Abstract:
Objectives: To address the challenge of high-precision tropospheric delay correction for Global Navigation Satellite System (GNSS) in complex terrain conditions, this study proposes a fusion method integrating GNSS observations with numerical weather prediction (NWP) products.
Methods: The proposed method first achieves temporal alignment of multi-source data through AutoRegressive Moving Average (ARMA) extrapolation and linear interpolation. To accurately characterize the heterogeneous spatial variation of zenith wet delay (ZWD), a vertical-turbulent component separation modeling strategy is introduced: the vertical component is fitted using an exponential decay model based on ERA5 reanalysis data, while the turbulent component is modeled by a quadratic polynomial surface. For zenith hydrostatic delay (ZHD), which varies stably with pressure and altitude, a quadratic polynomial incorporating elevation is directly applied without component decomposition. A distance-precision dual dynamic weighting strategy is then developed to balance the advantages of high-precision GNSS point data and spatially continuous NWP grid data, where GNSS data with higher accuracy receive greater weights than NWP data. Ridge regression regularization is incorporated to prevent overfitting. The fused ZHD and ZWD components are finally combined to recover the zenith total delay (ZTD).
Results: The method was validated using data from 24 GNSS stations in Yunnan Province, China, and VMF3 (Vienna Mapping Functions 3) grid products covering the entire year of 2025. Four GNSS stations were randomly selected daily as an independent validation set, with the remaining 20 stations used for model training. The performance was evaluated using bias, standard deviation (STD), and root mean square error (RMSE), with GNSS precise solutions serving as the reference truth. The fusion model achieved an annual average ZTD prediction RMSE of 12.2 mm and a bias of -1.6 mm. Compared with the GNSS-only scheme, the proposed method reduced RMSE by 16.4%; compared with the VMF3-only scheme, it reduced RMSE by 10.3% and corrected the systematic bias of VMF3 from -4.4 mm to -1.6 mm, representing an improvement of 63.6%.
Conclusions: The proposed method effectively integrates the high precision of GNSS data with the spatial continuity of NWP products through ZWD component separation, ZHD direct fitting, and dual dynamic weighting. The fusion model significantly outperforms single-data-source schemes, providing a reliable tropospheric delay correction solution for highprecision GNSS positioning in complex terrain areas, with potential applications in real-time meteorological services and geological disaster monitoring.