Optimal fault detection with nuisance parameters and a general covariance matrix

Optimal fault detection is addressed within a statistical framework. A linear model with nuisance parameters and a general covariance matrix (not necessarily diagonal) is considered. It is supposed that the nuisance parameters are unknown but non-random; practically, this means that the nuisance can be intentionally chosen to maximize its negative impact on the monitored system (for instance, to mask a fault). Two different invariant tests can be designed in such a case. It is shown that these methods are equivalent. An example of the ground-based Global Navigation Satellite System (GNSS) integrity monitoring in the case of an arbitrary diagonal covariance matrix of the pseudorange errors illustrates the relevance of the proposed approaches. Copyright © 2007 John Wiley & Sons, Ltd.