已知e或a的先验值的初轨迭代算法

AN ITERATIVE ALGORITHEM OF THE INITIAL ORBIT DETERMINATION WITH A PRIORI VALUE OF THE ELEMENT e OR a

本文讨论由短弧测角资料，已知偏心率ｅ 或半长轴ａ 的先验值时，初轨的迭代算法。某根数的先验值可看作是对该根数的具有一定精度的观测量，在加权残差平方和达到极小意义下，本文导出了最小二乘估计的迭代算法。仿真结果显示，周期的估计精度主要取决于偏心率先验值的精度；当ｅ 足够小时，可用园轨道计算的ａ′作为ａ 的先验值，定出的初轨有较高精度。

With a priori value of the orbital element e or a ,an iterative algorithem to determine the initial orbit,using the short arc angle data,is investigated in this paper.A priori value of orbital element can be regarded as an observation with proper precision,and the residual term corresponding to the observation of e or a can be put in the weighted square sum of residuals.Minimizing the weighted square sum of the residuals,the iterative algorithem of initial orbit determination with a priori value of e or a is derived.In fact,This method is an iterative algorithem of the least square estimation.Simulations show that the accuracy of the orbital period mainly depends on the precision of the priori value of eccentricity e .When the eccentricity e is small enough,the semi major axis a′ estimated with circular orbit may be regarded as the priori value of the orbital element a .Then,using the above algorithem with the priori value of the semi major axis a ,the result of initial orbit can be got with high accuracy.