Improving Predictions in LPV-PBSIDopt

System identification of linear parameter varying systems has been thesubject of numerous recent developments. One such method, LPV-PBSIDoptpresented in \cite{wingerden:2009}, is an extension of the PBSIDmethod for time-invariant systems. In order to deal with time-varyingsystems, certain approximations are made in the output predictors. Asshown in this paper, these approximations are not necessary, and thepredictions can be greatly improved with no significant increase incomputational cost. However, improving the predictions does notnecessarily improve the resulting model. Therefore, simple guidelinesfor choosing between the two prediction methods are also presented.