DISTRIBUTED DECISION FUSION USING EMPIRICAL ESTIMATION

The problem of optimal data fusion in multiple detection systems is st udied in the case where training examples are available, but no a prio ri information is available about the probability distributions of err ors committed by the individual detectors. Earlier solutions to this p roblem require some knowledge of the error distributions of the detect ors, for example, either in a parametric form or in a closed analytica l form. Here we show that, given a sufficiently large training sample, an optimal fusion rule can be implemented with an arbitrary level of confidence. We first consider the classical cases of Bayesian rule and Neyman-Pearson test for a system of independent detectors. Then we sh ow a general result that any test function with a suitable Lipschitz p roperty can be implemented with arbitrary precision, based on a traini ng sample whose size is a function of the Lipschitz constant, number o f parameters, and empirical measures. The general case subsumes the ca ses of nonindependent and correlated detectors.