Java Toolbox for Data Assimilation with Scalar Conservation Laws

The Riemann problem is a building block for constructing solutions to the Cauchy problem, and the initial-boundary value problem associated with a hyperbolic conservation law. The solution to the Riemann problem characterizes the propagation of discontinuities in the solution, corresponding to the propagation of queues of vehicles in partial differential equation models of traffic flow.

This package proposes a Java implementation of several advanced filtering methods for data assimilation with a macroscopic traffic flow model discretized using the Godunov finite volume numerical scheme and initial conditions corresponding to a Riemann problem.

A graphical interface is designed to allow efficient comparative analysis of the estimates produced by the EKF, the EnKF, and a Monte-Carlo forward simulation, in the case a scalar conservation law with flux function corresponding to a Greenshields, Newell-Daganzo, or quadratic-linear flux function. The values of the initial and boundary conditions noise, state noise, observation noise, and sampling rate can be set through the graphical interface.

A specific module is designed to illustrate the emergence of multi-modal distributions of the uncertainty on the true state, in the case of entropic shock waves.

Reproducible research

The joint use of the two testers allows reproduction of the main results presented in the manuscript “On sequential data assimilation for scalar macroscopic traffic flow models”, by Sebastien Blandin, Adrien Couque, Alexandre Bayen, and Daniel Work, accepted for publication to Physica D: Nonlinear Phenomena on May 2012.

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