Quick Coverage Analysis Method for Mega Constellation Based on High-Order Expansion

This paper presents a coverage analysis method with high precision and efficiency for mega constellations. The proposed method is based on using differential algebraic techniques to construct the high-order Taylor expansions of complex functions. Initially, a clustering strategy for the mega Walker constellation is introduced. The orbits of all satellites within the constellation are analytically represented using high-order orbital expansion models derived from a selected number of nominal satellites. Subsequently, utilizing these high-order orbital expansion models, the high-order expansion of the visibility function corresponding to the nominal target is constructed, which can provide an analytical approximation of the visibility function between any satellites and targets within the cluster. The calculation of rise and set times is simplified to polynomial operations. Simulation results demonstrate that the proposed method achieves high prediction accuracy across various payload types. Furthermore, the computational efficiency is significantly enhanced for large-scale coverage analysis missions that involve mega constellations.