Area Coverage

Area Coverage

Sensor Deployment and Target Localization in Distributed Sensor Networks

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Area Coverage

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Area Coverage Objective

Maximize the coverage for a given number of sensors within a wireless sensor networks.

Propose a Virtual force algorithm (VFA)

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Area Coverage Virtual Force Algorithm(VFA)

Attractive force

Repulsive force

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Each sensor behaves as a “source of force” for all other sensors

S2

S1

S3

S4

F13

→

F12→Attractive force

Repulsive force F14=0→

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Fij: the vector exerted on Si by another sensor Sj

Obstacles and areas of preferential coverage also have forces acting on Si

FiA : the total (attractive) force on Si due to preferential coverage areas

FiR : the total (repulsive) force on Si due to obstacles

The total force Fi on Si

→

→

→

→

iRiA

k

ijjiji FFFF

,1

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Uses a force-directed approach to improve the coverage after initial random deployment

Advantages Negligible computation time Flexibility

Area Coverage

Movement-Assisted Sensor Deployment

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Area Coverage Motivation senso

r

sensing

range

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Area Coverage Deploying more static sensors cannot solve the

problem due to wind or obstacles

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Area Coverage

Detecting

coverage

hole

Move to

heal the hole

General idea:

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Area Coverage Coverage Hole Detection

sensing range

Only check local Voronoi cell

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Area Coverage

Calculate the target

location(by VEC, VOR or Minimax)

Coverage hole exists?

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Area Coverage The VECtor-Based Algorithm (VEC)

Motivated by the attributes of electrical particles Virtual force pushes sensors away from dense area

B

C

AB

C

A

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Area Coverage The VORonoi-Based Algorithm (VOR)

Move towards the farthest Voronoi vertex Avoid moving oscillation: stop for one round if move

backwards

B

M

BM

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Area Coverage The Minimax Algorithm

Move to where the distance to the farthest voronoi vertex is minimized

BM

NB

M

N

Target Coverage

Energy-Efficient Target Coverage in Wireless Sensor Networks

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Area coverage problem Sensing overall area Minimizing active nodes Maximizing network lifetime

Target Coverage

Active

Sleep

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Target coverage problem Sensing all targets Minimizing active nodes Maximizing network lifetime

Target Coverage Target

Active

Sleep

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Target Coverage Disjoint Set Covers

Divide sensor nodes into disjoint sets Each set completely monitor all targets One set is active each time until run out of energy Goal: To find the maximum number of disjoint sets This is NP-Complete

Disjoint set cover same time

interval

Non-disjoint set cover different time interval

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Target Coverage

r1

r2

r3

s3

s1

s2

s4

All sensors are activeLifetime = 1

s3

s2

s1

s4

r2

r1

r3

Sensor Target

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Target Coverage

r1

r2

r3

s3

s1

s2

s4

Disjoint setsS1 = {s1, s2}S2 = {s3, s4}Lifetime = 2

s3

s2

s1

s4

r2

r1

r3

Sensor Target

Target Coverage

r1

r2

r3

s3

s1

s2

s4

s3

s2

s1

s4

r2

r1

r3

Another Approach:

S1 = {s1, s2} with t1 = 0.5

S2 = {s2, s3} with t2 = 0.5

S3 = {s1, s3} with t3 = 0.5

S4 = {s4} with t4 = 1

Lifetime = 2.5

t1 t2 t3 t4

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Target Coverage

r1

r2

r3

s3

s1

s2

s4

s3

s2

s1

s4

r2

r1

r3

Minimum Set elementS1 s1, s2

S2 s1, s3

S3 s2, s3

S4 s4

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Set active interval = 0.5 choose a available set

Target Coverage

remainder life time

s1 1

s2 1

s3 1

s4 1

remainder life time

0.5

0.5

1

1

S1remainder

life time

0

0.5

0.5

1

S2remainder

life time

0

0

0

1

S3remainder

life time

0

0

0

0.5

S4remainder

life time

0

0

0

0

S4

This order is not unique, tried all the orders and pick up the order with the maximum life time

Minimum Set elementS1 s1, s2

S2 s1, s3

S3 s2, s3

S4 s4

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Target Coverage Maximum Set Covers (MSC) Problem

Given: C : set of sensors R : set of targets

Goal: Determine a number of set covers S1, …, Sp and t1,…, tp

where: Si completely covers R Maximize t1 + … + tp

Each sensor is not active more than 1 MSC is NP-Complete

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Target Coverage Using Linear Programming Approach Given:

A set of n sensor nodes: C = {s1, s2, …, sn} A set of m targets: R={r1, r2, …, rm} The relationship between sensors and targets:

Ck = {i|sensor si covers target rk}

C = {s1, s2, s3}; R = {r1, r2, r3}C1 = {1, 3}; C2 = {1, 2}; C3 = {2, 3}

Variables: xij = 1 if si ∈ Sj, otherwise xij = 0 tj [0, 1], represents the time allocated for ∈ Sj

s3

s2

s1

r2

r1

r3

)1(1,0

,..,1,1

1

...

1

1

jiijij

Cikij

ij

p

jij

p

Ssiffxxwhere

pjRrx

Cstxtosubject

ttMaximize

k

maximize network lifetime

sensor’s lifetime constraint

all targets must be covered

Target Coverage

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Barrier Coverage

Strong Barrier Coverage of Wireless Sensor Networks

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Barrier Coverage

USA

MEXICO

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Barrier Coverage How to define a belt region?

Parallel curves Region between two parallel curves

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Barrier Coverage Two special belt region

Rectangular:

Donut-shaped:

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Barrier Coverage Crossing paths

A crossing path is a path that crosses the complete width of the belt region.

Crossing paths Not crossing paths

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Barrier Coverage

Weak barrier coverage

Strong barrier coverage

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Barrier Coverage k-covered

A crossing path is said to be k-covered if it intersects the sensing disks of at least k sensors.

3-covered 1-covered 0-covered

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k-barrier covered A belt region is k-barrier covered if all crossing paths are k-

covered.

Barrier Coverage

Not barrier coverage

1-barrier coverage

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Reduced to k-connectivity problem Given a sensor network over a belt region Construct a coverage graph G(V, E)

V: sensor nodes, plus two dummy nodes L, R E: edge (u,v) if their sensing disks overlap

Region is k-barrier covered if L and R are k-connected in G.

Barrier Coverage

L R

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Barrier Coverage3-

barrier

3-barrier

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Barrier Coverage Characteristics

Improved robustness of the barrier coverage Lower communication overhead and computation costs Strengthened local barrier coverage

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failurefailure

without vertical strip with vertical strip

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Surface Coverage in Wireless Sensor Networks

IEEE INFOCOM 2009

Ming-Chen Zhao, Jiayin Lei, Min-You Wu, Yunhuai Liu, Wei Shu

Shanghai Jiao Tong Univ., Shanghai

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Motivation Existing studies on Wireless Sensor Networks

(WSNs) focus on 2D ideal plane coverage and 3D full space coverage.

The 3D surface of a targeted Field of Interest is complex in many real world applications.

Existing studies on coverage do not produce practical results.

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Motivation In surface coverage, the targeted Field of

Interest is a complex surface in 3D space and sensors can be deployed only on the surface.

Existing 2D plane coverage is merely a special case of surface coverage.

Simulations point out that existing sensor deployment schemes for a 2D plane cannot be directly applied to surface coverage cases.

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Introduction volcano monitoring

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Introduction Surface Coverage

use triangularization to partition a surface

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Models Sensor models

sensing radius r in 3D Euclid space statically deployed

Surface models z = f(x, y)

z = c, if the surface is a plane ax + by + c, if the surface is a slant

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Problem Statement Problems in WSN surface coverage:

1. The number of sensors that are needed to reach a certain expected coverage ratio under stochastic deployment.

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Problem Statement Problems in WSN surface coverage:

2. The optimal deployment strategy with guaranteed full coverage and the least number of sensors when sensor deployment is pre-determined.

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Optimum Partition Coverage Problem (OPCP) Convert optimum surface coverage problem

to a discrete problem and then relate those results back to the original continuous problem.

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S: P = {SA, SB, SC, SD, SE, SF}

　　　　　　　　　　　　　　 h*(Lα)=h(1)∪h(3)∪h(4)∪h(5)　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 Lα = {1, 3, 4, 5}

　　　　　　　　　　　　　　 |Lα| = 4

　　　　　　　　　　　　　　 Lβ = {3, 6, 7}

　　　　　　　　　　　　　　 |Lβ| = 3　minimum

Optimum Partition Coverage Problem (OPCP)

A BC

DEF

2

4

37

5

16

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Algorithm 1: Greedy algorithm


A BC

DEF

1

2

4

5 37

6

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Greedy algorithm selects a position that can increase the

covered region the most Time complexity

O(|P|2) log (|P|) approximation algorithm

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Trap Coverage

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Motivation Tracking of movements such as that of

people, animals, vehicles, or of phenomena such as fire can be achieved by deploying a wireless sensor network.

Real-life deployments, will be at large scale and achieving this scale will become prohibitively expensive if we require every point in the region to be covered (i.e., full coverage), as has been the case in prototype deployments.

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Motivation Trap Coverage scales well with large

deployment regions.

A sensor network providing Trap Coverage guarantees any moving object can move at most a displacement before it is guaranteed to be detected by the network.

Trap Coverage generalizes the real model of full coverage by allowing holes of a given maximum diameter.

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Trap Coverage: Allowing Coverage Holes of Bounded Diameter in Wireless Sensor Networks

Paul Balister, Santosh Kumar, Zizhan Zheng, and Prasun Sinha IEEE INFOCOM 2009

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Introduction Real-life deployments, will be at large scale

and achieving this scale will become prohibitively expensive if we require every point in the region to be covered (i.e., full coverage), as has been the case in prototype deployments.

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Introduction Trap Coverage

Guarantees that any moving object or phenomena can move at most a (known) displacement before it is guaranteed to be detected by the network.

Hole Diameter

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Introduction Trap Coverage

d is the diameter of the largest hole Full Coverage: d is set to 0

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Introduction Define a Coverage Hole in a target region of

deployment A to be a connected component1 of the set of uncovered points of A.

Trap Coverage with diameter d to A if the diameter of any Coverage Hole in A is at most d.

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Estimating the Density for Random Deployments Example of Poisson deployment

holes of larger diameters are typically long and thin

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Computing the Trap Coverage Diameter Discovering Hole Boundary Diameter Computation Coping with Sensing Region Uncertainty

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Computing the Trap Coverage Diameter Discovering Hole Boundary

Boundary node

S1 S2

Boundary node

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Computing the Trap Coverage Diameter Discovering Hole Boundary

Hole Boundary: hole loop–outermost curves

diamH

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Diameter Computation Crossing: intersection point of perimeters

Computing the Trap Coverage Diameter

diamXH

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Diameter Computation Crossing: intersection point of perimeters

Computing the Trap Coverage Diameter

diamXH +2D

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Computing the Trap Coverage Diameter Diameter Computation

H : denote a hole loop XH : denote the set of crossings on the loop

Crossing: an intersection point of either two sensing perimeters

D : the maximum diameter of all sensing regions

Lemma 5.1: diamXH ≤ diamH ≤ diamXH

+2D

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Adaptive k-Coverage Contour Evaluation and Deployment in Wireless Sensor Networks This paper, considers two sub-problems: k-

coverage contour evaluation and k-coverage rate deployment.

The former aims to evaluate the coverage level of any location inside a monitored area, while the latter aims to determine the locations of a given set of sensors to guarantee the maximum increment of k-coverage rate when they are deployed into the area.

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k-Fully covered and k-partially covered An area A’ is called to be fully covered by a

sensor s if each point in A’ is covered by s. A’ is called to be partially covered by s if some

points in A’ are covered by s and some are not. If A’ is not fully covered or partially covered by

any sensor, then A’ is uncovered. For simplicity, an area fully covered by exactly

k distinct sensors is called to be exactly k-fully and an area partially covered by exactly k distinct sensors is called to be exactly k-partially covered.

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An example of fully covered, partially covered, and uncovered grids. Each grid has side length r/2.

g1 g5

Zero-Partially Covered

Non-Zero Partially Covered

g4 g2

g3 s2

s1

s3

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k-COVERAGE CONTOUR EVALUATION SCHEME (K-CCE) When a grid g is partially covered by s,

evaluating what percentage of g is covered by s requires complex computation.

The matter goes worse as grids are partially covered by more than one sensor.

Instead of applying complex computation, we can divide the grid into sub-grids to obtain more precise coverage information.

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da bc

Zero - Partially Covered Grid

2-Fully Covered Grid

s2

Uncertain Grids1

s3

An example of each grid with side length r/4.

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K-CCE Besides, for k-coverage contour evaluation,

grids which are fully covered by at least k sensors do not need any more division. Hence, division shall be performed on those grids which are partially covered by at least one sensor and fully covered by less than k distinct sensors.

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s2

Zero - Partially Covered Grid

2-Fully Covered Grid

Uncertain Grids1

s3

An example of non-uniform-sized grids.

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Maximum Tolerable Evaluation Error (MTEE) Maximum Evaluation Error (MEE) is the ratio of

uncertainly covered area relative to whole monitored area, i.e., MEE = ∑g U |g|/|A|, where U denotes the set of uncertain grids, and |g| and |A| denote the area size of g and A, respectively.

Maximum Tolerable Evaluation Error (MTEE) is the maximum evaluation error that is permitted for a target application.

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An example of grid division.

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k-COVERAGE RATE DEPLOYMENT SCHEME (K-CRD) The basic idea of this scheme is to deploy

sensors to locations that increase the total area of k-fully covered grids most economically

Given a grid g, we define a deployment region with respect to g, denoted by DR(g), as an area within which a sensor is deployed can fully cover g.

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The original deployment region with respect to grid g.

The dashed circle is a simplified deployment region with respect to grid g.

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Two Heuristics We employ the following two heuristics to deploy

the sensors economically (in terms of the number of sensors used).

First, consider λ = {max i | there exists some grid g that is i-fully covered and i < k}. It is clear that deploying sensors to fully cover the λ-fully covered grids improves the k-coverage rate

Second, define a candidate grid to be a λ -fully covered grid. Among all candidate grids, deploying sensors to fully cover the ones with the largest area is an even more economic way.

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Intersection of deployment regions. (a) Intersection of DR(g1) and DR(g2); (b) Points Pb Pc, and Pe are best_fits.

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k-CRD1 Define grid-weight of grid g, GW(g), to be |

g| if g is a candidate grid and 0 otherwise. The main idea is based on the observation

that there is a high possibility that a best_fit is a fit with respect to a higher-grid-weight grid.

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The first three candidate grids are at left-up, right-up, and left-down corner.

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k-CRD1 Clearly, fits with respect to grids at left-up, right-up,

and left-down corner are in I1, I2, and I3, respectively. Besides, fit with respect to the grid at left-down

corner has the highest weight. So, we deploy a sensor in fit with respect to grid at left-down corner.

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k-CRD2 In order to further reduce the computation

cost, the main motivation of scheme k-CRD2 is to avoid high computation cost of determining fits.

In k-CRD2, only highest-grid-weight candidate grids are considered.

Let C1 denote the set of highest-grid-weight candidate grids. Randomly choose a candidate grid g from C1. Deploy k sensors at a point p satisfying that (1) p is located in DR(g); and (2) maximal number of grids in C1 can be fully

covered.

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An example of 4-CRD2. C1={g1, g2, … , g8 }.

Randomly choose a grid fromC1, say g6. Then deploy (4-3) sensor at point u because maximum number of grids (i.e., g5 and g6) in C1 can be fully covered.

Documents

Area Coverage