Continuous vibration-based Structural Health Monitoring (SHM) can be successfully exploited to assess the health of civil structures throughout their lifecycle by analyzing the evolution over time of relevant structural parameters. Machine learning techniques are frequently applied for anomaly detection in the context of data-driven SHM: in this framework, deviations from their normal trends are interpreted as indicators of anomalous behavior, triggering timely inspection and investigation. However, data-driven approaches usually limit the performance of SHM systems to damage detection and localization. In order to enhance the informative content of SHM, experimental data should be coupled with refined numerical model to indirectly track relevant structural parameters useful for a more detailed assessment of damage. The present study describes a continuous model updating strategy and its application to the analysis of data collected from the SHM system installed on a roadway bridge. It allows to analyze the changes in relevant structural parameters under varying environmental and operational conditions, providing baseline data useful for enhanced structural health assessment through the integration of experimental monitoring data and numerical models. To this aim, the study also investigates computational aspects associated with continuous model updating for SHM purposes: surrogate models are therefore employed to keep the computational efforts associated with optimization low. The obtained results show how the proposed approach enables the effective tracking of the evolution of structural parameters, not directly measured by the monitoring system and under varying environmental conditions, while keeping computational burdens to a minimum.