On Distributed Detection with Correlated Local Detectors

Recently, Chair and Varshney have solved the data fusion problem for n fixed binary local detectors with statistically independent decisions. We generalize their solution by using the Bahadur-Lazarfeld expansion of probability density functions. The optimal data fusion rule is developed for correlated local binary decisions, in terms of the conditional correlation coefficients of order 1, 2, ..., n. We show that when all these coefficients are zero, the rule coincides with the original Chair-Varshney design.