Slighly improved discussion of UKF weights.
I wrongly stated that weights must sum to one. they don't. I clarified this, but did not explain *why* Merwe weights are so large, and/or negative. this needs to be improved.
This commit is contained in:
Roger Labbe committed
1 parent
2743b78db5
commit
81ab95d5a9
1 file changed
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-143
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@@ -16,7 +16,7 @@
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{
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"execution_count": 55,
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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@@ -289,7 +289,7 @@
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"<IPython.core.display.HTML object>"
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]
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},
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"execution_count": 55,
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -317,7 +317,7 @@
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},
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"cell_type": "code",
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"execution_count": 56,
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"execution_count": 2,
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"metadata": {
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"collapsed": false,
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"scrolled": true
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@@ -325,9 +325,9 @@
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.figure.Figure at 0x15b3cb83f60>"
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]
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},
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"metadata": {},
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@@ -378,7 +378,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"execution_count": 3,
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"metadata": {
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"collapsed": false,
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"scrolled": false
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@@ -386,9 +386,9 @@
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"outputs": [
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{
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"data": {
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1d11198>"
|
||||
"<matplotlib.figure.Figure at 0x15b3ad02cf8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -425,7 +425,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 58,
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -435,14 +435,14 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Difference in mean x=-0.008, y=42.577\n"
|
||||
"Difference in mean x=0.121, y=43.207\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c31e0cc0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e138048>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -495,7 +495,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 59,
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -503,9 +503,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c31f6dd8>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e1abda0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -546,7 +546,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 60,
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -556,7 +556,7 @@
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c108b9b0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e263d68>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -586,16 +586,16 @@
|
||||
"\n",
|
||||
"For the moment, assume an algorithm for selecting the sigma points and weights exists. How are the sigma points used to implement a filter?\n",
|
||||
"\n",
|
||||
"The *unscented transform* is the core of the algorithm yet it is remarkably simple. We pass the sigma points $\\boldsymbol{\\chi}$ through a nonlinear function yielding a transformed set of points.\n",
|
||||
"The *unscented transform* is the core of the algorithm yet it is remarkably simple. It passes the sigma points $\\boldsymbol{\\chi}$ through a nonlinear function yielding a transformed set of points.\n",
|
||||
"\n",
|
||||
"$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n",
|
||||
"\n",
|
||||
"We then compute the mean and covariance of the transformed points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. "
|
||||
"It then compute the mean and covariance of the transformed points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 61,
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -603,9 +603,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c0fc92b0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3dc36f28>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -639,12 +639,12 @@
|
||||
"source": [
|
||||
"### Accuracy of the Unscented Transform\n",
|
||||
"\n",
|
||||
"Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now pass 5 sigma points through the same function, and compute their mean with the unscented transform."
|
||||
"Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now pass 5 sigma points through the same function, and compute their mean with the unscented transform. We will use the FilterPy function *MerweScaledSigmaPoints()* to create the sigma points and *unscented_transform* to perform the transform; we will learn about these functions later."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 62,
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -659,9 +659,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAjMAAAEWCAYAAACT2xbaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c204ba58>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f2e0ef0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -669,8 +669,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"from filterpy.kalman import unscented_transform\n",
|
||||
"from filterpy.kalman import MerweScaledSigmaPoints as SigmaPoints\n",
|
||||
"from filterpy.kalman import unscented_transform, MerweScaledSigmaPoints\n",
|
||||
"import scipy.stats as stats\n",
|
||||
"\n",
|
||||
"#initial mean and covariance\n",
|
||||
@@ -678,7 +677,7 @@
|
||||
"p = np.array([[32., 15], [15., 40.]])\n",
|
||||
"\n",
|
||||
"# create sigma points - we will learn about this later\n",
|
||||
"points = SigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n",
|
||||
"points = MerweScaledSigmaPoints(n=2, alpha=.3, beta=2., kappa=.1)\n",
|
||||
"Wm, Wc = points.weights()\n",
|
||||
"sigmas = points.sigma_points(mean, p)\n",
|
||||
"\n",
|
||||
@@ -845,16 +844,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 63,
|
||||
"execution_count": 9,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1dd9320>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f37f1d0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -869,7 +868,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We can see that the sigma points lie between the first and second standard deviation, and that the larger $\\alpha$ spreads the points out. Furthermore, the larger $\\alpha$ weights the mean (center point) higher than the smaller $\\alpha$, and weights the rest 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."
|
||||
"We can see that the sigma points lie between the first and second standard deviation, and that the larger $\\alpha$ spreads the points out. Furthermore, the larger $\\alpha$ weights the mean (center point) higher than the smaller $\\alpha$, and weights the rest 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."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -911,7 +910,7 @@
|
||||
"\n",
|
||||
"It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to $\\pm 1\\sigma$ times some scaling factor. There is an $n$ term in the denominator, so with more dimensions the points will be spread out and weighed less.\n",
|
||||
"\n",
|
||||
"**Important note:** Ordinarily these weights do not sum to one. I get many questions about this. Getting weights that sum to greater than one, or even negative values is expected.\n",
|
||||
"**Important note:** Ordinarily these weights do not sum to one. I get many questions about this. Getting weights that sum to greater than one, or even negative values is expected. I cover this in more detail below.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"### Reasonable Choices for the Parameters\n",
|
||||
@@ -966,7 +965,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 64,
|
||||
"execution_count": 10,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -974,9 +973,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c31beda0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f4336a0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1025,7 +1024,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 65,
|
||||
"execution_count": 11,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1074,7 +1073,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 66,
|
||||
"execution_count": 12,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1089,9 +1088,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1ff5ba8>"
|
||||
"<matplotlib.figure.Figure at 0x15b3d2b4400>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1103,7 +1102,7 @@
|
||||
"\n",
|
||||
"import numpy as np\n",
|
||||
"\n",
|
||||
"sigmas = SigmaPoints(4, alpha=.1, beta=2., kappa=1.)\n",
|
||||
"sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=1.)\n",
|
||||
"ukf = UKF(dim_x=4, dim_z=2, fx=f_cv,\n",
|
||||
" hx=h_cv, dt=dt, points=sigmas)\n",
|
||||
"ukf.x = np.array([0., 0., 0., 0.])\n",
|
||||
@@ -1146,7 +1145,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"execution_count": 13,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1154,9 +1153,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1cc5ac8>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f445ba8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1194,7 +1193,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 68,
|
||||
"execution_count": 14,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1230,7 +1229,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 69,
|
||||
"execution_count": 15,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1258,7 +1257,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 70,
|
||||
"execution_count": 16,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1326,16 +1325,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 71,
|
||||
"execution_count": 17,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c2035710>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f343358>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1343,9 +1342,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1d180f0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e169048>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1353,9 +1352,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1e108d0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e1db7b8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1375,7 +1374,7 @@
|
||||
"radar_pos = (0., 0.)\n",
|
||||
"h_radar.radar_pos = radar_pos\n",
|
||||
"\n",
|
||||
"points = SigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n",
|
||||
"points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n",
|
||||
"kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n",
|
||||
"\n",
|
||||
"kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
|
||||
@@ -1424,7 +1423,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 72,
|
||||
"execution_count": 18,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1440,9 +1439,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c20ff9b0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3dc4c2b0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1497,7 +1496,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 73,
|
||||
"execution_count": 19,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -1513,7 +1512,7 @@
|
||||
" return np.dot(F, x)\n",
|
||||
" \n",
|
||||
"def cv_UKF(fx, hx, R_std):\n",
|
||||
" points = SigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n",
|
||||
" points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n",
|
||||
" kf = UKF(4, len(R_std), dt, fx=fx, hx=hx, points=points)\n",
|
||||
"\n",
|
||||
" kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
|
||||
@@ -1527,7 +1526,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 74,
|
||||
"execution_count": 20,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1543,9 +1542,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1d97dd8>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e187b38>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1601,7 +1600,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 75,
|
||||
"execution_count": 21,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1609,9 +1608,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1f0c358>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e187da0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1661,7 +1660,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 76,
|
||||
"execution_count": 22,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -1684,7 +1683,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 77,
|
||||
"execution_count": 23,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1692,9 +1691,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1760828>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e234d30>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1761,7 +1760,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 78,
|
||||
"execution_count": 24,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1769,9 +1768,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c204c5c0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f276278>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1791,7 +1790,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 79,
|
||||
"execution_count": 25,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -1811,7 +1810,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 80,
|
||||
"execution_count": 26,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -1832,7 +1831,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 81,
|
||||
"execution_count": 27,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -1853,7 +1852,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 82,
|
||||
"execution_count": 28,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -1877,7 +1876,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 83,
|
||||
"execution_count": 29,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": true
|
||||
@@ -1885,9 +1884,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAmIAAAERCAYAAADYCMsUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAm4AAAEWCAYAAADfMRsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1eac6d8>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f52a940>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1896,7 +1895,7 @@
|
||||
],
|
||||
"source": [
|
||||
"def moving_target_filter(pos, std_noise, Q, dt=0.1, kappa=0.0):\n",
|
||||
" points = SigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n",
|
||||
" points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n",
|
||||
" f = UKF(dim_x=4, dim_z=2, dt=dt, \n",
|
||||
" hx=hx_VOR, fx=fx_VOR, points=points)\n",
|
||||
" f.x = np.array([pos[0], 1., pos[1], 1.])\n",
|
||||
@@ -1949,7 +1948,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 84,
|
||||
"execution_count": 30,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -1957,9 +1956,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c2045748>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f285208>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1995,7 +1994,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 85,
|
||||
"execution_count": 31,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2003,9 +2002,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c31bc278>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e126160>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2048,7 +2047,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 86,
|
||||
"execution_count": 32,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2056,9 +2055,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1cf97f0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f541320>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2089,7 +2088,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 87,
|
||||
"execution_count": 33,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2097,9 +2096,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c17b9a20>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e13b470>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2153,7 +2152,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 88,
|
||||
"execution_count": 34,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -2168,13 +2167,13 @@
|
||||
" [ 0.0, -0.172]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 88,
|
||||
"execution_count": 34,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"points = SigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n",
|
||||
"points = MerweScaledSigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n",
|
||||
"points.sigma_points(x=[0.,0], P=[[1.,.1],[.1, 1]])"
|
||||
]
|
||||
},
|
||||
@@ -2261,7 +2260,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 89,
|
||||
"execution_count": 35,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -2273,7 +2272,7 @@
|
||||
" [ 0.122, 2.99]])"
|
||||
]
|
||||
},
|
||||
"execution_count": 89,
|
||||
"execution_count": 35,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -2318,7 +2317,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 90,
|
||||
"execution_count": 36,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2330,7 +2329,7 @@
|
||||
"array([410, 520, 630])"
|
||||
]
|
||||
},
|
||||
"execution_count": 90,
|
||||
"execution_count": 36,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -2498,7 +2497,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 91,
|
||||
"execution_count": 37,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2506,9 +2505,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1f8f748>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f5119b0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2516,9 +2515,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1d670f0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e25fda0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2526,9 +2525,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1eab080>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f4a72e8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2545,7 +2544,7 @@
|
||||
"radar_pos = (0., 0.)\n",
|
||||
"h_radar.radar_pos = radar_pos\n",
|
||||
"\n",
|
||||
"points = SigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n",
|
||||
"points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n",
|
||||
"kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n",
|
||||
"\n",
|
||||
"kf.Q[0:2 ,0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
|
||||
@@ -2590,7 +2589,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 92,
|
||||
"execution_count": 38,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2601,14 +2600,14 @@
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Difference in position in meters:\n",
|
||||
"\t [-0.7717 -0.1195 0.0426 -1.1727 -1.0871]\n"
|
||||
"\t [-0.7714 -0.1196 0.0421 -1.1724 -1.0864]\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1d6db70>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f3ef9e8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2616,9 +2615,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
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||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c208b908>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f3a3c18>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2626,9 +2625,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c20289b0>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e237cc0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2660,7 +2659,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 93,
|
||||
"execution_count": 39,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -2707,7 +2706,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 94,
|
||||
"execution_count": 40,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": true
|
||||
@@ -2733,7 +2732,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We can see that the sigma point spread over 100 standard deviations.If our data was Gaussian we'd be incorporating data many standard deviations away from the mean; for nonlinear problems this is unlikely to produce good results. But suppose our distribution was not Gaussian, but instead had very fat tails? We might need to sample from those tails to get a good estimate, and hence it would make sense to make $kappa$ larger (not 200, which was absurdly large to make the change in the sigma points stark). \n",
|
||||
"We can see that the sigma point spread over 100 standard deviations. If our data was Gaussian we'd be incorporating data many standard deviations away from the mean; for nonlinear problems this is unlikely to produce good results. But suppose our distribution was not Gaussian, but instead had very fat tails? We might need to sample from those tails to get a good estimate, and hence it would make sense to make $\\kappa$ larger (not 200, which was absurdly large to make the change in the sigma points stark). \n",
|
||||
"\n",
|
||||
"With a similar line of reasoning, suppose that our distribution has nearly no tails - the probability distribution looks more like an inverted parabola. In such a case we'd probably want to pull the sigma points in closer to the mean to avoid sampling in regions where there will never be real data.\n",
|
||||
"\n",
|
||||
@@ -2751,7 +2750,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 95,
|
||||
"execution_count": 41,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -2812,16 +2811,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 96,
|
||||
"execution_count": 42,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1f0e908>"
|
||||
"<matplotlib.figure.Figure at 0x15b3dbf44e0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -2904,7 +2903,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 97,
|
||||
"execution_count": 43,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -2939,7 +2938,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 98,
|
||||
"execution_count": 44,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -3010,7 +3009,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 99,
|
||||
"execution_count": 45,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -3025,7 +3024,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 100,
|
||||
"execution_count": 46,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -3051,7 +3050,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 101,
|
||||
"execution_count": 47,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -3088,7 +3087,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 102,
|
||||
"execution_count": 48,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -3121,7 +3120,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 103,
|
||||
"execution_count": 49,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -3174,7 +3173,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 104,
|
||||
"execution_count": 50,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -3190,7 +3189,7 @@
|
||||
" sigma_bearing, ellipse_step=1, step=10):\n",
|
||||
"\n",
|
||||
" plt.figure()\n",
|
||||
" points = SigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n",
|
||||
" points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n",
|
||||
" subtract=residual_x)\n",
|
||||
" ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=fx, hx=Hx,\n",
|
||||
" dt=dt, points=points, x_mean_fn=state_mean, \n",
|
||||
@@ -3248,7 +3247,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 105,
|
||||
"execution_count": 51,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -3256,9 +3255,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1fde9e8>"
|
||||
"<matplotlib.figure.Figure at 0x15b3e263e80>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -3299,7 +3298,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 106,
|
||||
"execution_count": 52,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -3338,7 +3337,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 107,
|
||||
"execution_count": 53,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -3346,9 +3345,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c1e6a080>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f3b8e80>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -3379,7 +3378,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 108,
|
||||
"execution_count": 54,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": false
|
||||
@@ -3387,9 +3386,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x1f8c20bdb70>"
|
||||
"<matplotlib.figure.Figure at 0x15b3f2b93c8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
|
||||
Reference in new issue
Block a user