基于微分改正和圆轨道约束的广义Laplace方法初轨确定  

Initial orbit determination using the generalized Laplacian method with differential correction and circular-orbit constraint

作　　者：汤靖师[1,2,3] 程昊文 TANG JingShi;CHENG HaoWen(School of Astronomy and Space Science,Nanjing University,Nanjing 210023,China;Key Laboratory of Astronomy and Astrophysics,Ministry of Education,Nanjing 210023,China;Institute of Space Environment and Astrodynamics,Nanjing University,Nanjing 210023,China;National Astronomical Observatories,Chinese Academy of Sciences,Beijing 100012,China;School of Astronomy and Space Science,University of Chinese Academy of Sciences,Beijing 100012,China)

机构地区：[1]南京大学天文与空间科学学院,南京210023 [2]现代天文与天体物理教育部重点实验室,南京210023 [3]南京大学空间环境与航天动力学研究所,南京210023 [4]中国科学院国家天文台,北京100012 [5]中国科学院大学天文与空间科学学院,北京100012

出　　处：《中国科学：物理学、力学、天文学》2022年第6期117-129,共13页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:11873031)资助项目。

摘　　要：航天器的初轨确定在卫星测控、空间碎片监测等场景中有重要的作用.广义Laplace方法以经典的Laplace方法为基础,支持摄动和多种观测类型,过程清晰、原理简单、构造方便,在实测场景中可以取得较好的使用效果.但在处理中高轨目标的观测数据时,现有的广义Laplace方法仍时有失效的情况出现.事实上,由于中高轨目标弧段较短,特别是同步轨道目标相对地面静止,短弧段定轨相对观测几何较差.受观测误差的影响,即使观测量均方根差(RMS)收敛到极小值,所得初轨中的轨道面内根数有时也会出现较大的偏差.本文在现有的广义Laplace方法基础上,使用微分改正来求解法化方程,提高收敛稳定性.同时对于明确的圆轨道目标,引入额外的约束.结果表明,通过这两项改进,初轨计算的收敛和结果的合理性有明显改善.以往很难收敛或不合理的初轨结果仅通过数次迭代就能稳定地得到圆轨道结果.Initial orbit determination(IOD)for spacecraft is crucial in various scenarios,including telemetry,tracking,and space debris surveillance.The generalized Laplacian method,based on the classic Laplacian method,supports various perturbations and measurement types.It is simple to comprehend,implement,and convenient to use and has been proven effective in practical applications.However,the current implementation of the generalized Laplacian method can fail when dealing with certain medium earth orbit(MEO)or geosynchronous orbit(GEO)objects.IOD solutions suffer from reduced observation geometry due to the short tracking length of MEO and GEO.The measurement error can cause inplane elements in IOD solutions,such as the semi-major axis and eccentricity,to be significantly biased even if IOD converges and the measurement residual RMS(root mean square)appears small.In this paper,differential correction(Newton-Raphson iteration)is used to improve the convergence of the generalized Laplacian method.We show that using the first-order derivative(Jacobian matrix)reduces the number of iterations significantly.It also helps in the convergence of iteration procedures when simple iteration techniques fail to solve the condition equation iteratively.Tracking data can be too short or sparse in some cases to effectively constrain the IOD solution to a reasonable level.An eccentric orbit solution can result from the measurements of a circular-orbit object.To overcome the inappropriate solution induced by insufficient tracking data,we introduce an external circular-orbit constraint in the condition equation when dealing with tracking data whose orbit is known to be circular.This constraint is effective in producing a suitable IOD solution when used with the measurements in the generalized Laplacian method.Our results indicate that,with a slight adjustment,the circular-orbit constraint can perform effectively in the generalized Laplacian method even when the tracking data are extremely sparse.

关 键 词：初轨确定 广义Laplace方法 地球同步轨道 空间碎片监测 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]