However, observation shows that, if sensors are densely deployed in a field,
readings at sensors in the same event region are spatially correlated and sensor
160
Chapter 6 Boundary Detection for Sensor Networks
Fig. 7. An illustration of random trisection. The sector yielding the largest |di| is
the union of i and iii.
errors are likely spatially uncorrelated. By exploiting this notion, the Bayesian
algorithm takes a similar approach in the faulty sensor detection described in
Section 2.4. Each sensor collects readings of its neighbors and identifies an
event or a false alarm locally.
Event disambiguation
The Bayesian algorithm takes a probability reasoning approach to decide
whether an event is correctly detected by a sensor node. Assume the probability
of an erroneous measurement at a sensor node equals p, then the probability
of a correct measurement at the same node is (1 ??’ p). If there are
N neighbors around sensor Si and k of them have the same reading e as Si
does, the probability P(E) that a sensor in the neighborhood of Si has the
same reading e can be modeled as P(E) = k
N . By the definition of Bayesian
calculation, the probability Pt that Si detects an event and its reading e is
also a correct one can be calculated as:
Pt =
P(E) ?· P(e|E)
P(E) ?· P(e|E) + P( ??E) ?· P(e| ??E
)
=
k
N ?· (1 ??’ p)
k
N ?· (1 ??’ p) + (1 ??’ k
N ) ?· p
. (22)
Based on the result of equation (22), the Bayesian algorithm incorporates
the following three di?®erent schemes to decide whether an event is correctly
detected at Si:
??? Randomized Decision Scheme: If Pt is larger than a randomly generated
value u 2 (0, 1), it is claimed that an event is correctly detected by Si.
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