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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.