An approach to noncausal hybrid estimation for linear continuous-time systems with non-Gaussian noises

In this paper we study hybrid estimation for linear continuous-time systems with non-Gaussian noises. It is assumed that modes of the systems are not directly accessible. We consider optimal estimation problems to find both estimated states of the systems and a candidate of the distributions of the modes over the finite time interval. We adopt most probable trajectory (MPT) approach. Q. Zhang (2000) has presented hybrid filtering algorithm by MPT approach. We consider both filtering and smoothing problems in this paper. We can expect better estimation performance by taking into consideration noncausal information of observations. The hybrid smoother is realized by two filters approach.