Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Asymptotic optimality of multicenter Voronoi
configurations for random field estimation
R. Graham, J. Cortés
Proceedings of the IEEE Conference on Decision and Control, New Orleans, Louisiana, USA, pp. 3127-3132
Abstract
This paper deals with multi-agent networks performing optimal
estimation tasks. Consider a network of mobile agents with
footprint sensors that can take measurements of a spatial process in
an environment of interest. Using the measurements, one can
construct a kriging interpolation of the spatial field over the
whole environment, with an associated prediction error at each
point. We study the continuity properties of the prediction error,
and consider as global objective functions the maximum prediction
error and the spatially-averaged prediction error. We study the
network configurations that give rise to optimal field
interpolations. Specifically, we show how, as the correlation
between any two different locations tends to vanish, circumcenter
and incenter Voronoi configurations become network configurations
that optimize the maximum and spatially-averaged prediction errors,
respectively. The technical approach draws on tools from
geostatistics, computational geometry, linear algebra, and dynamical
systems.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
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