Skip to main content
SpringerLink
Log in

Range-free localization algorithm based on connectivity and motion

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

Information about the position of entities is very valuable in many fields. People, animals, robots and sensors are some examples of entities that have been targeted as nodes of interest for localization purposes. Technical advances in ubiquitous computing and wireless communications properties are very valuable means to obtain localization information. This paper presents a novel range-free localization algorithm based on connectivity and motion (LACM). The core of the algorithm is an error function that measures the error of the obtained trajectories with respect to the localization solution space, a multi-dimensional space that encompasses all solutions that satisfy completely the constraints of a range-free localization problem. LACM is a centralized method that can be used standalone or as a refinement phase for other localization methods. Limited-memory Broyden–Fletcher–Goldfarb–Shanno, an unconstrained optimization algorithm, is the numerical method used to minimize the error function. The performance of LACM is validated both through extensive simulations with excellent results in scenarios with irregular communications and by transforming real Bluetooth connectivity traces into localization information.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Notes

  1. Bold non-capital letters are used to denote vectors. Bold capital letters are used to denote matrices. All non-bold letters will represent variables of scalar nature or functions. \(d_{ij}\) denotes the scalar in the row \(i\) and column \(j\) of the matrix \(\mathbf{D}\).

  2. The possibility of perturbing exclusively stationary points has been considered, but preliminary tests produced unsatisfactory results.

References

  1. Baggio, A., & Langendoen, K. (2008). Monte Carlo localization for mobile wireless sensor networks. Ad Hoc Networks, 6(5), 718–733.

    Article  Google Scholar 

  2. Shang, Y., Ruml, W., Zhang, Y., & Fromherz, M. P. J. (2003). Localization from mere connectivity. In Proceedings of the 4th ACM international symposium on mobile ad hoc networking and computing (pp. 201–212).

  3. Shang, Y., Rumi, W., Zhang, Y., & Fromherz, M. (2004). Localization from connectivity in sensor networks. IEEE Transactions on Parallel and Distributed Systems, 15(11), 961–974.

    Article  Google Scholar 

  4. Zhang, S., Cao, J., Li-Jun, C., & Chen, D. (2010). Accurate and energy-efficient range-free localization for mobile sensor networks. IEEE Transactions on Mobile Computing, 9(6), 897–910.

    Article  Google Scholar 

  5. Borg, I., & Groenen, P. (2005). Modern multidimensional scaling, theory and applications. Berlin: Springer.

    MATH  Google Scholar 

  6. Shang, Y., & Ruml, W. (2004). Improved MDS-based localization. In Proceedings of the 23rd annual joint conference of the IEEE computer and communications societies (Vol. 4, pp. 2640–2651).

  7. Costa, J. A., Patwari, N., & Hero, A. O. (2006). Distributed weighted-multidimensional scaling for node localization in sensor networks. ACM Transactions on Sensor Networks, 2(1), 39–64.

    Article  Google Scholar 

  8. Ji, X., & Zha, H. (2004). Sensor positioning in wireless ad-hoc sensor networks using multidimensional scaling. In Proceedings of the 23rd annual joint conference of the IEEE computer and communications societies (pp. 2652–2661).

  9. Hou, C., Hou, Y., Huang, Z., & Zhang, H. (2011). The multidimensional scaling and barycentric coordinates based distributed localization in wireless sensor networks. In Proceedings of the 12th international conference on parallel and distributed computing, applications and technologies (pp. 156–160).

  10. Popescu, D., Hedley, M., & Sathyan, T. (2012). A manifold flattening approach for anchorless localization. Wireless Networks, 18(3), 319–333.

    Article  Google Scholar 

  11. Jin, M., Xia, S., Wu, H., & Gu, X. (2011). Scalable and fully distributed localization with mere connectivity. In Proceedings of the 30th annual joint conference of the IEEE computer and communications societies (pp. 3164–3172).

  12. Yang, Z., Wu, C., & Liu, Y. (2012). Locating in fingerprint space: Wireless indoor localization with little human intervention. In Proceedings of the 18th annual international conference on mobile computing and networking (pp. 269–280).

  13. Handschin, J. E. (1970). Monte Carlo techniques for prediction and filtering of non-linear stochastic processes. Automatica, 6(4), 555–563.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hu, L., & Evans, D. (2004). Localization for mobile sensor networks. In Proceedings of the 10th annual international conference on mobile computing and networking (pp. 45–57).

  15. Rudafshani, M., & Datta, S. (2007). Localization in wireless sensor networks. In Proceedings of the 6th international conference on information processing in sensor networks (pp. 51–60).

  16. Stevens-Navarro, E., Vivekanandan, V., & Wong, V. (2007). Dual and mixture Monte Carlo localization algorithms for mobile wireless sensor networks. In Proceedings of IEEE wireless communications and networking conference (pp. 4024–4028).

  17. Wang, Y., & Wang, Z. (2011). Accurate and computation-efficient localization for mobile sensor networks. In Proceedings of international conference on wireless communications and signal processing (pp. 1–5).

  18. Mei, J., Chen, D., Gao, J., Gao, Y., & Yang, L. (2012). Range-free Monte Carlo localization for mobile wireless sensor networks. In Proceedings of the international conference on computer science service system (pp. 1066–1069).

  19. Doucet, A., Defreitas, N., & Gordon, N. (2001). An introduction to sequential Monte Carlo methods. New York: Springer.

    Book  Google Scholar 

  20. Chiou, Y.-S., Wang, C.-L., & Yeh, S.-C. (2010). An adaptive location estimator using tracking algorithms for indoor WLANs. Wireless Networks, 16(7), 1987–2012.

    Article  Google Scholar 

  21. Chiou, Y.-S., Wang, C.-L., & Yeh, S.-C. (2011). Reduced-complexity scheme using alpha–beta filtering for location tracking. IET Communications, 5(13), 1806–1813.

    Article  MathSciNet  MATH  Google Scholar 

  22. Vivekanandan, V., & Wong, V. (2006). Ordinal MDS-based localization for wireless sensor networks. In Proceedings of the 64th IEEE vehicular technology conference, 2006 (pp. 1–5).

  23. Nocedal, J. (1980). Updating quasi-Newton matrices with limited storage. Mathematics of Computation, 35(151), 773–782.

    Article  MathSciNet  MATH  Google Scholar 

  24. Broyden, C. G. (1970). The convergence of a class of double-rank minimization algorithms. IMA Journal of Applied Mathematics, 6(1), 76–90.

    Article  MathSciNet  MATH  Google Scholar 

  25. Fletcher, R. (1970). A new approach to variable metric algorithms. The Computer Journal, 13(3), 317–322.

    Article  MathSciNet  MATH  Google Scholar 

  26. Goldfarb, D. (1970). A family of variable-metric methods derived by variational means. Mathematics of Computation, 24, 23–26.

    Article  MathSciNet  MATH  Google Scholar 

  27. Shanno, D. F. (1970). Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation, 24, 647–656.

    Article  MathSciNet  Google Scholar 

  28. Armijo, L. (1966). Minimization of functions having Lipshitz continuous first partial derivatives. Pacific Journal of Mathematics, 16(1), 1–3.

    Article  MathSciNet  MATH  Google Scholar 

  29. Wolfe, P. (1969). Convergence conditions for ascent methods. Society for Industrial and Applied Mathematics (SIAM), 11(2), 226–235.

    MathSciNet  MATH  Google Scholar 

  30. Dennis, J. E., & Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations. Society for Industrial and Applied Mathematics. doi:10.1137/1.9781611971200.

  31. Nocedal, J., & Wright, S. J. (2006). Line search methods. In Numerical optimization, Springer series in operations research and financial engineering (pp. 30–65). New York: Springer.

  32. Bulusu, N., Bychkovskiy, V., Estrin, D., & Heidemann, J. (2002). Scalable, ad hoc deployable RF-based localization. In Proceedings of the grace hopper conference on celebration of women in computing.

  33. (2010). MATLAB version 7.10.0. Natick. Massachusetts: The MathWorks Inc.

  34. (2013). http://www.di.ens.fr/mschmidt/Software/minFunc.html. Accessed July 2013.

  35. Kuhn, F., Wattenhofer, R., & Zollinger, A. (2003). Ad-hoc networks beyond unit disk graphs. In Proceedings of the 2003 joint workshop on foundations of mobile computing, New York, USA (pp. 69–78).

  36. Cabero, J. M., Molina, V., Urteaga, I., Liberal, F., & Martín, J. L. (2012). Acquisition of human traces with Bluetooth technology: Challenges and proposals. Ad Hoc Networks. doi:10.1016/j.adhoc.2012.05.007.

  37. (2013). http://crawdad.org/tecnalia/humanet. Accessed July 2013.

Download references

Acknowledgments

The authors would like to thank Virginia Molina and Iñigo Urteaga for their inestimable work in the generation and processing of the real database. This work has been partially supported by the European Project SAIL (Project 257448).

Author information

Authors and Affiliations

  1. Tecnalia Research and Innovation, Parque Tecnológico, Edificio 202, 48170, Zamudio, Spain

    José María Cabero, Ignacio Olabarrieta, Sergio Gil-López & Javier Del Ser

  2. Department of Electronics and Telecommunication, Faculty of Engineering, University of the Basque Country, Alda. Urquijo s/n, 48013, Bilbao, Spain

    José Luis Martín

Authors
  1. José María Cabero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ignacio Olabarrieta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergio Gil-López
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Javier Del Ser
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. José Luis Martín
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José María Cabero.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cabero, J.M., Olabarrieta, I., Gil-López, S. et al. Range-free localization algorithm based on connectivity and motion. Wireless Netw 20, 2287–2305 (2014). https://doi.org/10.1007/s11276-014-0741-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-014-0741-y

Keywords

Search

Navigation