1. Deployment Strategies for Differentiated Detection in Wireless Sensor Network Jingbin Zhang, Ting Yan, and Sang H. Son University of Virginia From SECON 2006

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

3. 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.

4. 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.

5. 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 MethodSMART A Scan-based Movement-Assisted Sensor Deployment Method (2)On Multiple Point Coverage in Wireless Sensor Networks On Multiple Point Coverage in Wireless Sensor Networks (3)Sensor Placement and Lifetime of Wireless Sensor Networks: Theory and Performance AnalysisSensor Placement and Lifetime of Wireless Sensor Networks: Theory and Performance Analysis

6. 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)

7. 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)

8. Collective Miss Probability The collective miss probability distribution where Logarithmic collective miss probability distribution I( x, y) = ln M(x, y) I( x, y) =

9. Problem Formulation Let m th denote the miss probability threshold distribution of the whole field, in which m th ( 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 m th ( x, y)

10. Linear Shift Invariant System (LSI) (5) [ Proof ] Proof I( x, y) =

11. Linear Shift Invariant System (LSI) Impulse response in this LSI system. Matrix multiplication Convolution

12. Matrix multiplication (0, 0) (N, N)

13. Integer Linear Programming Let m th denote the miss probability threshold distribution. Set I p = ln m th

14. Differentiated Deployment Algorithm Based on matrix algebra, if we know the miss probability threshold distribution and the detection model, Matrix multiplication

15. Differentiated Deployment Algorithm The result D p computed from Equation (9) can be any real number, including negative values. Therefore, the result D p can not be used directly. Idea:  the maximum value in D p might be the location that contributes the most in satisfying the detection requirement if a sensor is deployed at the location.

17. Performance Evaluation Grid dimension: 5  50 Sensing range: 7 The parameter: a = 0.5 Matlab

18. Evaluation Set 1: Uniform Detection Requirement [MIN_MISS]MIN_MISS

19. Evaluation Set 1: Uniform Detection Requirement

21. Evaluation Set 2: Differentiated Detection Requirement

26. 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.

27. Proof of LSI System

29. [back]back

30. 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

31. MIN_MISS Algorithm Overall miss probability M overall ( i, j): MIN_MISS  Iteratively select next location to deploy a new sensor  Candidate location (i, j) which has the minimum M overall ( i, j) among all the candidate locations is selected for the next sensor to deploy.