In this work, we consider the problem of localizing multiple signal sources based on time-difference of arrival (TDOA) measurements. In the blind setting, in which the source signals are not known, the localization task is challenging due to the data association problem. That is, it is not known which of the TDOA measurements correspond to the same source. Herein, we propose to perform joint localization and data association by means of an optimal transport formulation. The method operates by finding optimal groupings of TDOA measurements and associating these with candidate source locations. To allow for computationally feasible localization in three-dimensional space, an efficient set of candidate locations is constructed using a minimal multilateration solver based on minimal sets of receiver pairs. In numerical simulations, we demonstrate that the proposed method is robust both to measurement noise and TDOA detection errors. Furthermore, it is shown that the data association provided by the proposed method allows for statistically efficient estimates of the source locations.

翻译：本文研究了基于到达时间差（TDOA）测量对多个信号源进行定位的问题。在盲场景下，由于信号源未知，定位任务因数据关联问题而颇具挑战性——即无法确定哪些TDOA测量值对应同一信号源。为此，我们提出通过最优传输框架实现联合定位与数据关联。该方法通过寻找TDOA测量值的最优分组，并将其与候选信源位置建立关联来运作。为在三维空间中实现计算可行的定位，我们利用最少接收器对集合构建最小多边定位求解器，生成高效的候选位置集。数值仿真表明，所提方法对测量噪声和TDOA检测误差均具有鲁棒性。此外，实验证明该方法提供的数据关联能使信源位置估计达到统计高效性。