System modeling in distributed adaptive networks remains challenging under sensor aging-induced nonlinear data censoring and non-Gaussian interference. This brief proposes a robust hierarchical control framework that incorporates a Laguerre-based random Fourier filter to capture network nonlinearities. To address censored measurements and impulsive noise, a robust Laguerre RFF Diffusion Hierarchical (LRFF-DH) algorithm is developed. It leverages maximum likelihood estimation to correct bias and introduces a connectivity-adaptive robustness strategy based on node connectivity, enhancing edge-node resilience while reducing computational load on critical nodes. Simulations on a 20-node ad-hoc network verify the algorithm's effectiveness in interference suppression and mean squared error reduction under complex nonlinear conditions.

Kernel adaptive filters (KAF) have emerged as a prominent method for nonlinear system identification (NSI). However, the KAF becomes computationally intensive as the input signal grows. In complex systems, traditional KAF with a unit time-delay structure may struggle with insufficient control capability. Moreover, KAFs adapted to second-order statistics can be susceptible to non-Gaussian noise. In this letter, we introduce the Laguerre kernel adaptive filter (LKAF) for NSI, using a block-oriented nonlinear model. The LKAF leverages the Laguerre series to approximate the linear block, benefiting from infinite impulse response (IIR) characteristics and a simple feedforward structure. To address non-Gaussian noise, the LKAF employs an arctangent (AT) criterion. This integration leads to the development of the Laguerre kernel arctangent least mean square (L-KATLMS) algorithm and its variations, which utilize random Fourier approximation. Simulation results demonstrate the superiority of our proposed algorithms for NSI.

To acquire an improvement of the performance of the subband adaptive filter with impulsive interference, the normalized subband adaptive filter (NSAF) algorithm-based maximum correntropy criterion (MCC), called MCC-NSAF, has been developed. However, it is hard for the MCC criterion to take into account both the fast convergence rate and low steady-state error with a fixed kernel bandwidth. To handle this dilemma, in this paper, the normalized subband adaptive filter algorithm-based maximum mixture correntropy criterion (MMC) algorithm, called MMC-NSAF, is proposed. The MMC-NSAF algorithm integrates two correntropies with complementary control sizes of Gaussian kernel and can not only converge quickly but also has a small misalignment. Yet the MMC-NSAF still has some limitations because of its fixed step size. Therefore, a convexly combined MMC-NSAF algorithm, namely MMC-CNSAF, is proposed. The MMC-CNSAF algorithm utilizes two Gaussian kernels of different size and can combine overall improvement between convergence rate and steady-state error simultaneously. Eventually, the convergence and the computational complexity are analyzed. To achieve the test and verification of the robustness of proposed algorithms, simulations are carried out to discuss the effect of the parameters algorithm under colored input signals in impulsive interference environments for system identification. Meanwhile, the performances of the proposed algorithms under the influence of the acoustic echo cancellation in practical application are studied.

The random Fourier filter-based filtered-x least mean square (RF-FxLMS) algorithm has been proposed for the nonlinear active noise control (NANC) system to reduce the computational burden of the kernel filter. However, the RF-FxLMS algorithm markedly fluctuates when dealing with impulsive noise. In addition, the computing cost for the RF-FxLMS algorithm is still pricey in practice. In this work, a random Fourier filter based filtered-x generalized hyperbolic secant function (RF-FxGHSF) algorithm is presented to deal with impulsive noise. In virtue of the bilinear scheme, a cascaded random Fourier filter model is designed for concise computations, and the cascaded RF-FxGHSF (CRF-FxGHSF) algorithm is derived. Moreover, the steady-state convergence conditions are analyzed. The calculation complexity of the proposed algorithms is compared, and experiments emphatically analyze the principle for the presented model. Numerical simulations with α-stable noise and real noise carried out in different nonlinear path scenarios verify the convergence ability of proposed algorithms.

As a robust nonlinear similarity measure, the maximum correntropy criterion (MCC) has been successfully applied to active noise control (ANC) for impulsive noise. The default kernel function of the filtered-x maximum correntropy criterion (FxMCC) algorithm is the Gaussian kernel, which is desirable in many cases for its smooth and strict positive-definite. However, it is not always the best choice. In this study, a filtered-x generalized maximum correntropy criterion (FxGMCC) algorithm is proposed, which adopts the generalized Gaussian density (GGD) function as its kernel. The FxGMCC algorithm has greater robust ability against non-Gaussian environments, but, it still adopts a single error norm which exhibits poor convergence rate and noise reduction performance. To surmount this problem, an improved FxGMCC (IFxGMCC) algorithm with continuous mixed Lp-norm is proposed. Moreover, to make a trade-off between fast convergence rate and low steady-state misalignment, a convexly combined IFxGMCC (C-IFxGMCC) algorithm is further developed. The stability mechanism and computational complexity of the proposed algorithms are analyzed. Simulation results in the context of different impulsive noises as well as the real noise signals verify that the proposed algorithms are superior to most of the existing robust adaptive algorithms.