A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks

1
A Beacon-Less Location Discovery Scheme for
Wireless Sensor Networks

• Lei Fang (Syracuse)
• Wenliang (Kevin) Du (Syracuse)
• Peng Ning (North Carolina State)

2
Location Discovery in WSN

• Sensor nodes need to find their locations
• Rescue missions
• Geographic routing protocols
• Many other applications
• Constraints
• No GPS on sensors
• Cost must be low

3
Existing Positioning Schemes
Beacon Nodes
4
Two Important Elements

• Reference points
• They must know their locations.
• e.g. beacon nodes, satellites.
• Relationship between nodes and reference points
• Distance
• Angle of arrival
• Time of arrival
• Time difference of arrival

5
The Beacon-Less Scheme

• Without using beacon nodes
• Beacon nodes are more expensive
• They can be the main target of attacks
• Nonetheless, we still have to find reference
  points and the corresponding relationships.
• Remember the locations of the reference points
  must be known.

6
A Group-Based Deployment Scheme
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A Group-Based Deployment Scheme
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Modeling of The Group-Based Deployment Scheme
Deployment Points Their locations are known.
We still need another important element The
relationship between nodes and reference points.
9
The Relationships
A
10
The Relationships
A
B
11
Modeling of the Deployment Distribution

• Using pdf function to model the node
  distribution.
• Example two-dimensional Gaussian Distribution.
• Other distribution can also be used.

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The Idea

• Observation at location O
• See more nodes from A and D than from H and I.
• Observation at location P
• Quit different from location O.
• See more nodes from H and I than from A and D.
• Given a location, we can derive the observation.
• Given the observation, can we derive the
  location?

13
The Problem Formulation
Observation a (a1, a2, an)
Location Estimation
Location ? (x, y)
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A Geometric Approach

• Pick the three nearest deployment points (the
  three highest ai values).
• Estimate the distance between the sensor and
  these points.
• MLE (Maximum Likelihood Estimation)
• f (Xi ai Z) The probability of
  observing ai nodes from Group i when
  the distance is Z.
• Find Z, such that f (Xi ai Z) is maximized.

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A More General Solution

• Instead of considering only three groups, we
  consider all the groups.
• a (a1, a2, an) The observation.
• fn(a ?) The probability of observing a at
  location ?.
• MLE Principle find ?, such that fn(a ?) is
  maximized.

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Maximum Likelihood Estimation

• Likelihood Function
• fn(a ?) Pr (X1a1, , Xnan ?)
• Pr (X1a1 ?) Pr (X1an
  ?)
• L(?) log fn(a ?)
• Find ?

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Finding ?

• Brute-Force Search search all possible ?.
• Small Area Search
• Find an initial point (accuracy can be low).
• Conduct brute-force search around the initial
  point.
• Gradient Descent A standard solution.

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Gradient Descent

• A 2-dimensional function is represented as a
  surface in a 3-dimensional space
• The maximum point (peak) holds a zero gradient
• Find the shortest path to reach the peak.
• Could be expensive

19
Evaluation

• Setup
• A square plane 1000 meters by 1000 meters
• 10 by 10 grids (each is 100m X 100m)
• s 50 (Gaussian Distribution)
• What to evaluate?
• Accuracy vs. Density
• Accuracy vs. Transmission Range
• Boundary Effects
• Computation Costs.

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Effect of Density m
An Improvement Dummy Nodes
m number of sensors in each group
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Effect of Transmission Range R
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Effect of Boundary
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Comparing the Three Numeric Approaches (Cost)
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Comparing the Three Numeric Approaches (Accuracy)
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Comparisons
Beacon-Less Beacon-Based
Communication Overhead Low Low
Computation Cost High Low
Device Cost Low High
Robustness/Security High Low
Mobility None Good
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Conclusion and Future Work

• Beacon-Less Location Discovery
• Formulate the location discovery problem as an
  estimation problem
• Use the Maximum Likelihood Estimation to solve
  the estimation problem
• Future work
• How the inaccuracy of the deployment model affect
  the result?
• Resilience and Security
• IPDPS05 paper (Best Paper Award in the Algorithm
  Track)
• Google Wenliang Du can get the paper.