# Study of Fast and Reliable Time Transfer Methods Using Low Earth Orbit Enhancement
## 4 Example Analysis
### Analysis of LEO-Augmented GPS Time Transfer Convergence Performance
(**a**) The first-order difference results of the clock offset sequence for the area station, (**b**) The first-order difference results of the clock offset sequence for the hard station, (**c**) The first-order difference results of the clock offset sequence for the ons1 station. Figure 5: Receiver clock offset convergence time. Figure 3: Receiver clock offset time series of stations (black denotes GPS alone; blue, GPS + LEOs. was determined. The results are presented in Figure 7. The first-order difference of the clock offset clearly showed faster convergence after LEO enhancement. The results of the convergence time calculations are presented in Table 5 and Figure 8.  
Figure 6: Time transfer link clock offset time series (black denotes GPS alone; blue GPS + LEOs). (**a**) The clock offset sequence of the areg-mci time transfer link, (**b**) The clock offset sequence of the gold-piel time transfer link, (**c**) The clock offset sequence of the pie1-ons1 time transfer link, (**d**) The clock offset sequence of the ons1-bor1 time transfer link, (**e**) The clock offset sequence of the bor1-usud time transfer link, (**f**) The clock offset sequence of the kiru-dlf1 time transfer link, (**g**) The clock offset sequence of the dlf1-harb time transfer link, (**h**) The clock offset sequence of the harb-sydn time transfer link, (**i**) The clock offset sequence of the kiru-syog time transfer link, (**j**) The clock offset sequence of the ohi2-syog time transfer link. sequence for the gold-piel time transfer link, (**c**) The first-order difference results of the clock offset sequence for the piel-ons1 time transfer link, (**d**) The first-order difference results of the clock offset sequence for the ons1-bor1 time transfer link, (**e**) The first-order difference results of the clock offset sequence for the bor1-usud time transfer link, (**f**) The first-order difference results of the clock offset sequence for the kiru-dlf1 time transfer link, (**g**) The first-order difference results of the clock offset sequence for the dlf1-harb time transfer link, (**h**) The first-order difference results of the clock offset sequence for the harb-sydn time transfer link, (**i**)The first-order difference results of the clock offset sequence for the kiru-syog time transfer link, (**j**) The first-order difference results of the clock offset sequence for the ohi2-syog time transfer link. The convergence speed of the time transfer link constructed by the rubidium clock link and the hydrogen-cesium hybrid clock group was the slowest. The performance of the rubidium clock link was consistent with the convergence speed of the receiver clock offset, which reflected the atomic clock performance. The kiru-dif1 link had the greatest increase in convergence speed among the cesium atomic clock links and was the link with the shortest baseline length among the four cesium atomic clock links. In the hydrogen atomic clock link, convergence time was consistently within four minutes. Therefore, LEO-augmented PPP exhibited different convergence speed improvements in time transfer links with different atomic clock and baseline lengths. There were no significant differences among time transfer links at different latitudes because the LEO constellations had wide latitude coverage. Thus, there was no significant latitude difference in the convergence speed of clock offsets in the LEO-augmented PPP time transfer links. Figure 8: Time transfer link convergence time histogram. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Links** & **GPS** & **GPS + LEO** &
\begin{tabular}{c} **Percentage of** \\ **Improvement** \\ \end{tabular} \\ \hline areg-mcl & 4.5 & 3 & 33.3\% \\ gold-piel & 11.5 & 4 & 65.2\% \\ piel-ons1 & 11.5 & 4 & 65.2\% \\ ons1-bor1 & 2.5 & 1.5 & 40.0\% \\ borl-usud & 6 & 2 & 66.7\% \\ kiru-dif1 & 13 & 3.5 & 73.1\% \\ dlf1-harb & 11 & 6 & 45.5\% \\ harb-sydn & 11 & 6 & 45.5\% \\ kiru-syog & 3.5 & 2 & 42.9\% \\ ohi2-syog & 6 & 4 & 33.3\% \\ \hline \hline \end{tabular}
\end{table}