Freeway traffic state estimation: A Lagrangian-space Kalman filter approach

Abstract

Recent researches have shown the potential benefits of using Lagrangian coordinates in modeling mobile sensor data such as GPS, Bluetooth, Wi-Fi, and cellphone probe data. Research shows the numerical accuracy and convenience of Lagrangian traffic flow models in traffic state estimation. In this paper, a new traffic state estimation model by using Lagrangian-space Kalman filter is proposed based on the travel time transition model (TTM). The proposed methodology reformulates the TTM model into a state-space form to fit the Kalman filter framework. The corresponding state-updating matrices for various traffic conditions are also provided. A numerical experiment is conducted based on a simulation model calibrated with the field loop detector data on IH-894 in Milwaukee, Wisconsin for model evaluation. The proposed TTM-based method is compared with a CTM-based Kalman filter estimator on Eulerian coordinate under different penetration rates of the input Bluetooth, Wi-Fi, or Cellular probe vehicle data in which vehicles are re-identified between two consecutive physical or virtual readers. The evaluation results indicate that TTM-based estimation model performs well especially during congestion and can track traffic breakdowns and recovery effectively. The TTM-based estimator outperforms CTM-based methods at all penetration rates levels. Furthermore, the 4% penetration rate is found to be a threshold beyond which TTM-based estimation results improve significantly. With increased penetration rates, the TTM-based model can achieve a mean absolute percentage error around 10%; while CTM-based model remains higher than 13%.