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Sensor Network Localization Using Semidefinite Representations and Facial Reductions

Karkhaneh, Mohammad Mehdi | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44089 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezamoddin
  7. Abstract:
  8. Use of wireless sensor networks (WSNs) to record environmental data such as temperature, sound level, and light intensity has grown dramatically. The specification of the locations of sensors is important. Using tools such as global positioning system (GPS) to find the location of sensors is not economical. Sensors can record their distances from neighboring sensors. On the other hand, the locations of some sensors are fixed. In wireless sensor network localization (SNL), we want to find the location of sensors using the available information. An approach for solving the SNL problem is to model the problem as an optimization problem and use an interior point method for its solution. Interior point methods require the existence of a strictly feasible solution of the problem, while such a solution in general may not exist for semidefinite models of the SNL problem. By using this feature of the semidefinite model, Krislock and Wolkowicz in 2010 showed that the size of the problem could be reduced successively to either determine the exact locations of some or of all the sensors or alternatively reach small semidefinite optimization problem for finding the locations of the sensors. Here, we describe this approach, implement the algorithm and test resulting programs
  9. Keywords:
  10. Sensor Network Localization ; Euclidean Distance Matrix Completion ; Graph Realization ; Semidefinite Optimization ; Facial Reduction Method ; Convex Cone Faces ; Graph Rigidity

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