# A Precise and Stable Space-Based Time System for Navigation in Smart Cities
## 6 Conclusions  
As an important national infrastructure that provides all-weather, all-day, high-precision positioning, navigation, and timing services for global users, it is crucial to research a precise and stable navigation constellation space-based time system to better  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Satellite Number**} & \multicolumn{2}{c}{**Satellite-Ground**} & \multirow{2}{*}{**Anchor Station**} & \multirow{2}{*}{**Centralized**} \\  & & **and Inter-Satellite** & & **Observation** & **Estimation** \\ \hline C19 & 0.23 & 0.16 & 0.22 \\ C20 & 0.53 & 0.09 & 0.21 \\ C21 & 0.51 & 0.07 & 0.28 \\ C22 & 0.30 & 0.08 & 0.18 \\ C23 & 0.67 & 0.08 & 0.21 \\ C24 & 0.37 & 0.08 & 0.22 \\ C25 & 0.35 & 0.12 & 0.24 \\ C26 & 0.28 & 0.08 & 0.24 \\ C27 & 0.33 & 0.12 & 0.19 \\ C28 & 0.48 & 0.09 & 0.17 \\ C29 & 0.36 & 0.09 & 0.17 \\ C30 & 0.11 & 0.07 & 0.24 \\ C32 & 0.49 & 0.09 & 0.19 \\ C33 & 0.48 & 0.08 & 0.17 \\ C34 & 0.49 & 0.13 & 0.17 \\ C35 & 0.65 & 0.08 & 0.22 \\ C36 & 0.49 & 0.09 & 0.19 \\ C37 & 0.41 & 0.08 & 0.23 \\ C59 & 0.13 & 0.15 & 0.22 \\ \hline \multicolumn{3}{c}{The average value of} \\ \multicolumn{3}{c}{MEO satellites} & \multicolumn{1}{c}{0.42} & \multicolumn{1}{c}{0.09} & \multicolumn{1}{c}{**0.21**} \\ \hline \hline \end{tabular}
\end{table}
Table 5: The RMS values of satellite clock offset prediction error through different methods.  
support smart city applications such as transportation, route planning, and self-driving cars. The purpose of establishing the space-based integrated atomic time of the navigation constellation is to obtain a stable and real-time space-based time reference, improve the system's timekeeping accuracy, and reduce the dependence on the ground.  
This paper proposes a space-based time system established under the autonomous time scale of navigation satellites. It consists of the establishment process, a centralized time comparison method based on the two-way time comparison of the inter-satellite link, the elimination of the magneto-frequency shift effect of space-borne atomic clocks, and the space-based integrated atomic time algorithm realized based on the ALGOS algorithm. As summarized in Table 6, simulations conducted on real collected Beidou navigation systems when providing services to smart cities around the world show the high accuracy and stability of the centralized estimation time system compared with the widely used anchor-based estimation. Moreover, the clock offset monitoring arc coverage is satisfied. Thus, the centralized estimation adopted in this paper has the potential to be used for satellite clock offset modeling and centralized clock offset prediction accuracy assessment for the next generation of navigation constellations.  
**Author Contributions:** Conceptualization, S.L., B.L., R.L. and R.D.; methodology, S.L. and X.H.; software, S.L. and X.H.; validation, S.L.; formal analysis, S.L.; investigation, S.L. and X.H.; resources, S.L.; data curation, S.L.; writing--original draft preparation, S.L. and R.L.; writing--review and editing, B.L., R.L. and R.D.; visualization, S.L.; supervision, B.L.; project administration, S.L.; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Youth Innovation Promotion Association of Chinese Academy of Sciences OF FUNDER grant number 2021292.  
**Conflicts of Interest:** The authors declare no conflicts of interest.