## 4 Data Processing  
According to Equations (8) and (9), the geopotential difference between QDDS and SFDS, \(\Delta\hat{W}_{QD-SF}(t)\), can be measured as a time series  
\[\Delta\hat{W}_{QD-SF}(t)=\Delta\hat{y}_{QD-s}(t)-\Delta\hat{y}_{SF-s}(t)+(Z_{SF}- Z_{QD}), \tag{14}\]  
where \(\Delta\hat{y}_{QD-s}(t)\) and \(\Delta\hat{y}_{SF-s}(t)\) are, respectively, the observed gravitational potential differences between QDDS and the satellite as well as between SFDS and the satellite at time \(t\), and \(Z_{QD}\) and \(Z_{SF}\) are the centrifugal force potentials of QDDS and SFDS, respectively. The observed values \(\Delta\hat{W}_{QD-SF}(t)\) are different from the true geopotential difference \(\Delta W_{QD-SF}\), because various error sources influence them. In this simulation experiment, we considered the clock error \(e_{clk}\), ionosphere residual error \(e_{ion}\), troposphere residual error \(e_{tro}\), and the satellite position and velocity errors \(e_{pos}\) and \(e_{vel}\), tidal correction residual error \(e_{tide}\), and asynchronism error \(e_{asy}\). We expect that \(\Delta\hat{y}_{QD-s}(t)\) and \(\Delta\hat{y}_{SF-s}(t)\) are measured at the same time \(t\), but in practice, they might have slight differences, which will introduce the asynchronism error. The above-mentioned various errors are regarded as noise which is added to the true values. The total errors \(e_{all}\) are expressed in the following form:  
\[e_{all}=e_{clk}+e_{ion}+e_{tro}+e_{pos}+e_{vel}+e_{tide}+e_{asy}, \tag{15}\]  
The magnitude and behavior of each type of error play important roles in this experiment. Therefore, it is necessary to investigate error models based on these sources to ensure that the simulation accurately reflects the real-world scenario. Currently, precise OACs have achieved a stability of \(4.8\times 10^{-17}\) at 1 s and \(6.6\times 10^{-19}\) in 1 h for a two clock comparison [19]; therefore, we set the error magnitude of \(e_{clk}\) as \(4.8\times 10^{-17}\). Although many kinds of random noises affect OAC signals [53], the most prominent components are white frequency modulation and random walk frequency modulation [54]. Correspondingly, the behaviors of clock errors are modeled as the following equation:  
\[e_{clk}(t)=a_{clk}+b_{clk}\cdot t+c_{clk}\cdot\phi(t)+d_{clk}\cdot\int_{0}^ {t}\xi(t)dt, \tag{16}\]  
where \(a_{clk}\), \(b_{clk}\), \(c_{clk}\), and \(d_{clk}\) are constant coefficients, and \(\phi(t)\) and \(\xi(t)\) are both standard white Gaussian noise. Each term on the right side of Equation (16) has a clear physical meaning; specifically, \(a_{clk}\) denotes the initial frequency difference, \(b_{clk}\cdot t\) is the drift term, \(c_{clk}\cdot\phi(t)\) is the white noise component, and \(d_{clk}\cdot\int_{0}^{t}\xi(t)dt\) represents the random \begin{table}
\begin{tabular}{l l l} \hline \hline
**Entities** & \multicolumn{2}{c}{**Values of Parameters**} \\ \hline Satellite & ID & SVN-56 (GPS Navigation Sat.) \\  & Coord. & from (\(-\)19,167.235509, 3652.729794, 18,038.749481) \\  & to (\(-\)26,493.102586, 424.868408, 3830.004962) \\ Qingdao DS & LLA & (36.06974\({}^{*}\)N, 120.32172\({}^{*}\)E, 77.472 m) \\  & ECEF (m) & (\(-\)2,605,813.108, 4,455,436.499, 3,734,494.956) \\  & OH (m) & 72.260 \\ San Francisco DS & LLA & (37.76985\({}^{*}\)N, 122.46616\({}^{*}\)W, 75.878 m) \\  & ECEF(m) & (\(-\)2,709,867.959, \(-\)4259189.792, 3,885,328.909) \\  & OH (m) & 109.126 \\ Gravity field model & \multicolumn{2}{c}{EGML2008} \\ Ionospheric model & \multicolumn{2}{c}{International Reference Ionosphere} \\ Tropospheric model & \multicolumn{2}{c}{Global Pressure and Temperature} \\ Tide correction & \multicolumn{2}{c}{Tidal Potential} \\ Observation duration & \multicolumn{2}{c}{from 6:00 a.m. to 7:30 a.m., 1 March 2023,} \\ Measurement interval & \multicolumn{2}{c}{5 s} \\ Height systems diff. & \multicolumn{2}{c}{1.000 m (China HS is higher than US HS)} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The input data used in the simulation experiments. The coordinates are based on ITRF14 walk effect.