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The normalized subband adaptive filtering algorithm provides fast convergence rate for colored input signals as compared to the normalized least mean square algorithm, but it suffers from a poor convergence issue in the α -stable noise. In light of this, the normalized subband p-norm (NSPN) algorithm, which is based on the least mean p-power error (MPE) criterion, is proposed in this study. This technique is not only robust against impulsive noise samples, but it also maintains a fast convergence rate when colored input signals are used. In addition to this, we develop both the steady-state and the transient models of the NSPN algorithm and provide some insights. Then, in order to solve the problem of making a choice regarding the order p in the NSPN algorithm, we design an autonomous system and come up with the NSPN algorithm with a variable p-norm (VP-NSPN). In addition, we offer the TFC-based VP-NSPN algorithm with a fast convergence rate and low steady-state misadjustment simultaneously by making use of the tap-weights feedback-based convex combination (TFC) scheme. In conclusion, simulation results on system identification and acoustic echo cancellation are undertaken in order to validate the superiority of the proposed algorithms and validate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Recently, the kernel adaptive filtering algorithm with the generalized maximum correntropy criterion (GMCC) has gained attention due to its excellent nonlinear system modeling ability and robustness to non-Gaussian noise. However, since the default center of the GMCC is located at zero, it hampers its performance in the non-zero mean noise environment. To overcome the problem, this paper proposes a kernel adaptive filtering algorithm based on the GMCC with variable center (GMCC-VC) called generalized kernel maximum correntropy criterion with variable center (GKMCC-VC). In addition, the online vector quantization (VQ) method is introduced to the GKMCC-VC algorithm for suppressing the increasing network size. The probability of divergence, the mean-square steady-state behavior, and the convergence condition of the GKMCC-VC algorithm are also obtained under some assumptions. The potential relationship between the GMCC-VC and the generalized minimum error entropy (GMEE) criteria is discussed in the paper. Finally, the simulation results verify the superiority of the proposed algorithm in modeling nonlinear systems and the correctness of the theoretical model. • This paper proposes the GKMCC-VC algorithm for non-zero mean and non-Gaussian noise. • The steady-state performance of the proposed algorithm is analyzed. • Simulation results show the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) detection plays a vital role in on-line condition monitoring of electrical apparatus in the power systems. However, the noise of PD measurements significantly degrades the performance of detection algorithms. In this paper, we focus on developing an adaptive filtering technique for the PD denoising problem. Heretofore, there are just a few literature reviews addressing the PD denoising based on such a method. The proposed recursive continuous S-shaped (RCSS) algorithm integrates the advantages of recursive strategy and continuous S-shaped function into adaptive noise cancellation (ANC) system, yielding enhanced filtering performance. The proposed algorithm can tackle PD noises in both Gaussian and impulsive scenarios, which is easy to implement in practical applications. The convergence behavior is also analyzed. Extensive simulation and experimental results confirm that the proposed algorithm can address polluted PD pulses, even in excessively noisy conditions, resulting in smaller mean square error (MSE) as compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• The kernel adaptive filter with generalized tanh function (KAF-GT) is proposed, which shows favourable performance in combating impulsive noise. • The convergence analysis of the proposed KAF-GT algorithm is conducted using energy conservation relation. • By using the pre-tuned dictionary strategy to model the unknown nonlinear system, we perform the EMSE analysis and arrive at a closed-form solution for predicting the steady-state behavior. • To further improve the performance of KAF-GT, an optimization scheme for scale factor is designed. Recently, online learning algorithms in machine learning have been imposed much attention. As a typical family, kernel adaptive filtering algorithms receive particular interest due to their sequential learning-based features. However, the kernel least mean square (KLMS) algorithm is not suitable for nonlinear tasks corrupted by non-Gaussian noise, especially impulsive noise. This is because the derivation of the KLMS algorithm is on the basis of the mean square error (MSE) criterion which only captures information of second-order statistics. In this paper, motivated by tanh function, we develop its generalized variant by introducing a scale factor for better representation capability; then we incorporate kernel adaptive filter with the generalized tanh function to propose a robust sequential learning algorithm. Based on establishing the energy conservation relation, we derive a sufficient condition for ensuring the algorithm convergence. In addition, to perform the steady-state excess mean square error (EMSE) analysis, we use the pre-tuned dictionary strategy to model the unknown nonlinear system in form of a finite-order combination; by Taylor expansion, we arrive at a closed-form solution for predicting the steady-state behavior. To further improve the algorithm performance, we design an optimization scheme for scale factor. Simulations for nonlinear time series prediction show that the designed schemes yield better performance than some state-of-art algorithms. The steady-state EMSE analysis is validated to provide accurate prediction results. [ABSTRACT FROM AUTHOR]

Ø The KRSL based adaptive filtering algorithm with sinusoidal signal is derived; Ø A recursive MKRSL based harmonic estimation method is developed; Ø A RMKRSL with adaptive gain factor is proposed to enhance the tracking ability. The development of effective harmonics estimation method plays a crucial role for safe operation of power system. Recently several existing parametric estimation approaches, however, are mainly developed and discussed under the assumption of Gaussian noise which is always unsuitable in real power systems. This work is mainly concerned with the robust parametric estimation methods. The kernel risk sensitive loss (KRSL) shows an advantage in that its performance surface is flat around the optimal solution while sharp far away from the optimal solution and it may exhibit outstanding performance in terms of faster convergence rate and higher estimation accuracy under non-Gaussian noise cases. Therefore, a minimum KRSL (MKRSL) algorithm with sinusoidal signal is designed, and we further develop a novel recursive MKRSL (RMKRSL) algorithm for harmonics estimation in non-Gaussian noise cases. In addition, an adaptive gain factor is introduced into the gain matrix of RMKRSL algorithm to enhance its tracking capability. Some simulations by using the signal generated from the given models and IEEE-1159-PQE databases are conducted to illustrate the performance of the proposed methods under different conditions. [ABSTRACT FROM AUTHOR]