Structures are exposed to aging and extreme events that can decrease the relevant safety margins or even lead to (partial) collapse mechanisms under the foreseen loading conditions. Structural health monitoring (SHM) looks therefore compulsory to avoid accidents, by tracking the evolution of the state of the system and sending out warnings as soon as critical conditions are met or drifts from the response of the undamaged structure are identified. One of the approaches to online SHM rests on Kalman filtering, which is able to build the time evolutions of the structural state upon the Bayes’ rule. In a customary joint version of the filtering procedure, state variables and health parameters are joined together in an extended state vector: while state variables, like e.g. lateral displacement of shear buildings, can be observed thanks to pervasive sensor networks, the health parameters usually linked to the structural stiffness cannot, leading to possible divergence issues characterized by biases in the estimates. This is further enhanced by epistemic uncertainties and related difficulties in setting the covariance terms allowing for modelling strategies not in perfect agreement with reality. In this work, we propose the use of an adaptive strategy to the online tuning of the aforementioned covariance terms, so that the accuracy of filtering outcomes is improved without issues linked to filter instability. Results are proposed for the SHM of shear buildings, showing that the proposed method outperforms other strategies available in the literature, both in terms of accuracy of the estimations and readiness to track their time evolutions.