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Reconstruction of geodetic time series with missing data and time-varying seasonal signals using Gaussian process for machine learning

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Abstract

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.

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Data availability

The software package used in this paper can be downloaded from the website (https://github.com/SBH08180815/GP_Time_Series_Tool). GNSS data used in this study were obtained from Nevada Geodetic Laboratory (http://geodesy.unr.edu). The data for GRACE are available at http://icgem.gfz-potsdam.de/series. And the data for GLDAS and Precipitation are available at https://disc.gsfc.nasa.gov/.

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Acknowledgements

The research is supported by the National Natural Science Foundation of China (41774041). We are grateful to International GNSS Service (IGS) for providing GNSS data.

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  1. Shuanggen Jin

    Present address: Henan Polytechnic University, Jiaozuo, 454000, China

Authors and Affiliations

  1. Henan Polytechnic University, Jiaozuo, 454000, China

    Keke Xu, Shaobin Hu, Jun Li, Wei Zheng, Jian Wang, Yongzhen Zhu, Kezhao Li, Ankang Ren & Yifu Liu

  2. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, 200030, China

    Shuanggen Jin

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  1. Keke Xu
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Contributions

KX proposed this study and wrote the manuscript. SH conducted the numerical computation and experiments. SJ modified the manuscript. JL and JW wrote the program code. WZ reviewed and modified the manuscript. YZ and AR analyzed and validated the method. KL and YL revised the manuscript. KX and All authors were involved in discussions throughout the development.

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Correspondence to Keke Xu or Shuanggen Jin.

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Xu, K., Hu, S., Jin, S. et al. Reconstruction of geodetic time series with missing data and time-varying seasonal signals using Gaussian process for machine learning. GPS Solut 28, 79 (2024). https://doi.org/10.1007/s10291-024-01616-8

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