daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Fixed equation for update covariance.

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Equation for P at the end of the chapter was wrong. The
equation in code is correct, I just made a mistake in the LaTex.
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Roger Labbe 2015-03-12 18:35:08 -07:00
parent 0d8036a109
commit 1d1866d00d
1 changed files with 1 additions and 1 deletions
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06_Multivariate_Kalman_Filters.ipynb
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@ -34587,7 +34587,7 @@
"\n",
"it implements the somewhat more complicated form \n",
"\n",
"$$\\mathbf{P} = (\\mathbf{I} - \\mathbf{KH})\\mathbf{P}^-(\\mathbf{I} - \\mathbf{KRK})^\\mathsf{T} + \\mathbf{KRK}^\\mathsf{T}$$.\n",
"$$\\mathbf{P} = (\\mathbf{I} - \\mathbf{KH})\\mathbf{P}^-(\\mathbf{I} - \\mathbf{KH})^\\mathsf{T} + \\mathbf{KRK}^\\mathsf{T}$$.\n",
"\n",
"The reason for this altered equation is that it is more numerically stable than the former equation, at the cost of being a bit more expensive to compute. It is not always possible to find the optimal value for $\\text{K}$, in which case the former equation will not produce good results because it assumes optimality. The longer reformulation used in the code is derived from more general math that does not assume optimality, and hence provides good results for non-optimal filters (such as when we can not correctly model our measurement error).\n",
"\n",