We propose an adaptive, data-driven framework for model identification with structural dynamics as main application. This method combines SINDy (Sparse Identification of Non-linear Dynamics) for model identification and the Extended Kalman Filter (EKF) for data assimilation. Specifically, SINDy enables the extraction of the governing equation of a dynamical system by solving a sparse regression problem starting from time-series data. This regression problem determines a set of coefficients that weigh a dictionary of pre-defined functions, such as polynomials or trigonometric functions. The inputs of these functions include kinematic variables describing the system dynamics (typically displacements, velocities, and accelerations); the inputs of the system (e.g. the forcing terms); and possibly parameters describing the physical properties of the system. In the context of modelling the dynamics of a structure, these parameters may be related to stiffness and damping properties. Such properties can be known at a certain time, but they may evolve, for example due to degradation phenomena. While one option to update the system dynamics description is to perform SINDy again, doing so disregards information about the previously identified system, preventing quick adaptation to an evolving scenario. A more convenient alternative is to modify the values of the physical parameters used as inputs for the SINDy functions. For this reason, the Extended Kalman Filter (EKF) has been here exploited. At variance with previous applications of the EKF, for example in structural identification, identifying the filter transition and observation models with SINDy enables to partly overcome issues related to the inadequacy of the modelling assumptions. Moreover, SINDy allows to automatically compute the function derivatives necessary for the definition of the Jacobian matrices required by the EKF. As a result, the coupling with the EKF allows to obtain a digital twin of the structure that assimilates incoming data. The potential of the method is demonstrated through case studies involving both linear and non-linear dynamic behaviours.