# 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  
Three representative stations, namely areg, harb, and ons1, were selected to analyze the receiver clock offset calculated by LEO-augmented PPP. The three stations--areg, harb, and ons1--used rubidium, cesium, and hydrogen, respectively, as their clock frequencies. The first 30 min receiver clock offsets of the three stations are shown in Figure 3a-c, and the first-order difference results of the clock offsets are shown in Figure 4a-c. In the calculation, the three stations involved an average of eight low-orbit satellites. According to the clock offset variation diagram of the three stations, receiver clock offsets converge faster under LEO enhancement than under the sole GPS. To quantify the convergence time, by calculating the first-order difference of the receiver clock offset, the mean and standard deviation were calculated using the converged first-order difference data, and the convergence confidence interval was obtained by adding and subtracting the mean from two times the standard deviation. The convergence criterion was that the first-order difference result of the receiver clock offset should be within the range of the convergence confidence interval for 10 min. The red lines in Figure 4a-c represent the boundaries of the convergence confidence interval. The results of the statistical convergence time calculation are presented in Table 4 and Figure 5. According to the statistics, the convergence period was significantly shorter compared to processing sole GPS data and moreover significantly different at the three stations. The convergence speed increased the most (65.0%) at station harb, with its cesium clock; second-most (50.0%) at station ons1, with its hydrogen clock; and least (18.8%) at station area, with its rubidium clock. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station** & **GPS** & **GPS + LEO** & \begin{tabular}{c} **Percentage of** \\ **Improvement** \\ \end{tabular} \\ \hline \begin{tabular}{c} areg \\ harb \\ ons1 \\ \end{tabular} & \begin{tabular}{c} 8 \\ 10 \\ \(11\) \\ \end{tabular} & \
\begin{tabular}{c} 6.5 \\ 3.5 \\ 5.5 \\ \end{tabular} &
\begin{tabular}{c} 18.8\% \\ 65.0\% \\ 50.0\% \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Receiver clock offset convergence time improvement (min). \begin{table}
\begin{tabular}{c c} \hline \hline
**Type** & **Descriptions** \\ \hline \begin{tabular}{c} Data sources \\ Data characteristics \\ \end{tabular} & \begin{tabular}{c} GPS, LEO \\ GPS is measured data \\ LEO is analogue data \\ \end{tabular} \\ \
\begin{tabular}{c} Type of observation \\ Frequency \\ \end{tabular} &
\begin{tabular}{c} Pseudorange and phase observations \\ L1, L2 \\ 70 satellites in polar orbit and 90 satellites in \\ inclined orbit \\ 1000 km \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data introduction. In light of the aforementioned conclusions, it can be posited that the receiver clock offset obtained by LEO-augmented PPP can effectively enhance convergence speed. The clock offset of a time transfer link calculated for the established 10 links are shown in Figure 5. The time transfer link clock offset had the same performance as the receiver clock offset. The time transfer link achieved using LEO-augmented PPP exhibited a faster performance compared to that attained by the GPS system (Figure 6). Concurrently, the 10 links had different latitude distributions, baseline lengths, and clock sources. Although the different time transfer links had different characteristics, they exhibited similar performances. A first-order differential calculation was applied to the clock offset sequence of the time transfer link, and the convergence confidence interval  
Figure 4: The first-order difference of the receiver clock offset time series of the stations (black denotes GPS alone; blue, GPS + LEOs).