LEO satellite clock analysis and prediction for positioning applications

The positioning service aided by low Earth orbit(LEO)mega-constellations has become a hot topic in recent years.To achieve precise positioning,accuracy of the LEO clocks is important for single-receiver users.To bridge the gap between the applicable time of the clock products and the time of positioning,the precise LEO clocks need to be predicted over a certain period depending on the sampling interval of the clock products.This study discusses the prediction errors for periods from 10 s to 1 h for two typical LEO clock types,i.e.the ultra-stable oscillator(USO)and the oven-controlled crystal oscillator(OCXO).The prediction is based on GNSS-determined precise clock estimates,where the clock stability is related to the GNSS estimation errors,the behaviors of the oscillators themselves,the systematic effects related to the environment and the relativistic effects,and the stability of the time reference.Based on real data analysis,LEO clocks of the two different types are simulated under different conditions,and a prediction model considering the systematic effects is proposed.Compared to a simple polynomial fitting model usually applied,the proposed model can significantly reduce the prediction errors,i.e.by about 40%-70%in simulations and about 5%-30%for real data containing different miss-modeled effects.For both clock types,short-term prediction of 1 min would result in a root mean square error(RMSE)of a few centimeters when using a very stable time reference.The RMSE amounts to about 0.1 m,when a typical real-time time reference of the national center for space studies(CNES)real-time clocks was used.For long-term prediction of 1 h,the RMSE could range from below 1 m to a few meters for the USOs,depending on the complexity of the miss-modeled effects.For OCXOs,the 1 h prediction could lead to larger errors with an RMSE of about 10 m.

Applications of two-way satellite time and frequency transfer in the BeiDou navigation satellite system

A two-way satellite time and frequency transfer(TWSTFT) device equipped in the BeiDou navigation satellite system(BDS)can calculate clock error between satellite and ground master clock. TWSTFT is a real-time method with high accuracy because most system errors such as orbital error, station position error, and tropospheric and ionospheric delay error can be eliminated by calculating the two-way pseudorange difference. Another method, the multi-satellite precision orbit determination(MPOD)method, can be applied to estimate satellite clock errors. By comparison with MPOD clock estimations, this paper discusses the applications of the BDS TWSTFT clock observations in satellite clock measurement, satellite clock prediction, navigation system time monitor, and satellite clock performance assessment in orbit. The results show that with TWSTFT clock observations, the accuracy of satellite clock prediction is higher than MPOD. Five continuous weeks of comparisons with three international GNSS Service(IGS) analysis centers(ACs) show that the reference time difference between BeiDou time(BDT) and golbal positoning system(GPS) time(GPST) realized IGS ACs is in the tens of nanoseconds. Applying the TWSTFT clock error observations may obtain more accurate satellite clock performance evaluation in the 104 s interval because the accuracy of the MPOD clock estimation is not sufficiently high. By comparing the BDS and GPS satellite clock performance, we found that the BDS clock stability at the 103 s interval is approximately 10.12, which is similar to the GPS IIR.