1. Performance Analysis of Relative Location Estimation for Multihop Wireless Sensor Networks Qicai Shi; Kyperountas, S.; Correal, N.S.; Feng Niu Selected Areas in Communications, IEEE Journal April 2005

2. Outline Introduction to Positioning Techniques for Wireless Sensor Networks The Contributions of This Paper Mathematical Formulation of Relative Location Estimation –Assume range estimation error is i.i.d zero- mean additive white Gaussian noise General Theoretical Analysis Simulation Results

3. Introduction Why Location is important for Wireless Sensor Networks? –Applications HVAC( heating, ventilating, and air conditioning) –Average temperature over room A? Battlefield Surveillance –Where is the enemy? Ecosystem monitoring –Where exists a bear? –Geographical Routing

4. Location-Aided Routing (LAR) to limit the area to search for the route –I will forward the ROUTE_REQ; –J will not forward the ROUTE_REQ. S AB C I J D Route search zone Expected zone of D

5. The Node Positioning Problem Reference node – nodes with global location Blindfolded node – nodes want to estimate their location Localize nodes in an ad-hoc multihop network based on a set of inter-node distance (range) measurements Reference (beacon) node Blindfolded (unknown) node

6. Types of Range Measurements How to obtain range measurements? –Received Signal Strength (RSS) –Time based methods (ToA,TDoA) Related Materials –Positioning Techniques in Sensor Network By Pei-Chi Chu http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=81&1127318744 –Novel Self-Configurable Positioning Technique for Multi-hop Wireless Networks By C. Y. Chen http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=305&1127318855 –TPS-A Time-Based Positioning Scheme for Outdoor Wireless Sensor Networks By C. Y. Chen http://vc.cs.nthu.edu.tw/ezLMS/show.php?id=214&1127318940

7. Contributions of This Paper Assume range estimation error is identical, independent additive zero-mean white Gaussian noise ~ n(0,  2 ) –Analyze error accumulation when applying relative location estimation to multihop sensor networks

8. Mathematical Formulation of Relative Location Estimation Accurate distance Distance with error [go ref.]

9. Maximum-likelihood Estimator EX: R1R1 N1N1 N2N2 R2R2 D 11 D 21 d 12

10. Analysis of Simple Schemes

11. [go ref.]

13. General Theoretical Analysis

19. Simulation Results 20m x 20m x 6m sensing field  =1m 4 reference nodes (m=4)

21. K=4 K=8 K=10 K=4 K=8 K=10

22. References N. Patwari, R. J. O'Dea, and Y. Wang. Relative Location in Wireless Networks. In Proc. Int’l conf. Vehicular Technology, 2001. N. Patwari, A. Hero, M. Perkins, N. Correal, and R. O’Dea, “Relative location estimation in wireless sensor networks,” IEEE Trans. Signal Process., Special Issue on Signal Processing in Networks, vol. 51, no. 8, pp. 2137–2148, Aug. 2003. K. Whitehouse, A. Woo, C. Karlof, F. Jiang, and D. Culler, “The Effects of Ranging Noise on Multi-hop Localization: An Empirical Study,” IPSN, 2005. [back]

23. Let X 1, X 2,….X n be independent and identically Normal distributed random variables with mean  i and variance  i 2. Then Y= X 1 +X 2 +…+X n is a normal distribution with mean  1 +  2 +…+  n variance  1 2 +  2 2 +….+  n 2 [back]