Analysis of Prior-Subspace Estimation Schemes

In the context of the direction-of-arrival (DOA) estimation problem, we can sometimes assume that we have a priori knowledge of a subset of the DOA for several sources. In that situation, some works have proposed to tacking into account of this knowledge to improve the localization of the unknown sources. The key idea is based on an orthogonal deflation of the signal subspace. In a companion paper, we have derived and analyzed the CRB associated to this model and we have shown that the prior-knowledge of a subset of the DOA is beneficial only for coherent or highly correlated sources associated to closely-spaced DOA. In particular, for uncorrelated sources with closely-spaced DOA, the orthogonal deflation cannot help the estimation of the unknown DOA. Finally, we suggest that a possible solution could be to use oblique projectors. In this paper, we follow this line and we propose two algorithms based on the MinNorm principle