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arXiv · 1807.08604

A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter

Song Fang·Hideaki Ishii·Jie Chen·Karl Henrik Johansson
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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.

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Song Fang, Hideaki Ishii, Jie Chen, Karl Henrik Johansson. 2018-07-23. A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter. https://arxiv.org/abs/1807.08604

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