Efficient Localization of Low-Frequency Sound Source With Non-Synchronous Measurement at Coprime Positions by Alternating Direction Method of Multipliers

The low-frequency sound source localization is fundamentally restricted by the array aperture. The non-synchronous measurement (NSM) is a powerful method to achieve excellent performance in low-frequency acoustic localization by sequentially scanning the sound field. Nevertheless, the existing methods can only perform sound source localization at a frequency of above 800 Hz. An efficient acoustic localization method is proposed in this article for low-frequency sound source localization by moving the array at coprime positions (CPs) to perform the NSM and solving the corresponding inverse problem by an alternating direction method of multipliers (ADMM) algorithm. First, the prototype array is moved at the CPs to perform the NSM, enlarging the aperture of the array for the first time. Second, the virtual array is constructed by the difference of the actual positions of the array element at each CP, expanding the synthetic aperture again. Third, the virtual signal propagation model is derived from the corresponding virtual signal to further increase spatial resolution by vectorizing the synthetic cross-spectral matrix of the NSM. Finally, the ADMM with the
$L_{1}$
-norm regularization algorithm is derived and applied to solve the virtual signal propagation model, which is also compared with the interior-point algorithm in solving the virtual signal propagation model. To verify the efficiency and robustness of the proposed method, simulations and experiments with different sound sources at low frequencies and noise disturbances are performed in this article.