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In this paper, a robust adaptive filter based on kernel risk-sensitive loss for bilinear forms is proposed. The proposed algorithm, called minimum kernel risk-sensitive loss bilinear form (MKRSL-BF), is derived by minimizing the cost function based on the minimum kernel risk-sensitive loss (MKRSL) criterion. The proposed algorithm can obtain the excellent performance when the system is corrupted by the impulsive noise. In addition, to further improve the performance of the MKRSL-BF algorithm, the novel algorithm based on the convex scheme is proposed, which can suppress the confliction between the fast convergence rate and the low steady-state error. Finally, simulations are carried out to verify the advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

• To analyze the performance of three proportionate algorithms in impulsive noises. • To reveal the ranges and relations of the step-sizes in three proportionate algorithms. • To develop a decorrelation technique based variable step-size scheme to deal with the trade-off between convergence rate and steady-state error. In the literature, the proportionate least mean M-estimate (PLMM) algorithm exhibits good performance when dealing with sparse systems in the presence of impulsive noises. In this paper, the mean and mean-square behaviors of three recursion types of the PLMM algorithm are studied in depth. We derive analytically the stability, transient and steady-state results of these PLMM recursions, and find that they can achieve the same performance when properly choosing the step-size and the proportionate matrix. To improve the filter performance in both convergence rate and steady-state error, we derive a variable step-size (VSS) scheme and then present the VSS-based PLMM algorithms. In addition, based on the adaptive decorrelation strategy aiming at the colored input signals, the VSS adaptive decorrelation PLMM algorithms are developed to further speed up the convergence. Computer simulations have verified our theoretical analyses and the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

An incremental least‐mean M‐estimate algorithm is proposed for distributed network, which minimises a robust M‐estimator‐based cost function against impulsive noise via the gradient descent method. Moreover, based on the same frame for implementation, an incremental distributed least‐mean p‐power algorithm is presented for combating impulsive noise. Simulations verify the superiority of the proposed algorithms in the presence of impulsive noise relative to some existing incremental distributed algorithms. [ABSTRACT FROM AUTHOR]

• By incorporating the sparsity-aware technique, we propose the S-IWF-SSAF algorithm, and analyze its performance in-depth in impulsive noise. • The proposed analysis covers the behaviors of the IWF-SSAF algorithm in impulsive noise, with better accuracy than the analysis in [15]. • We devise a joint optimization scheme to automatically choose the step-size and the sparsity penalty parameter for the S-IWF-SSAF algorithm. • To make the proposed algorithms suitable for AEC, we develop delayless implementation of the proposed algorithms. In this paper, we propose and analyze the sparsity-aware sign subband adaptive filtering with individual weighting factors (S-IWF-SSAF) algorithm, and consider its application in acoustic echo cancellation (AEC). Furthermore, we design a joint optimization scheme of the step-size and the sparsity penalty parameter to enhance the S-IWF-SSAF performance in terms of convergence rate and steady-state error. A theoretical analysis shows that the S-IWF-SSAF algorithm outperforms the previous sign subband adaptive filtering with individual weighting factors (IWF-SSAF) algorithm in sparse scenarios. In particular, compared with the existing analysis on the IWF-SSAF algorithm, the proposed analysis does not require the assumptions of large number of subbands, long adaptive filter, and paraunitary analysis filter bank, and matches well the simulated results. Simulations in both system identification and AEC situations have demonstrated our theoretical analysis and the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

• This paper provides the robust SAF-LHC-MNAG algorithm for nonlinear system identification in impulsive noise scenarios. • The proposed algorithm can accelerate the convergence under the premise of low steady-state error. • The convergence condition and the mean square performance of the SAF-LHC-MNAG algorithm are given. • The proposed algorithm is implemented to identify the hysteresis model of the piezoelectric actuator. This paper proposes a novel spline adaptive filtering (SAF) algorithm for nonlinear system identification under impulsive noise environments. This algorithm combines the logarithmic hyperbolic cosine (LHC) cost function and the modified Nesterov accelerated gradient (MNAG) learning method, which is called the SAF-LHC-MNAG algorithm. The LHC cost function can reduce the sensitivity of SAF to large outliers and improve the robustness to impulsive noises. Additionally, the MNAG method can further accelerate the convergence under the premise of low steady-state error. Performance analysis of this algorithm is carried out and supported by simulations. Numerical results show that the SAF-LHC-MNAG algorithm has better convergence performance than some existing SAF algorithms. Besides, experimental results confirm the effectiveness of SAF-LHC-MNAG for the accurate identification of nonlinear hysteresis system. [ABSTRACT FROM AUTHOR]

Highlights • This paper provides the development of the robust censored adaptive algorithm for the impulsive noise. • This paper gives Consideration of non-Gaussian background noise as different from previous literature which only consider the Gaussian noise. • Theoretical insights into the mean and mean square performance of the CR-MCC algorithm are provided. • Simulation examples to demonstrate the performance of the proposed algorithm in impulsive noise scenarios are given. Abstract Censored observations and impulsive measurement noise are encountered in many practical applications of adaptive signal processing. Traditional adaptive filtering algorithms may fail to work in such cases. This paper proposes a robust adaptive filter algorithm predicated on maximum correntropy criteria (MCC) for censored regression. A detailed performance analysis in terms of mean and mean-square behaviour is provided. Simulations with Gaussian and non-Gaussian noise are presented to verify the theoretical results, and to demonstrate the superior performance of the proposed algorithm over existing algorithms. [ABSTRACT FROM AUTHOR]