A New Hybrid Wireless Sensor
Network Localization System
Ahmed A. Ahmed, Hongchi Shi, and Yi Shang
Department of Computer Science
University of Missouri-Columbia
Columbia, Missouri, USA
Outline
Introduction
Related Work
Network Properties
Adaptive Localization System (ALS)
Experimental Results
Conclusion
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Introduction
A wireless sensor network is represented
as an undirected connected graph with
vertices (nodes) V and edges E.
Edges are:
– Connectivity information or
– Estimated distances to neighbors.
Some of the nodes are anchors (with
known positions).
Relative vs. absolute localization.
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Related Work (1/3)
Ad-hoc Positioning System (APS)
Niculescu et al., GLOBECOM’01
1. Each anchor k
– broadcasts its position,
– receives the positions of all m anchors, and
– computes the shortest-path distance p to each anchor.
2. Each anchor k computes its distance correction value, ck.
3. Each unknown node
– computes the corrected shortest-path distances to all anchors, and
– multilaterates based on all anchors to determine its position.
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Related Work (2/3)
MultiDimensional Scaling (MDS-MAP)
Shang et al., MobiHoc’03.
1. Set the range for local maps to Rlm.
2. Compute relative maps for individual nodes
within Rlm .
– Compute all-pair shortest paths.
– Apply MDS to the distance matrix and construct the
local maps.
3. Merge the relative maps to form one global
map.
4. Given sufficient anchors, transform the relative
map to an absolute one.
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Related Work (3/3)
SemiDefinite Programming (SDP)
Biswas et al., IPSN’04
The problem is considered in the presence of
measurement errors.
By introducing slack variables and then relaxing
the problem, it is rewritten as a standard SDP
problem.
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Network Properties
1.
Network topology
–
–
–
2.
3.
Average network connectivity
Measurement error
–
–
–
4.
5.
Random uniform (isotropic)
Grid
C-shape (anisotropic)
Received Signal Strength Indicator (RSSI)
Time of Arrival (ToA)
Time Difference of Arrival (TDoA)
Anchor ratio
Anchor placement
–
–
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Random
Outer
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Adaptive Localization System (ALS)
Phase 1: Discover network properties.
Phase 2: Run the three localization
methods: APS, MDS, and SDP.
Phase 3: Using the appropriate weights,
compute the weighted centroid of the three
position estimates.
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Simulation Setup
Total # of network instances = 2 X 8 X 3 X 3 X 2 = 288
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Topologies
Isotropic network, 100 nodes
Average node connectivity = 14.7
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Anisotropic network, 100 nodes
Average node connectivity = 14.9
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Determining the Weights (1/2)
Find the values of the weights that give the
minimum localization error under a specific set
of network properties.
Train off-line using 30 network instances for
every one of a 288-combination set.
Find the values of the weights by solving the
constrained linear least-squares problem.
Test on a different set of 30 networks for every
combination.
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Determining the Weights (2/2)
For node i, let
–
–
–
–
xi = [xi yi]T be the true position,
xia = [xia yia ]T be the estimated position using APS,
xim = [xim yim ]T be the estimated position using MDS,
xis = [xis yis ]T be the estimated position using SDP,.
Define the weighted centroid of the three
estimates as xic = [xic yic ]T where
xic = wa xia + wmxim + wsxis
yic = wa yia + wmyim + wsyis
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Experimental Results (1/4)
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Experimental Results (2/4)
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Experimental Results (3/4)
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Experimental Results (4/4)
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Conclusion
We have identified 5 network properties that may affect
performance.
We present our Adaptive Localization System (ALS)
method based on 3 existing algorithms. ALS has 3
phases:
1. Discover network properties.
2. Run three localization methods.
3. Compute a new position estimate that is the weighted centroid of
the three estimates.
We use machine learning to compute the values of the
weights.
ALS outperforms the individual algorithms under a broad
range of networks conditions.
In the future, we will consider
– the performance-cost tradeoff in localization.
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Thanks!
Questions / Comments
?
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