Abstract
In this paper, we address the received signal strength (RSS)-based indoor localization problem in a wireless local area network (WLAN) environment and formulate it as a multi-class classification problem using survey locations as classes. We present a discriminatively regularized least square classifier (DRLSC)-based localization algorithm that is aimed at making use of the class label information to better distinguish the RSS samples taken from different locations after proper transformation. Besides DRLSC, two other regularized least square classifiers (RLSCs) are also presented for comparison. We show that these RLSCs can be expressed in a unified problem formulation with a closed-form solution and convenient assessment of the convexity of the problem. We then extend the linear RLSCs to their nonlinear counterparts via the kernel trick. Moreover, we address the missing value problem, utilize clustering to reduce the training and online complexity, and introduce kernel alignment for fast kernel parameter tuning. Experimental results show that, compared with other methods, the kernel DRLSC-based algorithm achieves superior performance for indoor localization when only a small fraction of the data samples are used.
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M. Rodriguez, J. Favela, E. Martinez, and M. Munoz, Location-aware access to hospital information and services, IEEE Transactions on Information Technology in Biomedicine, Vol. 8, No. 4, pp. 448–455, 2004.
H. Harroud, M. Ahmed, and A. Karmouch, Policy-driven personalized multimedia services for mobile users, IEEE Transactions on Mobile Computing, Vol. 2, No. 1, pp. 16–24, 2003.
C. Patterson, R. Muntz, and C. Pancake, Challenges in location-aware computing, IEEE Pervasive Computing, Vol. 2, No. 1, pp. 80–89, 2003.
J. Pan, J. Kwok, Q. Yang, and Y. Chen, Multidimensional vector regression for accurate and low-cost location estimation in pervasive computing, IEEE Transactions on Knowledge and Data Engineering, Vol. 18, No. 9, pp. 1181–1193, 2006.
A. Kushki, K. Plataniotis, and A. Venetsanopoulos, Kernel-based positioning in wireless local area networks, IEEE Transactions on Mobile Computing, Vol. 6, No. 6, pp. 689–705, 2007.
P. Bahl and V. Padmanabhan, RADAR: an in-building RF-based user location and tracking system, in INFOCOM 2000. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE, Vol. 2. Ieee, pp. 775–784, 2002.
T. Roos, P. Myllymäki, H. Tirri, P. Misikangas, and J. Sievänen, A probabilistic approach to WLAN user location estimation, International Journal of Wireless Information Networks, Vol. 9, No. 3, pp. 155–164, 2002.
X. Li, RSS-based location estimation with unknown pathloss model, IEEE Transactions on Wireless Communications, Vol. 5, No. 12, pp. 3626–3633, 2006.
R. Ouyang, A. Wong, and C. Lea, Received signal strength-based wireless localization via semidefinite programming: noncooperative and cooperative schemes, IEEE Transactions on Vehicular Technology, Vol. 59, No. 3, pp. 1307–1318, 2010.
X. Li and K. Pahlavan, Super-resolution TOA estimation with diversity for indoor geolocation, IEEE Transactions on Wireless Communications, Vol. 3, No. 1, pp. 224–234, 2004.
C. Yang, Y. Huang, and X. Zhu, Hybrid TDOA/AOA method for indoor positioning systems, in Location Technologies, 2007. The Institution of Engineering and Technology Seminar on. IET, London, pp. 1–5, 2008.
M. Kjærgaard, A taxonomy for radio location fingerprinting, in Proceedings of the 3rd International Conference on Location-and Context-Awareness. Springer-Verlag, Heidelberg, pp. 139–156, 2007.
N. Patwari, I. Hero, A. O., M. Perkins, N. S. Correal, and R. J. O’Dea, Relative location estimation in wireless sensor networks, IEEE Transactions on Signal Processing, Vol. 51, No. 8, pp. 2137–2148, 2003.
K. Pahlavan and A. Levesque, Wireless Information Networks. Wiley Online Library, 1995.
A. Molisch, K. Balakrishnan, C. Chong, S. Emami, A. Fort, J. Karedal, J. Kunisch, H. Schantz, U. Schuster, and K. Siwiak, IEEE 802.15. 4a channel model-final report, IEEE P, Vol. 15, pp. 802–1504, 2006.
A. Haeberlen, E. Flannery, A. Ladd, A. Rudys, D. Wallach, and L. Kavraki, Practical robust localization over large-scale 802.11 wireless networks, in Proceedings of the 10th Annual International Conference on Mobile Computing and Networking. ACM, New York, pp. 70–84, 2004.
M. McGuire, K. Plataniotis, and A. Venetsanopoulos, Location of mobile terminals using time measurements and survey points, IEEE Transactions on Vehicular Technology, Vol. 52, No. 4, pp. 999–1011, 2003.
Z. Wu, C. Li, J. Ng, and K. Leung, Location estimation via support vector regression, IEEE Transactions on Mobile Computing, Vol. 6, No. 3, pp. 311–321, 2007.
C. Bishop et al., Pattern Recognition and Machine Learning. Springer, New York, 2006.
E. Alpaydin, Introduction to Machine Learning, 2nd ed. The MIT Press, Cambridge, 2010.
M. Brunato, C. Kalló, et al., Transparent location fingerprinting for wireless services, in Proceedings of Med-Hoc-Net, Vol. 2002. Citeseer, 2002.
M. Youssef, A. Agrawala, U. Shankar, et al., WLAN location determination via clustering and probability distributions, in Proceedings of the First IEEE International Conference on Pervasive Computing and Communications, 2003 (PerCom 2003). IEEE, pp. 143–150, 2003.
Y. Chen, Q. Yang, J. Yin, and X. Chai, Power-efficient access-point selection for indoor location estimation, IEEE Transactions on Knowledge and Data Engineering, pp. 877–888, 2006.
H. Xue, S. Chen, and Q. Yang, Discriminatively regularized least-squares classification, Pattern Recognition, Vol. 42, No. 1, pp. 93–104, 2009.
J. Suykens and J. Vandewalle, Least squares support vector machine classifiers, Neural Processing Letters, Vol. 9, No. 3, pp. 293–300, 1999.
M. Belkin, P. Niyogi, and V. Sindhwani, Manifold regularization: a geometric framework for learning from labeled and unlabeled examples, The Journal of Machine Learning Research, Vol. 7, pp. 2399–2434, 2006.
K. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, An introduction to kernel-based learning algorithms, IEEE Transactions on Neural Networks, Vol. 12, No. 2, pp. 181–201, 2001.
B. Marlin, Missing data problems in machine learning, Ph.D. dissertation, Citeseer, 2008.
N. Cristianini, J. Kandola, A. Elisseeff, and J. Shawe-Taylor, On kernel target alignment, Innovations in Machine Learning, pp. 205–256, 2006.
Z. Chen and S. Haykin, On different facets of regularization theory, Neural Computation, Vol. 14, No. 12, pp. 2791–2846, 2002.
J. Ye and T. Xiong, SVM versus least squares SVM, in Proceedings of the International Conference on Artificial Intelligence and Statistics. Citeseer, pp. 640–647, 2007.
L. Doherty, K. S. J. pister, and L. El Ghaoui, Convex position estimation in wireless sensor networks, in INFOCOM 2001. Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE, Vol. 3, pp. 1655–1663, 2001.
B. Schölkopf and A. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, 2002.
J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge, 2004.
H. Li, T. Jiang, and K. Zhang, Efficient and robust feature extraction by maximum margin criterion, IEEE Transactions on Neural Networks, Vol. 17, No. 1, pp. 157–165, 2006.
H. Hashemi, The indoor radio propagation channel, Proceedings of the IEEE, Vol. 81, No. 7, pp. 943–968, 2002.
S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, 1993.
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Ouyang, R.W., Wong, A.KS. & Woo, K.T. Indoor Localization via Discriminatively Regularized Least Square Classification. Int J Wireless Inf Networks 18, 57–72 (2011). https://doi.org/10.1007/s10776-011-0133-5
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DOI: https://doi.org/10.1007/s10776-011-0133-5