This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Understanding Node Localizability of Wireless Ad Hoc and Sensor Networks
Aug. 2012 (vol. 11 no. 8)
pp. 1249-1260
Yunhao Liu, Hong Kong University of Science and Technology, Hong Kong
Zheng Yang, Hong Kong University of Science and Technology, Hong Kong
Location awareness is highly critical for wireless ad-hoc and sensor networks. Many efforts have been made to solve the problem of whether or not a network can be localized. Nevertheless, based on the data collected from a working sensor network, it is observed that the network is not always entirely localizable. Theoretical analyses also suggest that, in most cases, it is unlikely that all nodes in a network are localizable, although a (large) portion of the nodes can be uniquely located. Existing studies merely examine whether or not a network is localizable as a whole; yet two fundamental questions remain unaddressed: First, given a network configuration, whether or not a specific node is localizable? Second, how many nodes in a network can be located and which are them? In this study, we analyze the limitation of previous works and propose a novel concept of node localizability. By deriving the necessary and sufficient conditions for node localizability, for the first time, it is possible to analyze how many nodes one can expect to locate in sparsely or moderately connected networks. To validate this design, we implement our solution on a real-world system and the experimental results show that node localizability provides useful guidelines for network deployment and other location-based services.

[1] N.B. Priyantha, A. Chakraborty, and H. Balakrishnan, "The Cricket Location-Support System," Proc. ACM MobiCom, 2000.
[2] S.Y. Seidel and T.S. Rappaport, "914 MHz Path Loss Prediction Models for Indoor Wireless Communications in Multifloored Buildings," IEEE Trans. Antennas and Propagation, vol. 40, no. 2, pp. 209-217, Feb. 1992.
[3] T. Eren, D.K. Goldenberg, W. Whiteley, Y.R. Yang, A.S. Morse, B.D.O. Anderson, and P.N. Belhumeur, "Rigidity, Computation, and Randomization in Network Localization," Proc. IEEE INFOCOM, 2004.
[4] B. Hendrickson, "Conditions for Unique Graph Realizations," SIAM J. Computing, vol. 21, no. 1, pp. 65-84, 1992.
[5] B. Jackson and T. Jordan, "Connected Rigidity Matroids and Unique Realizations of Graphs," J. Combinatorial Theory Series B, vol. 94, no. 1, pp. 1-29, 2005.
[6] G. Laman, "On Graphs and Rigidity of Plane Skeletal Structures," J. Eng. Math., vol. 4, pp. 331-340, 1970.
[7] "OceanSense Project," http://www.cse.ust.hk/~liu/Ocean index.html , 2010.
[8] D. Goldenberg, A. Krishnamurthy, W. Maness, Y.R. Yang, A. Young, A.S. Morse, A. Savvides, and B. Anderson, "Network Localization in Partially Localizable Networks," Proc. IEEE INFOCOM, 2005.
[9] D.J. Jacobs and B. Hendrickson, "An Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game," J. Computational Physics, vol. 137, pp. 346-365, 1997.
[10] J.E. Hopcroft and R.E. Tarjan, "Finding The Triconnected Components of a Graph," Technical Report TR 140, Dept. of Computer Science, Cornell Univ., 1972.
[11] Z. Yang, M. Li, and Y. Liu, "Sea Depth Measurement with Restricted Floating Sensors," Proc. IEEE 28th Int'l Real-Time Symp. (RTSS), 2007.
[12] J. Aspnes, T. Eren, D.K. Goldenberg, A.S. Morse, W. Whiteley, Y.R. Yang, B.D.O. Anderson, and P.N. Belhumeur, "A Theory of Network Localization," IEEE Trans. Mobile Computing, vol. 5, no. 12, pp. 1663-1678, Dec. 2006.
[13] D. Moore, J. Leonard, D. Rus, and S. Teller, "Robust Distributed Network Localization with Noisy Range Measurements," Proc. ACM Second Int'l Conf. Embedded Networked Sensor Systems (SenSys), 2004.
[14] A. Savvides, C. Han, and M.B. Strivastava, "Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors," Proc. ACM MobiCom, 2001.
[15] Z. Yang and Y. Liu, "Quality of Trilateration: Confidence Based Iterative Localization," IEEE Trans. Parallel and Distributed Systems, vol. 21, no. 5, pp. 631-640, May 2010.
[16] L. Mo, Y. He, Y. Liu, J. Zhao, S. Tang, X.-Y. Li, and G. Dai, "Canopy Closure Estimates with GreenOrbs: Sustainable Sensing in the Forest," Proc. ACM Seventh ACM Conf. Embedded Networked Sensor Systems (SenSys), 2009.
[17] M. Li and Y. Liu, "Underground Coal Mine Monitoring with Wireless Sensor Networks," ACM Trans. Sensor Networks, vol. 5, no. 2, 2009.
[18] P. Bahl and V.N. Padmanabhan, "RADAR: An In-Building RF-Based User Location and Tracking System," Proc. IEEE INFOCOM, 2000.
[19] Z. Yang, Y. Liu, and X.-Y. Li, "Beyond Trilateration: On the Localizability of Wireless Ad-Hoc Networks," Proc. IEEE INFOCOM, 2009.
[20] C. Peng, G. Shen, Y. Zhang, Y. Li, and K. Tan, "BeepBeep: A High Accuracy Acoustic Ranging System Using COTS Mobile Devices," Proc. ACM Int'l Conf. Embedded Networked Sensor Systems (SenSys), 2007.
[21] D. Goldenberg, P. Bihler, M. Cao, J. Fang, B. Anderson, A.S. Morse, and Y.R. Yang, "Localization in Sparse Networks Using Sweeps," Proc. ACM MobiCom, 2006.
[22] T. Eren, W. Whiteley, and P.N. Belhumeur, "Further Results on Sensor Network Localization Using Rigidity," Proc. European Workshop Sensor Networks, 2005.
[23] J. Liu, Y. Zhang, and F. Zhao, "Robust Distributed Node Localization with Error Management," Proc. ACM MobiHoc, 2006.
[24] T. He, C. Huang, B.M. Blum, J.A. Stankovic, and T.F. Abdelzaher, "Range-Free Localization Schemes in Large Scale Sensor Networks," Proc. ACM MobiCom, 2003.
[25] Y. Shang, W. Ruml, Y. Zhang, and M.P.J. Fromherz, "Localization from Mere Connectivity," Proc. ACM MobiHoc, 2003.
[26] H. Lim and J.C. Hou, "Localization for Anisotropic Sensor Networks," Proc. IEEE INFOCOM, 2005.
[27] Y. Wang, J. Gao, and J. Mitchell, "Boundary Recognition in Sensor Networks by Topological Methods," Proc. ACM MobiCom, 2006.
[28] M. Li and Y. Liu, "Rendered Path: Range-Free Localization in Anisotropic Sensor Networks with Holes," Proc. ACM MobiCom, 2007.
[29] S. Lederer, Y. Wang, and J. Gao, "Connectivity-Based Localization of Large Scale Sensor Networks with Complex Shape," Proc. IEEE INFOCOM, 2008.
[30] W. Whiteley, "Rigidity and Scene Analysis," Handbook of Discrete and Computational Geometry, J. Goodman and J.O. Rourke, eds., pp. 893-916, CRC Press, 1997.
[31] B. Jackson and T. Jordan, "A Sufficient Connectivity Condition for Generic Rigidity in the Plane," Technical Report TR-2008-01, Operations Research Dept., Eotvos Univ., Budapest, 2008.
[32] L. Lovasz and Y. Yemini, "On Generic Rigidity in the Plane," SIAM J. Algebraic and Discrete Methods, vol. 3, no. 1, pp. 91-98, 1982.
[33] C. Bettstetter, "On the Minimum Node Degree and Connectivity of a Wireless Multihop Network," Proc. ACM MobiHoc, 2002.
[34] H. Dette and N. Henze, "Some Peculiar Boundary Phenomena for Extremes of rth Nearest Neighbor Links," Statistics & Probability Letters, vol. 10, no. 5, pp. 381-390, 1990.
[35] P. Gupta and P. Kumar, "Critical Power for Asymptotic Connectivity in Wireless Networks," Stochastic Analysis, Control, Optimization and Applications, vol. 16, pp. 347-358, 1998.
[36] X.-Y. Li, Y. Wang, P.-J. Wan, and C.-W. Yi, "Fault Tolerant Deployment and Topology Control for Wireless Ad Hoc Networks," Proc. ACM MobiHoc, 2003.
[37] M. Penrose, "The Longest Edge of the Random Minimal Spanning Tree," Annals of Applied Probability, vol. 7, pp. 340-361, 1997.
[38] M. Penrose, "On k-Connectivity for a Geometric Random Graph," J. Random Structures and Algorithms, vol. 15, pp. 145-164, 1999.
[39] F. Xue and P. Kumar, "The Number of Neighbors Needed for Connectivity of Wireless Networks," Wireless Networks, vol. 10, no. 2, pp. 169-181, 2004.

Index Terms:
Sufficient conditions,Ad hoc networks,Wireless communication,Wireless sensor networks,Mobile radio mobility management,ad hoc networks.,Localization,localizability,graph rigidity,wireless sensor networks
Citation:
Yunhao Liu, Zheng Yang, "Understanding Node Localizability of Wireless Ad Hoc and Sensor Networks," IEEE Transactions on Mobile Computing, vol. 11, no. 8, pp. 1249-1260, Aug. 2012, doi:10.1109/TMC.2011.122
Usage of this product signifies your acceptance of the Terms of Use.