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分析了空间近程高速相对运动的特点,建立了描述近程高速相对运动的线性微分方程组,并给出了状态转移矩阵与解析解。仿真结果表明:对于HEO-GEO近程高速相对运动,所建方程的相对距离计算误差仅为16 cm,不足Hill方程计算误差的15%。所给出的状态转移矩阵对于实现空间目标拦截等任务的实时高精度相对导航和制导算法具有一定的应用价值。
The characteristics of relative motion at high speed in space are analyzed. A set of linear differential equations describing the relative motion at high speed in short range is established. The state transition matrix and analytic solution are also given. The simulation results show that the relative distance between the HEO-GEO and the HEO-GEO is only 16 cm, which is less than 15% of the error calculated by the Hill equation. The given state transition matrix has certain application value for real-time high-precision relative navigation and guidance algorithm of space target interception.