Aligning GPS/Galileo/BDS satellite integer clock products across day boundaries for continuous time and frequency transfer

GNSS integer ambiguity precision point positioning (IPPP) with satellite integer clock products is currently one of the most precise techniques for time and frequency transfer. However, a challenging issue that hampered the long-term performance of IPPP is the day-boundary discontinuity (DBD) that manifests at UTC (Coordinated Universal Time) midnights during the processing of multi-day GNSS observations. Users’ remedy to eliminate such receiver clock DBDs is to identify the integer offset of ambiguities across days, but residual DBDs could still potentially exceed 100 ps. In this study, we propose an alternative but more efficient approach to eliminate the DBDs of satellite orbit/clock/bias products as an integral, while users would directly achieve receiver clocks without DBDs rather than being troubled to fix them through carrier-phase ambiguity connection. Such a post-processing alignment approach is applicable to IGS satellite integer products processed in daily batches and does not rely on the respective smoothness of orbits or clocks. After application to the rapid multi-GNSS Experiment (MGEX) product at Wuhan University, the residual discontinuities of satellite integer clocks for each GPS/Galileo/BDS-3 satellite typically do not exceed 0.05 cycles of narrow-lane wavelengths. In continuous time and frequency transfer over a 31-day period, DBDs in all nine IPPP time links are smaller than 25 ps with a standard deviation of 10 ps, compared to 60–90 ps for the legacy strategy and unaligned products. This day-boundary alignment approach is suitable for common satellite integer products in the International GNSS Service (IGS) and has been routinely implemented in Wuhan University’s rapid MGEX satellite orbit/clock/bias products since January 1, 2023.