Moved chapter 6 as part of reorg.
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Roger Labbe committed
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"This notebook creates the animations for the Multivariate Kalman Filter chapter. It is not really intended to be a readable part of the book, but of course you are free to look at the source code, and even modify it. However, if you are interested in running your own animations, I'll point you to the examples subdirectory of the book, which contains a number of python scripts that you can run and modify from an IDE or the command line. This module saves the animations to GIF files, which is quite slow and not very interactive. "
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"input": [
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"import stats\n",
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"import numpy as np\n",
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"from matplotlib.patches import Ellipse\n",
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"import matplotlib.pyplot as plt\n",
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"from matplotlib import cm\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"\n",
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"# this code lets me animate the 3d covariance. to be honest I do not find it\n",
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"# very instructive or compelling so I am not using it for now.\n",
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"def plot_3d_covariance(ax, mean, cov):\n",
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" \"\"\" plots a 2x2 covariance matrix positioned at mean. mean will be plotted\n",
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" in x and y, and the probability in the z axis.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" mean : 2x1 tuple-like object\n",
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" mean for x and y coordinates. For example (2.3, 7.5)\n",
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"\n",
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" cov : 2x2 nd.array\n",
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" the covariance matrix\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" # compute width and height of covariance ellipse so we can choose\n",
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" # appropriate ranges for x and y\n",
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" o,w,h = stats.covariance_ellipse(cov,3)\n",
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" # rotate width and height to x,y axis\n",
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" wx = abs(w*np.cos(o) + h*np.sin(o))*1.2\n",
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" wy = abs(h*np.cos(o) - w*np.sin(o))*1.2\n",
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"\n",
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" # ensure axis are of the same size so everything is plotted with the same\n",
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" if wx > wy:\n",
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" w = wx\n",
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" else:\n",
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" w = wy\n",
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"\n",
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" minx = mean[0] - w\n",
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" maxx = mean[0] + w\n",
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" miny = mean[1] - w\n",
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" maxy = mean[1] + w\n",
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" #print (minx, maxx, miny, maxy)\n",
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" \n",
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" minx = -9.57238091319 \n",
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" maxx= 13.5723809132 \n",
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" miny = -4.57238091319 \n",
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" maxy = 18.5723809132\n",
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"\n",
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" xs = np.arange(minx, maxx, (maxx-minx)/40.)\n",
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" ys = np.arange(miny, maxy, (maxy-miny)/40.)\n",
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" xv, yv = np.meshgrid (xs, ys)\n",
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"\n",
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" zs = np.array([100.* stats.multivariate_gaussian(np.array([x,y]),mean,cov) \\\n",
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" for x,y in zip(np.ravel(xv), np.ravel(yv))])\n",
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" zv = zs.reshape(xv.shape)\n",
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"\n",
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" ax.plot_surface(xv, yv, zv, rstride=1, cstride=1, cmap=cm.autumn)\n",
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"\n",
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" ax.set_xlabel('X')\n",
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" ax.set_ylabel('Y')\n",
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" ax.set_zlim([0,10])\n",
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" #ax.set_xlim([-10,10])\n",
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"\n",
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" ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)\n",
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" ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)\n"
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"import numpy as np\n",
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"import mkf_internal\n",
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"import matplotlib.pyplot as plt\n",
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"from gif_animate import animate\n",
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"import stats\n",
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"def mkf_animate(frame):\n",
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" global ax\n",
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" plt.cla()\n",
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" var = (31-frame) / 3\n",
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" plot_3d_covariance(ax, (2,7), np.array([[var,0],[0,4.]]))\n",
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" \n",
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" \n",
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"def ellipse_animate(frame):\n",
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" \n",
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" plt.cla()\n",
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" cov = frame/15.\n",
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" P = np.array([[2,cov],[cov,2]])\n",
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" stats.plot_covariance_ellipse((2,7), cov=P, facecolor='g', alpha=0.2, \n",
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" title='|2.0 {:.1f}|\\n|{:.1f} 2.0|'.format(cov, cov))\n",
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"\n",
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"fig = plt.figure()\n",
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"#ax = fig.add_subplot(111, projection='3d')\n",
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"animate('multivariate_ellipse.gif', ellipse_animate, 30, 125)"
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7effd7d90898>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<img src='multivariate_ellipse.gif'>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"import numpy as np\n",
|
||||
"from matplotlib.patches import Ellipse\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"from matplotlib import cm\n",
|
||||
"from mpl_toolkits.mplot3d import Axes3D\n",
|
||||
"from gif_animate import animate\n",
|
||||
"import numpy.random as random\n",
|
||||
"from DogSensor import DogSensor\n",
|
||||
"import stats\n",
|
||||
"from filterpy.common import Q_discrete_white_noise\n",
|
||||
"from filterpy.kalman import KalmanFilter\n",
|
||||
"\n",
|
||||
"def dog_tracking_filter(R,Q=0,cov=1.):\n",
|
||||
" dog_filter = KalmanFilter (dim_x=2, dim_z=1)\n",
|
||||
" dog_filter.x = np.array([0, 0]) # initial state (location and velocity)\n",
|
||||
" dog_filter.F = np.array([[1,1],\n",
|
||||
" [0,1]]) # state transition matrix\n",
|
||||
" dog_filter.H = np.array([[1,0]]) # Measurement function\n",
|
||||
" dog_filter.R *= R # measurement uncertainty\n",
|
||||
" dog_filter.P *= cov # covariance matrix \n",
|
||||
" if np.isscalar(Q):\n",
|
||||
" dog_filter.Q = Q_discrete_white_noise(2, var=Q)\n",
|
||||
" else:\n",
|
||||
" dog_filter.Q = Q\n",
|
||||
" return dog_filter\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"R = 5\n",
|
||||
"Q = .01\n",
|
||||
"noise = 2.\n",
|
||||
"P=20.\n",
|
||||
"dog = DogSensor(velocity=1,noise_var=noise)\n",
|
||||
"f = dog_tracking_filter(R=R, Q=Q, cov=P)\n",
|
||||
"random.seed(200)\n",
|
||||
"zs = []\n",
|
||||
"xs = []\n",
|
||||
"def animate_track(frame):\n",
|
||||
" if frame > 30: return\n",
|
||||
" \n",
|
||||
" plt.gca().set_xlim(-100,100)\n",
|
||||
" if frame == 0:\n",
|
||||
" stats.plot_covariance_ellipse ((0, f.x[0]), cov=f.P, axis_equal=True, \n",
|
||||
" facecolor='g', edgecolor=None, alpha=0.2)\n",
|
||||
" xs.append (f.x[0])\n",
|
||||
" \n",
|
||||
" z = dog.sense()\n",
|
||||
" zs.append(z)\n",
|
||||
" f.update(z)\n",
|
||||
" xs.append (f.x[0])\n",
|
||||
" \n",
|
||||
" stats.plot_covariance_ellipse ((frame+1, f.x[0]), cov=f.P, axis_equal=True, \n",
|
||||
" facecolor='g', edgecolor=None, alpha=0.5,\n",
|
||||
" xlim=(-5,30), ylim=(-5,30))\n",
|
||||
" \n",
|
||||
" plt.plot(zs, c='r', linestyle='dashed')\n",
|
||||
" plt.plot(xs, c='b')\n",
|
||||
" f.predict()\n",
|
||||
"\n",
|
||||
"animate('multivariate_track1.gif', animate_track, 37, 200, figsize=(10.5, 10.5))"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7effd05c44a8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 5
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<img src='multivariate_track1.gif'>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
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Reference in new issue
Block a user