### Jorge Cortés

#### Professor

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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