Sensor Deployment Strategy for Target Detection

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Sensor Deployment Strategy for Target Detection
Thomas Clouqueur, Veradej Phipatanasuphorn
Parmesh Ramanathan, Kewal K. Saluja
Acknowledgments DARPA grant F30602-00-2-055.
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Big picture
How to deploy sensors in region to monitor?
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Outline

• Sensor networks
• Target detection
• Evaluation of deployment
• Deployment strategy
• Analytical
• Simulation - Example
• Conclusion

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Sensor network model

• Set of nodes with ability to
• Sense environment (acoustic, seismic, )
• Process information
• Communicate with each other (e.g. wireless)
• Estimate their position (GPS)

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Target detection Unauthorized Traversal problem

• Target produces signal measurable by sensors
• Decaying with distance
• Corrupted by noise
• How to detect a target traversing region using
  path P?
• How to evaluate detection performance of a given
  sensor deployment?

Region to monitor
Target in
Target out
sensors
Path P
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Path detection

• Target is detected if it is detected at any point
  of path P
• Sensors collaborate for point detection
• Each sensor measures signal continuously
• Energy at sensor i is given by
• u position of target, K max energy
• position of sensor i, k decay factor,
  noise
• Signal energies of all sensors are fused every T
  seconds

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Fusion method data fusion

• Algorithm
• Exchange energy values
• Compare average energy to threshold
• Metrics
• Detection probability at point u
• False alarm probability (same at every point u)

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Path exposure definition

• The exposure of path P is the net probability of
  detecting a target that traverses the region
  using P
• Goodness of deployment is measured by the minimum
  exposure when considering all possible paths
  through the region

Path P1
Path P2
Exposure(P1) lt Exposure(P2)
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Finding least exposed path

• Path is subdivided into segments corresponding to
  detection attempts
• Assume target traveling at constant speed
• Detection probability associated with
• segment i reflects the measurements performed
• during time T
• Problem is to find least exposed path P, i.e.
  path that minimizes
• Path constrained on grid
• Compute least weight path P using Dijkstras
  algorithm

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Least exposed path example
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Deployment

• Problem formulation
• Assume
• Sensors randomly deployed, maximum of M sensors
  available
• Known target max energy K, and noise distribution
• Find a deployment strategy that results in a
  desired performance level for unauthorized
  traversal detection

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Deployment metrics

• Performance
• Minimum exposure
• False alarm rate
• Goal obtain desired minimum exposure at constant
  false alarm rate
• Cost
• Cost of individual sensors
• Cost of sensor deployment
• Tradeoff number of sensors vs number of
  deployments

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Deployment proposed solution

• Strategy
• Deploy part of the sensors
• Figure sensors position and determine if desired
  performance is reached
• If not, deploy more sensors until desired
  performance is reached or until M sensors are
  deployed
• Problem
• For given performance level, find the optimal
  number of sensors to deploy at each step to
  minimize cost

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Cost expression

• Expected cost
• cdf of min exposure when n sensors are
  deployed
• number of sensors deployed after step i
• cost of deployment
• cost of each sensor

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Simulation

• Goal determine distribution of minimum exposure
• Simulator implements algorithm to find minimum
  exposure for given deployment and collects
  statistics
• Example with following settings
• Chi square noise distribution
• Signal characteristics K60, k2
• Uniformly distributed deployment over 20x20
  region
• Fixed false alarm probability of 5 for path of
  20 segments

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Simulation results

• pdf for minimum exposure

• function of n

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Result for cost

• Assuming p sensors are deployed at every step (
  )

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Conclusion

• Summary
• Method for collaborative target detection with
  sensors
• Method to derive exposure of paths for given
  deployment
• Strategy for sensor deployment to achieve desired
  exposure at minimum cost
• Future work
• Investigate impact of faults on deployment
• Investigate sensor deployment strategy for other
  applications such as target localization