Construction and Evaluation of the Stochastic Model in Precise Point Positioning based on Triple-Frequency Geometry-Free Combination

The Global Navigation Satellite System (GNSS) carrier phase and pseudorange measurements exhibit different levels of accuracy, and there are differences in observation accuracy among different observation systems, satellites and receivers. A reasonable stochastic model is crucial for improving Precise Point Positioning (PPP) results. We propose a method for constructing stochastic models in PPP using triple-frequency observations. By forming geometry-free and ionosphere-free (GFIF) combinations and subtracting inter-frequency clock biases (IFCB), the accuracies of phase and pseudorange observations are evaluated using residuals to determine weights. Data from 278 International GNSS Service (IGS) stations on September 1, 2023 are processed to calculate the accuracies of carrier phase and pseudorange observations in GPS, Galileo, and BDS-3 systems. The results show that the accuracies of carrier phase observations among different receivers are relatively close, while there are obvious disparities in pseudorange observation accuracies. The average Root Mean Square (RMS) of Galileo carrier phase and pseudorange observations is the smallest among three systems. In BDS-3 system, there are certain disparities in carrier phase observation accuracies among different types of satellites. Specifically, for LEICA and SEPT receivers, the average RMS of IGSO satellites is greater than that of MEO satellites. To validate the effectiveness of the proposed model, the static and dynamic PPP solutions are conducted using 80 IGS stations. The results demonstrate that compared to the empirical model, the proposed model shortens the average convergence time by 22.5%, 31.5%, and 24.1% in static PPP for GPS, Galileo, and BDS-3 systems, respectively. At 0.5h, the average three dimensions (3D) positioning accuracies improve by 2.1, 3.5 and 2.9 cm, respectively. For dynamic PPP within the range of 0.5 to 1 hour, the average RMS of the 3D positioning are reduced by 2.6, 4.7 and 3.0 cm, respectively. Furthermore, for multi-system PPP of GPS+Galileo+BDS-3, the average convergence time and positioning accuracy are also improved with the proposed stochastic model.