Weiss–Weinstein Lower Bounds for Markovian Systems. Part 2: Applications to Fault-Tolerant Filtering

摘要

Characterized by sudden structural changes, fault-prone systems are modeled using the framework of systems with switching parameters or hybrid systems. Since a closed-form mean-square optimal filtering algorithm for this class of systems does not exist, it is of particular interest to derive a lower bound on the state estimation error covariance. The well known CramÉr–Rao bound is not applicable to fault-prone systems because of the discrete distribution of the fault indicators, which violates the regularity conditions associated with this bound. On the other hand, the Weiss–Weinstein lower bound is essentially free from regularity conditions. Moreover, a sequential version of the Weiss–Weinstein bound, suitable for Markovian dynamic systems, is presented by the authors in a companion paper. In the present paper, this sequential version is applied to several classes of fault-prone dynamic systems. The resulting bounds can be used to examine fault detectability and identifiability in these systems. Moreover, it is shown that several recently reported lower bounds for fault-prone systems are special cases of, or closely related to, the sequential version of the Weiss–Weinstein lower bound.