Adaptive Subspace Signal Detection with Uncertain Partial Prior Knowledge

This paper is concerned with signal detection in strong disturbance with a subspace structure. Unlike conventional subspace detection techniques relying on the availability of ample training data, we consider a knowledge-aided subspace detection approach for training limited scenarios by incorporating partial prior knowledge of the subspace. A unique advantage of the proposed approach is that it allows the prior knowledge to be incomplete and uncertain, consisting of both correct and incorrect basis vectors. However, the correct and incorrect bases cannot be identified a priori. Two hierarchical models are introduced for knowledge representation. One is suitable for the case when the prior knowledge is largely accurate, while the other tries to identify possible errors in the prior knowledge by checking it against and learning from the observed data. The proposed hierarchical models are integrated within a sparse Bayesian framework, which promotes parsimonious subspace representation of the observed data. Variational Bayesian inference algorithms are developed based on the proposed models to recover parameters and subspace structures associated with the disturbance, which are then used in a generalized likelihood ratio test to perform signal detection. Numerical results are presented to illustrate the performance of the proposed subspace detectors in comparison with several notable existing methods.