# Improved Short-Term Clock Prediction Method for Real-Time Positioning
## 1 Introduction  
Precise point positioning (PPP) has been vigorously developed since its introduction. High-precision orbit and clock products are required by PPP technology [1]. The Global Navigation Satellite System (GNSS) ranging measurement in substance is equal to the time measurement between the satellite clock and receiver clock and usually, the users fix satellite clock corrections and estimate receiver clock corrections to eliminate the error of the clock. In short, the accuracy of the satellite clock is directly related to the accuracy of PPP. However, a 12-day to 18-day delay occurs before International GNSS Service (IGS) final orbit and clock products are released, and even IGS rapid products are released after 17 h to 41 h [2,3]. Therefore, such products can only be utilized by users in post PPP applications. Real-time PPP has graduallybecome a research focus in satellite navigation and positioning, but IGS final and rapid products cannot meet real-time demands. IGS also provides ultra-rapid products (IGU-P). The precision of IGU-predicted orbit products is about 5 cm, which is equivalent to that of IGS final products and satisfies post PPP applications. By contrast, the official accuracy of IGU-P clock products is only 3 ns. Besides, the sampling rate of the clock has a significant impact on the PPP solution in kinematic PPP [4]. Apparently, 15-min interval IGU-P clocks cannot be used for high-precision PPP. To promote real-time PPP application, IGS set up a real-time working group in 2002 to start the prototype research, and the IGS Real Time Service (RTS) was officially launched in 2013 to provide service for real-time applications [2]. The accuracy of real-time clocks is about 0.3 ns, the broadcast delay is 25 s, and the sampling interval is 5 s [5]. This can be regarded as a reference for real-time clocks estimation. Apart from the integrated products provided by IGS, the analysis center of IGS also provides users their own products. Nevertheless, several problems are encountered in real-time clock applications. First, a delay occurs in real-time observation receiving and product broadcasting. Second, the processing of real-time clock correction estimation software results in a delay. Third, the data stream often loses information or encounters interruption. Table 1 shows the loss rate of real-time clock products in each analysis center between days 349 and 358 in 2015 (except for day 357). The sampling interval is 5 s. In the most ideal case, nearly 10% of the epoch is lost, and this loss seriously affects the accuracy and stability of real-time PPP. The current Global Positioning System (GPS) constellation can be grouped into three types. Block IIR and Block IIR-M satellites carry rubidium clocks, and the newest generation of Block IIF is equipped with an improving cesium and rubidium atomic frequency standard (AFS). Previous studies have shown that AFS operated on Block IIF is more stable than other types [6; 7], and rubidium AFS is more stable than cesium AFS [7; 8]. The type of satellite and atomic clock on 1 May 2016 is shown in Table 2. Moreover, the behavior of GPS on-board clocks has been fully discussed by researchers. Periodic signals related to orbital dynamics have been detected in all clock types [9]. Knowing these variations in the satellite clock is important for improving the prediction model of clock. Most studies and models focused on medium- and long-term forecast analyses, such as one day or several days, the purpose of which is to provide products similar to IGU ultra-fast products to realize real-time PPP with ultra-fast orbit products. This case is obviously different from the short-term clock prediction required for real-time clock difference calculation. Therefore, the introduction of short-term