# BDS Satellite Clock Prediction Considering Periodic Variations
## 3 Results
### BDS Satellite Clock Prediction Analysis  
In order to evaluate the prediction performance of the TFAM, we give and compare the prediction results of the TFAM and the SAM. The fitting and prediction are processed on a daily basis. To evaluate the prediction accuracy with different prediction time, 6 h, 12 h, 18 h, and 24 h prediction results are given in this section. As the data length of precise clock products publicly released by GFZ is limited, 300-day (DOY 166, 2020 to 099, 2021) clock offsets are used as the FFT length in this section. As shown in Table 2, the BDS-3 satellites are manufactured by CAST and SECM, and they have been partitioned to analyze  
Figure 9: Improvement of the TFAM relative to the SAM. the prediction performance, respectively. RMS after quadratic difference processes is used as the evaluation standard of the prediction accuracy. Clock prediction results of 30-day (DOY 140 to 169, 2021) are analyzed statistically. The mean RMS of 30 days for 30 satellites are listed in Table 3.  
Table 3 shows the mean prediction RMS of the WHU and GFZ clock offsets using the SAM and TFAM. It can be seen that the TFAM improves the mean prediction accuracy of the SAM, which indicates that the effect of the periodic noise can be further weakened by considering the time-varying periodic term. For different satellite types, IGSO satellites have maximum improvement, and the 24 h accuracy improvement of GFZ and WHU clock offsets achieve 19.5% and 8.8%, respectively. For the GEO satellites, there is little accuracy improvement both for WHU and GFZ clock offsets. Figure 10 gives the frequency variations of the main periodic term for GFZ and WHU clock offsets of 30 days (DOY 140 to 169, 2021). As shown in Figure 10, there is little periodic variations for GEO satellites. Therefore, little accuracy improvement is achieved for GEO satellites. The periodic variations of IGSO satellites are more frequent than MEO satellites. The improvement of MEO satellites is lower than that of IGSO, which is mainly because the MEO periodic variations generally only occur around the \(\beta\) angle peak value. Compared with WHU, the GFZ improvement is more obvious. It is caused by the different periodic variations between WHU and GFZ clock offsets. As shown in Figure 10, the variations of the main periodic term are mostly consistent for GFZ and WHU clock offsets. The prediction accuracy improvement of the 6 h, 12 h, 18 h, and 24 h are in the range of 6.4% to 10.0% for WHU clock offsets, while 11.1% to 14.4% for GFZ clock offsets. In addition, the prediction accuracy of different satellites is discussed. Compared with the BDS-2 MEO satellites, the prediction accuracy of BDS-3 MEO satellites is better. Figure 10: Frequency variations of main periodic term from DOY 140 to 169 in 2021. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Clock** \\ **Products** \\ \end{tabular}  } & \multirow{2}{*}{**System**} & \multirow{2}{*}{**Satellite Type**} & \multicolumn{3}{c}{**6 h**} & \multicolumn{3}{c}{**12 h**} & \multicolumn{3}{c}{**18 h**} & \multicolumn{3}{c}{**24 h**} \\  & & & **SAM** & **TFAM** & **IMP** & **SAM** & **TFAM** & **IMP** & **SAM** & **TFAM** & **IMP** & **SAM** & **TFAM** & **IMP** \\ \hline \multirow{6}{*}{WHU} & \multirow{4}{*}{BDS-2} & GEO (CASC) & 1.52 & 1.46 & 3.9\% & 2.52 & 2.52 & 0\% & 3.73 & 3.68 & 1.3\% & 5.16 & 5.09 & 1.4\% \\  & & IGSO (CASC) & 1.75 & 1.50 & 14.3\% & 3.52 & 3.00 & 14.7\% & 5.31 & 4.63 & 12.8\% & 6.97 & 6.36 & 8.8\% \\  & & MEO (CASC) & 0.91 & 0.80 & 12.1\% & 1.56 & 1.43 & 8.3\% & 2.32 & 2.16 & 6.9\% & 2.77 & 2.57 & 7.2\% \\  & & MEG (CASC) & 0.48 & 0.43 & 10.4\% & 0.85 & 0.79 & 7.1\% & 1.28 & 1.19 & 7.0\% & 1.77 & 1.66 & 6.2\% \\  &  
Because the BDS-3 satellites are equipped with the new generation high-quality atomic clocks, they have better frequency stability than the atomic clocks on BDS-2.