Abstract
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.
Supported by the National Natural Science Foundation of China under Grants 41761086, 41401519, 61461037, 61761035 and 61661041, the National Science and Technology Major Project of the Ministry of Science and Technology of China under Grant No. 2016YFB0502102, the Natural Science Foundation of Inner Mongolia Autonomous Region of China under Grant 2017JQ09, and the Grassland Elite Project of the Inner Mongolia Autonomous Region under Grant CYYC5016.
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References
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)
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)
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)
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)
Huang, Y., Li, B., Liang, S., Ma, H., Liu, Z.: Generalized format-preserving encryption for character data. J. Netw. 7(8), 1239–1244 (2016)
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)
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). https://doi.org/10.1007/11669463_14
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)
Huang, B., Yu, C., Anderson, B.: Understanding error propagation in multi-hop sensor network localization. IEEE Trans. Ind. Electron. 60(12), 5811–5819 (2013)
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)
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)
Akaike, H.: Block toeplitz matrix inversion. SIAM J. Appl. Math. 24(2), 234–241 (1973)
Meurant, G.: A review on the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM J. Matrix Anal. Appl. 13(3), 707–728 (1992)
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Jia, B., Huang, B., Zhou, T., Li, W. (2018). Quantitatively Investigating Multihop Localization Errors in Regular 2-D Sensor Networks. In: Vaidya, J., Li, J. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2018. Lecture Notes in Computer Science(), vol 11336. Springer, Cham. https://doi.org/10.1007/978-3-030-05057-3_36
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DOI: https://doi.org/10.1007/978-3-030-05057-3_36
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