Seasonal signals in satellite geodesy time series are mainly derived from a number of loading sources, such as atmospheric pressure and hydrological loading. The most common method for modeling the seasonal signal with quasi-period is to use the sine and cosine functions with the constant amplitude for approximation. However, due to the complexity of environmental changes, the time-varying period part is very difficult to model by the geometric or physical method. We present a machine learning method with Gaussian process to capture the quasi-periodic signals in the geodetic time series and optimize the estimation of model parameters by means of maximum likelihood estimation. We test the performance of the method using the synthetic time series by simulating the time-varying and quasi-periodic signals. The results show that the fitting residuals of the new model show a better random fluctuation, while the traditional models still leave the clear periodic systematics signals without being fully modeled. The new model illustrates a higher reliability of linear trend estimation, and a lower uncertainty and model fitting RMSE, even in time series with shorter time span. On the other hand, it shows a strong capacity to restore the missing data and predict the future changes in time series. The method is successfully applied to modeling the real coordinate time series of the GNSS site (BJFS) from IGS network, and the equivalent water height (EWH) time series in North China obtained from gravity satellites. Therefore, it is recommended as an alternative for precise model reconstruction and signals extraction of satellite geodesy time series, especially in modeling the complex time-varying signals, estimating the secular motion velocity, and recovering the large missing data.

卫星大地测量时间序列中的季节信号主要来自多种载荷源，例如大气压力和水文载荷。对准周期季节信号进行建模的最常见方法是使用具有恒定幅度的正弦和余弦函数进行近似。然而，由于环境变化的复杂性，时变周期部分很难用几何或物理方法建模。我们提出了一种采用高斯过程的机器学习方法来捕获大地时间序列中的准周期信号，并通过最大似然估计来优化模型参数的估计。我们通过模拟时变和准周期信号，使用合成时间序列测试该方法的性能。结果表明，新模型的拟合残差表现出更好的随机波动，而传统模型仍然留下清晰的周期性系统信号，没有完全建模。新模型表明线性趋势估计的可靠性更高，不确定性和模型拟合 RMSE 更低，即使在时间跨度较短的时间序列中也是如此。另一方面，它显示出强大的恢复丢失数据和预测时间序列未来变化的能力。该方法成功应用于对IGS网络的GNSS站点（BJFS）真实坐标时间序列和重力卫星获得的华北地区等效水高（EWH）时间序列进行建模。因此，建议将其作为卫星大地测量时间序列的精确模型重建和信号提取的替代方案，特别是在对复杂时变信号进行建模、估计长期运动速度和恢复大量丢失数据方面。