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.

为了支持实时全球导航卫星系统（GNSS）精确应用，需要以高速率更新间隔精确估计卫星时钟校正，由于多GNSS星座的快速发展，这仍然是一个挑战。在本研究中，我们开发了一种无差 (UD) 模糊度解析 (AR) 程序，以提高通过平方根信息滤波器实现的实时多 GNSS 时钟估计的精度和计算效率。在所提出的方法中，在校正同时估计的未校准相位延迟（UPD）后解决UD模糊度，并立即从滤波器中消除固定的UD模糊度参数，从而显着减少计算负担。此外，基于双差（DD）和UD模糊度之间的线性关系，我们研究了DD和UD AR在时钟估计中的差异。我们发现，DD AR 对时钟估计贡献不大，而 UD AR 能够显着加快收敛速度​​的主要原因是，与 DD AR 相比，UD AR 额外提供了稳定的时钟数据。使用所提出的方法处理来自全球约 100 个分布站的 GNSS 观测结果，为 GPS、伽利略和 BDS 卫星生成一个月内的模拟实时时钟和 UPD。结果表明，宽巷（WL）UPD残差在±0.25个周期内的百分比和窄巷（NL）UPD残差在±0.15个周期内的百分比分别超过97.0％和90.0％，这有助于歧义修复率三个系统均超过90%。 UD固定解决方案的时钟相对于欧洲定轨中心30秒最终产品的平均日标准偏差（STD）为0.021，0。GPS、伽利略、北斗卫星分别为0.020、0.035 ns，比浮点方案提高了78.1%、58.3%、79.8%。受益于固定歧义的去除，每个 epoch 的平均计算时间从 3.88 秒减少到 1.05 秒，显着提高了 72.9%。卫星时钟和UPD产品的质量还通过运动精密单点定位（PPP）的性能进行评估。结果表明，使用衍生的UD固定时钟和UPD可以实现快速可靠的多GNSS PPP-AR，其性能优于使用DD固定时钟和离线UPD产品，平均提高7.9%和19.9%分别在收敛时间和定位精度方面。此外，我们通过为期 7 天的实时时钟估计实验证明了所提出的 UD AR 方法的有效性。