Prete Carlos A, Nascimento Vítor H, Lopes Cássio G
Department of Electronic Systems Engineering, University of São Paulo, São Paulo 3566-590, Brazil.
Entropy (Basel). 2021 Nov 27;23(12):1585. doi: 10.3390/e23121585.
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.
声发射是一种无损检测方法，其中传感器监测结构的某个区域，以检测和定位诸如扩展裂纹等弹性波的无源源。基于到达时间（TOA）的无源源定位方法利用从传感器接收到的噪声信号估计出的TOA来估计源位置。在这项工作中，我们推导了TOA的概率分布，假设它们是通过固定阈值技术（一种流行的低复杂度TOA估计技术）获得的，并表明，如果采样率足够高，TOA可以由一个根据高斯分布混合分布的随机变量近似，在低噪声情况下简化为高斯分布。假设混合参数已知，推导了最优源位置估计器，在这种情况下其均方误差与克拉美罗下界匹配，并提出了一种从噪声信号估计混合参数的算法。我们还表明，固定阈值技术会产生有偏差的到达时间差（TDOA），并提出了对该方法的一种修改以消除偏差。所提出的源位置估计器在使用有偏差和无偏差TDOA的仿真中得到验证，在大多数情况下比其他基于TOA的无源源定位方法表现更好。
