Robust fault and state estimation for linear discrete-time systems with unknown disturbances using PI Three-Stage Kalman Filter

The problem of simultaneously estimating the state and the fault of linear time varying stochastic systems in the presence of unknown input with uncertain noise covariances is presented. The approach suggested rests on the use of the Proportional Integral Three-Stage Kalman Filter (PI-ThSKF). This technique is qualified to be robust against the noise covariance matrices uncertainty. The proposed filter is tested by an illustrative example.