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.
Low-Complexity Gridless Single-Snapshot DoA Estimation via Truncated Hankel Newton-MUSIC
The Hong Kong University of Science and Technology（香港科技大学）；Southern University of Science and Technology（南方科技大学）；The University of British Columbia（不列颠哥伦比亚大学）
Beyond $λ/2$: Can Arbitrary EMVS Arrays Achieve Unambiguous NLOS Localization?
Ningbo University（宁波大学）；South China University of Technology（华南理工大学）；The Hong Kong Polytechnic University（香港理工大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；Kyung Hee University（庆熙大学）；West Virginia University（西弗吉尼亚大学）
South China University of Technology（华南理工大学）；Ningbo University（宁波大学）；Nanjing University of Science and Technology（南京理工大学）；West Virginia University（西弗吉尼亚大学）；City University of Hong Kong（香港城市大学）
