OPTIMAL FILTERING AND ROBUST FAULT DIAGNOSIS OF STOCHASTIC SYSTEMS WITH UNKNOWN INPUTS AND COLORED OBSERVATION NOISES

摘要

This paper studies the optimal filtering and robust fault diagnosis for discrete-time stochastic time varying systems with both unknown inputs and colored observation noises. Under natural conditions, systems with colored observation noises are transformed into systems with white Gaussian noises whose unknown disturbances can be decoupled. The gain matrices of the optimal filter are determined so that the variance of its estimation error is made minimal without losing unknown disturbance decoupling. The output estimation error with both disturbance decoupling and minimum variance properties is used for a residual signal to diagnose faults. The method proposed is applied to an illustrative example, and numerical experiments show that the optimal filter gives good state estimation and that the fault diagnosis process developed is able to detect faults reliably.