Sensor selection for hypothesis testing in wireless sensor networks: a Kullback-Leibler based approach

We consider the problem of selecting a subset of p out of n sensors for the purpose of event detection, in a wireless sensor network (WSN). Occurrence or not of the event of interest is modeled as a binary Gaussian hypothesis test. In this case sensor selection consists of finding, among all n p combinations, the one maximizing the Kullback-Leibler (KL) distance between the induced p-dimensional distributions under the two hypotheses. An exhaustive search is impractical if n and p are large, as the resulting optimization problem is combinatorial. We propose a suboptimal approach with computational complexity of order O(n3 p). This consists of relaxing the 0/1 constraint on the entries of the selection matrices to let the optimization problem search over the set of Stiefel matrices. Although finding the Stiefel matrix is a nonconvex problem, we provide an algorithm that guarantees to produce a global optimum for p = 1, through a series of judicious problem reformulations. The case p >...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Dragana Bajovic, Bruno Sinopoli, João Xavier
• Keywords: CDC 2009, Control Systems, Optimization Problem, Sensor Selection, Stiefel Matrix