distributed selection of references for localization in wireless sensor networks dominik lieckfeldt,...

Distributed Selection of References for Localization in

Wireless Sensor Networks

Dominik Lieckfeldt, Jiaxi You, Dirk TimmermannInstitute of Applied Microelectronics and Computer Engineering

University of Rostock, 18119 Rostock, GermanyEmail: {dominik.lieckfeldt, jiaxi.you}@uni-rostock.de

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 > ConclusionIntroduction > 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 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks" 3


Baseline Algorithm for Localization


1. Phase Refinement


Unknown

Beacon

TX range

Reference/Beacon

Sources of Error


Error Systematic Random

RF Shadowing, orientation of antenna Noise , Fading (interference)

Hardware Tolerances Noise

EnvironmentTemperature, Humidity, Location of References

(Geometry )-

• Selection of beacons that contribute most to accurate localization Distributed Beacon Selection1


• 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


Finding a Selection Criteria

Need 3 reference points for localization!

Need 3 reference points for localization!??

CRLBCRLB


CR

LB

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:


23

4

12,1d

3,1d

4,1d

Distances


… path loss coefficient… deviation of RSS… true parameter… estimated parameter

• Example: 2 references, 1 unknown

8

0 0.1 0.2 0.3 0.41

10

100

Distance/ [rad]

CR

LB

no

rmal

ized

linearcircular

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

Reference Unknown

Impact of Geometry on CRLB

Linear vector

Circular vector


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

Need 5 reference points for

localization.


localization.




• 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




• Phase III: Recalculation of

based on previous responses and on CRLB

Reference i responds with probability

End condition:– Sufficient number of

references has responded


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" 12P

EP

More

effi

cient

More

effi

cient

PEP schematic


= 0.3 mJ

= 0.81 mJ

2 4 6 8 10 12 144

6

8

10

12

14

16

18

number of references in subset

loc

ati

on

err

or

[m]

Local-DistanceLocal-CRLBLocal-CRLB with circle ruleGlobal-DistanceGlobal-CRLB


Simulation Results (RSS)Reference

Unknown

Distance-based

CRG-based 2 4 6 8 10 12 1410

-1

100

101

102

103


PE

P [

mJ

]

Local-CRLBLocal-CRLB with circle ruleLocal-Distance


2 4 6 8 10 12 140.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


loc

ati

on

err

or

[m]

Local-DistanceGlobal-DistanceLocal-CRLBLocal-CRLB with circle ruleGlobal-CRLB


Simulation Results (TOA)Reference

Unknown

2 4 6 8 10 12 1410

-2

10-1

100

101


PE

P [

mJ

]

Local-CRLBLocal-CRLB with circle ruleLocal-Distance


Distance-based

CRG-based


• 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


Questions?

- Thank you for your attention -

Literature:1 Lieckfeldt, D; You, Jiaxi; Timmermann, D.: “An algorithm for distributed for

distributed beacon selection”, IEEE PerSeNS, 20082 Patwari, N.; O. Hero III, A.; Perkins, M.; Correal, N. & O'Dea, R.: “Relative location

estimation in wireless sensor networks“, IEEE TSP, 2003


LocalizationLocalization Wireless Sensor NetworksWireless Sensor Networks

Accuracy Limited resources

Auswahl von ReferenzenAuswahl von Referenzen

CRLBCRLBDistanceDistance

Introduction > Selecting References > Simulations > Conclusion

Summary

Formeln

I

XTEXT

2

Var

XT

22

1

2 1

2

2,1

2,1

,,1

2

2,1

rss )~()~(E1

yyxx

dd

dd

d

bCRLB

N

i

N

ij ji

jiji

N

ij

2

rss

p

10ln

10

n

b

pn

rssx

x~

iPresp

2

tx

,1resp 1

d

dP ii

id ,1txd

iRCRLB

RCRLBiRCRLBPi

resprss

resprssresprssresp

)(

T

i

yyxxT

e1

22 )~()~(1

eΔEPEP

M

ii

i

ntδEtΔE

EnEntntδE

1

(i)tx

tx(i)txrx

(i)tx

(i)tx

),()(

)(),(

txE

rxE

Beacon Selection: CRLB explained

19

CRLBCRLB

Error model of RSS

measurements

Error model of RSS

measurements

Number of beacons

Number of beacons GeometryGeometry

Lower bound on variance of

position error

Lower bound on variance of

position errorRSS [dBm]

Pro

ba

bili

ty

Motivation > SotA > Beacon Selection > Conclusion


-5 0 2.5-2.5 5 x

Cramer-Rao-Lower-Bound

-5 0 2.5-2.5 5 x

-5 0 2.5-2.5 5

0

0.2

0.4

x

Pro

bab

ilit

y

• Beispiel 1 Dimension Wahre Position: x=0 Fehlerhafte Positionsschätzungen PDF der Positionsschätzungen Standardabweichung -> intuitives Maß um Fehler zu

charakterisieren

20

22rss )ˆ()ˆ(E yyxxCRLB

2


Unknown Reference Beacon/Reference Tx range

Baseline Algorithm for Localization


1. Phase Refinement

23

4

12,1d

3,1d

4,1d

24,1

241

241

23,1

231

231

22,1

221

221

)()(

)()(

)()(

dyyxx

dyyxx

dyyxx

y

x

),( 11 yx

Localization in WSN > Distributed Beacon Selection > Conclusion



• 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

iPant2

tx

,1ant 1

d

dP ii

iPant


localization.


localization.




• Phase II: Recalculation of

based on the decrease of CRLB

Reference i response with probability

End condition:– Sufficient number of

references has responded

iPant

iRCRG

RCRGiRCRGPi

antrss

antrssantrssant

)(

iPant


Drahtlose Sensornetzwerke

• Definition: Netz aus kleinsten Knoten Zufällige Positionierung Drahtlose Kommunikation Erfassung von Umwelt-

parametern

• Eigenschaften: Ressourcenarm Fehleranfällig

• Anwendungsbereiche:

Analyse, Beobachtung, Überwachung24WPNC 2008 - "Distributed Selection of References for Localization in Wireless Sensor Networks"

Einleitung > Positionsbestimmung > Auswahlverfahren > Zusammenfassung

distributed selection of references for localization in wireless sensor networks dominik lieckfeldt,...

Documents

introduction localization

selection criteria

crlb slide

crlb introduction

selection description

wireless sensor networks

wireless sensor networks7

parameter slide