## 5 Discussion  
The experimental results demonstrate that the proposed experimental system, constructed using the carrier-phase proportional active compensation method, exhibits the potential to achieve picosecond synchronization accuracy. Moreover, it is comparable to existing satellite-borne atomic clocks regarding short-term stability and exhibited long-term stability an order of magnitude better than existing satellite-borne atomic clocks. The system exhibits a stability level comparable to that of a partially active hydrogen maser. Compared with satellite atomic clocks, which are characterized by their structural complexity and environmental demands, the proposed method requires only the incorporation of a channel into a conventional transparent transponder to facilitate the continuous reproduction of precise and stable terrestrial atomic frequency standards in GEO satellites. Additionally, the satellite motion data obtained from the compensation amount in this experiment could be roughly used to estimate the radial acceleration level of Zhongxing-10 relative to the ground station. A dynamic platform was constructed based on these data. The results of the satellite-ground link active compensation experiment demonstrated that our proposed method has the potential to achieve picosecond-level accuracy. The accuracy of the ground experiment characterizes a key factor, namely whether the compensation system has the ability to track satellite motion. Under conditions simulating the acceleration of geostationary satellite motion, the transponder end achieved a picosecond-level reproduction, demonstrating the feasibility of proportional compensation in dynamic scenarios. Since the Ku-band is widely used in satellite communications, and  
Figure 16: Result of frequency-synchronization experiments with the moving platform under equivalent distance of 5 km. (**a**) Closed-loop phase differences between the recovery clock and local frequency standard. (**b**) Allan deviation of the phase difference between the recovery clock and local frequency standard. some of our previous work was also conducted in the Ku-band, we use this band as an example to discuss further extensions of the ground experiment. Beyond the ground experiments, a crucial aspect yet to be addressed is the extent to which the residual error level of this active compensation method can be reached in an actual satellite-ground link. In our previous study, we constructed a link between a ground station and a synchronous orbiting satellite, during which we conducted a self-generated and self-received carrier-phase active compensation experiment. The results demonstrated that the phase residual error of the locked satellite-ground link could reach 0.896 ps. The stability performance achieved in this experiment can reach the level of \(10^{-12}\) at 1 s and \(10^{-16}\) at 1 day. The experimental results can be found in Figures 8 and 10 of reference [27]. This demonstrates the noise floor attainable by our system within the ground station-to-satellite link. This also demonstrates that our developed compensation system can function properly under the signal-to-noise ratios (SNRs) present in realistic satellite communication scenarios. The main difference between the short-distance ground experiment and the long-distance satellite-to-ground link experiment, excluding the ionospheric and relativistic effects which will be considered later, lies in the time delay and the noise introduced by the atmospheric link. In our previous ground experiments, we found that changing the equivalent distance did not significantly affect the precision and stability of the recovery clock. Furthermore, the full-link noise compensation experiment for satellite-to-ground links demonstrated that the control system could compensate for long-distance links with a delay of about 0.25 s. Therefore, the primary influencing factor for the extrapolation of the ground experiment results should be the noise introduced by the atmospheric link.