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, Rostock, Germany {dominik.lieckfeldt,

Outline 2WPNC "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

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

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

Sources of Error WPNC "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

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 "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

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 "Distributed Selection of References for Localization in Wireless Sensor Networks" Distances Introduction > Selecting References > Simulations > Conclusion …path loss coefficient … deviation of RSS …true parameter …estimated parameter

Example: 2 references, 1 unknown 8WPNC "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

Distributed Selection Procedure 9WPNC "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

Distributed Selection Procedure 10WPNC "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

Distributed Selection Procedure WPNC "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

Performance Metrics Error of location estimates: Power-Error-Product (PEP): Simple Energy Model (TDMA): WPNC "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

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

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

15WPNC "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

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

WPNC "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

Formeln

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 "Distributed Selection of References for Localization in Wireless Sensor Networks"

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

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

Distributed Selection Procedure 22WPNC "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

Distributed Selection Procedure WPNC "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

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