On the Fixed-Interval Smoothing for Jump Markov Nonlinear Systems

This paper considers the fixed-interval smoothing for jump Markov systems. An optimal backward-time recursive equation for computing the joint posterior of the state vector and model index is established first. A suboptimal algorithm is then developed to approximate the new Bayesian smoother under nonlinear state-space models with additive Gaussian noise. The proposed method utilizes the well-known assumed density filtering with Gaussian assumption and the expression for the quotient of two Gaussian densities to compute the smoothing posterior. It eliminates the need for finding the inverse of the state dynamics and can handle singular process noise covariance, compared with several existing multiple model smoothers. Promising results are obtained in simulations using a maneuvering target tracking task.