# A Precise and Stable Space-Based Time System for Navigation in Smart Cities
## 5 Evaluation Results
### Satellite Clock Offset Prediction Error  
The primary goal of establishing a space-based time system is to serve users in various scenarios, such as smart cities. Therefore, it is crucial to evaluate the accuracy of the satellite broadcast clock parameters. The satellite clock offset prediction is traditionally calculated under the anchor station scale. However, this paper proposes to conduct the satellite clock offset prediction under the autonomous time scale. The evaluation strategy includes both short-term and long-term predictions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Satellite** & \begin{tabular}{c} **Anchor** \\ **Station** \\ **Reference** \\ \end{tabular} & \begin{tabular}{c} **Autonomous** \\ **Time Scale** \\ **Reference** \\ \end{tabular} & \begin{tabular}{c} **Satellite** \\ **Number** \\ **Reference** \\ \end{tabular} & \
\begin{tabular}{c} **Anchor** \\ **Station** \\ **Reference** \\ \end{tabular} &
\begin{tabular}{c} **Autonomous** \\ **Time Scale** \\ **Reference** \\ \end{tabular} \\ \hline C25 & 0.61 & 0.33 & C22 & 0.35 & 0.48 \\ C26 & 0.40 & 0.14 & C23 & 0.78 & 0.42 \\ C27 & 0.43 & 0.10 & C24 & 0.56 & 0.31 \\ C28 & 0.40 & 0.13 & C32 & 0.42 & 0.17 \\ C29 & 0.38 & 0.10 & C33 & 0.70 & 0.40 \\ C30 & 0.43 & 0.16 & C34 & 0.40 & 0.39 \\ C59 & 0.62 & 0.43 & C35 & 0.42 & 0.20 \\ C20 & 0.82 & 0.58 & C36 & 0.36 & 0.21 \\ C21 & 0.62 & 0.56 & C37 & 0.39 & 0.42 \\ Average & & & Average & & \\ value of & & & value of & & \\ hydrogen & 0.47 & **0.20** & rubidium & 0.50 & **0.38** \\ clock & & & clock & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: RMS comparison of satellite clock offset fitting residuals under different references (unit: ns).  
Figure 2: Evaluation of clock offset fitting residuals for two satellites relative to anchor station (red) and to autonomous time scale (blue). (**a**) Fitting residual evaluation on satellite C27. (**b**) Fitting residual evaluation on satellite C36.  
In the short-term prediction, first-order polynomial fitting is applied to 2-h clock offset data to predict the next 2 h. The 2-h prediction error RMS is then analyzed. Conversely, the long-term prediction involves fitting on 48-h clock offset data. Hydrogen clocks and C34 use a first-order polynomial, while other rubidium clocks use a second-order polynomial. The 24-h clock offset data are further predicted, and the prediction error RMS is calculated accordingly. The short-term and long-term prediction accuracy of the satellite clock offset under the anchor station clock and the autonomous time scale are summarized in Table 2.  
The statistical results of the prediction error show that by converting the time reference from the anchor station clock to the autonomous time scale, the 2-h prediction error RMS of the satellite clock is decreased from 0.20 ns to 0.15 ns. The 24-h prediction error RMS of the hydrogen clock is decreased from an average of 1.07 ns to 0.45 ns, and the RMS prediction error of the rubidium clock in the 24 th h is decreased from an average of 1.98 ns to 1.40 ns. In summary, the satellite clock offset prediction demonstrates higher short-term and long-term accuracy under the autonomous time scale reference.