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Distributed Selection of References for Localization in Wireless Sensor Networks

Distributed Selection of References for Localization in Wireless Sensor Networks. Dominik Lieckfeldt , Jiaxi You, Dirk Timmermann Institute of Applied Microelectronics and Computer Engineering University of Rostock, 18119 Rostock, Germany

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Distributed Selection of References for Localization in Wireless Sensor Networks

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  1. Distributed Selection of References for Localization in Wireless Sensor Networks Dominik Lieckfeldt, Jiaxi You, Dirk Timmermann Institute of Applied Microelectronics and Computer Engineering University of Rostock, 18119 Rostock, Germany Email: {dominik.lieckfeldt, jiaxi.you}@uni-rostock.de

  2. Introduction • Localization in Sensor Networks • Sources of errors regarding localization Selecting references for localization • Finding a criteria for selection • Description of the algorithm Simulation results Summary and conclusions Introduction > Selecting References > Simulations > Conclusion Outline WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  3. Why? • Mapping of location ↔ sensor data Problem: • Nodes randomly deployed • GPS not on every node possible Solution: • Few nodes with GPS → Beacons • Remaining nodes → Unknowns Introduction > Selecting References > Simulations > Conclusion Localization in Wireless Sensor Networks WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  4. Introduction > Selecting References > Simulations > Conclusion Baseline Algorithm for Localization 1. Phase Refinement WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  5. Selection of beacons that contribute most to accurate localization • Distributed Beacon Selection1 Introduction > Selecting References > Simulations > Conclusion Sources of Error WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  6. Theory of Estimation • Comparison of estimators based on variance of estimates • Fundamental lower bound on Variance → Cramer-Rao-Lower-Bound (CRLB) Here: Use CRLB as selection criteria Introduction> Selecting References > Simulations > Conclusion Finding a Selection Criteria CRLB subset Selection using CRLB Need 3 reference points for localization! ? CRLB WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  7. Poses lower bound on variance of any estimator CRLB for localization based on: • Time-of-Arrival (ToA) or received signal strength (RSS) derived by Patwari et al.2 RSS: Introduction> Selecting References > Simulations > Conclusion Inequality of Cramér and Rao 2 3 1 4 Distances … path loss coefficient … deviation of RSS … true parameter … estimated parameter WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  8. Example: 2 references, 1 unknown Introduction> Selecting References > Simulations > Conclusion Impact of Geometry on CRLB Linear vector Circular vector Reference Unknown WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  9. Phase I: • Inquiry send by unknown • All beacons compute response probability ( … maximal tx range) • TDMA: Beacon i responds with probability and broadcasts its position and estimated distance • End condition: • One beacon has responded Introduction> Selecting References > Simulations > Conclusion Distributed Selection Procedure Need 5 reference points for localization. WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  10. Phase II: • After first response: • Use estimated distances and position of first responder to avoid collinear beacons • How? Utilize CRLB • End condition: • 2 beacons have responded Introduction> Selecting References > Simulations > Conclusion Distributed Selection Procedure WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  11. Phase III: • Recalculation of based on previous responses and on CRLB • Reference i responds with probability • End condition: • Sufficient number of references has responded Introduction> Selecting References > Simulations > Conclusion Distributed Selection Procedure WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  12. Error of location estimates: Power-Error-Product (PEP): Simple Energy Model (TDMA): Introduction> Selecting References > Simulations > Conclusion Performance Metrics More efficient PEP = 0.3 mJ = 0.81 mJ PEP schematic WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  13. Introduction> Selecting References > Simulations > Conclusion Simulation Results (RSS) Reference Unknown Distance-based CRG-based WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  14. Introduction> Selecting References > Simulations > Conclusion Simulation Results (TOA) Reference Unknown Distance-based CRG-based WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  15. Contribution: • Analysis of distributed algorithms for selecting references for localization • Investigation of error of localization • Comparison regarding Power-Energy-Product Conclusions: • Use of CRLB can improve selection regarding accuracy • Convergence of CRLB-based algorithms should be improved to increase energy efficiency Introduction> Selecting References > Simulations > Conclusion WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  16. Questions? - Thank you for your attention - Literature: 1 Lieckfeldt, D; You, Jiaxi; Timmermann, D.: “An algorithm for distributed for distributed beacon selection”, IEEE PerSeNS, 2008 2 Patwari, N.; O. Hero III, A.; Perkins, M.; Correal, N. & O'Dea, R.: “Relative location estimation in wireless sensor networks“, IEEE TSP, 2003

  17. Introduction> Selecting References > Simulations > Conclusion Summary Localization Wireless Sensor Networks Accuracy Limited resources Distance Auswahl von Referenzen CRLB WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  18. Formeln

  19. Motivation > SotA > Beacon Selection > Conclusion Beacon Selection: CRLB explained Number of beacons Error model of RSS measurements Geometry CRLB Lower bound on variance of position error WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  20. Beispiel • 1 Dimension • Wahre Position: x=0 • Fehlerhafte Positionsschätzungen • PDF der Positionsschätzungen • Standardabweichung -> intuitives Maß um Fehler zu charakterisieren Cramer-Rao-Lower-Bound WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  21. Localization in WSN > Distributed Beacon Selection > Conclusion Baseline Algorithm for Localization 2 3 1. Phase Refinement y 1 4 x WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  22. Phase I: • Inquiry sent by unknown • References calculate response probability • TDMA: Reference i response with probability • After first response: • Utilize CRLB to avoid collinear references Introduction> Selecting References > Simulations > Conclusion Distributed Selection Procedure Need 5 reference points for localization. WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  23. Phase II: • Recalculation of based on the decrease of CRLB • Reference i response with probability • End condition: • Sufficient number of references has responded Introduction> Selecting References > Simulations > Conclusion Distributed Selection Procedure WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

  24. Definition: • Netz aus kleinsten Knoten • Zufällige Positionierung • Drahtlose Kommunikation • Erfassung von Umwelt-parametern Eigenschaften: • Ressourcenarm • Fehleranfällig Einleitung > Positionsbestimmung > Auswahlverfahren > Zusammenfassung Drahtlose Sensornetzwerke • Anwendungsbereiche: • Analyse, Beobachtung, Überwachung WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

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