This article presents the identification of a web winding system and the estimation of its reel radius as time-varying parameter. This system is non-linear and time-varying, then, a set of Linear, Time Invariant models are estimated for local operation regions. The reel radius estimator is a direct virtual sensor (DVS) directly designed from experimental data. The estimated models are compared to a single model, identified for the complete operation range and better results are obtained with the local models on fresh data not used in the identification phase. The DVS is able to estimate the reel radius from voltage, speed and tension measurements, with good precision.