TDOA-based source localization with distance-dependent noises

This paper focuses on the problem of source localization using time-difference-of-arrival (TDOA) measurements in both 2-D and 3-D spaces. Different from existing studies where the variance of TDOA measurement noises is assumed to be independent of the associated source-to-sensor distances, we consider the more realistic model where the variance is a function of the source-to-sensor distances, which dramatically complicates TDOA-based source localization. After formulating the distance-dependent noise model, we prove that using the extra information about the source location in the functional variance improves the estimation accuracy of TDOA-based source localization, but contributes little under a sufficiently small noise level. Further, we theoretically analyze the problem of optimal sensor placement, and derive the necessary and sufficient conditions for optimizing localization performance under different circumstances. Then, a localization scheme based on the iteratively reweighted generalized least squares (IRGLS) method is proposed to efficiently exploit the extra source location information. Finally, a simulation analysis confirms our theoretical studies, and shows that the performance of the proposed localization scheme is comparable to the Cramer-Rao lower bound (CRLB) given moderate TDOA measurement noises.