Wireless Personal Communications

, Volume 96, Issue 3, pp 4467–4484 | Cite as

Localization in Wireless Sensor Networks Using Rigid Graphs: A Review

  • Shamantha Rai
  • Shirshu Varma


The applications of wireless senor networks (WSN) vary in diversified field, at different geographic locations. Location aware computing is the key for the success of such applications. Henceforth, there is a need of efficiently estimating the location of individual WSN nodes deployed in the remote geographic locations. Manually estimating the locations of these densely deployed nodes is impossible, therefore the WSN nodes must be able to localize themselves collecting local information from its neighboring nodes, which is called as the localization technique. The information used for localization is generally distance and bearing information obtained from the ranging techniques which are not accurate and are prone to error. Therefore there is a need for techniques which can cope up with this perturbed distance information. Rigid graphs have the property of sustaining various kind of deformations due to translation, rotation and reflection. Hence, it is more fruitful using the concepts of rigid graphs, for estimating accurate location coordinates from error prone distance measurements. In this paper we will scrutinize the sound theoretical background which defines the need of rigid graph based localization and different localization techniques, with associated algorithms which uses the concepts of rigid graphs.


Wireless sensor network Localization Localizability Localizable Rigid graphs 


  1. 1.
    Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., & Cayirci, E. (2002). A survey on sensor networks. IEEE Communications magazine, 40(8), 102–114.CrossRefGoogle Scholar
  2. 2.
    Anderson, B. D., Belhumeur, P. N., Eren, T., Goldenberg, D. K., Morse, A. S., Whiteley, W., et al. (2009). Graphical properties of easily localizable sensor networks. Wireless Networks, 15(2), 177–191.CrossRefGoogle Scholar
  3. 3.
    Anderson, B. D., Shames, I., Mao, G., & Fidan, B. (2010). Formal theory of noisy sensor network localization. SIAM Journal on Discrete Mathematics, 24(2), 684–698.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Aspnes, J., Eren, T., Goldenberg, D. K., Morse, A. S., Whiteley, W., Yang, Y. R., et al. (2006). A theory of network localization. IEEE Transactions on Mobile Computing, 5(12), 1663–1678.CrossRefGoogle Scholar
  5. 5.
    Aspnes, J., Goldenberg, D., & Yang, Y. R. (2004). On the computational complexity of sensor network localization. In: Algorithmic aspects of wireless sensor networks (pp. 32–44). SpringerGoogle Scholar
  6. 6.
    Connelly, R. (2005). Generic global rigidity. Discrete and Computational Geometry, 33(4), 549–563.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Eren, T. (2011). Cooperative localization in wireless ad hoc and sensor networks using hybrid distance and bearing (angle of arrival) measurements. EURASIP Journal on Wireless Communications and Networking, 2011(1), 1–18.CrossRefGoogle Scholar
  8. 8.
    Eren, T., Anderson, B. D., Morse, A. S., Whiteley, W., Belhumeur, P. N., et al. (2003). Operations on rigid formations of autonomous agents. Communications in Information and Systems, 3(4), 223–258.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Eren, T., Belhumeur, P. N., Anderson, B. D., & Morse, A. S. (2002). A framework for maintaining formations based on rigidity. In: Proceedings of the 15th IFAC world congress (pp. 2752–2757), Barcelona, SpainGoogle Scholar
  10. 10.
    Eren, T., Goldenberg, O., Whiteley, W., Yang, Y. R., Morse, A. S., & Anderson, B. D., et al. (2004). Rigidity, computation, and randomization in network localization. In: INFOCOM 2004. Twenty-third annual joint conference of the IEEE computer and communications societies (Vol. 4, pp. 2673–2684). IEEEGoogle Scholar
  11. 11.
    Fang, J., & Morse, A. S. (2009). Merging globally rigid graphs and sensor network localization. In: Proceedings of the 48th IEEE conference on decision and control, 2009 held jointly with the 2009 28th Chinese control conference, CDC/CCC 2009 (pp. 1074–1079). IEEEGoogle Scholar
  12. 12.
    Goldenberg, D. K., Bihler, P., Cao, M., Fang, J., Anderson, B., & Morse, A. S., et al. (2006). Localization in sparse networks using sweeps. In: Proceedings of the 12th annual international conference on mobile computing and networking (pp. 110–121). ACMGoogle Scholar
  13. 13.
    Goldenberg, D. K., Krishnamurthy, A., Maness, W. C., Yang, Y. R., Young, A., & Morse, A. S., et al. (2005). Network localization in partially localizable networks. In: Proceedings IEEE, 24th annual joint conference of the IEEE computer and communications societies INFOCOM 2005 (Vol. 1, pp. 313–326). IEEEGoogle Scholar
  14. 14.
    Gortler, S. J., Healy, A. D., & Thurston, D. P. (2010). Characterizing generic global rigidity. American Journal of Mathematics, 132(4), 897–939.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Hendrickson, B. (1992). Conditions for unique graph realizations. SIAM Journal on Computing, 21(1), 65–84.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2004). Unit disk graph approximation. In: Proceedings of the 2004 joint workshop on foundations of mobile computing (pp. 17–23). ACMGoogle Scholar
  17. 17.
    Laman, G. (1970). On graphs and rigidity of plane skeletal structures. Journal of Engineering mathematics, 4(4), 331–340.MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Liu, Y., Yang, Z., Wang, X., & Jian, L. (2010). Location, localization, and localizability. Journal of Computer Science and Technology, 25(2), 274–297.CrossRefGoogle Scholar
  19. 19.
    Mao, G., Fidan, B., & Anderson, B. (2007). Wireless sensor network localization techniques. Computer Networks, 51(10), 2529–2553.CrossRefMATHGoogle Scholar
  20. 20.
    Moore, D., Leonard, J., Rus, D., & Teller, S. (2004). Robust distributed network localization with noisy range measurements. In: Proceedings of the 2nd international conference on embedded networked sensor systems (pp. 50–61). ACMGoogle Scholar
  21. 21.
    Wang, X., Liu, Y., Yang, Z., Lu, K., & Luo, J. (2014). Robust component based localizationin sparse networks. IEEE Transactions on Parallel and Distributed Systems, 25(5), 1317–1327.CrossRefGoogle Scholar
  22. 22.
    Wang, X., Luo, J., Liu, Y., Li, S., & Dong, D. (2011). Component-based localization in sparse wireless networks. IEEE/ACM Transactions on Networking (ToN), 19(2), 540–548.CrossRefGoogle Scholar
  23. 23.
    Xiao, Q., Bu, K., Wang, Z., & Xiao, B. (2013). Robust localization against outliers in wireless sensor networks. ACM Transactions on Sensor Networks (TOSN), 9(2), 24.CrossRefGoogle Scholar
  24. 24.
    Yang, Z., Jian, L., Wu, C., & Liu, Y. (2013). Beyond triangle inequality: Sifting noisy and outlier distance m for localization. ACM Transactions on Sensor Networks (TOSN), 9(2), 26.CrossRefGoogle Scholar
  25. 25.
    Yang, Z., & Liu, Y. (2012). Understanding node localizability of wireless ad hoc and sensor networks. IEEE Transactions on Mobile Computing, 11(8), 1249–1260.CrossRefGoogle Scholar
  26. 26.
    Yang, Z., Liu, Y., & Li, X. Y. (2010). Beyond trilateration: On the localizability of wireless ad hoc networks. IEEE/ACM Transactions on Networking (ToN), 18(6), 1806–1814.CrossRefGoogle Scholar
  27. 27.
    Yang, Z., Wu, C., Chen, T., Zhao, Y., Gong, W., & Liu, Y. (2013). Detecting outlier measurements based on graph rigidity for wireless sensor network localization. IEEE Transactions on Vehicular Technology, 62(1), 374–383.CrossRefGoogle Scholar
  28. 28.
    Zhang, Y., Chen, Y., & Liu, Y. (2012). Towards unique and anchor-free localization for wireless sensor networks. Wireless Personal Communications, 63(1), 261–278.CrossRefGoogle Scholar
  29. 29.
    Zhang, Y., Liu, S., Zhao, X., & Jia, Z. (2012). Theoretic analysis of unique localization for wireless sensor networks. Ad Hoc Networks, 10(3), 623–634.CrossRefGoogle Scholar
  30. 30.
    Zhu, Y., Gortler, S., & Thurston, D. (2009). Sensor network localization using sensor perturbation. In: INFOCOM 2009, IEEE (pp. 2796–2800). doi: 10.1109/INFCOM.2009.5062234

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.IIIT-AllahabadAllahabadIndia

Personalised recommendations