## 5 Results  
Since the length of the experiment period (from 6:00 a.m. to 7:30 a.m., 1 March 2023) was 1.5 h, and the measurement interval was 5 s, there were 1080 observation values in total. The results from the first experiment (namely from 6:00 a.m. to 7:30 a.m., 1 March 2023) are shown in Figure 6, with a mean offset of \(-3.6\) cm and an STD value of 12.1 cm (see the first row of Table 3).  
Figure 6: The offset between true values and estimated values of the height datum difference determined by the SVN-56 satellite.  
We can see that the mean offset was at the centimeter level, while the STD was one magnitude higher at the decimeter level. The reason for this is the main component of the clock errors is white noise, while the drift and random walk effects are not apparent in the results. Since we can significantly improve the stability of the clock after a period (e.g., one hour) of integration, as demonstrated by [19], the height unification accuracy could be improved after a period of integration.  
To estimate the reliability of the SFST method, we ran 10 difference simulation experiments with different randomly chosen coefficients, \(a_{i}\), \(b_{i}\), \(c_{i}\) and \(d_{i}\), in Equations (16) and (17) in total. The behaviors of the offset signals were similar. Thus, we only display the mean offsets and STDs in Figure 7. We can see that the mean offsets are limited to the centimeter level, and the most significant mean offset is \(-7.5\) cm in the eighth experiment. The final results are listed in Table 3.  
We may use several days of data to estimate the height difference in practical applications. For instance, we can improve the final results after taking the average of ten different experiments conducted in different periods (e.g., continuous ten days, everyday from 6:00 to 7:30). We may also conduct the experiment via several satellites, such as communication satellites and GNSS satellites, as long as the satellites can simultaneously connect with Qingdao and San Francisco. This could further improve the robustness of the height datum difference result. In the future, we can set up appropriate equipment on multiple satellites  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Experiment** & **Height Diff. between China’s** & **Offset to True** & **STD** \\
**No.** & **VHS and the US’ VHS (m)** & **Value (1 m)** & **(m)** \\ \hline
1 & 0.964 & \(-0.036\) & 0.121 \\
2 & 1.072 & 0.072 & 0.133 \\
3 & 0.998 & \(-0.002\) & 0.128 \\
4 & 0.965 & \(-0.035\) & 0.116 \\
5 & 1.005 & 0.005 & 0.119 \\
6 & 0.992 & \(-0.008\) & 0.118 \\
7 & 1.014 & 0.014 & 0.118 \\
8 & 0.925 & \(-0.075\) & 0.124 \\
9 & 1.049 & 0.049 & 0.126 \\
10 & 1.027 & 0.027 & 0.124 \\ \hline Average & 1.001 & 0.001 & 0.123 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The results of 10 simulation experiments. Relevant parameters are listed in Table 1.  
Figure 7: The mean offset values and STD values of the height datum difference from 10 different simulation experiments.  
orbiting the Earth and establish continuous SFST links with major benchmark stations on Earth to measure the height differences between stations. This overlapping observation at multiple time periods and from multiple satellites can significantly improve the precision and reliability of the results, thereby achieving centimeter-level high-precision global height system unification.