Abstract
Accurately modeling and prediction the nonlinear motion of GNSS (Global Navigation Satellite System) coordinate time series holds significant theoretical and practical value for the study of geodynamics. A novel integrated network, named Ensemble Learning method based on Signal Source Driver (ELSSD), is proposed, which leverages the strengths of Long Short-Term Memory (LSTM) and Deep Self-Attention Neural Network (DSANN), while integrating GNSS loading data as an additional data source. Additionally, a multi-track synchronous sliding window data processing strategy is designed to address the challenge of multi-source data fusion input. The effectiveness of this algorithm is validated using GNSS coordinate time series from 186 global stations over a period of 10 years. Experimental results initially illustrate that, when accounting for displacement caused by environmental loading effects, there is a marked improvement in the modeling and prediction accuracy compared with GNSS input-only. Furthermore, the application of three ensemble network strategies-Bagging, Boosting, and Stacking-have further been demonstrated to enhance modeling and prediction accuracy. Compared with LSTM and DSANN networks, the proposed ELSSD algorithm achieves an average RMSE (Root Mean Square Error) of 3.6 mm for both modeling and prediction, with modeling accuracy improvements of 4.8% and 6.2%, while prediction accuracy improvements of 5.4% and 5.9%, respectively. With respect to the traditional Least Square method, there is an improvement of 22.1% and 27.9% in modeling and prediction accuracy, respectively. Regarding noise characteristics, there is a significant reduction in colored noise amplitude, with decreases of 36.7% and 36.0% observed in modeling and prediction, respectively. Simultaneously, the velocity uncertainty experiences an average reduction of 27.1% and 27.5%. The average velocity differences are measured at 0.06 mm/year and 0.24 mm/year, respectively. Hence, our findings suggest that the ELSSD algorithm emerges as an effective methodology for handling multi-source data input in GNSS coordinate time series, presenting promising practical applications in the field.
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Data availability
The GNSS data is provided by International Terrestrial Reference Frame (ITRF, https://itrf.ign.fr/, accessed on 13 May 2024). Global surface atmospheric pressure products are available at the National Centers for Environmental Prediction (NCEP, https://www.weather.gov/ncep/, accessed on 13 May 2024). Land water storage models are provided by The Global Land Data Assimilation System (GLDAS, https://ldas.gsfc.nasa.gov/gldas, accessed on 13 May 2024).Global seafloor pressure grid data is obtained from the National Oceanographic Partnership Program (NOPP, https://www.boem.gov/environment/environmental-studies/national-oceanographic-partnership-program, accessed on 13 May 2024). The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Ackonwledgments
The study is supported by the Major Science and Technology Program for Hubei Province (No.2022AAA002),National Science Foundation of China (No. 42174030, 42004017), Special fund of Hubei Luojia Laboratory (No. 220100020), Special Fund for Wuhan Knowledge Innovation Program(No. 2022010801010107), Open Fund of Hubei Luojia Laboratory (No. 220100048) ,Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University (No. 21-02-08), National Science Foundation of China (NO. 42104028 ), State Key Laboratory of Spatial Datum (No. SKLGIE2024-M-1-1).
Funding
Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,Wuhan University,21-02-08,National Science Foundation of China,42174030,42004017,Special fund of Hubei Luojia Laboratory,220100020,Major Science and Technology Program for Hubei Province,2022AAA002,Special Fund for Wuhan Knowledge Innovation Program,2022010801010107,Open Fund of Hubei Luojia Laboratory,220100048
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Jian Wang: Methodology, Software, Writing—original draft. Zhao Li and Weiping Jiang: Conceptualization, Methodology, Resources, Writing—review & editing. Wenlan Fan: Data analysis, Visualization, Validation. Qusen Chen and Hua Chen: Supervision.
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Wang, J., Li, Z., Fan, W. et al. A new ensemble learning method based on signal source driver for GNSS coordinate time series prediction. GPS Solut 29, 68 (2025). https://doi.org/10.1007/s10291-025-01829-5
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DOI: https://doi.org/10.1007/s10291-025-01829-5