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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

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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

Email: {dominik.lieckfeldt, jiaxi.you}@uni-rostock.de

outline

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"

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

Introduction > Selecting References > Simulations > Conclusion

Localization in Wireless Sensor Networks

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

baseline algorithm for localization
Introduction > Selecting References > Simulations > ConclusionBaseline Algorithm for Localization

1. Phase

Refinement

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

sources of error

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"

slide6

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"

inequality of cram r 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:

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"

slide8

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"

distributed selection procedure

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"

distributed selection procedure1

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"

distributed selection procedure2

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"

performance metrics

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"

slide13
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"

slide14
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"

slide15

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"

questions

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

summary
Introduction> Selecting References > Simulations > ConclusionSummary

Localization

Wireless Sensor Networks

Accuracy

Limited

resources

Distance

Auswahl von Referenzen

CRLB

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

beacon selection crlb explained
Motivation > SotA > Beacon Selection > ConclusionBeacon 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"

cramer rao lower bound

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"

baseline algorithm for localization1
Localization in WSN > Distributed Beacon Selection > ConclusionBaseline Algorithm for Localization

2

3

1. Phase

Refinement

y

1

4

x

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

distributed selection procedure3

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"

distributed selection procedure4

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"

drahtlose sensornetzwerke

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"