Blind System Identification

  • J. K. Richardson
  • A. K. Nandi
Chapter

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.

Keywords

Move Average Filter Coefficient Input Distribution ARMA Process Order Cumulants 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    H. Akaike. A new look at the statistical model identification. IEEE Transactions Automatic Control, AC-19:716–723, 1974.MathSciNetCrossRefGoogle Scholar
  2. [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.MATHGoogle Scholar
  3. [3]
    H. Bartelt, A. W. Lohman, and B. Wirnitzer. Phase and amplitude recovery from bispectra. Applied Optics, 23:3121–3129, 1984.CrossRefGoogle Scholar
  4. [4]
    M. Boumahdi. Blind identification using the kurtosis with applications to field data. Signal Processing, 48:205–216, 1996.MATHCrossRefGoogle Scholar
  5. [5]
    D. R. Brillinger. The identification of a particular nonlinear time series system. Biometrika, 64:509–515, 1977.MathSciNetMATHCrossRefGoogle Scholar
  6. [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.CrossRefGoogle Scholar
  7. [7]
    J. R. Dickie and A. K. Nandi. A comparative study of AR order selection methods. Signal Processing, 40:239–255, 1994.CrossRefGoogle Scholar
  8. [8]
    P. M. Djuric and S. M. Kay. Order selection of autoregressive models. IEEE Transactions on Signal Processing, 40:2829–2833, 1992.CrossRefGoogle Scholar
  9. [9]
    J. A. Fonollosa and J. Vidal. System identification using a linear combination of cumulant slices. Proceedings of IEEE, 41:2405–2411, 1993.MATHGoogle Scholar
  10. [10]
    G. B. Giannakis. Cumulants: A powerful tool in signal processing. Proceedings of IEEE, 75:1333–1334, 1987.CrossRefGoogle Scholar
  11. [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.MathSciNetMATHCrossRefGoogle Scholar
  12. [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.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    S. M. Kay. Modern Spectral Estimation. Prentice Hall, Englewood Cliffs, New Jersey, 1988.MATHGoogle Scholar
  14. [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.CrossRefGoogle Scholar
  15. [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.MATHCrossRefGoogle Scholar
  16. [16]
    K. S. Lii. Non-gaussian ARMA model identification and estimation. Proc Bus and Econ Statistics (ASA), pages 135–141, 1982.Google Scholar
  17. [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.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    K. S. Lii and M. Rosenblatt. Non-gaussian linear processes, phase and deconvolution. Statistical Signal Processing, pages 51–58, 1984.Google Scholar
  19. [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. [20]
    P. Lin and S. Mao. Non-gaussian ARMA identification via higher order cumulant. Signal Processing, 33:357–362, 1993.MATHCrossRefGoogle Scholar
  21. [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.CrossRefGoogle Scholar
  22. [22]
    S. L. J. Marple. Digital Spectral Analysis with Applications. Prentice Hall, Englewood Cliffs, New Jersey, 1987.Google Scholar
  23. [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.MathSciNetMATHCrossRefGoogle Scholar
  24. [24]
    T. Matsuoka and T. J. Ulrych. Phase estimation using the bispectrum. Proceedings of IEEE, 72:1403–1411, 1984.CrossRefGoogle Scholar
  25. [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.CrossRefGoogle Scholar
  26. [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.CrossRefGoogle Scholar
  27. [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. [28]
    A. K. Nandi. Blind identification of FIR systems using third order cumulants. Signal Processing, 39:131–147, 1994.MATHCrossRefGoogle Scholar
  29. [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. [30]
    A. K. Nandi and D. Mampel. Improved estimation of third order cumulants. FREQUENZ, 49:156–160, 1995.CrossRefGoogle Scholar
  31. [311.
    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.CrossRefGoogle Scholar
  32. [32]
    C. L. Nikias. ARMA bispectrum approach to nonminimum phase systemn identification. IEEE Transactions on Accoustics, Speech and Signal Processing, 36:513–524, 1988.MATHCrossRefGoogle Scholar
  33. [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. [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.MATHCrossRefGoogle Scholar
  35. [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. [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.MathSciNetMATHCrossRefGoogle Scholar
  37. [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. [38]
    J. Rissanen. Modeling by shortest data description. Automatica, 14:465–471, 1978.MATHCrossRefGoogle Scholar
  39. [39]
    J. Rissanen. A predictive least-squares principle. I M A J. Math. Control Inform., 3:211–222, 1986.MATHCrossRefGoogle Scholar
  40. [40]
    G. Schwarz. Estimation of the dimension of a model. Annals of Statistics, 6:461–464, 1978.MathSciNetMATHCrossRefGoogle Scholar
  41. [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.CrossRefGoogle Scholar
  42. [42]
    A. G. Stogioglou and S. McLaughlin. MA parameter estimation and cumulant enhancement. IEEE Transactions on Signal Processing, 44:1704–1718, 1996.CrossRefGoogle Scholar
  43. [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.MathSciNetCrossRefGoogle Scholar
  44. [44]
    I. The MathWorks. HOSA toolbox for use with MATLAB.Google Scholar
  45. [45]
    J. K. Tugnait. Identification of non-minimum phase linear stochastic systems. Automatica, 22:457–464, 1986.MATHCrossRefGoogle Scholar
  46. [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.MATHCrossRefGoogle Scholar
  47. [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.MATHCrossRefGoogle Scholar
  48. [48]
    J. K. Tugnait. New results on FIR system identification using higher order statistics. IEEE Transactions on Signal Processing, 39:2216–2221, 1991.CrossRefGoogle Scholar
  49. [49]
    X. Zhang and Y. Zhang. FIR system identification using higher order statistics alone. IEEE Transactions on Signal Processing, 42:2854–2858, 1994.CrossRefGoogle Scholar
  50. [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.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • J. K. Richardson
  • A. K. Nandi

There are no affiliations available

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