Investigation of Precise Single-Frequency Time and Frequency Transfer with Galileo E1/E5a/E5b/E5/E6 Observations

With the rapid upgrade of global navigation satellite system (GNSS) single-frequency (SF) receivers and the increasing market demand for low-cost hardware, SF precise point positioning (PPP) technology has been widely applied in the time and frequency field. The five-frequency signals provided by the whole constellation of Galileo bring more opportunities for the application of SF PPP in time and frequency transfer. In this contribution, using Galileo's multi-frequency observations, three SF PPP time and frequency transfer models, i.e., the un-combined (UC) model, the ionosphere-free-half (IFH) model, and the ionosphere-weighted constraints (IWCs) model are established. SF PPP time and frequency transfer performance with Galileo E1, E5a, E5b, E5, and E6 multi-frequency observations is evaluated using four links (947.7 km to 1331.6 km) with five external high-precision atomic clocks stations. The results show that the time and frequency transfer performance of SF-UC and SF-IWC is better than that of SF-IFH, and the timing accuracy of SF-UC and SF-IWC is similar. SF PPP time and transfer performance with E5, E5a, E5b, and E6 signals is improved compared with traditional E1 signal. Among them, the frequency stability of E5 improves the most (about 58%), and that of E6 improves the least (about 14%). In addition, the difference in frequency stability between SF and double-frequency (DF) PPP decreases gradually with an increase in average time, and the frequency stability difference between SF and DF PPP can reach 2 x 10(-16) in 120,000 s, indicating that SF PPP has the potential to achieve DF PPP frequency stability. Considering the possible frequency data loss during actual observation, the cost of the GNSS SF receiver, and the advantages of Galileo multi-frequency observations, SF PPP can also meet the long-time time and frequency transfer requirements, and the SF-IWC model based on Galileo E5 observations is more recommended.