A Comparison of Equivalent Source Method and Monopole Time Reversal Method for Noise Source Localization

The equivalent source method (ESM) and monopole time reversal method (MTRM) are two popular techniques for noise source localization. These two methods have some similar characteristics, such as using the pressure field measured by a microphone array as the input and using similar propagation matrices obtained from the Green's function. However, the spatial resolutions of results obtained by these two methods are different. The aim of this paper is to reveal the reason resulting in this difference from a theoretical analysis and compare the performance of these two methods using results from numerical simulations and experiments. Using the singular value decomposition (SVD) technique, the difference between the two methods is found to be only the diagonal matrices of singular values, and the two methods are equivalent after simply replacing the diagonal matrix in the MTRM with its inverse. Comparison of the results demonstrates that the ESM can calculate the real source strength and obtain a high spatial resolution due to the significant amplification of evanescent waves in the inverse process. However, it does not work when the signal-to-noise ratio (SNR) is low or the measurement distance is large. The performance of ESM under these situations can be significantly improved by introducing a regularization procedure. While the MTRM fails to calculate the real source strength and locate the source at low frequencies due to the loss of information of evanescent waves, it works well at high frequencies even with a low SNR and a large measurement distance.