Eavesdropper Selection Strategies in Wireless Source Localization Networks

Abstract

We consider a wireless source localization network in which a target node emits localization signals that are used by anchor nodes to estimate the target node position. In addition to target and anchor nodes, there can also exist eavesdropper nodes and jammer nodes which aim to estimate the position of the target node and to degrade the accuracy of localization, respectively. We first propose the problem of eavesdropper selection with the goal of optimally placing a given number of eavesdropper nodes to a subset of possible positions in the network to estimate the target node position as accurately as possible. As the performance metric, the Cramér-Rao lower bound (CRLB) related to the estimation of the target node position by eavesdropper nodes is derived, and its convexity and monotonicity properties are investigated. By relaxing the integer constraints, the eavesdropper selection problem is approximated by a convex optimization problem and algorithms are proposed for eavesdropper selection. Moreover, in the presence of parameter uncertainty, a robust version of the eavesdropper selection problem is developed. Then, the problem of jammer selection is proposed where the aim is to optimally place a given number of jammer nodes to a subset of possible positions for degrading the localization accuracy of the network as much as possible. A CRLB expression from the literature is used as the performance metric, and its concavity and monotonicity properties are derived. Also, a convex optimization problem and its robust version are derived after relaxation. Moreover, the joint eavesdropper and jammer selection problem is proposed with the goal of placing certain numbers of eavesdropper and jammer nodes to a subset of possible positions. Simulation results are presented to illustrate performance of the proposed algorithms.

Anchor Placement in TOA based Wireless Localization Networks via Convex Relaxation

“…can be written as a ratio of two non-decreasing supermodular functions. In addition, after relaxation, from Proposition 2 in [19], the anchor selection problem for the TDOA based approach can be shown to be convex, as well. Hence, the algorithms proposed for the TOA based approach in the previous section can also be used for TDOA based wireless localization networks.…”

“…First, we can simply set the largest N A components of the solution of ( 16) to one, and the others to zero (called largest-N A algorithm). Second, starting from this solution, we can use the swap algorithm [19]. In this algorithm, for each run, one checks whether there is a decrease in the objective function by simply swapping one of the N A selected locations with one of the R − N A locations that are not selected.…”

“…As in the previous section, due to the difficulty of the continuous optimization problem (see ( 7)), we discretize the set R as R. After the discretization, via similar steps to those in [19], one can show that the CRLB related to the estimation of the ith target location, x i , by anchor nodes is given by…”

“…Remark 2: In this manuscript, we rely on the perfect knowledge of λ (k) i 's. In fact, due to the monotonic behavior of the CRLB with respect to λ (k) i 's, it is straightforward to extend the analyses if we have some uncertainty region for each λ (k) i 's as in [19]. V. SIMULATION RESULTS AND CONCLUSIONS In this section, numerical examples are presented to evaluate the proposed approaches in Section III.…”

“…In the simulations, the same parameters as in [19], [20] are used. In particular, α (l) i (y j ) and ξ i (y j ) are modeled as α (l) i (y j ) = x i − y j −2 and ξ i (y j ) = 0.…”