Subscribe

Issue No.09 - September (2011 vol.10)

pp: 1276-1282

Enyang Xu , University of California, Davis, Davis

Zhi Ding , University of California, Davis, Davis

Soura Dasgupta , University of Iowa, Iowa

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TMC.2010.263

ABSTRACT

We investigate the problem of source localization based on measuring time difference of signal arrivals (TDOA) from the source emitter. Taking into account the colored measurement noise, we adopt a min-max principle to develop two lower complexity semidefinite relaxation algorithms that can be reliably solved using semidefinite programming. The reduction of algorithm complexity is achieved through a simple, but effective method to select a reference node among participating measurement nodes such that only selective time differences of signal arrival are exploited. Our estimation methods are insensitive to the source locations and can be used either as the final location estimate or as the initial point for more traditional search algorithms.

INDEX TERMS

Source localization, time difference of arrival, semidefinite programming.

CITATION

Enyang Xu, Zhi Ding, Soura Dasgupta, "Reduced Complexity Semidefinite Relaxation Algorithms for Source Localization Based on Time Difference of Arrival",

*IEEE Transactions on Mobile Computing*, vol.10, no. 9, pp. 1276-1282, September 2011, doi:10.1109/TMC.2010.263REFERENCES

- [1] E.Y. Xu, Z. Ding, and S. Dasgupta, “Robust and Low Complexity Source Localization in Wireless Sensor Networks Using Time Difference of Arrival Measurement,”
Proc. IEEE Wireless Comm. and Networking Conf. (WCNC '10), Apr. 2010.- [2] N. Patwari, J.N. Ash, S. Kyperountas, A. Hero, R.L. Moses, and N.S. Correal, “Locating the Nodes: Cooperative Localization in Wireless Sensor Networks,”
IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 54-69, July 2005.- [3] A.H. Sayed, A. Tarighat, and N. Khajehnouri, “Network-Based Wireless Location: Challenges Faced in Developing Techniques for Accurate Wireless Location Information,”
IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 24-40, July 2005.- [4] P. Biswas, T.-C. Liang, K.-C. Toh, Y. Ye, and T.-C. Wang, “Semidefinite Programming Approaches for Sensor Network Localization with Noisy Distance Measurements,”
IEEE Trans. Automation Science and Eng., vol. 3, no. 4, pp. 360-371, Oct. 2006.- [5] C. Meng, Z. Ding, and S. Dasgupta, “A Semidefinite Programming Approach to Source Localization in Wireless Sensor Networks,”
IEEE Signal Processing Letter, vol. 15, pp. 253-256, May 2008.- [6] Y.T. Chan and K.C. Ho, “A Simple and Efficient Estimator for Hyperbolic Location,”
IEEE Trans. Signal Processing, vol. 42, no. 8, pp. 1905-1915, Aug. 1994.- [7] A. Beck, P. Stoica, and J. Li, “Exact and Approximate Solutions of Source Localization Problems,”
IEEE Trans. Signal Processing, vol. 56, no. 5, pp. 1770-1778, May 2008.- [8] K. Yang, G. Wang, and Z. Luo, “Efficient Convex Relaxation Methods for Robust Target Localization by a Sensor Network Using Time Differences of Arrivals,”
IEEE Trans. Signal Processing, vol. 57, no. 7, pp. 2775-2784, July 2009.- [9] K.W.K. Lui, F.K.W. Chan, and H.C. So, “Semidefinite Programming Approach for Range-Difference Based Source Localization,”
IEEE Trans. Signal Processing, vol. 57, no. 4, pp. 1631-1633, Apr. 2009.- [10] A. Host-Madsen, “On the Existence of Efficient Estimators,”
IEEE Trans. Signal Processing, vol. 48, no. 11, pp. 3028-3031, Nov. 2000.- [11] L. Vandenberghe and S. Boyd, “Semidefinite Programming,”
SIAM Rev., vol. 38, no. 1, pp. 49-95, Mar. 1996.- [12] J.F. Sturm, “Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over Symmetric Cones,”
Optimization Methods Software, vols. 11/12, pp. 625-653, http:/sedumi.mcmaster.ca, 1999.- [13] Z. Ding and Z. Luo, “A Fast Linear Programming Algorithm for Blind Equalization,”
IEEE Trans. Comm., vol. 48, no. 9, pp. 1432-1436, Sept. 2000.- [14] Y. Ding, D. Ge, and H. Wolkowicz, “On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming,” Technical Report CORR 2010-02, Univ. of Waterloo, 2010.
- [15] J. Nocedal and J. Stephen Wright,
Numerical Optimization. Springer Verlag, 1999. |