Linear parameter varying (LPV) models are an extension of linear time varying systems as their parameters are expressed as a function of some scheduling variables: exogenous ones in the standard setup and internal ones in the case of so called quasi-LPV models. If the dependency on internal variables is chosen to be sufficiently general, quasi-LPV models boil down to a different representation of nonlinear systems. In contrast to classical nonlinear identification approaches, like artificial neural networks or NARMAX models, the NLPV approach offers the possibility to interpret the behavior of a complex system as the effect of a basically linear dynamic and a scheduling variable responsible for the nonlinearity. This paper proposes a new identification approach, whose main advantage lies in the fact that it presents a compact and precise nonlinear model with a small number of parameters. Our proposal yields to the time evolution of the scheduling variable which explains the nonlinear behavior of the system. The approach has been tested on an test bench with a diesel engine, experimental results are presented.