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Abstract

To support real-time global navigation satellite systems (GNSS) precise applications, satellite clock corrections need to be precisely estimated at a high-rate update interval, which remains a challenge due to the rapid development of multi-GNSS constellations. In this study, we developed an undifferenced (UD) ambiguity resolution (AR) procedure to improve both the accuracy and computational efficiency for real-time multi-GNSS clock estimation realized by a square root information filter. In the proposed method, UD ambiguities are resolved after correcting the simultaneously estimated uncalibrated phase delays (UPD) and the fixed UD ambiguity parameters are eliminated immediately from the filter, so that the computational burden is significantly reduced. Moreover, based on the linear relationship between double-differenced (DD) and UD ambiguities, we investigated the difference between DD and UD AR in clock estimation. We found that the major reason why DD AR contributes little to the clock estimation while UD AR can speed up the convergence remarkably is that UD AR additionally provides a stable clock datum compared with DD AR. GNSS observations from about 100 globally distributed stations were processed with the proposed method to generate simulated real-time clocks and UPDs for GPS, Galileo, and BDS satellites over a one-month period. The results show that the percentage of wide-lane (WL) UPD residuals within  ± 0.25 cycles and narrow-lane (NL) UPD residuals within  ± 0.15 cycles are over 97.0% and 90.0%, respectively, which contributes to an ambiguity fixing rate of more than 90% for three systems. The mean daily standard deviation (STD) of the clocks of the UD-fixed solution with respect to Center for Orbit Determination in Europe 30 s final products is 0.021, 0.020, and 0.035 ns for GPS, Galileo, and BDS satellite, respectively, which is improved by 78.1%, 58.3%, and 79.8% compared to the float solution. Benefiting from the removal of fixed ambiguities, the average computation time per epoch was reduced from 3.88 to 1.05 s with a remarkable improvement of 72.9%. The quality of the satellite clock and UPD products was also evaluated by the performance of kinematic precise point positioning (PPP). The results show that fast and reliable multi-GNSS PPP-AR can be achieved with the derived UD-fixed clocks and UPDs, which outperforms that using DD-fixed clock and off-line UPD products with an average improvement of 7.9% and 19.9% in terms of convergence time and positioning accuracy, respectively. Furthermore, we demonstrated the effectiveness of the proposed UD AR method through a 7-day real-time clock estimation experiment.