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![Page 1: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/1.jpg)
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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
![Page 2: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/2.jpg)
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Outline Introduction GPS-Free-Free Algorithm Details Simulation Conclusion
![Page 3: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/3.jpg)
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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
![Page 4: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/4.jpg)
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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
![Page 5: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/5.jpg)
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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
![Page 6: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/6.jpg)
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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
![Page 7: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/7.jpg)
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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
![Page 8: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/8.jpg)
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Calculate coordinate of λ1, λ2, λ3
q
pi(dip, 0)
( , )
Is the angle of
λ1 λ2
λ3
![Page 9: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/9.jpg)
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Local coordinates computation
λ1 λ2
λ3
(0, 0) (d λ1λ2, 0)
a
c
b
Node n
( , )
![Page 10: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/10.jpg)
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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 ( , )
![Page 11: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/11.jpg)
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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
![Page 15: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/15.jpg)
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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
![Page 16: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/16.jpg)
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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
![Page 18: 1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062413/5a4d1b257f8b9ab059996c4a/html5/thumbnails/18.jpg)
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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