The objective of this paper is to describe recent progress in the area of the Ground Based Augmentation System (GBAS) σpr_gnd establishment to ensure aircraft precision approach navigation integrity. In particular, this paper details: (1) the development and testing of a new adaptive binning algorithm for processing GBAS reference station empirical data to account for ranging error non-stationarity; (2) an introduction of a practical empirical method to quantify and compensate for the effects of seasonal variations of ranging error; and (3) the synthesis of these empirical results with existing theoretical ground-multipath models toward a quantitative establishment σpr_gnd for GBAS.