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Uncertainty in timing information pertaining to the start time of microphonerecordings and sources' emission time pose significant challenges in variousapplications, such as joint microphones and sources localization. Traditionaloptimization methods, which directly estimate this unknown timing information(UTIm), often fall short compared to approaches exploiting the low-rankproperty (LRP). LRP encompasses an additional low-rank structure, facilitatinga linear constraint on UTIm to help formulate related low-rank structureinformation. This method allows us to attain globally optimal solutions forUTIm, given proper initialization. However, the initialization process ofteninvolves randomness, leading to suboptimal, local minimum values. This paperpresents a novel, combined low-rank approximation (CLRA) method designed tomitigate the effects of this random initialization. We introduce three new LRPvariants, underpinned by mathematical proof, which allow the UTIm to draw on aricher pool of low-rank structural information. Utilizing this augmentedlow-rank structural information from both LRP and the proposed variants, weformulate four linear constraints on the UTIm. Employing the proposed CLRAalgorithm, we derive global optimal solutions for the UTIm via these fourlinear constraints.Experimental results highlight the superior performance ofour method over existing state-of-the-art approaches, measured in terms of boththe recovery number and reduced estimation errors of UTIm.

Low Rank Properties for Estimating Microphones Start Time and Sources Emission Time