Normalised least‐mean‐square algorithm for adaptive filtering of impulsive measurement noises and noisy inputs

Jung, Sang Mok; Park, PooGyeon

doi:10.1049/el.2013.2482

Cited by 57 publications

(33 citation statements)

References 5 publications

(7 reference statements)

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“…Furthermore, the following unbiasedness criterion [28] is employed E[ w(n + 1)|u(n) ] = 0 whenever E[ w(n)|u(n) ] = 0 (8) and by some simplified calculations, we have…”

Section: Bcnmccmentioning

confidence: 99%

“…As a result, more and more bias-compensated aware AFAs with the unbiasedness criterion have been developed to eliminate the influence from noisy input signals [28][29][30][31]. These include, for example, the bias-compensated NLMS (BCNLMS) algorithm [28][29][30], bias-compensated NLMF algorithm [31], bias-compensated affine projection algorithm [32], bias-compensated NMCC (BCNMCC) [33], and so on. However, they do not consider the sparsity of the system.On the basis of the analysis above, we develop two novel algorithms called bias-compensated NMCC with CIM penalty (CIM-BCNMCC) and bias-compensated proportionate NMCC (BCPNMCC) in this work.…”

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confidence: 99%

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Sparse-Aware Bias-Compensated Adaptive Filtering Algorithms Using the Maximum Correntropy Criterion for Sparse System Identification with Noisy Input

Zheng

Zhang

et al. 2018

Entropy

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To address the sparse system identification problem under noisy input and non-Gaussian output measurement noise, two novel types of sparse bias-compensated normalized maximum correntropy criterion algorithms are developed, which are capable of eliminating the impact of non-Gaussian measurement noise and noisy input. The first is developed by using the correntropy-induced metric as the sparsity penalty constraint, which is a smoothed approximation of the 0 norm. The second is designed using the proportionate update scheme, which facilitates the close tracking of system parameter change. Simulation results confirm that the proposed algorithms can effectively improve the identification performance compared with other algorithms presented in the literature for the sparse system identification problem.Entropy 2018, 20, 407 2 of 15 developed to address the SSI problem: one using the compressed sensing approach [17,18], and the other employing the proportionate update scheme [19]. At present, the zero attracting (ZA) algorithm and reweight zero attracting algorithm belonging to the former (such as ZANLMS [20], ZANLMF [21], ZAMCC [22] and General ZA-Proportionate Normalized MCC [23]) have been proposed based on the sparse penalty term (SPE). The correntropy-induced metric (CIM) [5], as an effective SPE, has been utilized to improve the performance of the algorithm in SSI, resulting in the CIM-NLMS, CIM-NLMF, CIM-LMMN, and CIM-MCC algorithms [22,24,25]. Correspondingly, the latter algorithms are proportionate-type AFAs (including proportionate NLMS [19], proportionate NLMF [26], proportionate MCC [27], and so on) which use the gain matrix to improve performance. Although those algorithms above make full use of the sparsity of the system, they lack consideration of the noisy input problem. As a result, more and more bias-compensated aware AFAs with the unbiasedness criterion have been developed to eliminate the influence from noisy input signals [28][29][30][31]. These include, for example, the bias-compensated NLMS (BCNLMS) algorithm [28][29][30], bias-compensated NLMF algorithm [31], bias-compensated affine projection algorithm [32], bias-compensated NMCC (BCNMCC) [33], and so on. However, they do not consider the sparsity of the system.On the basis of the analysis above, we develop two novel algorithms called bias-compensated NMCC with CIM penalty (CIM-BCNMCC) and bias-compensated proportionate NMCC (BCPNMCC) in this work. The former introduces the CIM into the BCNMCC algorithm, while the latter combines the unbiasedness criterion and the PNMCC algorithm. Both of them can achieve better performance than MCC, CIM-MCC, and BCNMCC for SSI under noisy input and non-Gaussian measurement noise.The rest of the paper is organized as follows: In Section 2, the BCNMCC algorithm is briefly reviewed. In Section 3, the CIM-BCNMCC and BCPNMCC algorithms are developed. In Section 4, simulation results are presented to evaluate the performance of the proposed algorithms. Finally, conclusions are made in Section 5.

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“…Furthermore, the following unbiasedness criterion [28] is employed E[ w(n + 1)|u(n) ] = 0 whenever E[ w(n)|u(n) ] = 0 (8) and by some simplified calculations, we have…”

Section: Bcnmccmentioning

confidence: 99%

mentioning

confidence: 99%

Sparse-Aware Bias-Compensated Adaptive Filtering Algorithms Using the Maximum Correntropy Criterion for Sparse System Identification with Noisy Input

Zheng

Zhang

et al. 2018

Entropy

View full text Add to dashboard Cite

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“…Using higher order model and increasing the signal-to-noise ratio (SNR) can mitigate the adverse impact of input noise in some degree but can never be eliminated completely [27]. To overcome this drawback, some improved algorithms for unbiased estimation have been investigated [28]- [39]. The total least squares (TLS) and the biascompensated least squares (TL) methods can handle the bias issue but suffer to computational inefficiency [40].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the bias-compensated algorithms under least mean square criterion obtain more attention relay on their easy implementation and low complexity. In [28], the unbiased criterion for steady state is utilized to provide a simple approach of bias compensation via the statistical property of the input noise. Since then, unbiased algorithms deriving from the unbiased criterion have been developed.…”

Section: Introductionmentioning

confidence: 99%

The Bias-Compensated Proportionate NLMS Algorithm With Sparse Penalty Constraint

Jin

Guo

2020

IEEE Access

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For compensating the bias caused by the noisy input which is always ignored by ordinary algorithms, two novel algorithms with zero-attraction (ZA) penalties are proposed in this paper. The first one constructs a bias-compensated term in the updating recursion of the zero-attraction proportionate normalized least mean square (PNLMS) algorithm which is named BC-ZA-PNLMS algorithm. The second one employs the bias-compensated term and the correntropy induced metric (CIM) constraint to renew the updating recursion of the PNLMS algorithm which is named BC-CIM-PNLMS algorithm. Both of these two algorithms are derived on the basis of unbiased criterion. Simulation examples are carried out, and the results indicate that the two newly developed unbiased algorithms outperform the related algorithms previously presented in other literatures for combating noisy input and measurement noises. INDEX TERMS Unbiased adaptive filtering, zero-attraction (ZA), correntropy induced metric (CIM), PNLMS algorithm.

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“…Adaptive filtering algorithms can be widely used for signal processing [1][2][3][4][5]. However, in some practical applications such as image processing or emission spectra in chemistry [6][7][8][9], systems require non-negative (NN) coefficients when their physical behaviour is parameterised by only NN values.…”

Section: Introductionmentioning

confidence: 99%

Variable step‐size non‐negative normalised least‐mean‐square‐type algorithm

Jung

Seo

Park

2015

IET signal process.

Self Cite

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This paper proposes a fast and precise adaptive filtering algorithm for online estimation under a non-negativity constraint. A novel variable step-size (VSS) non-negative normalised least-mean-square (NLMS)-type algorithm based on the mean-square deviation (MSD) analysis with a non-negativity constraint is derived. The NLMS-type algorithm under the non-negativity constraint is derived by using the gradient descent of the given cost function and the fixed-point iteration method. Furthermore, the VSS derived by minimising the MSD yields improvement of the filter performance in the aspects of the convergence rate and the steady-state estimation error. Simulation results show that the proposed algorithm outperforms existing algorithms.

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Normalised least‐mean‐square algorithm for adaptive filtering of impulsive measurement noises and noisy inputs

Cited by 57 publications

References 5 publications

Sparse-Aware Bias-Compensated Adaptive Filtering Algorithms Using the Maximum Correntropy Criterion for Sparse System Identification with Noisy Input

Sparse-Aware Bias-Compensated Adaptive Filtering Algorithms Using the Maximum Correntropy Criterion for Sparse System Identification with Noisy Input

The Bias-Compensated Proportionate NLMS Algorithm With Sparse Penalty Constraint

Variable step‐size non‐negative normalised least‐mean‐square‐type algorithm

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