Nonlinear system identification in impulsive environments

Nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics. In many practical applications, impulsive measurement noise severely weakens the effectiveness of conventional methods. In this paper, /spl alpha/-stable noise is used as a noise model. In such case, the minimum mean square error (MMSE) criterion is no longer an appropriate metric for estimation error due to the lack of finite second-order statistics of the noise. Therefore, we adopt minimum dispersion criterion, which in turn leads to the adaptive least mean pth power (LMP) algorithm. It is shown that the LMP algorithm under the /spl alpha/-stable noise model converges as long as the step size satisfies certain conditions. The effect of p on the performance is also investigated. Compared with conventional methods, the proposed method is more robust to impulsive noise and has better performance.

[1]  Gail D. Baura,et al.  Nonlinear System Identification , 2002 .

[2]  Abdelhak M. Zoubir,et al.  Optimal selection of model order for a class of nonlinear systems using the bootstrap , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[3]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[4]  D. Falconer.  Adaptive equalization of channel nonlinearities in QAM data transmission systems , 1978, The Bell System Technical Journal.

[5]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[6]  B. Stuck.  Minimum error dispersion linear filtering of scalar symmetric stable processes , 1978 .

[7]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[8]  Nicholas Kalouptsidis,et al.  Nonlinear system identification using Gaussian inputs , 1995, IEEE Trans. Signal Process..

[9]  Taiho Koh,et al.  Second-order Volterra filtering and its application to nonlinear system identification , 1985, IEEE Trans. Acoust. Speech Signal Process..

[10]  G. E. Ellis,et al.  Statistical Characteristics of Ocean Acoustic Noise Processes , 1989 .

[11]  Hugo Van.  A Stochastical Limit to the Resolution of Least Squares Estimation of the Frequencies of a Double Complex Sinusoid , 1991 .

[12]  竹中 茂夫.  G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance , 1996 .

[13]  C. L. Nikias,et al.  Signal processing with fractional lower order moments: stable processes and their applications , 1993, Proc. IEEE.

[14]  V. J. Mathews,et al.  Polynomial Signal Processing , 2000 .

[15]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[16]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[17]  Anthony J. Weiss,et al.  Effects of modeling errors on the resolution threshold of the MUSIC algorithm , 1994, IEEE Trans. Signal Process..

[18]  Peyman Milanfar,et al.  Local detectors for high-resolution spectral analysis: Algorithms and performance , 2005, Digit. Signal Process..

[19]  Harry B. Lee,et al.  Resolution threshold of beamspace MUSIC for two closely spaced emitters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[20]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[21]  Giovanni Ramponi,et al.  Quadratic digital filters for image processing , 1988, IEEE Trans. Acoust. Speech Signal Process..

[22]  P. Mertz.  Model of Impulsive Noise for Data Transmission , 1961 .

[23]  Walter A. Frank.  An efficient approximation to the quadratic Volterra filter and its application in real-time loudspeaker linearization , 1995, Signal Process..

[24]  L. Scharf,et al.  Cramer-Rao bounds for deterministic modal analysis , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[25]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[26]  Ezio Biglieri,et al.  Analysis and compensation of nonlinearities in digital transmission systems , 1988, IEEE J. Sel. Areas Commun..

[27]  Robert Nowak.  Nonlinear system identification , 2002 .

[28]  Louis L. Scharf,et al.  Information measures and performance bounds for array processors , 1975 .

[29]  S.T. Smith.  Statistical Resolution Limits and the Complexified , 2005 .

[30]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound: further results and comparisons , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[31]  S.T. Smith,et al.  Resolution and ambiguity bounds for interferometric-like systems , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).