  This paper presents a mesoscopic traffic flow model that explicitly describes
the spatio-temporal evolution of the probability distributions of vehicle
trajectories. The dynamics are represented by a sequence of factor graphs,
which enable learning of traffic dynamics from limited Lagrangian measurements
using an efficient message passing technique. The approach ensures that
estimated speeds and traffic densities are non-negative with probability one.
The estimation technique is tested using vehicle trajectory datasets generated
using an independent microscopic traffic simulator and is shown to efficiently
reproduce traffic conditions with probe vehicle penetration levels as little as
10\%. The proposed algorithm is also compared with state-of-the-art traffic
state estimation techniques developed for the same purpose and it is shown that
the proposed approach can outperform the state-of-the-art techniques in terms
reconstruction accuracy.
