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Introduction
With high accuracy GNSS time series, it is possible to determine the crust velocity field and its uncertainty of the global GNSS reference stations [1, 2–3], it is also widely applied to the establishment of international terrestrial reference frame [4], crustal plate movement monitoring [5, 6–7], Drought monitoring [8], and global coordinate frame maintenance [9, 10]. Therefore, analyzing and predicting GNSS time series is of significance for geodynamics and geophysics studies.
Time series prediction methods primarily include physical modeling and numerical modeling [11, 12], which typically rely on geophysical theories, linear terms and periodic components in the construction of coordinate time series models [13]. However, these models, requiring manual establishment of feature information and modeling parameters, struggle to capture complex nonlinear data features, which resulted in systematic biases and limitations [14]. In contrast, deep learning (DL), as an emerging technology used for many areas including image recognition [15, 16], natural language processing [17, 18, 19–20], and time series prediction [21, 22, 23–24], can process highly nonlinear data and capture deeper patterns and regularities [25]. DL algorithms do not require manual feature selection. These networks build complex and precise networks to automatically learn and extract relevant data features, reducing the need for domain knowledge and enhancing the generalization ability of the models [26]. However, neural networks are purely data-driven and unable to account for the physical significance and inherent patterns that may exist within the time series. Therefore, ensemble models based on the 'decomposition, prediction, and integration' concept have emerged as a novel approach for time series prediction. First, the time series data is decomposed on multiple scales, which break down the complex time series data into simpler modes that more interpretable modes with specific significance, reducing the modeling difficulty of complex systems. Then, each simple mode component is analyzed and predicted individually. Finally, the prediction for each component is integrated to produce the overall result, enhancing the model's analysis and prediction performance.
To enhance the Long Short-Term Memory (LSTM) model performance, numerous studies have combined Ensemble Empirical Mode Decomposition (EEMD) and LSTM to model and predict time series in various fields. For instance, Zou et al. applied the EEMD-LSTM model to bearing fault diagnosis, it demonstrated that the EEMD method can preprocess signals to...