Title: GNSS VERTICAL TIME SERIES PREDICTION BASED ON THE INTEGRATION OF CEEMDAN-VMD-LSTM AND COMPOSITE ENTROPY
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Authors: Lu Tieding, Jiang Chen, He Xiaoxing, Yang Houming and Zhang Yuan
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DOI: 10.13168/AGG.2026.0016
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Journal: Acta Geodynamica et Geomaterialia, Vol. 23, No. 2 (222), Prague 2026
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Full Text:  PDF file (1.5 MB)
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Keywords: GNSS vertical time series; Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN); Variational Mode Decomposition (VMD); Long Short-Term Memory (LSTM); prediction
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| Abstract: GNSS vertical time series exhibit nonlinear and non-stationary characteristics, making it difficult for traditional time series forecasting methods to achieve high-precision predictions. To address this challenge, this study proposes a hybrid prediction model—CEEMDAN-VMD-LSTM—which integrates Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Variational Mode Decomposition (VMD), and Long Short-Term Memory (LSTM) networks. The model first applies the CEEMDAN algorithm to decompose the original GNSS time series into a set of Intrinsic Mode Functions (IMFs), and computes the Permutation Entropy (PE) and Sample Entropy (SE) of each IMF. A Composite Entropy (CE) is constructed by taking the equal-weighted average of PE and SE. Based on the composite entropy values, the K-Nearest Neighbors (KNN) algorithm is used to classify the IMFs into high-frequency and low-frequency components. These components are then linearly aggregated into high-frequency and low-frequency sequences, respectively. The high-frequency sequence undergoes a second decomposition using the VMD algorithm, resulting in k IMFs and a residual sequence. The low-frequency sequence (from the first decomposition), the IMFs, and the residual sequence (from the second decomposition) are separately modeled and predicted using the LSTM network. The final forecast is reconstructed by aggregating the predictions of the subcomponents. Experimental results on GNSS vertical time series from ten stations show that the proposed CEEMDAN-VMD-LSTM model achieves Root Mean Square Error (RMSE) values ranging from 2.20 mm to 3.69 mm, Mean Absolute Error (MAE) values between 1.75 mm and 2.95 mm, and coefficients of determination (R²) ranging from 0.80 to 0.89. Compared with baseline models including LSTM, VMD-LSTM, CEEMDAN-VMD-RNN, and CEEMDAN-VMD-GRU, the proposed model demonstrates varying degrees of improvement, validating its effectiveness for GNSS vertical time series prediction. |
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