The LMMSE estimation for Markovian jump linear systems with stochastic coefficient matrices and one-step randomly delayed measurements

This paper presents the state estimation problem of discrete-time Markovian jump linear systems (MJLSs) with stochastic coefficient matrices (SCMs) and one-step randomly delayed measurements (RODs). Here, the SCMs are modeled as the randomly weighted sum of a series known basis matrices while the RODs are represented by a sequence of independent Bernoulli random variables. The proposed system is the MJLS with multiple stochastic parameters, including stochastic system matrices leading the uncertainty coupling between system matrices and state/noises, and ranndom Bernoulli variables leading the real measurement correlated with that at previous instant. By geometry augmentation, the state coupled with mode uncertainty is estimated instead of estimating the original state directly. Then, the linear minimum-mean-square error (LMMSE) estimator is derived in a recursive structure according to the orthogonality principle. A numerical simulation is presented to testify the proposed method.