Efficient Large-Scale Constellation Coverage Analysis via Visibility Manifold Surrogates

This article proposes a visibility manifold surrogate framework for satellite and constellation coverage analysis under generalized sensor footprints and secular [Formula: see text] perturbations. To characterize generalized field-of-view constraints, a unified mathematical model utilizing a signed distance field is established, reducing the visibility problem to a bounded parameter space via equivalence mapping. Building upon the resulting high-dimensional visibility boundary manifold, a topological layered decomposition approach constructs locally single-valued interpolation surrogate models. To mitigate nonlinear interpolation errors near the manifold boundaries, a vectorized tubular-parameter correction mechanism is integrated, transforming large-scale constellation coverage computations into efficient analytical queries. The framework is further extended to rapidly evaluate dynamic accumulated coverage for regional targets by incorporating polygon Boolean intersections and one-dimensional boundary extremum optimization. Simulation results demonstrate that, compared to traditional numerical root-finding approaches, the proposed method accelerates computational speed by over an order of magnitude while maintaining access window timing errors predominantly below [Formula: see text]. Consequently, the proposed visibility manifold surrogate framework provides a geometric tool for large-scale constellation design, agile resource scheduling, and Earth observation missions.