Optimum fusion of correlated local decisions

A distributed detection system consisting of a number of local detectors and a fusion center is considered. Each detector makes a decision for the underlying binary hypothesis testing problem based on its own observations and transmits its decision to the fusion center where the global decision is derived. The local decision rules are assumed to be given, but the local decisions are correlated. The correlation model is expressed by a finite number of conditional probabilities. The optimum decision fusion rule in the Neyman-Pearson sense is derived and analyzed. The performance of the distributed detection system versus the degree of correlation between the local decisions is studied for a special correlation structure that can be indexed by a single parameter. It is shown that system performance degrades as the degree of correlation between local decisions increases