Dynamic Traffic Reconstruction using Probe Vehicles

TL;DR

This paper introduces a moving boundary observer for traffic flow estimation using probe vehicles, demonstrating exponential convergence and effectiveness across different traffic regimes through numerical simulations.

Contribution

It proposes a novel moving boundary observer based on probe vehicle trajectories for traffic state estimation, achieving exponential convergence of the observation error.

Findings

Exponential convergence of the observation error is proven.

Finite-time convergence is achieved in some cases.

Numerical simulations validate the approach across various traffic regimes.

Abstract

This article deals with the observation problem in traffic flow theory. The model used is the semilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the measurements here are obtained from Probe Vehicles (PVs). We propose then a moving dynamic boundary observer whose boundaries are defined by the trajectories of the PVs. The main result of this article is the exponential convergence of the observation error, and, in some cases, its finite-time convergence. Finally, numerical simulations show that it is possible to observe the traffic in the congested, free-flow, and mixed regimes provided that the number of PVs is large enough.