Incremental and online learning through extended kalman filtering with constraint weights for freeway travel time prediction

Providing travel time information to travelers on available route alternatives in traffic networks is widely believed to yield positive effects on both individual drive and (route/departure time) choice behavior as well as on collective traffic operations in terms of for example overall time savings and - if nothing else - on the reliability of travel times. As such there is an increasing need for fast and reliable online travel time prediction models. In an operational context, also adaptivity of such models is a crucial property. This paper describes a method to calibrate (train) a data driven travel time prediction model (a so-called state-space neural network - SSNN) in an incremental fashion. Since travel times are available only for realized trips, travel time prediction is not a one-step prediction task, and thus online incremental learning methods such as the extended Kalman filter (EKF) can not be applied directly. We propose a delayed EKF method which can be applied online. By constraining the model parameters within particular bounds, an automatic regularization scheme is incorporated, which guarantees a smooth mapping