On Distributed Composite Tests with Dependent Observations in WSN

We consider a distributed detection problem with statistically spatial dependent measurements in a sensor network, when there is not a fusion center. Thus, each node takes some measurements, does some processing, exchanges messages with its neighbors and finally makes a decision (typically the same for all nodes) about the phenomenon of interest. A cooperative algorithm is proposed for reducing the number of communications between sensors and thus make an efficient use of the energy budget of a wireless sensor network (WSN). The problem is formulated as a composite hypothesis test using a general probability density function with unknown parameters leading naturally to the use of the generalized likelihood ratio (GLR) test. As the sensors observe statistically spatial dependent samples, which makes difficult the implementation of fully distributed detection procedures, we propose a simpler algorithm for making a decision about the true hypothesis. We also compute its asymptotic distribution to characterize its performance. Interestingly, despite the fact that our proposal is more simple and efficient to implement than the GLR test, we find relevant scenarios for which it outperforms the latter, even in finite length regimes.