On Estimating Noncausal Nonminimum Phase ARMA Models of Non-Gaussian Processes

Georgios B. Giannakis, Ananthram Swami

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


We address the problem of estimating the parameters of non-Gaussian ARMA processes using only the cumulants of the noisy observation. The measurement noise is allowed to be colored Gaussian or independent and identically non-Gaussian distributed. The ARMA model is not restricted to be causal or minimum phase and may even contain all-pass factors. The unique parameter estimates of both the MA and AR parts are obtained via linear equations. The structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulatant statistics. The method is computationally simple and can be viewed as the least-squares solution to a quadratic model fitting of a sampled cumulant sequence. Identifiability issues are addressed. Simulations are presented to illustrate the proposed algorithm.

Original languageEnglish (US)
Pages (from-to)478-495
Number of pages18
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Issue number3
StatePublished - Mar 1990

Bibliographical note

Funding Information:
Manuscript received May 10, 1988; revised April 26, 1989. Part of the work reported in this paper was presented at SPIE'87 Symposium, San Diego, CA, August 1987, and at the 4th ASSP Workshop on Spectrum Estimation and Modeling, Minneapolis, MN, August 1988 and was performed when the first author was at the University of Southern California, Los Angeles, under National Science Foundation Grant ECS-8602531, and NOSC Contract N66001-85-D-0203. G. B. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22901. A. Swami is with the Department of Electrical Engineering-Systems, University of Southern California, Signal and Image Processing Institute, Los Angeles, CA 90089-0781. IEEE Log Number 8933428.


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