# Study of Fast and Reliable Time Transfer Methods Using Low Earth Orbit Enhancement
## 4 Example Analysis
### Stability Analysis of LEO-Augmented GPS Time Transfer  
For the sustained and dependable application of GNSS time transfer, the reliability of the clock offset in the time transfer link is of paramount importance. Considering that LEO-augmented PPP can improve the convergence speed of time transfer links, the standard deviation of the clock offset obtained by the two methods in the convergence interval was examined. As evident from the results presented in Table 6 and Figure 9, the standard deviation of the clock offset for the LEO-augmented time transfer link exhibited a marked improvement within the convergence interval, when compared to that of GPS. Therefore, LEO-augmented PPP provides a higher stability in the initial convergence period of time transfer and can better ensure the stability and reliability of real-time fast convergence time transfer.  
The time and frequency signals of the time transfer link are continuous. Time and frequency signals are not always fixed due to the influence of frequency source performance variation characteristics. However, this alteration has the same impact on the two data processing schemes [1], whether long-term or short-term. The Allan deviation is employed to assess the frequency stability of the time transfer clock offset sequence in the convergence time span. The Allan deviation results for each time transfer link are shown in Figure 10. The blue curve represents the Allan deviation obtained by the sole GPS time transfer scheme, and the orange curve represents the Allan deviation obtained by the GPS + LEO time transfer scheme. The Allan deviation obtained by the GPS + LEO time transfer scheme obviously shows a smaller variance. Thus, adding low-orbit satellites to the sole GPS data improves the frequency stability of the time transfer clock error sequence within  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time Transfer Link** & **GPS** & **GPS + LEO** & \begin{tabular}{c} **Percentage of** \\ **Improvement** \\ \end{tabular} \\ \hline \begin{tabular}{c} areg-mci \\ gold-piel \\ piel-ons1 \\ \end{tabular} & 0.491 & 0.358 & 27.1\% \\ \begin{tabular}{c} gold-piel \\ piel-ons1 \\ \end{tabular} & 0.228 & 0.047 & 79.3\% \\ \begin{tabular}{c} piel-ons1 \\ \end{tabular} & 0.226 & 0.064 & 71.9\% \\ \begin{tabular}{c} ons1-bor1 \\ bort-uusd \\ kiru-dlf1 \\ \end{tabular} & 0.302 & 0.133 & 55.9\% \\ \begin{tabular}{c} bort-uusd \\ kiru-dlf1 \\ \end{tabular} & 0.158 & 0.081 & 48.8\% \\ \begin{tabular}{c} dllf1-harb \\ \end{tabular} & 0.141 & 0.051 & 63.4\% \\ \
\begin{tabular}{c} harb-sydn \\ kiru-syog \\ \end{tabular} & 0.170 & 0.038 & 77.4\% \\
\begin{tabular}{c} kiru-syog \\ ohi2-syog \\ \end{tabular} & 0.108 & 0.098 & 8.9\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Standard deviation of time transfer link clock offset in the convergence interval (ns).  
Figure 9: Histogram of standard deviation of time transfer link clock offsets in the convergence interval.  
the convergence time range. The Allan deviation results for the 10 links were calculated and averaged. As depicted in Table 7, the frequency stability was improved after LEO enhancement over different sampling time intervals, with a minimum improvement of 25.7%. Consequently, within the time transfer convergence interval, LEO-enhanced PPP time transfer can effectively improve the frequency stability of the time transfer link's clock error sequence. The principal rationale is the fast geometry change in the low-orbit satellites, which allows for a faster and more stable estimation of the receivers' position and clock offset.  
Figure 10: The Allan deviation results of the time transfer link in the convergence interval.