Bayesian State Estimation for Markovian Jump Systems: Employing Recursive Steps and Pseudocodes

In this article, we review several existing Bayesian state-estimation algorithms for Markovian jump systems (MJSs) and illustrate their distinctive properties. Specifically, we analyze the jump Markov linear systems (JMLSs), for which autonomous multiple-model (AMM) algorithms, first-order generalized pseudo-Bayesian (GPB1) algorithms, second-order generalized pseudo-Bayesian (GPB2) algorithms, interacting multiple-model (IMM) algorithms, and reweighed IMM (RIMM) algorithms are introduced. For nonlinear MJSs, we consider the sampling importance resampling (SIR) particle filter (PF) as well as the IMM PF to demonstrate how to handle nonlinearity in the framework of MJSs. For convenience, the realization codes of GPB1 and IMM algorithms and SIR PFs are provided.