State estimation for systems with sojourn-time-dependent Markov model switching

A switching process in which the switching probabilities depend on a random sojourn time is a class of semi-Markov processes and is encountered in target tracking, systems subject to failures, And also in the socioeconomic environment. In such a system, knowledge of the sojourn time is needed for the computation of the conditional transition probabilities. It is shown how one can infer the transition probabilities through the evaluation of the conditional distribution of the sojourn time. Subsequently, a recursive state estimation for such systems is obtained using the conditional sojourn time distribution for dynamic systems with imperfect observations and changing structures (models)