Compared with traditional global satellite navigation systems and fiber-optic time transfer techniques, satellite time transfer based on free-space laser links has higher accuracy and better flexibility, making them widely applicable. However, they are not capable of meeting the timing needs of a large number of users with uncertain positions and lacking precise bi-directional alignment abilities in real life. In this article, we propose a unidirectional Beidou time transfer scheme based on laser links which adopts the terminal user unidirectional timing scheme in the Beidou/GPS navigation system. The proposed scheme combines the flexibility of a unidirectional timing mechanism and the high-precision of laser link based satellite timing systems. However, one of the factors that restrict the performance of this laser link based Beidou unidirectional time transfer is the timing deviation introduced by atmospheric refraction experienced by the laser transmission. Our study focuses on the influence of atmospheric refraction on the laser link, which causes unidirectional timing deviation. The results can pave the way for our future research in correcting the timing deviation and improving the time transfer accuracy and, in turn, promote the development of satellite-to-earth laser link based unidirectional time transfer.

In our study, several typical climate representative cities are chosen and the atmospheric refractive index models are established using the monthly average and daily basic observation meteorological data provided by the China Meteorological Data Service Centre (CMDC). Then, with the help of the precise ephemeris data from the International GNSS Service (IGS) data center of Wuhan University, the Beidou satellites are screened, and then the timing deviation caused by atmospheric refraction is computed using the laser signal transmission model and pseudo-range measurement equations. Using this method, the influence of satellite orbit parameters on the unidirectional timing deviation caused by the atmospheric refraction is simulated and studied. Then, the comprehensive impact of satellite orbit parameters and atmospheric conditions on the unidirectional timing deviation is analyzed. Finally, by comparing the differences between the above two results, the magnitude of the impact of atmospheric condition changes on the unidirectional timing deviation is analyzed.

When the monthly average atmospheric refractive index layered model is used, the overall impact of atmospheric refraction on the unidirectional timing deviation fluctuates in the order of tens of nanoseconds (Fig. 4, Table 1), with a timing deviation of about 15.97-42.46 ns. For a specific ground station, the fluctuation of timing deviation is greatly affected by the orbit parameters of the Beidou satellites, and the timing deviation increases with the increase of the ground station’s zenith angle to the satellites. For different ground stations, we find that the fluctuation of timing deviation is influenced by the position of the ground stations as well as the orbit parameters of the Beidou satellites. For example, the relatively high ground station position of Lhasa station results in smaller timing deviations and fluctuations. When using the measured daily atmospheric refractive index layered model, the overall impact of atmospheric refraction on the unidirectional timing deviation still fluctuates in the order of tens of nanoseconds (Fig. 5, Table 2) and the timing deviation range is about 15.88-42.34 ns. Comparing the difference between the two timing deviation results acquired based on the monthly average and the measured daily atmospheric refractive index layered models (Fig. 6), we can see that the maximum difference in timing deviation calculated based on the two models does not exceed 0.5 ns. Besides, the impact of daily meteorological conditions on the unidirectional laser Beidou timing deviation caused by atmospheric refraction is on the order of 100 ps, which is much smaller compared with the influence of Beidou satellite orbit parameters.

We study the timing deviation caused by atmospheric refraction in the laser link based Beidou unidirectional time transfer and propose a method to compute the timing deviation caused by the atmospheric refraction. Then the timing deviation caused by atmospheric refraction is computed and analyzed based on the proposed method and the IGS data in several reprehensive cities in China. The results show that the unidirectional timing deviation caused by atmospheric refraction in the laser link based Beidou time transfer is on the order of 10 ns. The timing deviation calculated using the monthly average atmospheric refractive index model fluctuates between 15.97 ns and 42.46 ns, while the timing deviation calculated using the measured daily atmospheric refractive index model fluctuates between 15.88 ns and 42.34 ns, which is much smaller than the time deviation caused by the ionosphere on the microwave link based Beidou time transfer. The comparison between the timing deviations acquired based on the two atmospheric refractive index layering models shows that the difference between the timing deviation caused by atmospheric refraction computed based on these two models is on the order of 100 ps. Additionally, compared with the impact of Beidou satellite orbit parameters on the timing deviation, the impact of meteorological condition induced atmospheric refraction is much smaller. Based on our study, it is expected that the unidirectional timing deviation caused by the atmospheric refraction in the laser link based Beidou time transfer can be predicted and corrected based on the comprehensive use of precise satellite orbit parameters and atmospheric refraction data modeling. Also, it is predicted that the timing deviation can be possibly reduced to be on the order of picoseconds.