Mobileassisted localization in wireless sensor networks

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Mobile-assisted localization in wireless sensor
networks

• Authors N. B. Priyantha, H. Balakrishnan,
  E. D. Demaine, and S. Teller
• From IEEE INFOCOM, vol. 1, pp. 172-183,
  Mar. 2005.
• Date 2005/11/29

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Outline

• Introduction
• Related work
• The case for mobile-assisted localization
• Theoretical framework and movement strategies
• Anchor-free localization
• Performance evaluation
• Conclusion

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1. Introduction

• Implement a localization algorithm in real-world
  system
• Prob. 1 physical obstacles
• Prob. 2 too few distance constraints to obtain a
  consistent coordinate assignment
• Mobility can help solve these problems
• Mobile-assisted localization
• A roving robot wanders through an area, collect
  distance info. between the nodes and itself.

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2. Related work

• User-friendly surveying tech. for location-aware
  systems
• Node localization using mobile robots in
  delay-tolerant sensor networks
• Networked robots flying robot navigation using a
  sensor net
• Localization of WSNs with a mobile beacon
• RADAR

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3. The case for mobile-assisted localization

• A localization algorithm
• needs a sufficient number of pairwise node
  distance to be able to compute node coordinates
  correctly.
• For indoor environment
• Obstructions
• Sparse node deployments
• Geometric dilution of precision (GDOP)

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4. Theoretical framework and movement strategies

• Connections to rigidity
• Engineering rigidity
• MAL distance measurement
• Calculating distance between two nodes
• Calculating distances between three nodes
• Calculating distances between four (or more) nodes

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• Global rigid in d dimensions
• The removal of any d vertices must leave the
  graph connected (d1 connectivity)
• The removal of any edge must leave the graph
  generically locally rigid.

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Engineering rigidity
TH1 a graph is globally rigid if it is formed by
starting from a clique of 4 non-coplanar nodes
and repeatedly adding a node connected to at
least 4 non-coplanar existing nodes.
P4
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MAL distance measurement
Mobile node
Computing distance between two nodes by measuring
distances from 3 points.
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• Proposition 2 the geometry of 5 coplanar points
  where are
  collinear, is determined by the distances
  for i 0, 1 and j 0, 1, 2
• Proposition 3 the geometry of 3 non-collinear
  points above the plane containing 6
  coplanar points no 3 of
  which are collinear, is determined by the
  distances for i 0, 1, 2 and j 0, 1,
  2, 3 ,4 ,5

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• Proposition 4 the geometry of 11 non-collinear
  points no 4 of which are coplanar,
  is determined by the distances for i
  1, 2, 3, 4 and j 1, 2, 3 ,4 ,5, 6, 7

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• MAL movement strategy
• Initialize
• Find 4 stationary nodes that can all be seen from
  a common mobile location
• Move the mobile to at least 7 nearby localtions
  and measure distances.
• Compute the pairwise distances between the 4
  stationary nodes
• Localize the resulting tetrahedron
• Loop
• Pick a stationary node that has been localized
  but not yet been examined by this loop (DFS)
• Move the mobile around the visibility region of
  that stationary node
• For each such mobile position
• Compute the distances among those 2, 3, or 4
  stationary nodes
• If the not-yet-localized stationary node now has
  4 known distances to localized stationary nodes,
  localize it according to TH 1.

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• TH 5 the mobile movement strategy described
  above is guaranteed to find a globally rigid
  graph on the stationary nodes of the type
  described in TH1 provided that such a graph can
  be constructed using 1 mobile
• TH 6 the number of distance measurements made by
  the mobile movement strategy described above is
  linear in the number of stationary nodes.
• TH 7 the total distance traveled by the
  depth-first mobile movement strategy described
  above is proportional to the product of the
  number of stationary nodes and the perimeter of a
  stationary nodes visibility region.

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5. Anchor-free localization (AFL)

• AFL runs in 2 phases
• Computes an initial coordinate assignment for
  nodes.Uses the shortest path hop count from
  these elected nodes to compute the initial
  coordinates of each node i.
• Uses a non-linear optimization algorithm to
  minimize the sum-squared energy

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The shortest path hop count between 3 and i The
range of the nodes in the graph dij denote the
(true) Euclidean distance between i and j
The computed distance between i and j obtained
from the current coordinate assignment of the
node The measured distance between the node i and
j obtained by MAL
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6. Performance evaluation

• End-to-end localization performance of MAL runing
  in conjunction with AFL
• Using 24-node real-world Cricket-based testbed.

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lt5 cm
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The node connectivity graph obtained by
MAL Mobile at 1592 pointsUsed 3 nodes at a time
approachDistance estimation algo. on 52
different triangles formed by different node
combinationsThe edge of these triangles
represented 59 unique edges connecting the nodes
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0.9
0.5
1.5
( edge length error)
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Graph obtained after running the AFL
initialization using RF connectivity information
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Coordinates obtained after running the AFL
optimization
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with r10
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7. Conclusion

• MAL method which employs a mobile user to assist
  in measuring distances between node pairs until
  these distance constraints from a globally rigid
  structure that guarantees a unique localization.