VMF3-XGB: a novel site-wise tropospheric mapping function based on VMF3 and machine learning

Accurate mapping functions (MFs) are essential for estimating tropospheric delays and enhancing global navigation satellite system (GNSS) positioning. Commonly used mapping function models include Niell mapping function (NMF), Global Mapping Function (GMF), Vienna Mapping Function (VMF) series, and the empirical Global Pressure and Temperature 3 (GPT3) model. However, their relatively simplified modeling approaches or limitations in the data often result in limited accuracy or unsuitability for real-time applications. To address these limitations, we propose a novel tropospheric MF model based on site-wise VMF3 operational (VMF3-OP) and XGBoost (VMF3-XGB). The model requires only basic inputs—coordinates (latitude, longitude, height), time (day-of-year and hour-of-day), and meteorological parameters (temperature, pressure, and water vapor pressure)—to estimate the coefficients a_h and a_w. Site-wise VMF3-OP products from 2018 to 2023 were used for training. Results from station-based tests show that VMF3-XGB consistently outperforms the traditional empirical models NMF, GMF, and GPT3 at stations covered by the VMF3 station products. Even without meteorological inputs, the XGB-based model shows clear advantages over traditional models, indicating the benefit of the machine-learning approach. When meteorological parameters are included, the model achieves further improvements and achieves performance closer to VMF3-FC at station locations. However, global 1°×1° gridded evaluation shows that the proposed station-based models do not yet outperform GPT3 or gridded VMF3-FC under full spatial extrapolation. These results indicate that the main contribution of VMF3-XGB lies in providing a practical and accurate offline alternative for station-based applications, especially when VMF3-FC station products are unavailable, incomplete, or difficult to access.