On the identifiability of non-Gaussian ARMA models using cumulants

A fixed set of output cumulants of order greater than two guarantees unique identification of known-order causal ARMA (autoregressive moving-average) models, which are driven by unobservable non-Gaussian i.i.d. noise. The models are allowed to be non-minimum-phase, and their outputs may be corrupted by additive colored Gaussian noise of unknown covariance. The ARMA parameters can be estimated either by means of linear equations and closed-form expressions or by minimizing quadratic cumulant matching criteria. The latter approach requires computation of cumulants in terms of the ARMA parameters, which is carried out in the state space using Kronecker products. >

[1]  M. Rosenblatt,et al.  Deconvolution and Estimation of Transfer Function Phase and Coefficients for NonGaussian Linear Processes. , 1982 .

[2]  A. Lohmann,et al.  Triple correlations , 1984, Proceedings of the IEEE.

[3]  Chrysostomos L. Nikias,et al.  Bispectrum estimation: A parametric approach , 1985, IEEE Trans. Acoust. Speech Signal Process..

[4]  Jitendra K. Tugnait,et al.  Identification of non-minimum phase linear stochastic systems , 1986, Autom..

[5]  M.R. Raghuveer,et al.  Bispectrum estimation: A digital signal processing framework , 1987, Proceedings of the IEEE.

[6]  G. Giannakis.  Cumulants: A powerful tool in signal processing , 1987, Proceedings of the IEEE.

[7]  Georgios B. Giannakis,et al.  WAVELET PHASE RECONSTRUCTION USING CUMULANTS. , 1987 .

[8]  G. Giannakis,et al.  On estimating noncasual ARMA nonGaussian processes , 1988, Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling.

[9]  J. Mendel,et al.  ARMA parameter estimation using only output cumulants , 1988, Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling.

[10]  J. Mendel,et al.  Adaptive Cumulant-Based Estimation of ARMA Parameters , 1988, 1988 American Control Conference.

[11]  Jitendra K. Tugnait,et al.  On selection of maximum cumulant lags for noncausal autoregressive model fitting , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[12]  Georgios B. Giannakis,et al.  ARMA modeling and phase reconstruction of multidimensional non-Gaussian processes using cumulants , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[13]  Jitendra K. Tugnait,et al.  Recovering the Poles from Fourth-Order Cumulants of System Output , 1988, 1988 American Control Conference.

[14]  Chrysostomos L. Nikias,et al.  Adaptive Filtering via Cumulants and LMS Algorithm , 1988, 1988 American Control Conference.

[15]  Georgios B. Giannakis,et al.  Wavelet parameter and phase estimation using cumulant slices , 1989 .

[16]  Georgios B. Giannakis,et al.  Signal reconstruction from multiple correlations: frequency- and time-domain approaches , 1989 .

[17]  Benjamin Friedlander,et al.  Adaptive IIR algorithms based on high-order statistics , 1989, IEEE Trans. Acoust. Speech Signal Process..

[18]  Jerry M. Mendel,et al.  Identification of nonminimum phase systems using higher order statistics , 1989, IEEE Trans. Acoust. Speech Signal Process..

[19]  J. Mendel,et al.  Cumulant based identification of multichannel moving-average models , 1989 .

[20]  Jerry M. Mendel,et al.  A unified approach to modeling multichannel ARMA processes , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[21]  G.B. Giannakis,et al.  Cumulant-based order determination of non-Gaussian ARMA models , 1990, IEEE Trans. Acoust. Speech Signal Process..

[22]  Benjamin Friedlander,et al.  Asymptotically optimal estimation of MA and ARMA parameters of non-Gaussian processes from high-order moments , 1990 .

[23]  J. Mendel,et al.  Time and lag recursive computation of cumulants from a state-space model , 1990 .