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A Cluster-based and Range Free Multidimensional Scaling-MAP Localization Scheme in WSN

1 Ke Xu, Yuhua Liu ( ), Cui Xu

School of Computer, Central China Normal University, Wuhan 430079, China

e-mail: yhliu@mail.ccnu.edu.cn2 Kaihua Xu

College of Physical Science and Technology, Central China Normal University, Wuhan 430079, China

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• Introduction

• MDS-MAP

• Improved MDS-MAP

• Experiments and Simulations

• Conclusion

• References

Outline

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• A sensor network is composed of a large number of sensor nodes, which are densely deployed either inside the phenomenon or very close to it

• The goal of a sensor network is to perceive, collect and process the information of specific objects, and send the information to observers

• Localization plays a key role within the application of WSN

Introduction (1/ 1)

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• What is MDS-MAP

• Procedure of MDS-MAP

MDS-MAP (1/ 3)

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MDS-MAP (2/ 3)

• What is MDS-MAP ?

MDS( Multidimensional Scaling) is a set of data analysis technology which can transform the given data into geometry model, thus problems can be visually solved. Torgerson firstly given the terminology MDS based on the work of Richardson, and proposed the first MDS method.

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MDS-MAP (3/ 3)

• Procedure of MDS-MAP– Calculate the shortest distances between nodes i

n WSN– Calculate the first r maximum eigenvalues of r di

mensional space to construct the relative location map of nodes

– Transforms the relative location map to absolute location map

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• Clustering

• Building Cluster Location Map

• Merging Cluster Location Map

Improved MDS-MAP (1/ 9)

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Improved MDS-MAP (2/ 9)

• Clustering– Selection of Cluster Heads– Inter-cluster Nodes

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Improved MDS-MAP (3/ 9)

• Clustering– Selection of Cluster Heads

Selection of cluster heads

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Improved MDS-MAP (4/ 9)

• Clustering– Inter-cluster Nodes

Result of k-hop clustering

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Improved MDS-MAP (5/ 9)

• Building Cluster Location Map– Step 1: After k-hop clustering completed, each cluster head node calc

ulates distance based on RSSI and the IDs of neighboring nodes[7]. Using the distance information which is expressed in a distance matrix and the shortest path algorithm, Dijkstra or Floyd, the cluster head node constructs a shortest distance matrix;

– Step 2: Using this shortest distance matrix, the MDS-MAP algorithm produces a relative location map within the cluster;

– Step 3: Refine cluster location map.

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• Merging Cluster Location MapIf have more than 3 nodes, than using formula (6) can transform the coordinates of nodes in Cluster-j to coordinates in Cluster-i:

(6)

where is zoom factor, depicts rotation transformation, indicates translation transformation, the technique of compute , , is shown as below.

Suppose are coordinate matrices of nodes of in Cluster-i and Cluster-j. The row vector of are depicted by .The central points of are computed through formula (7).

　　 (7)

Improved MDS-MAP (6/ 9)

0)R( XXX jclustericluster s

( ) ( )NB i NB j

)(R 0Xs

s )(R 0X

jclutericluster SS , ( ) ( )NB i NB j

jclutericluster SS , ijclusteriicluster SS ,, ,

n

k

kjclusterjcluster

n

k

kiclustericluster Xn

SXn

S1

,

1

,1

,1

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• Merging Cluster Location Map Assume

, the zoom factor s in formula (6) is calculated through formula (8).

(8)

　　

The covariance matrix of can be computed by using formula (9).

(9)

　　

Improved MDS-MAP (7/ 9)

jclusterkjclusterkjclustericlusterkiclusterkicluster SSSSSS ,,'

,,' ,

n

kkjcluster

n

kkicluster SSs

1

2,

'

1

2,

' ||||/||||

zzzyzx

yzyyyx

xzxyxxn

kkicluster

Tkjcluster

CCC

CCC

CCC

SS1

,,''

C

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• Merging Cluster Location MapDefine matrix as formula (10):

(10)

　　

Compute which is composed by eigenvalue of matrix :

　　Compute R(•) of formula (6) using formula (11).

(11)

Improved MDS-MAP (8/ 9)

U

m ),,,( 3210 m

zzyyxxzyyzxzzxyxxy

zyyzzzyyxxyxxyxzzx

xzzxyxxyzzyyxxzyyz

yxxyxzzxzyyzzzyyxx

CCCCCCCCC

CCCCCCCCC

CCCCCCCCC

CCCCCCCCC

U

23

22

21

2010232013

103223

22

21

203012

2031302123

22

21

20

)(2)(2

)(2)(2

)(2)(2

R

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• Merging Cluster Location MapCompute through formula (12):

(12)

Using formula (6), (8), (11), (12), the matrix D (the nodes’ coordinate matrix of ) can be transformed to the coordinate system of Cluster-i, the technique is shown as formula (13).

(13)

where is a all-1 matrix which has an equal row number as matrix .

　Using this technique, all clusters’ location map can be merged to one location map.

Improved MDS-MAP (9/ 9)

Tjclustericluster SSX R 0

0T XIDRF

0X

)NB()NB()NB( jij

I D

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Experiments and Simulations (1/ 4)

• Simulations of Two Types of WSN

• Localization Error with Connectivity

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• Simulations of Two Types of WSN

localization results where a sensor topology is configured in a C shape

Experiments and Simulations (2/ 4)

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• Simulations of Two Types of WSN

localization results in a sensor topology with a horseshoe-shaped hole

Experiments and Simulations (3/ 4)

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• Localization Error with Connectivity

Localization error with connectivity in C-shaped WSNs(a), horseshoe-shaped WSNs(b)

Experiments and Simulations (4/ 4)

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Conclusion (1/ 1)

This article proposes MDS-MAP(C,RF) algorithm based on conventional MDS-MAP. Simulation results indicate that MDS-MAP(C,RF) is better than MDS-MAP for it can improve localization accuracy. Since MDS-MAP(C,RF) is a cluster based technique which can reduce the burden of center nodes, it can extend lifespan of WSN. The next stage work is focus on the effect to WSN’s lifespan of MDS-MAP(C,RF).

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Referencs(1/ 1)

1 G. Mao, B. Fidan, B. Anderson. Wireless sensor network localization techniques[J]. Computer Networks. 51(10), 2529-2553(2007).

2 A. Pal. Localization algorithm in wireless sensor networks: Current approaches and future challenges. Network Protocols and Alogriths. 2(1), 45-73(2010).

3 G.D.Stefano and A. Petricola. A distributed AOA based localization algorithm for wireless sensor networks. Journal of Computers. 3(4), 1-8(2008).

4 Ewa Niewiadomska-szynkiewicz. Localization in wireless sensor networks: classification and evaluation of techniques. International Journal of Applied Mathematics and Computer Science. 22(2), 281-297(2012)

5 Y. Shang, W. Ruml, Y. Zhang and M. Fromherz. Localization from mere connectivity. Proceeding of the 4th ACM international symposium on Mobile ad hoc networking & computing,ACM New York. pp, 201-212(2003)

6 W. S. Torgeson. Multidimensional scaling of similarity. Psychometrika. 30(4),379–393(1965)

7 Kaihua Xu, Ya Wang and Yuhua Liu. A Clustering Algorithm Based on Power for WSNs.Lecture Notes in Computer Science, Springer. 4489, 153-156(2007)

8 Y. Shang, W. Ruml. Improved MDS-Based Localization[C]. INFOCOM 2004, Twenty-third Annual Joint Conference of the IEEE Computer and Communications Societies, Hong Kong, China. pp, 2640-2651(2004)