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A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks. Lei Fang (Syracuse) Wenliang (Kevin) Du (Syracuse) Peng Ning (North Carolina State). Location Discovery in WSN . Sensor nodes need to find their locations Rescue missions Geographic routing protocols

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a beacon less location discovery scheme for wireless sensor networks

A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks

Lei Fang (Syracuse)

Wenliang (Kevin) Du (Syracuse)

Peng Ning (North Carolina State)

location discovery in wsn
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
two important elements
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
the beacon less scheme
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.
modeling of the group based deployment scheme
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.

modeling of the deployment distribution
Using pdf function to model the node distribution.

Example: two-dimensional Gaussian Distribution.

Other distribution can also be used.

Modeling of the Deployment Distribution
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?

The Idea
the problem formulation
The Problem Formulation

Observation a = (a1, a2, … an)

Location

Estimation

Locationθ = (x, y)

a geometric approach
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.
a more general solution
A More General Solution
  • Instead of considering only three groups, we consider all the groups.

a = (a1, a2, … an): The observation.

fn(a|θ): The probability of observing a at location θ.

  • MLE Principle:find θ, such thatfn(a|θ)is maximized.
maximum likelihood estimation
Maximum Likelihood Estimation
  • Likelihood Function

fn(a|θ) =Pr (X1=a1, …, Xn=an|θ)

= Pr (X1=a1|θ) · · · Pr (X1=an|θ)

L(θ)=logfn(a|θ)

  • Find θ:
finding
Finding θ
  • Brute-Force Search: search all possible θ.
  • Small Area Search:
    • Find an initial point (accuracy can be low).
    • Conduct brute-force search around the initial point.
  • Gradient Descent: A standard solution.
gradient descent
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
evaluation
Evaluation
  • Setup
    • A square plane: 1000 meters by 1000 meters
    • 10 by 10 grids (each is 100m X 100m)
    • σ = 50 (Gaussian Distribution)
  • What to evaluate?
    • Accuracy vs. Density
    • Accuracy vs. Transmission Range
    • Boundary Effects
    • Computation Costs.
effect of density m
Effect of Density m

An Improvement:

Dummy Nodes

m: number of sensors in each group

conclusion and future work
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:
      • IPDPS’05 paper (Best Paper Award in the Algorithm Track)
      • Google “Wenliang Du” can get the paper.