Analysis of array gain degradation of near-field passive synthetic aperture method

A previous study established a method for localizing low-frequency acoustic sources in the near field using a passive synthetic aperture method [Lei et al., 2015]. Sound fields sampled at different positions (sub-apertures) and times are synthesized to improve the spatial resolution of conventional beamforming. However, in practice, the position errors of the sub-apertures could significantly degrade the performance of the method. In this work, the analysis is extended to measure the sensitivity of the method to the position errors of the sub-apertures using array gain degradation (AGD). First, the position errors in three directions are assumed to be independent and obey the same Gaussian distribution to present a simple expression for AGD. Then, the analysis is generalized to the case of different Gaussian distributions to obtain an expression with explicit physical meaning. The two expressions are verified by simulations and partially validated using the experimental data sampled by a planar array in a semi-anechoic chamber. Finally, the results of localizing the sources on a transformer in a 750 kV substation are revealed.