Source localization and denoising: a perspective from the TDOA space

In this manuscript, we formulate the problem of source localization based on Time Differences of Arrival (TDOAs) in the TDOA space, i.e., the Euclidean space spanned by TDOA measurements. More specifically, we show that source localization can be interpreted as a denoising problem of TDOA measurements. As this denoising problem is difficult to solve in general, our analysis shows that it is possible to resort to a relaxed version of it. The solution of the relaxed problem through linear operations in the TDOA space is then discussed, and its analysis leads to a parallelism with other state-of-the-art TDOA denoising algorithms. Additionally, we extend the proposed solution also to the case where only TDOAs between few pairs of microphones within an array have been computed. The reported denoising algorithms are all analytically justified, and numerically tested through simulative campaign.