Initial Orbit Determination of Space Targets Based on Spatial Filtering Velocimetry

Han Pei; Sheng Cai; Jiulong Wang; Yan Xing; Luwei Zhang; Jinfeng Li; Le Liu

doi:10.3788/AOS241712

Acta Optica Sinica, Volume. 45, Issue 12, 1211001(2025)

Initial Orbit Determination of Space Targets Based on Spatial Filtering Velocimetry

Han Pei^1,2, Sheng Cai^1、*, Jiulong Wang¹, Yan Xing¹, Luwei Zhang¹, Jinfeng Li^1,2, and Le Liu^1,2

¹Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, Jilin , China

²University of Chinese Academy of Sciences, Beijing 100039, China

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Abstract Get PDF(in Chinese)

Figures & Tables(17)

Fig. 1. Geometric structure of optical observation

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Fig. 2. Schematic diagram of spatial filter

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Fig. 3. Filter (grating) shape and modulation waveform

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Fig. 4. Projection mode

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Fig. 5. Schematic diagram of space filter fixed orbit imaging

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Fig. 6. Target simulation images at different time. (a) t=0 s; (b) t=8 s; (c) t=12 s; (d) t=20 s

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Fig. 7. Changes in target brightness in two directions. (a) x direction; (b) y direction

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Fig. 8. Signal processing and smoothing. (a) Time-domain spectrum of x; (b) smooth the frequency in the x direction before and after smoothing; (c) time-domain spectrum of y; (d) smooth the frequency in the y direction before and after smoothing

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Fig. 9. Calculated and actual values of target angular velocity and angular acceleration. (a) $\frac{d α}{d t}$ ; (b) $\frac{d δ}{d t}$ ; (c) $\frac{d^{2} α}{d t^{2}}$ ; (d) $\frac{d^{2} δ}{d t^{2}}$

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Fig. 10. Relative error of target distance varies with the standard deviation of error. (a) ISS (ZARYA); (b) DELTA 1 DEB; (c) STARLINK-1019; (d) SL-14 R/B; (e) CZ-4B R/B; (f) INTERCOSMOS

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Fig. 11. Relationship between window length and spectral bandwidth

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Fig. 12. Relationship between window length and distance error

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Table 0. [in Chinese]

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Table 0. [in Chinese]

Target	Error /（″）	Relative error /%
Target	Error /（″）	Filtered	AURORAS	Gauss	Laplace	Gooding
SL-14 R/B	0	1.42	3.59	0.66	0.67	0.68
	5	1.42	6.22	2.55	2.55	2.54
	10	1.41	14.81	5.42	5.42	5.41
	15	1.45	32.13	4.92	4.92	4.91
	20	1.40	NaN	12.27	12.27	12.27
	25	1.43	NaN	15.40	15.40	14.08
CZ-4B R/B	0	3.19	1.47	0.01	0.02	64.73
	5	3.19	5.19	1.13	1.14	52.65
	10	3.20	8.75	2.38	2.40	52.53
	15	3.18	14.57	3.97	3.97	61.43
	20	3.21	17.29	5.43	5.43	53.31
	25	3.21	24.65	9.52	9.52	52.28
INTERCOSMOS 24	0	1.32	1.99	2.84	3.00	2.83
	5	1.33	2.52	2.87	3.03	2.93
	10	1.33	3.85	2.51	3.29	2.56
	15	1.32	5.80	3.15	3.80	11.32
	20	1.31	8.39	3.70	3.80	29.51
	25	1.33	10.98	4.50	4.57	NaN

Table 1. Observation platform and scene parameter

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Table 1. Observation platform and scene parameter

Parameter	Value
Field of view /［（°）×（°）］	8×8
Exposure frequency /Hz	10
Pixel	1024×1024
Pixel size /μm	20.48
F number	3
Entrance pupil diameter /cm	5
Noise equivalent irradiance /（W·cm^-2）	1×10^-11
Detector irradiation saturation /（W·cm^-2）	1×10^-8
Station site	（43.817°N， 125.324°E）
Observation mode	Gaze

Table 2. Target effective simulation parameter

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Table 2. Target effective simulation parameter

NORAD ID	Name	Apogee /km	Perigee /km	Inclination /（°）	Observed time /s	Proportion of arc length
25544	ISS （ZARYA）	423	410	51.64	20	1/276
07049	DELTA 1 DEB	1914	1507	101.76	30	1/241
44724	STARLINK-1019	548	546	53.05	20	1/286
16194	SL-14 R/B	1247	1222	82.65	30	1/220
25732	CZ-4B R/B	858	806	98.73	25	1/243
20261	INTERCOSMOS 24	2359	499	82.61	30	1/230

Table 3. Calculation results of relative error of slant distance for different targets

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Table 3. Calculation results of relative error of slant distance for different targets

Target	Error /（″）	Relative error /%
Target	Error /（″）	Filtered	AURORAS	Gauss	Laplace	Gooding
ISS （ZARYA）	0	0.83	0.34	0.22	0.09	1.55
	5	0.82	4.98	1.31	1.29	1.76
	10	0.80	8.72	2.27	2.29	2.43
	15	0.75	13.64	4.32	4.32	4.10
	20	0.88	21.59	4.14	4.10	4.10
	25	0.77	9.56	5.34	5.29	5.43
DELTA 1 DEB	0	4.32	6.00	0.56	0.55	4.79
	5	4.28	6.79	1.88	1.87	4.38
	10	4.26	15.64	3.91	3.91	11.19
	15	4.27	18.24	5.31	5.31	16.34
	20	4.27	NaN	8.56	8.56	20.32
	25	4.24	NaN	7.05	7.05	13.01
STARLINK-1019	0	1.23	3.53	0.78	0.80	0.78
	5	1.22	8.13	3.29	3.30	3.26
	10	1.25	17.50	5.52	5.51	5.45
	15	1.30	27.97	9.99	9.99	9.12
	20	1.25	36.21	8.18	8.18	26.44
	25	1.27	NaN	16.66	16.64	34.65

Table 4. Error of initial orbit determination

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Table 4. Error of initial orbit determination

Target	$σ = 0^{″}$			$σ = 10^{″}$			$σ = 25^{″}$
Target	$\|∆ a\|$ /km	$\|∆ e\|$	$\|∆ i\|$ /（°）	$\|∆ a\|$ /km	$\|∆ e\|$	$\|∆ i\|$ /（°）	$\|∆ a\|$ /km	$\|∆ e\|$	$\|∆ i\|$ /（°）
ISS （ZARYA）	141.60	0.020	0.040	151.87	0.021	0.048	183.80	0.026	0.061
DELTA 1 DEB	659.66	0.067	0.083	660.36	0.067	0.085	665.87	0.068	0.096
STARLINK-1019	75.19	0.009	0.071	72.03	0.012	0.080	76.02	0.009	0.074
SL-14 R/B	159.47	0.015	0.137	182.93	0.017	0.148	184.54	0.017	0.162
CZ-4B R/B	111.64	0.015	0.027	116.96	0.015	0.022	134.83	0.017	0.008
INTERCOSMOS 24	251.61	0.021	0.140	268.61	0.022	0.146	270.20	0.023	0.152

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Han Pei, Sheng Cai, Jiulong Wang, Yan Xing, Luwei Zhang, Jinfeng Li, Le Liu. Initial Orbit Determination of Space Targets Based on Spatial Filtering Velocimetry[J]. Acta Optica Sinica, 2025, 45(12): 1211001

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Paper Information

Category: Imaging Systems

Received: Nov. 5, 2024

Accepted: Jan. 8, 2025

Published Online: Jun. 23, 2025

The Author Email: Sheng Cai (caisheng@ciomp.ac.cn)

DOI:10.3788/AOS241712

CSTR:32393.14.AOS241712

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology