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Energy-Based Localization in Wireless Sensor Networks Using Second-Order Cone Programming Relaxation

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Abstract

Source localization in wireless sensor networks (WSNs) aims to determine the position of a source in a network, given inaccurate position-bearing measurements. This paper addresses the problem of locating a single source from noisy acoustic energy measurements in WSNs. Under the assumption of Gaussian energy measurement errors, the maximum likelihood (ML) estimator requires the minimization of a nonlinear and nonconvex cost function which may have multiple local optima, thus making the search for the globally optimal solution hard. In this work, an approximate solution to the ML location estimation problem is presented by relaxing the minimization problem to a convex optimization problem, namely second-order cone programming. Simulation results demonstrate the superior performance of the convex relaxation approach. More precisely, the new approach shows an improvement of 20 % in terms of localization accuracy when compared to the existing approaches at moderate to high noise levels. Simulation results further show comparable performance of the new approach and the state-of-art approaches at low noise levels.

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Notes

  1. It is possible to generalize the SLCP algorithm to the weighted case, i.e., to the case when \(y_i \ne g_i P\). However, numerical experiments indicate that the SLCP provides a meaningless solution. This is due to the fact that the almost convexity property of the resulting constraints is not preserved.

  2. Remark that the WDC method [28] can be easily generalized to the case when the source transmit power \(P\) is known.

  3. When the noise is relatively large, the energy measurements generated according to the energy decay model (1) are likely to be negative, which is unreasonable. Hence, in the simulations, if \(y_i < 0\) then \(y_i = 0.001\) is set.

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Acknowledgments

This work was partially supported by Fundação para a Ciência e a Tecnologia under Projects PEst-OE/EEI/UI0066/2011,PTDC/EEA-TEL/099973/2008–ADCOD, PTDC/EEA-TEL/115981/2009–OPPORTUNISTIC-CR, PTDC/EEI-TEL/2990/2012–ADIN and EXPL/EEI-TEL/0969/2013, and Ciência 2008 Post-Doctoral Research Grant. The author is a collaborative member of INESC–INOV, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal. The author would like to thank João Xavier, ISR–IST, Portugal, and Rui Dinis, DEE–UNL, Portugal, for their very constructive suggestions.

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  1. Universidade Lusófona de Humanidades e Tecnologias, Campo Grande 376, 1749-024, Lisboa, Portugal

    Marko Beko

  2. UNINOVA, Campus da FCT/UNL, Monte de Caparica, 2829-516, Caparica, Portugal

    Marko Beko

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Beko, M. Energy-Based Localization in Wireless Sensor Networks Using Second-Order Cone Programming Relaxation. Wireless Pers Commun 77, 1847–1857 (2014). https://doi.org/10.1007/s11277-014-1612-7

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