Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization

Details Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization

2006-12-14

arxiv.org/abs/math/0612388v1

Mathematics

Optimization and Control

33 pages

Scientific paper

We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular \SDP relaxation is equivalent to known relaxations in the literature for \EDM completions. The existence of anchors in the problem is {\em not} special. The set of anchors simply corresponds to a given fixed clique for the graph of the \EDM problem. We next propose a method of projection when a large clique or a dense subgraph is identified in the underlying graph. This projection reduces the size, and improves the stability, of the relaxation. In addition, viewing the problem as an \EDM completion problem yields better low rank approximations for the low dimensional realizations. And, the projection/reduction procedure can be repeated for other given cliques of sensors or for sets of sensors, where many distances are known. Thus, further size reduction can be obtained. Optimality/duality conditions and a primal-dual interior-exterior path following algorithm are derived for the \SDP relaxations We discuss the relative stability and strength of two formulations and the corresponding algorithms that are used. In particular, we show that the quadratic formulation arising from the \SDP relaxation is better conditioned than the linearized form, that is used in the literature and that arises from applying a Schur complement.

Affiliated with

Also associated with

No associations

Rating

Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-476920