Proof that the Kalman gain minimizes the generalized variance
Systems and Control
2021-03-15 v1 Systems and Control
Optimization and Control
Atmospheric and Oceanic Physics
Abstract
The optimal gain matrix of the Kalman filter is often derived by minimizing the trace of the posterior covariance matrix. Here, I show that the Kalman gain also minimizes the determinant of the covariance matrix, a quantity known as the generalized variance. When the error distributions are Gaussian, the differential entropy is also minimized.
Cite
@article{arxiv.2103.07275,
title = {Proof that the Kalman gain minimizes the generalized variance},
author = {Eviatar Bach},
journal= {arXiv preprint arXiv:2103.07275},
year = {2021}
}