Design and Analysis of Distributed Detection Networks with Uncertainties

A distributed detection network is an acyclic directed graph with detectors as nodes. Each detector has the ability to process its input data consisting of external observations and decisions from preceding detectors, to produces a decision regarding an underlying binary hypothesis testing problem. The local observations are assumed conditionally independent given either hypothesis. Each local detector has an unknown probability to be jammed or defective and an unknown probability to provide an incorrect decision when jammed or defective. The resulting binary hypothesis testing problem is solved using concepts of Dempster-Shafer theory. Each detector employs Dempster´s combining rule to aggregate its input information for a decision. The uncertainty that is introduced by the unknown probabilities is treated by discounting the degree of confidence on decisions. It is shown that each detector employs a likelihood ratio test and that the thresholds can be expressed as a function of the local performance characteristics and the uncertainty discount rates. By analysing a special distributed detection network with four detectors we show that the proposed decision rule has very robust behaviour and that with few exception, it significantly outperforms the minimax decision rule and the decision rule that is optimum when there are no jammed or defective detectors.