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1.18.0
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EmrysFilter 0.1.0
State estimation utilities in C++23 using Eigen
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The Joseph covariance update: \( (I - K H) P (I - K H)^T + K R K^T \), with \( H \) and \( R \) from the statistical linearization of the output in the input (see statisticalLinearization()). More...
#include <EmrysFilter/Models/Condition.h>
The Joseph covariance update: \( (I - K H) P (I - K H)^T + K R K^T \), with \( H \) and \( R \) from the statistical linearization of the output in the input (see statisticalLinearization()).
It is correct for any gain, an error in the gain changes it only at second order, and it is a sum of two positive semidefinite terms, so it stays positive semidefinite whenever \( R \) is. It costs a solve against the prior covariance and products of the state's size cubed.
\( R \) is everything in \( \Sigma_{yy} \) that \( H \) does not explain: input noise, and the error of the linearization. A measurement's additive noise is kept apart and added to \( R \) rather than being subtracted back out of \( \Sigma_{yy} \), which would cancel the digits that make a precise measurement hard. With a negative sigma-point weight the linearization error can come out indefinite, and then so can the result.
The Joseph stabilized form (Bar-Shalom, Li, and Kirubarajan (2001)), with the measurement matrix and noise replaced by the statistical linearization's, so that it applies to every transform method.
1.18.0