Improving Stochastic Model of GNSS Precise Point Positioning with Triple-Frequency Geometry-Free Combination

The triple-frequency global positioning system (GPS), BeiDou navigation satellite system-3 (BDS-3), and Galileo can form the geometry-free and ionosphere-free (GFIF) carrier phase and pseudorange combinations, respectively. These combinations provide a precondition for which the accuracies of the carrier phase and pseudorange observations can be evaluated, respectively. The stochastic model of precise point positioning (PPP) processing is constructed using the evaluated results. The 176 International GNSS Service (IGS) stations are used to validate the presented method. The evaluated results show that accuracies of the GPS, BDS-3, and Galileo carrier phase observations are at the millimeter level, while those of pseudorange observations reach the decimeter level. In addition, BDS-3, GPS, and Galileo have different precisions. The stochastic model, which is reestablished from the evaluated accuracies, is tested using single Global Navigation Satellite System (GNSS) and multiGNSS PPP performances. The single-GNSS PPP shows that its convergence time has a mean improvement of 24%, and its 1- and 2-h mean three dimensions (3D) positioning accuracies are improved by about 17.7% and 4.5%, respectively, compared with those of empirical accuracies-based stochastic models. It also has the best performance in the multiGNSS PPP. Its mean convergence time of GPS+Galileo for 3 days is shorter than 35 min, while that of GPS+BDS-3 is less than 30 min. The mean improvements for the convergence time and 1- and 2-h 3D positioning reach 28%, 9.4%, and 2.8%, respectively, when the GPS+Galileo and GPS+BDS-3 PPP use the reestablished stochastic model instead of the empirical methods.