Non-linear kalman filtering algorithms for on-line calibration of dynamic traffic assignment models

The problem of on-line calibration of dynamic traffic assignment (DTA) models is receiving increasing attention from researchers and practitioners. The problem can be formulated as a non-linear state-space model. Because of its nonlinear nature, the resulting model cannot be solved by the Kalman filter and therefore non-linear extensions need to be considered. In this paper, three extensions to the Kalman filter algorithm are presented: extended Kalman filter (EKF), limiting EKF (LimEKF), and unscented Kalman filter (UKF). The solution algorithms are applied to the calibration of the state-of-the-art DynaMIT-R DTA model and their use is demonstrated in a freeway network in Southampton, U.K. The LimEKF shows accuracy comparable to that of the best algorithm, but vastly superior computational performance