A Zenith Tropospheric Delay Prediction Model Based on VMD-LSTM Neural Network

Zenith Tropospheric Delay (ZTD) is one of the primary error sources impacting the accuracy of Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) and Very Long Baseline Interferometry (VLBI). Enhancing the accuracy of ZTD prediction is critical for improving navigation, positioning, and VLBI precision. This study introduces an innovative tropospheric prediction model that integrates Variational Mode Decomposition (VMD) with a Long Short-Term Memory (LSTM) neural network to improve ZTD prediction accuracy and long-term stability. The experimental data used in this study were obtained from the Vienna Mapping Function 3 Optimized (VMF3_OP) ZTD dataset. VMD was employed to decompose the ZTD into periodic and residual components, allowing for deeper exploration of its informational characteristics. Each component is then individually used to train an enhanced LSTM neural network model integrated with the Self-Attention mechanism, enabling accurate prediction of the global ZTD. By combining all VMD-LSTM forecasted components, the final ZTD prediction was obtained. The results demonstrate that the VMD-LSTM model's average Root Mean Square Error (RMSE) in 2023 showed improvements of 62.3%, 61.9%, 76.1%, and 74.2% compared to the GPT2w, LSTM, Hopfield, and Saastamoinen models, respectively. These findings highlight the superior performance of the VMD-LSTM model in ZTD forecasting.