Kernel Smoothing Method Applicable to the Dynamic Calibration of Traffic Flow Models

Real time traffic flow simulation models are used to provide traffic information for dynamic traffic management systems. Those simulation models are supplied by traffic data in order to estimate and predict traffic conditions in unobserved sections of a traffic network. In general, most of recent real time traffic simulators are based on the macroscopic model because the macroscopic model replicates the average traffic behavior in terms of observable variables such as (time–space) flow and speed at a relatively fast computational time. Like other simulation models, an important aspect of the real time macroscopic simulator is to calibrate the model parameters online. The most conventional way of the online calibration is to add a random walk to the parameters to constitute an augmentation of the traffic variables and the model parameters to be estimated. Actually, this method allows the parameters to vary at every time step and, therefore, describes the adaptation of the model to the prevailing traffic conditions. However, it has been reported that the use of the random walk results in a loss of information and an increase of the covariance of parameters, which consequently leads to posteriors that are far more diffuse than the theoretical posteriors for the true parameters. To this end, this article puts forward a Kernel density estimation technique in the calibration process to handle the covariance issue and to avoid the information loss. The Kernel density estimation technique is embedded in the particle filter algorithm, which is extended to the calibration problems. The proposed framework is investigated using real-life data collected in a freeway in England.