The international GNSS service (IGS) has been providing an open-access real-time service (RTS) since 2013, which allows users to carry out real-time precise point positioning (RT-PPP). As the availability of RTS products is vital for RT-PPP, a disruption in receiving RTS products will be a concern. Currently, the IGS Ultra-rapid (IGU) orbit is accurate enough to be used as an alternative orbit for RTS during RTS outages, while the precision of the IGU predicted clock offsets is far below that of the RTS clock product. The existing clock prediction methods based on received RTS clock data will not work well if the discontinuity arises shortly after the start of the RT-PPP processing due to the lack of RTS clock data to fit the prediction model or to predict clock offsets at a high precision. Even if there is a sufficient amount of RTS clock data available, saving large amounts of RTS clock data would also use processor memory. An alternate approach for GPS clock prediction is proposed. The prediction model, composed of linear polynomial and sinusoidal terms, is similar to those used by the precious methods. The main innovation is the determination of the model coefficients: coefficients of linear and sinusoidal terms are estimated with the epoch-differenced clock offsets from the IGU observed part, while the constant coefficient is computed with the latest RTS clock corrections. There is no need to save the received RTS clock corrections, and clock prediction can be carried out even with only one epoch of RTS data. Evaluation of the proposed method shows that the predicted clock offsets within a short period of prediction time, e.g., 5 min, are slightly worse than RTS clock data. Even when the predicted time reaches up to 1 h, the precision of the predicted clock offsets is still higher than that of IGU predicted clock offsets by about 50%.

The GPS satellite clock offset prediction is investigated and applied to a real-time PPP system. First, the current situation of GPS satellite clock is introduced and analysed with respect to their stability. Then the satellite clock prediction with different update intervals is presented, in which the satellite clock day boundary jump is addressed. Afterwards, the investigation of the satellite clock prediction model for GPS satellite IIF clocks is carried out and the effects of periodic terms are discussed. After that, the verification of the satellite clock offset prediction will be carried out both in the time and positioning domain. Positioning accuracy at 0.021, 0.049, and 0.017 m in the east, north, and vertical directions can be obtained for 6-h static positioning using the predicted clock offset updating every hour, while the 3D RMS for kinematic real-time PPP is 0.360 m, with 28% improvement over that utilising the IGU predicted products.

This paper proposed the high-precision satellite orbit prediction process at the user end for the real-time precise point positioning (PPP) system. Firstly, the structure of a new real-time PPP system will be briefly introduced in the paper. Then, the generation of satellite initial parameters (IP) at the sever end will be discussed, which includes the satellite position, velocity, and the solar radiation pressure (SRP) parameters for each satellite. After that, the method for orbit prediction at the user end, with dynamic models including the Earth’s gravitational force, lunar gravitational force, solar gravitational force, and the SRP, are presented. For numerical integration, both the single-step Runge–Kutta and multi-step Adams–Bashforth–Moulton integrator methods are implemented. Then, the comparison between the predicted orbit and the international global navigation satellite system (GNSS) service (IGS) final products are carried out. The results show that the prediction accuracy can be maintained for several hours, and the average prediction error of the 31 satellites are 0.031, 0.032, and 0.033 m for the radial, along-track and cross-track directions over 12 h, respectively. Finally, the PPP in both static and kinematic modes are carried out to verify the accuracy of the predicted satellite orbit. The average root mean square error (RMSE) for the static PPP of the 32 globally distributed IGS stations are 0.012, 0.015, and 0.021 m for the north, east, and vertical directions, respectively; while the RMSE of the kinematic PPP with the predicted orbit are 0.031, 0.069, and 0.167 m in the north, east and vertical directions, respectively.