The satellite gravity mission GRACE(-FO) has not yet reached its designed baseline accuracy. Previous studies demonstrated that the deficiency in the sensor system or the related signal processing might be responsible, which in turn motivates us to keep revising the sensor data processing, typically the spacecraft’s attitude. Many efforts in the past have been made to enhance the attitude modeling for GRACE, for instance, the latest release reprocesses the attitude by fusing the angular acceleration with the star camera/tracker (SC) measurements, which helps to reduce the error in Level-2 temporal gravity fields. Therefore, in addition to GRACE, revising GRACE-FO attitude determination might make sense as well. This study starts with the most original raw GRACE-FO Level-1A data including those from three SCs and one IMU (Inertial Measurement Unit) sensors, and manage to generate a new publicly available Level-1B attitude product called HUGG-01 covering from June 2018 to December 2020, using our independently-developed software. The detailed treatment of individual payload is present in this study, and an indirect Kalman filter method is introduced to fuse the multiple sensors to acquire a relatively stable and precise attitude estimation. Unlike the direct SC combination method with a predefined weight as recommended in previous work, we propose an involvement of each SC measurement in the Kalman filter to enable a dynamic weight adjustment. Intensive experiments are further carried out to assess the HUGG-01, which demonstrate that the error level of HUGG-01 is entirely within the design requirement, i.e., the resulting KBR pointing variations are well controlled within 1 mrad (pitch), 5 mrad (roll) and 1 mrad (yaw). Moreover, comparisons with the official JPL-V04 attitude product demonstrate an equivalent performance in the low-to-middle spectrum, with even a slightly lower noise level (in the high spectrum) than JPL-V04. Further analysis on KBR range-rate residuals and gravity recovery on January 2019 indicates that, i.e., RMS of the difference (HUGG-01 minus JPL-V04) for the range rate is less than $3.234\times {10}^{-8}$ m/s, and the amplitude of geoid height difference is approximately $0.5$ cm. Both differences are below the sensitivity of the state-of-the-art satellite gravity mission, demonstrating a good agreement between HUGG-01 and JPL-V04.

When using the dynamic approach to recover the time-variable gravity field, the reference orbit generated by the perturbation model and the non-conservative force observed from the accelerometer should be introduced at first, and then the observation equations of the residual orbit and the residual range rate are established. This introduces a perturbation model error and instrument noise. Thus, there are low-frequency errors in the residual orbit and the residual range rate. Currently, most studies only focus on the low-frequency error of the residual range rate, neglecting the influence of the low-frequency error in the residual orbit. Therefore, under the condition of the perturbation model error and instrument noise including the constant term and 1CPR term, the low-frequency error formulas of the residual orbit and residual range rate are derived according to the characteristics of the solution of the Hill equation. Then, the influence of the low-frequency error on the residuals is analyzed by using the simulation and the real data processing respectively. In the simulation and real data processing, the accuracy of the recovered gravity field can maintain a good consistency for different arc lengths by removing the low-frequency error in the residual orbit. Finally, the time-variable gravity field model UCAS-IGG (University of Chinese Academy of Sciences-Institute of Geodesy and Geophysics) was solved from January 2005 to February 2010 by removing the low-frequency error of the residual orbit and residual range rate. Compared with the official institutions, the UCAS-IGG presents a good consistency in the estimating time-variable gravity field signal. This study demonstrates how the effect of the low-frequency error of the residual orbit should be taken into consideration when the longer arc length is used to recover a time-variable gravity field. Using a long arc length can reduce the variables of the initial state and recover the influence of the small force.