Automated modal parameter tracking is an essential part of vibration-based structural health monitoring of engineering structures, e.g., bridges, high-rise building, wind turbines, amongst others. In this work, we conceive a robust algorithm for accomplishing this task. First, the modal parameters are extracted with by greedy clustering the stabilization diagram, which is based on covariance-driven subspace identification and the related uncertainty quantification. After the selection of a set of relevant modal parameters to be monitored, the tracking is performed by an active search of stable modes close to the reference ones, again using statistical criteria and automated clustering. The applied strategies allow for a robust method, allowing also for relatively strong variations in the natural frequencies or the MAC without losing track of the monitored modes. Finally, when EOVs (Environmental and Operational Variables) are measured and training and testing periods are defined, a neural network is trained based on the tracked frequencies and the EOVs, with the goal of correcting the environmental influence on the estimated frequencies based on the model predictions. In doing so, a distance metric is defined for damage detection, which is robust to environmental perturbations under the measured EOVs. The whole framework is showcased on monitoring data of a full-scale bridge.