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 here is that we express the jump process in terms of the initial value and the jump times instead of its instantaneous values and that in order to apply Lainiotis' formula we regard the initial value and jump times as the unknown system parameter vector. The parameter vector is, however, infinite dimensional so that Lainiotis' formula cannot be applied directly. This is because the formula is applicable only to linear systems with a finite dimensional parameter vector. Therefore, the minimum variance estimator algorithm is derived by using some limiting procedure. The resultant optimal algorithm is infinite dimensional, so that feasible approximate algorithms should be developed for practical implementation. A simple illustrating example is also worked out.