqNbl3EFBQXA9u3AwIHS0zN9e+kl\nYN484OZNoGFD/e9fJpgAkFHI7gu9BmMs5KHSccjL094gr0wj/kmYQUbXgafa1llZ6dRgcK6GU6Ly\nyf676b//BbKzpYYzAKxbB4waJSXSxRuyU6ZIA8fHjZP+W2zZUlr28wOOH5fe0vvOO0B6upQcPPec\nlFx06iR9Pj1dSgz++QeYMAHw8HjcGC9tPErxu/h5ecCAAcChQ9LvV16REo6zZ4Ft26TzePll4NYt\nqQ4ffww8+ywUABzd3Erfb0YG0L078OefUveZjh2B+Hjgm2+AgweBkyelv72iQkKAnBzpTcQWFlLZ\nsWOlZKR797Kve1yc1J3Py6vsclUxaBCwZg0wc6bhjmFkTACIiKpbQYH+pn3MyTH22WhnYaG/waiV\nmEGGyOBSUqTGs7W1tDx+PNCunXSXfsQIzfEYOTlS3/qi6776SmqM790L9Ov3eP3EiUDr1lLSoJrZ\nZ8ECIClJSjJUycVbbwHvvw98/bX2+hXvOvfVV1LSMGMG8Omn2j/Ttq3UAF+9WqpTr17l73fBAunp\nxfLl0jVQad8eePttYOFC6alCUbm5QGzs44R86FBpJqOlS8tPAM6fl5KQoklJUatWAffuAZcuSUnO\nX38BycnSrEELFwKNGpW9f0A67w8/ZAJARFTjqWaQqWqDPSNDumsoR6amjxvhVWmw29rKo58wkSFN\nnPi48Q9I/92/9ZbUwI6Kku7uFy1bfID2pk3As89Kd8xTUh6vFwLo3x8IC5OeJlhYSF1ennlGatAW\n9d//lp4AFPf991J3HH03an/5ReqP/+abmuvHj5ca/tu2lUwAJk3SfBrXsCHQogVw+XL5x7t7V/pd\ntGuRyurVUuLRtStw6pR0HdevlwYzf/yxlDzpkgB07iwld3l5xh/wbCBMAMgoZNu3swZ6qmMhhNTY\nrpxV1xcAACAASURBVGqDXTXfuxwplVV/uZLq3xYWHIyKp/xv4gki6zgoFFLjvbhWraTvnT//1Czr\n7l6y7IUL0pOBevW07x+Q7mQ3aiTtz8ur5N9ngwZAnTq61fnyZSnZqGByXm4crl0DunQpOSbGxERq\n1MfHa65XKICmTUvup25d6SlHeVTXQNvkACkpUuMfkPZlYgIMGSJ1k4qKkrpRqURFAW3aAI6OJfdj\nYyMd59o16RyeQkwAyChk+YVeQ8kuFkJI/1OsaoNd9buw0NhnVJJqBhl9zCLDGWT0TnZ/EzXUUxUH\nS8uS64SQutx89VXpM11pSw6qmUHiUNpYHF1m/FJdk9TUkts++ujxv6OjH3dhql1bs/EPAFOnSoOW\nS1O3LnD/fvn1eUIxASAi/cjN1d8MMvn5xj4b7ays9NOv3cqKM8gQPcmEkO7gDxyouT4hQUrImzUr\nfx/u7lJ3Fh+f8ss2aybdwS8+Reft20Bamm51btECuHix/G4tFb2h0KyZ1N++sFDze62gQJppSJdr\nURFt2kjXobzuQgcPAm+8oX3bgwfS0+EGDUr/fH7+U/1eDSYARDWZagYZffRrz8019tloV7t21WaO\nUf3b2towU84R0ZPpm2+kPv+2ttJyero0rWWdOtILs8oTFCS9dfaLL6QBp8UlJz9+I+3gwdJg27Aw\naZ56lf/7P93rGxgoHW/u3JJ98ouytpYa2NrusGszZAjw2WfAt99KsxyprFolJTgTJuheR1107Chd\n8+PHNdcXFkqDpvv2lY6bkKCeyhSANAB42jTgxx+Bn38G7O2B+fOB997T/oTm/v2n+o3ATADIKGTd\nt1PuCgqkwaj66Nde2vRxxmZuXvU77apG+xMygIt/E/LBWMiD7OPg6Cj1Nx87Vmowr1snzWm/Zo00\nvaZKad1aJk+W3g8wbZrUcPX1lb63kpKkefJr15Z+A1KZ77+XBtrGxkqzBEVFSY1gbX3YSzvezp1S\nAnDypDQVaK1aUkM5MVF6vwDwuD//vHlAaiqu3r6N3EaN4FE08Shq2jRg61ZpYG9cnNRA//13YO1a\nabrSqVM1y1f1xX5KpTRd6fbtmk8zVq6U6nDxonQulpaA87+T+u7YIT05AIBhw4AzZ6QBwmPHaj9G\naqo0KcIzz1StrjJm9AQgJiYGixYtQlxcHG7evIn169cjqMj8uWPHjsWGDRs0PtOtWzccPXpUvXzn\nzh1MmTIFERERyMjIgLu7O6ZNm4bRo0dX23lQ+YQQyMjIwLlz53Djxg0AwKNHj9CmTRvY2tpC8TT3\nYy4sBLKy9NOvPSvL2GejnYlJ1WeQKToYtYaRbSOnBmIs5EHWcVAopDvyMTHS9Jd37khdbL7/XvNF\nYKqy2piaArt2SZ/fuBEIDZXWN2woDfgt2uCuUwc4fFiaYnTjRmldnz5SN5e+fbUfo/g6MzMp4fji\nC6meM2ZICYC7O/Daa4/LubhIycyCBcDEiXDLy5PqoqpP8f3a2kovOZs1S2por18vNZwnTpTOqfg7\nAMr6f72u7YAJE6SXiv36q/TiLgDo0QMYPRrYskWaCWjlSik5cXWVBh2PGfP484cOlZxRqajjxwFP\nz6f6qa9CCOO+Y3337t04cuQIOnXqhKCgICxfvrxEAnDz5k189913UFXV3NwcdYqMeh8wYADS0tKw\nfPlyODo64ueff8bUqVMRHR0Nb29vjeOlp6er/21nZ2fgsyMVIQROnDiBWbNmYZ/qLsO//Pz8MHv2\nbHh5eckrCRBCukNe1TvtGRnSHXvj/qlpp1DobwaZWrU4GJWInn4bNkgN5oMHtc+TT9UjIEDqxx8d\nXbHP5eZKSc9ff0mzLGl7gvLf/0pJzAcf6KeueqLPNqzRnwAEBAQgICAAABBcyuMlCwsL1CtjJPyx\nY8ewdOlS9d2CDz74AEuWLMHJkydLJABU/VSNf39/f43/eFX27t2L48ePY8+ePejatWvVkgAhpHmT\n9XGnPSNDnjPIAPqbQcbSko12IiJ68nzxBdChAxARofkitfKcPSu9sA0AvvtOGgNQVG6u1L3o2DH9\n1VWGjJ4A6OLw4cN45plnUKdOHfTu3Rvz5s3TSAh69uyJLVu2YODAgbC3t8eOHTtw79499KvIfxBk\nMBkZGZg1a5bWxr9Keno6QkNDEb55M+xu3JAGU1W2EZ+XV41nVwGWlvqZQcbaWq8zyMi+n20NwTjI\nB2MhD7KOgxyf6BqIbOPQqlXlJp9wc5PGV6xdK72BuLj166XuTvb2Va6inMk+AQgICMDQoUPRtGlT\nXL9+HTNmzEDfvn0RFxcHs38HfoSHh2PkyJFwdHSEqakpatWqhc2bN6OdKsMjozp37lyJbj/aHNi7\nF6ZeXsCVK9VQKx3VqlX1BrtqMKqpPP/cZPelXkMxDvLBWMiDrONQg56cyjoOlVGnjjROQJurV6Vx\nEj/8UL11MgYhI9bW1mLDhg1llrl586YwMzMT27ZtU6975513RNeuXcXBgwfFmTNnxJw5c4SdnZ04\nc+ZMic+npaWpf1ROnTqlUYbL+l1eu3atAFDuj5t0T6XKPwWmpkLUrStE06ZCtGsnMjp0ECIgQIgR\nI4R44w1xa/RoIUJDhfjiCyFWrxZX5s0TYtcuIQ4fFuL0aXF6+3Yh7t0T4tEjWVw/LnOZy1zmMpe5\nbPjlf958U4jMTNnUp/iytjZsZcnzlmQZnJyc4OzsjMv/vgDizz//xNKlS3HmzBm0+XeKp7Zt2+LQ\noUP43//+h1WrVhmzulQBVwGc/c9/0OzMGVg5OKjvoN/NzUW9Zs3Ud9Ovp6bCtW1b9faEv/9G627d\n1Hfffz97VuOOxaXYWI3lG7GxaFBk+X5srDTa/1+5ubnSGwCJiIioxrg5bhwaFp+16Cll9FmAirKx\nscGyZcs0ZgEq7u7du3B2dsaaNWswZswYnDt3Du3bt8fZs2fRqlUrdTl/f384Ozvj22+/1fg8ZwGq\nfkeOHNF5MPaRI0fQo0cPA9eIipJt/84ahnGQD8ZCHhgHeWAc5OOpmgUoK+v/27vzoCjONAzgzwww\ncggiijAeKCJqvA+8CxAV0TUiEWOpCeCRkuhqPLJriEtWxGMTTTyisiqooFhG47GgwZVTFI3GYCCK\nF4pK1EWRrOABcsy3fxhmHTl0uGaceX5VVMnXX/e83S9O99v9dfdTXL9+HUIIKBQKZGdnIz09HVZW\nVrCyskJQUBC8vb0hl8tx8+ZNLF68GLa2tnjvj+e+du7cGQ4ODpg9ezZWr16NZs2a4dChQ4iPj0d0\ndLSG144AoFu3bhg5cuRr7wPw8PBA165dGygqKscvde3APGgP5kI7MA/agXnQTRq/ApCcnAw3N7cK\nj3708/NDSEgIvLy8kJaWhkePHkEul2PYsGEIDg5Gq1atlH1v3LiBgIAApKSk4MmTJ+jQoQM+/fRT\nfPjySx/+wCsADU8IgZ9++gkeHh5VPgnI0tISR48erf1jQImIiIh0UF0ew2q8AGhoLAA0Q/zxLoCg\noCAcO3ZMZdqoUaOwZMkSHvwTERERVYEFQC2wANAcIQQKCgqQkZGBq1evAgA6deqErl27wsLCggf/\nGsLxndqBedAezIV2YB60A/OgPVgA1AILACIiIiJ629TlMWzdvU6UtFJycjKkUil27typ6VDq3cWL\nF2FkZISEhIRq+127dq2BIqpadHQ0GjVqhBs3bmg6FCIiItIzLAB0QHp6OpYuXYrs7OxKp2vD0JrX\nxVgXFi5cCGdnZwwfPrzKPlu3bsXkyZOxbdu2eovjTXh6eqJ79+747LPPNBoHERER6R8WADogLS0N\nS5cuxa1btypMc3V1RWFhIXx8fBo+sJe8GuPPP/+sHFdYF3788UfEx8dj4cKFVfYJDQ1FQUEBUlNT\n8eDBA2zfvr3OPr8m5s2bh0OHDuHy5csajaOuc0E1wzxoD+ZCOzAP2oF50E0afw8A1Z4Qotqz/DKZ\nrAGjqdyrMdb1zUQhISGwtrbG6NGjq+zj6uqKjh07AgA+//xz5Y3ImjJ+/HjMmjULmzdvxvr16zUW\nB2/s0g7Mg/ZgLrQD86AdmAfdxCsAGlJcXIyVK1eiW7duMDExQdOmTeHp6Ym0tDSVfs+fP0dQUBA6\nd+4MMzMzNG3aFD169MCiRYsAAEuXLsX06dMBAEOHDoVUKoVUKlW2VXYPQEREBKRSKRITExEcHIx2\n7drB1NQUAwcOxNmzZ5XzOTs7o3HjxmjZsiWWL19eYR2ePHmCwMBADBw4ENbW1jA2NoajoyM+//xz\nFBYWKvu9LkZ1tkdlysrKEBUVhREjRsDAwKDKfuUH/+U6der02mXXJzMzMzg7O2P//v0ajYOIiIj0\nC68AaEBpaSk8PDxw5swZ+Pj4YO7cucjPz0doaCiGDBmCkydPok+fPgCA2bNnIzw8HH5+fhg0aBBK\nS0uRmZmJpKQkAC/OIv/nP/9BaGgoAgMD0blzZwCAg4OD8vOqujoQEBAAhUKB+fPno7i4GF9//TU8\nPDwQERGBGTNm4OOPP8aHH36Iffv2YcmSJWjfvj2mTJminP/u3bvYvn07vL298cEHH8DQ0BDJyclY\ntWoV0tLScPToUQCAt7d3tTGqsz0qk5qaiidPnqB///41TYnGDBo0CLGxsbh27VqFAoWIiIioXgg9\n8+jRI+WPpqxZs0ZIpVIRFxen0v748WNhZ2cn3NzclG1WVlZizJgx1S4vPDxcSKVSkZycXGHa8ePH\nhUQiERERESr9JRKJ6Nu3rygpKVG2R0dHC4lEImQymTh//ryyvbi4WMjlcjF48GCVZZeUlIjS0tIK\nn/nFF18IqVQqzp07V2WM586dU05XZ3tUZseOHUIqlYrDhw9XOn3Lli1ixYoVwtfXV8TFxYmwsDCx\ncuVKMWXKFHHnzp1ql13fIiMjhVQqFQcPHtRYDC/ngjSHedAezIV2YB60A/OgPeryGJZXADRg9+7d\n6Ny5M3r37o28vDxluxAC7u7u2LlzJ54/f45GjRqhSZMmyMjIQEZGBrp27VqnccyePRuGhv//E3B2\ndgYADBw4EL1791a2GxkZoX///jh9+rTK/C/PW1ZWhsePH6OsrAzDhw/H8uXLcfbs2SrHDr7crs72\nqExubi4AwMrKqsK00NBQ9OzZEwMGDMC5c+fg7u6O8PBw2NnZITAwEL6+vmjVqlWV26i+NWvWDEII\nPHjwQGMxcHyndmAetAdzoR2YB+3APOgmFgAacPnyZRQVFcHa2rrCtPLhOg8fPkSrVq2wbt06+Pr6\nonv37mjfvj3c3NwwduxYjB07tlaP95RIJLC3t1dps7S0BAC0a9euQv+mTZuqHJyXCwkJwZYtW5CR\nkQGFQqGy/P/+979vFIs626OqdQFeFAyvysvLw4ABAwAA2dnZMDAwgJeXFwoLC3H8+HFl0fOy48eP\no1u3bmjevPkbxV+VrKwsLF++vNqnDZXHrA2PaiUiIiL9wAJAA4QQ6N69O9auXVvpQSsA5cGwp6cn\nbt26hZiYGCQnJyM+Ph7btm2Di4sL4uPjVc7Cq6uqG2aru5H2ZWvWrMFf/vIXjBo1CvPmzUPLli0h\nk8lw9+5d+Pn5qRQE1VFne1Q37ffff68wLSAgQPnv5ORkuLi4AABMTEwqPfgHgL/+9a84fPjwG8Ve\nlY0bNyI1NRW3b9+utt/vv/8OiURS7foRERER1SUWABrg6OiI3NxcuLm5vVF/S0tLTJkyRXkDbkBA\nAFavXo2oqCh4e3tr7OxxZGQk7O3tERMTo9J+7NixCn1fjbH8mcJOTk5qb49XdevWDUIIZGZmVtsv\nKSkJH330UbV9Hj9+jGfPnsHW1rZGsZSbM2cOkpOTsXTp0mr7Xb9+HcCLddCUl3NBmsM8aA/mQjsw\nD9qBedBNfAyoBvj6+iInJwfffPNNpdPLx4MrFArk5+dXmN6rVy8IIZRnvBs3bqzye0MxMDCARCJR\nOWtfWlqKf/zjHxUO+F+N0cnJSfll8qbboyq9e/eGhYUFzpw5o9KuUCgQHx+vHGOfkZGBoUOHKqev\nWrVKpf/+/fvh7++Ppk2bYuXKlXj27Fn1G6AOnDlzBjY2NnB0dKz3z6rKy7kgzWEetAdzoR2YB+3A\nPOgmXgHQgHnz5iEuLg6LFi1CYmIihg0bBgsLC2RnZyMhIQEmJiZISEjA48ePIZfL4enpid69e6NF\nixbIysrC5s2b0axZM4wdOxYA0K9fP0ilUqxYsQK///47zMzMYG9vX+1jMasaaqOOCRMmYPHixRg1\nahTGjx+P/Px87NmzBzKZrMLyq4vxTbdHVaRSKcaPH4+oqCiUlJTAyMgIALBlyxb8+c9/xpUrVxAb\nGwtTU1O0bt0aABAdHV3hrPuECRPw66+/wt3dHdOmTav19nmdp0+f4uTJk6+9KkFERERUlzReAJw8\neRJff/01UlNTce/ePYSHh8PX11c5fdq0aYiIiFCZZ+DAgcon0ty+fRv29vYVzkQDwOrVq/Hpp5/W\n/0qoydDQEDExMQgJCcGuXbsQFBQEAGjZsiX69+8PPz8/AICpqSkWLFiAhIQEJCQk4MmTJ5DL5fDy\n8kJAQIBymEqbNm2wY8cOfPXVV5g9ezZKSkrg5+enLAAqGyJU1bAhiURS7bSXlb+MbNu2bZg/fz5s\nbW0xadIkTJ06FV26dFHpX12Mb7o9qjNr1ixERETgyJEjeO+99wAAgwcPxpQpU7Bv3z707NkTW7Zs\nwaJFi9CuXTvY29vjww8/rLCcEydOwMfHp0L7unXrUFBQoNIm/ni7cdeuXeHt7f3aGF+1f/9+FBYW\nwt/fX+15iYiIiGpKIuriVHAtHD16FKdOnUKfPn3g6+uLkJCQCgXAvXv3EBkZqTzAl8lkyifWCCGU\nj4Esd/DgQcyZMwdZWVmws7NTmfbykJomTZrU12rRa9THmMLRo0fj2bNnSE5OrtH8xcXFcHR0xO3b\nt/Hw4cNaPwWo/B6AxMTESqf36dMHDg4O+P7772v1ObXF8Z3agXnQHsyFdmAetAPzoD3q8hhW41cA\nRo8ejdGjRwNAlWd6GzVqVOVTUiQSCVq0aKHSduDAAYwYMaLCwT9pj/r4Ivnmm2/Qq1cvxMfHY8SI\nEWrPf+HCBfTo0QPAixuc58+fX6t4hBBVDrWKiorCpUuXsH///lp9Rl3gl7p2YB60B3OhHZgH7cA8\n6CaNFwBvIiUlBTY2NrC0tISrqytWrFhRZUGQlZWFxMRErTiwoobVpUsXFBcX13h+BwcHmJiYYPv2\n7TUa0vOy0NBQREVF4cKFCwgMDISfn5/Kjb7jxo1DUVFRrT6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- "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 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", - "if set the Kalman gain $K = 0.9$ we can 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 relate to 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 *covariance* (denoted by $COV$), so you may not fully understand this equation. Think of the numerator as the variance between the position 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. The Kalman filter is a g-h filter where $g$ and $h$ vary over time according to the variance of the measurements and our current beliefs." - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1634,7 +1618,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 26, "metadata": { "collapsed": false }, @@ -1643,7 +1627,7 @@ "data": { "image/png": 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5U6ZMQUBAgIhRkc7QarUoLS1FYWEhCgsLUVlZ2aVR1b3J0dFR94Wg7YeeL0GI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\n6enpQpIk4e/vL/bu3SuKioqEWq0W8fHx4plnnhm17uH27ds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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1659,38 +1643,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We've been doing the same thing in this chapter. And, as already mentioned, each filter makes a prediction, takes a measurement, and then forms a new estimate somewhere between the two." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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TsX//fkybNg2RkZHw9fWFra0tkpKScODAAdSuXRsHDhxQl+/Tpw+USiUuXryI\nV199Vb3ew8MDDRo0wPnz59G9e3dYWVnp9dgPHjyAk5MTBg0ahI4dO6J+/fr4888/sWLFCtStWxcD\nBw4EIL2YU6lUYt68eUhNTYWVlRWaNm0KLy+vSl2re/fulXsew4YNQ0hICPz9/fHyyy8jPT0dmzdv\nhrm5udZ9l1XHisajOKVSiZdffhnbt29HXl4ezMzMAAArV67EpEmT1C8stbS0VN9t37Fjh8ad/GHD\nhuHMmTPo378/xo4dW+IYWVlZiImJKfMJQmXZ2tpizpw5OHHihNaED5CeAoWGhsLW1lbvx6fqo3MC\ncO/ePRw9ehTnz5/HvXv3oFAo4OjoCA8PD/To0QOOjo6GrCc9ZdjIkQ/GQh4YB/nQRyzK6mZSdJup\nqSl27dqF5cuXY+PGjQgNDQUgDX718vJCcHCwxmfr1KmDDh06ID4+Hn379tXY5uvri82bN5dYX5qK\nHNvS0hLvv/8+Dhw4gAMHDiAzMxNOTk4YMmQIPvroI3VXFRcXF6xbtw4LFizAxIkTkZeXh+DgYHUC\noO26lHatFAqF1sG4xT8zbdo0AMCaNWvw3nvvoUGDBhg5ciReffVVtGrVqsT+y6pjReOhzYQJE7Bh\nwwb8+uuveOmllwAAPXr0wOjRo7Flyxa0b98eK1euxLRp0+Dq6oqmTZtizJgxGvs4dOgQXnnlFa37\n//HHH/Hw4UOMHz++3LpUlEKhgJeXF/bs2YPQ0NAS3aj8/f0xa9YsdO3a1ehvdKaqUYgyUu/c3Fxs\n2rQJ69atw5EjR0rN0hUKBbp3747XXnsNgYGBsLCwMFiFq6poRmtnZ2fEmhAREdHTKCAgANnZ2YiO\njq7wZ3Nzc+Hu7o6//voL9+7dK3GDtVOnTnBzc8PWrVv1Vd0ShBDIyMjAsWPHEBAQAECabfHvv/+G\nra0tG/9Gos82bKljAFasWIFmzZphwoQJqFOnDhYvXozDhw/j5s2bePjwIbKzs/HPP//g8OHD+Oqr\nr+Dg4ICJEyfCzc0NK1eurFKliIiIiJ5UX3zxBY4dO4aIiIgKf/bs2bNo164dAGmAc1Hbt2/H+fPn\nsWDBAr3UszQKhQJ2dnYaXbdMTU1hZ2fHxv9TotQnAC4uLvjggw/w2muv6ZxlpKenY82aNVi8eDGS\nkpL0WlF94RMAeWB/Z/lgLOSBcZAPxkIeamoc0tLSMG7cOPj7+6N///5GnW0nNTUVdevWBSC9f6E6\nB3dTSfpt2Bk0AAAgAElEQVRsw5aaABQdvFJRVfmsoTEBICIiIiofEwB5qZYuQFVpwMu18U9ERERE\nVNPp/B6AO3fuID4+XmPdxYsXMX78eIwYMQLbtm3Te+WIiIiIiEi/dJ4GdNKkSUhOTsahQ4cASI+F\nevXqhbS0NNSuXRs//vgjtm/fzrfvkk5qat9OOWIs5IFxkA/GQh4YByLDKXMa0KIaNWqESZMmISQk\nBACwZMkSfPjhh4iPj0fLli3Rt29fKBSKSk15VZ04BoCIiIiofBwDIC/VMgaguJSUFDg5OamXd+7c\niV69eqFNmzYwMzPDyJEjkZCQUKXKEBERERGRYemcADg4OODWrVsAgOzsbBw5cgQDBgxQb1coFMjJ\nydF/DYmIiIiISG90HgPg7e2N5cuXw8PDA3v27MGjR48waNAg9fZLly6hUaNGBqkkPX3Yt1M+GAt5\nYBzkg7GQB8aByHB0HgNw9epVDBgwANeuXQMAfPjhh/j8888BAAUFBWjSpAmef/55rFq1ynC11QOO\nASAiIiIqH8cAyIs+27A6PwFwc3PDpUuXcP78edja2sLV1VW9LTs7G8uWLUP79u2rVBkiIiIiIjIs\nnZ8APC34BICIiIiofHwCIC9GeQIAAPn5+QgLC8Ovv/6K69evAwBcXV3x4osvIigoCKamFdod1WDs\n2ykfjIU8MA7ywVjIA+NAZDg6zwKUnJyMLl264I033kBUVBQUCgUUCgWioqLwxhtvwNPTE3fu3Klw\nBWJiYjB48GA4OztDqVQiLCysRJnExEQMHToU9vb2sLKygqenJy5dugQAuH//Pt599114eHjA0tIS\njRs3xsSJE5mlypynpye/1GWCsZAHxkE+GAt5YByIDEfnBOCdd97B+fPnsWbNGty9exdxcXGIi4vD\n3bt38e233+LChQt49913K1yBzMxMtG3bFkuWLIGlpWWJ7devX4e3tzfc3NwQFRWFhIQEzJ07F9bW\n1gCAmzdv4ubNm1i0aBHOnTuHTZs24dChQxg9enSF60JERERE9LTTeQyAra0txo8fr575p7gPP/wQ\nq1evRkZGRqUrY2Njg2XLliEoKEi9LjAwEEqlEhs3btR5P7t378bAgQORlpamThRUOAaAiIiIqHwc\nAyAvRnkTsIWFBZo0aVLq9qZNm6JWrVpVqkxxQgjs3LkTrVq1QkBAAOrXrw8vLy9s2bKlzM+lp6fD\nwsJC6xMFkofY2Fh1/04yLsZCHhgH+WAs5IFxIDIcnROAESNGYPPmzcjLyyuxLTc3F5s3b8aIESP0\nWrnk5GRkZmZi/vz58Pf3R0REBEaNGoXAwEDs3r1b62fS0tLwySefYNy4cVAqdTu94l8wXDb8ctG+\nnXKoT01eBjQH2Rm7PjV1WfU3IZf61ORlfj/JY1lb/3851a8mLMfHx8uqPjV9WZ9Knbbn5MmTGsv/\n+c9/EBMTgy5duuCtt95C8+bNAQCXL1/GypUrAQDDhg3Ta+UKCwsBAEOGDMHkyZMBAO3atUNsbCyW\nLl2KgIAAjfJZWVkYOHAgXFxcsGDBAr3WhYiIiIjoaVDqGAClUgmFQqGxrmhR1bbi6woKCipdmeJj\nAPLy8mBlZYXQ0FCEhISoy82dOxfh4eE4e/asel1WVhYCAgKgVCqxa9euUrv/cAwAERERUfk4BkBe\nquU9AOvWravSjvXBzMwMXbp0UU/5qZKYmKgxHiEzMxMBAQFQKBRlNv5JPop2eyDjYizkgXGQD8ZC\nHhgHIsMpNQEIDg6ulgpkZWXhypUrEEKgsLAQSUlJOH36NBwcHODi4oJp06ZhxIgR8Pb2hq+vLyIj\nIxEeHo7t27cDkBr//fv3R2ZmJn755Rc8ePAADx48AAA4ODjAzMysWs6DKoZf6PLBWMgD4yAfjIU8\nMA5EhqPzNKCGEh0dDR8fnxLdjYKDg7F27VoAQFhYGObNm4cbN27A3d0dISEhGD58uPrzvr6+Gp8V\nQkChUODgwYPo1auXxjZ2ASIiIiIqH7sAyYs+27ClJgBz5syp+M4UCsycObNKFTI0JgBERERE5WMC\nIC/VkgDoOoWmxs6qOAi4OjABkAf27ZQPxkIeGAf5YCzkgXEwPiYA8lItCcDTigkAERERUfmYAMiL\nUd4ETERERERETz4mAERERERENUipCUDv3r2xb9++Cu9w79696N27d5UqRU+/2NhYg77imnTHWMgD\n4yAfjIU8MA5EhlPqewDatWuHQYMGoWHDhhg+fDj69esHT09P1KlTR6Pc/fv3ERcXh/3792Pr1q24\ndesWxo0bZ/CK05ONg7rkg7GQB8ZBPhgLeWAciAynzEHA169fx9dff41Nmzbh3r17UCgUsLOzg729\nPYQQuH//PjIyMiCEQL169fDKK6/g3XffRePGjavzHCqEg4CJiIiIysdBwPJS7bMA5efnIyYmBseO\nHcPFixeRkpICAHB0dISHhweee+45dO/eHaampT5QkA0mAERERETlYwIgL5wGtAqYAMgD53eWD8ZC\nHhgH+WAs5IFxMD4mAPLCBKAKmAAQERERlY8JgLzwPQBERERERFQpTACIiIiIiGoQJgBkFJzfWT4Y\nC3lgHOSDsZAHxoHIcDgGgIiIiIhK4BgAeeEYACIiIiIiqhSdEwATExN8//33pW4PDw+HiYlJhSsQ\nExODwYMHw9nZGUqlEmFhYSXKJCYmYujQobC3t4eVlRU8PT1x6dIl9fbVq1fD19cX9vb2UCqVSEpK\nqnA9iIiIiIhqAp0TgPJ6ChUWFkKhUFS4ApmZmWjbti2WLFkCS0vLEtuvX78Ob29vuLm5ISoqCgkJ\nCZg7dy6sra3VZbKzs+Hn54fZs2dXqg5U/di3Uz4YC3lgHOSDsZAHxoHIcCr06t6yGtcnTpyAvb19\nhSsQEBCAgIAAAEBwcHCJ7TNmzICfnx8WLlyoXufq6qpRZvLkyQCAuLi4Ch+fjIMvdpEPxkIeGAf5\nYCzkgXEgMpwynwB8/fXXaNasGZo1awYAeO+999TLRX8cHBzwv//9Dy+++KJeKyeEwM6dO9GqVSsE\nBASgfv368PLywpYtW/R6HCIiIiKimqLMBKB+/fpo3bo1WrduDQBo1KiReln106ZNG/Ud+uXLl+u1\ncsnJycjMzMT8+fPh7++PiIgIjBo1CoGBgdi9e7fejlP8ESOXucxlLnOZy1zmck1fjo+Pl1V9avqy\nPpXZBWjUqFEYNWoUAMDHxwcff/wx+vbta7DKFFdYWAgAGDJkiLqbT7t27RAbG4ulS5equw7Rk0f1\nHzUf8cpDbGwsY2Fkhvyip4rh95M88G+CyHBk9R4AGxsbLFu2DEFBQQCAvLw8WFlZITQ0FCEhIepy\nc+fORXh4OM6ePavx+bi4OHh5eeHatWto3Lix1mPwPQBERERE5eN7AORFn23YCg0CBoDz58/jzz//\nxP3797XODKRqvOuDmZkZunTpojHlJyBNC9qkSRO9HYeIiIiIqKbQOQG4evUqxowZg5MnT5Y6JahC\noahwApCVlYUrV65ACIHCwkIkJSXh9OnTcHBwgIuLC6ZNm4YRI0bA29sbvr6+iIyMRHh4OLZv367e\nx507d3D79m1cunQJQggkJCTg/v37aNy4caVmJiIiIiIielrp3AWoX79+OH78OD777DP07Nmz1IZ1\nRe/MR0dHw8fHp8QUo8HBwVi7di0AICwsDPPmzcONGzfg7u6OkJAQDB8+XF129uzZWt8BsG7duhIJ\nCbsAyQP72MoHYyEPjIN8MBbywDgYH7sAyYs+27A6JwC1a9dGSEgIZs6cWaUDGhsTACIiIqLyMQGQ\nF322YXV+E7CjoyMbzERERERETzidE4AJEybgu+++Q0FBgSHrQ0REREREBlTqIODib9t1c3NDfn4+\n2rVrh+DgYLi4uMDExKTE54r2zScqDft2ygdjIQ+Mg3wwFvLAOBAZTqljAJRKJRQKhXrGn6L/LnVn\nCoXsnxBwDAARERFR+TgGQF6q5T0ABw8erNKOiYiIiIhIfkpNAHr37l2d9SAiIiIiomqg8yBgIn2K\njY1V9+8k42Is5IFxkA/GQh4YByLD0fk9AL6+vmXvSKFArVq14OzsDB8fHwwbNgympjq/aLjacAwA\nERERUfk4BkBeqmUMQHGFhYX4559/cPXqVdjb28PV1RUAcP36ddy/fx/NmzeHnZ0dTpw4gdWrV+P/\n/u//EBERAUdHxypVkIiIiIiI9EfnLkCffvopUlNTsWHDBiQnJyMuLg5xcXFITk7GunXrkJqaisWL\nF+Pu3btYu3YtEhISMH36dEPWnYiIiIiIKkjnLkDdunVDr169sHDhQq3bp06dikOHDuHEiRMAgPHj\nx2Pnzp24efOm/mqrB+wCJA+c31k+GAt5YBzkg7GQB8bB+NgFSF6M0gXozJkzeOWVV0rd3qRJE5w9\ne1a93LlzZ2zYsKFKlaOnF7/Q5YOxkAfGQT4YC3lgHIgMR+cuQE5OTti6davWF30VFBRgy5YtaNCg\ngXpdSkoKHBwc9FNLIiIiIiLSC52fAHzwwQd455130K1bN7z55ptwc3MDAFy5cgWrV69GfHw8lixZ\noi6/detWeHl56b/GRERERERUaTonAJMmTYJSqcQnn3yCt956CwqFAgAghEDdunWxZMkSTJo0CQDw\n6NEjfPXVV+qZgoiKY99O+WAs5IFxkA/GQh4YByLD0XkQsEpeXh5iY2Px119/AZD6/nt6esLMzKxS\nFYiJicGiRYsQFxeHmzdvYv369QgKCtIok5iYiOnTpyMyMhK5ubnw8PDApk2b0LJlSwBAbm4uPvzw\nQ/zwww94+PAh+vbti+XLl6NRo0YljsdBwERERETl4yBgedFnG7bCbwI2MzND9+7dMXLkSIwcORLd\nu3evdOMfADIzM9G2bVssWbIElpaWJbZfv34d3t7ecHNzQ1RUFBISEjB37lxYW1ury0yePBnbtm1D\neHg4Dh8+jIyMDLz44ouoYG5DRERERPTUK/UJQFJSEgCgcePGGsvlUZWvDBsbGyxbtkzjCUBgYCCU\nSiU2btyo9TMZGRmoV68eNmzYgJEjRwIAbty4gSZNmmDPnj3o37+/Rnk+ASAiIiIqH58AyEu1TAPq\n6uoKhUKBhw8fwtzcXL1cHm2zBFWWEAI7d+7E9OnTERAQgLi4OLi6umLKlCkYPnw4ACAuLg75+fka\nDX1nZ2d4eHjg6NGjJRIAkgf27ZQPxkIeGAf5YCzkgXEgMpxSuwCtXbsWa9euVXfvUS2X96NPycnJ\nyMzMxPz58+Hv74+IiAiMGjUKgYGB2L17NwDg9u3bMDExUWeoKs888wxu376t03FUXzJcrr5lT09P\n9Ze6HOpTk5cBzf/BGrs+NXVZ9Tchl/rU5GV+P8ljWVvDX071qwnL8fHxsqpPTV/Wp1KfALz66qtl\nLleHwsJCAMCQIUMwefJkAEC7du0QGxuLpUuXIiAgoNrrRERERET0JKvwLEAAkJOTg5SUFNSrVw/m\n5uZ6q0zxMQB5eXmwsrJCaGgoQkJC1OXmzp2L8PBwnD17FgcPHkS/fv2QnJys8RSgTZs2+M9//oNZ\ns2ZpHINjAIiIiIjKxzEA8mK0WYAOHToEb29v2NjYoHHjxjh8+DAA4N69e+jbty/27dtXpcoUZ2Zm\nhi5duuDSpUsa6xMTE9GkSRMAQOfOnWFqaor9+/ert9+4cQMXLlzAc889p9f6kP7ExsYa9NEW6Y6x\nkAfGQT4YC3lgHIgMR+cXgUVFRWHAgAFo0aIF3n77bXz99dfqbY6OjgCAb7/9FgMGDKhQBbKysnDl\nyhUIIVBYWIikpCScPn0aDg4OcHFxwbRp0zBixAh4e3vD19cXkZGRCA8Px/bt2wEAtra2eP311zFt\n2jTUq1cPDg4O+PDDD9GhQwf07du3QnWh6sNBXfLBWMgD4yAfjIU8MA5EhqNzF6CePXsiNzcXR44c\nQVpaGurXr4+IiAj4+voCAObMmYN169bh2rVrFapAdHQ0fHx8SswwFBwcrB5UHBYWhnnz5uHGjRtw\nd3dHSEiIehYgQOoqNGXKFHz//fd4+PAh+vXrh2XLlvFFYERERESVxC5A8lIt04AWFxcXh4ULF8LU\n1FTrdKANGzbUedadonr37q0e7FuaoKCgEm8HLsrMzAxff/21xlMJIiIiIiIqSecxAObm5sjLyyt1\n+40bN2Bra6uXStHTj3075YOxkAfGQT4YC3lgHIgMR+cuQM8//zzS0tJw9OhR9QxAqi5AmZmZaNWq\nFbp3747w8HBD17lK2AWIiIiIqHzsAiQvRpkFaPbs2YiPj4efnx927twJAPj999+xYsUKdOrUCamp\nqZg5c2aVKkNERERERIZVofcAREdH46233ioxLWfz5s2xZs0a9OzZU+8V1Dc+ASAiIiIqH58AyItR\nBgED0oDdCxcu4PTp00hMTERhYSHc3NzQuXNnrQODiUqj6tfJad6Mj7GQB8ZBPhgLeWAciAynUm8C\nfpLxCQARERFR+fgEQF6M8gSgadOm6N27N3r27ImePXuiRYsWVTowERERERFVP50TAG9vb0RHRyMs\nLAwKhQL169eHt7c3evXqhV69eqF9+/aGrCcREREREemBzgnAxo0bAUjz/R86dAgxMTE4fPgwfv75\nZwCAra0tvL291TMEEZWFfTvlg7GQB8ZBPhgLeWAciAynSmMA7t+/j+3bt2PBggW4dOkSFAoFCgoK\n9Fk/veMYACIiIqLycQyAvBhtFqA7d+7g0KFD6p+EhASYmpqic+fO+O9///tETANKRERERFST6ZwA\ntGzZEleuXIGVlRW6deuGYcOG4euvv0a3bt1Qq1YtQ9aRiIiIiIj0ROcE4PLly1AqlejTpw98fX3R\nq1cvdOzYkfP/U6Wwb6d8MBbywDjIB2MhD4yD8VlYWMDExAQFBQWwtrY2dnVIj3QeA5CYmKge/Hvo\n0CH89ddfsLW1RY8ePdQzAXl5ecHUtEK9iqodxwAQERER6eaTTz7B6tWrMXv2bIwbN87Y1anR9NmG\nrfQg4KKzAUVERODPP/9E7dq1kZmZWaUKGRoTACIiIiLdCSHY40MG9NmGVVbmQw8ePMDZs2dx9uxZ\nnD59GklJSRBCIDc3t8L7iomJweDBg+Hs7AylUomwsDCN7WPHjoVSqdT46dGjh0aZP//8Ey+//DLq\n168POzs7jBw5EsnJyZU5NSIiIqIaTQiBvPR0PDxyBDnh4Xi0ZQseHjmCvPR0VGHySJIRnROAbdu2\n4f3330fnzp3h4OCAF154AUuWLEHt2rUxffp07N+/H2lpaRWuQGZmJtq2bYslS5bA0tJSa5n+/fvj\nzp07uH37Nm7fvo1du3apt2VnZ2PAgAEAgKioKBw9ehSPHj3CwIEDK1wXqj6xsbHq/p1kXIyFPDAO\n8sFYyAPjYBxCCOScOAHF8OGo5e2NWiNHSj/e3lCMGIGckyeZBDwFdO4CpFQqYW9vj+eeew49e/ZE\nz5494enpqdc+/zY2Nli2bBmCgoLU68aOHYuUlBTs2LFD62f279+PgIAApKamwtbWFgCQkZEBe3t7\n7N+/H76+vhrl2QWIiIiIapTCQiA4GPj1V8DHB5g8GejVCyjWrUfV+K/l7w9FkfaSRhk7O+Ts2YNa\nXbuyW1A1M0oXoDNnzqgb4lOnTkW3bt2qbcDv4cOH8cwzz6Bly5YYN24c7t69q9726NEjKBQKWFhY\nqNdZWFhAqVTi8OHD1VI/IiIiItl6+BD47jsgLQ3Ytg3o0wfo2BFYvx7IyVEXy8/IgNmsWaU2/gFA\nkZ4Os9BQ5GdkGL7eZDA6JwBt2rQxZD1KFRAQgLCwMERGRuLLL7/EyZMn0bdvX+Tl5QEAunXrBmtr\na0yZMgXZ2dnIysrClClTUFhYiFu3bhmlzkRERERGJQSQlQXcvg3cuAGMHq25/fRpYOxYoG5dYNgw\nICcH+efOwWTfvnJ3bbJ3L/ITEgxUcaoOlRoEXJ2GDx+OF198Ea1bt8YLL7yA3bt34+LFi/jtt98A\nAI6Ojti6dSv27NkDGxsb2NvbIyMjAx07doRSqdvpFe9jyGXDLxft2ymH+tT05aLr5FCfmrhc/O/C\n2PWpycv8fpLHco38ezh1Srojn5wMXL2KhE2bgOhoqevO99/jekgI8PnnwMyZwHvv4d6gQcB//gP4\n+QHdu+OhmxvQuDFgbw+YmgLW1oCTE/Dss8D330Or7Gzgp5+A11/Hw8RE6NKpRwFA8fffxr9eNWxZ\nn+Q9ab8WTk5OcHZ2xuXLl9Xr+vXrh8uXLyM1NRWmpqawtbWFk5MTmjVrZsSaUln4Yhd5YTyMTxUD\nQ37hk2749yAPnp6eT87fQ24u8OABzP/5BzAzAx48ADIyYP/HH0B8PJCRATx4AOfLlwFLS2k5IwMt\nb92S+uf/W75TejpQUKDebetih3EttuxYbLl2Vc6BL/qqUSr9HgBD0DYIuLi7d+/C2dkZa9aswZgx\nY7SWiYyMxIABA3DhwgW4u7trbOMgYCIiIkJ+vrrhXeJ3Rdc9emTss9GuVi3A1hawsQGsrKQnC7dv\nlywTFAR88w0eHjsmzfZTzm4FgJwjR1C72LTsZFj6bMMa/QlAVlYWrly5AiEECgsLkZSUhNOnT8PB\nwQEODg4IDQ3F0KFD4eTkhGvXriEkJAQNGjTASy+9pN7H+vXr8eyzz6J+/fo4evQo3nvvPXzwwQcl\nGv9ERET0BCsoADIzK99QL/r74UNjn412ZmZSo13VcC/+74qsMzN7vN9XXpEGAquYmABvvQWEhgKO\n0rME0zZtUDBgAEzLGQdQ4OcH09bFn0/Qk8ToTwCio6Ph4+NTYiqp4OBgLF++HEOGDMEff/yBtLQ0\nODk5wdfXF3PmzEGjRo3UZadPn47169fj/v37cHV1xYQJEzB58mStx+MTAHlQPdblo3bjYyzkgXGQ\nD8ZCz1SDUSvYYM/45x+YZGXBqrDwcbmsLGOfjXYmJvppsNvaAkVmNdSroUOBn3+W/u3vD3zxBdCq\nlUYRIQRyTp5ELT+/UmcCKqxTB4927+Y0oEagzzas0ROA6sYEgIiIqBxCSHfI9dE95sEDaX9yo1BU\nraFedFutWiXm1JedtDRp2s/27aV3AZRC9S4As9BQmOzdq+4OJAAU+Psjb9YsNv6NhAlAFTABICKi\np5IQUl90fXSPefBAYzCqrFhb6+duu5WV/BvtRiKEQH5GBvITEqD4+29pnYsLTFu3hqmtLRv/RvJU\njQEgIiKq0f6dQUYvd9v/fUeO7Fha6qd7jLU1oOMU31R5CoUCZnZ2MOMg36cWEwAyCvaxlQ/GQh4Y\nB/nQKRaqGWQqc2e9+DY5zyCjj+4x1tbSnPQVpI6Dh4e+z+zp4uoKNGsGREY+XhcdLXXzWb9emuGn\nCjT+HvS43yo7d056m/GePUDfvsatyxOICQAZBRs58sFYyAPjUA0KC6UZZMppsHuq1i1eXHo5uc8g\nU9W77TY2gLm5UU+FfxM6Kq07TmW76Zw+Dfzyi/SW4MaNS8ZBLt1/PvgA6NlTv43/KVOAadOA+vX1\nt0+ZYgJARETyVXQGmap2j8nMNPbZaFd8BpnK3nU35Awy9GTp3VtKUotOA6qrP/4AZs+W7vQ3bqy/\n/erTsWNARASwY4d+9zt9OvD668CWLUZPgA2NCQAREemXagYZfXSPkfMMMlVpqBddV7u2fO6qkuEV\nFkrdvmpX6b295atsA1aIsv97lEPDePlyoF49ICBAv/utWxcIDgZmzAA+/1y/+5YZJgBkFOzvLB+M\nhTzIIg6PHlV99pgnYQaZchrnN9LTUWBlhSZt2pReztKSg1ENTBZ/E9ps2CB1j9m/H4iJkfrD374N\ntGwJhIQAI0ZoL3v0qLT899/A6tVSH/rcXGDRIuD774GrV6VxFz17AnPmAB06aB73xg2p28u+fVIj\nvU8f4KuvtNextL76eXnSZzZvBhITpTv57u7Aq68CkyZJd/5nz5YSgD59AEjTf6a8+CIcd+wofb8p\nKcAnnwA7dwJ37gDPPAMMGiSdh4NDyetx4AAQFwesWCGdV5MmUqNbl3EFBQXA9u3AwIHS0zN9e+kl\nYN484OZNoGFD/e9fJpgAkFHI7gu9BmMs5KHSccjL094gr0wj/kmYQUbXgafa1llZ6dRgcK6GU6Ly\nyf676b//BbKzpYYzAKxbB4waJSXSxRuyU6ZIA8fHjZP+W2zZUlr28wOOH5fe0vvOO0B6upQcPPec\nlFx06iR9Pj1dSgz++QeYMAHw8HjcGC9tPErxu/h5ecCAAcChQ9LvV16REo6zZ4Ft26TzePll4NYt\nqQ4ffww8+ywUABzd3Erfb0YG0L078OefUveZjh2B+Hjgm2+AgweBkyelv72iQkKAnBzpTcQWFlLZ\nsWOlZKR797Kve1yc1J3Py6vsclUxaBCwZg0wc6bhjmFkTACIiKpbQYH+pn3MyTH22WhnYaG/waiV\nmEGGyOBSUqTGs7W1tDx+PNCunXSXfsQIzfEYOTlS3/qi6776SmqM790L9Ov3eP3EiUDr1lLSoJrZ\nZ8ECIClJSjJUycVbbwHvvw98/bX2+hXvOvfVV1LSMGMG8Omn2j/Ttq3UAF+9WqpTr17l73fBAunp\nxfLl0jVQad8eePttYOFC6alCUbm5QGzs44R86FBpJqOlS8tPAM6fl5KQoklJUatWAffuAZcuSUnO\nX38BycnSrEELFwKNGpW9f0A67w8/ZAJARFTjqWaQqWqDPSNDumsoR6amjxvhVWmw29rKo58wkSFN\nnPi48Q9I/92/9ZbUwI6Kku7uFy1bfID2pk3As89Kd8xTUh6vFwLo3x8IC5OeJlhYSF1ennlGatAW\n9d//lp4AFPf991J3HH03an/5ReqP/+abmuvHj5ca/tu2lUwAJk3SfBrXsCHQogVw+XL5x7t7V/pd\ntGuRyurVUuLRtStw6pR0HdevlwYzf/yxlDzpkgB07iwld3l5xh/wbCBMAMgoZNu3swZ6qmMhhNTY\nrpxV1xcAACAASURBVGqDXTXfuxwplVV/uZLq3xYWHIyKp/xv4gki6zgoFFLjvbhWraTvnT//1Czr\n7l6y7IUL0pOBevW07x+Q7mQ3aiTtz8ur5N9ngwZAnTq61fnyZSnZqGByXm4crl0DunQpOSbGxERq\n1MfHa65XKICmTUvup25d6SlHeVTXQNvkACkpUuMfkPZlYgIMGSJ1k4qKkrpRqURFAW3aAI6OJfdj\nYyMd59o16RyeQkwAyChk+YVeQ8kuFkJI/1OsaoNd9buw0NhnVJJqBhl9zCLDGWT0TnZ/EzXUUxUH\nS8uS64SQutx89VXpM11pSw6qmUHiUNpYHF1m/FJdk9TUkts++ujxv6OjH3dhql1bs/EPAFOnSoOW\nS1O3LnD/fvn1eUIxASAi/cjN1d8MMvn5xj4b7ays9NOv3cqKM8gQPcmEkO7gDxyouT4hQUrImzUr\nfx/u7lJ3Fh+f8ss2aybdwS8+Reft20Bamm51btECuHix/G4tFb2h0KyZ1N++sFDze62gQJppSJdr\nURFt2kjXobzuQgcPAm+8oX3bgwfS0+EGDUr/fH7+U/1eDSYARDWZagYZffRrz8019tloV7t21WaO\nUf3b2towU84R0ZPpm2+kPv+2ttJyero0rWWdOtILs8oTFCS9dfaLL6QBp8UlJz9+I+3gwdJg27Aw\naZ56lf/7P93rGxgoHW/u3JJ98ouytpYa2NrusGszZAjw2WfAt99KsxyprFolJTgTJuheR1107Chd\n8+PHNdcXFkqDpvv2lY6bkKCeyhSANAB42jTgxx+Bn38G7O2B+fOB997T/oTm/v2n+o3ATADIKGTd\nt1PuCgqkwaj66Nde2vRxxmZuXvU77apG+xMygIt/E/LBWMiD7OPg6Cj1Nx87Vmowr1snzWm/Zo00\nvaZKad1aJk+W3g8wbZrUcPX1lb63kpKkefJr15Z+A1KZ77+XBtrGxkqzBEVFSY1gbX3YSzvezp1S\nAnDypDQVaK1aUkM5MVF6vwDwuD//vHlAaiqu3r6N3EaN4FE08Shq2jRg61ZpYG9cnNRA//13YO1a\nabrSqVM1y1f1xX5KpTRd6fbtmk8zVq6U6nDxonQulpaA87+T+u7YIT05AIBhw4AzZ6QBwmPHaj9G\naqo0KcIzz1StrjJm9AQgJiYGixYtQlxcHG7evIn169cjqMj8uWPHjsWGDRs0PtOtWzccPXpUvXzn\nzh1MmTIFERERyMjIgLu7O6ZNm4bRo0dX23lQ+YQQyMjIwLlz53Djxg0AwKNHj9CmTRvY2tpC8TT3\nYy4sBLKy9NOvPSvL2GejnYlJ1WeQKToYtYaRbSOnBmIs5EHWcVAopDvyMTHS9Jd37khdbL7/XvNF\nYKqy2piaArt2SZ/fuBEIDZXWN2woDfgt2uCuUwc4fFiaYnTjRmldnz5SN5e+fbUfo/g6MzMp4fji\nC6meM2ZICYC7O/Daa4/LubhIycyCBcDEiXDLy5PqoqpP8f3a2kovOZs1S2por18vNZwnTpTOqfg7\nAMr6f72u7YAJE6SXiv36q/TiLgDo0QMYPRrYskWaCWjlSik5cXWVBh2PGfP484cOlZxRqajjxwFP\nz6f6qa9CCOO+Y3337t04cuQIOnXqhKCgICxfvrxEAnDz5k189913UFXV3NwcdYqMeh8wYADS0tKw\nfPlyODo64ueff8bUqVMRHR0Nb29vjeOlp6er/21nZ2fgsyMVIQROnDiBWbNmYZ/qLsO//Pz8MHv2\nbHh5eckrCRBCukNe1TvtGRnSHXvj/qlpp1DobwaZWrU4GJWInn4bNkgN5oMHtc+TT9UjIEDqxx8d\nXbHP5eZKSc9ff0mzLGl7gvLf/0pJzAcf6KeueqLPNqzRnwAEBAQgICAAABBcyuMlCwsL1CtjJPyx\nY8ewdOlS9d2CDz74AEuWLMHJkydLJABU/VSNf39/f43/eFX27t2L48ePY8+ePejatWvVkgAhpHmT\n9XGnPSNDnjPIAPqbQcbSko12IiJ68nzxBdChAxARofkitfKcPSu9sA0AvvtOGgNQVG6u1L3o2DH9\n1VWGjJ4A6OLw4cN45plnUKdOHfTu3Rvz5s3TSAh69uyJLVu2YODAgbC3t8eOHTtw79499KvIfxBk\nMBkZGZg1a5bWxr9Keno6QkNDEb55M+xu3JAGU1W2EZ+XV41nVwGWlvqZQcbaWq8zyMi+n20NwTjI\nB2MhD7KOgxyf6BqIbOPQqlXlJp9wc5PGV6xdK72BuLj166XuTvb2Va6inMk+AQgICMDQoUPRtGlT\nXL9+HTNmzEDfvn0RFxcHs38HfoSHh2PkyJFwdHSEqakpatWqhc2bN6OdKsMjozp37lyJbj/aHNi7\nF6ZeXsCVK9VQKx3VqlX1BrtqMKqpPP/cZPelXkMxDvLBWMiDrONQg56cyjoOlVGnjjROQJurV6Vx\nEj/8UL11MgYhI9bW1mLDhg1llrl586YwMzMT27ZtU6975513RNeuXcXBgwfFmTNnxJw5c4SdnZ04\nc+ZMic+npaWpf1ROnTqlUYbL+l1eu3atAFDuj5t0T6XKPwWmpkLUrStE06ZCtGsnMjp0ECIgQIgR\nI4R44w1xa/RoIUJDhfjiCyFWrxZX5s0TYtcuIQ4fFuL0aXF6+3Yh7t0T4tEjWVw/LnOZy1zmMpe5\nbPjlf958U4jMTNnUp/iytjZsZcnzlmQZnJyc4OzsjMv/vgDizz//xNKlS3HmzBm0+XeKp7Zt2+LQ\noUP43//+h1WrVhmzulQBVwGc/c9/0OzMGVg5OKjvoN/NzUW9Zs3Ud9Ovp6bCtW1b9faEv/9G627d\n1Hfffz97VuOOxaXYWI3lG7GxaFBk+X5srDTa/1+5ubnSGwCJiIioxrg5bhwaFp+16Cll9FmAirKx\nscGyZcs0ZgEq7u7du3B2dsaaNWswZswYnDt3Du3bt8fZs2fRqlUrdTl/f384Ozvj22+/1fg8ZwGq\nfkeOHNF5MPaRI0fQo0cPA9eIipJt/84ahnGQD8ZCHhgHeWAc5OOpmgUoK+v/27vzoCjONAzgzwww\ncggiijAeKCJqvA+8CxAV0TUiEWOpCeCRkuhqPLJriEtWxGMTTTyisiqooFhG47GgwZVTFI3GYCCK\nF4pK1EWRrOABcsy3fxhmHTl0uGaceX5VVMnXX/e83S9O99v9dfdTXL9+HUIIKBQKZGdnIz09HVZW\nVrCyskJQUBC8vb0hl8tx8+ZNLF68GLa2tnjvj+e+du7cGQ4ODpg9ezZWr16NZs2a4dChQ4iPj0d0\ndLSG144AoFu3bhg5cuRr7wPw8PBA165dGygqKscvde3APGgP5kI7MA/agXnQTRq/ApCcnAw3N7cK\nj3708/NDSEgIvLy8kJaWhkePHkEul2PYsGEIDg5Gq1atlH1v3LiBgIAApKSk4MmTJ+jQoQM+/fRT\nfPjySx/+wCsADU8IgZ9++gkeHh5VPgnI0tISR48erf1jQImIiIh0UF0ew2q8AGhoLAA0Q/zxLoCg\noCAcO3ZMZdqoUaOwZMkSHvwTERERVYEFQC2wANAcIQQKCgqQkZGBq1evAgA6deqErl27wsLCggf/\nGsLxndqBedAezIV2YB60A/OgPVgA1AILACIiIiJ629TlMWzdvU6UtFJycjKkUil27typ6VDq3cWL\nF2FkZISEhIRq+127dq2BIqpadHQ0GjVqhBs3bmg6FCIiItIzLAB0QHp6OpYuXYrs7OxKp2vD0JrX\nxVgXFi5cCGdnZwwfPrzKPlu3bsXkyZOxbdu2eovjTXh6eqJ79+747LPPNBoHERER6R8WADogLS0N\nS5cuxa1btypMc3V1RWFhIXx8fBo+sJe8GuPPP/+sHFdYF3788UfEx8dj4cKFVfYJDQ1FQUEBUlNT\n8eDBA2zfvr3OPr8m5s2bh0OHDuHy5csajaOuc0E1wzxoD+ZCOzAP2oF50E0afw8A1Z4Qotqz/DKZ\nrAGjqdyrMdb1zUQhISGwtrbG6NGjq+zj6uqKjh07AgA+//xz5Y3ImjJ+/HjMmjULmzdvxvr16zUW\nB2/s0g7Mg/ZgLrQD86AdmAfdxCsAGlJcXIyVK1eiW7duMDExQdOmTeHp6Ym0tDSVfs+fP0dQUBA6\nd+4MMzMzNG3aFD169MCiRYsAAEuXLsX06dMBAEOHDoVUKoVUKlW2VXYPQEREBKRSKRITExEcHIx2\n7drB1NQUAwcOxNmzZ5XzOTs7o3HjxmjZsiWWL19eYR2ePHmCwMBADBw4ENbW1jA2NoajoyM+//xz\nFBYWKvu9LkZ1tkdlysrKEBUVhREjRsDAwKDKfuUH/+U6der02mXXJzMzMzg7O2P//v0ajYOIiIj0\nC68AaEBpaSk8PDxw5swZ+Pj4YO7cucjPz0doaCiGDBmCkydPok+fPgCA2bNnIzw8HH5+fhg0aBBK\nS0uRmZmJpKQkAC/OIv/nP/9BaGgoAgMD0blzZwCAg4OD8vOqujoQEBAAhUKB+fPno7i4GF9//TU8\nPDwQERGBGTNm4OOPP8aHH36Iffv2YcmSJWjfvj2mTJminP/u3bvYvn07vL298cEHH8DQ0BDJyclY\ntWoV0tLScPToUQCAt7d3tTGqsz0qk5qaiidPnqB///41TYnGDBo0CLGxsbh27VqFAoWIiIioXgg9\n8+jRI+WPpqxZs0ZIpVIRFxen0v748WNhZ2cn3NzclG1WVlZizJgx1S4vPDxcSKVSkZycXGHa8ePH\nhUQiERERESr9JRKJ6Nu3rygpKVG2R0dHC4lEImQymTh//ryyvbi4WMjlcjF48GCVZZeUlIjS0tIK\nn/nFF18IqVQqzp07V2WM586dU05XZ3tUZseOHUIqlYrDhw9XOn3Lli1ixYoVwtfXV8TFxYmwsDCx\ncuVKMWXKFHHnzp1ql13fIiMjhVQqFQcPHtRYDC/ngjSHedAezIV2YB60A/OgPeryGJZXADRg9+7d\n6Ny5M3r37o28vDxluxAC7u7u2LlzJ54/f45GjRqhSZMmyMjIQEZGBrp27VqnccyePRuGhv//E3B2\ndgYADBw4EL1791a2GxkZoX///jh9+rTK/C/PW1ZWhsePH6OsrAzDhw/H8uXLcfbs2SrHDr7crs72\nqExubi4AwMrKqsK00NBQ9OzZEwMGDMC5c+fg7u6O8PBw2NnZITAwEL6+vmjVqlWV26i+NWvWDEII\nPHjwQGMxcHyndmAetAdzoR2YB+3APOgmFgAacPnyZRQVFcHa2rrCtPLhOg8fPkSrVq2wbt06+Pr6\nonv37mjfvj3c3NwwduxYjB07tlaP95RIJLC3t1dps7S0BAC0a9euQv+mTZuqHJyXCwkJwZYtW5CR\nkQGFQqGy/P/+979vFIs626OqdQFeFAyvysvLw4ABAwAA2dnZMDAwgJeXFwoLC3H8+HFl0fOy48eP\no1u3bmjevPkbxV+VrKwsLF++vNqnDZXHrA2PaiUiIiL9wAJAA4QQ6N69O9auXVvpQSsA5cGwp6cn\nbt26hZiYGCQnJyM+Ph7btm2Di4sL4uPjVc7Cq6uqG2aru5H2ZWvWrMFf/vIXjBo1CvPmzUPLli0h\nk8lw9+5d+Pn5qRQE1VFne1Q37ffff68wLSAgQPnv5ORkuLi4AABMTEwqPfgHgL/+9a84fPjwG8Ve\nlY0bNyI1NRW3b9+utt/vv/8OiURS7foRERER1SUWABrg6OiI3NxcuLm5vVF/S0tLTJkyRXkDbkBA\nAFavXo2oqCh4e3tr7OxxZGQk7O3tERMTo9J+7NixCn1fjbH8mcJOTk5qb49XdevWDUIIZGZmVtsv\nKSkJH330UbV9Hj9+jGfPnsHW1rZGsZSbM2cOkpOTsXTp0mr7Xb9+HcCLddCUl3NBmsM8aA/mQjsw\nD9qBedBNfAyoBvj6+iInJwfffPNNpdPLx4MrFArk5+dXmN6rVy8IIZRnvBs3bqzye0MxMDCARCJR\nOWtfWlqKf/zjHxUO+F+N0cnJSfll8qbboyq9e/eGhYUFzpw5o9KuUCgQHx+vHGOfkZGBoUOHKqev\nWrVKpf/+/fvh7++Ppk2bYuXKlXj27Fn1G6AOnDlzBjY2NnB0dKz3z6rKy7kgzWEetAdzoR2YB+3A\nPOgmXgHQgHnz5iEuLg6LFi1CYmIihg0bBgsLC2RnZyMhIQEmJiZISEjA48ePIZfL4enpid69e6NF\nixbIysrC5s2b0axZM4wdOxYA0K9fP0ilUqxYsQK///47zMzMYG9vX+1jMasaaqOOCRMmYPHixRg1\nahTGjx+P/Px87NmzBzKZrMLyq4vxTbdHVaRSKcaPH4+oqCiUlJTAyMgIALBlyxb8+c9/xpUrVxAb\nGwtTU1O0bt0aABAdHV3hrPuECRPw66+/wt3dHdOmTav19nmdp0+f4uTJk6+9KkFERERUlzReAJw8\neRJff/01UlNTce/ePYSHh8PX11c5fdq0aYiIiFCZZ+DAgcon0ty+fRv29vYVzkQDwOrVq/Hpp5/W\n/0qoydDQEDExMQgJCcGuXbsQFBQEAGjZsiX69+8PPz8/AICpqSkWLFiAhIQEJCQk4MmTJ5DL5fDy\n8kJAQIBymEqbNm2wY8cOfPXVV5g9ezZKSkrg5+enLAAqGyJU1bAhiURS7bSXlb+MbNu2bZg/fz5s\nbW0xadIkTJ06FV26dFHpX12Mb7o9qjNr1ixERETgyJEjeO+99wAAgwcPxpQpU7Bv3z707NkTW7Zs\nwaJFi9CuXTvY29vjww8/rLCcEydOwMfHp0L7unXrUFBQoNIm/ni7cdeuXeHt7f3aGF+1f/9+FBYW\nwt/fX+15iYiIiGpKIuriVHAtHD16FKdOnUKfPn3g6+uLkJCQCgXAvXv3EBkZqTzAl8lkyifWCCGU\nj4Esd/DgQcyZMwdZWVmws7NTmfbykJomTZrU12rRa9THmMLRo0fj2bNnSE5OrtH8xcXFcHR0xO3b\nt/Hw4cNaPwWo/B6AxMTESqf36dMHDg4O+P7772v1ObXF8Z3agXnQHsyFdmAetAPzoD3q8hhW41cA\nRo8ejdGjRwNAlWd6GzVqVOVTUiQSCVq0aKHSduDAAYwYMaLCwT9pj/r4Ivnmm2/Qq1cvxMfHY8SI\nEWrPf+HCBfTo0QPAixuc58+fX6t4hBBVDrWKiorCpUuXsH///lp9Rl3gl7p2YB60B3OhHZgH7cA8\n6CaNFwBvIiUlBTY2NrC0tISrqytWrFhRZUGQlZWFxMRErTiwoobVpUsXFBcX13h+BwcHmJiYYPv2\n7TUa0vOy0NBQREVF4cKFCwgMDISfn5/Kjb7jxo1DUVFRrT6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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gh_internal.plot_estimate_chart_3()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**This is extremely important to understand**: Every filter in this book implements the **same algorithm**, just with different mathematical details. The math can become challenging in later chapters, but the idea is easy to understand.\n", + "We've been doing the same thing in this chapter. And, as already mentioned, each filter makes a prediction, takes a measurement, and then forms a new estimate somewhere between the two.\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 and what problems can be represented, but not the underlying ideas.\n", + "**This is extremely important to understand**: Every filter in this book implements the same algorithm, just with different mathematical details. 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. They all use different math to implement the same algorithm. The choice of math affects the quality of results and what problems can be represented, but not the underlying ideas.\n", "\n", "Here is the generic algorithm:\n", "\n", @@ -1715,7 +1672,7 @@ " 5. update belief in the state based on how certain we are \n", " 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." + "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. The simple thought experiments in **g-h Filter** chapter result in this algorithm." ] }, { @@ -1724,12 +1681,12 @@ "source": [ "## Comparison with g-h Filter and discrete Bayes Filter\n", "\n", - "Now is a good time to be understand the differences between these three filters in terms of how we model errors. For the g-h filter we modeled our measurements as shown in this graph" + "Now is a good time to be understand the differences between these three filters in terms of how we model errors. For the g-h filter we modeled our measurements as shown in this graph:" ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 27, "metadata": { "collapsed": false }, @@ -1738,7 +1695,7 @@ "data": { "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1754,7 +1711,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this graph sensor A returned a measurement of 160, and sensor B returned 170. The bars are *error bars* - they illustrate the possible range of error for the measurement. Hence, the actual value that A is measuring can be betwee 157 to 163, and B is measuring a value between 161 to 179.\n", + "Sensor A returned a measurement of 160, and sensor B returned 170. The bars are *error bars* - they illustrate the possible range of error for the measurement. Hence, the actual value that A is measuring can be between 157 to 163, and B is measuring a value between 161 to 179.\n", "\n", "I did not define it at the time, but this is a *uniform distribution*. A uniform distribution assigns equal probability to any event in the range. According to this model it is equally likely for sensor A to read 157, 160, or 163. Likewise, 161, 170, and 179 are equally likely. Any value outside these ranges have 0 probability. \n", "\n", @@ -1763,16 +1720,17 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 28, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "outputs": [ { "data": { "image/png": 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u3YzrDxgwABcXFwYPHsyxY8f45ZdfmDZtGh98YPrQfOaZZ1i3bh3z58/n/Pnz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\npuDtrXxBEMISSPIuyr2Pd37M+lPrjfX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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1806,16 +1764,16 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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ixWL9iTW2D9kubJ9+cBqTDk/iEpJEJCi1eC8oKEBsbCxsbW2LtdvZ2SE6OrrE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\nKrmE1Lup+Pzu5/im6huL2O7eblwpv4Ir5Vfwl4y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y5EgAnJycCAsLo02bNkyaNInq1avnet+urq5575UQKvvrjFBZPV51Oh0fbv2Q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\nus3Ro0dp06YNRkZGSq1Tp06MGzeO69e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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1839,9 +1797,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "I used random numbers to form the discrete distribution to illustrate that it can model any arbitrary probability distribution. This provides it with enormous power. With enough discrete buckets we can model the error characteristics of any sensor no matter how complicated. But with this power comes mathematical intractability. Multiplying or adding Gaussians takes two lines of math. Multiplying or adding a discrete distribution requires looping over the data, and we have no easy way to characterize the result. In contrast, multiplying two Gaussians results in another Gaussian, as does adding them. This regularity allows us to perform powerful analysis on the performance and behavior of our filters. Analyzing the performance characteristics of a filter based on a discrete distribution is extremely difficult to impossible.\n", + "I used random numbers to form the discrete distribution to illustrate that it can model any arbitrary probability distribution. This provides it with enormous power. With enough discrete buckets we can model the error characteristics of any sensor no matter how complicated. But with this power comes mathematical intractability. Multiplying or adding Gaussians takes two lines of math, and the result is another Gaussian. This regularity allows us to perform powerful analysis on the performance and behavior of our filters. Multiplying or adding a discrete distribution requires looping over the data, and we have no easy way to characterize the result. Analyzing the performance characteristics of a filter based on a discrete distribution is extremely difficult to impossible.\n", "\n", - "There is no 'correct' choice here. Later in the book we will introduce the *particle filter* which uses a discrete distribution It is an extremely powerful technique because it can handle arbitrarily complex situations. This comes at the cost of very slow performance, and resistance to analytical analysis. \n", + "There is no 'correct' choice here. Later in the book we will introduce the *particle filter* which uses a discrete distribution. It is an extremely powerful technique because it can handle arbitrarily complex situations. This comes at the cost of slow performance, and resistance to analytical analysis. \n", "\n", "For now we will ignore these matters and return to using Gaussians for the next several chapters. As we progress you will learn the strengths and limitations of using Gaussians in our mathematical models." ] @@ -1850,13 +1808,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Implementation in a Class" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Implementation in a Class\n", + "\n", "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", "```python\n", @@ -1892,10 +1845,23 @@ "Now we can implement the `update()` and `predict()` methods. 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", "```python\n", - "def update(z):\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", + " self.P = (self.P * self.R) / (self.P + self.R)\n", "```\n", + "or\n", + "\n", + "```python\n", + "def update(self, z): \n", + " y = z - self.x # residual\n", + " K = self.P / (self.P + self.R) # Kalman gain\n", + "\n", + " self.x = self.x + K*y\n", + " self.P = (self.P * self.R) / (self.P + self.R)\n", + "```\n", + "\n", + "I'm going to go with the latter as you need to transition to understanding this form of the equations.\n", + "\n", "\n", "Finally, the movement is usually called `u`, and so we will use that. So for the predict method we might write:\n", "\n", @@ -1910,7 +1876,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 47, "metadata": { "collapsed": false }, @@ -1923,9 +1889,12 @@ " 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", + " def update(self, z): \n", + " y = z - self.x # residual\n", + " K = self.P / (self.P + self.R) # Kalman gain\n", + "\n", + " self.x = self.x + K*y\n", + " self.P = (self.P * self.R) / (self.P + self.R)\n", "\n", " def predict(self, u=0.0):\n", " self.x += u\n", @@ -1936,13 +1905,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Introduction to Designing a Filter" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Introduction to Designing a Filter\n", + "\n", "So far we have developed filters for a position sensor. 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. Following chapters 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 volts.\n", "\n", "We can simulate the temperature sensor measurement with this function:" @@ -1950,7 +1914,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 31, "metadata": { "collapsed": false }, @@ -1973,7 +1937,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 48, "metadata": { "collapsed": false, "scrolled": false @@ -1981,9 +1945,9 @@ "outputs": [ { "data": { - "image/png": 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o+ODP172E08nJKfO+sLAwevQYyIkTZ+jWrVu+xvY4SimqVStBiRLplC7tQMmS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\nW1uzwMfN6frL5cYIQiW1Lg7I5QkIwqN8qQ/vOW3MoPkViE1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llJTgCNWcLDhCh33nTHj5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\n", 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IercULVoUT09Ppk+fTmBgIG5ubrRv316ep/ect7c3RYsWJSbmAYcPLyFPnucMHTqEQoWK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\nvCQoPz8/3+wQvmrgwIHKy8vTiBEjFB4ernfffVd1d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YGAhXV1eoVCpkZWV1Gl9YWIjIyEjI5XL4+/tjxYoVBsc1Gg2efvpphISEwMHB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\nq9UG7Wq1GhERERbKinqyQYMGQalUGsy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+ "image/png": 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6BCen5lTvvvtui/lyhZ6IiIiIOguLW24aGxuRl5eH6Ohok/aYmBjk5OSY7XPkyBGMGDEC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\nEaNoQMnlMyi5fAZymRMG3H0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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2060,13 +2024,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Animation" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "### Animation\n", + "\n", "For those reading this in a browser here is an animation showing the filter working. If you are not using a browser you can see this plot at https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/animations/05_volt_animate.gif.\n", "\n", "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", @@ -2092,19 +2051,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Exercise: Plot Histogram of Measurements" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Exercise: Plot Histogram of Measurements\n", + "\n", "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. Use `plt.hist(data, bins=100)` to plot the histogram. After 10,000 runs do the results look normally distributed? Does this match your intuition of what should happen?" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 33, "metadata": { "collapsed": false }, @@ -2122,16 +2076,16 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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WLFmiyspK2Ww2JSUlaeXKlcrNzdWcOXNGdAAAAIxXl2+v+G2RNrvirr8hCBUB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\nK7W0tCgpKUlXX321nn32Wd1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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2147,9 +2101,9 @@ " N = 50\n", " voltage = (14, 1000)\n", " for i in range(N):\n", - " Z = volt(actual_voltage, variance)\n", - " voltage = predict(voltage[0], voltage[1], 0, process_var)\n", - " voltage = update(voltage[0], voltage[1], Z, variance)\n", + " z = volt(actual_voltage, variance)\n", + " voltage = predict(voltage, (0, process_var))\n", + " voltage = update(voltage, (z, variance))\n", " return voltage[0]\n", "\n", "vs = []\n", @@ -2176,28 +2130,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Example: Extreme Amounts of Noise" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Example: Extreme Amounts of Noise\n", + "\n", "With the dog filter 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? I will start by injecting more noise in the RFID sensor while leaving the process variance at 2 m$^2$. I will inject an extreme amount of noise - noise that apparently swamps the actual measurement. What does your intuition say about the filter's performance if the has a standard deviation of 300 meters?. In other words, an actual position of 1.0 m might be reported as 287.9 m, or -589.6 m, or any other number in roughly that range. Think about it before you scroll down." ] }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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IAFgdwlT90qVLS10n0X+x3PNuDRo0KPNaga5duxKQG3axX79+BOSGG3z69GmZ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\n4vDhw3KnRA2kUCiEUqms87VgwQK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1orlz59LNmzepbt26cu1tzJgxpbp85Nw4tm7dmgICAqhly5YEgObMmSOXNicn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hgdTUVFhZWeHhw4fMNcbKygq+vr4lrrdnzx6cPn0aFhYW+OGHH3Dw4EEEBQVh5syZiIuLU9sx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\nOnXQrl07bNi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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2205,18 +2154,18 @@ } ], "source": [ - "velocity = 1\n", "sensor_var = 300**2\n", "process_var = 2\n", + "process_model = (1, process_var)\n", "pos = (0,500)\n", "N = 1000\n", - "dog = DogSimulation(pos[0], velocity, sensor_var, process_var)\n", + "dog = DogSimulation(pos[0], 1, sensor_var, process_var)\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_var) \n", - " pos = update(pos[0], pos[1], zs[i], sensor_var)\n", + " pos = predict(pos, process_model) \n", + " pos = update(pos, (zs[i], sensor_var))\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", @@ -2246,16 +2195,16 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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5FBUVRatWrbSB+tChQ+zZs4dTp05hYWHxj/3t7e2xtbXl1q1btGrVChMTE86f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GtrY2jRo10kxREUWbBG8hhBBCiEKSmpoKQJ06ddDV1aVatWrs27ePlJSUF76ubNmymjna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\nHD16FFNTU/z8/GjatCnBwcEMGzZMU3/Tpk2cOXOGoKAgjh07xvTp04m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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2263,21 +2212,21 @@ } ], "source": [ - "velocity = 1\n", "sensor_var = 20\n", "process_var = .001\n", + "process_model = (1, process_var)\n", "pos = (0,500)\n", "N = 100\n", - "dog = DogSimulation(pos[0], velocity, sensor_var, process_var*10000)\n", + "dog = DogSimulation(pos[0], 1, sensor_var, process_var*10000)\n", "zs = []\n", "for _ in range(N):\n", " dog.velocity += 0.04\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_var) \n", - " pos = update(pos[0], pos[1], zs[i], sensor_var)\n", + "for z in zs:\n", + " pos = predict(pos, process_model) \n", + " pos = update(pos, (z, sensor_var))\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", @@ -2296,29 +2245,24 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Example: Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Example: Bad Initial Estimate\n", + "\n", "\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 1000 meters. Can the filter recover from a 1000 meter error?" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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27FmWNl4IIYT4FK1cuRKA4cOHc+/ePcaPHw+QLUHxxYsX/PnnnwCcOXOGR48e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G+Pk7DUULZN7NiJGRkYDu+2NiYkK1atWApBsohcgMGvX8skfPMTc3R6PRMGjQ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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2326,18 +2270,18 @@ } ], "source": [ - "velocity = 1\n", "sensor_var = 30\n", "process_var = 2\n", "pos = (1000, 500)\n", + "process_model = (1, process_var)\n", "N = 100\n", - "dog = DogSimulation(0, velocity, sensor_var, process_var)\n", + "dog = DogSimulation(0, 1, sensor_var, process_var)\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_var) \n", - " pos = update(pos[0], pos[1], zs[i], sensor_var)\n", + "for z in zs:\n", + " pos = predict(pos, process_model) \n", + " pos = update(pos, (z, sensor_var))\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", @@ -2356,28 +2300,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Example: Large Noise and Bad Initial Estimate" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Example: Large Noise and Bad Initial Estimate\n", + "\n", "What about the worst of both worlds, large noise and a bad initial estimate?" ] }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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XX7Fhw4bi2bq4uOjZM1asWFFMxLSysqK5uTkBsHHjxm/8vNQFjipWrMixY8eK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\n7++vmBXOaBMW3oX13LlzAAAfHx8wJkpNoqOjERkZCcbkzim68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CArK4v/7JycHHAchyFD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\nIGh2AAAAAElFTkSuQmCC\n", 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RnTp1Kkly165dwnKcmJhoYmWvUaOGCBbMnTs3bW1txf8cHR0/yjmkpqby+PHjDA8P5927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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2388,14 +2327,16 @@ "sensor_var = 30000\n", "process_var = 2\n", "pos = (1000, 500)\n", + "process_model = (1, process_var)\n", + "\n", "N = 1000\n", - "dog = DogSimulation(0, velocity, sensor_var, process_var)\n", + "dog = DogSimulation(0, 1, sensor_var, process_var)\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_var) \n", - " pos = update(pos[0], pos[1], zs[i], sensor_var)\n", + "for z in zs:\n", + " pos = predict(pos, process_model) \n", + " pos = update(pos, (z, sensor_var))\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", @@ -2414,16 +2355,16 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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YBAUFMcGeU1xuIkJERATu3LkDGxsbeHh4sDCAoaGhmDBhAhOnQUFB8PX1hZ+f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JDw/HnTt3sGXLFgD/ZYjhcDgcDofD4cK8iLl//z4AwNbWFgBgZWWFypUrS0qFDx06FFOmTMHT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\nzJkzkMlkRT0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J72j0r4+iBTp27IgBAwaIpD1PnjyBsbExevXqhYoVK+Lx48fo0aPHG/czaNAgtGzZErNm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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2433,15 +2374,16 @@ "source": [ "sensor_var = 30000\n", "process_var = 2\n", + "process_model = (1, process_var)\n", "N = 1000\n", - "dog = DogSimulation(0, velocity, sensor_var, process_var)\n", + "dog = DogSimulation(0, 1, sensor_var, process_var)\n", "zs = [dog.move_and_sense() for _ in range(N)]\n", "\n", "pos = (zs[0], 500)\n", "ps = []\n", - "for i in range(N):\n", - " pos = predict(pos[0], pos[1], velocity, process_var)\n", - " pos = update(pos[0], pos[1], zs[i], sensor_var)\n", + "for z in zs:\n", + " pos = predict(pos, process_model) \n", + " pos = update(pos, (z, sensor_var))\n", " ps.append(pos[0])\n", "\n", "bp.plot_measurements(zs, lw=1)\n", @@ -2462,19 +2404,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Exercise: Interactive Plots" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Exercise: Interactive Plots\n", + "\n", "Implement the Kalman filter using Jupyter 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 **Gaussians** 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 written the boilerplate for this; you fill in the required code." ] }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 40, "metadata": { "collapsed": false }, @@ -2501,28 +2438,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Solution" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "### Solution\n", + "\n", "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. Process noise 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": 38, + "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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Pr32u8eabMGcOvPgifPSRWY5yiikqrSCroAzHhLQTBuPyyqr6Qbru/vLa9tXt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\n4OTYyEcnFov5Ma2cUGFJWW35SEJas8u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B+WQVFqpfOt55p67t5pvVxbceHk3vJ4QQ7aRFwbukpITExESmTp3aIHADPPnk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\nZbXLHO9vvvmG4uJi+vXrR3Z2No8++ih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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2531,6 +2463,8 @@ ], "source": [ "from numpy.random import seed \n", + "from IPython.html.widgets import FloatSlider\n", + "\n", "def plot_kalman_filter(start_pos, \n", " sensor_noise, \n", " velocity,\n", @@ -2541,10 +2475,11 @@ " dog = DogSimulation(start_pos, velocity, sensor_noise, process_noise)\n", " zs = [dog.move_and_sense() for _ in range(N)]\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", + " process_model = (velocity, process_noise)\n", + " \n", + " for z in zs: \n", + " pos = predict(pos, process_model)\n", + " pos = update(pos, (z, sensor_noise))\n", " ps.append(pos[0])\n", "\n", " plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", @@ -2562,13 +2497,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Exercise - Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Exercise - Nonlinear Systems\n", + "\n", "Our equations for the Kalman filter are linear:\n", "\n", "$$\\begin{aligned}\n", @@ -2590,7 +2520,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 42, "metadata": { "collapsed": false }, @@ -2608,16 +2538,16 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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oOT7GCjfQaqopYfnAPzj9DCiMuoqwf9rqwv5FJqRj7oGntKytjNKzcjB1zyOk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P08bPgnyMT4H7/MPcKHLTmhWwZERbnlslG/3b1MSkfpK1j147r3DZGIi0F28+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\n50tOTsbJkycxevRojBkzBhUqVDDML5iWpj/NnnekjxVPSIguS0l0NI2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Mb/lyymEOUGYl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\n4qLKKiYAAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2625,19 +2555,21 @@ } ], "source": [ + "import math\n", + "\n", "sensor_var = 30\n", "process_var = 2\n", "pos = (100,500)\n", - "\n", + "process_model = (1, process_var)\n", "zs, ps = [], []\n", "\n", "for i in range(100):\n", - " pos = predict(pos[0], pos[1], velocity, process_var)\n", + " pos = predict(pos, process_model)\n", "\n", - " Z = math.sin(i/3.)*2\n", - " zs.append(Z)\n", + " z = math.sin(i/3.)*2\n", + " zs.append(z)\n", " \n", - " pos = update(pos[0], pos[1], Z, sensor_var)\n", + " pos = update(pos, (z, sensor_var))\n", " ps.append(pos[0])\n", "\n", "plt.plot(zs, c='r', linestyle='dashed', label='input')\n", @@ -2649,13 +2581,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Discussion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "### Discussion\n", + "\n", "Here we use 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", @@ -2667,19 +2594,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Exercise - Noisy Nonlinear Systems" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "## Exercise - Noisy Nonlinear Systems\n", + "\n", "Implement the same system, but add noise to the measurement." ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 44, "metadata": { "collapsed": false }, @@ -2697,16 +2619,16 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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FjDNtJ+IRlR8Gg4GFY7vT98edoE8I/0fqlVCUe8GfcfslVTmeyWRg63Txqehd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\nh1qTmvpG+3kAAAAASUVORK5CYII=\n", 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dZ9ya0yxyuQpAUEg4+y48ovuMfWRuMZtqQ9Yxb5c7z3w+6XroKYIZWy/ID6xF\n89hqRBOTG2UcJSeg79HbJ2/8qPfX5t96tlRbePt+YaHLFXl5cvfqya6Zn216Swa1KCsv/7PuDBGi\njiVGPF9/ZPIGtcvO5B7VyZE5jpSTv/8GZ2ews4OLF2PfVkskyVV46tSpn5xXoqNpxQLy630XHumk\neMHl3ANueEpTyqnNTfi7o+FObTpky8ic/nV5vWMYi/5Xn+/PNmdvv2D4kmP6HVwSEh6hZIbLPXm5\neWVH6pXNp8cRJT3ZbNIyt786jWXuLncu3n2lxxEZBisOeNBj5n5ZkBfNY8uJOV3IqEcv+vzZMzKj\nTy15eea2i1y6F/3fapHLFaZuOhfte0qlCrdbLxi6+Ch5Oiygw+TdBItC3xjx+fiFpfuvyctTetRI\ndkLrR2qUys328a3keqKbT97SePRWMVP2i0xYd0b+LJXOb0cLA0thiC8j2lQgjYU0m/LghS/bTt2N\nY4/fE5VKRb+5h+Q8/FIOdgxqUS72nd69k6LkAL6+kD9pOmsb1DdW1eK5sI6MBr545/9T4eOvEhGh\nlIs6AAY2K5ssvKstUpkyoHlZpvSoIa9b6HJFI3Kcktl96YVsC5Xa3ERDnP5OdK9fgrplJF9slQq6\nzdjLl28hceyVclnkcoU/ojT9yW+fllP/dTWI5lADmpWlRsncgCSuu07f+5OQ2nnmHv9bqO4iWr9c\nPu6t7c+MPrWoUDg7P04wbj11l8ajtxIYQ5fg353pW85rCK3GFZLmJqprmlVyZNWIxvLy+TsvaTF+\nuxDmieTBiw+sdlV3zPy3V81k2/Aro7UFQ1uVl5cnrHcTrk8/oFKpGDj/MCevPwOkNMOVIxpjEtcD\nu4cHGEfWGFSqBJmSxprUoES5mamxnDsLCU9hGb3yJOkaTafW8A3sdrv/U4rHjjP3uPdcyieySm3G\nn+2TV07y3x0raVQJ9/3vIFcjc+NTKm/9vrI0inXluM5VyJklnR5HpD8UCgUrhjeWIyOer/3o+9+h\n39IOa84OqVHPdwplt2bpH+UNQpCD9MW/5s8mGn+rqA2gTt94Rqd/XeQIf7mCWdn5T2sK5bLhz/YV\nubCoB967hrNieCONBkUnPLyo++cm/EUKgwZvPgSw/ICHvDyxW7VkK7Sio3v9kszpV0dePnr1KQ1G\nbf6tH8oTy98rT8pFkbVK56FOmbxx7GHYDG3tLHf6fPLGjw1Hb+l5RIaDSqXifwtdWbJPPYM2rHX5\n+HWNb9DAHOE1AAAgAElEQVRAipBv2wZ//aXDUWpiUKIc0MgrT0h3z11u95m25Tz+gSGcvP6MVhN2\nkqv9fCasO8ObDwGE/xAlH9yynMHcwOOLQqFg7V9NKZJb8q4OCYug+bjtKbr4Z/iSYwQGS9Gv/Nkz\nMqy1s55HpF9yZLZmyZCG8vKWk3dYdei6HkeU9EzbfI4RS4/Ly86Fs7G4d7kEe4zrmpxZ0jF/YD15\neaHLFU5df8bNJ29pOnYboZFTqQWyZ+RgNJ2Es2Swonej0hyd1YkpPavL6y/cfUWtERv5KApBZaZt\nOS9PTZd1zEqD8g5x7JH8GNbGmQnd1B2y3W69oNbwjTF2Nhb8zIU7LzV0RdQ0s+RKOqtUjGirvi9O\n2uAmf7f8zqhUKoYsOiLX6wC0r1GEab0T8De3toa2bSWBnkQYnCivVzYfpibSsG4+eRsvF5YPnwPp\nP+/QT+u9fb8wcb0bOdvNo+LANXi+llrTWluaM7xN8hR3VqnN2Du5rfxk/Mb3C60m7EyRH8Idp++x\n5aS6Ccyi/9XH/Dcp7oyNTrWL0auhuoBt0AJXbiXAei+5olKpmLj+DKNXqYtcqxTLydGZnWJti61P\nutUrQSNndRpFtxl7qf/XZtn1wT5TGo7O7BRngGBMpyrMjWKNee2RN9WGrudtCn4gjy+v3vuzMsqD\n6cTuKStKHpV/ulZj5h9qUXHl4RuqD12fogMz2kKlUvHncvVsVYeaReMXMU0G/K9FOdlC88U7f9ZE\nSc/5HVGpVAxdfJQFe9TFvG2rF2bD6OZxp63oGYMbXVpLcxqWV9/E2kzcic/HL7HuM2DeYT58lqJG\nWTOlYUynymSO4jscoVTJFogAw9s4x+hdnBzImzUD28a1lIt/zt95ydDFR/Q8Ku3y5kMAfeeq84Ub\nls5KbafkPc2oTRYMqk/RPOoZk9YTdxIQmDymslUqFR6PvOP8XEfFLyCIP+YcZMI6N3ldjZK5OTy9\nA2kszHUxTK2gUEj5i9+dYF69D5CFtLWlOUdmdIx3OtaQVuVZPqyRnGt+99l7qg5Zx6v3/rHvmML5\nd/M5OSjhXDibXHeRUhnZriKLB6sjd7e93lFlyDpef4i+HbtAYt+FR1yMLLg2MzXWmH1K7qSxMOev\nKOm4Uzae/W2LwlUqFcOXHGP+7svyutZVC7FpTAuDF+QAxhMmTJigr5OHhKhFRKpUats/50LZ2Hj8\nNkEh4XwNCuXygzd0rl0MY6Of/0N3nL7HxA3qG/X28a34o7ET/2tRjqK5bfH1/6bRdCFD2tRsHdcq\n2Udc82XNQCozY054SMULVx958+SNHw9efuC5z2c+BgQRHqHEwtwUUxPDbYgQHUqlilYTdnI/Mv/f\nLn1q5nRzIlfO7HoemeFgamJMjZK5WXf0FqHhEfgFBPHM5xMtqxQ0+CjhlI1naT9lD/N2ufP87WcK\n57aN0b4wIkLJioMeNB+3nfNR3GbqlsnL/qntsEglpXx4e3sDYG9vH+1x9IlVajNyZ0nHLje1j7C5\nqTGuMzpSxjFrgo5VuoA9ee0zsP/CI1Qq+BgQxJ5zD2jsnF8vFpD65sXbz3SfuU/OEV77V1Py2meI\ncXtDvk4SQhnHrOSxS8/+i+rrwOXcw9/2OoiL8AglLf/ZIXv/D2pRlnY1isa4fXK8Tkrms2P14esE\nBofx5VsotuksKRfZM+F3QaVSMXLZcf7b6S6va1W1EFvGttCJDopJw/4KBinK01mlolR+OzafuINK\nBS/f++MfGEz9cpp5gu8/BdLw7y18i+yC17NBSYa3qQBIfsGFc9vSrV4J2lQrjKmJERnTWrB0aEPy\nZYv5Szs5UbFIdh688JWLV+94vefUjefsPf+QDcdusTDSbm3FQQ8ypbWgRL4seh5x/Fiw+7JcmKFQ\nwJxuZchpa5WsviCTgkzWFuTOko7dZx8AcO/5B7JksMKpgOH+PwWHhtN6wk6CQ8NRqaQUtcV7r/Lk\njR+FctpopHGcu/2C5uN3sPrwDYJC1FGfFpULsnNCa1Kbq1NWDP0mWji3LU/e+HHH6z1GRgp2TmhN\n3TKJs/UsljczRXLb4nL+AUqlCv/AEPace0jTCgV+O0H257LjXH0k/e0rFc3B5B7VY30oNfTrJCEU\nz5eFIrlscDn/EKVSxeevwex0u0/9sg7YpPu1DrUpjVWHrstuZWktzdk1sQ0WqWJOeUuO14mpiTFm\nJsYcufIEgBuePvRvWibZBeUSS0SE8idB3qJyQbaOa5mw/4PHj+H8eciRA2LoQP+d30aUA+SxT68R\nCb784A35smagWN7MgPRE1G36Xjwe+wCSj/O+Ke2ibShjk86SemXz0bFWUbLbxmEWn4xQKBQ0KJeP\nEx7PeOMbcyrA16BQXK88oWOtogaftnP32XvaTNxJRGTka1SHitQolB5IXl+QSUXRPJnx+fhF/hyc\n8PCiYXkH7DKm0fPIomeX2302Hb+jsU6lkqbgl+y7yoMXvmRMm5oxq04xfOkxjZzpXFnSsfavpozv\nUuWnL9nkcBNtUrEARXLZ8neHSlSPtEtMLAVz2uBUwJ7dZx8QHqEk4NvvJ8y9vD/Rc9Z+lJEWNutG\nNSW3XfpY90kO10lCKJRL8zr4GhTK5hO3KZ3fLtYZg9+JwKBQWozfwddIK9HxXapSN44+F8n1Oime\nLwvrj94i4FsIgcFhmJkaUa1ELn0PS+d4+36h2bjtbI3i0968siPbx7dK+EPJrFkwaBD8959U6Fku\nZj9zXYhyg06w+bNdRVpGMfXvM+eAXNC24/Q9OUIIsGpE42TZTvlXsUxtxsVFPTg0rQMLBtVjZNsK\ntKtRhIpFspMzs7WcQxUSFsEwA284FBIaTqepe2QXhZIOWZjYLeXk/emKeQPrUTzyYTUkLILWEww3\nvzyqU0zn2sWo7ZRHXlapYPvpe9QYtkHjyzW1uQmTe1Tn/rr+NKvkaPDpOTFhYmxEm+qFKemgneKy\n+uUcODStg9w99PWHAKoPW4+X9+/R/XPKxrOyJ3O1Erl++UEnuVK/nAOuMzpiFene4x8YQv2/NrN0\n39U49vw9mLvLXX64t8+UhiFRfL1TGqnMTBjTSd0QccI6N+bvco9lj+TPoUuPKd5rGWduPpfXNa1Y\ngG3jEiHIAfbvl/4NDoacObUzyASgdVG+ZMkSihcvjrW1NdbW1lSoUIHDhw8n6ljfLQAdc0im7UEh\n4TQfv52HL30ZMF99zF4NS8b55BsrAQFw5w4kU79nY2MjGpR3YFCLcszsW5ut41pyfmEPnm8bwrkF\n3eXt9p5/yLGrT/U40tgZv/a03DAqlZkJm0a3kFtMC2ImtbkpO/5pLd+Un3p/omC3xfSbexDXy54G\nU/Dj5f1Jo4HDv71rcmxWZy4t7qnRnyAqbasX5uH6gYztXEUjXUUgUaNUbg5MbS/PEL56H0C1oetS\nvDB/8saPDcfUfswTu1XT32AMgGolcnF2fjeyZpJmyCKUKvrPO8z/Frj+1s1kPnwOZOa2C/LyxG7V\nYk1bSQn0qF8S58LqXPIhi48yc+uFWPZInoSGRTB8yVEajd4q1woYGSn4p2tVdk1skzjt4OkJDyKD\nvalTQ62kt8zUuijPnj07M2fO5MaNG3h4eFCjRg2aNWvG3buJa/+axsIcl8lt5SYcz3w+U7L3cj5G\nerNmt03LnH6/0OHx2zcoVAiKFQP9ZfLojPKFstG1bnF5+X8LXQ3SPtHt5nNmbb8oL8/oU4tCuWz0\nOKLkRf7sGTW6/nn7fmHZfg8ajNpCpqYzaTl+B+uP3OTD50C9jXHtEbVNV70y+chmkxaQrtFD0ztw\nbVnvyEi4NEtyZm5Xto1vRY7MKSflTBfULJ2Hg/9qCvPqw9bzzCd5C3OPR950+deFJmO2UnfkJqoP\nXU/FgWso03cl1Yask1PcapbKTZXiSR/RMjRKOthxZWlvjZqShS5XaDx662/bbGrKxrOy/WjBnJno\nVq9E7Dt4ecHr10kwMt1hZmrMkRmdqFhEbYzw14oTTI5iiJHcefLGjwoDV2vkj9tnSsPJOV2Y0K1a\n4l1WDhxQv65dGyySvpeNQpUE7QAzZszI9OnT6d27t8Z6f3+1lZe1dew33j1nH9Dynx0/rT82q9Ov\nWeUdPQr11A0+ePcObG0TfzwD5K3fV/J3Xih/Oc3uV1suiDUE/L8GU6zXMl6+k66HOk55cZ3RUbZ8\nvHZNKvp0cnLS2xiTCwt2X2biBrcYG4qYmhixakQTukR5UEsKIiKU5Gw3T6592D2xDS2ipKZFJTg0\nPNrakNgQ14hUT9B49FZ5ZiRHZmvOzO0aZ561IfLpSxAFuiySrW5j4/yC7lQsmiNex5WvExsbvUxN\nJwXfgsPoOn2vhttPoZw2HJzWPlleC4nF5dwD2kzcJc8U7JvSjiYVC8S+U6tWsH8/vvXq4d2rF8Wa\nNEmCkeqGr0GhNB69VSOtY0ynynEWQxs6m4/fpt+8Q7KeAWhY3oF1o5r9ekPIqlXh7Fnp9apV0LNn\nrJsnRMPGF53mlCuVSrZt20ZgYCAVKvyaCGxRpSCjOlTUWNenUalf965+GaU5kaUlZMz4a8czQLJk\nsGJC12ry8sT1brF6RL9670+TMVsp2mOpxgdaF6hU0jTrd0GeIW1q1v7VVBbkgoTxv5bleLdnBG7z\nujG8jTP5smoWe4WFK/njv4O8iGITmhQcvfpUFuS26S01Gur8SEIFuUCiVuk87J+qLnZ/+c6f6kOT\nZ8R83JrT8RLknWsXi7cg/46ZtzcUKQLt2sHHj4kdosFikcqU7eNbMbazOrf4/osPlO23isv3k3cU\nOL6sdb1Bqwk7ZUFeuVgOGleI+TsHgEePYM8eCAsj04EDmPr5SU4cyRSr1GYcmtZBo25n6qZz/Ln8\nOEkQi9U6fgFBtJ+8m07/usiC3NTEiLkD6nLg3/ba6dDety+0bi0VeDZq9OvHSwQ6iZTfvXsXZ2dn\ngoODSZMmDZs3b6Z+/fo/bRf1KcPT0zPO40YoVYxYd43zD96TO7MVawZWwOoX88Psly7Ffs0aALx7\n9sS7b99fOp6hEh6hpMN/53j2Xip4aVg6KxPa/TyVd+fFJ0as88Dvq1QoaGluwqoBzuSzS6uTcR24\n+opJO27Ly9M7l6JmsZTRZc0QUKlUvPgQyNl779h96QXen6QIeq3idkzrVCrJxjFy/TXO3JXqBTpV\nzcPgRgW/DxCScdTGEHF/9IHh664RGi4JElvrVCzuU45ctlZ6Hln8ePTGny7zzxOZncKA+gXIb58W\nUxMjzIyNMDExwtTYCMtUJtinT52wqJ9SSf4BA0gbGTEPy5CBF6NH87lq1Th2TJ4c9njNlJ13CIsU\np2lTm7JygDN5MhumO5M22OzmxbyDahOIHJksWfxHObKki92VKOeUKdjs2/fT+hunTxNhlTw+O9ER\nEhbBXxs8uPDwg7yubaVcDG9SKNlEzC8/9mXSjlu891enYWXLaMG/nUpRMJv20xsV4eGoTOIODjk4\nqGuhDDpS7ujoyK1bt7hy5Qr9+vWjS5cu3L9/P+4d48DYSMGcbk5sGFyJdYMq/rIgBzCPtD4CCLVL\nuWLQxNiI4U0Ly8uHPN5w67mfxjaHPV7Td5m7LMgBAkPCGbrmGr4B2s9JfP7+KzNd7snLTcpkE4Jc\nyygUCnLZWtGlel4mtlc/hJ245cN1r6SJEn78EsK5++/l5d7PL1G4VStK1KhBhmOG7QiUHClfwIY5\n3ZwwM5G+3t/7B9NnySUeext+x0elUsVMl3uyIC/nkImu1fNSwdGWMvkyUTx3BgpnT0d++7RkzWCR\nYFGhCA0lJIrNnamfH/lGjCDXP/9gHGD4/z8JpUHpbCzrW550llJNVkBQGINWXuHt5+jT25IzKpWK\npUceaQjy/PZpWTnAOU5Bbvr+PRkPHYr+vbdvtTrOpMbc1JiZXUtTrXBmed3288+ZH+X/yVAJDotg\n9r57DFx5WUOQNy2bnU1DKutEkAPxEuS6IklyymvXrk2uXLlYuXKlxnpd5OMkmKVL4fRpePECZs+G\nypXj3icZ03L8Dvackz6MpRzsuLK0FwqFgrGrTzFty3l5u4xpUxMaHiFPE5VxtOfM3G5aq1wPDg2n\nXL9V3PaSoqeOOTJxbVlvLCMdRKIi8oW1R/vJu9kWaTdYIl8Wri3rjbGOWw/P2naBP5efAKSGV+e5\nAYsWSW/+9x8MHfrL5xDXyM+c9PCiydhtfAuWmquls0rF4ekdcC5suJ1x1x+5SbcZUrTS1MSIO6v7\nUSDSfSvBhITAxYtQXW2rKl8n795B797gI/n7Y2oKHh5QNOYuj8kZj0feVBu6XvbqLpgzE+cX9Egx\nnvZKpYqB8w+zdP81eV3lYjk4MLV9/KySR46U7v8AFSoQEBoqz6Zw+DBEM9Of3AgLj6DTVBd2nFEH\nwhYMqsegFjH7cOuT64996PTvHh688JXXZbK2YOWIxjSr5KjHkalJdjnl31EqlRom6wZFv36wYwdc\nvpziBTnAnP515JzT654+zN99mZb/7NAQ5IVy2nBlaW92/NNazu2++tCbLtNc5HbWv8rIZcdkQW5u\nasz28a2iFeQC7TLzj1qyr/XNJ29Z43ojjj3A5+MXHr9KXFRdpVKx+rD6HL0aloIsUTrLvnuXqOMK\n4qZm6Twcn9UZa0tzAD5/Dab2iI2c9PDS88ii5/PXYEYuPy4vD2vt/GuCvEULydJs+/af32/YEO7e\nhY4dpeWJE1OsIAcoXcAel8ltMY2cPXnwwpdGo7fID2yGTFh4BFtO3KHXrP38b4Er0zafY63rDVwv\ne3LD04c3HwLoNHWPhiBvWN6BIzM6xb93Sa9eUlGfqSmMGkVoZnVUmVevtPwb6QdTE2M2j21B88pq\nQTt40RH2nn+ox1FFz7L91yjXf5WGIG/knJ+7a/oZjCDXFVoX5X///Tfnz5/nxYsX3L17l7///hs3\nNzc6deqk7VPpjoAAWL062fqWx0auLOk0CmaHLz2m8aFsUM6BS4t7ksc+PfXK5mPhIHWEYPfZB4xe\ndfKXx7D3/EMWuagbW8wdUFfu1CrQLdltrRnVvpK8PGb1KT7HYpe27shNcrabR4Eui2g7cRfvPyXM\nUvHC3Vc8ihT0aSzMaF21EES94SXzqWFDp0KR7JyZ1w2bdFIRVGBwGA3+3sL+C4/0PLKfGR+luDOb\nTVrGdq6SuAN9F+SHD4NSCR06SH0ofiRDBti0CY4dkyKlKZxapfOw8e/mcgnHpXuvaTNxJ2HhhmeR\nCxAQGMJ/Oy6Rt+MCOk7dw+rDN1jocoXRq07RY+Z+GozaQqk+K8jWZq5Gs7EONYviMrltwmZ1CxSQ\n3DaeP4eGDVOkKAcpjXXT6BaULyT5mKtU0uypuwEVAJ+5+ZwB8w/LRbqWqUxZMbwR+6e2I3MGHeX2\nKw3Hy1/rovzt27d07twZR0dHatWqhYeHB0eOHKFOnTraPpVumDgRsmeXnpxP/roANUT+bFeRXFnS\n/bR+eBtn9k9tR9rIyBpA/2ZlGNJKPb01Y+sFja6MCeXlO396zFQX07SoXJC+TUTKQVIyom0F2fv7\nw+dv0frXqlQqpm46S/cZ+wiLLBjcceYehbotZsuJO/Gu3o8aJW9fo4g0GxL1hici5TqnRL4snJ3f\nXfaFDw2LoMX47Ww5EY1Q1RO3nrxlcZQOlP/1ryM3w0owXbpIgvw7o0dLbisxUbs26DGHNClpW6MI\n8weqLYAPuXvSZ85Bg3LjeP0hgD+XHSd727kMX3qMV+/jn+s/oFkZNo5unrhOjgD29mBkRGiWLKiM\njCBrVjBLWTO4FqlM2T+1HXntJXvM4NBwGo/eytM3fnHsqXt8/b/RceoeeUa+pEMWbq7qS+9GpXVX\nlKpUSr1qWrWCDRsgNDTufXRIkuSUx4RB5JT/yMCBsHix9Lp2bSmKkgJxOfeAFuMl33dTEyOWDW1E\njwYlo902IkJJs3HbOXhJsocyMTbiyIyO1CydJ9rtYyI8Qkm1Ieu4cFeKPOTIbM3NlX+QPk3seY0x\n5gufPg0rVkC3blD3FxpI/YbsOH2PtpN2AdLf886afnLn3IgIJYMWuGpMB/9II+f8LBvakKw2Mbvy\nBASGYNdqjjxFfnlJL8oG+kCZMuqNSpaE64l/yPuOyCmPmxdvP1Nz+AaeRnb7VChgUvfqjOpQKfHN\nNrSASqWiyuB1nL8j2dPWLJWb47M7J+4m/OwZ5InyvTR2LEyaJDv8iOtEYsyqk/y7WZ2yOKpDRab1\nTvruhVF59d6fMatOsfXU3Z+6kNqks6BvYyfSWaXird9XfPy+8jbyx+fjF4JDwxnVoRJjOlXWinjz\nuHgRlZERTuXL//KxDBXP1x9xHrBabsTokC0DFxf11I61YCJQqVQ0GbNN1hmZrC24taov9pl07BR0\n7Zr6npQxozR7G8+H9GSbU56sGDYMjCL/W44fhxtx59wmR5pVcmROvzo0r+zImbndYhTkAMbGRmwd\n15IS+aRc4PAIJS3/2cGjl74x7hMdk9a7yYLc2EjBljEt4hTkMfLtmzRFvW2b5Des56fb5EbraoWo\nXEzydw6PUDJsyVEAgkLCaDVhp4Ygr1kqN3smtdHorHnw0mMKdV/CqkPXY4yybTt1VxbkRfPYUsbR\nHt68UW/g5ARXr0a7r0D75MySjnMLulMkt9QcTaWS/MArDVqT6JoBbbDp+G1ZkJuaGLFocIPEC6un\nT9Wvy5XTEOQCNVN61qBHfbUb0/QtF+g/9xCBQfr5HvX2/ULFQWvYePy2hiAvkD0jK4Y34uX2oUzq\nUZ1hbZyZ2bc2G0c35/jsztxZ0w/ffX/y1XU0YztX0Vo0VWVmluJnTxyyZeRAlE7Anq/9aDpmG0Eh\n+qkzWLD7sizIAdb91VT3ghwgqutOgwZ6/7v/3qL8+HEpKn7woLoKP08eaRrjO98rslMYCoWCYW2c\n2TOpLRWKxO3GYJXajAP/tpc/JP6BIbSeuDPeH+CTHl5M2XRWXp7UvXqCm35oYGEhCXOAz59BC5ab\nvxMKhYL5A+vJesX18hM2HrtFzeEbNGoMOtQsyuHpHWleuSB31/Sjf1N1hDEgMITesw/gPGA1fy0/\nzsZjt7j55C0hkR0lVx1WR8B71i8p3TDfq60RKVIEjBM5zSxIFHYZ03BmblcqRfnsXX7whhK9l7HI\n5UqshdwhoeG43XzO6RvP5K6hv4r/12BGLlMXdw5tVV6esUkUzs7Sg97u3TBhQsIE+ZEjUm5548bS\nLFwKRqFQsHx4Y42GOkv3X6N4r2VcuPMylj21T0BgCA1GbdZIU6lSLCf7p7bj/roB9G5UWjcNxS5e\nhNu3494uBeNcODubx7SQPyYX772i01QX/GOpM9IF1x/7aBR5D21VnoaxNJjTKkeOqF83bJg054yF\n3zt9pXt3WLdOer1sGfzxh/Q66nSGsbHU9TOKt+3vzPXHPlQctEa+KfdtUpqlQ2PvfOXl/Ymy/VbK\n02Q1Subm2KxO8bbii3HKuWVLqQMbwJo10t/zV/HxkaavSsY8c5CS6DP7ACtjqBEY2bYC0/vU+qm7\nqtvN5/SafYAnMeQgGhspyJc1g1zgaWZqjPfOYWS0toB//4UxY6QN//wTZszQyu8h0hISRkSEklnb\nLzJ+7Wm5ZgCkYsA1fzYhu630ffz+UyCHL3ty8NJjjl59KlvqpTY3oWapPDQol4/65RyirVH5keDQ\ncO4+e8/NJ2+54enDjSdvufX0nTybkjVTGh5uGJj4XPJ4EOt1EjV1cebM36L4MygkjI5T9+ByTv0g\nrlDAiDYVmNSjus6764aFR9Dw7y0cvyY5AhkbKdgzqS1NKhbQ6XlRqaTv+Fu3pOjowoUaaU+/2/fJ\n/F3uDFl8VF42MzWmjlNeWlctRJOKBUgXXxebRPDlWwil/1iB52vpflLKwY6Li3pgnhSdnT9+BFtb\nKa/cyEgKGiWgq7suNGzKmp+5fl1KZ2jfPn6i6vlz9etcudSvnZygZk2wtJSEgxDkMqXy2zF3QF36\nzZWmfJbt96BGydy0rlY42u2/fAuh6dhtsiDPksGKjaOba8cbu0QJtSi/efPXj/fqFRQrJkXee/WC\n5cvVqUwplCk9a7D9zD0CAtWWpQoFzO1fl8Gtos+nrFoiF7dW9eWfdaf5b6f7T9HVCKVKFuQAzSs5\nSoIcNCPlNjba+0UECcLY2IhRHSpRv2w+Ok9z4Y6X9Hc54eFF0R5L6dmgJBfvvebyg9fRmlAFhYRz\n8NJjebq5UE4bGpTPR+4s6fn0NQi/gCD8vgRH/huEr/83nrzx+ylXOCr/9a+rU0EeJwWiCMGHhmcT\npwtSm5uye2IbNh67zaCFrgQEhqBSwaztFznk7smGv5tRuoBu7n8qlYresw/Ighxg5YjGuhfkAOfO\nSYIc4MwZqa26NklmnYoHtyrP83efmbfrMiAVg3//fJuaGFG7dF5aVS1Is0qOiU85jYEB8w7Lgtwq\ntRnbxrdMGkEO0kyJqank2FSmTIIEua5IOaI8IgKaNZOE1c6dUm5hXILqxQv165w5Nd87fDjFVV1r\niz8al+bk9WfscpNSRnrNPoBTAXty26XX2E6pVNH5XxfuPpNu+GamxrhMbqu9PLGoD17ayP1ft04S\n5CDZY5mYwJIlyerLNaHYprfkny5VGb5UKmg2MzVm0+jmMT5kfccilSmz+tZhUPNyuN9/zZ1n77jj\n9Z67z97j5fNJFnLGRgqGRBX3H9StnoUo1z/F82Xh6tLe/LPuDDO3XUClklLT/tvpHu32eezTY2Js\n9FMO+v0XH7j/4kO0+8RFlgxWdK9XgtbVCiVqf60RVZQ/MjzLSF2hUCjoUrc41UvmosfM/ZyI9LG/\n/+ID5QesZkynyozuWBkzU+2mmk1Yd4b1R2+pl7tVpXv9JJqhPK8ucqV9++jFmEolRVJfvgQ7O83+\nCj8SGipZKZ86Bfv3S6mxFy9C3rzaH7uOmNOvLvmzZWTVoRtc9/SR14eFKzl82ZPDlz0ZuMCVMR0r\nM6LvacUAACAASURBVLyNs1aE84ajt9h4XJ1CtHRoQxyyJaEwrl4d/Pzg7Nm4t00iUk76ip+f5gfr\nxQvIEUvOckQEpEoF4ZG5kYGBUp6yIF58/hpMyd7Lef5WErFlHbNybkF3jS/ucWtOMWXjOXl53V9N\n6VqvxE/HiosYpxLfvIFs2STbqipVYMuWRPwmUTh1Spohicr//gfz5qVoYR4WHsHQxUe5++w9k3tU\np3KxnHHvFAuBQaHce/6BR698KZjTBqeokbaPH8HbWxLnjo7SzS4i4peLa3636WZdcP7OS7pO34tX\npDsLgJGRgopFstPYOT+NnPPjmCMTCoWCp2/8cL3yhMOXPTl943m8c8zzZc1AyXxZKOmQhRL5slDS\nwY4suvIejoZYr5OXL9XBmUyZNB8gY+LECWnbQoVSRBBHpVKxbP81Riw7rtFYyDFHJhYPbkCNUrm1\ncp5Vh67Te/YBeblH/RKsGtlEd7Z3P9KiBbi4SK9Xr4YePTTevnbtGjlmzMB2l+RQxYIFMGhQzMdz\nd5fqGaKydCn07avFQScdT9/4sfvsA3a63efaI++f3s9rn555A+vR6Bfyvh+/+kipPssJjLzOutYt\nzrpRzRJ9PH2gi/SVlCPKQerI+f0J+MiR2G3yXr1Si3ZbW+GXnAiuPHhDxUFr5CnpEW2dmdVX8qPf\nfuou7Sbvlrcd3saZ2f0S51WvcSM9e1aKWOTPL0UyfH21G3GNiJDcXL5/GWfIIKXGZDfc1uTJktmz\npRvdu3dSnvnw4b90OCHKtcPXoFBmbD3Pmw9fqFU6D/XK5ouzFfu34DDO3HzOcY+nBAaFkdE6NRnS\nRP6kTU36NKlJb5WK3HbpNXog6INYrxOlEqysIEhKtcPXN+7p7OzZ4fVr6aHywQPIl0/LI9YPT974\n0W36Xtkt6zsdaxVldr86v/Qg5XrZk8ajtxIRmfZWt0xeDvzbPvHe4okhZ07pIQykNJZixTTevnbt\nGnarV5N12TJpxciRUp1BTGzcKPnjR6V5c3V6ZTLmmc8ndp99wFrXmz/NhjUo58C8gXUTHN32Cwii\n8v/WysfLnz0jHsv76Dd9LRGInPK4KFRILcrv349dlJubw7hxUkQ9tXZzpH4XyhbMyrTeNWX3hNnb\nL1GjZG4yp7eie5QGQXXL5GVGHy144KpU0Ls3PH4sRbRXroTc2oncyBgbw9atUmT8zBmpgZQQ5Non\nNFTdKU88EBsMVqnNmNyjRoL2sUhlSoPyDjQo76CjUcWTjx+leqDs2aV7wXdBFV+MjGDaNCm/2NER\n0sSRZvfxoyTIQfreiFqXlMzJlzUDbvO6scjlCuPWnubLN6nAd/OJOxy49JipPWvQr4lTgmuDjl97\nSusJO2VBXtIhCzsntE5aQR4WBlWrgoeHdP8vFH3aVIK6enp6/rzu5ElpJj6ZWyvmtkvPiLYVGNKq\nPMv3X2PsmtNyF+jDlz05cd2LYa3LM6ZTlXiJ6qCQMJqM2SoLcjNTY7aNa5nsBLmuSN5Xy48ULKh+\nHZdFnq2t5GEbX0JCpA+zVdJNtSYHhrV25tSNZ7hefgJAl2l7SWVmQlCINJ2dP3tGto1vpZ3CztOn\nJUEOku2Zre2vHzM6TExg82bphvuroj84WKrsz5ZNyl0USETNz3z7Vn/jiI1Dh6Sxde6cIlITUjwv\nX0rF+8+fw6dPcW0dPYMHx3/bW+p8aIoWTfbi60eMjY0Y3Ko8rasVZvjSY2yLbGUfEBjCoAWurHW9\nycL/1ce5cLY4007uP//An8uPc8hdLV5zZrbm0LQOpLFI4tkTU1OpcyNI388x/N1Co35HJUaUBwTA\nlStQoUIiB2pYmBgbMaB5WdrWKMKYVSdZeeg6KpVUFDp9ywU2n7jD9vGtcC4ccxArIkJJhyl7NGZg\n1v7ZlJIOdknxKyQLtG4tMW3aNMqWLYu1tTW2trY0adKEe/fuafs00VOoEKRPDxUrSukN2mDrVulD\nlTatlHsm0MDISMH6Uc3k4k1f/2+8/iD5zVpbmrN/Sjvt2SktXap+3aWL5I6jK0xNtROFP3ECpk+H\nDh00i4t+d6JGoQwxUn7hAjRqJLnwzJ+v79EI4sPLKP7aSTG7FdXxqXhxKWCQAtIVfsQ+Uxq2jmvJ\nsVmdcMiWQV5/3VOyxy3cfQmTN7jh+frnBlRv/b7yx5wDFO25VEOQZ0ibGtcZHbHLmATNYWIjVcz3\npkRHyh0iZ4yMjVNk/4xM1hYsH96Yq0t741w4m7z+1fsAqgxex/xd7tE2lFOpVAxccFijD8acfnXo\nUKtokoxbg8BAKUX1u7GDAaF1UX727FkGDhzIpUuXOH36NCYmJtSqVYvPSfHL16olTSmeP689j9lP\nn+DSJWm6/eJF7RwzhWGTzpLNY1po+FkbGSnYOq4lBX6lEUgUTH19Ye9e9QptFtAoY7Zp+2WePpXy\nFS0tNZsU/O4YeqQ86izan3/qbxyC+BNVlMdW5K8toory1asl95b27aUbfgqktlNe7qzux+Qf/Msf\nvPBl/Noz5O+8CKc/VjB7+0Uev/rIpPVu5Ou4gBUHr8u2qQqFVNB3a1VfCuY0bPelUFtbKbXVwUFK\nZ4qt/M7YWArkAMydK92r/Pykh/oUSukC9pxf0IP1o5qRPo30cBMeoWTI4qO0m7SbL99CNLafuukc\ny/Z7yMvDWpdnWJsfimOTitOnoXVrqUj7hyJffaP1+TZXV1eN5Y0bN2Jtbc2FCxdoqKtuSc+eSUK8\nWDHpw2OuxemwqBXVQpTHSLUSufinS1X+WXcGgJl/1KJ+Oe3lmGbat0/tlFO5MhSOYtkXEiJFJG7c\nkIpr0qeP/iAxUb26lEfasqX0QY3JhSc0VHq6PnlSskyMj1OApaWUmw7w5EnCxpXScHeXuuXa2Gha\nhQUExLyPvvD11VxOZr7DvyVJLcpLlZKajd28qb5eQkOlz7sBdAbUBeZmJoztXIUONYvyz7oz7Dn3\nQMOlxeOxDx6PfTS6tH6nVuk8zOpbmxL5YrEWNCBU5ubSA1Z8PveXL0v3p5cvpRnW3+S7wshIstOs\nUjwnrSfslJ1adpy5x62nb9k9sQ2Fc9uy5vANxq1Rd8ltX6OIbAqhF74HyCIiDM6aV+dJcAEBASiV\nStInVCglhGPH1JHTDh2kfGBtUbSoJKwCA6Uc41evROFfDIzrUoXS+e0wNzOhVuk8ce+QAD7Wr0/W\n9OmliNSPUfKaNaV0A5DsEWMr8P2Rly/VHqWurlKL7ehEeXi4VLPgFdnookcPKU0qLooUUb++ezf+\n40qJ+PhINpZv3kgNuTw9pTQWQ6zTiPp9VaSI9Pk3xHEK1CR1+sqQIdKPSgUjRsD/2Tvv8KbKL45/\nb7rSQlsotNACZRYoLSBDhrJlyBJQ9pChbAREZYqAslQEfsgSEUWZIggIsmQjimXvWUqB0kJL6aQr\neX9/nKb3Jk2a3STN+3mePL25ueNt8t57z3vec75n8WJaf+BAkTXKVVQJKolfpvfA6pedseef29h8\n5Cr2/XcXWdmKfNuGVw7A16PaocOrVQtP8tBSGNNeV1e1qqDORKWyJXBq2VBMXLE/zxt+62ECGo1Z\nizHdGmKJpO5B2wZV8NPU7vkqRRcq0llrY+yFQsDqkoi9e/dGZGQkIiIi8l2QUjmZO9oSJQxEqif6\naNw4xA4eXPAOSiUqLFmCrDJlkBkUhBetWxd48VUfPRo+uVJa9+bPR2K7dia3lWMeQnY2IAhgkuSc\n4IULEbCd5BcN+v0lBGzahOAlSwAASU2a4M633+rctuLcufDfRaoyCe3b4/68eXqPL0tNRf3WrQEA\nShcXXDh5Ekw1zelklN6xA5UWLAAAPHvrLTyYOdPGLSoYl+RkyB8+RHpICBhP9LR7ZGlpcI+NhXts\nLF6GhCDbxETwwHXrUPzSJcijonB72TJkahaW04LPmTOoPm4cACAjOBhXt2/Xs0fRI+VlNo5eicXB\nizGIuBuP0j5yjGxfHZ0bloeLLQ0wCV43b8I7IgLptWohrUYNKPlA2+L8ee4RFmy/igwtA7TqQT74\nbnQTFJfb7hno8fAhar/9NgBA4emJi3/9ZfL9PSREjAZwCEnESZMm4fTp0/j777+tOkL2lIQFpBug\nE+v2/DnKbNkCAMjx8cHFNgVLgKXVrg2fs2eR4+sLl5QU8xrLMQttBm26JKnXy8hKfCWPHMlbTtTT\nD5726pVnlJc8fBiPPvwQ2aULjplXFi+OzLJl4REbC5lCAY/oaGQ4UJU3S+ImUcTIsebMmeZ54+JQ\n7No1JDdtCqUR8qcKHx+khRVc2ZRjPyiLFUNG1apmX1/eZ8/CJyICACCPijLIKE955RUoPDzgkpkJ\neXQ03B8/Rla5cma1w9Hw9nTDW40q4K1GFZCRpYCbq8xujHEVvidPotyaNQCAuD598PDjj23coqJH\npwblUb2cL6b8fA7Rz8T8iiA/T/zvvVdtapADgM8//+QtpzRsaH8OF2YlJk6cyIKCgtjt27d1bvPi\nxYu8l8kolYz5+DBGk4iMRUUxdv06Y9u3M/bzz9r3OX1a3L5ePf3niI5m7NYtOhen0ImIiGARERG6\nNzhzRvw9a9Qw/MCPHzMmCLSfTMbY06f692nWTDzX7Nnat8nKYqxzZ8bWrmUsJYWxwYMZa9eOsYkT\nGbt3z/D2FTXGjxe/u2++seihdfaRx48ZK1aMzjl0qEXPyXE89N5LGGNs7Fixn371leEH79yZnifT\npjH26JF5DeVYh65dxd92/XqdmxnUTwwhNZWxvXsZe/LE/GM5GEmpGaz37G0MrWaz4D5L2K3oeFs3\niTh+nLEhQxgrW5ax5cvNOpRFbFgNrOIpnzBhArZt24Zjx46pufetwoMHYqKYnx9piauKAZQtSxrD\n2vZRYYAXhMeQ2znh4VT4Q6kkWbLUVMPif69dowIhyclAq1aGJXyMGydKG/75JzBrVv5t9uwhjeu9\ne6kK3M2bTpP4UyDSsuWFlVzj4wMEBlKS7bZtlKArs7joFKcoUaOGuHzzpu7tNPn9d1GBg2Of5Iah\nAqBCU/pQKCgX5uFDer5oyyM6f57uMWXLqt/np00DvvmGbJLVq4GRI81vvwPhU8wDW2f1xDdj2sPf\n1wse7nai49+iBb0Yo9/GzrD4tzR27Fhs2LABu3btgq+vL+JyNYiLFy+OYtbQlXZxASZNAi5fBkqU\noMxnDw9S5IiNJUlDzalyqVFehKqwFTmePCHDtk6dgg0pLy+gWTP63evVo9/eEKO8XTvg6VPSEjc0\nrOHtt0lBpF8/4K23tG8j1bPv2ZMb5CrWrAHmzqXvXJoQlZVFN0dr3B+KFQNUIWepqTRoq1nT8ufh\nFB2kRrm2cDjGqBp0aCjpk4eF0TXODXL7JiaGnikA3Rekv7Mu/v2Xni0AGfG5YU15MEbVQVWOoOho\n0d4oU0Y0+g4dcjqjXEV5fx9bN0E7gmCXReEsbpSvWrUKgiDgjTfeUFs/a9YsfPbZZ5Y+HXmxv/lG\nfV3NmmK1tRs38lfUiooSl7lRbr989BGweTNqhofjwbRpBXs2jh837RweHsYpJbi5kcdVF48ekYqL\nCjvTQLUpxYvTS2WQr10LTJlCer4ffQQsWmT5cwoC9Zu9e+l9RIR+o1y1jbc3FZc4f55erVoZ5l3j\nFD6WlKzUZ5Q/fAiokrxLlKD+y7F/zoka2ahXjxx6+pBKa2orIBQXRwY5QI6jEiXEz9pLJP8OHyav\nuyHn5Dg1Fp/HVSqVUCgU+V5WMch1ERoqLmurqNWnDzB/PjBiBPDqq4XXLo7hHDlC1VQBFL96Fa4S\npR675qefxGJEbdqo63Fz1HF1FQ0aa1b1lF7jmp4uTRISgEaNKOwlNJSKCL3xBhUj++MP67WRYx5f\nfknhA6++StegOVSoAPzyC5VIv3cv/+cqhw9AnnI+E+YYhIYCCxZQPYqOHQ3bJzBQnKWNi6NZWCma\nlTylfSE0lKRfARrcS0NnOBwd2EmQj4VRxZQD5CnXpFUrehkLYzT9ffYs6aHzm7F1yMoCxo7Ne5vQ\noQNSHGXw9Ndf4nIRruZmESxd1ZMxMp779ydPmAqpd1tf2WuplryXF9Cggfj+/Hnz28ixDg8ekNEU\nFweYO4CXyYCBA3V/Lq3k+cor5p2LU3hUqwZMnWrcPq6uZFg/ekTvHz1Sd7RoGuVSBIG85apB4sGD\nQOPGRjeb41wUzYyn+vWp6uOIERTQbwkYo4u6Zk26YUtDYDiWZfFiMcHK2xuPJk60bXuM4fBhKh7y\n7rtUXVTFvXvAhg2U/HP0qO79nYkyZcRlC3jKg1avphCYli0phlPFa69RQbHbt+nBWBBXrojLtWvT\nvUQFN8oLl8uXgVWrgNGjAYmMmVakoQXWruYpNcrr1s3/+cmTdJ03aED5ExzHpqAQFmmVZm2iFu3b\nA6VK0ey8dIDPKXw2baJQ1WXL7Np+K5qe8s6dLV9RTRBohKyq6Hj6NCWVciwLY+ox2Z9/rlcL3GgO\nHaKba7dudMM0h6Qk8oSUKAEMHkwxg+3bq8cTArTN3Lm0rFQCuQWFnBoLespL79iBoHXr6E1KCrB9\nOyXyApR41b+/YQeSesrDw4Hq1cljnp5OiWKxserttgRpacBvv5FHrkIFnoiqYvVqMsoByv1p2lT3\ntoVZzVMavqLNUz59uqjQdOgQMGCAddvDsS5hYXRPqVABkMvVP/Pzo/vE3bvajfKePckg54pPtmfX\nLlJM+/NPCkP65BNbt0grjt1TDh2i6ahNmwpn5CNNGNXnueGYhiBQPPnKlRRilFslzyCiosgj+vHH\n6mEkmixdCrz3Hnlqf/3V9LaePg2UK0eltufMoUQeXYSHi8vXrpl+Tkfl1CkyjqtXB0aNonX+/mII\nmCAU/P0VRGwsgqXJ3p06AQVUZi0QTU+5i4u64XXhgmnHLYj794EhQ2ggFxpK/ZdDqksqLl8ueFup\nUW5NT7lKeWXCBBpYS0MlVUjLdh84YL22cAqHNWuo/+3dCzRpov7Zxx/TPSMtDejbN/++bm7cILcH\ncnLUZ0/ffNN2bdGDffaW8+fpwbpwYcHb7d1LCT4DBpAxZm2knhpulFsPFxeasj5yhGL6DOXHHym0\n6Jtv1L3tUuLjxYtToaCkPlOpV4/UWwAyrHSdE1A3yqXeWGchLo6Sne7cEWXJXF2Bx48phyAuznRl\ngtWrIcvKouXatWmgZao8XeXKoiKT6jfr1Ano1YuSxCTVYy1GTIz6+8WLRUUHZ0ZqlEsHS5qkpopx\n5B4eltfAlyb3CQLNiC1dSvcn1fUvRWqUHzwoJn5zii4yGZfEtGdOniR5bIBmJKXPYzvDPsNXpkwh\nT+e+fRSHpZqG1kQ6jSi9gRfEjh103EqVyDNlTAKhNEnj0iUaHVtDW5lDGJtIK03u0+XRnDlT1I5t\n2NA8SUxPT/K4f/01vV++HOjSRfu2ISFkhObkUFJaSgpJ7jkL0sJBAQHicmCg+cd++RJKd3cyzGfM\nMO+a3LCB/iYni7/PjBnmt7EgVIMUFYzR/UVboRJnYfhw9djtGzdo8KZNV7h4cSAjgwZ4cXGWScBX\nKGgwdvMmhSylphpudNWvT2FxCQnUnkuX1O9NnMJn/Hh6XjdoQAPswipexrEPvvhCXO7a1a5FOuzT\nUy4NPZgzR/s2jKlPaRpqlB87RvrIn35qvLZ1iRJ0w23ShKYvX740bn+OddEMM2BM/fNLl2gqUsXM\nmeafc8wYcfnAAUom1Ia7u7r+sT4VkKKGNat5fvklLv/xBx6OH0/FnQpCqSRvvcqzrgsfn8K7cWt6\nygGeVHrqlLqEXE5OwdU1PTxI/76guHNjcHGhazQ6mvrK/fvG7SvNKVHFl3NsA2PA1q3AunWk6qXy\nmHKcg+RkcbbLxcVuY8lV2J+nXFV9T0VmpnbR/ZgYUePYxyd/HGFiIilhXL9OnrOPPqL10tjzihWN\nb19EBI8RszSPHlECjbkJnRUr0sDpxQt6RUer/8ZHj4qGevv2NGI2l0qVSPNWFbpy8KDuEIf+/ck4\nDQ93vqJVUhUKqafcQuT4+SFu0CBUKMib+d57lACalESV+uxFnowb5erk5Kjrg3/4IeXzWFtVRZMa\nNUQpvJs3jQtdev99GiB06KA9AZBTeDx6JN5/vL1JRa2wefEC2LkT2LKFnj2TJhV+G5wVHx8aGO/f\nT2Fwdl47xP6M8thYymhWGdz//afdY6XpJdfcJiqKpqkAuimqjPIHD8RtTDGMuEFueUaPpqTJhQvJ\ncDL1OxYE8pYfO0bvL1xQN8onTiSJzI8+ophQS3lCv/yS+qmbW8EJJNOnW+Z8jog1PeWGkpEhxh5H\nRNiPUV6/PtC7t3rSsTMb5Q8eiCFmQUEUY28LatQgxw6gvbJnQbRpQy+O7ZFW8mzQwLTny7171C+j\no+la9fICzpyhsKaQEKB8+YKPu2sXMHQoLT99yo3ywkYQyHlmaNEoG2IVC/PkyZPo1q0bypcvD5lM\nhp9//tnwnUNCKBYvMZGmmXUZTnXqUBjK+PEkO6RJjRrivvfuidMX5nrKOZblxAlgzx4ahI0caX5Y\nR+/eFFr044/akzjr1yePubTqq7nUrk2DyUePbOOFcQQ2bKDv6PLl/DdGxshYjo+3bhuk+SP2VF1v\n6FCaXk9KomqD8+eT3rqzIg0Bs0ZiraFIpSlv3aLnUefONLjeu9d27eIYh/RaN1UrvEMHquw7dKho\nQ3z1FdC2LdkRudWnddK9u5gPceGC8YM8jtNgFU95amoqateujcGDB+Pdd9817SAlStBLF+XKkVdV\nF15epKQQGUlxpLdvk85ocjJ97unJkz1sDWPA5Mni+0GDzM+KHj3avP1NxRiVGGfE1ZUkKKUFgwDS\n5x44kAbN/fqRvKkhKJXGe7yklT0jItQ/y8khLfnatUmXuHhx9c+fPKHQl/PnKfxGnzKUKfj40Pfh\n7BhrlKen0/3e0khzQJ4/J4+rSue4UyfL18LgWAepUS69BxhDcLAYUvXwIUlhFlTNUxNfX+ozO3fS\n+61bgc8+M60tnCKNVSyJjh07omOuN2zw4MHWOIVhhIaKxX6uXycv5o4dNNJNT7frDFyn4PffaQoQ\noEQtaYY0xznw8RFnsYwpIDR1KklLTpyoW51Jk3r1yJBXKknNQ6qAc+cOKX4ANHiX6l4DpOzxwQe0\nXK2adYxyDjFiBIV+3L5NYQH6qF2bwqOCgylu1JB9DKFpUzLEq1enQZq0RLu2okH6yM7msnm2YN06\nMszPnjVd0UhakCo6mu4h+qp5atK3r2iUb95MQgPcBrEOCgVFW1i68GAhULQDpKWFHa5fJ+94jx6U\nOGSOzFlyMvDHHzSNuWSJ+e10RhQK9RjrceOsk8glTRjj2B9Sz3lcnGH7pKaSis6+fTStrIr71Uex\nYuQF9/CgeHJp8qlUB1vbbE14uDgbcveuGJvOsTyenmRov/OO/rh/pZI8lykpVJSrZEnLtcPbm8Ld\nVLMmUonGunWNO9a+fRQOU1BRM451CAoC3noL+Pxz06u9Svd7+JCSs1Xqa35+hvW7Ll1EudZnz8yu\nYlykmTOHrr+PP86vomYIv/5KkRIzZ1KSrQNhN3PuZwuI8fR4+BCld+7Ey6pV8bxTJ4OP6VO+PEq8\n8w4yKldGSs2aeGmhOFLviAjUyJXCS69WDdebN7fIcZ2N4pMmofzy5ZDfv48rb74JhZ7fp6A+ovX4\n58+jxqhRSOjcGY/GjkWOHYyai126hBInT8IzMhLPO3TAc2mhESfENT4eKp9j9uPHuGTAb+z/66+o\nmGsUZwQH46qPT95n+vqI2/z5yCldGszVlTwpudsHHTiAoNxtnvj747GW49SqXBleuVPWN7dsQaqp\n8akcoyh+7hz8Dh+G5927SOjYEfE9euR95hYfj7q5SaE5vr64eOOGQcc09l4CAHXOnoVKJf2Kiwsy\nDTxGwJYteRVnM957D9c2bwbTprfOsTtU/aS0UolKueviL1xAwp49UAU3pQYF4aaBfcF/3DhkBgYi\npXFjsMePaQaOo4ZHVBRqz55Nb775BncDAvDCmKTpnByET50KeWoqMHcuHj99iieqWVALE2IFZSW7\nMcoBAAoF5NHRyAwKAsutlFbiyBFUmzIFAJBevTqed+xo8JRP8muvIfm11yzezLSwMDCZDIJSCc97\n9yBLTYVSMwaVo5fU+vVx84cf4PHwIRQF5Q+YgkKB4EWLIDCG0nv2AACiZs2y7DlMwPvSJQSuXw8A\nyCpTxjmMcpWnQ8t1m1OyZN615JaUBCEnhwxmXSiVKLN1a97buD59jIotzy5bVut6T1WYG4CXOiSz\n0mvWzDPKi926ZRGj3OPBA/hERCDb3x8ZFSsiw9mkMg3A6/ZtBGzbBgDIqFBBzSh3l8yuZGnmK1gQ\n1/h4uCckAAAUcjkyjQiRed62LYJWr4ZrWhrk0dEo+8sveFJQPhTH7sgMDkZqeDiyypRBWng4FF5e\neN62LTwePkS6NPdAD8+0iVJw1Mj298fLSpXgmZtQG/z110hp1AgKA22sUn/+CXlu+GGOtzee9u1r\nraZaB2ZlihcvztavX6/1sxcvXuS9GGOMRUYyBjAmCIw1aEDrnj9nTC6n9QBjERGMLVjAWOfOjE2f\nztjly9b+F7Tzyitimw4csE0bnISIiAgWERFh+A537jBWqpT4+3h6MhYdbb0GGsOePWK7WrSwdWsK\nh+PHGXN3Z6x8ecaGDs3/eUAAYx4ejAUHM/b0acHH2rtX/P58fRlLSWGMmdBHNKlaVTzuhQvat1m+\nXNxmwADTzyVl7VrxmO++S+s2bmTsvfcYq1ePsStXLHMeR+bIEfE7athQ/bNt28TPunbVeyiT+0lW\nFmNnzjD23XeMffml8ft/+63YTrmcsXv3jD8Gp9Aw+37CMY/ERMZKlxavmdGjDdsvM5OxihXF/ebO\ntWoz89mwFsC+YspV8b+MUTEZgGK1VHrjAPD998CRIyRJNX++7gqK1kZaOW76dF7d0554+pRktdvt\nTwAAIABJREFUNVVMm2Z6LKGlkcYrX7tmWryco/H0KVVFfPRIezW9u3fp+nnwQL8i0rNnFMMJkPqS\nJWaoGAP69CE1jcqV1aXwpLRuDcyaBezeTXJolkBaOCgoN4Bm2zbghx9IOk2qsewMKJX519WuLS5f\nvUr5KCoSE8XkSWsWF8rMpKSxESPUFaMMZfRoSjQGSC//gw+c49q3JYyRqhLH8ShRAli1Snz/44+k\ngKWPH34Qa9GULk2S2Q6GVYzytLQ0XLp0CRcvXoRSqUR0dDQuXbqEhw8fFryjZApZreqSNB5o0yYq\nNKOiTh3DG9a5M8nuzZxJN0ZzkEyhom5dcRDBsT2vvCIm3lSuTMki9kJwsGhIJiQYntzoyOgrHOTt\nbbgKweDBlGj13XeiGoq5CAIwbx7p5UdG6r6Wa9UCZs+mSrAqA9pctBnl9euL65ytiNCCBUDZslTk\nSxWmVLq0+N1kZKirXgwfTutiYsxL3tfF3buk5uLtTZJ2puLiQkaGIJCu9ahRXHnD2kRFkbpT06bW\n6Rsc6/LOO3SvbdGCkqwDA/Xv8/rrYqXuKVNEdS0HwipG+dmzZ1GvXj00aNAAGRkZmDVrFurXr49Z\n+mJ6pUoZVaqIy82aid6r1FQgLY2WvbzUtyuI1FTSl92wgbxc5ibatGtH2dw9e5ISBL/B6icykpRv\nrF0kxsuLpNE+/ZTUDjw9rXs+YxAEUgBRcfWq7dpSWEhVTixRG8DLizyW5sRfP3lCHu/jx81vjzlo\nM8pVHlXA+Yzy27dpoHrypPqsitRbfumS+j4yGT2wDXloG0vZsmIy3r17YqVRU2jcmCR5r18XDQeO\n9fj3X5qB+/dfqrhsb8THA6tXO981biiCAGzcSMX+DI3br1OH7uv//gvkinE4GlZJ9GzZsiWU2qYh\n9SE1yqWeckEAPvmEtIQrVhQLxISHkwdC3zE3bKApYRXBwaaXcpcyc6ZpRUyclZkzaaZj3Tpg5Upg\nwADrnatRI+0VPe2BCRNoYBkebtxMj6Mi9ZQHBNiuHSo2bRL7XrduQMuWtmuLPk/5hQvOdY/RVTho\n4kRg2DAyzq2geKCT4sWpUN3jxxQKcf++eVVGu3e3XNs4BSOdUbeC4INZrFhBzwGFgipZr15t6xbZ\nFqWSZKY7d1YvxGeqp1uflKodY1/qK76+5O148kTdKAfohgwAixeL6wzRio2JoSlnKRUrmtVMNZzl\nYWku58+L1RqTk83zcjo6/frZugWFy/Pn4rI9VNGVDoQ0K3sWNr160eAsJkaMiQ4MJP32uDgavN25\nY7inyNGRGuXS//nNNwu/LdJ2qLzlt26ZZ5RzdJOZSc+JWrXIFjAXSxvl0dHA5cs0+/rsGYXChoWZ\nlq9Ut66YG/Hbb8C33zp3Yak9e2jAWqkSzXAbok7EGP0O9uDosSD2ZVH+8AM9nNLSdJfDHTmSpibW\nrDHM0xoamn+dtQ3C+HiqSHf5snXP40h895243K2b6ZXVOI7Hxo00ELt3T3dp8uxsuvZzZbCsSs2a\nYln2mBh1b7UxmDIbqMnkyZTEdOAAeWQBmhn8+muq/vfggfMYgQkJ4gDOy8tycfvmIi2nvnKl7dpR\n1Bkxgoznpk0p3NQcUlPFMCdBsIzndP16Cjv63//IwdSxIxmQpvDaa2Ll2YQEXlRq0SL6GxVlmHhH\nVBQVHKxXjwQEihD2ZZSr8PLSPWosVowusOHDDZt2Ll06v3fOkp5yTZKTyatz9CjQpAklhK5d61hF\nAiIiKClp927LGUnS0CQrCflz7BRBoGnIKlW0e8COHqUcj3LlgKFDtR/j++/JuFdl1puDq6t6iEiL\nFhRSZUhsp1IJjB1L13bJkuYnjOti0CAavAYHO0++SlSUOPNYvbr+/zsjg6oiWmJwVBAqgwFQT/C3\nFFyFhX7Hn3+m5Rs3gKVLzTve/fuk4AGQN9sSdTC0ecRNDaWSyUjxScWWLaYdpyjw33+UQwLQvbmg\nBP7Hjymfr3JlGiDHxJCjJyWlcNpaCNinUW5ppN7yrl11e+sswd27ojrAy5fk7Ro+nEbF9+9b77yW\n5I8/KEmiWzcyViyB1BtpROENjhMgrbSqrfQ0Y8BnnwEDB9IslyWSY6Uzcffu0XTpyJH695PJgIMH\ngTNnaADuDIm6hUWDBkB6OiVCrlmjf/vTpynUx9MT6N3beu1SJfMvXy6GUZrL0aNA+/bkIHLQhDSL\nsmuX+ntdM+WGUrs2hTbcuqU+S2sOljTKAfUwxt9/t94A397JrXYLgL4TXfYBY8Bbb+WfVahVq0iF\n/thXTLm1qFULOHGCllu2VPeSWZr69YFjx4B33wWuXBHXV63qOHHUUq++akrdXKZMIfUVaewsh2DM\nebyh2pBWYtQmERkZKRrrvr7aQ9KMpUkTiuWWGtVSDfmCaNBAHHifPWu+AcER8fDQ//syRvHHKond\nrCz15DBLI5NZfnbv5Uvg0CFavnHDssd2RHbsEJe/+cYyOQSCQDMulgr/srRRXr8+zfrXrQv07Vuk\nDEuDiYqimHoVH32ke1tBIOW8tm3FdTNmkApeEcrtcw6jvE8fmsKqVcuw5FBzeeUVime7fZtkGPfu\npdgnRzG8rGGUDx5smeMUFXbvphyKq1dJs/iTT2zdIttRqhSpKCkUJIOXmUnGmQrV1CZAsZj6FJcM\noU8feo0cKXplpbJ7BdGokaihvW8f/X4c63P4MDB3LuXq9OmjLoFoL8XBDEWaxHrrlu3aYQ8oFEBS\nkvjeXkvRa/PgmmOUCwLwzz+OYxdYg3LlSB1v0SIqCqfPPnvjDYrp37aNVPj69y+cdhYi9mOUnz9P\nD9sqVSwv+N6qFb0KE0GgG2+NGqTN7Uhxg9LEidRUSlyVhhhwzOfRIzLMAfUZFXvj2DGa3QgKIk+y\nsf0gJ4f6fkFeIBcXyvtQecOfPlU3sk6dEpebNTPu/PqQfveGesrfekv06Bw4QGEsPj7Gn/vAARqU\nBQWRx0xXzQWFgqa2ixUz/hxFiexs6o8AGeZSzXBHm32rVInyKLKyqN+b2oeKAi4uJN4QFUUz2vb6\nW3p5UTyzaoajVSvzbRVnNsgBei7060czBcnJhu0zfrxDVuo0FPvx+X/4IXmYfXzII1LU0Hbx/fMP\nJZlJdZztAamnvF8/YPt227WlqCI1AK9ds1079PHdd6Ry1Lo1zfoYy6lTZHz4+RXs1ShblrYJDaW4\nYs1jqGje3Pg26IIx08JXqlWjexVAMcGmJkNv307VZvv3p2JXmvz+O80M+PhQpUtnRzqTcfkySdSp\nsFdDThcuLupeVmf3lgM0UHn3XVu3omAOHqT7BmOUF8CxDIJgGRnMIoD9eMojI8VlDXUUxhiysrLA\nHMnbrI/oaBoZTp9OsZH2Ug6WMUqgkqpcBAfbNAmlYm5/yHDARBhBEODu7g5Bc1Amrep5/Tp5Qy0R\nlmFppAm6poQyqQaciYkF96GzZ7X//4xRzODJk+RNs2T8tkJBRTyuXqX7jzEVIZcupUFEeLjp3i5t\nhYOkZGTQwB2gIkJFmYwMGoz5+eneJiiIPn/+nNQWYmOpuE9qquOFrwA0i6oakEdFAa++atPm2CXJ\nyZQEOmiQ4fucOkUzb4Yo+HA4dobVjPKVK1di0aJFePLkCcLCwrB06VI0K2jqWeWdlcnUvB5KpRKZ\nmZlwd3eHiz0aLaZiyQQUSxMaaplkOgshl8tt3QSTUSgUyMjIgIeHB2TSZJRSpcg7HBtLBklkZOFW\nKjQUqeH42WdkyLZvb/j+T5+KywUVedB1bQsCKWtYQ13D1dW4h70US1QB1WeUSxPSi3op7pMnqV+V\nKkUxxdoqHAoCFX5ShbB88QWpaSUlOWZoz6xZpHMdEkKDC446335LA/L4eJLAMzR0bfhw4OZN6kvH\nj6s7QOydx4+pL3CvsdNilfCVrVu3YuLEifj0009x8eJFvPbaa+jYsSMeFSTyrvKCBwfTdHcuWVlZ\nkMvlRcsg5zgNLi4ukMvlyMrKyv+hqrKkl1fhFM0xFsbUDcfTp42fspWGZtlDNU97Qp9RHhIiGpux\nsVTpuKiiKhiSkEBx1rpQXTNubvR9CAJpUDuickWdOiQAwA1y7fz3HxnkAKl3GTJTnpBABjlAgzVd\neRr2xp9/UsHBChWAX36xdWs4NsQqRvmSJUswbNgwDBs2DDVq1MCyZcsQGBiIVatW6d+5atV8q/JN\n/XM4DoTO/jt5Mql3JCRQApG9kZycP77b2Ph3Qz3lzkZ2tvjdCIK6LKQKmUyMXQeKtrdcWsVPqkyi\nyfjxlJyblmaYrjzHfsnKovDNf//VXgDq88/Fwdbp01Q/Qx///isu169PGvaOQHQ0OTwYoyJphpCT\nQ7VPDh8mxSpH4uRJmo3v3BlYssTWrbErLG6UZ2dn49y5c2inYWS0b98ep0+f1r1jmzaU6GGvIR0c\njqV54w3S47XX8ByFgqpXSgfKxhrlL1+Ky9xTLpKTQ+EXY8ZQCI0uT68qhMXbW32AU9SQGuUFPQOq\nVqU4fkf0jHPUOXKEEpibNiXBA00qVybZOxXTp9M9qSCkNsZrr1mmnYVBr16i1v6//6pXwNZFeDjN\nBLRtK9ZNcBRu36YZjT//BM6ds3Vr7AqLx5THx8dDoVCgjIbnp0yZMjhcgKrK2S+/pAXGKOkrl4oV\nKzp0TDGHAwApKSm46ojVH4cMgdC/P+q3aAFBoQC7fx8XTp6E0lAP1NixwMiRcE1KgtLTE0rJta2J\nLD0dbgkJkGVm4mW1aiY192wBx7cW8nv3UPLIEaTWrYuURo0M37FDB3FZR7vd33gDQqtWyCxfnjzn\nNvj/CoPwK1egustfzcpChpX/T1v0E446Fb/7DqphemylSnik5Tdx7dwZtdeuhUt6OnDtGm6vWoXk\nJk10HrP6gQNQCUveK1MGiWb+zoXZT6o1aYISuUpTjxctwpP33itw+5ASJaCKPL9z4ACSpA4QO6fc\n339DlVYfI5cjxkGvxxAr5IHZjySiCh6qwuHYFczdHRm5hTMExiC/f9+4A7i6IqdUKSi9vHRuIr93\nD/VbtkTtt99GlalTAQBlfvkF1ceMQdCaNZBL1ZnsiIBNmxDety/KrVmD0pqlwi1AVrlyyAwOLlIV\n6/KhUIC5u0Pp4gImCDQA0YP748dwf/wYglSr3IGRpaVBlpZm62YUHgoFShw/nvc2sXVrrZvl+Pkh\nduBApNSti5vff1+gQQ4Aqa+8gtTataF0c0OqocXA7ISEjh3zlv3279caQy9kZaHcypVwf/RI7Trx\nkMoYOwDukvZmWqpAYRFBYBbWGczOzoaXlxe2bNmCd955J2/9uHHjcO3aNRyVJIolSap4+erINs7I\nyOCeco7D4/D9eOlSiuMNC6OiGSVKWPb48fFieIuvL/DiBalxqAp1bNhAeuk6UHm0GhZ2yfsrV8Tk\nw+LFKcTEUeJY7Y3sbJKHNSQ5r39/YPNmcuJs3Ej1FAzAZv1EF4sWUUxtTAywbBnwwQe2blHhcPy4\nWNAvMJCKqekaeGZnU2iHMQ67jAyzwgJt0k/S0ii3pHhxKqazcGH+/+GXX0jLXRDUjfbx46nSpaPQ\nuDEl8gLUF7SFLzkAhtiwxmJx94ubmxsaNGiAQ6qHaS6HDh3C66+/bunTcTiFypMnTzBnzhxcvnzZ\nsgd+/hzYtEldH96emDgRmDED6N7d8gY5QPrTKoWlpCR6QKk0ugHLV/K0FOHhYgx0aioVF+GYhpub\n4WoZqsJBjGlPknUUpApHzlRAaMcOcblHj4JngtzcjJ9Bd0QHSLFiFE/+6BE5QTT/B8ZEw5sxoEED\n8TNDYtDtCenMp6Mo5BQSVpkTnTRpEn766Sf88MMPuHnzJiZMmIAnT55gJM+W5zg4MTExmDNnDi5e\nvGi5g376KXmJBwwAtm2z3HEdCZlM3bg6eJCMXAAoX95+KzYKAulqq3DW368wOXUK+Ptv8b299g1D\nkCrNOJNRPmkSsHgxDbYlM+pOT3i4mPCpyenTYlKkXE5Jsn5+VFCtZs3Ca6MluH4dOHOGHFHa5GCd\nGKsUD+rduzeeP3+OefPm4cmTJwgPD8e+fftQoaCqaxERVL66ZElrNIljB6Snp8OrgLhiR8AqVWWr\nVBElwfbsodLr9sC6ddSuoCCaXjRWTzkri9RXfHwM83SVKSN6DbdvF9c3b27fuSa9egHz59Py7t0k\nT+bhUfA+335LITpBQVQAxxC5yDt3gN9/B957jwqjOCualVcNiEG3W5zVKK9YEfjwQ3pxDGPZMnF5\nwABSXUlIsF17zMHfn17GJMY7CVbLHho1ahQiIyPx8uVLRERE6A9dadSI5MGciNmzZ0Mmk+HmzZsY\nOHAgSpQoAX9/f8yYMQMA8PjxY/To0QO+vr4oW7YsFi1apLZ/VlYW5syZg+rVq0Mul6N8+fKYNGkS\nXmpkYf/0009o164dAgMDIZfLUb16dSxcuDCfgXnv3j307t0bQUFBkMvlKFeuHHr27Im4uDgAwIMH\nDyCTyfDzzz/n+19kMhk+//zzfP/btWvXMGjQIJQqVQq1JYk3sbGxeP/99/PaVKtWLazWqOJ3/Phx\nyGQybN68GXPmzEH58uXh7e2Nd955B0lJScjOzsakSZNQtmxZeHt7Y8iQIcjUote6adMmNGrUCF5e\nXvDz80Pv3r0RpVGsp1WrVqhVqxZu3LiBNm3aoFixYihfvjy+/vprtfY0atQIgiBgyJAhkMlk+f5v\nk+jUSVw+dYqMNXvg88+pOl7nzlS8xlhOnaJQF7ncMG9YcDAZWA0bkhdFhb2GrqioWxfo0gWYM4em\nn/UZ5ACwdi1VSH3/fYqj1se771KYzJQphuk1F2UqV6bvHKDKqo4YqqCiShXRM/rwIYVtcQomLo48\n7VIjtajz/Dmwc6f4fvx4+3ZUcEzGKp5yk9FSOKgooyoq069fP4SGhuLLL7/En3/+iYULF8LPzw/r\n1q1Dy5Yt8dVXX2Hjxo2YMmUKGjZsiFa5CTLdu3fHyZMnMWLECISGhuLGjRtYsWIFrl+/jv379+ed\nZ+XKlahVqxY6d+4MuVyOw4cPY/r06UhOTsb8XA9fTk4O2rdvj8zMTIwbNw6BgYF48uQJ9u/fj5iY\nmHwSl4b+b3369EGVKlUwb968vKqWz549Q+PGjcEYw9ixYxEQEIDDhw9jzJgxeP78OaZPn652rK++\n+gqenp6YNm0a7t69i2+//RbDhw+Hl5cXnj59itmzZ+PMmTNYv349KlWqhNmzZ+ftu3DhQsyYMQO9\ne/fGsGHDkJiYiOXLl6NZs2a4dOkSSuV6HAVBwIsXL9CpUyf06NEDffr0wW+//YapU6eiTp066NCh\nA0JDQ/H555/js88+w8iRI9G8eXMAQB1Vop+plC0LvPoqzRYpFMCBA0CfPuYd01w0q3lqeicNQVXN\nMyvLsAeI9KGTkwNcvkyG/ZtvGn/uwkQQjDeU9VXz1ESqJLFjBzBkiHHns2dOn6ZZUn9/w/qJTEYJ\nwMeO2WfRLWNQxdHfuUPe49hYp3sOGsWZM1TTJD2dZouGDiUN/+PH6b7ZtCnpkxelmSTGKEzlxg1g\nxQqKxzb3mcOxX5gNefHiRd6LAYz98EO+bV6+fGncQWfNomNpvmbNssz2FmT27NlMEAQ2fPjwvHUK\nhYJVqFCBubi4sAULFuStf/HiBfPy8mKDBg1ijDG2ceNG5uLiwk6ePKl2zE2bNjGZTMYOHTqUt07b\ndzhixAjm7e3NsrKyGGOMXbp0iQmCwHbs2KGzvVFRUUwQBLZ+/fp8nwmCwObMmZPvf+vVq1e+bYcP\nH84CAwNZQkJCvvXFihVjSUlJjDHGjh07xgRBYGFhYSw7Oztvu/79+zOZTMbefPNNtf1fe+01VqFC\nhbz30dHRzM3Njc2dO1dtu8jISCaXy9mMGTPy1rVq1YrJZDK2YcOGvHVZWVksMDBQ7X84e/aszu+g\nIPT24zlzxL43cKBRx7YKz56J7fH1pXV//snY++8z1qQJYxs36j/GsmXiMUaNsmpzIyIiWEREhFXP\nYTEyMsTvRSZjLCdH/z537oj7eHgwlpJi/XYWBomJ4v9VpgxjSqVVT2eX/SQqirH0dFu3wjHIzGSs\nUiWxz8yfT+s//FBcN3262aexeT958oSx//2PsUaNGCvgmcyxLWo2rIWwL/FbJ/QQCIKA9yRFAmQy\nGRo2bAjGGIYNG5a33tfXFzVq1EBkbtbytm3bUL16dYSGhiIhISHvpfLeSqUnVVJ8SqUSL168QEJC\nAlq0aIG0tDTcvHkTAODjQyUX9u/fj3TN0upm/G+jRo3Kt3779u3o3LkzGGNqbW/Xrh3S09NxRhq6\nAODdd9+FqyT5pXHjxgCg9v2o1sfExCA7V7t4+/btUCgU6N27t9p5vL29Ubt2bbXvCAA8PT0xQCK7\n5+bmhkaNGuV951alc2eKqR42rEDpv0JDqnur0pE9e5bCLv7917AiNipPOWBYzLSzIA0FKltWVJ0p\niGrVRG95ZiYgmQlzaO7cEZdLl3bOKfmKFZ1HRvPJEzF/xhTc3YGZM8X3X39Nak2OWslTFytWABMm\nkGzghg22bo1lMef3dwLsyyh3UmmcYA31AF9fX7i5uSFAw5Dx9fVFYmIiAOD27du4desW/P391V6q\nYz2VlOQ+deoUWrRokRdT7e/vj0GDBgEQdTYrVaqEjz76CGvXrkXp0qXRrl07LFu2DM+fPzfrf6uq\nMdB69uwZEhMTsW7dunxt79OnDwRBUGs7gHwJwio90PIaCV6+vr5gjOFFbkz2nTt3wBhDjRo11M4T\nEBCAc+fO5TtPOS1FDEqWLJn3nVuV+vUppOGHH+wjXENbeEVYmLju2jX9x5B+vyoNco7xoSsqevQQ\nl6WScoWNUmk56c7bt8VllbQkp+jStStQoQIwbpxpeSoAMGiQ6MBLTCQ97/Pnxc/1FBhyCPr3F5f3\n7tWdZ5SVJZardxQ51tq1ydZr21bd+cMBYE8x5eHhokfOHGbPppe1trcCLlo8ZTIduq0sNzlTqVSi\nVq1aWLZsmVZFkKDch/39+/fRrl071KhRA//73/9QoUIFyOVynDt3DlOnToVSMmr9+uuvMWzYMOze\nvRsHDx7ERx99hLlz5+LEiROoWbNmXpy4JsoCRr6eGh4g1bb9+vXL5+lWESY1/qD9+ylovfQ7EgQB\n+/fv17qtZtv0Hc+qCIJ9eQkrVAA++YQMyPBwWmesUa5UUtJjZqZzecoZo6JCoaEUM6xJ+fIkBxcT\nQ55yQ+nRgyQXe/RQl2EsLDIyaNC4bBkZA3fvGublLwhulDsPz56R8cwYsHo1MG+eacdxc6Mk6cGD\nxXwOVWXXmjWLRjx5aChQrx5w4QLdP3fsoFlUTf7+m2LsAYqnb9++cNtpLAoF3TeysoD79ykfgKOG\n/RjlV67YugUORdWqVXH+/Hm01lGeWMXu3buRlZWFPXv2qHmW7+koNhAaGorQ0FBMmTIFV69eRf36\n9bFkyRJ89913KJkrV/lCY9T+wAivmb+/P7y9vZGTk4M2qpuJlVB56StUqICaFtJx1TUwcRiysmgK\nWB/h4cBXX6mvq1qV9s3KIg/HixcFFxJaswb47jvSG9dmnGqiVAJRUaRh6+tLUoiOxtKlwMqVFJZx\n4ID2h2SFCqZJwdWtS9+NrWAMmDVLlGHbvVvde28K0lA5qTwgp+hx6JBYhbJpU7rGTWXAAAqhGzGC\nPMlTp9L6ohC6omLAADLKAdLz1maUS6MLCiPM0lxiYuj5AVC4Wm7YLEfEvsJXOAbTp08fxMbGYtWq\nVfk+y8rKQmpu4RWV91fqzc7MzMTy5cvV9klJSYFCoVBbV6NGDXh6euYZ4d7e3ihdujROnDihtt2K\nFSsMNlZlMhl69uyJnTt3aq2KGR8fb9BxDOGdd94pULIwwQSN12LFigFA4YS0WJKcHAqL8fEh/XFT\ncHUlD44KQ7zlgkDeEENk6168IMO/a1fSRf/iC9PaaUuiosQ4aamajCWw9YDQ05OMIBVLl5p/zE8/\nFZVkQkLMP54jk5REMcSqollFjQMHxOUOHcw7losLzdiEh1OdgNWryXPeubN5x7Un+vYVr/nUVJqp\n0qR8eVFSMy7O/iU1pQMHJ8whNAT78ZRzjGLgwIH47bffMG7cOBw/fhzNmjUDYww3b97Etm3b8Ntv\nv6FFixbo0KED3Nzc0LlzZ4wcORIZGRnYsGGDWuIkABw5cgRjx45Fz549UaNGDTDGsGXLFqSmpqJv\n3755273//vtYuHAhhg8fjoYNG+LEiRN5sduGsnDhQhw/fhxNmzbF8OHDERYWhsTERFy4cAG7du0y\nKNHUkPNVrlwZCxcuxOTJkxEVFYXu3bujRIkSuH//Pnbt2oW+ffvis88+M7jdAHnfS5YsiVWrVqFY\nsWLw9vZGeHh4vpAbi8CY5QyxHTvEh+LYsdq9LoagCvUKC7N8Dohm4TALDtAKjR49xFLYu3YBy5cX\nXELc0RgzhpLrcnKAEycoHKF+fdOP5+sLfPklyb29+qrl2ulodOoE7NtHy4cPiyEJRQXG1GOezTXK\npVSpAowcSa+iRLlylNS6ZAn1B22ODRcXoFIlCgkBKCREFW5oj0iNcifNIdQHN8rtFF2eZ9V6QRDw\n+++/Y+nSpVi/fj12794NT09PVKlSBePGjcvTzg4JCcGuXbswffp0TJkyBaVLl8bgwYPRsmVLtJdM\nrdetWxedOnXCvn37sHbtWsjlcoSFhWHXrl3o0qVL3nafffYZ4uPj8dtvv2Hbtm15+wQEBBjsLff3\n98eZM2fwxRdfYNeuXVi9ejX8/PwQGhqKxYsXG/U96OOjjz5C9erVsXjxYsybNw9KpRLly5fHG2+8\ngV69ehl9LldXV2zYsAHTpk3DuHHjkJ2djVmzZlnOKH/+HNi4kSp7FitmuYQ+aYGajAyKwTQkpEST\n7t0t0x5taH7/jqjF+/rrFNOakEBTtefOFS1js3x58kxu3kzv//c/YP16/fsxBly8SHG6PVi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QHUNbINZcIE8nDFxKgrQeiCq/8YTps2FHqUnGzbOO358yk3YfVqMqIuXABatqTZFSmGqq5wiiap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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2717,16 +2639,17 @@ "sensor_var = 30\n", "process_var = 2\n", "pos = (100,500)\n", + "process_model = (1, process_var)\n", "\n", "zs, ps = [], []\n", "\n", "for i in range(100):\n", - " pos = predict(pos[0], pos[1], velocity, process_var)\n", + " pos = predict(pos, process_model)\n", "\n", - " Z = math.sin(i/3.)*2 + randn()*1.2\n", - " zs.append(Z)\n", + " z = math.sin(i/3.)*2 + randn()*1.2\n", + " zs.append(z)\n", " \n", - " pos = update(pos[0], pos[1], Z, sensor_var)\n", + " pos = update(pos, (z, sensor_var))\n", " ps.append(pos[0])\n", "\n", "p1, = plt.plot(zs, c='r', linestyle='dashed', label='measurement')\n", @@ -2738,13 +2661,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Discussion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "### Discussion\n", + "\n", "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. Later chapters are devoted to this problem." @@ -2770,94 +2688,59 @@ "## 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", + "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. 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, some 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(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", + "Write the posterior as $P(x \\mid z)$. Now we can use Bayes Theorem to state\n", "\n", - "$$P(x|z) = \\frac{P(z|x)P(x)}{P(z)}$$\n", + "$$P(x \\mid z) = \\frac{P(z \\mid 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)$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "$$P(x \\mid 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]$$\n", + "$$P(z \\mid 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_p)^2}{2\\sigma_p^2}\\Big]$$\n", "\n", - "$$P(x) = \\frac{1}{\\sqrt{2\\pi\\sigma_p^2}}\\exp \\Big[-\\frac{(x-\\mu_p)^2}{2\\sigma_p^2}\\Big]$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ "We can drop the leading terms, as they are constants, giving us\n", "\n", "$$\\begin{aligned}\n", - "P(x|z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\mu_p)^2}{2\\sigma_p^2}\\Big]\\\\\n", + "P(x \\mid z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\mu_p)^2}{2\\sigma_p^2}\\Big]\\\\\n", "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\mu_p)^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_p)^2]\\Big]\n", - "\\end{aligned}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "\\end{aligned}$$\n", + "\n", "Now we multiply out the squared terms and group in terms of the posterior $x$.\n", "\n", "$$\\begin{aligned}\n", - "P(x|z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z^2 -2xz + x^2) + \\sigma_z^2(x^2 - 2x\\mu_p+\\mu_p^2)]\\Big ] \\\\\n", + "P(x \\mid z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z^2 -2xz + x^2) + \\sigma_z^2(x^2 - 2x\\mu_p+\\mu_p^2)]\\Big ] \\\\\n", "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_p + \\sigma_p^2z) + (\\sigma_p^2z^2+\\sigma_z^2\\mu_p^2)]\\Big ]\n", - "\\end{aligned}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "\\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_p + \\sigma_p^2z)}{\\sigma_z^2\\sigma_p^2}\\Big ]\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "$$P(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_p + \\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_p + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "$$P(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\mu_p + \\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_p + \\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", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "$$P(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\mu_p + \\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 ]$$\n", "\n", - "So we can see that $P(x|z)$ has a mean of\n", + "So we can see that $P(x \\mid z)$ has a mean of\n", "\n", "$$\\mu_\\mathtt{posterior} =\\frac{\\sigma_z^2\\mu_p + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2}$$\n", "\n", @@ -2907,7 +2790,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.0" + "version": "3.5.1" } }, "nbformat": 4, diff --git a/code/kf_internal.py b/code/kf_internal.py index b0280e2..a277ab1 100644 --- a/code/kf_internal.py +++ b/code/kf_internal.py @@ -19,9 +19,9 @@ from __future__ import (absolute_import, division, print_function, import book_plots as bp import matplotlib.pyplot as plt -def plot_dog_track(xs, measurement_var, process_var): +def plot_dog_track(xs, dog, measurement_var, process_var): N = len(xs) - bp.plot_track([0, N-1], [1, N]) + bp.plot_track(dog) bp.plot_measurements(xs, label='Sensor') bp.set_labels('variance = {}, process variance = {}'.format( measurement_var, process_var), 'time', 'pos') diff --git a/code/mkf_internal.py b/code/mkf_internal.py index f31b1b8..acd9349 100644 --- a/code/mkf_internal.py +++ b/code/mkf_internal.py @@ -104,9 +104,11 @@ def show_residual_chart(): plt.text (0.5, 159.6, "prediction", ha='center',va='top',fontsize=18,color='red') plt.text (1.0, 164.4, r"measurement ($z$)",ha='center',va='bottom',fontsize=18,color='blue') plt.text (0, 157.8, r"posterior ($x_{t-1}$)", ha='center', va='top',fontsize=18) - plt.text (1.02, est_y-1.5, "residual", ha='left', va='center',fontsize=18) + plt.text (1.02, est_y-1.5, "residual($y$)", ha='left', va='center',fontsize=18) + plt.text (1.02, est_y-2.2, r"$y=z-\bar x_t$", ha='left', va='center',fontsize=18) plt.text (0.9, est_y, "new estimate ($x_t$)", ha='right', va='center',fontsize=18) plt.text (0.8, est_y-0.5, "(posterior)", ha='right', va='center',fontsize=18) + plt.text (0.75, est_y-1.2, r"$\bar{x}_t + Ky$", ha='right', va='center',fontsize=18) plt.xlabel('time') ax.yaxis.set_label_position("right") plt.ylabel('state')