Global navigation satellite system (GNSS) site coordinate time series provides essential data for geodynamic and geophysical studies, realisation of a regional or global geodetic reference frames, and crustal deformation research. The coordinate time series has been conventionally modelled by least squares (LS) fitting with harmonic functions, alongside many other analysis methods. As a key limitation, the traditional modelling approaches simply use the functions of time variable, despite good knowledge of various underlying physical mechanisms responsible for the site displacements. This paper examines the use of machine learning (ML) models to reflect the effects or residential effects of physical variables related to Sun and the Moon ephemerides, polar motion, temperature, atmospheric pressure, and hydrology on the site displacements. To form the ML problem, these variables are constructed as the input vector of each ML training sample, while the vertical displacement of a GNSS site is regarded as the output value. In the evaluation experiments, three ML approaches, namely the gradient boosting decision tree (GBDT) approach, long short-term memory (LSTM) approach, and support vector machine (SVM) approach, are introduced and evaluated with the time series datasets collected from 9 GNSS sites over the period of 13 years. The results indicate that all three approaches achieve similar fitting precision in the range of 3–5 mm in the vertical displacement component, which is an improvement in over 30% with respect to the traditional LS fitting precision in the range of 4–7 mm. The prediction of the vertical time series with the three ML approaches shows the precision in the range of 4–7 mm over the future 24- month period. The results also indicate the relative importance of different physical features causing the displacements of each site. Overall, ML approaches demonstrate better performance and effectiveness in modelling and prediction of GNSS time series, thus impacting maintenance of geodetic reference frames, geodynamics, geophysics, and crustal deformation analysis.

Accurate and reliable vehicle positioning during extended Global Navigation Satellite System/Inertial Navigation System outages remains challenging due to noise, outliers, and biases in input data. This study evaluates the robustness of machine learning (ML) models under two specific conditions: (1) noise and outliers present in training target data, and (2) errors and biases within input data. Two ML methods–Long Short-Term Memory (LSTM) and Gradient Boosting Decision Tree (GBDT)–were evaluated using the proposed methodology. Results indicate that both ML methods significantly enhance horizontal positioning accuracy compared to the conventional Kalman filter (KF). Specifically, LSTM reduces horizontal RMSE by approximately 85.8% (from 39.5 to 5.6 m), while GBDT achieves a reduction of approximately 77.7% (to 8.8 m). Additionally, the robustness analysis confirms that the proposed LSTM-based strategy demonstrates substantial robustness by maintaining consistent prediction accuracy, even in the presence of significant errors and outliers in training data, as well as being minimally impacted by errors and biases introduced in input variables.