Gridless Methods for Two-Dimensional Direction-of-Arrival Estimation in Single-Snapshot Scenario

Two-dimension (2D) direction-of-arrival (DOA) estimation in single-snapshot super-resolution scenarios constitutes a pivotal challenge in radar detection for unmanned aerial vehicles (UAVs). Existing algorithms can generally be categorized into two main types: those based on atomic norm minimization (ANM) and those relying on enhanced matrix techniques. However, the ANM-based methods are constrained by the need for prior knowledge of noise power, while the enhanced matrix-based approaches suffer from a reduction in array aperture due to the reconstruction process of the enhanced matrix. To address these issues, we introduce a gridless version of the sparse iterative covariance-based estimation (SPICE) method, termed GLS, which estimates noise power in a vectorized atom form for 2D DOA estimation, leading to the development of a novel approach called V-GLS. Like ANM, V-GLS lev-erages semi-definite programming (SDP) optimization, ensuring that the array aperture is not compromised. Additionally, we ingeniously reconfigure the 2D single-snapshot received signal vector into an approximated 1D multiple-snapshot matrix, thereby decoupling the 2D DOAs into two separate 1D DOAs. Furthermore, we propose a decoupled version of GLS for 2D DOA estimation, referred to as D-GLS. Compared to V-GLS, D-GLS exhibits supe-rior computational efficiency due to its low-dimensional SDP optimization. Both V-GLS and D-GLS demonstrate robust performance in noisy environ-ments and show promise for estimating multiple sources. Extensive simulations are presented to illustrate the superiority of the proposed method over the state-of-the-art methods.