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

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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!