Prediction of Zenith Tropospheric Delay in GNSS Application Using Machine Learning Models

Abstract

Satellite System (GNSS) positioning and atmospheric modelling. Traditional tropospheric delay models, including numerical weather models, analytical models, and empirical approaches, often struggle to capture the complex nonlinear variations in ZTD. To overcome these limitations, this study explores the use of five machine learning models (Kolmogorov–Arnold Network (KAN), Long Short-Term Memory (LSTM), Multilayer Perceptron Neural Network (MLPNN), Extreme Gradient Boosting (XGBoost), and Random Forest) to predict ZTD across four GNSS COR stations in Ghana: Accra, Ho, Kumasi, and Akim Oda. Meteorological parameters (pressure, temperature, and relative humidity) and geospatial features (latitude and ellipsoidal height) were utilised as input variables. Model performance was assessed using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R²). Results showed that the KAN model consistently outperformed all other models, achieving test RMSEs of approximately 10 mm and R² above 0.976, demonstrating its capacity to model nonlinear and sequential atmospheric patterns with interpretability and efficiency. LSTM and MLPNN also yielded competitive results, while ensemble methods, particularly Random Forest, lagged in generalisation and accuracy. The findings highlight the potential of interpretable deep learning techniques like KAN to improve GNSS-based atmospheric modelling and precise positioning applications in tropical regions.