Sensor Network Localization Using Least Squares Kernel Regression

  • Anthony Kuh
  • Chaopin Zhu
  • Danilo Mandic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4253)


This paper considers the sensor network localization problem using signal strength. Unlike range-based methods signal strength information is stored in a kernel matrix. Least squares regression methods are then used to get an estimate of the location of unknown sensors. Locations are represented as complex numbers with the estimate function consisting of a linear weighted sum of kernel entries. The regression estimates have similar performance to previous localization methods using kernel classification methods, but at reduced complexity. Simulations are conducted to test the performance of the least squares kernel regression algorithm. Finally, the paper discusses on-line implementations of the algorithm, methods to improve the performance of the regression algorithm, and using kernels to extract other information from distributed sensor networks.


Sensor Network Signal Strength Localization Algorithm Kernel Matrix Kernel Regression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Akyildiz, I., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor networks. IEEE Communications Magazine, 102–114 (August 2002)Google Scholar
  2. 2.
    Bulusu, N., Heidemann, J., Estrin, D.: GPS-less low cost outdoor localization for very small devices. Tech. Rep. 00-0729, Computer Science Dept., Univ. of Southern California (2000)Google Scholar
  3. 3.
    Castro, P., Chiu, P., Kremenek, T., Muntz, R.: A probabilistic room location service for wireless networked environments. In: ACM Ubicomp 2001, Atlanta, GA (2001)Google Scholar
  4. 4.
    de Kruif, B.: Function approximation for learning control, a key sample based approach. Ph.D. thesis, University of Twente, Netherland (2004)Google Scholar
  5. 5.
    Guestrin, C., Bodik, P., Thibaux, R., Paskin, M., Madden, S.: Distributed regression; an efficient framework for modeling sensor network data. In: Information Processing in Sensor Networks 2004, Berkeley, CA (April 2004)Google Scholar
  6. 6.
    Hightower, J., Borriello, G.: Real-time error in location modeling for ubiquitous computing, in Location, Modeling for Ubiquitous Computing. In: Ubicomp 2001 Workshop Proceedings, pp. 21–27 (2001)Google Scholar
  7. 7.
    Kuh, A.: Intelligent recursive kernel subspace estimation algorithms. In: The 39th Annual Conference of Information Sciences and Systems (CISS 2005), Baltimore, MD, pp. 216–221 (2005)Google Scholar
  8. 8.
    Muller, K., Mika, S., Ratsch, G., Tsuda, K., Scholkopf, B.: An Introduction to Kernel-Based Learning Algorithms. IEEE Trans. on Neural Networks 12(2), 181–202 (2001)CrossRefGoogle Scholar
  9. 9.
    Nguyen, X., Jordan, M., Sinopoli, B.: A kernel-based learning approach to ad hoc sensor network localization. ACM Transactions on Sensor Networks 1(1), 134–152 (2005)CrossRefGoogle Scholar
  10. 10.
    Patwari, N., Hero, A., Perkins, M., Correat, N., O’Dea, R.: Relative location estimation in wireless sensor networks. IEEE Transaction on Signal Processing 51(8), 2137–2148 (2003)CrossRefGoogle Scholar
  11. 11.
    Predd, J.B., Kulkarni, S.R., Poor, H.V.: Distributed Regression in Sensor Networks: Training Distributively with Alternating Projections. In: Proceedings of the SPIE Conference and Advanced Signal Processing Algorithms, Architectures, and Implementations XV, San Diego, CA (August 2005)Google Scholar
  12. 12.
    Roos, T., Myllymaki, P., Tirri, H.: A statistical modeling approach to location estimation. IEEE Transactions on Mobile Computing 1(1), 59–69 (2002)CrossRefGoogle Scholar
  13. 13.
    Seidel, S., Rappaport, T.: 914MHz path loss prediction models for indoor wireless communications in multifloored buildings. IEEE Transactions on Antennas and Propagation 40(2), 207–217 (1992)CrossRefGoogle Scholar
  14. 14.
    Suykens, J., Van Gestel, T., De Brabanter, J., De Moor, B., Vandewalle, J.: Least squares support vector machines. World Scientific Publishing Co., Singapore (2002)MATHCrossRefGoogle Scholar
  15. 15.
    Vapnik, V.: Statistical learning theory. John Wiley, New York (1998)MATHGoogle Scholar
  16. 16.
    Zhu, C., Kuh, A.: Sensor network localization using pattern recognition and least squares kernel methods. In: Proceedings of 2005 Hawaii, IEICE and SITA Joint Conference on Information Theory (HISC 2005), May 25-27, 2005, Honolulu, HI (2005)Google Scholar
  17. 17.
    Zhu, C., Kuh, A.: Dynamic Ad Hoc network localization using online least squares kernel subspace methods. In: 2006 IEEE International Symposium on Information Theory, Seattle, WA (July 2006) (submitted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Anthony Kuh
    • 1
  • Chaopin Zhu
    • 1
  • Danilo Mandic
    • 2
  1. 1.University of Hawaii 
  2. 2.Imperial College London 

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