Bias analysis in Kalman filter with correlated mode mismatch errors

In this paper, we investigate the impact of inaccurate mode knowledge on a mode-based Kalman filter used for state estimation in a Markov jump linear system (MJLS). Specifically, we consider correlated mode mismatch errors that can effectively capture the influence of communication network errors or cyber-attacks in a cyber-physical system. Interpreting the bias dynamics as a transformed switching system, we derive, for the first time, an algebraically solvable sufficient condition (with respect to mode mismatch error probabilities) that guarantees convergence of the bias. The theoretical result, validated via simulations, provides insights on the fidelity of discrete state knowledge required for maintaining the continuous state estimate quality.