# A New BDS-2 Satellite Clock Bias Prediction Algorithm with an Improved Exponential Smoothing Method
## 1 Introduction  
The Chinese Beidou Navigation Satellite System (BDS), to date, has completed the construction of its regional system BDS-2, which consists of 15 satellites [1]. The system can provide positioning, navigation, timing, and short message communication services for users in the Asia and Pacific. Over the past few years, it has made great strides in building global navigation systems such as BDS-3. By the end of 2018, a total of 19 BDS-3 satellites had been launched to enable the primary system for global services. With a total of 33 operational satellites, namely, 5 geostationary earth orbits (GEO), 7 inclined geosynchronous orbits (IGSO), and 21 medium earth orbits (MEO), the standard positioning accuracy of the orbits is achieved 5 m in both horizontal and vertical directions for the Asia-Pacific users and 10 m for global users approximately. By 23 June 2020, with the successful launch of the 55 th networking satellite, it marks the complete networking of the BDS [2]. As one of the vital payloads of the Global Navigation Satellite System (GNSS), the performance of the satellite clocks and the accuracy, stability, and reliability of satellite clock bias (SCB) prediction are one of the critical factors affecting the positioning, navigation, and timing (PNT) service capabilities of the whole system [3, 4, 5]. Due to the rapid development of navigation satellite technology and its widespread use in practical applications, users' requirements for accuracy are getting higher and higher. Many factors affect the capability of the PNT services, among which the impact of the SCBs is one of the most important factors [6, 7]. Even a clock bias of 1 ns will produce a range error of 0.3 m approximately, which seriously influences the positioning and timing accuracy of navigation systems [8, 9]. In order to meet the requirements of users for centimeter-level positioning, it is essential to establish a high-precision time system. The clock bias products released by the international IGS server are a post-precision clock bias file with high accuracy, but the acquisition time is longer and cannot fulfill the necessities of real-time positioning [10, 11, 12]. The improvement of the precision of clock bias forecast will contribute to the acquisition of a priori information required for satellite autonomous navigation and the ability to improve precise point positioning (PPP) accuracy [13, 14, 15]. Therefore, studying how to further the stability and accuracy of clock bias prediction is of paramount importance for boosting the quality of clock bias products and the ability of navigation and positioning. At present, in order to enhance the precision level of SCBs prediction, many scholars had conducted multi-angle, multi-directional, and in-depth studies on SCBs prediction from various aspects, and a variety of clock bias prediction models had been established, e.g., polynomial prediction model, gray model (GM), auto-regressive moving average model (ARMA), spectrum analysis model (SAM), Least Squares Support Vector Machines (LSSVM), functional network, etc. [16, 17, 18, 19, 20, 21]. Since the interruption of satellite clock information will affect the accuracy of real-time PPP, some methods, such as the optimal arc length identifying, diverse polynomial power forecasting and empirical model made of a sixth-power harmonic function, etc., were proposed as a way to build up the performance of real-time PPP [22, 23, 24]. Furthermore, a predicted method of clock bias with a wavelet neural network (WNN) model was put forth, and some outcomes were obtained via the prediction tests. Compared with the IGU-P clock bias products, this method could better improve the prediction accuracy, but this approach did not consider the periodic errors and the frequency shift errors [25].