顾及星敏感器安装矩阵校正的GRACE-FO姿态数据处理研究

doi:10.11947/j.AGCS.2026.20250361

测绘学报 ›› 2026, Vol. 55 ›› Issue (2): 287-300.doi: 10.11947/j.AGCS.2026.20250361

• 大地测量学与导 • 上一篇

顾及星敏感器安装矩阵校正的GRACE-FO姿态数据处理研究

梁磊¹^,²^,³(), 王长青⁴^,⁵(), 黄令勇³, 黄志勇³, 于瑶瑶⁶, 钟敏⁷, 闫易浩⁸, 穆庆禄⁹

^1.滁州学院地理信息与旅游学院，安徽　滁州　239099
^2.安徽省实景地理环境重点实验室，安徽　滁州　239009
^3.智能空间信息国家级重点实验室，北京　100029
^4.中国科学院精密测量科学与技术创新研究院，湖北　武汉　430077
^5.华中科技大学国家精密重力测量科学中心，湖北　武汉　430074
^6.北京市遥感信息研究所，北京　100124
^7.中山大学遥感科学与技术学院，广东　珠海　519082
^8.马克斯-普朗克引力物理研究所（阿尔伯特-爱因斯坦研究所），德国　汉诺威　30167
^9.江苏海洋大学海洋技术与测绘学院，江苏　连云港　222005

收稿日期:2025-09-04 修回日期:2025-11-10 发布日期:2026-03-13
通讯作者: 王长青 E-mail:lianglei@chzu.edu.cn;whiggsdkd@asch.whigg.ac.cn
作者简介:梁磊（1990—），男，博士，副教授，研究方向为物理大地测量、卫星重力。 E-mail：lianglei@chzu.edu.cn
基金资助:
国家自然科学基金(42204091; 42174103);安徽省高校自然科学研究重点项目(2024AH051436);智慧地球重点实验室基金(KF2023YB02-04);滁州学院科研启动基金(2023qd08);国家精密重力测量科学中心开放课题(NGL-2025-010)

GRACE-FO attitude data determination with consideration of star camera alignment matrix calibration

Lei LIANG¹^,²^,³(), Changqing WANG⁴^,⁵(), Lingyong HUANG³, Zhiyong HUANG³, Yaoyao YU⁶, Min ZHONG⁷, Yihao YAN⁸, Qinglu MU⁹

^1.School of Geographic Information and Tourism, Chuzhou University, Chuzhou 239099, China
^2.Anhui Provincial Key Laboratory of Physical Geographic Environment, Chuzhou 239009, China
^3.National Key Laboratory of Intelligent Spatial Information, Beijing 100029, China
^4.Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China
^5.National Gravitation Laboratory, Huazhong University of Science and Technology, Wuhan 430074, China
^6.Capital Institute of Geographic Information, Beijing 100124, China
^7.School of Geospatial Engineering and Science, Sun Yat-Sen University, Zhuhai 519082, China
^8.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institute), Hannover 30167, Germany
^9.School of Marine Technology and Geomatics, Jiangsu Ocean University, Lianyungang 222005, China

Received:2025-09-04 Revised:2025-11-10 Published:2026-03-13
Contact: Changqing WANG E-mail:lianglei@chzu.edu.cn;whiggsdkd@asch.whigg.ac.cn
About author:LIANG Lei (1990—), male, PhD, associate professor, majors in physical geodesy and satellite gravity. E-mail: lianglei@chzu.edu.cn
Supported by:
The National Natural Science Founding of China(42204091; 42174103);The Key Project of Natural Science Research in Universities of Anhui Province(2024AH051436);Funded by Key Laboratory of Smart Earth(KF2023YB02-04);Chuzhou University Research Initiation Fund Project(2023qd08);National Gravitation Laboratory(NGL-2025-010)

摘要/Abstract

摘要：

如何获取高精度的姿态数据是重力卫星载荷数据处理的重要研究内容。GRACE-FO的每颗卫星均搭载了3颗星敏感器和1个陀螺仪，融合这两类载荷的测量数据是获得高精度姿态数据的重要途径。本文首先根据星敏感器测量噪声具有各向异性的特点，建立了星敏感器安装矩阵标定算法；其次，建立了星敏感器低频误差处理方法，使用滑动平均方法抑制低频误差；然后，基于Gibbs矢量建立了四元数改正量和陀螺仪偏差改正量为状态向量的间接Kalman滤波算法；最后，使用GRACE-FO Leve-l1A数据进行验证，并分析其对时变重力场的影响。结果表明，以其中1个星敏感器为基准，校正另外两颗星敏感器安装矩阵时，解算的卫星姿态差异较小，经过星敏感器安装矩阵校正后，可以降低姿态数据在1个轨道周期（CPR）处的低频误差。根据建立的星敏感器低频误差处理策略，可以较好地压制30 CPR频段内的星敏感器低频误差。对于星敏感器和陀螺仪融合，相较于JPL结果，本文解算的姿态数据为0.000 5~0.1 Hz，具有更低的噪声，充分发挥了载荷最大性能。对时变重力场模型反演的影响，从反演的时变重力场的阶方差和等效水高差异上看，基于不同姿态数据解算的时变重力场模型精度基本一致，目前姿态数据精度的提升对时变重力场模型精度影响较小。

关键词: GRACE-FO, 卫星姿态, 星敏感器低频误差, 安装矩阵校正, 间接Kalman滤波

Abstract:

The acquisition of high-precision attitude data is a crucial research aspect in the processing of gravity satellite payload raw data. Each GRACE-FO satellite is equipped with three star cameras and a gyroscope to measure the satellite's attitude data. The fusion of these two types of data is an important approach to obtain high-precision attitude data. Firstly, we establish a calibration algorithm for the star cameras installation matrix according to the anisotropic noise of star camera measurements. Secondly, a low-frequency error processing strategy for star cameras is developed, utilizing a moving average method to suppress low-frequency errors. Then, an indirect Kalman filtering algorithm is proposed, with the quaternion correction based on the Gibbs vector and gyroscope bias correction as state vectors. Finally, the GRACE-FO Level-1A data is used for validation and analysis. The computational results show that using different star cameras as references to calibrate the installation matrix of the other star cameras yields only minor differences in the derived satellite attitude and the low-frequency errors at the 1 CPR frequency band in the attitude data are significantly reduced. The established low-frequency error processing strategy for star cameras can effectively suppress low-frequency errors within the 30 CPR frequency band. For the fusion of star cameras and gyroscope data, compared to the JPL results, the attitude data calculated in this paper reduces noise in the 0.000 5~0.1 Hz frequency band, demonstrating that the fusion fully exploits the instruments'maximum performance. Regarding the impact on time-variable gravity field recovery, both the degree variances of the recovered gravity fields and the equivalent water height differences show that the accuracies of the time-variable gravity models derived from different attitude datasets are essentially identical. At the current level, further improvements in attitude data accuracy have only a minor effect on enhancing the precision of time-variable gravity field models.

Key words: GRACE-FO, satellite attitude, star camera low-frequency error, installation matrix calibration, indirect Kalman filter

中图分类号:

P228

梁磊, 王长青, 黄令勇, 黄志勇, 于瑶瑶, 钟敏, 闫易浩, 穆庆禄. 顾及星敏感器安装矩阵校正的GRACE-FO姿态数据处理研究[J]. 测绘学报, 2026, 55(2): 287-300.

Lei LIANG, Changqing WANG, Lingyong HUANG, Zhiyong HUANG, Yaoyao YU, Min ZHONG, Yihao YAN, Qinglu MU. GRACE-FO attitude data determination with consideration of star camera alignment matrix calibration[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(2): 287-300.

图/表 10

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参考文献 44

[1]	TAPLEY B D, BETTADPUR S, RIES J C, et al. GRACE measurements of mass variability in the Earth system[J]. Science, 2004, 305(5683): 503-505.
[2]	KORNFELD R P, ARNOLD B W, GROSS M A, et al. GRACE-FO: the gravity recovery and climate experiment follow-on mission[J]. Journal of Spacecraft and Rockets, 2019, 56(3): 931-951.
[3]	LANDERER F W, FLECHTNER F M, SAVE H, et al. Extending the global mass change data record: GRACE follow-on instrument and science data performance[J]. Geophysical Research Letters, 2020, 47(12): e2020GL088306.
[4]	肖云, 杨元喜, 潘宗鹏, 等. 中国卫星跟踪卫星重力测量系统性能与应用[J]. 科学通报, 2023, 68(20): 2655-2664.
	XIAO Yun, YANG Yuanxi, PAN Zongpeng, et al. Performance and application of the Chinese satellite-to-satellite tracking gravimetry system[J]. Chinese Science Bulletin, 2023, 68(20): 2655-2664.
[5]	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.
[6]	李建成, 吴云龙, 姚宜斌, 等. 面向“数据-场景-模式”驱动的卫星重力技术研究进展、挑战与趋势[J]. 测绘学报, 2025, 54(9): 1537-1560. DOI: . doi: 10.11947/j.AGCS.2025.20250274
	LI Jiancheng, WU Yunlong, YAO Yibin, et al. Satellite gravity technology oriented towards data-scenario-model driven approach: developments, challenges and outlook[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(9): 1537-1560. DOI: . doi: 10.11947/j.AGCS.2025.20250274
[7]	梁磊, 闫易浩, 王长青, 等. 基于卡尔曼滤波重构GRACE-FO姿态数据[J]. 地球物理学报, 2022, 65(12): 4602-4615.
	LIANG Lei, YAN Yihao, WANG Changqing, et al. Results from GRACE-FO attitude determination based on Kalman filter[J]. Chinese Journal of Geophysics, 2022, 65(12): 4602-4615.
[8]	GOSWAMI S, KLINGER B, WEIGELT M, et al. Analysis of attitude errors in GRACE range-rate residuals: a comparison between SCA1B and the fused attitude product (SCA1B+ACC1B)[J]. IEEE Sensors Letters, 2018, 2(2): 1-4.
[9]	PATEL R C. Analyzing and monitoring GRACE-FO star camera performance in changing environment[D]. Austin: The University of Texas at Austin, 2020.
[10]	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.
[11]	BANDIKOVA T. The role of attitude determination for inter-satellite ranging[D]. Hannover: Leibniz Universität Hannover, 2015.
[12]	WEN H Y, KRUIZINGA G, PAIK M, et al. Gravity recovery and climate experiment follow-on (GRACE-FO) level-1 data product user handbook[R]. Pasadena: Jet Propulsion Laboratory, 2019.
[13]	庞博, 黎康, 汤亮, 等. 星敏感器误差分析与补偿方法[J]. 空间控制技术与应用, 2017, 43(1): 17-24.
	PANG Bo, LI Kang, TANG Liang, et al. Error analysis and compensation for star sensor[J]. Aerospace Control and Application, 2017, 43(1): 17-24.
[14]	胡丹怡, 吴云龙, 肖云, 等. 顾及温度效应改正的多星敏感器角速度重建方法[J]. 测绘学报, 2024, 53(9): 1748-1760. DOI: . doi: 10.11947/j.AGCS.2024.20240093
	HU Danyi, WU Yunlong, XIAO Yun, et al. Multi-star tracker angular velocity reconstruction method considering temperature effect correction[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(9): 1748-1760. DOI: . doi: 10.11947/j.AGCS.2024.20240093
[15]	叶立军, 刘付成, 尹海宁, 等. 基于纵向滤波的星敏感器低频误差在线估计[J]. 航空学报, 2019, 40(10): 238-248.
	YE Lijun, LIU Fucheng, YIN Haining, et al. Online estimation of low frequency error for star tracker based on vertical filter[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(10): 238-248.
[16]	WANG Jiongqi, XIONG Kai, ZHOU Haiyin. Low-frequency periodic error identification and compensation for star tracker attitude measurement[J]. Chinese Journal of Aeronautics, 2012, 25(4): 615-621.
[17]	熊凯, 汤亮, 刘一武. 基于地标信息的星敏感器低频误差标定方法[J]. 空间控制技术与应用, 2012, 38(3): 11-15.
	XIONG Kai, TANG Liang, LIU Yiwu. Calibration of star sensor's low frequency error based on landmark information[J]. Aerospace Control and Application, 2012, 38(3): 11-15.
[18]	霍德聪, 黄琳, 李岩, 等. 星敏感器在轨测量误差分析[J]. 遥感学报, 2012, 16(S1): 57-60.
	HUO Decong, HUANG Lin, LI Yan, et al. An analytical method of star tracker measurement errors[J]. National Remote Sensing Bulletin, 2012, 16(S1): 57-60.
[19]	WANG F. Study on center of mass calibration and K-banding system calibration of the GRACE mission[D]. Austin: The University of Texas at Austin, 2003.
[20]	KO U D, WANG Furun, EANES R J. Improvement of Earth gravity field maps after pre-processing upgrade of the GRACE satellite's star trackers[J]. Korean Journal of Remote Sensing, 2015, 31(4): 353-360.
[21]	黄志勇, 李姗姗, 李世忠, 等. GRACE-FO卫星星敏感器/加速度计安装矩阵校准[J]. 地球物理学进展, 2024, 39(1): 87-99.
	HUANG Zhiyong, LI Shanshan, LI Shizhong, et al. SCA/ACC alignment algorithm for GRACE-FO[J]. Progress in Geophysics, 2024, 39(1): 87-99.
[22]	黄志勇. GRACE型重力卫星载荷在轨定标理论与方法研究[J]. 测绘学报, 2025, 54(3): 583. DOI: . doi: 10.11947/j.AGCS.2025.20230499
	HUANG Zhiyong. Research on theory and method of on-orbit calibration of GRACE-type gravity satellite payloads[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(3): 583. DOI: . doi: 10.11947/j.AGCS.2025.20230499
[23]	WANG Aoming, GU Defeng, HUANG Zhiyong, et al. GRACE-FO attitude determination: star camera installation matrix calibration and incremental quaternion integrator[J]. Acta Astronautica, 2024, 219: 774-784.
[24]	YANG Fan, LIANG Lei, WANG Changqing, et al. Attitude determination for GRACE-FO: reprocessing the level-1A SC and IMU data[J]. Remote Sensing, 2022, 14(1): 126.
[25]	HARVEY N, SAKUMURA C. Results from a GRACE/GRACE-FO attitude reconstruction Kalman filter[J]. Journal of Geodesy, 2019, 93(10): 1881-1896.
[26]	熊凯, 宗红, 汤亮. 星敏感器低频误差在轨校准方法研究[J]. 空间控制技术与应用, 2014, 40(3): 8-13.
	XIONG Kai, ZONG Hong, TANG Liang. On star sensor low frequency error in-orbit calibration method[J]. Aerospace Control and Application, 2014, 40(3): 8-13.
[27]	王炯琦, 矫媛媛, 周海银, 等. 复杂卫星抖动下的星敏感器姿态测量数据处理技术[J]. 电子与信息学报, 2010, 32(8): 1885-1891.
	WANG Jiongqi, JIAO Yuanyuan, ZHOU Haiyin, et al. Star sensor attitude measuring data processing technique in condition of complex satellite dithering[J]. Journal of Electronics & Information Technology, 2010, 32(8): 1885-1891.
[28]	ROMANS L. Optimal combination of quaternions from multiple star cameras[R]. Pasadena: Jet Propulsion Laboratory, 2003.
[29]	MANDEA M, HOLSCHNEIDER M, LESUR V, et al. The Earth's magnetic field at the CHAMP satellite epoch[M]//System Earth via geodetic-geophysical space techniques. Berlin: Springer, 2010: 475-526.
[30]	WU S C, KRUIZINGA G, BERTIGER W. Algorithm theoretical basis document for GRACE Level-1B data processing: version 1.2[R]. Pasadena: Jet Propulsion Laboratory, 2006.
[31]	SIEMES C. GOCE gradiometer calibration and Level 1b data processing[R]. Noordwijk: European Space Agency, 2011.
[32]	STUMMER C, FECHER T, PAIL R. Alternative method for angular rate determination within the GOCE gradiometer processing[J]. Journal of Geodesy, 2011, 85(9): 585-596.
[33]	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.
[34]	JAFARI M. Optimal redundant sensor configuration for accuracy increasing in space inertial navigation system[J]. Aerospace Science and Technology, 2015, 47: 467-472.
[35]	FROMMKNECHT B. Integrated sensor analysis of the GRACE mission[D]. München: Technische Universität München, 2007.
[36]	SFIKAS K. Reconstructing the attitude of the GRACE-FO mission based on fusion of star sensor, gyroscope and steering mirror data[D]. Delft: Delft University of Technology, 2024.
[37]	LEFFERTS E J, MARKLEY F L, SHUSTER M D. Kalman filtering for spacecraft attitude estimation[J]. Journal of Guidance, Control, and Dynamics, 1982, 5(5): 417-429.
[38]	MARKLEY F L. Attitude error representations for Kalman filtering[J]. Journal of Guidance, Control, and Dynamics, 2003, 26(2): 311-317.
[39]	TRAWNY N, ROUMELIOTIS S I. Indirect Kalman filter for 3D attitude estimation[R]. Minneapolis: University of Minnesota, 2005.
[40]	KLINGER B. A contribution to GRACE time-variable gravity field recovery: improved Level-1B data pre-processing methodologies[D]. Graz: Technischen Universität Graz, 2018.
[41]	KLINGER B, MAYER-GÜRR T. Combination of GRACE star camera and angular acceleration data: impact on monthly gravity field models[C]//Proceedings of 2014 RACE Science Team Meeting. Potsdam: [s.n.], 2014.
[42]	王燕清, 杜伟峰, 吴永康, 等. 星敏感器在轨精度分析[J]. 光学学报, 2025, 45(12): 1228002.
	WANG Yanqing, DU Weifeng, WU Yongkang, et al. Analysis of star sensor in-orbit accuracy[J]. Acta Optica Sinica, 2025, 45(12): 1228002.
[43]	LIANG Lei, YU Jinhai, WANG Changqing, et al. Influence of the low-frequency error of the residual orbit on recovering time-variable gravity field from the satellite-to-satellite tracking mission[J]. Remote Sensing, 2021, 13(6): 1118.
[44]	梁磊, 于锦海, 朱永超, 等. 顾及非线性改正的动力学方法反演GRACE时变重力场模型[J]. 地球物理学报, 2019, 62(9): 3259-3268.
	LIANG Lei, YU Jinhai, ZHU Yongchao, et al. Recovered GRACE time-variable gravity field based on dynamic approach with the non-linear corrections[J]. Chinese Journal of Geophysics, 2019, 62(9): 3259-3268.

星间指向角	JPL-Cal1	JPL-Cal2	JPL-Cal3	JPL-NoCal
Yaw	3.33×10^－5	3.11×10^－5	2.82×10^－5	7.25×10^－5
Pitch	3.38×10^－5	3.43×10^－5	3.67×10^－5	5.02×10^－5
Roll	2.82×10^－5	2.57×10^－5	2.65×10^－5	6.68×10^－5

结果差异	ω_x	ω_y	ω_z
CHZU_LFE-IMU1B	1.58×10^－7	1.30×10^－7	1.37×10^－7
CHZU_NLFE-IMU1B	1.84×10^－7	1.49×10^－7	1.60×10^－7
JPL-IMU1B	6.00×10^－7	3.55×10^－7	3.93×10^－7

顾及星敏感器安装矩阵校正的GRACE-FO姿态数据处理研究

GRACE-FO attitude data determination with consideration of star camera alignment matrix calibration

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