1. A New Hybrid Wireless Sensor Network Localization System Ahmed A. Ahmed, Hongchi Shi, and Yi Shang Department of Computer Science University of Missouri-Columbia Columbia, Missouri, USA

2. 06/26/2006 ICPS 2006 2 Outline Introduction Introduction Related Work Related Work Network Properties Network Properties Adaptive Localization System (ALS) Adaptive Localization System (ALS) Experimental Results Experimental Results Conclusion Conclusion

3. 06/26/2006 ICPS 2006 3 Introduction A wireless sensor network is represented as an undirected connected graph with vertices (nodes) V and edges E. Edges are: –Connectivity information or –Estimated distances to neighbors. Some of the nodes are anchors (with known positions). Relative vs. absolute localization.

4. 06/26/2006 ICPS 2006 4 Related Work (1/3) Ad-hoc Positioning System (APS) Related Work (1/3) Ad-hoc Positioning System (APS) Niculescu et al., GLOBECOM’01 1. Each anchor k –broadcasts its position, –receives the positions of all m anchors, and –computes the shortest-path distance p to each anchor. 2. Each anchor k computes its distance correction value, c k. 3. Each unknown node –computes the corrected shortest-path distances to all anchors, and –multilaterates based on all anchors to determine its position.

5. 06/26/2006 ICPS 2006 5 Related Work (2/3) MultiDimensional Scaling (MDS-MAP) Related Work (2/3) MultiDimensional Scaling (MDS-MAP) Shang et al., MobiHoc’03. 1. Set the range for local maps to R lm. 2. Compute relative maps for individual nodes within R lm. –Compute all-pair shortest paths. –Apply MDS to the distance matrix and construct the local maps. 3. Merge the relative maps to form one global map. 4. Given sufficient anchors, transform the relative map to an absolute one.

6. 06/26/2006 ICPS 2006 6 Related Work (3/3) SemiDefinite Programming (SDP) Related Work (3/3) SemiDefinite Programming (SDP) Biswas et al., IPSN’04 The problem is considered in the presence of measurement errors. By introducing slack variables and then relaxing the problem, it is rewritten as a standard SDP problem.

7. 06/26/2006 ICPS 2006 7 Network Properties 1. Network topology –Random uniform (isotropic) –Grid –C-shape (anisotropic) 2. Average network connectivity 3. Measurement error –Received Signal Strength Indicator (RSSI) –Time of Arrival (ToA) –Time Difference of Arrival (TDoA) 4. Anchor ratio 5. Anchor placement –Random –Outer

8. 06/26/2006 ICPS 2006 8 Adaptive Localization System (ALS) Phase 1: Discover network properties. Phase 1: Discover network properties. Phase 2: Run the three localization methods: APS, MDS, and SDP. Phase 2: Run the three localization methods: APS, MDS, and SDP. Phase 3: Using the appropriate weights, compute the weighted centroid of the three position estimates. Phase 3: Using the appropriate weights, compute the weighted centroid of the three position estimates.

9. 06/26/2006 ICPS 2006 9 Simulation Setup Total # of network instances = 2 X 8 X 3 X 3 X 2 = 288

10. 06/26/2006 ICPS 2006 10 Topologies Isotropic network, 100 nodes Average node connectivity = 14.7 Anisotropic network, 100 nodes Average node connectivity = 14.9

11. 06/26/2006 ICPS 2006 11 Determining the Weights (1/2) Find the values of the weights that give the minimum localization error under a specific set of network properties. Train off-line using 30 network instances for every one of a 288-combination set. Find the values of the weights by solving the constrained linear least-squares problem. Test on a different set of 30 networks for every combination.

12. 06/26/2006 ICPS 2006 12 Determining the Weights (2/2) For node i, let – –x i = [x i y i ] T be the true position, – –x i a = [x i a y i a ] T be the estimated position using APS, – –x i m = [x i m y i m ] T be the estimated position using MDS, – –x i s = [x i s y i s ] T be the estimated position using SDP,. Define the weighted centroid of the three estimates as x i c = [x i c y i c ] T where x i c = w a x i a + w m x i m + w s x i s y i c = w a y i a + w m y i m + w s y i s

13. 06/26/2006 ICPS 2006 13 Experimental Results (1/4)

14. 06/26/2006 ICPS 2006 14 Experimental Results (2/4)

15. 06/26/2006 ICPS 2006 15 Experimental Results (3/4)

16. 06/26/2006 ICPS 2006 16 Experimental Results (4/4)

17. 06/26/2006 ICPS 2006 17 Conclusion We have identified 5 network properties that may affect performance. We present our Adaptive Localization System (ALS) method based on 3 existing algorithms. ALS has 3 phases: 1.Discover network properties. 2.Run three localization methods. 3.Compute a new position estimate that is the weighted centroid of the three estimates. We use machine learning to compute the values of the weights. ALS outperforms the individual algorithms under a broad range of networks conditions. In the future, we will consider –the performance-cost tradeoff in localization.

18. 06/26/2006 ICPS 2006 18 Thanks! Questions / Comments ?