Optimal Decision Fusion Given Sensor Rules

Abstract—Optimal distributed fusion assuming that sensor decision rules are given is considered. A general and computationally tractable optimal fusion rule is presented, which relies only on the joint conditional probability densities of all sensor observations and all local decision rules. It is valid for general decision systems with any sensor observations and sensor decision rules, regardless of their interdependence, and any network structure. It is also valid for -ary Bayesian decision problems and binary problems under the Neyman-Pearson criterion. Local decision rules of a sensor that are optimal for the sensor itself are also presented, which take the form of a generalized likelihood ratio test. Numerical examples are given, which reveal some interesting phenomena.