Critical-Point n-Fold Coverage Evaluation for Continuous Coverage in Mega-Constellation Design

Coverage evaluation in the orbital design of satellite constellations is a major driver of project cost because it dictates the required number of satellites. This becomes particularly critical when the objective is continuous 24/7 coverage, which requires eliminating coverage gaps while maintaining an optimal satellite count. Numerous methods have been proposed for evaluating coverage, each involving trade-offs between accuracy and computational load. Considering the limitations of previous methods, this paper presents a critical-point-based approach that focuses on spatial boundary locations and footprint intersections where coverage loss within the target area is most likely. The method improves coverage-evaluation accuracy while reducing computational complexity and sensitivity to spatial and temporal discretization. After presenting the underlying theory, we assess performance through case studies. We define mission parameters and perform orbit design via numerical optimization using particle swarm optimization (PSO) under simultaneous n-fold coverage constraints. The resulting designs are re-evaluated with the conventional grid point approach (GPA), yielding consistent outcomes. Although the numerical evaluation in this paper focuses on Walker-Delta orbital patterns and conical sensor footprints, the proposed critical-point framework is conceptually general and can be applied to other orbit families and footprint geometries.