Added MM filter bank.
This commit is contained in:
Roger Labbe committed
1 parent
1b92397175
commit
24e70d7c77
2 files changed
+232
-113
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+202
-113
@@ -30,7 +30,7 @@
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"@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
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"\n",
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" div.cell{\n",
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" width: 850px;\n",
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" width: 900px;\n",
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" margin-left: 0% !important;\n",
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" margin-right: auto;\n",
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" }\n",
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@@ -117,9 +117,6 @@
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" font-family: 'Arimo',verdana,arial,sans-serif;\n",
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" line-height: 125%;\n",
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" font-size: 120%;\n",
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" width:740px;\n",
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" margin-left:auto;\n",
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" margin-right:auto;\n",
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" text-align:justify;\n",
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" text-justify:inter-word;\n",
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" }\n",
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@@ -240,7 +237,10 @@
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" },\n",
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" displayAlign: 'center', // Change this to 'center' to center equations.\n",
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" \"HTML-CSS\": {\n",
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" scale:85,\n",
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" scale:100,\n",
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" availableFonts: [\"Neo-Euler\"],\n",
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" preferredFont: \"Neo-Euler\",\n",
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" webFont: \"Neo-Euler\",\n",
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" styles: {'.MathJax_Display': {\"margin\": 4}}\n",
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" }\n",
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" });\n",
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@@ -401,9 +401,9 @@
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"outputs": [
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{
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"data": {
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"image/png": 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"image/png": 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truncated
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"text/plain": [
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"<matplotlib.figure.Figure at 0x7b0b6d8>"
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"<matplotlib.figure.Figure at 0x6e6cc50>"
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]
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},
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"metadata": {},
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@@ -466,9 +466,9 @@
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"outputs": [
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{
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"data": {
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||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7ae9f28>"
|
||||
"<matplotlib.figure.Figure at 0x6e7cb70>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -497,7 +497,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 10,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -506,15 +506,17 @@
|
||||
"from filterpy.kalman import KalmanFilter\n",
|
||||
"from filterpy.common import Q_discrete_white_noise\n",
|
||||
"\n",
|
||||
"dt = 0.1\n",
|
||||
"cvfilter = KalmanFilter(dim_x = 2, dim_z=1)\n",
|
||||
"cvfilter.x = array([0., 0.])\n",
|
||||
"cvfilter.P *= 3\n",
|
||||
"cvfilter.R *= noise_factor\n",
|
||||
"cvfilter.F = array([[1, dt],\n",
|
||||
" [0, 1]], dtype=float)\n",
|
||||
"cvfilter.H = array([[1, 0]], dtype=float)\n",
|
||||
"cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
|
||||
"def make_cv_filter(dt):\n",
|
||||
" cvfilter = KalmanFilter(dim_x = 2, dim_z=1)\n",
|
||||
" cvfilter.x = array([0., 0.])\n",
|
||||
" cvfilter.P *= 3\n",
|
||||
" cvfilter.R *= noise_factor\n",
|
||||
" cvfilter.F = array([[1, dt],\n",
|
||||
" [0, 1]], dtype=float)\n",
|
||||
" cvfilter.H = array([[1, 0]], dtype=float)\n",
|
||||
" cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
|
||||
" \n",
|
||||
" return cvfilter\n",
|
||||
"\n",
|
||||
"def initialize_filter(kf):\n",
|
||||
" \"\"\" helper function - we will be reinitialing the filter\n",
|
||||
@@ -549,16 +551,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 11,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAu8AAAE6CAYAAACmmLxQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8267d30>"
|
||||
"<matplotlib.figure.Figure at 0x8098748>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -569,7 +571,9 @@
|
||||
"# extract the x coordinates\n",
|
||||
"import numpy as np\n",
|
||||
"\n",
|
||||
"dt = 0.1\n",
|
||||
"# initialize filter\n",
|
||||
"cvfilter= make_cv_filter(dt)\n",
|
||||
"initialize_filter(cvfilter)\n",
|
||||
"\n",
|
||||
"xs = pos[:, 0]\n",
|
||||
@@ -595,16 +599,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"execution_count": 12,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8bd3978>"
|
||||
"<matplotlib.figure.Figure at 0x850d278>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -640,16 +644,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"execution_count": 13,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8bf8240>"
|
||||
"<matplotlib.figure.Figure at 0x808df28>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -682,16 +686,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"execution_count": 14,
|
||||
"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 0x7b7d940>"
|
||||
"<matplotlib.figure.Figure at 0x830ca58>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -725,40 +729,41 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"execution_count": 23,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"cafilter = KalmanFilter(dim_x=3, dim_z=1)\n",
|
||||
"cafilter.x = array([0., 0., 0.])\n",
|
||||
"cafilter.P *= 3\n",
|
||||
"cafilter.R *= 1\n",
|
||||
"cafilter.F = array([[1, dt, 0.5*dt*dt],\n",
|
||||
" [0, 1, dt], \n",
|
||||
" [0, 0, 1]], dtype=float)\n",
|
||||
"cafilter.H = array([[1, 0, 0]], dtype=float)\n",
|
||||
"def make_ca_filter(dt):\n",
|
||||
" cafilter = KalmanFilter(dim_x=3, dim_z=1)\n",
|
||||
" cafilter.x = array([0., 0., 0.])\n",
|
||||
" cafilter.P *= 3\n",
|
||||
" cafilter.R *= 1\n",
|
||||
" cafilter.Q = Q_discrete_white_noise(dim=3, dt=dt, var=0.02)\n",
|
||||
" cafilter.F = array([[1, dt, 0.5*dt*dt],\n",
|
||||
" [0, 1, dt], \n",
|
||||
" [0, 0, 1]], dtype=float)\n",
|
||||
" cafilter.H = array([[1, 0, 0]], dtype=float)\n",
|
||||
" return cafilter\n",
|
||||
"\n",
|
||||
"def initialize_const_accel(f):\n",
|
||||
" f.x = array([0., 0., 0.])\n",
|
||||
" f.P = np.eye(3) * 3\n",
|
||||
"\n",
|
||||
"cafilter.Q = Q_discrete_white_noise(dim=3, dt=dt, var=0.02)"
|
||||
" f.P = np.eye(3) * 3"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"execution_count": 25,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAE6CAYAAAB0yLYIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7b63a58>"
|
||||
"<matplotlib.figure.Figure at 0x8447c88>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -766,6 +771,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"cafilter = make_ca_filter(dt)\n",
|
||||
"initialize_const_accel(cafilter)\n",
|
||||
"\n",
|
||||
"kxs2, _, _, _ = cafilter.batch_filter(z_xs2)\n",
|
||||
@@ -816,9 +822,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7b0b320>"
|
||||
"<matplotlib.figure.Figure at 0x6f3e630>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -839,16 +845,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"execution_count": 39,
|
||||
"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 0x8e0dbe0>"
|
||||
"<matplotlib.figure.Figure at 0x84650f0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -856,36 +862,30 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"pos2, zs2 = generate_data(120, noise_factor=0.2)\n",
|
||||
"xs2 = pos2[:, 0]\n",
|
||||
"z_xs2 = zs2[:, 0]\n",
|
||||
"from adaptive_internal import plot_track_and_residuals\n",
|
||||
"\n",
|
||||
"# reinitialize filter\n",
|
||||
"initialize_filter(cvfilter)\n",
|
||||
"cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
|
||||
"xs = []\n",
|
||||
"res = []\n",
|
||||
"for z in z_xs2:\n",
|
||||
" cvfilter.predict()\n",
|
||||
" cvfilter.update([z])\n",
|
||||
" xs.append(cvfilter.x[0])\n",
|
||||
" res.append(cvfilter.y[0])\n",
|
||||
"xs = np.asarray(xs)\n",
|
||||
"plt.subplot(121)\n",
|
||||
"bp.plot_measurements(t, z_xs2, label='z')\n",
|
||||
"bp.plot_filter(t, xs)\n",
|
||||
"plt.legend(loc=2)\n",
|
||||
"plt.xlabel('time (sec)')\n",
|
||||
"plt.ylabel('X')\n",
|
||||
"plt.title('estimates vs measurements')\n",
|
||||
"plt.subplot(122)\n",
|
||||
"# plot twice so it has the same color as the plot to the left!\n",
|
||||
"plt.plot(t, res)\n",
|
||||
"plt.plot(t, res)\n",
|
||||
"plt.xlabel('time (sec)')\n",
|
||||
"plt.ylabel('residual')\n",
|
||||
"plt.title('residuals')\n",
|
||||
"plt.show()"
|
||||
"def show_residual_chart():\n",
|
||||
" dt = 0.1\n",
|
||||
" # initialize filter\n",
|
||||
" cvfilter= make_cv_filter(dt)\n",
|
||||
" initialize_filter(cvfilter)\n",
|
||||
" pos2, zs2 = generate_data(120, noise_factor=0.2)\n",
|
||||
" xs2 = pos2[:, 0]\n",
|
||||
" z_xs2 = zs2[:, 0]\n",
|
||||
"\n",
|
||||
" cvfilter.Q = Q_discrete_white_noise(dim=2, dt=dt, var=0.02)\n",
|
||||
" xs = []\n",
|
||||
" res = []\n",
|
||||
" for z in z_xs2:\n",
|
||||
" cvfilter.predict()\n",
|
||||
" cvfilter.update([z])\n",
|
||||
" xs.append(cvfilter.x[0])\n",
|
||||
" res.append(cvfilter.y[0])\n",
|
||||
" \n",
|
||||
" xs = np.asarray(xs)\n",
|
||||
" plot_track_and_residuals(t, xs, z_xs2, res)\n",
|
||||
" \n",
|
||||
"show_residual_chart()"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -960,9 +960,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAvsAAAE6CAYAAACI3Z3CAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8c5ccf8>"
|
||||
"<matplotlib.figure.Figure at 0x81dc828>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1014,9 +1014,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8ffcac8>"
|
||||
"<matplotlib.figure.Figure at 0x838c438>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1102,9 +1102,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8e71e10>"
|
||||
"<matplotlib.figure.Figure at 0x81c26d8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1204,9 +1204,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8267e10>"
|
||||
"<matplotlib.figure.Figure at 0x83e7588>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1233,9 +1233,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8f3f048>"
|
||||
"<matplotlib.figure.Figure at 0x748c160>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1262,9 +1262,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8bd3438>"
|
||||
"<matplotlib.figure.Figure at 0x83ca550>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1272,9 +1272,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7b576d8>"
|
||||
"<matplotlib.figure.Figure at 0x950f518>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1304,9 +1304,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8be6358>"
|
||||
"<matplotlib.figure.Figure at 0x82cd860>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1314,9 +1314,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8be6208>"
|
||||
"<matplotlib.figure.Figure at 0x84417f0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1324,9 +1324,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x826bbe0>"
|
||||
"<matplotlib.figure.Figure at 0x75060b8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1334,9 +1334,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8d8c160>"
|
||||
"<matplotlib.figure.Figure at 0x6edd240>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1344,9 +1344,9 @@
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x8f56ba8>"
|
||||
"<matplotlib.figure.Figure at 0x8465e10>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
@@ -1389,15 +1389,15 @@
|
||||
"\n",
|
||||
"The fading memory filter accounts for this problem by giving less weight to older measurements, and greater weight to the more recent measurements. \n",
|
||||
"\n",
|
||||
"There are many formulations for the fading memory Filter; I use the one provided by Dan Simon in *Optimal State Estimation* [3]. I will not go through his derivation, but only provide the results.\n",
|
||||
"There are many formulations for the fading memory filter; I use the one provided by Dan Simon in *Optimal State Estimation* [3]. I will not go through his derivation, but only provide the results.\n",
|
||||
"\n",
|
||||
"The Kalman filter equation for the covariances of the estimation error is\n",
|
||||
"\n",
|
||||
"$$ \\mathbf{P} = \\mathbf{FPF}^\\mathtt{T} + \\mathbf{Q}$$\n",
|
||||
"$$ \\mathbf{P} = \\mathbf{FPF}^\\mathsf{T} + \\mathbf{Q}$$\n",
|
||||
"\n",
|
||||
"We can force the filter to forget past measurements by multiplying a term $\\alpha$\n",
|
||||
"\n",
|
||||
"$$ \\tilde{\\mathbf{P}} = \\alpha^2\\mathbf{FPF}^\\mathtt{T} + \\mathbf{Q}$$\n",
|
||||
"$$ \\tilde{\\mathbf{P}} = \\alpha^2\\mathsf{FPF}^\\mathtt{T} + \\mathbf{Q}$$\n",
|
||||
"\n",
|
||||
"where $\\alpha > 1.0$. If $\\alpha == 1$ then we get the normal Kalman filter performance. $\\alpha$ is an attribute of `FilterPy`s Kalman filter class; its value defaults to 1 so the filter acts like a Kalman filter unless $\\alpha$ is assigned a value other than 1. There is no hard and fast rule for choosing $\\alpha$, but it is typically very close to 1, such as 1.01. You will need to make many runs with either simulated or real data to determine a value that responds to maneuvers without causing the estimate to become too noisy due to overly weighting the noisy measurement.\n",
|
||||
"\n",
|
||||
@@ -1417,9 +1417,9 @@
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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"text/plain": [
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"<matplotlib.figure.Figure at 0x8ed1898>"
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"<matplotlib.figure.Figure at 0x95d9fd0>"
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]
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},
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"metadata": {},
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@@ -1558,14 +1558,103 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The example I have been using in this chapter entails a target moving in a steady state, performing a maneuver, and then returning to a steady state. We have been thinking of this as two models - a constant velocity model, and a constant acceleration model. Whenever you can describe the system as obeying one of a finite set of models you can use *Multiple Model (MM) Estimation*. This means what it sounds like. We use a bank multiple filters, each using a different process to describe the system, and either switch between them or blend them based on the dynamics of the tracked object. \n",
|
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"The example I have been using in this chapter entails a target moving in a steady state, performing a maneuver, and then returning to a steady state. We have been thinking of this as two models - a constant velocity model, and a constant acceleration model. Whenever you can describe the system as obeying one of a finite set of models you can use *Multiple Model (MM) Estimation*. This means what it sounds like. We use a bank of multiple filters, each using a different process to describe the system, and either switch between them or blend them based on the dynamics of the tracked object. \n",
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"\n",
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"As you might imagine this is a broad topic, and there are many ways of designing and implementing MM estimators. But consider a simple approach for the target we have been tracking in this chapter. One idea would be to simultaneously run a constant velocity and a constant acceleration filter, and to switch between their outputs when we detect a maneuver by inspecting the residuals. Even this choice gives us many options. Consider the dynamics of a turning object. For example, an automobile turns on a wheelbase - the front wheels turn, and the car pivots around the rear wheels. This is a nonlinear process, so for best results we would want to use some type of nonlinear filter (EKF, UKF, etc) to model the turns. On the other hand, a linear constant velocity filter would perform fine for the steady state portions of the travel. So our bank of filters might consist of a linear KF and an EKF filter for the turns. However, neither is particularly well suited for modeling behaviors such as accelerating and braking. So a highly performing MM estimator might contain a bank of many filters, each designed to perform best for a certain performance envelope of the tracked object.\n",
|
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"\n",
|
||||
"Of course, you do not need to just base your filters on the order of the model. You can use different noise models, different adapters in each. For example, in the section above I showed many plots depicting the effects of changing parameters on the estimate of the velocity and position. Perhaps one setting works better for position, and a different setting for velocity. Put both in your bank of filters. You could then take the best estimates for the position from one filter, and the best estimate for the velocity from a different filter.\n",
|
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"\n",
|
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"I trust the idea of switching between filters to get the best performance is clear, but what mathematical foundations should we use to implement it? The problem that we face is trying to detect via noisy measurements when a change in regime should result in a change in model. \n",
|
||||
"\n"
|
||||
"### A Two Filter Adaptive Filter\n",
|
||||
"\n",
|
||||
"I trust the idea of switching between filters to get the best performance is clear, but what mathematical foundations should we use to implement it? The problem that we face is trying to detect via noisy measurements when a change in regime should result in a change in model. What aspect of the Kalman filter measures how far the measurement deviates from the prediction? Yes, the *residual*.\n",
|
||||
"\n",
|
||||
"Let's say we have a two state (constant velocity) Kalman filter. As long as the target is not maneuvering the filter will track it's behavior closely, and roughly 68% of the measurements should fall within 1$\\sigma$. Furthermore the residual should fluctuate around 0 because as many if the sensor is Gaussian an equal number of measurement should have positive error as have negative errors. If the residual grows and stays beyond predicted bounds then the target must not be performing as predicted by the state model. We saw this earlier in this chart where the residual switched from bouncing around 0 to suddenly jumping and staying above zero once the tracked object began maneuvering."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 18,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x6ed7940>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"show_residual_chart()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"For this problem we saw that the constant velocity filter performed better the constant acceleration filter while the object was in steady state, and the opposite was true when the object is maneuvering. In the chart above that transition occurs at 4 seconds. \n",
|
||||
"\n",
|
||||
"So the algorithm is easy. Initialize both a constant velocity and constant acceleration filter and run them together in a predict/update loop. After every update examine the residual of the constant velocity filter. If it falls within theoretical bounds use the estimate from the constant velocity filter as the estimate, otherwise use the estimate from the constant acceleration filter. If you have enough insight into your problem, you can also choose to blend the outputs of the two filters proportional to the size of the residual."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 76,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x81f2710>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"def run_filter_bank(threshold):\n",
|
||||
" dt = 0.1\n",
|
||||
" cvfilter= make_cv_filter(dt)\n",
|
||||
" cafilter = make_ca_filter(dt)\n",
|
||||
"\n",
|
||||
" pos2, zs2 = generate_data(120, noise_factor=0.2)\n",
|
||||
" z_xs2 = zs2[:, 0]\n",
|
||||
" t = np.arange(0, len(z_xs2) * dt, dt)\n",
|
||||
" xs, res = [], []\n",
|
||||
"\n",
|
||||
" for z in z_xs2:\n",
|
||||
" cvfilter.predict()\n",
|
||||
" cafilter.predict()\n",
|
||||
" cvfilter.update([z])\n",
|
||||
" cafilter.update([z])\n",
|
||||
" \n",
|
||||
" std = np.sqrt(cvfilter.R[0,0])\n",
|
||||
" if cvfilter.y[0] < 1.4 * std:\n",
|
||||
" xs.append(cvfilter.x[0])\n",
|
||||
" else:\n",
|
||||
" xs.append(cafilter.x[0])\n",
|
||||
" res.append(cvfilter.y[0])\n",
|
||||
" xs = np.asarray(xs)\n",
|
||||
" plot_track_and_residuals(t, xs, z_xs2, res)\n",
|
||||
"\n",
|
||||
"run_filter_bank(threshold=1.4)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Here we get nearly ideal performance. While the target is not maneuvering our estimate is nearly noise free, and then once it does maneuver we quickly detect that and switch to the constant acceleration filter. "
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -1603,7 +1692,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.4.3"
|
||||
"version": "3.4.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@@ -0,0 +1,30 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Created on Tue Jun 30 19:48:21 2015
|
||||
|
||||
@author: rlabbe
|
||||
"""
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import book_plots as bp
|
||||
|
||||
|
||||
def plot_track_and_residuals(t, xs, z_xs, res):
|
||||
plt.subplot(121)
|
||||
bp.plot_measurements(t, z_xs, label='z')
|
||||
bp.plot_filter(t, xs)
|
||||
plt.legend(loc=2)
|
||||
plt.xlabel('time (sec)')
|
||||
plt.ylabel('X')
|
||||
plt.title('estimates vs measurements')
|
||||
plt.subplot(122)
|
||||
# plot twice so it has the same color as the plot to the left!
|
||||
plt.plot(t, res)
|
||||
plt.plot(t, res)
|
||||
plt.xlabel('time (sec)')
|
||||
plt.ylabel('residual')
|
||||
plt.title('residuals')
|
||||
plt.show()
|
||||
|
||||
|
||||
|
||||
Reference in new issue
Block a user