Projection operations for failure detection and isolation

The problem of failure detection and isolation in linear systems is discussed. Typically the solutions to this problem have included a statistical test being performed on the measurement residual generated by a Kalman filter. These solutions are usually based on one or more of the assumptions: the type of failure is known, or the failure location (in sensor or state) is known, so that the failure can be estimated. In this paper a technique is developed which is based on a set of projection operators which, under appropriate conditions, can both detect and isolate the failures when the type, location, time of occurrence and magnitude of the failure are not known a priori.