Initial Orbit Determination for Space-Based Optical Surveillance of Space Debris

Lingling Guo; Shaolin Wang; Haishan Dai; Zepeng Wu; Bo Liu; Jun Zhou; Feng Sang

doi:10.3788/AOS240738

Acta Optica Sinica, Volume. 44, Issue 24, 2412002(2024)

Initial Orbit Determination for Space-Based Optical Surveillance of Space Debris

Lingling Guo, Shaolin Wang^*, Haishan Dai, Zepeng Wu, Bo Liu, Jun Zhou, and Feng Sang

Author Affiliations

Shanghai Institute of Satellite Engineering, Shanghai 200240, China

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Figures & Tables(18)

Fig. 1. Admissible region border. (a) Range-range; (b) range-range difference

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Fig. 2. Contour lines of loss function and corresponding orbital parameters. (a) Cost function; (b) semi-major axis; (c) eccentricity

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Fig. 3. Contour lines of loss function with additional eccentricity constrains

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Fig. 4. Contour lines of extended loss function

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Fig. 5. Updated routes of the initial orbit determination procedure for different arcs. (a)-(i) Arc 1-9

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Fig. 6. Updated routes of different optimalization methods with first initial value. (a) SGD; (b) Momentum; (c) AdaGrad; (d) Adam

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Fig. 7. Updated routes of different optimalization methods with second initial value. (a) SGD; (b) Momentum; (c) AdaGrad; (d) Adam

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Fig. 8. Statistical comparison of initial orbit determination results using different methods. (a) Position error; (b) semi-major axis error; (c) inclination error

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Fig. 9. Statistical comparison of initial orbit determination results derived from measurements with different durations. (a) Position error; (b) semi-major axis error; (c) inclination error

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Fig. 10. Statistical comparison of initial orbit determination results derived from measurements with different sampling intervals. (a) Position error; (b) semi-major axis error; (c) inclination error

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Table 1. Target orbits of different types

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Table 1. Target orbits of different types

Target type	GEO	MEO	LEO
Semi-major axis /km	42171.06718	26570.99877	6943.796906
Eccentricity	0.001023892	0.006966028	0.011296452
Inclination /（°）	31.93220111	63.68409379	50.30592977
Argument of perigee /（°）	184.6836616	222.9662792	206.3723500
Right ascension of the ascending node /（°）	314.0553419	311.9303899	177.6147107
Mean anomaly /（°）	16.69060785	344.0309035	145.8372277

Table 2. Orbital parameters of space-based optical surveillance platform

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Table 2. Orbital parameters of space-based optical surveillance platform

Parameter	Value
Semi-major axis /km	7198.291671
Eccentricity	0.003136516
Inclination /(°)	98.47119867
Argument of perigee /(°)	102.9257714
Right ascension of the ascending node /(°)	129.1838602
Mean anomaly /(°)	168.7278390

Table 3. Duration of measured optical arcs
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Table 3. Duration of measured optical arcs
Target type GEO MEO LEO
Arc 1 Arc 2 Arc 3 Arc 4 Arc 5 Arc 6 Arc 7 Arc 8 Arc 9
Duration /s 102.02 84.01 135.00 66.01 116.99 102.03 57.01 132.03 101.95

Table 4. Iterations of different optimalization methods
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Table 4. Iterations of different optimalization methods
Method First initial value Second initial value
SGD 90 308
Momentum 45 301
AdaGrad 14 167
Adam 6 72

Table 5. Comparison of time consumption of different algorithms
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Table 5. Comparison of time consumption of different algorithms
Target type GEO MEO LEO
Arc 1 Arc 2 Arc 3 Arc 4 Arc 5 Arc 6 Arc 7 Arc 8 Arc 9
Revised AR-PSO 35.76 37.04 37.92 36.43 38.77 35.38 36.56 38.78 35.26
Proposed 0.05 0.56 0.25 0.16 0.16 0.18 0.58 2.37 1.04

Table 6. Comparison of statistical results of initial orbit determination using different methods
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Table 6. Comparison of statistical results of initial orbit determination using different methods
Method Position error /km Semi-major error /km Inclination error /(°)
Proposed 16.37 148.24 0.081257
Improved Gooding 322.51 4336.27 1.399618
AR-PSO 136.64 1748.57 0.588587
Revised AR-PSO 82.70 958.40 0.421945

Table 7. Comparison of statistical results of initial orbit determination derived from measurements with different durations
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Table 7. Comparison of statistical results of initial orbit determination derived from measurements with different durations
Duration /min Position error /km Semi-major error /km Inclination error /(°)
2.5 49.82 554.62 0.254784
3.0 34.73 395.61 0.187434
3.5 16.37 148.24 0.081257

Table 8. Comparison of statistical results of initial orbit determination derived from measurements with different sampling intervals
View table
Table 8. Comparison of statistical results of initial orbit determination derived from measurements with different sampling intervals
Interval /s Position error /km Semi-major error /km Inclination error /（°）
3.0 34.73 395.61 0.187434
6.0 51.65 599.68 0.276120
9.0 66.24 785.82 0.338042

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Lingling Guo, Shaolin Wang, Haishan Dai, Zepeng Wu, Bo Liu, Jun Zhou, Feng Sang. Initial Orbit Determination for Space-Based Optical Surveillance of Space Debris[J]. Acta Optica Sinica, 2024, 44(24): 2412002

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Mar. 15, 2024

Accepted: May. 27, 2024

Published Online: Sep. 3, 2024

The Author Email: Wang Shaolin (shaolin_w@126.com)

DOI:10.3788/AOS240738

CSTR:32393.14.AOS240738

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Target orbits of different types

Table 1. Target orbits of different types

Table 2. Orbital parameters of space-based optical surveillance platform

Table 2. Orbital parameters of space-based optical surveillance platform

Table 3. Duration of measured optical arcs

Table 3. Duration of measured optical arcs

Table 4. Iterations of different optimalization methods

Table 4. Iterations of different optimalization methods

Table 5. Comparison of time consumption of different algorithms

Table 5. Comparison of time consumption of different algorithms

Table 6. Comparison of statistical results of initial orbit determination using different methods

Table 6. Comparison of statistical results of initial orbit determination using different methods

Table 7. Comparison of statistical results of initial orbit determination derived from measurements with different durations

Table 7. Comparison of statistical results of initial orbit determination derived from measurements with different durations

Table 8. Comparison of statistical results of initial orbit determination derived from measurements with different sampling intervals

Table 8. Comparison of statistical results of initial orbit determination derived from measurements with different sampling intervals