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.Comment: 13 pages for main content; 9 pages for proof of proposed low rank
properties; 13 figure