State estimation for discrete-time Markov jump linear systems with time-correlated and mode-dependent measurement noise

Abstract The state estimation problem for discrete-time Markov jump linear systems corrupted by time-correlated and mode-dependent measurement noise is considered where the time-correlated and mode-dependent measurement noise is described via a discrete-time stochastic system with Markov parameter and Kronecker delta function. By defining the measurement noise in this manner, both time-correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise. A novel “distributed measurement differencing method” is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper. The first algorithm is optimal in the sense of minimum mean-square error, which can exactly compute the minimum mean-square error estimate of system state. The second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some Gaussian hypotheses. The two proposed algorithms are recursive and the proposed suboptimal algorithm has a time-independent complexity. The performance of the proposed suboptimal algorithm is illustrated using computer simulations.

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