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

Abstract

Abstract-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(n 3 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 > 1 is tackled by an incremental, greedy approach. The obtained Stiefel matrix is then used to determine the sensor selection matrix which best approximates its range space. Extensive simulations are used to assess near optimality of the proposed approach. They also show how the proposed approach performs better than exhaustive searches once an upper bound on the computation time is set.

Sensor Selection for Event Detection in Wireless Sensor Networks

“…The orientations of the uncertainty ellipsoids in (3) are induced by the covariance matrices S 0 and S 1 . (3).…”

Adaptive sensor selection in sequential hypothesis testing

“…Joshi et al [8] present a convex optimization-based heuristic to select multiple sensors for optimal parameter estimation. Bajović et al [1] discuss sensor selection problems for Neyman-Pearson binary hypothesis testing in wireless sensor networks. Castañón [4] study an iterative search problem as a hypothesis testing problem over a fixed horizon.…”

Robust linear dimensionality reduction for hypothesis testing with application to sensor selection

“…This problem has already been addressed in [3]. This reference solved the problem globally for case p = 1 reducing it to a grid search over an interval and proposed suboptimal greedy approach for case p > 1.…”

“…However, finding the linear projection that maximizes any of the mentioned distances is in general a hard nonconvex problem. In our previous work [3], we solve the problem of maximizing KL distance globally for the case of LDR to one dimension and in full generality.…”

“…However, it results in the Bayes optimal classifier only for the case of equal covariance matrices of the two Gaussian distributions. Moreover, its performance To overcome this problem, the authors in [12], [3] try to find the linear map that maximizes the Kullback-Leibler (KL) distance between the two projected distributions. This paper also uses the KL distance as optimality criterion.…”