State estimation for jump Markov linear systems by variational Bayesian approximation

This article studies the problem of state estimation for jump Markov linear systems with unknown measurement noise variance parameters. By using the concept of conjugate prior distributions for noise statistics, a novel estimator is developed by applying the basic interacting multiple model (IMM) approach and the Kalman filtering theory. The main difficulties encountered are the exponentially growing terms in the interacting stage of the IMM and the coupled state and noise variance in the likelihood functions. They are overcome by employing the merging scheme via matching the first two moments and the variational Bayesian approximation technique, respectively. Simulation results are presented to verify the effectiveness of the proposed filter via a manoeuvring target tracking example.