# Considering Inter-Frequency Clock Bias for BDS Triple-Frequency Precise Point Positioning
## 3 Results
### Performance Evaluation of Triple-Frequency PPP  
In order to validate the correctness of IFCB estimates, the performance of triple-frequency PPP is evaluated. The IFCB corrections are derived by prediction. As the precise satellite orbit and clock products of BDS-3 satellites are still unavailable, only BDS-2 satellites are used. For the purpose of comparison, the traditional B1/B2-based PPP processing is also carried out. The epoch-wise positioning errors for dual- and triple-frequency cases in the east, north and vertical directions at JFNG on 12 September 2016 are shown in Figure 10, and their variations are consistent for the two different cases in all three directions. Nevertheless, the convergence performance of triple-frequency case in the first two hours is slightly better than that of dual-frequency case. Compared to the dual-frequency PPP solutions, the triple-frequency PPP solutions are more stable even after a long convergence time. The RMS values of positioning errors over the last 15 min as well as the convergence time for dual- and triple-frequency PPP solutions are presented in Table 7. In this study, the position filter is considered to have converged when the positioning errors reach 0.1 m and keep within 0.1 m. According to [PERSON] et al. [38], the BDS B1/B2 PPP requires more than two hours to achieve a positioning accuracy better than 0.1 m for all three coordinate components. Therefore, our results are comparable to theirs. The reason for the longer convergence time of BDS PPP in comparison to GPS PPP is that the BDS satellite orbit and clock are at a relatively lower accuracy [9], and BDS measurements exhibit relatively higher noise level [17]. In addition, BDS position dilution of precision (PDOP) values are larger in most times than the GPS case although the former has more visible satellites at the station JFNG with the coverage of BDS service. For comparison, the epoch-wise positioning errors and the corresponding statistical values for the triple-frequency PPP without IFCB consideration are also shown in Figure 10 and Table 7. Its positioning accuracy and convergence performance are worse than those of the other two BDS PPP cases. The results indicate that the positioning performance will degrade without careful consideration of the IFCB, even if B1/B3 observations are added to the B1/B2 PPP processing. The datasets from 9 stations covered by the BDS service of the Asia-Pacific area on 12-13 September 2016 are used for the accuracy statistics. For each 24-h session, the RMS statistics are computed using the positioning errors of the last 15 min. Theoretically, the position solution at the last epoch for the PPP with the use of Kalman filter has the highest positioning accuracy. However, the position solutions may still show fluctuations after a long observation time of approximately 24 hours if the re-convergence occurs due to the frequent cycle slips, the gross errors, the insufficient satellite number or even the signal blockage. For reliability, it may be better to use a period of time rather than an epoch at the end of a session for RMS calculation. [PERSON] et al. [39] also adopted a time span of 15 min at the end of each session for RMS calculation. The average positioning errors for all 24-h cases are calculated based on the RMS values. An accuracy of 1.7, 0.4 and 2.0 cm in the east, north and vertical coordinate components is achieved for B1/B2 PPP, respectively. Taking IFCB into account, the triple-frequency PPP improves the positioning accuracy by 12%, 25% and 10% over the B1/B2 PPP to 1.5, 0.3 and 1.8 cm in the three coordinate components, respectively. As there are mainly measurement noises as well as other unmodeled errors in observation residuals, they can be used for the evaluation of triple-frequency PPP model. The residuals of B1/B2 and B1/B3 ionospheric-free combined carrier phase observations in the triple-frequency PPP from JFNG of 12 September 2016 are shown in Figure 11. Different satellites are identified by different colors.