Area Coverage Sensor Deployment and Target Localization in Distributed Sensor Networks

Area Coverage 2

 Objective  Maximize the coverage for a given number of sensors within a wireless sensor networks.  Propose a Virtual force algorithm (VFA) 3

Area Coverage  Virtual Force Algorithm(VFA)  Attractive force  Repulsive force 4

Area Coverage  Virtual Force Algorithm(VFA)  Each sensor behaves as a “source of force” for all other sensors S2S2 S1S1 S3S3 S4S4 F 13 → F 12 → Attractive force Repulsive force F 14 =0 → 5

Area Coverage  Virtual Force Algorithm(VFA)  F ij : the vector exerted on S i by another sensor S j  Obstacles and areas of preferential coverage also have forces acting on S i  F iA : the total (attractive) force on S i due to preferential coverage areas  F iR : the total (repulsive) force on S i due to obstacles  The total force F i on S i → → → → 6

Area Coverage  Virtual Force Algorithm(VFA)  Uses a force-directed approach to improve the coverage after initial random deployment  Advantages  Negligible computation time  Flexibility 7

Area Coverage Movement-Assisted Sensor Deployment

Area Coverage  Motivation sensor sensing range 9

Area Coverage  Deploying more static sensors cannot solve the problem due to wind or obstacles 10

Area Coverage Detecting coverage hole Move to heal the hole  General idea: 11

Area Coverage  Coverage Hole Detection sensing range Only check local Voronoi cell 12

Area Coverage Calculate the target location (by VEC, VOR or Minimax ) Coverage hole exists? 13

Area Coverage  The VECtor-Based Algorithm (VEC)  Motivated by the attributes of electrical particles  Virtual force pushes sensors away from dense area B C A B C A 14

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 B M 15

Area Coverage  The Minimax Algorithm  Move to where the distance to the farthest voronoi vertex is minimized B M N B M N 16

Target Coverage Energy-Efficient Target Coverage in Wireless Sensor Networks

 Area coverage problem  Sensing overall area  Minimizing active nodes  Maximizing network lifetime Target Coverage Active Sleep 18

 Target coverage problem  Sensing all targets  Minimizing active nodes  Maximizing network lifetime Target Coverage Target Active Sleep 19

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 20

Target Coverage r1r1 r2r2 r3r3 s3s3 s1s1 s2s2 s4s4 All sensors are active Lifetime = 1 21 s3s3 s2s2 s1s1 s4s4 r2r2 r1r1 r3r3 Sensor Target

Target Coverage r1r1 r2r2 r3r3 s3s3 s1s1 s2s2 s4s4 Disjoint sets S 1 = {s 1, s 2 } S 2 = {s 3, s 4 } Lifetime = 2 22 s3s3 s2s2 s1s1 s4s4 r2r2 r1r1 r3r3 Sensor Target

Target Coverage r1r1 r2r2 r3r3 s3s3 s1s1 s2s2 s4s4 s3s3 s2s2 s1s1 s4s4 r2r2 r1r1 r3r3 Another Approach: S 1 = {s 1, s 2 } with t 1 = 0.5 S 2 = {s 2, s 3 } with t 2 = 0.5 S 3 = {s 1, s 3 } with t 3 = 0.5 S 4 = {s 4 } with t 4 = 1 Lifetime = 2.5 t1t1 t2t2 t3t3 t4t4

Target Coverage r1r1 r2r2 r3r3 s3s3 s1s1 s2s2 s4s4 s3s3 s2s2 s1s1 s4s4 r2r2 r1r1 r3r3 24 Minimum Setelement S1S1 s 1, s 2 S2S2 s 1, s 3 S3S3 s2, s3s2, s3 S4S4 s4s4

 Set active interval = 0.5  choose a available set Target Coverage 25 remainder life time s1s1 1 s2s2 1 s3s3 1 s4s4 1 remainder life time S1S1 remainder life time S2S2 remainder life time S3S3 remainder life time S4S4 remainder life time S4S4  This order is not unique, tried all the orders and pick up the order with the maximum life time Minimum Setelement S1S1 s 1, s 2 S2S2 s 1, s 3 S3S3 s2, s3s2, s3 S4S4 s4s4

Target Coverage  Maximum Set Covers (MSC) Problem  Given:  C : set of sensors  R : set of targets  Goal:  Determine a number of set covers S 1, …, S p and t 1,…, t p  where:  S i completely covers R  Maximize t 1 + … + t p  Each sensor is not active more than 1  MSC is NP-Complete 26

Target Coverage  Using Linear Programming Approach  Given:  A set of n sensor nodes: C = {s 1, s 2, …, s n }  A set of m targets: R={r 1, r 2, …, r m }  The relationship between sensors and targets: C k = {i|sensor s i covers target r k } C = {s 1, s 2, s 3 }; R = {r 1, r 2, r 3 } C 1 = {1, 3}; C 2 = {1, 2}; C 3 = {2, 3}  Variables:  x ij = 1 if s i ∈ S j, otherwise x ij = 0  t j ∈ [0, 1], represents the time allocated for S j s3s3 s2s2 s1s1 r2r2 r1r1 r3r3 27

maximize network lifetime sensor’s lifetime constraint all targets must be covered Target Coverage 28

0 ≤ y ij ≤ t j ≤ 1 Target Coverage 29 relaxation

LP-MSC Heuristic Initial: G = 0 1. Let be the optimal solution of the LP formulated before 2. First approximation can be obtained as follows: 1) Set 2) For each k, choose an 3) Update the network lifetime 4) Update the remaining lifetime for each sensor Target Coverage 30

3. Iteratively repeat step 1 and 2 by solving this 4. Return G if there is no longer any set that can cover all targets Target Coverage 31

Barrier Coverage Strong Barrier Coverage of Wireless Sensor Networks

Barrier Coverage USA MEXICO 33

Barrier Coverage  How to define a belt region?  Parallel curves  Region between two parallel curves 34

Barrier Coverage  Two special belt region  Rectangular:  Donut-shaped: 35

Barrier Coverage  Crossing paths  A crossing path is a path that crosses the complete width of the belt region. Crossing pathsNot crossing paths 36

Barrier Coverage Weak barrier coverage Strong barrier coverage 37

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-covered1-covered0-covered 38

 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 39

 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 40

Barrier Coverage 41 3-barrier

Barrier Coverage 42  Characteristics  Improved robustness of the barrier coverage  Lower communication overhead and computation costs  Strengthened local barrier coverage 42 failure without vertical strip with vertical strip

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 43

Motivation 44  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.

Motivation 45  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.

Introduction  volcano monitoring 46

Introduction  Surface Coverage  use triangularization to partition a surface 47

Models 48  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

Problem Statement 49  Problems in WSN surface coverage:  1. The number of sensors that are needed to reach a certain expected coverage ratio under stochastic deployment.

Problem Statement 50  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.

Optimum Partition Coverage Problem (OPCP) 51  Convert optimum surface coverage problem to a discrete problem and then relate those results back to the original continuous problem.

Optimum Partition Coverage Problem (OPCP) 52  Definition  A Partition is a set defined on a surface S: P = {S 1, S 2,..., S k } which satisfies: S i ⊆ S(i = 1... k), S i ∩ i=j S j = ∅, and S i = S.  The function h : P → 2 P is a function defined on partition P.  The function h ∗ : 2 P → 2 P is a set function defined as: L ⊆ P, h ∗ (L) = h(t).  A set L satisfying L ⊆ P and h ∗ (L) ⊇ P.  The Optimum Partition Coverage Problem (OPCP) is defined as: minimize |L|, L is a feasible solution.

 S: P = {S A, S B, S C, S D, S E, S F } h * (L α )=h(1) ∪ h(3) ∪ h(4) ∪ h(5) L α = {1, 3, 4, 5} |L α | = 4 L β = {3, 6, 7} |L β | = 3 minimum Optimum Partition Coverage Problem (OPCP) 53 A B C D E F

 Algorithm 1: Greedy algorithm Optimum Partition Coverage Problem (OPCP) 54 A B C D E F

Optimum Partition Coverage Problem (OPCP) 55  Greedy algorithm  selects a position that can increase the covered region the most  Time complexity  O(|P| 2 )  log (|P|) approximation algorithm

Trap Coverage 56

Motivation 57  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.

Motivation 58  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.

Trap Coverage: Allowing Coverage Holes of Bounded Diameter in Wireless Sensor Networks Paul Balister, Santosh Kumar, Zizhan Zheng, and Prasun Sinha IEEE INFOCOM

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. 60

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. 61 Hole Diameter

Introduction  Trap Coverage  d is the diameter of the largest hole  Full Coverage: d is set to 0 62

Introduction 63  Define a Coverage Hole in a target region of deployment A to be a connected component 1 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.

Estimating the Density for Random Deployments 64  Example of Poisson deployment  holes of larger diameters are typically long and thin

Computing the Trap Coverage Diameter 65  Discovering Hole Boundary  Diameter Computation  Coping with Sensing Region Uncertainty

Computing the Trap Coverage Diameter 66  Discovering Hole Boundary  Boundary node S1S1 S2S2 Boundary node

Computing the Trap Coverage Diameter 67  Discovering Hole Boundary  Hole Boundary: hole loop–outermost curves diamH

 Diameter Computation  Crossing: intersection point of perimeters Computing the Trap Coverage Diameter 68 diam X H

 Diameter Computation  Crossing: intersection point of perimeters Computing the Trap Coverage Diameter 69 diam X H +2D

Computing the Trap Coverage Diameter 70  Diameter Computation  H : denote a hole loop  X H : 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: diamX H ≤ diamH ≤ diamX H +2D

71 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.

k-Fully covered and k-partially covered 72  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.

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

k-COVERAGE CONTOUR EVALUATION SCHEME (K-CCE) 74  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.

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

K -CCE 76  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.

77 An example of non-uniform-sized grids.

Maximum Tolerable Evaluation Error (MTEE) 78  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.

79 An example of grid division.

k -COVERAGE RATE DEPLOYMENT SCHEME (K-CRD) 80  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.

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

Two Heuristics 82  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.

83 Intersection of deployment regions. (a) Intersection of DR(g 1 ) and DR(g 2 ); (b) Points P b P c, and P e are best_fits.

k -CRD1 84  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.

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

k -CRD1 86  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.

k -CRD2 87  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 C 1 denote the set of highest-grid-weight candidate grids. Randomly choose a candidate grid g from C 1. Deploy k sensors at a point p satisfying that (1) p is located in DR(g); and (2) maximal number of grids in C 1 can be fully covered.

88 An example of 4-CRD2. C 1 ={g 1, g 2, …, g 8 }. Randomly choose a grid from C 1, say g 6. Then deploy (4-3) sensor at point u because maximum number of grids (i.e., g5 and g6) in C1 can be fully covered.