Fault detection is addressed within a statistical framework. The goal of this paper is to propose an optimal statistical tool to detect a fault in a linear stochastic (dynamical) system with uncertainties (nuisance parameters or nuisance faults). 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). Examples of ground station based and receiver autonomous Global Positioning System (GPS) integrity monitoring illustrate the proposed method. (c) 2005 Elsevier Ltd. All rights reserved.