A simplified variable step-size LMS algorithm for Fourier analysis and its statistical properties

Huang, Boyan; Xiao, Yegui; Ma, Yaping; Wei, Guo; Sun, Jinwei

doi:10.1016/j.sigpro.2015.04.021

Cited by 28 publications

(17 citation statements)

References 18 publications

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“…Practice shows that these algorithms can achieve fast convergence at a small tracking error, and effectively eliminate interferences. Besides, these algorithms are easy to implement with hardware, thanks to their small parameter size and computing load [15][16].…”

Section: Lms Algorithm With Variable Step Sizementioning

confidence: 99%

Design and Application of an Improved Least Mean Square Algorithm for Adaptive Filtering

Zhao-jun¹,

Ru-Gang²

2019

EJEE

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This paper enumerates the strengths and defects of the traditional least mean square (LMS) algorithm for adaptive filtering, and then designs a novel LMS algorithm with variable step size and verifies its performance through simulation. In our algorithm, the step size is no longer adjusted by the square of the error (e2(n)), but by the correlation between the current error and the error of a previous moment e(n-D). In this way, the algorithm becomes less sensitive to the noise with weak autocorrelation, and manages to achieve fast convergence, high time-varying tracking accuracy, and small steady-state error. The simulation results show that our algorithm outperformed the traditional LMS algorithm with fixed step size in convergence speed, tracking accuracy and noise suppression. The research findings provide a new tool for many other fields of adaptive filtering, such as adaptive system identification and adaptive signal separation.

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Section: Lms Algorithm With Variable Step Sizementioning

confidence: 99%

Design and Application of an Improved Least Mean Square Algorithm for Adaptive Filtering

Zhao-jun¹,

Ru-Gang²

2019

EJEE

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“…y ¼ 2nþake min 1þn (27) where k ¼ arccotð e min j jÞ. Note that 0 < n < 1, 0 < a < 1 and 0 < k < p 2 , then y < 4nþpae min 1þn (28) From equations (21) and (26), a sufficient condition on parameters n and a for convergence of the MSE is 0 < 4nþpae min 1þn 1 3trðRÞ (29) Substituting equation (26) in equation 22, we have…”

Section: Steady-state Misadjustmentmentioning

confidence: 99%

New feedforward filtered-x least mean square algorithm with variable step size for active vibration control

Fang

Zhu

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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The step size of least mean square (LMS) algorithm is significant for its performance. To be specific, small step size can get small excess mean square error but results in slow convergence. However, large step size may cause instability. Many variable step size least mean square (VSSLMS) algorithms have been developed to enhance the control performance. In this paper, a new VSSLMS was proposed based on Kwong's algorithm to evaluate the robustness. The approximate analysis of dynamic and steady-state performance of this developed VSSLMS algorithm was given. An active vibration control system of piezoelectric cantilever beam was established to verify the performance of the VSSLMS algorithms. By comparing with the current VSSLMS algorithms, the proposed method has better performance in active vibration control applications.

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“…The step-size parameter is critical to the performance of the LMS algorithm and evaluates how fast the algorithm converges along the error performance surface. To accelerate the speed of convergence and minimize the excess mean squared error (MSE), several time-varying step-size techniques have been reported in the literature [25]- [32]. The basic principle is that at the starting stages of convergence or transients, the step-size parameter should be large, in order to achieve a faster convergence rate and minimum error.…”

Section: Introductionmentioning

confidence: 99%

A High-Speed Master-Slave ADALINE for Accurate Power System Harmonic and Inter-Harmonic Estimation

2020

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This paper presents a unique twofold adaptive linear neural network (ADALINE) for fast and accurate measurement of fundamental, harmonics, sub-harmonics, inter-harmonics and decaying DC components of a distorted current signal with additive noise. The preceding parallel approach is termed as Master-Slave ADALINE (MS ADALINE). The Slave-ADALINE adopts least mean square (LMS) algorithm with a fixed and large step-size for weight vector adjustment. During the training interval or transients, this filter performs a significant role. On the other hand, the Master-ADALINE uses a variable step-size LMS algorithm for achieving a small steady-state error. At the end of each iteration, the local averages of the squared errors of both the ADALINE's are calculated and weights of the Master-ADALINE are updated accordingly. The amplitudes and phases of desired frequency components can be worked out from Master-ADALINE's weights. The proposed architecture improves the convergence speed by establishing an independent control action between the steady-state error and the speed of convergence. The simulation results of this method under various operating situations are analyzed and compared with single fold ADALINE structure that obeys dynamic step-size LMS (DSSLMS) adaptation rule. Eventually, a scaled laboratory prototype has been developed for the validation of the proposed technique in real-time utilization. This innovative research finding makes the power system smart and precise. INDEX TERMS Adaptive linear neural network (ADALINE), dynamic step-size least mean square (DSSLMS), harmonic estimation, power quality assessment, master-slave (MS).

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A simplified variable step-size LMS algorithm for Fourier analysis and its statistical properties

Cited by 28 publications

References 18 publications

Design and Application of an Improved Least Mean Square Algorithm for Adaptive Filtering

Design and Application of an Improved Least Mean Square Algorithm for Adaptive Filtering

New feedforward filtered-x least mean square algorithm with variable step size for active vibration control

A High-Speed Master-Slave ADALINE for Accurate Power System Harmonic and Inter-Harmonic Estimation

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