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Novel Self-Configurable Positioning Technique for Multi-hop Wireless Networks

Hongyi Wu, Chong Wang,and Nian-Feng Tzeng

IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 13, NO. 3, JUNE 2005

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Outline Introduction Proposed self-configurable positioning

technique Euclidean distance estimation Coordinates system establishment

Simulation Conclusion

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Introduction Many application are need to know node

location Target tracking, routing…

We propose a self-configurable positioning technique

1. Euclidean distance estimation model

2. Coordinates system establishment Range-based GPS-free

AB

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Proposed self-configurable positioning technique – Euclidean distance estimation

This can be done off-line by each node or a central controller

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Euclidean distance estimation Assume the node distribution is uniform Euclidean distance d is given

(0,0) (d,0)

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Euclidean distance estimation The distance between node D and node i

(within S’s transmission range)

(0,0) (d,0)

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Euclidean distance estimation where Xi and Yi are random variables with a un

iform distribution

(0,0) (d,0)

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Euclidean distance estimation Accordingly, we can derive the density functio

n of Zi

(0,0) (d,0)

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Euclidean distance estimation Assume a node has the shortest

Euclidean distance to D

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Euclidean distance estimation Consequently, we can derive the pdf of Z

And obtain its mean value

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Euclidean distance estimation We draw an arc ACB with node D as the center

and as the radius

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Euclidean distance estimation Assuming node is uniformly distributed

along AC (or BC) We can obtain the first hop along the shortest

path from S to D

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Euclidean distance estimation

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Euclidean distance estimation Recursively applying the above method,

we can obtain the shortest path

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Euclidean distance estimation

This can be done off-line by each node or a central controller

r=0.25, network=1*1

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How to use the Euclidead distance estimation model Estimate the distance between A and B

A B1 2 3 4

ControlPacket

0

Include a route length field

Assume the control packet follow the shortest path

ControlPacket

0.17

0.17 0.12 0.1 0.18 0.2

ControlPacket

0.29

ControlPacket

0.39

ControlPacket

0.57

ControlPacket

0.77

DAB= 0.77

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How to use the Euclidead distance

DAB= 0.77

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Coordinates system establishment : Localize landmarks Each landmark flooding a control packet to

every one of all other landmarks In order to learn the Euclidean distance

L1 L2 … Li

L1 0 L21 … Li1

L2 L12 0 … Li2

… … … … …

Li L1i L2i … 0

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Coordinates system establishment: Localize landmarks1. The landmark with the lowest ID : (0, 0)2. The landmark with the second lowest ID : (X, 0)3. The landmark with the third lowest ID: negative Y

(0, 0)(LAB, 0)

(LacCos , - LacSin )

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Minimize the errors of the landmark’s coordination

(0, 0)

(LAB, 0)

(LacCos , - LacSin )

Minimize the error function:

Lij can be learned through the Euclidean distance estimation model

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Coordinates system establishment : Localize regular nodes Landmarks flooding control packet that

include their coordinates and length field

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Minimize the errors of the regular node’s coordination

Minimize the error function:

Lip can be learned through the Euclidean distance estimation model

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Locations of landmarks The more the landmarks, the higher the

accuracy But computational complexity increases

exponentially Simulation show that typical # of

landmark vary from 4 to 7 Locations of landmarks

We consider 4 landmarks in a 1*1 area Assume 4 landmark located at the vertices of a

square and has an edge of G

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Locations of landmarks

G = 0.5

1

1

0.5

(Xc,Yc)

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Locations of landmarks

G = 0.7G = 0.9

G = 0.7

1

1

0.7

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Selection of landmarks ： a set of all landmark candidates

If the node is stability and power are high Each candidate node discovers the shortest path to

all other candidate nodes

Ci ： Candidacy degree of node i. Lower value of C, higher probability to be selected as landmark

Si,j : the length of the shortest path from i to j

1

3 42

5

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Selection of landmarks

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Simulation parameters Use Matlab Assume a number (N=50 to 400) of nodes 1 * 1 unit area R=0.25 unit An average of about 10 to 80 neighbors

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Simulation: Node density V.S Euclidean distance estimation

N = 50 N = 100N = 400

Shortest path length

Euclidean distance

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Simulation: Node density V.S Coordinates system

N = 50 N = 100N = 400

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Simulation: Node density V.S Coordinates error

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The number of landmarks

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Conclusion We have proposed a self-configurable

positioning technique Do not depend on GPS Accuracy

We plan to implement the technique in real world