Distributed decision fusion using empirical estimation

摘要

The problem of optimal data fusion in multiple detection systems is studied in the case where training examples are available, but no a priori information is available about the probability distributions of errors committed by the individual detectors. Earlier solutions to this problem require some knowledge of the error distributions of the detectors, for example, either in a parametric form or in a closed analytical form. Here the authors show that, given a sufficiently large training sample, an optimal fusion rule can be implemented with an arbitrary level of confidence. They first consider the classical cases of Bayesian rule and Neyman-Pearson test for a system of independent detectors. Then they show a general result that any test function with a suitable Lipschitz property can be implemented with arbitrary precision, based on a training sample whose size is a function of the Lipschitz constant, number of parameters, and empirical measures. The general case subsumes the cases of non-independent and correlated detectors.