Abstract
High-precision coordinate time series prediction of global navigation satellite system (GNSS) stations provides a vital fundamental for geodesy and geodynamics applications. This study aimed to investigate the performance of data-driven algorithms in fitting and predicting GNSS height time series. First, long short-term memory (LSTM), Transformer, and temporal convolutional network (TCN) were compared using the height time series of 13 GNSS stations in Hongkong, China, with a time span of 15 years (Jan 01, 2009–Dec 31, 2023). LSTM and Transformer are found to perform better than TCN in RMSE and MAE. Then, the data sample length and sliding window size were changed artificially to analyze their impacts on the aforementioned three methods. The maximum differences both in RMSE and MAE are basically within 1 mm between different dataset partitioning options, indicating these options have little influence on the model performance when predicting GNSS height time series. Finally, an integrated LSTM model based on variational mode decomposition (VMD), Kalman filter, and attention mechanism (VKA-LSTM) was established. The experiment results show that the VKA-LSTM model significantly improves height time series prediction accuracy without bringing excessive time costs. Compared with the original LSTM model, the improvements in RMSE and MAE are basically 19.79% to 45.23% and 16.83% to 42.86%, respectively, while the time cost only increased by about 8%.
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The data used in this paper are publicly available on the websites of the Nevada Geodetic Laboratory. The other detailed files can be available upon reasonable request by contacting the authors.
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Acknowledgements
This contribution was supported by National Natural Science Foundation of China (Project No. 42474049), the Science and Technology Major Project of Jiangsu Province, China (Grant No.BG2024003) and the Fundamental Research Funds for the Central Universities of China (Grant No. 2242025RCB0023). The authors appreciate the Nevada Geodetic Laboratory for providing data for this research.
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Jiafu Wang: Methodology, software, experiment, validation, writing—original draft Qi Liu: Data curation, validation, supervision Dehao Ma: Software, experiment Yunfei Zhang: Writing and revision—original draft Xianwen Yu: Methodology, revision—original draft.
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Wang, J., Liu, Q., Ma, D. et al. An integrated VKA-LSTM model for GNSS height time series prediction. GPS Solut 30, 29 (2026). https://doi.org/10.1007/s10291-025-01994-7
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DOI: https://doi.org/10.1007/s10291-025-01994-7