From 49c8c8df3182d6e4a076c2f69517adb26422892a Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Mon, 1 Sep 2014 18:57:13 -0700 Subject: [PATCH] added chapter 8 --- Chapter02_Discrete_Bayes/discrete_bayes.ipynb | 4 +- .../Designing_Kalman_Filters.ipynb | 1833 +++++++++++++++++ Designing_Kalman_Filters.ipynb | 1831 ---------------- 3 files changed, 1835 insertions(+), 1833 deletions(-) create mode 100644 Chapter08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb delete mode 100644 Designing_Kalman_Filters.ipynb diff --git a/Chapter02_Discrete_Bayes/discrete_bayes.ipynb b/Chapter02_Discrete_Bayes/discrete_bayes.ipynb index 7464b1a..066a8fa 100644 --- a/Chapter02_Discrete_Bayes/discrete_bayes.ipynb +++ b/Chapter02_Discrete_Bayes/discrete_bayes.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:063b7f8661d95b15baf3a227206a7c70003948c2f16023329df63903d9ecccbb" + "signature": "sha256:15e9f5d13095957c1cb52ad9b164d8d64eb30075da904eb586599abf442ea6ec" }, "nbformat": 3, "nbformat_minor": 0, @@ -25,7 +25,7 @@ "from __future__ import division, print_function\n", "import matplotlib.pyplot as plt\n", "import sys\n", - "sys.path.insert(0,'../') # allow us to format the boo\n", + "sys.path.insert(0,'../') # allow us to format the book\n", "import book_format\n", "book_format.load_style()" ], diff --git a/Chapter08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb b/Chapter08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb new file mode 100644 index 0000000..58165ab --- /dev/null +++ b/Chapter08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb @@ -0,0 +1,1833 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:4ab6426303b8e42b01e0c28dbe8acb5f6f138ede5afd19f2ba0ca549d9b04260" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Designing Kalman Filters" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#format the book\n", + "%matplotlib inline\n", + "from __future__ import division, print_function\n", + "import matplotlib.pyplot as plt\n", + "import sys\n", + "sys.path.insert(0,'../') # allow us to format the book\n", + "import book_format\n", + "book_format.load_style()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this chapter we will work through the design of several Kalman filters to gain experience and confidence with the various equations and techniques.\n", + "\n", + "\n", + "For our first multidimensional problem we will track a robot in a 2D space, such as a field. We will start with a simple noisy sensor that outputs noisy $(x,y)$ coordinates which we will need to filter to generate a 2D track. Once we have mastered this concept, we will extend the problem significantly with more sensors and then adding control inputs. \n", + "blah blah" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking a Robot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This first attempt at tracking a robot will closely resemble the 1-D dog tracking problem of previous chapters. This will allow us to 'get our feet wet' with Kalman filtering. So, instead of a sensor that outputs position in a hallway, we now have a sensor that supplies a noisy measurement of position in a 2-D space, such as an open field. That is, at each time $T$ it will provide an $(x,y)$ coordinate pair specifying the measurement of the sensor's position in the field.\n", + "\n", + "Implementation of code to interact with real sensors is beyond the scope of this book, so as before we will program simple simulations in Python to represent the sensors. We will develop several of these sensors as we go, each with more complications, so as I program them I will just append a number to the function name. `pos_sensor1()` is the first sensor we write, and so on.\n", + "\n", + "So let's start with a very simple sensor, one that travels in a straight line. It takes as input the last position, velocity, and how much noise we want, and returns the new position. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy.random as random\n", + "import copy\n", + "class PosSensor1(object):\n", + " def __init__(self, pos = [0,0], vel = (0,0), noise_scale = 1.):\n", + " self.vel = vel\n", + " self.noise_scale = noise_scale\n", + " self.pos = copy.deepcopy(pos)\n", + " \n", + " def read(self):\n", + " self.pos[0] += self.vel[0]\n", + " self.pos[1] += self.vel[1]\n", + " \n", + " return [self.pos[0] + random.randn() * self.noise_scale,\n", + " self.pos[1] + random.randn() * self.noise_scale]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A quick test to verify that it works as we expect." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "pos = [4,3]\n", + "s = PosSensor1 (pos, (2,1), 1)\n", + "\n", + "for i in range (50):\n", + " pos = s.read() \n", + " plt.scatter(pos[0], pos[1])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks correct. The slope is 1/2, as we would expect with a velocity of (2,1), and the data seems to start at near (6,4).\n", + "\n", + "##### Step 1: Choose the State Variables\n", + "\n", + "As always, the first step is to choose our state variables. We are tracking in two dimensions and have a sensor that gives us a reading in each of those two dimensions, so we know that we have the two *observed variables* $x$ and $y$. If we created our Kalman filter using only those two variables the performance would not be very good because we would be ignoring the information velocity can provide to us. We will want to incorporate velocity into our equations as well. I will represent this as\n", + "\n", + "$$\\mathbf{x} = \n", + "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n", + "\n", + "There is nothing special about this organization. I could have listed the (xy) coordinates first followed by the velocities, and/or I could done this as a row matrix instead of a column matrix. For example, I could have chosen:\n", + "\n", + "$$\\mathbf{x} = \n", + "\\begin{bmatrix}x&y&v_x&v_y\\end{bmatrix}$$\n", + "\n", + "All that matters is that the rest of my derivation uses this same scheme. However, it is typical to use column matrices for state variables, and I prefer it, so that is what we will use. \n", + "\n", + "It might be a good time to pause and address how you identify the unobserved variables. This particular example is somewhat obvious because we already worked through the 1D case in the previous chapters. Would it be so obvious if we were filtering market data, population data from a biology experiment, and so on? Probably not. There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n", + "\n", + "Beyond this you can start looking at how you might combine the data from two or more different sensors to produce more information. This opens up the field of *sensor fusion*, and we will be covering examples of this in later sections. For now, recognize that choosing the appropriate state variables is paramount to getting the best possible performance from your filter. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 2:** Design State Transition Function\n", + "\n", + "Our next step is to design the state transition function. Recall that the state transition function is implemented as a matrix $\\mathbf{F}$ that we multipy with the previous state of our system to get the next state, like so. \n", + "\n", + "$$\\mathbf{x}' = \\mathbf{Fx}$$\n", + "\n", + "I will not belabor this as it is very similar to the 1-D case we did in the previous chapter. Our state equations for position and velocity would be:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) \\\\\n", + "v_x &= (0*x) + (1*v_x) + (0*y) + (0 * v_y) \\\\\n", + "y' &= (0*x) + (0* v_x) + (1*y) + (\\Delta t * v_y) \\\\\n", + "v_y &= (0*x) + (0*v_x) + (0*y) + (1 * v_y)\n", + "\\end{aligned}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Laying it out that way shows us both the values and row-column organization required for $\\small\\mathbf{F}$. In linear algebra, we would write this as:\n", + "\n", + "$$\n", + "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}' = \\begin{bmatrix}1& \\Delta t& 0& 0\\\\0& 1& 0& 0\\\\0& 0& 1& \\Delta t\\\\ 0& 0& 0& 1\\end{bmatrix}\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n", + "\n", + "So, let's do this in Python. It is very simple; the only thing new here is setting `dim_z` to 2. We will see why it is set to 2 in step 4." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from filterpy.kalman import KalmanFilter\n", + "import numpy as np\n", + "\n", + "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", + "dt = 1. # time step\n", + "\n", + "f1.F = np.array ([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 3**: Design the Motion Function\n", + "We have no control inputs to our robot (yet!), so this step is trivial - set the motion input $\\small\\mathbf{u}$ to zero. This is done for us by the class when it is created so we can skip this step, but for completeness we will be explicit." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f1.u = 0." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### **Step 4**: Design the Measurement Function\n", + "The measurement function defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. At first this is a bit counterintuitive, after all, we use the Kalman filter to go from measurements to state. But the update step needs to compute the residual between the current measurement and the measurement represented by the prediction step. Therefore $\\textbf{H}$ is multiplied by the state $\\textbf{x}$ to produce a measurement $\\textbf{z}$. \n", + "\n", + "In this case we have measurements for (x,y), so $\\textbf{z}$ must be of dimension $2\\times 1$. Our state variable is size $4\\times 1$. We can deduce the required size for $\\textbf{H}$ by recalling that multiplying a matrix of size $m\\times n$ by $n\\times p$ yields a matrix of size $m\\times p$. Thus,\n", + "\n", + "$$ \n", + "\\begin{aligned}\n", + "(2\\times 1) &= (a\\times b)(4 \\times 1) \\\\\n", + "&= (a\\times 4)(4\\times 1) \\\\\n", + "&= (2\\times 4)(4\\times 1)\n", + "\\end{aligned}$$\n", + "\n", + "So, $\\textbf{H}$ is of size $2\\times 4$.\n", + "\n", + "Filling in the values for $\\textbf{H}$ is easy in this case because the measurement is the position of the robot, which is the $x$ and $y$ variables of the state $\\textbf{x}$. Let's make this just slightly more interesting by deciding we want to change units. So we will assume that the measurements are returned in feet, and that we desire to work in meters. Converting from feet to meters is a simple as multiplying by 0.3048. However, we are converting from state (meters) to measurements (feet) so we need to divide by 0.3048. So\n", + "\n", + "$$\\mathbf{H} =\n", + "\\begin{bmatrix} \n", + "\\frac{1}{0.3048} & 0 & 0 & 0 \\\\\n", + "0 & 0 & \\frac{1}{0.3048} & 0\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "which corresponds to these linear equations\n", + "$$\n", + "\\begin{aligned}\n", + "z_x' &= (\\frac{x}{0.3048}) + (0* v_x) + (0*y) + (0 * v_y) \\\\\n", + "z_y' &= (0*x) + (0* v_x) + (\\frac{y}{0.3048}) + (0 * v_y) \\\\\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "To be clear about my intentions here, this is a pretty simple problem, and we could have easily found the equations directly without going through the dimensional analysis that I did above. In fact, an earlier draft did just that. But it is useful to remember that the equations of the Kalman filter imply a specific dimensionality for all of the matrices, and when I start to get lost as to how to design something it is often extremely useful to look at the matrix dimensions. Not sure how to design $\\textbf{H}$? \n", + "Here is the Python that implements this:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", + " [0, 0, 1/0.3048, 0]])\n", + "print(f1.H)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 3.2808399 0. 0. 0. ]\n", + " [ 0. 0. 3.2808399 0. ]]\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 5**: Design the Measurement Noise Matrix\n", + "\n", + "In this step we need to mathematically model the noise in our sensor. For now we will make the simple assumption that the $x$ and $y$ variables are independent Gaussian processes. That is, the noise in x is not in any way dependent on the noise in y, and the noise is normally distributed about the mean. For now let's set the variance for $x$ and $y$ to be 5 for each. They are independent, so there is no covariance, and our off diagonals will be 0. This gives us:\n", + "\n", + "$$\\mathbf{R} = \\begin{bmatrix}5&0\\\\0&5\\end{bmatrix}$$\n", + "\n", + "It is a $2{\\times}2$ matrix because we have 2 sensor inputs, and covariance matrices are always of size $n{\\times}n$ for $n$ variables. In Python we write:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f1.R = np.array([[5,0],\n", + " [0, 5]])\n", + "print (f1.R)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 5. 0.]\n", + " [ 0. 5.]]\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Step 6: Design the Process Noise Matrix\n", + "Finally, we design the process noise. We don't yet have a good way to model process noise, so for now we will assume there is a small amount of process noise, say 0.1 for each state variable. Later we will tackle this admittedly difficult topic in more detail. We have 4 state variables, so we need a $4{\\times}4$ covariance matrix:\n", + "\n", + "$$\\mathbf{Q} = \\begin{bmatrix}0.1&0&0&0\\\\0&0.1&0&0\\\\0&0&0.1&0\\\\0&0&0&0.1\\end{bmatrix}$$\n", + "\n", + "In Python I will use the numpy eye helper function to create an identity matrix for us, and multipy it by 0.1 to get the desired result." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f1.Q = np.eye(4) * 0.1\n", + "print(f1.Q)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 0.1 0. 0. 0. ]\n", + " [ 0. 0.1 0. 0. ]\n", + " [ 0. 0. 0.1 0. ]\n", + " [ 0. 0. 0. 0.1]]\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### **Step 7**: Design Initial Conditions\n", + "\n", + "For our simple problem we will set the initial position at (0,0) with a velocity of (0,0). Since that is a pure guess, we will set the covariance matrix $\\small\\mathbf{P}$ to a large value.\n", + "$$ \\mathbf{x} = \\begin{bmatrix}0\\\\0\\\\0\\\\0\\end{bmatrix}\\\\\n", + "\\mathbf{P} = \\begin{bmatrix}500&0&0&0\\\\0&500&0&0\\\\0&0&500&0\\\\0&0&0&500\\end{bmatrix}$$\n", + "\n", + "In Python we implement that with" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f1.x = np.array([[0,0,0,0]]).T\n", + "f1.P = np.eye(4) * 500.\n", + "print(f1.x)\n", + "print()\n", + "print (f1.P)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 0.]\n", + " [ 0.]\n", + " [ 0.]\n", + " [ 0.]]\n", + "\n", + "[[ 500. 0. 0. 0.]\n", + " [ 0. 500. 0. 0.]\n", + " [ 0. 0. 500. 0.]\n", + " [ 0. 0. 0. 500.]]\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Implement the Filter Code" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Design is complete, now we just have to write the Python code to run our filter, and output the data in the format of our choice. To keep the code clear, let's just print a plot of the track. We will run the code for 30 iterations." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", + "dt = 1.0 # time step\n", + "\n", + "f1.F = np.array ([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]])\n", + "f1.u = 0.\n", + "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", + " [0, 0, 1/0.3048, 0]])\n", + "\n", + "f1.R = np.eye(2) * 5\n", + "f1.Q = np.eye(4) * .1\n", + "\n", + "f1.x = np.array([[0,0,0,0]]).T\n", + "f1.P = np.eye(4) * 500.\n", + "\n", + "# initialize storage and other variables for the run\n", + "count = 30\n", + "xs, ys = [],[]\n", + "pxs, pys = [],[]\n", + "\n", + "s = PosSensor1 ([0,0], (2,1), 1.)\n", + "\n", + "for i in range(count):\n", + " pos = s.read()\n", + " z = np.array([[pos[0]],[pos[1]]])\n", + "\n", + " f1.predict ()\n", + " f1.update (z)\n", + "\n", + " xs.append (f1.x[0,0])\n", + " ys.append (f1.x[2,0])\n", + " pxs.append (pos[0]*.3048)\n", + " pys.append(pos[1]*.3048)\n", + "\n", + "p1, = plt.plot (xs, ys, 'r--')\n", + "p2, = plt.plot (pxs, pys)\n", + "plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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lFFXY5+/tcXzWhrJe3v4/L6CNoxDr+RdR0qcPeHs7qWoR51IQFhERqcUKiq18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\nAOS8+CL599yDq2lTX8YTERGRSkIflpOryunyMGZ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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I encourage you to play with this, setting $\\mathbf{Q}$ and $\\mathbf{R}$ to various values. However, we did a fair amount of that sort of thing in the last chapters, and we have a lot of material to cover, so I will move on to more complicated cases where we will also have a chance to experience changing these values.\n", + "\n", + "Now I will run the same Kalman filter with the same settings, but also plot the covariance ellipse for $x$ and $y$. First, the code without explanation, so we can see the output. I print the last covariance to see what it looks like. But before you scroll down to look at the results, what do you think it will look like? You have enough information to figure this out but this is still new to you, so don't be discouraged if you get it wrong." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import stats\n", + "\n", + "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", + "dt = 1.0 # time step\n", + "\n", + "f1.F = np.array ([[1, dt, 0, 0],\n", + " [0, 1, 0, 0],\n", + " [0, 0, 1, dt],\n", + " [0, 0, 0, 1]])\n", + "f1.u = 0.\n", + "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", + " [0, 0, 1/0.3048, 0]])\n", + "\n", + "f1.R = np.eye(2) * 5\n", + "f1.Q = np.eye(4) * .1\n", + "\n", + "f1.x = np.array([[0,0,0,0]]).T\n", + "f1.P = np.eye(4) * 500.\n", + "\n", + "# initialize storage and other variables for the run\n", + "count = 30\n", + "xs, ys = [],[]\n", + "pxs, pys = [],[]\n", + "\n", + "s = PosSensor1 ([0,0], (2,1), 1.)\n", + "\n", + "for i in range(count):\n", + " pos = s.read()\n", + " z = np.array([[pos[0]],[pos[1]]])\n", + "\n", + " f1.predict ()\n", + " f1.update (z)\n", + "\n", + " xs.append (f1.x[0,0])\n", + " ys.append (f1.x[2,0])\n", + " pxs.append (pos[0]*.3048)\n", + " pys.append(pos[1]*.3048)\n", + "\n", + " # plot covariance of x and y\n", + " cov = np.array([[f1.P[0,0], f1.P[2,0]], \n", + " [f1.P[0,2], f1.P[2,2]]])\n", + " \n", + " #e = stats.sigma_ellipse (cov=cov, x=f1.x[0,0], y=f1.x[2,0])\n", + " #stats.plot_sigma_ellipse(ellipse=e)\n", + " stats.plot_covariance_ellipse((f1.x[0,0], f1.x[2,0]), cov=cov)\n", + "\n", + " \n", + "p1, = plt.plot (xs, ys, 'r--')\n", + "p2, = plt.plot (pxs, pys)\n", + "plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", + "plt.show()\n", + "print(\"final P is:\")\n", + "print(f1.P)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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gYf5ulxwoO5tfyne/x7Jw83FKKrQ0d7KhrYcTkbFn+GJ9NBv3J9En2JO9J7M4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B/bleHdgs9bMWFbTDr3/nsVmX+aOdaoVcy8rTcv/aN/XRAd95y1PNmcewdz/5hotsWk88Xqw6zd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\ngg==\n", + "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "final P is:\n", + "[[ 0.30660483 0.12566239 0. 0. ]\n", + " [ 0.12566239 0.24399092 0. 0. ]\n", + " [ 0. 0. 0.30660483 0.12566239]\n", + " [ 0. 0. 0.12566239 0.24399092]]\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Did you correctly predict what the covariance matrix and plots would look like? Perhaps you were expecting a tilted ellipse, as in the last chapters. If so, recall that in those chapters we were not plotting $x$ against $y$, but $x$ against $\\dot{x}$. $x$ *is correlated* to $\\dot{x}$, but $x$ is not correlated or dependent on $y$. Therefore our ellipses are not tilted. Furthermore, the noise for both $x$ and $y$ are modeled to have the same value, 5, in $\\mathbf{R}$. If we were to set R to, for example,\n", + "\n", + "$$\\mathbf{R} = \\begin{bmatrix}10&0\\\\0&5\\end{bmatrix}$$\n", + "\n", + "we would be telling the Kalman filter that there is more noise in $x$ than $y$, and our ellipses would be longer than they are tall.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The final P tells us everything we need to know about the correlation between the state variables. If we look at the diagonal alone we see the variance for each variable. In other words $\\mathbf{P}_{0,0}$ is the variance for x, $\\mathbf{P}_{1,1}$ is the variance for $\\dot{x}$, $\\mathbf{P}_{2,2}$ is the variance for y, and $\\mathbf{P}_{3,3}$ is the variance for $\\dot{y}$. We can extract the diagonal of a matrix using *numpy.diag()*." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print(np.diag(f1.P))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 0.30660483 0.24399092 0.30660483 0.24399092]\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The covariance matrix contains four $2{\\times}2$ matrices that you should be able to easily pick out. This is due to the correlation of $x$ to $\\dot{x}$, and of $y$ to $\\dot{y}$. The upper left hand side shows the covariance of $x$ to $\\dot{x}$. Let's extract and print, and plot it." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "c = f1.P[0:2,0:2]\n", + "print(c)\n", + "stats.plot_covariance_ellipse((0,0), cov=c)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 0.30660483 0.12566239]\n", + " [ 0.12566239 0.24399092]]\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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UreVrdCwRqSZ7MnIBCA+tZXASkeqhsiwiF2T6dxv5bs0efL09+GLStXrDFHEx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\n/w++fKSlWtMUFAAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The covariance contains the data for $x$ and $\\dot{x}$ in the upper left because of how it is organized. Recall that entries $\\mathbf{P}_{i,j}$ and $\\mathbf{P}_{j,i}$ contain $p\\sigma_1\\sigma_2$.\n", + "\n", + "Finally, let's look at the lower left side of $\\mathbf{P}$, which is all 0s. Why 0s? Consider $\\mathbf{P}_{3,0}$. That stores the term $p\\sigma_3\\sigma_0$, which is the covariance between $\\dot{y}$ and $x$. These are independent, so the term will be 0. The rest of the terms are for similarly independent variables." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking a Ball" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's turn our attention to a situation where the physics of the object that we are tracking is constrained. A ball thrown in a vacuum must obey Newtonian laws. In a constant gravitational field it will travel in a parabola. I will assume you are familiar with the derivation of the formula:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "y &= \\frac{g}{2}t^2 + v_{y0} t + y_0 \\\\\n", + "x &= v_{x0} t + x_0\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "where $g$ is the gravitional constant, $t$ is time, $v_{x0}$ and $v_{y0}$ are the initial velocities in the x and y plane. If the ball is thrown with an initial velocity of $v$ at angle $\\theta$ above the horizon, we can compute $v_{x0}$ and $v_{y0}$ as\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "v_{x0} = v \\cos{\\theta} \\\\\n", + "v_{y0} = v \\sin{\\theta}\n", + "\\end{aligned}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because we don't have real data we will start by writing a simulator for a ball. As always, we add a noise term independent of time so we can simulate noise sensors." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import radians, sin, cos\n", + "import math\n", + "\n", + "def rk4(y, x, dx, f):\n", + " \"\"\"computes 4th order Runge-Kutta for dy/dx.\n", + " y is the initial value for y\n", + " x is the initial value for x\n", + " dx is the difference in x (e.g. the time step)\n", + " f is a callable function (y, x) that you supply to compute dy/dx for\n", + " the specified values.\n", + " \"\"\"\n", + " \n", + " k1 = dx * f(y, x)\n", + " k2 = dx * f(y + 0.5*k1, x + 0.5*dx)\n", + " k3 = dx * f(y + 0.5*k2, x + 0.5*dx)\n", + " k4 = dx * f(y + k3, x + dx)\n", + " \n", + " return y + (k1 + 2*k2 + 2*k3 + k4) / 6.\n", + "\n", + "def fx(x,t):\n", + " return fx.vel\n", + " \n", + "def fy(y,t):\n", + " return fy.vel - 9.8*t\n", + "\n", + "\n", + "class BallTrajectory2D(object):\n", + " def __init__(self, x0, y0, velocity, theta_deg=0., g=9.8, noise=[0.0,0.0]):\n", + " self.x = x0\n", + " self.y = y0\n", + " self.t = 0\n", + " \n", + " theta = math.radians(theta_deg)\n", + "\n", + " fx.vel = math.cos(theta) * velocity\n", + " fy.vel = math.sin(theta) * velocity\n", + " \n", + " self.g = g\n", + " self.noise = noise\n", + " \n", + " \n", + " def step (self, dt):\n", + " self.x = rk4 (self.x, self.t, dt, fx)\n", + " self.y = rk4 (self.y, self.t, dt, fy)\n", + " self.t += dt \n", + " return (self.x +random.randn()*self.noise[0], self.y+random.randn()*self.noise[1])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So to create a trajectory starting at (0,15) with a velocity of $60 \\frac{m}{s}$ and an angle of $65^\\circ$ we would write:\n", + "\n", + " traj = BallTrajectory2D (x0=0, y0=15, velocity=100, theta_deg=60)\n", + " \n", + "and then call `traj.position(t)` for each time step. Let's test this " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def test_ball_vacuum(noise):\n", + " y = 15\n", + " x = 0\n", + " ball = BallTrajectory2D(x0=x, y0=y, theta_deg=60., velocity=100., noise=noise)\n", + " t = 0\n", + " dt = 0.25\n", + " while y >= 0:\n", + " x,y = ball.step(dt)\n", + " t += dt\n", + " if y >= 0:\n", + " plt.scatter(x,y)\n", + " \n", + " plt.axis('equal')\n", + " plt.show()\n", + " \n", + "test_ball_vacuum([0,0]) # plot ideal ball position\n", + "test_ball_vacuum([1,1]) # plot with noise " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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VHk9YM2YE9PDDLknShAkhZWSwJCdwJARsAJ0cOBBShO4PAJ9jt5uaP79Fp5wS\nkt8vlZUFlZkZjHdZQEIiYAOI2brVrRtvdCoQsOk3vwmptLQ13iUBSCD9+wf1jW8QqoGv0uWt0gH0\nDk1NKZo/P13vvOPQBx/YddFF6aqvZ5UAAF9fIGBXW5v9q78Q6OUI2AAkRVcIaP3MhLXfbyhMeyWA\nr2n7dpfmzs3W2WfnaNMmdn5E30bABiBJysoK6p57WuV2m3I6Tf3+9y0aOJBLwQC+ms+Xohtu8Grj\nRofefTdFF1yQzjrZ6NPowQYQ8y//0qLXX7cpEpGys1tkGAm7iieABBIKSY2NHXN2LS2GQiEjjhUB\n8cUMNoBOioocOuEEB+EawNeWkRHSXXe1yOUyZbebuv/+Fg0cGIh3WUDcMIMN9DGmaWjPnlRFItJx\nx7XL4SBIA+i6SZNatX59SJGIoUGD2mW387sFfRcz2EAfs2GDR+Xl/TR5cj8995yXy7gALHPcce0a\nMqSNcI0+j4AN9CFNTQ794hceBQKGTNPQDTd4uREJQI/Yv9/J0p/oMwjYQB+SkmKqf/+ObRozM01a\nRAB0u7ff9mjmzGxNm5atV17xxrscoNsRsIE+xO0OafHiFp1+ekATJwb16KNN6t+fG5EAdJ/GRoeu\nvdarjz+2qaHBpksvTdcnnzCTjd6NmxyBPqaw0K9ly9oViRhyONhJBkD3MozPf24e9hjQ2zCDDfRB\ndnuEcA2gR2RkBLVkSYsGD44oNzeiP/2pWQMGcOUMvRsz2EAvtX+/Q+GwoQEDgpLoswYQPyed1Kq1\nawMyTUM5OYRr9H7MYAO90HvvufWNb+RoypRsvfyyR6bJ9VgA8ZWdHSRco88gYAO9jN9v109+4tXe\nvTY1Ntp02WXp+vhjbigCkLgMw5BBYzZ6EVpEgF7GNDvfVGQYh99kBACJoqbGpSVL3AqHpWuv9amw\n0B/vkoAuI2ADvYzbHdbixS364Q/T1dJi6He/a9GgQVyWBZB4mptTdO21Xm3a5JAkvfuuXU89FVJm\nZjDOlQFdQ8AGeqHRo31atSqocJgbigAkrvZ2m3btssc+373brvZ2Lrkh+dGDDfRSWVncUAQgsfXr\nF9S//VurDMOUZOrf/q1V2dnMXiP5MYMNAADiwm43deaZLSopCUmS8vPblZLCsqJIfgRsIEnt3+/Q\nP/+ZKp/P0PjxQQ0e3BbvkgDgqDmdpk44gRsb0bsQsIEkZJqG/vhHj+691y1JKi0NafnysPr149Iq\nAADxRg+570zZAAAgAElEQVQ2kIR8PrteeCE19vnbb6eosdH+Jc8AgOQTCBjavt2l7dtdCga5+RHJ\ng4ANJCG3O6w5czpaQk4/PaB+/cJxrAgArBUOG3r22XSdfnqWpk7N0vPPexUOE7KRHGgRAZKQYZj6\nwQ9adeKJIfn9hk48McC6sQB6lYYGhxYu9EgyZJrSwoUenXZau/r3Z3UkJD4CNpCk0tNDmjw5FO8y\nAKBbpKaaGjQorObmaFQZMiQipzMS56qAr4eADQAAEk5mZlB//GOzfvMbt+x26cYbfcrIYFIByYGA\nDSQ4w4j2HJoma8MC6FsKC/168MHo/Sb8DkQyIWADCeyjj1L1xBMu7dtn0yWXtGnUKF+8SwKAHkWw\nRjIiYAMJyjRtuucejx57LE2StGaNU3/7W0h5edzgAwBAIiNgAwkqGDT0/vsdL9GGBpt8PlbWBABJ\nam21q6oqVXa7qaKidqWlcQMkEgd/rYEE5XSG9ZOf+GSzRS+PXnGFX7m53OADAIGATX/6k1ezZ2dp\n1qws/fWvrJGNxMIMNpDATj+9VS+9FJbfLxUUBOXxELAB4MABh37zG/f/fmbo7rvdmj27TdnZtNAh\nMRCwgQRmt5s64QR/vMsAgISSlhbRyJFhvfdeNMaMHh1SWhq72SJxELABAEBSycwM6qGHmvX446ly\nOqU5c9rkdhOwkTgI2AAAIOnk5/v1y1+yRjYSEwEbiLOGBofefDNN+/cbmjQpoPz8tniXBABJgWCN\nREXABuLIMAz9+c8e3XVX9Gad/PyQnnkmogEDuFEHAIBkxTJ9QBwFg4b++7+dsc9ra1N04IA9jhUB\nQPIzTUOffOJUfb3zq78Y6AYEbCCOUlIiuuCCjpaQ004LqH9/luIDgGNlmob+/neP/vVfczR1arb+\n+U9PvEtCH0SLCBBnZ57ZqoKCkFpaDBUXB5WdHYx3SQCQtOrqnLriinT5/YYkQ9df79Xzz7crPZ3J\nC/QcAjYQZy5XWBMm+OJdBgD0CoZhKuUz6cbplGxcr0cP40cOAAD0Grm5AS1b1qShQ8M64YSwfve7\nZnbBRY/rUsAOhUL62c9+ptNOO00TJkzQhRdeqKqqKklSMBjUggULNG7cOE2dOlVr1qzp9Nxly5Zp\n8uTJKisr0+LFi7tSBgAAQExZWavWrt2vZ59t0OjRXCFEz+tSwI5EIho+fLhWrFihN998U9OmTdP8\n+fMlSY888oiqqqq0fv163XnnnVqwYIH27dsnSdq8ebOWLFmiZcuW6bnnntPzzz9/WAAHeptPP3Vq\nz540tbdz4QgAultWVpC+a8RNl/7SO51OzZ8/X7m5uZKkc889Vzt37tT+/fu1du1azZs3T16vV2Vl\nZSotLVVlZaUkae3atZo5c6YKCwuVm5urOXPmaPXq1V3/boAEtWWLW9OnZ+vUU/vp0UfT1dZGyAYA\noLey9CbHt99+W7m5uerXr59qa2tVUFCgm266SdOmTVNhYaF27NghSaqtrdXEiRO1dOlS7du3T+PH\nj9eqVauOeM6cnBwrS0QPcDgckhi7Q4LBsO64I0UNDdFQ/atfuTV9uqlx4xxxruzIGL/kxvglL8Yu\nuTF+yevQ2FnJsoDd3NysRYsW6Re/+IUMw5Df75fb7db27dtVUlIij8cTaxE5dKyqqkofffSRysvL\n5fMduUfqtttui31cXl6uKVOmWFUy0CNsNik7u2M735QUqRteywCAr2HnzpD++U8pNVWaMEEaOJAF\n1fqidevWaf369ZIku92u8vJyS89vyU9VIBDQ/Pnz9c1vflMVFRWSJJfLJb/fr5UrV0qSbr/9dnk8\nntgxn8+nhQsXSpIqKyvldruPeO6rr7660+cNDQ1WlIxudOjdO2PV4frr09TQYGj3brtuuaVVeXmt\namgwv/qJccD4JTfGL3kxdt2vuTlFN92UqVWrUiVJv/hFq+bP3y+breu/jxm/5FJSUqKSkhJJ0bHb\nsGGDpefvciNoOBzWjTfeqPz8fP34xz+OPZ6fn6/q6urY59XV1SooKIgdq6mpiR2rqqrSiBEjuloK\nkLDy89v0H/9xQKtWNej001ss+WUOADg6Bw+maNWqju3TH388TS0t9jhWhN6qywH75ptvls1m0y23\n3NLp8YqKCi1fvlzNzc3auHGjNm3apBkzZsSOVVZWqqqqSnV1dVqxYkVs5hvorZzOsLxe7mgHgHjJ\nyAhr4sSO38MzZgTkdofjWBF6qy61iOzdu1crVqyQy+XS+PHjY4//8Y9/1MUXX6yamhpNmTJFmZmZ\nWrRoUWy1kbFjx2r+/Pm68MILFQqFNHfuXAI2AADoVpmZQS1Z0qQ33nAqLU2aMKFdKSlcUYT1jG3b\ntiXsT9bu3btVXFwc7zJwlOhDS26MX3Jj/JIXY5fcGL/kdagHe+jQoZadk1tnAYuYpqGamjS1tEjD\nh4eUlRWMd0kAACAO2O0CsMjrr7t1xhlZmj27n37963Q1NrIWHwAAfREBG7CAzWbT73/vUiBgSJL+\n+tc07d3LBSIAAPoiAjZgAdM0NWZMx53pXq8pjydhb28AABzBxx+nau1ar/7+d68OHOAqJI4dU2yA\nBUzT1Lx5PrndpqqrU3TxxX4NH94W77IAAF/TwYMOXXNNul57LbpO9k9/6tN11zXKMJgswdEjYAMW\nycsL6Jprojc2mia/kAEgmTQ22mPhWpJWrkzVFVfY5fGwfwGOHi0igIVM0yRcA0ASysoK61/+JRD7\n/Oyz29mEBseMGWwAANDnZWYGdd99zdq82aG0NOmkk9ppD8ExI2ADAABIystrV15ee7zLQC9Aiwhw\nlOrrndq7N03t7bx8AADA4UgIwFH48EOXvvGNbJ1ySj/94Q/p8vns8S4JAAAkGAI28DUZhqEHHnDr\n449tMk1D/+//ebRjh/OrnwgAAPoUerCBo5CZGYl9bLOZcrAPAQD0Ca2tKdq506HUVKmgoE02GzdA\n4osxgw18TaZp6vLL/ZoxI6ARI8J6+OEWjRjBZjIA0Nv5fHY98IBXM2b007RpWfqf//HEuyQkOGaw\ngaMwdGibHn44qLY2QxkZYUnMYABAb7dvn0O//a1bkhQKGbrjDrdOPdWv1FTWycaRMYMNHCWnM6yM\njJAI1wDQN7jdprKyOloEi4rCcjr5G4Avxgw2AADAl8jLa9eTTzbp3ntdGjQoossv98swIl/9RPRZ\nBGwAAICvMHq0Tw8/7JcUvScH+DIEbAAAgK+BYI2vi4ANfE5zc4refjtNdXU2lZYGVVTkj3dJAAAg\niRCwgc958UWXrrkmXZLUv39Ezz8f0ZAh7XGuCgAAJAtWEQE+wzAMrVvXsTtjfb1N9fVshw4A+HKm\nadJCghgCNvAZpmnqrLPadWgJvuOPDykvLxTfogAACa221qX77jP12GMRNTSwxS9oEQEOc9ppPq1a\nFdH+/TaNHBlSXl4g3iUBABLUJ584df756dq5MxqpbrpJuvHGRmaz+zhmsIHPSU2NqLTUp+nTWzRk\nCFuhAwC+WGOjPRauJenll50KBolXfR0/AQAAAMdowICQpk07dKXT1EUX+ZWSwhbqfR0tIgAAAMco\nKyuoxYubtH27S16vqeOPb413SUgABGwAAIAuGDAgoFGjosu7NjSwhTpoEUEfZxhGvEsAAAC9DDPY\n6JMaGhx64QWXtm5N0bnntqu0lEt6AADAGgRs9EkvvODST3/qlSQ99liqXnghwpboAADAErSIoM8x\nDEPvv9/x3rKtzVBjI60iAADAGgRs9Dmmaeq889qVmhrdBGDSpICGDWO3RgCA9aqqXHrggUw99VS6\n6uvZ5bGvoEUEfdK4cT698EJETU2Ghg0LacAAdmsEAFhr375Uffe7maqri85n/vSndt1wA7s89gXM\nYKOPMnX88X6NH+8jXAMAukVjoy0WriVpwwaHIhFaEvsCAjYAAEA3GDgwpOnTO3Z5vOyyNhkG62T3\nBbSIAAAAdIN+/YK6++4mbd/ukNdratQoVqvqKwjYAAAA3WTAgACtiH0QLSIAAACAhZjBRq/V1mbT\nu++6VFdnU3FxSIWFXJoDAADdj4CNXuu119z6wQ/SJRnq3z+i554zNWxYW7zLAgAAvRwtIuiVDMPQ\n+vUOSdHlkOrrbdq3jx93AADQ/Ugc6JVM01R5eVBSdDH/AQMiystjaSQAQOKor3dq40a33n/fpVCI\n9bF7E1pE0GtNmuTTypWmPvnE0KhRYdpDAAAJY/9+h268MUMvveSUzWZq6dJmTZvWEu+yYBECNnqt\n1NSIJkxojXcZAAAcZt++FL30klOSFIkY+tOf0jR9uk+mydXW3qBLLSIvvviivve97+nEE0/UL3/5\ny9jjwWBQCxYs0Lhx4zR16lStWbOm0/OWLVumyZMnq6ysTIsXL+5KCQAAAEknIyOifv06wvQpp4R0\nqK0Rya9LM9gZGRm6/PLL9corr6itrePy+yOPPKKqqiqtX79eW7Zs0ZVXXqnS0lLl5eVp8+bNWrJk\niR577DF5vV6df/75Ki4uVkVFRZe/GQAAgGQwZEi7Vqxo1KpVqRo6NKJp0/wyTQJ2b9GlgF1WViZJ\nev/99zsF7LVr1+riiy+W1+tVWVmZSktLVVlZqXnz5mnt2rWaOXOmCgsLJUlz5szR6tWrCdgAAKBP\nGTnSr5Ej2aOhN7KkB/vz77hqa2tVUFCgm266SdOmTVNhYaF27NgROzZx4kQtXbpU+/bt0/jx47Vq\n1SorygAAAADizpKAbRidl5bx+/1yu93avn27SkpK5PF4tG/fvk7Hqqqq9NFHH6m8vFw+n+8Lz52T\nk2NFiehBDodDUs+MnWmaamqKqKXFVP/+NqWmsvJkV/Xk+MF6jF/yYuySG+OXvA6NnZW6ZQbb5XLJ\n7/dr5cqVkqTbb79dHo8ndszn82nhwoWSpMrKSrnd7i8892233Rb7uLy8XFOmTLGiZPQSH34Y0i9+\n4dRbb6Xo2mvbdcUVYWVl2eNdFgAASGDr1q3T+vXrJUl2u13l5eWWnr9bZrDz8/NVXV2tMWPGSJKq\nq6s1ffr02LGamprY11ZVVWnEiBFfeO6rr7660+cNDQ1WlIxudOjde0+M1cqVmVqzJrrM0a9+5VJp\n6UGVln7xFRF8tZ4cP1iP8UtejF1yY/ySS0lJiUpKSiRFx27Dhg2Wnr9L19MjkYja29sVDocVDocV\nCAQUCoVUUVGh5cuXq7m5WRs3btSmTZs0Y8YMSVJFRYUqKytVVVWluro6rVixghscccwCgc6fh0Lx\nqQMAAKt9fgITyaNLM9jPPPOMFixYEPv82Wef1TXXXKOrrrpKNTU1mjJlijIzM7Vo0SLl5uZKksaO\nHav58+frwgsvVCgU0ty5cwnYOGbf/Ga7Vq926p13UnT11X6NHBn46icBAJDg3n/fraefTtWIEWHN\nnOlX//7BeJeEo2Bs27YtYRdd3L17t4qLi+NdBo5ST18ma2x0yO+3KSsrqLQ0dsDqKi5zJjfGL3kx\ndsnNyvHbuTNNs2b1U3NzdAb7179u1ZVXNrFOdjc51CIydOhQy87JkgtIepmZQeXltROuAQC9QlOT\nEQvXkvTGG5bcMoceRMAGAABIIIMHhzR9erTlMSXF1MUXtzN7nWR4SwQAAJBAsrODWry4STt2pCgj\nw1RRUdtXPwkJhYANAACQYPr3D6h/f27cT1a0iAAAAAAWImAjKRw44NCePWlqbWWXRgAAkNgI2Eh4\nu3alae7cfjrllH76v/83UwcPOuJdEgAAwBciYCPhVVam6r33UiQZWro0TVu3OuNdEgAAwBciYCPh\nuVydlyZyOlmqCADQt7GNemJjFREkvKlT2/Td7zr02msp+uEP21Rc3B7vkgAAiJt33nHrqadSdcIJ\nYc2a5VdODtuoJxoCNhLeoEEB3XXXQfn9Nnm9IdlszGADAPqmHTvS9J3vZKq1NTqD3d5u6JJLGuNc\nFT6PgI2k4HCE5XCE410GAABx1dRkxMK1JL3zTooMw2CnxwRDDzYAAECSGDIkrClTohvQOBym5s5t\nI1wnIGawAQAAkkROTkC/+12TamtTlJnJNuqJioANAACQRNhGPfHRIgIAAABYiICNBGIoELCzticA\nAEhqBGwkhPp6h+66K1PnnJOjJ5/0qq2NH00AAJCc6MFGQnj11TTde69bknTddV6NGBHWuHG+OFcF\nAABw9JgmREI4cOCzbSGGfD7aRAAAQHIiYCMhlJcHNXx4SJI0Y0ZAI0ey7SsAAEfr449TtWGDR1u2\nuBQOM1kVL7SIICHk5/u1cmVYTU129e8fUmYmARsAgKNRV+fUJZdk6t13U2S3m3riiWZNmtQS77L6\nJGawkTAGDAiosNBPuAYA4Bjs2ZOid9+Nzp2Gw4ZWrnSyMlecELABAAB6gezsiNLTO7ZNnzAhxDbq\ncUKLCAAAQC9QUNCmp59u1N//7lBBQUSnnuqPd0l9FgEbAACglygu9qm4ON5VgBYRAAAAwEIEbAAA\nAMBCtIigR+3cmaaGBpsGDQpp0KBAvMsBAACwHAEbPebDD10655xMHTxo0/HHh/Too40aPLg93mUB\nAABYihYR9Jg33nDo4MHoj9z27Sn68EPe3wEAgN6HgI0eM3hwJPaxYZjKzmZtTgAAehIbz/QMphDR\nY8aPb9MDDxj6xz8cOvPMgEaPZn1OAAB6hqG333Zr5UqnxowJa/p0v7Kz2Tm5uxCw0WPS00P69reb\ndfbZBjtLAQDQg7ZvT9N552WovT06g33vvdJ3vkPA7i60iKDHEa4BAOhZBw8asXAtSVu32mkX6UYE\nbAAAgF5u+PCQJk6MzlinpZk688wAE17diBYRAACAXm7gwIAefrhRu3alKCvLVFER90F1JwI2AABA\nHzBwYEADB7LJW0+gRQQAAACwEAEbAAAAsBABGwAAALAQARsAAACwEAEbAAAAsBABGwAAAGw8YyGW\n6QMAAOjDTNPQ22+7tWaNUyUlIU2Z4ldWVijeZSU1AjYAAEAftn17ms47L0OBQHQG+8EHpbPOao5z\nVcktbi0i+/bt07x583TyySfr3HPP1fbt2+NVCgAAQJ+1f78RC9eS9MEHdtpFuihuAftXv/qVRo4c\nqddff10VFRW64YYb4lUKAABAnzV8eEglJdGWkLQ0UzNnBmSaZpyrSm5xCdgtLS165ZVXdMUVV8jp\ndOqiiy7S3r179eGHH8ajHAAAgD5r0KCAli49qKefPqi1aw/qpJN88S4p6cUlYO/cuVNOp1Nut1vn\nn3++9uzZo2HDhqmmpiYe5QAAAPRpeXkBlZX5dPzx/niX0ivE5SZHv98vj8ej1tZWVVdXq6mpSR6P\nR37/4YOak5MThwrRFQ6HQxJjl6wYv+TG+CUvxi65MX7J69DYWSkuAdvlcqm1tVV5eXnauHGjJKm1\ntVVut/uwr73ttttiH5eXl2vKlCk9VicAAAB6n3Xr1mn9+vWSJLvdrvLyckvPH5eAPXz4cLW3t6uu\nrk65ubkKBALatWuXCgoKDvvaq6++utPnDQ0NPVUmjtGhd++MVXJi/JIb45e8GLvkxvgll5KSEpWU\nlEiKjt2GDRssPX9cerC9Xq9OO+00Pfzww2pvb9cjjzyiwYMH64QTTohHOQAAAIBl4rZM36233qoP\nP/xQZWVlWrt2re655554lQIAAABYJm47Oebl5Wn58uXx+ucBAACAbhG3GWwAAACgNyJgAwAAABYi\nYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJg\nAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImAD\nAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMA\nAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAA\nABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAAFiJgAwAAABYiYAMAAAAWImADAAAA\nFiJgAwAAABYiYAMAAAAWImADAAAAFjrmgF1TU6PLLrtMEydO1LRp0w47vmzZMk2ePFllZWVavHhx\np2MbN27UrFmzVFpaqvnz56ulpeVYywAAAAASyjEHbIfDobPOOks/+9nPDju2efNmLVmyRMuWLdNz\nzz2n559/XmvWrJEk+f1+XXfddfrxj3+sV199VYZh6O677z727wAJaevWrfEuAV3A+CU3xi95MXbJ\njfHDIcccsIcOHaqzzz5bgwcPPuzY2rVrNXPmTBUWFio3N1dz5szR6tWrJUVnrzMyMvTNb35TaWlp\nuvTSS2PH0HvwSya5MX7JjfFLXoxdcmP8cEi39GDX1taqoKBAS5cu1Z133qmioiLt2LFDkrRjxw6N\nGDFCb731li677DINHz5cjY2NOnDgQHe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api68MKhHHnGrvt7QOeeENHgwL7SBkyFgA2i2b59L999vyueTJk1KbrWmtdMZ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\neXnKzs7WlVdeqXXr1kmKzV6npqbqoos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+ "text": [ + "" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks reasonable, so let's continue (excercise for the reader: validate this simulation more robustly)." + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "Step 1: Choose the State Variables" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We might think to use the same state variables as used for tracking the dog. However, this will not work. Recall that the Kalman filter state transition must be written as $\\mathbf{x}' = \\mathbf{F x}$, which means we must calculate the current state from the previous state. Our assumption is that the ball is traveling in a vacuum, so the velocity in x is a constant, and the acceleration in y is solely due to the gravitational constant $g$. We can discretize the Newtonian equations using the well known Euler method in terms of $\\Delta t$ are:\n", + "\n", + "$$\\begin{aligned}\n", + "x_t &= v_{x(t-1)} {\\Delta t} \\\\\n", + "v_{xt} &= vx_{t-1}\n", + "\\\\\n", + "y_t &= -\\frac{g}{2} {\\Delta t}^2 + vy_{t-1} {\\Delta t} + y_{t-1} \\\\\n", + "v_{yt} &= -g {\\Delta t} + v_{y(t-1)} \\\\\n", + "\\end{aligned}\n", + "$$\n", + "> **sidebar**: *Euler's method integrates a differential equation stepwise by assuming the slope (derivative) is constant at time $t$. In this case the derivative of the position is velocity. At each time step $\\Delta t$ we assume a constant velocity, compute the new position, and then update the velocity for the next time step. There are more accurate methods, such as Runge-Kutta available to us, but because we are updating the state with a measurement in each step Euler's method is very accurate.*\n", + "\n", + "This implies that we need to incorporate acceleration for $y$ into the Kalman filter, but not for $x$. This suggests the following state variables.\n", + "\n", + "$$\n", + "\\mathbf{x} = \n", + "\\begin{bmatrix}\n", + "x \\\\\n", + "\\dot{x} \\\\\n", + "y \\\\\n", + "\\dot{y} \\\\\n", + "\\ddot{y}\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "**Step 2:** Design State Transition Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our next step is to design the state transistion function. Recall that the state transistion function is implemented as a matrix $\\mathbf{F}$ that we multipy with the previous state of our system to get the next state$\\mathbf{x}' = \\mathbf{Fx}$.\n", + "\n", + "I will not belabor this as it is very similar to the 1-D case we did in the previous chapter. Our state equations for position and velocity would be:\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) + (0 * a_y) \\\\\n", + "v_x &= (0*x) + (1*v_x) + (0*y) + (0 * v_y) + (0 * a_y) \\\\\n", + "y' &= (0*x) + (0* v_x) + (1*y) + (\\Delta t * v_y) + (\\frac{1}{2}{\\Delta t}^2*a_y) \\\\\n", + "v_y &= (0*x) + (0*v_x) + (0*y) + (1*v_y) + (\\Delta t * a_y) \\\\\n", + "a_y &= (0*x) + (0*v_x) + (0*y) + (0*v_y) + (1 * a_y) \n", + "\\end{aligned}\n", + "$$\n", + "\n", + "Note that none of the terms include $g$, the gravitational constant. This is because the state variable $\\ddot{y}$ will be initialized with $g$, or -9.81. Thus the function $\\mathbf{F}$ will propagate $g$ through the equations correctly. \n", + "\n", + "In matrix form we write this as:\n", + "\n", + "$$\n", + "\\mathbf{F} = \\begin{bmatrix}\n", + "1 & \\Delta t & 0 & 0 & 0 \\\\\n", + "0 & 1 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 1 & \\Delta t & \\frac{1}{2}{\\Delta t}^2 \\\\\n", + "0 & 0 & 0 & 1 & \\Delta t \\\\\n", + "0 & 0 & 0 & 0 & 1\n", + "\\end{bmatrix}\n", + "$$" + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "Interlude: Test State Transition" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Kalman filter class provides us with useful defaults for all of the class variables, so let's take advantage of that and test the state transistion function before continuing. Here we construct a filter as specified in Step 2 above. We compute the initial velocity in x and y using trigonometry, and then set the initial condition for $x$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin,cos,radians\n", + "\n", + "def ball_kf(x, y, omega, v0, dt):\n", + "\n", + " g = 9.8 # gravitational constant\n", + "\n", + " f1 = KalmanFilter(dim_x=5, dim_z=2)\n", + "\n", + "\n", + " ay = .5*dt**2\n", + "\n", + " f1.F = np.array ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", + " [0, 1, 0, 0, 0], # dx = dx\n", + " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", + " [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt \n", + " [0, 0, 0, 0, 1]]) # ddy = -g.\n", + " \n", + " # compute velocity in x and y\n", + " omega = radians(omega)\n", + " vx = cos(omega) * v0\n", + " vy = sin(omega) * v0\n", + " \n", + " f1.Q *= 0.\n", + "\n", + " f1.x = np.array([[x, vx, y, vy, -g]]).T\n", + " \n", + " return f1" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can test the filter by calling predict until $y=0$, which corresponds to the ball hitting the ground. We will graph the output against the idealized computation of the ball's position. If the model is correct, the Kalman filter prediction should match the ideal model very closely. We will draw the ideal position with a green circle, and the Kalman filter's output with '+' marks." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y = 15.\n", + "x = 0.\n", + "theta = 20. # launch angle\n", + "v0 = 100.\n", + "dt = 0.1 # time step\n", + "\n", + "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[0,0])\n", + "f1 = ball_kf(x,y,theta,v0,dt)\n", + "t = 0\n", + "while f1.x[2,0] > 0:\n", + " t += dt\n", + " f1.predict() \n", + " x,y = ball.step(dt)\n", + " p1 = plt.scatter(f1.x[0,0], f1.x[2,0], color='black', marker='+', s=75)\n", + " p2 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + "\n", + "plt.legend([p1,p2], ['Kalman filter', 'idealized'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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L8a1oNBr0Gj3z5s0DYGraVMYkjekxdr/7hrDKXsVe8160VVpMOhMl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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see, the Kalman filter agrees with the physics model very closely. If you are interested in pursuing this further, try altering the initial velocity, the size of dt, and $\\theta$, and plot the error at each step. However, the important point is to test your design as soon as possible; if the design of the state transistion is wrong all subsequent effort may be wasted. More importantly, it can be extremely difficult to tease out an error in the state transition function when the filter incorporates measurment updates." + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "**Step 3**: Design the Motion Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have no control inputs to the ball flight, so this step is trivial - set the motion transition function $\\small\\mathbf{B}=0$. This is done for us by the class when it is created so we can skip this step." + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "**Step 4**: Design the Measurement Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The measurement function defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. We will assume that we have a sensor that provides us with the position of the ball in (x,y), but cannot measure velocities or accelerations. Therefore our function must be:\n", + "\n", + "$$\n", + "\\begin{bmatrix}z_x \\\\ z_y \\end{bmatrix}= \n", + "\\begin{bmatrix}\n", + "1 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 1 & 0 & 0\n", + "\\end{bmatrix} * \n", + "\\begin{bmatrix}\n", + "x \\\\\n", + "\\dot{x} \\\\\n", + "y \\\\\n", + "\\dot{y} \\\\\n", + "\\ddot{y}\\end{bmatrix}$$\n", + "\n", + "where\n", + "\n", + "$$\\mathbf{H} = \\begin{bmatrix}\n", + "1 & 0 & 0 & 0 & 0 \\\\\n", + "0 & 0 & 1 & 0 & 0\n", + "\\end{bmatrix}$$" + ] + }, + { + "cell_type": "heading", + "level": 5, + "metadata": {}, + "source": [ + "**Step 5**: Design the Measurement Noise Matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As with the robot, we will assume that the error is independent in $x$ and $y$. In this case we will start by assuming that the measurement error in x and y are 0.5 meters. Hence,\n", + "\n", + "$$\\mathbf{R} = \\begin{bmatrix}0.5&0\\\\0&0.5\\end{bmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Step 6: Design the Process Noise Matrix\n", + "Finally, we design the process noise. As with the robot tracking example, we don't yet have a good way to model process noise. However, we are assuming a ball moving in a vacuum, so there should be no process noise. For now we will assume the process noise is 0 for each state variable. This is a bit silly - if we were in a perfect vacuum then our predictions would be perfect, and we would have no need for a Kalman filter. We will soon alter this example to be more realistic by incorporating air drag and ball spin. \n", + "\n", + "We have 5 state variables, so we need a $5{\\times}5$ covariance matrix:\n", + "\n", + "$$\\mathbf{Q} = \\begin{bmatrix}0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\end{bmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Step 7: Design the Initial Conditions\n", + "\n", + "We already performed this step when we tested the state transistion function. Recall that we computed the initial velocity for $x$ and $y$ using trigonometry, and set the value of $\\mathbf{x}$ with:\n", + "\n", + " omega = radians(omega)\n", + " vx = cos(omega) * v0\n", + " vy = sin(omega) * v0\n", + "\n", + " f1.x = np.mat([x, vx, y, vy, -g]).T\n", + " \n", + " \n", + "With all the steps done we are ready to implement our filter and test it. First, the implementation:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sin,cos,radians\n", + "\n", + "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.):\n", + "\n", + " g = 9.8 # gravitational constant\n", + " f1 = KalmanFilter(dim_x=5, dim_z=2)\n", + "\n", + " ay = .5*dt**2\n", + " f1.F = np.mat ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", + " [0, 1, 0, 0, 0], # dx = dx\n", + " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", + " [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt \n", + " [0, 0, 0, 0, 1]]) # ddy = -g.\n", + "\n", + " f1.H = np.mat([\n", + " [1, 0, 0, 0, 0],\n", + " [0, 0, 1, 0, 0]])\n", + " \n", + " f1.R *= r\n", + " f1.Q *= q\n", + "\n", + " omega = radians(omega)\n", + " vx = cos(omega) * v0\n", + " vy = sin(omega) * v0\n", + "\n", + " f1.x = np.mat([x,vx,y,vy,-9.8]).T\n", + " \n", + " return f1" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will test the filter by generating measurements for the ball using the ball simulation class." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y = 1.\n", + "x = 0.\n", + "theta = 35. # launch angle\n", + "v0 = 80.\n", + "dt = 1/10. # time step\n", + "\n", + "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[.2,.2])\n", + "f1 = ball_kf(x,y,theta,v0,dt)\n", + "\n", + "t = 0\n", + "xs = []\n", + "ys = []\n", + "while f1.x[2,0] > 0:\n", + " t += dt\n", + " x,y = ball.step(dt)\n", + " z = np.mat([[x,y]]).T\n", + "\n", + " f1.update(z)\n", + " xs.append(f1.x[0,0])\n", + " ys.append(f1.x[2,0])\n", + " \n", + " f1.predict() \n", + " \n", + " p1 = plt.scatter(x, y, color='green', marker='.', s=75, alpha=0.5)\n", + "\n", + "p2, = plt.plot (xs, ys,lw=2)\n", + "plt.legend([p2,p1], ['Kalman filter', 'Measurements'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + 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kYK7lnmj2BOsS19HQks/4vuEcOWTk42/3kn5By7JlWurV09Omw0VyG+fe0WXN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\n8/QezdK7NE/v0jy9R7P0Ln9/f6+8z48W5xdeeIGXXnrpe9tHjx7Niy+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+ "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that the Kalman filter reasonably tracks the ball. However, as already explained, this is a silly example; we can predict trajectories in a vacuum with arbitrary precision; using a Kalman filter in this example is a needless complication." + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Tracking a Ball in Air" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are now ready to design a practical Kalman filter application. For this problem we assume that we are tracking a ball traveling through the Earth's atmosphere. The path of the ball is influenced by wind, drag, and the rotation of the ball. We will assume that our sensor is a camera; code that we will not implement will perform some type of image processing to detect the position of the ball. This is typically called *blob detection* in computer vision. However, image processing code is not perfect; in any given frame it is possible to either detect no blob or to detect spurious blobs that do not correspond to the ball. Finally, we will not assume that we know the starting position, angle, or rotation of the ball; the tracking code will have to initiate tracking based on the measurements that are provided. The main simplification that we are making here is a 2D world; we assume that the ball is always traveling orthogonal to the plane of the camera's sensor. We have to make that simplification at this point because we have not yet discussed how we might extract 3D information from a camera, which necessarily provides only 2D data. " + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Implementing Air Drag" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our first step is to implement the math for a ball moving through air. There are several treatments available. A robust solution takes into account issues such as ball roughness (which affects drag non-linearly depending on velocity), the Magnus effect (spin causes one side of the ball to have higher velocity relative to the air vs the opposite side, so the coefficient of drag differs on opposite sides), the effect of lift, humidity, air density, and so on. I assume the reader is not interested in the details of ball physics, and so will restrict this treatment to the effect of air drag on a non-spinning baseball. I will use the math developed by Nicholas Giordano and Hisao Nakanishi in *Computational Physics* [1997]. \n", + "\n", + "**Important**: Before I continue, let me point out that you will not have to understand this next piece of physics to proceed with the Kalman filter. My goal is to create a reasonably accurate behavior of a baseball in the real world, so that we can test how our Kalman filter performs with real-world behavior. In real world applications it is usually impossible to completely model the physics of a real world system, and we make do with a process model that incorporates the large scale behaviors. We then tune the measurement noise and process noise until the filter works well with our data. There is a real risk to this; it is easy to finely tune a Kalman filter so it works perfectly with your test data, but performs badly when presented with slightly different data. This is perhaps the hardest part of designing a Kalman filter, and why it gets referred to with terms such as 'black art'. \n", + "\n", + "I dislike books that implement things without explanation, so I will now develop the physics for a ball moving through air. Move on past the implementation of the simulation if you are not interested. \n", + "\n", + "A ball moving through air encounters wind resistance. This imparts a force on the wall, called *drag*, which alters the flight of the ball. In Giordano this is denoted as\n", + "\n", + "$$F_{drag} = -B_2v^2$$\n", + "\n", + "where $B_2$ is a coefficient derived experimentally, and $v$ is the velocity of the object. $F_{drag}$ can be factored into $x$ and $y$ components with\n", + "\n", + "$$F_{drag,x} = -B_2v v_x\\\\\n", + "F_{drag,y} = -B_2v v_y\n", + "$$\n", + "\n", + "If $m$ is the mass of the ball, we can use $F=ma$ to compute the acceleration as\n", + "\n", + "$$ a_x = -\\frac{B_2}{m}v v_x\\\\\n", + "a_y = -\\frac{B_2}{m}v v_y$$\n", + "\n", + "Giordano provides the following function for $\\frac{B_2}{m}$, which takes air density, the cross section of a baseball, and its roughness into account. Understand that this is an approximation based on wind tunnel tests and several simplifying assumptions. It is in SI units: velocity is in meters/sec and time is in seconds.\n", + "\n", + "$$\\frac{B_2}{m} = 0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}}$$\n", + "\n", + "Starting with this Euler discretation of the ball path in a vacuum:\n", + "$$\\begin{aligned}\n", + "x &= v_x \\Delta t \\\\\n", + "y &= v_y \\Delta t \\\\\n", + "v_x &= v_x \\\\\n", + "v_y &= v_y - 9.8 \\Delta t\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We can incorporate this force (acceleration) into our equations by incorporating $accel * \\Delta t$ into the velocity update equations. We should subtract this component because drag will reduce the velocity. The code to do this is quite straightforward, we just need to break out the Force into $x$ and $y$ components. \n", + "\n", + "I will not belabor this issue further because the computational physics is beyond the scope of this book. Recognize that a higher fidelity simulation would require incorporating things like altitude, temperature, ball spin, and several other factors. My intent here is to impart some real-world behavior into our simulation to test how our simpler prediction model used by the Kalman filter reacts to this behavior. Your process model will never exactly model what happens in the world, and a large factor in designing a good Kalman filter is carefully testing how it performs against real world data. \n", + "\n", + "The code below computes the behavior of a baseball in air, at sea level, in the presence of wind. I plot the same initial hit with no wind, and then with a tail wind at 10 mph. Baseball statistics are universally done in US units, and we will follow suit here (http://en.wikipedia.org/wiki/United_States_customary_units). Note that the velocity of 110 mph is a typical exit speed for a baseball for a home run hit." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, exp, cos, sin, radians\n", + "\n", + "def mph_to_mps(x):\n", + " return x * .447\n", + "\n", + "def drag_force(velocity):\n", + " \"\"\" Returns the force on a baseball due to air drag at\n", + " the specified velocity. Units are SI\"\"\"\n", + "\n", + " return (0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))) * velocity\n", + "\n", + "v = mph_to_mps(110.)\n", + "y = 1\n", + "x = 0\n", + "dt = .1\n", + "theta = radians(35)\n", + "\n", + "def solve(x, y, vel, v_wind, launch_angle):\n", + " xs = []\n", + " ys = []\n", + " v_x = vel*cos(launch_angle)\n", + " v_y = vel*sin(launch_angle)\n", + " while y >= 0:\n", + " # Euler equations for x and y\n", + " x += v_x*dt\n", + " y += v_y*dt\n", + "\n", + " # force due to air drag \n", + " velocity = sqrt ((v_x-v_wind)**2 + v_y**2) \n", + " F = drag_force(velocity)\n", + "\n", + " # euler's equations for vx and vy\n", + " v_x = v_x - F*(v_x-v_wind)*dt\n", + " v_y = v_y - 9.8*dt - F*v_y*dt\n", + " \n", + " xs.append(x)\n", + " ys.append(y)\n", + " \n", + " return xs, ys\n", + " \n", + "x,y = solve(x=0, y=1, vel=v, v_wind=0, launch_angle=theta)\n", + "p1 = plt.scatter(x, y, color='blue')\n", + "\n", + "x,y = solve(x=0, y=1,vel=v, v_wind=mph_to_mps(10), launch_angle=theta)\n", + "p2 = plt.scatter(x, y, color='green', marker=\"v\")\n", + "plt.legend([p1,p2], ['no wind', '10mph wind'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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sgfCA8FJrjAyMZG6fuWX6fpqGN2Xen+ed89oAEeEGxvcYxLsf59LoChe33JLNZZcVnnFc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\nWDhfp8+ukOXAdzX+eouysjxmjwUAQK+Tl+fS44/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+ "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can easily see the difference between the trajectory in a vacuum and in the air. I used the same initial velocity and launch angle in the ball in a vacuum section above. We computed that the ball in a vacuum would travel over 240 meters (nearly 800 ft). In the air, the distance is just over 120 meters, or roughly 400 ft. 400ft is a realistic distance for a well hit home run ball, so we can be confident that our simulation is reasonably accurate.\n", + "\n", + "Without further ado we will create a ball simulation that uses the math above to create a more realistic ball trajectory. I will note that the nonlinear behavior of drag means that there is no analytic solution to the ball position at any point in time, so we need to compute the position step-wise. I use Euler's method to propagate the solution; use of a more accurate technique such as Runge-Kutta is left as an exercise for the reader. That modest complication is unnecessary for what we are doing because the accuracy difference between the techniques will be small for the time steps we will be using. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import radians, sin, cos, sqrt, exp\n", + "\n", + "class BaseballPath(object):\n", + " def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)): \n", + " \"\"\" Create 2D baseball path object \n", + " (x = distance from start point in ground plane, y=height above ground)\n", + " \n", + " x0,y0 initial position\n", + " launch_angle_deg angle ball is travelling respective to ground plane\n", + " velocity_ms speeed of ball in meters/second\n", + " noise amount of noise to add to each reported position in (x,y)\n", + " \"\"\"\n", + " \n", + " omega = radians(launch_angle_deg)\n", + " self.v_x = velocity_ms * cos(omega)\n", + " self.v_y = velocity_ms * sin(omega)\n", + "\n", + " self.x = x0\n", + " self.y = y0\n", + "\n", + " self.noise = noise\n", + "\n", + "\n", + " def drag_force (self, velocity):\n", + " \"\"\" Returns the force on a baseball due to air drag at\n", + " the specified velocity. Units are SI\n", + " \"\"\"\n", + " B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))\n", + " return B_m * velocity\n", + "\n", + "\n", + " def update(self, dt, vel_wind=0.):\n", + " \"\"\" compute the ball position based on the specified time step and\n", + " wind velocity. Returns (x,y) position tuple.\n", + " \"\"\"\n", + "\n", + " # Euler equations for x and y\n", + " self.x += self.v_x*dt\n", + " self.y += self.v_y*dt\n", + "\n", + " # force due to air drag\n", + " v_x_wind = self.v_x - vel_wind\n", + " v = sqrt (v_x_wind**2 + self.v_y**2)\n", + " F = self.drag_force(v)\n", + "\n", + " # Euler's equations for velocity\n", + " self.v_x = self.v_x - F*v_x_wind*dt\n", + " self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt\n", + "\n", + " return (self.x + random.randn()*self.noise[0], \n", + " self.y + random.randn()*self.noise[1])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can test the Kalman filter against measurements created by this model." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y = 1.\n", + "x = 0.\n", + "theta = 35. # launch angle\n", + "v0 = 50.\n", + "dt = 1/10. # time step\n", + "\n", + "ball = BaseballPath(x0=x, y0=y, launch_angle_deg=theta, velocity_ms=v0, noise=[.3,.3])\n", + "f1 = ball_kf(x,y,theta,v0,dt,r=1.)\n", + "f2 = ball_kf(x,y,theta,v0,dt,r=10.)\n", + "t = 0\n", + "xs = []\n", + "ys = []\n", + "xs2 = []\n", + "ys2 = []\n", + "\n", + "while f1.x[2,0] > 0:\n", + " t += dt\n", + " x,y = ball.update(dt)\n", + " z = np.mat([[x,y]]).T\n", + "\n", + " f1.update(z)\n", + " f2.update(z)\n", + " xs.append(f1.x[0,0])\n", + " ys.append(f1.x[2,0])\n", + " xs2.append(f2.x[0,0])\n", + " ys2.append(f2.x[2,0]) \n", + " f1.predict() \n", + " f2.predict()\n", + " \n", + " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + "\n", + "p2, = plt.plot (xs, ys, lw=2)\n", + "p3, = plt.plot (xs2, ys2, lw=4, c='#e24a33')\n", + "plt.legend([p1,p2, p3], \n", + " ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)'],\n", + " loc='best')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": 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h+AHkA6nIR/dBZbljFzo5Q6v2SG1ikcIfgMAQpHpuId6QSZIEAUFIAUHwoHkS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\nY/HixThz5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+ "text": [ + "" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin blue line, and a Kalman filter with R=10 as a thick red line. These R values are chosen merely to show the effect of measurement noise on the output, they are not intended to imply a correct design.\n", + "\n", + "We can see that neither filter does very well. At first both track the measurements well, but as time continues they both diverge. This happens because the state model for air drag is nonlinear and the Kalman filter assumes that it is linear. If you recall our discussion about nonlinearity in the g-h filter chapter we showed why a g-h filter will always lag behind the acceleration of the system. We see the same thing here - the acceleration is negative, so the Kalman filter consistently overshoots the ball position. There is no way for the filter to catch up so long as the acceleration continues, so the filter will continue to diverge.\n", + "\n", + "What can we do to improve this? The best approach is to perform the filtering with a nonlinear Kalman filter, and we will do this in subsequent chapters. However, there is also what I will call an 'engineering' solution to this problem as well. Our Kalman filter assumes that the ball is in a vacuum, and thus that there is no process noise. However, since the ball is in air the atmosphere imparts a force on the ball. We can think of this force as process noise. This is not a particularly rigorous thought; for one thing, this force is anything but Gaussian. Secondly, we can compute this force, so throwing our hands up and saying 'it's random' will not lead to an optimal solution. But let's see what happens if we follow this line of thought.\n", + "\n", + "The following code implements the same Kalman filter as before, but with a non-zero process noise. I plot two examples, one with `Q=.1`, and one with `Q=0.01`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_ball_with_q(q, r=1., noise=0.3):\n", + " y = 1.\n", + " x = 0.\n", + " theta = 35. # launch angle\n", + " v0 = 50.\n", + " dt = 1/10. # time step\n", + "\n", + " ball = BaseballPath(x0=x, \n", + " y0=y, \n", + " launch_angle_deg=theta, \n", + " velocity_ms=v0, \n", + " noise=[noise,noise])\n", + " f1 = ball_kf(x,y,theta,v0,dt,r=r, q=q)\n", + " t = 0\n", + " xs = []\n", + " ys = []\n", + "\n", + " while f1.x[2,0] > 0:\n", + " t += dt\n", + " x,y = ball.update(dt)\n", + " z = np.mat([[x,y]]).T\n", + "\n", + " f1.update(z)\n", + " xs.append(f1.x[0,0])\n", + " ys.append(f1.x[2,0]) \n", + " f1.predict() \n", + "\n", + "\n", + " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + "\n", + " p2, = plt.plot (xs, ys,lw=2)\n", + " plt.legend([p1,p2], ['Measurements', 'Kalman filter'])\n", + " plt.show()\n", + " \n", + "plot_ball_with_q(0.01)\n", + "plot_ball_with_q(0.1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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tHJxZSqxVtPyc+nM9RSmuFma9mcc6P0Y7v3a4VBdljjJQoUNgBx7p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jj8ybN4+///3v3HzzzaSkpJxXHJ07d2bz5s2sW7eORx55hDlz5tCoUaNKXSXa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\nxcV6wsN93HlnOf37OwkIqEg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/hfv/NZcNe/NpFGFj+mu38vTvOqLXVf/vIy4ojhGtRmAz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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second filter tracks the measurements fairly well. There appears to be a bit of lag, but very little.\n", + "\n", + "Is this a good technique? Usually not, but it depends. Here the nonlinearity of the force on the ball is fairly constant and regular. Assume we are trying to track an automobile - the accelerations will vary as the car changes speeds and turns. When we make the process noise higher than the actual noise in the system the filter will opt to weigh the measurements higher. If you don't have a lot of noise in your measurements this might work for you. However, consider this next plot where I have increased the noise in the measurements." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plot_ball_with_q(0.01, r=3, noise=3.)\n", + "plot_ball_with_q(0.1, r=3, noise=3.)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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Jc/M3AvD6vUl0aH3hSz5vztpc8Tg83E14uP23Z0FAECWOEgZFDmRc53FA9XPF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O3w6mADAkMpAFU4by5jdxfP3bcZ5bHMe2I6m88eBAnB1rXuTElvam7621BAcq\nb9zcmbaz2oeSlkRRFCwWC+rLMMovRF0sFkuTzO18gSTGQgjxX/nl+Sw+vJhiU7E1kUkpSmHn+Z1M\n6DyBINcgDDoDowJHNXOk1ZWaSkkqSKqSFP+dTqUjtSi11sQYoMJSQWZ+CUs2HOWLTfFkF1Su8OXj\n5sB9w7pwz9BwPF1qL7WoS3ZpNrvTdmPUGnn7qW68u+wMZ9ILKCk3YTIrFJYaKSyteZGUjX+cZfEv\nR5g2rgf3j4jAQV/zny6zxcJnv8bz+rd7KCk34Waw48W7+vLoTX1RqVS8+VAM13Zpx6xP41iz8xQH\nT2fx4eND6B7UtNOQmS3mOken1agxWVr2jZvu7u5kZGTg4+MjybFoNhaLhYyMDOsUjE1BEmMhhKBy\nRGzp0aWYFXOV0T17rT2KovDN8W94KuqpWhPP5pZTlkOFuaLW+Oy0dpgVc63H5+er+GOfCx/9+xvK\njZX7dQ305KGR3RjXLxi9tnE3rRktRpYfX86p/FPYaezQqDSUmA4w8hYX7gq7Cy8HL4xmC6XlJkor\nTJSUm6yPS8tN5BeX8/mGeHYcPc+8r3fzyfrDPH1zL+4Y1Amt5q8E7VhyDjM+/p0/EjMAGBsdzNz7\n+uHt6lglKb25fyg9gr14dOFmjiRlM27OGv55ZzQPXh/RZKUVHVw6kJifWGv9domphI7uHZvk3Lai\n0+nw9PSkoKAARVEwmVp2It9aaLWVaZj0Z/0oioKnpyc6XdOVrUliLIQQwNnCs2SXZddYB6pSqbAo\nFnan7SbGP6YZors4O41dnSN5OrUODzsPzBYzGvVfSW5mppo9e+w4flyLoqgAM9f36sDDo7oRHdbm\nkpPFlSdWklyYXKVfDToDJouJz+M/58nIJ9Fr9ei1mlpLJUb3CSL20DleXb6HQ2eymLn4dz78+U9m\n3tabEVEd+PeaP/n3mgMYzRbauBt4dVJ/RvSqfYaQkLZurHlpHHO/2sXnG+KZ8+UOth1J5e0pMbg7\n2f6DT2/f3sSmxNZ646aTzolwj5a/EJZOpyMkJASQxVJsRRafaXkkMRZCCOBozlHsNLXXsNpr7Ukq\nSLqMETWMp70n7nbuGC01lyMYLUbGhozldP5pys3lZKY5sHu3ntOnK0de1Gq4ZUBHpo3tQUc/d5vE\nVFBRwIn8Exi0NX/YKDeVszttNwP8BtTZjkqlYlB3fwZ29eOn3ad447u9nE4r4NGFm3G001JSXjna\ndu+wcGYoxneAAAAgAElEQVTf0QeXetQN2+u1/Ov+/lzbpR0zPo7l1/1JjHh+FR9MG8o1nXwb94Jr\nodfouaPzHXx9/GtUqNBrKuMrM5WhVWu5O/zuOufIFkJcPpIYCyEElSOqdd3QUdNoX0uiUqkYGjCU\nVYmrqt3oZVEsaNAwov0Ith5M5fUftpOQVAGATqcwoq8XL9wyjABvF5vGdDjrMBpqL8Gw19pzIvfE\nRRPjC9RqFeP6hjCqdxDfxp7g7VX7SMstIaStKwsmDyQ6rOHLTo/uE0S3QE+m/nszfyRmcsvcH3nu\n9t48OroHarXt/r+DXIOYHjmduNQ4kguTAQjxCaFv274ttjxHiKuRJMZCCAFEekeyPXW7dRq2/1Vq\nKqWbV7fLHFXDRHhFYMHCprObyCvPAyqnYvNxbIMhpw/jX1xvnWHCzWDHpBERPHB9BB7OTZOYWRTL\nxT9MNCL31GnV3DUkjJsHhLL3RDrXdPLFvpYb8uqjvY8Lq14cy+vf7uWjnw8y/5s9bI8/z7/u70+g\nr+0+LDjqHBnRYYTN2hNC2J4kxkIIAXg4eBDiGkJSYZL1UvcFZsWMs50zXT27NlN09dfNqxtdPbty\nvvg8uSWFxO4r5LNvTpKcuRuANu6OPHxDN+4aHIaTQ9NOVRbuEc7m5M21lqiUm8sJcApodPsOei0D\nu/o1+vi/02s1vHBnNP3C2zL9o9/47WAKg579lonXhTH9pkjauNdvvmYhROsmibEQQvzXbZ1vY8WJ\nFSTkJaBVa1GpVFSYK/Bx8OHu8Lur3LTW0lgsCilZhRw9m0N8cg5Hz+aw89h565RrwW1dmTqmOzf3\n73jZlkX2dPDE38mfzNJMtOqqf24ulK3Ut4zichkW2Z4Nr97C69/uYWVcAl9uOsp3v5/ggRERPDqm\nh01G10tNpeSV52Gvscfd3jb13EII25DEWAgh/kun1jExbCJ55XkcyDiASTER7h6On7NtRiVtpaCk\ngmPJOcSfzeHo2WyOJedyLDmHorLqN951D/Ji2riejOzd4bIswfy/JoZN5PMjn5NRkoFBZ0ClUlFm\nKkOj0jCx88Q6l6BuLm09DLz7yHVMHdODBSv2snbPGT746SBfbjrKI6O789CobhjsGz5dVLGxmFUJ\nqzhbcBajxYhKpcLbwZsR7UcQ6h7aBK9ECNFQquPHjzfd8iFAcnIy4eEtfxqa1kCmdbEt6U/bkb60\nrQv9mZ6Ryem0fOLP5nAsOYej/x0JTskqqvE4HzcHwgM8CG/vSViAOxEdPAkP8Gj2mwYVReFk3kn2\npe/DgoUOzh3o06ZPtZKVpnKp788DiZm8/u0eYg+fq2zPxZ4nxkdyz9Dweo++l5nK+ODgB5jMpmpX\nHkpMJUzsNLHByXGJsYQtKVtIyE3AaDHirHcmuk00Pbx7NNn/ufys25b0p215enoSFxdHQEDjS7Rk\nxFgIIVqY7IJSJr3xI1v/TLIutvF39joNnfzdCW/vQXiAB2EBlV+9XFve6CtUzpgR6haKj6MPKlS4\n6F2aPVlviJ4h3nw9+wa2HUnltW/3sD8hgzlf7mDR2kM8fXMUtw7sWGWxkZpsTdlKuam8xg8DjlpH\nfkn6pUGJcX55PosOLcKsmNGpdahUKoqMRaw5tYaEvARu6XhLq+pjIVoKSYyFEKKFefrDDfy69xQA\nAd5OhAd4Et7eg7AAd7q09yTQ1+WiiVhLoSgKv5/7nX0Z+yisKATAVe9KdNto+rbt28zRNUz/iHas\neWkcG/af5fVv93AsJZdnPo7lw58P8uytvbjhmqBap3g7kXeizhHyrLIscspy8LD3qFcsK06uACrL\nf/7OoDMQnxNPWHYYXb1a/s2iQrQ0khgLIUQL8uu+JJZvicfRTse6eTcS2s6tuUO6JGtOreFQ1iEc\ntA7W1e9MiokNSRsoNBYyvP3wZo6wYVQqFSN6dWBoZABrdpzizZX7SEjNY8r/baJboBfP3BLFgK5+\nOPzP9HEVpoo6p6azWCyUmkrrFUNBRQGpRak46hxr3O6odWRn2k5JjIVoBEmMhRCihcgrLmfWp3EA\nvDIpptUnxTmlORzIPICTzqnaNkedI7vO7+LattfWuAx3S6dRq7mpfyhjooP5Zutx3v1+P4fOZHH/\nW7+i1agID/AkMtSbnsE+RIZ4Y9A5UWyquTYcQKfR4WZXv//vnNKcWlc4hMrkvaii9nMJIWonibEQ\nQrQQLy/dSXpeCX27+PHo2F7k5eXarG1FUaiwVKBT6y7b8sO/n/sdB03tdc8alYZd53cxpP2QyxJP\nU9Bp1dwzNJxbB3bk81+PsDIugeMpuRw6k8WhM1l8wVEAHO21uHvZ4dcO2rQx06aNGSenynvfzYqZ\nAOcADDoDFSYzaTnFpGYXcz6nmNScIlKzi2nnaWDqmMqb6hx1jhf9P7xcNzYKcaWRxFgIIVqAzQeS\n+Tb2BPY6DYueugGNjWqIy83l/HrmV47nHafMVIZWraWDcwduCLoBVztXm5yjNiWmkjrnftZr9OSW\n2y75b04Oei2PjunBo2N6UFxm5ODpLA4kZrA/IZMDpzJIzS6mJMWOcyl/HePkZMHHt3LaNgeTE+/k\nLiUzv/ZyigERfvQI9sbbwRsPe49aR43LTGVE+UTZ+iUKcVWQxFgIIZpZYUkFMxf/DsCMW3vRKcDT\nJu1WmCv45NAnFFQUoNforXMGpxSl8OHBD5nSbUqTLjDhYe9BUkFSrctsl5nKaGNo02Tnby4Gex39\nwtvSL7yt9bn03BL+SMxg3cGD7E04T+p5FUVFaoqKLqwKWLlUt1qlwtfdkbYeBtp5Gmjn4cQfiRns\nOZHOjqPn6RHsjUqlYniH4aw4saJanbHJYsKgM3Btu2sv18sV4opy0cR4xowZ7Ny5k9LSUvz8/Hjy\nyScZOnQoRqOROXPmsH79elxdXZk5cyajRo26HDELIcQVZe7XuzifU0zPYG8eGtXNZu3+lvIb+RX5\n1ZZkvnAZfs2pNdzX5T6bne9/9W/Xn91pu2tNjNUqNb19ezfZ+VsSX3dHRvYOZGTvQKBypcLE83kc\nPJ2FTqumrYcT7TwN+Lo5Vptx5LvfT1gT40dGdwcql9u+rdNtbDy7kezSbCxY0Kv1dHDpwC0db6l1\nGW4hRN0umhhPnjyZ+fPno9fr2bZtG1OmTGH37t0sW7aMhIQEYmNjiY+PZ8qUKURGRtKmzZX36V8I\nIZrK74fPsWzzMfRaNW9PibHpNGzx2fG1JkhqlZqUwhRKTaVNtvqck96JwQGD2Zy8GUeto3VeXUVR\nKDWVMjpo9FWbwKnVKjr6udPR7+Ij9v3CKkeedx9Pw2yxWFcwDPMIo7N7Z3LLcykzleFu794iVxIU\nojW56G/gsLAw9Ho9iqJgNBoxGCqX9Fy/fj333HMPTk5O9OnTh8jISDZs2HA5YhZCiCtCcZmRZz+J\nBWD6TVF09q/fHLb1dbHpv8yKmRJjiU3P+b8G+A1gQucJuNm5UWGuwGQx4engyd3hdxPlK3Ww9eHv\n7Yy/lxMFJRUcPVu1JlulUuFh70E7p3aSFAthA/WqMX7ppZdYuXIl9vb2/Oc//8HBwYEzZ84QFBTE\njBkzGDJkCCEhIZw+fbrG4y8seSgujU5XeTlS+tM2pD9tR/qyceZ98CvJmUX0DPHlhfsGo9NW3qhm\nq/70cPbArFRfOc9KB/6+/rXOh2sr/Tz70S+0X5Oeoy6X+/1pNBs5mH6Q3PJc2ru0p6NHx0tehe66\nnoEs3XiYQ8n5DOrVyUaRNpz8rNuW9KdtXejPS1HvxPif//wny5cv59lnn2Xt2rWUlpbi6OjIyZMn\n6dq1KwaDgbS0tBqPnzt3rvVxTEwMgwYNuuTAhRCiNfv90Fk+XLMfrUbNomdusCbFthThE8Gec3uw\n01YvV7AoFtq7tm/ypLilMlvMbE/Zzp7zeyg1lmKntSOqTRQDAwbWWhNdH7+d+Y0tSVsoM5ehU+kw\nKkbc7NyYEDGBILegRrc7sHt7lm48zNebjuDn5Uz3YF+C2rjVutKeEFeLrVu3EhtbeeVNo9EQExNz\nSe2pjh8/rjTkgFGjRvHcc8/xzDPP8MUXXxAREQHAvHnzUBSFF154ocr+ycnJhIeHX1KQotKFT5TZ\n2dnNHMmVQfrTdqQvG6a03MSw2Ss5k17AUzdFMePWXlW226o/y83lLDq4iGJTcZWlgy2KBZPFxMPd\nHsbT4cofqfrf/jRZTHwR/wWpxalVyg/KTGV4OHhwW+ht7M3YS5GxCD+DH718e9VrXuC9aXtZf2Y9\nDrqqJQ2KolBmLmNq96l4ODSuXCYls5C+T32D8re/2E72Orp08CCig6f1Xyc/d+z1TTfhlPys25b0\np215enoSFxdHQEBAo9to8E+PoigoikJgYCCJiYnWxDgxMZGhQ4c2OhAhhLhavPHdXs6kFxDm784T\nN/ZssvPYaex4qNtDrD+znhO5J6iwVKBRaWjv0p5RgaPwsK9fkmZRLFSYKxcHqWte4tZiS/IWzhef\nr1aTa6exY0/aHnam7qSLZxe0ai3Hco6xNWUrY4PHEuEVUWubiqLwe+rv1ZJiqKwD1mv0bEzeyO2d\nbm9UzP7eziyfPZrYw+eIT8rmSFI26Xkl7D6ezu7j6db9NGoVHdu5ERHoycOjutM18Mr/4COELdWZ\nGGdlZbFlyxZGjRqFvb09K1asICcnh8jISEaNGsWXX37J4MGDiY+P58CBA7z22muXK24hhGiV/kjM\n4OP1h9CoVbw9ZRD6Jiih+Dt7rT03ht6IRbFQbi5Hp9ahVddvTOTC4iDHco/9tTiISwduCLwBN/vW\nuVy1oigczj6Mvda+2rYzBWfILs1Go9JYp7S7kDyvTFiJp4NnrfMuZ5dlU1BRUOPy11C5yl9KYUqN\n2+qrf0Q7+ke0s36fmV9CfFIOR/6bKMefzSYhNZ9jKbkcS8ll7Z4zLHz0OkZd0/gSDiGuNnX+dlSr\n1fz000+89dZbGI1GQkND+eCDD3Bzc+P+++/n1KlTDBo0CFdXV+bPn4+vr+/lilsIIVodo8nCsx//\njqLAlNHd6BHsfdnOrVapGzRrwf8uDnKhFvlc0Tk+PPhhqy3DMCtmio3F1frColg4X3werVqLyWLC\nZDFVKZ9w0DqwJXkLE8Mm1tiuyWJCUequTLQolkt/AX/j7erIoO6ODOrub32utMLE8eRcPttwhBW/\nn+Sh9zby/B19eHRM90u+AVCIq0GdibGHhwdLliyp+UCtlvnz5zN//vwmCUwIIa40H/78J0eTc+jg\n48zTN/e6+AHNaGvK1loXB9Gqtaw5tYZJEZOaKbrG06g0NY6YlxhLqDBXWJNhjarqSL5apSatuOYb\nzKFylb+6PngoioKbXdOPsjvotfQM8ebd4EF0bOfGq8v38K9vdpNwPo/XHhjQ5FcohGjtbDeTvBBC\niFolns/j3e//AOD1BwfiYNd0N0jZQnxO3YuDnCs61+RzIDcFlUpFB+cONY7eKqrKEV9nvXONtdQK\ntY8I6zV6wtzDqDBX1Li9xFTCQL+BjYy64VQqFdPG9eTj6cOw12tYvvUEd762jpzCsssWgxCtkSTG\nQgjRxCwWhecWx1FuNHPHoE4M7OrX3CFd1EUXB7FUliS0RtcHXo/RYqxS+uCoc0Sn0mGymAh1C612\njEWx4OPoU2e7o4NH4+voS7Gx2Nq2WTFTWFHIte2upbNHZ9u+kHq44Zogvn9xLL5ujuw4ep6xc1aT\nkJp32eMQorWQxFgIIZrY178dZ8fR83i5OPDCndHNHU69XKweWaPWYNAZLlM0tuVh78HkiMm42LlQ\nbCymoKKAElMJga6BhHuE46x3rnZMqbGUwf6D62xXq9YyKWISd3S+A19HX9zs3AhyCWJqj6kMaz+s\nqV7ORXUP8uanV8bTNdCTM+kFjJuzmm1HUpstHiFaspZ9LU8IIVq5tNxi5n29C4BX7u2Hu1P12RBa\nonCPcPam762xnMKiWPBz8mvVi4P4GHx4uNvD5JfnU1hRiEFnwNXOlRUnV3As5xj2Wns0Kg3l5nIs\nioUxwWPwc774SL9KpaKze2c6u1/+0eG6tPN0YtULY3n8gy38si+JO19fy6uTBnDn4LDmDk2IFkUS\nYyGEaEIvLNlOQUkFwyLbM65vcHOHU2/X+V/HydyTFFYUVlkJ7sLiIOOCxzVjdLbjaueKq52r9fvb\nO91OVkkW21K3UWoqxdfgS9+2fRs0o0dLZbDX8fH0Ybz6zR4+/Pkgz37yO4nn83l+wjVo1HIBWQiQ\nxFgIIS6Z0WLkfNF5FBTaGNpYR1nX7TnN2j1nMNjrmD+pf6uaLkuv0TO522R+OfMLx3OPU2YuQ6uq\nnMd4ZODIei8O0hp5OXoxPnR8c4fRJDRqNf+8M5qQdq7M+jSOj34+yKnz+fz7scEY7Bu/FLYQVwpJ\njIUQopEUReGXpF84mHmQYlMxKJULanTx6MJA3+H84/PtADx/xzX4eda88ENLZqexY1zIOOviIHq1\n/opY+U7AxOvCaO/twsPvbeTX/UncOu8nvpl9A66GmmciEeJqIddOhBCikX5I/IG96XvRqDW46F1w\nsXNBr9FzJPsIkxd9Q3peCb06+nDvsC7NHeolubA4iCTFV5b+Ee1Y8/I4Ovg4c/B0Fvcu+IWSMmNz\nhyVEs5IRYyFEq6UoCoeyDrEzbSf55floVVoCXQMZEjCkSt1oU8gvz+dw1uEab0DLTHNk134zWo2K\nBZMHola3nhIKcXUJaevGt8+P5qa5P7L3ZDqT3v6VJTOux14v6YG4OsmIsRCiVVIUhZ9O/cQPiT9Q\nUF6AWqXGgoUTuSf44M8PyCjOaNLz7zy/s8pNaReYTLBhQ+XME8MG2NHZ/8qtxRWtl8li4lzROVKL\nUmnj6cA3s2/A29WBuCOpPLpwM0aTbZevFqK1kI+EQohW6XTBafZn7sdJV7V2V6vWoigK3538jsd6\nPtZk5y82FqNVVf8VumuXHbm5Gjw8zAy6VsYeRMtiUSz8cqayLj6rNAsLFjztPenl24uvZo3itnk/\n8+v+JJ76z2+89+h1MluFuOpIYiyEaJW2nduGQVvzAhMqlYqssizSi9PxNfg2yfkDXQOJz4m3TuOl\nKHDqlJY9e/QAXDe0AH/XTk1ybiEaa+XJlWxN2Up6Sbp1dUOdWkd8Tjxjg/NY+txI7pi/lu+3J+Jo\np+P1Bwe0qtlUhLhU8lFQCNEqFRoL6/yDrUJFeml6k52/u1d39JrKJDgjQ83KlY6sXu2IxaKiR48K\n2rQ10q9tvyY7vxANlV2azaazmzhbeBaLYsFOY4edxg61Sk1RRRHLTyzHv42qssZYp2HZlmO8smxX\nlaWzhbjSSWIshGiV9Gp9ndstiqVamYUtadVaBnjcwNp1OpYuNXD2rBY7O4WYmFL69M9hTPCYK2JR\nCHHl+D3ld9KL09Gpq9fGa9QajGYjy08up194Wz6ePhydRs2idYd4Z9X+ZohWiOYhpRRCiFaph3cP\nfkn6pdbk00XvQqBLYJOcu6i0gg9+Osh/1h6krMIBjRqiIk3062skyLMNgwMm4u3o3STnFqKxzhSc\nwYQJPTV/qNRr9BzPPQ7AkJ4B/PuxwTy6cDNvrdqPwUHHlBu62ySOYmMxacVp6NQ6/Jz8ZBpA0aJI\nYiyEaJUifSLZm76X/PL8arNDlBhLGBM8BrXKthfFTGYLX/92nDdX7COroLI+c0x0ELPv6EOgr4tN\nzyWErRn0BiwWS63Xik0WE07av66yjIkOprjMxNOLtvLKsl0Y7HU8eduARp+/zFTGipMrKhN0iwkF\nBSedE33b9GWAn9Qyi5ZBEmMhRKukVWt5oOsDrElcQ0JeAuXmclSo8LD34PrQ6+nq1dVm51IUhU0H\nkpn31S5OpuYB0KujDy/c2ZdrOjXNzX1C2NoQ/yF8n/B9nftEeEVU+f6OQZ0oKTfyzyXbmfVpHL5e\n7kwYHFHL0bUzW8wsPryYQmNhtas8W89txaSYGBwwuMHtCmFrkhgLIVotO40dt3W6jXJzOXnleejU\nOtzt3G068nT4TBavfLWLbUdSAejg48zsCX0Y0ydIRrhEqxLsFkykTyQHMw+i0+hQUfn+VVAwWUx0\ncO7AkIAh1Y6bNCKColIjr327hwcX/ATA8O5tGnTug1kHySnLqXFBHAetA7vTdtO/XX/rDa1CNBdJ\njIUQrZ6dxg5fR9uO3J7LLuKN7/ayMu4kigJuBjuevCmS+4Z1wU4nNZGi9VGpVDzR8wn+78D/cbbw\nLGWmMgAMWgNtDG0Y2mEo7Zza1Xjs4+N7UlJu5P9WH2DSGz/yr/v7c18Dljo/kHmgxqT4gnJzOcdy\nj9HdyzZ1zEI0liTGQgjxN4UlFbz/0598vPYQZUYzOo2aSSMiePKmSNwMds0dnhCXxNfgy6xrZrH5\n7GbOFJzBrJhxs3NjoN9AOrp3rPPY526/Bh9PN/756W88/9k28orKeWJ8z3pdOTFZTHVu16g0FFcU\nN+i1CNEUJDEWQrRKJ8/l8tWW45SUG7FYFMyKgtmiVD62KJgtFutjSx3b/vf51Jxi8orKARgbHczs\nCdfQwUdurBNXDme9M+NDx9e6XVEU8ivyURQFVzvXKjexzri9L25O9jy+cD1vfLeXvKJyXrwr+qLJ\nsbudO7nluWhUNV9tMVvMtHdu37gXJIQNSWIshGh1ftp1iqf+s5WS8rpHoRqrd0dfXrgrmt4d5cY6\ncXXZnbabHed3kFeeB0plEt3TuyeDAwZbk9/JN/REo1TwxAe/sWjdIfJLynnjwYFoNbXPAnOd/3XE\n/xmPQV99tUpFUfBw8Ki1jEOIy0kSYyFEq2G2WHj92728/+OfQOVUadd2aYdGrUKjVqFWqf96/N+v\nlf/UqNUq1Krq29Rq9d/2U2Gv1xLS1lVurBNXnc1nN7MtdRuOOkfr4jgKCtvPbye3PJdbOt5i3Xdc\n3xCcHfRMfncDy7eeoKC4gvenDam1/t7L0Ysh7YewKXkTjlpH6yi00WwEFUzoPKFeP3NlpjK2pmzl\nWO4xKswVOGodifKJIrpttM2nZxRXJ0mMhRCtQk5hGY/9ezOxh8+hUat44c5oJo/sKgmsEDZQaipl\nx/kdtc4acTjrMAPaDcDT09P6/OAeAXwz6wbuffMX1u09w2vL9zDn7r61nmOA3wCCXILYkrKF3LJc\nNGoNXTy7MMhvUJ035v09xv8c/A+lplL0Gj1qlZoycxmbkjdxPPc493a5V5JjcckkMRZCtHiHz2Qx\n+d0NJGcW4eliz0ePD+XaLnLZVQhb2ZO2p84PmQ46B7albqNL+6ozUVzTuQ3LnhvFuJdW89mvR7hv\neJc6F7vxc/bj7vC7GxXjDwk/UG4urzalm4PWgZSiFLalbmOg38BGtS3EBfLRSgjRoq2MO8n4l9aQ\nnFlEz2Bv1s27SZJiIWwspywHvbr2OYQ1Kg0lppIat0WF+nDrgI4YzRZeW76nSeIrN5dzuuA0WnXN\n43kOWgf+zPyzSc4tri6SGAshWiSjycKLX2zniQ9/o8xoZuJ1nVn5whj8PJ0ufrAQokH8nPys8xrX\nxGgx4m7vXuv2mbf1xl6n4cddp9h3Mt3m8RVWFFbWI9ehyFhk8/OKq89FE2OTycTMmTMZMGAAvXv3\n5t577yUhIQGAhQsXEhERQWRkJJGRkQwdOrTJAxZCXPky80uY8OrPLP7lCDqNmtceGMCCyQOx10v1\nlxBNoadPT3QaXa3bK8wVdZYptPN0YvKobgDM/WoXiqLYND57jT1qdd0pS10j3kLU10UTY4vFQocO\nHVi5ciV79+5lyJAhPPbYY9bto0eP5o8//uCPP/5g06ZNTRqsEOLK90diBiP/8QM7j6Xh6+bIihfG\ncM/QcLnJTogmpFPrGBU4ihJjSZWkVlEUio3FDPIfhIu+7vm8p43tgaeLPXtOpLN+7xmbxuekd8LX\nwbfWhNtkMRHiGmLTc4qr00UTY71ez2OPPYavb+V8njfffDNJSUnk5OQA2PxToRDi6vXVlmPc/MqP\npOUWc00nX9bNu0nmEhbiMunu3Z37I+7H29Ebk8WE0WLE1c6V2zvdziD/QRc93tlRz9M3RQHwr292\nYzRZbBrfyMCRlJnLquUdFsWCWqVmWIdhNj2fuDo1+LrkH3/8ga+vL+7ulbVGW7ZsITo6mrZt2/Lk\nk08yePBgmwcphLiylRvNvPDFdpZtPgbApBFdePGuvui1Nc+JKoRoGgHOAdzX5b5GH3/XkHAW/3qE\nU+fzWbr5KJNGRNgstvYu7bk3/F7WnllLRkkGFsWCVq0lwDmAm0JuwqCrvniIEA2lOn78eL2HfAsL\nC7n11luZPn06o0aNIjExEU9PT5ydndm8eTMzZ85k1apVBAUFWY9JTk5mwIABTRL81Uanq6z/Mhrr\nvgFB1I/0p+1cSl+eyyrkznnfs+tYKnY6Df9+YiT3DO9m6xBbFXlv2pb0p+3Upy/XbD/B7a+swtPF\ngfjPpuBqsLd5HHlleRQbi3Gzc6txNb3WQt6btqXT6diyZQsBAQGNbqPeI8YVFRU89thjjB49mlGj\nRgEQEvJXPc/w4cPp06cPcXFxVRJjgLlz51ofx8TEMGjQxS/JCCGal6IoJOUnkV6cjpejF8FuwXXW\n+RaWlLN25wmcHfS093WlvY8LDna138wDEHc4mbv+9QPpucUE+Liw/IWbierYxtYvRQhxGY3t15H+\nXf3ZdjiFBct3Mu+B62x+Djd7N9zs3Wzermh9tm7dSmxsLAAajYaYmJhLaq9eibHZbObpp58mMDCQ\nJ554osEnmTp1apXvs7OzG9yGwLrikPSfbUh/1u5U/inWJK4hvyIfjUqD2WLGWe/MqKBRhHuEV9u/\nHD1j//EtR85kVnne29UBfy8n/L2cCfB2wu+/XwO8nIk7co6Xl+3EZFboH9GOD6cNwdNFJ/8fyHvT\n1qQ/bae+fTn79l6MOZzCwu/3cHv/IPy8ZJrFmsh789J17dqVrl27ApX9GRcXd0nt1SsxfvHFF1Gr\n1XeAAeAAACAASURBVLz00ktVnt+wYQPR0dE4OTkRGxvL7t27mTVr1iUFJIRoXqlFqXx17CvsNfY4\n6f76Y6agsOLkCu4Ku4tg12Dr86fT8rl7wS+cScung48z/t7OpGQWci67iMz8UjLzS/kjMbOmUwHw\nyOjuzL7jGrQamVZdiCtFZIgP4/uFsHpHIq9/t4f/e1TuPxKtw0UT43PnzrFy5UocHBzo1asXACqV\nikWLFvHzzz8ze/ZszGYzgYGBvPvuu9XKKIQQrcuGsxuw19jXWDbhoHFg49mNPNztYQCOJGVz1+vr\nyMwvpXentnz29DA8nCvrCc0WC+m5JaRkFZGSVURyZiEpmYWVj7MKsVgUnrv9Gsb3kymWhLgSzbq9\nN+v2nGbVtgQeGtmNbkFe/8/efcdXWd7/H3/dZyUnJyQhg4SdMMIKG8IQgmwRV3EP3LSKo7Vfv1pp\na61YvrVWpc7W1larv7qqggsVWWHJUJZA2GGFBEjIHmfdvz+isTSJQHKSk/F+Ph4+HuTc59z3O5cZ\nn1znc19XsCOJnNEZC+OOHTuSkZFR47Fhw4YFPJCIBI/f9JNVnIXDWvNC+YZhcKL0BOXecrbsPcXN\nT35OYamb8YO68vbDM3CXfb/zlNVioUNMOB1iwknt1VifgYg0FV3aRXDz5H68tGgbc99Yx1sPXaj1\nyKXJ03uXIlLFb/rxmz+89qjf9PPFpkNc9/tFFJa6uXB4EgsevZI2YSGNlFJEmot7LxtElCuE1duz\nWLrlcLDjiJyRCmMRqWKz2GjjaPODzzm4J5LZz6RT7vFx/fje/PneCYRoq2YRqUHb8FDuvWwQAI/9\nax1eX2A3/RAJNBXGInKawe0GU+Ytq/HY+q8sLPrUic9vcvfFA3n8tjFYLfoxIiK1u3lyP7rEtWH3\n0XzeWrE72HFEfpB+o4nIacZ0GEOPqB4Ue4qrtl71+02WrzRYtaJylYpfXzeCh65JVb+giJxRiN3K\nL64eDsAT/95ISbk2s5CmS4WxiJzGMAyuTr6aa3tdS1xYHKHWMNakR/H1hjZYDIOnfpzGHdMHBDum\niDQjl4zsxuDu7ThRUMafP94a7DgitVJhLCLVGIZBcttkrk2+gW9WJrP+a5MQu5W//mwSV4/TEhMi\ncm4Mw+Dh60cA8OLHW8k+VRLkRCI1U2EsIjUqLfdwy5Of88GX+wkPtfP6AxdwwbDEYMcSkWYqtVcC\n04YlUlbh5Y///qqqVUukKdGt5CJSzanicm584jO+3nucmIhQ/t8D07Q4/1kwTZNSbykGBk6bUz3Y\nIv/loWuGs3jTQd5YvosPvtxP13ZtSIyPoGu7CLrGV/6X2K4NHWPDdWOvBIUKY5EGVuIpYU3WGvIr\n8olxxjCq/SicNmewY9Xqy53HeODllew7VkDHmHDeeGga3dtHBTtWk2aaJhtyNrDu2DryK/LBgLaO\ntozsMJJh8doISeQ73dtH8cgNo3jinY0UlLrZcSiPHYfyqj3PbrXQvX0ko/t24Lx+HRjZpz1RLq2V\nLg1PhbFIA1p6aClrjq3BalhxWB3syd/D2qy1nN/5fM7rcF6w453meH4pc/+1jvdW7wWgV6e2vP7A\nBXSICQ9ysqbvs4OfsTFnI06bkzB7GAAV/go+zfyUgooCJnaZGOSEIk3HLVP6ccuUfpwqLudgThGZ\nOQVk5hRy8HgRB3MKOXi8kOxTpWQcOUXGkVP8/fPtGAb0T4zlvL4dGJPSgdTkBMJC7cH+VKQFUmEs\n0kC+zvmaNcfWnDY7HGKtnPFYcmgJ0SHR9InpE6x4Vbw+P68s3sEf/72RojIPoXYrd18yiDsvGkCo\nNu44o0J3Ietz1uOyuaodc9qcrD22lpHtR+KyVz8u0pq1DQ+lbXgog7rHVTtWVuFlW+ZJVm/PYvWO\nLL7ak8PWAyfZeuAkL368FbvVwuAecYzq0574DiWExZ6kTUg4I9uPJCpE73BJ3em3nkgDME2zWlH8\nn8JsYaQfTQ96Ybx+VzZzXlnNzm/fypw0uAuP3jiKru0igpqrOVl9dDUOi6PW41bDypqsNUzuOrkR\nU4k0b84QG6m9EkjtlcB9M4ZQVuFlw+7sqkJ5y/6TrN+Vw/pdOQAMHFjBuPElbMjeQN+Yvvyox4+w\nGOpRlnOnwlikAZT7yjlVcYowW1iNxw3D4GTZSXx+H1aLtZHTwYmCUn73xnreWbkHgM5x4Tx642im\nDOna6Fmau0J3IXZL7W/pOqyOyr5jEakzZ4iNtP6dSOvfCYBDecf57WevcPSgi23bHBw8aMNmqfxv\nZ95OwjLDmJY0LcippTlSYSwSRCaNu1yR1+fntSU7+cM7GyksdRNitzL7ooHcdclAnGqbqJO2oW05\nUHAAu7Xm4rjCV0Gcs/pbxSJSdxtyV5Lcw6RX93J27LCTn2+logJCQipbmLae3MqkrpN+8I9WkZro\nN6FIAwi1hhLliMLtd9f6nFhnLDZL430LbtyTw5x/rGb7wVwAxg/oxNybRpOUENloGVqi8zqcx/rs\n9dip+RewaZqMaD+ikVOJtGxZxVlVPz9jY/3k5FjJybHSpYsPgFJvKVnFWXSN0Ltgcm5UGIs0AMMw\nGNVhFJ8e+BSnvXqfcZm3jKldpzZ4Dp/fz9LNh3l9aQZfbDoEQMeYcB69cRRTh3bVOrsB4LK7GNdx\nHMuPLj+tdcY0Tcq8ZUzqMqlJL88n0tzFx/vIybFy/Pj3hTEm+E1/cINJs6TCWKSBDIsfRl5ZHl9m\nf4nD6sBusePxefCYHtI6ppESm9Jg184+VcIby3fxr2UZZOVWbr3qsFn4yfQB3HvJIC1zFGBjO40l\nxhnDyqMrOVl2Egxo52zHRd0uond072DHE2lx4l3xZBZmYjWsxMdXFsM5Od/frxFqC6VDeIdgxZNm\nTIWxSAOakjiFkR1GsjprNYUVhbQNbcvo9qMJdwR+bWC/3yT9myO8tmQni78+hM9f2b+cGB/B9eN7\nc1VaMrGRmrlsKH1j+tI3pm/VLJXuiBdpOOM7jefPW/9MmD3sPwrjyu+5Cm8F/WL6VS2PKXIuVBiL\nNLAIRwTTEhvu7ugTBaW8uXw3/1qWwaETRQDYrAYXDk9i5sTejOnXEYtFLRONRQWxSMOLC4vjsh6X\n8eH+D3FFmlitLvLzreQVl9CnXTcu6nZRsCNKM6XCWKQZ8vtNVu/I4vWlO/l0YyZeX+XscKfYcK6f\n0Jur03oR37bmpeJERFqC/rH96RHVg3XH1vFxu30cOeZnZPhlXNxnQLCjSTOmwlikGcktLOPt9N28\nvjSDzJxCACyGwdShXblhQh/GDeiI1aIZSxFpHZw2J+d3Pp/z+1h5/VgGWTnBTiTNnQpjkSbONE2+\nzMjm9SU7+WTDAdzeyh7W9tEurju/F9ec34sOMYHvWRYRaS4GJMUBGWw7cDLYUaSZU2Es0kSdKi7n\n3yv38PrSDPZmVe6cZhgwYVBnZk7sw4SBnbFZNTssItI/KQaArSqMpZ5UGIs0MYWlbh55fS0L1+yj\n3FN5t3V8VBjXnN+L687vRae4NkFOKCLStPTqFI3damF/dgHFZW7CnY5gR5JmSoWxSBPz4Msr+eDL\n/QCM69+RGyb2YfLgrthtmh0WEalJiN1K787RbMs8yTeZuQzoEcmO3B14/B56te1FtDM62BGlmVBh\nLNKELFizlw++3E9YiI0PHrmUPl30w1xE5GwMSIplW+ZJXt+wlPaFmZiYGBgsPrSYTuGduLb3tdqF\nUs5IU1AiTURWbjFz/rEagEduGKWiWETkHPRPigVge2YeobZQnDYnobZQXHYXJ8pO8PI3L2ubaDmj\nMxbGXq+XBx54gDFjxjBs2DBuvPFG9u7dC4DH42HOnDkMGTKE8ePHs2jRogYPLNIS+f0m//NSOgWl\nbiYN7sJ143sFO5KISLPSvVPlbHDWUQdFRadvamSz2Mgrz2NH7o5gRJNm5IyFsd/vp2vXrrz77rts\n3LiRCRMmcNdddwHwyiuvsHfvXtLT03n88ceZM2cO2dnZDR5apLGVeErIKs4ivyK/Qc7/6hc7SP/m\nKG3DQ3ji9rEYhnaqExE5F6WOA0RG+igutvDPf4aze/fp3aJhtjA2n9gcpHTSXJyxx9jhcFQVwgAz\nZszg97//PXl5eXz66afcfPPNhIeHk5qayuDBg1m8eDEzZ85s0NAijaWgooD3977P4aLDeE0vVsNK\nXFgc07pOIzEyMSDX2JuVz2NvrAPgD7ePpV2UdqwTETlXPsPNlVcXsmRxOAcO2PnoozD69XMzfnw5\nDgcYhoHP9AU7pjRx59xjvGnTJuLj42nbti2ZmZkkJSVx//3388knn9C9e3cOHDjQEDlFGl2Jp4SX\ntr3EibIThNnDiHBE4LK7KHGX8HrG6xwqPFTva3i8fn764nLK3T6uGNuTC4cn1flcpmnWO4+ISHPV\ns21PLCFlXHZZGRMmlGG1mmzf7uC118I5dsxKha+CjuEdgx1TmrhzWpWiqKiIefPm8Ytf/ALDMCgr\nKyMsLIw9e/aQkpKCy+WqsZUiJiYmYIFbM7vdDmg8A+VM47lkxxJCQkOwWap/mzhNJ+kn0vlp0k/r\nleGx11exef8JOreL4PmfTSfSFXpOrzdNk/TD6aw/up6CigKshpXEqEQu6nkRcWFx9cp2LvS1GVga\nz8DSeAZOUx7L6OholmYvpdxbzqhRFnr08LJggY3jxy28+WYYo8fYeOR/ptMmtOnsFNqUx7M5+m48\n6+OsC2O3281dd93F9OnTmTZtGgBOp5OysjIWLlwIwGOPPYbL5ar22rlz51b9Oy0tjXHjxtU3t0iD\n25O3p8aiGCrfkjtWfIyiiiLahNRtw40Nu7L4v39VrkLx1/+pW1H82rbXyDiZgdPuJMQaAsChgkPM\nXzefO4feSaeITnXKJiLSEDw+D+uPrmfL8S14TS/twtoxKWkSsWGx9T63YRjcNug2Xtj4AuXecuLi\nQrnlFi9LlsLGDXZWrwzhslMLeO2hS+kQo42SWooVK1aQnp4OgNVqJS0trV7nO6vC2Ofz8fOf/5zE\nxETuvffeqscTExPZt28f/fr1A2Dfvn1MnDix2utnz5592se5ubn1ydxqffcXpcYvMM40nvnF+dgt\ntf/1WeouJetEFrHOc/+BXlbh5abfL8TnN5k1LYX+ncLP+f/rztydbDy0kXBHOGXestOOmabJyxte\n5u5Bd59ztrrQ12ZgaTwDS+MZOPUZyxJPCX/d9leKPcVV6wkfyT3Cmsw1XJh4IcMThtc7n4HB7b1v\nZ332enaf2o3DMPnxpe2ZPS6Zh/62ntXfHOHaR9/l37+6CIsl+Dc562uz/lJSUkhJSQEqx3PVqlX1\nOt9Z9Rg//PDDWCwWHnnkkdMenzZtGq+99hpFRUWsW7eOzZs3M3ny5HoFEmkqwu0//Hab3WqnjaNu\nsw6/e3Md+48VkNwxil9cVbdfBl8e+xKXvfo7NFA5c5JblktOSU6dzi0iEmhv7HoDt8992iYbNouN\ncHs4izIXkVsWmOIwxBrC2I5juS3lNm7vfzvTk6YzdXBPPp83g7hIJ+t2ZfPmil0BuZa0PGcsjI8e\nPcq7777LypUrGTp0KIMHD2bw4MF89dVX3HzzzfTs2ZNx48bxi1/8gnnz5hEfH98YuUUa3KC4QdVm\nYr/j9XtJikiqal84F+nbjvCPz3dgsxo8O3s8oY66bUBZ6i394WXdDDhZdrJO5xYRCQS/6ScjL4NP\n9n/C1hNba/2ZFWoNZfmR5Q2aJTbSyW9njgLgsX+t40RBaYNeT5qnM/5G7tixIxkZGbUenzdvHvPm\nzQtoKJGmYHSH0ewr2MehokOE2b5fQu27GY/Lelx2zufML6ngvr9U9kL9fMZQUhLr3lcXYg2h3Fde\n63HTNIkMiazz+f9TkbuIlUdXkleeR6g1lNEdRtMhvENAzi0iLVNGXgYfH/iYEk8JueW57Dm1hyPF\nR+ge2Z0EV8Jpz7VarI3yh/wlI7vxTvpulm09wiOvfcnzd09o8GtK86ItoUVqYTEszOwzkyldpxBm\nD8M0TRxWB0Pjh3LHgDtOezvwbP3yH6vJPlXCkB7tuOvigfXKNyR+CKWe2mc8okKiArI00eqs1czf\nNJ+tJ7eSU5rDgcID/PWbv/Lmrje1vaqI1OhI0RHe2f0OAC67i1BrKDaLDQODXad21VgEWw1rg+cy\nDIN5t5xHqMPKgrX7WLblcINfU5oXFcYiP8BiWBiRMII7B9zJ/cPu555B9zCl6xRCbee2ggTAwrX7\nWLB2H84QG8/ceT42a/2+/QbGDiTBlYDb5z7tcdM0KfWWckHiBfXeQW9//n4WH1yM0+qsuhHRYlgI\nt4ezL38fiw8urtf5RaRlWnxo8WmTB9Gh0VWr/NgMG5mFmac9v9xbTq/oXo2SrUu7CO6/fCgAD/1j\nFaXlnka5rjQPKoxFGsGxvBLm/KNyabaHrxtBUkL9WxysFis397uZlJgUfH4fJZ4SSr2lRIREcF2v\n6+gd3bvO5/b6vXyW+Rm/Wfsbvs75mtVZq9l2cttpPdehtlC2ntyKz6+dpETke6Zpcqz42Gl/mNss\nNtq72uP1ezEMgxJPCR5/ZUHqN/2EWENITUhttIy3X9Cfvl2iOXyimKfe+7rRritNX93u+hGRs2aa\nJvf/NZ38kgomDOzMzIl9AnZuu8XOxd0vZlrSNIo9xTgsDsLs9dtS2uv38vftf+dk6UlKvCXYrZUz\nxYXuQjbmbGRou6FV1yjxlJBXnkc72tX7cxGRlsFv+jGpvhNnt8humJgcKzmG1+elzFNGhVFBgiuB\na3pdU6ebmevKbrPwh9vHcvFvFvLSom1cNroHKYnaZEM0YyzS4F79YifLtx4hKjyEP85Kq3d7Q01s\nFhtRIVH1LooB1h5by/HS44TYQjD4PquBgdWwknHq+5txDcNokM9HRJovq8Va442/hmHQI6oHo9qP\nIiUuhamJU7ljwB38ZMBPAnaj8LkY3L0dt07ph89v8uDLK/H5dc+EqDAWaVD7juUz919fAvD7W8cQ\n37b+hWtD23pya1VvYLgjHNM8feanyF1U1dcc4YggJlSzLCJyuuHxw2td7tLj93BB1wsY3WE08a7g\nLvH6wJXDaB/tYvP+E7y6eEdQs0jToMJYpIF4fX5++uIKyt0+ZpzXg4tHdAt2pLNS5vn+l1lSRBJe\n03vacb/pp8JXQZm3jNSEVM0Yi0g1qQmppMSkUOwurlq9xjRNit3FdI/qzvmdzw9uwG+FOx387qbR\nAPz+7Y1k5RYHOZEEmwpjkQbywkdb2LTvOO2jXTz27Q/e5iDU+v2KG20cbegb0xfTNPH4PZimiWma\n+E0/qfGpjG7ffD4vEWk8hmFwafdLuTXlVjqFdyLSEUmCK4GZfWdyTfI1WIymU35MHZbItGGJlJR7\n+PU/1wQ7jgSZbr4TaQAZh/N46t3KO52fnJVGpKvxbiqpr76xfVmbtbZqSbo4ZxwxHWLILsmm0F1I\ndGg0vxj+i4D0M4tIy2UYBp3bdOba3tcGO8oZzb1pNCu/OcqnGw+yaMMBpg1PCnYkCZKm8yebSAvh\n8fq57y8r8Pj8XD++N+MGdAp2pHMytuNYokKi8Pi+X9vTYlho72pPYkQiPxvyMxXFItKitI928Yur\nhwPwq1fXUlTqPsMrpKVSYSwSYC98tIWtB07SMSacX183IthxzpndYmdW/1n0ju6Nz++j1FNKhbeC\nuLA4ZqXMor2rfbAjiogE3I2T+jC4ezuyT5Xw+Dsbgh1HgkStFCIBtPNQHk9/u1j8H2eNpU2YI8iJ\n6sZhdXBZj8vw+X2U+8qxW+w4rM3zcxERORtWi4U/3D6Gab96n1cW7+Cacb21tnErpBljkQD5zxaK\nGyb0Jq1/82qhqInVYsVld6koFpFWoW+XGK4f3wfThPfX7A12HAkCFcYiAfL8h5vZlnmSTrHNs4VC\nRETgkpGVS2t+ujGz2jru0vKplUIkAHYcymX++5sA+OOsNMKdmmEVEWkO8sryWHJ4Cdkl2QDEOtvR\nNtxBZk4he47mk9ypbZATSmPSjLFIPf1nC8XMiX0Ym9Ix2JFEROQsZORl8MLWFzhQcAC3343b7+Zw\n8UHadc4H4NOvMoMbUBqdCmORenruw818k5lLp9hwfnVtarDjiIjIWfD4PSzYtwCnzYnVYq163GpY\n6dWz8t+fbswMTjgJGhXGIvWw41Auf/q2heLJH6uFQkSkudiYvRGvz1vjsa5dvdhsJlv2nyT7VEkj\nJ5NgUmEsUkf/2UJx46Q+jOmnFgoRkebicPFhnHZnjcfs9sriGODzrw42ZiwJMhXGInX03AeVLRSd\n48L51bVahUJEpDkJs4Xh8/tqPZ7UvXL3u89UGLcqKoxF6mD7wVzmL6jcyOPJWeNwhdqDnEhERM7F\nqPajKPeV13q8Q5diLAas3p6lLaJbERXGIufouxYKr8/kpkl9Oa9fh2BHEhGRcxTjjKF3dG/KvdWL\n4wpfBQM79GB4cgIen5+lWw4HIaEEgwpjkXP07MJNbD+YS5e4NvxSq1CIiDRbV/S8gkHtBuHxeyis\nKKSwohCPz0P/mP5clXwVU4d1BdRO0Zpogw+Rc/BNZi5/Wvj9KhRqoRARab4shoXpSdOZ3GUyx0qO\nAdDe1R6HtXKFoalDE3n0/61j6eZDuL0+HDbrD51OWgDNGIucJbfXx31/WY7XZ3Lz5L6M7qsWChGR\nlsBhddA1oitdI7pWFcUAifER9O7UlqIyD2t3HAtiQmksKoxFztKzCzez41AeXeLaMOcatVCIiLQG\nU4clAmqnaC1UGIuchW8yc3lGLRQiIq3O1KHf9xmbphnkNNLQzlgYf/HFF1x99dX079+fhx56qOrx\nZ599ln79+jF48GAGDx7MxIkTGzSoSLAcPlHEXc8vxeszuWWKWihERFqTAUmxJLR1kX2qhK0HTgY7\njjSwMxbGERER3H777VxxxRWnPW4YBtOnT2fTpk1s2rSJJUuWNFhIkWBJ33aEC371Pnuz8unRIYo5\nV6uFQkSkNTEMo2rW+NONmcENIw3ujIVxamoqkydPJjIy8rTHTdPUWwrSYpmmyXMfbOb6xz8lv7iC\nCQM7s/CRSwhTC4WISKtzwbfLtml76JbvrHuM/7sINgyDZcuWMWLECC677DKWLVsW8HAiwVBc5ubH\nf1rC/721Ab9pct+PhvDq/VOJcoUEO5qIiATByD7taeO0k3HkFJk5hcGOIw3orNcxNgzjtI+nTZvG\nDTfcQJs2bVi6dCk///nPee+990hKSqr22piYmPonFez2ytlKjWdg1DSeuw/nctXcj8g4lEtEWAh/\n/9+LuGhUz2BFbDb0tRlYGs/A0ngGTmsey2kjevL28h3c8tRifH6TvMIyHr5xLHdeMrTO52zN49kQ\nvhvP+jjrwvi/Z4y7d+9e9e/JkyeTmprKqlWraiyM586dW/XvtLQ0xo0bV5esIg3qgzW7ue2PH1FU\n6qZPl1je+vWPSO6sH1YiIgJXjuvN28t3sPtIXtVjj7yaznUT+xHpCg1istZtxYoVpKenA2C1WklL\nS6vX+eo8Y3wuZs+efdrHubm5dT5Xa/bdX5Qav8D4bjyPnzjBH//9Fc8s3AzA9NQknvpxGuFOjfXZ\n0tdmYGk8A0vjGTiteSxH9YzmrTkXApDQ1sWDL6/ky4xsnn5rNfdcOqhO52zN4xkoKSkppKSkAJXj\nuWrVqnqd74w9xn6/n4qKCnw+Hz6fD7fbjdfrZfHixRQWFuL3+1m+fDnr169nzJgx9Qoj0tjyisq4\n6YnPeGbhZiyGwa+uTeUv904k3Ok484tFRKTVMAyDMf06MqZfR3p0iOKnlw0G4K+fbqOswhvkdBIo\nZ5wxXrBgAXPmzKn6+IMPPuDuu+9m7969PPTQQ/h8PhITE5k/f36NbRQiTdXW/Tlc9eh7ZGYX0DY8\nhBfumUhaSsdgxxIRkWZgbEpHBnaLZcv+k/xrWQa3XZAS7EgSAGcsjGfMmMGMGTMaI4tIo3l/9V7+\n9+WVlFV46Z8Yy99+NolOcW2CHUtERJoJwzC499LB3Pb0Yl78eCszJ/XBYbMGO5bUk7aElmbB5/ex\nP38/209uJ78iv87n8Xj9PPzaWu5+YRllFV5mTu7P+7+5WEWxiIicsylDutKrU1uO5ZXw7qo9wY4j\nAXDWN9+JBMvKIyv5cP+HHCyq3Kc+zB5GakIqN/a5kXBH+Fmf50RBKXc8s4QvM7KxWy08eeckZk0f\nTF5e3plfLCIi8l8sFoO7LxnEPS8s47kPtnDl2GRsVs05Nmf6vydN2tJDS5m/eT4ZpzLw+r34TB8F\nFQUsOrCIR798FLfPfVbn+WpPDhf88n2+zMgmPiqMd351ET++aEi9VlsRERG5ZGQ3urZrQ2ZOIR+t\n2x/sOFJPKoylyfL6vfxj+z/w+/3YLd8v2m0xLDisDr7J/YbFBxf/4DlM0+S1JTu5fO5HZJ8qJbVX\nPJ/+7kcMT44/5zwev4eCigIqfBXn/FoREWmZbFYLd11cuVzbsws34/ebZ3iFNGVqpZAm65uT33Ci\n/AQum6vG46HWUD4+8DHTu02v9RwvfLSFeW9uAODWKf349fUjzvnmiFJPKR/u/5D9Bfvx+D3YLDY6\nhXdietJ0YpzaAEREpKUxTZOvcr5iffZ6Cj2FWA0rXSO6MqXLFKJCo6o9/4qxPXnqva/JOHKKLzYd\nYsrQrkFILYGgGWNpsg4UHvjB44ZhUOQpqvX4ht05PP72RgCe+vE45t40+pyL4jJvGS9ufZGDhQdx\nWB247C5CrCHklObw0raXyC3TouwiIi2JaZq8u+ddFh1cRJmvDLvFjsWwkFmYyQtbXyCnJKfaa0Ls\nVu6Y3h+AZxZuqrZbsDQfKoylyWof1h5+4GeLaZo4rc4ajxWUVHD380vx+U3umD6Aq8cl1ynDZ5mf\n4fV7sVpOL6gthgWbxcbHBz6u03lFRCQ4/KafYyXHOFp8lHJvebXju07tYnvedsJsYac9bjWss2Wu\nVgAAIABJREFU+Hw+fvvlb3l1+6u8vettjhQdqSqCrx/fm+g2oWzad4JV27Ma5XORwFMrhTRZQ+KH\nEOWIosJfgcWo/jdcha+C8Z3HV3vcNE0eeHklR04WM7BbLA9eNazOGfbk78FmqfnbxGJYOFJ8hApf\nBSHWkDpfQ0REGp5pmqzOWs26Y+so9BQClS15yW2TuaT7JVX3sqw9trbGFr79Bfs5XHgYE5OEsASc\ndicZ32SQHJ3MVclXERZq5/YLUvjDOxt5ZuEmxmrDqGZJM8bSZDmsDq5MvhK/6cfr/367TdM0cfvc\ndInowmU9Lqv2ujeW7+KjdQdwhdp5/q4JdV5w3TRN3P4fXvXC6/fWOOMgIiJNy9LDS1l+ZDkYEOGI\nIMIRgcPqYM+pPby6/dWqmd8ST0m1FYtOlJ7gcNFh7NbK4rnEW4LFsOByuNiXv48lh5cAcPPkvrRx\n2lmz4xgb91RvuZCmT4WxNGkzes7gpr43keBKwGJYKleksDlIjU/ltyN/i9N2eivF7iOn+PU/1wDw\nf7ecR1JCZJ2vbRhGra0a37Fb7NUyiIhI01LuLWdd9roaf17brXaySrLYnb8boMZ3AA8VHfp+dSSj\ncqb5O6G2ULYc34LP7yPSFcLNU/oB8PwHWxrgM5GGplYKadIMw2BGzxlckHgBm09sptRbSrfIbiRF\nJFX7i77c7WX2c0spd/u4YmxPLh/Ts97X7xPdh80nNuOwOqod8/l9JEYk1nhMRESajm0nt+Hz+6CW\nNxDDbGGsz15Pr7a9GBQ3iM8OfnZaEV3mLatq6Qu1htLGcfpuqSWeEgrcBUSHRnP71BT+8vFWvth0\niKMni+kYe/YbUUnwacZYmoUwexijO4xmUpdJdIvsVuPGHHP/tY6dh/NIjI/gdzeNDsh1J3aZSIQj\notpGIl6/F4th4ZLulwTkOiIi0nCK3EVVbRA1MQwDj98DwJB2Q4hzxtW4gZTH76F7ZPdqv4MMw8Bq\nVFbdsZFOpg1Pwm+avLliVwA/C2kMKoylRfhsYyavLN6B3WrhxXsmEO4MzCyuw+pgVv9ZDIobhIFB\nubccv+knuW0yswfOxmWveY1lERFpOrq06UKFt/bNmbx+L9Eh0QBYLVZu6XcLvaJ74fV7KfGUEGIN\nwWax0S+mH3FhcdVeHxUSRYQjourj68f3BirvefH6/AH+bKQhqZVCmr2s3GJ+/td0AOZcm8qApOo/\ntOrDYXUwLWka05Km4Tf9Na6QISIiTVf3qO60cbTBb/prfMexwldBWse0qo8dVgczeszA4/dQWFHI\nyfKTvL3rbcLsYdVeW+Yp4/yk80877+i+7UmMjyAzp5BlWw4zeUjlhh/l3nLcfjcum6vaMqDSNKgw\nlmbN5/dzzwvLyC+uYMLAztw+NaVBr6eiWESk+TEMg6uSr+LVHa9is9iqluE0TZNSbykTOk8g2hld\n7XV2i50YZwwxzhiuSL6CD/d/SLm3nFBrKG6/G6thZVzncQyNH1rtejdM6M1jb6zn/y3LoG+yjc8y\nPyOrJAvTNAmxhpDcNpmZUTN1n0oTo8JYmrVnFmzmy4xs2kU5efon47BYqs8EiIiIdGrTibsG3sWy\nI8s4VHgIE5NoZzTjOo2ja8SZt3DuE92H5KhktudtJ6s4i7ahbRkUN6jWdeyvHJvM429vZMmmQySs\n/YrYto7TbujbmbeT5zY8xz3D7wnY5yj1p8JYmq31u7J56r2vMQz4053jiY3UsmkiIlK7qNAoftTj\nR3V+vdViZUDsAAbEDjjjc2MjnVwwLJEP1+1nT0Yb4kaffjOfw+rgZNlJVh9eTf82/eucSQJL7wtL\ns3SquJy7nl+K3zS566KBpGmHIRERaWIuGVP5u+mbbxz4a7gHz2lz8lX2V42cSn6ICmNpdkzT5IG/\nrSQrt4TB3dtx/xV13/JZRESkofTrHkZEhJfiYguZmTW/Sa/dU5sWFcbS7Ly+NINPNmTSxmnnhbvH\nY7fpy1hERJqeyNAI+qSUAbBtW83rKLscWvazKVFFIc1KxuE8HnltLQCP3zaWLu0izvAKERGR4IgK\niWLskHAsFpP9+23k5Z1edpV4SkjtkBqkdFITFcbSbJR9t+Wzx8c145K5dFT3YEcSERH5QdcPuIze\nfcsxTYPVq79fwaLCV0FiZCIjO44MYjr5byqMpdn47etfsuvIKbq3j2TujYHZ8llERKQhtXO145mb\nL8dmgz177Bw86sVqWBnZfiSzBs/S+vhNjP5vSLPwzpptvLZkJ1arybDxmfw94y+szVqLaZrBjiYi\nIvKD+rTvyE+mDQQg55sUfjbkZ0zoPEG73zVBKoylydt8ZD8PvrwGgLFjK+iYYKXCV8EXh77g7d1v\nqzgWEZEmb/bFA4kMc7Bqexbp244EO47UQoWxNGk+v5/Zzy+motxCUpKHwYO/XyA9zB7GrlO72JG3\nI4gJRUREzizKFcLsiytnjf/vrQ34/ZrUaYpUGEuT9uT7azl4yEJYmJ+pU8sx/mvH5zBbGOuOrQtO\nOBERkXNw29QU4qPC2HrgJB9vOBDsOFKDMxbGX3zxBVdffTX9+/fnoYceqnrc4/EwZ84chgwZwvjx\n41m0aFGDBpXWZ8v+Ezy3YCcAU6eWExZW/a9rwzAo8ZQ0djQREZFz5gyxcd+MIQA8/vYGPF5fkBPJ\nfztjYRwREcHtt9/OFVdccdrjr7zyCnv37iU9PZ3HH3+cOXPmkJ2d3WBBpXUpKfdw1/NL8flNUgYU\nk5TkrfW5IdaQWo+JiIg0JdeM60VifAQHsgt59fNtwY4j/+WMhXFqaiqTJ08mMjLytMc//fRTZs6c\nSXh4OKmpqQwePJjFixc3WFBpXR7+5xoOZBfSu3Nbpkyo/cu0zFvG4HaDGzGZiIhI3dltFh64chgA\n8/7fKkrLPUFOJP/prHuM//vO/8zMTJKSkrj//vv55JNP6N69OwcOqF9G6u+jdft5c8VuQu1WXrh7\nAtO7T6XUU1rteW6fmzhnnApjERFpVi4e0Y2UxBiycot58cOvgh1H/oPtbJ9o/NddT2VlZYSFhbFn\nzx5SUlJwuVy1tlLExMTUL6UAYLdX7rPeksfz8IlCHvz7KgB+P2sCowf2BHoSFx3HJ/s+Ibu48mss\n1BbKwNiBzOg1A7u15v3nz6Q1jGdj0VgGlsYzsDSegaOxDJz/mzWJi3/5Fk+89SW3XjCItm1Cgx2p\n2fvu67M+zrow/u8ZY6fTSVlZGQsXLgTgsccew+Vy1fjauXPnVv07LS2NcePG1SWrtHA+n59b/vAh\n+cUVXDiiOz+5eEjVseSYZJJjkil2F1PhqyDCEVHnglhERCTYJg1JZPygRJZtzuTJd77ksVvPD3ak\nZmnFihWkp6cDYLVaSUtLq9f56jxjnJiYyL59++jXrx8A+/btY+LEiTW+dvbs2ad9nJube645he//\nQm+p4/fMwk2s2naYdlFOfn/zKPLy8mp9bmFpYb2v19LHszFpLANL4xlYGs/A0VgG1m9vTmPZzzJ5\nbsEGrk3rRkLbmicYpXYpKSmkpKQAlV+fq1atqtf5zthj7Pf7qaiowOfz4fP5cLvdeL1epk2bxmuv\nvUZRURHr1q1j8+bNTJ48uV5hpPXatO84T75b2Wc1/yfnExPhDHIiERGRhpXauwOXjk6m3O1j/vub\ngh1HOIsZ4wULFjBnzpyqjz/44APuvvtu7rjjDvbv38+4ceOIjIxk3rx5xMfHN2hYaZmKy9zc/fwy\nvD6TWdNSGDegU7AjiYiINIrf3pzGh2v38K9lGfz4wv50S4g884ukwZyxMJ4xYwYzZsyo8di8efOY\nN29ewENJ6/KrV9eQmVNI3y7RPHR1arDjiIiINJreXWK5Kq0nb67YzR///RUv3D0h2JFaNW0JLUG1\ncO0+3lm5h1C7lefvmkCI3RrsSCIiIo3q5zOGEmK3snDtPrYdOBnsOK2aCmMJmiMnivjFt0uz/eaG\nkSR3ahvkRCIiIo2vY2w4N03qC8D//DWdEm36ETQqjCUovD4/97y4jMJSN1OHdmXmxD7BjiQiIhI0\nP/3RYBLjI9h+MJc7n12Cz+8PdqRWSYWxBMWzH2xm/a4c4qPC+OOstGrLAYqIiLQmUa4Qnrt3JC6n\nwZLNh7n5+TcprKj/0qRyblQYS6PbuCeHp9/7GoD5d4wjWrv9iIhIK2aaJh/u+5APs1/lgosKsFpN\nln5Zwm2v/JX0I+nBjteqqDCWRlVU6uae55fh85vcMX0Aaf21NJuIiLRuq7NWs+XkFlx2F107w5Qp\nZQCsSW/DK+lfsjNvZ5ATth4qjKVRzXllNYdOFJGSGMODVw0LdhwREZGgMk2TjTkbcdq+39iqTx8v\no0eXAwZLPovirY0rgxewlTnrLaGl9SrxlLDq6CqOlhzFwKB3294MSxiG3WI/p/O8v3ov763eS6ij\ncmk2h01Ls4mISOtWWFFIkbuIMHvYaY+PGOEmP9/Cjh0O3lrg4zeTTd2P0whUGMsP2n1qN+/sfgeL\nYcFhdQCw5NAS1hxbw239biMqNOqsznPoeCEP/aNyabbfzhxFjw5n9zoREZGWrLZi1zBg8uRydu2y\nU1hgpaTcQ7jT0cjpWh+1Ukityrxl/HvPvwm1hVYVxQBOuxO/6ef1jNcxTfOM5/H6/Nz9wjKKyjxM\nG5bI9eN7N2RsERGRZqONow2RITVvA221gstV+Xv2ZGF5Y8ZqtVQYS63WZK2p9ZjFsJBXnsehokNn\nPM/89zfx1Z7jJLQN4w+3j9VbQSIiIt8yDINR7UdR6imt8Xio0wvAifyaj0tgqTCWWh0pPkKINaTW\n4yHWEHad2vWD5/ho3X6efv9rDAP+dOf5WppNRETkvwxPGM7oDqMp95bj9rkBqPBW4Pa5SYyNA+B4\nQVkwI7Ya6jGWWlkNK6ZZe7O/3/TjsNTe7/TVnhx++uJyAOZcncqYfh0bIqaIiEizN7HLREa1H8WX\nx77kVMUp4sPiGZ4wnF9vW8/67QWcUGHcKFQYS636x/Znf8F+XHZXjce9ppch8UNqPHbweCG3PPU5\n5R4f10/ozZ0XDWjIqCIiIs1emD2MCV0mnPZYu8jK1SpOFKiVojGolUJqlRKTQlRIFD6/r9qxCm8F\nvdr2IsIRUe1YfkkFNz7xGbmF5Yzr35Hf3XSe+opFRETqIDaycn1jzRg3DhXGUiurxcptKZVLspV4\nSnD73JR7yynzlpEcnczlPS6v9hq318es+YvZm5VPn87R/OXeSdht+jITERGpi3ZR3xbG+SqMG4Na\nKeQHuewuftz/x+SU5LA7fzc2w0b/2P6EO8KrPdc0TR7420rW7DhGuygnr94/lTZhWnNRRESkruLU\nStGoVBjLWYl3xRPviv/B5/xpwSbeWbkHZ4iNV++fSsfY6sWziIiInL04tVI0Kr3HLQHx/uq9PPHv\nrzAMeOGuCQxIigt2JBERkWbvPwvjs9lUS+pHhbHU27qMY/z8pRUAPHLDKKYM7RrkRCIiIi2DK9SO\nK9ROhcdHYak72HFaPBXGUi/7juVz69OLcXv93DKlL7dN7RfsSCIiIi2K2ikajwpjqbO8onJufOIz\n8osrmDS4C7+dOUrLsomIiASYCuPGo8JY6qTc7eXWpz4nM6eQlMQYXrh7AlaLvpxEREQCTStTNB5V\nMnLO/H6T/3kpnQ27c2gf7eLV+6fiCrUHO5aIiEiLVDVjrLWMG5wKYzlnf3z3Kxas3Ycr1M6r908l\noW3NW0aLiIhI/cV9u8nHcbVSNDgVxnJO3lqxmz8t2ITVYvDneybSr2tMsCOJiIi0aO2+baU4qVaK\nBqfCWM7aqu1HeeDldADm3jSaCYM6BzmRiIhIy/ddK4VmjBueCmM5K3uOnmLW/C/w+kx+cmF/bprU\nN9iRREREWoXvWilOqjBucPXeEnrmzJls2bIFq9UKwJQpU3j88cfrHUyajhMFpcx84lMKS91MG5bI\nr64dEexIIiIirUZcxLczxrr5rsHVuzAGePjhh7niiisCcSppYsrcXm55cjGHTxQzqFscz84ej8Wi\ntYpFREQaS+y3rRQnC0vx+039Hm5AAWml0N7dLZPfb3LvC8vZtO84nWLD+cf/TME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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This output is terrible. The filter has no choise but to give more weight to the measurements than the process (prediction step), but when the measurements are noisy the filter output will just track the noise. This inherent limitation of the linear Kalman filter is what lead to the development of nonlinear versions of the filter.\n", + "\n", + "With that said, it is certainly possible to use the process noise to deal with small nonlinearities in your system. This is part of the 'black art' of Kalman filters. Our model of the sensors and of the system are never perfect. Sensors are non-Gaussian and our process model is never perfect. You can mask some of this by setting the measurement errors and process errors higher than their theoretically correct values, but the trade off is a non-optimal solution. Certainly it is better to be non-optimal than to have your Kalman filter diverge. However, as we can see in the graphs above, it is easy for the output of the filter to be very bad. It is also very common to run many simulations and tests and to end up with a filter that performs very well under those conditions. Then, when you use the filter on real data the conditions are slightly different and the filter ends up performing terribly. \n", + "\n", + "For now we will set this problem aside, as we are clearly misapplying the Kalman filter in this example. We will revisit this problem in subsequent chapters to see the effect of using various nonlinear techniques. In some domains you will be able to get away with using a linear Kalman filter for a nonlinear problem, but usually you will have to use one or more of the techniques you will learn in the rest of this book." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Tracking Noisy Data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we are applying a Kalman filter to a thermometer in an oven in a factory then our task is done once the Kalman filter is designed. The data from the thermometer may be noisy, but there is never doubt that the thermometer is reading the temperature of *some other* oven. Contrast this to our current situation, where we are using computer vision to detect ball blobs from a video camera. For any frame we may detect or may not detect the ball, and we may have one or more spurious blobs - blobs not associated with the ball at all. This can occur because of limitations of the computer vision code, or due to foreign objects in the scene, such as a bird flying through the frame. Also, in the general case we may have no idea where the ball starts from. A ball may be picked up, carried, and thrown from any position, for example. A ball may be launched within view of the camera, or the initial launch might be off screen and the ball merely travels through the scene. There is the possibility of bounces and deflections - the ball can hit the ground and bounce, it can bounce off a wall, a person, or any other object in the scene.\n", + "\n", + "Consider some of the problems that can occur. We could be waiting for a ball to appear, and a blob is detected. We initialize our Kalman filter with that blob, and look at the next frame to detect where the ball is going. Maybe there is no blob in the next frame. Can we conclude that the blob in the previous frame was noise? Or perhaps the blob was valid, but we did not detect the blob in this frame.\n", + "\n", + "**author's note: not sure if I want to cover this. If I do, not sure I want to cover this here.**" + ] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Designing_Kalman_Filters.ipynb b/Designing_Kalman_Filters.ipynb deleted file mode 100644 index ecc2534..0000000 --- a/Designing_Kalman_Filters.ipynb +++ /dev/null @@ -1,1831 +0,0 @@ -{ - "metadata": { - "name": "", - "signature": "sha256:d6b001b78dc6570e35ed9c44483a5418f73da8c384f456475479b75494374801" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "heading", - "level": 1, - "metadata": {}, - "source": [ - "Designing Kalman Filters" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "#format the book\n", - "%matplotlib inline\n", - "from __future__ import division, print_function\n", - "import matplotlib.pyplot as plt\n", - "import book_format\n", - "book_format.load_style()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Introduction" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this chapter we will work through the design of several Kalman filters to gain experience and confidence with the various equations and techniques.\n", - "\n", - "\n", - "For our first multidimensional problem we will track a robot in a 2D space, such as a field. We will start with a simple noisy sensor that outputs noisy $(x,y)$ coordinates which we will need to filter to generate a 2D track. Once we have mastered this concept, we will extend the problem significantly with more sensors and then adding control inputs. \n", - "blah blah" - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking a Robot" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This first attempt at tracking a robot will closely resemble the 1-D dog tracking problem of previous chapters. This will allow us to 'get our feet wet' with Kalman filtering. So, instead of a sensor that outputs position in a hallway, we now have a sensor that supplies a noisy measurement of position in a 2-D space, such as an open field. That is, at each time $T$ it will provide an $(x,y)$ coordinate pair specifying the measurement of the sensor's position in the field.\n", - "\n", - "Implementation of code to interact with real sensors is beyond the scope of this book, so as before we will program simple simulations in Python to represent the sensors. We will develop several of these sensors as we go, each with more complications, so as I program them I will just append a number to the function name. `pos_sensor1()` is the first sensor we write, and so on.\n", - "\n", - "So let's start with a very simple sensor, one that travels in a straight line. It takes as input the last position, velocity, and how much noise we want, and returns the new position. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy.random as random\n", - "import copy\n", - "class PosSensor1(object):\n", - " def __init__(self, pos = [0,0], vel = (0,0), noise_scale = 1.):\n", - " self.vel = vel\n", - " self.noise_scale = noise_scale\n", - " self.pos = copy.deepcopy(pos)\n", - " \n", - " def read(self):\n", - " self.pos[0] += self.vel[0]\n", - " self.pos[1] += self.vel[1]\n", - " \n", - " return [self.pos[0] + random.randn() * self.noise_scale,\n", - " self.pos[1] + random.randn() * self.noise_scale]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A quick test to verify that it works as we expect." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "pos = [4,3]\n", - "s = PosSensor1 (pos, (2,1), 1)\n", - "\n", - "for i in range (50):\n", - " pos = s.read() \n", - " plt.scatter(pos[0], pos[1])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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Jg/COHTu0adMmvfzyy2ptbZXD4dB1112npqam/sc0NTUpGAwO+Pw1a9b0f11ZWamqqqqk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\nTkSuQmCC\n", - "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "That looks correct. The slope is 1/2, as we would expect with a velocity of (2,1), and the data seems to start at near (6,4).\n", - "\n", - "##### Step 1: Choose the State Variables\n", - "\n", - "As always, the first step is to choose our state variables. We are tracking in two dimensions and have a sensor that gives us a reading in each of those two dimensions, so we know that we have the two *observed variables* $x$ and $y$. If we created our Kalman filter using only those two variables the performance would not be very good because we would be ignoring the information velocity can provide to us. We will want to incorporate velocity into our equations as well. I will represent this as\n", - "\n", - "$$\\mathbf{x} = \n", - "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n", - "\n", - "There is nothing special about this organization. I could have listed the (xy) coordinates first followed by the velocities, and/or I could done this as a row matrix instead of a column matrix. For example, I could have chosen:\n", - "\n", - "$$\\mathbf{x} = \n", - "\\begin{bmatrix}x&y&v_x&v_y\\end{bmatrix}$$\n", - "\n", - "All that matters is that the rest of my derivation uses this same scheme. However, it is typical to use column matrices for state variables, and I prefer it, so that is what we will use. \n", - "\n", - "It might be a good time to pause and address how you identify the unobserved variables. This particular example is somewhat obvious because we already worked through the 1D case in the previous chapters. Would it be so obvious if we were filtering market data, population data from a biology experiment, and so on? Probably not. There is no easy answer to this question. The first thing to ask yourself is what is the interpretation of the first and second derivatives of the data from the sensors. We do that because obtaining the first and second derivatives is mathematically trivial if you are reading from the sensors using a fixed time step. The first derivative is just the difference between two successive readings. In our tracking case the first derivative has an obvious physical interpretation: the difference between two successive positions is velocity. \n", - "\n", - "Beyond this you can start looking at how you might combine the data from two or more different sensors to produce more information. This opens up the field of *sensor fusion*, and we will be covering examples of this in later sections. For now, recognize that choosing the appropriate state variables is paramount to getting the best possible performance from your filter. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 2:** Design State Transition Function\n", - "\n", - "Our next step is to design the state transition function. Recall that the state transition function is implemented as a matrix $\\mathbf{F}$ that we multipy with the previous state of our system to get the next state, like so. \n", - "\n", - "$$\\mathbf{x}' = \\mathbf{Fx}$$\n", - "\n", - "I will not belabor this as it is very similar to the 1-D case we did in the previous chapter. Our state equations for position and velocity would be:\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) \\\\\n", - "v_x &= (0*x) + (1*v_x) + (0*y) + (0 * v_y) \\\\\n", - "y' &= (0*x) + (0* v_x) + (1*y) + (\\Delta t * v_y) \\\\\n", - "v_y &= (0*x) + (0*v_x) + (0*y) + (1 * v_y)\n", - "\\end{aligned}\n", - "$$\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Laying it out that way shows us both the values and row-column organization required for $\\small\\mathbf{F}$. In linear algebra, we would write this as:\n", - "\n", - "$$\n", - "\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}' = \\begin{bmatrix}1& \\Delta t& 0& 0\\\\0& 1& 0& 0\\\\0& 0& 1& \\Delta t\\\\ 0& 0& 0& 1\\end{bmatrix}\\begin{bmatrix}x\\\\v_x\\\\y\\\\v_y\\end{bmatrix}$$\n", - "\n", - "So, let's do this in Python. It is very simple; the only thing new here is setting `dim_z` to 2. We will see why it is set to 2 in step 4." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from filterpy.kalman import KalmanFilter\n", - "import numpy as np\n", - "\n", - "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", - "dt = 1. # time step\n", - "\n", - "f1.F = np.array ([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 3**: Design the Motion Function\n", - "We have no control inputs to our robot (yet!), so this step is trivial - set the motion input $\\small\\mathbf{u}$ to zero. This is done for us by the class when it is created so we can skip this step, but for completeness we will be explicit." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f1.u = 0." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### **Step 4**: Design the Measurement Function\n", - "The measurement function defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. At first this is a bit counterintuitive, after all, we use the Kalman filter to go from measurements to state. But the update step needs to compute the residual between the current measurement and the measurement represented by the prediction step. Therefore $\\textbf{H}$ is multiplied by the state $\\textbf{x}$ to produce a measurement $\\textbf{z}$. \n", - "\n", - "In this case we have measurements for (x,y), so $\\textbf{z}$ must be of dimension $2\\times 1$. Our state variable is size $4\\times 1$. We can deduce the required size for $\\textbf{H}$ by recalling that multiplying a matrix of size $m\\times n$ by $n\\times p$ yields a matrix of size $m\\times p$. Thus,\n", - "\n", - "$$ \n", - "\\begin{aligned}\n", - "(2\\times 1) &= (a\\times b)(4 \\times 1) \\\\\n", - "&= (a\\times 4)(4\\times 1) \\\\\n", - "&= (2\\times 4)(4\\times 1)\n", - "\\end{aligned}$$\n", - "\n", - "So, $\\textbf{H}$ is of size $2\\times 4$.\n", - "\n", - "Filling in the values for $\\textbf{H}$ is easy in this case because the measurement is the position of the robot, which is the $x$ and $y$ variables of the state $\\textbf{x}$. Let's make this just slightly more interesting by deciding we want to change units. So we will assume that the measurements are returned in feet, and that we desire to work in meters. Converting from feet to meters is a simple as multiplying by 0.3048. However, we are converting from state (meters) to measurements (feet) so we need to divide by 0.3048. So\n", - "\n", - "$$\\mathbf{H} =\n", - "\\begin{bmatrix} \n", - "\\frac{1}{0.3048} & 0 & 0 & 0 \\\\\n", - "0 & 0 & \\frac{1}{0.3048} & 0\n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "which corresponds to these linear equations\n", - "$$\n", - "\\begin{aligned}\n", - "z_x' &= (\\frac{x}{0.3048}) + (0* v_x) + (0*y) + (0 * v_y) \\\\\n", - "z_y' &= (0*x) + (0* v_x) + (\\frac{y}{0.3048}) + (0 * v_y) \\\\\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "To be clear about my intentions here, this is a pretty simple problem, and we could have easily found the equations directly without going through the dimensional analysis that I did above. In fact, an earlier draft did just that. But it is useful to remember that the equations of the Kalman filter imply a specific dimensionality for all of the matrices, and when I start to get lost as to how to design something it is often extremely useful to look at the matrix dimensions. Not sure how to design $\\textbf{H}$? \n", - "Here is the Python that implements this:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", - " [0, 0, 1/0.3048, 0]])\n", - "print(f1.H)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 3.2808399 0. 0. 0. ]\n", - " [ 0. 0. 3.2808399 0. ]]\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 5**: Design the Measurement Noise Matrix\n", - "\n", - "In this step we need to mathematically model the noise in our sensor. For now we will make the simple assumption that the $x$ and $y$ variables are independent Gaussian processes. That is, the noise in x is not in any way dependent on the noise in y, and the noise is normally distributed about the mean. For now let's set the variance for $x$ and $y$ to be 5 for each. They are independent, so there is no covariance, and our off diagonals will be 0. This gives us:\n", - "\n", - "$$\\mathbf{R} = \\begin{bmatrix}5&0\\\\0&5\\end{bmatrix}$$\n", - "\n", - "It is a $2{\\times}2$ matrix because we have 2 sensor inputs, and covariance matrices are always of size $n{\\times}n$ for $n$ variables. In Python we write:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f1.R = np.array([[5,0],\n", - " [0, 5]])\n", - "print (f1.R)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 5. 0.]\n", - " [ 0. 5.]]\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Step 6: Design the Process Noise Matrix\n", - "Finally, we design the process noise. We don't yet have a good way to model process noise, so for now we will assume there is a small amount of process noise, say 0.1 for each state variable. Later we will tackle this admittedly difficult topic in more detail. We have 4 state variables, so we need a $4{\\times}4$ covariance matrix:\n", - "\n", - "$$\\mathbf{Q} = \\begin{bmatrix}0.1&0&0&0\\\\0&0.1&0&0\\\\0&0&0.1&0\\\\0&0&0&0.1\\end{bmatrix}$$\n", - "\n", - "In Python I will use the numpy eye helper function to create an identity matrix for us, and multipy it by 0.1 to get the desired result." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f1.Q = np.eye(4) * 0.1\n", - "print(f1.Q)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 0.1 0. 0. 0. ]\n", - " [ 0. 0.1 0. 0. ]\n", - " [ 0. 0. 0.1 0. ]\n", - " [ 0. 0. 0. 0.1]]\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### **Step 7**: Design Initial Conditions\n", - "\n", - "For our simple problem we will set the initial position at (0,0) with a velocity of (0,0). Since that is a pure guess, we will set the covariance matrix $\\small\\mathbf{P}$ to a large value.\n", - "$$ \\mathbf{x} = \\begin{bmatrix}0\\\\0\\\\0\\\\0\\end{bmatrix}\\\\\n", - "\\mathbf{P} = \\begin{bmatrix}500&0&0&0\\\\0&500&0&0\\\\0&0&500&0\\\\0&0&0&500\\end{bmatrix}$$\n", - "\n", - "In Python we implement that with" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f1.x = np.array([[0,0,0,0]]).T\n", - "f1.P = np.eye(4) * 500.\n", - "print(f1.x)\n", - "print()\n", - "print (f1.P)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 0.]\n", - " [ 0.]\n", - " [ 0.]\n", - " [ 0.]]\n", - "\n", - "[[ 500. 0. 0. 0.]\n", - " [ 0. 500. 0. 0.]\n", - " [ 0. 0. 500. 0.]\n", - " [ 0. 0. 0. 500.]]\n" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Implement the Filter Code" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Design is complete, now we just have to write the Python code to run our filter, and output the data in the format of our choice. To keep the code clear, let's just print a plot of the track. We will run the code for 30 iterations." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", - "dt = 1.0 # time step\n", - "\n", - "f1.F = np.array ([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]])\n", - "f1.u = 0.\n", - "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", - " [0, 0, 1/0.3048, 0]])\n", - "\n", - "f1.R = np.eye(2) * 5\n", - "f1.Q = np.eye(4) * .1\n", - "\n", - "f1.x = np.array([[0,0,0,0]]).T\n", - "f1.P = np.eye(4) * 500.\n", - "\n", - "# initialize storage and other variables for the run\n", - "count = 30\n", - "xs, ys = [],[]\n", - "pxs, pys = [],[]\n", - "\n", - "s = PosSensor1 ([0,0], (2,1), 1.)\n", - "\n", - "for i in range(count):\n", - " pos = s.read()\n", - " z = np.array([[pos[0]],[pos[1]]])\n", - "\n", - " f1.predict ()\n", - " f1.update (z)\n", - "\n", - " xs.append (f1.x[0,0])\n", - " ys.append (f1.x[2,0])\n", - " pxs.append (pos[0]*.3048)\n", - " pys.append(pos[1]*.3048)\n", - "\n", - "p1, = plt.plot (xs, ys, 'r--')\n", - "p2, = plt.plot (pxs, pys)\n", - "plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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2o0lUkJsrEg17EBERETkbiot5/J3FpGYV0C0uilsHtXV3RYJ6fkVERESqnCknh9W3P8AX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\n4ccUOyH+NmY+eBGtYsLcUKCIiIicSD2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- "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I encourage you to play with this, setting $\\mathbf{Q}$ and $\\mathbf{R}$ to various values. However, we did a fair amount of that sort of thing in the last chapters, and we have a lot of material to cover, so I will move on to more complicated cases where we will also have a chance to experience changing these values.\n", - "\n", - "Now I will run the same Kalman filter with the same settings, but also plot the covariance ellipse for $x$ and $y$. First, the code without explanation, so we can see the output. I print the last covariance to see what it looks like. But before you scroll down to look at the results, what do you think it will look like? You have enough information to figure this out but this is still new to you, so don't be discouraged if you get it wrong." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import stats\n", - "\n", - "f1 = KalmanFilter(dim_x=4, dim_z=2)\n", - "dt = 1.0 # time step\n", - "\n", - "f1.F = np.array ([[1, dt, 0, 0],\n", - " [0, 1, 0, 0],\n", - " [0, 0, 1, dt],\n", - " [0, 0, 0, 1]])\n", - "f1.u = 0.\n", - "f1.H = np.array ([[1/0.3048, 0, 0, 0],\n", - " [0, 0, 1/0.3048, 0]])\n", - "\n", - "f1.R = np.eye(2) * 5\n", - "f1.Q = np.eye(4) * .1\n", - "\n", - "f1.x = np.array([[0,0,0,0]]).T\n", - "f1.P = np.eye(4) * 500.\n", - "\n", - "# initialize storage and other variables for the run\n", - "count = 30\n", - "xs, ys = [],[]\n", - "pxs, pys = [],[]\n", - "\n", - "s = PosSensor1 ([0,0], (2,1), 1.)\n", - "\n", - "for i in range(count):\n", - " pos = s.read()\n", - " z = np.array([[pos[0]],[pos[1]]])\n", - "\n", - " f1.predict ()\n", - " f1.update (z)\n", - "\n", - " xs.append (f1.x[0,0])\n", - " ys.append (f1.x[2,0])\n", - " pxs.append (pos[0]*.3048)\n", - " pys.append(pos[1]*.3048)\n", - "\n", - " # plot covariance of x and y\n", - " cov = np.array([[f1.P[0,0], f1.P[2,0]], \n", - " [f1.P[0,2], f1.P[2,2]]])\n", - " \n", - " #e = stats.sigma_ellipse (cov=cov, x=f1.x[0,0], y=f1.x[2,0])\n", - " #stats.plot_sigma_ellipse(ellipse=e)\n", - " stats.plot_covariance_ellipse((f1.x[0,0], f1.x[2,0]), cov=cov)\n", - "\n", - " \n", - "p1, = plt.plot (xs, ys, 'r--')\n", - "p2, = plt.plot (pxs, pys)\n", - "plt.legend([p1,p2], ['filter', 'measurement'], 2)\n", - "plt.show()\n", - "print(\"final P is:\")\n", - "print(f1.P)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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AnPVH0Gs1fNS9KiU7PU7pc+dwHi3OlZd6ER5+LUAH+ngyp2slvlvyCcPLtWDR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\ncDiYOXMmi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- "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "final P is:\n", - "[[ 0.30660483 0.12566239 0. 0. ]\n", - " [ 0.12566239 0.24399092 0. 0. ]\n", - " [ 0. 0. 0.30660483 0.12566239]\n", - " [ 0. 0. 0.12566239 0.24399092]]\n" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Did you correctly predict what the covariance matrix and plots would look like? Perhaps you were expecting a tilted ellipse, as in the last chapters. If so, recall that in those chapters we were not plotting $x$ against $y$, but $x$ against $\\dot{x}$. $x$ *is correlated* to $\\dot{x}$, but $x$ is not correlated or dependent on $y$. Therefore our ellipses are not tilted. Furthermore, the noise for both $x$ and $y$ are modeled to have the same value, 5, in $\\mathbf{R}$. If we were to set R to, for example,\n", - "\n", - "$$\\mathbf{R} = \\begin{bmatrix}10&0\\\\0&5\\end{bmatrix}$$\n", - "\n", - "we would be telling the Kalman filter that there is more noise in $x$ than $y$, and our ellipses would be longer than they are tall.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The final P tells us everything we need to know about the correlation between the state variables. If we look at the diagonal alone we see the variance for each variable. In other words $\\mathbf{P}_{0,0}$ is the variance for x, $\\mathbf{P}_{1,1}$ is the variance for $\\dot{x}$, $\\mathbf{P}_{2,2}$ is the variance for y, and $\\mathbf{P}_{3,3}$ is the variance for $\\dot{y}$. We can extract the diagonal of a matrix using *numpy.diag()*." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print(np.diag(f1.P))" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ 0.30660483 0.24399092 0.30660483 0.24399092]\n" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The covariance matrix contains four $2{\\times}2$ matrices that you should be able to easily pick out. This is due to the correlation of $x$ to $\\dot{x}$, and of $y$ to $\\dot{y}$. The upper left hand side shows the covariance of $x$ to $\\dot{x}$. Let's extract and print, and plot it." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "c = f1.P[0:2,0:2]\n", - "print(c)\n", - "stats.plot_covariance_ellipse((0,0), cov=c)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 0.30660483 0.12566239]\n", - " [ 0.12566239 0.24399092]]\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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CNXYsb66BEyEYAwHizTej1L59ja6+2ml0KQAC1MsvR2vcuErFxPiMLgXwS0y+\nAwJAXp5ZL78crZUr840uBUCA+v57ae1au/72t0NGlwL4LXqMgQDw9NMxGjGiSh07ssMdgIZ57jmr\nRo+uUEICvcXAydBjDPi5rVtt2rAhQhs3Hja6FAAB6qefpIwMs3JyGFsMnEqDe4zXrFmjtLQ0paWl\nKScnp9GOBfBfPp/0yCNxmjq1VLGx9PIAaJjnn7do9GiPHA6WeQROpUE9xi6XS+np6crMzJTT6dSY\nMWPUt2/fMz4WwLHefdcut1v6zW9YbxRAwxQWmrRggUX/+pfL6FIAv9egHuNt27YpJSVFiYmJatWq\nlZKTk7Vjx44zPhbAf3k8Unp6jKZPL5WZ2QA4iY0bTUaXAD/3xhvRGjrUq7PPNroSwP81qMc4Pz9f\nDodDGRkZiouLk8Ph0OHDh9WpU6czOjYpKakh5fg9m80mKXh/PzSen7eVpUvNSk42a8iQGJnIPjgB\nm82mTz4xqU8fzi04sZISaeHCMP3jHz7ZbDZeh1AnoZxbzmjy3ciRIyVJWVlZMp3mlbsux86cObP2\n6969e6tPnz5nUh4QsLxeafZsi2bNqiEU44Q2bjTpk09Mevxxkzwei3r39qpPH8ah41ivvWZRWppX\n557LiQShbePGjdq0aVPt9ZMN621QMHY4HMrLy6u9npeXJ4fDccbHTpgw4ZjrBQUFDSnP7xx9xxUs\nvw+aztG28s47FbJYotWzZ75oNjiR1FSpT58keTwWTZhwZMUS2gp+rrLSpBdfbKllywrkdsdJ4nUI\ndROMuSU1NVWpqam113Nzc094XIOCcdeuXbV7924VFhbK6XTq0KFDtUMj0tPTZTKZNGnSpNMeC+B4\nPp/0wgvR+sMfyuktBtBgb78dqUsvdSklpcboUoCA0aBgHBYWpsmTJ2vUqFGSpGnTptXel5+fX+dj\nARxv/XqTqqtNSkurNroUBIDevVl+C8crKDiyW+by5cHT4wc0B9POnTv9YlDa/v371blzZ6PLaBLB\n+JEEmkZiYpL69bPplltKdOONLNGGU+PcgpOZMiVOERE+Pf54qSTaCuonFNpLbm6u2rZte9zt7HwH\n+JGPPzYpL08aMoRQDKBhtm+3at06dssEGoLVUQE/8vTTVj3wgEcWi9GVAAhEPp80Y0acHnigTHFx\nfvGBMBBQCMaAn/j8c5t27zZp9GjGjAJomPfei1BlpUmjRlUaXQoQkBhKAfiJF16I0QMP1CgszOhK\nAASiykr0COV3AAAe1UlEQVSTnngiVi+9VMynTkADEYwBP7B9u1XbttmUmcmySgAa5uWXo/WrX7l0\n6aUuo0sBAhbBGPADL74YozvvLFdERITRpQAIQPv3W7RgQZTWrWPCHXAmGGMMGOy77yz6+9/DdOut\njAkE0DCPPx6r8ePL1aYNcxSAM0EwBgy2aFGkRoyoUmQkM8gB1N8nn4Tpyy9tuuuucqNLAQIeQykA\nA7lc0tKlkVqxIv/0BwPAL9TUSI88EqcZM0pltxtdDRD46DEGDPTBBxE6//wanXeex+hSAASgv/wl\nUomJXg0axBbyQGOgxxgw0F/+EqVbbqkwugwAAaiw0KS5c2O0ZEmBTCajqwGCAz3GgEH27rVo506r\nrr2Wnh4A9TdzZpxuuKFKnTuzzCPQWOgxBgyyaFGURoyoYkMPAPW2bl24/vnPMGVl5RldChBUCMaA\nAdxuadkyu1auZNIdgPopLDTroYfi9eqrRYqKYjUboDExlAIwwEcfhat9e4/OPZdJdwDqzueTHnoo\nTjfeWMUOd0AToMcYMMCyZZG66SY29ABQP++9F6Fdu6x64YUio0sBghI9xkAzKy42adOmcA0ZUmV0\nKQACyKFDZj3ySJyef75Y7B4PNA2CMdDM3n/frt69nYqPZ2wggLrx+aQHHojXrbdW6qKL3EaXAwQt\ngjHQzBhGAaC+MjIidfiwWX/4Q5nRpQBBjTHGQDP69luLvvvOoquuchpdCoAAsX+/RU89FaOlSwtY\n3hFoYvQYA83ogw8idO211bLZjK4EQCDweqVJk+J1110VbOQBNAOCMdCMcnIi1K8fO90BqJsFC6Lk\ndJp0113lRpcChASGUgDNpKLCpC1bbLriCtYeBXB633xj0dy50XrvvXxZLEZXA4QGeoyBZvLJJ2Hq\n3t3NTlUATqumRpo4MUGTJ5exERDQjAjGQDPJyYlQ374MowBwei++GC273aexY1nBBmhOBGOgGfh8\nUk5OuPr2ZTUKAKeWkxOuv/wlSi++WCQzr9JAs2KMMdAMvvnGIrfbpAsuYFY5gJP7/nuLJk6M17x5\nRTrrLK/R5QAhh/eiQDP46KMjq1GYTEZXAsBfVVVJv/tdgu65p1yXXsokXcAIBGOgGXz0UTibegA4\nKZ9PmjYtXuedV6Px4yuMLgcIWQRjoIlVVUn/+leYevUiGAM4sUWLIrV1q03PPFPCJ0uAgRhjDDSx\nf/wjXF26uBUXxzJtAI73xRc2zZkTo5Ur81nOETAYPcZAE8vJYRgFgBMrKDDrzjsT9MwzJTrvPNYr\nBoxGMAaa2EcfsUwbgOPV1EgTJiRo6NAqpaWxxjngDwjGQBM6dMisggKLunRxG10KAD/zzDMxMpmk\nKVPKjC4FwH8wxhhoQrm5Nl14oZtF+gEcY+3aCK1cadfatfmyWIyuBsBRBGOgCe3YYVXnzvQWA/iv\nb76xaOrUOL39dqGSktjEA/An9GMBTSg316ZOndjtDsARFRUmjR+fqKlTy9S9O2+aAX9DMAaa0I4d\nVnXqxIsfAMnjkSZOjFfPni6NHl1pdDkAToChFEATqamR9uyx6oIL6DEGQp3PJ/3xj7EqLjbrpZeK\n2MQD8FMEY6CJfPedVcnJXhbsB6BXX43WP/4RrhUr8hUebnQ1AE6GYAw0kdxchlEAkFassGvBgkit\nWpWv2FjeKAP+jGAMNBEm3gHYtClMjz0Wq6VLC9SqFStQAP6OyXdAE2HiHRDatm+36p57EjRvXhFz\nDYAAQTAGmsiOHTZ17syLIRCKfvjBorFjk/TUUyW69FKX0eUAqCOCMdAEKipMOnTIrPbtCcZAqCkq\nMum3v03UhAnlGjy42uhyANQDwRhoAjt3WpWSUiMro/iBkFJVJd12W6IGDHDqf/+3wuhyANRTg4Lx\nmjVrlJaWprS0NOXk5Jzy2EOHDmnUqFEaPHiwhg0bpk8//bRBhQKBZP9+i845x2N0GQCakccj3Xtv\ngtq08WjatFKjywHQAPXuz3K5XEpPT1dmZqacTqfGjBmjvn37nvwBrFY9+uijuuCCC3TgwAGNHDlS\nmzZtOqOiAX9XUmJWXBwz0IFQ4fNJM2bEqbTUrIULC2Tm81ggINU7GG/btk0pKSlKTEyUJCUnJ2vH\njh3q1KnTCY9PSkpSUlKSJKl169Zyu91yu92y2WxnUDbg30pLCcZAKHn55Wh99lkYG3gAAa7ewTgv\nL08Oh0MZGRmKi4uTw+HQ4cOHTxqMf+7jjz9Wly5dCMUIeqWlJsXFsZA/EAqWLbNr4UI28ACCwSmD\n8YIFC7R8+fJjbvP5fOrRo4dGjhwpScrKypKpDpu+5+Xlac6cOXrllVdOeszRnuVgc/SNQLD+fjhe\ndbVVnTp5lZRUv64j2grqg/ZivMxMs2bNsmrtWrc6d04wupyToq2gPkK5vZwyGI8bN07jxo075rbN\nmzdr/vz5tdeP9iCfitPp1H333aepU6eqbdu2Jz1u5syZtV/37t1bffr0OeXPBfxVSYkUF2d0FQCa\n0tKlZk2ZYtXq1W517kxPMeDPNm7ceMwct5PNj6v3UIquXbtq9+7dKiwslNPp1KFDh44ZRpGeni6T\nyaRJkyZJOtLD/PDDD2vw4MHq1avXKX/2hAkTjrleUFBQ3/L80tF3XMHy++D08vISZTZXqKDAWa/v\no62gPmgvxlm50q6ZM2O1eHGeWrWqkb8/BbQV1EcwtpfU1FSlpqbWXs/NzT3hcfUOxmFhYZo8ebJG\njRolSZo2bdox9+fn5x9zffPmzVq3bp327t2rpUuXSpLmz59/2l5mIJCxKgUQvFassOuJJ2K1eHGB\nOnViEx8gmDRo+4FBgwZp0KBBJ7xv1qxZx1y/+OKLtX379oY8DBCwSkrMio0lGAPBZvlyu558Mlbv\nvFOgCy4gFAPBhn25gCbAqhRA8Fm2zK5Zs2KVkVGg888nFAPBiGAMNDKfjx5jINhkZtr19NNHQnFK\nCqEYCFYEY6CRVVWZZLX6WOQfCBJLl9o1ezahGAgFBGOgkVVWmmS3M4wCCAZLltg1Z06sliwpUMeO\nhGIg2BGMgUYWGelTVdXpN70B4N8yMux65plYLVmSr44dPUaXA6AZmI0uAAg2drtPLpdJHl5HgYBF\nKAZCE8EYaGQm05Fe48pKeo2BQPTOO5F69tlYLV1KKAZCDUMpgCYQFeVTeblJMTGMNQYChc8nvfJK\ntBYsiNTSpfk691xCMRBqCMZAE4iM9Kmigh5jIFB4PNKMGXH67LMwvfdevlq1YrlFIBQRjIEmEB3t\nVWWlWRI9ToC/q6oy6e6741VRYdaKFfmKjeWTHiBUMcYYaAJHh1IA8G8FBWaNGJGk6GifFi4sIBQD\nIY5gDDSBqCiGUgD+7rvvLLr++ha68kqnnn++WGFhRlcEwGgMpQCaQHy8V4WFvO8E/NUXX9h0++2J\nmjSpTLfeWml0OQD8BMEYaAJt23q0fz9/XoA/WrcuXJMnx2vu3GINGOA0uhwAfoRXbqAJtGtXo08/\nDTe6DAC/8PbbkfrTn2K0cGGhund3G10OAD9DMAaawNlne/TDDxajywDwHz6f9PTTMfrrX+1asSJf\n7duzYgyA4xGMgSbQtq1H339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- "text": [ - "" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The covariance contains the data for $x$ and $\\dot{x}$ in the upper left because of how it is organized. Recall that entries $\\mathbf{P}_{i,j}$ and $\\mathbf{P}_{j,i}$ contain $p\\sigma_1\\sigma_2$.\n", - "\n", - "Finally, let's look at the lower left side of $\\mathbf{P}$, which is all 0s. Why 0s? Consider $\\mathbf{P}_{3,0}$. That stores the term $p\\sigma_3\\sigma_0$, which is the covariance between $\\dot{y}$ and $x$. These are independent, so the term will be 0. The rest of the terms are for similarly independent variables." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking a Ball" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now let's turn our attention to a situation where the physics of the object that we are tracking is constrained. A ball thrown in a vacuum must obey Newtonian laws. In a constant gravitational field it will travel in a parabola. I will assume you are familiar with the derivation of the formula:\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "y &= \\frac{g}{2}t^2 + v_{y0} t + y_0 \\\\\n", - "x &= v_{x0} t + x_0\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "where $g$ is the gravitional constant, $t$ is time, $v_{x0}$ and $v_{y0}$ are the initial velocities in the x and y plane. If the ball is thrown with an initial velocity of $v$ at angle $\\theta$ above the horizon, we can compute $v_{x0}$ and $v_{y0}$ as\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "v_{x0} = v \\cos{\\theta} \\\\\n", - "v_{y0} = v \\sin{\\theta}\n", - "\\end{aligned}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Because we don't have real data we will start by writing a simulator for a ball. As always, we add a noise term independent of time so we can simulate noise sensors." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from math import radians, sin, cos\n", - "import math\n", - "\n", - "def rk4(y, x, dx, f):\n", - " \"\"\"computes 4th order Runge-Kutta for dy/dx.\n", - " y is the initial value for y\n", - " x is the initial value for x\n", - " dx is the difference in x (e.g. the time step)\n", - " f is a callable function (y, x) that you supply to compute dy/dx for\n", - " the specified values.\n", - " \"\"\"\n", - " \n", - " k1 = dx * f(y, x)\n", - " k2 = dx * f(y + 0.5*k1, x + 0.5*dx)\n", - " k3 = dx * f(y + 0.5*k2, x + 0.5*dx)\n", - " k4 = dx * f(y + k3, x + dx)\n", - " \n", - " return y + (k1 + 2*k2 + 2*k3 + k4) / 6.\n", - "\n", - "def fx(x,t):\n", - " return fx.vel\n", - " \n", - "def fy(y,t):\n", - " return fy.vel - 9.8*t\n", - "\n", - "\n", - "class BallTrajectory2D(object):\n", - " def __init__(self, x0, y0, velocity, theta_deg=0., g=9.8, noise=[0.0,0.0]):\n", - " self.x = x0\n", - " self.y = y0\n", - " self.t = 0\n", - " \n", - " theta = math.radians(theta_deg)\n", - "\n", - " fx.vel = math.cos(theta) * velocity\n", - " fy.vel = math.sin(theta) * velocity\n", - " \n", - " self.g = g\n", - " self.noise = noise\n", - " \n", - " \n", - " def step (self, dt):\n", - " self.x = rk4 (self.x, self.t, dt, fx)\n", - " self.y = rk4 (self.y, self.t, dt, fy)\n", - " self.t += dt \n", - " return (self.x +random.randn()*self.noise[0], self.y+random.randn()*self.noise[1])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So to create a trajectory starting at (0,15) with a velocity of $60 \\frac{m}{s}$ and an angle of $65^\\circ$ we would write:\n", - "\n", - " traj = BallTrajectory2D (x0=0, y0=15, velocity=100, theta_deg=60)\n", - " \n", - "and then call `traj.position(t)` for each time step. Let's test this " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def test_ball_vacuum(noise):\n", - " y = 15\n", - " x = 0\n", - " ball = BallTrajectory2D(x0=x, y0=y, theta_deg=60., velocity=100., noise=noise)\n", - " t = 0\n", - " dt = 0.25\n", - " while y >= 0:\n", - " x,y = ball.step(dt)\n", - " t += dt\n", - " if y >= 0:\n", - " plt.scatter(x,y)\n", - " \n", - " plt.axis('equal')\n", - " plt.show()\n", - " \n", - "test_ball_vacuum([0,0]) # plot ideal ball position\n", - "test_ball_vacuum([1,1]) # plot with noise " - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This looks reasonable, so let's continue (excercise for the reader: validate this simulation more robustly)." - ] - }, - { - "cell_type": "heading", - "level": 5, - "metadata": {}, - "source": [ - "Step 1: Choose the State Variables" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We might think to use the same state variables as used for tracking the dog. However, this will not work. Recall that the Kalman filter state transition must be written as $\\mathbf{x}' = \\mathbf{F x}$, which means we must calculate the current state from the previous state. Our assumption is that the ball is traveling in a vacuum, so the velocity in x is a constant, and the acceleration in y is solely due to the gravitational constant $g$. We can discretize the Newtonian equations using the well known Euler method in terms of $\\Delta t$ are:\n", - "\n", - "$$\\begin{aligned}\n", - "x_t &= v_{x(t-1)} {\\Delta t} \\\\\n", - "v_{xt} &= vx_{t-1}\n", - "\\\\\n", - "y_t &= -\\frac{g}{2} {\\Delta t}^2 + vy_{t-1} {\\Delta t} + y_{t-1} \\\\\n", - "v_{yt} &= -g {\\Delta t} + v_{y(t-1)} \\\\\n", - "\\end{aligned}\n", - "$$\n", - "> **sidebar**: *Euler's method integrates a differential equation stepwise by assuming the slope (derivative) is constant at time $t$. In this case the derivative of the position is velocity. At each time step $\\Delta t$ we assume a constant velocity, compute the new position, and then update the velocity for the next time step. There are more accurate methods, such as Runge-Kutta available to us, but because we are updating the state with a measurement in each step Euler's method is very accurate.*\n", - "\n", - "This implies that we need to incorporate acceleration for $y$ into the Kalman filter, but not for $x$. This suggests the following state variables.\n", - "\n", - "$$\n", - "\\mathbf{x} = \n", - "\\begin{bmatrix}\n", - "x \\\\\n", - "\\dot{x} \\\\\n", - "y \\\\\n", - "\\dot{y} \\\\\n", - "\\ddot{y}\n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "heading", - "level": 5, - "metadata": {}, - "source": [ - "**Step 2:** Design State Transition Function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our next step is to design the state transistion function. Recall that the state transistion function is implemented as a matrix $\\mathbf{F}$ that we multipy with the previous state of our system to get the next state$\\mathbf{x}' = \\mathbf{Fx}$.\n", - "\n", - "I will not belabor this as it is very similar to the 1-D case we did in the previous chapter. Our state equations for position and velocity would be:\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) + (0 * a_y) \\\\\n", - "v_x &= (0*x) + (1*v_x) + (0*y) + (0 * v_y) + (0 * a_y) \\\\\n", - "y' &= (0*x) + (0* v_x) + (1*y) + (\\Delta t * v_y) + (\\frac{1}{2}{\\Delta t}^2*a_y) \\\\\n", - "v_y &= (0*x) + (0*v_x) + (0*y) + (1*v_y) + (\\Delta t * a_y) \\\\\n", - "a_y &= (0*x) + (0*v_x) + (0*y) + (0*v_y) + (1 * a_y) \n", - "\\end{aligned}\n", - "$$\n", - "\n", - "Note that none of the terms include $g$, the gravitational constant. This is because the state variable $\\ddot{y}$ will be initialized with $g$, or -9.81. Thus the function $\\mathbf{F}$ will propagate $g$ through the equations correctly. \n", - "\n", - "In matrix form we write this as:\n", - "\n", - "$$\n", - "\\mathbf{F} = \\begin{bmatrix}\n", - "1 & \\Delta t & 0 & 0 & 0 \\\\\n", - "0 & 1 & 0 & 0 & 0 \\\\\n", - "0 & 0 & 1 & \\Delta t & \\frac{1}{2}{\\Delta t}^2 \\\\\n", - "0 & 0 & 0 & 1 & \\Delta t \\\\\n", - "0 & 0 & 0 & 0 & 1\n", - "\\end{bmatrix}\n", - "$$" - ] - }, - { - "cell_type": "heading", - "level": 5, - "metadata": {}, - "source": [ - "Interlude: Test State Transition" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Kalman filter class provides us with useful defaults for all of the class variables, so let's take advantage of that and test the state transistion function before continuing. Here we construct a filter as specified in Step 2 above. We compute the initial velocity in x and y using trigonometry, and then set the initial condition for $x$. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from math import sin,cos,radians\n", - "\n", - "def ball_kf(x, y, omega, v0, dt):\n", - "\n", - " g = 9.8 # gravitational constant\n", - "\n", - " f1 = KalmanFilter(dim_x=5, dim_z=2)\n", - "\n", - "\n", - " ay = .5*dt**2\n", - "\n", - " f1.F = np.array ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", - " [0, 1, 0, 0, 0], # dx = dx\n", - " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", - " [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt \n", - " [0, 0, 0, 0, 1]]) # ddy = -g.\n", - " \n", - " # compute velocity in x and y\n", - " omega = radians(omega)\n", - " vx = cos(omega) * v0\n", - " vy = sin(omega) * v0\n", - " \n", - " f1.Q *= 0.\n", - "\n", - " f1.x = np.array([[x, vx, y, vy, -g]]).T\n", - " \n", - " return f1" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we can test the filter by calling predict until $y=0$, which corresponds to the ball hitting the ground. We will graph the output against the idealized computation of the ball's position. If the model is correct, the Kalman filter prediction should match the ideal model very closely. We will draw the ideal position with a green circle, and the Kalman filter's output with '+' marks." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "y = 15.\n", - "x = 0.\n", - "theta = 20. # launch angle\n", - "v0 = 100.\n", - "dt = 0.1 # time step\n", - "\n", - "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[0,0])\n", - "f1 = ball_kf(x,y,theta,v0,dt)\n", - "t = 0\n", - "while f1.x[2,0] > 0:\n", - " t += dt\n", - " f1.predict() \n", - " x,y = ball.step(dt)\n", - " p1 = plt.scatter(f1.x[0,0], f1.x[2,0], color='black', marker='+', s=75)\n", - " p2 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", - "\n", - "plt.legend([p1,p2], ['Kalman filter', 'idealized'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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R6YN1WZec3E99d76+Onv00uawnTd5NelNOL3Oc7YDnHaf7rV6Tg9/wM+BpgNM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\nAgDY7Xbs3bsXBw4cgM1mw44dO7B+/fqgBSUiIiIKNw63A0ajEW3GNs/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- "text": [ - "" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As we can see, the Kalman filter agrees with the physics model very closely. If you are interested in pursuing this further, try altering the initial velocity, the size of dt, and $\\theta$, and plot the error at each step. However, the important point is to test your design as soon as possible; if the design of the state transistion is wrong all subsequent effort may be wasted. More importantly, it can be extremely difficult to tease out an error in the state transition function when the filter incorporates measurment updates." - ] - }, - { - "cell_type": "heading", - "level": 5, - "metadata": {}, - "source": [ - "**Step 3**: Design the Motion Function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have no control inputs to the ball flight, so this step is trivial - set the motion transition function $\\small\\mathbf{B}=0$. This is done for us by the class when it is created so we can skip this step." - ] - }, - { - "cell_type": "heading", - "level": 5, - "metadata": {}, - "source": [ - "**Step 4**: Design the Measurement Function" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The measurement function defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. We will assume that we have a sensor that provides us with the position of the ball in (x,y), but cannot measure velocities or accelerations. Therefore our function must be:\n", - "\n", - "$$\n", - "\\begin{bmatrix}z_x \\\\ z_y \\end{bmatrix}= \n", - "\\begin{bmatrix}\n", - "1 & 0 & 0 & 0 & 0 \\\\\n", - "0 & 0 & 1 & 0 & 0\n", - "\\end{bmatrix} * \n", - "\\begin{bmatrix}\n", - "x \\\\\n", - "\\dot{x} \\\\\n", - "y \\\\\n", - "\\dot{y} \\\\\n", - "\\ddot{y}\\end{bmatrix}$$\n", - "\n", - "where\n", - "\n", - "$$\\mathbf{H} = \\begin{bmatrix}\n", - "1 & 0 & 0 & 0 & 0 \\\\\n", - "0 & 0 & 1 & 0 & 0\n", - "\\end{bmatrix}$$" - ] - }, - { - "cell_type": "heading", - "level": 5, - "metadata": {}, - "source": [ - "**Step 5**: Design the Measurement Noise Matrix" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As with the robot, we will assume that the error is independent in $x$ and $y$. In this case we will start by assuming that the measurement error in x and y are 0.5 meters. Hence,\n", - "\n", - "$$\\mathbf{R} = \\begin{bmatrix}0.5&0\\\\0&0.5\\end{bmatrix}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Step 6: Design the Process Noise Matrix\n", - "Finally, we design the process noise. As with the robot tracking example, we don't yet have a good way to model process noise. However, we are assuming a ball moving in a vacuum, so there should be no process noise. For now we will assume the process noise is 0 for each state variable. This is a bit silly - if we were in a perfect vacuum then our predictions would be perfect, and we would have no need for a Kalman filter. We will soon alter this example to be more realistic by incorporating air drag and ball spin. \n", - "\n", - "We have 5 state variables, so we need a $5{\\times}5$ covariance matrix:\n", - "\n", - "$$\\mathbf{Q} = \\begin{bmatrix}0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\\\0&0&0&0&0\\end{bmatrix}$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Step 7: Design the Initial Conditions\n", - "\n", - "We already performed this step when we tested the state transistion function. Recall that we computed the initial velocity for $x$ and $y$ using trigonometry, and set the value of $\\mathbf{x}$ with:\n", - "\n", - " omega = radians(omega)\n", - " vx = cos(omega) * v0\n", - " vy = sin(omega) * v0\n", - "\n", - " f1.x = np.mat([x, vx, y, vy, -g]).T\n", - " \n", - " \n", - "With all the steps done we are ready to implement our filter and test it. First, the implementation:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from math import sin,cos,radians\n", - "\n", - "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.):\n", - "\n", - " g = 9.8 # gravitational constant\n", - " f1 = KalmanFilter(dim_x=5, dim_z=2)\n", - "\n", - " ay = .5*dt**2\n", - " f1.F = np.mat ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", - " [0, 1, 0, 0, 0], # dx = dx\n", - " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", - " [0, 0, 0, 1, dt], # dy = dy0 + ddy*dt \n", - " [0, 0, 0, 0, 1]]) # ddy = -g.\n", - "\n", - " f1.H = np.mat([\n", - " [1, 0, 0, 0, 0],\n", - " [0, 0, 1, 0, 0]])\n", - " \n", - " f1.R *= r\n", - " f1.Q *= q\n", - "\n", - " omega = radians(omega)\n", - " vx = cos(omega) * v0\n", - " vy = sin(omega) * v0\n", - "\n", - " f1.x = np.mat([x,vx,y,vy,-9.8]).T\n", - " \n", - " return f1" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we will test the filter by generating measurements for the ball using the ball simulation class." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "y = 1.\n", - "x = 0.\n", - "theta = 35. # launch angle\n", - "v0 = 80.\n", - "dt = 1/10. # time step\n", - "\n", - "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[.2,.2])\n", - "f1 = ball_kf(x,y,theta,v0,dt)\n", - "\n", - "t = 0\n", - "xs = []\n", - "ys = []\n", - "while f1.x[2,0] > 0:\n", - " t += dt\n", - " x,y = ball.step(dt)\n", - " z = np.mat([[x,y]]).T\n", - "\n", - " f1.update(z)\n", - " xs.append(f1.x[0,0])\n", - " ys.append(f1.x[2,0])\n", - " \n", - " f1.predict() \n", - " \n", - " p1 = plt.scatter(x, y, color='green', marker='.', s=75, alpha=0.5)\n", - "\n", - "p2, = plt.plot (xs, ys,lw=2)\n", - "plt.legend([p2,p1], ['Kalman filter', 'Measurements'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - 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G0e9LTmfY2LXdl8yzBl6Zu5O/LbfTq3cFLaNLuDn4JoZGDnV1VHEdVFX91bWO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\n7rSYlJTExo0bA36ugF6498ADD7By5Uo++OADbrn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- "text": [ - "" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that the Kalman filter reasonably tracks the ball. However, as already explained, this is a silly example; we can predict trajectories in a vacuum with arbitrary precision; using a Kalman filter in this example is a needless complication." - ] - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Tracking a Ball in Air" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We are now ready to design a practical Kalman filter application. For this problem we assume that we are tracking a ball traveling through the Earth's atmosphere. The path of the ball is influenced by wind, drag, and the rotation of the ball. We will assume that our sensor is a camera; code that we will not implement will perform some type of image processing to detect the position of the ball. This is typically called *blob detection* in computer vision. However, image processing code is not perfect; in any given frame it is possible to either detect no blob or to detect spurious blobs that do not correspond to the ball. Finally, we will not assume that we know the starting position, angle, or rotation of the ball; the tracking code will have to initiate tracking based on the measurements that are provided. The main simplification that we are making here is a 2D world; we assume that the ball is always traveling orthogonal to the plane of the camera's sensor. We have to make that simplification at this point because we have not yet discussed how we might extract 3D information from a camera, which necessarily provides only 2D data. " - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Implementing Air Drag" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our first step is to implement the math for a ball moving through air. There are several treatments available. A robust solution takes into account issues such as ball roughness (which affects drag non-linearly depending on velocity), the Magnus effect (spin causes one side of the ball to have higher velocity relative to the air vs the opposite side, so the coefficient of drag differs on opposite sides), the effect of lift, humidity, air density, and so on. I assume the reader is not interested in the details of ball physics, and so will restrict this treatment to the effect of air drag on a non-spinning baseball. I will use the math developed by Nicholas Giordano and Hisao Nakanishi in *Computational Physics* [1997]. \n", - "\n", - "**Important**: Before I continue, let me point out that you will not have to understand this next piece of physics to proceed with the Kalman filter. My goal is to create a reasonably accurate behavior of a baseball in the real world, so that we can test how our Kalman filter performs with real-world behavior. In real world applications it is usually impossible to completely model the physics of a real world system, and we make do with a process model that incorporates the large scale behaviors. We then tune the measurement noise and process noise until the filter works well with our data. There is a real risk to this; it is easy to finely tune a Kalman filter so it works perfectly with your test data, but performs badly when presented with slightly different data. This is perhaps the hardest part of designing a Kalman filter, and why it gets referred to with terms such as 'black art'. \n", - "\n", - "I dislike books that implement things without explanation, so I will now develop the physics for a ball moving through air. Move on past the implementation of the simulation if you are not interested. \n", - "\n", - "A ball moving through air encounters wind resistance. This imparts a force on the wall, called *drag*, which alters the flight of the ball. In Giordano this is denoted as\n", - "\n", - "$$F_{drag} = -B_2v^2$$\n", - "\n", - "where $B_2$ is a coefficient derived experimentally, and $v$ is the velocity of the object. $F_{drag}$ can be factored into $x$ and $y$ components with\n", - "\n", - "$$F_{drag,x} = -B_2v v_x\\\\\n", - "F_{drag,y} = -B_2v v_y\n", - "$$\n", - "\n", - "If $m$ is the mass of the ball, we can use $F=ma$ to compute the acceleration as\n", - "\n", - "$$ a_x = -\\frac{B_2}{m}v v_x\\\\\n", - "a_y = -\\frac{B_2}{m}v v_y$$\n", - "\n", - "Giordano provides the following function for $\\frac{B_2}{m}$, which takes air density, the cross section of a baseball, and its roughness into account. Understand that this is an approximation based on wind tunnel tests and several simplifying assumptions. It is in SI units: velocity is in meters/sec and time is in seconds.\n", - "\n", - "$$\\frac{B_2}{m} = 0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}}$$\n", - "\n", - "Starting with this Euler discretation of the ball path in a vacuum:\n", - "$$\\begin{aligned}\n", - "x &= v_x \\Delta t \\\\\n", - "y &= v_y \\Delta t \\\\\n", - "v_x &= v_x \\\\\n", - "v_y &= v_y - 9.8 \\Delta t\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "We can incorporate this force (acceleration) into our equations by incorporating $accel * \\Delta t$ into the velocity update equations. We should subtract this component because drag will reduce the velocity. The code to do this is quite straightforward, we just need to break out the Force into $x$ and $y$ components. \n", - "\n", - "I will not belabor this issue further because the computational physics is beyond the scope of this book. Recognize that a higher fidelity simulation would require incorporating things like altitude, temperature, ball spin, and several other factors. My intent here is to impart some real-world behavior into our simulation to test how our simpler prediction model used by the Kalman filter reacts to this behavior. Your process model will never exactly model what happens in the world, and a large factor in designing a good Kalman filter is carefully testing how it performs against real world data. \n", - "\n", - "The code below computes the behavior of a baseball in air, at sea level, in the presence of wind. I plot the same initial hit with no wind, and then with a tail wind at 10 mph. Baseball statistics are universally done in US units, and we will follow suit here (http://en.wikipedia.org/wiki/United_States_customary_units). Note that the velocity of 110 mph is a typical exit speed for a baseball for a home run hit." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from math import sqrt, exp, cos, sin, radians\n", - "\n", - "def mph_to_mps(x):\n", - " return x * .447\n", - "\n", - "def drag_force(velocity):\n", - " \"\"\" Returns the force on a baseball due to air drag at\n", - " the specified velocity. Units are SI\"\"\"\n", - "\n", - " return (0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))) * velocity\n", - "\n", - "v = mph_to_mps(110.)\n", - "y = 1\n", - "x = 0\n", - "dt = .1\n", - "theta = radians(35)\n", - "\n", - "def solve(x, y, vel, v_wind, launch_angle):\n", - " xs = []\n", - " ys = []\n", - " v_x = vel*cos(launch_angle)\n", - " v_y = vel*sin(launch_angle)\n", - " while y >= 0:\n", - " # Euler equations for x and y\n", - " x += v_x*dt\n", - " y += v_y*dt\n", - "\n", - " # force due to air drag \n", - " velocity = sqrt ((v_x-v_wind)**2 + v_y**2) \n", - " F = drag_force(velocity)\n", - "\n", - " # euler's equations for vx and vy\n", - " v_x = v_x - F*(v_x-v_wind)*dt\n", - " v_y = v_y - 9.8*dt - F*v_y*dt\n", - " \n", - " xs.append(x)\n", - " ys.append(y)\n", - " \n", - " return xs, ys\n", - " \n", - "x,y = solve(x=0, y=1, vel=v, v_wind=0, launch_angle=theta)\n", - "p1 = plt.scatter(x, y, color='blue')\n", - "\n", - "x,y = solve(x=0, y=1,vel=v, v_wind=mph_to_mps(10), launch_angle=theta)\n", - "p2 = plt.scatter(x, y, color='green', marker=\"v\")\n", - "plt.legend([p1,p2], ['no wind', '10mph wind'])\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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HR5+U4bguXbpQWFhIcXExzz77LDt27GDFihV8/fXX3HrrrTXH1TWSe7pzfvjhh/ztb3/D\nx8eHiy++mPbt29e3+xpMhbCISCuUn29kyhQbe/dW/2/8q68s4JNNlz77ah0X5hvGlVeaeOMNfw4e\nrJ72EBNjZ8KEMjomzWT1j6vZVbSLYEswc/rMITzcxcsv5+N0wq8Hh44Xt35mPwbFDQIgLu7U8xIM\nBgPT0qbxbcG3BPgEEBDlJCrq1P8WX5Mvl3W6DIfLwexpR3G5jnK662Tu6rWIO3b8F9f+AVDYmS5d\nqhgypPYHALPBQsWn18O5i8DkgMJEjm15BC6sq0fFG92dfjdf5X5F3rE8ksOSGddl3EnHzO07l2vf\nu5bUiFR6t+td67H4oHjOiz2Pt/e+DVSPBk9NndqgLKcqIP39/Tl27Bhr1lQX6/fccw8BAScuNjWZ\nTBiNxpqRXLPZjN1+4puUiIiImv2hoaHk5uaSmJgIUDMVw2KpHhGvqDj1B+njjEYj3bt35+uvv+aT\nTz6hpKSEoqIi8vLy6Nq161n9G093zoKCAmy2E99EHc/dHOoshAsLC5k6dSp2ux2Xy8VNN93EqFGj\nWL16NY8++igAd911F0OHDm2WsCIiUm3tWt+aIhiqL1b791tZbNt/KU5XdXHqdDmZljaN2X1ms2JF\nIStWBOJywU03lZCSYgf8GJU4ir9s+QspthQGxJz4OvNU35AaDAZm9pyJzc928oOncHnny7mcy8/q\n2Fm9Tswhruti8fEXxrEybzA+u+7FdnkZCxceISSkdgFRVGSET26HqOeh3TbYO5TDP0UDeSe1N/2D\n6Xxf9D0Gqk9abi/ntUtfI8Kv+d6IxXM6h3amV2QvMvdncl3KdRgNJ7/w+0f3p3No55NGg49b1H8R\nm3M2k38snyu7XInZ2LAxxlONCHfs2JFdu3aRllY9wvz9998zcuTZf7ORm5tLfHw8drudoqKiRheY\nvXv35vPPPwegf//+PPfcc/To0aNRbQLYbDby8vLo3LkzAHl5J/+tNpU6f1tBQUH83//9H35+fhQW\nFjJq1CguvPBCli9fzksvvURFRQVTpkxRISwi4iZOJ/zwgwmTCRITHactCiMiHFgsTiorT7xxJ5h7\n4gg/l40HNwLVb/LTe0wHID29kvT0gpPamdlrJi9+/yJz+sw5q3wXd7i4nv+is1OfpZJenvQXmARQ\ndMrHQ0KchARayPn6KhjwKKx9kLD+J49cu1zgs/06vveZgsPnCAAZcRkqgr3MovRFXF98PVd0ueK0\nx7w65tXTFrgJwQn0bdeXXYW7uCH1hnqf3+l0UllZicPhwOFwUFFRgdlsxmQyMWbMGP71r38xfPhw\ntm/fzpdffskjjzxy1m0/+eSTLFy4kGeeeYb4+Hg6dOhQ73y/1Lt3b+68805uuOEGevbsycyZM087\nl7c+F7sNHz6cp59+mt69e7N27Vp++umnRuWsjzpXjTCbzfj5VS+SfvToUSwWC1u3bqVLly6Eh4cT\nExNDdHQ03333XbOEFRFpy6qq4NJLzVx6aSSjR0cwdWrYaVdEGDaskuHDK/D3d2I2u+jevZKFC48w\np+8cQnxDMGBgVOIo/Mynv9EFgJ/Zj5dHv1xrNLi1M5ng4YftJBfeTuiX99E7OZhHHjm5aP7jH4NY\n9egYHNnVI1qmChtze9/V3HHFwzqFduK9se/V+WHsTKO8iwcsZlbvWQ0aDX7ppZfo3LkzK1as4NVX\nX6VTp0785S9/AWDatGkkJSXRr18/brvtNpYvX05MTAxwYi3gutYEDg8Pp3v37jz//POnvNDtuLP9\nINq7d29yc3MZMmQI/fr1o6SkhN69q6eLbNq0ia5duzJs2DAMBgPdunWja9eu7N2795Rt/fKc8+bN\no6Kigu7du/Paa6/Rt2/fs8rjDoadO3fWWbKXlpYyceJE9u3bx5/+9CccDgcbN24kJSWFkJAQ1qxZ\nw29/+1syMjJqPS8rK4tu3bo1aXhvcXzeTH5+voeTtH7qS/dSf7rXk09Gct99ZpzO6jcIH79yYhec\nT3TkiSXNovyjeOw3jwHVI5rbtvlQVmagZ89KrD8v/zv+rfEcKjvEe2PfO2Mh3FbZbDZcLjhwIL+m\nX35t7Fgbn33mCx3WwoRxmA+ls27aMzXLwP3Sqj2reHnXy5gM1b+LKmcVv0v7HYPjBjflP6PFaO1/\n67m5uURGRno6RrPJyspi4MCB7Nu3r86VIFqjU/0ubTYbGzZsICEhod7tnfGjS0BAAKtWrWL37t3c\ndNNNzJgxA4CJEycCsGbNmtN+kvjlxGdpOJ/qS7bVn26gvnQv9ad77dtnqimCAaqOWfGpbMdnh6ov\nxDEbzNw35L5a/X2qmWnLfrOM9VnriW8X3+SZW6rjr824uNO/NoOCfn4L3Dsc8pMI/2oZHTqEEh5+\n8rGDDINY/OlickpzAGgf0p6BnQZiC/CO135r/1v/5UoK0rqZzeaTXofHX58Nau9sD+zUqROxsbHE\nxcXxzjvv1Oyv61PWkiVLan7OyMhgyJAhDQ4qItLWTZkCb73lIienuhiOi3Py4PDfc/Nnn3O47DDJ\nEcnc2u/WM7QCA+IHMCC+7Ux1aCoPP2xnwgQDe/YYCH17PTffaCI8vPZosMsFDz1kYs2ac3H07A8R\n1be4zUjIICrgNMtgiLQAzXWLYk9Zt24dmZnVazibTKaTZiacrToL4ZycHCwWC2FhYeTm5rJ37146\ndOjArl27KCgooKKigpycHJKTk0/5/OnTp9fabq1fqXhaa/9KqiVRX7qX+vPMysoM3HlnCPv3m4iM\ndPLHPxYRGnrqGWnp6Tb+/GcDK1Y4MRjglltKGNDZRvfd3fko6yMu63AZR4qONPO/oHU6m9emzQZv\nvGFg1y4zkZEO4uKc/PrwJ58M4MEHgygrM8I3f8I49b9ER1iY03OOV73uW/vf+i+XFPMGCQkJZGVl\nnfnAVshut5Ofn09qaiqpqanAiakRDVFnIXzw4EEWLVpUs33XXXdhs9mYPXt2zVWCCxYsaNCJRUS8\nwYwZobz33s/zdI12tkT+kRGXnPiaNjYgllt63lKzffnlLjIyaq/usCh9Ed8VfMe0tGnNktmbBAS4\n6NnzNPebBtav960uggEKuuLc15/O0QGnXVliQ/YGntj+BGZD9dur0+VkfNfxTbbahog0Tp2FcM+e\nPVm1atVJ+0eNGsWoUaOaLJSISFvxy7V+cZrJ89/Ev7/5rGbXmI5jzthG59DOvDf2PXyMDZ8HJw0T\nFlZ7qkRQ5j+4c2rZaY/vGtaVbwu+JbskG4AovygWDVh02uNFxLPa1qWEIiItjL9/7WkQkd8uJNAn\nEKgeDV48YPFZtRPqG+r2bHJm999/hN69KwkNdRAdbWfK5cH06hZw0nEuV/Xd/oKNUQyIPjE/u1dU\nLzqGdGzOyHIKLperXuvaSsvkdDrd/nvULZZFRJrQ/fcXcccdYeTnGwkNdXL/DQP5S0k3Ps/5nH7R\n/YgJiPF0RKlDcLCL11/PIyvLRFCQC5vt5IWdCwsNXHONjawsE1ari6tuXEZc4KdUOaq4O/1uD6SW\nXwsMDKS4uLjmFr/S+jidTg4fPuz2lUtUCIuI1NNPP5l48UV/wsIcXHNNGRbL6Y/t08fO++/ncuiQ\niagoB35+wL5bmbVuFovS9ZV5a3D8Ln+ns2BBKF98ceJF8J8Vnei9dAB2Y4lGg1sIf39/Kisryc3N\n9XQUoHoJMPC+i/gaw+VyYbPZGrVU2qmoEBYRqYdvvzVz3XXhZGWZwVLCS5/8wNKlxZh+vudFhF8E\n7YPb13qOry+0b3+ikBp2zjAeyXhEo8FtRH5+7VmGxcVGrm23jE5dTz+X+D/f/Id/7/g3viZfAI7Z\nj7EgfQEj249s0qzerCWNBrf2VTjaEs0RFhGph4cfDqouggEsR9nR/QqueHsc494ax9hVY/nH1n+c\nVTvD2w9vwpTSnLp3r8RsPjFvMTbWQY+uwbQLaHfa54zpOIZyRznb8rexLX8bRoORC+IvaIa0IvJL\nKoRFROqh1nUaJTGwZzgOqqhyVhEfFM/8/vM9lk08Y/78o1x9dSm9elUycGAF//hHIQEBdV/QE24N\nJyOu+gYARoyM6TimZnRYRJqPpkaIiNTDjBlH2brVhwMHzICL7jlLyU1fx8GyAwyNH0qIb4inI0oz\nM5nggQfqvtFJeTncd18IP/1komNHO/fcc4S7+t1FZnYmVpO11lrSItJ8VAiLiNRDz552nnkmn2ee\nCSA83Mn06VbmfNKfzTmbmdt3rqfjSQs1fXoY771nBQysX+8iL8/IY4/B+XHnE+0frdFgEQ9RISwi\nXs/lgtxcI35+LoKCzrxGZXKyg2XLTowA3p1+Ny/velmjwXJaO3f6AAYAnE4D335bfeX7skHLMBlM\np33emp/WsPfI3pptAwYmJk0kyBLUpHlFvIUKYRHxamVlBqZMCeeHH8yYfRyMu6KEuXNLah43GUwY\nDIY624gJiGFmz5lNHVVaMV9f16+2q/97prsFfrDvA5757pma7fZB7ZncbbLb84l4K10sJyJebcmS\nID75xJfcXBMHz5vMCp/u9Pu/8zjvhfPo+1zfmlvlijTGrFlHiY+34+PjIiHBzh131D2n+Lj5/eeT\nGJwIVI8GX975cqxmaxMmFfEuKoRFxKsdOvSLr6U/WIYLB4crsskuzSYtIo34oHjPhZM247LLynn7\n7TxefjmPt9/O46KLKs7qeSG+ITXLqnUO7axvHkTcTIWwiHi1wYMr8ff/+ba5hZ2xFvQHwGa1sbD/\nQg8mk7YmIsJJ375Vp7xNM8C+fSZmzgxl+vRQduw4MXPxzr53Eu0fzSUdLtFosIibaY6wiHi1668v\npbDQwPr1vpjNMGXEQhbv+4S0iDSSw5M9HU+8xOHDRq66ysbevdVvy5s3W3jmmXySkhyE+IYwv998\nRncc7eGUIm2PCmER8WoGA8yZU8KcOccvkIvn7bX9uaP3HR7NJd5l5Ur/miIYIDvbzFNPBfLQQ8UA\nXNH1itM+1+F0sLt4d619AT4BxAXGNU1YkTZEhbCIyK/8c/g/PR1BvExwsBODwYXLdWKFkoCAU0+h\n+LVKZyVXvXMVRyuP1uzrFdmLFy55we05RdoazREWkTaltNTA9OmhXHaZjRtvDKO4uO6lz0RaggkT\nyujXrxKjsXqZtdTUSm6/veQMz6rmZ/ZjdIfRlFSVUFJVgtVk5b6B9zVlXJE2QyPCItKmTJ8extq1\nVuj0LvSby7onrHTubKfKUcXEpIlcn3q9pyOKnMTXF158MZ8PPrBSWQkXXliBv/+Zb+5y3Jw+c1i7\nby17j+ylR2QPksKTmjCtSNuhQlhE2pQff/x5ObSfLgCDk5KQzWzJhfjAeMZ0HOPRbCJ1sVjg4ovL\nG/TcQEsgw88Zzku7XtJqJyL1oEJYRNqUgICfR9HsVthxJUQsAaOTATEDiPSP9Gw4kUYoKjIwd24o\nublG2rd38Ic/FOHnd+LxOX3mUOGo0GiwSD2oEBaRNuX++4uYPTuM/HwjIdmzqbK+gMFSyt397/Z0\nNJFGmTo1nE8+qb438+efuzh2zMA//1lY83igJZDfD/69p+KJtEoqhEWkTenb18777+eSk2MiKsrB\nih2XsO/IPo0GS6tmt0NW1i/ugoiB3bvr9xb+Q9EPHCo9VGtfj8geBFmC3JBQpHVSISwibY6vL5xz\njgOA23rdRpWzysOJRBrHZOKki+f8/M7+YjqAZ797ln9uO7E0YJhvGGvHrVUhLF5Ny6eJSJtmMpp0\nW1pp9QwGuOuuIyQmVhEa6qBz5yqWLCmqVxtz+8ylU0inmu2M+AyiA6LdHVWkVdGIsIi0aDk5Rv73\nfwPw83Nx/fWl9VpSSqQtGTmygoyMPHJyjERHO7DW8/Odv48/I9qP4B9f/4PYgFgWpS9qmqAirYgK\nYRFpsbKzjUycaGNP+VcwZCkrHjIyYEAlBqOTixMv5squV3o6okiz8vNzkZjoaPDz7+h9B6v3rqZX\nVC9iAmLcmEykdVIhLCIt1iOPBLFnjw9Yu0LENxyx7eb9LAj1DWVmz5mejifS4uTlGfnySx/OOcdB\ncrL9pMf9ffyZmjqViztc7IF0Ii2P5giLSIvldP78Q3ko/HBRzf7uEd3pFdXLM6FEWqgvvjAzZkwE\n111nY+yUHQJMAAAgAElEQVRYGw88cOqL4K5PvV6jwSI/UyEsIi3WrFkltG//86jWR0vxKelIqCWU\nO/ve6dlgIi3Q738fwr591V/0FhebePVVP4qKDB5OJdKyaWqEiLRY7ds7WLkynyeeCMDf30Rezwx+\nKtul0WCRU3D8aupwZaWB0lIDoaFnf4Hpjvwd3P/p/VhMFgBcLhcXxF/AvAvmuTOqSIuhQlhEWrT4\neAf33XcEgNKqBRSV12/JKBFvMWRIBTt2+FBaWv1lb+fOdmJinGd4Vm2dQjqRU5bDrqJdAIRYQpjV\ne5bbs4q0FCqERaTVCPAJIMAnwNMxRFqk224rISTESWamL1FRTu655wjGek6AtJqtXNLhEh796lFc\nuEi1pdKvXb+mCSzSAqgQFhERaSOuu66M664ra1QbM3vO5O29b3P42GHm9pvrpmQiLVOdhXBOTg63\n3XYbR48exWKxMGfOHM477zy6detGUlISAP369WPhwoXNElZEWr+qn+927OPj2RwicmrHR4U/OfiJ\nRoOlzauzEDabzdx7770kJSVx4MABJk6cSGZmJlarlddff725MopIG+BywZ13hrDmuy+pCt9K16Qq\nLrusHIMBLmp/Ee0C2nk6okib53DAwYMmQkKcBAWd/iK6W3vdyuRuk5sxmYhn1FkI22w2bDYbALGx\nsVRVVVFZWdkswUSkbXnpJT9efdWP8h5fwMA5/Nfk4L+bINIvkpHtR3o6nkibl5dnZMqUcLKyTPj5\nubjhhlJ+97vSUx7ra/IlOiC6mROKNL+znka/fv16UlJSsFgsVFZWMnbsWCZNmsTmzZubMp+ItBFb\nt/pQXm6Ez2dAbmrN/sGxg/WGK9IM5s8PYetWCwUFJrKzzTzxRAC5ubqdgHi3s7pYLjc3l4ceeoi/\n//3vAGRmZmKz2di2bRszZsxgzZo1WCyWk553fDRZGsfn58mU6s/GU1+6V33687e/NfDGGy4KC83w\n1bUwYi4R1hiWX7QcW5B+H6DXpzupL09WVlZ7Yv7RoyYqK8Ox2c68zvAv+7OsqozHvnwMh+vEwsUd\nQjpwRbcr3Bu4DdPr0718GnHRyRkL4YqKCmbNmsW8efNISEgATvzi0tLSiIqKYv/+/XTs2PGk5y5Z\nsqTm54yMDIYMGdLgoCLSul10kYt58+y8+KIJV9V0Dvo8wdAu3YkNivV0NBGv0K+fk02bDFRWVt9t\nLiHBRefOZ3+zjeMsJgv/3vpvvi/4vmbf/6T+jwphaVbr1q0jMzMTAJPJREZGRoPaMezcufO0fwUu\nl4vZs2fTt29frrrqKgCKi4vx9fXFarWyf/9+rrrqKt5//32sVmut52ZlZdGtW7cGhZLajn/wyM/P\n93CS1k996V6N6c+3975N33Z9aeevi+SO0+vTfdSXJ3M6YcmSYL76yger1cWyZcV06uQ48xM5uT//\nue2fLPtsGXaXnYTABFZfvppwa3iTZW9r9Pp0L5vNxoYNG2oGbOujzhHhL774gvfff589e/awcuVK\nDAYD99xzD/Pnz8disWAymVi2bNlJRbCIyJlc0uEST0cQ8SpGIyxefMQtbV2fcj0rv1/JtwXfMjhu\nsIpgabXqLIT79u3L9u3bT9r/7rvvNlkgERERadnMRjNXdrmSx75+jAX9F3g6jkiD6c5yIiIiUm83\npN5AhF+ERoOlVdO6KSIiIgJAdraR116zsmPHmcfJzEYz47qMa4ZUIk1HI8Ii0iDvvuvL2+9AZKSL\nWbMcBAS4MGDAZDR5OpqINMDHH1uYOzeUAwfMhIQ4ueaaEubNK/F0LJEmpRFhEam3l1/2Y/YCA6+e\n04HHfZPo+a9BDHxhIJNWT/J0NBFpoEceCebAgerxseJiI6+84s+xYx4OJdLENCIsIvX2yit+FOVY\n4ceh0P05KoEj5aHMGTbH09FEpIEcv1pJzW6vXnPYz6/+aw1XOCpY/sVyKh2VNfviA+OZmja1sTFF\n3EqFsIjUm+n47Ic1f4Rz1kNoFl2DU+kf3d+juUSk4TIyKti500xZmRGDwUVychUhIfUvggEsRguZ\n2Zlsy9tWs29cZ80nlpZHUyNEpN7mzTvCOefY4Wgsxuzz8XGEcM/5Gg0Wac3mzj3KggVHuPjiY0yb\nVsLTTxc0uC2DwcD07tPxM/kB1aPB9wy4x11RRdxGI8IiUm9paXZefz2P//7XRkC7B3gq/yD92vXz\ndCwRaQSDAa67rozrritzS3tjOo7h8W2PsyV3CwNjBhLhF+GWdkXcSSPCItIg7do5ufZaJ1deHM2z\nF/+fp+OISAtjMBj4XdrvsFlt3J1+t6fjiJySRoRFRESkSYzpOAZfs69Gg6XF0oiwiIiINAmDwcDI\n9iM9HUPktDQiLCIiImf0ww8wbZqNo0cNdOxo5+GHixu0tJpIS6JCWEREROrkdMKkST5s21b9RfL2\n7RZMJvjb34o8nEykcTQ1QkRwuU5eTF9E5LjcXDh8uPa+vXs1liatn17FIl7u6af9+cO3t+MwHyU4\nyEnvPpUE+wby8JCHPR1NRFqI8HAIDoacnBP7QkOdjWqzoLyAy1ddjtVkrdnXMaQj//jNPxrVrkh9\naERYxIv9+KOJRx8NoqTyKMc6vEJOxGu889PblFSWeDqaiLQgPj7w+9/b6dSpiuhoOz16VPKnPzVu\nWkS4NZy4gDi2529ne/529hbv5couV7opscjZ0YiwiBfbtctMbq6p+lbJCZ9A8AF8K2JYlL7I09FE\npIUZPdpFenoepaUGAgNdGAyNb/Ou/nexbfU2CioKONd2LsPOGdb4RkXqQSPCIl4sJaWK2Fg7FHWA\nrIEAnGPsT0JwgoeTiUhLZDRCUJB7imCA7hHdSYtII8AcwK09b3VPoyL1oEJYxIvFxjpZvLiYtLRK\nOu55AIvdxn+unu/pWCLiReb3n0+HkA4aDRaP0NQIES83enQFo0dXAIHsyH+e9iEaDRaR5pMWkcaq\ny1Z5OoZ4KY0Ii0iNFFuKpyOIiBeymCyejiBeSoWwiIiINNqLL/oxbpyNK6+08cEHvp6OI3JWNDVC\nREREGuXjjy0sXRpMQYEJgD17TDz7bAHJyXYPJxOpm0aERUREpFHeeMOvpggGOHTIzLvvWut4hkjL\noBFhERERaZTERAcmkwuHo3pdNavVSadOjR8N/uzgZ/x1y1/xMfoA4HA5uKzTZYzrMq7RbYuACmER\nERFppOnTS9i82cLWrT4YjXD++RWMHl3e6HaTwpPYU7yHn47+BECENYKF/Rc2ul2R41QIi7Qh6zc5\nycoyM3hwBe2inRgNxpqRFBGRpuLjA//7vwUcOGDCZHIRHe10S7uhvqFkxGfwzLfPANAjsgdJ4Ulu\naVsEVAiLtBmz5/nyQlRPcBowrXQRFubknLBorc8pIs3CYIC4OIfb272r311k7s+ktKpUo8HidrpY\nTqQNOHDAyJp3QuG70RCahSNwPwVlR7m91+2ejiYi0ijHR4U1GixNQSPCIm1AWZmBqioDfPgAdFoD\ntt0ElKTqlqUi0ibc3f9uSqtKPR1D2iCNCIu0AR06OEhOroLyMNh9IVQGMDbyNk/HEhFxi0BLIO0C\n2nk6hrRBKoRF2gCTCZ59toDrrithhM8ikgP68sB1gz0dS0SkhsMBRUUGXC5PJxE5QVMjRNoIf38X\nS5ce+XnrOY9mERH5pffe82XZsmBKSoxERTl46qkC4uLcs7KESGPUOSKck5PDpEmTGD16NGPHjmXT\npk0ArF69mpEjRzJy5Eg++uijZgkqIiIirY/dDkuXhrB7tw85OSa2bbMwZ06op2OJAGcYETabzdx7\n770kJSVx4MABJk6cyAcffMDy5ct56aWXqKioYMqUKQwdOrS58oqIiEgrUlxspKTEUGvfkSOamSkt\nQ52FsM1mw2azARAbG0tVVRVbtmyhS5cuhIeHAxAdHc13331HcnJy06cVERGRViUszElkpIPDh001\n+9q3b/ztl4+bvW42PxT9ULNd7ijnuYufw+Znc9s5pO066znC69evJyUlhfz8fCIjI3nhhRcICQkh\nMjKSw4cPqxAWERGRkxiN8MQThcyZE0pJiYHERDvLlxe7rf2hCUN5c8+blNnLABgYM1BFsJy1syqE\nc3Nzeeihh/j73//Ojh07AJg4cSIAa9aswWAwnPJ5x0eTpXF8fKpvkav+bDz1pXupP91L/ek+6kv3\namx/2mzw4YcALsAEhLsrGlPCp/DkN0/y+cHPCfUN5f6h97f437ten+51vD8b4oyFcEVFBbNmzWLe\nvHkkJCRw+PBhcnNzax7Pzc0lMjLylM9dsmRJzc8ZGRkMGTKkwUFFREREfs1gMHB7+u1MfWsq3dt1\n5/xzzvd0JGkG69atIzMzEwCTyURGRkaD2qmzEHa5XMyfP5/Ro0czeHD1mqRpaWns2rWLgoICKioq\nyMnJOe20iOnTp9fazs/Pb1BIb3f8E6P6r/HUl+6l/nQv9af7qC/dq6X3Z0ZEBglBCdyadmuLzfhL\nLb0/W4PU1FRSU1OB6v7csGFDg9qpsxD+4osveP/999mzZw8rV67EYDDw+OOPM3v2bCZNmgTAggUL\nGnRiETm1z/f+wPIXdmKvgmHDKohq5yQ9Op2EoARPRxMRaZEMBgNvXPoGQZYgT0eRVqbOQrhv375s\n3779pP2jRo1i1KhRTRZKxFsVFxuYfu9BDqTfCj7lfPIt+H8fyEtjXlQhLCJSBxXB0hBayE+kBXn1\nVT8OrB0Ph3rU7Asq7k/PyJ4eTCUiItI2qRAWaUF8fX/+YdMcqPSHsnB6F9zryUgiIk3KbodFi4IZ\nO9bGtdeGcfiwShNpPnq1ibQgY8eW0bt3FXw7Fg6n4l/Ui9/f2sXTsUREmsyiRcH85z8BfPaZL2vW\n+HHNNeE4nZ5OJd7irG+oISJNz2qFlSvzWLnSnx3l8/jthcFERuodQUTaru3bLTgcJ+5HcOCAiZwc\nIzEx+n+fND0VwiItjJ8fXHNNGTDA01FERJpcQEDtgtff30VoqMtt7RdXFPPOj+/U2pcYnMiAGP0/\nVlQIi4iIiActW1bMtGkmDh0yERTkZPr0o/j5ua8QBvjj5j9yqOxQzfa01GkqhAVQISwiIiIe1KmT\ng3feyWX/fhMREU5CQtxbBIf4hjCy/Uj+8+1/qs8X0ok7+97p1nNI66WL5URERMSjfH2rC2J3F8HH\nzes3j/ZB7QEY0X4E/j7+TXIeaX1UCIuIiEibFuIbwgXxF5AQlMAdve/wdBxpQTQ1QkRERNq8ef3m\n0SOyh0aDpRaNCIuIiEibF+IbwoSkCZ6OIS2MCmERERER8UoqhEVERETEK2mOsEgTOFyay60vPMWB\ng0YiIhz07FFFj6geXNbpMk9HExFpNRwOWLAghC1bfPDxgQULjnDeeZWejiVtiAphkSbwl+XRrPd9\nB9r9wG7gs20m7uo319OxRERalYceCuKFF/yx26tvwTxnTihvvZVHeLhuvyzuoakRIk1g08fhsGMc\n/Lwkpk9hN6al/s6zoUREWpnt231qimCA/ftN/PCDxvDEffRqEmkCJpMLMhdB8usQ/gOBP07E12zx\ndCwRkVYlJsZRazsy0kF8vN3t5/ns4GccqTxSs200GLkg/gJMRpPbzyUtiwphkSYweXIpf/pTMPnf\n/RZj6itcn3wjBkOVp2OJiLQq999/hP37TezebcZicXHjjaXExrp/WsTyL5ez8cDGmu32Qe1ZP369\n288jLY8KYZEmMGXKMfr0qWLdppn4dO7JtKEqgkVE6svf38ULLxRw7Fj1bZiNTTShc8nAJYx/ezx5\n5XmYDWauT7leo8FeQoWwSBNJSbGTkmIAMjwdRUSkVfPza9r2k8KT6BnZk7VZa+ka1pVrU65t2hNK\ni6GL5URERMTrLei/gFDfUCZ0nYDZqHFCb6FCWERERLxeUngSN6bdqNFgL6OPPCIiIiLArF6zPB1B\nmplGhEVERETEK6kQFhERERGvpKkRIiIi0ir9+KOJN9/0Iy7OzuWXlzfZ8mrSdqkQFhERkVbniy/M\n3HxzONnZZnx8XLz1Vjn/+lchBsOZnytynD47iYiISKvz5z8Hk51dPZ5XVWVg0yZfdu7U+J7Ujwph\nERERaXWczpO37XbPZJHWSx+dRE4j71ge/9jwBt98ayLC5iItrYpzbecyOG6wp6OJiHi9a68t5Ztv\nfDh82AS46N69iuTkpqmE/73j33yY9SFGQ/X4YaWjkoXpC0mxpTTJ+aT5qBAWOY3Mj/3453eP4wzM\nhjJ49VMjd/abo0JYRKQFuPDCCh57rJAXXvAjJsbJrbcexdxEVc25tnN56IuHKK4oBqBzaGc6hnRs\nmpNJs1IhLHIazz11Dk7bKOj7BACmgnO5IuYWD6cSEZHj0tMrSU+vbPLz9I/uT2p4KhsPbsSAgVGJ\no/Az+zX5eaXpaY6wyGm4XMAHv4eCDuAwYdk5EYPT4ulYIiLiAXP6ziHEN4ROoZ24tdetno4jbnLG\nEeEHH3yQN998k/DwcFatWgVAt27dSEpKAqBfv34sXLiwaVOKeMCECWXs2hVK/p7h0GEdA10ziIkp\n9XQsERHxgP7R/UkOSyY9Ol2jwW3IGQvhESNGcMkllzB//vyafVarlddff71Jg4l42vjxx4iOdrBy\n1SIIHsSfnyzV+pQiIl5sxbAVhPmGeTqGuNEZC+FevXqxf//+5sgi0uJkZFSSkWECLvR0FBER8bCY\ngBhPRxA3a9DFcpWVlYwdOxZfX19mz55N3759T3mczWZrVDip5uPjA6g/3UF96V7qT/dSf7qP+tK9\n1J/upf50r+P92RANKoQzMzOx2Wxs27aNGTNmsGbNGiyWky8iWrJkSc3PGRkZDBkypMFBRUREREQA\n1q1bR2ZmJgAmk4mMjIwGtdOgQvj4J5i0tDSioqLYv38/HTuevJ7e9OnTa23n5+c35HRe73h/q/8a\nT33pXupP91J/uo/60r1aY39+952ZzEwLaWlVDBxY5ek4tbTG/mxpUlNTSU1NBar7c8OGDQ1qp96F\ncFFREVarFavVyv79+8nJySE2NrZBJxcRERFxt9de8+P++4M5fNhEUJCTyZNLWbjwqKdjSQt0xkL4\nvvvuY82aNRQVFTFkyBDGjx/PqlWrsFgsmEwmli1bhtVqbY6sIiIiImf05JMBP996GY4eNfLmm37M\nnXuUU8ziFC93xkJ48eLFLF68uNa+W27R3bVERESkZXI6T952ODyTRVo23WJZRERE2pQLLyxn924T\npaUmzGYXvXpV4teE98DYnLOZ1XtX19o3puMYekX1arqTiluoEBYREZE25Y47SoiPd7BunS9du9qZ\nMaOkSc/nY/ThhZ0vUFxZDECYbxjjOo9r0nOKe6gQFhERkTZn/PhjjB9/rFnO1SOyBz0ie5CZnVmz\nnRKR0iznlsYxejqAiIiISGt3V7+7CPMNI9w3nAX9Fng6jpwljQhLm1ZWVcbRijKKioyEhjpxWB2E\n+4V7OpaIiLQxPSJ7kBaRhtFg1GhwK6JCWNq0uasf5s19K3E5zBiNEBTs5J2r3+Qcn3M8HU1ERNqY\newfei8lg8nQMqQdNjZA27fsn78VZGoorIAeHXw72A6n0itZVvCIi4n5JYUl0Du3s6RhSDyqEpU07\nVhgOP1xUvVEWRsgX93k2kIiIiLQYKoSlTYuLs8NHSyG/ExzqSVe/8zwdSURERFoIFcLSpj3+eCEj\nMnyJzL+M/iWLeO45u6cjiYiISAuhi+WkTQsNdfH004XAbADCwjybR0REPGvPHhMLF4ZQVmagR48q\nFi8+gknXt3ktFcIiIiLiFcrLYerUcHbu9AFgyxYLPj6waNERDycTT9HUCBEREfEKWVlmDhw4Mfxr\ntxvYssXHg4nE01QIi4iIiFew2RwEBztr7QsJcZ7maPEGmhohIiIiXiE83MVNN5Xw+OOBHDtmIC7O\nwR/+UNzk5129dzVP73gaH+PPo88mmNF3BufZtJKRp6kQFhEREa9x/fVlTJhwjKIiA9HRzma5UK5v\nu77c++m9ZJdkA3BO8Dmkx6VDedOfW+qmqREiIiLiVQICXMTFNU8RDBDlH8WA6AE12xnnZBAVENU8\nJ5c6qRAWERERaWJ3p99NXGAc8YHxPDD0AU/HkZ9paoSIiIhIEzs+Kmw0GDUa3IKoEBYRERFpBksH\nLcWAwdMx5BdUCIuIiIg0g2BLsKcjyK9ojrCIiIiIeCUVwiIiIiLilTQ1Qlq07JJs5q69lx92+YIB\nunaxk9GhNzd2v9HT0URERKSVUyEsLZq9MJpNO/dRFb4dgOwDVga3G+bhVCIi0ha98oofr7/uh8Xi\nYtGiIyQmOjwdSZqYpkZIi/afp0Op2jwFHD9/ZstJIf/D6zwbSkRE2pxVq3xZvDiYDz+08u67fkyZ\nEk5hoVZ4aOtUCEuLFhDggk9vg9xuUGWF/95CYID+xyQiIu71xhv+FBaeuNXc7t0+fPqpxYOJpDmo\nEJYW7Xe/K6V7qgu+ngyFHenOJKZOLfV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- "text": [ - "" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can easily see the difference between the trajectory in a vacuum and in the air. I used the same initial velocity and launch angle in the ball in a vacuum section above. We computed that the ball in a vacuum would travel over 240 meters (nearly 800 ft). In the air, the distance is just over 120 meters, or roughly 400 ft. 400ft is a realistic distance for a well hit home run ball, so we can be confident that our simulation is reasonably accurate.\n", - "\n", - "Without further ado we will create a ball simulation that uses the math above to create a more realistic ball trajectory. I will note that the nonlinear behavior of drag means that there is no analytic solution to the ball position at any point in time, so we need to compute the position step-wise. I use Euler's method to propagate the solution; use of a more accurate technique such as Runge-Kutta is left as an exercise for the reader. That modest complication is unnecessary for what we are doing because the accuracy difference between the techniques will be small for the time steps we will be using. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from math import radians, sin, cos, sqrt, exp\n", - "\n", - "class BaseballPath(object):\n", - " def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)): \n", - " \"\"\" Create 2D baseball path object \n", - " (x = distance from start point in ground plane, y=height above ground)\n", - " \n", - " x0,y0 initial position\n", - " launch_angle_deg angle ball is travelling respective to ground plane\n", - " velocity_ms speeed of ball in meters/second\n", - " noise amount of noise to add to each reported position in (x,y)\n", - " \"\"\"\n", - " \n", - " omega = radians(launch_angle_deg)\n", - " self.v_x = velocity_ms * cos(omega)\n", - " self.v_y = velocity_ms * sin(omega)\n", - "\n", - " self.x = x0\n", - " self.y = y0\n", - "\n", - " self.noise = noise\n", - "\n", - "\n", - " def drag_force (self, velocity):\n", - " \"\"\" Returns the force on a baseball due to air drag at\n", - " the specified velocity. Units are SI\n", - " \"\"\"\n", - " B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))\n", - " return B_m * velocity\n", - "\n", - "\n", - " def update(self, dt, vel_wind=0.):\n", - " \"\"\" compute the ball position based on the specified time step and\n", - " wind velocity. Returns (x,y) position tuple.\n", - " \"\"\"\n", - "\n", - " # Euler equations for x and y\n", - " self.x += self.v_x*dt\n", - " self.y += self.v_y*dt\n", - "\n", - " # force due to air drag\n", - " v_x_wind = self.v_x - vel_wind\n", - " v = sqrt (v_x_wind**2 + self.v_y**2)\n", - " F = self.drag_force(v)\n", - "\n", - " # Euler's equations for velocity\n", - " self.v_x = self.v_x - F*v_x_wind*dt\n", - " self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt\n", - "\n", - " return (self.x + random.randn()*self.noise[0], \n", - " self.y + random.randn()*self.noise[1])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 21 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we can test the Kalman filter against measurements created by this model." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "y = 1.\n", - "x = 0.\n", - "theta = 35. # launch angle\n", - "v0 = 50.\n", - "dt = 1/10. # time step\n", - "\n", - "ball = BaseballPath(x0=x, y0=y, launch_angle_deg=theta, velocity_ms=v0, noise=[.3,.3])\n", - "f1 = ball_kf(x,y,theta,v0,dt,r=1.)\n", - "f2 = ball_kf(x,y,theta,v0,dt,r=10.)\n", - "t = 0\n", - "xs = []\n", - "ys = []\n", - "xs2 = []\n", - "ys2 = []\n", - "\n", - "while f1.x[2,0] > 0:\n", - " t += dt\n", - " x,y = ball.update(dt)\n", - " z = np.mat([[x,y]]).T\n", - "\n", - " f1.update(z)\n", - " f2.update(z)\n", - " xs.append(f1.x[0,0])\n", - " ys.append(f1.x[2,0])\n", - " xs2.append(f2.x[0,0])\n", - " ys2.append(f2.x[2,0]) \n", - " f1.predict() \n", - " f2.predict()\n", - " \n", - " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", - "\n", - "p2, = plt.plot (xs, ys, lw=2)\n", - "p3, = plt.plot (xs2, ys2, lw=4, c='#e24a33')\n", - "plt.legend([p1,p2, p3], \n", - " ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)'],\n", - " loc='best')\n", - "plt.show()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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7WKeVq0xZKSLxZyyvzsXy2t8Rx1NvbGMlG7PZzJQpUwgKCmLRokW27Rs2bGDQ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- "text": [ - "" - ] - } - ], - "prompt_number": 32 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I have plotted the output of two different Kalman filter settings. The measurements are depicted as green circles, a Kalman filter with R=0.5 as a thin blue line, and a Kalman filter with R=10 as a thick red line. These R values are chosen merely to show the effect of measurement noise on the output, they are not intended to imply a correct design.\n", - "\n", - "We can see that neither filter does very well. At first both track the measurements well, but as time continues they both diverge. This happens because the state model for air drag is nonlinear and the Kalman filter assumes that it is linear. If you recall our discussion about nonlinearity in the g-h filter chapter we showed why a g-h filter will always lag behind the acceleration of the system. We see the same thing here - the acceleration is negative, so the Kalman filter consistently overshoots the ball position. There is no way for the filter to catch up so long as the acceleration continues, so the filter will continue to diverge.\n", - "\n", - "What can we do to improve this? The best approach is to perform the filtering with a nonlinear Kalman filter, and we will do this in subsequent chapters. However, there is also what I will call an 'engineering' solution to this problem as well. Our Kalman filter assumes that the ball is in a vacuum, and thus that there is no process noise. However, since the ball is in air the atmosphere imparts a force on the ball. We can think of this force as process noise. This is not a particularly rigorous thought; for one thing, this force is anything but Gaussian. Secondly, we can compute this force, so throwing our hands up and saying 'it's random' will not lead to an optimal solution. But let's see what happens if we follow this line of thought.\n", - "\n", - "The following code implements the same Kalman filter as before, but with a non-zero process noise. I plot two examples, one with `Q=.1`, and one with `Q=0.01`." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def plot_ball_with_q(q, r=1., noise=0.3):\n", - " y = 1.\n", - " x = 0.\n", - " theta = 35. # launch angle\n", - " v0 = 50.\n", - " dt = 1/10. # time step\n", - "\n", - " ball = BaseballPath(x0=x, \n", - " y0=y, \n", - " launch_angle_deg=theta, \n", - " velocity_ms=v0, \n", - " noise=[noise,noise])\n", - " f1 = ball_kf(x,y,theta,v0,dt,r=r, q=q)\n", - " t = 0\n", - " xs = []\n", - " ys = []\n", - "\n", - " while f1.x[2,0] > 0:\n", - " t += dt\n", - " x,y = ball.update(dt)\n", - " z = np.mat([[x,y]]).T\n", - "\n", - " f1.update(z)\n", - " xs.append(f1.x[0,0])\n", - " ys.append(f1.x[2,0]) \n", - " f1.predict() \n", - "\n", - "\n", - " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", - "\n", - " p2, = plt.plot (xs, ys,lw=2)\n", - " plt.legend([p1,p2], ['Measurements', 'Kalman filter'])\n", - " plt.show()\n", - " \n", - "plot_ball_with_q(0.01)\n", - "plot_ball_with_q(0.1)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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VOaVGWAghGpjCQoWD21uxc58Xp7MsMQsJ8dCjh5OEBBdObIzuMKmeo7wyRQVE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\nowSS1iHnnIufzVkHwGO3j6RDYnSQE4mIiATHoG6J9OkYz74TBSzacow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Ofvr1U9iVv0sS4UuQzWbjueee41e/+hWjRo0iKSkJp9NJZGQkOp2OjRs3snr1\nalJTq//fpqSksGnTpmqlAFB7iYKmabjdbhRFweFw4Pf7eeuttygrK7vgeQ2ptvaio6MJCwur9V4A\nYmJiOHjwYLUa4REjRvCHP/yBL774gmuuuQav18vq1asZNGhQtVHt5lDvrBEGgyFYxFxeXo7JZGL3\n7t107NiRqKgo2rRpQ2xsLAcPHmySYIUQoiXwqb56R2UNOgN5ZWXc+/eV/P7dDbg9ftq31TF2rIsZ\nM8oZMaLye0lwFYvews6cnY0dumgAfVr3qff/3xfwVY3coxARoTF6dCV33VVB9+5e9Ho4fNjInDmh\nvPWRk11H8+tsR7Qs3/8/HzlyJCNGjOB3v/sdAM8//zx//vOfSU9P57333qtWM3zeo48+ypIlS+jY\nsSPPPvtstXbP//n+to4dOzJjxgzGjx9Pr169cDqdJCQk1Divrhgv5n5+eHwgEKBjx46kpqZy9uxZ\n7rjjDlJTU/nPf/4TPEav1/Pcc8/x0EMPkZqayrJly6q18dhjjzF79mx69+7NCy+8AEBISAhz5szh\n/fffp3v37vTv359PPvmkRSzIoWRlZdX79sHpdDJlyhSys7N58cUXCQQCbNiwgc6dOxMeHs7y5cuZ\nNGlSjXcFp06dIiMjo1GDv1I4HA4ACgsLmzmSS5/0ZcO6Uvtz0dFFHCg6UOcMEcdPedn0dQI5hZWE\nWIz85e4hlEVsJM+VV2ebftXP0JShTOg44Yrrz8bQ2K/NzTmb+erEV8Hlr89z+VwMiR9CrD2WeYfm\n1SifqahQ2LbNxJ49Jvz+qvOu6pbAwzelERWpEWmJJMoS1Sgx/xxN9b2en59PdHT0hQ8UV6zaXiMO\nh4P169eTmJj4o9u74MNydrudRYsWcfToUe677z5mzpwJwJQpUwBYvnx5ne9Azn/jiJ/nfD2O9OfP\nJ33ZsK7U/pxkn0TWxqwaSxlrGmzerLBqVSiqWkmvjrG8/8REUuIi2Xjaz6JDi4IzDfyQ0+tkQNIA\njEbjFdefjaGxX5vjHONo37o9K46vIMeZg6qpxNhjuCrpKnrE9kDTNNbmrcUb8FZbnMNqhWuu0Rg6\nJIByZiD/XLSd1XtOs+7AKfoNdNG7j5e4sFimdJpCm9A2jRL7T9FU3+vFxcUXPkhc0QwGQ43X4Q9X\nxftR7V3sgSkpKcTFxREfH8+SJUuC2+t79/b9of+hQ4cybJjUuQkhLn0RlggmdJzAosOLsBqs6BQd\nLhd8/rlpgCtSAAAgAElEQVSOo0erHvZ4cHImf7zzKsymqh+zfeP6svL4ylqn5PIFfCRFJBEbEtvk\n9yJ+uvRW6aS3SkfVqspcvp/wKorCjF4z+Of2f1LhrQi+AXL5XFgNVh4ecjduvxt37Ao2rLGzd6+e\njWvtHDtkY/z4Cl5zv8Zv+v0Gh1XeFAlRmzVr1rB27Vqgqlyjtnrli1FvIpybm4vJZCIyMpL8/HyO\nHz9OcnIyhw8fpqioCI/HQ25uLunp6bWe/6tf/ara1/Jx309zpX783BikLxvWldyf6bZ0wlLCWH16\nNbsOF/H5lybKyxXC7SZemTGMMZntqCgvpeJ759ycfDPvf/s+Zd4ybAYbGhpuv5s29jZMTJgYnBbp\nSuzPhtZSXpv3pN3DnoI9HCg6gIZG39Z96RHTA4PHwLt738Vq1Bg1ykmHDnpWrLCSk6PjnXcMZGYG\niNbN5ZbOU5o1/vOaqj/9fn+jti8ufX6/n8LCQrp06UKXLl2A70ojfop6E+Fz587x5JNPBr9+/PHH\ncTgczJo1i6lTpwLw+9///iddWAghLnWxtjYUZGUwd8F2AqpG744xvDFzBPGtQmo93mF18FDPh8gq\nyuJA0QH0ip4+rfsQFxInU6JdpvQ6PT1jetIzpvriAG6/m1xnbnCkODk5wO23V7B+vZldu0xs3Wrh\n8JESOs48R7/0llMiIcTlpt5EuEePHtXWtT5v3LhxjBs3rtGCEkKIli6/1MVDr69m7b4zADxwbXd+\nd0MmRkP9T0HrFB0ZjgwyHPIw8ZXME/CgUf1ZdZMJhg/3kJ7uZ9kyC0VFeq5/9gtuG5nBEzf1wWTW\nMOlN1UowhBA/j6wsJ4QQP9K6fWd48PVV5Je6iQq18Pf7r+Lq7j/+aWVx5QoxhtQ5D3FcXIBbbnGy\nbYuNLVuN/O+Kb/lk835GjCkhMUGjbWhbxiWPI9zcvPOvNgZN02qtoxcCQFXVBp8rWd5WCiHERTpy\ntoR7/76CKX9aTH6pmwEZbVj+p+slCRY/mkFnIDUiFW+g9iVxfbi5f2Iat91SSUyMn/JyHZ8tjGTr\nNyGcLDvFG3veoKSypImjbnwhISGUlpY2dxiiBVJVlby8PCIjIxu0XRkRFkKIOhS5i1h7Zi2nC8tZ\nsx427/IQUDUsRj0zr+vBQ5N6oG8BE8KLS9O45HHkuHIocBUEp+LTNA2X30X78PZUBiqxRZQzdaqJ\njRvNbN1q4ptvzGRn67lmrJPPj3/ObRm3NfNdNCybzYbX6yU///JeaMRgqEq/5OHAi6dpGg6H42dN\nlVYbSYSFEOIHNE1j6YmlrDuxjb07Iti920wgoKAoGkMy7bx820TiHLU/ECfExTLpTdzd5W625mxl\nd8FuPAEPdoOdUUmj6Bbdjf/e+d+Y9CYAhgzx0LatnyVLrJw9a+CDOWEMuzqfmzpW1llicamKiIho\n7hAaXUuZ1URIIiyEEDWsP7WFf31xkF07WuP1VtUqpqb6GDTIgzk0l1Pe/cTRr5mjFJcDg87AgLgB\nDIgbUGOf2+fGbDAHv05KCnDbbU6WLbNw9KiRZUvDmFW+lr/cdTV2S8OOkglxpZDP9IQQ4v94fAHe\n/mofdz27my3fhOD1KrRt62f69AomTHATGaliM9jYkrOlwR/YEOKHfrhyIYDVqnHddW5GjHCj12t8\nuuEkY2Z/zJ7jl3cpgRCNRUaEhRBXvICq8smGo7y4cBun8isAhTZt/Awe7CExMVDj+FJvKZ6A57L7\nSFq0LGmRaezO3x0sjzhPUaBrNw9dUkJZtiSMb08Vcd3Tn/Nftw3gthEZMuOCED+CJMJCiCuWpmks\n35HNC/O2knW6GIDU+AhSepwgPVVHffmEJBuisY1IGsGRkiO4/C6Muu9KH1RNxa/6ubffRB4aEMYf\nP9rMu8sO8Pt3N7Dl8CnGjQa9XqOroyvxofHNeAdCtHySCAshrkh7jufz1P9uYuuhXAASWoXw2xt6\nc/2gDry97y3KvGVA7cluK2srzHpzrfuEaChmvZkZXWew9MRSDhUfwqN6MCpGksKSGNduHBGWqofK\n/nj7ILq2j+LRt9bz6fpsNh3xM35COVtythBji+HWjFuxG+3NfDdCtEySCAshrih5JS7+PG8r/1l7\nCE0DR5iFhyf1ZPrwDMxGPQBDE4Yy/9D84PK33+f0ORmXLCtriqZhMViY1GESqqbiCXgw6Uzodfoa\nx7kiv+EXN5WweFEYuTkG/vNROBMmmLC0KeOdfe/wQI8HZEU6IWoh3xVCiCuC1x/gn1/uYcisecxd\ncwiDTsevJnRjw0s3c9eYLsEkGCA9Kp0x7cbgDXhx+91omkalvxJvwMvotqPJiJLlkUXT0ik6rAZr\nrUnwOec5siuyiY/VMX26k8REP06njvnzbezba6GospisoqxmiFqIlk9GhIUQlzW3z83i7Ud4ed5+\nTuSWAzCqVxJPTe9P+9i6l6jtG9uX7tHd2ZG7g3x3PtHWaHq17iUlEaLF2Za7DZuh6tMLm03jF79w\nsXatmR07zKxcaSU3V0+HsN1kOOQNnBA/JImwEOKy5PK5ePObj5m3pJTsk1VP3bdyaDw5rQ839O95\nUW2Y9eZa53cVoiUJqAGU79Wz63Rw1VUeYmJUli+3sG+fideKnYx4wklspNQKC/F9kggLIS47OaUl\n3PPvD9i5y4immTCbNQYM8NCtm4eD2pecLo8mITShucMUokF0cXRhT8GeGg/Ederkw+EI8NlnVk6e\ngbH/7xP+PnMQZZYDlHhKsBvsDIkfgsPqaKbIhWh+kggLIS4bAVXlw1VZ/HHuRipcJhRFo1s3LwMH\nerDZNEBBr1lYfHwxM7rNaO5whWgQKREphJvD8Qa8NR6Ii4kJMG16BXvWpvHNtzlM/9NyRoyqoEsn\njYAaYHfBbnpE9+C69tfJlIDiiiQPywkhLgtbD+UyZvYnPP7OeipcKgkJfqZPdzJyZOX/JcFVFEUh\n15VLube8GaMVouEoisKtGbeiV/S4/K7gdrffjaqp3NNrGk/PSKZTFxeBgMKypaGsX29Gp+gJMYaw\nt2Av68+ub8Y7EKL5yIiwEOKScX4KKaPOiEFX9eNL0zTeXLyX5+duIaBqJLQKoVu/HNJS1ToXxAho\nAdx+N6Gm0CaMXojGE2WJ4qGeD7E7fzffFn0LQPvw9mS2zsSkN7Ho2CJGj/QRG+Nm1SoLW7aYKSzU\nMXasG6vJyvbc7QyOGyyjwuKKI4mwEKLF8wa8LD2xlKziLCoDlegVPQmhCQyJGcUf/3cvS7edBOC+\n8d347Q29eefAm1QGKutsz6gzShIsLjsGnYHerXvTu3Xvats1TaPAXYDFYKFHDx+RkSpffGHj6FEj\nc+fqmDTJhcFaTrmvnDBTWDNFL0TzkNIIIUSL5lN9vLXvLfYX7ken6LAZbJj1ZvYdL2Dck5+xdNtJ\nwmwm3vnNKJ6c1g+ryUD36O64/e5a2wtoARLDErEarE18J0I0n+/XDrdtG2DaNCeRkQEKCvR88IGd\nc2eN6CQlEFcgedULIVq0dWfWUVxZjElvCm7bt8/I3LkhlJXqiY2BJX+czJjMdsH9A9oMID4knkp/\n9VFhn+pDQWFy+8lNFb4QzU5RFKJt0Wjad7XykZEqU6c6advWj9utY9EnUXy56UwzRilE85BEWAjR\noh0oOIDFYAHA54OvvrKwbJmVQEChSxcvE27IwRFZva5Rr9NzW8ZtDE0Yillvxqf60KGjc1RnHuj+\nAKFmKYsQV5bhicNrfEpiscDkyS66dnehqgqP/GstLy3c3kwRCtE8pEZYCNGiuQIu9Iqe4mKFL76w\nkZ+vR6/XGDmyks6dfZR5/Th9zho1v3qdniHxQxgSP6SZIhei5Wgf3p7xyeP5KvsrAmoAi96CV/UC\n8PjU3pzJjOX3763n5Y930LVdK0b3btvMEQvRNCQRFkK0aDaDjX0HA3z1lRWvVyEiIsC117qJjlaB\nqgeEQowhzRylEC1fr9a96NKqC9tzt5PryiXKEkWf2D5V9fKJUO728uyHm/nNm2tY9vz1xLeS7ytx\n+ZNEWAjRYvn8Kns2x/Ll2mIAOnTwMWaMG7O5ar+macTZ4wgxyS9sIS6GSW+qc9nwGWO7svHAWVbu\nOsUDr33Ngv83AYNeKijF5U0SYSFEk/OpPnbk7eBYyTH0Oj29onuREpFSbQ7TnGIn97+6ki1ZxSiK\nxsDBTvpmfjc3sKqp+FU/k1ImNdNdCHFpO1V+irVn1lLmLcOoGOke3Z0XZwxm7OzP2XoolxcXbufx\nm/o0d5hCNCpJhIUQTSq7LJu5WXPxql6sBiuapnGw6CDRtmju6HQHVoOVjQfOcv+rX1NQ5iY20sar\nDwyjxLKHbwu/xe13o9fpaRvalmvaXUOUJaq5b0mIS85XJ77im5xvsBlswanVvjr5FZHmLbxy3wSm\nv7Ccf3y+i4EZbRjaNaGZoxWi8UgiLIRoMpX+Sj44+AFGnTE4j6+iKNiNdso8ZczNmkurimE8+Noq\nfAGVQZ3jeP2B4bQKtwIJjG03Fq/qxagzVpsXVQhx8Q4XH2ZzzuYatfVWg5VyXzlnLBt55Be9eHHB\ndh58fTXL/3Q9DoejmaIVonHJbxIhRJPZdG4TqqbWuoyrQWfgq00F3P/qSnwBlV9e04WPHh/7f0lw\nFUVRMOvNkgQL8TOsO7MOm8FW6z6jzsjx0uPcMz6NQZ3jKChzM/P1VQQCahNHKUTTkBFhIUSTOVF2\nIjgn8A9t2WJi/fqqfY/emMlDE3vUmjALIX6eUk9pvd9bHtVDiaeYV++/mlG/X8iG/We5+/X/oVf/\nCpxOJwkhCQyJHyIPqYrLggyrCCGalabB2rXm/0uCNe6a1JpfT+opSbAQjcSgq38MTEHBqDfSOtLG\n03d2BWDu4hx2fltKmbeM3fm7+dvOv3Gs9FhThCtEo5JEWAjRZDpGdKy27LGqwvLlFrZtM6PTaYwY\nU8qs64Y2Y4RCXP7ahbXDp/rq3B9uDifGGkNADXBct4I+fSrRNIV58/RkZ+sx6o2Y9WbmZc3DG/A2\nYeRCNDxJhIUQTaZvbF9MehOapuH3w+LFVvbtM6HXa4ybUMboPm2IMEc0d5hCXNaGJw0HrWoe7h9y\n+V0MjR+KoijsL9qP2+9m8GAv3bur+P0Kn35qIztbj6Io+DU/23NlSWZxaZNEWAjRZEx6E7dn3E7A\nr+fjT8wcOmTEZNIYN7GQgV2juSn1puYOUYjLnt1o556u92Az2qjwVeDyuSj3lqOhMbrtaHq37g1U\nzS5hNVhRFBg/PlAjGbYarJwsO9nMdyPEz1NvoVBubi4PP/ww5eXlmEwmfvvb3zJw4EAyMjJIS0sD\noE+fPsyePbtJghVCXPqMWhjrlyRz+lQ+oXaFB29z8Iue1xFrj23u0IS4YjisDn7V/VfkOHPIceZg\nN9lpH9YevU4fPMakN6GiokcfTIYDAT/79pn49FMbEyc6Seqir+cqQrR89SbCBoOBZ555hrS0NM6e\nPcuUKVNYu3YtFouFTz/9tKliFEJcJnKLXUx7YTEHTxcT7wjhoyfGktJGSiGEaC6x9tg634T2i+3H\nzryd2I12ABQFRo2qqvHft8/EZ5/ZGZbQocliFaIx1Fsa4XA4giO/cXFx+Hw+vF4pjBdC/HgncsuY\n9F+fc/B0MR3iIvj06WslCRaiBYuxxdA+vH21B+LOJ8OdOlfi9ys8+sZO1u0704xRCvHzXHSN8Lp1\n6+jcuTMmkwmv18v111/P1KlT2bZtW2PGJ4S4DHybXcTkP3xOdn453du34pOnriXOIXOQCtHSTUmb\nQkpECm6/G6fPidvvxh1wcdukSKZc1ZFKb4A7XvpKkmFxyVKysrJqPjb6A/n5+dx11128/vrrJCYm\nUlhYiMPhYO/evcycOZPly5djMpmqnXPq1CkGDx7caIFfSYxGIwA+X93T3YiLI33ZsC6mP785cIZJ\nT82jpMLDsO5JLHj6F4TazE0V4iVFXp8NR/qyYXk0D/vz9+P1eukU3YkwcxiqqjHz1aW8s2Q3FpOB\nz569kWHd25LvyqfcU064JRyHVZZmro28PhuW0Whk1apVJCYm/uhzL7iynMfj4de//jWPPfZY8ALn\n1xzv2rUrMTExnD59mvbt29c499lnnw3+e+jQoQwbNuxHByiEuHQt2nSI219YhMvj49oBHXn/iYlY\nTLKgpRCXmhBTCP3i+1VL3HQ6hX88eA0A7yzZzeSn5jN9uobVkY+qquh1emJDYrmp003Eh8Y3V+ji\nMrVmzRrWrl0LgF6vZ+jQnzYHfb0jwpqmMWvWLDIzM5k2bRoApaWlmM1mLBYLp0+fZtq0aSxbtgyL\npfqyqadOnSIjI+MnBSWqO//Go7CwsJkjufRJXzasuvpTVTVe+WQHL3+8A4Abh3TkxXuGYtDLjI31\nkddnw5G+bFj19aeqatz3+lK+3HQak0njF79w0qaNClTlEZ6Ah/u63Sejw98jr8+G5XA4WL9+fcOP\nCG/fvp1ly5Zx7Ngx5s2bh6IoPPXUUzzxxBOYTCb0ej3PPfdcjSRYCHHlCagBclw5lDk9vDAnixU7\nTqMo8Pub+3L/hG6yZLIQlymdTqHfsHMcKfKSlWXi44/t3Hijk5gYFUVRMOlNLD25lOnp05s7VCFq\nqDcRzszMZN++fTW2L126tNECEkJcWjRNY93pdWzO2czpPDfLFzsoKTZitSi88eAIRvVIbu4QhRCN\nyBvwkuM6xzXXWAgEFI4cMbJggY2bbnLRqpWKTtGRXZ6NqlX9W4iWRF6RQoifZenRpaw+s5rjx418\nvqA1JcVGHI4Av7i5kBP6FbUu4yqEuHz4VB+qpqLXw7hxbpKTfVRW6liwwEZRUVWaoaoqAS3QzJEK\nUZMkwkKIn6zSX8n6UxvYtyOCTz+14vEopKT4mDrVSYzDwDnnOQ4WHWzuMIUQjchqsGIxVJVIGgxw\n7bVukpL8uFw65s+3UVKiYDPaMCjyoKxoeSQRFkL8ZBtPbuPzT02sX28BFAYOrOS669ycn03RZrCx\nLVfmGhficqZTdGREZQQX3jAYYOJEF/HxfpxOHfPm24jTZ8hzAqJFkkRYCPGTZOeV8avnt3E4y4TJ\npDFxoov+/b18/3edoij4NJknU4jL3Zh2Y3BYHbh9bgCMRpg82UXrWC8V5Xr++70ScoqdzRylEDVJ\nIiyE+NHW7TvD2Cc/5cSZSiIiA0yb5iQlxV/jOL/qJ8oc1QwRCiGaklFn5K7OdzEiaQR2ox29oifK\nHsJLM3vRNdlBdl45v/nnGnlmQLQ4UrAjhLhomqbx76X7ePaDzaiaxti+KXQbdgSvPwDU/NjTE/Aw\nNP6nTXIuhLi0GHQGBsQNYEDcgGrbu/7OzbDfzWftvjN8seU41/aruQCXEM1FRoSFEBfF7fXz63+u\n5r/mfIOqaTw0sQcLnv4F9/S5FW/Ai1/9bkRY0zQqfBWMSBpBlFVGhIW4krUKt/L4zX0AeOb9TVS4\nvc0ckRDfkURYCHFBZworuP4Pi1i4/gg2s4E3HxrBYzf1Qa/XkRCWwMyeM0mPTMekM6FX9MTYY7ir\n810MihvU3KELIVqAaVen0TMlmpxiV3DFSSFaAimNEELUa9vhXH758nIKytwkRYfyziOjyUiqPsob\nZgpjYoeJzRShEKIl0jSNwspCnD4nEeYInr9zEOOe/JS3lu7jxiGpNX6OCNEcJBEWQtRp4frD/Pbf\na/H6VQZ3juOfD40gMkSWVBdC1O9oyVGWnFhCYWUhATWAQWegjb0NN1/VnrmrjvH799bz8ZPXypRq\notlJaYQQogZV1Xhh3lYeemM1Xr/K7SM7MefRsZIECyEu6HjpcT48+CGV/kpCjCGEm8OxG+2UeEoI\nS9uGI8zMlqxc5q873NyhCiGJsBCiutzyYqa9+CmvfrYLvU7hudsH8vydgzAa5MeFEOLClp1chtVg\nrTHaq1N0WC0KY0dUfRj9x482U+L0NEeIQgTJbzYhBABuv5u/ffMeo5/8iHW7CzCZVK6bVE5KpyKZ\n+1MIcVEqvBXkufLqLHnQ6/S0aneW/umxFJZV8ud5W5s4QiGqk0RYCIFf9fOHZW/zj7c9FOQbiYgI\nMG2ai+R2KqtPr2bN6TXNHaIQ4hLgVb2oqPUe41d9PHfHIAx6hfdXfsvuY/lNFJ0QNUkiLITg7199\nzQdzTbhcOhIT/Uyd6iQqquqXmc1oY0vOFnyqLJUshKhfiDEEs85c7zGhplDSE6O4+5quaBo88e56\nAmr9ybMQjUUSYSGuYKqq8eKC7bw05ySBgELXrl6uv96F1Vr9OLffzaGiQ80TpBDikmHSm0iJSKnz\njbPb76ZXTC8AHrm+F7GRdnYfK+DDVVlNGaYQQZIIC3GFcnv83P+PlbzyyQ4UReOqqyoZObISvb7m\nsXqdHpff1fRBCiEuOde2v5YQYwiV/spq250+J8lhyfRv0x8Au8XI07f0A+CFeVspKq+s0ZYQjU0S\nYSGuQOeKnFz/7CK+2HycUKuRe6bZ6d7TTV1Tega0AImhiU0bpBDikmQxWLi3270MiR+C1WBFr+gJ\nM4VxbftrmZY+DZ3yXepxbb/2DO4cR0mFhxfkwTnRDGRBDSEuEwE1wL7CfezI24Ff9RNuDueqhKuI\nscVUO27P8XzufGkZOcUu2saE8t6sMURE+XhjzxuEGENqtKtqKjHWGGLtsU11K0KIS5xRZ2RowlCG\nJgyt9zhFUfjj7QMZ+cRCPlx1kGlXpdMjJbqJohRCRoSFuCx4Ah7+te9ffH70cwrdhZR5yzhRdoI3\n9rxRbcaHRZuPMfkPi8gpdtE/PZYv/jCJ1IRIYmwxDE8YToWvAlVTq7WLBjen3dwctyWEuAJ0jI/k\nnv97cG72extQVZmuUTQdGREW4jLw6ZFPKfWUYjPagtv0ip4QYwirTq2ibVhblq4r49kPNwMwZVgq\nf7prMCbDdwXBQxKG0D68PavPrKa4shidoqNbq24Mjh+M1WCtcU0hhGgoD0/uyScbj7DrWD4frc5i\n+vD05g5JXCEkERbiEuf2uzlachSzofYpi0KMIfz3kq+Z/3kARYEnp/VjxtiutU54Hx8az/T06Y0d\nshBCBJV4SijwFPDgL9KY/dZOnv/PFsb2aUdUqCzpLhqfJMJCXOLyXHl4Ap46E+FTpwx8/IUfUPjD\nrQO4a0yXpg1QCCFqUVRZxILDC8hx5qBqKqpZIykpluxs+PO8rfz5l0OaO0RxBZAaYSEucUadEU2p\nvaausFDHokU2VFXhnrFdJAkWQrQITp+Tf+/9N6WeUuxGO6GmUMLNYVx9dSU6ncYHqw7KinOiSUgi\nLMQlLtYeS7gxvMZ2p1Phk09seDwKPTLMPDmtXzNEJ4QQNX2d/TUaWrWp1AAcDpWePb1oGvxeHpwT\nTUASYSEucTpFx4C4Abh83y144fPBp5/aKCvT0TrWx3u/vg69Tr7dhRAtw9HSoxh1xlr3DRjgwWYP\nsOtoPnPXyIpzonHJb0YhLgMD4wYyLGEYftVPeaWTRV+Yyc3VEx6u8sFvJxAdGtHcIQohRJBf9de5\nz2SCfoNKAHh+7hZZcU40KkmEhbhMDE0YysM9HyZ3Xw9OHDcTZjPy+eybyGiT1NyhCSFENWHmsHr3\nZ6Sr9EtvTXGFh/tfXYnPHyC7LJtPjnzCgsML2F+4v9qc50L8VJIIC3EZ+d/lh/h8bS4mg453HxlD\nh/jI5g5JCCFq6BfbD6fPWes+v+qnfXgyr/5qOK3CrKzff5apr73Newfe42jJUU6UnmDh4YX8bcff\nKHQXNnHk4nIjibAQl4klW4/zXx98A8DLM4bRP6NNM0ckhBC169aqG10cXajwVaBp3z0QV+mvxGqw\nMqnDJOIdIbz50Ah0Oti0ReHU0XAURUFRFOxGOwEtwLv73623zEKIC5FEWIjLwI4jecx8bRWaBo/d\nlMnkQR2aOyQhhKiToihM7jCZmzreRJQlCqPOiN1oZ2jCUO7rdl9wNct2SQr9B1fVCy9bZiU/X1et\njcpAJbvydjXLPYjLgyyoIcQl7mReGXe89BWVvgDTrkrjwet6NHdIQghxQYqikOHIIMORUecxu/J3\n0bunSkmBlwMHTHz2mY3p051YrVWjyFaDlYPFB8mMzWyqsMVlRkaEhbiEFVdUcutfllJYVsmwrvE8\nf+fgWpdOFkKIS5VOURg5spLWrQOUlen48ksrqjwnJxpIvYlwbm4uU6dOZcKECVx//fVs3LgRgMWL\nFzNmzBjGjBnDqlWrmiRQIUR1Hl+Au19ZztFzpWQkRfHmQyMxGuS9rRDi8tGtVTcqA5UYDHDddS6s\nVpXsbAPr11ctKe/2u+kY2bGZoxSXsnpLIwwGA8888wxpaWmcPXuWKVOmsHLlSl566SXmz5+P5/+3\nd+fxUdX3/sdfZ7ZMJisJCUlYZJUtYV9EMAFFQFRKsVVxoYu1VerSXtvbq95fvb3U9tqqtde2Ll3U\ntlbaulAtiwQUAgpYNllCANnDkoQEyD7r+f2RSxQJ22SSk2Tez78yZyYz78cnA/POyfec4/UyZ84c\nJk2a1Fp5RQQIhUz+7YWVrC06RkYnD3/83lQSPC6rY4mIRFRWfBYZcRmcqD9BQoKDG26o4403PKxf\nH0N6epDL+8cwIn2E1TGlHTvv7qPU1FT69+8PQFZWFn6/n82bN9OvXz9SUlLIzMwkIyODoqKiVgkr\nIg1+9vp6FqzZQ5zbySvfm0ZWarzVkUREWsSdA+8k0ZVIjb+Gbt0C5OY2XGBj6dJYroifec4r1Ilc\njIs+WG7VqlUMHjyY8vJy0tLSmD9/PklJSaSlpVFaWsqAAQNaMqdIVKuoq2DtsbXUBerYVRjPr/5x\nELvN4IUHriG7Z6rV8UREWkysI5Z7htzD3lN72Vi6ke5XhbBXO1m+vpx/f34Di37cnU7xbqtjSjt1\nUUW4rKyMn/3sZ/zmN79h+/btANx6660A5Ofnn/PgnNRUfUBHgtPZ8Nuu5tl87W2WITPEa9teY1vZ\nNrXCTL8AACAASURBVFx2F7uKnCxYUA4YPPq1YXzpamvPENHe5tnWaZ6Ro1lGVluYZ+fOnRnTZwwA\nXxvl55rvvcrG3cf4/dKd/PTuqy3LFY62MM+O5PQ8w3HBIuz1ennwwQf5wQ9+QPfu3SktLaWsrKzx\n/rKyMtLS0pr83nnz5jV+nZubS15eXthBRaLRgp0LKDxeiMfpYccOgwUL7JimwYQJQao7r+RE3Rg6\nxerqcSISXWJjnPzvfVOZ8OAr/H7xxzx823gS42KsjiWtaOXKlRQUFABgt9vJzc0N63nOW4RN0+Th\nhx/mhhtuYMKECQDk5OSwe/duKioq8Hq9lJSUnHNZxNy5c8+4XV6uSyGG4/RvjJpf87WnWfqCPtbs\nW4PT7uTj7X4WLozFNA3GjvUyerSXgDfAm1veZGbfmZZlbE/zbA80z8jRLCOrLc6zV2cXY/tnsG7n\nMX791hq+eV2O1ZEuWlucZ3uTnZ1NdnY20DDP1atXh/U85y3CGzZsYOnSpezdu5e//e1vGIbBCy+8\nwEMPPcTs2bMBeOSRR8J6YRE5v0NVh6gP1LN/byyLFjWU4DFjvFx5pRfDAIfhoLi62OqYIiKWuef6\nIazbeYzfLd7G16cMxmHXKSTl0py3CI8aNYpt27adtX369OlMnz69xUKJSIP9+2JYviSWUMhg9Ggv\n48c3lGAREYHJw3vQOzOJvUdPsfCjfXxhXB+rI0k7o1+dRNqoHbtCLF+SSihkMGqUlwkTzizBwVCQ\nLp4u1gUUEbGYzWY0Lol4fuEWTNO0OJG0NyrCIm1Q/sYD3PerAkIhg2HDa7nqqrP3BHuDXq7pfo01\nAUVE2ogvXdWPlAQ3W/YdZ23RMavjSDujIizSxizbdJBv/nIZ/mCIu6YO4tbpKdQEqgmZIQDqA/V4\ng15u6ncTKbEpFqcVEbFWrMvBV68dBDTsFRa5FBd9QQ0RaXnvbT7E3c/k4wuEuGvqYH505zgMYzyH\nqw6z9thafEEfXeO7MiZjDG6HTiAvIgLwlcmD+PU7H7Ns00E+OXKSvlnJVkeSdkJ7hEXaiBVbDvGN\n/yvBX5sy6P9KcMN6iK4JXbmp303MHjCb3G65KsEiIp/ROSmWL13VD4AXF2+1OI20JyrCIm3Ayi3F\nfP3pfLz+IF+ZPIh5c6485xUbRUTkbKcPmnt91W6On6qzOI20FyrCIhYr2HaYrz+9FK8/yJzJA3n8\nqyrBIiIXUh+o52DlQQ5XHyYQCtA3K5lrR/TA6w/yyrJCq+NJO6E1wiIWWrXtMF978l3q/UHuuHoA\nj39lvEqwiMh5BEIB3tn7DjsqduANeDExiXfGM7LLSL55XQ75Gw/ycn4hc28cSqxLNUfOT3uERSzy\nwfYjfPWphhJ8+6QB/PRrE7DZVIJFRM7FNE3+vOPPFFUUEWOPITEmkaSYJOw2O2uOrqHCvZEhvTpT\nUVXP66t2Wx1X2gEVYRELfFh4hDlPLqHeF2T2xP78z9dVgkVELmR/5X4OVB7AZXeddV+sI5bNZZv5\n6tTLAXhh0Rb8gVBrR5R2Rn8zEGlla3ccZc6T71LvC3JL3uX87K6rVIJFRC7CR8c+Is4Zd877bYaN\ntB5lXJaewL5jlfzH/LcYP9YgKz6LEekjmizQEt20R1ikFX1YeIQ7f76EOm+Am3Mv58lv5KoEi4hc\nJF/Qd97jKJw2J9WBSr50vQeA1/PL2XhgH8sOLuPpDU/zcenHrRVV2gkVYZFW8s91e7n9icXUegPc\nNKEvT96tPcEiIpeis6cz/qD/nPfXBeqo8lVRm7CFAQN8BAIG773nwW2PxWl38vbetzlUdagVE0tb\npyIs0gpeXrqde55d3nixjF98Kw+7Tf/8REQuxVVZVxEwA03eZ5omHoeH0rpSYh2xTJzoxe0OceCA\ngx07nEDDOuL3Dr3XmpGljdMnsUgLMk2TJ/72Lx595UNME35w8yjmzblSJVhEJAzxrnim9ZxGja+G\nkPnpgXCBUID6YD1TekyhylcFgMdjkpfnBWDFihjq6gwMw6CkpsSS7NI26WA5kRYSCIb4we9XMX/l\nLuw2g59/4ypuuLIbJ7wnSHAl4LQ5rY4oItLujOoyiq5xXXm/+H3K6sowMOid1JtJ3SYRIoSJ2fjY\nQYP8FBY6OXTIwcqVMUybVn/G/SIqwiItoM4b4J5nl7Ns00HcLjv/dVc2JxNX8PSGUkKEcNvd9OvU\njxt63aCjmEVELlFmfCa3DbjtrO0hM0SCM6Gx7BoGTJ5cxx//GE9hoYsBA/wM65/c2nGlDdPfZ0Ui\nrKKqnlt+upBlmw6SHB/Dk/flsN/5LlW+KjxOD/HOeBw2B7sqdvH7bb8nEGp6vZuIiFwam2FjWNow\n6gJ1jds6dTIZN65hicSyZTGMSRtvVTxpg1SERSLo8PFqvvjf77BhdyldU+NZ8MMbOWSswePwnHXK\nH6fdSXldOf869i+L0oqIdDyTuk9iUMogqv3VBM0gAEOG15Ca6qey0sHb752yOKG0JVoaIRIhOw5W\ncMfPFnPsRC0Du6fw5x9Mw4ippuJgBQmuhCa/J9YZy5bjWxiXNa6V04qIdEyGYTCr3yxyu+ay+shq\nagO1pLhTmHjvAG55PJ/nF27B33kTl2XFMLrLaAalDsJmaL9gtNJPXiQC1u44yqx573DsRC1XDMjg\njf93Axmd4hqPXj4fb9DbCglFRKJLZ09nZvadyW0DbmPqZVMpdW5icE41IRPeXgxlNeW8+cmbvFL4\nipaoRTEVYZFmWvSvfdz2xGIqa31MH92TV39wHUlxMQCkuFPOexUk0zTxOD2tFVVEJCqtL1nP9uPb\nmZgbIiEhREmJna1bXcQ54zhafZR3D7xrdUSxiIqwSDO8sqyQb/5yGV5/kDmTB/L8A9fgdn264ijF\nnUKX2C6YZtOn66kN1DI2Y2xrxRURiUofHfuIWGcsLhdMnFgPwAcfuKmtNYhxxFBYXkgwFLQ4pVhB\nRVgkDKZp8vPX1/PISx9gmvD9L43kJ18d3+SFMmb1nYUv5Gs8aOO0On8d/ZL7kZ2a3VqxRUSijmma\nnPJ+eoBc374BevYM4PUarFrV8Ne7ukAdlb5KqyKKhVSERS5Rw4UyVvPMW5uwGQ0XyvjOF0eccwlE\nelw6c4fMpWdiT0JmCF/QR4w9hqt7XM2t/W8979IJERFpHsMwcNgcn7kNkybVY7ebbN/u4vBhOwaG\nLnIUpXTWCJFLUOcLMPfZ91i68QBup53n7r+GKSMvu+D3JbuTufnym1shoYiIfF63hG4crj7ceHaI\nTp1CjBrlY926GJYvd/PNr8UQ74q3OKVYQXuERS6CaZrsO36Mm378D5ZuPEByXAzzH7n+okqwiIhY\n69oe1+IL+s44XmPMGC+JiSGOH7dzau/lFqYTK6kIi1zAx2Uf89RHv2Lmj9/g4z0VxMcHmftVN8P6\nplgdTURELkKaJ407Bt6B0+ak2ldNXaAOL9VMmtRw4NwfFx2i5EStxSnFCloaIXIe60vW884ni3n3\nnc4cL3OQlBTi5ptrqXSc4KXtL3HX4Luw2+xWxxQRkQu4LPEyHhj+AMVVxZTUltDJ3YleY3tRczCf\nZZsO8uPX1vHs3ElWx5RWpj3CIucQDAV578AKVixN5dAhB3FxIW66qYaEBBOX3cWxmmNsO77N6pgi\nInKRDMOge2J3RmWMok9yH2yGjf+eMw63086bH3zC2h1HrY4orUxFWOQcPjn5CUvyHXzyiZOYGJNZ\ns2pJTv50fZnH4WFD6QYLE4qISHNdlp7IfTOGAfDIyx/gD4QsTiStSUVY5Bx+9WYROwvjcDhMZs6s\nJS3tzP8cDcPAF/JZlE5ERCLl3huGcFl6AjuLT/Dq+0VWx5FWpCIs0oTn/vkxb75fimEzueGGOrp2\nPfuKQ6ZpEu/U6XZERNo7t8vBI7eOAeDFRVsIhrRXOFpcsAg/8cQTjB8/nhtvvLFx28CBA5k5cyYz\nZ87k8ccfb9GAIq1t/oqd/Pi1jwC4fpqfXr38TT6uxl9Dbtfc1owmIiIt5LrRPbksPYEDpVUsWX/A\n6jjSSi5YhKdMmcILL7xwxja3282CBQtYsGABjz76aIuFE2ltS9bv5/u/WwXAf985jse+8MWGyyN/\n5hr0pmlS469hVMYoeiT2sCqqiIhEkN1m45vX5QDw/MItFqeR1nLBIjx8+HCSk5NbI4uIpT7YfoS5\nv3qPkGny3S+O4K5p2WTFZzF3yFz6JPfBwCBoBkmKSWJW31lc3+t6qyOLiEgE3Zx7OclxMWz8pJR/\n7SqxOo60grDOI+zz+Zg1axYxMTE89NBDjBo1qsnHpaamNiucNHA6G65/rnk237lmuXH3Me56Jh+v\nP8i3bhjBT755LYZhNDyWVPp07dPqWdsDvTcjS/OMHM0ysqJlnqnAt24cyRPzP+Sl/CKmjRvUIq8T\nLfNsLafnGY6winBBQQGpqals3bqV++67j/z8fFwu11mPmzdvXuPXubm55OXlhR1UpKXsOlTOjP/8\nK1W1Pr6cN5BfzP20BIuISHS5d8YIfvHGOt5es4tPDlfQt6uuItoWrVy5koKCAgDsdju5ueEdsxNW\nET79G0xOTg7p6ekUFxfTu3fvsx43d+7cM26Xl5eH83JR7/S8Nb/m+/wsj5RXM/NH73D8VB0Th3Tj\nZ18fx4kTFVZGbFf03owszTNyNMvIiqZ5OoGbxvfltRU7+dlrq/jp1yZE/DWiaZ4tJTs7m+zsbKBh\nnqtXrw7reS759GknT56kvr7h2tzFxcWUlJSQlZUV1ouLWKmiqp7b/mcxh8urGdE3nd8+OBmXQ5dL\nFhGJdqcPmvvbyl2UV9ZZnEZa0gX3CP/oRz8iPz+fkydPkpeXx80338w777yDy+XCbrfz+OOP43a7\nWyOrSMTU1PuZ8/Ml7D5ykv7dOvHH70/F4w5/jZGIiHQcl3frxDXDurN88yH+uGwH3501wupI0kIu\nWIQfe+wxHnvssTO2ffvb326xQCItzesL8I1f5LNpTxnd0+J59QfX0Slev8yJiES7vSf3surIKiq9\nlXQd6ILNNl5aup17bxiC2xXWalJp43RlOYkqwWCIu578JwXbDtM5MZa//Md0MlPirI4lIiIWW7hv\nIX/a8SfKasvwhXykZlSTluanvKqe1woKrY4nLURFWKKGaZo8+OulvF5QREKsk1d/MI3eGUlWxxIR\nEYvtOrGL9cfWE++KbzxrkGHA6NENVxb95dsfEQqZVkaUFqIiLFHj569v4HeLNuN2OXj5oalk9+xs\ndSQREWkDVh9eTZzz7L8O9usXICEhRFm5ycL1uyxIJi1NRVg6vAOVB/jWK3/glws2YTPgnjtSGdwn\n3upYIiLSRlT6Kps8f7zdDiNG+AB4ftHW1o4lrUBFWDq01YdX88N//JV/Lg0CcP0NAWK67OfZzc9y\npPqIxelERKQtsNvOferMnBwfLleIzbtPsHlPWSumktagIiwdVkVdBX9eu5r385MBuOqqeoYMMXHY\nHLhsLv6262+YptZ8iYhEu37J/fAFfU3e53LB0CEBAH67WHuFOxoVYemw/rJhGe/+sxPBoMGwYT5G\njfr0PznDMKj0VbKvcp+FCUVEpC3I65aHw+YgZIbOuq/WX8vc6aOw2wzeWbeXw+XVFiSUlqIiLB3S\nkfJqfv3nU/h8Nvr29TNxYj2fX/7ltDk5WHnQmoAiItJmxDpiuTv7bpJjkqnx11Dlq2pYN4zB9F7T\nmdJ/LDeM7U0wZPLy0u1Wx5UI0tmhpcM5VePlzp8tobIKsrICXHddHbYmfuULhoIkxiS2fkAREWlz\nkt3J3J1zNyfqT3Cs9hhxjji6JXTDZjR8gNx9XTb/WLOHP79XxHe+OII4XY20Q9AeYelQvP4gd/0i\nn6LiE/ToEsu11x/HeY7/q+w2O4NTB7duQBERadM6uTsxMGUgPRJ7NJZggOF90hnTvwuVtT7+unKn\nhQklklSEpcMIhUy+8/wK1uw4SpdkD399+EZ6pnZp8gCIukAdYzPGEmOPsSCpiIi0R9+8LgeA3y3Z\nRjB09npiaX9UhKXD+PFr63h77V7i3U7++P1p9EhL4quDvkrf5L54A14qvZWc8p4CYGK3iUzqPsni\nxCIi0p5MGXkZl6UncKC0ivyNOsakI9AaYekQfrt4Ky8s2orDbvDb715Lds9UAFx2F1++/MvUBeoo\nqy0jLTWNrIQsTlScsDixiIi0N3abjbumZvPDP63hxUVbmTaqp9WRpJm0R1javXfW7eVHr64F4Olv\n5pGb3fWsx8Q6YumR2INuid3OWPMlIiJyKW7Ju5xEj4t1O4/pAhsdgBqBtGtrdhzlgd+8j2nCw7eM\n5qYJ/ayOJCIiHdDh6sP8cccfeW77L+k3sBKAX7y9xuJU0lwqwtJu7Syu4K6nl+ILhPjqtYP49o1D\nrY4kIiId0JayLfxh2x8orSnFZtgYMcKPYZi8t/EYC3essjqeNIOKsLRLRytquP2JJZyq9XHdqJ78\n95xxGJ+/YoaIiEgz+YI+Fu1bhMfpafycSUgwufzyAKGQwW8Wb6DWX2txSgmXirC0O5W1Pu782RKO\nVtQwql8Xnv32JOxNXTFDRESkmTaUbCBgBs7aPmKEF4DCrbEs21fQ2rEkQnTWCGmTTNNkX+U+Npdt\nxjRNcjrn0C+5H75AiLt+sZQdhyrok5nESw9NIdalt7GIiLSMIzVHiHXEnrU9MzNEVlaAI0ccvLu2\nhBmXWxBOmk0NQtqcWn8tL29/mbL6MuIccQBsO76N5JhObF/dnw8Lj5KeHMurP7iOlAS3xWlFRKQj\nS3Ql4g/6cdrPvkzpyJE+jhxxsPpfAYJ3hPTXyXZIPzFpU0zT5JXCV6j2VxPvjMcwDAzDIN4Vz/IV\nBgvXHSTO7eRP359G97QEq+OKiEgHNy5zHP6Qv8n7+vQJkJgU4HhFiH+s2dvKySQSVISlTdlfuZ+y\n2jLsNvsZ2zdudLFhgxubzeSHX7+c7J6dLUooIiLRJN4Vz6guo6gL1J11nzdUx/V5iQA889ZGXXa5\nHVIRljbl47KP8Tg9Z2zbtcvBihUxAFx7bR2uzsVWRBMRkSg1rec0JnabiM2wUe2vptpXjWmajMsc\nx09m3UqPtAT2HD3F29or3O5ojbC0KSbmGbePHrWzeHEsYDBhQj2DBvnPeoyIiEhLMgyDCV0ncGXW\nlZyoP4GJSaeYTo1/vXxg5jC+99tVPLNgEzPG9dZa4XZEPylpU4Z0HkJtoOF8jHV1sHBhLMGgwZAh\nPkaP9lEbqGVw6mCLU4qISDSyGTZSY1PpHNv5jCV8N43vR2Z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- "text": [ - "" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The second filter tracks the measurements fairly well. There appears to be a bit of lag, but very little.\n", - "\n", - "Is this a good technique? Usually not, but it depends. Here the nonlinearity of the force on the ball is fairly constant and regular. Assume we are trying to track an automobile - the accelerations will vary as the car changes speeds and turns. When we make the process noise higher than the actual noise in the system the filter will opt to weigh the measurements higher. If you don't have a lot of noise in your measurements this might work for you. However, consider this next plot where I have increased the noise in the measurements." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plot_ball_with_q(0.01, r=3, noise=3.)\n", - "plot_ball_with_q(0.1, r=3, noise=3.)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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HkRye+M8vZRBDk1rzdB1lEBfr14li3P/W873UKYrCkzf3w2jQ8trCXcx8fQ12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Q5cuXYzQa2bVrFwCBgYEsXryYo0eP8uyzz/Lwww+Tk5PjOX/Lli289dZbbNiwgZUrV7Jn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\nJ9ojJoRNQJRvVJuZK2ySDRa7BbcPu90l56FvdFkIp6SkIDDwm3nxTp8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- "text": [ - "" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This output is terrible. The filter has no choise but to give more weight to the measurements than the process (prediction step), but when the measurements are noisy the filter output will just track the noise. This inherent limitation of the linear Kalman filter is what lead to the development of nonlinear versions of the filter.\n", - "\n", - "With that said, it is certainly possible to use the process noise to deal with small nonlinearities in your system. This is part of the 'black art' of Kalman filters. Our model of the sensors and of the system are never perfect. Sensors are non-Gaussian and our process model is never perfect. You can mask some of this by setting the measurement errors and process errors higher than their theoretically correct values, but the trade off is a non-optimal solution. Certainly it is better to be non-optimal than to have your Kalman filter diverge. However, as we can see in the graphs above, it is easy for the output of the filter to be very bad. It is also very common to run many simulations and tests and to end up with a filter that performs very well under those conditions. Then, when you use the filter on real data the conditions are slightly different and the filter ends up performing terribly. \n", - "\n", - "For now we will set this problem aside, as we are clearly misapplying the Kalman filter in this example. We will revisit this problem in subsequent chapters to see the effect of using various nonlinear techniques. In some domains you will be able to get away with using a linear Kalman filter for a nonlinear problem, but usually you will have to use one or more of the techniques you will learn in the rest of this book." - ] - }, - { - "cell_type": "heading", - "level": 3, - "metadata": {}, - "source": [ - "Tracking Noisy Data" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If we are applying a Kalman filter to a thermometer in an oven in a factory then our task is done once the Kalman filter is designed. The data from the thermometer may be noisy, but there is never doubt that the thermometer is reading the temperature of *some other* oven. Contrast this to our current situation, where we are using computer vision to detect ball blobs from a video camera. For any frame we may detect or may not detect the ball, and we may have one or more spurious blobs - blobs not associated with the ball at all. This can occur because of limitations of the computer vision code, or due to foreign objects in the scene, such as a bird flying through the frame. Also, in the general case we may have no idea where the ball starts from. A ball may be picked up, carried, and thrown from any position, for example. A ball may be launched within view of the camera, or the initial launch might be off screen and the ball merely travels through the scene. There is the possibility of bounces and deflections - the ball can hit the ground and bounce, it can bounce off a wall, a person, or any other object in the scene.\n", - "\n", - "Consider some of the problems that can occur. We could be waiting for a ball to appear, and a blob is detected. We initialize our Kalman filter with that blob, and look at the next frame to detect where the ball is going. Maybe there is no blob in the next frame. Can we conclude that the blob in the previous frame was noise? Or perhaps the blob was valid, but we did not detect the blob in this frame.\n", - "\n", - "**author's note: not sure if I want to cover this. If I do, not sure I want to cover this here.**" - ] - } - ], - "metadata": {} - } - ] -} \ No newline at end of file