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