Two-stage Multiple Hypotheses LAO Test of Distributed Detection System for Many Families of Distributions

Problem of multiple hypotheses of distributed detection forming many families of possible probability distributions is considered. Reliabilities matrix and Logarithmically Asymptotically Optimal (LAO) hypotheses testing for a pair of stages are studied. The fusion center detects one of some known probability distributions of the source inside many disjoint families of probability distributions. In first stage the first fusion center identifies one family of probability distributions on the base of a messages sample, then in second stage the second fusion center denotes exact distribution in the mentioned family on the base of another messages sample and the result of the first fusion center. The results show the compatibility conditions to happen of characteristics of LAO hypotheses testing of distributed detection.