On Gridless Sparse Methods for Multi-snapshot Direction of Arrival Estimation

The authors have recently proposed two kinds of gridless sparse methods for direction of arrival estimation in the presence of multiple snapshots that exploit joint sparsity among the snapshots and completely resolve grid mismatches of previous grid-based sparse methods. One is termed as gridless SPICE (GL-SPICE, GLS) that is a gridless version of the covariance-based SPICE method; the other uses deterministic atomic norm optimization which extends the recent super-resolution and continuous compressed sensing framework from the single- to multi-snapshot case. In this paper, we unify these two techniques by interpreting theoretically GLS as atomic norm methods in various scenarios and under different assumptions of noise. The new interpretations of GLS enable us to provide theoretical guarantees of GLS in the case of finite snapshots. Besides, they are applied to show that GLS is robust to source correlations though it was derived under the assumption of uncorrelated sources. Numerical results are also provided to validate our findings.