单点弹道精度与轨道半长轴远地点高度计算精度的映射关系

在仅使用单点位置、速度信息计算轨道的奈件下,针对轨道半长轴、远地点高度的精度问题,在轨道面内,应用活力公式和二体运动学理论推导得出了轨道计算精度与弹道测量精度间映射关系的解析表达式,并采用数值分析方法给出了不同的位置、速度误差与半长轴、远地点高度最大误差之间的数值关系.仿真结果表明,对于位置误差和速度误差大小分别为100 m和1 m/s的算例,半长轴最大误差和远地点高度最大误差分别约为2 km和4 km.基于此方法,可以将弹道误差传递至轨道参数误差,进一步分析故障误判和漏判概率;也可根据轨道参数精度要求反算弹道测量精度要求,以作为地面测量系统建设的技术依据.

Mapping Relationship between Single Point Trajectory Accuracy and Accuracy of Semi Major Axis and Altitude of Apogee

This paper analyses precision of the semi major axis and altitude of the apogee of orbits under the conditions of single point position and velocity information. In the orbit plane, this paper derives analytical expressions for precision relationship of orbit determination to trajectory by using equations and kinematic theory of two bodies, and gives their numerical error relationship by method of numerical analysis. Simulation results show the errors of semi major axis and altitude of the apogee can reach 2 km and 4 km respectively when the error of position and velocity are 100 m and 1 m/s. Our method is practically significant for surface measuring systems. Errors of orbit parameters can be derived from the errors of trajectory, which are used to compute the probability of inaccurate judgment or missing judgment, and the accuracy of trajectory needed can be derived from the accuracy of orbit conversely