A probabilistic approach to the intermittent measurements problem

We present some preliminary results of a research on the state estimation problem for a linear stochastic system under the hypothesis that observations may be lost randomly. This scenario is becoming more and more relevant, and it is currently investigated by many authors, because of many applications where sensors are connected to the controller through networked or wireless links. In such links measurements may be lost or delayed, so that they cannot be used for feedback control. We investigate the potential divergence of the estimator using a probabilistic approach, which may hopefully give a deeper insight on the problem, and also compare our scenario with the case of periodic observations, for which it is well known that divergence never occurs, even in the case of rare observations.