近地天体与空间目标初轨确定的多解问题

doi:10.12305/j.issn.1001-506X.2022.09.26

系统工程与电子技术 ›› 2022, Vol. 44 ›› Issue (9): 2914-2921.doi: 10.12305/j.issn.1001-506X.2022.09.26

近地天体与空间目标初轨确定的多解问题

赵柯昕^1,^2,³, 甘庆波^1,^2,^3,*, 杨志涛^1,^2,³, 刘静^1,^2,³

1. 中国科学院国家天文台, 北京 100012
2. 国家航天局空间碎片监测与应用中心, 北京 100012
3. 中国科学院大学, 北京 100049

收稿日期:2021-08-27 出版日期:2022-09-01 发布日期:2022-09-09
通讯作者: 甘庆波
作者简介:赵柯昕(1995—), 男, 博士研究生, 主要研究方向为天基空间目标的初始轨道确定|甘庆波(1982—), 男, 研究员, 博士, 主要研究方向为天体测量与天体力学|杨志涛(1986—), 男, 助理研究员, 博士, 主要研究方向为航天器轨道力学|刘静(1970—), 女, 研究员, 博士, 主要研究方向为空间碎片监测与预警技术
基金资助:
国家自然科学基金(12073045);国防科工局空间碎片十四五专项(KJSP2020020205);国防科工局空间碎片十四五专项(KJSP2020020102)

Multiple-roots problem of initial orbit determination of near-Earth object and space target

Kexin ZHAO^1,^2,³, Qingbo GAN^1,^2,^3,*, Zhitao YANG^1,^2,³, Jing LIU^1,^2,³

1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
2. Space Debris Observation and Data Application Center, China National Space Administration, Beijing 100012, China
3. University of Chinese Academy of Sciences, Beijing 100049, China

Received:2021-08-27 Online:2022-09-01 Published:2022-09-09
Contact: Qingbo GAN

摘要/Abstract

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。

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

Abstract:

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.

Key words: initial orbit determination, near-earth object, space target, space-based space target surveillance, 8th-degree polynomial equation

中图分类号:

V412.41

赵柯昕, 甘庆波, 杨志涛, 刘静. 近地天体与空间目标初轨确定的多解问题[J]. 系统工程与电子技术, 2022, 44(9): 2914-2921.

Kexin ZHAO, Qingbo GAN, Zhitao YANG, Jing LIU. Multiple-roots problem of initial orbit determination of near-Earth object and space target[J]. Systems Engineering and Electronics, 2022, 44(9): 2914-2921.

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观测时刻	MJD	赤经/(°)	赤纬/(°)	地球X/AU	地球Y/AU	地球Z/AU
t₁	59 243.266 710	47.719 328	17.782 398	-0.616 715 716	0.704 510 08	0.305 402 78
t₂	59 253.277 130	37.983 650	14.938 175	-0.743 577 968	0.594 637 62	0.257 776 60
t₃	59 264.183 290	27.591 571	11.353 189	-0.855 605 760	0.454 102 59	0.196 856 38

正实根	ρ₁	ρ₂	ρ₃
1	-1.073 154 12	-0.948 024 74	-0.779 208 16
2	0.170 215 00	0.145 732 50	0.124 410 83

观测时刻	MJD	赤经/(°)	赤纬/(°)	观测平台X/km	观测平台Y/km	观测平台Z/km
t₁	59 410.192 361 11	14.412 735	-32.412 455	-6 323.548	-2 290.293	547.849
t₂	59 410.194 444 44	12.478 481	-29.897 754	-5 779.067	-3 482.275	115.328
t₃	59 410.196 527 78	12.891 181	-26.900 668	-4 992.551	-4 528.415	-322.023

非伪解	ρ₁/R_Earth	ρ₂/R_Earth	ρ₃/R_Earth	f₁	f₃
1	0.777 383 57	0.588 538 89	0.444 578 59	0.007 445 23	0.005 868 73
2	4.647 871 44	3.459 195 58	2.658 074 77	1.634 331 24	1.653 806 37

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近地天体与空间目标初轨确定的多解问题

Multiple-roots problem of initial orbit determination of near-Earth object and space target

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