Pretty graphs are pretty.
Added a fill for the covariance to many of the charts. I also fixed a code typo in the ensemble chapter.
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Roger Labbe committed
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|
||||
"prompt_number": 5
|
||||
"prompt_number": 3
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -469,7 +469,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 7
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -487,7 +487,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 8
|
||||
"prompt_number": 5
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -506,7 +506,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 10
|
||||
"prompt_number": 6
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -532,7 +532,7 @@
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 12
|
||||
"prompt_number": 7
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -563,7 +563,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cced3a9e8>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc4de3c8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -616,7 +616,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce9dc668>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc20f160>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -714,7 +714,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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||||
"text": [
|
||||
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|
||||
"<matplotlib.figure.Figure at 0x7f4ebc1a2908>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -741,7 +741,7 @@
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||||
"output_type": "display_data",
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||||
"png": 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|
||||
"text": [
|
||||
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|
||||
"<matplotlib.figure.Figure at 0x7f4ebc3f0d68>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -768,7 +768,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cceab8b70>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc3b76d8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -799,7 +799,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce89ff28>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc1bf860>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -864,7 +864,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cceb12f28>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc3d7c50>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1950,14 +1950,24 @@
|
||||
" ps, zs, cov = filter_dog(noise_var=noise_var, data=data, count=count,\n",
|
||||
" R=R_var, Q=Q_var, P=P, initial_x=initial_x)\n",
|
||||
" \n",
|
||||
" cov = np.asarray(cov)\n",
|
||||
" std3 = cov[:,0,0]*1\n",
|
||||
" std3_top = np.minimum(ps+std3, [count+10])\n",
|
||||
" std3_btm = np.maximum(ps-std3, [-50])\n",
|
||||
"\n",
|
||||
" plt.plot([0, count],[0, count], label='actual')\n",
|
||||
" plt.plot(range(1, count+1), zs, linestyle='dashed', label='measurement')\n",
|
||||
" plt.plot(range(1, count+1), ps, label='filter')\n",
|
||||
" plt.legend(loc=2)\n",
|
||||
" plt.ylim((-10, count+10))\n",
|
||||
" plt.plot(range(count), ps+std3, linestyle='--', c='k')\n",
|
||||
" plt.plot(range(count), ps-std3, linestyle='--', c='k')\n",
|
||||
" plt.fill_between(range(count), std3_btm, std3_top,\n",
|
||||
" facecolor='yellow', alpha=0.2)\n",
|
||||
" plt.legend(loc=4)\n",
|
||||
" plt.ylim((-50, count+10))\n",
|
||||
" plt.title(title)\n",
|
||||
" plt.show()\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" if plot_P:\n",
|
||||
" ax = plt.subplot(121)\n",
|
||||
" ax.set_title(\"$\\sigma^2_x$\")\n",
|
||||
@@ -1989,7 +1999,7 @@
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plot_track(noise_var=10, R_var=10, Q_var=0.01, count=50)"
|
||||
"plot_track(noise_var=10, R_var=10., Q_var=0.01, count=50)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -1997,9 +2007,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4ccec74b70>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc50f828>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2007,7 +2017,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cd8030358>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc4bc518>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2019,9 +2029,9 @@
|
||||
"source": [
|
||||
"There is still a lot to learn, but we have implemented our first, full Kalman filter using the same theory and equations as published by Nobert Kalman! Code very much like this runs inside of your GPS and phone, inside every airliner, inside of robots, and so on. \n",
|
||||
"\n",
|
||||
"The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely.\n",
|
||||
"The first plot plots the output of the Kalman filter against the measurements and the actual position of our dog (drawn in green). After the initial settling in period the filter should track the dog's position very closely. The yellow shaded portion between the black dotted lines shows 1 standard deviations of the filter's variance, which I explain in the next paragrah.\n",
|
||||
"\n",
|
||||
"The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that."
|
||||
"The next two plots show the variance of $x$ and of $\\dot{x}$. If you look at the code, you will see that I have plotted the diagonals of $\\mathbf{P}$ over time. Recall that the diagonal of a covariance matrix contains the variance of each state variable. So $\\mathbf{P}[0,0]$ is the variance of $x$, and $\\mathbf{P}[1,1]$ is the variance of $\\dot{x}$. You can see that despite initializing $\\mathbf{P}=(\\begin{smallmatrix}500&0\\\\0&500\\end{smallmatrix})$ we quickly converge to small variances for both the position and velocity. We will spend a lot of time on the covariance matrix later, so for now I will leave it at that. For now we can look at the top plot and see that the filter's output stays within the 3 standard deviation lines, so we should feel confident that the filter is performing well."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2157,10 +2167,13 @@
|
||||
" plt.scatter(range(len(x2)), x2, c='r')\n",
|
||||
" plt.title('State')\n",
|
||||
" plt.plot(x1)\n",
|
||||
" plt.xlim([0, 50])\n",
|
||||
"\n",
|
||||
" plt.figure()\n",
|
||||
" plt.plot(p1)\n",
|
||||
" plt.scatter(range(len(x2)), p2, c='r')\n",
|
||||
" plt.title('Variance')\n",
|
||||
" plt.xlim([0, 50])\n",
|
||||
" plt.show()\n",
|
||||
" \n",
|
||||
"plot_kf_compare(x0=0., p0=500., R=5., Q=.2, move=1.)"
|
||||
@@ -2171,17 +2184,17 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce993208>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc50fc88>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cceb549b0>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebbfc1588>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2404,6 +2417,7 @@
|
||||
" plt.scatter(range(len(x2)), x2, c='r', label='2D Filter')\n",
|
||||
" plt.title('State')\n",
|
||||
" plt.legend(loc=4)\n",
|
||||
" plt.xlim([0,50])\n",
|
||||
" plt.show()\n",
|
||||
" \n",
|
||||
"plot_compare_pos_vel(x0=0., p0=500., R=5., Q=.2, move=1.) "
|
||||
@@ -2414,9 +2428,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce993f28>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc4bc1d0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2484,17 +2498,17 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce84dd30>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc19c0f0>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce848cf8>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc28e550>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2535,9 +2549,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
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||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cd8046240>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc4e2ac8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2547,7 +2561,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The effect of this can be subtle. We have created an suboptimal filter because the actual measurement noise variance is 30 m, not 10,000 m. By setting the filter's noise variance so high we force the filter to favor the prediction over the measurement. This can lead to apparently very smooth and good looking results. In the chart above the track may look extremely good to you since it follows the ideal path very closely. But, the 'great' behavior at the start should give you pause - the filter has not converged yet ($\\mathbf{P}$ is still large) so it should not be able to be so close to the actual position. Let's make $\\mathbf{R}$ larger yet. Let's see the result of a bad initial guess for the position by guessing the initial position to be 20 m and the initial velocity to be 1 m/s."
|
||||
"The effect of this can be subtle. We have created an suboptimal filter because the actual measurement noise variance is 30 m, not 10,000 m. By setting the filter's noise variance so high we force the filter to favor the prediction over the measurement. This can lead to apparently very smooth and good looking results. In the chart above the track may look extremely good to you since it follows the ideal path very closely. But, the 'great' behavior at the start should give you pause - the filter has not converged yet ($\\mathbf{P}$ is still large) so it should not be able to be so close to the actual position. We can see that $\\mathbf{P}$ has not converged because the entire chart is colored with the yellow background denoting the size of $\\mathbf{P}$. Let's make $\\mathbf{R}$ larger yet. Let's see the result of a bad initial guess for the position by guessing the initial position to be 20 m and the initial velocity to be 1 m/s."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2564,9 +2578,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cd8030978>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc543fd0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2593,9 +2607,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4ccedb4320>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc534390>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2664,7 +2678,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cceca15c0>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc0040f0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2694,7 +2708,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4ccea60a20>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc427be0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2756,7 +2770,7 @@
|
||||
" 47.769, 56.855, 53.693, 61.534, 70.665, 60.355, 65.095, 63.386]\n",
|
||||
"\n",
|
||||
"plot_track(data=zs, R_var=50., Q_var=.2, P=500., count=len(zs), \n",
|
||||
" plot_P=True, title='P=500 m')"
|
||||
" plot_P=False, title='P=500 m')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -2764,17 +2778,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4ccea8e278>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cceb56390>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc33a278>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2794,7 +2800,7 @@
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plot_track(data=zs, R_var=50., Q_var=.2, P=1., count=len(zs), \n",
|
||||
" plot_P=True, title='P=1 m')"
|
||||
" plot_P=False, title='P=1 m')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -2802,17 +2808,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
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||||
"text": [
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||||
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||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce9d9550>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc20e320>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2843,9 +2841,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cce84bbe0>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc534ef0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2874,9 +2872,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cceb84e48>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc262ac8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -2947,17 +2945,17 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cced2cb70>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc28ec88>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4cced4d710>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc1a7978>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -3032,7 +3030,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7f4ccebeceb8>"
|
||||
"<matplotlib.figure.Figure at 0x7f4ebc1aed68>"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
{
|
||||
"metadata": {
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"name": "",
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"signature": "sha256:2b626ac51cd84e0593614b830cc5ea8b9d2af5ca92e0863eaba39906bb9cd0af"
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||||
"signature": "sha256:27673fb70676d96004e87e31970b90211c1085f207b54be7493d754343d3e67f"
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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 0x7fc25989a588>"
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"<IPython.core.display.HTML at 0x7fd6b1d87588>"
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]
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}
|
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],
|
||||
@@ -311,9 +311,9 @@
|
||||
{
|
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"metadata": {},
|
||||
"output_type": "display_data",
|
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||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAsQAAAF2CAYAAABpv45gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fc23c43b780>"
|
||||
"<matplotlib.figure.Figure at 0x7fd6b1d7c240>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -552,8 +552,8 @@
|
||||
"kf.x = np.array([x]).T\n",
|
||||
"kf.F = F.copy()\n",
|
||||
"kf.P = P.copy()\n",
|
||||
"kf.R = f.R.copy()\n",
|
||||
"kf.Q = f.Q.copy()\n",
|
||||
"kf.R = enf.R.copy()\n",
|
||||
"kf.Q = enf.Q.copy()\n",
|
||||
"kf.H = np.array([[1., 0.]])\n",
|
||||
"\n",
|
||||
"measurements = []\n",
|
||||
@@ -574,10 +574,10 @@
|
||||
" kf.update(np.asarray([[z]]))\n",
|
||||
"\n",
|
||||
" # save data\n",
|
||||
" results.append (f.x[0])\n",
|
||||
" results.append (enf.x[0])\n",
|
||||
" kf_results.append (kf.x[0,0])\n",
|
||||
" measurements.append(z)\n",
|
||||
" ps.append(3*(f.P[0,0]**.5))\n",
|
||||
" ps.append(3*(enf.P[0,0]**.5))\n",
|
||||
"\n",
|
||||
"results = np.asarray(results)\n",
|
||||
"ps = np.asarray(ps)\n",
|
||||
@@ -587,6 +587,7 @@
|
||||
"plt.plot(measurements, c='r', label='z')\n",
|
||||
"plt.plot (results-ps, c='k',linestyle='--', label='3$\\sigma$')\n",
|
||||
"plt.plot(results+ps, c='k', linestyle='--')\n",
|
||||
"plt.fill_between(range(100),results-ps, results+ps, facecolor='yellow', alpha=.3)\n",
|
||||
"plt.legend(loc='best')\n",
|
||||
"plt.show()"
|
||||
],
|
||||
@@ -596,13 +597,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fc234731208>"
|
||||
"<matplotlib.figure.Figure at 0x7fd68d6a6cf8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 13
|
||||
"prompt_number": 7
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
|
||||
Reference in new issue
Block a user