A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter
Systems and Control
2018-07-24 v1 Robotics
Signal Processing
Optimization and Control
Abstract
In this paper, we discover that the trace of the division of the optimal output estimation error covariance over the noise covariance attained by the Kalman-Bucy filter can be explicitly expressed in terms of the plant dynamics and noise statistics in a frequency-domain integral characterization. Towards this end, we examine the algebraic Riccati equation associated with Kalman-Bucy filtering using analytic function theory and relate it to the Bode integral. Our approach features an alternative, frequency-domain framework for analyzing algebraic Riccati equations and reduces to various existing related results.
Keywords
Cite
@article{arxiv.1807.08604,
title = {A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter},
author = {Song Fang and Hideaki Ishii and Jie Chen and Karl Henrik Johansson},
journal= {arXiv preprint arXiv:1807.08604},
year = {2018}
}