A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks

1. A Beacon-Less Location Discovery Scheme for Wireless Sensor Networks Lei Fang (Syracuse) Wenliang (Kevin) Du (Syracuse) Peng Ning (North Carolina State)

2. Location Discovery in WSN • Sensor nodes need to find their locations • Rescue missions • Geographic routing protocols • Many other applications • Constraints • No GPS on sensors • Cost must be low

3. Existing Positioning Schemes Beacon Nodes

4. Two Important Elements • Reference points • They must know their locations. • e.g. beacon nodes, satellites. • Relationship between nodes and reference points • Distance • Angle of arrival • Time of arrival • Time difference of arrival

5. The Beacon-Less Scheme • Without using beacon nodes • Beacon nodes are more expensive • They can be the main target of attacks • Nonetheless, we still have to find reference points and the corresponding relationships. • Remember: the locations of the reference points must be known.

6. A Group-Based Deployment Scheme

7. A Group-Based Deployment Scheme

8. Modeling of The Group-Based Deployment Scheme Deployment Points: Their locations are known. We still need another important element: The relationship between nodes and reference points.

9. The Relationships A

10. The Relationships A B

11. Using pdf function to model the node distribution. Example: two-dimensional Gaussian Distribution. Other distribution can also be used. Modeling of the Deployment Distribution

12. Observation at location O See more nodes from A and D than from H and I. Observation at location P Quit different from location O. See more nodes from H and I than from A and D. Given a location, we can derive the observation. Given the observation, can we derive the location? The Idea

13. The Problem Formulation Observation a = (a1, a2, … an) Location Estimation Locationθ = (x, y)

14. A Geometric Approach • Pick the three nearest deployment points (the three highest ai values). • Estimate the distance between the sensor and these points. • MLE (Maximum Likelihood Estimation): f (Xi = ai|Z): The probability of observing ai nodes from Group i when the distance is Z. • Find Z, such that f (Xi = ai|Z)is maximized.

15. A More General Solution • Instead of considering only three groups, we consider all the groups. a = (a1, a2, … an): The observation. fn(a|θ): The probability of observing a at location θ. • MLE Principle:find θ, such thatfn(a|θ)is maximized.

16. Maximum Likelihood Estimation • Likelihood Function fn(a|θ) =Pr (X1=a1, …, Xn=an|θ) = Pr (X1=a1|θ) · · · Pr (X1=an|θ) L(θ)=logfn(a|θ) • Find θ:

17. Finding θ • Brute-Force Search: search all possible θ. • Small Area Search: • Find an initial point (accuracy can be low). • Conduct brute-force search around the initial point. • Gradient Descent: A standard solution.

18. Gradient Descent • A 2-dimensional function is represented as a surface in a 3-dimensional space • The maximum point (peak) holds a zero gradient • Find the shortest path to reach the peak. • Could be expensive

19. Evaluation • Setup • A square plane: 1000 meters by 1000 meters • 10 by 10 grids (each is 100m X 100m) • σ = 50 (Gaussian Distribution) • What to evaluate? • Accuracy vs. Density • Accuracy vs. Transmission Range • Boundary Effects • Computation Costs.

20. Effect of Density m An Improvement: Dummy Nodes m: number of sensors in each group

21. Effect of Transmission Range R

22. Effect of Boundary

23. Comparing the Three Numeric Approaches (Cost)

24. Comparing the Three Numeric Approaches (Accuracy)

25. Comparisons

26. Conclusion and Future Work • Beacon-Less Location Discovery • Formulate the location discovery problem as an estimation problem • Use the Maximum Likelihood Estimation to solve the estimation problem • Future work • How the inaccuracy of the deployment model affect the result? • Resilience and Security: • IPDPS’05 paper (Best Paper Award in the Algorithm Track) • Google “Wenliang Du” can get the paper.