Entropy, Vol. 23, Pages 1585: Optimal Passive Source Localization for Acoustic Emissions (Entropy)

Acoustic emission is a non-destructive testing method where sensors monitor an area of a structure to detect and localize passive sources of elastic waves such as expanding cracks. Passive source localization methods based on times of arrival (TOAs) use TOAs estimated from the noisy signals received by the sensors to estimate the source position. In this work, we derive the probability distribution of TOAs assuming they were obtained by the fixed threshold technique—a popular low-complexity TOA estimation technique—and show that, if the sampling rate is high enough, TOAs can be approximated by a random variable distributed according to a mixture of Gaussian distributions, which reduces to a Gaussian in the low noise regime. The optimal source position estimator is derived assuming the parameters of the mixture are known, in which case its MSE matches the Cramér–Rao lower bound, and an algorithm to estimate the mixture parameters from noisy signals is presented. We also show that the fixed threshold technique produces biased time differences of arrival (TDOAs) and propose a modification of this method to remove the bias. The proposed source position estimator is validated in simulation using biased and unbiased TDOAs, performing better than other TOA-based passive source localization methods in most scenarios.