Semi-definite programming-based localization algorithm in networks with inhomogeneous transmission medium

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Abstract

We study the asymptotic properties of a semi-definite programming (SDP) based localization algorithm in a network of wireless sensors with an inhomogeneous RF transmission interface given incomplete and inaccurate pairwise distance measurements between sensor-sensor and sensor-anchors. A novel relaxed SDP approach based on a graph realization problem with noisy time-of-arrival (TOA) measurements with additive Gaussian noise and inaccurate transmission permittivity and permeability coefficients both with additive standard Gaussian noise and a varying dielectric constant is proposed. Denoting-the true distance between a pair of sensors i and j by d¯ ij and the set of known pair-wise distances between sensors-sensors and sensors-anchors by Λ, an upper bound for the expected value of the optimal objective relaxed SDP problem is obtained, showing that its asymptotic properties can potentially grow as fast as Σ (i, j)∈ Λ2 ij(1 + (1 + μ ij) 2 + σ 2 ij).

Original languageEnglish
Title of host publicationProceedings of the 2015 Conference on research in adaptive and convergent systems
PublisherAssociation for Computing Machinery
Publication date2015
Pages223-226
ISBN (Electronic)978-1-4503-3738-0
DOIs
Publication statusPublished - 2015
EventConference on research in adaptive and convergent systems - Prague, Czech Republic
Duration: 9. Oct 201512. Oct 2015

Conference

ConferenceConference on research in adaptive and convergent systems
Country/TerritoryCzech Republic
CityPrague
Period09/10/201512/10/2015

Keywords

  • Inhomogeneous transmission media
  • Linear matrix inequality
  • Semi-definite programming

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