Conditions for Correct Sensor Network Localization Using SDP Relaxation

Part of the Fields Institute Communications book series (FIC, volume 69)


A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them. In this paper, we analyze and determine new sufficient conditions and formulations that guarantee that the SDP relaxation is exact, i.e., gives the correct solution. These conditions can be useful for designing sensor networks and managing connectivities in practice. Our main contribution is threefold: First, we present the first non-asymptotic bound on the connectivity (or radio) range requirement of randomly distributed sensors in order to ensure the network is uniquely localizable with high probability. Determining this range is a key component in the design of sensor networks, and we provide a result that leads to a correct localization of each sensor, for any number of sensors. Second, we introduce a new class of graphs that can always be correctly localized by an SDP relaxation. Specifically, we show that adding a simple objective function to the SDP relaxation model will ensure that the solution is correct when applied to a triangulation graph. Since triangulation graphs are very sparse, this is informationally efficient, requiring an almost minimal amount of distance information. Finally, we analyze a number of objective functions for the SDP relaxation to solve the localization problem for a general graph.

Key words

Sensor network localization Graph realization Semidefinite programming 

Subject Classifications

90C22 90C46 90C90 90B18 


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Department of Management Science and Engineering, Huang Engineering CenterStanford UniversityStanfordUSA
  2. 2.IBM Research, Smarter Cities Technology CentreDublinIreland
  3. 3.IBM CorporationFoster CityUSA
  4. 4.Department of Management Science and Engineering, Huang Engineering Center 308, School of EngineeringStanford UniversityStanfordUSA

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