Variational Bayesian Inference for Jump Markov Linear Systems with Unknown Transition Probabilities

Jump Markov linear systems (JMLSs) switch among simpler models according to a finite Markov chain, whose parameter, namely transition probability matrix (TPM), is rarely known and would cause significant loss in performance of estimator if not sufficient, thus needs to be estimated in practice. This paper considers the general situation where TPM is unknown and random, and presents a variational Bayesian method for recursive joint estimation of system state and unknown TPM. Under the assumption of transition probabilities following Dirichlet distributions, a variational Bayesian approximation is made to the joint posterior distribution of TPM, system and modal state on each time step separately. The resulting recursive method is applicable to various Bayesian multiple model state estimation algorithms for JMLSs and an application to IMM algorithm is demonstrated as an example. The performance of proposed method is illustrated by numerical simulations of maneuvering target tracking.