Penalized maximum-likelihood estimation of covariance matrices with linear structure

Author

Schulz, Timothy J.

Author_Institution

Dept. of Electr. Eng., Michigan Technol. Univ., Houghton, MI, USA

Volume

45

Issue

12

fYear

1997

fDate

12/1/1997 12:00:00 AM

Firstpage

3027

Lastpage

3038

Abstract

In this paper, a space-alternating generalized expectation-maximization (SAGE) algorithm is presented for the numerical computation of maximum-likelihood (ML) and penalized ML (PML) estimates of the parameters of covariance matrices with linear structure for complex Gaussian processes. By using a less informative hidden-data space and a sequential parameter-update scheme, a SAGE-based algorithm is derived for which convergence of the likelihood is demonstrated to be significantly faster than that of an EM-based algorithm that has been previously proposed. In addition, the SAGE procedure is shown to easily accommodate penalty functions, and a SAGE-based algorithm is derived and demonstrated for forming PML estimates with a quadratic smoothness penalty

Keywords

Gaussian processes; convergence of numerical methods; covariance matrices; maximum likelihood estimation; signal processing; EM-based algorithm; SAGE-based algorithm; complex Gaussian processes; convergence; covariance matrices; data space; linear structure; maximum-likelihood; penalized maximum-likelihood estimation; penalty functions; quadratic smoothness penalty; sequential parameter-update scheme; space-alternating generalized expectation-maximization algorithm; Acoustic measurements; Additive noise; Covariance matrix; Discrete Fourier transforms; Filtering theory; Maximum likelihood estimation; Noise measurement; Parameter estimation; Signal processing algorithms; Spectral analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.650262

Filename

650262