Identification of Nonminimum Phase Systems Using Higher Order Statistics

IEEE Transactions on Acoustics, Speech, and Signal Processing

Volumn 37, Issue 3, 1989, Pages 360-377

  Giannakis, Georgios B ^a   Mendel, Jerry M ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS, STOCHASTIC--IDENTIFICATION; MATHEMATICAL STATISTICS; MATHEMATICAL TECHNIQUES--TRANSFER FUNCTIONS; NOISE, SPURIOUS SIGNAL--WHITE NOISE; PROBABILITY;

ARMA MODEL; HIGHER ORDER STATISTICS; LINEAR TIME INVARIANT SYSTEMS; NONMINIMUM PHASE SYSTEMS; POLYSPECTRA;

SYSTEMS SCIENCE AND CYBERNETICS;

EID: 0024627342     PISSN: 00963518     EISSN: None     Source Type: Journal    
DOI: 10.1109/29.21704     Document Type: Article

References (23)

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23. G.U. Yule, “On a method of investigating periodicities in disturbed series, with special reference to Wolfer's sunspot numbers,” Philosoph. Trans. Roy. Soc. London, Ser. A., vol. 226A, pp. 267–298, 1927. Maximum Likelihood Estimation of the Parameters of Multiple Sinusoids from Noisy Measurements PETRE STOICA, RANDOLPH L. MOSES, member, ieee, BENJAMIN FRIEDLANDER, fellow, ieee. and TORSTEN SOÖDERSTRO ÖM, senior member, ieee Abstract-The problem of estimating the frequencies, phases, and amplitudes of sinusoidal signals is considered. A simplified maximum-likelihood Gauss-Newton algorithm which provides asymptotically efficient estimates of these parameters is proposed. Initial estimates for this algorithm are obtained by a variation of the overdetermined Yule-Walker method and a periodogram-based procedure. Use of the maximum-likelihood Gauss-Newton algorithm is not, however, limited to this particular initialization method. Some other possibilities to get suitable initial estimates are briefly discussed. An analytical and numerical study of the shape of the likelihood function associated with the sinusoids-in-noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure. Some numerical examples are presented to illustrate the performance of the proposed estimation procedure. Comparison to the performance corresponding to the Cramer-Rao lower bound is also presented, using a simple expression for the asymptotic Cramer-Rao bound covariance matrix derived in the paper. P. Stoica is with the Facultatea de Automatica, Institutul Politehnic Bucuresti, Splaiul Independentei 313, Sector 6, R-77 206 Bucharest, Romania. R.L. Moses is with the Department of Electrical Engineering, The Ohio State University, Columbus, OH 43210. B. Friedlander is with Signal Processing Technology, Ltd., 703 Coast-land Drive, Palo Alto, CA 94303. T. Soderstroöm is with the Department of Automatic Control and Systems Analysis, Institute of Technology, Uppsala University, P.O. Box 534, S-751 21 Uppsala, Sweden.