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Boundary conditions estimation on a road network using compressed sensing.
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2016-02-01
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[PDF-529.25 KB]
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Abstract:This report presents a new boundary condition estimation framework for transportation networks in which
the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a
Hamilton-Jacobi equation, we pose the problem of estimating the boundary conditions of the system on a
network, as a Mixed Integer Linear Program (MILP). We show that this framework can handle various
types of traffic flow measurements, including floating car data or flow measurements. To regularize the
solutions, we propose a compressed sensing approach in which the objective is to minimize the variations
over time (in the L1 norm sense) of the boundary flows of the network. We show that this additional
requirement can be integrated in the original MILP formulation, and can be solved efficiently for small to
medium scale problems.
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