area coverage
DESCRIPTION
Area Coverage. Sensor Deployment and Target Localization in Distributed Sensor Networks. Area Coverage. Area Coverage. Objective Maximize the coverage for a given number of sensors within a wireless sensor networks. Propose a Virtual force algorithm (VFA). Area Coverage. - PowerPoint PPT PresentationTRANSCRIPT
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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Area Coverage Virtual Force Algorithm(VFA)
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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Area Coverage Virtual Force Algorithm(VFA)
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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Area Coverage Virtual Force Algorithm(VFA)
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
Optimum Partition Coverage Problem (OPCP)
A BC
DEF
1
2
4
5 37
6
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Optimum Partition Coverage Problem (OPCP)
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.