# BDS Satellite Clock Prediction Considering Periodic Variations
## 4 Discussion  
This research focused on the characteristics of the BDS satellite clock offset periodic variations, and proposed TFAM to analyze the impact of the periodic variations on the performance of clock prediction model. According to previous researchers, the amplitude of the periodic terms is time-varying. From the FFT results of different clock offset lengths, it can be seen that the FFT is not suitable to detect and quantify the periodic variations. Considering that the STFT has a unique advantage in processing non-stationary signals, it is used to analyze the periodic variations of BDS satellite clocks in this paper. Comparing the amplitude spectrums obtained by FFT and spectrograms obtained by STFT, it can be seen that both the amplitude and frequency of periodic terms vary with time, and the variations are diverse for different satellites. By analyzing the PSD variations of four significant periodic terms with respect to the \(\beta\) angle of BDS satellite, it is found that the amplitude variations of periodic terms due to the orbit determination errors vary significantly, and it tracks the eclipse season. For other periodic terms, the PSD variations may be caused by perturbation errors and environment variations. As the PSD variations of each periodic term are inconsistent, the frequency of main periodic term varies over time, which is found both in the WHU and GFZ clock offsets. Awareness of periodic variations may be used to improve the clock prediction model, and the TFAM considering the time-varying periodic term is established. Using STFT instead of FFT in obtaining the main periodic term, the periodic variations of the clock offsets are properly considered in the clock prediction model.  
Compared with the fitting and prediction performance of the TFAM and SAM, it can be concluded that adding a time-varying periodic term to the TFAM indeed improves the fitting and prediction accuracy. Since the periodic variations of different satellites occur at different times, the overall improvement of TFAM is limited. For the satellites with marked periodic variations, the TFAM can significantly improve the fitting and prediction accuracy. Although there are some differences between the periodic variations of the WHU and GFZ clock offsets, the TFAM can improve the fitting and prediction accuracy for both WHU and GFZ clock offsets.  
Due to the inconsistency performance of different satellites, the fitting and prediction results are discussed, and some conclusions have been drawn. The fitting and prediction accuracy of BDS-3 MEO satellites is better than that of BDS-2 MEO satellites. This may be because the BDS-3 satellites are equipped with high-quality atomic clocks, which have more stable frequency than atomic clocks on BDS-2 satellites. MEO satellites present better fitting and prediction performance than the GEO and IGSO satellites, and this is mainly  
Figure 15: Mean RMS of the SAM and the TFAM prediction errors.  
because the orbit model performs better for MEO satellites than other satellites. Comparing the prediction accuracy of satellites from different manufacturers, the prediction accuracy of SECM satellites is higher than that of CAST satellites. It may be affected by the distinct orbit accuracy of CAST satellites and SECM satellites, which is caused by different attitude control models.  
It is noted that the TFAM performs well for satellites with marked periodic variations. Except for the periodic noise, the characteristics of residual noise will be further studied in future work.