ABSTRACT
This chapter presents a local threshold rule based on random graph and percolation theory as opposed to traditional methods, which are not appropriate due to the nonfixed infrastructure of an ad hoc wireless sensor network. The sensors collect environmental measurements that are subject to independent additive noise. Each sensor node employs a local threshold rule on the measurements to detect a target in the presence of random background noise. The chapter also presents an analytical model of the proposed sensor network and provides the local threshold rule based on random graph theory for the system to remain in viable state despite of topological dynamics. It discusses threshold bounds for accumulated decisions using Chebyshev’s inequality based on individual hit and false-alarm probabilities calculated from probability density function and local threshold but without requiring an a priori knowledge of the underlying probabilities.
