On the Performance of Kalman Filter for Markov Jump Linear Systems with Mode Mismatch

Abstract

Markov jump linear system (MJLS) is a class of hybrid systems where the continuous states evolve linearly and the discrete state transitions are modeled via a Markov chain. It has been shown that the optimal estimator for MJLS is a mode-based Kalman filter when the discrete mode is given. However, in practical applications, there are situations where the mode information is inaccurate and mode mismatches result in a biased estimate from the mode-based Kalman filter. This paper, for the first time, studies the impact of time correlated mode mismatch errors on MJLS state estimation using a mode-based Kalman filter. Unlike prior efforts that (1) assume mode mismatches are independent and identically distributed and (2) are limited to bi-modal systems, this paper is built on a general MJLS setup with a Markovian model for mode mismatch errors. The main contribution of this work lies in deriving the statistics of the bias term from a mode-based Kalman filter estimation with the aforementioned system setup. The sufficient conditions based on the probabilities of mode mismatch errors for the bias to be statistically convergent are derived. Since time correlated mode mismatch errors can effectively capture communication link impairments in a cyber-physical system, this new fundamental result provides guidance on the design of estimation strategies for MJLS and sheds light on their resilience in the presence of mode mismatch errors.