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

This research explores innovative adaptive localization algorithms designed to improve coverage in Wireless Sensor Networks (WSNs). The algorithms consider fine-grain and coarse-grain localization methods, addressing the critical importance of accurate position information for applications such as wildlife tracking, military operations, and environmental monitoring. By leveraging graph theory and rigidity concepts, the study identifies feasible initial-anchor sets to optimize localization while minimizing noise impacts. The findings contribute significantly to the efficiency and reliability of WSNs, enhancing their application scope in real-world scenarios.

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

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  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()

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

  6. 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. …

  7. Related works and Main Results

  8. 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 .

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

  10. 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

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

  13. Non-rigid Infinite Initial-anchor Unknown

  14. Rigid graph Finite

  15. Globally rigid graph Unique

  16. 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 .

  17. 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.

  18. 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

  19. 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

  20. 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

  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 *MaxDegreeChoose *AdaptiveChoose

  22. 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.

  23. 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

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

  25. 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

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

  27. Trilateration anchor unknown initial-anchor

  28. Trilateration anchor unknown initial-anchor

  29. Sweep2(+Tri)

  30. Sweep2(+Tri)

  31. 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.

  32. Rigid(+Tri) Localizedsubgraph Subgraph

  33. Rigid(+Tri) Localizedsubgraph Subgraph

  34. Rigid(Tri) Localizedsubgraph Subgraph

  35. 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

  36. 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

  37. 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

  38. 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

  39. Simulation

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

  41. 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,

  42. *200 graphs for each

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

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

  45. 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.

  46. Thank you for your attention!

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