A non-linear, single-degree-of-freedom model is developed to describe the vortex-induced, transverse vibration of a circular cylinder, elastically suspended in a wind flow. The model is appropriate for predicting the dynamic response during lock-in conditions. The ''linear-in-the parameters'' nature of the model allows the formulation of a relatively simple and computationally very efficient procedure for estimating all the unknown parameters in the model. The method, based on the use of a state variable filter, enables the parameters to be estimated recursively by processing digitized records of the cylinder dynamic response. The technique is validated by applying it to both simulated data, where the parameters are known a priori, and to real data obtained from an experimental rig placed in a wind tunnel. For the experimental data, which relates to time-varying wind flow conditions, representing the natural wind, it is shown that the estimation technique allows the response during lock-in events to be isolated and treated separately. A reasonably good fit to the experimental data is obtained and the resulting estimates of the mean values of the parameters are found to converge satisfactorily.