基于时谱信号分析的在轨空间目标姿态感知

谭凡教; 苏金宇; 侯晴宇; 王佳轩; 王一惠

doi:10.7498/aps.69.20200098

摘要

为了在天基远距离条件下估计空间目标的姿态参数, 提出了基于时序光谱信号分级求解目标表面参数及姿态参数的方法. 第一级, 在三轴稳定状态下将空间目标等效为“双面模型”, 引入双向反射分布函数(bidirectional reflectance distribution function, BRDF)的多级融合模型表征复杂材料的光谱反射特性, 基于时谱信号与时谱信号模型对双面光谱BRDF与面积乘积进行重构. 第二级, 为了抑制双面耦合特性对姿态估计的影响, 构建双面特性分离度, 并基于该度量最大化实现光谱波段优选. 第三级, 构建目标姿态运动状态下的时序光谱信号模型, 以模型值与观测值之间的误差为目标函数, 利用Levenberg-Marquardt算法对姿态参数进行估计. 仿真表明, 该方法更适用于方形本体的目标, 且反演误差会随相位角和探测器噪声的增大而增大, 在信噪比SNR ≥ 10条件下反演误差在2%以内.

关键词:

Abstract

In order to estimate the attitude parameters of space objects under the condition of space-based long-distance observation, a hierarchical solving method based on the time-series spectral signal is proposed to estimate the parameters of surface reflection characteristics and the attitude of the space objects. The first step is to let the space object in three-axis stabilization state be equivalent to a two-facet model. Then multi-level fusion model of bidirectional reflectance distribution function (BRDF) is introduced to describe the spectral reflection characteristics of complex material surfaces. Based on the time-series spectral signal and its model, the product of area and spectral BRDF of the two-facet can be reconstructed. The second step is to set up the two-facet characteristic difference model to select the optimum wavelength based on the maximum of the difference thereby minimizing the influence of coupling characteristics on of the two-facet on attitude estimate. The third step is to construct the time-series spectral signal model under the change of object attitude. The objective function is defined as the error between the model data and the measured data, then the attitude parameter can be estimated using Levenberg-Marquardt algorithm. The simulation result shows that the method is more suitable for the object with cube body, and the error between inversion value and real value will increase as the phase angle and the detector noise increase. When signal-to-noise ratio is greater than or equal to 10, the inversion error is within 2%.

Keywords:

space object /
attitude estimate /
time-series spectral signal /
visible light /
bidirectional reflectance distribution function

作者及机构信息

哈尔滨工业大学, 空间光学工程研究中心, 哈尔滨　150001

通信作者: 侯晴宇, houqingyu@126.com

基金项目: 国家自然科学基金(批准号: 61705052)资助的课题

Authors and contacts

Research Center for Space Optical Engineering, Harbin Institute of Technology, Harbin 150001, China

Corresponding author: Hou Qing-Yu, houqingyu@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61705052)

文章全文 : translate this paragraph

参考文献

[1]	Wang H Y, Zhang W, Dong A T 2012 Appl. Opt. 51 7810 Google Scholar
[2]	Wang H Y, Zhang W, Wang F G 2012 Sci. China: Technol. Sci. 55 982 Google Scholar
[3]	袁艳, 孙成明, 张修宝 2010 物理学报 59 2097 Google Scholar Yuan Y, Sun C M, Zhang X B 2010 Acta Phys. Sin. 59 2097 Google Scholar
[4]	Wang H Y, Zhang W, Dong A T 2013 Measurement 46 3654 Google Scholar
[5]	Hou Q Y, Zhi X Y, Zhang H L, Zhang W 2014 Proc. SPIE. 9299 929914
[6]	Wang H Y, Zhang W 2012 J. Mod. Opt. 59 547 Google Scholar
[7]	袁艳, 孙成明, 张修宝, 赵慧洁, 王潜 2010 光学学报 30 2748 Google Scholar Yuan Y, Sun C M, Zhang X B, Zhao H J, Wang Q 2010 Acta Opt. Sin. 30 2748 Google Scholar
[8]	Chaudhary A B, Payne T, Gregory S, Dao P 2011 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 13–16, 2011 p1
[9]	Cegarra Polo M, Abay R, Gehly S, Lambert A 2018 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 11–14, 2018 p1
[10]	Wetterer C J, Jah M 2009 J. Guid. Control. Dynam. 32 1648 Google Scholar
[11]	Holzinger M J, Alfriend K T, Wetterer C J, Luu K K, Sabol C, Hamada K 2014 J. Guid. Control. Dynam. 37 921 Google Scholar
[12]	Linares R, Crassidis J L 2013 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 10–13, 2013 p1
[13]	Linares R, Jah M, Crassidis J, Leve F 2014 Acta Astronautica. 99 1 Google Scholar
[14]	Linares R, Shoemaker M, Walker A, Mehta P M, Palmer D M, Thompson D C, Koller J, Crassidis J L 2013 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 10–13, 2013 p1
[15]	Linares R, Jah M K, Crassidis J L, Nebelecky C K 2014 J. Guid. Control. Dynam. 37 13 Google Scholar
[16]	Furfaro R, Linares R, Reddy V 2018 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 11–14, 2018 p1
[17]	Jia B, Pham K D, Blasch E, Wang Z H 2018 Proceedings of IEEE Aerospace Conference Big Sky, Montana, United States, March 3–10, 2018 p1
[18]	Arakawa R, Matsushita Y, Hanada T 2019 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 17–20, 2019 p1
[19]	Furfaro R, Linares R, Reddy V 2019 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 17–20, 2019 p1
[20]	Hou Q Y, Wang Y H, Tan F J, Huo Y J 2018 J. Mod. Opt. 65 2171 Google Scholar
[21]	Hall D 2010 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 14–17, 2010 p1
[22]	Hall D, Hamada K M, Kelecy T, Kervin P 2012 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 11–14, 2012 p1
[23]	Levenberg K 1944 Q. Appl Math. 2 164 Google Scholar
[24]	Lourakis M, Argyros A 2004 The Design and Implementation of a Generic Sparse Bundle Adjustment Software Package (Heraklion, Greece: Institute of Computer Science-FORTH) Technical Report 340
[25]	侯晴宇, 巩晋南, 樊志鹏, 王一惠 2017 物理学报 66 154201 Google Scholar Hou Q Y, Gong J N, Fan Z P, Wang Y H 2017 Acta Phys. Sin. 66 154201 Google Scholar

施引文献

图 1 空间目标姿态参数估计方法的流程图

Fig. 1. Flow chart of attitude parameter estimation of space object.

下载: 全尺寸图片幻灯片

图 2 三轴稳定卫星的在轨观测示意图

Fig. 2. Observation diagram of the on-orbit three-axis stabilized satellite.

下载: 全尺寸图片幻灯片

图 3 坐标系旋转变换关系示意图　(a)绕Z轴转动; (b)绕Y轴转动; (c)绕X轴转动

Fig. 3. Diagram of coordinate system rotation transformation: (a) Rotate around Z-axis; (b) rotate around Y-axis; (c) rotate around X-axis.

下载: 全尺寸图片幻灯片

图 4 卫星结构图　(a)面元划分前; (b)面元划分后

Fig. 4. Diagram of satellite structure: (a) Before surface division; (b) after surface division.

下载: 全尺寸图片幻灯片

图 5 材料BRDF与波长和反射角的关系　(a) 本体包覆材料BRDF; (b)帆板材料BRDF

Fig. 5. Material BRDF changes with wavelength and reflected angle: (a) BRDF of body coating material; (b) BRDF of solar panel

下载: 全尺寸图片幻灯片

图 6 在不同光谱波段仿真得到的光度信号曲线　(a) 400 nm; (b) 450 nm; (c) 500 nm; (d) 550 nm; (e) 600 nm; (f) 650 nm; (g) 700 nm; (h) 750 nm

Fig. 6. Simulation curves of photometric signal at different wavelengths: (a) 400 nm; (b) 450 nm; (c) 500 nm; (d) 550 nm; (e) 600 nm; (f) 650 nm; (g) 700 nm; (h) 750 nm

下载: 全尺寸图片幻灯片

图 7 650 nm波段下本体及帆板光学特性重构曲线　(a)本体表面光学特性重构曲线; (b)帆板表面光学特性重构曲线

Fig. 7. Optical characteristic reconstruction curve of body and solar panel at 650 nm: (a) Reconstruction curve of body; (b) reconstruction curve of solar panel

下载: 全尺寸图片幻灯片

图 8 时序光谱信号重构结果　(a)本体重构结果; (b)帆板重构结果; (c)目标整体重构结果

Fig. 8. Reconstruction result of time-series spectral signals: (a) Reconstruction result of body signal; (b) reconstruction result of solar panel signal; (c) reconstruction result of total signal.

下载: 全尺寸图片幻灯片

图 9 绕Y轴转动得到的时序光谱信号

Fig. 9. Time-series spectral signals when rotating around Y-axis.

下载: 全尺寸图片幻灯片

图 10 绕Z轴转动得到的时序光谱信号

Fig. 10. Time-series spectral signals when rotating around Z-axis.

下载: 全尺寸图片幻灯片

图 11 不同本体形状的目标模型　(a)圆柱体本体; (b)球体本体; (c)六棱柱本体

Fig. 11. Object model with different body structure: (a) Cylinder body; (b) sphere body; (c) hexagonal prism body.

下载: 全尺寸图片幻灯片

图 12 误差随信噪比变化曲线　(a)绕Y轴旋转; (b)绕Z轴旋转

Fig. 12. Error curve changes with SNR: (a) Rotate around Y-axis; (b) rotate around Z-axis

下载: 全尺寸图片幻灯片

表 1 目标卫星与观测卫星的轨道参数

Table 1. Orbit parameter of object satellite and observe satellite.

卫星	半长轴/km	偏心率/(°)	轨道倾角/(°)	近地点幅角/(°)	升交点赤经/(°)	真近点角/(°)
目标卫星	42378.1	0	0	0	181.803	0
观测卫星	42408.0	0	0	0	184.860	359.93

下载: 导出CSV

表 2 观测星探测系统参数

Table 2. Detection system parameter of observe satellite.

参量	光谱宽度/nm	入瞳直径/m	焦距/m	面阵大小	像元尺寸/m	瞬时视场/rad
数值	10	0.1505	0.8	512 × 512	1.5 × 10^–5	1.8750 × 10^–5

下载: 导出CSV

表 3 不同光谱波段的双面特性分离度

Table 3. Two-facet characteristics difference at different wavelengths.

光谱波长/nm	$\sigma $	光谱波长/nm	$\sigma $
400	0.1593	600	0.6664
450	0.3850	650	0.8574
500	0.4576	700	0.8284
550	0.5862	750	0.8031

下载: 导出CSV

表 4 650 nm参数重构结果

Table 4. Parameter reconstruction results at 650 nm

序号	本体		帆板
序号	${A_{\rm{b}}} \cdot {b_j}$	${\mu _j}$	${A_{\rm{p}}} \cdot {b_i}$	${\mu _i}$
1	0.1722	0.01	0.0003	0.01
2	0.0248	0.02	0.0103	0.02
3	0.0102	0.04	0.0837	0.04
4	0.0517	0.05	0.1046	0.05
5	0.0312	0.07	0.8049	0.07
6	0.0083	0.08	0.1153	0.08
7	0.0137	0.10	0.0489	0.10
8	0.0077	0.20	0.0345	0.20
9	0.0002	0.30	0.0003	0.30
10	0	0.50	0.0103	0.50

下载: 导出CSV

表 5 在不同相位角开始估计得到的姿态角速度

Table 5. Estimate results of attitude angular velocity at different phase angles.

开始相位角/(°)	估计得到的姿态参数/rad·帧^–1	相对误差/%
3	[0.0125 –0.00182 0.2567]	1.43
5	[–1.35 × 10^–4 0.0176 0.2489]	1.76
10	[–0.0163 –0.0034 0.2567]	1.79
15	[–0.0125 0.0223 0.2458]	2.59
20	[–0.0233 –0.0028 0.2742]	3.37
25	[–0.0132 0.0321 0.2533]	3.49
30	[0.0713 –0.0019 0.3057]	9.05
35	[–0.0679 0.1301 –0.1986]	47.25
40	无解	—

下载: 导出CSV

表 6 不同模型重构曲线误差

Table 6. Errors of reconstruction curves with different models.

模型	整体信号	本体信号	帆板信号
球体	41.68%	61.24%	26.77%
圆柱体	29.77%	46.73%	23.82%
六棱柱	3.56%	15.09%	1.21%

下载: 导出CSV

表 7 不同信噪比下的姿态估计结果

Table 7. Attitude estimate results with different SNR.

信噪比	绕Y轴旋转	绕Z轴旋转
SNR = 1	[8.3448 × 10^–7 0.2437 0.0081006]	[0.069 0.074087 0.21274]
SNR = 3	[4.5801 × 10^–7 0.24959 0.0072132]	[0.0853 0.003516 0.27007]
SNR = 5	[1.9843 × 10^–8 0.25191 0.0072818]	[0.073 1.1668 × 10^–8 0.26576]
SNR = 10	[1.2073 × 10^–10 0.24933 0.0057039]	[0.013255 2.0514 × 10^–8 0.25114]
SNR = 20	[7.8452 × 10^–7 0.25027 0.0059434]	[0.007916 4.4372 × 10^–6 0.25177]
SNR = 50	[8.8736 × 10^–8 0.24997 0.0047093]	[0.009675 2.0484 × 10^–8 0.25056]

下载: 导出CSV

[1]	Wang H Y, Zhang W, Dong A T 2012 Appl. Opt. 51 7810 Google Scholar
[2]	Wang H Y, Zhang W, Wang F G 2012 Sci. China: Technol. Sci. 55 982 Google Scholar
[3]	袁艳, 孙成明, 张修宝 2010 物理学报 59 2097 Google Scholar Yuan Y, Sun C M, Zhang X B 2010 Acta Phys. Sin. 59 2097 Google Scholar
[4]	Wang H Y, Zhang W, Dong A T 2013 Measurement 46 3654 Google Scholar
[5]	Hou Q Y, Zhi X Y, Zhang H L, Zhang W 2014 Proc. SPIE. 9299 929914
[6]	Wang H Y, Zhang W 2012 J. Mod. Opt. 59 547 Google Scholar
[7]	袁艳, 孙成明, 张修宝, 赵慧洁, 王潜 2010 光学学报 30 2748 Google Scholar Yuan Y, Sun C M, Zhang X B, Zhao H J, Wang Q 2010 Acta Opt. Sin. 30 2748 Google Scholar
[8]	Chaudhary A B, Payne T, Gregory S, Dao P 2011 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 13–16, 2011 p1
[9]	Cegarra Polo M, Abay R, Gehly S, Lambert A 2018 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 11–14, 2018 p1
[10]	Wetterer C J, Jah M 2009 J. Guid. Control. Dynam. 32 1648 Google Scholar
[11]	Holzinger M J, Alfriend K T, Wetterer C J, Luu K K, Sabol C, Hamada K 2014 J. Guid. Control. Dynam. 37 921 Google Scholar
[12]	Linares R, Crassidis J L 2013 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 10–13, 2013 p1
[13]	Linares R, Jah M, Crassidis J, Leve F 2014 Acta Astronautica. 99 1 Google Scholar
[14]	Linares R, Shoemaker M, Walker A, Mehta P M, Palmer D M, Thompson D C, Koller J, Crassidis J L 2013 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 10–13, 2013 p1
[15]	Linares R, Jah M K, Crassidis J L, Nebelecky C K 2014 J. Guid. Control. Dynam. 37 13 Google Scholar
[16]	Furfaro R, Linares R, Reddy V 2018 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 11–14, 2018 p1
[17]	Jia B, Pham K D, Blasch E, Wang Z H 2018 Proceedings of IEEE Aerospace Conference Big Sky, Montana, United States, March 3–10, 2018 p1
[18]	Arakawa R, Matsushita Y, Hanada T 2019 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 17–20, 2019 p1
[19]	Furfaro R, Linares R, Reddy V 2019 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 17–20, 2019 p1
[20]	Hou Q Y, Wang Y H, Tan F J, Huo Y J 2018 J. Mod. Opt. 65 2171 Google Scholar
[21]	Hall D 2010 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 14–17, 2010 p1
[22]	Hall D, Hamada K M, Kelecy T, Kervin P 2012 Proceedings of the Advanced Maui Optical & Space Surveillance Technologies Conference Maui, Hawaii, United States, September 11–14, 2012 p1
[23]	Levenberg K 1944 Q. Appl Math. 2 164 Google Scholar
[24]	Lourakis M, Argyros A 2004 The Design and Implementation of a Generic Sparse Bundle Adjustment Software Package (Heraklion, Greece: Institute of Computer Science-FORTH) Technical Report 340
[25]	侯晴宇, 巩晋南, 樊志鹏, 王一惠 2017 物理学报 66 154201 Google Scholar Hou Q Y, Gong J N, Fan Z P, Wang Y H 2017 Acta Phys. Sin. 66 154201 Google Scholar

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