Optimal Decentralized Detection for Conditionally Independent Sensors

The optimal fusion rule for decentralized detection is easily shown to be a likelihood ratio test on the data transmitted by the sensors. It is more difficult to determine the procedure whereby the sensors reduce their observations in order to transmit over a bandlimited channel. Intuitively, it seems that the optimal sensor processor would compute and transmit as close a facsimile to the local (sensor) likelihood ratio as the channel will allow. This, in fact, is the case. We show that the sensor decision rule which is optimal under both the Neyman-Pearson and the Bayes criteria partitions the sensor observation space by the value of the likelihood ratio at the sensor input. We also show that sensor decision rules based on likelihood ratio partitions maximize the Ali-Silvey distance between the distributions under the two hypotheses at the fusion center input.