Improving real-time clock estimation with undifferenced ambiguity fixing

Real-time clock products are essential and a prerequisite for global navigation satellite system (GNSS) real-time applications, which are usually estimated from real-time observations from reference stations of a ground network without fixing the phase ambiguities. To improve the precision of real-time clock products further, an undifferenced ambiguity fixing algorithm is proposed for the classical real-time clock estimation method without requiring modifications to the current data processing strategy and product consistency. Combined with the wide-lane (WL) ambiguities, the ionospheric-free (IF) ambiguity estimates generated by the traditional clock estimation method are fed to an independent ambiguity fixing process to estimate the WL and narrow-lane (NL) uncalibrated phase delays (UPDs) and fix the WL/NL undifferenced ambiguities at each epoch. The fixed IF ambiguities are recovered from these WL/NL UPDs and integer ambiguities and then used to constrain the float-ambiguity clock solution. The proposed strategy is tested on 30 days of observations of 85 globally distributed reference stations of the international GNSS service (IGS) and multi-GNSS experiment (MGEX) networks. In the experiment, 99.96% of the post-fit residuals of WL ambiguities and 99.31% of the post-fit residuals of NL ambiguities fall in the range of (− 0.3, 0.3), with standard deviations (STD) of 0.045 and 0.074 cycles, respectively, which demonstrates the high precision and consistency of UPDs and fixed ambiguities. With the constraint of fixed ambiguities, the traditional float-ambiguity clock solution is further refined, resulting in ambiguity-fixed clock solution. Comparison with the IGS 30 s final clock products shows that ambiguity-fixing brings as much as 50–87% precision improvement to the float-ambiguity clock solution, and with an average improvement over 30 days of 24–50% for each satellite. When used in the float-ambiguity kinematic PPP test, the ambiguity-fixed clock brings at least 5% improvement to the north component and at least 10% improvement to the east and vertical components.