2024/01/12 by Yifan Wu, Wu, Yifan, Michael B. Wakin +3 · 1 citation
Earth and Planetary Sciences · Engineering · #FOS: Electrical engineering #Signal Processing (eess.SP) #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation #Underwater Acoustics Research #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2401.06313
openalex publication_date 2024/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gridless direction-of-arrival (DOA) estimation with multiple frequencies can be applied in acoustics source localization problems. We formulate this as an atomic norm minimization (ANM) problem and derive an equivalent regularization-free semi-definite program (SDP) thereby avoiding regularization bias. The DOA is retrieved using a Vandermonde decomposition on the Toeplitz matrix obtained from the solution of the SDP. We also propose a fast SDP program to deal with non-uniform array and frequency spacing. For non-uniform spacings, the Toeplitz structure will not exist, but the DOA is retrieved via irregular Vandermonde decomposition (IVD), and we theoretically guarantee the existence of the IVD. We extend ANM to the multiple measurement vector (MMV) cases and derive its equivalent regularization-free SDP. Using multiple frequencies and the MMV model, we can resolve more sources than the number of physical sensors for a uniform linear array. Numerical results demonstrate that the regularization-free framework is robust to noise and aliasing, and it overcomes the regularization bias.