The Averaged, Overdetermined, and Generalized LMS Algorithm

• Published in: IEEE transactions on signal processing Vol. 55; no. 12; pp. 5593 - 5603
• Main Authors: Alameda-Hernandez, E., Blanco, D., Ruiz, D.P., Carrion, M.C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithm; Adaptive algorithms; Adaptive filters; Algorithms; Applied sciences; Derivation; Detection, estimation, filtering, equalization, prediction; Eigenvalues and eigenfunctions; Exact sciences and technology; Exports; Information, signal and communications theory; Instrumental variable; Instruments; International trade; least squares; Least squares approximation; Least squares method; Least squares methods; Mathematical analysis; orthogonality conditions; Recursive; recursive algorithms; Resonance light scattering; Signal and communications theory; Signal processing algorithms; Signal, noise; Statistics; stochastic gradient; Stochastic processes; Studies; Telecommunications and information theory; Instrumental variable; recursive algorithms; stochastic gradient; least squares; orthogonality conditions; Adaptive algorithm; Adaptive filtering; Stochastic method; Orthogonality; Recursive algorithm; Simulation; Least squares method; Recursive method; Least mean squares methods
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.899375

This paper provides and exploits one possible formal framework in which to compare and contrast the two most important families of adaptive algorithms: the least-mean square (LMS) family and the recursive least squares (RLS) family. Existing and well-known algorithms, belonging to any of these two families, like the LMS algorithm and the RLS algorithm, have a natural position within the proposed formal framework. The proposed formal framework also includes - among others - the LMS/overdetermined recursive instrumental variable (ORIV) algorithm and the generalized LMS (GLMS) algorithm, which is an instrumental variable (IV) enable LMS algorithm. Furthermore, this formal framework allows a straightforward derivation of new algorithms, with enhanced properties respect to the existing ones: specifically, the ORIV algorithm is exported to the LMS family, resulting in the derivation of the averaged, overdetermined, and generalized LMS (AOGLMS) algorithm, an overdetermined LMS algorithm able to work with an IV. The proposed AOGLMS algorithm overcomes - as we analytically show here - the limitations of GLMS and possesses a much lower computational burden than LMS/ORIV, being in this way a better alternative to both algorithms. Simulations verify the analysis.