Maximum-Consistency Extension of Combined Weighted Method for Outlier-Robust Acoustic TDOA Localization

Time difference of arrival (TDOA) measurements and corresponding hyperbolic localization techniques are widely utilized across diverse domains, including pedestrian tracking, wildlife monitoring, autonomous vehicle navigation, underwater positioning, and defense applications. The combined weighted (COM-W) method and its enhanced version (E-COM-W) provide location estimates in closed form in two dimensions. These methods are attractive candidates for hyperbolic localization problems because they offer a low, deterministic computational cost; require a minimal number of sensors; and incorporate geometric dilution of precision (GDOP) directly into the location estimate. While the accuracy of the location estimate approaches the Cramér–Rao lower bound (CRLB) under low-noise conditions, it degrades significantly in the presence of higher measurement errors that are common in practice. This paper elucidates the mechanisms driving this suboptimal behavior and proposes a robust method, designated as R-COM-W. The proposed algorithm not only rectifies the performance degradation of both COM-W and E-COM-W in high-noise environments but also ensures resilience against erroneous measurements, such as those caused by non-line-of-sight (NLOS) propagation. We extend this methodology to three dimensions and demonstrate the superior performance of R-COM-W using both numerical simulations and experimental measurements.