Made sensor fusion code a function.
The function takes the wheel and gps variance in as parameters so I can easily vary the values and display them to the reader.
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@@ -1,7 +1,7 @@
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{
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"metadata": {
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"name": "",
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"signature": "sha256:99ce1d42001f74032bcccc6919adcf581e234259ab9db1c2aa8da6551ff2c728"
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"signature": "sha256:7abdbb6792be112481394d0099141b4a4c633b66c486d753cbcc2f6d854636d7"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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@@ -261,7 +261,7 @@
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"output_type": "pyout",
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"prompt_number": 1,
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"text": [
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"<IPython.core.display.HTML at 0x7f7a9b19c5c0>"
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"<IPython.core.display.HTML at 0x7fe3077d45f8>"
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]
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}
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],
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@@ -354,9 +354,9 @@
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{
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"metadata": {},
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"output_type": "display_data",
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"png": 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truncated
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"png": 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truncated
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"text": [
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"<matplotlib.figure.Figure at 0x7f7a7e5d63c8>"
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"<matplotlib.figure.Figure at 0x7fe2eac40400>"
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]
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}
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],
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@@ -707,9 +707,9 @@
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{
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"metadata": {},
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"output_type": "display_data",
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"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a7e21df98>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2ea87cf98>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -797,9 +797,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a7df5ffd0>"
|
||||
"<matplotlib.figure.Figure at 0x7fe3077c9908>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -884,7 +884,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a7e207908>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2ea871710>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -957,48 +957,50 @@
|
||||
"from filterpy.kalman import KalmanFilter\n",
|
||||
"from numpy import array, asarray\n",
|
||||
"\n",
|
||||
"dt = 0.1\n",
|
||||
"wheel_sigma = 1.5\n",
|
||||
"gps_sigma = wheel_sigma*2\n",
|
||||
"kf = KalmanFilter(dim_x=2, dim_z=2)\n",
|
||||
"def fusion_test(wheel_sigma, gps_sigma, do_plot=True):\n",
|
||||
" dt = 0.1\n",
|
||||
" kf = KalmanFilter(dim_x=2, dim_z=2)\n",
|
||||
"\n",
|
||||
"kf.F = array ([[1., dt], [0., 1.]])\n",
|
||||
"kf.H = array ([[1., 0.], [1., 0.]])\n",
|
||||
"kf.X = array ([[0.], [1.]])\n",
|
||||
"kf.Q *= 0.01\n",
|
||||
"kf.P *= 100\n",
|
||||
"kf.R[0,0] = wheel_sigma**2\n",
|
||||
"kf.R[1,1] = gps_sigma**2 \n",
|
||||
" kf.F = array ([[1., dt], [0., 1.]])\n",
|
||||
" kf.H = array ([[1., 0.], [1., 0.]])\n",
|
||||
" kf.X = array ([[0.], [1.]])\n",
|
||||
" kf.Q *= array([[(dt**3)/3, (dt**2)/2],\n",
|
||||
" [(dt**2)/2, dt ]]) * 0.02\n",
|
||||
" kf.P *= 100\n",
|
||||
" kf.R[0,0] = wheel_sigma**2\n",
|
||||
" kf.R[1,1] = gps_sigma**2 \n",
|
||||
"\n",
|
||||
"random.seed(1123)\n",
|
||||
"xs = []\n",
|
||||
"zs = []\n",
|
||||
"nom = []\n",
|
||||
"for i in range(1, 100):\n",
|
||||
" m0 = i + randn()*wheel_sigma\n",
|
||||
" m1 = i + randn()*gps_sigma\n",
|
||||
" z = array([[m0], [m1]])\n",
|
||||
" random.seed(1123)\n",
|
||||
" xs = []\n",
|
||||
" zs = []\n",
|
||||
" nom = []\n",
|
||||
" for i in range(1, 100):\n",
|
||||
" m0 = i + randn()*wheel_sigma\n",
|
||||
" m1 = i + randn()*gps_sigma\n",
|
||||
" z = array([[m0], [m1]])\n",
|
||||
"\n",
|
||||
" kf.predict()\n",
|
||||
" kf.update(z)\n",
|
||||
" kf.predict()\n",
|
||||
" kf.update(z)\n",
|
||||
"\n",
|
||||
" xs.append(kf.X.T[0])\n",
|
||||
" zs.append(z.T[0])\n",
|
||||
" nom.append(i)\n",
|
||||
" xs.append(kf.X.T[0])\n",
|
||||
" zs.append(z.T[0])\n",
|
||||
" nom.append(i)\n",
|
||||
"\n",
|
||||
"xs = asarray(xs)\n",
|
||||
"zs = asarray(zs)\n",
|
||||
"nom = asarray(nom)\n",
|
||||
" xs = asarray(xs)\n",
|
||||
" zs = asarray(zs)\n",
|
||||
" nom = asarray(nom)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"res = nom-xs[:,0]\n",
|
||||
"print('fusion std: {:.3f}'.format (np.std(res)))\n",
|
||||
" res = nom-xs[:,0]\n",
|
||||
" print('fusion std: {:.3f}'.format (np.std(res)))\n",
|
||||
" if do_plot:\n",
|
||||
" plt.plot(xs[:,0], label='Kalman filter')\n",
|
||||
" plt.plot(zs[:,0],linestyle=':', label='wheel')\n",
|
||||
" plt.plot(zs[:,1],linestyle=':', label='GPS')\n",
|
||||
" plt.legend(loc=4)\n",
|
||||
" plt.show()\n",
|
||||
"\n",
|
||||
"plt.plot(xs[:,0], label='Kalman filter')\n",
|
||||
"plt.plot(zs[:,0],linestyle=':', label='wheel')\n",
|
||||
"plt.plot(zs[:,1],linestyle=':', label='GPS')\n",
|
||||
"plt.legend(loc=4)\n",
|
||||
"plt.show()"
|
||||
"fusion_test(1.5, 3.0)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -1007,15 +1009,15 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"fusion std: 0.422\n"
|
||||
"fusion std: 0.391\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a769411d0>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2fa3ac8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1033,13 +1035,35 @@
|
||||
"\n",
|
||||
"##### Solution 1\n",
|
||||
"\n",
|
||||
"Force the Kalman filter to disregard the GPS measurement by setting the measurement noise for the GPS to a near infinite value. Re-run the filter and observe the standard deviation of the residual. \n",
|
||||
"\n",
|
||||
"For example, if I edit the cell above with\n",
|
||||
"\n",
|
||||
" kf.R[1,1] = 1.e80\n",
|
||||
"\n",
|
||||
"and run the cell again I get a standard deviation of 0.494, vs the standard deviation of 0.422 when the GPS measurement is used. \n",
|
||||
"Force the Kalman filter to disregard the GPS measurement by setting the measurement noise for the GPS to a near infinite value. Re-run the filter and observe the standard deviation of the residual. "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fusion_test(1.5, 3.0, do_plot=False)\n",
|
||||
"fusion_test(1.5, 1e80, do_plot=False)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"fusion std: 0.391\n",
|
||||
"fusion std: 0.438\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 15
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Here we can see the error in the filter where the GPS measurement is almost entirely ignored is greater than that where it is used.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"##### Solution 2\n",
|
||||
@@ -1112,11 +1136,11 @@
|
||||
"output_type": "display_data",
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a768a9198>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2fa39e8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 15
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1217,7 +1241,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 16
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1260,7 +1284,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a768f84a8>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2f9d780>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -1268,11 +1292,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a76900978>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2f9dba8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 17
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1410,7 +1434,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 18
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1450,11 +1474,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a76784fd0>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2df0198>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 19
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1595,7 +1619,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 20
|
||||
"prompt_number": 21
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1645,11 +1669,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a7e3109e8>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2f03be0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 21
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1786,11 +1810,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a767aa588>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e3026860>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 22
|
||||
"prompt_number": 23
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1860,7 +1884,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 23
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1919,11 +1943,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a768d3668>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2f02240>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 24
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -1987,7 +2011,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a88145f98>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2ea92fcf8>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -1995,11 +2019,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a768e9cc0>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2ddcef0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 25
|
||||
"prompt_number": 26
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2025,7 +2049,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a76796668>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2fb7be0>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2033,11 +2057,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f7a767ecef0>"
|
||||
"<matplotlib.figure.Figure at 0x7fe2e2cc9e80>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 26
|
||||
"prompt_number": 27
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
|
||||
+11
-11
@@ -43,17 +43,17 @@ if __name__ == '__main__':
|
||||
#merge_notebooks(sys.argv[1:])
|
||||
merge_notebooks(
|
||||
['Preface.ipynb',
|
||||
'Chapter01_gh_filter/g-h_filter.ipynb',
|
||||
'Chapter02_Discrete_Bayes/discrete_bayes.ipynb',
|
||||
'Chapter03_Least_Squares/Least_Squares_Filters.ipynb',
|
||||
'Chapter04_Gaussians/Gaussians.ipynb',
|
||||
'Chapter05_Kalman_Filters/Kalman_Filters.ipynb',
|
||||
'Chapter06_Multivariate_Kalman_Filter/Multivariate_Kalman_Filters.ipynb',
|
||||
'Chapter07_Kalman_Filter_Math/Kalman_Filter_Math.ipynb',
|
||||
'Chapter08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb',
|
||||
'Chapter09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb',
|
||||
'Chapter10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb',
|
||||
'Chapter11_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb',
|
||||
'01_gh_filter/g-h_filter.ipynb',
|
||||
'02_Discrete_Bayes/discrete_bayes.ipynb',
|
||||
'03_Least_Squares/Least_Squares_Filters.ipynb',
|
||||
'04_Gaussians/Gaussians.ipynb',
|
||||
'05_Kalman_Filters/Kalman_Filters.ipynb',
|
||||
'06_Multivariate_Kalman_filter/Multivariate_Kalman_Filters.ipynb',
|
||||
'07_Kalman_Filter_Math/Kalman_Filter_Math.ipynb',
|
||||
'08_Designing_Kalman_Filters/Designing_Kalman_Filters.ipynb',
|
||||
'09_Extended_Kalman_Filters/Extended_Kalman_Filters.ipynb',
|
||||
'10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb',
|
||||
'11_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb',
|
||||
'Appendix_A_Installation/Appendix_Installation.ipynb',
|
||||
'Appendix_B_Symbols_and_Notations/Appendix_Symbols_and_Notations.ipynb'])
|
||||
|
||||
|
||||
Reference in new issue
Block a user