The absence of unknown timing information about the microphones recording start time and the sources emission time presents a challenge in several applications, including joint microphones and sources localization. Compared with traditional optimization methods that try to estimate unknown timing information directly, low rank property (LRP) contains an additional low rank structure that facilitates a linear constraint of unknown timing information for formulating corresponding low rank structure information, enabling the achievement of global optimal solutions of unknown timing information with suitable initialization. However, the initialization of unknown timing information is random, resulting in local minimal values for estimation of the unknown timing information. In this paper, we propose a combined low rank approximation method to alleviate the effect of random initialization on the estimation of unknown timing information. We define three new variants of LRP supported by proof that allows unknown timing information to benefit from more low rank structure information. Then, by utilizing the low rank structure information from both LRP and proposed variants of LRP, four linear constraints of unknown timing information are presented. Finally, we use the proposed combined low rank approximation algorithm to obtain global optimal solutions of unknown timing information through the four available linear constraints. Experimental results demonstrate superior performance of our method compared to state-of-the-art approaches in terms of recovery rate (the number of successful initialization for any configuration), convergency rate (the number of successfully recovered configurations), and estimation errors of unknown timing information.

翻译：麦克风记录起始时间与声源发射时间的未知时序信息缺失对多个应用场景构成挑战，包括联合麦克风与声源定位问题。相较于试图直接估计未知时序信息的传统优化方法，低秩特性（LRP）包含额外的低秩结构，该结构可为未知时序信息构建线性约束以形成对应的低秩结构信息，从而在适当初始化条件下实现未知时序信息的全局最优解。然而，未知时序信息的初始化具有随机性，导致其估计结果陷入局部极小值。本文提出一种联合低秩逼近方法，以缓解随机初始化对未知时序信息估计的影响。我们通过理论证明定义了三种新型LRP变体，使未知时序信息能够获益于更丰富的低秩结构信息。进而，利用LRP及其变体的低秩结构信息，构建了未知时序信息的四类线性约束。最终，采用所提出的联合低秩逼近算法，通过四类可用线性约束获取未知时序信息的全局最优解。实验结果表明，在恢复率（任意配置下的成功初始化次数）、收敛率（成功恢复的配置数量）以及未知时序信息估计误差方面，本方法均优于现有最佳技术方案。