Recursive linear optimal filter for Markovian jump linear systems with multi-step correlated noises and multiplicative random parameters

This paper presents the state estimation problem for discrete-time Markovian jump linear systems with multi-step correlated additive noises and multiplicative random parameters (termed as MCNMP). A recursive linear optimal filter for the considered MCNMP (which is abbreviated as RLMMF) is derived based on state augmentation between the original state and mode uncertainty, with the help of estimating the multi-step correlated additive noises online simultaneously. A maneuvering target tracking example under one-step and two-step correlated additive noises scenarios with different cases (i.e. Gaussian/Gaussian mixture distribution and no multiplicative noises) is simulated to validate the designed filter.