# Considering Inter-Frequency Clock Bias for BDS Triple-Frequency Precise Point Positioning
## 3 Results
### Characteristics of IFCB
The multipath will have significant effect on the measurements for GEO satellites because of their almost constant elevation angles, especially for C05 with lowest elevation angles. The multipath is also an important attribution for the obvious bias variations of GEO satellites. \begin{table}
\begin{tabular}{c c} \hline \hline
**Combination** & **Coefficient** \\ \hline (B1, B2, B3) & (\(-\)0.457, \(-\)1.487, 1.944) \\ (B1, B2a, B3) & (\(-\)0.629, \(-\)1.314, 1.944) \\ (B1, B2b, B3) & (\(-\)0.457, \(-\)1.487, 1.944) \\ (B1C, B2a, B3) & (\(-\)0.583, \(-\)1.261, 1.844) \\ (B1C, B2b, B3) & (\(-\)0.422, \(-\)1.422, 1.844) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Coefficients for triple-frequency carrier phase combinations. Figure 3: Time series of triple-frequency carrier phase combinations at station SGG1 on 13 July 2016. The root mean square (RMS) values of low-frequency and high-frequency components in the triple-frequency carrier phase combination time series for each BDS satellite are calculated using the datasets collected at SGG1 on 7-13 July 2016, and the results are shown in Figure 4. The wavelet decomposition and reconstruction is used to separate the low-frequency and high-frequency components from their combination. In this contribution, the threshold value for the distinction between low-frequency and high-frequency components is roughly 3 \(\times\) 10\({}^{-4}\) Hz, which is a compromise between different satellites since they show different noise level. It is important to note that the frequency threshold may be only appropriate for the datasets used in this paper. If we analyze the triple-carrier combination time series for GPS satellites, the frequency threshold should be determined once again. The Symlet wavelet'sym5' is employed [36]. The high-frequency components mainly contain the PMN, while the low-frequency components mainly reflect the longer-term changes, namely IFCB variations. The RMS values of low-frequency components range from 0.2 to 0.9 mm for BDS-3 satellites, indicating that no significant IFCB variations can be observed for these satellites. The RMS values of low-frequency components vary within a range of 4.5-12.2 mm for BDS-2 GEO satellites, while the corresponding varying range is 0.8-5.2 and 0.7-0.9 mm for BDS-2 IGSO and MEO satellites, respectively. A further characterization and analysis of IFCB for BDS-2 satellites is required. It is interesting to note that the GEO satellites with relatively higher sun elevations above the satellite orbital plane such as C01 and C04 also have larger low-frequency components. This is because the low-frequency components may also contain partial multipath. Alternatively, other unknown factors may affect the variations of triple-frequency carrier phase combination with respect to a single station, which needs further investigation. Due to the comprehensive effects of multipath and IFCB, all the GEO satellites and the IGSO satellite C06 show larger RMS statistics of triple-carrier combination time series. For the purpose of assessing the PMN level, the variation of RMS statistics of high-frequency components in the triple-carrier combination time series with elevation at SGG1 is plotted in Figure 5. The RMS values are computed with respect to the increment of satellite elevation angles in steps of 5\({}^{\circ}\). The PMN variations are quite consistent for the four different triple-frequency carrier phase  
Figure 4: RMS statistics of low-frequency and high-frequency components in the triple-frequency carrier phase combination time series for each BDS satellite at station SGG1. combinations of BDS-3 tracking. The BDS-2 satellites show larger carrier phase errors compared with BDS-3 satellites at mid and high elevation angles. At elevation angle of 87.5\({}^{\circ}\), the RMS PMN for all four triple-carrier combinations of BDS-3 satellites is 0.8 mm, while the RMS PMN for the B1/B2/B3 triple-carrier combination of BDS-2 satellites is 1.7 mm.