diff --git a/Designing_Kalman_Filters.ipynb b/Designing_Kalman_Filters.ipynb index 7b08a3a..bcf274e 100644 --- a/Designing_Kalman_Filters.ipynb +++ b/Designing_Kalman_Filters.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:1176e606a0fbcfee32c2c1282d705afff40c345291d62a713bbb17979900fd8d" + "signature": "sha256:dc7abfb3c31bceb18f38ed34d63ab344a0e937dfb0c1b339c16885b1cc985f8a" }, "nbformat": 3, "nbformat_minor": 0, @@ -246,13 +246,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 93, + "prompt_number": 1, "text": [ - "" + "" ] } ], - "prompt_number": 93 + "prompt_number": 1 }, { "cell_type": "heading", @@ -313,7 +313,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 94 + "prompt_number": 2 }, { "cell_type": "markdown", @@ -340,13 +340,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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Smp+gJ4BtgKJSLOIC/KXP6FEUXtqQzfiIGtKtdZrF4S/59AWSS215W8B7AjFA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\nQxFCCJ/SJsPUNWvWKIMGDWq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qOYJfeg61s2bB1KePrUNqFPOT7AWLXyIiIhs6kVeJOC8FoNej5umnbR0Okd1j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\nsj/+sEFERERE9HcsfsnhtEffmtEsIKW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8LEQFLgiPmf37lezcqcRq9Q0ffPJJN2XKePlxfyJP6a4z4gMHU2YGM3q0nqef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\nHR34Hsl/7Gbj3PUcVKrZUuMJcrmcmN0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z58zPunpVxdKlOmbP9uTZZ82MHZv2SCxMc5fM/AohhBDikXbwoIb+/Y20amXl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\ndK9bkmm3Jb6uRERE0Lq1lX/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JXxrKNXsag348yk+HE7DYsl/0dlODBnZ++cVZXBwaamPX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X/Xe7s9nMrgQwD6MUEWLVWR0Yd7RZCYWke+5JUv/+Xp11FucVxzvWFtTXkbJS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\nIV5dcYVPbu4qDgC1qm3GmB1jIEYlJ0s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3HN7aQ/63IqSr6pamqe5YtmaNlaNHDaZM8fHhh5UsWlTNsGGRu8JY57qszrGB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\nh9raFU9744zGQnU+4FaPx5M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6CmjFkbfpdblsZWa2vASC7MxGfubqqdl98olLF12UqylT8vXEE2kKBJyeUdfo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\nWWedRX5JbPny5frggw+UnZ2tG264QVL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kO7ORn7kSNTu/X/rkE5f++U+XAgGnZ9N1EjU/HD2KaCBBZWZKP/tZgyZM8Oui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\n3z725jwaTmeHY0N+5iI7s5E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"text": [ - "" + "" ] } ], - "prompt_number": 107 + "prompt_number": 15 }, { "cell_type": "markdown", @@ -1134,7 +1134,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 108 + "prompt_number": 16 }, { "cell_type": "markdown", @@ -1173,13 +1173,13 @@ { "metadata": {}, "output_type": "display_data", - "png": 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74ELlVClofUEflS2VHOw9SFAJkhafxjrLOvKSz26gIfwc/1L3Fw70HCAghwdB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\nj3tW3uPYGFaxcKpGvxVoB0bfY7wJaAIagRtjeG8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65s6bC4CKyswxM/nHa/8xvDT7SMtIKXcoxDByIXOS5ZNAiCHoU+en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"text": [ - "" + "" ] } ], - "prompt_number": 109 + "prompt_number": 17 }, { "cell_type": "markdown", @@ -1292,15 +1292,12 @@ "from KalmanFilter import KalmanFilter\n", "from math import sin,cos,radians\n", "\n", - "def ball_kf(x, y, omega, v0, dt):\n", + "def ball_kf(x, y, omega, v0, dt, r=0.5, q=0.02):\n", "\n", " g = 9.8 # gravitational constant\n", - "\n", " f1 = KalmanFilter(dim_x=5, dim_z=2)\n", "\n", - "\n", " ay = .5*dt**2\n", - "\n", " f1.F = np.mat ([[1, dt, 0, 0, 0], # x = x0+dx*dt\n", " [0, 1, 0, 0, 0], # dx = dx\n", " [0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2\n", @@ -1311,8 +1308,8 @@ " [1, 0, 0, 0, 0],\n", " [0, 0, 1, 0, 0]])\n", " \n", - " f1.R *= 0.5\n", - " f1.Q *= 0.02\n", + " f1.R *= r\n", + " f1.Q *= q\n", "\n", " omega = radians(omega)\n", " vx = cos(omega) * v0\n", @@ -1325,7 +1322,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 110 + "prompt_number": 34 }, { "cell_type": "markdown", @@ -1338,10 +1335,10 @@ "cell_type": "code", "collapsed": false, "input": [ - "y = 15.\n", + "y = 1.\n", "x = 0.\n", - "theta = 20. # launch angle\n", - "v0 = 100.\n", + "theta = 35. # launch angle\n", + "v0 = 50.\n", "dt = 1/10. # time step\n", "\n", "ball = BallTrajectory2D(x0=x, y0=y, theta_deg=theta, velocity=v0, noise=[1,1])\n", @@ -1361,8 +1358,7 @@ " \n", " f1.predict() \n", " \n", - " #p1 = plt.scatter(f1.x[0,0], f1.x[2,0], color='black', marker='+', s=75)\n", - " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", "\n", "p2, = plt.plot (xs, ys,lw=2)\n", "plt.legend([p2,p1], ['Kalman filter', 'Measurements'])\n", @@ -1374,13 +1370,20 @@ { "metadata": {}, "output_type": "display_data", - "png": 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89gnTIvQWNp+dNZuucFf0PF3X8Yf9pDnT+O6M7xLorUx+HPyKn3nZ806p5UTl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\n+vvk0lx0dFjbDFaV59DRv5Lu4XJ8sTdZubwSBw4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am+ttogxR5MTmjHaYQowb0jMshBiTnj/8PHVddUHbIPyqn8yoTP4p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"text": [ - "" + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "237.122227572\n" ] } ], - "prompt_number": 111 + "prompt_number": 26 }, { "cell_type": "markdown", @@ -1403,7 +1406,11 @@ "source": [ "We are now ready to design a practical Kalman filter application. For this problem we assume that we are tracking a ball travelling 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 travelling 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. \n", "\n", - "Our first step is to learn 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 nonspinning, smooth ball, such as a cannonball. I will use the math developed by Nicholas Giordano and Hisao Nakanishi in *Computational Physics* [1997]. \n", + "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 nonspinning 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 $\\mathbf{Q}$ and $\\mathbf{R}$ 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", @@ -1420,73 +1427,254 @@ "$$ a_x = -\\frac{B_2}{m}v v_x\\\\\n", "a_y = -\\frac{B_2}{m}v v_y$$\n", "\n", - "Giordano provides this 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. \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", - "$$\\frac{B_2}{m} = 0.0039 + \\frac{0.0058}{1+e^{(v-35)/5}}$$\n", + "$$\\frac{B_2}{m} = 0.0039 + \\frac{0.0058}{1+\\exp{[(v-35)/5]}}$$\n", "\n", - "\n" + "Starting with this Euler discretation of the ball path in a vacuum:\n", + "$$\\begin{aligned}\n", + "x &= v_x \\Delta t \\\\\n", + "y &= v_y \\Delta t \\\\\n", + "v_x &= v_x \\\\\n", + "v_y &= v_y - 9.8 \\Delta t\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We can incorporate this force (acceleration) into our equations by incorporating $accel * \\Delta t$ into the velocity update equations. We should subtract this compenent 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 presense 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 customary units, and we will follow suit here (http://en.wikipedia.org/wiki/United_States_customary_units). Note that the velocity of 50 m/s corresponds to a velocity of 110 mph, which is a typical exit speed for a baseball for a home run hit." ] }, { "cell_type": "code", "collapsed": false, "input": [ - "from math import sqrt, exp\n", - "def a_drag(v):\n", - " #return 4.0E-5 * v\n", - " return 0.0039 + 0.0058 / (1. + exp((v-35.)/5.))\n", + "from math import sqrt, exp, cos, sin, radians\n", "\n", - "mph_to_m_s = 0.447 # mph to meters/sec\n", - "v = 50\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 = 50.\n", "y = 1\n", "x = 0\n", - "dt = .001\n", + "dt = .1\n", "theta = radians(35)\n", "\n", - "def solve(x,y,v, v_wind):\n", - " vx = v*cos(theta)\n", - " vy = v*sin(theta)\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 += vx*dt\n", - " y += vy*dt\n", + " x += v_x*dt\n", + " y += v_y*dt\n", "\n", " # force due to air drag \n", - " v = sqrt ((vx-v_wind)**2 + vy**2) \n", - " F = a_drag(v)*v\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", - " vx = vx - F*(vx-v_wind)*dt\n", - " vy = vy - 9.8*dt - F*vy*dt\n", - " \n", - " #plt.scatter(x,y)\n", - " return x, y\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", - "x,y = solve(0, 1, v, 10*mph_to_m_s)\n", - "x2,y2 = solve(0, 1, v, -10*mph_to_m_s)\n", - "print (x,x2)\n", - "(x-x2)*3.28" + " xs.append(x)\n", + " ys.append(y)\n", + " \n", + " return xs, ys\n", + " \n", + "x,y = solve(x=0, y=1, vel=v, v_wind=0, launch_angle=theta)\n", + "p1 = plt.scatter(x, y, color='blue')\n", + "\n", + "x,y = solve(x=0, y=1,vel=v, v_wind=4.47, launch_angle=theta) # roughly 10 mph wind\n", + "p2 = plt.scatter(x, y, color='green', marker=\"v\")\n", + "plt.legend([p1,p2], ['no wind', '10mph wind'])\n", + "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "132.904542049 115.061343571\n" - ] - }, { "metadata": {}, - "output_type": "pyout", - "prompt_number": 289, + "output_type": "display_data", + "png": 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EPMLixYvp378/9erV4/bbby93X3FxMZMmTSIxMZHWrVvz0UcfueSYFovlrB+jfL4aNGhA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\n+nIVTqe+EZ+LzinjlJUxysmY2pTT9On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"text": [ - "58.52569100894303" + "" ] } ], - "prompt_number": 289 + "prompt_number": 29 + }, + { + "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 propogate the solution; use of a more accurate technique such as Runge-Kutta is left as an exercise for the reader. That modest complication is unnessesary for what we are doing because the accuracy difference between the techniques will be small for the time steps we will be using. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import radians, sin, cos, sqrt, exp\n", + "\n", + "class BaseballPath(object):\n", + " def __init__(self, x0, y0, launch_angle_deg, velocity_ms, noise=(1.0,1.0)): \n", + " \"\"\" Create 2D baseball path object \n", + " (x = distance from start point in ground plane, y=height above ground)\n", + " \n", + " x0,y0 initial position\n", + " launch_angle_deg angle ball is travelling respective to ground plane\n", + " velocity_ms speeed of ball in meters/second\n", + " noise amount of noise to add to each reported position in (x,y)\n", + " \"\"\"\n", + " \n", + " omega = radians(launch_angle_deg)\n", + " self.v_x = velocity_ms * cos(omega)\n", + " self.v_y = velocity_ms * sin(omega)\n", + "\n", + " self.x = x0\n", + " self.y = y0\n", + "\n", + " self.noise = noise\n", + "\n", + "\n", + " def drag_force (self, velocity):\n", + " \"\"\" Returns the force on a baseball due to air drag at\n", + " the specified velocity. Units are SI\n", + " \"\"\"\n", + " B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.))\n", + " return B_m * velocity\n", + "\n", + "\n", + " def update(self, dt, vel_wind=0.):\n", + " \"\"\" compute the ball position based on the specified time step and\n", + " wind velocity. Returns (x,y) position tuple.\n", + " \"\"\"\n", + "\n", + " # Euler equations for x and y\n", + " self.x += self.v_x*dt\n", + " self.y += self.v_y*dt\n", + "\n", + " # force due to air drag\n", + " v_x_wind = self.v_x - vel_wind\n", + " v = sqrt (v_x_wind**2 + self.v_y**2)\n", + " F = self.drag_force(v)\n", + "\n", + " # Euler's equations for velocity\n", + " self.v_x = self.v_x - F*v_x_wind*dt\n", + " self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt\n", + "\n", + " return (self.x + random.randn()*self.noise[0], \n", + " self.y + random.randn()*self.noise[1])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 30 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can test the Kalman filter against measurements created by this model. There is truly a significant difference in the predictions by the process model; the Kalman filter assumes that the ball is in a vacuum, and thus predicts that the ball would travel about twice as far as it actually does." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y = 1.\n", + "x = 0.\n", + "theta = 35. # launch angle\n", + "v0 = 50.\n", + "dt = 1/10. # time step\n", + "\n", + "ball = BaseballPath(x0=x, y0=y, launch_angle_deg=theta, velocity_ms=v0, noise=[.3,.3])\n", + "f1 = ball_kf(x,y,theta,v0,dt,r=1.)\n", + "f2 = ball_kf(x,y,theta,v0,dt,r=10.)\n", + "t = 0\n", + "xs = []\n", + "ys = []\n", + "xs2 = []\n", + "ys2 = []\n", + "\n", + "while f1.x[2,0] > 0:\n", + " t += dt\n", + " x,y = ball.update(dt)\n", + " z = np.mat([[x,y]]).T\n", + "\n", + " f1.update(z)\n", + " f2.update(z)\n", + " xs.append(f1.x[0,0])\n", + " ys.append(f1.x[2,0])\n", + " xs2.append(f2.x[0,0])\n", + " ys2.append(f2.x[2,0]) \n", + " f1.predict() \n", + " f2.predict()\n", + " \n", + " p1 = plt.scatter(x, y, color='green', marker='o', s=75, alpha=0.5)\n", + "\n", + "p2, = plt.plot (xs, ys,lw=2)\n", + "p3, = plt.plot (xs2, ys2,lw=4, c='r')\n", + "plt.legend([p1,p2, p3], ['Measurements', 'Kalman filter(R=0.5)', 'Kalman filter(R=10)'])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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jR44wbtw4evbsSWRkpOuYRx99lBUrVjBy5Mjrv7jrJEaEm4hb8S7ypkrE0rtE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+ "text": [ + "" + ] + } + ], + "prompt_number": 48 + }, + { + "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 $\\textbf{R}$ on the output, they are not intended to imply a correct design.\n", + "\n", + "With R=0.5 we see that the Kalman filter follows the measurements quite closely, albeit slightly overshooting at the end of the trajectory. This small value of R tells the Kalman filter that we expect there to be about 1/2 meter error in the ball measurements, which is quite small, so the Kalman filter prefers the position implied by the measurement vs the process model. The small amount of overshoot is attributable to the incorrect assumption that the ball is travelling in a vacuum during the predict step. We see the effect of this when we set R=10, which incorrectly tells the Kalman filter that the noise in the measurments is on order of 10 meters. In this case the Kalman filter weights the prediction more, and the trajectory ends up overshoooting the measurements because air drag is not being considered by the filter. \n", + "\n", + "At this point we should question the value of $\\textbf{Q}$, which tells the Kalman filter how much process noise there is in the system. We can think of air drag as process noise, and setting $Q=\\verb,I*0.1,$, for example, would cause the Kalman filter to fit the measurements quite well. If you are reading this in IPython Notebook I urge you to modify the code above to see the effects of various values for $\\textbf{Q}$ and $\\textbf{R}$. \n", + "\n", + "However, the errors caused by our process model are anything but Gaussian, so a large $\\textbf{Q}$ is a poor representation of the errors in the model. A better approach is to redesign the Kalman filter to model the behavior of a ball in air.\n", + "\n", + "This is where Kalman filter design becomes an 'art'. I prefer to think of it as emperical engineering. We try designs, measure their performance, work to understand the limits of the mathematical model that we are using, make changes based on that new understanding, and measure the performance of that new system to see if it matches our expectations. Blithely changing $\\textbf{Q}$ and $\\textbf{R}$ will eventually give you a filter that performs very well for a specific set of data, but the filter is likely to perform badly in different situations. Much of this theory and practice was developed by the radar folks in the 1960s and beyond. They were trying to develop filters to track aircraft and missles based on signals generated by radar. Testing was (and is) cumbersome and expensive, and they endlessly faught against overtuning their filters to the rather sparse data they had available. Your application may be less expensive and difficult to test, and you must do everything you can to ensure that your filter is robust in the presense of various process noise. There is significant literature devoted to this topic, and you will have to read it and master it if your application is critical. An excellent introduction to the topic (and excellent introduction to Kalman filters taking a g-h filters approach is the book *Tracking and Kalman Filters Made Easy* by Eli Brookner. I highly recommend this book even if tracking is not your primary interest, as its approach to the math is very clear, yet still rigorous." + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Kalman Filter with Air Drag" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will dispense with the step 1, step 2, type approach and proceed in a more natural style that you would use in a non-toy engineering problem. We have already developed a Kalman filter that does excellently at tracking a ball in a vacuum, but that does not incorporate the effects of air drag into the model. We know that the process model is implemented with $\\textbf{F}$, so we will turn our attention to that immediately.\n", + "\n", + "Notionally, the computation that $\\textbf{F}$ computes is\n", + "\n", + "$$x' = Fx$$\n", + "\n" + ] }, { "cell_type": "heading", diff --git a/exp/ball.py b/exp/ball.py index feac7d8..baad47d 100644 --- a/exp/ball.py +++ b/exp/ball.py @@ -7,89 +7,136 @@ Created on Sat Jul 5 16:07:29 2014 import numpy as np from KalmanFilter import KalmanFilter -from math import radians, sin, cos +from math import radians, sin, cos, sqrt, exp import numpy.random as random import matplotlib.markers as markers +import matplotlib.pyplot as plt + class BallPath(object): def __init__(self, x0, y0, omega_deg, velocity, g=9.8, noise=[1.0,1.0]): omega = radians(omega_deg) self.vx0 = velocity * cos(omega) self.vy0 = velocity * sin(omega) - + self.x0 = x0 self.y0 = y0 - + self.g = g self.noise = noise - + def pos_at_t(self, t): """ returns (x,y) tuple of ball position at time t""" x = self.vx0*t + self.x0 y = -0.5*self.g*t**2 + self.vy0*t + self.y0 - + return (x +random.randn()*self.noise[0], y +random.randn()*self.noise[1]) + + + +class BaseballPath(object): + def __init__(self, x0, y0, omega_deg, velocity, noise=[1.0,1.0]): + omega = radians(omega_deg) + self.v_x = velocity * cos(omega) + self.v_y = velocity * sin(omega) + + self.x = x0 + self.y = y0 + + self.noise = noise + + + def drag_force (self, velocity): + """ Returns the force on a baseball due to air drag at + the specified velocity. Units are SI + """ + B_m = 0.0039 + 0.0058 / (1. + exp((velocity-35.)/5.)) + return B_m * velocity + + + def update(self, dt, vel_wind=0.): + """ compute the ball position based on the specified time step and + wind velocity. Returns (x,y) position tuple. + """ + + # Euler equations for x and y + self.x += self.v_x*dt + self.y += self.v_y*dt + + # force due to air drag + v_x_wind = self.v_x - vel_wind + v = sqrt (v_x_wind**2 + self.v_y**2) + F = self.drag_force(v) + + # Euler's equations for velocity + self.v_x = self.v_x - F*v_x_wind*dt + self.v_y = self.v_y - 9.81*dt - F*self.v_y*dt + + return (self.x + random.randn()*self.noise[0], + self.y + random.randn()*self.noise[1]) + + + +def test_baseball_path(): + ball = BaseballPath (0, 1, 35, 50) + while ball.y > 0: + ball.update (0.1, 0.) + plt.scatter (ball.x, ball.y) - - -y = 15 -x = 0 -omega = 0. -noise = [1,1] -v0 = 100. -ball = BallPath (x0=x, y0=y, omega_deg=omega, velocity=v0, noise=noise) -t = 0 -dt = 1 -g = 9.8 - - -f1 = KalmanFilter(dim=6) -dt = 1/30. # time step - -ay = -.5*dt**2 - -f1.F = np.mat ([[1, dt, 0, 0, 0, 0], # x=x0+dx*dt - [0, 1, dt, 0, 0, 0], # dx = dx - [0, 0, 0, 0, 0, 0], # ddx = 0 - [0, 0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2 - [0, 0, 0, 0, 1, dt], # dy = dy0 + ddy*dt - [0, 0, 0, 0, 0, 1]]) # ddy = -g -f1.B = 0. - -f1.H = np.mat([ - [1, 0, 0, 0, 0, 0], - [0, 0, 0, 1, 0, 0]]) - -f1.R = np.eye(2) * 5 -f1.Q = np.eye(6) * 0. - -omega = radians(omega) -vx = cos(omega) * v0 -vy = sin(omega) * v0 - -f1.x = np.mat([x,vx,0,y,vy,-9.8]).T - -f1.P = np.eye(6) * 500. - - - - -z = np.mat([[0,0]]).T -count = 0 -markers.MarkerStyle(fillstyle='none') - -np.set_printoptions(precision=4) -while f1.x[3,0] > 0: - count += 1 - #f1.update (z) - f1.predict() - print f1.x[0,0], f1.x[3,0] - #markers.set_fillstyle('none') - plt.scatter(f1.x[0,0],f1.x[3,0], color='green') - +def test_ball_path(): + + y = 15 + x = 0 + omega = 0. + noise = [1,1] + v0 = 100. + ball = BallPath (x0=x, y0=y, omega_deg=omega, velocity=v0, noise=noise) + dt = 1 + f1 = KalmanFilter(dim=6) + dt = 1/30. # time step + + ay = -.5*dt**2 + + f1.F = np.mat ([[1, dt, 0, 0, 0, 0], # x=x0+dx*dt + [0, 1, dt, 0, 0, 0], # dx = dx + [0, 0, 0, 0, 0, 0], # ddx = 0 + [0, 0, 0, 1, dt, ay], # y = y0 +dy*dt+1/2*g*dt^2 + [0, 0, 0, 0, 1, dt], # dy = dy0 + ddy*dt + [0, 0, 0, 0, 0, 1]]) # ddy = -g + f1.B = 0. + + f1.H = np.mat([ + [1, 0, 0, 0, 0, 0], + [0, 0, 0, 1, 0, 0]]) + + f1.R = np.eye(2) * 5 + f1.Q = np.eye(6) * 0. + + omega = radians(omega) + vx = cos(omega) * v0 + vy = sin(omega) * v0 + + f1.x = np.mat([x,vx,0,y,vy,-9.8]).T + + f1.P = np.eye(6) * 500. + + z = np.mat([[0,0]]).T + count = 0 + markers.MarkerStyle(fillstyle='none') + + np.set_printoptions(precision=4) + while f1.x[3,0] > 0: + count += 1 + #f1.update (z) + f1.predict() + plt.scatter(f1.x[0,0],f1.x[3,0], color='green') +if __name__ == '__main__': + test_baseball_path() + #test_ball_path() +