A Quadratic Constraint Total Least-squares Algorithm for Hyperbolic Location

DOI: 10.4236/ijcns.2008.12017   PDF   HTML     7,955 Downloads   15,929 Views   Citations


A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system model contains error or is not known exactly, and quadratic constraint, which could be realized via Lagrange multipliers technique, could constrain the solution to the location equations to improve location accuracy. Comparisons of performance with ordinary least-squares are made, and Monte Carlo simulations are performed. Simulation results indicate that the proposed algorithm has high location accuracy and achieves accuracy close to the Cramer-Rao lower bound (CRLB) near the small TDOA measurement error region.

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K. YANG, J. AN and Z. XU, "A Quadratic Constraint Total Least-squares Algorithm for Hyperbolic Location," International Journal of Communications, Network and System Sciences, Vol. 1 No. 2, 2008, pp. 130-135. doi: 10.4236/ijcns.2008.12017.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] N. Patwari, J. N. Ash, S. Kyperountas, A. O. Hero III, 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. 54–68, July 2005.
[2] X. Jun, L. R. Ren, and J. D. Tan, “Research of TDOA based self-localization approach in wireless sensor network,” in proceedings of IEEE International Conference on Intelligent Robots and Systems, Beijing, pp. 2035–2040, October 2006.
[3] J. Smith and J. Abel, “Closed-form least-squares source location estimation from range-difference measurements,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 35, pp. 1661–1669, December 1987.
[4] Y. T. Chan and K. C. Ho, “A simple and efficient estimation for hyperbolic location,” IEEE Transactions on Signal processing, vol. 42, no. 8, pp. 1905-1915, August 1994.
[5] R. Schmidt, “Least squares range difference location,” IEEE Transactions on Aerospace and Electronic Systems, vol. 32, no. 1, pp. 234-242, January 1996.
[6] Y. Huang, J. Benesty, G. W. Elko, and R. M. Mersereau, “Real-time passive source localization: a practical linear-correction least-squares approach,” IEEE Transactions On Speech And Audio Processing, vol. 9, no. 8, pp. 943–956, November 2001.
[7] T. J. Abatzoglou, J. M. Mendel, and G. A. Harada, “The constrained total least squares technique and its applications to harmonic superresolution,” IEEE Transactions on Signal Processing, vol. 39, no. 5, pp. 1070–1087, May 1991.
[8] S. V. Huffel and J. Vandewalle, "The Total Least Squares Problem: Computational Aspects and Analysis," Philadelphia: SIAM, 1991.
[9] I. Markovsky and S. V. Huffel, “Overview of total least-squares methods,” Signal Processing, vol. 87 no. 10, pp. 2283–2302, October 2007.
[10] X. Li, "Super-Resolution TOA Estimation with Diversity Techniques for Indoor Geolocation Applications," Ph.D. Dissertation, Worcester Polytechnic Institute, Worcester, MA, 2003.
[11] S. D. Hodges and P. G. Moore, “Data Uncertainties and Least Squares Regression,” Applied Statistics, vol. 21, pp. 185–195, 1972.
[12] J. A. Cadzow, “Spectral estimation: An overdetermined rational model equation approach,” Proceedings of the IEEE, vol. 70, no. 9, pp.907–939, September 1982.

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