Result and discussion The medium earth orbit (MEO) satellite is selected as the navigation satellite. On this basis, we investigate the influence of atmospheric dispersion on the single-satellite-to-earth unidirectional time transfer deviation first. Simulation results of the unidirectional time transfer deviation are obtained with the laser wavelength of 815 nm (Fig. 3) and 1550 nm (Fig. 4) respectively. The range of unidirectional time transfer deviation is from 7.52 ns to 17.69 ns at 815 nm and slightly decreases from 7.38 ns to 17.36 ns at 1550 nm. The results show that the unidirectional time transfer deviation caused by atmospheric dispersion decreases with the increasing atmospheric temperature and potential height, and it also reduces with the decrease in atmospheric pressure and receiving zenith, with a more significant influence of potential height. The unidirectional time transfer deviation of Jiuquan station with higher altitude is significantly lower than that of other stations. Then, the effect of atmospheric dispersion on the unidirectional time transfer deviation of four satellites to the earth is studied, and the fluctuations of unidirectional time transfer deviation are obtained when the laser wavelength is 815 nm (Fig. 5) and 1550 nm (Fig. 6) respectively. The unidirectional time transfer deviation ranges from 15.02 ns to 35.36 ns at 815 nm and from 14.74 ns to 34.70 ns at 1550 nm. The trend of the time transfer deviation influenced by temperature, potential height, and receiving zenith angle is similar to that with the wavelength of 815 nm. Finally, a comprehensive analysis of the unidirectional time transfer deviation of the four ground stations in different months with a laser wavelength of 1550 nm (Fig. 7, Table 1). This shows that the mean square error of the unidirectional time transfer deviation at each ground station is in the order of 100 ps throughout the year when the relative position between the four satellites and ground stations is fixed.

Free-space laser time transfer techniques have a wide range of application prospects as they have higher accuracy than the traditional global navigation satellite system (GNSS) and better flexibility than fiber-optic time transfer techniques. However, the current research on free-space laser time transfer techniques requires two-way signal transmission and antenna alignment to meet the symmetric reciprocity of channel time delay, resulting in the high complexity and cost of terminal equipment. Consequently, these techniques are mainly utilized for high-precision time transfer of satellite-to-satellite, satellite-to-earth crucial time-frequency nodes and users. Characterized by small user terminal size, low power consumption, good concealment, and plug-and-play convenience without the need for precise two-way alignment, satellite-to-earth laser unidirectional time transfer can combine the high precision of free-space laser time transfer techniques and the flexibility of unidirectional time transfer techniques to overcome the limitation. A significant factor limiting the performance of satellite-to-earth laser unidirectional time transfer is the time transfer deviation introduced by atmospheric dispersion. We can lay a solid foundation for further correcting the deviation and improving the time transfer accuracy by studying the range and fluctuation of atmospheric dispersion on the deviation of satellite-to-earth laser unidirectional time transfer.

We employ the meteorological data from China Meteorological Data Network to build a standard atmospheric refractive index layering model using Murray's classical spherically symmetric atmospheric refractive index layering theory, and then build a time transfer deviation model based on the unidirectional time transfer mechanism. On this basis, firstly, the variation of single-satellite-to-earth unidirectional time transfer deviation is simulated and studied. Secondly, the variation of four-satellite-to-earth unidirectional laser time transfer deviation is analyzed. Finally, the fluctuations of the single-satellite-to-earth and four-satellite-to-earth unidirectional time transfer biases are compared and analyzed under the laser wavelength of 815 nm (Fig. 3) and 1550 nm, respectively.

We investigate the mechanism of the influence of atmospheric dispersion on the deviation of satellite-to-earth laser unidirectional time transfer link, build a time transfer deviation calculation model, and simulate and study the deviation caused by atmospheric dispersion in the satellite-to-earth laser unidirectional time transfer link. The results show that the unidirectional time transfer deviation introduced by atmospheric dispersion is related to the user receiving zenith angle, laser wavelength, ground temperature, and potential height. The receiving zenith angle exerts the most significant influence, resulting in time deviation fluctuation of up to 10 ns. When the relative position between the four satellites and ground stations is not fixed, the unidirectional time transfer deviation fluctuates within the range of 15 ns to 35 ns. However, when the relative position between the four satellites and ground stations is fixed, the annual unidirectional time transfer deviation fluctuation is less than 1 ns. Therefore, in non-extreme weather conditions, the peak deviation of satellite-to-earth laser unidirectional time transfer is expected to be reduced to the order of 100 ps by compensating the deviation with empirical values.