Localized Extended Kalman Filter for Scalable Real-Time Traffic State Estimation

Current or historic traffic states are essential input to advanced traveler information, dynamic traffic management, and model predictive control systems. As traffic states are usually not perfectly measured and are everywhere, they need to be estimated from local and noisy sensor data. One of the most widely applied estimation methods is the Lighthill-Whitham and Richards (LWR) model with an extended Kalman filter (EKF). A large disadvantage of the EKF is that it is too slow to perform in real time on large networks. To overcome this problem, the novel localized EKF (L-EKF) is proposed in this paper. The logic of the traffic network is used to correct only the state in the vicinity of a detector. The L-EKF does not use all information available to correct the state of the network; the resulting accuracy is equal, however, if the radius of the local filters is sufficiently large. In two experiments, it is shown that the L-EKF is much faster than the traditional Global EKF (G-EKF), that it scales much better with the network size, and that it leads to estimates with nearly the same accuracy as the G-EKF and when the spacing between detectors is varied somewhere between 0.7 and 5.1 km. Compared with the G-EKF, the L-EKF is a highly scalable solution to the state estimation problem.