Improving the stability of real-time PPP solutions by receiver clock modeling

In precise point positioning (PPP) solutions, stochastic modeling of the receiver clock parameter affects solution stability, especially the station up component. This study analyzes GPS + Galileo static and kinematic PPP solutions for 14 GNSS stations equipped with ultra-stable hydrogen masers, utilizing real-time orbit and clock products, such as HAS, IGS, and CNES, as well as final products from CODE. The solution with modeling of the receiver clock parameter enhances stability and precision compared to the reference solution, in which the receiver clocks are estimated independently for each epoch. In static PPP solutions, receiver clock modeling reduces spikes in the clock parameter and improves short-term stability. The most notable improvement of the station up component reaches up to 59, 21, 25, and 38% for HAS, IGS, CNES, and CODE, respectively, in terms of the interquartile range (IQR) of the estimated parameter during the first three processing hours. For kinematic PPP solutions, the maximum reduction of the up component standard deviation is 38, 50, 18, and 26% for HAS, IGS, CNES, and CODE, respectively across all analyzed GNSS stations. Additionally, the IQR analysis of epoch-wise differences in the station up component indicates even greater enhancements, with reductions reaching up to 63, 70, 52, and 83% for HAS, IGS, CNES, and CODE, respectively. Epoch-wise differences indicate short-term stability. The proposed clock modeling improves both the common clock parameter and the vertical component, enhancing PPP solution by increasing stability (reduced variability) and precision (reduced dispersion) across real-time and post-processed GNSS products.