{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Designing Kalman Filters" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "from __future__ import division, print_function\n", "from book_format import load_style, figsize\n", "load_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Author's note: clean up ball example, add control input example.**\n", "\n", "In the last chapter we worked with 'textbook' problems. These are problems that are easy to state, program in a few lines of code, and teach. Real world problems are rarely 'textbook'. In this chapter, and the remainder of the book, we will work with more realistic examples. \n", "\n", "We will begin by tracking a robot in a 2D space, such as a field or warehouse. 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", "\n", "We will then move to a nonlinear problem. The world is nonlinear, but the Kalman filter is linear. Sometimes you can get away with using it for mildly nonlinear problems, sometimes you can't. I'll show you examples of both. This will set the stage for the remainder of the book, where we learn techniques for nonlinear problems. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking a Robot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This first attempt at tracking a robot will closely resemble the 1D dog tracking problem of previous chapters. This will allow us to 'get our feet wet' with Kalman filtering. Instead of a sensor that outputs position in a hallway, we now have a sensor that supplies a noisy measurement of position in a 2D space. At each time $t$ it will provide an $(x,y)$ coordinate pair of the noisy 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 of 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. \n", "\n", "So let's start with a very simple sensor, one that travels in a straight line. It is initialized with the initial position, velocity, and noise standard deviation. Each call to `read()` updates the position by one time step and returns the new measurement." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from numpy.random import randn\n", "import copy\n", "class PosSensor1(object):\n", " def __init__(self, pos=(0, 0), vel=(0, 0), noise_std=1.):\n", " self.vel = vel\n", " self.noise_std = noise_std\n", " self.pos = [pos[0], pos[1]]\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] + randn() * self.noise_std,\n", " self.pos[1] + randn() * self.noise_std]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A quick test to verify that it works as we expect." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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fffaZOnToUOpcmzZtFBkZqdTU1JJjeXl5SktLU+/evatRMoAq+eILae5cs5Td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\nyIqMjLRmz55d0iY3N9cKCwu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import book_plots as bp\n", "\n", "pos, vel = (4, 3), (2, 1)\n", "sensor = PosSensor1(pos, vel, noise_std=1)\n", "ps = np.array([sensor.read() for _ in range(50)])\n", "bp.plot_measurements(ps[:, 0], ps[:, 1]);" ] }, { "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). It doesn't look realistic. This is still a 'textbook' representation. As we continue we will add complications that adds real world behavior. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 1: Choose the State Variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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", "$$\\mathbf{x} = \n", "\\begin{bmatrix}x & \\dot{x} & y & \\dot{y}\\end{bmatrix}^\\mathsf{T}$$\n", "\n", "There is nothing special about this organization. I could have used $\\begin{bmatrix}x & y & \\dot{x} & \\dot{y}\\end{bmatrix}^\\mathsf{T}$ or something less logical. I just need to be consistent in the rest of the matrices. I like keeping positions and locations next to each other because it keeps the covariances between positions and velocities in the same sub block of the covariance matrix. In my formulation `P[1,0]` contains the covariance of of $x$ and $\\dot{x}$. In the alternative formulation that covariance is at `P[2, 0]`. This gets worse as the number of dimension increases (e.g. 3D space, accelerations).\n", "\n", "Let's pause and address how you identify the hidden variables. This example is somewhat obvious because we've already worked through the 1D case, but other problems won't be obvious 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. Once you have chosen hidden variables, you must run many tests to ensure that you are generating real results for them. The Kalman filter runs whatever model you give it; if your model cannot generate good information for the hidden variables the Kalman filter output will be nonsense." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 2:** Design State Transition Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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 multiply 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. The state equations are\n", "\n", "$$\n", "\\begin{aligned}\n", "x^- &= 1x + \\Delta t \\dot{x} + y + 0 \\dot{y} \\\\\n", "v_x &= 0x + 1\\dot{x} + 1y + 0 \\dot{y} \\\\\n", "y^- &= 0x + 0\\dot{x} + 1y + \\Delta t \\dot{y} \\\\\n", "v_y &= 0x + 0\\dot{x} + 0y + 1 \\dot{y}\n", "\\end{aligned}\n", "$$" ] }, { "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", "$$\n", "\\begin{bmatrix}x \\\\ \\dot{x} \\\\ y \\\\ \\dot{y}\\end{bmatrix}^- = \\begin{bmatrix}1& \\Delta t& 0& 0\\\\0& 1& 0& 0\\\\0& 0& 1& \\Delta t\\\\ 0& 0& 0& 1\\end{bmatrix}\\begin{bmatrix}x \\\\ \\dot{x} \\\\ y \\\\ \\dot{y}\\end{bmatrix}$$\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", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from filterpy.kalman import KalmanFilter\n", "tracker = KalmanFilter(dim_x=4, dim_z=2)\n", "dt = 1. # time step 1 second\n", "\n", "tracker.F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 3: Design the Process Noise Matrix\n", "\n", "We will use FilterPy's functions to compute the $\\mathbf{Q}$ matrix for us. For simplicity I will assume the noise is a discrete time Wiener process - that it is constant for each time period. This assumption allows me to use a variance to specify how much I think the model changes between steps. Revisit the Kalman Filter Math chapter if this is not clear." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.0125 0.025 0. 0. ]\n", " [ 0.025 0.05 0. 0. ]\n", " [ 0. 0. 0.0125 0.025 ]\n", " [ 0. 0. 0.025 0.05 ]]\n" ] } ], "source": [ "from scipy.linalg import block_diag\n", "from filterpy.common import Q_discrete_white_noise\n", "\n", "q = Q_discrete_white_noise(dim=2, dt=dt, var=0.05)\n", "tracker.Q = block_diag(q, q)\n", "print(tracker.Q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I assume the noise in x and y are independent, so the covariances between any x and y variable should be zero. This allows me to compute $\\mathbf{Q}$ for one dimension, and then use `block_diag` to copy it for the x and y axis. The printed result shows how much noise we add during each evolution (prediction). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 4**: Design the Control Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We haven't yet added controls to our robot, so there is nothing to be done for this step. The `KalmanFilter` class initializes `B` to zero under the assumption that there is no control input,\n", "so there is no code to write. If you like, you can be explicit and set `tracker.B` to 0, but as you can see it already has that value." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n" ] } ], "source": [ "print(tracker.B)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 5**: Design the Measurement Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The measurement function $\\mathbf{H}$ defines how we go from the state variables to the measurements using the equation $\\mathbf{z} = \\mathbf{Hx}$. In this case we have measurements for (x,y), so we will design $\\mathbf{z}$ as $\\begin{bmatrix}x & y\\end{bmatrix}^\\mathsf{T}$ which is dimension 2x1. Our state variable is size 4x1. We can deduce the required size for $\\textbf{H}$ by recalling that multiplying a matrix of size MxN by NxP yields a matrix of size MxP. Thus,\n", "\n", "$$(2\\times 1) = (a\\times b)(4 \\times 1) = (2\\times 4)(4\\times 1)$$\n", "\n", "So, $\\textbf{H}$ is 2x4.\n", "\n", "Filling in the values for $\\textbf{H}$ is easy 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 slightly more interesting by deciding we want to change units. The measurements are returned in feet, and that we desire to work in meters. $\\textbf{H}$ changes from state to measurement, so the conversion is $\\mathsf{feet} = \\mathsf{meters} / 0.3048$. This yields\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", "$$\n", "\\begin{aligned}\n", "z_x &= (\\frac{x}{0.3048}) + (0* v_x) + (0*y) + (0 * v_y) = \\frac{x}{0.3048}\\\\\n", "z_y &= (0*x) + (0* v_x) + (\\frac{y}{0.3048}) + (0 * v_y) = \\frac{y}{0.3048}\n", "\\end{aligned}\n", "$$\n", "\n", "This is a simple problem, and we could have found the equations directly without going through the dimensional analysis that I did above. 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 useful to look at the matrix dimensions.\n", "\n", "Here is my implementation:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "tracker.H = np.array([[1/0.3048, 0, 0, 0],\n", " [0, 0, 1/0.3048, 0]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 6**: Design the Measurement Noise Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this step we model the noise in our sensor. For now we will make the simple assumption that the $x$ and $y$ variables are independent white 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 0. For now let's set the variance for $x$ and $y$ to be 5 meters$^2$. They are independent, so there is no covariance, and our off diagonals will be 0. This gives us:\n", "\n", "$$\\mathbf{R} = \\begin{bmatrix}\\sigma_x^2 & \\sigma_y\\sigma_x \\\\ \\sigma_x\\sigma_y & \\sigma_{y}^2\\end{bmatrix} \n", "= \\begin{bmatrix}5&0\\\\0&5\\end{bmatrix}$$\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", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[5 0]\n", " [0 5]]\n" ] } ], "source": [ "tracker.R = np.array([[5, 0],\n", " [0, 5]])\n", "print(tracker.R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initial Conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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", "\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", "The Python implementation is" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "tracker.x = np.array([[0, 0, 0, 0]]).T\n", "tracker.P = np.eye(4) * 500." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implement the Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Design is complete, now we just have to write the code to run the filter and output the data in the format of our choice. We will run the code for 30 iterations." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WoEEwciSULGkTUOLjDTb9BSt/CsNj8Vz+NEpz2KM019yKginx67dgXni5AbR5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\nw6KglXT6Mid3cv1jJWD91+D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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def tracker1():\n", " tracker = KalmanFilter(dim_x=4, dim_z=2)\n", " dt = 1.0 # time step\n", "\n", " tracker.F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])\n", " tracker.u = 0.\n", " tracker.H = np.array([[1/0.3048, 0, 0, 0],\n", " [0, 0, 1/0.3048, 0]])\n", "\n", " tracker.R = np.eye(2) * 5\n", " q = Q_discrete_white_noise(dim=2, dt=dt, var=0.05)\n", " tracker.Q = block_diag(q, q)\n", " tracker.x = np.array([[0, 0, 0, 0]]).T\n", " tracker.P = np.eye(4) * 500.\n", " return tracker\n", "\n", "# simulate robot movement\n", "N = 30\n", "sensor = PosSensor1 ([0, 0], (2, 1), 1.)\n", "zs = np.array([np.array([sensor.read()]).T for _ in range(N)])\n", "\n", "# run filter\n", "robot_tracker = tracker1()\n", "mu, cov, _, _ = tracker.batch_filter(zs)\n", "\n", "# plot results\n", "zs *= .3048 # convert to meters\n", "bp.plot_filter(mu[:, 0], mu[:, 2])\n", "bp.plot_measurements(zs[:, 0], zs[:, 1])\n", "plt.legend(loc=2)\n", "plt.gca().set_aspect('equal')\n", "plt.xlim((0, 20));" ] }, { "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", "execution_count": 11, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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f9DoD4AGyRCLBEUccwf3334+qqpRKJU444YQ+xy1dupR8Pk9zc3O/7XR2dvZ8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "\n", "# simulate robot movement\n", "N = 30\n", "sensor = PosSensor1([0, 0], (2, 1), 1.)\n", "zs = np.array([np.array([sensor.read()]).T for _ in range(N)])\n", "\n", "# run filter\n", "robot_tracker = tracker1()\n", "mu, cov, _, _ = robot_tracker.batch_filter(zs)\n", "\n", "for x, P in zip(mu, cov):\n", " # covariance of x and y\n", " cov = np.array([[P[0, 0], P[2, 0]], \n", " [P[0, 2], P[2, 2]]])\n", " mean = (x[0, 0], x[2, 0])\n", " plot_covariance_ellipse(mean, cov=cov, fc='g', alpha=0.15)\n", " \n", "# plot results\n", "zs *= .3048 # convert to meters\n", "bp.plot_filter(mu[:, 0], mu[:, 2])\n", "bp.plot_measurements(zs[:, 0], zs[:, 1])\n", "plt.legend(loc=2)\n", "plt.gca().set_aspect('equal')\n", "plt.xlim((0, 20));" ] }, { "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", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.25675401, 0.10095634, 0.25675401, 0.10095634])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.diag(tracker.P)" ] }, { "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 $\\dot{x}$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.25675401 0.10192183]\n", " [ 0.10192183 0.10095634]]\n" ] }, { "data": { "image/png": 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FVtmqQjSPRWkg3L9/P1atWgW/34+BgQG8/PLL86774osv4vrrr0dnZyeCwSA2bNiARx55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\nAj6Jf9glouXBtm+zYrGIhx9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5n+F2u/F7v/d7dpVERERERNTQbAvjO3bswNNPP40nn3wS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\nAAAAADJBMw4AAAAAIBM04wAAAAAAMvkPw44fWXfVpHYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "c = tracker.P[0:2, 0:2]\n", "print(c)\n", "plot_covariance_ellipse((0, 0), cov=c, fc='g', alpha=0.2)" ] }, { "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 $\\sigma_1\\sigma_2$.\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": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0., 0.],\n", " [ 0., 0.]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tracker.P[2:4, 0:2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Effect of Filter Order" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have only studied tracking position and velocity. It has worked well, but only because I have been selecting problems for which this is an appropriate choice. You know have enough experience with the Kalman filter to consider this in more general terms.\n", "\n", "What do I mean by **order**? In the context of these system models it is the number of derivatives required to accurately model a system. Consider a system that does not change, such as the height of a building. There is no change, so there is no need for a derivative, and the order of the system is zero. We could express this in an equation as $x = 312.5$.\n", "\n", "A first order system has a first derivative. For example, change of position is velocity, and we can write this as\n", "\n", "$$ v = \\frac{dx}{dt}$$\n", "\n", "which we integrate into the Newtonian equation\n", "\n", "$$ x = vt + x_0.$$\n", "\n", "This is also called a **constant velocity** model, because of the assumption of a constant velocity.\n", "\n", "A second order has a second derivative. The second derivative of position is acceleration, with the equation\n", "\n", "$$a = \\frac{d^2x}{dt^2}$$\n", "\n", "which we integrate into \n", "\n", "$$ x = \\frac{1}{2}at^2 +v_0t + x_0.$$\n", "\n", "This is also known as a **constant acceleration** model.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another, equivalent way of looking at this is to consider the order of the polynomial. The constant acceleration model has a second derivative, so it is second order. Likewise, the polynomial $x = \\frac{1}{2}at^2 +v_0t + x_0$ is second order.\n", "\n", "When we design the state variables and process model we must choose the order of the system we want to model. Let's say we are tracking something with a constant velocity. No real world process is perfect, and so there will be slight variations in the velocity over short time period. You might reason that the best approach is to use a second order filter, allowing the acceleration term to deal with the slight variations in velocity. \n", "\n", "In practice that doesn't work well. To thoroughly understand this issue lets see the effects of using a process model that does not match the order of the system being filtered. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we need a system to filter. I'll write a class to simulate an object with constant velocity. Essentially no physical system has a truly constant velocity, so on each update we alter the velocity by a small amount. I also write a sensor to simulate Gaussian noise in a sensor. The code is below, and a plot an example run to verify that it is working correctly. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VIU8e6NABwsOhfXtbIu3jk7QbuLnBCy8kfq55c9i3D/Lle9zHkHQo3SXTYEuo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\nIpJESqZFMpA7m6AAREZGUqBAAaKiogD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class ConstantVelocityObject(object):\n", " def __init__(self, x0=0, vel=1., noise_scale=0.06):\n", " self.x = x0\n", " self.vel = vel\n", " self.noise_scale = noise_scale\n", "\n", " def update(self):\n", " self.vel += randn() * self.noise_scale\n", " self.x += self.vel\n", " return (self.x, self.vel)\n", "\n", "def sense(x, noise_scale=1.):\n", " return x[0] + randn()*noise_scale\n", "\n", "np.random.seed(124)\n", "obj = ConstantVelocityObject()\n", "\n", "xs, zs = [], []\n", "for i in range(50):\n", " x = obj.update()\n", " z = sense(x)\n", " xs.append(x)\n", " zs.append(z)\n", "\n", "xs = np.asarray(xs)\n", "bp.plot_track(xs[:, 0])\n", "bp.plot_measurements(range(len(zs)), zs)\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I am satisfied with this plot. The track is not perfectly straight due to the noise that we added to the system - this could be the track of a person walking down the street, or perhaps of an aircraft being buffeted by variable winds. There is no *intentional* acceleration here, so we call it a constant velocity system. Again, you may be asking yourself that since there is in fact a tiny bit of acceleration going on why would we not use a second order Kalman filter to account for those changes? Let's find out.\n", "\n", "How does one design a zero order, first order, or second order Kalman filter? We have been doing it all along, but just not using those terms. It might be slightly tedious, but I will elaborate fully on each - if the concept is clear to you feel free to skim a bit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Zero Order Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A zero order Kalman filter is just a filter that tracks with no derivatives. We are tracking position, so that means we only have a state variable for position (no velocity or acceleration), and the state transition function also only accounts for position. Using the matrix formulation we would say that the state variable is\n", "\n", "$$\\mathbf{x} = \\begin{bmatrix}x\\end{bmatrix}$$\n", "\n", "The state transition function is very simple. There is no change in position, so we need to model $x=x$; in other words, *x* at time t+1 is the same as it was at time t. In matrix form, our state transition function is\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix}1\\end{bmatrix}$$\n", "\n", "The measurement function is very easy. Recall that we need to define how to convert the state variable $\\mathbf{x}$ into a measurement. We will assume that our measurements are positions. The state variable only contains a position, so we get\n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}1\\end{bmatrix}$$\n", "\n", "Let's write a function that constructs and returns a zero order Kalman filter." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def ZeroOrderKF(R, Q, P=20):\n", " \"\"\" Create zero order Kalman filter. Specify R and Q as floats.\"\"\"\n", " kf = KalmanFilter(dim_x=1, dim_z=1)\n", " kf.x = np.array([0.])\n", " kf.R *= R\n", " kf.Q *= Q\n", " kf.P *= P\n", " kf.F = np.eye(1)\n", " kf.H = np.eye(1)\n", " return kf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First Order Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A first order Kalman filter tracks a first order system, such as position and velocity. We already did this for the dog tracking problem above, so this should be very clear. But let's do it again.\n", "\n", "A first order system has position and velocity, so the state variable needs both of these. The matrix formulation could be\n", "\n", "$$ \\mathbf{x} = \\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}$$\n", "\n", "So now we have to design our state transition. The Newtonian equations for a time step are:\n", "\n", "$$\\begin{aligned} x_t &= x_{t-1} + v\\Delta t \\\\\n", " v_t &= v_{t-1}\\end{aligned}$$\n", " \n", "Recall that we need to convert this into the linear equation\n", "\n", "$$\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix} = \\mathbf{F}\\begin{bmatrix}x\\\\\\dot{x}\\end{bmatrix}$$\n", "\n", "Setting\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix}1 &\\Delta t\\\\ 0 & 1\\end{bmatrix}$$\n", "\n", "gives us the equations above.\n", "\n", "Finally, we design the measurement function. The measurement function needs to implement\n", "\n", "$$z = \\mathbf{Hx}$$\n", "\n", "Our sensor still only reads position, so it should take the position from the state, and 0 out the velocity, like so:\n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}1 & 0 \\end{bmatrix}$$\n", "\n", "This function constructs and returns a first order Kalman filter." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def FirstOrderKF(R, Q, dt):\n", " \"\"\" Create zero order Kalman filter. Specify R and Q as floats.\"\"\"\n", " kf = KalmanFilter(dim_x=2, dim_z=1)\n", " kf.x = np.zeros(2)\n", " kf.P *= np.array([[100, 0], [0, 1]])\n", " kf.R *= R\n", " kf.Q = Q_discrete_white_noise(2, dt, Q)\n", " kf.F = np.array([[1., dt],\n", " [0., 1]])\n", " kf.H = np.array([[1., 0]])\n", " return kf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Second Order Kalman Filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A second order Kalman filter tracks a second order system, such as position, velocity and acceleration. The state variable will be\n", "\n", "$$ \\mathbf{x} = \\begin{bmatrix}x\\\\\\dot{x}\\\\\\ddot{x}\\end{bmatrix}$$\n", "\n", "So now we have to design our state transition. The Newtonian equations for a time step are:\n", "\n", "$$\\begin{aligned} x_t &= x_{t-1} + v_{t-1}\\Delta t + 0.5a_{t-1} \\Delta t^2 \\\\\n", " v_t &= v_{t-1} \\Delta t + a_{t-1} \\\\\n", " a_t &= a_{t-1}\\end{aligned}$$\n", " \n", "Recall that we need to convert this into the linear equation\n", "\n", "$$\\begin{bmatrix}x\\\\\\dot{x}\\\\\\ddot{x}\\end{bmatrix} = \\mathbf{F}\\begin{bmatrix}x\\\\\\dot{x}\\\\\\ddot{x}\\end{bmatrix}$$\n", "\n", "Setting\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix}1 & \\Delta t &.5\\Delta t^2\\\\ \n", "0 & 1 & \\Delta t \\\\\n", "0 & 0 & 1\\end{bmatrix}$$\n", "\n", "gives us the equations above. \n", "\n", "Finally, we design the measurement function. The measurement function needs to implement\n", "\n", "$$z = \\mathbf{Hx}$$\n", "\n", "Our sensor still only reads position, so it should take the position from the state, and 0 out the velocity, like so:\n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}1 & 0 & 0\\end{bmatrix}$$\n", "\n", "This function constructs and returns a second order Kalman filter." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def SecondOrderKF(R_std, Q, dt):\n", " \"\"\" Create zero order Kalman filter. Specify R and Q as floats.\"\"\"\n", " kf = KalmanFilter(dim_x=3, dim_z=1)\n", " kf.x = np.zeros(3)\n", " kf.P[0, 0] = 100\n", " kf.P[1, 1] = 1\n", " kf.P[2, 2] = 1\n", " kf.R *= R_std**2\n", " kf.Q = Q_discrete_white_noise(3, dt, Q)\n", " kf.F = np.array([[1., dt, .5*dt*dt],\n", " [0., 1., dt],\n", " [0., 0., 1.]])\n", " kf.H = np.array([[1., 0., 0.]])\n", " return kf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evaluating the Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can run each Kalman filter against the simulation and evaluate the results. \n", "\n", "How do we evaluate the results? We can do this qualitatively by plotting the track and the Kalman filter output and eyeballing the results. However, a rigorous approach uses mathematics. Recall that system covariance matrix $\\mathbf{P}$ contains the computed variance and covariances for each of the state variables. The diagonal contains the variance. Remember that roughly 99% of all measurements fall within $3\\sigma$ if the noise is Gaussian. If this is not clear please review the Gaussian chapter before continuing, as this is an important point. \n", "\n", "So we can evaluate the filter by looking at the residuals between the estimated state and actual state and comparing them to the standard deviations which we derive from $\\mathbf{P}$. If the filter is performing correctly 99% of the residuals will fall within $3\\sigma$. This is true for all the state variables, not just for the position. \n", "\n", "I must mention that this is only true for simulated systems. Real sensors are not perfectly Gaussian, and you may need to expand your criteria to, say, $5\\sigma$ with real sensor data.\n", "\n", "So let's run the first order Kalman filter against our first order system and access it's performance. You can probably guess that it will do well, but let's look at it using the standard deviations.\n", "\n", "First, let's write a routine to generate the noisy measurements for us." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def simulate_system(Q, count):\n", " obj = ConstantVelocityObject(x0=.0, vel=0.5, noise_scale=Q)\n", " xs, zs = [], []\n", " for i in range(count):\n", " x = obj.update()\n", " z = sense(x)\n", " xs.append(x)\n", " zs.append(z)\n", " return np.asarray(xs), np.asarray(zs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now a routine to perform the filtering." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def filter_data(kf, zs):\n", " xs, ps = [], []\n", " for z in zs:\n", " kf.predict()\n", " kf.update(z)\n", "\n", " xs.append(kf.x)\n", " ps.append(kf.P.diagonal()) # just save variances\n", " \n", " return np.asarray(xs), np.asarray(ps)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And to plot the track results." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_kf_output(xs, filter_xs, zs, title=None, aspect_equal=True):\n", " bp.plot_filter(filter_xs[:, 0])\n", " bp.plot_track(xs[:, 0])\n", " \n", " if zs is not None:\n", " bp.plot_measurements(zs)\n", " bp.show_legend()\n", " bp.set_labels(title=title, x='meters', y='time (sec)')\n", " if aspect_equal:\n", " plt.gca().set_aspect('equal')\n", " plt.xlim((-1, len(xs)))\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we are prepared to run the filter and look at the results." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QunfvjqmpaZJOVLZsWcqWLcu4ceP47bffkq1AIYQQmc/Tp0+JiorCxsYGRVGw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\n/wcHQserPzMOmQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R, Q = 1, 0.03\n", "xs, zs = simulate_system(Q=Q, count=50)\n", "\n", "kf = FirstOrderKF(R, Q, dt=1)\n", "filter_xs1, ps1 = filter_data(kf, zs)\n", "\n", "plt.figure()\n", "plot_kf_output(xs, filter_xs1, zs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like the filter is performing well, but it is hard to tell exactly how well. Let's look at the residuals and see if they help. You may have noticed that in the code above I saved the covariance at each step. I did that to use in the following plot. The ConstantVelocityObject class returns a tuple of (position, velocity) for the real object, and this is stored in the array `xs`, and the filter's estimates are in `filter_xs1`." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_residuals(xs, filter_xs, Ps, title, y_label, stds=1):\n", " res = xs - filter_xs\n", " plt.plot(res)\n", " bp.plot_residual_limits(Ps, stds)\n", " bp.set_labels(title, 'time (sec)', y_label)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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e7RCJKpGRkY7Roz0werQaDJOHXbv2IjCQwS23+IDjKvH55/8ExzXhllsiwHEN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\nw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(xs[:, 0], filter_xs1[:, 0], ps1[:, 0], \n", " title='First Order Position Residuals(1$\\sigma$)',\n", " y_label='meters') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we interpret this plot? The residual is drawn as the jagged line - the difference between the measurement and the predicted position. If there was no measurement noise and the Kalman filter prediction was always perfect the residual would always be zero. So the ideal output would be a horizontal line at 0. We can see that the residual is centered around 0, so this gives us confidence that the noise is Gaussian (because the errors fall equally above and below 0). The yellow area between dotted lines show the theoretical performance of the filter for 1 standard deviations. In other words, approximately 68% of the errors should fall within the dotted lines. The residual falls within this range, so we see that the filter is performing well, and that it is not diverging.\n", "\n", "Let's look at the residuals for velocity. " ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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x6CUmhBBCCCHNi6CpA2iuikrLkJCaxpV7uKuuClTJ0coC+kIhykQiFJWVI3jv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(xs[:, 1], filter_xs1[:, 1], ps1[:, 1], \n", " title='First Order Velocity Residuals(1$\\sigma$)',\n", " y_label='meters/sec') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, as expected, the residual falls within the theoretical performance of the filter, so we feel confident that the filter is well designed for this system. Actually, almost all \n", "\n", "\n", "Now let's do the same thing using the zero order Kalman filter. All of the code and math is largely the same, so let's just look at the results without discussing the implementation much." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AY8fCq02MHz9+TKNGjbh58ya2traUKVOGAwcOvHe4gTl4GKwyex3MXgdPnhmW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\nMLnYzp07+d/SpYzq0wf3vHkxXl4cPn2aQkWKwJ13pr3ToEE3t5HnJZ0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kf0 = ZeroOrderKF(R, Q)\n", "filter_xs0, ps0 = filter_data(kf0, zs)\n", "plot_kf_output(xs, filter_xs0, zs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we would expect, the filter has problems. Think back to the g-h filter, where we incorporated acceleration into the system. The g-h filter always lagged the input because there were not enough terms to allow the filter to adjust quickly enough to the changes in velocity. The same thing is happening here, just one order lower. On every `predict()` step the Kalman filter assumes that there is no change in position - if the current position is 4.3 it will predict that the position at the next time period is 4.3. Of course, the actual position is closer to 5.3. The measurement, with noise, might be 5.4, so the filter chooses an estimate part way between 4.3 and 5.4, causing it to lag the actual value of 5.3 by a significant amount. This same thing happens in the next step, the next one, and so on. The filter never catches up.\n", "\n", "This raises a very important point. The assumption of 'constant' is an assumption of constant-ness between discrete samples only. The filter's output can still change over time.\n", "\n", "Now let's look at the residuals. We are not tracking velocity, so we can only look at the residual for position." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Nh79DfkmOvs5CKMJj/adjWO9xEPCCNt1/Rl4qdsT8hMuJsQb1YpEUD0dOwrDe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\nyMhwdykiIiIiImWiWgX6vn2H8MUXX2jteRERERGpMqrFHPrCwiIMwwP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(xs[:, 0], filter_xs0[:, 0], ps0[:, 0], \n", " title='Zero Order Position Residuals(3$\\sigma$)',\n", " y_label='meters',\n", " stds=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the filter diverges almost immediately. After a few seconds the residual exceeds the bounds of three standard deviations. It is important to understand that the covariance matrix $\\mathbf{P}$ is only reporting the *theoretical* performance of the filter *assuming* all of the inputs are correct. In other words, this Kalman filter is diverging, but $\\mathbf{P}$ implies that the Kalman filter's estimates are getting better and better with time because the variance is getting smaller. The filter has no way to know that you are lying to it about the system. This is sometimes referred to a *smug* filter - it is overconfident in its performance.\n", "\n", "In this system the divergence is immediate and striking. In many systems it will only be gradual, and/or slight. It is important to look at charts like these for your systems to ensure that the performance of the filter is within the bounds of its theoretical performance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's try a second order system. This might strike you as a good thing to do. After all, we know there is a bit of noise in the movement of the simulated object, which implies there is some acceleration. Why not model the acceleration with a second order model? If there is no acceleration, the acceleration should just be estimated to be 0, right?. But is that what happens? Think about it before going on." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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99hmmpqZYWVlhaWmJmZkZrq6u9O7dm4CAgDR/ACGEENmcqsKzZ2BgoJu8Dzx/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\ncVHwIiIiIiL3FfXA3Gl2O/z+O6xZA6tXO35u347x8ODtD88weJorycn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kf2 = SecondOrderKF(R, Q, dt=1)\n", "filter_xs2, ps2 = filter_data(kf2, zs)\n", "plot_kf_output(xs, filter_xs2, zs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Did this perform as you expected?\n", "\n", "We can see that second order filter performs poorly compared to the first order filter. Why? This filter models acceleration, and so the large changes in the measurement gets interpreted as acceleration instead of noise. Thus the filter close tracks the noise. Not only that, but it *overshoots* the noise in places if the noise is consistently above or below the track because the filter incorrectly assumes an acceleration that does not exist, and so it's prediction goes further and further away from the track on each measurement. This is not a good state of affairs.\n", "\n", "Still, the track doesn't look *horrible*. Let's see the story that the residuals tell. I will add a wrinkle here. The residuals for the second order system do not look terrible in that they do not diverge or exceed three standard deviations. However, it is very telling to look at the residuals for the first order vs the second order filter, so I have plotted both on the same graph." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CAEII0TF3MzWXXb5LQQAhpPP55JNPIJFIcOrUKXh6egIApk+fDl9fX8yfPx/x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8Tf8pcT7ogIaMDUMaGYEh4CGwtzo7eb1DX61AOcSUrBpZQM8vb8mAhEBWnv7hk7LBbRDThwitjx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\nARsbGwQHM9bn3Llz8dxzz9GT9tWr1+DTTz8Hn+8OP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OXlQavVwt3dHbIs48KFC3d9z6ef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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = xs[:, 0] - filter_xs2[:, 0]\n", "res1 = xs[:, 0] - filter_xs1[:, 0]\n", "\n", "plt.plot(res1, ls=\"--\", label='order 1')\n", "plt.plot(res, label='order 2')\n", "bp.plot_residual_limits(ps2[:, 0])\n", "bp.set_labels('Second Order Position Residuals', 'meters', 'time (sec)')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second order position residuals are slightly worse than the residuals of the first order filter, but they still fall within the theoretical limits of the filter. There is nothing very alarming here.\n", "\n", "Now let's look at the residuals for the velocity." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vRt++fREcHAxvb2+l9rNmzYK5uTkWL14MqVQKADh16hRGjRqFdu3aYcWKFUhP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\nIYQQQoiG+f/Q46CJerMl7wAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = xs[:, 1] - filter_xs2[:, 1]\n", "res1 = xs[:, 1] - filter_xs1[:, 1]\n", "plt.plot(res, label='order 2')\n", "plt.plot(res1, ls='--', label='order 1')\n", "bp.plot_residual_limits(ps2[:, 1])\n", "bp.set_labels('Second Order Velocity Residuals', 'meters/sec', 'time (sec)')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the story is very different. While the residuals of the second order system fall within the theoretical bounds of the filter's performance, we can see that the residuals are *far* worse than for the first order filter. This is the usual result for this scenario. The filter is assuming that there is acceleration that does not exist. It mistakes noise in the measurement as acceleration and this gets added into the velocity estimate on every predict cycle. Of course the acceleration is not actually there and so the residual for the velocity is much larger than is optimum." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I have one more trick up my sleeve. We have a first order system; i.e. the velocity is more-or-less constant. Real world systems are never perfect, so of course the velocity is never exactly the same between time periods. When we use a first order filter we account for that slight variation in velocity with the *process noise*. The matrix $\\mathbf{Q}$ is computed to account for this slight variation. If we move to a second order filter we are now accounting for the changes in velocity. Perhaps now we have no process noise, and we can set $\\mathbf{Q}$ to zero! " ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bWuDppsRFRORlpo0sRUQkyZ04cYJRo0ZFHbdr1oyTJ09imiZnLpp8NDYtbw/w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\nvfGG7cP9Tf7w3crcuXOZO3cuCxcuhOeewy00lF9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IkYSGhhIdHU2ePHkyu3qSVSQlwbJl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\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kf2 = SecondOrderKF(R, 0, dt=1)\n", "filter_xs2, ps2 = filter_data(kf2, zs)\n", "plot_kf_output(xs, filter_xs2, zs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To my eye that looks quite good! The filter quickly converges to the actual track. Success!\n", "\n", "Or, maybe not. Setting the process noise to 0 tells the filter that the process model is perfect. I've yet to hear of a perfect physical system. Let's look at the performance of the filter over a longer period of time.\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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o6Gg6duxosm3Xrl3MmjWL+fPn06lTJ5PPqlmzJj///DM9e/YEDCP258+fZ82a\nNTRp0iQdzki8qjSH+MKFC/PHH3/Qv39/pk+fbrKtdu3aTJs2jaJFM/ZXvDlz5sTb25tz584BkCNH\nDlJTU4mKijIZjY+IiKBWrVrPPE7FihUztE7x3/4Z2ZJrYX5yLTJOQqJi/S5YtBnW74bEJEN7xdj9\nLDjTGYDhdoUo0eEdfmY+6oDG3SpVuBMcJNcjC5C/G1lHTExMuh9z9E+KsXPS/bBGn3eD0d3Tbx76\ntGnTKFasmElbWh/I+SxLly7F0dGRhg0bmozyFylSBE9PT8LCwowhHiBPnjwS4LOQNId4MIyG//77\n70RGRhrnx/v6+pI9e/YMKe7fIiMjuX79Ojlz5gQMT4m1srJi06ZNdOjQAYBr165x6tSpJ5aiFEKI\nzPAgQbFxL6z4Hdb+AffiTLer5EiG3/gGC/SceLcP6y6Fs6btBXx9u0APfy5cumR8IqsQQvyjUqVK\nT9zYeunSpVc65pkzZ7h//z5eXl5P3f74fYgABQoUeKXPE+nrhUL8Pzw8PPDw8HjlD4+Li+Ps2bMA\n6PV6Ll++zOHDh3F3d8fNzY1Ro0bRunVrcuTIwaVLl/j444/x8vIyTqVxdname/fuBAcH4+npaVxi\nskyZMvj5+b1yfUIIkRaxcYr1uw3B/dfd8CDh6f3KF1bc2OqH7n8j4UJhSgwaxBF390fLw3l4wOXL\nmVa3EOLtptfrcXd3Z8mSJU/d7urqavJeVqLJWl4oxJ8+fZqxY8cSFhZGZGQkGzdupF69ekRGRhIc\nHEyfPn2oUqVKmo+3f/9+482wmqYxatQoRo0aRUBAADNmzOD48ePMnz+f6OhocubMSb169Vi+fDkO\njz3IZPLkyVhaWtKuXTvi4+Px8/NjwYIFGbKUkhBC/OPOPcWanbBiO2ze/2iqzOOcU6JpmTiPFrYH\nKDFqGPn9y7JkyaccPnmCFuPGAS85kiKEeGWju2uM7m7uKjLHszKRr68vW7ZsoUqVKibZSrwe0vz9\n48iRI9SsWRM7Oztq1KjBypUrjds8PDw4fvw4P/zwwwuF+Dp16qDX65+5/bfffvvPY1hbWzN16lSm\nTp2a5s8VQoiXcfOOYtUOw4h72CFISX16v5J5kpkUN466W75BlxAPgOr0Kxw7ZnLDvhBCZAYHBwfu\n3r37RHv79u354YcfGDt2LOPHjzfZlpqaSmxsLC4uLplVpnhBaQ7xI0aMIGfOnOzdu5eUlBSTEA+G\nO5kXL17W6d7LAAAgAElEQVSc7gUKIYS5KKU4fQU27oWV2yH8KDxt3MFGn0BJXx1N61tTrfBVTnap\nS/2H9w2pypW5ee0aHr17Y5ErVyafgRBCGObTL126lMGDB1O5cmV0Oh3t27enZs2a9O/fnwkTJnD0\n6FEaNmyIjY0N586d45dffuGLL76gS5cu5i5fPEOaQ3x4eDijR4/GxcXlqeuU5s2bl+vXr6drcUII\nkdluRyu2HjBMkdm8H64++5ETVCkOLetAx+NTyDVvKtp736KqtSfy/n0SXV2xWbECrU4dcmRa9UKI\nN9GLThH+d/9+/fpx7NgxFixYwLRp0wDDKDwYVr0pX748P/74IyNHjsTS0hIfHx/atWtn8vwfmaac\n9bzQdMznLWV069atV17qSAghMtvde4qdR2D7YQg7CIfPPruvpkHNMobg3tblEDm+GAKRbrB6taGD\ngwOaptFo4UKsS5cGT89MOQchxJsrICCAgICAp27Lly/fE9OSn9bfzs6OkJCQZ35GYGAggYGBz63j\n4sWLaSlXZKI0h/jy5cuzbt06+vfv/8S25ORkFi1axDvvvJOuxQkhRHpKSVH8dRkOnoKDpyH8CBw9\nD0o9e59sDlCvAjSqAs1rgZebRkpMDBRtAhERxn5/OzmR8+H6ya6yOpYQQogMluYQ/+mnn+Lv70+P\nHj2Ma7Jfv36dDRs2MG7cOE6fPs2PP/6YYYUKIURapaYqrkXC6ctw6gr8dQkOn4Ej5yDhKavIPM7C\nwjBNpkFlaFAJKhcDS0sNYmPB0hKwY9+JE/SxseHQ6NFYpqSAnR052rQBnS4zTk8IIYRIe4hv2LAh\n8+fPZ8CAAcyZY3jEWdeuXQFwcXFh4cKF1KhRI2OqFEKIf0lOUVz6G85ehXPXDf89f93wuvQ3JKek\n7TgWFlChCNQqC7XLQa0y4OTwcO5nRATEWEFyMslFiqBWrcK6bl2qVatGtcaNOd++PUWKFAFAZosK\nIYTITC80J75jx440a9aMzZs3c+bMGfR6Pb6+vjRq1Ihs2bJlVI1CiLeUXq+4ctMwkn7mKpy79uh1\nKQJSn7HE4/Pk8YLyhaF8EahcHKqVfCy0P+7OHShWDB48AL0eq5QUNs+dS4O6dQHkN49CCCHM6oWf\nM+Lg4EDz5s0zohYhxFssPlFx7Dz8eQYOnTFMfzlx8dlPP/0vXm7gmxuK+kCxfFAivyG4e7o+Z8w8\nKQmsrEDTuBAdTeSnn1Llo48e1ejo+HLFCCGEEOkszSH+5MmTnD17lmbNmhnbtm/fzldffUVMTAzt\n27dnyJAhGVKkEOLNkpKiOHER9pyAvScMN5mevPTiI+u5PaCQNxTMAwW9DX/2zQ0FcoGj/QtMcElK\ngvr1ITwcateGbdu4d+8ezb/9loshIdgGBICvL00fLs0mhBBCmFuaQ/ywYcPQNM0Y4q9du0aTJk2w\ntbXFw8ODDz/8EFdX12cugySEeHsppTh8FlbvhB1/wv5TEBeftn3dnaGYDxTxgUJ5Hob2h2Hd3jad\nZqKvXm0I8IA6cgTt7FnKli3LF198QVyTJtgeOAAeHoYJ9EIIIUQWkOYQf+jQIZOR9vnz55Oamsrh\nw4fJnTs3zZo1Y8aMGRLihRCAIbiHH4ElW2HtH89/aBIY1mAv5A3lCkO5IlCuEJQp9B/TX9LLTz8B\n8IePD7s6duSjhzer9ujRw7Dd3T3jaxBCCCFeQJpDfHR0NJ6PPbjk119/pV69euTOnRuAd999l+Dg\n4PSvUAjxWomNUyzYBD+sgOMXnt3P2xPeKQFVShiWcSxb6Bk3mGagzZs382DlSppt3Ag2NuRdvRrb\nlDQuayOEEEKYUZpDvIeHh/FpXXfv3mXv3r1MmDDBuD0xMRH1vCemCCHeaH9dUsxYAT9vgNgHT253\ncYL3qkKT6lC9NHh7mn9RxgIFCvDOkiX4+/tj3aoVecqUIY+5ixJCCCHSIM0hvlGjRkybNg0XFxfC\nwsJQSpnc5Hry5Eny5JFvf0K8TfR6xZpwmLYMwg49ud3BDjo2hHb1oWYZsLI0b3BPTk6mUaNGLFmy\nBA8PD3x9fdmybRtWpUrJg5qEEEK8VtIc4r/66itOnz7NsGHDsLa2ZuLEieTLlw+A+Ph4li5dSufO\nnTOqTiFEFpKUrAjdBN8shFOXn9xe1Af6toAu/uDsaP4Rd6XXo40Zg9X33/OzpjFr4kQ+HT8egDJl\nypi5OiGEEOLFpTnEe3l5sXPnTqKjo7Gzs8PGxsZk+7Zt28ibN2+6FyiEyDri4hWz18J3i5+8UdXC\nAprVgH6toG550DQzh3e9HnQ6li1bRuSyZfRbtgwAb2D41avmrU0IIV5Dv//+O/Xq1WPx4sW0bdvW\n3OW89V74YU8uLi5PtNnZ2VG2bNl0KUgIkfXcuaeYvhymLYeoGNNtTvbQpwUEtc4a89wBbm3Zgmdg\nIAwcSL2KFXF/GOAZOhTeew/Lx27SF0KIrEyXxql+c+fOpWvXrhlcjchKnhniw8LCqPvw8eIv6lX2\nFUJkHUnJium/wJchEB1rus3TFQa1NUybcXHKAuE9JQU6diSlQAE2T55Mp8REuHQJ9x49UE5OaJaW\nMHIkuLqau1IhhEizBQsWmLyfOXMme/bsYe7cuSbt1apVy8yyRBbwzBD/7rvvUrZsWfr06UOLFi3I\nli3bcw8UExPDypUrmTlzJkeOHOHBg6csTyGEeC0opVj3B3w4Dc5dM92WLycM6wiB74GdjRnC+717\nhsDu5mZs6t+/P+3ataNWeDiWy5bR6Z8N3bqBqyvaoUOGG1clwAshXjMdO3Y0eb9p0yb27dv3RPu/\nxcXF4eDgkJGlCTN75u9ozp07R6lSpejVqxceHh7UqFGDwYMHM3XqVObPn8/PP//MlClTGDx4MNWr\nV8fT05M+ffpQpkwZzp07l5nnIIRIRycvKvyHQrPhpgG+oDf8/DmcWQz9WmoZH+A3boRZs+DxpWuT\nk6FKFXB350aFCpCYCEDu3LlZtmwZfPEF5MoFNjaGqTPlyz8sviAUKJCx9QohhJkEBARgZ2fH5cuX\nadq0Kc7OzjRp0gSAo0ePEhgYiK+vL3Z2dnh4eNChQweuPuXeoJiYGD766CMKFCiAra0t3t7edOrU\niRs3bjzzs5OTk2nTpg2Ojo5s3bo1w85RPOmZI/G5c+dm1qxZfPXVVyxYsIBVq1Yxa9YsEhISTPrZ\n29tTpUoVJkyYQKdOnXCXJxsK8Vq6e08xeg7MWAGpqY/aXZzgswDo3wqsrdIQ3BMT4eZNePxGd70e\n4uLAyen5+27dCsuX83flyuTs1s3Qli8fi+/cISwsjJkxMXDqFAC5Dh2C/fuhRg369u1r6OvqCp06\nGT7P3j7tJy+EEK85vV5Pw4YNqVKlChMnTsTS0hDxtmzZwpkzZwgICCBXrlycO3eOH3/8kX379nH8\n+HHs7OwAw8h97dq1OXHiBIGBgVSsWJHbt2+zYcMGzp8/T65cuZ74zMTERFq3bs3OnTvZuHEj1atX\nz9Rzftv9542tHh4eDBkyhCFDhpCcnMyVK1eIiooCIHv27OTNm9f4hSKEeP0oBRsPujJtFERGP2rX\n6aBXMxjbA7K7pCG8p6bCzp3Qqxfq/HmuTJqEz8CBAEStWIF7mzbg5wchIVwHwsPDadeuHQDbt29n\n7ty5hPz4I/zvf+T88cdHxz16FM/y5XHctQuOHwcgoW1bzlauTKkaNQBwfXyajK3tK/3/EEK8HTRN\nM3lIZXq/z2zJycm8//77TJw40aS9b9++DB061KStadOmVK9enRUrVtCpk2EC4oQJEzh69CjLli2j\nVatWxr6ffPLJUz/vwYMHNGvWjEOHDrF582YqVaqUzmck/ssLpW8rKyt8fX3x9fXNqHqEEJnownXF\nwB8LsveUs0l73fIwaRCULviv8B4TAydPQtWqJs2Hly3Dc+BAckVEAKABl8eMwScoCDSNs7lzc93R\nkdJbtoCPD04lS7JarzeGeAcHB44ePQqaBtWrow8PR5eQAJs3g58fNZKSeCc8HHr2hMhIbH/+mVL/\nWuZWCCHedv369Xui7Z+RdoD79++TmJhIoUKFcHFx4dChQ8YQv3z5ckqWLGkS4J/l3r17NG7cmNOn\nTxMWFkbp0qXT7yREmskjCoV4CyWnKL5ZqCj1ASYBPo8XLPsStkx9LMAfPgwtW8KlS9ClC1SrRvSy\nZcyYMcO4X3ZLS0OAz5ULBg8mrn59KsTGwjXDpPqcuXKxbdAgqFULUlPJduQIoceOwdGjAJQqVYp1\n69YZ5rKPHo0uIgIiIgwj94C1tTX2zs6wdCmEhRn6CSHEK/j3qHl6v89sOp3O+BDOx929e5fevXvj\n7u5OtmzZ8PDwwNPTk+joaGJiHq0ZfP78eUqWLJmmzxo6dCi7d+9my5YtEuDNSObBCPEWUUqxJhw+\n/RFOXnrUrmmKoNYaX/QEJ4d/jb7nyEGqrS2pJUtiHRcHgGW1agwvWpSOHTvi4uKCt78/57t0ocC0\naWjZsuGglGGezsP1jX18fBj85ZeGtlOnDCPqp04Z5q4DNjY2pvMtnZ0NLyGEEGlibW391DXl27Zt\ny65duxg2bBjlypXD6eG9Se3bt0f/8N9geLEH9DVv3pzFixfz1VdfERoamua17EX6khAvxFvi2i1F\n4Few9YBpe6HcD/i03WW6tCpu0p6QkICVlRUW1tbodu7E4mGAp2dPHHPnZsqUKSQlJRnabG3xnTfv\n0c6aZnj9m6ZBsWKGufNJSTKiLoQQ6eRpvwm4e/cuW7duZcyYMXz22WfG9oSEBO7cuWPS19fXl2PH\njqXps5o0acK7775L586dcXBw4Keffnq14sVLkR+dhHjDKaVYtFlRpotpgHeyh/H9YN6Hf1Hc5wHc\nuAHffw8VK8IXX9CiUSPDcmFubmgbNnC5ZEni8+eH4cMB6NatG54v++RTTZMAL4QQL+lpo+ZPa7Ow\nsAAwGXEHmDRp0hOhv3Xr1pw4cYLly5enqYb27dszc+ZM5s6dy6BBg9JaukhHMhIvxBvsxAVF0Hfw\n+5+P2nQ6w3KRI7uCh6vGgQOAXk9MvXo4nz5t6HTzJv6DBxMeHk7Dhg2hZEl80jhCI4QQImM9bdT9\naW3ZsmWjTp06fPPNNyQlJZE3b17Cw8PZsWMH7u7uJvt89NFH/PLLL3To0IFNmzZRvnx5oqOj+e23\n3xg7diy1atV64vjdu3fn/v37DBkyBEdHR7766qv0PVHxXBLihXgDpaYqJoTCqNmQnPKoPa8XzP8c\napY1jNj8Mzpjf+bMowAPMGQIAwYPlnmOQgiRxWia9sSo+9Pa/hEaGsqgQYOYOXMmycnJ1K5dm23b\ntuHn52eyj729PTt27GD06NGsWLGCefPm4eXlRe3atSlcuLDJZz1u0KBBxMbG8vnnn+Pk5MSIESPS\n8WzF82jqBW6nPn36NGPHjiUsLIzIyEg2btxIvXr1uH37Nh999BF9+vShSpUqGVnvS3v8DmxnuWHO\n7A4cMMzrqFixopkrefOcvaro+gXsOfGozcICglrDqG7g7Gj4B/jEjh10++gjpk+fjgZU6NyZg6VK\nUcHfH61rV5DnP5iF/N3IOuRaZB1p/R6ekJCArTwrQrxBnvc1nebv0keOHKFmzZrY2dlRo0YNVq5c\nadyWPXt2jh8/zg8//JBlQ7wQbzq9XjFjBQyfAfGJj9orFYM5n0CJAhqxsbHo9Q7oEhMp7u9PCHDw\n8GGKliuHtnUrFb29zVW+EEIIIV5Amn9XPmLECHLmzMnp06eZOXPmE9sbN27MH3/8ka7FCSHS5nKE\nouFgGDjpUYC3tICxPeGPHw0BHqBT69Yc/+ADcHJCe/CAIsWKUbRcOcMOEuCFEEKI10aaQ3x4eDi9\nevXCxcXlqdvz5s3L9evX060wIcR/U0oxd72i9Aew7eCj9pIFYO9sGOm8Cl3ZUrBnDwBBH36I77Jl\nkJoKgK51a3OULYQQQohX9EJ3rT1vntmtW7dkHpoQmSg6VtH6E+g+DmIfGNp0OhjeGfb/BOX0p6Fl\nS3QnTkDVqnDhAn4NGmAfGGjoXLo0POUR3UIIIYTI+tIc4suXL294LPpTJCcns2jRIt555510K0wI\n8WwHTykqdIOVOx61FfSGHTPgs67xWOhSYcwY0518fdEOHUL7+mtYsAB274Zs2TK3cCGEEEKkizSH\n+E8//ZRNmzbRo0cPjhw5AsD169fZsGED9erV4/Tp03zyyScZVqgQwjB95oeViup94OKNR+19W8KR\nbr9TLd99unfvbnh63g8/wIQJ6JcsgYYNYdMmqFAB3NygUyewtzffiQghhBDilaR5dZqGDRsyf/58\nBgwYwJw5cwDo2rUrAC4uLixcuJAaNWpkTJVCCO4/UPT5BkI3P2pzsU1hlf/vlKrjhl3VRmBtzYiN\nG/n4q6/o3bs3DBtm+Em9bVtzlS2EEEKIDPBCC0F37NiRZs2asXnzZs6cOYNer8fX15fGjRvj5OSU\nUTUK8dY7fkHRdiScuvyorUxB2B7fi2wfhTxqrFmTMtWrs379+kyvUQghhBCZ54Ufx+jg4EDz5s0J\nDg5mxIgRtGnT5qUD/I4dO2jatCne3t7odDrmzZv3RJ/Ro0eTO3du7O3tqVu3LidPnjTZnpiYSFBQ\nEB4eHjg6OtKsWTNZJUe8UX7eoKjSwzTAB/jHs330dbLt3mLauXdv4Mkn6gkhhBDizfLCIT4xMZFz\n586xf/9+9u3b98TrRcTFxVG6dGmmTJmCnZ3dE8Fj/PjxfPfdd0yfPp39+/fj6elJgwYNuH//vrHP\n4MGDWbFiBYsXL2bnzp3cu3ePJk2aGB8nL8Tr6kGCosfXioAvH639bm8L8z4Dq6tD+H7xfPjzT9i4\nEZKSIDZWps0IIYQQb4k0T6eJiopi6NChLF68mOTk5Kf20TSN1IfrT6eFv78//v7+AAQEBJhsU0ox\nefJkPv74Y1q0aAHAvHnz8PT0JDQ0lF69ehETE8OcOXMICQmhfv36AMyfPx8fHx+2bNlCw4YN01yL\nEFnJyYuKdp/BiYsPG5SiXM4Yfp7gQokCGtULD6d79+4MHz4c3T9f51ZWZqtXCCGEEJkrzSG+W7du\nrFu3jvbt21O5cmWcnZ0zsi4uXrzIzZs3TYK4ra0ttWrVYteuXfTq1YuDBw+SnJxs0sfb25tixYqx\na9cuCfHitaOUIuRXGPDto9H3yrF7+e1CM+4ejMY5eAcUqEKBAgXYtm2bTJsRQggh3lJpDvGbN29m\n4MCBTJo0KSPrMYqIiADAy8vLpN3T05MbN24Y+1hYWODu7m7Sx8vLi5s3b2ZKnUKkl/sPFP0mwoKN\nhvfOKdFUSj7KmkstsY27g4OlJWtmzKBVlSqAzHsXQoi3QUhICN26dQMM9xI+bSXAggULcuHCBWrX\nrk1YWFhmlyge2rVrF5s3b2bw4MEZPtgNLxDi3dzcKFiwYEbWkmavGl4OHDiQTpWIVyXXwuDMdTs+\nCSnAlVuGpx7Xi97Kr3/5Y61SAEjMkYPDixeT194+w/6fybXIWuR6ZB1yLcyvUKFC5i7B7Ozs7AgN\nDX0ixO/Zs4cLFy5ga2srgztmtmvXLsaMGUNgYGCmhPg039jau3dvFi5c+EJz3l9Fjhw5AJ4YUb95\n86ZxW44cOUhNTSUqKsqkT0REhLGPEFmZUvBLeHa6fVfUGOABXOsX5tjAwfxlYUFUoUJc+uwzLBwc\n5B9oIYR4S/n7+7Ns2TJSUlJM2kNDQylatCi+vr5mqix9xMXFmbuEdKOUyrQPSpPU1FQVHBysSpUq\npcaPH69CQ0PVkiVLnni9LEdHRzVv3jzje71er3LmzKnGjRtnbIuPj1fZsmVTs2bNUkopFR0drayt\nrVVoaKixz9WrV5VOp1ObNm0yOX50dLTxJcxv//79av/+/eYuw6yiY/Wq3Ui90qo9etkUn6sm/XzZ\n2Of8+fNKr9dnaB1yLbIWuR5Zh1yLrCOt38Pj4+MzqaLMM3fuXKVpmlq+fLnS6XRq3bp1xm0pKSnK\ny8tLffnll6pkyZKqbt26xm16vV5NnTpVlSxZUtna2ipPT0/VvXt3dfv2bZPjr169WjVp0kR5e3sr\nGxsb5ePjoz766COVkJBg0i8iIkJ1797d2M/Ly0v5+/urEydOGPtomqZGjx79xDn4+PiogICAJ85p\n27ZtKigoSHl6eipN04zb9+3bp/z9/ZWzs7Oys7NTNWrUUGFhYSbHHDVqlNI0Tf3111+qU6dOytnZ\nWWXPnl198sknSimlrly5opo2baqyZcumvLy81IQJE56oKyEhQY0ePVoVLFhQ2djYqNy5c6shQ4ao\nBw8emPTTNE316dNHrVy5UpUoUULZ2NioEiVKqN9+++2Jev792r59u1JKqYMHDyp/f3/l4eGhbG1t\nlY+Pj/rggw/+82v2edvTPJ3m2rVr/P777xw/fpwRI0Y8tY+mabR9gSXu4uLiOHv2LAB6vZ7Lly9z\n+PBh3N3dyZMnD4MHD2bcuHEULVqUQoUK8eWXX+Lk5ETHjh0BcHZ2pnv37gQHB+Pp6YmbmxtDhw6l\nTJky+Pn5pbkOITLbgb8U7T+HCzceNijFcItFdEj8H6Hf/4jqvBtN0yhQoIBZ6xRCCJE1eHt7U7Nm\nTUJDQ3nvvfcA2LJlC7du3aJDhw4sWrTIpH/fvn2ZM2cOAQEBDBw4kCtXrjBt2jT27dvH/v37sbGx\nAQxz7u3s7Bg0aBDOzs7s3r2bSZMmcfXqVZNjtm7dmuPHjxMUFET+/Pm5desWO3bs4OzZsxQvXtzY\n72m/MdY07antQUFBuLm58dlnnxETEwPA9u3badSoEeXLl2fUqFFYWloyf/58GjZsyObNm6ldu7bJ\nMTp06ECxYsUYP34869ev5+uvv8bZ2ZnZs2fj5+fHN998w4IFCwgODqZChQrUrVsXMIyWt2jRgh07\ndtCrVy+KFy/OyZMnmTFjBidOnGDjxo0mn7N7927Wrl1Lv379cHR0ZOrUqbRq1YorV67g5uZGq1at\nOHv2LIsWLWLy5Mlkz54dgGLFihEZGUmDBg3w9PRk+PDhuLq6cuXKFdauXcuDBw+wtbXlpTw3/j+m\nfv36ysbGRn3yySdq1apVKiws7KmvFxEWFmb8SUWn0xn/HBgYaOwzevRolTNnTmVra6vq1Klj8hOf\nUkolJiaqoKAg5e7uruzt7VXTpk3VtWvXnvgsGYnPWt7WES69Xq8mL9Er61qGkfdiZY6qy1aeKs7O\nRSnD7Bp1sXHjDB99f9zbei2yKrkeWYdci6xDRuI1tXfvXjVz5kzl4OBgHCn+4IMPVNWqVZVSSpUo\nUcI4Ev/HH38oTdPUggULTI4VHh6uNE0zzmhQSj0x6qyUUuPGjVM6nU5dvXpVKaXU3bt3laZp6ttv\nv31urZqmqTFjxjzRni9fPpNs9885vfPOOyo1NdXYrtfrVZEiRVSDBg1M9k9KSlIlSpRQ1apVM7b9\nM/Ldo0cPY1tqaqrKkyeP0jTNZCZHdHS0sre3V507dza2LVy4UOl0OrVjxw6Tz1q4cKHSNM1kRoem\nacrGxkadP3/e2Hb06FGlaZqaPn26sW3ChAlK0zR1+fJlk2OuWrVKaZqmDh48+JT/a8+XLiPxu3fv\nJjg4mLFjx77cTwtPUadOnf98KNOoUaMYNWrUM7dbW1szdepUpk6dmm51CZERomIU3cfBmvBHbQF3\n55E3+RYkA7lywcCB5Bs0CGTuuxBCZKxn/Tv7rPnML9o/A7Rp04agoCBWrVpF8+bNWbVqFV9//fUT\n/ZYuXYqjoyMNGzbk9u3bxvYiRYrg6elJWFgYPXv2BAw3zIJhRkRsbCzJyclUr14dpRR//vkn3t7e\n2NnZYW1tTVhYGIGBgbi6uqbL+fTs2ROd7tHtmUeOHOHMmTMMHz7cpG4APz8/pk+fTkJCgsnIdY8e\nPYx/1ul0VKhQgevXr9O9e3dju7OzM0WKFOHixYvGtqVLl1K4cGGKFy9u8lm1atVC0zTCwsJo0KCB\nsb1u3bomvx0vVaoU2bJlMznms7i4uACwdu1aSpcujaVlmuP3c6X5KF5eXri5uaXLhwrxtgk/oug4\nGq7dAqVSICWaiiWz06t4KsyGMwEB/H979x0eZZW3cfw7k94INQQSauhNWgSytNAEREBBIQpSRRQp\niyyCogQIYFARlCJS3EhZKeKLi4gB6SJK7wRZotRECDUYEsic9w+WWUIoESGTcn+uK9eVOXPmeX7P\nHCN3Ts6cp9yMGeDq6uhSRUQki8qXLx9PPPEE8+bNw2q1kpSURKdOndL1O3z4MImJiem26b7pzJkz\n9u/37dvH0KFDWb9+PUlJSWn63Vzi4ubmRmRkJEOGDKFw4cLUqVOH1q1b07VrVwIDAx/4em7/MO7h\nw4cB0gTwW1ksFhISEggICLC3FS9ePE0fX19fXFxc8PPzS9OeJ0+eNNd9+PBhYmJiKFSo0B3Pc2vf\nO50HbozH+fPn71jrrRo1akTHjh0ZNWoUEydOpFGjRrRt25bnn38eT0/P+77+bjIc4ocMGcKUKVPo\n2bMnefLkeeATiuQmNpvh3bkwcjakpkL5Pw6xcl8Dlnl78tL6o3h4fAhTIykHCvAiIpnpz86gZ+KM\n+708//zzvPjii1y6dInmzZvb117fymazUaBAARYuXHjHY9ycSb948SKhoaH4+Pgwbtw4ypQpg4eH\nBydOnKB79+5pVksMHDiQdu3asWzZMlatWsWYMWMYN24cy5cvT7dO/Xa376hz082/AtxaN0BkZCS1\natW642tuv14nJ6d0fe62k5u5ZQxtNhuVK1dm8uTJd+xbtGjR+57n9mPey6JFi9i6dSvLly9n1apV\n9OnTh/Hjx7Nly5Y7/iKRERkO8ZcvX8bNzY0yZcrQoUMHihcvfscLGjp06AMVIpLTxJ8zdB0Fq7eB\nMalYLE4MOjedEtcTGHAhgeN7d1Ds8ccV3kVEJMPatWuHm5sbmzdvJioq6o59goKCWL16NXXq1MHL\ny1Cwp18AACAASURBVOuux1q7di0JCQksXbqUBg0a2NtXrVp1x/4lS5Zk4MCBDBw4kJMnT1K9enXG\njh1rD/H58uXjwoULaV6TkpLC6dOnM3RtN2fmvb29adKkSYZe86DKlCnD9u3bH+p57rcNdHBwMMHB\nwYwaNYqVK1fSunVrZs6cyZtvvvlA58twiB8+fLj9+xkzZty1n0K8COyIMXQceo3nd03gWIGOxMS+\nzlNVWvPysY9vdPj00xsBXkRE5E/w8PBg+vTpHD16lPbt29+xT+fOnZk+fTqjR48mMjIyzXOpqalc\nvnyZvHnz2idjb51xt9lsTJw4Mc1rbi6zuXXmPCAggEKFCtmX3MCNEL5+/fo0r/3000/v+/nHm2rX\nrk2ZMmWYOHEiXbt2xdvbO83zZ86cydCsdUbuqdKpUydWrFjB9OnTeeWVV9I8l5yczLVr19Kd/35u\n/sJ07ty5NMtvLly4gK+vb5q6atSoAZDm/fuzMhzijx49+sAnEclNFn1v6DEWOh7/F40urueb/G3o\n0nMIE6e0/F+nWz6IIyIi8md06dLlju03l3Y0aNCAfv368d5777Fnzx5atGiBm5sbR44c4csvv2TM\nmDG8+OKL1K9fnwIFCtCtWzf69++Ps7MzS5YsSXfjpZiYGJo0acJzzz1HpUqVcHNzY8WKFRw6dIgP\nPvjA3q9379707duXjh070qxZM3bv3k10dDQFCxbM0LITi8XC7NmzadmyJZUqVaJnz54EBARw6tQp\n+y8Ha9asue9x7nauW9u7dOnCkiVL6NevH+vXr7d/mDcmJobFixezZMkSGjZs+KfOExwcDNyY+A4L\nC8PV1ZWmTZsyf/58pk6dyjPPPEPp0qVJSkris88+w9nZmY4dO973eu4mwyG+ZMmSD3wSkdzAZjOE\nz4aIf4KxJfPy8XcIST7G/MbrqfTBQFKf3wxhYTBkiHafERGRDMvIzPLte7F//PHH1KxZk08++YQR\nI0bg7OxMiRIl6NSpk30JSb58+fjmm294/fXXGTlyJD4+PnTo0IG+fftSrVo1+7GKFy9Oly5d+P77\n71mwYAEWi4Xy5cvb96G/6aWXXiI2NpbZs2ezcuVKGjZsyKpVq2jatGm6a7jbNTVo0IAtW7YwZswY\npk2bxqVLlyhSpAjBwcFpdqK5297zGW23WCwsXbqUSZMmERUVxbJly/Dw8CAoKIh+/fpRtWrV+7zj\n6a+hVq1ajB8/nmnTptGzZ0+MMaxdu5bGjRuzbds2Fi1aRFxcHHny5KFmzZpMnTrVHvwfhMVkdEV+\nNnfrnyt8fX0dWIkAbNu2Dbjxp7OcIPEPQ7cx8NWGG4+XH2hN6wsrbzw4eBAqVHBccfeR08Yiu9N4\nZB0ai6wjo/+G3779oEh2d6//pu86Ex8aGorFYiE6OhpnZ2f747sxxmCxWDL0Zw6RnOTX04b2w2DP\nETApv2Nx9cPP18DNz/aUL+/Q+kRERCTnsd7tCWNMmrU+xhhsNttdv27vL5IbbNxlqNsrlafWRvDa\nb2/D7ur0anGS6sveB19fGDVKS2dERETkobvrTPy6devu+VgkN7PZDB8thjenXmfe/k48c+4rEq1e\nXO70Ok8+tg3nx9rD+fMK8CIiIvJIZPiDrRs2bKBixYp33drnzJkzHDx48L6f5BXJ7q4kGbqOhv/b\nAB2OjeWZc19xwTkvx6cs4rOX/3eLZgV4EREReVTuupzmdo0bN77r5v8A33//PaGhoQ+lKJGs6uhJ\nw9/63gjwAM/8sRuAU927UfXWAC8iIiLyCGV4Jv5+UlJSMrQFkkh2Ff2TIWwknDt3Fkwqbs55efrK\n9wBUHNbfwdWJiIhIbnLPEH/x4kUuXrxo/8Dq2bNnOXbsWLp+586d41//+hcBAQGPpkoRBzLGMP3j\nE7T9Rz3e921OT4+KWC4uZ+YHc3GfXQXi47H891bRIiIiIpnhniF+0qRJjBo1yv540KBBDBo06K79\nx48f//AqE8kCriQZeo2DmnM+JjDlJD3O/BOX4i8R3bEeLZ90g+Qu0KCBo8sUEZH/urnltUh2d79d\nH+8Z4ps3b46XlxcAQ4cOJSwsjBo1aqTpY7FY8PLyIjg4mFq1av3FckWyjv+cMDzzJqTsPcTs05Ps\n7Z18t9Fl1o4bD1591UHViYjI7VxdXe03x1GQl+zMGMPVq1dxc3O7a597hviQkBBCQkIASExMpEOH\nDhm6Da1Idrdyi+H5cLhwGaqYa3iY62x2cqXqTz/hE1jE0eWJiMgdWK1W3NzcSE5OdnQpIn+Zm5sb\nVuvd96DJ8Adbw8PDH0Y9IlmaMYbIefDWDLBd2Q8eFTictyqbBs2hUt96+OjuqyIiWZrVar3rbepF\ncpKHtjuNSHaX+IdhQt+NfLHPH+NRFn59A5+CVVi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MC62m/dtFRERE5JHIMSF+2rRpvPfe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\niEiWpDXxIiIiIiLZjEK8iIiIiEg2oxAvIiIiIpLNKMSLiIiIiGQzCvE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Pl7rN0tqLX/PKK69cc1+dOnWqXDncSsW5lfXgtNL2u7OzM1988QVRUVGcPn2aBQsW0KVL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(25944)\n", "xs500, zs500 = simulate_system(Q=Q, count=500)\n", "\n", "kf2 = SecondOrderKF(R, 0, dt=1)\n", "filter_xs2, ps2 = filter_data(kf2, zs500)\n", "\n", "plot_kf_output(xs500, filter_xs2, zs500)\n", "plot_residuals(xs500[:, 0], filter_xs2[:, 0], ps2[:, 0], \n", " 'Zero Order Position Residuals',\n", " 'meters') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the performance of the filter is abysmal. We can see that in the track plot where the filter diverges from the track for an extended period of time.The residual plot makes the problem more apparent. Just before the 100th update the filter diverges sharply from the theoretical performance. It *might* be converging at the end, but I doubt it. The entire time, the filter is reporting smaller and smaller variances. **Do not trust the filter's covariance matrix to tell you if the filter is performing well**!\n", "\n", "Why is this happening? Recall that if we set the process noise to zero we are telling the filter to use only the process model. The measurements end up getting ignored. The physical system is *not* perfect, and so the filter is unable to adapt to this imperfect behavior. \n", "\n", "Maybe just a really low process noise? Let's try that." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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+/fsTFhZGlSpVCAoKsljrNGvWLKytrWnbti1RUVHUq1ePpUuX6ptNRFJNXLzB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\nRERgx44dup4GERFRveGTMIlIr1laWmL48OFYs2aNrqdCRER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kHkoUCCGEEEJIbaZR3QGoq3fv3ujduzcAYMKECaXW//PPP5GdnQ1fX19oa2uj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\n65ycHIwcO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(32594)\n", "xs2000, zs2000 = simulate_system(Q=0.0001, count=2000)\n", "\n", "kf2 = SecondOrderKF(R, 0, dt=1)\n", "filter_xs2, ps2 = filter_data(kf2, zs2000)\n", "\n", "plot_kf_output(xs2000, filter_xs2, zs2000)\n", "plot_residuals(xs2000[:, 0], filter_xs2[:, 0], ps2[:, 0], \n", " 'Seceond Order Position Residuals',\n", " 'meters') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, the residual plot tells the story. The track looks very good, but the residual plot shows that the filter is diverging for significant periods of time.\n", "\n", "How should you think about all of this? You might argue that the last plot is 'good enough' for your application, and perhaps it is. I warn you however that a diverging filter doesn't always converge. With a different data set, or a physical system that performs differently you can end up with a filter that veers further and further away from the measurements.\n", "\n", "Also, let's think about this in a data fitting sense. Suppose I give you two points, and tell you to fit a straight line to the points. " ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter([1, 2], [1, 1], s=100, c='r')\n", "plt.plot([0, 3], [1, 1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A straight line is the only possible answer. Furthermore, the answer is optimal. If I gave you more points you could use a least squares fit to find the best line, and the answer would still be optimal (in a least squares sense).\n", "\n", "But suppose I told you to fit a higher order polynomial to those two points. There is now an infinite number of answers to the problem. For example, infinite number of parabolas (which are second order) pass through those points. When the Kalman filter is of higher order than your physical process it also has an infinite number of solutions to choose from. The answer is not just non-optimal, it often diverges and never recovers. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For best performance you need a filter whose order matches the system's order.. In many cases that will be easy to do - if you are designing a Kalman filter to read the thermometer of a freezer it seems clear that a zero order filter is the right choice. But what order should we use if we are tracking a car? Order one will work well while the car is moving in a straight line at a constant speed, but cars turn, speed up, and slow down, in which case a second order filter will perform better. That is the problem addressed in the Adaptive Filters chapter. There we will learn how to design a filter that *adapts* to changing order in the tracked object's behavior.\n", "\n", "With that said, a lower order filter can track a higher order process so long as you add enough process noise and you keep the discretization period small (100 samples a second are usually locally linear). The results will not be optimal, but they can still be very good, and I always reach for this tool first before trying an adaptive filter. Let's look at an example with acceleration. First, the simulation." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gAQBg27ZtUKvV2LlzJ5YtWwaj0YgtW7Zg69atSExMFN8nJCQEBw4cQEpKigO+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\neHIaCREREd0RAzkNGBZLOxpN9Wgw2Yb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "class ConstantAccelerationObject(object):\n", " def __init__(self, x0=0, vel=1., acc=0.1, acc_noise_scale=.1):\n", " self.x = x0\n", " self.vel = vel\n", " self.acc = acc\n", " self.acc_noise_scale = acc_noise_scale\n", " \n", " def update(self):\n", " self.acc += randn() * self.acc_noise_scale \n", " self.vel += self.acc\n", " self.x += self.vel\n", " return (self.x, self.vel, self.acc)\n", " \n", "R, Q = 6., 0.02\n", "def simulate_acc_system(R, Q, count):\n", " obj = ConstantAccelerationObject(acc_noise_scale=Q)\n", " zs = []\n", " xs = []\n", " for i in range(count):\n", " x = obj.update()\n", " z = sense(x, R)\n", " xs.append(x)\n", " zs.append(z)\n", " return np.asarray(xs), zs\n", "\n", "np.random.seed(124)\n", "xs, zs = simulate_acc_system(R=R, Q=Q, count=80)\n", "plt.plot(xs[:, 0]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will filter the data using a second order filter." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dOsTFixfx9/fPcHt8fLzN++LFi9/X8cR+7irAXufr62t9lM29slgst93u7u7O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\nlXNOXfjJqQs5qJC8nmrlbWjXABpVus2U0T2YOuBTatasycX92Vyrd5u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AnjEGkUiY8i8SiVDXA4akpKTWaFa7ceLECQCuf14Pny8CLppe6w1ViOzSEUF+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\nG7t3d8Phq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(124)\n", "xs, zs = simulate_acc_system(R=R, Q=Q, count=80)\n", "\n", "kf2 = SecondOrderKF(R, Q, dt=1)\n", "fxs2, ps2 = filter_data(kf2, zs)\n", "\n", "plot_kf_output(xs, fxs2, zs, aspect_equal=False)\n", "plot_residuals(xs[:, 0], fxs2[:, 0], ps2[:, 0], \n", " 'Second Order Position Residuals',\n", " 'meters') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the filter is performing within the theoretical limits of the filter. \n", "\n", "Now let's use a lower order filter. As already demonstrated the lower order filter will lag the signal because it is not modeling the acceleration. However, we can account for that (to an extent) by increasing the size of the process noise. The filter will treat the acceleration as noise in the process model. The result will be suboptimal, but if designed well it will not diverge. Choosing the amount of extra process noise is not an exact science. You will have to experiment with representative data. Here, I've multiplied it by 10, and am getting good results." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fvoyfn1+m7QkJCRbvixUr9lDHE+u5rwB7k4+Pj/lRNg8qIyPjru3Ozs6sXbv2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\no/+xt3nht9G4558jy3Biqv9D4BwEIa8A4OgAru5BuLXazaRDo3Excih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5gJ6QhlSqykTBPABotGooVQp4uHi16rGyi1Oh1dUAAG4V3aCAnhBCCCEWYzMB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\nDgAJVxuC+nkF851eVepKyqN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o0Wqg02mRX5zNbxPOQlwf8cBYqkXfFmq0GpTfvaPHgYOX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\nmExkasqok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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kf2 = FirstOrderKF(R, Q * 10, dt=1)\n", "fxs2, ps2 = filter_data(kf2, zs)\n", "\n", "plot_kf_output(xs, fxs2, zs, aspect_equal=False)\n", "plot_residuals(xs[:, 0], fxs2[:, 0], ps2[:, 0], \n", " 'Second Order Position Residuals',\n", " 'meters') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Think about what will happen if you make the process noise many times larger than it needs to be. A large process noise tells the filter to favor the measurements, so we would expect the filter to closely mimic the noise in the measurements. Let's find out." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9+eSTT7LUNWzYkMmTJ1O+fPkcD1BERETkYbD3qEGzMDiV3grjrw8x+XZl0mt+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\nP/6gR48eVK9enXPnzvHTTz9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sFvz9/ZkwYcJ1caWkpDB69GjKlCmDi4sLgYGBhIWFkZSU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mUqd6zkrKi9i0dwXrdy/lWGGmxzpFpfms2v4Dq7b/gM3qT8dm3enYvAfNo9qh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\nKrcGdtauXWu8vLzMiy++aL799lszbdo0ExgYaDIyMlwdWqPx4Ycfmtm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kf1 = FirstOrderKF(R, Q * 10000, dt=1)\n", "fxs1, ps1 = filter_data(kf2, zs)\n", "\n", "plot_kf_output(xs, fxs1, zs, aspect_equal=False)\n", "plot_residuals(xs[:, 0], fxs1[:, 0], ps2[:, 0], \n", " 'Second Order Position Residuals',\n", " 'meters') " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sensor Fusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Early in the g-h filter chapter we discussed designing a filter for two scales, one accurate and one inaccurate. We determined that we should always include the information from the inaccurate filter - we should never discard any information. If you do not recall this discussion, consider this edge case. You have two scales, one accurate to 1 lb, the second to 10 lbs. You weigh yourself, and the first reads 170 lbs, and the second reads 181 lbs. If we only used the data from the first scale we would only know that our weight is in the range of 169 to 171 lbs. However, when we incorporate the measurement from the second scale we can decide that the correct weight can only be 171 lbs, since 171 lbs is exactly at the outside range of the second measurement, which would be 171 to 191 lbs. Of course most measurements don't offer such a exact answer, but the principle applies to any measurement.\n", "\n", "So consider a situation where we have two sensors measuring the system. How shall we incorporate that into our Kalman filter? \n", "\n", "Suppose we have a train or cart on a railway. It has a sensor attached to the wheels counting revolutions, which can be converted to a distance along the track. Then, suppose we have a GPS-like sensor which I'll call a 'position sensor' mounted to the train which reports position. I'll explain why I don't just use a GPS in the next section. Thus, we have two measurements, both reporting position along the track. Suppose further that the accuracy of the wheel sensor is 1m, and the accuracy of the position sensor is 10m. How do we combine these two measurements into one filter? This may seem quite contrived, but aircraft use sensor fusion to fuse the measurements from sensors such as a GPS, INS, Doppler radar, VOR, the airspeed indicator, and more.\n", "\n", "Kalman filters for inertial filters are very difficult, but fusing data from two or more sensors providing measurements of the same state variable (such as position) is quite easy. The relevant matrix is the measurement matrix $\\mathbf{H}$. Recall that this matrix tells us how to convert from the Kalman filter's state $\\mathbf{x}$ to a measurement $\\mathbf{z}$. Suppose that we decide that our Kalman filter state should contain the position and velocity of the train, so that\n", "\n", "$$ \\mathbf{x} = \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n", "\n", "We have two measurements for position, so we will define the measurement vector to be a vector of the measurements from the wheel and the position sensor.\n", "\n", "$$ \\mathbf{z} = \\begin{bmatrix}x_{wheel} \\\\ x_{ps}\\end{bmatrix}$$\n", "\n", "So we have to design the matrix $\\mathbf{H}$ to convert $\\mathbf{x}$ to $\\mathbf{z}$ . They are both positions, so the conversion is nothing more than multiplying by one:\n", "\n", "$$ \\begin{bmatrix}x_{wheel} \\\\ x_{ps}\\end{bmatrix} = \\begin{bmatrix}1 &0 \\\\ 1& 0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n", "\n", "To make it clearer, suppose that the wheel reports not position but the number of rotations of the wheels, where 1 revolution yields 2 meters of travel. In that case we would write\n", "\n", "$$ \\begin{bmatrix}x_{wheel} \\\\ x_{ps}\\end{bmatrix} = \\begin{bmatrix}0.5 &0 \\\\ 1& 0\\end{bmatrix} \\begin{bmatrix}x \\\\ \\dot{x}\\end{bmatrix}$$\n", "\n", "Now we have to design the measurement noise matrix $\\mathbf{R}$. Suppose that the measurement variance for the position is twice the variance of the wheel, and the standard deviation of the wheel is 1.5 meters. That gives us\n", "\n", "$$\n", "\\begin{aligned}\n", "\\sigma_{wheel} &= 1.5\\\\\n", "\\sigma^2_{wheel} &= 2.25 \\\\ \n", "\\sigma_{ps} &= 1.5*2 = 3 \\\\\n", "\\sigma^2_{ps} &= 9.\n", "\\end{aligned}\n", "$$\n", "\n", "That is pretty much our Kalman filter design. We need to design for $\\mathbf{Q}$, but that is invariant to whether we are doing sensor fusion or not, so I will just choose some arbitrary value.\n", "\n", "So let's run a simulation of this design. I will assume a velocity of 10 m/s with an update rate of 0.1 seconds." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fusion std: 0.391\n" ] }, { "data": { "image/png": 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OCrWrNnZan3zxLEkpJ4ts8/H047eeLXE5dAQiIq57zpNnDWavsDFr/kXWHvXDwAUo71AX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\nJEqWLJnt8RVF4cKFC+zZs4eAgAAAypcvT+PGjfnkk084e/Ysrq6uABQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy import array, asarray\n", "import numpy.random as random\n", "\n", "def fusion_test(wheel_sigma, ps_sigma, do_plot=True):\n", " dt = 0.1\n", " kf = KalmanFilter(dim_x=2, dim_z=2)\n", "\n", " kf.F = array([[1., dt], [0., 1.]])\n", " kf.H = array([[1., 0.], [1., 0.]])\n", " kf.x = array([[0.], [1.]])\n", " kf.Q *= array([[(dt**3)/3, (dt**2)/2],\n", " [(dt**2)/2, dt ]]) * 0.02\n", " kf.P *= 100\n", " kf.R[0, 0] = wheel_sigma**2\n", " kf.R[1, 1] = ps_sigma**2 \n", "\n", " random.seed(1123)\n", " xs, zs, nom = [], [], []\n", " for i in range(1, 100):\n", " m0 = i + randn()*wheel_sigma\n", " m1 = i + randn()*ps_sigma\n", " z = array([[m0], [m1]])\n", "\n", " kf.predict()\n", " kf.update(z)\n", "\n", " xs.append(kf.x.T[0])\n", " zs.append(z.T[0])\n", " nom.append(i)\n", "\n", " xs = asarray(xs)\n", " zs = asarray(zs)\n", " nom = asarray(nom)\n", " \n", " res = nom - xs[:, 0]\n", " print('fusion std: {:.3f}'.format(np.std(res)))\n", " if do_plot:\n", " bp.plot_measurements(zs[:, 0], label='Wheel')\n", " plt.plot(zs[:, 1], linestyle='--', label='Pos Sensor')\n", " bp.plot_filter(xs[:, 0], label='Kalman filter')\n", " plt.legend(loc=4)\n", " plt.ylim(0, 100)\n", "\n", "fusion_test(1.5, 3.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see the result of the Kalman filter in blue.\n", "\n", "It may be somewhat difficult to understand the previous example at an intuitive level. Let's look at a different problem. Suppose we are tracking an object in 2D space, and have two radar systems at different positions. Each radar system gives us a range and bearing to the target. How do the readings from each data affect the results?\n", "\n", "This is a nonlinear problem because we need to use a trigonometry to compute coordinates from a range and bearing, and we have not yet learned how to solve nonlinear problems with Kalman filters. So for this problem ignore the code that I use and just concentrate on the charts that the code outputs. We will revisit this problem in subsequent chapters and learn how to write this code.\n", "\n", "I will position the target at (100, 100). The first radar will be at (50, 50), and the second radar at (150, 50). This will cause the first radar to measure a bearing of 45 degrees, and the second will report 135 degrees.\n", "\n", "I will create the Kalman filter first, and then plot its initial covariance matrix. I am using a **unscented Kalman filter**." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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qCelvOWa4XqfIWek4rjo6OvrdP+g522VlZSgsLERdXV1sWygUwo4dO3DttdcC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\nNA9c/MWUpiS43dPgdl+BrKz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M2wMghIAs9/6fSpbl2EN6ysrKUFhYiLq6utj+UCiEHTt2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\nEIZtIiIiIqIE+f+w5ZJ+B/qw7QAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_design_internal import sensor_fusion_kf, set_radar_pos\n", "\n", "kf = sensor_fusion_kf()\n", "x0, p0 = kf.x.copy(), kf.P.copy()\n", "plot_covariance_ellipse(x0, cov=p0, fc='y', ec=None, alpha=0.6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are equally uncertain about the position in x and y, so the covariance is circular.\n", "\n", "Now we will update the Kalman filter with a reading from the first radar. I will set the standard deviation of the bearing error at 0.5$^\\circ$, and the standard deviation of the distance error at 3." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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y8nJMJhOzZs0iLS2NiRMnsmnTJl544QWqq6tJS0tj1KhR/PGPf4wkswB/+9vf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\ndjgcWL9+fVQKJiK6XUOD9tOPvpiQQftGA8sEioM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import radians\n", "\n", "# set the error of the radar's bearing and distance\n", "kf.R[0, 0] = radians (.5)**2\n", "kf.R[1, 1] = 3.**2\n", "\n", "# compute position and covariance from first radar station\n", "set_radar_pos((50, 50))\n", "dist = (50**2 + 50**2) ** 0.5\n", "kf.predict()\n", "kf.update([radians(45), dist])\n", "\n", "# plot the results\n", "x1, p1 = kf.x.copy(), kf.P.copy()\n", "\n", "plot_covariance_ellipse(x0, p0, fc='y', ec=None, alpha=0.6)\n", "plot_covariance_ellipse(x1, p1, fc='g', ec='k', alpha=0.6)\n", "\n", "plt.scatter([100], [100], c='y', label='Initial')\n", "plt.scatter([100], [100], c='g', label='1st station')\n", "plt.legend(scatterpoints=1, markerscale=3)\n", "plt.plot([92, 100], [92, 100], c='g', lw=2, ls='--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see the effect of the errors on the geometry of the problem. The radar station is to the lower left of the target. The bearing measurement is extremely accurate at $\\sigma=0.5^\\circ$, but the distance error is inaccurate at $\\sigma=3$. I've shown the radar reading with the dotted green line. We can easily see the effect of the accurate bearing and inaccurate distance in the shape of the covariance ellipse. \n", "\n", "Now we can incorporate the second radar station's measurement. The second radar is at (150,50), which is below and to the right of the target. Before you go on, think about how you think the covariance will change when we incorporate this new reading." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5nbBarU0eIy4kjsQRiTyz5Zk619Vr9cyMn4lBb2jyfutjxYoVFBQUUFBQAFQW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\nMMf6yEpLD/L6618yaNAZXHbZFeTm5vZ8gSIy4Hk9dFNfX8/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute position and covariance from first radar station\n", "set_radar_pos((150, 50))\n", "kf.predict()\n", "kf.update([radians(135), dist])\n", "\n", "plot_covariance_ellipse(x0, p0, fc='y', ec='k', alpha=0.6)\n", "plot_covariance_ellipse(x1, p1, fc='g', ec='k', alpha=0.6)\n", "plot_covariance_ellipse(kf.x, kf.P, fc='b', ec='k', alpha=0.6)\n", "\n", "plt.scatter([100], [100], c='y', label='Initial')\n", "plt.scatter([100], [100], c='g', label='1st station')\n", "plt.scatter([100], [100], c='b', label='2nd station')\n", "plt.legend(scatterpoints=1, markerscale=3)\n", "plt.plot([92, 100], [92, 100], c='g', lw=2, ls='--')\n", "plt.plot([108, 100], [92, 100], c='b', lw=2, ls='--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see how the second radar measurement altered the covariance. The angle to the target is orthogonal to the first radar station, so the effects of the error in the bearing and range are swapped. So the angle of the covariance matrix switches to match the direction to the second station. It is important to note that the direction did not merely change; the size of the covariance matrix became much smaller as well.\n", "\n", "The covariance will always incorporate all of the information available, including the effects of the geometry of the problem. This formulation makes it particularly easy to see what is happening, but the same thing occurs if one sensor gives you position and a second sensor gives you velocity, or if two sensors provide measurements of position.\n", "\n", "One final thing before we move on: sensor fusion is a vast topic, and my coverage is simplistic to the point of being misleading. For example, the Kalman Filter Math chapter talks about using iterated least squares to determine the position from a set of pseudorange readings from the satellites without using a Kalman filter. That is the usual but not exclusive way this computation is done in GPS receivers. If you are a hobbiest my coverage may get you started. A commercial grade filter requires very careful design of the fusion process. That is the topic of several books, and you will have to further your education by finding one that covers your domain. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Can you Kalman Filter GPS outputs?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the section above I have you apply a Kalman filter to 'GPS-like' sensor. Can you apply a Kalman filter to the output of a commercial Kalman filter? In other words, will the output of your filter be better than, worse than, or equal to the GPS's output?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Commercial GPS's have a Kalman filter built into them, and their output is the filtered estimate created by that filter. So, suppose you have a steady stream of output from the GPS consisting of a position and position error. Can you not pass those two pieces of data into your own filter?\n", "\n", "Well, what are the characteristics of that data stream, and more importantly, what are the fundamental requirements of the input to the Kalman filter?\n", "\n", "Inputs to the Kalman filter must be *Gaussian* and *time independent*. The output of the GPS is *time dependent* because the filter bases its current estimate on the recursive estimates of all previous measurements. Hence, the signal is not white, it is not time independent, and if you pass that data into a Kalman filter you have violated the mathematical requirements of the filter. So, the answer is no, you cannot get better estimates by running a KF on the output of a commercial GPS. \n", "\n", "Another way to think of it is that Kalman filters are optimal in a least squares sense. There is no way to take an optimal solution, pass it through a filter, any filter, and get a 'more optimal' answer because it is a logical impossibility. At best the signal will be unchanged, in which case it will still be optimal, or it will be changed, and hence no longer optimal.\n", "\n", "This is a difficult problem that hobbyists face when trying to integrate GPS, IMU's and other off the shelf sensors. \n", "\n", "Let's look at the effect. A commercial GPS reports position, and an estimated error range. The estimated error just comes from the Kalman filter's $\\mathbf{P}$ matrix. So let's filter some noisy data, take the filtered output as the new noisy input to the filter, and see what the result is. In other words, $\\mathbf{x}$ will supply the $\\mathbf{z}$ input, and $\\mathbf{P}$ will supply the measurement covariance $\\mathbf{R}$. To exaggerate the effects somewhat to make them more obvious I will plot the effects of doing this one, and then a second time. The second iteration doesn't make any 'sense' (no one would try that), it just helps me illustrate a point. First, the code and plots." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HXvmgSzNzW3iEwYm/Yiatx8+aY2MfeOd1GNbpoRPdvg0ZMyZaXCIiqZldE9TW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8AwuLWYb3Gu+8YykUEXmBaIiviIjIi+zOHfj9d9I7OvIwffrkv7+bG3z3HQQG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JqbMjTH0fZn2YDMkpQJMmULo0nDzJyaJFCbt8GYDy5cszYMAAwsLCkt6GiCSaElQRERER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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(124)\n", "xs, zs = simulate_acc_system(R=R, Q=Q, count=30)\n", "\n", "kf0 = SecondOrderKF(R, Q, dt=1)\n", "kf1 = SecondOrderKF(R, Q, dt=1)\n", "kf2 = SecondOrderKF(R, Q, dt=1)\n", "\n", "# Filter measurements\n", "fxs0, ps0 = filter_data(kf0, zs)\n", "\n", "# filter twice more, using P as error\n", "fxs1, ps1, _, _ = kf1.batch_filter(fxs0[:, 0], ps[:, 0])\n", "fxs2, _, _, _ = kf2.batch_filter(fxs1[:, 0], ps1[:, 0, 0])\n", "\n", "plot_kf_output(xs, fxs0, zs, title='KF', aspect_equal=False)\n", "plot_kf_output(xs, fxs1, zs, title='1 iteration', aspect_equal=False)\n", "plot_kf_output(xs, fxs2, zs, title='2 iterations', aspect_equal=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the filtered output of the reprocessed signal is smoother, but it also diverges from the track. What is happening? Recall that the Kalman filter requires that the signal not be time correlated. However the output of the Kalman filter *is* time correlated because it incorporates all previous measurements into its estimate for this time period. So look at the last graph, for 2 iterations. The measurements start with several peaks that are larger than the track. This is 'remembered' (that is vague terminology, but I am trying to avoid the math) by the filter, and it has started to compute that the object is above the track. Later, at around 13 seconds we have a period where the measurements all happen to be below the track. This also gets incorporated into the memory of the filter, and the iterated output diverges far below the track. \n", "\n", "Now let's look at this in a different way. The iterated output is *not* using $\\mathbf{z}$ as the measurement, but the output of the previous Kalman filter estimate. So I will plot the output of the filter against the previous filter's output." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HXvmgSzNzW3iEwYm/Yiatx8+aY2MfeOd1GNbpoRPdvg0ZMyZaXCIiqZldE9TW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CtYiKgr//hsKFwd4+6YJMJoVTEZH/UEAVERGRtLd2LcybZw6lf/5p7uIK5vsv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cisiLSyOoIiIiIk+wdOlS7O3tadasGQDNmzdn586d1KtXD4B333035uDoaNi1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_kf_output(xs, fxs0, zs, title='KF', aspect_equal=False)\n", "plot_kf_output(xs, fxs1, fxs0[:, 0], title='1 iteration', aspect_equal=False)\n", "plot_kf_output(xs, fxs2, fxs1[:, 0], title='2 iterations', aspect_equal=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I hope the problem with this approach is now apparent. In the bottom graph we can see that the KF is tracking the imperfect estimates of the previous filter, and incorporating delay into the signal as well due to the memory of the previous measurements being incorporated into the signal." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Prove that the position sensor improves the filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Devise a way to prove that fusing the position sensor and wheel measurements yields a better result than using the wheel alone." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Solution 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Force the Kalman filter to disregard the position sensor measurement by setting the measurement noise for the position sensor to a near infinite value. Re-run the filter and observe the standard deviation of the residual." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fusion std: 0.391\n", "fusion std: 0.438\n" ] } ], "source": [ "fusion_test(1.5, 3.0, do_plot=False)\n", "fusion_test(1.5, 1e80, do_plot=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we can see the error in the filter where the position sensor measurement is almost entirely ignored is greater than that where it is used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Solution 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is more work, but we can write a Kalman filter that only takes one measurement." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "std: 40.386\n" ] }, { "data": { "image/png": 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CtGm2z0XSSKrhe+LEieTOnZt+/foRHh5O/vz56d27NyNGjEisGTJkCNHR0fTr14+IiAgC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\nNmzIRx99xM2bNylSpAihoaFs2LCBvHn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = 0.1\n", "wheel_sigma = 1.5\n", "kf = KalmanFilter(dim_x=2, dim_z=1)\n", "kf.F = array([[1., dt], [0., 1.]])\n", "kf.H = array([[1., 0.]])\n", "kf.x = array([[0.], [1.]])\n", "kf.Q *= 0.01\n", "kf.P *= 100\n", "kf.R[0, 0] = wheel_sigma**2\n", "\n", "random.seed(1123)\n", "nom = range(1, 100)\n", "zs = np.array([i + randn()*wheel_sigma for i in nom])\n", "xs, _, _, _ = kf.batch_filter(zs)\n", "\n", "res = nom - xs[:, 0]\n", "print('std: {:.3f}'.format(np.std(res)))\n", "\n", "bp.plot_filter(xs[:, 0], label='Kalman filter')\n", "bp.plot_measurements(zs, label='Wheel')\n", "plt.legend(loc=4)\n", "plt.xlim((-1, 100));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On this run I got a standard deviation of 0.523 vs the value of 0.391 for the fused measurements. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Different Data Rates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is rare that two different sensor classes output data at the same rate. Assume that the position sensor produces an update at 1 Hz, and the wheel updates at 4 Hz. Design a filter that incorporates all of these measurements.\n", "\n", "**hint**: This is a difficult problem in that I have not explained how to do this. Think about which matrices incorporate time, and which incorporate knowledge about the number and kind of measurements. All of these will have to be designed to work with this problem. If you can correctly enumerate those matrices you are most of the way to a solution." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#your solution here!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can do this by setting the data rate to 0.25 seconds, which is 4 Hz. As we loop, on every iteration we call `update()` with only the wheel measurement. Then, every fourth time we will call `update()` with both the wheel and PS measurements. \n", "\n", "This means that we vary the amount of data in the z parameter. The matrices associated with the measurement are $\\mathbf{H}$ and $\\mathbf{R}$. In the code above we designed H to be \n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}1 &0 \\\\ 1& 0\\end{bmatrix}$$\n", "\n", "to account for the two measurements of position. When only the wheel reading is available, we must set\n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}1 &0\\end{bmatrix}.$$\n", "\n", "The matrix $\\mathbf{R}$ specifies the noise in each measurement. In the code above we set\n", "\n", "$$\\mathbf{R} = \\begin{bmatrix}\\sigma_{wheel}^2 &0 \\\\ 0 & \\sigma_{ps}^2\\end{bmatrix}$$\n", "\n", "When only the wheel measurement is available, we must set\n", "\n", "$$\\mathbf{R} = \\begin{bmatrix}\\sigma_{wheel}^2\\end{bmatrix}$$\n", "\n", "The two matrices that incorporate time are $\\mathbf{F}$ and $\\mathbf{Q}$. For example,\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix}1 & \\Delta t \\\\ 0& 1\\end{bmatrix}.$$\n", "\n", "Since the wheel and position sensor reading coincide once every 4 readings we can just set $\\delta t =0.25$ and not modify it while filtering. If the readings did not coincide in each iteration you would have to calculate how much time has passed since the last predict, compute a new $\\mathbf{F}$ and $\\mathbf{Q}$, and then call `predict()` so the filter could make a correct prediction based on the time step required.\n", "\n", "So here is the code. " ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fusion std: 0.452\n" ] }, { "data": { "image/png": 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AB1MN3v8Wln58hJ/znyAj6eKh1dcLurWEnm2hVxuoF2GCwnaQ2wz8/Suh1xeX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\n8KE3TtfCObHnnMGxpSztKG/vjKLoUKlkJRYhhBBCiH9LkvN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def fusion_test(wheel_sigma, ps_sigma, do_plot=True):\n", " dt = 0.25\n", " kf = KalmanFilter(dim_x=2, dim_z=2)\n", "\n", " kf.F = array([[1., dt], [0., 1.]])\n", " kf.H = array([[1., 0.], [1., 0.]])\n", " kf.x = array([[0.], [1.]])\n", " kf.Q *= array([[(dt**3)/3, (dt**2)/2],\n", " [(dt**2)/2, dt ]]) * 0.02\n", " kf.P *= 100\n", " kf.R[0, 0] = wheel_sigma**2\n", " kf.R[1, 1] = ps_sigma**2 \n", "\n", " random.seed(1123)\n", " xs = []\n", " zs_wheel = []\n", " zs_ps = []\n", " nom = []\n", " for i in range(1, 101):\n", " \n", " if i % 4 == 0:\n", " m0 = i + randn()*wheel_sigma\n", " m1 = i + randn()*ps_sigma\n", " z = array([[m0], [m1]])\n", " kf.H = array([[1., 0.], [1., 0.]])\n", " R = np.eye(2)\n", " R[0, 0] = wheel_sigma**2\n", " R[1, 1] = ps_sigma**2 \n", " \n", " zs_wheel.append(m0)\n", " zs_ps.append((i, m1))\n", " else: \n", " m0 = i + randn()*wheel_sigma\n", " z = array([m0])\n", " kf.H = array([[1., 0.]])\n", " R = np.eye(1) * wheel_sigma**2\n", " zs_wheel.append(m0)\n", "\n", " kf.predict()\n", " kf.update(z, R)\n", "\n", " xs.append(kf.x.T[0])\n", " nom.append(i)\n", "\n", " xs = asarray(xs)\n", " nom = asarray(nom)\n", "\n", " res = nom - xs[:, 0]\n", " print('fusion std: {:.3f}'.format(np.std(res)))\n", " if do_plot:\n", " bp.plot_measurements(zs_wheel, label='Wheel')\n", " plt.plot(*zip(*zs_ps), linestyle='--', label='Pos Sensor')\n", " bp.plot_filter(xs[:, 0], label='Kalman filter')\n", " plt.legend(loc=4)\n", " plt.ylim(0, 100)\n", "\n", "fusion_test(1.5, 3.0);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the standard deviation that the performance is a bit worse than when the PS and wheel were measured in every update, but better than the wheel alone.\n", "\n", "The code is fairly straightforward. The `update()` function optionally takes R as an argument, and I chose to do that rather than alter `KalmanFilter.R`, mostly to show that it is possible. Either way is fine. I modified `KalmanFilter.H` on each update depending on whether there are 1 or 2 measurements available. The only other difficulty was storing the wheel and PS measurements in two different arrays because there are a different number of measurements for each. " ] }, { "cell_type": "markdown", "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 gravitational 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", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [], "source": [ "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 \n", " compute dy/dx for 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, \n", " theta_deg=0., \n", " g=9.8, \n", " 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 + randn()*self.noise[0], \n", " self.y + randn()*self.noise[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So to create a trajectory starting at (0, 15) with a velocity of $100 \\frac{m}{s}$ and an angle of $60^\\circ$ 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", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def test_ball_vacuum(noise):\n", " y = 15\n", " x = 0\n", " ball = BallTrajectory2D(x0=x, y0=y, \n", " theta_deg=60., velocity=100., \n", " 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", " \n", "#test_ball_vacuum([0, 0]) # plot ideal ball position\n", "test_ball_vacuum([1, 1]) # plot with noise " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks reasonable, so let's continue (exercise for the reader: validate this simulation more robustly)." ] }, { "cell_type": "markdown", "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 $\\mathbf{x}^- = \\mathbf{Fx} + \\mathbf{Bu}$, 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", "$$\\begin{aligned}\n", "x_t &= x_{t-1} + v_{x(t-1)} {\\Delta t} \\\\\n", "v_{xt} &= vx_{t-1}\n", "\\\\\n", "y_t &= y_{t-1} + v_{y(t-1)} {\\Delta t}\\\\\n", "v_{yt} &= -g {\\Delta t} + v_{y(t-1)} \\\\\n", "\\end{aligned}\n", "$$\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.* If you need to use Runge-Kutta you will have to write your own `predict()` function which computes the state transition for $\\mathbf{x}$, and then uses the normal Kalman filter equation $\\mathbf{P}=\\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}$ to update the covariance matrix.\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", "$$\n", "\\mathbf{x} = \n", "\\begin{bmatrix}\n", "x \\\\\n", "\\dot{x} \\\\\n", "y \\\\\n", "\\dot{y} \\\\\n", "\\ddot{y}\n", "\\end{bmatrix}\n", "$$\n", "\n", "However, the acceleration is due to gravity, which is a constant. Instead of asking the Kalman filter to track a constant we can treat gravity as what it really is - a control input. In other words, gravity is a force that alters the behavior of the system in a known way, and it is applied throughout the flight of the ball. \n", "\n", "The equation for the state prediction is $\\mathbf{x^-} = \\mathbf{Fx} + \\mathbf{Bu}$. $\\mathbf{Fx}$ is the familiar state transition function which we will use to model the position and velocity of the ball. The vector $\\mathbf{u}$ lets you specify a control input into the filter. For a car the control input will be things such as the amount the accelerator and brake are pressed, the position of the steering wheel, and so on. For our ball the control input will be gravity. The matrix $\\mathbf{B}$ models how the control inputs affect the behavior of the system. Again, for a car $\\mathbf{B}$ will convert the inputs of the brake and accelerator into changes of velocity, and the input of the steering wheel into a different position and heading. For our ball tracking problem it will compute the velocity change due to gravity. We will go into the details of that in step 3. For now, we design the state variable to be\n", "\n", "$$\n", "\\mathbf{x} = \n", "\\begin{bmatrix}\n", "x \\\\\n", "\\dot{x} \\\\\n", "y \\\\\n", "\\dot{y} \n", "\\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 2:** Design State Transition Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our next step is to design the state transition function. Recall that the state transistion function is implemented as a matrix $\\mathbf{F}$ that we multiply 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", "$$\n", "\\begin{aligned}\n", "x' &= (1*x) + (\\Delta t * v_x) + (0*y) + (0 * v_y) \\\\\n", "v_x &= (0*x) + (1*v_x) + (0*y) + (0 * v_y) \\\\\n", "y' &= (0*x) + (0* v_x) + (1*y) + (\\Delta t * v_y) \\\\\n", "v_y &= (0*x) + (0*v_x) + (0*y) + (1*v_y) \n", "\\end{aligned}\n", "$$\n", "\n", "Note that none of the terms include $g$, the gravitational constant. As I explained in the previous function we will account for gravity using the control input of the Kalman filter.\n", "In matrix form we write this as:\n", "\n", "$$\n", "\\mathbf{F} = \\begin{bmatrix}\n", "1 & \\Delta t & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 \\\\\n", "0 & 0 & 1 & \\Delta t \\\\\n", "0 & 0 & 0 & 1\n", "\\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### **Step 3**: Design the Control Input Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use the control input to account for the force of gravity. The term $\\mathbf{Bu}$ is added to $\\mathbf{x^-}$ to account for how much $\\mathbf{x^-}$ changes due to gravity. We can say that $\\mathbf{Bu}$ contains $\\begin{bmatrix}\\Delta x_g & \\Delta \\dot{x_g} & \\Delta y_g & \\Delta \\dot{y_g}\\end{bmatrix}^\\mathsf{T}$.\n", "\n", "If we look at the discretized equations we see that gravity only affect the velocity for $y$.\n", "\n", "$$\\begin{aligned}\n", "x_t &= x_{t-1} + v_{x(t-1)} {\\Delta t} \\\\\n", "v_{xt} &= vx_{t-1}\n", "\\\\\n", "y_t &= y_{t-1} + v_{y(t-1)} {\\Delta t}\\\\\n", "v_{yt} &= -g {\\Delta t} + v_{y(t-1)} \\\\\n", "\\end{aligned}\n", "$$\n", "\n", "Therefore we want the product $\\mathbf{Bu}$ to equal $\\begin{bmatrix}0 & 0 & 0 & -g \\Delta t \\end{bmatrix}^\\mathsf{T}$. In some sense it is arbitrary how we define $\\mathbf{B}$ and $\\mathbf{u}$ so long as multiplying them together yields this result. For example, we could define $\\mathbf{B}=1$ and $\\mathbf{u} = \\begin{bmatrix}0 & 0 & 0 & -g \\Delta t \\end{bmatrix}^\\mathsf{T}$. But this doesn't really fit with our definitions for $\\mathbf{B}$ and $\\mathbf{u}$, where $\\mathbf{u}$ is the control input, and $\\mathbf{B}$ is the control function. The control input is $-g$ for the velocity of y. So this is one possible definition.\n", "\n", "$$\\mathbf{B} = \\begin{bmatrix}0&0&0&0 \\\\ 0&0&0&0 \\\\0&0&0&0 \\\\0&0&0&\\Delta t\\end{bmatrix}, \\mathbf{u} = \\begin{bmatrix}0\\\\0\\\\0\\\\-g\\end{bmatrix}$$\n", "\n", "To me this seems a bit excessive; I would suggest we might want $\\mathbf{u}$ to contain the control input for the two dimensions $x$ and $y$, which suggests\n", "\n", "$$\\mathbf{B} = \\begin{bmatrix}0&0 \\\\ 0&0 \\\\0&0 \\\\0&\\Delta t\\end{bmatrix}, \\mathbf{u} = \\begin{bmatrix}0\\\\-g\\end{bmatrix}$$.\n", "\n", "You might prefer to only provide control inputs that actually exist, and there is no control input for $x$, so we arrive at\n", "\n", "$$\\mathbf{B} = \\begin{bmatrix}0 \\\\ 0 \\\\0\\\\ \\Delta t\\end{bmatrix}, \\mathbf{u} = \\begin{bmatrix}-g\\end{bmatrix}$$.\n", "\n", "I've seen people use \n", "$$\\mathbf{B} = \\begin{bmatrix}0&0&0&0 \\\\ 0&0&0&0 \\\\0&0&0&0 \\\\0&0&0&1\\end{bmatrix}, \\mathbf{u} = \\begin{bmatrix}0\\\\0\\\\0\\\\-g \\Delta t\\end{bmatrix}$$\n", "\n", "While this does produce the correct result, I am resistant to putting time into $\\mathbf{u}$ as time is not a control input, it is what we use to convert the control input into a change in state, which is the job of $\\mathbf{B}$." ] }, { "cell_type": "markdown", "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", "$$\n", "\\begin{bmatrix}z_x \\\\ z_y \\end{bmatrix}= \n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0\n", "\\end{bmatrix} * \n", "\\begin{bmatrix}\n", "x \\\\\n", "\\dot{x} \\\\\n", "y \\\\\n", "\\dot{y} \\end{bmatrix}$$\n", "\n", "where\n", "\n", "$$\\mathbf{H} = \\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0\n", "\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are assuming a ball moving in a vacuum, so there should be no process noise. We have 4 state variables, so we need a $4{\\times}4$ covariance matrix:\n", "\n", "$$\\mathbf{Q} = \\begin{bmatrix}0&0&0&0\\\\0&0&0&0\\\\0&0&0&0\\\\0&0&0&0\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step 7: Design the Initial Conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We already performed this step when we tested the state transition 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.array([[x, vx, y, vy]]).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", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from math import sin,cos,radians\n", "\n", "\n", "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.):\n", "\n", " kf = KalmanFilter(dim_x=4, dim_z=2, dim_u=1)\n", "\n", " ay = .5*dt**2\n", " kf.F = np.array([[1, dt, 0, 0], # x = x0 + dx*dt\n", " [0, 1, 0, 0], # dx = dx0\n", " [0, 0, 1, dt], # y = y0 + dy*dt\n", " [0, 0, 0, 1]]) # dy = dy0\n", "\n", " kf.H = np.array([[1, 0, 0, 0],\n", " [0, 0, 1, 0]])\n", " \n", " kf.B = np.array([[0,0,0,.1]]).T\n", " \n", " kf.R *= r\n", " kf.Q *= q\n", "\n", " omega = radians(omega)\n", " vx = cos(omega) * v0\n", " vy = sin(omega) * v0\n", "\n", " kf.x = np.array([[x, vx, y, vy]]).T\n", " \n", " return kf" ] }, { "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", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2Z1JKCM826E/1wDp/JDCtWkkyIu4d10bZ+/fHu+9gnnhhAa89+X9E+DbCoqhs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\nY7HWYlX+DpR51aFNrTcmFWmh4BhGIiJqApR1Nkw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y = 1.\n", "x = 0.\n", "theta = 35. # launch angle\n", "v0 = 80.\n", "dt = 1/10. # time step\n", "g = 9.8 # gravitational constant\n", "\n", "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, \n", " noise=[.2, .2])\n", "kf = ball_kf(x, y, theta, v0, dt)\n", "\n", "t = 0\n", "xs = []\n", "ys = []\n", "u = -g\n", "while kf.x[2, 0] > 0:\n", " t += dt\n", " x, y = ball.step(dt)\n", " z = np.array([[x, y]]).T\n", "\n", " kf.update(z)\n", " xs.append(kf.x[0, 0])\n", " ys.append(kf.x[2, 0])\n", " \n", " kf.predict(u=u) \n", " \n", " p1 = plt.scatter(x, y, color='r', marker='.', s=75, alpha=0.5)\n", "\n", "p2, = plt.plot(xs, ys, lw=2)\n", "plt.legend([p2, p1], ['Kalman filter', 'Measurements'], scatterpoints=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the Kalman filter reasonably tracks the ball. However, as already explained, this is a trivial example because we have no process noise. We can predict trajectories in a vacuum with arbitrary precision; using a Kalman filter in this example is a needless complication. A least squares curve fit would give identical results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking a Ball in Air" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**author's note - I originally had ball tracking code in 2 different places in the book. One has been copied here, so now we have 2 sections on ball tracking. I need to edit this into one section, obviously. Sorry for the duplication.**\n", "\n", "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": "markdown", "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 discretization 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", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6dCmysrKQmZlpkIfz8ssv678ODQ3F008/je7du+PgwYOYPHlyg/PoPoYi8XBM\nTYPjahrGjuuNG/4AHlW6O5oI+OfAybkWs/xm8WfTBI6LaXBcDRn8buqPFSEnp6hV57l9+zbTUcgq\n3L59G7m5uY0+1lgBoPZodRC+ZMkSfP755zh+/Dh69OjRbFs/Pz8EBgbihx9+aGv/iIgwbdovOH7c\nAwUFLkCpEs7lgzAwqBq93DmjRmRJBr+bAIKD72DatF8s3CsyhkajsXQXOrxWBeGLFy/GF198gePH\njxtVWrS0tBTXr1/XV4GqjwtcxMNFQ6bBcTWNtozrN988/pj7+ZiN8PJiSfnG8DVrGhzXptX93VSr\nXeDtbXxRGd24uru7m6JrRK3m7u7e5O953YWZYjA6CF+4cCE+/fRT7N+/HzKZDMXFxQC0nXV1dUV1\ndTXi4uLw4osvwtfXFz/99BOWLVsGHx+fRlNRiIhaw7C8NoNvImth+LtJRMYyOgjfvHkzJBIJxo4d\na3A8Pj4eb7/9NhwcHJCbm4udO3eioqICfn5+GDNmDL788ku4urqK3nEisk1lZUDctmv4wfVLDL7i\nwq0Giexca7YwJOpIjA7CW8odcnJywqFDh9rdISKyX4+3GgwBXjmKy9xqkMiutWYLQ0EQ2lSmnEgs\n5q6m2eYtComIWotbDRJ1LMZuYejo6IiamhrU1taar3NEddTW1qKmpsasld7bXKyHiKhdHm016OLa\n8UpYE5EhqVQKJycn3L9/Hw8ePGi2bfX9anxX8h3u12prkDg6OCLMJwyujkx91bl9+zYALnhtDYlE\nAicnJ7N+GsMgnIjMRq3Wfhytmw13u6XC0FAJZ8GJ7JTB7zyA/v21xxojkUjQpUuXFs/p5OSE9796\nH6n5qQCA34b8FgenHxSry3ZBt881d/OxbgzCichsvL21+aBvvqkt5DHvL8nw8rJwp4jIZHS/82Iv\nzEwcm4ic6zkQwE/SyHYxCCcis/L2BubP1wbhqt6cpSGydy1tYVhR0QmxsdqvjQ3SlT5KqAJUkICf\npJHtYhBOREREFlFR0Qlz5vRBQYH2fnO7p9SXPCHZtJ0jMjEG4UTUJtz7l4jaa/duhb7kPfB49xRj\niv80VzE3ozADO77bYXCMtQjI2jAIJ6JW0+/9W5UBhO3AxjeASRMBJye+0RGR5Xk6eSLlUgpK77AW\nAVkv7hNORK2m3/v3rifQNwUVPbfi0wtbkXIpBV7OXGlJRMaZNu0XBAff0d9vbveU1lD6KBEewFoE\nZN04E04eWjYTAAAgAElEQVREbacrutNHu1UY3+iIqDU8PB5iy5bLOHHiNwDETW3jDipk7RiEE1Gr\nGez9ezQRDk/kwNODb3RE1HoeHg+NygFvLe6gQtaOQTgRtZrh3r9K/F9vFbo48o2OiKwLd1Aha8Yg\nnIjapO7evz/+yjc6IjKN9uzE1NwOKkSWxiCciNqNb3REZAr6nZgelb1vzT7iRNaOQTgRERFZJf1O\nTI+0Zh/xlnAvcbI0BuFEHRyL7hBRR8S9xMnSuE84UQdWVgaopmRg1fevYdX3ryHkjdcw8/PXkFGY\nYemuERFBrdbuHa4j1j7iAPcSJ8vjTDhRB5aUBBRe8AReSQHcSlEBYG+eHG+N4mwQEVme4U5M4n9a\nx73EyZIYhBN1dPUK7vgJnA0iIutRdycmsXEvcbIko9JR1qxZg/DwcMhkMigUCkRHR+P8+fMN2sXH\nxyMgIAAuLi4YPXo08uqupiAiq6P/qPdoIlClgEONHJ9M52wQEdmOsjIgNlZ7Kytr/fOTJyRj/YT1\n4neMqAVGBeFpaWl4/fXXcfLkSRw7dgydOnXCs88+i/Lycn2bxMRErFu3Dh988AGys7OhUCgwbtw4\nVFVVmazzRNQ+uo96V8xRopeLCmP6DsbwvpwNIiLboNvCcNUq7W3kyNYH4r28enGbVbIIo9JRDh06\nZHB/586dkMlkyMrKwsSJEyEIApKSkrBs2TJMnjwZALB9+3YoFArs2rULc+bMEb/nRCQK3Ue9r7Lg\nDhHZGFNuYUhkam3KCb916xY0Gg08PT0BAAUFBSgpKcH48eP1bZycnDBixAhkZWUxCCeyAZwJIiIy\nxL3EyZQkgiAIrX3S1KlT8eOPPyInJwcSiQRZWVkYPnw4rl69isDAQH272bNno6ioyGAmvbKyUv91\nfn5+O7tPREREHVVFRSfMmdMHBQUuAIDg4DvYsuUyPDweinL+H27/gAWnFqD8vjb91tPRE5uHbEYv\nd05adEQhISH6r2UyWbvP1+qZ8KVLlyIrKwuZmZmQSCQttjemDREREVFreXg8xJYtl7F7twIAMG3a\nL6IF4ADQ2703+sv64+vSrwEA/WX9GYCTaFoVhC9ZsgSff/45jh8/jh49euiP+/r6AgBKSkoMZsJL\nSkr0jzVGpVK1srvUlJycHAAcU7HZyrge+C4Db/9L+5GpUgk4OVn3R6a2Mq62iGNrGhxX0xBrXJ99\nVveVf/s61Ih/BP0DY3eMhQABH774oU1sZcjXq2nUzeYQg9EVMxcvXow9e/bg2LFj6NOnj8FjwcHB\n8PX1xZEjR/THampqkJmZiYiICPF6S0QNlJUB6nmeOHs3BWcdtuLTC1ux70IKvJy9LN01IiKbp9tL\nfHDAYJsIwMl2GDUTvnDhQnz66afYv38/ZDIZiouLAQDu7u5wdXWFRCKBWq3G6tWr0a9fP4SEhCAh\nIQHu7u6YPn26Sb8Boo4uKQm4ckoJ9HxccMfjDgvuEBGVlYlTbTN5AnePIvEZFYRv3rwZEokEY8eO\nNTgeHx+Pt99+GwDw17/+FXfv3sXChQtRXl6OIUOG4MiRI3B1dRW/10TU0NFEwD8HgICxXVhwh4g6\nNt0e4rotDPft09ZFaEsgzt2jyBSMCsI1Go1RJ4uLi0NcXFy7OkREraNWa99c8vKUQJEKbm4SrFrF\nWXAi6ti4hzhZuzbtE05E1kNX9TIpCfgVyXg1pu0fuRIRkfG4jzi1B4NwIjugq3oJ8CNTIiKg7qeE\n2vv9+2uPicnTyRMpl1JQeqcUACB3kUM9ROSLkN0yencUIiIiIluh+5RwxQrtra354M1R+igRHhCu\nvx8ewEXxZDzOhBMREZFdevwpoekkjk1EzvUcCBCw9lkuiifjMQgnIiIiaiPdPuISSDgLTq3CIJyI\niIioHbiPOLUFg3AiK2FrpeeJiGyZWIV8AO4jTm3DIJzICuhKz18ZngK4leLsBaCbE1fZExGZgpiF\nfIjaikE4kRVg6XkiIvMxZyEf7iVOTWEQTmRNWHqeiMiucC9xagr3CSeyAmq1tpAESh+Vnr81GKvU\nnAUnIjIF/d/cR0xRyEeHe4lTUzgTTmQFWHqeiMh86v7NBdq/MLMl3EucGsMgnMhKsPQ8EZH5mKOQ\njw73EqfGMAgnIiIiMjHuJU71MQgnIiIiMjHuJU71MQgnIiIiqkfMYj5EjWEQTkRERFQHi/mQOTAI\nJxIRZ06IiGyfOYv5ACzo01ExCCcSSVkZoJqSgUKZ9g/pxjeASROBOc/wDykRETWNBX06JqOL9aSn\npyM6OhqBgYGQSqXYvn27weMxMTGQSqUGt4iICNE7TGStkpKAwgueQN8U4OmtqOi5FXvzUuDl7GXp\nrhERUSuYs5gPwII+HZXRQXh1dTUGDhyI9evXw9nZGRKJxOBxiUSCcePGobi4WH9LTU0VvcNEVq1U\nCRQ9/kPqJ/APKRGRrdEV81mxQnszRz544thEKFwUkLvIWdCngzA6HSUqKgpRUVEAtLPe9QmCAEdH\nRygUCtE6R2RL1Grt4p28o4mAfw4cOgn4JIZ/SImIbJE5i/kALOjTEYmWEy6RSJCZmQkfHx94eHhg\n5MiRWLVqFeRyuViXILJqj8sgK/GZgwo9gyUY3pd/SImIyDgs6NOxSARBEFr7JHd3d2zcuBGzZs3S\nH9uzZw9cXV0RHByMgoICxMbGora2Ft9++y0cHR317SorK/Vf5+fnt7P7RNbpWvU1AECQa5CFe0JE\nRERiCAkJ0X8tk8nafT7RZsJffvll/dehoaF4+umn0b17dxw8eBCTJ08W6zJENoHBNxGR/aqo6ITd\nu7Xpt9Om/QIPj4cW7hHZIpNtUejn54fAwED88MMPTbZRqVSmunyHk5OTA4BjKjaOq2lwXE2HY2sa\nHFfTsMVxrV/I59Qpf6sr5GOL42oL6mZziMHo3VFaq7S0FNevX4efn5+pLkFERERkVk0V8iFqLaNn\nwqurq/U53BqNBoWFhTh79iy6desGLy8vxMXF4cUXX4Svry9++uknLFu2DD4+PkxFISIiImoHVtS0\nT0bPhGdnZ+Opp57CU089hZqaGsTFxeGpp55CXFwcHBwckJubi+effx59+/ZFTEwMnnzySZw8eRKu\nrq6m7D8RERGR2Zi7kA/wuKLm1jNbsfXMVqRcYiE4e2D0TPioUaOg0WiafPzQoUOidIiIiIjIWj3e\njlZ7X602fT64rqJmar62CCIratoHky3MJLJFB77LwNv/0n7kp1QCt6tKMTFwIlTg4hYiItIydyEf\nQFtRM+d6DgQIrKhpJxiEEz1SVgao53niyvAUwK0UZy8Ask6emBY8zdJdIyKiDo4VNe0Pg3CiR5KS\ngCunlEDPcKCP9iM/99uD0Mu9l4V7RkRExIqa9oZBOFF9RxMB/xwAAlS3Yi3dGyIiIgBALy9OCtkT\nk+0TTmRr9CveS5VAkQputwZj4Uuelu4WERHZkLIyIDZWeysrs3RvyJpxJpzokbor3n9FMl6NASQV\n5ZbuFhER2Yj61TT37YPVVdMk68GZcKI6dCveNyX0QnhvfuxHRETGYzVNag3OhBMRERHZsPoVNUvL\nuL2uLWAQTkRERCQCtVqbgqK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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', label='no wind')\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\", label='10mph wind')\n", "plt.legend(scatterpoints=1);" ] }, { "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", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from math import radians, sin, cos, sqrt, exp\n", "\n", "class BaseballPath(object):\n", " def __init__(self, x0, y0, launch_angle_deg, velocity_ms, \n", " noise=(1.0, 1.0)): \n", " \"\"\" Create 2D baseball path object \n", " (x = distance from start point in ground plane, \n", " y=height above ground)\n", " \n", " x0,y0 initial position\n", " launch_angle_deg angle ball is travelling respective to \n", " ground plane\n", " velocity_ms speeed of ball in meters/second\n", " noise amount of noise to add to each position\n", " 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 \n", " step and 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 + randn()*self.noise[0], \n", " self.y + randn()*self.noise[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can test the Kalman filter against measurements created by this model." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RGVZmfRFCtDulZYrXP4MX3oPcfPvHRPWEZ2ZBb+8UTKbaXnSlFIczU9mwO5Ht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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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,\n", " 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.array([[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='r', marker='o', s=75, alpha=0.5)\n", "\n", "p2, = plt.plot(xs, ys, lw=2)\n", "p3, = plt.plot(xs2, ys2, lw=4)\n", "plt.legend([p1, p2, p3], \n", " ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)'],\n", " loc='best', scatterpoints=1);" ] }, { "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", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SBx980JDu4ezszIYNG3j55ZeZM2cO9vb2jB8/nqeeeopOnToZ9tWiRQsmT57M1q1bWbVq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\na9euhuP610tj8bO315Jeamoqrly5gvDwcDg5OcHJyQlJSUlISEiAXC5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xzbVr13jmmWfw8PBAq9USFBTEV199VWA/27dvR6PRsGzZMqZPn07Dhg2xs7Pj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\nq9C5uCBv3jz4OTk1fVhPgyWkdfdkScaU4U9g7fcx+CXpfxH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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.array([[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", " p1 = plt.scatter(x, y, color='r', marker='o', s=75, alpha=0.5)\n", "\n", " p2, = plt.plot(xs, ys, lw=2)\n", " plt.legend([p1, p2], ['Measurements', 'Kalman filter'], scatterpoints=1)\n", " plt.show()\n", " \n", "plot_ball_with_q(0.01)\n", "plot_ball_with_q(0.1)" ] }, { "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", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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nZ2fD9jk5OcTExFS4AWmqJFAXQoh6KiwuIDMnjczcVDJy0ohPPk9U9DZyC7MM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\n9poMiq3PrLmSp9/grCysefy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5Mn5+fobtHn30URISEti4caNhWWZmpuH3s2fPNkTzhKgR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\nbPHrqIazszOioqKwe/dui+N79uyxu1y0Z9myZeYifejQoRbnQkJC4O/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79sTe3p6ff/653Nut0KDyKmQwGHjiiSeIiYnhk08+Yfny5TRs2BCNRlPkmAov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\nPlzy/TowQgjdUsxOSqVSd/WMeR28vuQwMjIStra2enPKyspQWFjIPPe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_ball_with_q(0.01, r=3, noise=3.)\n", "plot_ball_with_q(0.1, r=3, noise=3.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This output is terrible. The filter has no choice 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": "markdown", "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": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }