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<p>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&#xa0;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&#xa0;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%.</p>

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An integrated VKA-LSTM model for GNSS height time series prediction

  • 期刊论文

  • 发表日期：

    2025年11月22日

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  • Jiafu Wang,
  • Qi Liu,
  • Dehao Ma,
  • Yunfei Zhang,
  • Xianwen Yu

摘要

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%.