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

• 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
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2011.2131136

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.