Structured Least Squares Problems and Robust Estimators

• Published in: IEEE transactions on signal processing Vol. 58; no. 5; pp. 2453 - 2465
• Main Authors: Pilanci, Mert, Arikan, Orhan, Pinar, Mustafa C
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Applied sciences; Blind identification; Blinds; Coefficients; Deconvolution; Detection, estimation, filtering, equalization, prediction; Errors; errors-in-variables; Estimates; Exact sciences and technology; Frequency estimation; Information, signal and communications theory; least squares; Least squares approximation; Least squares methods; Mathematical analysis; Maximum likelihood estimation; Miscellaneous; Noise measurement; Regression; Regularization; robust least squares; Robustness; Signal and communications theory; Signal processing; Signal, noise; structured total least squares; Telecommunications and information theory; Vectors; Performance evaluation; Parameter estimation; errors-in-variables; Linear regression; Least squares problem; Signal estimation; Theoretical study; Frequency estimation; Robust estimation; Regression analysis; Blind identification; Mean square error; structured total least squares; Deconvolution; robust least squares; Simulation; Least squares method; least squares; Signal processing; Alternative method; System identification; Multiple frequency; Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2041279

A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values.