A Macroscopic Traffic Data-Assimilation Framework Based on the Fourier-Galerkin Method and Minimax Estimation

作者：Tchrakian Tigran T^*; Zhuk Sergiy

来源：IEEE Transactions on Intelligent Transportation Systems, 2015, 16(1): 452-464.

DOI：10.1109/TITS.2014.2347415

• Data assimilation
• Fourier-Galerkin
• macroscopic traffic flow models
• minimax
• shock waves
• viscosity solutions

In this paper, we propose a new framework for macroscopic traffic state estimation. Our approach is a robust "discretize" then "optimize" strategy, based on the FourierGalerkin projection method and minimax state estimation. We assign a Fourier-Galerkin reduced model to a macroscopic model of traffic flow, described by a hyperbolic partial differential equation. Taking into account a priori estimates for the projection error, we apply the minimax method to construct the state estimate for the reduced model that gives us, in turn, the estimate of the Fourier-Galerkin coefficients associated with a solution of the original macroscopic model. We illustrate our approach with a numerical example that demonstrates its shock capturing capability using only sparse measurements and under high uncertainty in initial conditions. We present implementation details for our algorithm, as well as a comparison of our method against the ensemble Kalman filter applied to a "local" discretization of the same traffic flow model.

• 出版日期2015-2
• 单位IBM