Microscopic simulation models have become widely applied tools in traffic engineering. Nevertheless, parameter identification of these models remains a difficult task. This is partially because parameters are generally not directly observable from common traffic data; also there is a lack of reliable statistical estimation techniques. This study puts forward a new general and structured approach to identifying parameters of car-following models. One of the main contributions of this study is joint estimation of parameters for multiple vehicles. Furthermore, prior information on the parameter values (or the valid range of values) can be estimated. The study also deals with serial correlation in the trajectory data. In doing so, the newly developed approach generalizes the maximum likelihood estimation approach proposed by the authors. The approach allows for statistical analysis of the model estimates, including the standard error of the parameter estimates and the correlation of the estimates. With the likelihood ratio test, models of different complexity (defined by the number of model parameters) can be cross-compared. A useful property of this test is that it takes into account the number of parameters of a model as well as the performance. The approach is applied to car-following behavior by using Dutch freeway vehicle trajectories collected from a helicopter.