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

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 sin...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-07, Vol.59 (7), p.3251-3261
Main Authors: Xue, Ming, Xu, Luzhou, Li, Jian
Format: Article
Language:English
Subjects:
Applied sciences
Computational efficiency
Covariance matrix
Detection, estimation, filtering, equalization, prediction
Estimation
Exact sciences and technology
Factorization
Generators
Gohberg-Semencul factorization
Information, signal and communications theory
iterative adaptive approach (IAA)
Least squares method
Mathematical analysis
Matrices
Matrix decomposition
Matrix methods
Noise
Polynomials
Sampled data
Signal and communications theory
Signal representation. Spectral analysis
Signal, noise
Spatial resolution
Spectra
spectral estimation
Telecommunications and information theory
Toeplitz matrices
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2131136