Incorporation of Lagrangian measurements in freeway traffic state estimation

Cell-phones equipped with a global positioning system (GPS) provide new opportunities for location-based services and traffic estimation. When traveling on-board vehicles, these phones can be used to accurately provide position and velocity of the vehicle as probe traffic sensors. This article presents a new technique to incorporate mobile probe measurements into highway traffic flow models, and compares it to a Kalman filtering approach. These two techniques are both used to reconstruct traffic density. The first technique modifies the Lighthill-Whitham-Richards partial differential equation (PDE) to incorporate a correction term which reduces the discrepancy between the measurements (from the probe vehicles) and the estimated state (from the model). This technique, called Newtonian relaxation, "nudges" the model to the measurements. The second technique is based on Kalman filtering and the framework of hybrid systems, which implements an observer equation into a linearized flow model. Both techniques assume the knowledge of the fundamental diagram and the conditions at both boundaries of the section of interest. The techniques are designed in a way in which does not require the knowledge of on- and off-ramp detector counts, which in practice are rarely available. The differences between both techniques are assessed in the context of the Next Generation Simulation program (NGSIM), which is used as a benchmark data set to compare both methods. They are finally tested with data from the Mobile Century experiment obtained from 100 Nokia N95 mobile phones on I-880 in California on February 8, 2008. The results are promising, showing that the proposed methods successfully incorporate the GPS data in the estimation of traffic.