近地轨道卫星的地影预报算法

针对传统地影预报算法计算量大，不适合星载计算机进行地影时刻自主预报的问题，提出一种地影预报星上算法。通过构造降维坐标系将卫星进出地影过程转换为“星-地-日”平面内的几何问题；基于常数变易法推导出阴影条件的隐式解析公式，其方程系数可由实时轨道参数确定。为简化计算，将星上算法设计为双层结构：构造迭代算法，依据实时轨道参数可精确预报卫星在每个节点上的地影时刻；而在任意两个节点之间采用解析算法进行近似预报。仿真结果表明，星上算法的预报精度高且计算量小，适合星载计算机进行地影时刻自主预报。

Umbra Prediction Algorithms for LEO Satellite

The traditional umbra prediction algorithms are of huge computational effort, and not suitable for the on-board computer to predict the shadow moments autonomously. Therefore, a on-board algorithm for shadow prediction is proposed in this paper. By constructing a reduced dimension coordinate system, the process of satellites′ entering or leaving the shadow is transformed into the geometry problem occurring in the plane containing the satellite, the Earth and the Sun. The implicit analytical formula of the shadow conditions can be derived based on the constant variation method, namely the coefficients of the equation are given by the real-time orbit parameters. The spaceborne algorithm is designed into two-layer structure to simplify calculations. The shadow moments of satellites at every node are precisely predicted by constructing an iteration algorithm according to the real-time orbit parameters, and the analytical algorithm can be used to approximatively predict the shadow moments between nodes. Numerical simulations have shown that the spaceborne algorithm is of high predicting accuracy and small computational effort, and is suitable for the on-board computer to predict the shadow moments autonomously.