State smoothing in Markov jump systems with lagged mode observation

Estimation involving Markov jump systems (MJSs) is widely used in target tracking, speech recognition and communication. It is assumed in MJSs that state measurement and mode observation are synchronous. In applications such as image-based target tracking, the target orientation, as one of the mode observations, needs additional computation time for pattern recognition and thus can be delayed. This motivates us to explore the smoothing problem of MJSs with mode observation lagged to state measurement. This brief paper presents a recursive estimator by deriving the conditional state mean and the conditional model probability from both delayed mode observation and state measurement. Simulations on maneuvering target tracking are carried out to validate the performance of the proposed smoother in comparison with existing methods.