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

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

3. 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. 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. 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. 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. 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. 8 Calculate coordinate of λ1, λ2, λ3 q p i (d ip, 0) (, ) Is the angle of λ1λ1 λ2λ2 λ3λ3

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

10. 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. 11 Local coordinates computation λ1λ1 λ2λ2 (0, 0) (d λ1λ2, 0) a b P1 P2 λ3λ3 (, ) c

12. 12 Problem n1, n2 share the same coordinate

13. 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. 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. 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. 16 Simulation: False negatives (I) Distance between λ1 and λ2 Virtual neighbor Real neighbor 70% of the neighbor are detected

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

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

19. 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. 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. 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