Abstract
An algorithm of minimal variance state estimation is shown for a class of continuous-time linear stochastic systems with coefficients depending on a finite state Markov chain. The class of the systems considered in this paper is more general than that of problems previously treated, in that the statistics of the observation noise can be also depend on the Markov chain. The minimal variance state estimate by using continuous-time observations is not feasible because the mathematical measurability of the noise covariance is guranteed by the differential operation which can not be realized in finite steps. For this reason, the available observations are assumed to be sampled from a continuous-time process in a short period on a finite set of time points. Except for a Bayesian type formula for the a posteriori probabilities of the Markov chain, the algorithm consists of a set of difference equations similar to stochastic differential equations in the case of continuous-time observations. A numerical example is shown to illustrate the performance of the algorithm.
