On the equivalence between likelihood ratio tests and counting rules in distributed detection with correlated sensors

We have considered in this paper the conditions for the equivalence of the counting rule and the likelihood ratio test when implementing the fusion rule of decisions corresponding to identically operated correlated sensors. A simple model of correlation, defined by two correlation indices, one for every hypothesis, has been considered. A main conclusion is that for properly operating sensors, the counting rule is almost a UMP test in the correlation indices.