The low Earth orbit (LEO) satellite internet network (LEO-SIN) has become a heated issue for the next generation of mobile communications, serving as a crucial means to achieve global wide-area broadband coverage and, especially, mobile phone directly to satellite cell (MPDTSC) communication. The ultra-high-speed movement of LEO satellites relative to the Earth results in serious Doppler effects, leading to signal de-synchronization at the user end (UE), and relative high-speed motion leading to frequent satellite handovers. Satellite ephemeris, which indicates the satellite’s position, has the potential to determine the position of the transmit (Tx) within the LEO-SIN, thereby enhancing the reliability and efficiency of satellite communication. The adoption of ephemeris in the LEO-SIN has met some new challenges: (1) how UEs can acquire ephemerides before signal synchronization is complete, (2) how to minimize the frequency of ephemeris broadcasting, and (3) how to decrease the overhead of ephemeris broadcasting. To address the above challenges, this paper proposes a method for extrapolating the LEO-SIN orbit based on multi-satellite ephemeris coordination (MSEC) and the multi-stream fractional autoregressive integrated moving average (MS-FARIMA). First, a multi-factor global error analysis model for ephemeris-extrapolation error is established, which decomposes it into three types; namely, random error (RE), trending error (TE), and periodic error (PE), with a focus on increasing the extrapolation accuracy by improving RE and TE. Second, RE is eliminated by utilizing the ephemerides from multiple satellites received at the same UE at the same time, as well as multiple ephemerides from the same satellite at different times. Subsequently, we propose a new FARIMA algorithm with the innovation of a multi-stream data time-series forecast (TSF), which effectively improves ephemeris extrapolation errors. Finally, the simulation results show that the proposed method reduces ephemeris extrapolation errors by 33.5% compared to existing methods, which also contributes to a performance enhancement in the Doppler frequency offset (DFO) estimation of MPDTSC.
