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

Abstract

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

CLC Number:

V412.41

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.

Figures/Tables 11

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References 30

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

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