TDOA-based Self-Calibration of Dual-Microphone Arrays

We consider the problem of determining the relative position of dual-microphone sub-arrays. The proposed solution is mainly developed for binaural hearing aid systems (HASs), where each hearing aid (HA) in the HAS has two microphones at a known distance from each other. However, the proposed algorithm can effortlessly be applied to acoustic sensor network applications. In contrast to most state-of-the-art calibration algorithms, which model the calibration problem as a non-linear problem resulting in high computational complexity, we model the calibration problem as a simple linear system of equations by utilizing a far-field assumption. The proposed model is based on target signals time-difference-of-arrivals (TDOAs) between the HAS microphones. Working with TDOAs avoids clock synchronization between sound sources and microphones, and target signals need not be known beforehand. To solve the calibration problem, we propose a least squares estimator which is simple and does not need any probabilistic assumptions about the observed signals