Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions

The sensor network localization, SNL , problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solution techniques relax this problem to a weighted, nearest, (positive) semidefinite programming, SDP , completion problem, by using the linear mapping between Euclidean distance matrices, EDM, and semidefinite matrices. The resulting SDP is solved using primal-dual interior point solvers, yielding an expensive and inexact solution. This relaxation is highly degenerate in the sense that the feasible set is restricted to a low dimensional face of the SDP cone, implying that the Slater constraint qualification fails. Cliques in the graph of the SNL problem give rise to this degeneracy in the SDP relaxation. In this paper, we take advantage of the absence of the Slater constraint qualification and derive a technique for t...

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Nathan Krislock, Henry Wolkowicz
• Keywords: SDP Cone, SIAMJO 2010, Slater Constraint Qualification, SNL Problem