Nonlinear Kalman Filtering Algorithms for On-Line Calibration of Dynamic Traffic Assignment Models

Abstract

An online calibration approach that jointly estimates demand and supply parameters of dynamic traffic assignment (DTA) systems is presented and empirically validated through an extensive application. The problem can be formulated as a nonlinear state-space model. Because of its nonlinear nature, the resulting model cannot be solved by the Kalman filter, and therefore, nonlinear extensions need to be considered. The following three extensions to the Kalman filtering algorithm are presented: 1) the extended Kalman filter (EKF); 2) the limiting EKF (LimEKF); and 3) the unscented Kalman filter. The solution algorithms are applied to the on-line calibration of the state-of-the-art DynaMIT DTA model, and their use is demonstrated in a freeway network in Southampton, U.K. The LimEKF shows accuracy that is comparable to that of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">best</i> algorithm but with vastly superior computational performance. The robustness of the approach to varying weather conditions is demonstrated, and practical aspects are discussed.