## 4 Results
Figure 12: Results of the frequency-synchronization experiments using the moving platform. (**a**) Open-loop and closed-loop phase differences between the transfer and receiver ends of the ground station, shown as time-difference changes. (**b**) Open-loop and closed-loop phase differences in the recovery clock at the transponder end and local frequency standard, shown as time-difference changes. The corresponding calculation formula is as follows:  
\[r=\frac{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)(y_{i}-\overline{y})}{\sqrt{ \sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}}\sqrt{\sum_{i=1}^{n}\left(y_ {i}-\overline{y}\right)^{2}}}. \tag{12}\]  
Figure 14: Device temperature fluctuations and transponder recovery clock phase fluctuations. Figure 13: Allan deviation of the frequency-synchronization experiments using the moving platform. (**a**) Allan deviation of the phase difference between the transfer and receiver end at the ground station. (**b**) Allan deviation of the recovery clock with local frequency standard. The Pearson product moment correlation coefficient, denoted by \(r\), measures the degree of correlation between two time series \(x_{i}\) and \(y_{i}\). The means of these time series are denoted as \(\overline{x}\) and \(\overline{y}\). Finally, to verify the repeatability of the experiment, we conducted four sets of dynamic experiments, using a sliding rail, each lasting 12 h. The speed and reciprocation distance settings were identical to those previously described. These experiments commenced on 20 September 2024 and concluded on 22 September 2024. The findings demonstrate the system's repeatable performance, highlighting its consistent precision and stability throughout multiple trials, as shown in Figure 15. This confirmed the system's reliability for frequency comparisons over extended periods and established its robustness for prolonged operations. Finally, we conducted dynamic experiments lasting 24 h under equivalent 5 km conditions to assess whether the introduction of a certain degree of equivalent distance would have an impact on the experimental results, as shown in Figure 16. Since the standard deviation of the phase difference between the transfer end and receiver end of the ground station was still very small at 0.79 ps, the figure focuses on showing the transponder end. Figure 16a depicts the time domain waveform and frequency stability of the remaining phase at the transponder end after proportional compensation. The standard deviation of the phase difference were 9.73 ps for the closed loop. Figure 16b illustrates the closed-loop frequency stability of the dynamic experiment over a 24 h period. The calculations demonstrate that the transponder end's 10,000 s stability reached 8.22 \(\times\) 10\({}^{-16}\). The experi  
Figure 15: Results of the four groups of frequency-synchronization experiments using the moving platform. (**a**) Closed-loop phase differences between the ground station’s transfer and receiver ends, shown as time-difference changes. (**b**) Standard deviation of the phase difference between the ground station’s transfer and receiver ends for the four groups. (**c**) Allan deviation of the phase difference between the ground station’s transfer and receiver ends. (**d**) Closed-loop phase differences between the recovery clock and local frequency standard. (**e**) Standard deviation of the phase difference between the recovery clock and local frequency standard. (**f**) Allan deviation of the phase difference between the recovery clock and local frequency standard. mental results are primarily influenced by fluctuations in room temperature, with minimal difference observed in the clock recovery performance before and after the equivalence.