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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Formeln

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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"

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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"

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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

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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

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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

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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

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