A nonlinear algorithm for traffic estimation with state constraints

Abstract

We present a real-time traffic state estimation algorithm for motorways. Natural constraints on the variables, like practical bounds on densities and velocities, are incorporated in the estimation process aiming to obtain better estimation results.The dynamic equation for the evolution of the traffic is defined by a second order macroscopic model which computes the density, the flow and the mean speed according to several nonlinear equations, but nothing avoids the results being out of those practical bounds. Different extensions of the Kalman method were already applied to this problem, but none of them consider natural constraints in the variables. On the other hand, general filter methods have been designed to cope with a constrained state. In order to incorporate the natural constraints of the traffic model, we adapt one of those methods based on the Unscented Kalman Filter. To validate the approach, many simulation cases over a freeway section were made using a microscopic simulation tool and comparing the Extended Kalman Approach with the proposed one.