Impact of Time Correlated Mode Mismatch on Markov Jump Linear System State Estimation

Abstract

State estimation in Markov jump linear systems has garnered interest for decades with a majority of the proposed strategies relying on mode-based Kalman filters. It has been shown that a mode-based Kalman filter is optimal if the discrete state is known at each time. However, in practical applications, there are situations where the mode information is inaccurate due to communication link failures or cyber-attacks. This letter addresses this issue by quantifying the bias resulting from mode mismatches in a mode-based Kalman filter. Specifically, we consider the scenario wherein the mode mismatch error is correlated across time and modeled via a Markov chain. Necessary and sufficient conditions for the statistical convergence of bias dynamics are derived. The relationship between bias dynamics and the transition probabilities associated with the mode mismatch Markov chain are quantified. The main results presented in this letter provide new insights on the fidelity in discrete state knowledge needed to maintain the performance of a mode-based Kalman filter.