# Dynamic Traffic Reconstruction using Probe Vehicles

arXiv: https://arxiv.org/abs/2007.09914 · HTML: https://mlsanity.com/paper/2007.09914/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Online Traffic Density Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2504.03483/) (2025)
- [Closed-Loop Neural Operator-Based Observer of Traffic Density](https://mlsanity.com/paper/2504.04873/) (2025)

## Abstract (arXiv)

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.