Xenaki Angeliki, Gerstoft Peter
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby 2800, Denmark.
Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92093-0238.
J Acoust Soc Am. 2015 Apr;137(4):1923-35. doi: 10.1121/1.4916269.
The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve high-resolution imaging. On a discrete angular grid, the CS reconstruction degrades due to basis mismatch when the DOAs do not coincide with the angular directions on the grid. To overcome this limitation, a continuous formulation of the DOA problem is employed and an optimization procedure is introduced, which promotes sparsity on a continuous optimization variable. The DOA estimation problem with infinitely many unknowns, i.e., source locations and amplitudes, is solved over a few optimization variables with semidefinite programming. The grid-free CS reconstruction provides high-resolution imaging even with non-uniform arrays, single-snapshot data and under noisy conditions as demonstrated on experimental towed array data.
到达方向（DOA）估计问题涉及从传感器阵列上的有限数量观测值中定位少数几个源，因此它可以被表述为一个稀疏信号重建问题，并通过压缩感知（CS）有效地求解以实现高分辨率成像。在离散角度网格上，当DOA与网格上的角度方向不一致时，CS重建会因基不匹配而退化。为克服这一限制，采用了DOA问题的连续表述形式，并引入了一种优化过程，该过程在连续优化变量上促进稀疏性。通过半定规划在少数几个优化变量上求解具有无限多个未知数（即源位置和幅度）的DOA估计问题。如在实验拖曳阵列数据上所展示的那样，无网格CS重建即使在非均匀阵列、单快照数据以及有噪声的条件下也能提供高分辨率成像。
