Continuous time smoothing for systems with interrupted observations

General continuous time smoothing results for state estimation with interrupted observations are derived. The interruption mechanism is characterized by a jump Markov process taking values 0 or 1. The approach followed for deriving the smoothing estimator is similar to the one used in [1] for the case of filtering where interruption process initial value and the jump instants are treated as the unknown system parameters. Lainiotis´s partition theorem is then applied to obtain the desired estimator based on smoothing.