Application of optimally distinguishable distributions to the detection of subspace signals in Gaussian noise of unknown level

A detection method based on optimally distinguishable distributions (ODD) was introduced recently. However, ODD testing as it was originally formulated has an important limitation because it does not accommodate models with nuisance parameters. This paper demonstrates how the difficulty can be circumvented in the case of subspace signals in Gaussian noise of unknown level. The key point is to define a partition of the parameter space. To this end, we analyze two different methods, and we choose one of them as basis for the new ODD detector. The performance of the detector is compared with that of the GLRT (generalized likelihood ratio test). Additionally, we compute the confidence indexes which are part of the ODD methodology.