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

doi:10.11947/j.AGCS.2026.20250454

Abstract

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

CLC Number:

P228

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.

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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