Multi-station Joint Initial Orbit-determination and Uncertainty Estimation Method

Xuefeng TAO; Shuailong ZHAO; Zhi LI

doi:10.19328/j.cnki.2096-8655.2024.06.003

AEROSPACE SHANGHAI, Volume. 41, Issue 6, 23(2024)

Multi-station Joint Initial Orbit-determination and Uncertainty Estimation Method

Xuefeng TAO*... Shuailong ZHAO and Zhi LI |Show fewer author(s)

Author Affiliations

Space Engineering University，Beijing101400，China

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Figures & Tables(12)

Fig. 1. Optical short-arc orbit-determination uncertainty and multi-station orbit-determination principle

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Fig. 2. Two-dimensional projection of the GEO satellite orbiting results （observation duration：60 s）

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Fig. 3. Two-dimensional projection of the LEO satellite orbit-determination results （observation duration：5 s）

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Fig. 4. Two-dimensional projection of the HEO satellite orbit-determination results （observation duration：30 s）

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Table 1. Tab.1Station-related parameters
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Table 1. Tab.1Station-related parameters
参数测站1（国家天文台）测站2（云南天文台）
测站坐标
(117.57 °E,40.40 °N,
960 m)
(102.79 °E,25.03 °N,
2 000 m)
测量频率/Hz 1 2
观测精度（1σ）/(") 1 5

Table 2. Tab.2Satellite-related parameters

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Table 2. Tab.2Satellite-related parameters

测试目标	GEO	LEO	HEO
初始状态历元(UTC)	2019-04-20 T12:32:00	2019-10-20 T12:00:00	2019-10-20 T12:00:00
$a / k m$	42 166.262	7 500	22 000
$e$	0.106	0	0.7
$i / (°)$	0	30	40
$Ω / (°)$	89.420	20	0
$ω / (°)$	60.720	30	30
$f / (°)$	5.923	60	90
观测时段	12:32:00— 12:33:00	12:05:00— 12:05:05	12:20:00— 12:20:30
观测弧长/s	60	5	30
定轨历元	2019-04-20 T12:32:00	2019-04-20 T12:05:00	2019-04-20 T12:20:00

Table 3. Tab.3<bold>Orbit-determination results of the GEO satellite </bold>（<bold>observation duration</bold>：<bold>60 s</bold>）

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Table 3. Tab.3<bold>Orbit-determination results of the GEO satellite </bold>（<bold>observation duration</bold>：<bold>60 s</bold>）

轨道参数	测站1	测站2	单站定轨结果融合	双站联合定轨	真值
a/km	13 190.017	13 309.018	42 170.189	42 164.975	42 166.262
e	0.818	0.811	0.011	0.001	0
i/（°）	4.918	3.551	0.099	0.107	0.106
Ω/（°）	65.72	41.645	77.892	91.494	89.42
u/（°）	90.096	112.34	78.172	64.569	66.643

Table 4. Tab.4Standard deviation of the GEO satellite orbit-determination results

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Table 4. Tab.4Standard deviation of the GEO satellite orbit-determination results

轨道参数	测站1	测站2	单站定轨结果融合	双站联合定轨
x/km	1 218.296	1 479.857	0.112 291	0.016 447
y/km	532.672 3	575.772 3	0.048 684	0.006 649
z/km	144.282 4	113.390 2	0.013 152	0.001 552
v_x/(km·s^-1)	0.083 666	0.112 772	0.003 16	0.000 473
v_y/(km·s^-1)	0.096 529	0.141 694	0.001 368	0.000 191
v_z/(km·s^-1)	0.009 009	0.009 718	0.000 361	0.000 045

Table 5. Tab.5<bold>Orbit-determination results of the LEO satellite </bold>（<bold>observation duration</bold>：<bold>5 s</bold>）

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Table 5. Tab.5<bold>Orbit-determination results of the LEO satellite </bold>（<bold>observation duration</bold>：<bold>5 s</bold>）

轨道参数	测站1	测站2	单站定轨结果融合	双站联合定轨	真值
a/km	11 526.411	-2 658.875	7 503.408	7 500.226	7 500
e	0.329	4.361	0.001	0	0
i/（°）	28.47	33.83	29.999	30	30
Ω/（°）	28.016	31.409	30.031	30.001	30
u /（°）	96.716	91.881	96.682	96.707	96.708

Table 6. Tab.6Standard deviation of the LEO satellite orbit-determination results

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Table 6. Tab.6Standard deviation of the LEO satellite orbit-determination results

轨道参数	测站1	测站2	单站定轨结果融合	双站联合定轨
x/km	0.818 495	0.572 089	0.000 243	0.000 072
y/km	24.715 32	4.358 184	0.001 433	0.000 135
z/km	3.924 835	5.268 926	0.000 302	0.000 138
v_x/(km·s^-1)	0.056 715	0.090 554	0.000 068	0.000 024
v_y/(km·s^-1)	0.056 261	0.431 648	0.000 354	0.000 044
v_z/(km·s^-1)	0.005 388	0.543 568	0.000 082	0.000 045

Table 7. Tab.7<bold>Orbit-determination results of the HEO satellite </bold>（<bold>observation duration</bold>：<bold>30 s</bold>）

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Table 7. Tab.7<bold>Orbit-determination results of the HEO satellite </bold>（<bold>observation duration</bold>：<bold>30 s</bold>）

轨道参数	测站1	测站2	单站定轨结果融合	双站联合定轨	真值
a/km	6 333.545	1 3402.397	21 939.745	21 996.611	22 000
e	0.87	0.673	0.699	0.7	0.7
i/（°）	41.023	38.755	40.006	40	40
Ω/（°）	31.147	31.146	29.98	30	30
ω/（°）	302.037	335.991	359.993	359.997	0
f/（°）	171.76	137.883	115.423	115.403	115.401

Table 8. Tab.8Standard deviation of the HEO satellite orbit-determination results

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Table 8. Tab.8Standard deviation of the HEO satellite orbit-determination results

轨道参数	测站1	测站2	单站定轨结果融合	双站联合定轨
x/km	406.991 5	469.810 4	0.012 153	0.001 25
y/km	211.786 1	136.661 8	0.006 294	0.000 492
z/km	290.486 3	422.605 3	0.008 683	0.001 04
v_x/(km·s^-1)	0.256 214	0.283 398	0.000 604	0.000 072
v_y/(km·s^-1)	0.088 742	0.096 182	0.000 31	0.000 028
v_z/(km·s^-1)	0.036 798	0.046 293	0.000 444	0.000 06

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Xuefeng TAO, Shuailong ZHAO, Zhi LI. Multi-station Joint Initial Orbit-determination and Uncertainty Estimation Method[J]. AEROSPACE SHANGHAI, 2024, 41(6): 23

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Paper Information

Category:

Received: Feb. 24, 2024

Accepted: --

Published Online: Mar. 7, 2025

The Author Email:

DOI:10.19328/j.cnki.2096-8655.2024.06.003

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Tab.1Station-related parameters

Table 1. Tab.1Station-related parameters

Table 2. Tab.2Satellite-related parameters

Table 2. Tab.2Satellite-related parameters

Table 3. Tab.3<bold>Orbit-determination results of the GEO satellite </bold>（<bold>observation duration</bold>：<bold>60 s</bold>）

Table 3. Tab.3<bold>Orbit-determination results of the GEO satellite </bold>（<bold>observation duration</bold>：<bold>60 s</bold>）

Table 4. Tab.4Standard deviation of the GEO satellite orbit-determination results

Table 4. Tab.4Standard deviation of the GEO satellite orbit-determination results

Table 5. Tab.5<bold>Orbit-determination results of the LEO satellite </bold>（<bold>observation duration</bold>：<bold>5 s</bold>）

Table 5. Tab.5<bold>Orbit-determination results of the LEO satellite </bold>（<bold>observation duration</bold>：<bold>5 s</bold>）

Table 6. Tab.6Standard deviation of the LEO satellite orbit-determination results

Table 6. Tab.6Standard deviation of the LEO satellite orbit-determination results

Table 7. Tab.7<bold>Orbit-determination results of the HEO satellite </bold>（<bold>observation duration</bold>：<bold>30 s</bold>）

Table 7. Tab.7<bold>Orbit-determination results of the HEO satellite </bold>（<bold>observation duration</bold>：<bold>30 s</bold>）

Table 8. Tab.8Standard deviation of the HEO satellite orbit-determination results

Table 8. Tab.8Standard deviation of the HEO satellite orbit-determination results

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