Abstract
In this paper we study hybrid estimation for linear discrete-time systems with noises not to be restricted to be Gaussian. 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 (1999, 2000) has presented hybrid filtering algorithm, i.e., causal estimation, by MPT approach for linear continuous- and discrete-time hybrid systems with non-Gaussian noises. We consider both filtering and smoothing problems for the linear discrete-time hybrid systems in this paper. Based on the principles of hybrid optimality we present filtering and smoothing algorithms, which give the solutions of these estimation problems. In the smoothing case, we can expect better estimation performance by taking into consideration noncausal information of observations. The hybrid smoother is realized by two filters approach ([23]).
