Rate distortion in the modal estimation of switching FIR linear systems

This paper is about the mode estimation of randomly switching linear systems. We follow up on previous results, where we posed the problem in a way which is well fitted for a worst-case analysis. The aforementioned investigation relies on a divergence measure and several other quantities, such as the entropy rate of the mode switching as well as the power ratio between the system´s excitation and the measurement noise. In this article we ascribe a natural interpretation to such divergence measure, while establishing a connection to rate-distortion theory. We also explore why and in what form estimation fidelity is affected by the entropy rate of the mode switching. Additionally, this analysis suggests that such entropy rate must be regarded as a fundamental quantity in the determination of the estimation fidelity.