.., yn} could be used to explain how large the step is compared to the standard
deviation for each of di. If i) the set of sensor readings x(i)
1 , x(i)
2 , ..., x(i)
k form a
sample of a normal distribution and ii) the number of sensor nodes within Si??™s
neighborhood is su?±ciently large, the set Y will also form a standard normal
population N(0, 1). A particularly large value, either positive or negative, in
a standard normal distribution will fall into the tail region of the probability
density function. A large |yi| would then imply that the reading of Si deviates
markedly compared to its neighbors, and could be a faulty sensor. Thus, to
determine whether a sensor node is faulty, a preselected threshold ?µ can be
introduced, which means if |yi| ?? ?µ, then Si is claimed to be a faulty sensor.
Let??™s go back to the discussion of the random bisection approach. To determine
the event boundary, we have to identify non-faulty sensor nodes whose
locations are near or on the boundary and their readings are extreme in their
neighborhoods as well. Although the faulty sensor detection algorithm presented
above can be of help in the process of identifying sensor nodes with
these two characteristics, in some cases, sensor nodes sitting near the boundary
cannot be detected e?±ciently.
158
Chapter 6 Boundary Detection for Sensor Networks
Let C1 denote the set of faulty sensor nodes detected by the faulty sensor
detection algorithm.
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