Suboptimal Bayesian Filters for Markov Jump Linear Systems with Unknown Noise Covariance

The quality of measurements plays a crucial role in industrial processes. This paper proposes a novel suboptimal filter for Markov jump linear systems (MJLSs) that deals with the challenge of unknown measurement covariance. To limit the number of feasible mode sequences, variational Bayesian (VB) inference is employed to approximate the posterior Gaussian mixture distribution. This is achieved by representing it as a product of Gaussian and categorical distribution, aiming to minimize the Kullback-Leibler (KL) divergence. The resultant recursion turns out to be a new suboptimal Bayesian estimator, adept at simultaneously estimating system states, modal state, and measurement noise covariance, all within a unified probabilistic framework. The target tracking example is presented to illustrate that the proposed method is a competitive alternative to existing suboptimal estimation methods.