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Abstract

In this chapter a comparison of blind system identification methods for linear time-invariant (LTI) systems using HOS is presented [37]. These methods [35] use only the system output data to identify the system model under the assumption that the system is driven by an independent and identically distributed (i.i.d.) non-Gaussian sequence that is unobservable.

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References

  1. H. Akaike. A new look at the statistical model identification. IEEE Transactions Automatic Control, AC-19:716–723, 1974.

    Article  MathSciNet  Google Scholar 

  2. S. A. Alshebeili, A. N. Venetsanopoulos, and A. E. Cetin. Cumulant based identification approaches for nonminimum phase FIR systems. Proceedings of IEEE, 41:1576–1588, 1993.

    MATH  Google Scholar 

  3. H. Bartelt, A. W. Lohman, and B. Wirnitzer. Phase and amplitude recovery from bispectra. Applied Optics, 23:3121–3129, 1984.

    Article  Google Scholar 

  4. M. Boumahdi. Blind identification using the kurtosis with applications to field data. Signal Processing, 48:205–216, 1996.

    Article  MATH  Google Scholar 

  5. D. R. Brillinger. The identification of a particular nonlinear time series system. Biometrika, 64:509–515, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  6. T. W. S. Chow and G. Fei. On the identification of non-minimum phase non-gaussian MA and ARMA models using a third-order cumulant. International Journal of Electronics, 79:839–852, 1995.

    Article  Google Scholar 

  7. J. R. Dickie and A. K. Nandi. A comparative study of AR order selection methods. Signal Processing, 40:239–255, 1994.

    Article  Google Scholar 

  8. P. M. Djuric and S. M. Kay. Order selection of autoregressive models. IEEE Transactions on Signal Processing, 40:2829–2833, 1992.

    Article  Google Scholar 

  9. J. A. Fonollosa and J. Vidal. System identification using a linear combination of cumulant slices. Proceedings of IEEE, 41:2405–2411, 1993.

    MATH  Google Scholar 

  10. G. B. Giannakis. Cumulants: A powerful tool in signal processing. Proceedings of IEEE, 75:1333–1334, 1987.

    Article  Google Scholar 

  11. G. B. Giannakis and J. M. Mendel. Identification of nonmimimum phase systems using higher order statistics. IEEE Transactions on Accoustics, Speech and Signal Processing, 37:360–377, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  12. G. B. Giannakis and A. Swami. On estimating noncausal nonminimum phase ARMA models of non-gaussian processes. IEEE Transactions on Accoustics, Speech and Signal Processing, 38(3):478–495, March 1990.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. M. Kay. Modern Spectral Estimation. Prentice Hall, Englewood Cliffs, New Jersey, 1988.

    MATH  Google Scholar 

  14. K. Konstantinides. Threshold bounds in svd and a new iterative algorithm for order selection in ar models. IEEE Transactions on Signal Processing, 39:757–763, 1991.

    Article  Google Scholar 

  15. G. Liang, D. M. Wilkes, and J. A. Cadzow. ARMA model order estimation based on the eignevalues of the covariance matrix. IEEE Transactions on Signal Processing, 41:3003–3009, 1993.

    Article  MATH  Google Scholar 

  16. K. S. Lii. Non-gaussian ARMA model identification and estimation. Proc Bus and Econ Statistics (ASA), pages 135–141, 1982.

    Google Scholar 

  17. K. S. Lii and M. Rosenblatt. Deconvolution and estimation of transfer function phase and coefficients for non-gaussian linear processes. Annals of Statistics, 10:1195–1208, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  18. K. S. Lii and M. Rosenblatt. Non-gaussian linear processes, phase and deconvolution. Statistical Signal Processing, pages 51–58, 1984.

    Google Scholar 

  19. K. S. Lii and M. Rosenblatt. A fourth-order deconvolution technique for non-gaussian linear processes. In P. R. Krishnaiah, editor, Multivariate Analysis VI. Elsevier, Amsterdam, The Netherlands, 1985.

    Google Scholar 

  20. P. Lin and S. Mao. Non-gaussian ARMA identification via higher order cumulant. Signal Processing, 33:357–362, 1993.

    Article  MATH  Google Scholar 

  21. D. Mampel, A. K. Nandi, and K. Schelhorn. Unified approach to trimmed mean estimation and its application to bispectrum of eeg signals. Journal of the Franklin Institute, 333B:369–383, 1996.

    Article  Google Scholar 

  22. S. L. J. Marple. Digital Spectral Analysis with Applications. Prentice Hall, Englewood Cliffs, New Jersey, 1987.

    Google Scholar 

  23. J. K. Martin and A. K. Nandi. Blind system identification using second, third and fourth order cumulants. Journal of the Franklin Institute of Science, 333B:1–13, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  24. T. Matsuoka and T. J. Ulrych. Phase estimation using the bispectrum. Proceedings of IEEE, 72:1403–1411, 1984.

    Article  Google Scholar 

  25. J. M. Mendel. Tutorial on higher-order statistics (spectra) in signal processing and system theory: Theoretical results and some applications. Proceedings of IEEE, 79:277–305, 1991.

    Article  Google Scholar 

  26. Y. J. Na, K. S. Kim, I. Song, and T. Kim. Identification of nonminimum phase FIR systems using third- and fourth-order cumulants. IEEE Transactions on Signal Processing, 43:2018–2022, 1995.

    Article  Google Scholar 

  27. A. K. Nandi. On the robust estimation of third-order cumulants in applications of higher-order statistics. Proceedings of IEE, Part F, 140:380–389, 1993.

    Google Scholar 

  28. A. K. Nandi. Blind identification of FIR systems using third order cumulants. Signal Processing, 39:131–147, 1994.

    Article  MATH  Google Scholar 

  29. A. K. Nandi and J. A. Chambers. New lattice realisation of the predictive least-squares order selection criterion. IEE Proceedings F, 138:545–550, 1991.

    Google Scholar 

  30. A. K. Nandi and D. Mampel. Improved estimation of third order cumulants. FREQUENZ, 49:156–160, 1995.

    Article  Google Scholar 

  31. A. K. Nandi and R. Mehlan. Parameter estimation and phase reconstruction of moving average processes using third order cumulants. Mechanical Systems and Signal Processing, 8:421–436, 1994.

    Article  Google Scholar 

  32. C. L. Nikias. ARMA bispectrum approach to nonminimum phase systemn identification. IEEE Transactions on Accoustics, Speech and Signal Processing, 36:513–524, 1988.

    Article  MATH  Google Scholar 

  33. C. L. Nikias. Higher-order spectral analysis. In S. S. Haykin, editor, Advances in Spectrum Analysis and Array Processing, volume I, chapter 7. Prentice Hall, Englewood Cliffs, New Jersey, 1991.

    Google Scholar 

  34. C. L. Nikias and H. H. Chiang. Higher-order spectrum estimation via noncausal autoregressive modeling and deconvolution. IEEE Transactions on Accoustics, Speech and Signal Processing, 36:1911–1913, 1988.

    Article  MATH  Google Scholar 

  35. C. L. Nikias and J. M. Mendel. Signal procesing with higher-order spectra. IEEE Signal Processing Magazine, pages 10 – 37, 1993.

    Google Scholar 

  36. C. L. Nikias and R. Pan. ARMA modelling of fourth-order cumulants and phase estimation. Circuits, Systems and Signal Processing, 7(13):291–325, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  37. J. K. Richardson. Parametric modelling for linear system identification and chaotic system noise reduction. PhD thesis, University of Strathclyde, Glasgow, UK, 1996.

    Google Scholar 

  38. J. Rissanen. Modeling by shortest data description. Automatica, 14:465–471, 1978.

    Article  MATH  Google Scholar 

  39. J. Rissanen. A predictive least-squares principle. I M A J. Math. Control Inform., 3:211–222, 1986.

    Article  MATH  Google Scholar 

  40. G. Schwarz. Estimation of the dimension of a model. Annals of Statistics, 6:461–464, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  41. L. Srinivas and K. V. S. Hari. FIR system identification using higher order cumulants — a generalised approach. IEEE Transaction on Signal Processing, 43:3061–3065, 1995.

    Article  Google Scholar 

  42. A. G. Stogioglou and S. McLaughlin. MA parameter estimation and cumulant enhancement. IEEE Transactions on Signal Processing, 44:1704–1718, 1996.

    Article  Google Scholar 

  43. A. Swami and J. M. Mendel. ARMA parmaeter estimation using only output cumulants. IEEE Transactions on Accoustics, Speech and Signal Processing, 38:1257–1265, 1990.

    Article  MathSciNet  Google Scholar 

  44. I. The MathWorks. HOSA toolbox for use with MATLAB.

    Google Scholar 

  45. J. K. Tugnait. Identification of non-minimum phase linear stochastic systems. Automatica, 22:457–464, 1986.

    Article  MATH  Google Scholar 

  46. J. K. Tugnait. Identification of linear stochastic systems via second- and fourth-order cumulant matching. IEEE Transactions on Information Theory, 33:393–407, 1987.

    Article  MATH  Google Scholar 

  47. J. K. Tugnait. Approaches to FIR system identification with noisy data using higher order statistics. IEEE Transactions on Accoustics, Speech and Signal Processing, 38:1307–1317, 1990.

    Article  MATH  Google Scholar 

  48. J. K. Tugnait. New results on FIR system identification using higher order statistics. IEEE Transactions on Signal Processing, 39:2216–2221, 1991.

    Article  Google Scholar 

  49. X. Zhang and Y. Zhang. FIR system identification using higher order statistics alone. IEEE Transactions on Signal Processing, 42:2854–2858, 1994.

    Article  Google Scholar 

  50. Y. Zhang, D. Hatzinakos, and A. N. Venetsanopoulos. Bootstrapping techniques in the estimation of higher-order cumulants from short data records. Proceedings of the International Conference of Accoustics, Speech and Signal Processing, IV:200–203, 1993.

    Article  Google Scholar 

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© 1999 Springer Science+Business Media Dordrecht

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Richardson, J.K., Nandi, A.K. (1999). Blind System Identification. In: Nandi, A.K. (eds) Blind Estimation Using Higher-Order Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2985-6_3

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  • DOI: https://doi.org/10.1007/978-1-4757-2985-6_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5078-9

  • Online ISBN: 978-1-4757-2985-6

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