The scope of this work is to investigate if and how it is possible to estimate the incident wave elevation on a floating wind turbine, with the purpose of improved control strategies. A Kalman based algorithm is proposed, which receives as input the rigid motions of the floater and estimates the wave elevation hitting the floating platform. The structure of the observer is described and the estimator is tested numerically on the OC3-Hywind platform coupled with the 5-MW reference wind turbine from NREL. Limitations to the estimation procedure are discussed. Finally the algorithm is tested on experimental data coming from a wave basin experimental campaign on a floating wind turbine model. The algorithm still needs improvements, but results are encouraging in the development of this technology.