Low rank properties for synchronizing microphones and sources in Ad-Hoc wireless acoustic sensor network

Wireless Acoustic Sensor Networks (WASNs) designed for joint localization of acoustic sources and microphones are increasingly utilized in applications such as intelligent speech interfaces, environmental monitoring, and robotic audition. However, uncertainties in timing information-such as imprecise microphone recording start times and unknown acoustic source emission times-pose significant challenges, particularly in ad-hoc WASNs. Traditional optimization methods typically address these issues by explicitly estimating unknown timing information (UTIm) to synchronize sensors and sources. In contrast, the Low-Rank Property (LRP) based methods exploit an inherent low-rank structure to impose linear constraints on UTIm, facilitating globally optimal solutions given proper initialization. Nonetheless, these methods often rely on random initialization, leading to convergence toward suboptimal local minima. Targeting this challenge, this paper introduces a novel combined low-rank approximation (CLRA) method to synchronize microphones and sources, mitigating random initialization effects. We present three new LRP variants, mathematically proven to enhance the UTIm with richer low-rank structural information. Using this augmented information, we formulate four linear constraints on UTIm and employ the CLRA algorithm to derive globally optimal solutions. Experimental results show our method outperforms state-of-the-art approaches in both recovery number and reduced estimation errors of UTIm.