# A New BDS-2 Satellite Clock Bias Prediction Algorithm with an Improved Exponential Smoothing Method
## 5 Conclusions  
In the applications of the GNSS, the clock bias forecast is a critical issue. The accuracy and stability of SCBs prediction determine the accuracy of satellite navigation and positioning directly. For purpose of improving the accuracy and stability of clock bias prediction, a new fusion prediction algorithm is proposed in this contribution to perform short-term and medium-term prediction of clock bias. The clock bias data of the BDS-2 satellites with the first day to the second day of the 737 weeks of the DOY released by the iGMAS are selected as experimental data to assess the prediction performance of these new models. For the comparison and analysis, the single GM, ES2, and ES3 models are regarded as reference, then the prediction performance of the ES2 + SW, ES3 + SW, ES2 + GM + SW, and ES3 + GM + SW model for clock bias are then analyzed. As for the short-term clock bias prediction, the method of predicting after learning the fitting error for the ES model during the modeling process using the GM model can enhance the forecast performance of the ES model dramatically: both the forecast accuracy and the stability of the forecast. In particular, the average forecast accuracy of the ES3 model has the greatest improvement, up to 25.30% going from 3.59 ns to 2.68 ns, and the average forecast stability of the ES3 model has the greatest improvement, up to 32.60% going from 2.98 ns to 2.01 ns. With respect to the medium-term prediction of clock bias, the fusion prediction algorithm using two processing strategies can improve the forecasting performance of the ES model, whether in terms of forecast accuracy or forecast stability. Above all, the most significant improvement in the prediction performance of the ES model is achieved by using a GM model to learn the fitting errors during the modeling process, followed by an SW processing strategy. Its average forecast accuracy is improved by 49.10% (56.40%) from 5.56 ns (6.77 ns) to 2.83 ns (2.95 ns), and the average forecast stability is improved by 53.40% (49.60%) from 8.99 ns (16.13 ns) to 4.19 ns (8.13 ns), compared with the single ES2 (ES3) model. Overall, this new fusion prediction algorithm is advantageous and can be used to forecast the BDS-2 clock bias with high-precision both in the short-term and medium-term. Therefore, it is recommended that this new algorithm can be utilized to predict clock bias for BDS-2 satellites. Furthermore, this study provides a theoretical reference for SCBs in terms of high-precision prediction and practical applications, and also provides a new guideline for continued research in SCBs forecast technology in the future. [PERSON] and [PERSON] designed the experiments. [PERSON] contributed to the tests and analyzed the data. [PERSON], [PERSON], and [PERSON] validated the experimental results and reviewed the paper. [PERSON] wrote the paper. All authors have read and agreed to the published version of the manuscript. Funding supports from the Postdoctoral Science Foundation of China (No. 2019M650801) and Director's Foundation of Institute of Microelectronics, Chinese Academy of Sciences (No. E0518101). We thank the editors and the anonymous reviewers for their valuable comments and suggestions to improve the paper. Many thanks go to the IGS MGEX for providing clock bias products. The authors declare no conflict of interest.