顾及月光和周期性噪声影响的GOCE卫星姿态四元数校正方法

doi:10.11947/j.AGCS.2026.20250454

测绘学报 ›› 2026, Vol. 55 ›› Issue (7): 1183-1198.doi: 10.11947/j.AGCS.2026.20250454

• 人工智能的大地测量与卫星重力反演前沿 • 上一篇

顾及月光和周期性噪声影响的GOCE卫星姿态四元数校正方法

郭泽华¹(), 徐新禹¹^,²(), 赵永奇¹, 蔺文奇¹, 丁嘉威¹

^1.武汉大学测绘学院，湖北　武汉　430079
^2.武汉大学地球空间环境与大地测量教育部重点实验室，湖北　武汉　430079

收稿日期:2025-10-27 修回日期:2026-06-18 发布日期:2026-08-18
通讯作者: 徐新禹 E-mail:zehuaguo@whu.edu.cn;xyxu@sgg.whu.edu.cn
作者简介:郭泽华（1992—），男，博士生，研究方向为重力卫星数据处理。 E-mail：zehuaguo@whu.edu.cn
基金资助:
国家自然科学基金(42388102; 42192533; 42574007; 42404005);中央高校自主科研项目(2042022dx0001)

A correction method for GOCE satellite attitude quaternions considering moonlight disturbance and orbit-periodic noise

Zehua Guo¹(), Xinyu Xu¹^,²(), Yongqi Zhao¹, Wenqi Lin¹, Jiawei Ding¹

^1.School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
^2.Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China

Received:2025-10-27 Revised:2026-06-18 Published:2026-08-18
Contact: Xinyu Xu E-mail:zehuaguo@whu.edu.cn;xyxu@sgg.whu.edu.cn
About author:Guo Zehua (1992—), male, PhD candidate, majors in gravity satellite data processing. E-mail: zehuaguo@whu.edu.cn
Supported by:
The National Natural Science Foundation of China(42388102; 42192533; 42574007; 42404005);Fundamental Research Funds for the Central Universities(2042022dx0001)

摘要/Abstract

摘要：

地球重力场和海洋环流探测（GOCE）卫星星敏感器（STR）的姿态观测数据，为静电重力梯度仪（EGG）高精度重力梯度测量与解算提供基准。然而，该姿态数据受周期性月光干扰和轨道周期相关噪声影响，导致星敏感器视轴夹角残差（ΔIBA）中出现局部偏差和轨道周期成分。本文提出一种顾及上述影响的姿态数据校正方法。首先，采用估计温度效应的校正方法估计STR常数偏差与温度系数；并结合STR有效观测状态、卫星-月球矢量与STR视轴夹角识别月光干扰数据段；然后，以仍有效的主星敏感器为参考，采用Levenberg-Marquardt（LM）方法估计STR3在组合切换时段的局部校准参数，以减小ΔIBA的局部异常偏差；最后，基于ΔIBA估计轨道周期噪声项并归算至实测姿态数据。利用GOCE卫星2012年1月－6月的姿态数据验证表明，本文估计的STR间相对常数偏差和相对温度系数与ESA标定结果基本一致，两者最大差异分别为0.257″和0.04（″/℃）；ΔIBA₁₃与ΔIBA₂₃周期均值异常出现的时间与卫星-月球矢量和相应STR视轴夹角小于14°的时段高度重合，并以约30天的周期出现。经LM局部校正后，ΔIBA₁₃和ΔIBA₂₃的周期均值分别降至3.95″和3.39″，标准差由0.87″和0.84″降低至0.44″和0.63″。去除轨道周期项后，角速度差值幅值谱密度（ASD）在1～30 CPR范围呈现与拟合阶数一致的谱峰。结果表明，本文方法可有效降低月光局部偏差和低频轨道周期误差的影响。

关键词: GOCE, 星敏感器, 参数估计, 周期性噪声, LM方法

Abstract:

The attitude observations acquired by the star trackers (STR) onboard the gravity field and steady state ocean circulation explorer (GOCE) satellite provide a reference for high-precision gravity gradient measurement and recovery using the electrostatic gravity gradiometer (EGG). However, these attitude data are affected by periodic moonlight interference and orbit-period-related noise, leading to local biases and orbit-periodic components in the inter-boresight angle residuals (ΔIBA) of the star trackers. This study proposes an attitude data correction method that simultaneously accounts for these effects. First, a correction method considering temperature effects is adopted to estimate the constant biases and temperature coefficients of the STRs; moonlight-contaminated data segments are then identified by combining the valid observation status of the STRs, the satellite-Moon vector, and the angle between this vector and the STR boresight. Then, the Levenberg-Marquardt (LM) method is used to minimize the sum of squared ΔIBA values and estimate local calibration parameters. Finally, orbit-periodic noise terms are estimated based on ΔIBA and reduced from the measured attitude data. Validation using GOCE attitude data from January to June 2012 shows that the estimated inter-STR relative constant biases and relative temperature coefficients are in good agreement with the ESA calibration results, with maximum discrepancies of 0.257″and 0.04″/℃, respectively. The times at which anomalies occur in the periodic mean values of ΔIBA₁₃ and ΔIBA₂₃ highly coincide with the periods when the angle between the satellite-Moon vector and the corresponding STR boresight is less than 14°, and recur with a period of approximately 30 days. After local correction using the LM algorithm, the periodic mean values of ΔIBA₁₃ and ΔIBA₂₃ are reduced to 3.95″and 3.39″, respectively, while their standard deviations decrease from 0.87″and 0.84″to 0.44″and 0.63″, respectively. After removing the orbit-periodic terms, the power spectral density (ASD) of the angular-rate differences exhibits spectral peaks consistent with the fitted orders over the range of 1～30 cycles per revolution (CPR). The results demonstrate that the proposed method can effectively reduce the effects of moonlight-induced local biases and low-frequency orbit-periodic errors.

Key words: GOCE, star sensor, parameter estimation, periodic noise, Levenberg-Marquardt method

中图分类号:

P228

郭泽华, 徐新禹, 赵永奇, 蔺文奇, 丁嘉威. 顾及月光和周期性噪声影响的GOCE卫星姿态四元数校正方法[J]. 测绘学报, 2026, 55(7): 1183-1198.

Zehua Guo, Xinyu Xu, Yongqi Zhao, Wenqi Lin, Jiawei Ding. A correction method for GOCE satellite attitude quaternions considering moonlight disturbance and orbit-periodic noise[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(7): 1183-1198.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: http://xb.chinasmp.com/CN/10.11947/j.AGCS.2026.20250454

http://xb.chinasmp.com/CN/Y2026/V55/I7/1183

图/表 17

图1

图2

图3

图4

表1

图5

表2

图6

表3

图7

图8

表4

表5

图9

表6

表7

图10

参考文献 28

[1]	Drinkwater M R, Floberghagen R, Haagmans R, et al. GOCE: ESA's first earth explorer core mission[J]. Space Science Reviews, 2003, 108(1): 419-432.
[2]	徐新禹, 李建成, 邹贤才, 等. GOCE卫星重力探测任务[J]. 大地测量与地球动力学, 2006, 26(4): 49-55.
	Xu Xinyu, Li Jiancheng, Zou Xiancai, et al. GOCE gravity explorer mission[J]. Journal of Geodesy and Geodynamics, 2006, 26(4): 49-55.
[3]	徐新禹, 赵永奇, 魏辉, 等. 利用先验重力场模型对GOCE卫星重力梯度观测值进行校准分析[J]. 测绘学报, 2015, 44(11): 1196-1201. DOI: . doi: 10.11947/j.AGCS.2015.20140414
	Xu Xinyu, Zhao Yongqi, Wei Hui, et al. Calibration and analysis of SGG observations of GOCE based on prior gravity models[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(11): 1196-1201. DOI: . doi: 10.11947/j.AGCS.2015.20140414
[4]	Siemes C. Improving GOCE cross-track gravity gradients[J]. Journal of Geodesy, 2018, 92(1): 33-45.
[5]	Rispens S, Bouman J. Calibrating the GOCE accelerations with star sensor data and a global gravity field model[J]. Journal of Geodesy, 2009, 83(8): 737-749.
[6]	Siemes C, Haagmans R, Kern M, et al. Monitoring GOCE gradiometer calibration parameters using accelerometer and star sensor data: methodology and first results[J]. Journal of Geodesy, 2012, 86(8): 629-645.
[7]	Visser P N A M. Exploring the possibilities for star-tracker assisted calibration of the six individual GOCE accelerometers[J]. Journal of Geodesy, 2008, 82(10): 591-600.
[8]	Siemes C, Rexer M, Schlicht A, et al. GOCE gradiometer data calibration[J]. Journal of Geodesy, 2019, 93(9): 1603-1630.
[9]	Frommknecht B, Lamarre D, Meloni M, et al. GOCE level 1b data processing[J]. Journal of Geodesy, 2011, 85(11): 759-775.
[10]	Romans L. Optimal combination of quaternions from multiple star cameras[R]. Los Angeles: Jet Propulsion Laboratory, 2003.
[11]	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.
[12]	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.
[13]	Siemes C, Rexer M, Haagmans R. GOCE star tracker attitude quaternion calibration and combination[J]. Advances in Space Research, 2019, 63(3): 1133-1146.
[14]	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.
[15]	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
[16]	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.
[17]	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.
[18]	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.
[19]	赵永奇, 李建成, 徐新禹, 等. 利用GOCE和GRACE卫星观测数据确定静态重力场模型[J]. 地球物理学报, 2023, 66(6): 2322-2336.
	Zhao Yongqi, Li Jiancheng, Xu Xinyu, et al. Determination of static gravity field model by using satellite data of GOCE and GRACE[J]. Chinese Journal of Geophysics, 2023, 66(6): 2322-2336.
[20]	邹贤才, 李建成. 单加速度计模式下的GOCE卫星重力场建模方法研究[J]. 地球物理学报, 2016, 59(4): 1260-1266.
	Zou Xiancai, Li Jiancheng. Study on the Earth gravity modeling by GOCE in individual accelerometer mode[J]. Chinese Journal of Geophysics, 2016, 59(4): 1260-1266.
[21]	Siemes C. GOCE gradiometer calibration and Level 1b data processing: ESA working paper EWP-2384[R]. Noordwijk: European Space Agency, 2011: 31-35.
[22]	Pail R. A parametric study on the impact of satellite attitude errors on GOCE gravity field recovery[J]. Journal of Geodesy, 2005, 79(4/5): 231-241.
[23]	Stummer C, Siemes C, Pail R, et al. Upgrade of the GOCE level 1b gradiometer processor[J]. Advances in Space Research, 2012, 49(4): 739-752.
[24]	乔兴, 王宏力, 王永胜, 等. 基于GA-LM融合的星敏感器参数标定算法[J]. 激光与红外, 2014, 44(11): 1224-1229.
	Qiao Xing, Wang Hongli, Wang Yongsheng, et al. Parameter calibration of star sensor based on GA-LM fusion algorithm[J]. Laser & Infrared, 2014, 44(11): 1224-1229.
[25]	赵健, 郭忠磊, 滕惠忠, 等. 基于LM方法的单位四元数光束法平差模型解算[J]. 海洋测绘, 2017, 37(5): 56-59.
	Zhao Jian, Guo Zhonglei, Teng Huizhong, et al. A solution to unit quaternion bundle adjustment model based on LM method[J]. Hydrographic Surveying and Charting, 2017, 37(5): 56-59.
[26]	王文超, 王夏莉, 王斌, 等. LCR-G型相对重力仪周期项参数的确定方法[J]. 大地测量与地球动力学, 2022, 42(1): 100-103, 110.
	Wang Wenchao, Wang Xiali, Wang Bin, et al. The method for periodic terms parameters of LCR-G gravity meters[J]. Journal of Geodesy and Geodynamics, 2022, 42(1): 100-103, 110.
[27]	Marquardt D W. An algorithm for least-squares estimation of nonlinear parameters[J]. Journal of the Society for Industrial and Applied Mathematics, 1963, 11(2): 431-441.
[28]	Welch P. The use of fast Fouriert Transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms[J]. IEEE Transactions on Audio and Electroacoustics, 1967, 15(2): 70-73.

方法	b₂－b₁/（″）	b₃－b₁/（″）	t₂－t₁/（″/℃）	t₃－t₁/（″/℃）
本文方法	[－5.910－18.100 4.230]	[－0.951－2.780 10.710]	[－0.476 0.704 0.117]	[－0.502 0.093 1.089]
ESA	[－5.839－18.341 4.487]	[－1.017－2.626 10.556]	[－0.479 0.712 0.090]	[－0.464 0.112 1.072]

视轴夹角残差	是否受影响段	最大值	最小值	均值	标准差
ΔIBA₁₃	未受影响	1.66	－1.58	－0.31	0.39
ΔIBA₁₃	受影响	9.73	－6.40	0.51	2.86
ΔIBA₂₃	未受影响	1.23	－2.35	－0.01	0.36
ΔIBA₂₃	受影响	5.99	－4.41	－0.25	1.15

方法	残差项	趋势斜率	均值/（″）	标准差/（″）
原始姿态	ΔIBA₁₂	－0.002 732	7.299	0.50
	ΔIBA₁₃	0.007 699	－9.827	1.44
	ΔIBA₂₃	－0.003 530	－8.900	0.51
常数偏差b_i/温度系数t_i校正	ΔIBA₁₂	－0.000 453	0.286	0.23
	ΔIBA₁₃	0.001 222	－0.310	0.87
	ΔIBA₂₃	0.001 537	－0.182	0.84
LM局部校正	ΔIBA₁₂	－0.000 454	0.286	0.23
	ΔIBA₁₃	0.001 179	－0.311	0.44
	ΔIBA₂₃	0.001 101	－0.185	0.63

星敏感器	欧拉角	方法	最大值	最小值	均值	标准差
STR₁	Roll	ESA	11.170	－11.979	0.045	1.759
	Roll	LM	13.576	－15.650	0.062	2.020
	Pitch	ESA	27.205	－9.204	0.101	1.514
	Pitch	LM	6.696	－5.746	0.032	0.890
	Yaw	ESA	330.797	－243.367	－0.663	35.710
	Yaw	LM	250.738	－243.716	－0.690	35.584
STR₂	Roll	ESA	10.107	－11.196	0.008	1.637
	Roll	LM	14.325	－14.711	－0.029	1.849
	Pitch	ESA	7.006	－7.329	0.078	1.102
	Pitch	LM	6.460	－7.148	0.022	0.911
	Yaw	ESA	159.742	－165.314	0.269	19.552
	Yaw	LM	154.114	－152.771	0.207	19.496
STR₃	Roll	ESA	11.599	－24.020	－0.251	2.146
	Roll	LM	16.893	－18.652	－0.262	3.183
	Pitch	ESA	6.601	－9.425	0.116	1.269
	Pitch	LM	5.291	－5.927	0.032	0.959
	Yaw	ESA	188.802	－217.493	1.687	27.247
	Yaw	LM	187.646	－186.051	1.493	27.252

方法	STR₁	STR₂	STR₃
ESA	2.388×10^－3	1.019×10^－3	1.174×10^－3
LM	1.931×10^－3	7.506×10^－4	1.085×10^－3

顾及月光和周期性噪声影响的GOCE卫星姿态四元数校正方法

A correction method for GOCE satellite attitude quaternions considering moonlight disturbance and orbit-periodic noise

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 17

参考文献 28

相关文章 15

编辑推荐

Metrics

本文评价

分量	最大值	最小值	均值	标准差
V_xx	1.976	－2.440	0.066	0.703
V_yy	0.478	－0.632	－0.111	0.182
V_zz	2.026	－2.622	0.070	0.740

迹	最大值	最小值	均值	标准差
Trace_ESA	－572 093.791	－577 148.577	－574 599.662	1 412.553
Trace_LM	－572 096.100	－577 149.188	－574 599.637	1 412.434

[1]	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.
[2]	王潜心, 胡超, 程彤. 基于GNSS钟差参数先验信息的超快速轨道钟差估计方法[J]. 测绘学报, 2025, 54(6): 982-994.
[3]	胡丹怡, 吴云龙, 肖云, 仇越, 吴晓辉, 钟玉龙. 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.
[4]	王珂, 刘国林, 付政庆, 王路遥. 基于Moore-Penrose广义逆及立体矩阵的可分离非线性最小二乘解算方法[J]. 测绘学报, 2022, 51(3): 340-350.
[5]	潘娟霞, 邹贤才. GOCE引力梯度内部校准方法[J]. 测绘学报, 2022, 51(2): 192-200.
[6]	陈鑑华, 张兴福, 沈云中, 陈秋杰, 李伟超. GOCE卫星重力梯度观测值的时变重力场变化改正及影响分析[J]. 测绘学报, 2021, 50(3): 324-332.
[7]	刘焕玲, 文汉江, 徐新禹, 赵永奇, 蔡剑青. GOCE实测数据反演高阶重力场模型的Torus方法[J]. 测绘学报, 2020, 49(8): 965-973.
[8]	邓兴升, 彭思淳, 游扬声. 加权整体最小二乘EIO模型与算法[J]. 测绘学报, 2019, 48(7): 926-930.
[9]	王乐洋, 余航, 邹传义, 鲁铁定. 加权整体最小二乘EIV模型与算法——与“加权整体最小二乘EIO模型与算法”一文的讨论[J]. 测绘学报, 2019, 48(7): 931-937.
[10]	孟令奎, 毛旭东, 魏祖帅, 张文. 结合先验概率估计的GF-3影像水体概率估计方法[J]. 测绘学报, 2019, 48(4): 439-447.
[11]	瞿庆亮, 常晓涛, 于胜文, 朱广彬. 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.
[12]	邹贤才. GOCE卫星重力梯度校准与无阻尼控制效果分析[J]. 测绘学报, 2018, 47(3): 291-297.
[13]	孟祥超, 万晓云, 于锦海, 朱永超, 冯炜. 利用引力梯度数据计算径向梯度的优化方法[J]. 测绘学报, 2016, 45(7): 775-781.
[14]	潘雄, 罗静, 汪耀. P范分布的实数阶与对数矩估计法[J]. 测绘学报, 2016, 45(3): 302-309.
[15]	刘焕玲, 文汉江, 徐新禹, 朱广彬. 利用GOCE模拟观测反演重力场的Torus法[J]. 测绘学报, 2015, 44(9): 965-972.