Linear minimum-mean-square error estimation of Markovian jump linear systems with randomly delayed measurements

This study presents the state estimation problem of discrete-time Markovian jump linear systems with randomly delayed measurements. Here, the delay is modelled as the combination of different number of binary stochastic variables according to the different possible delay steps. In the actually delayed measurement equation, multiple adjacent step measurement noises are correlated. Owing to the stochastic property from the measurement delay, the estimation model is rewritten as a discrete-time system with stochastic parameters and augmented state reconstructed from all modes with their mode uncertainties. For this system, a novel linear minimum-mean-square error (LMMSE, renamed as LMRDE) estimator for the augmented state is derived in a recursive structure according to the orthogonality principle under a generalised framework. Since the correlation among multiple adjacent step noises in the measurement equation, the measurement noises and related second moment matrices of corresponding previous instants in each current step are also needed to be estimated or calculated. A numerical example with possibly delayed measurements is simulated to testify the proposed method.