Stochastic analysis of the filtered-X LMS algorithm in systems with nonlinear secondary paths

Costa, Márcio Holsbach; Bermudez, J.C.M.; Bershad, N.J.

doi:10.1109/tsp.2002.1003058

Cited by 73 publications

(63 citation statements)

References 11 publications

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“…In fact, A1 and A2 only imply that the statistical dependence of weight and data vectors is not significant in determining the algorithm behaviour. Similar assumptions have been made in Reference [5] and extensively verified by numerical simulations.…”

Section: The Mean Weight Behaviour In a Non-linear Environment}analysismentioning

confidence: 55%

A new adaptive algorithm for reducing non‐linear effects from saturation in active noise control systems

Costa

Bermudez

2004

Adaptive Control & Signal

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Adaptive algorithms applied to active noise and vibration control are frequently designed for maximum performance in linear environments. In many cases, non-linear effects can severely impair the adaptive algorithm performance. One of the most common non-linear effects is saturation, which can occur at the electronic circuits that drive the acoustic or mechanical transducers. An effective solution to mitigate such non-linear distortions is to embed an automatic control of the non-linear effects within the adaptive algorithm. Algorithms that use this approach are called minimum effort adaptive filters. This work presents a new minimum effort algorithm (MOV-FXLMS), based on the minimum output variance least mean square estimator, for situations in which the influence of the secondary path cannot be neglected and its output is constrained by a saturation non-linearity. Analytical expressions are obtained for the behaviour of the mean weight vector and for the mean square error for Gaussian inputs and slow learning. Monte Carlo simulations show excellent agreement with the predictions of the theoretical model. The optimum penalty factor (a design parameter of the MOV-FXLMS algorithm) is determined as a function of the system's degree of non-linearity. The new algorithm provides an unbiased solution to the associated nonlinear mean square estimation problem for small estimation errors of the secondary path and degree of non-linearity. Robustness of the algorithm's performance to such errors is addressed. The new algorithm is compared with the conventional FXLMS algorithm for performance.

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Section: The Mean Weight Behaviour In a Non-linear Environment}analysismentioning

confidence: 55%

A new adaptive algorithm for reducing non‐linear effects from saturation in active noise control systems

Costa

Bermudez

2004

Adaptive Control & Signal

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“…This approximation preserves the mean (in odd order moments) and fluctuation behaviors of while keeping the mathematical problem tractable. It has been previously employed with success in analyses of adaptive algorithms with weight updates that are nonlinear with respect to the weight vector [34]. The simulation results will show that assumptions A1 and A2 and approximation A3 lead to analytical models which are accurate enough in predicting the behavior of the algorithms for design purposes.…”

Section: Second Moment Analysismentioning

confidence: 98%

“…We have again found out that using a zero-th order approximation of is sufficient to provide a reasonably good model for the mean weight error behavior. Thus, we make (34) Using (34) in (33), taking the expected value and considering the statistical properties of and yields (35) where is the identity matrix and is an diagonal matrix defined as with being the vector whose th component is . It is simple to verify that this model collapses to the NNLMS model derived in [20] for .…”

Section: Exponential Nnlms Algorithmmentioning

confidence: 99%

Variants of Non-Negative Least-Mean-Square Algorithm and Convergence Analysis

Chen

Richard

Bermudez

et al. 2014

IEEE Trans. Signal Process.

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Abstract-Due to the inherent physical characteristics of systems under investigation, non-negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate. The Non-Negative Least-Mean-Square algorithm (NNLMS) was proposed to adaptively find solutions of a typical Wiener filtering problem but with the side constraint that the resulting weights need to be non-negative. It has been shown to have good convergence properties. Nevertheless, certain practical applications may benefit from the use of modified versions of this algorithm. In this paper, we derive three variants of NNLMS. Each variant aims at improving the NNLMS performance regarding one of the following aspects: sensitivity of input power, unbalance of convergence rates for different weights and computational cost. We study the stochastic behavior of the adaptive weights for these three new algorithms for non-stationary environments. This study leads to analytical models to predict the first and second order moment behaviors of the weights for Gaussian inputs. Simulation results are presented to illustrate the performance of the new algorithms and the accuracy of the derived models.Index Terms-Adaptive signal processing, convergence analysis, exponential algorithm, least-mean-square algorithms, non-negativity constraints, normalized algorithm, sign-sign algorithm.

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“…Depending on the amount of additional delay the SPR condition (1) does not hold anymore, especially for high frequencies. The RPFxLMS algorithm has been applied for various choices of : 1) , i.e., the nominal case; 2) , which is such that (5) just holds for a delay of 1 10 s; 3) , which is such that (5) just holds for a delay of 2 10 s; and finally 4) estimated via the covariance of the model error due to a delay uniformly distributed from In all experiments, the normalized step size is chosen to be 0.1, the number of filter coefficients and the measurement noise is absent . Fig.…”

Section: Simulation Examplementioning

confidence: 99%

Increasing the Robustness of a Preconditioned Filtered-X LMS Algorithm

Fraanje

Verhaegen

Doelman³

2004

IEEE Signal Process. Lett.

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Abstract-This letter presents a robustification of the preconditioned Filtered-X LMS algorithm proposed by Elliott et al.. The method optimizes the average performance for probabilistic uncertainty in the secondary path and relaxes the SPR condition for global convergence. It also prevents large amplification in the preconditioning filters due to secondary path zeros on and/or close to the unit circle, which may yield overactuation in practical applications.Index Terms-Acoustic noise, adaptive control, adaptive signal processing, feedforward systems, robust filtering.

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Stochastic analysis of the filtered-X LMS algorithm in systems with nonlinear secondary paths

Cited by 73 publications

References 11 publications

A new adaptive algorithm for reducing non‐linear effects from saturation in active noise control systems

A new adaptive algorithm for reducing non‐linear effects from saturation in active noise control systems

Variants of Non-Negative Least-Mean-Square Algorithm and Convergence Analysis

Increasing the Robustness of a Preconditioned Filtered-X LMS Algorithm

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