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A convex optimization approach to arma(n,m) model design from covariance and cepstral data
KTH, Tidigare Institutioner                               , Matematik.
2004 (Engelska)Ingår i: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 43, nr 3, s. 1011-1036Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Methods for determining ARMA(n, m) filters from covariance and cepstral estimates are proposed. In [C. I. Byrnes, P. Enqvist, and A. Lindquist, SIAM J. Control Optim., 41 ( 2002), pp. 23-59], we have shown that an ARMA( n, n) model determines and is uniquely determined by a window r(0), r(1),..., r(n) of covariance lags and c(1), c(2),..., c(n) of cepstral lags. This unique model can be determined from a convex optimization problem which was shown to be the dual of a maximum entropy problem. In this paper, generalizations of this problem are analyzed. Problems with covariance lags r(0), r(1),..., r(n) and cepstral lags c(1), c(2),..., c(m) of different lengths are considered, and by considering different combinations of covariances, cepstral parameters, poles, and zeros, it is shown that only zeros and covariances give a parameterization that is consistent with generic data. However, the main contribution of this paper is a regularization of the optimization problems that is proposed in order to handle generic data. For the covariance and cepstral problem, if the data does not correspond to a system of desired order, solutions with zeros on the boundary occur and the cepstral coefficients are not interpolated exactly. In order to achieve strictly minimum phase filters for estimated covariance and cepstral data, a barrier-like term is introduced to the optimization problem. This term is chosen so that convexity is maintained and so that the unique solution will still interpolate the covariances but only approximate the cepstral lags. Furthermore, the solution will depend analytically on the covariance and cepstral data, which provides robustness, and the barrier term increases the entropy of the solution.

Ort, förlag, år, upplaga, sidor
2004. Vol. 43, nr 3, s. 1011-1036
Nyckelord [en]
cepstrum, covariance, ARMA, entropy, convex optimization
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:kth:diva-13176DOI: 10.1137/S0363012901399751ISI: 000225642700013Scopus ID: 2-s2.0-19944383824OAI: oai:DiVA.org:kth-13176DiVA, id: diva2:321484
Anmärkning
QC 20100601Tillgänglig från: 2010-06-01 Skapad: 2010-06-01 Senast uppdaterad: 2017-12-12Bibliografiskt granskad
Ingår i avhandling
1. Spectral Estimation by Geometric, Topological and Optimization Methods
Öppna denna publikation i ny flik eller fönster >>Spectral Estimation by Geometric, Topological and Optimization Methods
2001 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Ort, förlag, år, upplaga, sidor
Stockholm: KTH, 2001. s. xii, 32
Serie
Trita-MAT, ISSN 1401-2286 ; 01-OS-03
Nyckelord
Spectral Estimation, ARMA models, Covariance analysis, Cepstral analysis, Markov parameters, Global analysis, Convex Optimization, Continuation methods, Entropy maximization
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:kth:diva-3118 (URN)
Disputation
2001-04-06, 00:00 (Engelska)
Anmärkning
QC 20100601Tillgänglig från: 2001-03-29 Skapad: 2001-03-29 Senast uppdaterad: 2010-06-01Bibliografiskt granskad

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