A Cluster-based and Range Free Multidimensional Scaling-MAP Localization Scheme in WSN

1. A Cluster-based and Range Free Multidimensional Scaling-MAP Localization Scheme in WSN 1 Ke Xu, Yuhua Liu (), Cui Xu School of Computer, Central China Normal University, Wuhan 430079, China e-mail: yhliu@mail.ccnu.edu.cn 2Kaihua Xu College of Physical Science and Technology, Central China Normal University, Wuhan 430079, China

2. Outline • Introduction • MDS-MAP • Improved MDS-MAP • Experiments and Simulations • Conclusion • References

3. Introduction (1/ 1) • A sensor network is composed of a large number of sensor nodes, which are densely deployed either inside the phenomenon or very close to it • The goal of a sensor network is to perceive, collect and process the information of specific objects, and send the information to observers • Localization plays a key role within the application of WSN

4. MDS-MAP (1/ 3) • What is MDS-MAP • Procedure of MDS-MAP

5. MDS-MAP (2/ 3) • What is MDS-MAP ? MDS( Multidimensional Scaling) is a set of data analysis technology which can transform the given data into geometry model, thus problems can be visually solved. Torgerson firstly given the terminology MDS based on the work of Richardson, and proposed the first MDS method.

6. MDS-MAP (3/ 3) • Procedure of MDS-MAP • Calculate the shortest distances between nodes in WSN • Calculate the first r maximum eigenvalues of r dimensional space to construct the relative location map of nodes • Transforms the relative location map to absolute location map

7. Improved MDS-MAP (1/ 9) • Clustering • Building Cluster Location Map • Merging Cluster Location Map

8. Improved MDS-MAP (2/ 9) • Clustering • Selection of Cluster Heads • Inter-cluster Nodes

9. Improved MDS-MAP (3/ 9) • Clustering • Selection of Cluster Heads Selection of cluster heads

10. Improved MDS-MAP (4/ 9) • Clustering • Inter-cluster Nodes Result of k-hop clustering

11. Improved MDS-MAP (5/ 9) • Building Cluster Location Map • Step 1: After k-hop clustering completed, each cluster head node calculates distance based on RSSI and the IDs of neighboring nodes[7]. Using the distance information which is expressed in a distance matrix and the shortest path algorithm, Dijkstra or Floyd, the cluster head node constructs a shortest distance matrix; • Step 2: Using this shortest distance matrix, the MDS-MAP algorithm produces a relative location map within the cluster; • Step 3: Refine cluster location map.

12. Improved MDS-MAP (6/ 9) • Merging Cluster Location Map If have more than 3 nodes, than using formula (6) can transform the coordinates of nodes in Cluster-j to coordinates in Cluster-i: (6) whereis zoom factor, depicts rotation transformation, indicates translation transformation, the technique of compute , , is shown as below. Suppose are coordinate matrices of nodes of in Cluster-i and Cluster-j. The row vector of are depicted by .The central points of are computed through formula (7). 　　(7)

13. Improved MDS-MAP (7/ 9) • Merging Cluster Location Map Assume , the zoom factor s in formula (6) is calculated through formula (8). (8) The covariance matrix of can be computed by using formula (9). (9)

14. Improved MDS-MAP (8/ 9) • Merging Cluster Location Map Define matrix as formula (10): (10) Compute which is composed by eigenvalue of matrix : Compute R(•) of formula (6) using formula (11). (11)

15. Improved MDS-MAP (9/ 9) • Merging Cluster Location Map Compute through formula (12): (12) Using formula (6), (8), (11), (12), the matrix D (the nodes’ coordinate matrix of ) can be transformed to the coordinate system of Cluster-i, the technique is shown as formula (13). (13) whereis a all-1 matrix which has an equal row number as matrix . Using this technique, all clusters’ location map can be merged to one location map.

16. Experiments and Simulations (1/ 4) • Simulations of Two Types of WSN • Localization Error with Connectivity

17. Experiments and Simulations (2/ 4) • Simulations of Two Types of WSN localization results where a sensor topology is configured in a C shape

18. Experiments and Simulations (3/ 4) • Simulations of Two Types of WSN localization results in a sensor topology with a horseshoe-shaped hole

19. Experiments and Simulations (4/ 4) • Localization Error with Connectivity Localization error with connectivity in C-shaped WSNs(a), horseshoe-shaped WSNs(b)

20. Conclusion (1/ 1) This article proposes MDS-MAP(C,RF) algorithm based on conventional MDS-MAP. Simulation results indicate that MDS-MAP(C,RF) is better than MDS-MAP for it can improve localization accuracy. Since MDS-MAP(C,RF) is a cluster based technique which can reduce the burden of center nodes, it can extend lifespan of WSN. The next stage work is focus on the effect to WSN’s lifespan of MDS-MAP(C,RF).

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