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Localization using boundary sensors: An analysis based on graph theory

Published: 01 October 2007 Publication History

Abstract

We consider sensors, such as fibers, lasers, and pyroelectric motion detectors, that fire when objects cross a boundary. A moving object can be localized by analyzing sequences of boundary crossings. We consider the number of distinct sequences and object positions that can be achieved using boundary sensors in one- and two-dimensional spaces. For 1D systems we use representations of sensor sequences on graphs to derive limits on the number of object locations that can be monitored by a given sensor population and sequence length. For 2D systems we show that in certain circumstances the ratio of the number of unique sensor sequences to the number of unique object paths is exponential in the sequence length and we argue that the probability of unique identification is high for sufficiently large sequences. We also prove the triangle grid can track an object with error limited to a small neighborhood.

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      cover image ACM Transactions on Sensor Networks
      ACM Transactions on Sensor Networks  Volume 3, Issue 4
      October 2007
      148 pages
      ISSN:1550-4859
      EISSN:1550-4867
      DOI:10.1145/1281492
      Issue’s Table of Contents

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      Association for Computing Machinery

      New York, NY, United States

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      Publication History

      Published: 01 October 2007
      Published in TOSN Volume 3, Issue 4

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      Author Tags

      1. Boundary sensor
      2. deployment graph
      3. deployment sequence
      4. sensor sequence
      5. sequence graph

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      • (2011)An efficient local improvement operator for the multi-objective wireless sensor network deployment problemEngineering Optimization10.1080/0305215X.2010.54684043:10(1115-1139)Online publication date: Oct-2011
      • (2010)Multi-target tracking in distributed active sensor networks2010 - MILCOM 2010 MILITARY COMMUNICATIONS CONFERENCE10.1109/MILCOM.2010.5679524(1044-1049)Online publication date: Oct-2010
      • (2010)A Three-State Node Reliability Model for Sensor Networks2010 IEEE Global Telecommunications Conference GLOBECOM 201010.1109/GLOCOM.2010.5683750(1-5)Online publication date: Dec-2010
      • (2008)Probabilistic model of triangulationProceedings of the 2008 ACM symposium on Solid and physical modeling10.1145/1364901.1364943(301-306)Online publication date: 2-Jun-2008
      • (2008)Reliability of wireless sensor grids2008 33rd IEEE Conference on Local Computer Networks (LCN)10.1109/LCN.2008.4664177(252-257)Online publication date: Oct-2008

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