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We investigate the localization of multiple signal sources based on sensors performing time-of-arrival (TOA) measurement in wireless sensor networks. Moving beyond the widely studied single source localization problem, concurrently active multiple sources substantially complicate the problem since anchored sensor nodes are unaware of associations between measured signals and source nodes. At the same time, as the total number of possible source-measurement associations grows exponentially with the number of sensor nodes, it is inefficient to attempt conventional single-source localization algorithm for each possible association in a brute-force manner. In this work, we address this difficult problem from a joint optimization perspective. Specifically, we consider simultaneous estimation of source-measurement associations and the source locations, in addition to finding the initial signal transmission time. This joint optimization problem includes both discrete and continuous variables. We propose an efficient three-step algorithm that progressively simplifies the original problem through convex relaxation and sensible approximations. Our proposed algorithm demonstrates results comparable to a genie-aided method that utilizes known source-measurement associations.
Shen et al. (Tue,) studied this question.