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

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

9. The Relationships A

10. A B

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

12. The Idea 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?

13. The Problem Formulation Location θ = (x, y) Observation a = (a 1, a 2, … a n ) Location Estimation

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

15. A More General Solution Instead of considering only three groups, we consider all the groups. a = (a 1, a 2, … a n ): The observation. f n (a | θ): The probability of observing a at location θ. MLE Principle: find θ, such that f n (a | θ) is maximized.

16. Maximum Likelihood Estimation Likelihood Function f n (a | θ) = Pr (X 1 =a 1, …, X n =a n | θ) = Pr (X 1 =a 1 | θ) · · · Pr (X 1 =a n | θ) L( θ) = log f n (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 Beacon-LessBeacon-Based Communication Overhead Low Computation Cost HighLow Device Cost LowHigh Robustness/Security HighLow Mobility NoneGood

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.