AA New Hybrid Wireless Sensor New Hybrid Wireless Sensor Network Localization SystemNetwork Localization System

Ahmed A. Ahmed, Ahmed A. Ahmed, Hongchi ShiHongchi Shi, and Yi Shang, and Yi Shang

Department of Computer ScienceDepartment of Computer ScienceUniversity of Missouri-ColumbiaUniversity of Missouri-Columbia

Columbia, Missouri, USAColumbia, Missouri, USA

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OutlineOutline

IntroductionIntroduction

Related WorkRelated Work

Network PropertiesNetwork Properties

Adaptive Localization System (ALS)Adaptive Localization System (ALS)

Experimental ResultsExperimental Results

ConclusionConclusion

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IntroductionIntroduction

A wireless sensor network is represented A wireless sensor network is represented as an undirected connected graph with as an undirected connected graph with vertices (nodes) vertices (nodes) VV and edges and edges EE..Edges are:Edges are:– Connectivity information orConnectivity information or– Estimated distances to neighbors.Estimated distances to neighbors.

Some of the nodes are anchors (with Some of the nodes are anchors (with known positions).known positions).Relative vs. absolute localization.Relative vs. absolute localization.

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Related Work Related Work (1/3)(1/3)Ad-hoc Positioning System (APS)Ad-hoc Positioning System (APS)Niculescu et al., GLOBECOM’01

1. Each anchor 1. Each anchor kk– broadcasts its position,broadcasts its position,– receives the positions of all receives the positions of all mm anchors, and anchors, and– computes the shortest-path distance computes the shortest-path distance p p to each anchor.to each anchor.

2. Each anchor 2. Each anchor k k computes its distance correction value, computes its distance correction value, cckk..

3. Each unknown node3. Each unknown node– computes the corrected shortest-path distances to all anchors, andcomputes the corrected shortest-path distances to all anchors, and– multilaterates based on all anchors to determine its position.multilaterates based on all anchors to determine its position.

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Related Work Related Work (2/3)(2/3)MultiDimensional Scaling (MDS-MAP)MultiDimensional Scaling (MDS-MAP)Shang et al., MobiHoc’03.

1. Set the range for local maps to 1. Set the range for local maps to RRlmlm..

2. Compute relative maps for individual nodes 2. Compute relative maps for individual nodes within within RRlm lm ..– Compute all-pair shortest paths.Compute all-pair shortest paths.– Apply MDS to the distance matrix and construct the Apply MDS to the distance matrix and construct the

local maps.local maps.

3. Merge the relative maps to form one global 3. Merge the relative maps to form one global map.map.

4. Given sufficient anchors, transform the relative 4. Given sufficient anchors, transform the relative map to an absolute one.map to an absolute one.

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Related Work Related Work (3/3)(3/3)SemiDefinite Programming (SDP)SemiDefinite Programming (SDP)Biswas et al., IPSN’04

The problem is considered in the presence of The problem is considered in the presence of measurement errors.measurement errors.

By introducing slack variables and then relaxing By introducing slack variables and then relaxing the problem, it is rewritten as a standard SDP the problem, it is rewritten as a standard SDP problem.problem.

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NetworkNetwork PropertiesProperties

1.1. Network topologyNetwork topology– Random uniform (isotropic)Random uniform (isotropic)– GridGrid– C-shape (anisotropic)C-shape (anisotropic)

2.2. Average network connectivityAverage network connectivity3.3. Measurement errorMeasurement error

– Received Signal Strength Indicator (RSSI)Received Signal Strength Indicator (RSSI)– Time of Arrival (ToA)Time of Arrival (ToA)– Time Difference of Arrival (TDoA)Time Difference of Arrival (TDoA)

4.4. Anchor ratioAnchor ratio5.5. Anchor placementAnchor placement

– RandomRandom– OuterOuter

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Adaptive Localization System (ALS)Adaptive Localization System (ALS)

Phase 1Phase 1: Discover network properties.: Discover network properties.

Phase 2Phase 2: Run the three localization : Run the three localization methods: APS, MDS, and SDP.methods: APS, MDS, and SDP.

Phase 3Phase 3: Using the appropriate weights, : Using the appropriate weights, compute the weighted centroid of the three compute the weighted centroid of the three position estimates.position estimates.

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SimulationSimulation SetupSetup

Total # of network instances = 2 X 8 X 3 X 3 X 2 = 288

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TopologiesTopologies

Isotropic network, 100 nodesAverage node connectivity = 14.7

Anisotropic network, 100 nodesAverage node connectivity = 14.9

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Determining the Weights Determining the Weights (1/2)(1/2)

Find the values of the weights that give the Find the values of the weights that give the minimum localization error under a specific set minimum localization error under a specific set of network properties.of network properties.

Train off-line using 30 network instances for Train off-line using 30 network instances for every one of a 288-combination set.every one of a 288-combination set.

Find the values of the weights by solving the Find the values of the weights by solving the constrained linear least-squares problem.constrained linear least-squares problem.

Test on a different set of 30 networks for every Test on a different set of 30 networks for every combination.combination.

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Determining the Weights Determining the Weights (2/2)(2/2)

For node i, let– xi = [xi yi]T be the true position,

– xia = [xi

a yia ]T be the estimated position using APS,

– xim = [xi

m yim ]T be the estimated position using MDS,

– xis = [xi

s yis ]T be the estimated position using SDP,.

Define the weighted centroid of the three estimates as xi

c = [xic yi

c ]T where

xic = wa xi

a + wmxim + wsxi

s

yic = wa yi

a + wmyim + wsyi

s

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Experimental Results Experimental Results (1/4)(1/4)

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Experimental Results Experimental Results (2/4)(2/4)

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Experimental Results Experimental Results (3/4)(3/4)

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Experimental Results Experimental Results (4/4)(4/4)

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ConclusionConclusionWe have identified 5 network properties that may affect We have identified 5 network properties that may affect performance.performance.We present our Adaptive Localization System (ALS) We present our Adaptive Localization System (ALS) method based on 3 existing algorithms. ALS has 3 method based on 3 existing algorithms. ALS has 3 phases:phases:1.1. Discover network properties.Discover network properties.2.2. Run three localization methods.Run three localization methods.3.3. Compute a new position estimate that is the weighted centroid of Compute a new position estimate that is the weighted centroid of

the three estimates.the three estimates.

We use machine learning to compute the values of the We use machine learning to compute the values of the weights.weights.ALS outperforms the individual algorithms under a broad ALS outperforms the individual algorithms under a broad range of networks conditions.range of networks conditions.In the future, we will considerIn the future, we will consider– the performance-cost tradeoff in localization.the performance-cost tradeoff in localization.

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