Distributed detection by a large team of sensors in tandem

The problem of decentralized binary hypothesis testing by a team consisting of N decision makers (DMs) in tandem is considered. Each DM receives an observation and transmits a binary message to its successor; the last DM has to decide which hypothesis is true. The necessary and sufficient condition for the probability of error to go asymptotically to zero as N to infinity is that the log-likelihood ratio of the observation of each DM be unbounded. The result is generalized for multiple hypotheses and multiple messages. An easily implementable suboptimal decision scheme is also considered; in this case, the necessary and sufficient condition for the probability of error to asymptotically go to zero is that the log-likelihood ratio of the observation of each DM be unbounded from both above and below. The tradeoff between the complexity of the decision rules and their performance is examined, and numerical results are presented, in order to demonstrate that the performance of both decision schemes is comparable.<
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