A d-step fixed-lag smoothing algorithm for Markovian switching systems

A suboptimal approach to the d(d>0) step fixed-lag smoothing problem for Markovian switching systems is presented. Multiple Model Estimation techniques have been widely used in solving state estimation problems of these systems. We demonstrated that the mode probability of each fixed-lag smoother at time k-d (data up to time k), thus it is possible to use Markov transition probability and state estimates at time k-d to get the smoothed state estimates. We augment both the system state and mode probability, so the fixed-lag smoothing problem can be transformed to the filtering one of the new augmented system. Then a new d-step fixed-lag smoothing. algorithm is developed by applying the basic structure of IMM to the augmented systems. In addition, d step Markov transition probabilities are defined and calculated based on the one-step Markov transition probability for the augmented smoothing mode probability. The algorithm is illustrated by using a typical target tracking simulation example. Simulation results show that a significant improvement on the filtering algorithm is achieved at the cost of a small time delay.