In this work, the estimation of Linear ParameterVarying (LPV) models in Output-Error (OE) form is addressed. In particular, it is assumed that the scheduling variable is noisy, a condition often encountered in practice but not frequently considered in the literature. An instrumental variable based system identification method, recently proposed for continuoustime LPV models, is adapted to the discrete-time case. To deal with the noisy scheduling variable, it is assumed that its noisefree version is smooth, enabling us to estimate it using the local regression method. The proposed LPV model estimation approach is compared with other available methods, first through a discussion and afterwards through a numerical example.