# 100 Picosecond/Sub-10\({}^{-17}\) Level GPS Differential Precise Time and Frequency Transfer
## 5 DPT Time and Frequency Transfer Validations
### DPT Time Transfer in a Common Clock  
Data from two independent receivers, USN7 and USN8, are being operated at the United States Naval Observatory (USNO) in Washington, DC, using a common reference clock that is regularly calibrated using GPS time transfer. As the time transfer solution of the two stations is expected to constant and known, it is relatively easy to evaluate the expected results of DPT.  
To verify the accuracy of the DPT time difference, we conducted time transfer experiments on the USN7 and USN8 stations and performed daily re-initialization. We collected 7 days' CV time transfer results during MJD 59,764.0-59,770.0, as shown in Figure 5. For the estimated time difference over these 7 days, the standard deviation (STD) for the C1 code was 939 ps and for the P2 code it was 88 ps. As expected, it is well known that the precision of the P code is ten times that of the C1 code due to its narrower code chip width. Since the initial value of DPT time transfer depends on pseudorange time transfer, the accuracy of CV time transfer for different codes will affect DPT time transfer.  
The DPT time transfer results are shown in Figure 6. Note that the results have been calibrated using the calibration results published by BIPM, as shown in Table 3, by subtracting the time delays associated with the stations CAB, REF, and INT, along with their respective uncertainties [26]. The calculation is as follows:  
\[\Delta t(f)=t(f)-\left\{TOT(f)\right._{USN7}-TOT(f)_{USN8}\}\to 0 \tag{13}\]  
where \(f\) represents the L1 frequency or L2 frequency, \(t(f)\) represents the DPT solution, and \(TOT(f)\) represents the total time delay of a geodetic system for frequency \(f\), which is divided into six different parts, including antenna delay, antenna cable delay, receiver internal delay, short cable and splitter delay, internal reference delay, and 1 PPS delay [27].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station** & **TOT (C1)** & **TOT (P2)** & **Calibration Uncertainties** \\ \hline USN7 & 155.6 & 149.3 & 1.2 \\ USN8 & 202.6 & 197.4 & 1.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The calibration values for data from the BIPM Time Department’s published GPS calibration results (ns) [26].  
Figure 5: CV time transfer results using pseudorange measurements for USN7-USN8.  
For the time difference solutions estimated for 7 days in Figure 6, the STD and mean results of the GPS DPT and CV time transfer daily solutions after convergence are shown in Table 4. The STDs of the converged time difference for the GPS L1 and L2 frequencies were 18 ps and 4 ps, respectively. As expected, due to the heavy noise level in the C1 code, time transfer relying on the C1 code requires a long time to converge, making it difficult to determine the absolute time for DPT with high precision. Meanwhile, the estimated time difference solutions for the 7 days had mean convergence values of 291 ps for GPS L1 frequency and 70 ps for the GPS L2 frequency. As a time transfer experiment, the time difference solution between the USN7 and USN8 stations should be zero in theory, and the closure of the two stations shows the accuracy of the DPT time transfer. In Figure 6, there is a constant difference of about 300 ps using the C1 code. This difference may be due to uncertainties of DPT solution or the calibration uncertainties from BIPM, or the combination of DPT and the calibration. Furthermore, we validate the time transfer of DPT through closure experiments in the next sub-section.