Ass. Biljana Stojkoska

1. University “Ss. Cyril and Methodus”SKOPJECluster-based MDS Algorithm for Nodes Localization in Wireless Sensor Networks Ass. Biljana Stojkoska

2. Outline • Introduction • Localization Techniques • Distributed localization techniques • Centralized localization techniques • Multidimensional scaling • Cluster-based localization algorithm • Simulation results • Conclusion

3. Wireless Sensor Networks (WSN) • WSN consists of hundreds or thousands of sensor nodes that: • sense physical phenomena • communicate with each other • Why are they so popular? • low cost • small size • easy to install • Limitations • hardware • energy • мно

4. WSN localization • Localization is important for: • using datagathered from sensor nodes • position-aware routing algorithms

5. WSN localization • Localization: estimating the location of a node • Solution: • installingGPS devices (expensive) • manually (unreliable and inappropriate for many applications) • using algorithmic techniques

6. Distributed localization techniques

7. Trilateration • 2D trilateration • 3D trilateration a b b c d a c

8. 3 3 2 3 2 3 2 1 2 3 1 3 1 2 3 1 2 Ad-hoc positioning system • Niculesu и Nath (2001) • Savarese (2002) • Savvides (2002) 2 3 1 1 = 3 * Hop Metric = 6 = 4 2 3 = 2 (18, 24)

9. Centralized localization techniques

10. Problem definition Known: • a set of Npoints in a plane • coordinates of0  K<Npoints (anchors) • M  N x (N-1)distances between some of the points Should be found: • Positions of all N- Kpoints (found unknown coordinates) Abstraction:WSN can be abstracted withgraph nodesinWSN~ verticesingraph distancebetweennodes~edgesin weighted graph Analogy: Localizationin WSN is analogous with Graph realization(~ find coordinates of the verticesusinglength of the edges) • Semidefinite programming • Multidimensional scaling

11. Multidimensional scaling • Multidimensional scaling (MDS)is a well known technique used for dimensionality reduction when we have multidimensional data • MDS minimize 2 • MDS-MAPis an algorithm for nodes localization in WSN based on multidimensional scaling • If the distance between nodesiandjcan not be measured, it will be approximate with the “shortest path” distance

13. MDS-MAP a+c+d 0 0 0 c c 0 d e d 0 f 6 b b b 5 0 g h h e f g 0 g 9 d f 0 7 12 h 0 4 e 10 0 c 8 0 3 3 13 a a a 0 2 0 11 1

14. MDS-MAP

15. 5 6 6 4 5 7 9 9 MDS-MAP 3 1 8 7 12 10 12 4 10 2 8 8 3 3 13 13 11 2 11 1 anchor anchor anchor Linear transform

16. MDS-MAP characteristics 6 5 5 • Pros • One of the most accurate technique • Relative map creation requires only distances between neighbours • To generate the global map (in 2D) only 3 anchornodes are needed • The complexity depends on the number of nodes in the network • Cons • Centralized processing • Poor accuracy for irregular topologies 9 9 d 7 7 12 12 4 4 10 c 8 8 10 3 3 3 3 13 a 13 2 2 2 11 11 1 1

17. грешка =

18. Cluster-based MDS-MAP • Aim • To overcome the drawbacks ofMDS-MAP • Distributed approach • Improve accuracy for irregular topologies • Idea • Divide the network into subsets (clusters) • Apply MDS-MAP on each cluster • Merge local maps into one unique global map • Assumptions: • path existence between each pair of nodes in the network • nodes that belong to the same cluster are in close proximity to each other • Each node uses RSSI method for distance estimation • RSSI provide accurate neighboring sensor distance estimation

19. I phase: Initial clustering cluster-head cluster-head cluster members cluster members

20. II phase: Cluster extension gateways gateways gateways

21. III phase: Local map construction

22. MDS-MAP MDS-MAP MDS-MAP MDS-MAP III phase: Local map construction

23. IV phase: Local map merging Parallel or consecutive merging shifting, rotation andreflection of the coordinates Referent coordinate system

24. Network density (average connectivity of the graph) • k=(number_od_edges*2)/ number_of_nodes • -Number of anchor nodes

25. Simulation results • Random and grid based topologieswith shape C, Land H • Nodes location are obtained using MDS-MAP and cluster-basedMDS algorithm (with 5, 7, 10 and 15 clusters) • Using different number of anchornodes (3,4,6 and 10) to generate absolute map • Changing radio range, which changes average connectivity of the graph (k, average number of neighbors). • 600 different topologies were simulated(6 x 5 x 4 x 5)

26. Ltopology grid topology random topology MDS-MAP error CB-MDS error Random topology Grid topology

27. Ctopology MDS-MAP error CB-MDS error Random topology Grid topology

28. Htopology random topology grid topology

29. Results discussion • Greater connectivity improves the accuracy • More anchors improves the accuracy (but not significantly) • Number of clusters has a huge impact on the positioning accuracy • In dense graphs (networks), better results can be achieved if the number of clusters is greater • In sparse graphs, the accuracy is greater for small number of clusters

30. Conclusion • Which algorithm for nodes localization will be choose depends on: • Desired prediction accuracy • The region where WSN is deployed • The devices’ limitations • Cluster-basedMDS-MAP is a good solution for: -WSN with irregular topologies - WSN with only a few anchor nodes • Cluster-basedMDS-MAPas a distributed technique minimize communication cost

31. Any Questions ? THANKS …