DOI QR코드

DOI QR Code

Time-Delay Estimation in the Multi-Path Channel based on Maximum Likelihood Criterion

  • Xie, Shengdong (School of Information Science and Engineering, Southeast University) ;
  • Hu, Aiqun (School of Information Science and Engineering, Southeast University) ;
  • Huang, Yi (School of Information Science and Engineering, Southeast University)
  • Received : 2011.12.19
  • Accepted : 2012.03.19
  • Published : 2012.04.30

Abstract

To locate an object accurately in the wireless sensor networks, the distance measure based on time-delay plays an important role. In this paper, we propose a maximum likelihood (ML) time-delay estimation algorithm in multi-path wireless propagation channel. We get the joint probability density function after sampling the frequency domain response of the multi-path channel, which could be obtained by the vector network analyzer. Based on the ML criterion, the time-delay values of different paths are estimated. Considering the ML function is non-linear with respect to the multi-path time-delays, we first obtain the coarse values of different paths using the subspace fitting algorithm, then take them as an initial point, and finally get the ML time-delay estimation values with the pattern searching optimization method. The simulation results show that although the ML estimation variance could not reach the Cramer-Rao lower bounds (CRLB), its performance is superior to that of subspace fitting algorithm, and could be seen as a fine algorithm.

Keywords

References

  1. Y.S. Lu, C.F. Lai, C.C. Hu, Y.M. Huang and X.H. Ge, "Path loss exponent estimation for indoor wireless sensor positioning," KSII Transactions on Internet and Information Systems, vol.4, no.3, pp.243-257, 2010.
  2. H.K. Charles and G.C. Carter, "The generalized correlation method for estimation of time delay," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.24, no.4, pp.320-327, 1976. https://doi.org/10.1109/TASSP.1976.1162830
  3. F. Viola and F.W. Walker, "A spline based algorithm for continuous time delay estimation using sampled data," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol.52, no.1, pp.80-93, 2005. https://doi.org/10.1109/TUFFC.2005.1397352
  4. M.I. Clara, H. Ramona and D.K. Robin, "Variable time delay estimation for anesthesia control during intensive care," IEEE Transactions on Biomedical Engineering, vol.58, no.2, pp.363-369, 2011.
  5. F. Gianmarco and E.T. Gregg, "Continuous delay estimation with polynomial splines," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol.53, no.11, pp.2026-2035, 2006. https://doi.org/10.1109/TUFFC.2006.143
  6. Y.C. Bai, X.G. Zhang and X.J. Qiu, "Subsample time delay estimation based on weighted straight line fitting to cross-spectrum phase," Chinese Journal of Electronics, vol.19, no.3, pp.553-556, 2010.
  7. B. Francesco and G. Gaetano, "A fast delay estimator of PN signals," IEEE Transactions on Communications, vol.59, no.8. pp.2057-2062, 2011.
  8. H.C. So and P.C. Ching, "Comparative study of five LMS based adaptive time delay estimators," Radar, Sonar and Navigation, IEEE Proceedings, vol.148, no.1, pp.9-15, 2001. https://doi.org/10.1049/ip-rsn:20010145
  9. R.D. Saul and K.N. Asoke, "Adaptive subsample time delay estimation using lagrange interpolators," IEEE Signal Processing Letters, vol.6, no.3, pp.65-67, 1999. https://doi.org/10.1109/97.744626
  10. A. Grennberg and M. Sandell, "Estimation of subsample time delay differences in narrowband ultrasonic echoes using the Hilbert Transform Correlation," IEEE Transactions on ULtrasonics,Ferroelectrics, and Frequency Control, vol.41, no.5, pp.588-595, 1994.
  11. L.M. Douglas and S.W. Graham, "Adaptive subsample delay estimation using windowed correlation," IEEE Transactions on Circuits and Systems, vol.53, no.6, pp.478-482, 2006.
  12. J. Benesty, Y.T. Huang and J.D. Chen, "Time delay estimation via minimum entropy," IEEE Signal Processing Letters, vol.13, no.3, pp.157-160, 2007.
  13. D.L. Maskel and G.S. Woods, "Adaptive subsample delay estimation using a modified quadrature phase detector," IEEE Transactions on Circuits and Systems, vol.52, no.10, pp.669-674, 2005. https://doi.org/10.1109/TCSII.2005.852166
  14. M. Takeshi and T.Hitoshi, "Superresolution of Mltipath delay profiles measured by PN correlation method," IEEE Transactions on Antennas and Propagation, vol.40, no.5, pp.500-509, 1992. https://doi.org/10.1109/8.142624
  15. F.X. Ge, D.X. Shen, Y.N. Peng and Y.O.K. Li, "Super-resolution time delay estimation in multipath environments," IEEE Transactions on Circuits and Systems, vol.54, no.9, pp.1977-1986, 2007.
  16. C.L. Bastard, V. Baltazart and Y.D. Wang, "Modified ESPRIT (M-ESPRIT) Algorithm for time delay estimation in both any noise and any radar pulse context by a GPR Radar," Signal Processing, vol.90, pp.173-179, 2010. https://doi.org/10.1016/j.sigpro.2009.06.007
  17. X.R. Li, K.Pahlavan, "Super-Resolution TOA Estimation with Diversity for Indoor Geo-location," IEEE Transactions on Wireless Communications, vol.3, no.1, pp.224-234, 2004. https://doi.org/10.1109/TWC.2003.819035
  18. Y.H. Kim, "Multipath parameter estimation for radio propagation channel measurements with a vector network analyzer," IEEE Transactions on Vehicular Technology, vol.59, no.1, pp.48-52, 2010. https://doi.org/10.1109/TVT.2009.2035705
  19. P. Wang, G.J. Zhang, J.J. Xiong, C.Y. Xue and W.D. Zhang, "Root music algorithm with real valued Eigen decomposition for acoustic vector sensor array," International Conference on Pervasive Computing Signal Processing and Applications, pp.652-656, 2010.
  20. H. Abeida and J.P. Delmas "Statistical performance of MUSIC like algorithm in resolving noncircular sources," IEEE Transactions on Signal Processing, vol.56, no. 9,pp.4317-4329, 2008. https://doi.org/10.1109/TSP.2008.924143
  21. R.O. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Transactions on Antennas and Propagation, vol. 34, no.3, pp.276-280, 1986. https://doi.org/10.1109/TAP.1986.1143830
  22. I. Ziskind and M. WAX, "Maximum likelihood localization of multiple sources by alternating projection," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.36, no.10, pp.1553-1560, 1988. https://doi.org/10.1109/29.7543
  23. A. Monakov and G.A. Varfolomeev, "Resolution of signal sources via spectral moment estimation," IEEE Transactions on Aerospace and Electronic Systems, vol.42, no.3, pp.770-777, 2006.
  24. A. Monakov, "Spectral moment estimation of an extended target in ULA," IEEE Transactions on Aerospace and Electronic Systems, vol.44, no.1, pp.360-366, 2008. https://doi.org/10.1109/TAES.2008.4517010
  25. S. Peleg and B. Porat, "The Cramer Rao lower bound for signal with constant amplitude and polynomial phase," IEEE Transactions on Signal Processing, vol.39, no.3, pp.749-752, 1991. https://doi.org/10.1109/78.80864
  26. X.R. Li and K. Pahlavan, "Super resolution ToA estimation with diversity for indoor geo-location," IEEE Transactions on Wireless Communication, vol.3, no.1, pp.224-234, 2004. https://doi.org/10.1109/TWC.2003.819035
  27. M. Wax and T. Kailath, "Detection of signals by information theoretic criteria," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.33, no.10, pp.387-392, 1985. https://doi.org/10.1109/TASSP.1985.1164557
  28. R. Hooke, T.A. Jeeves, "Direct search solution of numerical and statistical problems," Journal of the Association for Computer Machinery, vol.8, no.2, pp.212-229, 1961. https://doi.org/10.1145/321062.321069

Cited by

  1. A New Statistical WRELAX Algorithm Under Nakagami Multipath Channel Based on Delay Power Spectrum Characteristic vol.82, pp.3, 2012, https://doi.org/10.1007/s11277-015-2294-5