Enhanced Fixed-Interval Smoothing for Markovian Switching Systems

This paper considers the problem of fixed-interval smoothing for Markovian switching systems with multiple linear state-space models. An enhanced algorithm that is capable of accurately approximating the Bayesian optimal smoother is proposed. It utilizes the exact expression for the quotient of two Gaussian densities to help solve the backward-time recursive equations of Bayesian smoothing, and computes the joint posterior of the state vector and model index. The proposed algorithm only involves the approximation of each model-matched state posterior, which is a Gaussian mixture, with a single Gaussian density for maintaining computational tractability in retrodiction. The validity of the newly developed smoother is verified using a simulated maneuvering target tracking task.