Goodness of fit function in the frequency domain for robust calibration of microscopic traffic flow models

In the field of traffic simulation, the calibration of uncertain inputs against real data is usually taken to cover both the epistemic uncertainty regarding the un-modeled details of the phenomena and the aleatory not predicted by the models. For this reason, model parameters are usually indirectly estimated within an optimization framework which tries to maximize the fit between real and simulated measures of the traffic system. This is the case, for example, of the calibration of car-following models’ parameters against vehicle trajectory data. Only recently, it has been proven that the capability of the optimization framework to provide the parameters’ values that allow the car-following model reproducing real trajectories at its best is strictly connected to the setting of the optimization framework itself. This, in particular, entails the necessity to carefully choose an appropriate combination of optimization algorithm and measure of goodness of fit (GOF). In this study, the authors focus attention on this latter issue. Specifically, it is claimed here that the commonly used GOFs are not able to capture the dynamics of the time-series which calibration is performed against. Therefore, a spectral analysis based approach to evaluate the overall performance of the simulation model in the objective function is proposed. The new measure of goodness of fit is tested in the calibration of the Intelligent Driver Model against synthetic and real trajectory data. Results with synthetic data, in particular, confirm that such a new optimization setting is always able to find the global optimum of the problem.