Traffic flow parameter estimation based on an adjoint method

This article deals with the problem of estimating the empirical parameters in a traffic flow modeled by the so-called Lighthill-Whitham-Richards equation. The optimal values of parameters are estimated by solving the inverse problem of minimizing the least square error between simulations and lumped observation values. The system equation and adjoint model equation, obtained by using adjoint method, are discretized and solved via the nonlinear implicit Preissmann scheme. The parameters to be estimated are then obtained through an optimization process containing steepest descent method and backtracking line search method. A numerical simulation is finally given in order to illustrate the effectiveness of here-proposed approach.