Mathematics – Optimization and Control
Scientific paper
2009-03-17
Mathematics
Optimization and Control
Scientific paper
In this paper we use the MAP criterion to locate a region containing a source. Sensors placed in a field of interest divide the latter into smaller regions and take measurements that are transmitted over noisy wireless channels. We propose implementations of our algorithm that consider complete and limited communication among sensors and seek to choose the most likely hypothesis. Each hypothesis corresponds to the event that a given region contains the source. Corrupted measurements are used to calculate conditional posteriors. We prove that the algorithms asymptotically find the correct region almost surely as long as information is available from three or more sensors. We also study the geometric properties of the model that make it possible in some situations to detect the correct region with a unique sensor. Our simulations confirm that the performance of algorithms with complete and limited information ameliorates with decreasing noise.
Bullo Francesco
Dandach Sandra H.
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