On the fusion of non-independent detectors

Independence between detectors is normally assumed in order to simplify the algorithms and techniques used in decision fusion. In this paper, we derive the optimum fusion rule of N non-independent detectors in terms of the individual probabilities of detection and false alarm and defined dependence factors. This has interest for the implementation of the optimum detector, the incorporation of specific dependence models and for gaining insights into the implications of dependence. This later is illustrated with a detailed analysis of the two equally-operated non-independent detectors case. We show, for example, that not any dependence model is compatible with an arbitrary point of operation of the detectors, and that optimality of the counting rule is preserved in presence of dependence if the individual detectors are “good enough”. We have derived also the expressions of the probability of detection and false alarm after fusion of dependent detectors. Theoretical results are verified in a real data experiment with acoustic signals.