Improved calibration method for dynamic traffic assignment models: Constrained extended kalman filter

The calibration of dynamic traffic assignment (DTA) models involves the estimation of model parameters to best replicate real-world measurements. Good calibration is essential to estimate and predict accurately traffic states, which are crucial for traffic management applications to alleviate congestion. A widely used approach to calibrate simulation-based DTA models is the extended Kalman filter (EKF). The EKF assumes that the DTA model parameters are unconstrained, although they are in fact constrained; for instance, origin–destination (O-D) flows are nonnegative. This assumption is typically not problematic for small-and medium-scale networks in which the EKF has been successfully applied. However, in large-scale networks (which typically contain numbers of O-D pairs with small magnitudes of flow), the estimates may severely violate constraints. In consequence, simply truncating the infea-sible estimates may result in the divergence of EKF, leading to extremely poor state estimations and predictions. To address this issue, a constrained EKF (CEKF) approach is presented; it imposes constraints on the posterior distribution of the state estimators to obtain the maximum a posteriori (MAP) estimates that are feasible. The MAP estimates are obtained with a heuristic followed by the coordinate descent method. The procedure determines the optimum and are computationally faster by 31.5% over coordinate descent and by 94.9% over the interior point method. Experiments on the Singapore expressway network indicated that the CEKF significantly improved model accuracy and outperformed the traditional EKF (up to 78.17%) and generalized least squares (up to 17.13%) approaches in state estimation and prediction.