Estimation in systems with a semi-Markov switching model

There are numerous examples of systems which have discrete models that randomly vary with time and experience switchings between different models after a random sojourn time. In some situations the switching probabilities depend on the sojourn time. Such a switching process, discussed in this paper, is a class of semi-Markov processes and is encountered in target tracking, manufacturing systems, power industry and also in the socio-economic environment. In this paper we use the recently derived conditional sojourn time distribution for systems with imperfect observations and changing structures or models and present the state estimation for such systems.