Multi-star tracker angular velocity reconstruction method considering temperature effect correction

doi:10.11947/j.AGCS.2024.20240093

Abstract

Abstract:

High-precision satellite attitude control is an important data preprocessing aspect of satellite gravity mission operation. The key payload star trackers onboard the gravity field and steady-state ocean circulation explorer (GOCE) satellite inevitably experience temperature variations in its low orbit, leading to inter-boresight angles (IBA) deviations ranging from 2 to 14 arcseconds, directly impacting the accuracy of satellite attitude. Quantitative analysis of temperature effects on satellite attitude and precise determination of satellite angular velocities are essential steps in the satellite data preprocessing workflow, directly influencing the accuracy of high-precision gravity gradient component reconstruction. In this study, based on the characteristics of the GOCE satellite mission, we develop a temperature effect correction method for joint attitude quaternion reconstruction using multiple star trackers. This method involves constructing a linear function of temperature-related relative attitude offsets between star trackers, establishing a weighted matrix considering the precision differences among sensor axes, and obtaining the optimal quaternion reconstruction of attitude velocities based on the principle of least squares. Additionally, in the original attitude data processing, we propose a logarithmic quaternion Hermite hypersurface interpolation method for data optimization. The research results demonstrate that the corrected attitude quaternions calculated from star tracker data exhibit no significant deviation when compared with reference frame information. Moreover, after temperature effect correction, the noise level of angular velocity for each tracker axis significantly decreases by approximately two orders of magnitude, achieving an accuracy of 10^-10 rad·s^-1 and significantly improving the precision of velocity reconstruction. Additionally, the angular velocity accuracy of each tracker axis maintains good consistency.The power spectral density of the gravity gradient trace calculated based on this method shows a more significant improvement in the whole frequency domain.

Key words: star tracker, inter-boresight angles, attitude quaternion, temperature effect, Hermite hypersurface interpolation

CLC Number:

P223

Danyi HU, Yunlong WU, Yun XIAO, Yue QIU, Xiaohui WU, Yulong ZHONG. Multi-star tracker angular velocity reconstruction method considering temperature effect correction[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(9): 1748-1760.

Figures/Tables 15

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Tab.1

Fig.6

Tab.2

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Tab.3

Fig.12

References 35

[1]	张林, 沈云中, 陈秋杰, 等. 红柳江区域陆地水储量变化及其驱动因素分析[J]. 测绘学报, 2022, 51(4):622-630. DOI: 10.11947/j.AGCS.2022.20220030.
	ZHANG Lin, SHEN Yunzhong, CHEN Qiujie, et al. Analysis of terrestrial water storage change and its driving factors of Hongliu River region[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(4):622-630. DOI: 10.11947/j.AGCS.2022.20220030.
[2]	马文静, 周浩, 何培培, 等. HUST-Grace2020模型反演中国大陆区域水储量变化特征分析[J]. 测绘学报, 2023, 52(12):2089-2102. DOI: 10.11947/j.AGCS.2023.20210693.
	MA Wenjing, ZHOU Hao, HE Peipei, et al. Analysis of terrestrial water storage variations in Chinese mainland based on HUST-Grace2020 model[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(12):2089-2102. DOI: 10.11947/j.AGCS.2023.20210693.
[3]	FENG Wei, XIONG Yuhao, YI Shuang, et al. Recent progress on hydrogeodesy in China[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(3):124-134.
[4]	CHEN J L, WILSON C R, TAPLEY B D, et al. GRACE detects coseismic and postseismic deformation from the Sumatra-Andaman earthquake[J]. Geophysical Research Letters, 2007, 34(13):L13302.
[5]	CHEN Jianli, TAPLEY B, WILSON C, et al. Global ocean mass change from GRACE and GRACE follow-on and altimeter and Argo measurements[J]. Geophysical Research Letters, 2020, 47(22):e90656.
[6]	王星星, 李斐, 郝卫峰, 等. GRACE RL05反演南极冰盖质量变化方法比较[J]. 武汉大学学报(信息科学版), 2016, 41(11):1450-1457.
	WANG Xingxing, LI Fei, HAO Weifeng, et al. Comparison of several filters in the rates of Antarctic ice sheet mass change based on GRACE RL05 data[J]. Geomatics and Information Science of Wuhan University, 2016, 41(11):1450-1457.
[7]	RUMMEL R, MÜLLER J, OBERNDORFER H, et al. Satellite gravity gradiometry with GOCE[C]//Proceedings of 2000 International Association of Geodesy Symposia. Berlin: Springer, 2000: 66-72.
[8]	瞿庆亮, 常晓涛, 于胜文, 等. 利用先验重力场模型求定GOCE卫星重力梯度仪校准参数[J]. 测绘学报, 2019, 48(2):176-184. DOI: 10.11947/j.AGCS.2019.20180137.
	QU Qingliang, CHANG Xiaotao, YU Shengwen, et al. Calibration for GOCE gradiometer data based on the prior gravity models[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(2):176-184. DOI: 10.11947/j.AGCS.2019.20180137.
[9]	FLOBERGHAGEN R, FEHRINGER M, LAMARRE D, et al. Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission[J]. Journal of Geodesy, 2011, 85(11):749-758.
[10]	QU Qingliang, CHANG Xiaotao, YU Shengwen, et al. Calibration for GOCE gradiometer data based on the prior gravity models[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(4):21-30.
[11]	陈逸峰, 朱广彬, 常晓涛, 等. 顾及姿态偏移的重力梯度卫星姿态确定方法[J]. 测绘科学, 2023, 48(4):46-53.
	CHEN Yifeng, ZHU Guangbin, CHANG Xiaotao, et al. A gravity gradient satellite attitude determination method by using attitude offset correction[J]. Science of Surveying and Mapping, 2023, 48(4):46-53.
[12]	吴云龙, 郭泽华, 肖云, 等. 卫星重力梯度观测数据L1级构建方法[J]. 地球物理学报, 2021, 64(12):4437-4448.
	WU Yunlong, GUO Zehua, XIAO Yun, et al. L1 level construction method of satellite gravity gradiometry observations[J]. Chinese Journal of Geophysics, 2021, 64(12):4437-4448.
[13]	BANDIKOVA T, FLURY J. Improvement of the GRACE star camera data based on the revision of the combination method[J]. Advances in Space Research, 2014, 54(9):1818-1827.
[14]	WU S C, KRUIZINGA G, BERTIGER W. Algorithm theoretical basis document for GRACE Level-l B data processing v1.2[R]. Los Angeles: Jet Propulsion Laboratory, 2006.
[15]	SPILLER D, CURTI F. A geometrical approach for the angular velocity determination using a star sensor[J]. Acta Astronautica, 2022, 196:414-431.
[16]	TAN Wenfeng, DAI Dongkai, WU Wei, et al. A comprehensive calibration method for a star tracker and gyroscope units integrated system[J]. Sensors, 2018, 18(9):3106.
[17]	LI Jian, WEI Xinguo, ZHANG Guangjun. An extended Kalman filter-based attitude tracking algorithm for star sensors[J]. Sensors, 2017, 17(8):1921.
[18]	HERCEG M, JØRGENSEN P S, JØRGENSEN J L. Characterization and compensation of thermo-elastic instability of SWARM optical bench on micro advanced stellar compass attitude observations[J]. Acta Astronautica, 2017, 137:205-213.
[19]	SIEMES C, REXER M, HAAGMANS R. GOCE star tracker attitude quaternion calibration and combination[J]. Advances in Space Research, 2019, 63(3):1133-1146.
[20]	ROMANS L. Optimal combination of quaternions from multiple star cameras[R]. Los Angeles: Jet Propulsion Laboratory, 2003.
[21]	郭泽华, 吴云龙, 肖云, 等. 联合星象仪四元数的卫星重力梯度测量角速度重建方法[J]. 武汉大学学报(信息科学版), 2021, 46(9):1336-1344.
	GUO Zehua, WU Yunlong, XIAO Yun, et al. Reconstruction method of satellite gravity gradient measurement angular velocity by combining star tracker quaternion[J]. Geomatics and Information Science of Wuhan University, 2021, 46(9):1336-1344.
[22]	XIAO Yun, YANG Yuanxi, PAN Zongpeng, et al. Chinese gravimetry augment and mass change exploring mission status and future[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(3):67-75.
[23]	GROVES P D. Principles of GNSS, inertial, and multisensor integrated navigation systems[J]. IEEE Aerospace and Electronic Systems Magazine, 2015, 30(2):26-27.
[24]	SIEMES C. GOCE gradiometer calibration and level 1b data processing[R]. Noordwijk: ESA, 2012.
[25]	LIEBE C C. Accuracy performance of star trackers-a tutorial[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38(2):587-599.
[26]	赖育网, 谷德峰, 刘俊宏, 等. 星敏感器/陀螺在轨系统误差分析与校准[C]//第三届高分辨率对地观测学术年会优秀论文集. 北京: [出版者不详], 2014: 33-43.
	LAI Yuwang, GU Defeng, LIU Junhong, et al. In-flight systematic error analysis and calibration for star tracker/gyro[C]//Proceedings of the 3rd High Resolution Earth Observation Academic Annual Conference. Beijing: [s.n.], 2014: 33-43.
[27]	PITTELKAU M. Everything is relative in system alignment calibration[C]//Proceedings of 2000 Astrodynamics Specialist Conference. Reston, Virigina: AIAA, 2000.
[28]	SHUSTER M D, PITONE D S, BIERMAN G J. Batch estimation of spacecraft sensor alignments: I. relative alignment estimation[J]. Journal of the Astronautical Sciences, 1991, 39:519-546.
[29]	YANG Fan, LIANG Lei, WANG Changqing, et al. Attitude determination for GRACE-FO: reprocessing the level-1A SC and IMU data[J]. Remote Sensing, 2021, 14(1):126.
[30]	PARKER J, IBARRA D, OBER D. Logarithm-based methods for interpolating quaternion time series[J]. Mathematics, 2023, 11(5):1131.
[31]	谢进, 檀结庆, 李声锋. 有理三次Hermite插值样条及其逼近性质[J]. 工程数学学报, 2011, 28(3):385-392.
	XIE Jin, TAN Jieqing, LI Shengfeng. Rational cubic Hermite interpolating spline and its approximation properties[J]. Chinese Journal of Engineering Mathematics, 2011, 28(3):385-392.
[32]	RISPENS S, BOUMAN J. External calibration of GOCE accelerations to improve derived gravitational gradients[J]. Journal of Geodetic Science, 2011, 1(2):114-126.
[33]	章仁为. 卫星轨道姿态动力学与控制[M]. 北京: 北京航空航天大学出版社, 1998: 147-153.
	ZHANG Renwei. Satellite orbit attitude dynamics and control[M]. Beijing: Beijing University of Aeronautics & Astronautics Press, 1998: 147-153.
[34]	SERCO/DATAMAT Consortium. GOCE L1b products user handbook[R]. Paris: European Space Agency, 2006.
[35]	RUMMEL R, YI Weiyong, STUMMER C. GOCE gravitational gradiometry[J]. Journal of Geodesy, 2011, 85(11):777-790.

数据产品	描述
STR_VC2_1b	星敏感器标识符(STR_ID)，四元数(Q₁，Q₂，Q₃，Q₄)，有效标志(Val_Flag)，星敏感器视场异物标志(BBO)
STR_VC3_1b	星敏感器标识符(STR_ID)，四元数(Q₁，Q₂，Q₃，Q₄)，有效标志(Val_Flag)，星敏感器视场异物标志(BBO)
AUX_NOM_1b	星敏感器CCD温度
AUX_EGG_DB	从星敏感器参考系(SSRF)到与卫星主轴对齐的公共参考系(梯度仪参考系GRF)的旋转

星敏感器	三轴总标准差	x^GRF轴标准差	y^GRF轴标准差	z^GRF轴标准差
温度改正前STR1	2.911 5×10^－4	3.173 7×10^－5	13.160 0×10^－5	8.257 2×10^－5
温度改正后STR1	2.777 0×10^－4	3.006 5×10^－5	1.164 2×10^－5	3.248 8×10^－5

结果对比	IBA12	IBA23	IBA31
飞行前/(°)	40.705 5	55.052 2	39.655 9
温度改正前飞行中/(°)	40.709 6	55.049 7	39.655 3
与飞行前的差异/(″)	14.760 0	9.000 0	2.160 0
温度改正后飞行中/(°)	40.705 6	55.052 2	39.655 9
与飞行前的差异/(″)	0.360 0	0.000 0	0.000 0