# Considering Inter-Frequency Clock Bias for BDS Triple-Frequency Precise Point Positioning
## 3 Results
### Characteristics of IFCB
At the 22.5\({}^{\circ}\) elevation, the RMS PMN for the four different combinations of BDS-3 satellites varies in a range of 5.5-6.9 mm, while the corresponding RMS PMN for BDS-2 satellites is 3.5 mm. For comparison, the right plot illustrates the results from XIA1 of 2-15 September 2016. The receiver and antenna information for the stations SGG1 and XIA1 is listed in Table 5. A prototype receiver is set up at the station SGG1, and it is developed by one university in China. The stations SGG1 and XIA1 are equipped with different types of receivers and antennas. The comparison reveals the PMN differences caused by the different tracking performance of the specific receiver and antenna quality with respect to its multipath sensitivity as well as surrounding of the receiving antenna. According to the results at the two stations, the representative RMS errors at low elevations are 10 mm for the high-frequency components in the triple-frequency carrier phase combination, while the corresponding errors at medium and high elevations are 2 mm. Assuming, for simplicity, equal error variances on all frequencies, the 1\(\sigma\) PMN for triple-frequency combination is 2.3-2.5 times larger than that of the individual signals. We can conclude that the PMN errors for BDS tracking on a single frequency vary in a range of 1 to 4 mm over the considered satellite elevation ranges. Based on ED strategy, the datasets on 32 consecutive days, i.e., 15 August-15 September 2016, are processed for all BDS-2 satellites. Figure 6 provides the time series of IFCB estimates. It is obvious that the IFCB changes over time, and the IFCB variations are generally confined to peak amplitudes of about 5 cm, except for C15. Most importantly, the IFCB exhibits notable periodic signal. The RMS statistics of IFCB estimates over the 32 days are also provided in each sub-figure. C01 has the smallest RMS values of 0.010 m, while C15 RMS values are the largest with value of 0.068 m. Compared with the results shown in Figures 3 and 4, the results shown in Figure 6 can be better used for IFCB  
Figure 5: Dependence of carrier phase multipath and noise errors on satellite elevation angles for triple-frequency carrier phase combination at stations SGG1 and XIA1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Station** & **Receiver Type** & **Receiver Number** & **Antenna Type** & **Antenna Number** & **Antenna Height** \\ \hline SGG1 & prototype & - & TRM59900.00 & - & 0 m \\  & receiver & & NONE & & \\ \hline XIA1 & gnss\_ggr & RINTMR20160006 & RINT-8 CH & RINT-8 CH-006 & 0.15 m \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Information of two stations. analysis. The IFCB estimation here is conducted based on a weighted average of solutions over the entire network, and thus the many influence factors such as measurement noises and multipath can be alleviated. Based on the law of random error propagation and reasonable assumption, the standard deviation (STD) of the IFCB estimates is computed and found to be usually smaller than 4 mm, except for C15. The sun elevation above the satellite orbital plane is highest for C01 during this period of time, and thus C01 has the smallest RMS IFCB. As to C06 and C08, they have the second largest RMS IFCB due to the relatively lower sun elevations. The reason for the largest RMS IFCB for C15 is that the number for stations with the capability of offering B1/B2/B3 tracking is not sufficient. The ED IFCB estimates for C15 are inaccurate at many epochs, and thus there are many accumulated errors when calculating the IFCB through accumulation. According to [PERSON] et al. (2016), the single-day IFCB time series of GPS show significant periods of 12, 8, 6, 4.8, 4 and 3 h. Some periods such as 8 h cannot be explained by the sun illumination, which indicates that other factors also affect the IFCB variations. Therefore, the factors that affect the IFCB variations need further investigation, but this does not limit the applications of IFCB to triple-frequency PPP.