GNSS-Based Displacement Estimation for Bridge Structural Health Monitoring: Comparison of Ensemble Kalman Filter and Random Forest Approaches

GNSS-based displacement monitoring provides important information for structural health monitoring (SHM) of bridges, but real-time kinematic (RTK) measurements are contaminated by noise and biases. This study investigates robust displacement estimation for a five-span steel box girder bridge monitored by RTK-GNSS. Two approaches are compared: an Ensemble Kalman Filter (EnKF) that assimilates noisy RTK-GNSS measurements into a state-space model, and a data-driven Random Forest (RF) model that exploits environmental variables such as member and air temperature, solar radiation and wind speed. Four GNSS antennas installed along the bridge were operated at five-minute intervals for 14 months, in parallel with static GNSS and displacement sensors used as reference measurements. The models are evaluated in terms of RMSE, MAE, maximum error and correlation coefficient, as well as their ability to reproduce daily thermal cycles and seasonal trends. Both approaches achieve millimetre-level accuracy; the best configurations provide RMSE below 2 mm and maximum error below 10 mm with correlation coefficients above 0.98. EnKF additionally provides time-varying confidence intervals, supporting reliability assessment and threshold setting for SHM decision-making. The results demonstrate that noisy RTK-GNSS data can be converted into reliable quasi-static displacement information and provide guidance for selecting estimation strategies in bridge SHM and digital twin applications.