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GPS-Free-Free Positioning System for Wireless Sensor Networks

Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge FdidaIEEE WCCN 2005

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Outline Introduction GPS-Free-Free Algorithm Details Simulation Conclusion

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Introduction The GPS is impractical in many situation

Cost Line of sight

Relative positioning algorithm Give reasonably precise coordinates Strong assumptions on the capabilities More Computation and communication cost

This paper proposes GPS-Free-Free Base on node communication

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GPS-Free-Free algorithm details: Distance determination of λ1

λ1 λ2

λ3

Floods a distance discovery packet

(DDP) 1. ID of λ1

2. Hop counter

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Distance determination of λ2

λ1 λ2

λ3Nodes keep the DDP with the smallest hop

counter

After receive λ1’s DDP, λ2 floods its

own DDP1. ID of λ22.Hop counter3.Distance to λ1

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Distance determination of λ3

λ1 λ2

λ3

λ3 include its distances to λ1

and λ2 1.ID of λ32.Hop counter3.Distance to λ14.Distance to λ2

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Local coordinates computation

λ1 λ2

λ3

Each node knows the hop-distance to the 3 landmarksand the hop-distance between λ1, λ2, λ3Then calculate the position of λ1, λ2, λ3

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Calculate coordinate of λ1, λ2, λ3

q

pi(dip, 0)

( , )

Is the angle of

λ1 λ2

λ3

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Local coordinates computation

λ1 λ2

λ3

(0, 0) (d λ1λ2, 0)

a

c

b

Node n

( , )

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Local coordinates computation

λ1 λ2(0, 0) (d λ1λ2, 0)

a b

X =

Y =

α = the angle ∠(n, λ 1,λ2)

dλ1λ2

(dλ1λ2)2

λ3 ( , )

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Local coordinates computation

λ1 λ2(0, 0) (d λ1λ2, 0)

a b

P1

P2

λ3 ( , )

c

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Problem

n1, n2 share the same coordinate

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Simulation Network environment is a square universe

of 200 meters on a side 3200 nodes are randomly spread

I II IIINodes that are virtually

located within a range of 1 hop from n

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False negatives (I)

c

d

b

a

(3, 5)

(10, 27)

(2, 3)

(3, 7)

I II III

Nodes that are c’s neighbor but when using virtual coordinate they are not one-hop neighbor

Virtual coordinate

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False positives (III)

c

db

a

(3, 5)

(2, 7)

(2, 3)(3, 7)

I II III

Nodes that are not c’s neighbor while they are using the real coordinates

Virtual coordinate

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Simulation: False negatives (I)Distance betwee

n λ1 and λ2

Virtual neighbor

Real neighbor

70% of the neighbor are detected

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Simulation: False positives ratio (III)

Virtual neighbor

Real neighbor

Distance between landmark seems to have no incidence

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Simulation: True positives ratio (II)

Virtual neighbor

Real neighbor

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Simulation: Average of localization error

Loca

lizat

ion

erro

r (m

eter

s)

Error is drastically reduced when densityup to 15

-hop distance is close to real distance

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Simulation: localization error VS distance to the first landmark

Loca

lizat

ion

erro

r (m

eter

s)

Density > 10, the error is about 10 metersEven for nodes located far from the first landmark

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Conclusion We proposed in this paper GPS-Free-Free,

a simple algorithm

GPS-Free-Free is low cost in terms of energy and bandwidth requirements

This algorithm is more efficient in high density networks