Cumulant-Based Order Determination of Non-Gaussian ARMA Models

Georgios B. Giannakis, Jerry M. Mendel

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148 Scopus citations

Abstract

Higher than second-order cumulants can be used for order determination of non-Gaussian ARMA processes. The two methods developed assume knowledge of upper bounds on the ARMA orders. The first method performs a linear dependency search among the columns of a higher order statistics matrix, via the Gram-Schmidt ortho-gonalization procedure. In the second method, the order of the AR part is found as the rank of the matrix formed by the higher order statistics sequence. For numerically robust rank determination the singular value decomposition approach is adopted. Furthermore, using the argument principle and samples of the polyspectral phase the relative degree of the ARMA model is obtained from which the order of the MA part can be determined. Statistical analysis is included for determining the correct MA order with high probability, when estimates of third-order cumulants are only available. Simulations verify the performance of our methods, and compare autocorrelation with cu-mulant-based order determination approaches.

Original languageEnglish (US)
Pages (from-to)1411-1423
Number of pages13
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Volume38
Issue number8
DOIs
StatePublished - Aug 1990

Bibliographical note

Funding Information:
Equation (23a) follows after substituting (14c) into (A4). Setting k = m, I = n in (23a), the estimated variance of sampled third-order cumulants is given by (23b). 0 ACKNOWLEDGMENT Part of this work was performed while the first author (G.B.G.) was at the University of Southern California, Los Angeles, supported by National Science Foundation Grant ECS-860253 1 and NOSC Contract N66001-85-D-0203.

Funding Information:
Manuscript received October 29, 1987; revised September 18, 1989. The first author (G.B.G.) was supported by HDL Contract 5-25227. Results from this paper were presented at the Conference of Mathematics The- ory of Networks and Systems, Phoenix, AZ. June 1987. G. B. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville. VA 22901. J. M. Mendel is with the Signal and Image Processing Institute. Department of Electrical Engineering-Systems, University of Southern California, Los Angeles. CA 90089-978 I. IEEE Log Number 9036515.

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