Skip to main content
Open Access Publications from the University of California

Real-time estimation of distributed parameters systems: Applicaton to traffic monitoring

  • Author(s): Work, Daniel Benjamin
  • Advisor(s): Bayen, Alexandre M
  • et al.

This dissertation is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway traffic is constructed, which results in a dynamical system in which the observation operator is linear. It presents a new scalar hyperbolic partial differential equation (PDE) model for traffic velocity evolution on highways, based on the seminal Lighthill-Whitham-Richards (LWR) PDE for density. Equivalence of the solution of the new velocity PDE and the solution of the LWR PDE is shown for quadratic flux functions. Because this equivalence does not hold for general flux functions, a discretized model of velocity evolution based on the Godunov scheme applied to the LWR PDE is proposed. Using an explicit instantiation of the weak boundary conditions of the PDE, the discrete velocity evolution model is generalized to a network, thus making the model applicable to arbitrary highway networks. The resulting velocity model is a nonlinear and nondifferentiable discrete time dynamical system with a linear observation operator, for which a Monte Carlo based ensemble Kalman filtering data assimilation algorithm is applied.

The model and estimation technique is evaluated with experimental data obtained from a large-scale field experiment known as Mobile Century. The velocity estimates using GPS data from cellphones is compared to velocity estimates using inductive loop detector data from the PeMS system. More than 900 estimation simulations are performed using various volumes of GPS data and inductive loop detector data collected during the experiment, which show travel times can be reconstructed to less than 10% error with sufficient GPS data, loop data, or a combination of both. All data collected during the field experiment and used in the simulations are available for download at

Main Content
Current View