Minimal error certificates for detection of faulty sensors using convex optimization

Authors:
Christian G. Claudel;Matthieu Nahoum;Alexandre M. Bayen
Affiliations:
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley and Research Intern, Mobile Internet Services Systems, Nokia Research Center, Palo Alto;Systems Engineering, Department of Civil and Environmental Engineering, University of California, Berkeley, CA;Systems Engineering, Department of Civil and Environmental Engineering, University of California, Berkeley, CA
Venue:
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Year:
2009

Citing 3
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Abstract

This article proposes a new method for sensor fault detection, applicable to systems modeled by conservation laws. The state of the system is modeled by a Hamilton-Jacobi equation, in which the Hamiltonian is uncertain. Using a Lax-Hopf formula, we show that any local measurement of the state of the system restricts the allowed set of possible values of other local measurements. We derive these constraints explicitly for arbitrary Hamilton-Jacobi equations. We apply this framework to sensor fault detection, and pose the problem finding the minimal possible sensor error (minimal error certificate) as a set of convex programs. We illustrate the performance of the resulting algorithms for a highway traffic flow monitoring sensor network in the San-Francisco Bay Area.