基于多边形距离的卫星对地时间窗口快速计算方法

A Fast Calculation Method for Satellite Earth Time Window Based on Polygonal Distance

摘要:

随着近地轨道上的卫星数量急剧上升、卫星之间通过组网以星座的方式协同工作,增加了对地监测的能力。“星链”是近年来低轨巨型星座的典范,“星链”星座卫星轨道高度低,周期短,重访率高；卫星携带传感器后对地球表面形成探测区域,星座不同卫星能够同时对重点区域实现多重覆盖,可对全球主要地区完成24小时不间断侦察监视。将建模计算得到的覆盖区域和目标区域在二维平面表示为多边形(星下点表示为平面内一点),可以把卫星对目标区域覆盖时间窗口计算问题转化为图形之间的几何关系判断问题。同时,针对固定步长耗时较长的问题,根据多边形之间的距离设计了求解时间窗口的快速计算方法。依据平面内多边形预测距离的变化率动态设置步长,一天内参与覆盖边界计算、与目标区域相交判断的采样点数目由86500个减少为457个,相比于固定步长方法效率提升约99.5%。

Abstract:

With the rapid increase of the number of satellites in low Earth orbit and the cooperation of satellites in constellation through networking, the ability of ground monitoring has increased. The "Starlink" is a model of low orbit giant constellations in recent years. The satellite orbit of the "Starlink" constellation is low, with short periods and high revisit rates; After carrying sensors, satellites form a detection area on the Earth"s surface, and different constellations of satellites can simultaneously achieve multiple coverage of key areas, completing 24-hour uninterrupted reconnaissance and monitoring of major regions around the world. This article represents the coverage area and target area obtained through modeling and calculation as polygons in a two-dimensional plane (the point below the star is represented as a point in the plane), which can transform the problem of calculating the time window for satellite coverage of the target area into a problem of determining the geometric relationship between the shapes. At the same time, a fast calculation method for solving the time window was designed based on the distance between polygons to address the problem of long time consuming fixed step sizes. By dynamically setting the step size based on the change rate of the predicted distance of polygons in the plane, the number of sampling points involved in coverage boundary calculation and intersection judgment with the target area within a day has been reduced from 86500 to 457, which improves the efficiency by about 99.5% compared to the fixed step size method.