# A New BDS-2 Satellite Clock Bias Prediction Algorithm with an Improved Exponential Smoothing Method
## 4 Results and Discussion
### Short-Term Forecast Performance Analysis  
The first day clock bias data of the 737 weeks (16 February 2020) are used to build a model. Then, the established model can be applied to forecast the clock bias data for the next 6 h. Since the length of the forecast is not long, SW processing is not adopted. The modeling strategies are as follows. (1) The ES2 and ES3 models are built using the first day clock bias data of the 737 weeks (16 February 2020), respectively, and the established ES2 and ES3 models can be employed to predict the next 6 h clock bias data. (2) To boost the forecast accuracy of the ES2 (ES3) model, the GM model is utilized to learn the fitting error of the ES2 (ES3) model during the modeling process. In other words, a combined forecasting model of the ES2 (ES3) model and the GM model (abbreviated as ES2 + GM and ES3 + GM) is developed. The coupling model algorithm is as follows. First, an ES2 (ES3) model is set up employing the clock bias data of the first day of the 737 weeks (16 February 2020), and the established ES2 (ES3) \begin{table}
\begin{tabular}{c c c c c c c} \hline
**PRN** & **Satellite No.** & **NORAD.ID** & **SVN** & **Int. sat. ID** & **Manuf.** & **Notes** \\ \hline C 01 & GEO-01 & 36287 & C 003 & 2010-001 A & 2G-CAST & 140.0\({}^{\circ}\) E; launched 17 January 2010 \\ C 05 & GEO-05 & 38091 & C 011 & 2012-008 A & 2G-CAST & 58.75\({}^{\circ}\) E; launched 25 February 2012 \\ C 10 & IGSO-05 & 37948 & C 010 & 2011-073 A & 2I-CAST & \(\sim\)95\({}^{\circ}\) E; launched 2 December 2011 \\ C 16 & IGSO-07 & 43539 & C 019 & 2018-057 A & 2I-CAST & \(\sim\)95\({}^{\circ}\) E; launched 10 July 2018 \\ C 11 & MEO-03 & 38250 & C 012 & 2012-018 A & 2M-CAST & Slot A-7; launched 30 April 2012 \\ C 12 & MEO-04 & 38251 & C 013 & 2012-018 B & 2M-CAST & Slot A-8; launched 30 April 2012 \\ \hline \end{tabular}
\end{table} 
Table 1: Information on selected satellites (as of February 2020). Figure 8: Boxplot change diagram of 6 h prediction accuracy (**a**) and stability (**b**) using different models. Figure 7: Variation diagram of 6 h forecast accuracy (RMS) and stability (Range) using different models: (**a**) is the changes of RMS, and (**b**) is the changes of Range. Figure 10: Variation diagram of 24 h satellite clock bias forecast errors using different models: (**a**) is the changes of the C 01 SCBs forecast, (**b**) is the changes of the C 05 SCBs forecast, (**c**) is the changes of the C 10 SCBs forecast; (**d**) is the changes of the C 16 SCBs forecast, (**e**) is the changes of the C 11 SCBs forecast, and (**f**) is the changes of the C 12 SCBs forecast. Figure 9: The average accuracy (RMS), stability (Range), and improvement percentage of 6 h forecast using different models: (**a**) is the changes of RMS and Range, and (**b**) is the changes of improvement percentage of RMS and Range. Figure 11: Variation diagram of 24 h forecast accuracy (RMS) and stability (Range) using different models: (**a**) is the changes of RMS, and (**b**) is the changes of Range. Figure 12: Boxplot change diagram of 24 h prediction accuracy (**a**) and stability (**b**) using different models. Figure 6 shows the error change of 6 h SCBs forecast using different models, where Figure 6a is the changes of the C 01 (GEO) SCBs forecast, Figure 6b is the changes of the C 05 (GEO) SCBs forecast, Figure 6c is the changes of the C 10 (IGSO) SCBs forecast, Figure 6d is the changes of the C 16 (IGSO) SCBs forecast, Figure 6e is the changes of the C 11 (MEO) SCBs forecast, and Figure 6f is the changes of the C 12 (MEO) SCBs forecast. Figure 7 shows the variation of 6 h forecast accuracy (RMS) and stability (Range) using different models, where Figure 7a is the changes of forecast accuracy (RMS) and average forecast accuracy (RMS), and Figure 7b is the changes of forecast stability (Range).