# 100 Picosecond/Sub-10\({}^{-17}\) Level GPS Differential Precise Time and Frequency Transfer
## 5 DPT Time and Frequency Transfer Validations
### Long-Term DPT Time and Frequency Transfer Validations  
We analyzed the common clock experiment between USN7 and USN8 and the three stations' baseline closure test and verified that DPT can accurately determine the initial value of DPT time transfer. In addition, we also selected four baselines, CEBR-VILL, ONSA-SPT0, KOUR-KOUG, and KOKV-KOVB, for continuous time transfer and further considered the long-term performance of DPT. Table 1 presents the details of the four baselines. To remove the trend effects of the time difference between two station clocks, a common reference time is introduced to subtract the inconsistency between the two clocks. Typically, IGS final station clock solutions are used as the reference times due to their precision of 20 ps (STD) [28]. The data sampling rate of the IGS final station clock solutions is 5 min. In order to better compare with the reference, the time difference solution of DPT is also set with a sampling interval of 300 s. The result of DPT is then:  
\[Time\ transfer=(T_{A}-T_{B})-(IGST_{A}-IGST_{B}) \tag{15}\]  
Figure 9 displays the time differences between different L1 and L2 frequencies and the dual-frequency IF combination DPT for four different baselines. It should be noted that none of the four baselines were calibrated and that a constant offset was added to each curve for comparison. It can be seen that the time difference estimated by the five curves shows the same trend. Among them, the KOKV-KOKB baseline was processed using single-frequency L1 or L2 time transfer, with STDs of 18 ps (the L1 frequency for KOKV-KOKB (L1)) and 17 ps (the L2 frequency for KOKV-KOKB (L2)) over a period of 30 days. The reason why the time difference results of the DPT time transfer are so flat is that the initial value of DPT time transfer depends on pseudorange time transfer, and  
Figure 8: The mean results of the three stations’ closure for the DPT daily solutions from MJD 59,764 to 59,770. Figure 7: Three stations’ closure. The closure is achieved by adding together the baselines of “NYA1-NYA2”, “NYA2-NYAL”, and “NYAL-NYA1”. after this initial value is determined, only the carrier phase is used, so the noise in the code is well eliminated. As the baseline distance between the reference station and the user station increases, the DD atmospheric delay cannot be ignored. Therefore, the CEBR-VILL, KOUR-KOUG, and ONSA-SPT0 baselines were processed using the dual-frequency IF combination, with STDs of 69, 75, and 94 ps, respectively. Compared with single-frequency processing, the IF combination used here amplifies the noise to a certain extent, especially for the ONSA-SPT0 baseline shown in Figure 9.  
From the above, we analyzed the long-term time transfer performance of DPT of four baselines, CEBR-VILL, ONSA-SPT0, KOUR-KOUG, and KOKV-KOVB. For the evaluation of frequency stability, compared with Allan deviation, modified Allan deviation (MDEV) has the advantage of distinguishing white and flickering phase modulation noise and is often used for frequency stability evaluation [29]. In addition, time deviation (TDEV) is used to characterize the time stability of time links [30]. In this work, we used TDEV and MDEV to analyze the time and frequency stability of DPT, respectively, which were obtained using the Stable32 software [31]. Smaller MDEV and TDEV values indicate better time and frequency stability. Figures 10 and 11 show the stability results of MDEV and TDEV for the four baselines. As shown in Figure 10, the single frequency DPT has an MDEV of \(9\times 10^{-17}\) at an averaging time of 1 day and \(3\times 10^{-18}\) at an averaging time of 7 days. The IF DPT has an MDEV of \(3\times 10^{-16}\) at an averaging time of 1 day and \(2\times 10^{-17}\) at an averaging time of 7 days. Figure 11 shows that the time stability of the IF DPT is less than 20 ps for an averaging time of 1 day, especially less than 10 ps within 7 days. As for the single-frequency DPT, the time stability is less than 4 ps for an averaging time of 1 day and approaches 1 ps within 7 days.