The gravity field recovery from GRACE (Gravity Recovery and Climate Experiment) mission data is contaminated by both observation noise and dynamic force errors, especially the temporal aliasing errors. To reduce their influence, four approaches are widely adopted, namely the estimation of empirical accelerations (ACC approach), the estimation of K-band range-rate parameters (KBR approach), the incorporation of the full variance–covariance matrix of observations into the least-squares adjustment (COV approach), and the time series model-based filtering (FILT approach). Essentially, the ACC and KBR approaches can be grouped into the method of functional model compensation, while the COV and FILT approaches belong to the method of stochastic model compensation. The four approaches are systematically revisited in this paper concerning their connections and differences from both theoretical perspectives and numerical simulations. Results show that all of them can significantly reduce errors in the recovered monthly gravity field models compared to the nominal approach not applying any of the four approaches. Moreover, their performances are quite consistent in the simulation case where only white observation noise is included. When both colored observation noise and temporal aliasing effects are considered, however, their performances are different. The noise reduction ratio can reach up to 87% by the ACC, COV and FILT approaches, while it is 79% in the KBR approach. The discrepancy can be explained by the compromise between noise reduction and signal absorption in the KBR approach due to the lack of constraints on empirical parameters. Moreover, in the spectral domain, ACC and KBR approaches function as high-pass filters, whereas the stochastic method, COV or FILT approach, can competently cope with colored noise in a full-spectrum manner.

GRACE（重力恢复和气候实验）任务数据的重力场恢复受到观测噪声和动力误差的污染，特别是时间混叠误差。为了减少它们的影响，广泛采用了四种方法，即经验加速度的估计（ACC方法），K波段距离速率参数的估计（KBR方法），将观测的全方差-协方差矩阵合并到最小二乘法调整（COV 方法）和基于时间序列模型的过滤（FILT 方法）。ACC和KBR方法本质上可以归为功能模型补偿方法，而COV和FILT方法属于随机模型补偿方法。本文从理论角度和数值模拟两个方面系统地重新审视了这四种方法的联系和差异。结果表明，与不应用四种方法中的任何一种的名义方法相比，它们都可以显着减少恢复的月度重力场模型中的误差。此外，在仅包含白观测噪声的模拟情况下，它们的性能非常一致。然而，当同时考虑有色观察噪声和时间混叠效应时，它们的表现是不同的。ACC、COV和FILT方法的降噪率最高可达87%，而KBR方法为79%。由于缺乏对经验参数的限制，KBR 方法中降噪和信号吸收之间的折衷可以解释这种差异。此外，在谱域中，ACC 和 KBR 方法充当高通滤波器，而随机方法、COV 或 FILT 方法可以以全谱方式胜任处理有色噪声。