# A Precise and Stable Space-Based Time System for Navigation in Smart Cities
## 5 Evaluation Results
### Space-Based Time System Stability Evaluation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Anchor Station Reference**} & \multicolumn{2}{c}{**Autonomous Time Scale Reference**} \\ \cline{2-5}
**Satellite Number** & **10,000-s** & **Day Stability** & **10,000-s** & **Day Stability** \\  & **Stability** & **Day Stability** & **Stability** & **Day Stability** \\ \hline C25 & \(2.50\times 10^{-14}\) & \(9.92\times 10^{-15}\) & \(1.39\times 10^{-14}\) & \(6.52\times 10^{-15}\) \\ C26 & \(2.52\times 10^{-14}\) & \(8.32\times 10^{-15}\) & \(1.48\times 10^{-14}\) & \(2.67\times 10^{-15}\) \\ C27 & \(2.50\times 10^{-14}\) & \(7.83\times 10^{-15}\) & \(1.48\times 10^{-14}\) & \(1.93\times 10^{-15}\) \\ C28 & \(2.96\times 10^{-14}\) & \(8.37\times 10^{-15}\) & \(2.30\times 10^{-14}\) & \(2.53\times 10^{-15}\) \\ C29 & \(2.67\times 10^{-14}\) & \(7.80\times 10^{-15}\) & \(1.47\times 10^{-14}\) & \(1.95\times 10^{-15}\) \\ C30 & \(3.12\times 10^{-14}\) & \(8.12\times 10^{-15}\) & \(2.20\times 10^{-14}\) & \(2.58\times 10^{-15}\) \\ C59 & \(3.43\times 10^{-14}\) & \(1.03\times 10^{-14}\) & \(2.62\times 10^{-14}\) & \(6.91\times 10^{-15}\) \\ C20 & \(2.62\times 10^{-14}\) & \(1.49\times 10^{-14}\) & \(1.94\times 10^{-14}\) & \(1.39\times 10^{-14}\) \\ C21 & \(2.87\times 10^{-14}\) & \(1.75\times 10^{-14}\) & \(2.25\times 10^{-14}\) & \(1.42\times 10^{-14}\) \\ C22 & \(2.59\times 10^{-14}\) & \(1.13\times 10^{-14}\) & \(1.80\times 10^{-14}\) & \(1.05\times 10^{-14}\) \\ C23 & \(2.73\times 10^{-14}\) & \(1.41\times 10^{-14}\) & \(2.09\times 10^{-14}\) & \(7.87\times 10^{-15}\) \\ C24 & \(3.08\times 10^{-14}\) & \(1.20\times 10^{-14}\) & \(2.14\times 10^{-14}\) & \(6.65\times 10^{-15}\) \\ C32 & \(2.16\times 10^{-14}\) & \(6.93\times 10^{-15}\) & \(1.31\times 10^{-14}\) & \(4.22\times 10^{-15}\) \\ C33 & \(2.74\times 10^{-14}\) & \(1.52\times 10^{-14}\) & \(2.08\times 10^{-14}\) & \(1.06\times 10^{-14}\) \\ C34 & \(2.39\times 10^{-14}\) & \(1.13\times 10^{-14}\) & \(1.34\times 10^{-14}\) & \(8.54\times 10^{-15}\) \\ C35 & \(2.74\times 10^{-14}\) & \(1.02\times 10^{-14}\) & \(1.79\times 10^{-14}\) & \(5.37\times 10^{-15}\) \\ C36 & \(2.54\times 10^{-14}\) & \(7.79\times 10^{-15}\) & \(1.99\times 10^{-14}\) & \(5.29\times 10^{-15}\) \\ C37 & \(2.47\times 10^{-14}\) & \(8.64\times 10^{-15}\) & \(1.47\times 10^{-14}\) & \(6.40\times 10^{-15}\) \\ \hline The average & & & & \\ value of the & \(2.81\times 10^{-14}\) & \(\textbf{8.67}\times 10^{-15}\) & \(1.85\times 10^{-14}\) & \(\textbf{3.59}\times 10^{-15}\) \\ hydrogen clock & & & & \\ \hline The average & & & & \\ value of the & \(2.63\times 10^{-14}\) & \(\textbf{1.18}\times 10^{-14}\) & \(1.84\times 10^{-14}\) & \(\textbf{8.51}\times 10^{-15}\) \\ rubidium clock & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The RMS values of satellite clock offset prediction error under different references. Figure 3: The Allan deviation and Hadamard deviation of space-based time system stability under anchor station reference (PHMs) and autonomous time scale reference (RAFSs). Based on the above results, it is reasonable that the frequency stability of autonomous time scales is higher than that of anchored station clocks. Furthermore, the Allan variance of the anchor station clock is evaluated by the clock offset of the anchor station relative to the autonomous time scale, and the results are shown in Figure 3c. The 10,000-s stability of the anchored station clock estimated by this method is about \(2.1\times 10^{-14}\), and the day stability is about \(7.6\times 10^{-15}\). Smoothing the time to the day, the stability of the space-borne hydrogen clock and some rubidium clocks is better than that of the anchor station clock. This also explains the phenomenon that the Allan variance curves of satellite clocks are difficult to distinguish under the anchor station reference. Accuracy Evaluation of the Proposed Centralized Two-Way Time Comparison Method Based on the Inter-Satellite Link  
The Beidou-3 satellite takes 1 min as a unit to complete the link establishment of different inter-satellite links.