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On the optimal anchor placement in single-hop sensor localization

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Abstract

In wireless sensor networks, the problem of anchor (whose locations are a priori known) placement plays a vital role in improving the estimation accuracy of sensor (whose locations are unknown and need to be determined) locations. This paper deals with single-hop sensor localization from a novel perspective. On the one hand, unlike existing studies relying on ideal independent identically distributed (i.i.d.) noises in distance measurements, namely distance-independent noises, this paper defines a more realistic noise model in the sense that the noise variance is a function of sensor-to-anchor distances, namely distance-dependent noises. On the other hand, other than evaluating the localization performance for sensors at deterministic locations, a statistical approach is adopted by assuming a uniform and random distribution within a unit disk for the sensor location and evaluating the mean value of the associated Fisher information matrix determinant as the optimality metric for anchor placement. Through this metric, the optimal anchor placement is investigated from both theoretical and simulative perspectives. In the literature of optimal anchor placement with distance-independent noises, it has been addressed or conjectured to be true that it is optimal to have anchors equally spaced on the boundary. However, after a thorough analysis, it is shown that this conclusion is generally incorrect, but approaches to be true provided that the number of anchors goes to infinity. This study not only provides useful guidance for optimally deploying anchors in practice, but also yields valuable insights for future research on optimal anchor placement.

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Notes

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    Having only two anchors in a plane, though results in flip ambiguities, is indicative of understanding the characteristics of localization performance.

References

  1. 1.

    Ho, K. C., Lu, X., & Kovavisaruch, L. (2007). Source localization using TDOA and FDOA measurements in the presence of receiver location errors: Analysis and solution. IEEE Transactions on Signal Processing, 55(2), 684–696.

  2. 2.

    Huang, Y., Benesty, J., Elko, G. W., et al. (2001). Real-time passive source localization: A practical linear-correction least-squares approach. IEEE Transactions on Speech and Audio Processing, 9(8), 943–956.

  3. 3.

    Yang, K., Wang, G., & Luo, Z. Q. (2009). Efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals. IEEE Transactions on Signal Processing, 57(7), 2775–2784.

  4. 4.

    Xu, E., Ding, Z., & Dasgupta, S. (2011). Reduced complexity semidefinite relaxation algorithms for source localization based on time difference of arrival. IEEE Transactions on Mobile Computing, 10(9), 1276–1282.

  5. 5.

    Huang, B., Xie, L., & Yang, Z. (2015). TDOA-based source localization with distance-dependent noises. IEEE Transactions on Wireless Communications, 14(1), 468–480.

  6. 6.

    Zou, H., Huang, B., Lu, X., Jiang, H., & Xie, L. (2016). A robust indoor positioning system based on the procrustes analysis and weighted extreme learning machine. IEEE Transactions on Wireless Communications, 15(2), 1252–1266.

  7. 7.

    Dissanayake, M. W. M. G., Newman, P., Clark, S., et al. (2001). A solution to the simultaneous localization and map building (SLAM) problem. IEEE Transactions on Robotics and Automation, 17(3), 229–241.

  8. 8.

    Pathirana, P. N., Bulusu, N., Savkin, A. V., et al. (2005). Node localization using mobile robots in delay-tolerant sensor networks. IEEE Transactions on Mobile Computing, 4(3), 285–296.

  9. 9.

    Van Trees, H. L. (2004). Detection, estimation, and modulation theory. Hoboken: Wiley.

  10. 10.

    Lanzisera, S. M., & Pister, K. (2009). RF ranging for location awareness. Berkeley: University of California.

  11. 11.

    Lanzisera, S., Zats, D., & Pister, K. S. J. (2011). Radio frequency time-of-flight distance measurement for low-cost wireless sensor localization. IEEE Sensors Journal, 11(3), 837–845.

  12. 12.

    Cassioli, D., Win, M. Z., & Molisch, A. F. (2002). The ultra-wide bandwidth indoor channel: From statistical model to simulations. IEEE Journal on Selected Areas in Communications, 20(6), 1247–1257.

  13. 13.

    Bishop, A. N., Fidan, B., Anderson, B. D. O., et al. (2010). Optimality analysis of sensor-target localization geometries. Automatica, 46(3), 479–492.

  14. 14.

    Meng, W., Xie, L., & Xiao, W. (2013). Decentralized TDOA sensor pairing in multihop wireless sensor networks. IEEE Signal Processing Letters, 20(2), 181–184.

  15. 15.

    Isaacs, J. T., Klein, D. J., & Hespanha, J. P. (2009). Optimal sensor placement for time difference of arrival 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. IEEE, pp. 7878–7884.

  16. 16.

    Salman, N., Maheshwari, H. K., Kemp, A. H., et al. (2011). Effects of anchor placement on mean-CRB for localization. In Ad hoc networking workshop (Med-Hoc-Net), 2011 The 10th IFIP annual mediterranean. IEEE, pp. 115–118.

  17. 17.

    Ling, Y., Alexander, S., & Lau, R. (2012). On quantification of anchor placement. In Proceedings IEEE, INFOCOM, 2012. IEEE, pp. 2192–2200.

  18. 18.

    Lasla, N., Younis, M., Ouadjaout, A., et al. (2015). On optimal anchor placement for efficient area-based localization in wireless networks. 2015 IEEE international conference on communications (ICC). IEEE, pp. 3257–3262.

  19. 19.

    Deora, S., & Krishnamachari, B. (2014). Harnessing non-uniform transmit power levels for improved sequence based localization. 2014 IEEE international conference on distributed computing in sensor systems. IEEE, pp. 43–50.

  20. 20.

    Huang, B., Yu, C., & Anderson, B. D. O. (2012). Analyzing localization errors in one-dimensional sensor networks. Signal Processing, 92(2), 427–438.

  21. 21.

    Huang, B., Li, T., Anderson, B. D. O., et al. (2013). Performance limits in sensor localization. Automatica, 49(2), 503–509.

  22. 22.

    Ash, J. N., & Moses, R. L. (2008). On optimal anchor node placement in sensor localization by optimization of subspace principal angles. In 2008 IEEE international conference on acoustics, speech and signal processing. IEEE, pp. 2289–2292.

  23. 23.

    Chan, Y. T., Hang, H. Y. C., & Ching, P. (2006). Exact and approximate maximum likelihood localization algorithms. IEEE Transactions on Vehicular Technology, 55(1), 10–16.

  24. 24.

    Zhu, S., & Ding, Z. (2010). Joint synchronization and localization using TOAs: A linearization based WLS solution. IEEE Journal on Selected Areas in Communications, 28(7), 1017–1025.

  25. 25.

    Patwari, N., Hero, A. O., Perkins, M., et al. (2003). Relative location estimation in wireless sensor networks. IEEE Transactions on Signal Processing, 51(8), 2137–2148.

  26. 26.

    Perez-Ramirez, J., Borah, D. K., & Voelz, D. G. (2013). Optimal 3-D landmark placement for vehicle localization using heterogeneous sensors. IEEE Transactions on Vehicular Technology, 62(7), 2987–2999.

  27. 27.

    Huang, B., Yu, C., & Anderson, B. D. O. (2013). Understanding error propagation in multihop sensor network localization. IEEE Transactions on Industrial Electronics, 60(12), 5811–5819.

  28. 28.

    Niculescu, D., & Nath, B. (2004). Error characteristics of ad hoc positioning systems (APS). In Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing. ACM, pp. 20–30.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant 41401519, the “Grassland Elite” Project of the Inner Mongolia Autonomous Region under Grant CYYC5016, and the Postgraduate Scientific Research Innovation Foundation of Inner Mongolia under Grant 11200-12110201.

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Correspondence to Baoqi Huang.

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Miao, Q., Huang, B. On the optimal anchor placement in single-hop sensor localization. Wireless Netw 24, 1609–1620 (2018). https://doi.org/10.1007/s11276-016-1424-7

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Keywords

  • Sensor localization
  • Optimal anchor placement
  • Single-hop
  • Heteroscedastic noises
  • Fisher information matrix (FIM)