Simultaneous estimation of states and parameters in Newell's simplified kinematic wave model with Eulerian and Lagrangian traffic data

- Propose a traffic estimation framework based on Newell's kinematic wave theory.
- Estimate traffic parameters and states simultaneously from Eulerian and Lagrangian data.
- Formulate and solve a single optimization problem.
- The method leads to multiple solutions under absolute steady traffic conditions.
- The proposed method yields better results than existing methods.

The traffic state estimation process estimates various traffic states from available data in a road network and provides valuable information for travelers and decision makers to improve both travel experience and system performance. In many existing methods, model parameters and initial states have to be given in order to estimate traffic states, which limits the accuracy of the results as well as their transferability to different locations and times. In this paper, we propose a new framework to simultaneously estimate model parameters and traffic states for a congested road segment based on Newell's simplified kinematic wave model (Newell, 1993). Given both Eulerian traffic count data and Lagrangian vehicle reidentification data, we formulate a single optimization problem in terms of the initial number of vehicles and model parameters. Then we decouple the optimization problem such that the initial number of vehicles can be analytically solved with a closed-form formula, and the model parameters, including the jam density and the shock wave speed in congested traffic, can be computed with the Gauss-Newton method. Based on Newell's model, we can calculate individual vehicles' trajectories as well as the average densities, speeds, and flow-rates inside the road segment. We also theoretically show that the optimization problem can have multiple solutions under absolutely steady traffic conditions. We apply the proposed method to the NGSIM datasets, verifying the validity of the method and showing that this method yields better results in the estimation of average densities than existing methods.