Geometric-Based Method for Regional-Target Coverage Analysis

Abstract

This study proposes a geometric-based method of providing regional target visibility from a satellite considering the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_2$</tex-math></inline-formula> perturbation. First, the basic mathematical model is introduced followed by the field-element equations for ground-point visibility analysis and envelope equations of a family of curves. Then, the concept of a regional-field-mapping envelope and its subset baseline field-mapping envelope are presented for calculating visible intervals. The envelopes transform the complex problem of calculating a visible interval into a simple intersection problem for a group of parallel lines representing a satellite's trajectory and the regional-field-mapping envelope. Based on the analytical partial differential of the field-element equations, the baseline-field-mapping envelope for smooth and non-smooth field of views can be rapidly calculated where the regional-field-mapping envelope can be obtained by splicing the baseline-field-mapping envelopes. The simulation results show that the proposed method is rapid, accurate, and intuitive, demonstrating its wide applications for regional-target coverage analysis.