Mobile Assisted Localization in Wireless Sensor Networks N.B. Priyantha, H. Balakrishnan, E.D. Demaine, S. Teller MIT Computer Science

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Mobile Assisted Localization in Wireless Sensor
NetworksN.B. Priyantha, H. Balakrishnan, E.D.
Demaine, S. TellerMIT Computer Science

• Presenters
• Puneet Gupta
• Sol Lederer

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Case for Mobile Assisted Localization

• Obstructions, especially in indoor environments
• Sparse node deployments
• Geometric dilution of precision (GDOP)
• Hence, finding 4 reference points for each node
  for localization is difficult

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Overview of scheme

• Initially no nodes know their location
• Mobile node finds cluster of nearby nodes
• Explores visibility region and measures
  distance
• of measurements required is linear in the of
  nodes
• Virtual nodes are discarded

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Theorem 1

• 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 nodes.

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MAL Distance Measurement

• First case Two nodes, n0 and n1 , single unknown
  n0 - n1
• Adding mobile node, m, introduces 3 unknowns (mx,
  my, mz), making problem more difficult
• Necessary condition deg of freedom (unknowns
  knowns) 0.
• Solution Use three mobile locations along the
  same line in a plane containing n0 and n1

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Case of 2 nodes solved

• 6 constraints from measurements of ni mj
  for I 0,1 and j 0,1,2
• Extra constraint obtained from colinearity of
  mobile points
• unknowns knowns 0
• Solve system of polynomial equations

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Case of 3 nodes

• Three nodes, n0 n1 n2, three unknowns, n0 -
  n1 n1 - n2 n0 - n2
• Each mobile position gives unknowns (mx, my, mz)
  3 constraints (m ni, i 0,1,2) 3
• Three additional constraints needed

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Case of 3 nodes ? Solution

• Restriction All mobile positions lie in a common
  plane
• k mobile locations ? k-3 additional co-planarity
  constraints
• Solution k 6, geometry of n0, n1, n2 above
  the plane containing 6 coplanar points m0, m1,
  m2, m3, m4, m5 no three of which are collinear,
  determined by the distances mi - nj, i 05
  j 0...2

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Case of 4 or More

• Number of nodes j 4
• Initially Number of unknowns (3j 5)
• 3 coordinates per node
• Minus 3 deg of translational motion
• Minus 2 deg of rotational motion
• Each mobile node adds (j 3) deg of freedom (j
  distances 3 coordinates of mobile position)
• j 3 gt 1

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Case of 4 or more ? Solution

• Require at least (3j 5)/(j 3) mobile
  positions
• E.g. for j 4, required mobile positions to
  uniquely determine the geometry 7
• But, no 4 of the 11 nodes (4 7) may be coplanar

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MAL Movement Strategy

• Initialize
• Find 4 nodes that can all be seen from a common
  location
• Move the mobile to 7 nearby locations measure
  distances
• Compute pair-wise distances
• Loop
• Pick a localized stationary node (not yet
  considered by this loop)
• Move mobile in perimeter of this node, searching
  for positions to hear a non-localized node
• Localize this node

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AFL Anchor-free localization

• Elect five nodes as shown
• Get crude coordinates based on hop count to
  anchors

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AFL

• Use non-linear optimization algorithm to minimize
  sum-squared energy E
• Coordinate assignments satisfy all 1-hop node
  distances when E 0

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• Graph from running AFLusing RF connectivity
  information
• Graph obtained by MAL

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Performance

• Layout of nodes in test scenario

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Estimate error
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Critique

• Pros
• Innovative stategy
• Cons
• In a cumbersome terrain (e.g. forest) it may not
  be feasible to deploy a roving node.

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The End