The constellation-to-ground coverage problem is a basic and important problem in satellite applications. The grid-point approach (GPA) is one of the most commonly used approaches to solving this problem. However, this approach also has some serious drawbacks. A group of strategies that can improve or overcome the drawbacks of this approach are proposed. The spatial and temporal characteristics of the GPA were analyzed, and a strategy that can compute the upper and lower bounds of the result was given. This strategy can not only acquire the result but can also yield the error range of the result. In addition, a strategy that uses low-precision results to compute a high-precision result is proposed. Simulation experiments of different types of coverage problems were conducted, and the results show that these strategies are effective.

This article studies the problem of analyzing the coverage capacity of satellite constellations with respect to ground regions. The coverage characteristics and formulations are first investigated, and a corresponding symbol system is established. On this basis, the coverage state function and the corresponding extension and intermediate modes for basic coverage analysis problems are defined. By introducing the parameter wildcard characters, the properties of three basic spatial and temporal factors are described. An integrated coverage theory system is constructed accordingly to formalize the general coverage analysis problems in a uniform way, which is versatile and works on representing any type of coverage analysis problems. Additionally, in accordance with the properties of the coverage theory, a boundary function is proposed. The corresponding algorithm framework is also constructed for the calculation of complicated practical coverage analysis problems. Experiments simulating different types of coverage analysis problems are carried out, and results reveal the correctness and the effectiveness of the proposed coverage theory system and algorithm framework.

Coverage capacity analysis of satellites constellation is the basis of satellite system design and performance evaluation, which is essential in the application of satellite technology. A characteristic area based method for continuous coverage analysis is proposed in this paper. The trajectory characteristics of the Walker constellation are first analyzed. The Earth's surface is partitioned into a group of characteristic areas, and the characteristic distance theory is defined and proposed accordingly. On this basis, the formulations of the characteristic point of each characteristic area and the corresponding characteristic distance with all different situations can be analytically obtained. Additionally, sufficient and necessary conditions for continuous coverage are given accordingly. The complex continuous coverage problem can be converted to the analysis of the relations between the critical geocentric angle of the satellite coverage range and the characteristic distance. Computational results indicate the effectiveness of the proposed method and reveal the feasibility in instructing the constellation design.

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.

This paper studies the influence of orbital element error on coverage calculation of a satellite. In order to present the influence, an analysis method based on the position uncertainty of the satellite shown by an error ellipsoid is proposed. In this error ellipsoid, positions surrounding the center of the error ellipsoid mean different positioning possibilities which present three-dimensional normal distribution. The possible subastral points of the satellite are obtained by sampling enough points on the surface of the error ellipsoid and projecting them on Earth. Then, analysis cases are implemented based on these projected subastral points. Finally, a comparison report of coverage calculation between considering and not considering the error of orbital elements is given in the case results.