A Stable Normalized Least Mean Fourth Algorithm With Improved Transient and Tracking Behaviors

Eweda, Eweda

doi:10.1109/tsp.2016.2573747

Cited by 18 publications

(12 citation statements)

References 18 publications

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“…In the absence of impulsive noise, and when the initial weight vector is assumed to be very large, both RNLMAT and VSSRNLMAT cannot provide fast convergence rate. The switching methods [3], [21] can solve this issue effectively, which is achieved by adaptively switching the original algorithm from one algorithm to the other in different filtering phases.…”

Section: Swrnlmat Algorithmmentioning

confidence: 99%

“…Inspired by NLMF5 [21], we propose a novel switching adaptive filtering algorithm, namely, the switching RNLMAT (SWRNLMAT) algorithm based on the LMAT algorithm (3) as follows:…”

Section: Swrnlmat Algorithmmentioning

confidence: 99%

“…Since SWRNLMAT behaves as a normalized LMS (NLMS) algorithm [41] with a unit step-size when the error is very large, it can be stable for large values of input variance, noise variance, and initial weights in nonimpulsive noises [1], [3], [18], [21]. Since SWRNLMAT behaves as a LMAT algorithm with a step-size being 1 ζ u(i) 3 when the error is small, it can provide performance improvement in most noise environments [6].…”

Section: Swrnlmat Algorithmmentioning

confidence: 99%

“…The mean square deviation (MSD) of NLMF4 has been shown to be bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment [19], [20]. To further address these limitations of NLMF4 efficiently, a switchable normalization is constructed by the product of the squared norm of the input and the maximum of the squared error and the scaled squared norm of the input, leading to a stable NLMF5 [21].…”

Section: Introductionmentioning

confidence: 99%

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Robust Normalized Least Mean Absolute Third Algorithms

2019

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This paper addresses the stability issues of the least mean absolute third (LMAT) algorithm using the normalization based on the third order in the estimation error. A novel robust normalized least mean absolute third (RNLMAT) algorithm is therefore proposed to be stable for all statistics of the input, noise, and initial weights. For further improving the filtering performance of RNLMAT in different noises and initial conditions, the variable step-size RNLMAT (VSSRNLMAT) and the switching RNLMAT (SWRNLMAT) algorithms are proposed using the statistics of the estimation error and a switching method, respectively. The filtering performance of RNLMAT is improved by VSSRNLMAT and SWRNLMAT at the expense of affordable computational cost. RNLMAT with less computational complexity than other normalized adaptive filtering algorithms, can provide better filtering accuracy and robustness against impulsive noises. The steady-state performance of RNLMAT and SWRNLMAT in terms of the excess mean-square error is performed for theoretical analysis. Simulations conducted in system identification under different noise environments confirm the theoretical results and the superiorities of the proposed algorithms from the aspects of filtering accuracy and robustness against large outliers.

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Section: Swrnlmat Algorithmmentioning

confidence: 99%

“…Inspired by NLMF5 [21], we propose a novel switching adaptive filtering algorithm, namely, the switching RNLMAT (SWRNLMAT) algorithm based on the LMAT algorithm (3) as follows:…”

Section: Swrnlmat Algorithmmentioning

confidence: 99%

Section: Swrnlmat Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Normalized Least Mean Absolute Third Algorithms

2019

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“…However, the tracking performance is limited when signal-tonoise ratio (SNR) is high. Eweda [15] propose a new stable NLMF algorithm, which is superior to the existing stable NLMF in both transient and steady states. Unfortunately, the NLMF algorithm can be biased by the input noise, which leads to degradation of its performance.…”

Section: Introductionmentioning

confidence: 99%

Novel Adaptive Filtering Algorithms Based on Higher-Order Statistics and Geometric Algebra

Wang

et al. 2020

IEEE Access

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Adaptive filtering algorithms based on higher-order statistics are proposed for multidimensional signal processing in geometric algebra (GA) space. In this paper, the proposed adaptive filtering algorithms utilize the advantage of GA theory in multi-dimensional signal processing to represent a multidimensional signal as a GA multivector. In addition, the original least-mean fourth (LMF) and least-mean mixed-norm (LMMN) adaptive filtering algorithms are extended to GA space for multi-dimensional signal processing. Both the proposed GA-based least-mean fourth (GA-LMF) and GA-based least-mean mixednorm (GA-LMMN) algorithms need to minimize cost functions based on higher-order statistics of the error signal in GA space. The simulation results show that the proposed GA-LMF algorithm performs better in terms of convergence rate and steady-state error under a much smaller step size. The proposed GA-LMMN algorithm makes up for the instability of GA-LMF as the step size increases, and its performance is more stable in mean absolute error and convergence rate. INDEX TERMS Adaptive filters, geometric algebra, least-mean fourth, least-mean mixed-norm.

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