IAA Spectral Estimation: Fast Implementation Using the Gohberg–Semencul Factorization

Author

Xue, Ming ; Xu, Luzhou ; Li, Jian

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Florida, Gainesville, FL, USA

Volume

59

Issue

7

fYear

2011

fDate

7/1/2011 12:00:00 AM

Firstpage

3251

Lastpage

3261

Abstract

We consider fast implementations of the weighted least-squares based iterative adaptive approach (IAA) for one-dimensional (1-D) and two-dimensional (2-D) spectral estimation of uniformly sampled data. IAA is a robust, user parameter-free and nonparametric adaptive algorithm that can work with a single data sequence or snapshot. Compared to the conventional periodogram, IAA can be used to significantly increase the resolution and suppress the sidelobe levels. However, due to its high computational complexity, IAA can only be used in applications involving small-sized data. We present herein novel fast implementations of IAA using the Gohberg-Semencul (G-S)-type factorization of the IAA covariance matrices. By exploiting the Toeplitz structure of the said matrices, we are able to reduce the computational cost by at least two orders of magnitudes even for moderate data sizes.

Keywords

Toeplitz matrices; covariance matrices; iterative methods; least mean squares methods; spectral analysis; Gohberg-Semencul factorization; IAA covariance matrices; IAA spectral estimation; Toeplitz structure; iterative adaptive approach; nonparametric adaptive algorithm; one-dimensional spectral estimation; two-dimensional spectral estimation; user parameter-free algorithm; weighted least-squares method; Covariance matrix; Estimation; Generators; Matrix decomposition; Noise; Polynomials; Spatial resolution; Gohberg–Semencul factorization; Toeplitz matrices; iterative adaptive approach (IAA); spectral estimation;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2011.2131136

Filename

5737801