A Cramer-Rao type lower bound for the estimation error of systems with measurement faults

A Cramer-Rao type lower bound for a class of systems with faulty measurements is presented. Lower bounds for both the state and the Markovian interruption variables of the system are derived, based on the recently presented sequential version of the Cramer-Rao lower bound (CRLB) for general nonlinear systems. To facilitate the calculation of the lower bound for this class of systems, the discrete distribution of the fault indicators is approximated by a continuous one and the lower bound is obtained via a limiting process applied to the approximating system. The results presented in this paper facilitate a relatively simple calculation of a nontrivial lower bound for the state vector of systems with faulty measurements. The CRLB-type lower bound for the interruption process variables is trivially zero, however, a non-trivial, non-CRLB-type bound for these variables has been recently presented elsewhere by the authors.