Fixed errors in display of std error.
For some reason I was displaying the std error as +/- the filter output, not the true path. I also neglected to take the sqrt of the variance.
This commit is contained in:
Roger Labbe committed
1 parent
6c9b693d7d
commit
917e66bf86
1 file changed
+83
-83
@@ -1,7 +1,7 @@
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@@ -261,7 +261,7 @@
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@@ -395,7 +395,7 @@
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@@ -563,7 +563,7 @@
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@@ -595,9 +595,9 @@
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd53dc9de48>"
|
||||
"<matplotlib.figure.Figure at 0x7fc65bc3d6d8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -655,7 +655,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519bc44a8>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636fe8ac8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -758,7 +758,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51983ddd8>"
|
||||
"<matplotlib.figure.Figure at 0x7fc63702fb00>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -785,7 +785,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519b46e48>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636da5a20>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -812,7 +812,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51993ac18>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636d9dfd0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -843,7 +843,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51963b208>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636dcc550>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -908,7 +908,7 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd5198004a8>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636e8e438>"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1776,8 +1776,8 @@
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 24,
|
||||
"text": [
|
||||
"array([[ 5.87500000e-05, 1.17500000e-03],\n",
|
||||
" [ 1.17500000e-03, 2.35000000e-02]])"
|
||||
"array([[ 0.00005875, 0.001175 ],\n",
|
||||
" [ 0.001175 , 0.0235 ]])"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1998,16 +1998,16 @@
|
||||
" 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",
|
||||
" actual = np.array(list(range(0,count)))\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",
|
||||
" std3 = np.sqrt(cov[:,0,0])*1\n",
|
||||
" std3_top = np.minimum(actual+std3, [count+10])\n",
|
||||
" std3_btm = np.maximum(actual-std3, [-50])\n",
|
||||
" plt.plot(actual, 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.plot(range(count), ps+std3, linestyle='--', c='k')\n",
|
||||
" plt.plot(range(count), ps-std3, linestyle='--', c='k')\n",
|
||||
" plt.plot(range(count), actual+std3, linestyle='--', c='k')\n",
|
||||
" plt.plot(range(count), actual-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",
|
||||
@@ -2033,7 +2033,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 28
|
||||
"prompt_number": 30
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2054,9 +2054,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519b34d68>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636daef28>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2064,11 +2064,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51982c588>"
|
||||
"<matplotlib.figure.Figure at 0x7fc6370cee80>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 29
|
||||
"prompt_number": 31
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2078,7 +2078,7 @@
|
||||
"\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. 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."
|
||||
"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. The covariance matrix $\\mathbf{P}$ tells us the *theoretical* performance of the filter *assuming* everything we tell it is true. Recall from the Gaussian chapter that the standard deviation is the square root of the variance, and that approximately 68% of a Gaussian distribution occurs within one standard deviation. Therefore, if at least 68% of the filter output is within one standard deviation we can be sure that the filter is performing well. In the top chart I have displayed the one standard deviation as the yellow shaded area between the two dotted lines. To my eye it looks like perhaps the filter is slightly exceeding that bounds, so the filter probably needs some tuning. We will discuss this later in the chaper."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2144,7 +2144,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 30
|
||||
"prompt_number": 32
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2173,7 +2173,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 31
|
||||
"prompt_number": 33
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2231,9 +2231,9 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519a5d390>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636e8e668>"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -2241,11 +2241,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519b3b3c8>"
|
||||
"<matplotlib.figure.Figure at 0x7fc6370c9fd0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 32
|
||||
"prompt_number": 34
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2409,7 +2409,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 33
|
||||
"prompt_number": 35
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2475,13 +2475,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519b1d0f0>"
|
||||
"<matplotlib.figure.Figure at 0x7fc637119a20>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 34
|
||||
"prompt_number": 36
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2545,21 +2545,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51962ba58>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636e8ea20>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
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"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51963b2b0>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636ea3860>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 35
|
||||
"prompt_number": 37
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2596,13 +2596,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51963a8d0>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636e0e438>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 36
|
||||
"prompt_number": 38
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2625,13 +2625,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519bbc550>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636d8b668>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 37
|
||||
"prompt_number": 39
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2654,13 +2654,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
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truncated
|
||||
"text": [
|
||||
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|
||||
"<matplotlib.figure.Figure at 0x7fc636ec4828>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 38
|
||||
"prompt_number": 40
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2725,11 +2725,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51976da58>"
|
||||
"<matplotlib.figure.Figure at 0x7fc637089d68>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 39
|
||||
"prompt_number": 41
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2755,11 +2755,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd5199c0dd8>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636b7ada0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 40
|
||||
"prompt_number": 42
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2825,13 +2825,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd5199ed668>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636f2d208>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 41
|
||||
"prompt_number": 43
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2855,13 +2855,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519a5cd68>"
|
||||
"<matplotlib.figure.Figure at 0x7fc63709c160>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 42
|
||||
"prompt_number": 44
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2888,13 +2888,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519bb1240>"
|
||||
"<matplotlib.figure.Figure at 0x7fc63714edd8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 43
|
||||
"prompt_number": 45
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2919,13 +2919,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519a4d710>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636dcc128>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 44
|
||||
"prompt_number": 46
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -2992,21 +2992,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519995d30>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636f7eeb8>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd5199994e0>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636b74860>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 45
|
||||
"prompt_number": 47
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -3077,11 +3077,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519798748>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636d35080>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 46
|
||||
"prompt_number": 48
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -3155,13 +3155,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519701710>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636cc81d0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 47
|
||||
"prompt_number": 49
|
||||
},
|
||||
{
|
||||
"cell_type": "heading",
|
||||
@@ -3215,11 +3215,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519701550>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636b94d68>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 48
|
||||
"prompt_number": 50
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -3259,11 +3259,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd51987b128>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636b94198>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 49
|
||||
"prompt_number": 51
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -3293,11 +3293,11 @@
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7fd519760a58>"
|
||||
"<matplotlib.figure.Figure at 0x7fc636ed7c88>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 50
|
||||
"prompt_number": 52
|
||||
},
|
||||
{
|
||||
"cell_type": "heading",
|
||||
|
||||
Reference in new issue
Block a user