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. Outline 2WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 1. Introduction  Localization in Sensor Networks  Sources of errors regarding localization 2. Selecting references for localization  Finding a criteria for selection  Description of the algorithm 3. Simulation results 4. Summary and conclusions Introduction > Selecting References > Simulations > Conclusion

3. Localization in Wireless Sensor Networks 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 WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"3 Introduction > Selecting References > Simulations > Conclusion

4. Baseline Algorithm for Localization 4WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 1. PhaseRefinement Introduction > Selecting References > Simulations > Conclusion Unknown Beacon TX range Reference/Beacon

5. Sources of Error WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"5 ErrorSystematicRandom RF Shadowing, orientation of antenna Noise, Fading (interference) HardwareTolerancesNoise Environment Temperature, Humidity, Location of References (Geometry ) - Selection of beacons that contribute most to accurate localization  Distributed Beacon Selection 1 Introduction > Selecting References > Simulations > Conclusion

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 6WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" Finding a Selection Criteria Need 3 reference points for localization! ? ? CRLB Introduction > Selecting References > Simulations > Conclusion CRLB subset Selection using CRLB

7. Inequality of Cramér and Rao 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: WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"7 2 3 4 1 Distances Introduction > Selecting References > Simulations > Conclusion …path loss coefficient … deviation of RSS …true parameter …estimated parameter

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

9. Distributed Selection Procedure 9WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 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 Need 5 reference points for localization. Introduction > Selecting References > Simulations > Conclusion

10. Distributed Selection Procedure 10WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 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

11. 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

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

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

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

15. 15WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 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

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

18. Formeln

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

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

21. UnknownReferenceBeacon/Reference Tx range Baseline Algorithm for Localization 21WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 1. PhaseRefinement 2 3 4 1 y x Localization in WSN > Distributed Beacon Selection > Conclusion

22. Distributed Selection Procedure 22WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 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 Need 5 reference points for localization. Introduction > Selecting References > Simulations > Conclusion

23. Distributed Selection Procedure 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

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