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Asymptotic optimality of multicenter Voronoi configurations for random field estimation
R. Graham, J. Cortés
IEEE Transactions on Automatic Control 54 (1) (2009), 153-158

Abstract

This paper deals with multi-agent networks performing estimation tasks. Consider a network of mobile agents with sensors that can take measurements of a spatial stochastic process. Using a statistical technique known as kriging, a field estimate may be calculated over the environment, with an associated error variance at each point. We study a single-snapshot scenario, in which the spatial process mean is known and each agent can only take one measurement. We consider two optimization problems with respect to the measurement locations, using as objective functions the maximum error variance and~the~extended prediction variance. We show that, as the correlation between distinct locations vanishes, circumcenter and incenter Voronoi configurations become network configurations that optimize the maximum error variance and the extended prediction variance, respectively. We also present distributed coordination algorithms that steer the network towards these configurations. The technical approach draws on tools from geostatistics, computational geometry, linear algebra, and dynamical systems.

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