二维动态网格压缩波束形成声源识别方法

基于平面传声器阵列测量和固定网格的传统二维压缩波束形成通过建立阵列传声器测量声压信号和假想声源网格点未知源强之间的欠定线性方程组，基于主声源通常为稀疏分布这一事实，利用稀疏促进算法求解上述方程组从而获得声源波达方向和源强的准确估计，进而准确识别声源。然而，当声源波达方向与网格点不一致、即发生基不匹配时，性能会劣化。为克服该问题，提出二维动态网格压缩波束形成声源识别方法。定义网格坐标和源强分布矢量为变量并采用对数求和罚函数构建目标函数以促进解的稀疏性；基于优化最小化框架在目标函数的基础上构造合适的替代函数以降低优化复杂度；通过梯度下降法对替代函数进行迭代优化求解，从而使网格坐标和源强分布矢量逐渐收敛至真实值附近。仿真和试验均表明，相较于传统固定网格的二维压缩波束形成，该方法能够克服基不匹配问题、获得更高的定位精度和量化精度；该方法能够适用于传声器随机分布的平面阵列，且无需先验的信噪比（噪声干扰）及声源稀疏度等信息，即使在传声器数量较少的情况下也能得到低污染高分辨率的声源成像，保证了高精度的二维波达方向估计和源强量化。

Two-dimensional Dynamic Grid Compressive Beamforming for Acoustic Source Identification

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.