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The quality of service of a network performing cooperative track detection is represented by the probability of obtaining multiple elementary detections over time along a target track. Recently, two different lines of research, namely, distributed-search theory and geometric transversals, have been used in the literature for deriving the probability of track detection as a function of random and deterministic sensors' positions, respectively. In this paper, we prove that these two approachesdoi:10.1109/tsmcb.2010.2041449 pmid:20236903 fatcat:tod7wboelreyldqcehc4d3uhdu