University Ss. Cyril and Methodus SKOPJE

Cluster-based MDS Algorithm for Nodes Localization in Wireless Sensor NetworksAss. Biljana Stojkoska

Outline

IntroductionLocalization TechniquesDistributed localization techniques Centralized localization techniquesMultidimensional scalingCluster-based localization algorithmSimulation resultsConclusion

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

WSN localizationLocalization is important for:

using data gathered from sensor nodes

position-aware routing algorithms

WSN localizationLocalization: estimating the location of a nodeSolution:installing GPS devices (expensive)manually (unreliable and inappropriate for many applications)using algorithmic techniques

Distributed localization techniques

Trilaterationabcabcd2D trilateration3D trilateration

Ad-hoc positioning system213123= 4= 2(18, 24)= 3 * Hop Metric= 6Niculesu Nath (2001)Savarese (2002)Savvides (2002)

anchordistance

Absolute position=

Centralized localization techniques

Problem definitionKnown:a set of N points in a planecoordinates 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 graphdistance between nodes ~ edges in weighted graphAnalogy: Localization in WSN is analogous withGraph realization (~ find coordinates of the vertices using length of the edges)

Semidefinite programming Multidimensional scaling

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

MDS-MAP1234567910111213380000000000000aaabbbcdefghcdefghcdefgha+c+d

anchoranchoranchorLinear transform

MDS-MAP characteristicsPros

One of the most accurate techniqueRelative map creation requires only distances between neighboursTo generate the global map (in 2D) only 3 anchor nodes are neededThe complexity depends on the number of nodes in the network

Cons

Centralized processingPoor accuracy for irregular topologies12345791011121338acd1234567910111213382

=

Cluster-based MDS-MAPAimTo overcome the drawbacks of MDS-MAPDistributed approachImprove accuracy for irregular topologiesIdeaDivide the network into subsets (clusters)Apply MDS-MAP on each clusterMerge local maps into one unique global mapAssumptions:path existence between each pair of nodes in the networknodes that belong to the same cluster are in close proximity to each otherEach node uses RSSI method for distance estimationRSSI provide accurate neighboring sensor distance estimation

I phase: Initial clusteringcluster-headcluster-headcluster memberscluster members

II phase: Cluster extensiongateways gateways gateways

III phase: Local map construction

III phase: Local map construction

IV phase: Local map mergingReferent coordinate systemshifting, 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 resultsRandom 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 topologyRandom topologyGrid topologyMDS-MAP errorCB-MDS error

random topologygrid topology

C topologyRandom topologyGrid topologyMDS-MAP errorCB-MDS error

random topologygrid topologyH topology

Results discussionGreater connectivity improves the accuracy

More anchors improves the accuracy (but not significantly)

Number of clusters has a huge impact on the positioning accuracyIn dense graphs (networks), better results can be achieved if the number of clusters is greaterIn sparse graphs, the accuracy is greater for small number of clusters

ConclusionWhich algorithm for nodes localization will be choose depends on:Desired prediction accuracyThe region where WSN is deployedThe 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

***