Comparison and application of the far-field identification algorithms for multiple sound sources based on microphone array

Based on the conventional beamforming (CBF), some algorithms for far-field sound source identification have been proposed in the past few decades. Typically, the functional beamforming (FBF) and the deconvolution methods, such as CLEAN, CLEAN with source coherence (CLEAN-SC), CLEAN-SC with compressed grids (CLEAN-SC-CG), CLEAN with cross spectral matrix function (CLEAN-CSM), High-resolution CLEAN-SC (HR-CLEAN-SC), are frequently mentioned and their advantages are widely discussed in the previous literatures. To assess their efficacy and suitability in engineering applications, with a focus on spatial resolution, computational efficiency, and dynamic range, a comparative study by locating two types of sound sources is carried out. The first scenario represents the case where the distance between two sound sources is smaller than the Rayleigh limit, while the second scenario represents the situation involving multiple sound sources, such as four or more complex sound sources. The analysis demonstrates that CBF, CLEAN, and CLEAN-SC cannot surpass the Rayleigh limit. However, FBF, CLEAN-SC-CG, CLEAN-CSM, and HR-CLEAN-SC have the potential to overcome it. In FBF, the grid mismatch results in a compromise between its dynamic range and source strength estimation. Meanwhile, HR-CLEAN-SC requires prior knowledge of the number of sound sources, which is challenging in applications. Because of superiority in the fundamental acoustic image and searching strategy, CLEAN-CSM and CLEAN-SC-CG exhibits superior features compared to the others. By compressing the number of grids, the CLEAN-SC-CG can improve the computational efficiency up to at least 46%. By constructing the cross spectral matrix function related to the real source, CLEAN-CSM uses the power function to simultaneously enhance the spatial resolution, dynamic range and source strength estimation. The conclusions are further validated through sound-source identification experiments involving two loudspeakers and an engine. The findings presented in this paper serve to guide the selection of suitable approaches for multi-sound source identification in engineering applications.