This work focuses on estimation of traffic using a Hamilton-Jacobi model of traffic. The recent explosion of smartphones with Internet connectivity and GPS created an increase in data available to monitor traffic. The talk will present theoretical results, algorithms and implementations designed to integrate mobile measurements obtained from smartphones into Hamilton Jacobi models of traffic. Using a Lax–Hopf formula, analytical solutions to the Hamilton–Jacobi equations are computed, which result in an explicit expression of the solution to an initial / boundary value problem for piecewise affine initial and boundary conditions. These results are extended to “internal” conditions (i.e. situations in which the value function is provided inside the computational domain). The dependency of the solution in the parameters of the piecewise affine functions (initial and boundary conditions) is studied and shown to result in convex formulations of estimation problems. The results are tried on data collected by the Mobile Millennium system, a system launched at Berkeley, which is operational in Northern California and streams more than 60 million data points a day into traffic models.