Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks

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Robust Positioning Algorithms for
DistributedAd-Hoc Wireless Sensor Networks

• ECE 7360
• FISP(Optimal and Robust Control)
• Anisha Arora
• anishaarora_at_cc.usu.edu
• Nov 24, 2003

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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Plume Detection using wireless sensor networks.
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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion.
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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Positioning Problem Ad-hoc Sensor Networks

• lack of infrastructure inherent to ad hoc
  networks.
• all nodes are considered equal, making it
  difficult to rely on centralized computation to
  solve network wide problems, such as positioning.
• there must exist within this network a minimum of
  four anchor nodes.
• all nodes being considered in an instance of the
  positioning algorithm must be included in the
  same connected network.

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Two most essential problems
At least I think they are

• RANGE ERROR PROBLEM
• SPARSE ANCHOR NODE PROBLEM

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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Geometric Interpretation

• Goal of these algorithms
• To determine a specific nodes location within a
  given global coordinate system.
• Done using Triangulation
• Triangulation
• Geometric technique
• Uses edges between objects to determine position
• Unique position of an object in a two-dimensional
  space triangle
• Ties between objects, in the form of measured
  distances and angles

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Geometric Interpretation
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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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The Two-Phase Algorithm

• Split in two parts
• Start up phase
• Addresses the sparse anchor node problem
• Awareness of the anchor nodes positions
  throughout the network
• Allowing all nodes to arrive at initial position
  estimates
• Refinement phase
• Uses the results of the start-up phase
• Improves upon initial position estimates
• Range error problem is addressed
• End goal
• To deliver reliable position estimates to other
  parts of the system

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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The Two-Phase Algorithm

• Start up phase algorithm 1
• TERRAIN ALGORITHM
• Triangulation via extended range and redundant
  associated of intermediate node
• Each node makes several independent maps one map
  for each anchor node
• Once a node is included in sufficient number of
  maps then it aligns itself in the global co
  ordinate system
• Suppose the node makes three maps with respect to
  three anchor nodes then it can use the
  triangulation method to find its position

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TERRAIN ALGORITHM
Example
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Pros and Cons of TERRAIN

• Pros
• Helps to position a node globally without
  complicated arithmetic deductions
• Easy to covert from a two dimensional positioning
  to a three dimensional positional system
• Cons
• Unacceptably high tendency to exponentially
  intensify error levels
• Final position estimates are too noisy to be
  useful

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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The Two-Phase Algorithm

• Start up phase algorithm 2
• HOP TERRAIN ALGORITHM
• Finds number of routing hops from a node to each
  of anchor nodes in a network
• Multiplies the number of routing hops by a shared
  metric (average hop distance)
• Estimates range between node and each anchor node
• Use these computed ranges to find positions using
  the triangulation method
• Each anchor node initializes this algorithm by
  broadcasting its location and a hop count of zero

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The Two-Phase Algorithm

• The neighbors who hear this broadcast then
  broadcast this further just changing the hop
  count to 1
• This procedure continues till it reaches the
  normal node whose position we are trying to
  determine

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Pros and Cons

• Pros
• Reduces network traffic
• Simplistic approach
• Does not use the magnitude of range measured
• Checks to see if communication is established.
• Does not iteratively compound errors
• More robust
• Yields more accurate and consistent positions

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Possible Error In Hop Terrain Algorithm

• strange or difficult topologies may cause strange
  positioning errors in the Hop Terrain algorithm

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Possible Error In Hop Terrain Algorithm

• Nodes that are physically close to each other,
  but separated by the obstacle, will receive hop
  counts that are artificially large from having
  had to travel around the obstacle
• Distort the estimated ranges used to compute
  positions, thus distorting the positions
  themselves
• The best solution to this warping effect would be
  to add more anchor nodes in key locations to
  mitigate the distortion created by the obstacle

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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The Refinement Algorithm

• Objective
• Obtain more accurate positions using the
  estimated ranges between nodes
• Algorithm
• A node broadcasts its position estimate
• Receives the positions and corresponding range
  estimates from its neighbors
• Computes a least squares triangulation solution
  to determine its new position

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Refinement Algorithm

• Refinement revealed two important error causes
• Errors propagate fast throughout the whole
  network. If the network has a diameter d, then an
  error introduced by a node in step s has
  (indirectly) affected every node in the network
  by step sd because of the triangulate-hop-triangu
  late-hop pattern
• Some network topologies are inherently hard, or
  even impossible to locate. For example, a cluster
  of n nodes (no anchors) connected by a single
  link to the main network can be simply rotated
  around the entry-point into the network while
  keeping the exact same intra-node ranges.

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Refinement Algorithm

• To mitigate error propagation the Refinement
  algorithm was modified to include a confidence
  metric associated with each nodes position
• Confidence metrics (between 0 and 1) are used to
  weigh the equations when solving the system of
  linear equations
• Anchors immediately start off with confidence
  value of 1
• Unknown nodes start off at a low value (0.1) and
  may raise their confidence after subsequent
  Refinement iterations
• A node performs a successful triangulation it
  sets its confidence level to the average of its
  neighbors confidence levels
• Triangulations sometimes fail or the new position
  is rejected on other grounds. In these cases the
  confidence is set to 0, so neighbors will not use
  erroneous information of the inconsistent node in
  the next iteration

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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Average Position Error After Hop - TERRAIN (5
Range Errors)
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(No Transcript)
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Fraction Of Located Nodes(2 Anchors, 5 Range
Error)
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Range Error Sensitivity Of Hop - TERRAIN And
TERRAIN
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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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Obstacles to Accuracy

• Poor topology
• Exaggerated range errors
• Excessive node mobility
• Stationary obstacles, such as walls, could be a
  large problem for Hop-TERRAIN due to the falsely
  inflated hop counts that result
• Obstacles artificially create poor topologies,
  leading to inaccurately estimated extended ranges
• obstacles create sections of the network that
  have low connectivity levels, another example of
  poor topology
• some objects may move through a network

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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Areas for Improvement and Future Study

• Improve the engine that drives both of these
  algorithmsUse the least squares triangulation
  method instead of the triangulation method
• Attempt to alleviate the shortcomings of
  Refinement in the presence of high range errors
  is introduced

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Presentation Outline

• Background
• Why I chose this topic
• The Positioning Problem within Ad-hoc Sensor
  Networks
• Geometric interpretation
• Two phase algorithm
• Terrain algorithm
• Hop Terrain algorithm
• Refinement algorithm
• Simulation Results
• Obstacles to Accuracy
• Areas for future improvement
• Conclusion
• Papers Reviewed
• Robust Positioning Algorithms for Distributed
• Ad-Hoc Wireless Sensor Networks by Chris
  Savarese

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In Conclusion

• Would use Hop-TERRAIN Algorithm
• More robust
• Less sensitive to error
• Second phase use the refinement algorithm

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References

• http//bwrc.eecs.berkeley.edu/Publications/2002/th
  esis/robst_pstng_algrthms_dstrbtd_adhoc/Savarese_M
  S_Thesis_FINAL.pdf
• http//mas-net.ece.usu.edu/

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Any Questions ???
Thanks for your patience