Performance Analysis of Relative Location Estimation for Multihop Wirele

ss Sensor Networks

Qicai Shi; Kyperountas, S.; Correal, N.S.; Feng Niu

Selected Areas in Communications, IEEE Journal April 2005

Outline

• Introduction to Positioning Techniques for Wireless Sensor Networks

• The Contributions of This Paper• Mathematical Formulation of Relative Loca

tion Estimation– Assume range estimation error is i.i.d zero-me

an additive white Gaussian noise

• General Theoretical Analysis• Simulation Results

Introduction

• Why Location is important for Wireless Sensor Networks?– Applications

• HVAC( heating, ventilating, and air conditioning)– Average temperature over room A?

• Battlefield Surveillance– Where is the enemy?

• Ecosystem monitoring– Where exists a bear?

– Geographical Routing

Location-Aided Routing (LAR)• to limit the area to search for the route

– I will forward the ROUTE_REQ; – J will not forward the ROUTE_REQ.

S

A B

C

IJ

D

Route search zone

Expected zone of D

The Node Positioning Problem

Beacon

Unkown Location

Randomly Deployed Sensor Network

•Reference node– nodes with global location

•Blindfolded node– nodes want to estimate their location

• Localize nodes in an ad-hoc multihop network based on a set of inter-node distance (range) measurements

Reference

(beacon) node Blindfolded (unknown) node

Types of Range Measurements• How to obtain range measurements?

– Received Signal Strength (RSS)

– Time based methods (ToA,TDoA)

• Related Materials– Positioning Techniques in Sensor Network

• By Pei-Chi Chu • http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=81&1127318744

– Novel Self-Configurable Positioning Technique for Multi-hop Wireless Networks • By C. Y. Chen • http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=305&1127318855

– TPS-A Time-Based Positioning Scheme for Outdoor Wireless Sensor Networks • By C. Y. Chen• http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=214&1127318940

Contributions of This Paper

• Assume range estimation error is identical, independent additive zero-mean white Gaussian noise ~ n(0,2)– Analyze error accumulation when applying rel

ative location estimation to multihop sensor networks

Mathematical Formulation of Relative Location Estimation

• Accurate distance

• Distance with error

[go ref.]

Maximum-likelihood Estimator

otherwise 0

andbetween existslink wirelessa if 1

otherwise 0

andbetween existslink wirelessa if 1

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,

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Analysis of Simple Schemes

1

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)ˆ(

1,11,111,111

21,11

x

nDDxDxx

Dx

816.03

2

3

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2

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2

1

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2

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dD

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General Theoretical Analysis

),ˆ,ˆ(

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1,1,1

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1

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1 1,,,

,

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abaa

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ddDXaxbxax

ddDXaxbxax

ddDXaxbxax

DDbdda

xxd

xXD

nn

m

jjn

n

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n

m

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kk

n

m

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kk

n

iin

n

niinini

n

jjn

m

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n

ii

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n

kk

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)(

1

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2

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nmm

m

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nm . . -

. . . .

. . . .

- ........ n m -

- ....... . -n m

ix

n

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niinini

ii

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ddDX

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niinini

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1,,,

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ˆ)ˆˆ(

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ˆ)ˆˆ(

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1 0

.2 10

0 1 21

0 0 12

Simulation Results

• 20m x 20m x 6m sensing field=1m

• 4 reference nodes (m=4)

K=4

K=8

K=10

K=4

K=8K=10

References

• N. Patwari, R. J. O'Dea, and Y. Wang. Relative Location in Wireless Networks. In Proc. Int’l conf. Vehicular Technology, 2001.

• N. Patwari, A. Hero, M. Perkins, N. Correal, and R. O’Dea, “Relative

location estimation in wireless sensor networks,” IEEE Trans. Signal

Process., Special Issue on Signal Processing in Networks, vol. 51, no. 8,

pp. 2137–2148, Aug. 2003.

• K. Whitehouse, A. Woo, C. Karlof, F. Jiang, and D. Culler, “The Effects of Ranging Noise on Multi-hop Localization: An Empirical Study,” IPSN, 2005.

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• Let X1, X2,….Xn be independent and identically Normal distributed random variables with mean i and variance i

2.

• ThenY= X1+X2+…+Xn is a normal distribution with

mean 1+ 2+…+ n

variance 12+ 2

2+….+ n2

[back]