Failure Detection Performance Analysis of the Optimal Nonlinear Filter for the Identification Problem

A popular nonlinear filter for failure detection in dynamic systems is the well-known Identification Filter. The filter consists of parallel Kalman filters, each tuned to a different system mode of operation, whose estimates parametrize a finite-dimensional system of equations for the conditional probabilities of being at each mode. The filter generates a sequence of decisions in finite time and this paper focuses on the performance analysis of such a filter. It is shown that after a long enough time a correct decision is expected for any decision threshold level.