Process and Sensor Noise Robustness in Detection Filter Design

A detection filter insensitive to process and sensor noise is developed. The approach is to minimize the H2 or H¿-norm of the transfer functions from the noise to the failure indicators with respect to the detection filter gain. Given a set of detection filter invariant state subspaces, the detection filter gain which preserves these subspaces is parameterized. Next the noise to failure indicator transfer functions are minimized one failure direction at a time. The output-separability condition is used to show that when the detection spaces fill the state-space, the gains thus found can be combined to form a detection filter gain that minimizes the noise in all failure indicators.