High-precision GNSS Real-Time Kinematic (RTK) positioning often suffers from gross errors caused by non-line-of- sight (NLOS) multipath and other anomalies, which can dramatically bias simple coordinate averages. This paper presents Entropic-Topological Barycentric Synthesis (ETBS), a novel framework that dynamically selects a reliable subset of GNSS coordinates and computes a weighted barycentric average. The method proceeds in phases: (1) Topological filtering of the raw point set using kernel density estimation to identify and remove outliers; (2) Entropy weighting of remaining points based on multiple quality metrics (e.g. carrier-to-noise ratio, PDOP, satellite elevation variability) to assign higher weight to more reliable observations; and (3) Barycentric coordinate synthesis by computing the Wasserstein (transport) barycenter of the weighted points, yielding the final coordinate estimate. In synthetic tests mimicking open-sky and harsh urban conditions, ETBS consistently isolates outliers and yields centimeter-level accuracy, whereas traditional mean/median or robust least-squares methods produce errors on the order of decimeters or more. The results demonstrate that ETBS effectively neutralizes extreme outliers and achieves superior positioning precision.
Kashyap et al. (Thu,) studied this question.