Sensor Placement for Effective Coverage and Surveillance in Distributed Sensor Networks

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Sensor Placement for Effective Coverage
andSurveillance in Distributed Sensor Networks

• Santpal Singh Dhillon
• Krishnendu Chakrabarty
• Duke University
• Presented by
• Amit Pendharkar
• WISER Group, UH

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Introduction

• A Challenge - To determine a sensor field
  architecture
• Optimize cost
• Provides high sensor coverage
• Resilience to sensor failures
• Appropriate computation/communication trade-offs.
• Unified design and operation of sensor network
• Decreases the need for excessive network
  communication for surveillance, target location
  and tracking

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Deployment Problems

• Nature of the terrain buildings or trees
• Uneven surfaces and elevations for hilly terrains
• Redundancy due to the likelihood of sensor
  failures
• Power needed to transmit information between
  deployed sensors
• Power needed to transmit information between a
  deployed sensor and the cluster head

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Where to place sensors?
Field
Obstacles
Target
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Modeling

• Sensor field as a 2D grid of points
• A target in the sensor field is a logical object
• An irregular sensor field as a collection of
  grids
• Model is inherently probabilistic due to the
  uncertainty associated with sensor detections
• Two algorithms for sensor placement with
  constraints of imprecise detections and terrain
  properties
• Preferential coverage of grid points
• Fixed Sensors

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AGP and Sensor Network

• AGP Art gallery Problem
• How the guards should be placed to cover every
  point in the art gallery?
• Although there is a close resemblance, sensor
  placement differs in two ways
• the sensors can have different ranges unlike
  basic AGP
• unlike the intruder detection by guards, sensor
  detection outcomes are probabilistic

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Paper Organization

• Explanation of sensor detection model and model
  of terrain
• Algorithms how they can be extended for
  preferential coverage
• Experimental Results
• Comparison with random and uniform sensor
  placement

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Assumptions

• Better the sensor detection model -gt better the
  sensor placement solution
• Sensor field is made up of grid points
• Granularity of the grid determined by the
  accuracy with which sensor placement is desired
• Probability of target detection varies
  exponentially with distance i.e.
• a - models the quality of the sensor and the rate
  at which its detection probability diminishes
  with distance

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Assumptions

• For every two grid points i and j in the sensor
  field
• Pij probability that a target at grid point j
  is detected by a sensor at grid point i
• Pji probability that a target at grid point i
  is detected by a sensor at grid point j
• The values are symmetric in absence of obstacles
• i.e. Pij Pji

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Sensor Detection Model
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Sensor Detection Model

• Algorithms are independent of the model - Can be
  used for other models
• Obstacles are modeled by altering the detection
  probabilities Pij
• If there is an obstacle between i j Pij 0 or
  some small value for partial occlusion
• Given the location of obstacle, the probabilities
  are found by equation of line
• For some practical scenarios even if

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Sensor Detection Model
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Sensor Placement Algorithms

• Goal To determine the minimum number of
• sensors and their locations such that every grid
  point is covered with a minimum confidence level
• T Coverage Threshold. So every point in the
  field should be covered with probability of at
  least T
• MAX_AVG_COV To maximize the average coverage of
  the grid points
• MAX_MIN_COV To maximize the coverage of the
  grid point that is covered least effectively

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Terminology

• For n x n grid, total grid points
• Hence rows and columns
• Total elements
• Miss Probability Matrix
• Vector Set
  of miss probabilities for grid points
• Probability that grid point i is not
  collectively covered by the sensors in the field

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Algorithm

• is initialized to all 1 vector
• As the sensors get placed, the values in
  get modified
• As the sensor is placed, the order of M is
  decreased by 1 by deleting corresponding row and
  column
• the maximum value of the
  miss probability permitted for any grid point

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Algorithm MAX_AVG_COV
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Algorithm MAX_AVG_COV

• For preferential coverage,
• Protection Probability
• Miss probability threshold
• Hence for those important points the threshold is
  different

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Algorithm MAX_MIN_COV
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Algorithm MAX_MIN_COV

• First sensor is placed randomly
• At each iteration, place a sensor at a point with
  minimum coverage
• Coverage at every grid point is then updated
• Next sensor is placed at point of minimum
  coverage
• Process continues till limit on number of sensors
  is reached or the threshold of coverage is
  achieved

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Algorithm complexity

• Complexity is O(kN)
• k Number of sensors required for given coverage
  threshold
• k is not known, its the one that we find out
• So complexity is O(NN)
• Sensor detections are independent so for two
  sensors p1 p2,
• Miss Probability (1-p1)(1-p2)

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How about other points??

• Is the region between the grid points covered?

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Theorem
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Illustration of theorem

• Miss probability of centers is lt threshold
  theorem verified

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Experimental Results

• Comparison of algorithms with random placement
  and uniform placement
• In absence of obstacles, random placement is as
  effective as MAX_AVG_COV
• Random placement performance is worse when there
  are obstacles or when preferential coverage is
  required

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Case Study 1

• 2 dimensional grid with 8 points
• a 0.6
• Two obstacles deterministically placed
• Both algorithms outperform random placement

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Case Study 1
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Case Study 2

• 2 dimensional grid with 20 points
• a 0.5
• Random obstacles
• Both algorithms outperform random placement
• MAX_AVG_COV performs better than MAX_MIN_COV

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Case Study 2
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Case Study 3

• 2 dimensional grid with 8 points
• a 0.6
• Eight obstacles
• Both algorithms outperform random placement

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Case Study 3
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Case Study 4

• 2 dimensional grid with 8 points
• a 0.6
• Four obstacles
• For some points threshold miss probability 0.01

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Case Study 4
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Case Study 5

• 2 dimensional grid with 10 points
• a 0.5
• No obstacles
• Uniform placement outperforms random placement
• MAX_MIN_COV is the best

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Case Study 5
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Conclusion

• Optimization problem on sensor placement
• Minimum number of sensors get deployed
• Polynomial time algorithm
• Optimizes coverage under imprecise detections
  terrain
• Preferential coverage issue also addressed
• Algorithms indeed work better in each case

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• Questions?

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• Libraries for computational geometry

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CGAL

• Computational Geometric Algorithmic Library
• Open source project to provide easy access to
  efficient and reliable geometric algorithms in
  the form of a C library
• Used in computer graphics, scientific
  visualization, computer aided design and
  modeling, geographic information systems,
  molecular biology, medical imaging, robotics and
  motion planning, mesh generation, numerical
  methods

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CGAL

• Offers data structures and algorithms for
• Triangulations
• Voronoi Diagrams
• Operations on polygons
• Convex hull algorithms
• Shape analysis, fitting and distances etc
• No license required if used with open source
  software.

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CGAL

• Homepage
• http//www.cgal.org
• Example
• Convex Hull
• http//www.cgal.org/Manual/3.3/doc_html/cgal_manua
  l/Convex_hull_2/Chapter_main.html

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LEDA

• C class library for efficient data types and
  algorithms by Algorithmic Solutions Software GMBH
• http//www.algorithmic-solutions.com/leda/about/in
  dex.htm
• Professional/Research editions are really
  expensive

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Other Sources

• http//compgeom.cs.uiuc.edu/jeffe/compgeom/softwa
  re.html
• Wykobi
• http//www.wykobi.com/
• Fastgeo
• http//www.partow.net/projects/fastgeo/index.html