# A New BDS-2 Satellite Clock Bias Prediction Algorithm with an Improved Exponential Smoothing Method
## 4 Results and Discussion
### Medium-Term Forecast Performance Analysis  
The clock bias data of the first day of the 737 weeks (16 February 2020) are employed to build a model. Then, the established model can be applied to predict the next 24 h clock bias. The modeling strategies are as follows. (1) The ES2 and ES3 models are established employing the clock bias data of the first day of the 737 weeks (16 February 2020), respectively, and the established ES2 and ES3 models can be employed to predict the next 24 h clock bias data. (2) Because of the longer forecast length, to boost the forecast accuracy of the ES2 (ES3) model, SW processing is adopted, that is, a combined forecasting model of the ES2 (ES3) model using the SW processing (abbreviated as ES2 + SW and ES3 + SW), is established. The coupling model algorithm is as follows. The length of the forecast is divided into two parts equally. First, an ES2 (ES3) model is developed by using the clock bias of the first day of 737 weeks (16 February 2020) to forecast the next 12 h clock bias data. Then, the 12 h clock bias predicted in the previous step and the last 12 h clock bias the first day of the 737 weeks (16 February 2020), the of 24 h clock bias data are used to establish an ES2 (ES3) model to forecast the clock bias for the next 12 h. Finally, the final forecasted clock bias is the combination of the clock bias of the first part of the forecast and the clock bias of the second part of the forecast. (3) Since the forecast time is relatively long, to further improve the forecast accuracy of the ES2 (ES3) model, the GM model is applied to learn the fitting error of the ES2 (ES3) model during the modeling process, and then, the SW processing method is employed to establish a combination forecast model: the ES2 (ES3) model and GM model using SW processing (abbreviated as ES2 + GM + SW and ES3 + GM + SW). The coupling model algorithm is as follows. The length of the forecast is divided into two parts equally. First, an ES2 (ES3) model is developed by using the clock bias of the first day of 737 weeks (16 February 2020) to predict the next 12 h clock bias data. Then, the GM model is applied to learn the fitting error of the ES2 (ES3) model during the modeling process, and the predicted values of the fitting error for the next 12 h will be obtained. The clock bias of the first part is equal to the sum of the clock bias predicted by the ES2 (ES3) model and the forecast value of the fitting error predicted by the GM model. Then, the SW processing is adopted, and the 12 h clock bias predicted in the previous step and the last 12 h clock bias of the first day of the 737 weeks (16 February 2020), the 24 h clock bias data, are used to establish an ES2 (ES3) model to forecast the clock bias for the next 12 h. Then, using the same processing method as the first part, the clock bias of the second part is equal to the sum of the clock bias predicted by the ES2 (ES3) model and the forecast value of the fitting error predicted by the GM model. Finally, the final forecasted clock bias is the combination of the clock bias of the first part and the clock bias of the second part. (4) Besides this, the single GM model as a comparison algorithm is established, employing the clock bias of the first day of the 737 weeks (16 February 2020) and forecast the clock bias data of the next 24 h.  
Figure 10 shows the error changes of 24 h SCBs forecast using different prediction models, where Figure 10a is the changes of the C 01 (GEO) SCBs forecast, Figure 10b is the changes of the C 05 (GEO) SCBs forecast, Figure 10c is the changes of the C 10 (IGSO) SCBs forecast, Figure 10d is the changes of the C 16 (IGSO) SCBs forecast, Figure 10e is the changes of the C 11 (MEO) SCBs forecast, and Figure 10f is the changes of the C 12 (MEO) SCBs forecast.