diff --git a/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb b/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb index cb1c85b..c562c2c 100644 --- a/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb +++ b/09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb @@ -259,13 +259,13 @@ ], "metadata": {}, "output_type": "pyout", - "prompt_number": 2, + "prompt_number": 1, "text": [ - "" + "" ] } ], - "prompt_number": 2 + "prompt_number": 1 }, { "cell_type": "markdown", diff --git a/10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb b/10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb index 8169d32..bc1a674 100644 --- a/10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb +++ b/10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb @@ -1,7 +1,7 @@ { "metadata": { "name": "", - "signature": "sha256:0c0bb47419d5cc93676b016c0494006e579ca5b7c7b773014800489a190f0e42" + "signature": 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OtOpgiYjag+PHVUhKUiMpSY3jx1Uuj2k0ciHQdASnWq3IZZtRo0xISwvApk2x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\n65l7//qXXQsX9nP+HgAAQAQRvQAAADDesNG7YcM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RmD59OgIDA5GXl4fU1FSEhIQgNjZWuJ+tW7diyZIlSElJwVtvvYWUlBTExsbC29u70WOn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\nX7t27Qr7wAAAAMBQGTCGe3p6dN9992n79u2qra1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oJulTiKhiLICJVEzrxrZo3VixMcwV6e3dEHkFYrmfn5WTj592nkddS+NXrmNV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\n6RR0EL+mAADOYLfbTSe0Y7PZJPlHl9PlVlhY2EXdpz89Xl3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9SMXq4AtYGxKHkd7OmD6sExzMZXt9B5GyYAFMJCfcHS1rtV5PFzuUvHL7GnPz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\nE3F/cjgcGjNmjPLz83XDDTdo48aNcrlcxvf/tre3q62tTe3t7ero6JD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"text": [ - "" + "" ] } ], @@ -361,7 +361,7 @@ "\n", "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. This is called a 'monte carlo' approach, and it used by some Kalman filter designs, such as the *Ensemble filter*. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the transfer function is, as long as we sample with enough points we will build an accurate output distribution.\n", "\n", - "\"Enough points\" is the rub. The graph above was created with 500,000 points, and the output is still not smooth. You wouldn't need to use that many points to get a reasonable estimate of the mean and variance, but it will require many points. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you need $50$ points for 1 dimension, you need $50^2$ for two dimensions, $50^3$ for three dimensions, and so on. So while this approach does work, it is very computationally expensive. The Unscented Kalman filter uses a somewhat similar technique but reduces the amount of computation needed by a drastic amount. " + "\"Enough points\" is the rub. The graph above was created with 500,000 points, and the output is still not smooth. You wouldn't need to use that many points to get a reasonable estimate of the mean and variance, but it will require many points. What's worse, this is only for 1 dimension. In general, the number of points required increases by the power of the number of dimensions. If you need $50$ points for 1 dimension, you need $50^2$ for two dimensions, $50^3$ for three dimensions, and so on. So while this approach does work, it is very computationally expensive. The Unscented Kalman filter uses a somewhat similar technique but reduces the amount of computation needed by a drastic amount, and also uses a deterministic method of choosing the points." ] }, { @@ -394,7 +394,7 @@ "output_type": "display_data", "png": 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juV88w5MxKKgZjUY0tvUiZYKXsWJJpU9zOIahkAIhXIc1YEnq6uqE0S5saWlB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\n+kqDkitfU+LeVyNqEfzI3/6xpj/6UcRGqvTwz/+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"text": [ - "" + "" ] } ], @@ -406,6 +406,111 @@ "source": [ "Here on the left we show an ellipse depicting the $1\\sigma$ distribution of two variables. The arrows show how three randomly sampled points might be transformed by some arbitrary nonlinear function to a new distribution. The ellipse on the right is drawn semi-transparently to indicate that it is an *estimate* of the mean and variance of this collection of points - if we were to sample, say, a million points the shape of the points might be very far from an ellipse. \n", "\n", + "Let's look at that. Let's run a bunch of points through a nonlinear function.\n", + "\n", + "###### Exercise: Plot 2D points\n", + "\n", + "Write a function to pass points through state transition:\n", + "\n", + "$$\\mathbf{Fx} = \\begin{bmatrix}1 & 1 \\\\ .1x &y\\end{bmatrix}\\begin{bmatrix}x\\\\y\\end{bmatrix}$$ \n", + "\n", + "for the mean $$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}$$ and the covariance\n", + "$$\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$\n", + "\n", + "Plot both the original points and the converted points. Plot the mean passed through the function vs the calculated value, and print the difference between the two." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# your answer here" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###### Solution\n", + "\n", + "Here is my answer." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy.random import randn\n", + "import numpy as np\n", + "from numpy import sin, cos, tan,log\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from numpy.random import multivariate_normal\n", + "\n", + "\n", + "def f(x,y):\n", + " return x+y, .1*x**2 +y*y\n", + "\n", + "mean = (0, 0)\n", + "p = np.array([[32, 15],[15., 40.]])\n", + "\n", + "xs ,ys = multivariate_normal(mean=mean, cov=p, size=5000).T\n", + "fxs, fys = [], []\n", + "for x,y in zip(xs,ys):\n", + " fx, fy = f(x,y)\n", + " \n", + " fxs.append(fx)\n", + " fys.append(fy)\n", + "\n", + "# Compute mean\n", + "mean_fx = f(*mean)\n", + "\n", + "computed_mean_x = np.average(fxs)\n", + "computed_mean_y = np.average(fys)\n", + "\n", + "plt.subplot(121)\n", + "plt.scatter (xs,ys, marker='.')\n", + "plt.axis('equal')\n", + "\n", + "plt.subplot(122)\n", + "plt.scatter(fxs, fys, marker='.')\n", + "plt.scatter(mean_fx[0], mean_fx[1], marker='v', s=120,c='r')\n", + "plt.scatter(computed_mean_x, computed_mean_y, marker='*',s=120,c='r')\n", + "plt.ylim([-10,290])\n", + "plt.xlim([-150,150])\n", + "plt.show()\n", + "print ('Difference in mean x={:.3f}, y={:.3f}'.format(\n", + " computed_mean_x-mean_fx[0], computed_mean_y-mean_fx[1]))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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FPBNjdrYWEmnmxJq+MNDIRX6+jh07ciGKAn78YxXBYG9OM8C8lXlqRrhA3rix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\nvM7u3Tbi43UuXjSRkKDzzjsOjhyxMHGiSkGBn6oqGwkJOhYL7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+ "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Difference in mean x=-0.037, y=42.097\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "So what would be fewest number of sampled points that we can use, and what kinds of constraints does this problem formulation put on the points? We will assume that we have no special knowledge about the nonlinear transform as we want to find a generalized algorithm. For reasons that come clear in the next section, we will call these points *sigma points*.\n", "\n", "Let's consider the simplest possible case, and see if it offers any insight. The simplest possible system is *identity* - the transformation does not alter the input. It should be clear that if our algorithm does not work for the identity transformation then the filter will never converge. In other words, if the input is 1 (for a one dimensional system), the output must also be 1. If the output was different, such as 1.1, then when we fed 1.1 into the transform at the next time step, we'd get out yet another number, maybe 1.23. The filter would run away (diverge). \n", @@ -433,11 +538,11 @@ "output_type": "display_data", "png": 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iTUPqMCKuNXY7PPtuEna7S56XTEScgIq0iLidsjI7z7y7AYAH+rUhNNDf4ETi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\nJhOxoYHE3hvIk3eN4S+p59j08Rm+PFvExr2n2bj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6zs1TCq1OB02Jiyf6ZGlkZAQGZyWLi4KYi62IpNXwer2io+QlFtYVGBsbg8Gp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\n3N7eZrlcpmmatNvttNvtrK6uZjAY5OHDh8KUL9p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"text": [ - "" + "" ] } ], - "prompt_number": 6 + "prompt_number": 8 }, { "cell_type": "markdown", @@ -485,7 +590,54 @@ "source": [ "Note that while I chose the points to lie along the major and minor axis of the ellipse, nothing in the constraints above require me to do that; however, it is fairly typical to do this. Furthermore, in each case I show the points evenly spaced; again, the constraints above do not require that. However, the technique that we develop in the next section *does* do this. It is a reasonable choice, after all; if we want to accurately sample our input it makes sense to sample in a symmetric manner.\n", "\n", - "There are many published ways for selecting the sigma points. For now I will stick with the original implementation by Julier and Uhlmann. This method defines a constant kappa ($\\kappa$) which controls how spread out the sigma points are. Their equations for the sigma points are" + "There are many published ways for selecting the sigma points. For now I will stick with the original implementation by Julier and Uhlmann. This method defines a constant kappa ($\\kappa$) which controls how spread out the sigma points are. Before we work through the derivation, let's just look at some examples. I will use the class UnscentedKalmanFilter from FilterPy to generate the sigma points for us. It is convention to import UnscentedKalmanFilter as UKF - UKF is the standarized shorthand used in the literature for this filter.\n", + "\n", + "I will plot the sigma points on top of a covariance ellipse showing the first and second deviations, and size them based on the weights assigned to them." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from numpy import array\n", + "import matplotlib.pyplot as plt\n", + "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", + "from filterpy.common import plot_covariance_ellipse\n", + "\n", + "x = array([0, 0])\n", + "P = array([[4, 1],\n", + " [1, 4]])\n", + "\n", + "sigmas_kp5 = UKF.sigma_points(x=x, P=P, kappa=.5)\n", + "sigmas_k2 = UKF.sigma_points(x=x, P=P, kappa=2)\n", + "W0 = UKF.weights(2, kappa=.5)\n", + "W1 = UKF.weights(2, kappa=2)\n", + "\n", + "for i in range(len(W0)):\n", + " plt.scatter(sigmas_kp5[i,0], sigmas_kp5[i,1], s=W1[i]*500, c='g')\n", + " plt.scatter(sigmas_k2[i,0], sigmas_k2[i,1], s=W0[i]*500, c='b')\n", + "\n", + "plot_covariance_ellipse(x, P, facecolor='g', alpha=0.2, std=[1,2])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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yIpq1cgbBgoLLRwGdSY+ECevNcj7PReO7JkmeMIkSsjL3sDUKpoFXAVdk0Sj0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\n3aa2GBaRW6KZQmTF+K5Nu1ahZtcYBKr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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that the sigma points lie between the first and second deviation, and that the larger $\\kappa$ spreads the points out further. Furthermore, the larger $\\kappa$ weighs the meaan (center point) higher than the smaller $\\kappa$, and weighs the rest of the sigma points less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know *how* these weights and sigma points are selected yet, but the choices look reasonable." ] }, { @@ -500,6 +652,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "**author's note:** needs rewrite, we already explained what kappa is\n", + "\n", "So our desire is to have an algorithm for selecting sigma points based on some criteria. Maybe we know something about our nonlinear problem, and we know we want our sigma points to be very close together, or very far apart. Or through experimentation we decide that a certain choice of basis vectors from our hyperellipse are the best axis to choose our sigma points from. But we want this to be an algorithm - we don't want to have to hard code in a specific selection algorithm for each different problem. So we are going to want to be able to set some parameters to tell the algorithm how to automatically select the points and weights for us. That may seem a bit abstract, so let's just launch into it, and try to develop an intuitive understanding as we go.\n", "\n", "Assume a n-dimensional state variable $\\mathbf{x}$ with mean $\\mu$ and covariance $\\Sigma$. We want to choose $2n+1$ sigma points to approximate the Gaussian distribution of $\\mathbf{x}$.\n", @@ -543,11 +697,11 @@ "output_type": "display_data", "png": 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zmTp1aolp4i61r6oo6x1pFdIVXFV8ApTL07i4cf5eRD8Q2oJZT3Qvt4uNlPdx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\nFaRk5PDz4XS2HUzlp0Np5BZerny+ibUld/m5E9bTg2HdO2j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"text": [ - "" + "" ] } ], - "prompt_number": 7 + "prompt_number": 10 }, { "cell_type": "markdown", @@ -734,7 +888,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 8 + "prompt_number": 11 }, { "cell_type": "markdown", @@ -804,7 +958,7 @@ "language": "python", "metadata": {}, "outputs": [], - "prompt_number": 9 + "prompt_number": 12 }, { "cell_type": "heading", @@ -818,9 +972,403 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We are now ready to consider implementing a Kalman filter using the approximations for the mean and covariances afforded by the unscented transform. " + "We are now ready to consider implementing a Kalman filter using the approximations for the mean and covariances afforded by the unscented transform. \n", + "\n", + "Let's solve the 'bearing only' target tracking problem. Here the idea is that we have a ship or other platform tracking a moving target. Our sensor only provides the bearing to the target relative to the ship.\n", + "\n", + "This is a nonlinear problem because the conversion between a target position and the bearing is:\n", + "\n", + "$$\\theta = \\tan^{-1}\\frac{y_{ship} - y_{target}}{x_{ship} - x_{target}}$$\n", + "\n", + "If we were solving this problem using and EKF we would need to compute the Jacobian of this transform to linearize the filter. With the UKF we do not have to do this - we will see how this works as we work the example.\n", + "\n", + "\n", + "### Define State\n", + "\n", + "First, lets define our filter state. Let's assume a constant velocity model for the target, so a reasonable state would be\n", + "\n", + "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x} \\\\ y \\\\ \\dot{y}\\end{bmatrix}$$\n", + "\n", + "\n", + "where $x$ and $y$ are the position of the target, and $\\dot{x}$ and $\\dot{y}$ are its velocity. \n", + "\n", + "### Define State Transition\n", + "\n", + "Now we need to tell the filter how to perform the state transition - how to predict the next position from the current position. In the linear Kalman filter this is the equation $\\mathbf{x}^- = \\mathbf{Fx}$ but the unscented Kalman filter is intended for nonlinear problems. We cannot implement nonlinear behavior using linear algebra, so instead of providing the filter with a matrix we need to provide the filter with a function that computes the transition.\n", + "\n", + "As it turns out our state transition is linear. We model the target movement using the standard Newtonian equation\n", + "$$x_k = x_{k-1} + \\dot{x}\\Delta t$$\n", + "\n", + "However, the UKF code does not differentiate between linear and nonlinear versions, so we will write a function. The signature of the function required by `filterpy.UnscentedKalmanFilter` is\n", + "\n", + " def fx(x, dt):\n", + " return x\n", + " \n", + "The filter implements the state as a one dimensional array, so our function can be implemented as" ] }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def fx(x,dt):\n", + " # pos = pos + vel\n", + " # vel = vel\n", + " x[0] += x[1]\n", + " x[2] += x[3]\n", + " return x" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define Measurement Function\n", + "\n", + "Now we define our measurement function. In the linear KF this is implemented with the $\\mathbf{H}$ matrix, but because the UKF is nonlinear we need to provide a function. We have already given the computation of the bearing from position as\n", + "\n", + "$$\\theta = \\tan^{-1}\\frac{y_{ship} - y_{target}}{x_{ship} - x_{target}}$$\n", + "\n", + "so all we have to do is compute that in a function. The signature of this function is required to be\n", + "\n", + " def hx(x):\n", + " return measurement\n", + " \n", + "The filter state does not includes the ship's position, so we will assume a global variable `ship_pos` is defined that specifies the (x,y) coordinate for the ship." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "def hx(x):\n", + " \"\"\" measurement function - convert position to bearing\"\"\"\n", + " return math.atan2(ship_pos[1] - x[2], ship_pos[0] - x[0])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And those two functions are the crux of the problem. All that remains is defining the noise in the system, and running the filter.\n", + "\n", + "**Important Note**: There is a nonlinearity that we are not considering, the fact that angles are modular. Kalman filters operate by computing the differences between measurements. The difference between $359^\\circ$ and $1^\\circ$ is $2^\\circ$, but a subtraction of the two values, as implemented by the filter, yields a value of $358^\\circ$. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later in the chapter I will show you how to handle this problem." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Design Noise Parameters\n", + "\n", + "We have spent a lot of time designing the $\\mathbf{R}$, $\\mathbf{Q}$, and $\\mathbf{P}$ matrices in past chapters, and nothing changes for the UKF filter, so I will just choose some arbitrary values without much discussion. Let's assume the variance in the bearing measurement is $\\sigma=0.35$ radians." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Implement the Filter\n", + "\n", + "So let's implement a filter given the design above. I'll just present the code; it should look very similar to the linear KF to you. The main difference is how we construct the filter:\n", + "\n", + " f = UKF(dim_x=4, dim_z=1, dt=dt, fx=fx, hx=hx, kappa=0.)\n", + " \n", + "When you construct the filter you have to provide the state transition function, the measurement function, and the value for $\\kappa$ along with the usual dimension and time step values." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", + "from filterpy.common import Q_discrete_white_noise\n", + "\n", + "\n", + "def fx(x,dt):\n", + " # pos = pos + vel\n", + " # vel = vel\n", + " x[0] += x[1]\n", + " x[2] += x[3]\n", + " return x\n", + "\n", + "def bearing(ship_pos, target_pos):\n", + " return math.atan2(target_pos[1]- ship_pos[1], target_pos[0] - ship_pos[0])\n", + "\n", + "def hx(x):\n", + " \"\"\" measurement function - convert position to bearing\"\"\"\n", + " return math.atan2(x[2] - ship_pos[1], x[0] - ship_pos[0])\n", + "\n", + "\n", + "dt = 0.1\n", + "ship_pos = [-40,20]\n", + "target_pos = [0,0]\n", + "\n", + "std_noise = math.radians(1)\n", + "\n", + "f = UKF(4, 1, dt, fx=fx, hx=hx, kappa=0.)\n", + "f.x = np.array([target_pos[0], 0., target_pos[1], 0.])\n", + "Q = Q_discrete_white_noise(2, dt, .01)\n", + "f.Q[0:2,0:2] = Q\n", + "f.Q[2:4, 2:4] = Q\n", + "\n", + "f.R *= std_noise**2\n", + "f.P *= 100\n", + "\n", + "N = 300\n", + "xs = []\n", + "for i in range(N):\n", + " target_pos[0] += 1 + randn()*0.0001 # add some process noise\n", + " angle = bearing(ship_pos, target_pos) + randn()*std_noise\n", + "\n", + " f.predict()\n", + " f.update(angle)\n", + " xs.append(f.x)\n", + "\n", + "xs = np.asarray(xs)\n", + "plt.plot([i/10 for i in range(N)], xs[:,0])\n", + "plt.xlabel('time')\n", + "plt.ylabel('target X position')\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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WJCIiIu5Va7PzxD9Xs3itFYBpdyTxzH198fH2cnNlIp7rum5fe3t706lTp/qq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\nItLE/g+8vOj9plWgoQAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we look at only the target's estimated position in x, the results look very good. After running for several seconds the filter appears to settle down and produce a reasonably linear output for the target's position. However, let's look at the 2D plot of position. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.ylabel('target X position')\n", + "plt.ylabel('target Y position')\n", + "plt.plot(xs[:,0], xs[:,2])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ikwt4atEwbC2MiIrP44/DSe3uq1AoGOpjT383m9bnHK1N+PXFedwxuT+1DU385bNQXv8x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\nB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+ "text": [ + "" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see the actual performance is abysmal. This is not an indictment of the UKF, but of the difficulty of the problem we are trying to solve. There are an infinite number of solutions for each measurement. For example, if our ship is at (0, 20), a bearing reading of 0 could reflect a target position of (0, 20) or (100, 20), or (1e300, 20). The Kalman filtering literature has many treatments of this problem; a common solution is to have the ship perform manuevers while tracking. This allows the filter to reduce the range of possibilities to something managable. This is rather outside the scope of this book so I will leave it to you to search the literature if you are interested in this specific problem.\n", + "\n", + "Instead, I will make the problem tractable by introducing a second sensor. In the Designing Nonlinear Filters chapter we solved the two sensor version of this problem by linearizing the problem while assuming a nominal position for the target track. Now we will solve this by using the UKF.\n", + "\n", + "The problem is as follows. Assume we have two sensors, each which provides a bearing only measurement to the target, as in the chart below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "circle1=plt.Circle((-4,0),5,color='#004080',fill=False,linewidth=20, alpha=.7)\n", + "circle2=plt.Circle((4,0),5,color='#E24A33', fill=False, linewidth=5, alpha=.7)\n", + "\n", + "fig = plt.gcf()\n", + "ax = fig.gca()\n", + "\n", + "plt.axis('equal')\n", + "plt.xlim((-10,10))\n", + "plt.ylim((-10,10))\n", + "\n", + "plt.plot ([-4,0], [0,3], c='#004080')\n", + "plt.plot ([4,0], [0,3], c='#E24A33')\n", + "plt.text(-4, -.5, \"A\", fontsize=16, horizontalalignment='center')\n", + "plt.text(4, -.5, \"B\", fontsize=16, horizontalalignment='center')\n", + "#plt.scatter ([-4],[0], 'r')\n", + "\n", + "ax.add_artist(circle1)\n", + "ax.add_artist(circle2)\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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TCeymu8DyCmWP8dHh0D6B4fAO5yFyFD2pYMQXwL+/cgyDI37VX2tpaQYFwoRo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+ "text": [ + "" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compute the bearing between a sensor and the target as follows:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def bearing(sensor, target_pos):\n", + " return math.atan2(target_pos[1] - sensor[1], target_pos[0] - sensor[0])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 79 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So our filter will need to receive a vector of 2 measurements during each update, one for each sensor. We can implement that as:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def measurement(A_pos, B_pos, pos):\n", + " angle_a = bearing(A_pos, pos)\n", + " angle_b = bearing(B_pos, pos)\n", + " return [angle_a, angle_b]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 80 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The design of the measurement function and state transition function can remain the same as nothing has changed that would affect them. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", + "from filterpy.common import Q_discrete_white_noise\n", + "\n", + "def bearing(sensor, target_pos):\n", + " return math.atan2(target_pos[1] - sensor[1], target_pos[0] - sensor[0])\n", + "\n", + "def measurement(A_pos, B_pos, pos):\n", + " angle_a = bearing(A_pos, pos)\n", + " angle_b = bearing(B_pos, pos)\n", + " return [angle_a, angle_b]\n", + "\n", + "\n", + "def fx(x,dt):\n", + " x[0] += x[1]\n", + " x[2] += x[3]\n", + " return x\n", + "\n", + "def hx(x):\n", + " # measurement to A\n", + " pos = (x[0], x[2])\n", + " return measurement(sa_pos, sb_pos, pos)\n", + "\n", + "def normalize(a):\n", + " if a > math.pi:\n", + " a -= math.pi*2\n", + "\n", + " if a < -math.pi:\n", + " a += math.pi*2\n", + " return a\n", + "\n", + "sa_pos = [-40, 0]\n", + "sb_pos = [40, 0]\n", + "\n", + "dt = .1\n", + "target_pos = [40, 20]\n", + "\n", + "std_noise = math.radians(1.)\n", + "\n", + "f = UKF(dim_x=4, dim_z=2, dt=dt, hx=hx, fx=fx, kappa=2.)\n", + "f.x = np.array([target_pos[0], 1., target_pos[1], 1.])\n", + "\n", + "Q = Q_discrete_white_noise(2, dt, 1.1)\n", + "f.Q[0:2,0:2] = Q\n", + "f.Q[2:4, 2:4] = Q\n", + "\n", + "f.R *= std_noise**2\n", + "f.P *= 1000\n", + "\n", + "xs = []\n", + "txs = []\n", + "\n", + "for i in range(300):\n", + " target_pos[0] += 1 + randn()*0.0001\n", + " target_pos[1] += 1 + randn()*0.0001\n", + " txs.append(target_pos.copy())\n", + " \n", + " z = measurement(sa_pos, sb_pos, target_pos)\n", + " z[0] += randn() * std_noise\n", + " z[1] += randn() * std_noise\n", + "\n", + " f.predict()\n", + " f.update(z)\n", + " xs.append(f.x)\n", + "\n", + "xs = np.asarray(xs)\n", + "txs = np.asarray(txs)\n", + "\n", + "plt.plot(xs[:,0], xs[:,2])\n", + "plt.plot(txs[:,0], txs[:,1])\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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EBXqZPaaItIArhnNtbS0vvPACGRkZVFZW0rdvX1588UWio6OpqanhpZdeIi0t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\nUFFRgTlz5uD48ePYvXu3mJsjIiIiIhKNrLy83C3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