Extended 2D Map for Satellite Coverage Analysis Considering Elevation-Angle Constraint

The analysis of satellite coverage to determine the visibility of ground targets from satellites has been extensively studied, particularly through geometric-based methods that provide analytical results. However, there exists a key limitation that these methods do not precisely consider the elevation-angle constraint. To address this limitation, this article provides a geometric approach for computing the visibility considering the elevation-angle constraint. First, the mathematical model of the elevation-angle constraint is established, and the elevation-element equation describing the geometrical relationship between satellite and ground target satisfying the elevation-angle constraint is deduced. Additionally, based on the analytical solution to the elevation-element equation, a two-dimensional map, named the elevation mapping, is proposed. Subsequently, the presented geometric approach is established by incorporating the elevation-angle constraint model into the satellite-target visibility model, and an extended field mapping is proposed to rapidly compute access intervals while adhering to the elevation-angle constraint. Specifically, it achieves this by converting the task into a straightforward problem involving the intersection of a set of lines with the time-invariant regions generated by the extended field mapping. Furthermore, the extended constellation field mapping is presented, which can simplify the multisatellite coverage problem into an easier single-satellite coverage problem, enabling it to solve the constellation coverage problem considering elevation-angle constraints analytically and rapidly. Simulation results demonstrate that the proposed intuitive methodology can accurately and rapidly compute access intervals while considering the elevation-angle constraint, which suggests its wide applications in satellite coverage analysis.