The use of regional coverage satellite constellations is on the rise, urging the need for an optimal constellation design method for complex regional coverage. Traditional constellations are often designed for continuous global coverage, and the few existing regional constellation design methods lead to suboptimal solutions for periodically time-varying or spatially-varying regional coverage requirements. This paper introduces a new general approach to design an optimal constellation pattern that satisfies such complex regional coverage requirements. To this end, the circular convolution nature of the repeating ground track orbit and common ground track constellation is formalized. This formulation enables a scalable constellation pattern analysis for multiple target areas and with multiple sub-constellations. The formalized circular convolution relationship is first used to derive a baseline constellation pattern design method with the conventional assumption of symmetry. Next, a novel method based on binary integer linear programming is developed, which aims to optimally design a constellation pattern with the minimum number of satellites. This binary integer linear programming method is shown to achieve optimal constellation patterns for general problem settings that the baseline method cannot achieve. Five illustrative examples are analyzed to demonstrate the value of the proposed new approach.

中文翻译：

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复杂区域覆盖的卫星星座图优化

区域覆盖卫星星座的使用正在增加，迫切需要针对复杂区域覆盖的最佳星座设计方法。传统星座通常设计用于连续的全球覆盖，而现有的少数区域星座设计方法导致针对周期性时变或空间变化的区域覆盖要求的次优解决方案。本文介绍了一种新的通用方法来设计满足这种复杂区域覆盖要求的最佳星座图。为此，形式化了重复地面轨道轨道和公共地面轨道星座的圆形卷积性质。该公式可以对多个目标区域和多个子星座进行可扩展的星座模式分析。形式化的圆形卷积关系首先用于推导出具有常规对称性假设的基线星座图案设计方法。接下来，开发了一种基于二进制整数线性规划的新方法，旨在以最少的卫星数优化设计星座图。这种二进制整数线性规划方法被证明可以实现基线方法无法实现的一般问题设置的最佳星座模式。分析了五个说明性示例以证明所提出的新方法的价值。其目的是用最少的卫星优化设计星座图。这种二进制整数线性规划方法被证明可以实现基线方法无法实现的一般问题设置的最佳星座模式。分析了五个说明性示例以证明所提出的新方法的价值。其目的是用最少的卫星优化设计星座图。这种二进制整数线性规划方法被证明可以实现基线方法无法实现的一般问题设置的最佳星座模式。分析了五个说明性示例以证明所提出的新方法的价值。