# A Precise and Stable Space-Based Time System for Navigation in Smart Cities
## 5 Evaluation Results
### Space-Based Time System Stability Evaluation
In other words, the relative clock offset data of the inter-satellite link within 1 min can complete the connection of the entire constellation. Therefore, the centralized prediction of the clock offset parameters of all constellation satellites can be completed by using the relative clock offset of all Ka links within 1 min. Due to the short duration, the influence of satellite clock drift is negligible. To avoid over-parameterization, only the \(A_{0}\) and \(A_{1}\) parameters are estimated for each satellite every minute. The relative clock offset parameters of all links within 1 min of the 18 MEO + 1 GEO + 1 anchor station are used to estimate the centralized clock offset parameters. The sliding window is 1 min, and the reference time is the starting time of each minute. Table 4 shows the link residual RMS value based on satellite statistics. It can be seen from the table that, according to satellite statistics, the maximum residual RMS of 1-min centralized clock offset estimation is 0.251 ns, the minimum is 0.081 ns, and the average is about 0.143 ns. The evaluation takes the parameter \(A_{0}\) sequence of each satellite as the satellite clock offset sequence sampled in 1 min and compares it with the satellite clock offset obtained by the satellite-ground inter-satellite joint method and anchor satellite method. The comparison is carried out by the second-order polynomial fitting. The fitting residuals are compared in Figure 4.  
In Figure 4, C19 on the left is a medium-Earth-orbit (MEO) satellite, and C59 on the right is a geostationary (GEO) satellite. The red curve in the figure is the satellite clock offset fitting residual sequence obtained by the satellite-ground inter-satellite joint method, the blue curve is the satellite clock offset fitting residual sequence obtained by the centralized clock offset estimation method, and the green curve is the sequence obtained by direct observations between the satellite and the anchor station. The following conclusions can be drawn from the figure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellite Number** & **Residual RMS** & **Satellite Number** & **Residual RMS** \\ \hline C19 & 0.12 & C29 & 0.19 \\ C20 & 0.11 & C30 & 0.16 \\ C21 & 0.16 & C32 & 0.15 \\ C22 & 0.13 & C33 & 0.12 \\ C23 & 0.22 & C34 & 0.16 \\ C24 & 0.10 & C35 & 0.13 \\ C25 & 0.19 & C36 & 0.19 \\ C26 & 0.25 & C37 & 0.09 \\ C27 & 0.15 & C59 & 0.10 \\ C28 & 0.16 & Anchor station & 0.08 \\ \hline Average & **0.14** & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The residual statistics of 1-min centralized inter-satellite clock offset parameter estimation (unit: ns). For MEO satellites, the satellite clock offset fitting residual accuracy obtained by the centralized clock offset estimation parameter sequence is higher than the one obtained by the satellite-ground inter-satellite joint method. The clock offset monitoring arc coverage is much higher than that of the direct observation between the satellite and anchor station. 2. For GEO satellites, the satellite clock offset obtained by the satellite-ground inter-satellite joint method is all L-band satellite-ground two-way time-frequency transfer clock offset. Since the GEO satellites are continuously visible, the three clock offset monitoring arc coverage is basically the same. 3. As for the noise level, the satellite clock offset noise of the L-band satellite-ground two-way time-frequency transmission is the smallest, followed by the satellite clock offset obtained by the direct observation of the anchor station, and the satellite clock offset obtained by the centralized clock offset estimation is slightly louder. The fitting residual statistics of the above three clock offsets are shown in Table 5. Due to the particularity of GEO satellites, only 18 MEO satellites are averaged. It can be seen from the table that using the satellite-ground inter-satellite joint method, the mean value of the RMS of the 24-h clock offset fitting residual of the MEO satellite is 0.42 ns.