Journal of Electrical Engineering and Technology

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지
DOI QR코드

DOI QR Code

Performance Analysis of the Robust Least Squares Target Localization Scheme using RDOA Measurements

  • Choi, Ka-Hyung (Dept. of Electrical and Electronic Engineering, Yonsei University) ;
  • Ra, Won-Sang (School of Mechanical and Control Engineering, Handong Global University) ;
  • Park, Jin-Bae (Dept. of Electrical and Electronic Engineering, Yonsei University) ;
  • Yoon, Tae-Sung (Dept. of Electrical Engineering, Changwon National University)
  • Received : 2011.03.15
  • Accepted : 2011.12.12
  • Published : 2012.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

A practical recursive linear robust estimation scheme is proposed for target localization in the sensor network which provides range difference of arrival (RDOA) measurements. In order to radically solve the known practical difficulties such as sensitivity for initial guess and heavy computational burden caused by intrinsic nonlinearity of the RDOA based target localization problem, an uncertain linear measurement model is newly derived. In the suggested problem setting, the target localization performance of the conventional linear estimation schemes might be severely degraded under the low SNR condition and be affected by the target position in the sensor network. This motivates us to devise a new sensor network localization algorithm within the framework of the recently developed robust least squares estimation theory. Provided that the statistical information regarding RDOA measurements are available, the estimate of the proposition method shows the convergence in probability to the true target position. Through the computer simulations, the omnidirectional target localization performance and consistency of the proposed algorithm are compared to those of the existing ones. It is shown that the proposed method is more reliable than the total least squares method and the linear correction least squares method.

Keywords

References

  1. K. W. Cheung, H. C. So, W. K. Ma, and Y. T. Chan, "A constrained least squares approach to mobile positioning: algorithms and optimality," EURASIP Journal on Applied Signal Processing, Vol. 2006, No. 20858, pp. 1-23, 2006. https://doi.org/10.1155/ASP/2006/96421
  2. H. C. So, and S. P. Hui, "Constrained location algorithm using TDOA measurements," IEICE Trans. Fundamentals, Vol. E86-A, pp. 3291-3293, 2003.
  3. F. Fletcher, B. Ristic, and D. Musicki, "Recursive estimation of emitter location using TDOA measurements from two UAVs," 10th Int. Conf. on Information Fusion, pp. 1 - 8, 2007.
  4. X. Sun, J. Li, P. Huang, and J. Pang, "Total leastsquares solution of active target localization Using TDOA and FDOA measurements in WSN," Proc. 22nd Int. Conf. on Advanced Information Networking and Applications, pp. 995-999, 2008.
  5. R. Schmidt, "A new approach to geometry of range difference location," IEEE Trans. Aero. Electron. Sys., pp. 821-835, 1972.
  6. W. H. Foy, "Position-location solutions by Taylorseries estimation," IEEE Trans. Aero. Electron. Sys., Vol. AES-12, pp. 187-194, 1976. https://doi.org/10.1109/TAES.1976.308294
  7. D.J. Torrieri, "Statistical theory of passive location systems," IEEE Trans. Aero. Electron. Sys., pp. 183- 198, 1984.
  8. B. T. Fang, "Simple solutions for hyperbolic and related position fixes," IEEE Trans. Aerospace and Electronic Systems, Vol. 26, No. 5, pp. 748-753, 1990. https://doi.org/10.1109/7.102710
  9. J.O. Smith, and J.S. Abel, "Closed-form least squares source location estimation from range-difference measurements," IEEE Trans. Acoust. Speech Sig. Proc., pp. 1661-1669, 1987.
  10. B. Friedlander, "A passive localization algorithm and its accuracy analysis," IEEE J. Ocean. Eng., vol. OE- 12, pp. 234-245, 1987.
  11. Y. T. Chan, and K. C. Ho, "A simple and efficient estimator for hyperbolic location," IEEE Trans. Sig. Process., Vol. 42, no. 8, pp. 1905-1915, 1994. https://doi.org/10.1109/78.301830
  12. Y. Huang, J. Benesty, G. W. Elko, and R. M. Mersereau, "Real-time passive source localization: a practical linear-correction least squares approach," IEEE Trans. Speech and Audio Processing, Vol. 9, No. 8, pp. 943-956, 2001. https://doi.org/10.1109/89.966097
  13. W. S. Ra, I. H. Whang, J. Y. Ahn, and J. B. Park, "Recursive robust least squares estimator for timevarying linear systems with a noise corrupted measurement matrix," IET control Theory & Applications, Vol. 1, No. 1, pp.104-112, 2007. https://doi.org/10.1049/iet-cta:20050331
  14. K. E. Lee, D. M. Ahn, Y. J. Lee, S. W. Cho, and J. W. Chun., "A total least squares algorithm for the source location estimation using GEO satellites," 21st Century Military Communications Conf. Proc., pp. 271-275, 2000.
  15. W. S. Ra, I. H. Whang, and J. B. Park, "Nonconservative robust Kalman filtering using a noise corrupted measurement matrix," IET control Theory & Applications, Vol. 3, No. 9, pp.1226-1236, 2009. https://doi.org/10.1049/iet-cta.2008.0224
  16. G. W. Stewart, "On the continuity of the generalized inverse," SIAM J. Appl. Math., vol. 17, no. 1, pp. 33- 45, 1969. https://doi.org/10.1137/0117004
  17. B. Patrick, Convergence of probability measures (2nd ed.), John Wiley & Sons, 1999.
  18. J. P. LE Cardre and C. Jauffret, "On the convergence of iterative methods for bearing-only tracking," IEEE Trans. Aero. Electron. Sys., pp. 801-818, vol. 35, no. 3, 1999. https://doi.org/10.1109/7.784053
  19. J. M. Mendel, Lessons in estimation theory for signal processing, Communications, and Control, Prentice Hall, Englewood Cliffs, New Jersey, 1995.
  20. W. S. Ra, and I. H. Whang, "Recursive Weighted Robust Least Squares Filter for Frequency Estimation," SICE-ICASE 2006 Int. Joint Conf., pp. 774-778, 2006.
  21. G. H. Choi, W. S. Ra, T. S. Yoon, and J. B. Park, "Low-cost tachometer based on the recursive frequency estimation for automotive application," SICE Annual Conference 2007, pp. 46-49, 2007.