New insights into the normalization of the least mean fourth algorithm

Eweda, Eweda; Zerguine, Azzedine

doi:10.1007/s11760-011-0231-y

Cited by 37 publications

(12 citation statements)

References 13 publications

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“…A combined estimation criterion to accelerate the identification process using a combination of quadratic criterion and fourth degree criterion, proposed and studied in [25], was developed in [26][27][28][29][30]. [26] investigated the stability of the algorithm under Gaussian input signals.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Robust identification of non-stationary objects with nongaussian interference

Rudenko¹,

Bezsonov²,

Lebediev³

et al. 2019

EEJET

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Robust identification of non-stationary objects with nongaussian interference

Rudenko¹,

Bezsonov²,

Lebediev³

et al. 2019

EEJET

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“…Consequently, NLMF3 is stabilized against the increase of the input variance. However, the stability of NLMF3 depends on the weight vector initialization and the noise variance [16], [17]. The fourth NLMF algorithm, NLMF4, is proposed in [18] and it is given by (11) The idea of this algorithm is a combination of the ideas of NLMF2 (9) and NLMF3 (10).…”

Section: Problem Formulationmentioning

confidence: 99%

“…Equations (1)-(4) and (11) imply that (14) (15) Due to (14) and (15), is a function of . Hence, Assumptions A1, A3-A5 imply that (16) Premultiplying (14) by and taking the expectation, (15) and (16) imply that (17) Rewrite (17) …”

Section: A Bounding Recurrence Of the Msdmentioning

confidence: 99%

“…This NLMF algorithm remains stable as the input variance increases. However, the stability of NLMF3 depends on both the initial weight deviation vector and the noise variance [16], [17]. Finally, [18] has proposed NLMF4 in which the weight vector update term is normalized by a term that is fourth order in the regressor and second order in the estimation error.…”

Section: Introductionmentioning

confidence: 99%

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Mean-Square Stability Analysis of a Normalized Least Mean Fourth Algorithm for a Markov Plant

Eweda¹

2014

IEEE Trans. Signal Process.

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Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations.Index Terms-Adaptive filters, least mean fourth algorithm, mean square stability, tracking. 1053-587X

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“…It is well known that the stability is one of the key factors for ASI. Standard LMF algorithm is unstable due to the fact that its stability depends on the following three factors: input signal power, noise power, and weight initialization [11]. In general, for a given gradient descend step-size, NLMS algorithm is stable and depends solely on the input signal power [4].…”

Section: Background and Motivationmentioning

confidence: 99%

Adaptive sparse system identification using normalized least mean fourth algorithm

Gui

Adachi

2013

Int J Communication

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SUMMARYNormalized least mean square (NLMS) was considered as one of the classical adaptive system identification algorithms. Because most of systems are often modeled as sparse, sparse NLMS algorithm was also applied to improve identification performance by taking the advantage of system sparsity. However, identification performances of NLMS type algorithms cannot achieve high-identification performance, especially in low signal-to-noise ratio regime. It was well known that least mean fourth (LMF) can achieve highidentification performance by utilizing fourth-order identification error updating rather than second-order. However, the main drawback of LMF is its instability and it cannot be applied to adaptive sparse system identifications. In this paper, we propose a stable sparse normalized LMF algorithm to exploit the sparse structure information to improve identification performance. Its stability is shown to be equivalent to sparse NLMS type algorithm. Simulation results show that the proposed normalized LMF algorithm can achieve better identification performance than sparse NLMS one.

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New insights into the normalization of the least mean fourth algorithm

Cited by 37 publications

References 13 publications

Robust identification of non-stationary objects with nongaussian interference

Robust identification of non-stationary objects with nongaussian interference

Mean-Square Stability Analysis of a Normalized Least Mean Fourth Algorithm for a Markov Plant

Adaptive sparse system identification using normalized least mean fourth algorithm

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