Anomaly detection with bounded nuisance parameters and safe train navigation

Anomaly detection is addressed within a statistical framework. Often the statistical model is composed of two types of parameters : the informative parameters and the nuisance ones. The nuisance parameters are of no interest for detection but they are necessary to complete the model. In the case of unknown, non-random nuisance parameters, their elimination is unavoidable. Some approaches addressing the cases where the nuisance parameters, belonging to a subspace, interfere with the informative ones in a linear manner, use the theory of invariance to reject the nuisance. Sometimes this leads to a certain degradation of the detector performances because some faults become undetectable, masked by the nuisance. Nevertheless, in many cases the physical nature of nuisance parameters is (partially) known, and this knowledge may allow us to define inequality bounds to limit the variations of these parameters. The goal of this paper is to study the statistical performances of the constrained generalized likelihood ratio test used to detect an additive anomaly in the case of bounded nuisance parameters. An example of the integrity monitoring of GNSS train navigation illustrates the relevance of the proposed method.