Networked Traffic State Estimation Involving Mixed Fixed-mobile Sensor Data Using Hamilton-Jacobi equations

TL;DR

This paper develops a robust traffic state estimation framework for highways using Hamilton-Jacobi equations, capable of integrating diverse sensor data and handling network junctions, demonstrated on real traffic data.

Contribution

It introduces a novel Hamilton-Jacobi based formulation for traffic estimation that accommodates mixed sensor data and complex network structures.

Findings

Effective integration of fixed and mobile sensor data.

Linear constraints derived from Hamilton-Jacobi equations.

Accurate traffic density estimation on real network data.

Abstract

Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for highways modeled by a system of Lighthill Whitham Richards equations that is able to assimilate different sensor data available. We first present an equivalent formulation of the problem using a Hamilton-Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton-Jacobi equation are linear ones. We then pose the problem of estimating the traffic density given incomplete and inaccurate traffic data as a Mixed Integer Program. We then extend the density estimation framework to highway networks with any available data constraint and modeling junctions. Finally, we present a travel estimation application for a small network using real traffic measurements obtained obtained during Mobile Century traffic experiment, and comparing the results with ground truth data.