# Considering Inter-Frequency Clock Bias for BDS Triple-Frequency Precise Point Positioning
## 3 Results
### Characteristics of IFCB
The number of stations in the ground tracking network mainly determines the accuracy and reliability of IFCB estimates (Kal  
In real-time triple-frequency PPP, the IFCB should be estimated in real time. In addition to the computational burden, the data streams with BDS observations broadcast by a global ground tracking network should be received in real time. The above real-time estimation process for IFCB will bring additional heavy workload for the real-time triple-frequency PPP users. The IFCB prediction with a high accuracy is a possible way to minimize the workload. Following [PERSON] et al. (2018), the IFCB periods roughly coincide with the orbital repeat periods of the satellites. Thus, the IFCB of the first day is utilized to predict that of the second day for GEO and IGSO satellites and of the day after a week for MEO satellites. The similarity degree between single-day IFCB time series of two different days can be assessed by the cross-correlation ([PERSON], 2016). A cross-correlation is performed on the single-day IFCB time series for two consecutive days or two days with an interval of a week. The normalized cross-correlation results at 1680 s lag for MEO satellites and at 240 s lag for GEO and IGSO satellites are shown in Figure 8. The time lag should be considered because of the difference between a solar day and a sidereal day. For all GEO and IGSO satellites except C01, C02 and C15, the cross-correlation values are larger than 0.6 for most cases. In addition, all MEO satellites show low similarity between waveforms of IFCB time series for two days, which may be attributed to the small IFCB variations and the long time span for IFCB prediction. Table 6 provides the average values of cross-correlation coefficient over 32 days for each BDS-2 satellite. According to the average results for the same orbit type of satellites, the cross-correlation coefficient between the IFCB series of two days is 0.625, 0.689 and 0.217 for GEO, IGSO and MEO satellites, respectively. Figure 8: Cross-correlations between IFCB time series of two days. Figure 7: Average values of sum of weights at an epoch over 32 days. After subtracting IFCB time series of the first day from those of the day after a week for MEO satellites and of the second day for GEO and IGSO satellites, the residuals are plotted in Figure 9. The time lag is considered. The residual series show a decrease of fluctuation amplitudes from about 5 cm to about 3 cm in comparison to the IFCB series for most satellites. The RMS statistics of residuals for the 32 days are also shown in each panel. According to the average results of the 14 satellites, the prediction accuracy of IFCB is 1.2 cm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Orbit Type** & **Satellite PRN** & **Cross-Correlation** \\ \hline  & C01 & 0.512 \\  & C02 & 0.292 \\ GEO & C03 & 0.678 \\  & C04 & 0.816 \\  & C05 & 0.828 \\ \hline  & C06 & 0.893 \\  & C07 & 0.592 \\  & C08 & 0.617 \\  & C09 & 0.786 \\  & C10 & 0.745 \\  & C15 & 0.501 \\ \hline  & C11 & 0.142 \\ MEO & C12 & 0.145 \\  & C14 & 0.363 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average cross-correlation values over 32 days for each BDS-2 satellite. Figure 9: Residuals obtained by subtracting IFCB time series of the first day from those of the day after a week for MEO satellites and of the second day for GEO and IGSO satellites.