天基光学空间目标监测的初轨确定

doi:10.7527/S1000-6893.2022.26465

Abstract

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

CLC Number:

V412.41

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.

Figures/Tables 10

Fig. 1

Fig. 2

Table 1

Actual measurements from LEO observation platform to LEO target

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

Table 1

Table 2

Slant-ranges corresponding to positive real roots at observed times

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

Table 2

Fig. 3

Table 3

Iterations and convergence results of LEO target corresponding to different slant-ranges

$ρ 1$ / $R E a r t h$	$ρ 3$ / $R E a r t h$	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

Table 3

Table 4

Simulation measurements from GEO observation platform to GEO target

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

Table 4

Table 5

Slant-ranges corresponding to positive real roots at observed times

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

Table 5

Fig. 4

Table 6

Iterations and convergence results of GEO target corresponding to different slant-ranges

$ρ 1$ / $R E a r t h$	$ρ 3$ / $R E a r t h$	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

Table 6

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Initial orbit determination for space-based optical space surveillance

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