摘要
针对近地天体与空间目标光学观测资料初轨确定过程中求解Laplace或Gauss八次方程时遇到的多个根无法判别的问题,提出了一种有效的选择算法。通过构建Laplace八次方程,分析了八次方程系数与根的个数之间的关系。利用观测平台地心距对八次方程进行归一化,消除了平凡解,并分析了方程非伪解个数与观测几何之间的关系。从求解半通径的方程出发,利用Shefer方程,推导了斜距约束,得到了观测时间间隔和斜距变化量之间应满足的方程组的解析形式,给出了利用该方程组判别非伪解的方法。最后,对近地天体和空间目标的初轨确定进行了仿真验证,仿真结果表明本方法能快速且有效地选择出正确的根,解决了多个非伪解难以选择的问题。
Aiming at the problem that multiple roots cannot be distinguished when solving 8th-degree polynomial equations of Laplace or Gauss form in the process of initial orbit determination(IOD)of near-Earth objects and space objects using optical measurements,this paper proposes an effective distinguishing method.By constructing Laplace form 8th-degree polynomial equation,the relationship between the coefficients of the equation and the number of roots is analyzed.The equation is normalized by using the distance between the observation platform and the geocentric to eliminate the trivial solution and analyze the relationship between the number of non-pseudo solutions and geometrical configuration.Starting from solving the semi-latus rectum,the constraint relationship that the slant range should be satisfied in IOD is derived,using the general equation proposed by Shefer.The analytic form of the equations which should be satisfied between the observation time intervals and the changes of slant range is obtained and the distinguishing method of multi non-pseudo solutions using the equations is given.Finally,the IOD of near-Earth objects and space objects is verified by simulation measurements.The results show that this method can quickly and effectively select the correct root,and solve the problem of multi non-pseudo solutions that cannot be selected.
作者
赵柯昕
甘庆波
杨志涛
刘静
ZHAO Kexin;GAN Qingbo;YANG Zhitao;LIU Jing(National Astronomical Observatories,Chinese Academy of Sciences,Beijing 100012,China;Space Debris Observation and Data Application Center,China National Space Administration,Beijing 100012,China;University of Chinese Academy of Sciences,Beijing 100049,China)
出处
《系统工程与电子技术》
EI
CSCD
北大核心
2022年第9期2914-2921,共8页
Systems Engineering and Electronics
基金
国家自然科学基金(12073045)
国防科工局空间碎片十四五专项(KJSP2020020205,KJSP2020020102)资助课题。
关键词
初轨确定
近地天体
空间目标
天基空间目标监测
八次方程
initial orbit determination
near-earth object
space target
space-based space target surveillance
8th-degree polynomial equation
