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fast QR algorithms based on backward prediction errors:: A new implementation and its finite precision performance

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2003年第4期22卷 335-349页

作者： Apolinario, JA Siqueira, MG Diniz, PSR Mil Inst Engn BR-22290270 Rio De Janeiro RJ Brazil Univ Fed Rio de Janeiro COPPE PEE BR-21945970 Rio De Janeiro RJ Brazil

QR decomposition techniques are well known for their good numerical behavior and low complexity. fast QRD recursive least squares adaptive algorithms benefit from these characteristics to offer robust and fast adaptive filters. This paper examines two different versions of the fast QR algorithm based on a priori backward prediction errors as well as two other corresponding versions of them fast QR algorithm based on a posteriori backward prediction errors. The main matrix equations are presented with different versions derived from two distinct deployments of a particular matrix equation. From this study, a new algorithm is derived. The discussed algorithms are compared, and differences in computational complexity and in finite-precision behavior are shown.

关键词： adaptive system fast rls algorithm QR decomposition

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Numerical performances of recursive least squares and predictor based least squares: A comparative study

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1997年第4期E80A卷 745-752页

作者： Wang, YH Nakayama, K Faculty of Engineering Kanazawa University Kanazawa-shi 920 Japan

The numerical properties of the recursive least squares (rls) algorithm and its fast versions have been extensively studied. However, very few investigations are reported concerning the numerical behavior of the predictor based least squares (PLS) algorithms that provide the same least squares solutions as the rls algorithm. This paper presents a comparative study on the numerical performances of the rls and the back ward PLS (BPLS) algorithms. Theoretical analysis of three main instability sources reported in the literature, including the over-range of the conversion factor, the loss of symmetry and the loss of positive definiteness of the inverse correlation matrix, has been done under a finite-precision arithmetic. Simulation results have confirmed the validity of our analysis. The results show that three main instability sources encountered in the rls algorithm do not exist in the BPLS algorithm. Consequently, the BPLS algorithm provides a much more stable and robust numerical performance compared with the rls algorithm.

关键词： adaptive filter rls algorithm fast rls algorithm stability finite-precision implementation

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A STABLE LEAST-SQUARE algorithm-BASED ON PREDICTORS AND ITS APPLICATION TO fast NEWTON TRANSVERSAL FILTERS

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1995年第8期E78A卷 999-1003页

作者： WANG, YH NAKAYAMA, K Kanazawa Univ Kanazawa-shi Japan

In this letter, we introduce a predictor based least square (PLS) algorithm. By involving both order- and time-update recursions, the PLS algorithm is found to have a more stable performance compared with the stable version (Version II) of the rls algorithm shown in Ref. [1]. Nevertheless, the computational requirement is about 50% of that of the rls algorithm. As an application, the PLS algorithm can be applied to the fast newton transversal filters (FNTF)[2]. The FNTF algorithms suffer from the numerical instability problem if the quantities used for extending the gain vector are computed by using the fast rls algorithms. By combing the PLS and the FNTF algorithms, we obtain a much more stable performance and a simple algorithm formulation.

关键词： ADAPTIVE FILTERS rls algorithm fast rls algorithm fast NEWTON TRANSVERSAL FILTERS STABILITY

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A stability analysis of predictor-based least squares algorithm

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1997年第11期E80A卷 2286-2290页

作者： Ikeda, K Wang, YH Nakayama, K Faculty of Engineering Kanazawa University Kanazawa-shi 920 Japan

The numerical property of the recursive least squares (rls) algorithm has been extensively studied. However, very few investigations are reported concerning the numerical behavior of the predictor-based least squares (PLS) algorithms which provide the same least squares solutions as the rls algorithm. In Ref. [9], we gave a comparative study on the numerical performances of the rls and the backward PLS (BPLS) algorithms. It was shown that the numerical property of the BPLS algorithm is much superior to that of the rls algorithm under a finite-precision arithmetic because several main instability sources encountered in the rls algorithm do not appear in the BPLS algorithm. This paper theoretically shows the stability of the BPLS algorithm by error propagation analysis. Since the time-variant nature of the BPLS algorithm, we prove the stability of the BPLS algorithm by using the method as shown in Ref. [6]. The expectation of the transition matrix in the BPLS algorithm is analyzed and its eigenvalues are shown to have values within the unit circle. Therefore we can say that the BPLS algorithm is numerically stable.

关键词： adaptive filter rls algorithm fast rls algorithm numerical stability analysis

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A Mechanism for Switching Adaptive Filter algorithms in Suddenly Time-Varying Environments 53

A Mechanism for Switching Adaptive Filter Algorithms in Sudd...

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SICE Annual Conference (SICE)

作者： Matsuzaki, Hidenori Hikawa Kohbou Saitama Japan

ISBN: (纸本)9784907764456

This paper proposes an adaptive filtering system where a least-square algorithm and a stochastic gradient algorithm are alternately switched depending on its operational mode. The switching mechanism is quite simple and realized with a small amount of computational cost. Several numerical examples show that the resulting filter could achieve both sufficiently fast convergence and enhanced robustness in suddenly time-varying system environments.

关键词： Adaptive filtering fast rls algorithm NLMS algorithm time-varying system

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