However, due to the influence of uncertain constraints like Earth's gravitational effects, the gravitational effects of other celestial bodies, satellite attitude deviations, and ephemeris transmission errors, the real positions and velocities of satellites would be different from the values of the extrapolation, and this difference would gradually enlarge with time [9;10]. There are two schemes used to optimize the performance of orbit extrapolation; namely, increasing the frequency of ephemeris broadcasting and measurements, and performing interpolation calculations. As for the first scheme, its prerequisite is that the link between the satellite and the UE must already be established; otherwise, the UEs cannot receive any data, including the ephemeris. This would be relevant in the case of the UE's initial access to a network or when the UE needs to re-access the network due to channel response degradation. Further, frequent ephemeris transmission requires extra overhead and radio resources, which decrease the efficiency of frequency utilization [11]. Additionally, increased measurement also requires an extensive number of ground stations (GSs) to continuously monitor the satellites, but this transmission is always much later than the time in which the UEs are in use [12]. In the latter scheme, interpolation is quite suitable in the case of limited ephemeris information and limited access to a referenced relative accurate location. Some algorithms such as Lagrange interpolation, Newton interpolation, and Chebyshev polynomial fitting can be used in orbit extrapolation improvement. The accuracy of interpolation methods depends on the accuracy of the boundary points of the observed ephemeris value and the interval of the interpolation [13;14]. In recent years, with the development of artificial intelligence (AI) algorithms, orbit extrapolation algorithms based on neural networks or deep learning have also gained a significant amount of attention. These methods primarily learn the uncertain errors of orbit extrapolation by measurements and fitting [15;16]. Based on the above analysis, the expected orbit extrapolation of the LEO-SIN needs to satisfy the following requirements, as shown in Figure 1: (1) the time of satellite ephemeris broadcasting should be limited, given the limited radio communication resources; (2) the outdated referenced ephemeris measured by GSs should be avoided, and (3) the accuracy of orbit extrapolation must improve. In our view, orbit extrapolation error is composed of distinct types of errors; if these errors can be separated, the total error would be expectedto improve. Under the premise of the limited time for ephemeris broadcasting, the determination of adjacent satellites' ephemeris information and the different timings of ephemeris information would be also expected to contribute to its enhanced performance. Here, we explore novel research on orbit extrapolation methods based on multi-satellite ephemeris coordination (MSEC) and the multi-stream fractional autoregressive integrated moving average (MS-FARIMA). The main contributions can be summarized as follows. * This work is the first to propose separating the broadcast ephemeris extrapolation errors into three types: random error (RE), trending error (TE), and periodic error (PE). It focuses on improving the extrapolation accuracy by diminishing and compensating for the RE and TE. We also derive the lower bound of the orbit extrapolation error based on single-satellite ephemeris information;
* This work first proposes a novel and accurate ephemeris extrapolation framework that involves the ephemerides of multi-satellite and multi-stream data time-series forecasting (TSF). By analyzing the spatial and temporal associations between corresponding and different satellites at different times, an MSEC orbit extrapolation error elimination algorithm can be designed.