Fast Algorithms with low Complexity for Adaptive Filtering (original) (raw)
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A FAST Algorithm for Adaptive Filtering
2009 16th International Conference on Systems, Signals and Image Processing, 2009
In this paper, we evaluate the possibility to develop algorithms of adaptation for the applications system of acoustic echo cancellation, while maintaining equilibrium between its reduced calculation complexity and its adaptive performances. We present new algorithms versions of fast recursive least squares numerically stable (NS-FRLS). They are obtained by means of redundant formulas, available in the fast recursive least squares (FRLS) algorithms, to estimate numerical errors and to retroact them in an unspecified point of the algorithm in order to modify its numerical properties. These algorithms represent a very important load of calculation that needs to be reduced. we propose a new (M-SMFTF) algorithm for adaptive filtering with fast convergence and low complexity. It is the result of a simplified FTF type algorithm, where the adaptation gain is obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. This algorithm presents a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal. Its calculation complexity is of 6L (L is the finite impulse response filter length) and this is considerably reduced to (2L+4P) when we use a reduced P-size (P<<L) forward predictor.
Advanced algorithms for adaptive filtering
2009
In this paper, we evaluate the possibility to develop algorithms of adaptation for the applications system of acoustic echo cancellation, while maintaining equilibrium between its reduced calculation complexity and its adaptive performances. We present new algorithms versions of fast recursive least squares numerically stable (NS-FRLS). They are obtained by means of redundant formulas, available in the fast recursive least squares (FRLS) algorithms, to estimate numerical errors and to retroact them in an unspecified point of the algorithm in order to modify its numerical properties. These algorithms represent a very important load of calculation that needs to be reduced. we propose a new (M-SMFTF) algorithm for adaptive filtering with fast convergence and low complexity. It is the result of a simplified FTF type algorithm, where the adaptation gain is obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. This algorit...
Fast Recursive Least Squares Algorithm for Acoustic Echo Cancellation Application
2007
Adaptive filtering is used in a wide range of applications including echo cancellation, noise cancellation and equalization. In these applications, the environment in which the adaptive filter operates is often non-stationary. For satisfactory performance under non-stationary conditions, an adaptive filtering is required to follow the statistical variations of the environment. Tracking analysis provides insight into the ability of an adaptive filtering algorithm to track the changes in surrounding environment. The tracking behavior of an algorithm is quite different from its convergences behavior. While convergence is a transient phenomenon, tracking is a steady-state phenomenon. Over the last decade a class of equivalent algorithms such as the Normalized Least Mean Squares algorithm (NLMS) and the Fast Recursive Least Squares algorithm (FRLS) has been developed to accelerate the convergence speed. In acoustic echo cancellation context, we propose in this paper to use numerically stable Fast Recursive Least Squares algorithm to improve the quality and the intelligibility of the enhanced speech.
Analysis of fast recursive least squares algorithms for adaptive filtering
In this paper, we present new version of numerically stable fast recursive least squares (NS-FRLS) algorithm. This new version is obtained by using some redundant formulae of the fast recursive least squares (FRLS) algorithms. Numerical stabilization is achieved by using a propagation model of first order of the numerical errors. A theoretical justification for this version is presented by formulating new conditions on the forgetting factor. An advanced comparative method is used to study the efficiency of this new version relatively to RLS algorithm by calculating their normalized square norm gain error (NGE). We provide a theoretical justification for this version by formulating new conditions on forgetting factor. It will be followed by an analytical analyze of the convergence of this version and we show, both theoretically and experimentally, their robustness. The simulation over a very long duration for a stationary signal did not reveal any tendency to divergence.
Improvement of the Simplified Fast Transversal Filter Type Algorithm for Adaptive Filtering
Journal of Computer Science, 2009
In this study, we proposed a new algorithm M-SMFTF for adaptive filtering with fast convergence and low complexity. Approach: It was the result of a simplified FTF type algorithm, where the adaptation gain was obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. Results: The computational complexity was reduced from 7L-6L, where L is the finite impulse response filter length. Furthermore, this computational complexity can be significantly reduced to (2L+4P) when used with a reduced P-size forward predictor. Conclusion: This algorithm presented a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal.
Signal Processing, 1994
In this paper, we derive a new fast algorithm for Recursive Least-Squares RLS adaptive ltering. This algorithm is especially suited for adapting very long lters such as in the acoustic echo cancellation problem. The starting point is to introduce subsampled updating SU in the RLS algorithm. In the SU RLS algorithm, the Kalman gain and the likelihood variable are matrices. Due to the shift invariance of the adaptive FIR ltering problem, these matrices exhibit a low displacement rank. This leads to a representation of these quantities in terms of sums of products of triangular Toeplitz matrices. Finally, the product of these Toeplitz matrices with a vector can be computed e ciently by using the Fast Fourier Transform FFT. Zusammenfassung Dieser Artikel beschreibt die Herleitung eines neuen Algorithmus zur schnellen adaptiven Recursive Least Square RLS Filterung. Dieser Algorithmus eignet sich besonders f uer aufwendige Filter, wie sie zum Beispiel zur akkustischen Echounterdr ueckung benutzt werden. Im Zentrum dieses Algorithmus steht die Einf uehrung von unterabgetastetem Updating SU. Der Kalman Gewinn und die Likelihood Variable treten im SU RLS Algorithmus als Matrizen auf. Aufgrund der Verschiebungsinvarianz in der adaptiven FIR Filterung zeigen diese Matrizen einen niedrigen Verschiebungsrang. Dies f uehrt zu einer Darstellung dieser Gr oessen als Summe von Produkten von triangul aeren Toeplitz Matrizen. Das Produkt dieser Matrizen mit einem Vektor k ann auf sehr e ziente Weise mit der Fast Fourier Transform FFT berechnet werden. R esum e Dans ce papier, nous pr esentons un nouvel algorithme des moindres carr es r ecursif rapide. Cet algorithme pr esente un int erêt certain pour l'adaptation de ltres tr es longs comme ceux utilis es dans les probl emes d'annulation d' echo acoustique. L'id ee de d epart est d'utiliser l'algorithme RLS avec une mise a jour sous-echantillonn ee" du ltre. Dans cet algorithme le SU RLS le gain de Kalman et la variable de vraisemblance sont des matrices qui ont des rangs de d eplacement faibles. Ces quantit es sont alors repr esent ees et mises a jour par le biais de leurs g en erateurs, sous forme de sommes de produits de matrices de Toeplitz triangulaires. Le produit de l'une de ces quantit es avec un vecteur peut alorsêtre calcul e en utilisant la transform ee de Fourier rapide FFT.
2005
In this paper, we present a new version of numerically stable fast recursive least squares (NS-FRLS) algorithm. This new version is obtained by using some redundant formulas of the fast recursive least squares FRLS algorithms. Numerical stabilization is realized by using a propagation model of first order of the numerical errors. An advanced comparative method is used to study the efficiency of this new version. The simulation over very long
Journal of Algorithms, 2000
In this paper, a new multichannel recursive least squares (MRLS) adaptive algorithm is presented which has a number of very interesting properties. The proposed computational scheme performs adaptive filtering via the use of a finite window, where the burdening past information is dropped directly by means of a generalized inversion lemma; consequently, the proposed algorithm has excellent tracking abilities and very low misjudgment. Moreover, the scheme presented here, due to its particular structure and to the proper choice of mathematical definitions behind it, is very robust; i.e., it is less sensitive in the finite precision numerical error generation and propagation. Also, the new algorithm can be parallelized via a simple technique and its parallel form and, when executed with four processors, is faster than all the already existing schemes that perform both infinite and finite window multichannel adaptive filtering. Finally, due to the particular structure of this scheme and to the intrinsic flexibility in the choice of the window length, the proposed algorithm can act as a full substitute of the infinite window MRLS ones.
A Practical Overview of Recursive Least-Squares Algorithms for Echo Cancellation
Due to its fast convergence rate, the recursive least-squares (RLS) algorithm is very popular in many applications of adaptive filtering. However, the computational complexity of this algorithm represents a major limitation in some applications that involve long filters, like echo cancellation. Moreover, the specific features of this application require good tracking capabilities and double-talk robustness for the adaptive algorithm, which further imply an optimization process on its parameters. In the case of most RLS-based algorithms, the performance can be controlled in terms of two main parameters, i.e., the forgetting factor and the regularization term. In this paper, we outline the influence of these parameters on the overall performance of the RLS algorithm and present several solutions to control their behavior, taking into account the specific requirements of echo cancellation application. The resulting variable forgetting factor RLS (VFF-RLS) and variable-regularized RLS (...
An efficient recursive total least squares algorithm for FIR adaptive filtering
IEEE Transactions on Signal Processing, 1994
Absbuct-An algorithm for recursively computing the total least squares (TLS) solution to the adaptive filtering problem is described. This algorithm requires O( N ) multiplications per iteration to effectively track the N-dimensional eigenvector associated with the minimum eigenvalue of an augmented sample covariance matrix. It is shown that the recursive least squares (RLS) algorithm generates biased adaptive filter coefficients when the filter input vector contains additive noise. The TLS solution on the other hand, is seen to produce unbiased solutions. Examples of standard adaptive filtering applications that result in noise being added to the adaptive filter input vector are cited. Computer simulations comparing the relative performance of RLS and recursive TLS are described.