New Adaptive Localization Algorithms That Achieve Better Coverage for Wireless Sensor Networks

1. New Adaptive Localization Algorithms That Achieve Better Coverage for Wireless Sensor Networks Advisor: Chiuyuan Chen Student: Shao-Chun Lin Department of Applied Mathematics National Chiao Tung University 2013/8/11

2. Introduction

3. 圖片來源:http://embedsoftdev.com/embedded/wireless-sensor-network-wsn/圖片來源:http://embedsoftdev.com/embedded/wireless-sensor-network-wsn/

4. Node : Sensor • Disk radius: transmission range()

6. Unit Disk Graph • Node : Sensor • Disk radius: Transmission range()

7. Applications of wireless sensor networks (WSNs) • Wildlife tracking, military, forest fire detection, temperature detection, environment monitoring Why localization? To detect and record events. When tracking objects, the position information is important. …

8. Related works and Main Results

9. Definitions • initial-anchor a node equipped with GPS • initial-anchor set () the set containing all initial-anchors • anchor a node knows its position. • feasible The initial-anchor set is called feasible if the position of each node in the given graph can be determined with .

10. Informations can be used to localize • For each node , the distances between where • The positions of anchors in

11. Localization types *Fine-grain Localization Coarse-grain Localization Resitrict [Rigid Theory] Consider noise [11~14, 2001~] *Find a feasible with as small as possible [8, 2011 Huang] Best Coverage[11~14, 2001~] 圖片來源:Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks

12. Localization types *Fine-grain Localization Coarse-grain Localization Resitrict [Rigid Theory] Consider noise [11~14, 2001~] *Find a feasible with as small as possible [8, 2011 Huang] Best Coverage[11~14, 2001~] 圖片來源:Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks

13. Rigidity Theory • non-rigid : localization solution is infinite. • rigid : localization solution is finite. • globally rigid : localization solution is unique.

14. Non-rigid Infinite Initial-anchor Unknown

15. Rigid graph Finite

16. Globally rigid graph Unique

17. Characterize globally rigid graph • Agraph which exists 3 anchors has unique localization solution if and only if the graph is globally rigid. • redundantly rigid:After one edge is deleted, the remaining graph is a rigid graph. • Laman’s Condition ([2], 1970 Laman) A graph with vertices is rigid in if and only if contains a subset consisting of edges with the property that, for any nonempty subset , the number of edges in cannot exceed , where is the number of vertices of which are endpoints of edges in .

18. Characterize globally rigid graph • 1982, Lovasz and Yemini shows 6-connected graph is redundantly rigid. • [7] 1992, Hendrickson proposed a polynomial-timealgorithm to determine the redundantly rigidity of a graph. • Hendrickson’s Conjecture A graph is called globally rigid if and only if the graph is 3-connectedandredundantly rigid. • [9] 2005, Jackson et al. proved thatHendrickson’s Conjecture is true. • [5] 2005, Connelly mentioned that there is an algorithm to determine if a graph is globally rigid (i.e. localizable) in polynomial-time. C-algorithm.

19. Characterize globally rigid graph • C-algorithm cannot compute position. • 2006, Aspnes shows that to compute position in globally rigid with 3 anchors is NP-hard

20. Localization types *Fine-grain Localization Coarse-grain Localization Resitrict [Rigid Theory] Consider noise [11~14, 2001~] *Find a feasible with as small as possible [8, 2011 Huang] Best Coverage[11~14, 2001~] 圖片來源:Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks

21. Grounded, generic, UDG A graph G Choose node to become initial-anchor Nodes with degree Trilateration *Tri + Sweep2 AnchorChoose-Phase Localization-Phase *Tri + Rigid No Check if all nodes are localized Yes HuangChoose[2011] Output a feasible initial-anchor set *AdaptiveChoose *MaxDegreeChoose

22. Grounded, generic, UDG A graph G Choose node to become initial-anchor Nodes with degree Trilateration *Tri + Sweep2 AnchorChoose-Phase Localization-Phase *Tri + Rigid No Check if all nodes are localized Yes HuangChoose[2011] Output a feasible initial-anchor set *MaxDegreeChoose *AdaptiveChoose

23. The graph we considered in this thesis • Unit Disk Graph • grounded([2], 2005 Aspnes et al.) A graph is groundedif implies that the distance can be measured or estimatedvia wireless communication. • generic A graph is called genericif node coordinates are algebraically independentover rationals.

24. A graph G Choose node to become initial-anchor Nodes with degree AnchorChoose-Phase Localization-Phase No Check if all nodes are localized Yes Output a feasible initial-anchor set

25. Theorem: • Let be any feasible initial-anchor set of . For all with degree , we have .

26. A graph G Choose node to become initial-anchor Trilateration *Tri + Sweep2 AnchorChoose-Phase Localization-Phase *Tri + Rigid No Check if all nodes are localized Yes Output a feasible initial-anchor set

27. Localization-Phase anchor Trilateration Sweep2+Tri Rigid+Tri unknown initial-anchor

28. Trilateration anchor unknown initial-anchor

29. Trilateration anchor unknown initial-anchor

30. Sweep2(+Tri)

31. Sweep2(+Tri)

32. Sweep2 • 2006 Goldenberg first propose this idea, and called this as sweep. • [8] 2011, Huang modified it to 2 neighbors version by two cases. • In 2013, this thesis simplifies it and achieves the same performance, called this algorithm as Sweep2.

33. Rigid(+Tri) Localizedsubgraph Subgraph

34. Rigid(+Tri) Localizedsubgraph Subgraph

35. Rigid(Tri) Localizedsubgraph Subgraph

36. A graph G Choose node to become initial-anchor AnchorChoose-Phase Localization-Phase No Check if all nodes are localized Yes HuangChoose[2011] Output a feasible initial-anchor set *AdaptiveChoose *MaxDegreeChoose

37. AnchorChoose-Phase • .ann : # of anchors in • MaxDegreeChoose (a straightforward approach) • HuangChoose ([8] 2011, Huang et al.)of with .ann Choose with maximum -> 1 -> 0 • AdaptiveChoose (This thesis) • Choose with maximum ann

38. A graph G Choose node to become initial-anchor AnchorChoose-Phase Localization-Phase No Check if all nodes are localized Yes Output a feasible initial-anchor set

39. A graph G Choose node to become initial-anchor AnchorChoose-Phase Localization-Phase No Check if all nodes are localized or Yes : The set of nodes that know their positions Output an initial-anchor set and

40. Simulation

41. Simulation • Localization-Phase • Trilateration (LocalTri) • Sweep2 • AnchorChoose-Phase • HuangChoose ([8] 2005, Huang et al.) • AdaptiveChoose • MaxDegreeChoose (MaxDegree)

42. Simulations Notation : Algorithm : The set of nodes that know their positions initial-anchor set : # of nodes • IAF: cardinality of an initial-anchor set • COVERAGE: the percentage of nodes that know their positions,

43. *200 graphs for each

44. G 圖片來源:Minimum cost localization problem in wireless sensor networks

47. Concluding remarks • Sweep2 are simpler than Sweep ([8] 2005, Huang) but cover all the cases. • A new algorithm for rigid in Localization-Phase

48. Future works • A much powerful Greedy algorithms to choose anchors. • Combine AdpativeChooseand HuangChooseto obtain better result. • Given a certain initial-anchor set, determine what kind of graphs are localizable. • Design a distributed version of AdaptiveChoose.

49. Thank you for your attention!