Deployment Strategies for Differentiated Detection in Wireless Sensor NetworkJingbin Zhang, Ting Yan, and Sang H. Son

University of Virginia

From SECON 2006

Outline

Introduction Sensor Detection Model Problem Formulation Differentiated Deployment Algorithm Performance Evaluation Conclusion

Introduction

The efficiency of a sensor network depends on the deployment and coverage of the monitoring area.

In most previous studies on sensing coverage, a binary detection model is assumed. In a binary detection model, sensor node can

detect a target with a 100% probability if the target is within its sensing range.

Introduction

This paper considers a probabilistic detection model. With a probability detection model, a target is detected by

the sensor is probabilistic.

In many surveillance system, the system might require different degrees of security at different locations. For example, the system might require extremely high

detection probability at certain sensitive areas. However, for some not so sensitive areas, relatively low detection probabilities are required to reduce the number of sensors deployed.

Introduction

This paper aim at finding the minimal number of nodes to satisfy

that, after these nodes are deployed, for any location in the sensing field, the collective miss probability satisfies the predefined detection threshold distribution.

Related presentations:

(1) SMART A Scan-based Movement-Assisted Sensor Deployment Method

(2) On Multiple Point Coverage in Wireless Sensor Networks  

(3) Sensor Placement and Lifetime of Wireless Sensor Networks: Theory and Performance Analysis

Terrain Model

Sensor Field

U

V

D( x, y) : the number of nodes deployed at grid point (x, y).

Typically, D( x, y) is either 1 or 0.

(x, y)

Probability Detection Model

Without taking into consideration of the time duration [10][13].

Considering the time duration a target stays at a certain grid (x, y)

Collective Miss Probability

The collective miss probability distribution

where

Logarithmic collective miss probability distribution I( x, y) = ln M(x, y)

I( x, y) =

Problem Formulation

Let mth denote the miss probability threshold distribution of the whole field, in which mth( x, y) is the miss probability threshold at location ( x, y) .

Objective: Find the minimal number of nodes to satisfy that,

after these nodes are deployed, for any ( x, y) Grid, the collective miss probability M( x, y) is smaller than or equal to mth( x, y)

Linear Shift Invariant System (LSI)

(5)

[ Proof ]

I( x, y) =

Linear Shift Invariant System (LSI)

Impulse response in this LSI system.

Matrix multiplication

Convolution

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Matrix multiplication

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Integer Linear Programming

Let mth denote the miss probability threshold distribution.

Set Ip = ln mth

Differentiated Deployment Algorithm

Based on matrix algebra, if we know the miss probability threshold distribution and the detection model,

Matrix multiplication

Differentiated Deployment Algorithm

The result Dp computed from Equation (9) can be any real number, including negative values. Therefore, the result Dp can not be used directly.

Idea: the maximum value in Dp might be the location that contributes t

he most in satisfying the detection requirement if a sensor is deployed at the location.

Performance Evaluation

Grid dimension: 550 Sensing range: 7 The parameter: a = 0.5 Matlab

Evaluation Set 1: Uniform Detection Requirement

[MIN_MISS]

Evaluation Set 1: Uniform Detection Requirement

Evaluation Set 1: Uniform Detection Requirement

Evaluation Set 2: Differentiated Detection Requirement

Evaluation Set 2: Differentiated Detection Requirement

Evaluation Set 2: Differentiated Detection Requirement

Evaluation Set 2: Differentiated Detection Requirement

Evaluation Set 2: Differentiated Detection Requirement

Conclusion

This paper focus on differentiated deployment problem, in which the required detection probability thresholds at different locations are different.

This paper shows that the relationship between the node deployment strategy and

the logarithmic collective miss probability distribution is Linear Shift Invariant (LSI).

A integer linear programming is formulated and a differentiated node deployment algorithm DIFF_DEPLOY is proposed.

Proof of LSI System

<proof>

[back]

MIN_MISS Algorithm

Candidate location: each location at which no sensor is deployed.

If we deploy a new node at candidate location ( x, y), the collective miss probability at location ( x, y) is

MIN_MISS Algorithm

Overall miss probability Moverall( i, j):

MIN_MISS Iteratively select next location to deploy a new sensor Candidate location (i, j) which has the minimum Moverall

( i, j) among all the candidate locations is selected for the next sensor to deploy.