Merging Kalman Filtering and Zonotopic State Bounding for Robust Fault Detection under Noisy Environment

A joint Zonotopic and Gaussian Kalman Filter (ZGKF) is proposed for the robust fault detection of discrete-time LTV systems simultaneously subject to bounded disturbances and Gaussian noises. Given a maximal probability of false alarms, a detection test is developed and shown to merge the usually mutually exclusive benefits granted by set-membership techniques (robustness to worst-case within specified bounds, domain computations) and stochastic approaches (taking noise distribution into account, probabilistic evaluation of tests). The computations remain explicit and can be efficiently implemented. A numerical example illustrates the improved tradeoff between sensitivity to faults and robustness to disturbances/noises.