# 100 Picosecond/Sub-10\({}^{-17}\) Level GPS Differential Precise Time and Frequency Transfer
## 4 Single-Difference Ambiguity Analysis  
The float SD carrier-phase ambiguity of the reference satellite can be obtained by using Equation (3). We took each visible satellite as a reference satellite separately and estimated the L1 and L2 SD ambiguities of the reference satellites. For the KOKV-KOVB baseline, the fractional part of the SD ambiguity of the reference satellite is shown in Figure 1. Note that KOKV-KOVB is the zero baseline. For the baseline of ONSA-SPT0 with a length of 67 km, the fractional part of the reference satellite SD ambiguity is shown in Figure 2. It is believed that when the peak-to-peak value of the SD carrier-phase ambiguity fractional part time series is less than 1/3 cycles and it remains stable in subsequent epochs, the integer ambiguity can be determined. As shown in the upper panel of Figure 1, the L1 SD carrier-phase ambiguities of eight visible satellites were obtained using the L1 carrier phase and the C1 code in MJD 59,764. It can be clearly seen that within 25 epochs (12.5 min for 30 s simple intervals), the peak-to-peak values of the L1 SD carrier-phase ambiguity fractional parts time series are less than 1/3 cycles, and the converged carrier-phase ambiguities remain stable in subsequent epochs. The bottom panel of Figure 1 plots the SD carrier-phase ambiguities obtained using the L2 carrier phase and the P2 code and shows the convergence of the solutions. It took 8 min to reduce the peak-to-peak values of the L2 SD carrier-phase ambiguity fractional parts time series to less than 1/3 cycles. In addition, for the ONSA-SPT0 baseline in Figure 2, it can be observed that the IF SD carrier-phase ambiguities for each visible satellite were resolved within 40 min. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Baseline** & **Receiver (B)** & **Antenna (B)** & **Receiver (U)** & **Antenna (U)** & **Distance (km)** \\ \hline USN7-USN8 &
\begin{tabular}{c} SEPT \\ POLARX5 TR \\ \end{tabular} & TPSCR.G5 & SEPT POLARX5 TR & TPSCR.G5 & 0 \\ NYA1-NYA2 & TRIMBE NETR8 & ASH701073.1 & SEPT POLARX5 & JAVRING & 0.17 \\ NYA2-NYAL & SEPT POLARX5 & JAVRINGANT\_G5 TRIBBLE NETR9 & AOAD/M\_B & 0.16 \\ NYAL-NYA1 & TRIMBE NETR9 & AOAD/M\_B & TRIMBE NETR8 & ASH701073.1 & 0.007 \\ KOKV-KOVB & JAVAD TRE\_G3 TH & ASH701945G\_M & SEPT POLARX5 TR & ASH7019 & 0 \\  & DELTA & & & 45G\_M & \\ CEBR-VILL & SEPT POLARX5 TR & SEPCHO & SEPT POLARX5 & SECTION & 35.30 \\  & KE\_B3E6 & & KE\_B3E6 & & \\ KOUR-KOUG & SEPT POLARX5 TR & LEIAR25.R3 & SEPT POLARX5 & SECTION & 25.07 \\ ONSA-SPT0 & SEPT POLARX5 TR & AOAD/M\_B & SEPT POLARX5 TR & TRM59800.00 & 67.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the eight baselines (B and U represent the base and user stations, respectively). \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Data Processing** \\ \hline Observation types & GPS L1, L2, C1, P2 \\ Sample rate & 30 s \\ Data period & 30 days, from Modified Julian Date (MJD) 59,764.0–59,793.0 \\ Tropospheric delay & Saastamoinen (dual frequency) \\ Ionospheric delay & IGS global ionosphere maps (single frequency) \\  & IF combination (dual frequency) \\ Cut-off angle & 10\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of DPT data processing. After determining the SD integer ambiguity of the reference satellite and the DD integer ambiguity, we used each visible satellite as a reference satellite to obtain the SD integer ambiguity of the other visible satellites by Equation (6). Figure 3 plots the L1 and L2 SD ambiguities of G07, G08, G10, G13, G18, G24, G27, and G28 for KOKV-KOVB. It is known that the ambiguity of each visible satellite remains continuous as long as the carrier-phase observation is continuously observed. It can be observed that the estimated SD ambiguities differ depending on the reference satellite used. Taking G18 as an example, when using five different satellites as a reference, the estimated L1 SD ambiguities were 6.