daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Replaced 'transverse' with 'transpose'.

Fixed creative commons license - it was pointing to the old
name of the book.
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Roger Labbe 2015-01-08 21:14:44 -08:00
parent f635810a70
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Preface.ipynb
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@ -483,7 +483,7 @@
" measurement_function_transpose) +\n",
" measurement_noise_covariance))\n",
"\n",
"I grant you this version has more context, but I cannot reasonable glance at this and see what math it is implementing. In particular, the linear algebra $HPH^T$ is doing something very specific - multiplying P by H and its transverse is changing the *basis* of P. It is nearly impossible to see that the Kalman gain is just a ratio of one number divided by a second number which has been converted to a different basis. If you are not solid in linear algebra perhaps that statement does not convey a lot of information to you yet, but I assure you that $K = PH^T[HPH^T + R]^{-1}$ is saying something very succinctly. There are two key pieces of information here - we are taking a ratio, and we are converting the *basis* of a matrix. I can see that in my first Python line, I cannot see that in the second line. \n",
"I grant you this version has more context, but I cannot reasonable glance at this and see what math it is implementing. In particular, the linear algebra $HPH^T$ is doing something very specific - multiplying P by H and its transpose is changing the *basis* of P. It is nearly impossible to see that the Kalman gain is just a ratio of one number divided by a second number which has been converted to a different basis. If you are not solid in linear algebra perhaps that statement does not convey a lot of information to you yet, but I assure you that $K = PH^T[HPH^T + R]^{-1}$ is saying something very succinctly. There are two key pieces of information here - we are taking a ratio, and we are converting the *basis* of a matrix. I can see that in my first Python line, I cannot see that in the second line. \n",
"\n",
"I will not *win* this argument, and some people will not agree with my naming choices. I will finish by stating, very truthfully, that I made two mistakes the first time I typed that second version and it took me awhile to find it. In any case, I aim for using the mathematical symbol names whenever possible, coupled with readable class and function names. So, it is `KalmanFilter.P`, not `KF.P` and not `KalmanFilter.apriori_state_covariance`. "
]
@ -502,7 +502,7 @@
"source": [
"<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"http://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\">Kalman Filters and Random Signals in Python</span> by <a xmlns:cc=\"http://creativecommons.org/ns#\" href=\"https://github.com/rlabbe/Kalman-Filters-and-Random-Signals-in-Python\" property=\"cc:attributionName\" rel=\"cc:attributionURL\">Roger Labbe</a> is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-sa/4.0/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />\n",
"\n",
"Based on a work at <a xmlns:dct=\"http://purl.org/dc/terms/\" href=\"https://github.com/rlabbe/Kalman-Filters-and-Random-Signals-in-Python\" rel=\"dct:source\">https://github.com/rlabbe/Kalman-Filters-and-Random-Signals-in-Python</a>."
"Based on a work at <a xmlns:dct=\"http://purl.org/dc/terms/\" href=\"https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python\" rel=\"dct:source\">https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python</a>."
]
},
{