The orbit and clock offset of GNSS are the prerequisite for the high-performance positioning, navigation and timing (PNT) services. To overcome the obvious problems of clock offsets estimation in multi-GNSS ultra-rapid orbit determination solution, such as the observation quality and model configurations, an improved model to estimate ultra-rapid clock offset is proposed by considering the BDS-3/GNSS satellite clock states. Firstly, the observation equation of clock offset estimation by inserting the clock offset velocity and acceleration terms is constructed based on the fixed ultra-rapid orbit and station positions. Secondly, the algorithms of time-difference carrier phase (TDCP) and singular decomposition are used to construct the quality control and epoch-transition model of clock offset estimation. Thirdly, with the introduction of clock parameter states transition equation and consideration of BDS-3/GNSS onboard clock frequency stability, the single-epoch estimated clock offset can be obtained. According to the proposed BDS-3/GNSS ultra-rapid clock offset estimation method, an accuracy improvement at least 46.9% can be obtained, where the instantaneous clock offset of epoch interval can be directly derived using the clock state values. In addition, compared with the traditionally issued BDS-3/GNSS ultra-rapid clock offsets, the four-system kinematics PPP performances of positioning and convergence are improved with 1.7%, 6.0%, 31.2% and 44.9%, 33.3%, 38.9% for E, N and U directions, respectively. Meanwhile, the accuracy of the predicted clock offset is also improved, which can lead to the decreasing of four-system static PPP positioning residuals and convergence time with 6.3%, 13.5%, 11.3% and 14.5%, 1.6%, 12.4% for E, N and U directions, respectively. Therefore, the quality of BDS-3/GNSS satellite ultra-rapid clock offset is significantly improved by the proposed estimation method, which can also be used to improve the multi-GNSS constellation performances of real-time and near-real-time services.
