State estimation for continuous-time system with interrupted observation

This paper considers the estimation problem for linear continuous-time systems with the interrupted observation mechanism which is characterized in terms of the jump Markov process taking on the values of 0 or 1. The minimum variance estimator algorithm is derived. The approach adopted is 1) to express the jump Markov interruption process in terms of the initial value and the jump times instead of its instantaneous values and 2) to regard the initial value and jump times as the unknown system parameter which may be infinite dimensional. Then employing some limiting procedure, Lainiotis' formula is applied to obtain the minimum variance estimator algorithm. The resultant optimal algorithm is infinite dimensional, so that feasible approximate estimator algorithms are presented for the practical implementation. Computer simulation studies are also carried out to demonstrate the feasibility of the approximate estimators.