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A powerful concept to cope with resource limitations and information redundancy in wireless sensor networks is the use of collaboration groups to distill information within the network and suppress unnecessary activities. When the phenomena to be monitored have large geographical extents, it is not obvious how to define these collaboration groups. This article presents the application of geometric duality to form such groups for sensor selection and non-local phenomena tracking. Using a dual-space transformation, which maps a non-local phenomenon (e.g., the edge of a half-plane shadow) to a single point in the dual space and maps locations of distributed sensor nodes to a set of lines that partitions the dual space, one can turn off the majority of the sensors to achieve resource preservation without losing detection and tracking accuracy. Since the group so defined may consist of nodes that are far away in physical space, we propose a hierarchical architecture that uses a small number of computationally powerful nodes and a massive number of power constrained motes. By taking advantage of the continuity of physical phenomena and the duality principle, we can greatly reduce the power consumption in non-local phenomena tracking and extend the lifetime of the network.
Date of Publication: Dec. 2004