A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter
This provides a theoretical insight for control systems researchers, but it is incremental as it builds on prior work.
The paper tackles the problem of characterizing the optimal error covariance in Kalman-Bucy filtering by deriving an explicit frequency-domain integral expression in terms of plant dynamics and noise statistics, reducing to existing results.
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.