Signal subspace change detection in structured covariance matrices

Testing common properties between covariance matrices is a relevant approach in a plethora of applications. In this paper, we derive a new statistical test in the context of structured covariance matrices. Specifically, we consider low rank signal component plus white Gaussian noise structure. Our aim is to test the equality of the principal subspace, i.e., subspace spanned by the principal eigenvectors of a group of covariance matrices. A decision statistic is derived using the generalized likelihood ratio test. As the formulation of the proposed test implies a non-trivial optimization problem, we derive an appropriate majorizationminimization algorithm. Finally, numerical simulations illustrate the properties of the newly proposed detector compared to the state of the art.