Satellite narrow beam pointing algorithm and simulation based on the ECEF coordinate system

In the scenario of low-Earth orbit (LEO) satellite narrow-beam coverage guarantee for ground stations, due to the high relative velocity and short zenith pass time of the satellite, it is necessary for the satellite to continuously autonomously calculate the beam pointing angle and adjust the antenna pointing in order to achieve stable tracking of the ground stations. Since the satellite position and velocity obtained through extrapolation using Kepler's six orbital elements are based on the inertial coordinate system, most traditional beam pointing algorithms calculate the beam pointing angle based on the satellite's position, velocity, and attitude data within the inertial coordinate system. The calculation process inevitably requires converting the ground station's longitude, latitude, and altitude information to the inertial coordinate system. This conversion process needs to consider the effects of precession, nutation, and polar motion, which not only complicates the calculation process but also requires regular maintenance of certain conversion matrices through table lookups, which is not conducive to on-orbit operation. On the other hand, traditional beam pointing algorithms rely on the velocity vector of the satellite within the inertial system to construct the orbital coordinate system, making the velocity calculation error a significant factor affecting the calculation results. To address these issues, based on the current situation where mainstream LEO satellite platforms in China can measure and output satellite attitude and position in the Earth-centered, Earth-fixed (ECEF) coordinate system, this paper proposes an algorithm for calculating the beam pointing angle based on the ECEF coordinate system. This algorithm can quickly calculate the two-dimensional rotation angle of the antenna based on the satellite's position within the ECEF coordinate system and its attitude angle with the ECEF coordinate system as the reference frame, achieving precise pointing of the LEO satellite narrow-beam at any station within the ground field of view. Compared to traditional algorithms, this approach avoids introducing matrices for precession, nutation, and polar motion, significantly reducing computational complexity. It also avoids introducing satellite velocity, ensuring that velocity errors do not affect the results. Simulation comparisons with STK calculation results indicate that this algorithm has minimal calculation error and is suitable for quickly determining the satellite narrow-beam pointing angle in an environment with limited on-board resources. It can significantly enhance the accuracy and response capability of satellite beam pointing.