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 ChenStudent: Shao-Chun Lin
Department of Applied Mathematics National Chiao Tung University
2013/8/11
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Introduction
3圖片來源 :http://embedsoftdev.com/embedded/wireless-sensor-network-wsn/
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• Node : Sensor• Disk radius: transmission range ()
𝑅
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Unit Disk Graph
• Node : Sensor• Disk radius:
Transmission range ()
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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.
…
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Related works and Main Results
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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 .
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• Informations can be used to localize – For each node , the distances between where – The positions of anchors in
Localization types
*Fine-grain Localization Coarse-grain Localization
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圖片來源 :Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks
Resitrict [Rigid
Theory]
*Find a feasible with as small as
possible [8, 2011 Huang]
Consider noise [11~14,
2001~]
Best Coverage[11~14, 2001~]
Localization types
*Fine-grain Localization Coarse-grain Localization
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圖片來源 :Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks
Resitrict [Rigid
Theory]
*Find a feasible with as small as
possible [8, 2011 Huang]
Consider noise [11~14,
2001~]
Best Coverage[11~14, 2001~]
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Rigidity Theory
• non-rigid : localization solution is infinite.• rigid : localization solution is finite.• globally rigid : localization solution is unique.
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Non-rigid
Initial-anchor
Unknown
Infinite
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Rigid graph
Finite
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Globally rigid graph
Unique
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Characterize globally rigid graph• A graph 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 .
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Characterize globally rigid graph• 1982, Lovasz and Yemini shows
6-connected graph is redundantly rigid.• [7] 1992, Hendrickson proposed a polynomial-time
algorithm 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-connected and redundantly 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.
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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
Localization types
*Fine-grain Localization Coarse-grain Localization
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圖片來源 :Efficient Location Training Protocols for Heterogeneous Sensor and Actor Networks
Resitrict [Rigid
Theory]
*Find a feasible with as small as
possible [8, 2011 Huang]
Consider noise [11~14,
2001~]
Best Coverage[11~14, 2001~]
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No
Choose node to become initial-
anchor
Check if all nodes are localized
Output a feasible initial-anchor set
Localization-Phase AnchorChoose-Phase
Yes
A graph G
Nodes with degree Trilateration
*Tri + Sweep2
*Tri + Rigid
HuangChoose[2011]
*AdaptiveChoose
Grounded, generic, UDG
*MaxDegreeChoose
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No
Choose node to become initial-
anchor
Check if all nodes are localized
Output a feasible initial-anchor set
Localization-Phase AnchorChoose-Phase
Yes
A graph G
Nodes with degree
HuangChoose[2011]
*AdaptiveChoose
Grounded, generic, UDG
Trilateration
*Tri + Rigid
*Tri + Sweep2
*MaxDegreeChoose
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The graph we considered in this thesis
• Unit Disk Graph• grounded ([2], 2005 Aspnes et al.)
A graph is grounded if implies that the distance can be measured or estimatedvia wireless communication.
• genericA graph is called generic if node coordinates are algebraically independentover rationals.
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No
Choose node to become initial-
anchor
Check if all nodes are localized
Output a feasible initial-anchor set
Localization-Phase AnchorChoose-Phase
Yes
A graph G
Nodes with degree
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• Theorem:• Let be any feasible initial-anchor set of . For all
with degree , we have .
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No
Choose node to become initial-
anchor
Check if all nodes are localized
Output a feasible initial-anchor set
Localization-Phase AnchorChoose-Phase
Yes
A graph G
Trilateration
*Tri + Rigid
*Tri + Sweep2
Localization-Phase
Trilateration
Sweep2+Tri
Rigid+Tri
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initial-anchor unknownanchor
Trilateration
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initial-anchor unknownanchor
Trilateration
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initial-anchor unknownanchor
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Sweep2(+Tri)
𝑢 𝑣
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Sweep2(+Tri)
𝑢 𝑣
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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.
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Rigid(+Tri)
𝑢 SubgraphLocalizedsubgraph
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Rigid(+Tri)
𝑢 SubgraphLocalizedsubgraph
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Rigid(Tri)
𝑢 SubgraphLocalizedsubgraph
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No
Choose node to become initial-
anchor
Check if all nodes are localized
Output a feasible initial-anchor set
Localization-Phase AnchorChoose-Phase
Yes
A graph G
HuangChoose[2011]
*AdaptiveChoose*MaxDegreeChoose
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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
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No
Choose node to become initial-
anchor
Check if all nodes are localized
Output a feasible initial-anchor set
Localization-Phase AnchorChoose-Phase
Yes
A graph G
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No
Choose node to become initial-
anchor
Check if all nodes are localized or
Output an initial-anchor set and
Localization-Phase AnchorChoose-Phase
Yes
A graph G |𝑆|≤𝑘
: The set of nodes that know their positions
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Simulation
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Simulation
• Localization-Phase– Trilateration (LocalTri)– Sweep2
• AnchorChoose-Phase– HuangChoose ([8] 2005, Huang et al.)– AdaptiveChoose– MaxDegreeChoose (MaxDegree)
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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,
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Average Degree
G200 nodes in 1200m 1000m
R=80
6.56 3.30%Vary Sparse*
200 nodes in 1200m 1000m R=70, k=100 and 120
1.19%Sparse*
200 nodes in 800m 600m R=70, k=30 and 50
5~7 2.89%Dense*
200 nodes in 800m 600mR=100, k=5 and 10
10~14 5.71%*200 graphs for each
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G
圖片來源 :Minimum cost localization problem in wireless sensor networks
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A=LocalTri IAF COVERAGEAdaptiveChoose No dataVary
SparseHuangChooseAdaptiveChoose The same
Sparse The same MaxDegreeAdaptiveChooseDense MaxDegreeAdaptiveChoose MaxDegreeAdaptiveChoose
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A=Sweep2 IAF COVERAGEAdaptiveChoose No dataVary
SparseHuangChooseAdaptiveChoose The same
Sparse HuangChooseAdaptiveChoose AdaptiveChooseMaxDegreeDense MaxDegreeAdaptiveChoose MaxDegreeAdaptiveChoose
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Concluding remarks
• Sweep2 are simpler than Sweep ([8] 2005, Huang) but cover all the cases.
• A new algorithm for rigid in Localization-Phase
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Future works
• A much powerful Greedy algorithms to choose anchors.
• Combine AdpativeChoose and HuangChoose to obtain better result.
• Given a certain initial-anchor set, determine what kind of graphs are localizable.
• Design a distributed version of AdaptiveChoose.
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Thank you for your attention!
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