Serial Distributed Detection Strategies

In the most common formulation of the binary hypothesis distributed detection problem, local detectors collect statistically independent and identically distributed observations under each hypothesis. Based upon these data, each detector independently decides which hypothesis it judges to be true and then transmits its decision to a fusion center. The fusion center in turn makes a final global decision. This paper analyzes two alternative distributed detection architectures from a Neyman-Pearson viewpoint. Here, the local detectors communicate their binary decisions to their immediate neighbors. (See figure 1). The first architecture is known in the literature as the serial or tandem architecture [1–3]. The second is a combination of the serial and the traditional parallel architecture. The serial architecture, like the parallel architecture, assumes all local detectors collect statistically independent observations. Unlike the parallel architecture the detectors are ordered. The first detector independently makes a decision solely based on its observation. This decision is passed to the second detector that makes a decision based not only on its observation but also the first detector’s decision. The second detector then relays its decision to the third detector and the process repeats. Assuming there are N local detectors, the decision of the N th detector is taken to be the final decision. All detectors perform likelihood ratio tests. To fully characterize any distributed detection scheme, the decision rules of each detector need to be specified. The optimal Neyman-Pearson decision rules for the serial architecture were found by Viswanathan et al. [3]. Unfortunately, the solution requires solving 2N − 1 coupled equations. This means the optimal decision rules become increasingly difficult to find as the number of systems grow. Furthermore the solution offers little insight. Here, we propose a suboptimal decision rule which uses a common decision rule for all interacting detectors. We denote the output of each detector as Yn(n = 1, . . . , N) and assume Yn = 1 if the n detector decides H1 and Yn = −1 if H0. The first detector is a standard Neyman-Pearson detector whose performance (or equivalently its threshold η) is determined by some specified false alarm probability. This threshold becomes a baseline threshold for all the other detectors. The n detector multiplies the decision of its predecessor by a linking parameter a and shifts its baseline threshold by aYn−1. Thus except for the first detector we associate two thresholds symmetrically placed about the baseline threshold to each detector. Specifically, the decision rule at the n detector is