On gridless sparse methods for multi-snapshot DOA estimation

The authors have recently proposed two kinds of gridless sparse methods for direction of arrival (DOA) estimation that exploit joint sparsity among snapshots and completely resolve the grid mismatch issue of previous grid-based sparse methods. One is based on covariance fitting from a statistical perspective and termed as the gridless SPICE (GL-SPICE, GLS); the other uses deterministic atomic norm optimization which extends the recent super-resolution and continuous compressed sensing framework from the single to the multi-snapshot case. In this paper, we unify the two techniques by interpreting GLS as atomic norm methods in various scenarios. As a byproduct, we are able to provide theoretical guarantees of GLS for DOA estimation in the case of limited snapshots.