# 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  
In this subsection, we focus on verifying the feasibility of our proposed time transfer method. There are more than 120 monitoring stations distributed around the world, all of which contribute to the calculation of the GBM product. In addition, the GBM product is calculated using the B1I/B3I IF observations of a three-day arc, which have a high accuracy of about 2.0 cm for orbit and about 75.0 ps for clock offset. Moreover, the accuracy of precise point positioning (PPP) time transfer can reach a sub-nanosecond level [32]. Therefore, the time transfer results calculated from BDS-3 PPP using the GBM product are taken as a reference. Since dual-frequency PPP has better time transfer performance than SF SPP [33], the B1I/B3I ionosphere-free observations are used to carry out GBM PPP. To better assess SF SPP time transfer performance, the following experiments are conducted with USUD and LCK3 stations as examples. Before performing time transfer, the number of BDS-3 visible satellites (NSAT) and the Position Dilution of Precision (PDOP) of the two stations are counted, as displayed in Figure 6. The average NSAT value of the USUD station is 6.9, and the mean PDOP is 4.7. For LCK3, the average NSAT value is 11.7, and the mean PDOP is 1.6. Figure 5: Correction ratio of BDGIM and Klobuchar model. Figure 6: NSAT and PDOP of USUD and LCK3 stations. Now turn to Figures 7 and 8, which present the receiver clock errors of the USUD and LCK3 stations relative to the GBM PPP solutions. Note that scheme 1 indicates the traditional SF SPP, and scheme 2 indicates the improved SF SPP. From the two figures, three findings can be found. First, it is easy to see that the clock error sequence of scheme 1 has many discrete points, while the clock error sequence of scheme 2 is quite smooth, and the discrete points are significantly reduced, almost becoming a thin line, which can be observed in the local enlargement in Figure 7. This shows that the smoothing algorithm has considerable potential in time transfer, and the pseudorange observations after smoothing are closer to the real value, reducing the noise of the pseudorange observations. The receiver clock errors are more stable after smoothing, which is more beneficial to improving time transfer performance. Second, we note that there is a convergence period of the clock error during the initial period; this is because the PPP algorithm uses a Kalman filter to estimate the receiver clock offset, which takes some time to converge to the \"true value\". However, there is no convergence in SPP, which uses the least squares method. When the receiver clock offsets solved by the SPP and PPP are differenced, there is a convergence problem in the clock errors, i.e., the left part of the red vertical line in Figure 7, which is removed to avoid the impact of the convergence problem on the performance evaluation of SPP time transfer. In this paper, the clock errors are considered to have converged when the clock error difference between 20 consecutive adjacent epochs is kept within 0.1 ns. Third, the clock error of the two stations does not fluctuate around the zero value. This is due to the various receiver hardware delays at various frequencies [34]. The receiver clock offset calculated by the GBM PPP absorbs the receiver hardware delay of the B1I/B3I signal, while that of the SF SPP absorbs the hardware delay of the B1I signal. To represent the performance of the phase-smoothed pseudorange more comprehensively, we present the pseudorange residuals for both the USUD and LCK3 stations, as shown in Figure 9. Each color represents each satellite. The fluctuation range of the pseudorange residuals is significantly reduced after smoothing. The RMSs of the pseudorange residuals for the USUD station in scheme 1 and scheme 2 are 1.26 m and 0.95 m, respectively, reducing by 24.6%.