Coverage Towards a realistic coverage model Chenyang Lu - - PDF document

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Coverage

Chenyang Lu

Department of Computer Science and Engineering Washington University in St. Louis

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Outline

• Integrate coverage and connectivity
• Towards a realistic coverage model

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Motivation

• Challenge: achieve very long operational

lifetime on limited battery energy

– Habitat monitoring, structural monitoring…

• Solution: energy conservation protocols

– Activate a subset of nodes to provide “sufficient” service – Schedule the others to sleep

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“Sufficient” Service

• Sensing: K-Coverage

– Every point in a region is monitored by at least K nodes – Applications often require more than 1-coverage – Applications require different degrees of coverage

• Different algorithms, environments, user requirement
• Communication: N-Connectivity

– Multi-hop network remains connected when any (N-1) nodes fail – Applications often need more than 1-connectivity for fault tolerance and good communication performance

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Goal: Integrated Coverage and Connectivity Configuration

• Integrated: must guarantee both coverage and

connectivity

• Configurable: can (re-)configure the network to

different degrees of coverage and connectivity

• Decentralized: can scale well in large networks

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Limitations of Existing Protocols

• Treat connectivity and coverage in isolation

– Connectivity only: ASCENT, AFECA, GAF, SPAN… – Coverage only: exposure, Ottawa protocol… – Density: PEAS

• Lack configurability: can only guarantee a fixed

degree of coverage (e.g., 1-coverage)

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Our Approach

1. Analyze the geometric relationship between coverage & connectivity 2. Design the Coverage Configuration Protocol (CCP) 3. Integrate CCP with SPAN (connectivity maintenance protocol from MIT)

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Assumptions

• Disc models for coverage and communication

– Point p is covered by node v if |pv| < Rs

• Rs: sensing range

– Nodes u and v are directly connected if |uv| < Rc

• Rc: communication range
• Intuition: Rc/Rs is important!

Rc Rs

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Connectivity Coverage?

• Connectivity cannot guarantee coverage

regardless of Rc/Rs

– Connectivity does not require “connection” with a location with no node – Coverage must cover all locations in a region

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Coverage Connectivity?

If Rc/Rs ≥ 2 (the double-range property)

• A covered network is always connected
• K-coverage connectivity ≥ K
• K-coverage interior connectivity ≥ 2K

– Interior node: node whose sensing circle locates inside the region – Interior connectivity: number of nodes that must be removed to disconnect any two interior nodes

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Implication of Analysis

• If Rc ≥ 2Rs

– To achieve K-coverage and N-connectivity, only needs to guarantee max(K.N)-coverage Coverage Configuration Protocol (CCP) is sufficient

• If Rc < 2Rs

– The protocol must consider both coverage and connectivity. Need to integrate CCP with a connectivity maintenance protocol

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Sufficient & Necessary Condition for K-Coverage

• A region is K-covered iff each intersection point

(between two sensing circles or a sensing circle and the region boundary) in the region is K-covered

• Implication: CCP only needs to worry about intersection

points!

S

p

Every point in a “patch” surrounded by sensing circles has the same degree of coverage

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CCP: K-Coverage Eligibility Rule

• A node is eligible if there exists an intersection point in its sensing

circle that is not K-covered Needs knowledge about the locations of its sensing neighbors (active nodes within 2Rs) to assess eligibility

• Incomplete knowledge about sensing neighbors leads to extra

active nodes, but will not cause insufficient coverage Active nodes Sleeping nodes Intersection point

• n?

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CCP: State Transition

• SLEEP state

– Periodically wake up and enter LISTEN state

• LISTEN state

– Receive location beacons and announcements (join/withdraw) – If becomes eligible: enter active state after randomized bidding – Otherwise return to SLEEP state

• ACTIVE state

– Receive location beacons and announcements – If becomes ineligible: enter SLEEP state after randomized bidding Sleep Listen Active

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Coverage Configurability

2 4 6 8 10 1 2 3 4 5 6 7 Required Coverage degree Achieved Coverage degree Min-500,700,900 Average-500 Average-700 Average-900

CCP strictly enforced desired coverage degree!

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What if Rc < 2Rs?

• CCP alone does not always guarantee connectivity
• Solution: CCP + SPAN
• Combined eligibility rules

– A sleeping node becomes eligible if it is eligible under SPAN or CCP – An active node becomes ineligible only if it is ineligible under both SPAN and CCP

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Coverage & Connectivity (Rc/Rs = 1.5)

SPAN+CCP is necessary when Rc < 2Rs SPAN CCP SPAN+CCP

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Coverage vs Rc/Rs

0.2 0.4 0.6 0.8 1 0.5 1 1.5 2 2.5 3 Coverage Percentage Rc/Rs Coverage Percentage CCP-2Hop SPAN+CCP-2Hop CCP SPAN+CCP SPAN

• CCP and SPAN+CCP always guarantees coverage
• SPAN cannot guarantee coverage regardless of Rc/Rs

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Packet Delivery Ratio

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0.5 1 1.5 2 2.5 3 Packet delivery ratio Rc/Rs Packet Delivery Ratio CCP-2Hop SPAN+CCP-2Hop CCP SPAN+CCP SPAN

• CCP successfully delivered all packets when Rc/Rs > 2
• SPAN+CCP and SPAN had higher deliver ratio than CCP when

Rc/Rs < 2

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Summary: Integrated Coverage and Connectivity Configuration

• Relationship between coverage and connectivity

– Rc ≥ 2Rs: K-coverage K-connectivity – Rc < 2Rs: Must worry about both requirements

• CCP can efficiently (re-)configure a network to different

degrees of coverage

• CCP+SPAN can maintain both coverage and

connectivity when Rc < 2Rs

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Outline

• Integrate coverage and connectivity
• Towards a realistic coverage model

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Limitations of Existing Coverage Models

• Deterministic Sensing Model

– Hard artificial boundary between “sensed” and “not sensed” – Fail to capture stochastic nature of signals

• Ignore sensor fusion

Network Topology with Sensing Coverage

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Problem Formulation

• Minimize the number of active sensors

under the coverage constraint

– Geographic region A is covered if

PD(x,y) – Detection probability of active sensors at point (x,y) PF – False alarm rate

) ( ) ) , ( , ) , ( ( α β ≤ ∧ ≥ ∈ ∀

F D

P y x P A y x

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Signal Detection Model

• Sensor observation

– Noise: Gaussian distribution with mean 0 – Event: Gaussian distribution with mean μ

• Introduce signal decay into detection model

– Observed event signal power decays with distance (2~4 power) – μ = square root of the target signal power

• Signal locality

– Detection performance decreases with distance – A sensor does not contribute to PD (x,y) if point (x,y) is far away

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Data Fusion

• Decide local fusion groups
• Design a set of decision rules in

a fusion group

– Single sensor: Likelihood Ratio Test (LRT) is optimal – Fusion center: Majority rule is used

PF<α Local PF thresholds Local PDi(x,y) PD(x,y)

Majority Rule LRT

How to compute PD(x,y)? S1: sensors with decision 1 S0: sensors with decision 0 O(2n) combinations

Data Fusion

∑ ∏ ∏

> ∈ ∈

− =

| | | |

1 1

) , ( )) , ( 1 ( ) , (

S S S i S j Dj Di D

y x P y x P y x P

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Goals

• Minimize the number of active sensors to

reduce energy consumption

• Minimize coverage configuration time

– Online reconfiguration due to sensor failures

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Centralized Coverage Algorithm

• Single fusion group
• Fusion center runs a coverage algorithm

– Uses a greedy strategy to activate sensors – Computes local PF for active sensors

• Active sensors perform detection using LRT

based on local PF

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while (PDmin < β) { Find point p(x,y) with min PD(x,y) Activate the sensor closest to p Compute local PF thresholds for active sensors }

• Fusing all sensor decisions at single fusion center

Ignore signal locality High computational cost O(2n) n – number of active sensors

Centralized Coverage Algorithm

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Se-Grid: Coverage Algorithm based on Separate Grids

– Configuration time is reduced via parallel processing Data fusion is restricted within each grid redundant active sensors

• Divide region into multiple grids
• Fusion center in each grid runs

the centralized algorithm

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Co-Grid: Coverage Algorithm with Inter-grid Coordination

• Overlapping grid layout
• Computing PD(x,y)

– Each point associates with up to 4 detection probabilities – Approximate PD(x,y) with the max probability

Each grid has 4 squares and each square belongs to (up to) 4 grids 2 X 2 Grids

G(1,1) G(2,1) G(2,2) G(1,2)

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G(2,3)

Turn on a new sensor Notify neighbors of new PF thresholds Restart the current iteration

Co-Grid: Inter-grid Coordination

3 X 3 Grids

G(2,2) G(3,2) G(3,1) G(2,1) G(1,1) G(1,2) G(1,3) G(3,3)

Increase local PF thresholds

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Turn on a new sensor Increase local PF thresholds Notify neighbors of new PF thresholds Restart the current iteration One iteration at G(i,j) Neighbors of G(i,j)

Co-Grid Algorithm

Find min PD(x,y)

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Number of Active Sensors

Co-Grid is competitive with Central when grid width > ¼ region width

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Configuration Time

– Parallelism & computational cost in each grid – When n > 17, Monte Carlo method is used in implementation

Co-Grid is orders of magnitude faster than Central (simulated time units)

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Summary: Co-Grid

• Probabilistic coverage model based on detection theory
• Co-Grid

– Maintains probabilistic coverage based on data fusion – Facilitates local signal processing by overlapping fusion groups – Outperforms the algorithm based on separate grids – Similar number of active sensors with the centralized algorithm while orders of magnitude faster

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References

• G. Xing, X. Wang, Y. Zhang, C. Lu, R. Pless and C. Gill, Integrated

Coverage and Connectivity Configuration for Energy Conservation in Sensor Networks, ACM Transactions on Sensor Networks, 1(1): 36-72, August 2005. Extended version of SenSys'03 paper.

• G. Xing, C. Lu, R. Pless, and J.A. O'Sullivan, Co-Grid: An Efficient

Coverage Maintenance Protocol for Distributed Sensor Networks, International Symposium on Information Processing in Sensor Networks (IPSN'04), April 2004.