Source localization using Poisson integrals

Carlos Canudas de Wit 1 Federica Garin 1, 2 Ruggero Fabbiano 1, 2 Pierre Rouchon 3 Antoine Rousseau 4
1 NECS - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
4 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : This paper deals with the problem of source localization in diffusion processes via several sensor devices providing pointwise concentration measures; sensors are assumed to be arranged in circular arrays, they can be fixed along the array or they can turn along a circular path defined by the array. The originality of the proposed source localization solution lies in the computation of the gradient and of higher-order derivatives (i. e., the Hessian) from Poisson integrals; in opposition to other solutions published in the literature, this computation does neither require specific knowledge of the solution of the difiusion process, nor the use of probing signals, but only exploits properties of the PDE. The Laplacian of the measured value is null on the studied domain; such an assumption is justified for isotropic diffusive sources in steady-state. The paper also presents some simulation results of a source-seeking torque control law for mobile non-holonomic robots looking for a heat source in a room, where the source is modeled as a small circular region.
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Carlos Canudas de Wit, Federica Garin, Ruggero Fabbiano, Pierre Rouchon, Antoine Rousseau. Source localization using Poisson integrals. 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys'12), Sep 2012, Santa Barbara, Californie, United States. pp.127-132, ⟨10.3182/20120914-2-US-4030.00021⟩. ⟨hal-00717193⟩

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