  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.
