Reverberation-Robust Self-Calibration and Synchronization of Distributed Microphone Arrays by Mitigating Heteroscedasticity and Outlier Occurrence in TDoA Measurements

Abstract

The network of distributed microphone arrays is usually established in an ad hoc manner; hence, network parameters such as the mutual positioning and rotation of the arrays, positions of sources, and synchronization of their recording onset times are initially unknown. In this article, we consider the problem of passively jointly self-calibrating and synchronizing distributed arrays in reverberant rooms. We use a typical two-step approach where, initially, the relative geometry of the network is estimated using Direction of Arrival (DoA) measurements. Subsequently, the absolute scale and synchronization parameters are estimated using Time Difference of Arrival (TDoA) measurements. This article presents methods to improve the robustness and accuracy of estimation of the absolute geometric scaling and synchronization parameters in reverberant conditions, in which TDoA measurements do not follow a normal distribution; furthermore, outliers often occur. To remedy these issues, we propose a Weighted Least Squares (WLS) estimator and schema for weighting the TDoA measurements to increase the estimation accuracy from heteroscedastic TDoA measurements. In addition, we propose an iterative reweighing algorithm with a binary weight to detect and reject TDoA outliers, which exploits the residuals of the parametric model in the least absolute value minimization. A numerical evaluation shows significant improvements in the proposed method over the state of the art in terms of the relative scaling error and mean absolute value of the synchronization parameters.