# A New BDS-2 Satellite Clock Bias Prediction Algorithm with an Improved Exponential Smoothing Method
## 1 Introduction
Then, considering the characteristics of the rate of change of the clock bias, an improved WNN model (its activation function was reconstructed) was put forward to predict SCBs of the GPS satellites, and the prediction results showed the model had higher prediction accuracy and robustness [26]. A mathematical approach based on stochastic differential equations was presented to forecast the behavior of in-orbit atomic clocks. Concurrently, they considered respective diverse situations with conclusive and stochastic signatures and optimized prediction results of clock bias. The most considerable issue was that the structure of this model was complex [27]. Nevertheless, the characteristics of the clock bias of the BDS are different from those of Galileo, GLONASS, and GPS because of its special constellation, which involves MEO satellites, GEO satellites, and IGSO satellites. Hence, the forecasting models of the Galileo, GLONASS, and GPS clock bias cannot be simply applied mechanically in the BDS-2 clock bias forecast. In 2020, the fractal behavior of the BDS clock bias was demonstrated by using the moving-average rescaled range analysis approach, and the results of this study suggested that the BDS clock bias had a memory [28]. Further, because of the advantages of simple modeling, easy calculation, less data to be stored, and the ability to quickly calculate new predicted values from recent observed values, the exponential smoothing (ES)model is widely concerned in time series forecasting, such as transportation, power load forecasting, industry, and finance [29; 30; 31; 32]. Up to now, very few studies have focused on the ES model in satellite clock forecasting. The ES model was first introduced into the short-term, medium-term, and long-term prediction of clock bias in 2017, but the selection of the smoothing coefficient was blind [33]. The 0.618 method was used to search for the best smoothing coefficient, and then, the model was established to predict the power load by using the found optimal smoothing coefficient. However, the optimization method was complex in operation and the forecast result was poor [34]. In the ES model, the determination of the smoothing coefficient is very complicated. In order to address this challenge, the \"thick near thin far (TNTF)\" principle is introduced to search for the best smoothing coefficient for better prediction. Then, in order to weaken the cumulative effect of errors due to the increase in forecast time, the idea of a sliding window (SW) is used to boost the forecast performance of the ES model employing the approach of a dynamic smoothing coefficient (ES based on SW). Besides, to further improve the forecast performance of the ES model, the GM model is used to learn the fitting error sequence of the ES model in the modeling process, and an SW is also adopted in the process (ES + GM based on SW), and then, the prediction results of the ES model and the GM model are combined as the final prediction clock bias. All these coupling algorithms are demonstrated by examples. The remaining paper is organized as follows. The prediction theory of the ES + GM based on the SW idea is introduced--which includes the prediction principle of the ES method, the process of searching for the best smoothing coefficients utilizing the TNTF principle, the prediction principle of the ES model based on the SW idea, and the prediction principle of the ES + GM based on the SW idea--in Section 2. The sources of experimental data and the evaluation criteria used to evaluate the prediction performance of these coupling algorithms are introduced in Section 3. In Section 4, the forecasting performance of these coupling algorithms is demonstrated through examples and the forecasting advantages of these coupling algorithms are also analyzed in this section. Finally, some outcomes are drawn in Section 5.