Quantitatively Investigating Multihop Localization Errors in Regular 2-D Sensor Networks

  • Bing Jia
  • Baoqi HuangEmail author
  • Tao Zhou
  • Wuyungerile Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11336)


In practice, a wireless sensor network normally includes a small portion of nodes with known locations, termed anchors, and the other nodes with unknown locations, termed sensors, have to be localized through dedicated algorithms. Since not every sensor is directly neighboring with anchors, sensor locations are determined in a multi-hop localization manner, and therein, localization errors of sensors display to rise up with their minimal hop count to anchors, which is termed error propagation. Grasping the rule of error propagation is critical to design and develop both localization algorithms as well as various applications. In this paper, we focus on quantitatively measuring how the localization errors vary across different sensors. To do so, regular 2-dimensional wireless sensor networks are taken into consideration, and formulae with respect to different sensors and different anchor placement are obtained. Simulation results are conducted to validate these formulae and analyze the characteristics of error propagation.


Localization errors Wireless sensor network Multihop Error propagation 


  1. 1.
    Albowicz, J., Chen, A., Zhang, L.: Recursive position estimation in sensor networks. In: 2001 Ninth International Conference on Network Protocols, pp. 35–41. IEEE (2001)Google Scholar
  2. 2.
    Huang, B., Yu, C., Anderson, B., Mao, G.: Estimating distances via connectivity in wireless sensor networks. Wirel. Commun. Mob. Comput. 14(5), 541–556 (2014)CrossRefGoogle Scholar
  3. 3.
    Liu, Z., Luo, D., Li, J., Chen, X., Jia, C.: N-mobishare: new privacy-preserving location-sharing system for mobile online social networks. Int. J. Comput. Math. 93(2), 384–400 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Han, G., Jiang, J., Zhang, C., Duong, T.Q., Guizani, M., Karagiannidis, G.K.: A survey on mobile anchor node assisted localization in wireless sensor networks. IEEE Commun. Surv. Tutor. 18(3), 2220–2243 (2016)CrossRefGoogle Scholar
  5. 5.
    Huang, Y., Li, B., Liang, S., Ma, H., Liu, Z.: Generalized format-preserving encryption for character data. J. Netw. 7(8), 1239–1244 (2016)Google Scholar
  6. 6.
    Liu, Z., Li, T., Li, P., Jia, C., Li, J.: Verifiable searchable encryption with aggregate keys for data sharing system. Futur. Gener. Comput. Syst. 78, 778–788 (2017)CrossRefGoogle Scholar
  7. 7.
    Dil, B., Dulman, S., Havinga, P.: Range-based localization in mobile sensor networks. In: Römer, K., Karl, H., Mattern, F. (eds.) EWSN 2006. LNCS, vol. 3868, pp. 164–179. Springer, Heidelberg (2006). Scholar
  8. 8.
    Liu, J., Zhang, Y., Zhao, F.: Robust distributed node localization with error management. In: Proceedings of the 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing, pp. 250–261. ACM (2006)Google Scholar
  9. 9.
    Huang, B., Yu, C., Anderson, B.: Understanding error propagation in multi-hop sensor network localization. IEEE Trans. Ind. Electron. 60(12), 5811–5819 (2013)CrossRefGoogle Scholar
  10. 10.
    Huang, B., Yu, C., Anderson, B.D.: Error propagation in sensor network localization with regular topologies. In: Global Telecommunications Conference, GLOBECOM 2009, pp. 1–6. IEEE (2009)Google Scholar
  11. 11.
    Huang, B., Yu, C., Anderson, B.D.: Analyzing error propagation in range-based multihop sensor 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. 865–870. IEEE (2009)Google Scholar
  12. 12.
    Akaike, H.: Block toeplitz matrix inversion. SIAM J. Appl. Math. 24(2), 234–241 (1973)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Meurant, G.: A review on the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM J. Matrix Anal. Appl. 13(3), 707–728 (1992)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Bing Jia
    • 1
    • 2
  • Baoqi Huang
    • 1
    • 2
    Email author
  • Tao Zhou
    • 1
    • 2
  • Wuyungerile Li
    • 1
    • 2
  1. 1.Inner Mongolia A.R. Key Laboratory of Wireless Networking and Mobile ComputingHohhotChina
  2. 2.College of Computer ScienceInner Mongolia UniversityHohhotChina

Personalised recommendations