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

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

Wireless Sensor Networks (WSN) мно 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

WSN localization Localization is important for: using data gathered from sensor nodes position-aware routing algorithms

WSN localization Localization: estimating the location of a node Solution: –installing GPS devices (expensive) –manually (unreliable and inappropriate for many applications) –using algorithmic techniques

Distributed localization techniques

Trilateration a b c ab c d 2D trilateration 3D trilateration

Ad-hoc positioning system anchordistance Absolute position = = 4 = 2 (18, 24) = 3 * Hop Metric= 6 Niculesu и Nath (2001) Savarese (2002) Savvides (2002)

Centralized localization techniques

Problem definition Known: a set of N points in a plane coordinates of 0  K < N points (anchors) M  N x (N-1) distances between some of the points Should be found: Positions of all N - K points (found unknown coordinates) Abstraction: WSN can be abstracted with graph nodes in WSN ~ vertices in graph distance between nodes ~ edges in weighted graph Analogy: Localization in WSN is analogous with Graph realization (~ find coordinates of the vertices using length of the edges) Semidefinite programming Multidimensional scaling

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

MDS-MAP aaa bbb c d e f g h c de f g h c d efg h a+c+d

MDS-MAP

anchor Linear transform

MDS-MAP characteristics Pros –One of the most accurate technique –Relative map creation requires only distances between neighbours –To generate the global map (in 2D) only 3 anchor nodes are needed –The complexity depends on the number of nodes in the network Cons –Centralized processing –Poor accuracy for irregular topologies a c d

грешка =

Cluster-based MDS-MAP Aim –To overcome the drawbacks of MDS-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

I phase: Initial clustering cluster-head cluster members

II phase: Cluster extension gateways

III phase: Local map construction

MDS-MAP

IV phase: Local map merging Referent coordinate system shifting, rotation and reflection of the coordinates Parallel or consecutive merging

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

Simulation results Random and grid based topologies with shape C, L and H Nodes location are obtained using MDS-MAP and cluster- based MDS algorithm (with 5, 7, 10 and 15 clusters) Using different number of anchor nodes (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)

L topology Random topologyGrid topology MDS-MAP error CB-MDS error random topology grid topology

C topology Random topologyGrid topology MDS-MAP error CB-MDS error

random topologygrid topology H topology

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

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

Any Questions ? THANKS …