In each square partition, the children partitions communicate
their estimation to a clusterhead. The leaf node in the tree is the sensor node,
and all other nodes represent the partitions in the field. In Figure 15, for
instance, each square can be considered a partition in the hierarchy.
In general, there are various methods that can be applied to process the collected
information at the clusterhead. Consider a simple example where sensor
measurements are assumed to be a Gaussion distribution, then in square (i, j),
the clusterhead computes an average from collected information to obtain the
value as follows,
xi,j ?» N(?µi,j ,
??2
mi,j
), (26)
where ?µi,j is the mean value, ??2 is the noise variance, and mi,j is the number
of nodes in square (i, j).
In [9], the authors present a hierarchical processing strategy that constructs
a non-uniform rectangular partition of the sensor field to adapt to the
boundary.
Suppose the sensor domain is a pn ?— pn square, and the side length pn
is the finest resolution. Theoretically, this can be achieved by a recursively
dyadic partition.
Fig. 16. An illustration of dyadic partition.
First divide a larger square into four sub-squares with equal sizes, as shown
in Figure 16, and then repeat this on each partition. So in iteration k, the
total number of partition changes from 22k??’2 to 22k. Obviously, the finest
resolution needs 1
2 log2n iterations. This process can be represented by a quadtree
structure.
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