Full text
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| Author(s): |
Manolis Tsakiris
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Escola Politécnica (EP/BC) |
| Defense date: | 2010-06-25 |
| Examining board members: |
Cassio Guimarães Lopes;
Marcio Eisencraft;
Miguel Arjona Ramirez
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| Advisor: | Cassio Guimarães Lopes |
| Abstract | |
This thesis is concerned with the issue of the regularization of the Recursive Least-Squares (RLS) algorithm. In the first part of the thesis, a novel regularized exponentially weighted array RLS algorithm is developed, which circumvents the problem of fading regularization that is inherent to the standard regularized exponentially weighted RLS formulation, while allowing the employment of generic time-varying regularization matrices. The standard equations are directly perturbed via a chosen regularization matrix; then the resulting recursions are extended to the array form. The price paid is an increase in computational complexity, which becomes cubic. The superiority of the algorithm with respect to alternative algorithms is demonstrated via simulations in the context of adaptive beamforming, in which low filter orders are employed, so that complexity is not an issue. In the second part of the thesis, an alternative criterion is motivated and proposed for the dynamical regulation of regularization in the context of the standard RLS algorithm. The regularization is implicitely achieved via dithering of the input signal. The proposed criterion is of general applicability and aims at achieving a balance between the accuracy of the numerical solution of a perturbed linear system of equations and its distance from the analytical solution of the original system, for a given computational precision. Simulations show that the proposed criterion can be effectively used for the compensation of large condition numbers, small finite precisions and unecessary large values of the regularization. (AU) | |
| FAPESP's process: | 09/06837-4 - Robust Affine Projection Algorithms |
| Grantee: | Manolis Tsakiris |
| Support Opportunities: | Scholarships in Brazil - Master |