Abstract: Conventional two-dimensional compressive beamforming, which is based on planar microphone array measurements and fixed discrete grids, establishes an underdetermined linear system of equations between the sound pressure signals measured by microphones and the unknown source strengths of the assuming acoustic sources corresponding to grids. Based on the fact that the main sources are generally sparse, the above equations can be solved by the sparsity promotion algorithms, then accurate estimation of the source direction-of-arrivals(DOAs) and quantification of the source strengths are achieved, thus identifying sources accurately. However, its performance deteriorates when sources do not coincide with the grids, namely the basis mismatch occurs. To solve this issue, a two-dimensional dynamic grid compressive beamforming for acoustic source identification is developed. First, the grid coordinates and the source strength distribution vector are defined as variables, and the objective function is constructed using a log-sum penalty function to promote the sparsity of the solution. Subsequently, a suitable surrogate function is formulated based on the objective function to reduce the optimization complexity under the majorization-minimization framework. Finally, a gradient descent method is used to iteratively optimize the surrogate function, leading to a gradual process to refine the grid coordinates and the source strength distribution vector. The results of numerical simulations and experiments demonstrate that the proposed technology can circumvent the basis mismatch and thus achieve higher location and quantification accuracy, comparing to the conventional two-dimensional fix-grid approach. It can be applied to a planar array with microphones randomly distributing and does not require prior knowledge of signal-to-noise ratio (noise interference) or source sparsity. The dynamic grid compressive beamforming can provide high-resolution and low contamination imaging, allowing accurate estimation of two-dimensional DOAs and quantification of source strengths, even with a small number of microphones.

Key words: compressive beamforming, dynamic grid, planar microphone array, sound source identification, direction-of-arrival