1 GPS-Free-Free Positioning System for Wireless Sensor Networks Farid Benbadis, Timur Friedman, Marcelo Dias de Amorim, and Serge Fdida IEEE WCCN 2005

2 Outline  Introduction  GPS-Free-Free Algorithm Details  Simulation  Conclusion

3 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

4 GPS-Free-Free algorithm details: Distance determination of λ 1 λ1λ1 λ2λ2 λ3λ3 Floods a distance discovery packet (DDP) 1.ID of λ 1 2.Hop counter

5 Distance determination of λ 2 λ1λ1 λ2λ2 λ3λ3 Nodes keep the DDP with the smallest hop counter After receive λ1’s DDP, λ2 floods its own DDP 1. ID of λ2 2.Hop counter 3.Distance to λ1

6 Distance determination of λ 3 λ1λ1 λ2λ2 λ3λ3 λ3 include its distances to λ1 and λ2 1.ID of λ3 2.Hop counter 3.Distance to λ1 4.Distance to λ2

7 Local coordinates computation λ1λ1 λ2λ2 λ3λ3 Each node knows the hop-distance to the 3 landmarks and the hop-distance between λ1, λ2, λ3 Then calculate the position of λ1, λ2, λ3

8 Calculate coordinate of λ1, λ2, λ3 q p i (d ip, 0) (, ) Is the angle of λ1λ1 λ2λ2 λ3λ3

9 Local coordinates computation λ1λ1 λ2λ2 λ3λ3 (0, 0) (d λ1λ2, 0) a c b Node n (, )

10 Local coordinates computation λ1λ1 λ2λ2 (0, 0) (d λ1λ2, 0) a b X = Y = α = the angle ∠ (n, λ 1,λ2) dλ1λ2dλ1λ2 (d λ1λ2 ) 2 λ3λ3 (, )

11 Local coordinates computation λ1λ1 λ2λ2 (0, 0) (d λ1λ2, 0) a b P1 P2 λ3λ3 (, ) c

12 Problem n1, n2 share the same coordinate

13 Simulation  Network environment is a square universe of 200 meters on a side  3200 nodes are randomly spread I IIIII Nodes that are virtually located within a range of 1 hop from n

14 False negatives (I) c d b a (3, 5) (10, 27) (2, 3) (3, 7) IIIIII Nodes that are c’s neighbor but when using virtual coordinate they are not one-hop neighbor Virtual coordinate

15 False positives (III) c d b a (3, 5) (2, 7) (2, 3) (3, 7) IIIIII Nodes that are not c’s neighbor while they are using the real coordinates Virtual coordinate

16 Simulation: False negatives (I) Distance between λ1 and λ2 Virtual neighbor Real neighbor 70% of the neighbor are detected

17 Simulation: False positives ratio (III) Virtual neighbor Real neighbor Distance between landmark seems to have no incidence

18 Simulation: True positives ratio (II) Virtual neighbor Real neighbor

19 Simulation: Average of localization error Localization error (meters) Error is drastically reduced when density up to 15 -hop distance is close to real distance

20 Simulation: localization error VS distance to the first landmark Localization error (meters) Density > 10, the error is about 10 meters Even for nodes located far from the first landmark

21 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