## 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)∈ Λ} d¯
^{2}
_{ij}(1 + (1 + μ
_{ij})
^{2} + σ
^{2}
_{ij}).

Original language | English |
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Title of host publication | Proceedings of the 2015 Conference on research in adaptive and convergent systems |

Publisher | Association for Computing Machinery |

Publication date | 2015 |

Pages | 223-226 |

ISBN (Electronic) | 978-1-4503-3738-0 |

DOIs | |

Publication status | Published - 2015 |

Event | Conference on research in adaptive and convergent systems - Prague, Czech Republic Duration: 9. Oct 2015 → 12. Oct 2015 |

### Conference

Conference | Conference on research in adaptive and convergent systems |
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Country/Territory | Czech Republic |

City | Prague |

Period | 09/10/2015 → 12/10/2015 |

## Keywords

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