In this paper a gray-box identification method is investigated for linear parameter varying (LPV) continuous-time systems. An algorithm is given to analyze the parameter identifiability problem. Since the initial conditions are not assumed to be known, an observer based identification scheme is proposed. This is an identification method with two steps. In the first step a Luenberger type observer is designed, and in the second step a parameter estimation for the observer system is performed. The role of an observer based identification scheme in the elimination of the effects caused by the unknown initial conditions is highlighted. The importance of the selection of sampling time is also shown. The method is demonstrated through an estimation of the features of the gravity center of heavy vehicles