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A Dual-Space Approach to Tracking and Sensor Management in Wireless Sensor Networks
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A Dual-Space Approach to Tracking and Sensor Management in Wireless Sensor Networks

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Wirelessly distributed, heterogeneous ad hoc sensor networks
are defined by several unique characteristics unparalleled to
those on conventional centralized sensor platforms. A wireless
sensor network can cover a large geographical region, and
hence can be used to detect and track multiple, simultaneous
events and support multiple active user queries. Because of its
dense spatial sampling and multi-aspect, multi-modality
sensing, the network can assemble information from spatially
diverse sources to improve signal/noise ratio. The redundancy
in the network can ensure a certain degree of robustness
against node failures. The network may be quickly deployed for
a particular application, and the ubiquity and low-cost nature of
the MEMS micro-sensors can potentially give users
unprecedented access to real-time situational information.

The approach we take to estimate the edge of the shadow is
based on the dual space principle in computational geometry,
(see e.g. [1], [5]). In the following, we assume the shadow is a
half plane, bounded by a line. We exploit the fact that both a
sensor location and the location (line equation) of the edge
shadow can be described by two parameters.

Line Arrangements
The arrangement of lines in the dual space and the cells they
create can be computed by using the topological sweep
algorithm of Edelsbrunner and Guibas [2], as modified by
Rafalin, Souvaine and Streinu to deal with degeneracies [6].
The details of topological sweep algorithm are beyond the
scope of this paper; we only describe how the sweep results are


Assume that the shadow is a half plane. By using the dual space
transform, we can easily determine the set of sensors at the
“frontier”, i.e., the ones that may detect a transition next. We use
light sensors to facilitate the discussion in this section.
Obviously, the mechanism applies to any sensors that give binary

This paper presents a shadow edge detection and power
management scheme in sensor networks using a dual-space
transformation. The approach converts non-local phenomena
into localized representations and solves the problem in an
appropriate configuration space. A testbed of distributed motes
was implemented to demonstrate this approach. A fully
distributed detection of shadows of more complicated shapes is
under development.

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