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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 5097324, 10 pages
Research Article

Judgement Theorems and an Approach for Solving the Constellation-to-Ground Coverage Problem

1School of Computer, China University of Geosciences, Wuhan 430074, China
2Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan 430074, China
3Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China

Correspondence should be addressed to Maocai Wang

Received 15 September 2017; Accepted 14 January 2018; Published 22 February 2018

Academic Editor: Raffaele Solimene

Copyright © 2018 Zhiming Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The satellite constellation-to-ground coverage problem is a basic and important problem in satellite applications. A group of judgement theorems is given, and a novel approach based on these judgement theorems for judging whether a constellation can offer complete single or multiple coverage of a ground region is proposed. From the point view of mathematics, the constellation-to-ground coverage problem can be regarded as a problem entailing the intersection of spherical regions. Four judgement theorems that can translate the coverage problem into a judgement about the state of a group of ground points are proposed, thus allowing the problem to be efficiently solved. Single- and multiple-coverage problems are simulated, and the results show that this approach is correct and effective.