Uncertainty in timing information pertaining to the start time of microphone recordings and sources' emission time pose significant challenges in various applications, such as joint microphones and sources localization. Traditional optimization methods, which directly estimate this unknown timing information (UTIm), often fall short compared to approaches exploiting the low-rank property (LRP). LRP encompasses an additional low-rank structure, facilitating a linear constraint on UTIm to help formulate related low-rank structure information. This method allows us to attain globally optimal solutions for UTIm, given proper initialization. However, the initialization process often involves randomness, leading to suboptimal, local minimum values. This paper presents a novel, combined low-rank approximation (CLRA) method designed to mitigate the effects of this random initialization. We introduce three new LRP variants, underpinned by mathematical proof, which allow the UTIm to draw on a richer pool of low-rank structural information. Utilizing this augmented low-rank structural information from both LRP and the proposed variants, we formulate four linear constraints on the UTIm. Employing the proposed CLRA algorithm, we derive global optimal solutions for the UTIm via these four linear constraints.Experimental results highlight the superior performance of our method over existing state-of-the-art approaches, measured in terms of both the recovery number and reduced estimation errors of UTIm.

翻译：时间信息的不确定性（包括麦克风记录的启动时间与声源的发射时间）在诸多应用中构成显著挑战，例如联合麦克风与声源定位。传统优化方法直接估计此类未知时间信息（UTIm），但效果往往不如利用低秩特性（LRP）的方法。LRP通过引入额外的低秩结构，为UTIm施加线性约束以构建相关低秩结构信息。在给定适当初始化的条件下，该方法可获取UTIm的全局最优解。然而初始化过程常伴随随机性，导致陷入次优局部极小值。本文提出一种新型组合低秩近似（CLRA）方法，旨在缓解随机初始化带来的影响。基于数学证明，我们引入三种新的LRP变体，使UTIm能够利用更丰富的低秩结构信息。结合LRP与所提变体所提供的增强型低秩结构信息，我们为UTIm构建了四个线性约束。通过提出的CLRA算法，利用这四个线性约束推导UTIm的全局最优解。实验结果表明，在UTIm恢复数量与估计误差降低方面，本方法显著优于现有最先进方法。