Posterior mixed distributions and optimal estimates of a vector discrete-continuous Markovian random process

The problem of optimal estimation of a discrete-continuous Markovian random process is solved in the case when its continuous part is a vector diffusion process and its discrete part is a vector consisting of two components, each characterized by a simple Markovian chain with several positions. Expressions for posterior probability densities (PPDs) and posterior mixed distributions (PMDs) are presented. Analytical relationships for optimal estimates of a vector discrete-continuous Markovian random process are derived. The possibility of practical implementation and efficiency of the proposed algorithms are illustrated by a device synthesized as an example.