An interacting multiple model fixed-lag smoothing algorithm for Markovian switching systems

We investigate a suboptimal approach to the fixed-lag smoothing problem for Markovian switching systems. A fixed-lag smoothing algorithm is developed by applying the basic interacting multiple model (IMM) approach to a state-augmented system. The computational load is roughly d (the fixed lag) times beyond that of filtering for the original system. In addition, an algorithm that approximates the “fixed-lag” mode probabilities given measurements up to current time is proposed. The algorithm is illustrated via a target tracking simulation example where a significant improvement over the filtering algorithm is achieved. The IMM fixed-lag smoothing performance for the given example is comparable to that of an existing IMM fixed-interval smoother. Compared to fixed-interval smoothers, the fixed-lag smoothers can be implemented in real-time with a small delay