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

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2 Author(s)
Ilia Rapoport ; Dept. of Aerosp. Eng., Technion-Israel Inst. of Technol., Haifa ; Yaakov Oshman

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 Crameacuter-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

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IEEE Transactions on Signal Processing  (Volume:55 ,  Issue: 5 )