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 at the cost of a time delay (i.e., data up to time k are used to produce the smoothed state estimate at time k-d where the fixed large d>0). the IMM fixed-lag smoothing performance for the given example is comparable to that of an existing IMM fixed-interval smoother. Compared with fixed-interval smoothers, the fixed-lag smoothers can be implemented in real-time with a small delay.