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.