天基光学空间目标监测的初轨确定

doi:10.7527/S1000-6893.2022.26465

电子电气工程与控制

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天基光学空间目标监测的初轨确定

赵柯昕¹^,²^,³, 甘庆波¹^,²^,³(), 刘静¹^,²^,³

^1.中国科学院国家天文台，北京 100101
^2.国家航天局空间碎片监测与应用中心，北京 100101
^3.中国科学院大学，北京 100049

收稿日期:2021-09-29 修回日期:2021-11-13 接受日期:2022-02-14 出版日期:2023-01-15 发布日期:2022-02-28
通讯作者: 甘庆波 E-mail:ganqingbo@nao.cas.cn
基金资助:
国家自然科学基金(12073045);中国科学院青年创新促进会(2018183)

Initial orbit determination for space-based optical space surveillance

Kexin ZHAO¹^,²^,³, Qingbo GAN¹^,²^,³(), Jing LIU¹^,²^,³

^1.The National Astronomical Observatories，Chinese Academy of Sciences，Beijing 100101，China
^2.Space Debris Observation and Data Application Center，China National Space Administration，Beijing 100101，China
^3.University of Chinese Academy of Sciences，Beijing 100049，China

Received:2021-09-29 Revised:2021-11-13 Accepted:2022-02-14 Online:2023-01-15 Published:2022-02-28
Contact: Qingbo GAN E-mail:ganqingbo@nao.cas.cn
Supported by:
National Natural Science Foundation of China(12073045);Youth Innovation Promotion Association of Chinese Academy of Sciences(2018183)

摘要/Abstract

摘要：

针对天基空间目标光学监测时初轨确定（IOD）困难的问题，讨论了计算结果收敛到平凡解的本因，提出了消去平凡解的改进定轨流程。通过构建Laplace初轨确定方法的八次方程，分析了空间目标处于不同相对位置时方程系数和根的性质之间的关系。针对传统Laplace型初轨确定方法收敛到观测平台轨道的现象，给出了平凡解的数学表征和数值验证并提出了消除方法。由于基于Lambert问题利用距离搜索的初轨确定方法进行天基目标监测时对初值相对敏感，利用平凡解消除方法对Gooding法进行了改造，提出了一种适用于天基空间目标初轨确定的方法与流程。最后利用低轨目标监测的实测数据和高轨目标监测的仿真数据对方法进行了验证。结果表明本方法可有效解决平凡解和初值敏感问题，方法具有收敛速度快、精度可靠的特点，且具有普适性，易于理解，便于推广。

关键词: 天基, 空间目标监测, 初轨确定, 平凡解, Lambert问题

Abstract:

Initial Orbit Determination （IOD） is a difficult problem in space-based optical space surveillance. Based on a discussion of the reason for the convergence of the calculation results converge to the trivial solution， an improved IOD procedure that eliminates the trivial solution is proposed. By constructing the 8th polynomial equation of the Laplace method， the relationship between the properties of coefficients and roots when the space target is at different relative positions is analyzed. For the phenomenon that the classical Laplace-type IOD method converges to the orbit of observation platform， the mathematical characterization and numerical verification of the trivial solution are given， and an elimination method is proposed. Since the IOD method using distance search based on the Lambert problem is relatively sensitive to the initial value of space-based target monitoring， the Gooding method is modified by the trivial solution elimination method， and a new method suitable for IOD of space-based space targets is proposed. Finally， the method is verified by measured data of low Earth orbit target monitoring and simulation data of geosynchronous orbit target monitoring. The results show that this method can effectively solve the trivial solution and initial value sensitive problems. The method has the characteristics of fast convergence speed and reliable accuracy， and is thus universal， easy to understand and generalize.

Key words: space-based, space target surveillance, initial orbit determination, trivial solution, Lambert problem

中图分类号:

V412.41

赵柯昕, 甘庆波, 刘静. 天基光学空间目标监测的初轨确定[J]. 航空学报, 2023, 44(1): 326465-326465.

Kexin ZHAO, Qingbo GAN, Jing LIU. Initial orbit determination for space-based optical space surveillance[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 326465-326465.

图/表 10

图1

图2

表 1

低轨平台观测低轨目标的实测数据

时间/s	赤经/（°）	赤纬/（°）	测站位置X/ $R E a r t h$	测站位置Y/ $R E a r t h$	测站位置Z/ $R E a r t h$
58 705.468 372	286.821	-31.672	-0.129 429	0.612 636	-0.886 445
58 705.469 784	290.464	-23.995	-0.072 997	0.501 337	-0.959 985
58 705.472 580	297.054	-8.171	0.041 627	0.256 631	-1.054 192

表 1

表2

正实根所对应的观测时刻斜距值

正实根	$ρ 1$ / $R E a r t h$	$ρ 2$ / $R E a r t h$	$ρ 3$ / $R E a r t h$
1.083 742 08	0.053 060 77	0.051 794 47	0.049 878 43
1.093 472 53	0.212 992 52	0.207 945 82	0.200 703 91
5.955 225 33	6.147 425 39	5.917 827 86	5.845 168 10

表2

图3

表3

LEO目标不同斜距的迭代次数和收敛结果

$ρ 1$ / $R E a r t h$	$ρ 3$ / $R E a r t h$	半长轴/km	迭代次数
0.05	0.05	6 925.613	7
0.1	0.1	6 925.613	8
0.15	0.15	7 039.847	8
0.212 993	0.200 704	7 039.847	4
0.3	0.3	7 039.847	6
0.4	0.4	7 039.847	7
0.5	0.5	7 039.847	7
0.8	0.8	7 039.847	7
1	1	6 925.613	10
2	2	-190.149 8	6

表3

表4

GEO平台观测GEO目标的仿真数据

时间/s	赤经/（°）	赤纬/（°）	测站位置X/ $R E a r t h$	测站位置Y/ $R E a r t h$	测站位置Z/ $R E a r t h$
59 367.166 666 7	52.341 6	8.649 2	5.567 008 8	3.214 114 1	0.000 001 2
59 367.170 138 9	51.391 7	6.587 5	5.501 123 3	3.324 885 4	0.069 971 3
59 367.173 611 1	50.426 4	4.476 0	5.432 374 3	3.433 926 1	0.139 907 5

表4

表5

正实根所对应的观测时刻斜距值

正实根	$ρ 1$ / $R E a r t h$	$ρ 2$ / $R E a r t h$	$ρ 3$ / $R E a r t h$
6.427 777 80	0.002 994	0.002 959	0.002 928
6.499 000 30	2.376 773	2.348 992	2.324 254
71.399 459 37	72.967 005	72.096 003	71.354 694

表5

图4

表6

GEO目标不同斜距的迭代次数和收敛结果

$ρ 1$ / $R E a r t h$	$ρ 3$ / $R E a r t h$	半长轴/km	迭代次数
0.5	0.5	40 996.089	7
1	1	40 996.089	8
2	2	42 672.451	6
2.376 773	2.324 254	42 672.451	4
3	3	42 672.451	6
4	4	42 672.451	7
5	5	42 672.451	6
6	6	42 672.451	7

表6

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天基光学空间目标监测的初轨确定

Initial orbit determination for space-based optical space surveillance

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