  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.
