# A BDGIM-Based Phase-Smoothed Pseudorange Algorithm for BDS-3 High-Precision Time Transfer
## 4 Results and Discussion
### Performance Evaluation of Phase-Smoothed Pseudorange SPP Time Transfer Based on BDGIM
The RMSs of the pseudorange residuals for the LCK3 station in scheme 1 and scheme 2 are 1.18 m and 0.97 m, respectively, reducing by 17.8%, which further indicates that the improved method enables better SPP performance. Figure 7: Receiver clock error sequence of USUD station. As described above, the smaller clock errors indicate better time transfer results. We give the clock difference of SF SPP time transfer for the LCK3-USUD time link, as shown in Figure 10. It is not difficult to see that scheme 2 has a certain smoothing effect on scheme 1. Similarly, the convergence problem in the initial period is caused by the PPP. Figure 8: Receiver clock error sequence of LCK3 station. Figure 9: Pseudorange residuals of USUD and LCK3 stations with two schemes. Each color represents each satellite. Due to limited space, only the LCK3 and USUD stations are analyzed in detail above. Next, we count the STD of the receiver clock errors after convergence for each station and the improvement of scheme 2 compared with that of scheme 1 in STD, as shown in Figure 11. Two findings are concluded. First, for all stations, the STDs of scheme 2 are smaller than those of scheme 1. The STDs of scheme 1 range from 1.16 ns to 2.11 ns, with an average STD of 1.75 ns, while the STDs of scheme 2 range from 1.08 ns to 1.81 ns, with an average STD of 1.51 ns. The average improvement of the STD values of scheme 2 is 13.6% with respect to those of scheme 1. This further validates the feasibility of our proposed method. Second, the STDs of the clock errors of the mid- and low-latitude stations are smaller than those of the high-latitude ones. On the one hand, this may be due to the relatively poor quality of the BDS-3 observations. On the other hand, this may be due to the ionospheric correction rate being lower at high latitudes than at low latitudes [19], which can also be seen in Figure 5:0  
Taking the time transfer results with the GBM products as a reference, we count the clock difference box display of five time links, as shown in Figure 5:1 The clock differences  
Figure 5:2 STDs of the receiver clock errors and the percentage improvement of scheme 2 compared with that of scheme 1 in STD. Figure 5:3 Clock difference of the SF SPP time transfer for the LCK3-USUD time link. of scheme 1 and scheme 2 are concentrated between \(\pm 5\) ns, but the box length of scheme 2 is shorter than that of scheme 1, which suggests that scheme 2 has a smaller clock error fluctuation range and a higher time transfer accuracy than scheme 1. It is not difficult to see that the outliers in scheme 2 are significantly less than those in scheme 1, which indicates that, after smoothing, a large number of outliers are pulled back to normal values. Similarly, the peak-to-peak value of the clock difference is also reduced after smoothing. To further evaluate the contribution of our proposed method to SF SPP time transfer, the STDs of the SF SPP solutions after convergence are calculated to evaluate the Type A uncertainty of the time links. Additionally, the improvement of time transfer in scheme 2 relative to that in scheme 1 in STD is also displayed, as shown in Figure 5:4 The STD values of scheme 1 range from 2.05 ns to 2.56 ns, with a mean STD of 2.34 ns, while the STD values of scheme 2 range from 1.92 ns to 2.40 ns, with a mean STD of 2.08 ns. The improvement of the STD values of scheme 2 ranges from 5.0% to 19.8% with respect to those of scheme 1, with an average value of 11.1%. In general, the BDGIM-based phase-smoothed pseudorange method provides a good improvement to the SF SPP time transfer performance in the time domain. Figure 5:5 The clock difference between the SF SPP time transfer solutions and GBM PPP time transfer solutions for five time links with the two schemes. Figure 5:6 STDs of clock difference of the SF SPP solutions and the percentage improvement of scheme 2 compared with that of scheme 1 in STD. We analyze the performance of SF SPP time transfer in the time domain.