The
hierarchical boundary estimation technique, which is described next, tries to
find a reasonable balance between energy cost and accuracy.
5 Hierarchical edge estimation
Other than centralized or distributed boundary estimation, Nowak and Mitra
[9] investigate a general class of boundaries in a hierarchical framework, which
tries to find a reasonable balance between energy cost and estimation accuracy
in terms of performance. As we mentioned before, there are two fundamental
problems in boundary detection in sensor networks. (1) Many messages transmitted
among active nodes and desired destination would consume the energy
so fast that the involved nodes could not work correctly after a short time. (2)
The spatial density of deployed nodes and unpredicted noise in the measurements
would limit the accuracy of boundary estimation. In real application,
it is very hard to quantify the tradeo?® between energy cost and estimation
accuracy under various conditions and unpredictable situations. However, if
we restrict some conditions in certain scenarios, say the distribution of the
boundary, we still might get a rough idea about the tradeo?®.
5.1 Lipschitz Boundary
Let us take an example from [9] to see how the tradeo?® between energy consumption
and estimation accuracy could be under certain constraints. Suppose
that there are n sensors arranged in a pn?—pn square cell field, and a boundary
separates two homogeneous regions, as seen in Figure 15.
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