Sensor Network Localization Using Least Squares Kernel Regression

  • Anthony Kuh
  • Chaopin Zhu

This chapter considers the sensor network localization problem using signal strength. Signal strength information is stored in a kernel matrix. Least squares kernel 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 as 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. We also consider the cases where sensors are mobile and on-line kernel regression learning algorithms are formulated to track moving sensors. Finally, we discuss some physical constraints on the sensor networks (i.e., communication and power constraints). To deal with these constraints, we proposed using distributed learning algorithms to cut down on communications between sensors. An ensemble of learners each solve a kernel regression algorithm and then communicate among each other to reach a solution. The communication costs are lowered using distributed learning algorithms and through simulations we show that the performance is comparable to the centralized kernel regression solution.


Sensor Network Signal Strength Fusion Center Kernel Matrix Base Node 
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 (2002)Google Scholar
  2. 2.
    Blake, C., Merz, C.: UCI repository of machine learning databases. Department of Information and Computer Science, UC Irvine, Irvine, CA (1998)Google Scholar
  3. 3.
    Breiman, L.: Bagging predictors. Machine Learning 26(2), 1579–1619 (1996)Google Scholar
  4. 4.
    Broch, J., Maltz, D., Johnson, D., Hu, Y.C., Jetcheva, J.: A performance comparison of multi-hop wireless ad hoc network routing protocols.In:Proceedings of the Fourth Annual ACM/IEEE International Conference on Mobile Computing and Networking (MobiCom’98). Dallas, TX (1998)Google Scholar
  5. 5.
    Bulusu, N., Heidemann, J., Estrin, D.: GPS-less low cost outdoor localization for very small devices. Technical Report 00-0729, Computer Science Department, University of Southern California (2000)Google Scholar
  6. 6.
    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
  7. 7.
    Cawley, G., Talbot, N.: A greedy training algorithm for sparse least-squares support vector machines. In: Proceedings of the International Conference on Artificial Neural Networks ICANN 2002, pp. 681–686. Madrid, Spain (2002)CrossRefGoogle Scholar
  8. 8.
    Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge, UK (2000)Google Scholar
  9. 9.
    Csato, L., Opper, M.: Sparse on-line gaussian processes. Neural Computation 14, 641–668 (2002)MATHCrossRefGoogle Scholar
  10. 10.
    Engel, Y., Mannor, S., Meir, R.: The kernel recursive least-squares algorithm. IEEE Transactions on Signal Processing 52(8), 2275–2285 (2004)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Freund, Y., Schapire, R.: Experiments with a new boosting algorithm. In: Machine Learning: Proceedings of the Thirteenth International Conference, pp. 148–156 (1996)Google Scholar
  12. 12.
    Freund, Y., Schapire, R.: A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer System and Sciences 55(1), 119–139 (1997)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    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 (2004)Google Scholar
  14. 14.
    Haykin, S.: Adaptive Filter Theory, 4th edn. Prentice-Hall, Englewood Cliffs, NJ (2003)Google Scholar
  15. 15.
    Hightower, J., Borriello., G.: Real-time error in location modeling for ubiquitous computing. In: Location, Modeling for Ubiquitous Computing, Ubicomp 2001 Workshop Proceedings, pp. 21–27 (2001)Google Scholar
  16. 16.
    Jagannathan, G., Wright, R.: Privacy-preserving distributed k-means clustering over arbitrarily partitioned data. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD) (2005)Google Scholar
  17. 17.
    Jordan, M.: Learning in Graphical Models. MIT Press, Cambridge, MA (1999)Google Scholar
  18. 18.
    de Kruif, B.: Function approximation for learning control, a key sample based approach. Ph.D. thesis, University of Twente, Netherland (2004)Google Scholar
  19. 19.
    Kuh, A.: Intelligent recursive kernel subspace estimation algorithms. In: The 39th Annual Conference of Information Sciences and Systems (CISS 2005), pp. 216–221. Baltimore, MD (2005)Google Scholar
  20. 20.
    Lazarevic, A., Obradovic, D.: The distributed boosting algorithm. In: KDD ’01, Proceedings of the seventh ACM KDD conference on Knowledge Discovery and Data Mining. San Francisco, CA (2001)Google Scholar
  21. 21.
    Muller, K., Mika, S., Ratsch, G., Tsuda, K., Scholkopf, B.: An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks 12(2), 181–202 (2001)CrossRefGoogle Scholar
  22. 22.
    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
  23. 23.
    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
  24. 24.
    Predd, J., Kulkarni, S., Poor, H.: 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 (2005)Google Scholar
  25. 25.
    Predd, J., Kulkarni, S., Poor, V.: Distributed learning in wireless sensor networks. IEEE Signal Processing Magazine 23(4), 56–69 (2006)CrossRefGoogle Scholar
  26. 26.
    Rabbat, M., Nowak, R.: Quantized incremental algorithms for distributed optimization. IEEE Journal on Selected Areas in Communications 23(4), 798–808 (2006)CrossRefGoogle Scholar
  27. 27.
    Rifkin, R.: Learning with kernels: Support vector machines, regularization, optimization and beyond. Ph.D. thesis, MIT (2002)Google Scholar
  28. 28.
    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
  29. 29.
    Seidel, S., Rappaport, T.: 914 MHz path loss prediction models for indoor wireless communications in multifloored buildings. IEEE Transactions on Antennas and Propagation 40(2), 207–217 (1992)CrossRefGoogle Scholar
  30. 30.
    Smola, A., Schölkopf, B.: Sparse greedy matrix approximation for machine learning. In: Proceedings of the 17th International Conference on Machine Learning, pp. 911–918. Morgan Kaufmann, USA (2000)Google Scholar
  31. 31.
    Stojmenovic, I.: Position-based routing in ad hoc networks. IEEE Communications Magazine 40(7), 128–134 (2002)CrossRefGoogle Scholar
  32. 32.
    Suykens, J., Gestel, T.V., Brabanter, J.D., Moor, B.D., Vandewalle, J.: Least Squares Support Vector Machines. World Scientific, Singapore (2002)MATHGoogle Scholar
  33. 33.
    Vapnik, V.: Statistical Learning Theory. Wiley, New York City, NY (1998)MATHGoogle Scholar
  34. 34.
    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). Honolulu, HI (2005)Google Scholar
  35. 35.
    Zhu, C., Kuh, A.: Ad hoc sensor network localization using distributed kern regression algorithms. In: 2007 International Conference on Acoustics, Speech, and Signal Processing, vol. 2, pp. 497–500. Honolulu, HI (2007)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Anthony Kuh
    • 1
  • Chaopin Zhu
    • 2
  1. 1.University of HawaiiHonoluluUSA
  2. 2.Juniper NetworksSunnyvaleUSA

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