An ideal-theoretic criterion for localization of an unknown number of sources

Source localization is among the most fundamental problems in statistical signal processing. Methods which rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC are some of the most widely used algorithms to solve this problem. As a common feature, these methods require both a-priori knowledge of the number of sources, and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms, and sources of potentially severe error. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace. An algorithm is proposed which adaptively learns the number of sources and estimates their locations. Simulation results show significant improvement over root-MUSIC, even when the correct number of sources is provided to the root-MUSIC algorithm.