Conventional active noise control (ANC) methods experience performance deterioration when exposed to impulsive noise (IN). Despite its transient nature, IN poses significant risks to auditory health. Recent approaches employing the maximum correntropy criterion (MCC) and its generalized version (GMCC) have attracted considerable interest for impulsive noise suppression. Nevertheless, these methods exhibit substantial steady-state misalignment, degrading their noise cancellation performance. To enhance ANC performance under impulsive conditions, this work introduces a novel robust filtered-x logarithmic hyperbolic secant adaptive filter (FxLHSAF) that minimizes a logarithmic hyperbolic secant loss function. Furthermore, an affine combination of FxLHSAF (A-FxLHSAF) is developed to attain accelerated convergence and reduced residual error. Experimental simulations demonstrate the superiority of both proposed techniques over other existing algorithms, with FxLHSAF and A-FxLHSAF delivering optimal noise suppression performance.

Active noise control (ANC) in the presence of impulsive/non-Gaussian disturbances remains challenging for the conventional adaptive algorithms. In recent years, information theory-based maximum correntropy criterion (MCC) and its variants have gained significant attention in environments with non-Gaussian disturbances. However, the MCC-based algorithm's performance suffers from high steady-state misalignment, which limits the noise control performance. In order to overcome this limitation, this paper proposes a filtered-x logistic distance metric adaptive filter (FxLDMAF) for robust ANC. It optimizes a logistic distance-based objective whose smooth saturation curtails the influence of significant instantaneous errors while maintaining sensitivity around the origin, thus promoting stable coefficient updates. Performance is examined under a symmetric alpha-stable interface and additional non-Gaussian conditions, including Laplacian, Uniform, and Binary noise. Across all scenarios, simulations show that FxLDMAF achieves lower steady-state misalignment and superior noise control performance compared to benchmark approaches (RFxLMS, FxMCC, and FxGMCC). The results indicate that FxLDMAF is well-suited for real-time ANC deployments operating in unpredictable, heavy-tailed acoustic environments.

Sparsity-based estimators (SBEs), including Lasso, have gained prominence in statistics and econometrics for handling high-dimensional datasets, where the number of potential predictors exceeds the observations. While traditional methods such as Ordinary Least Squares (OLS) falter in these scenarios, SBEs assume that only a small subset of predictors influences the outcome. However, the validity of the sparsity assumption has been challenged, questioning the robustness of SBEs when this assumption does not hold. This seminar paper critically reviews”The Fragility of Sparsity,” which examines the reliability of SBEs across empirical contexts, focusing on the sensitivity of these estimators to assumptions and methodological choices, such as the selection of tuning parameters, normalization methods, and the construction of control matrices. I extend these findings by applying SBEs to new datasets and testing their generalizability, while also exploring the impact of varying data sizes, predictor count, and regularization parameters on model performance. This paper underscores the importance of validating sparsity assumptions and methodological rigor in high-dimensional data analysis.

The performance of conventional active noise control (ANC) systems degrades under non-Gaussian conditions. In the recent past, generalized filtered-x maximum correntropy criterion (FxGMCC) algorithm has been widely used to tackle such non-Gaussian noises. However, noise reduction performance of maximum correntropy criterion (MCC) based algorithms degrades due to the high steady-state misalignment. To overcome this limitation, a filtered-x exponential hyperbolic cosine adaptive filter (FxEHCAF) algorithm is proposed in this paper. Later, an affine combination technique has been applied and the corresponding affine FxEHCAF (AFxEHCAF) algorithm has been developed here showing faster convergence rate in transient state along with low residual error in steady-state. Simulation study shows that the proposed FxEHCAF and A-FxEHCAF algorithms provide enhanced noise control performance over other existing algorithms.

Direction-of-arrival (DOA) estimation methods based on conventional adaptive signal processing are not robust to outliers. A robust DOA estimation technique based on an exponential hyperbolic cosine function under such situations is proposed in this letter. To further enhance the performance of the proposed approach, a variable scale parameter strategy has been incorporated into the proposed scheme. The new methods have been shown to offer improved and robust DOA estimation performance.

This brief introduces a novel cost function framework for developing robust algorithms for adaptive filtering by embedding the standard cost function into the arctangent framework. This proposed framework is called the arctangent cost function framework. Based on this, we propose an arctangent family of robust algorithms for adaptive filtering. The performance of the proposed family of algorithms is tested through simulation studies in system identification scenarios that confirm the enhanced performance achieved by the arctangent family of algorithms over standard algorithms.

In the recent past, logarithmic hyperbolic cosine based-cost function has been widely applied in adaptive filters as it offers robust performance against outliers. However, the performance of such adaptive filters suffers from high steady-state misalignment due to its significant weight update, even in the presence of outliers. This paper proposes a logistic distance metric-based novel robust cost function, and the corresponding logistic distance metric adaptive filter (LDMAF) has been developed. The proposed LDMAF provides negligible weight update when the desired signals are affected by significant outliers, resulting in low steady-state misalignment. The bound on learning rate has been estimated, and computational complexity comparison of the proposed and other existing algorithms has also been carried out. To further exploit the system's sparse nature and robustness against the outliers, zero attraction-based LDMAF (ZA-LDMAF) and re-weighted zero attraction-based LDMAF (RZA-LDMAF) algorithms have also been developed in this paper. In addition, a new sparse penalty function based on a generalized multivariate Geman-McClure function has been introduced, which provides smooth l(0)-norm approximation over other existing functions. Based on this new sparse penalty function, this paper has also developed a novel sparsity-aware robust adaptive filter called generalized Geman-McClure LDMAF (GGM-LDMAF). Simulation studies confirmed the improved convergence behaviour achieved by the proposed algorithms over other existing algorithms for system identification and acoustic echo cancellation scenarios.

Recently, the logarithmic hyperbolic cosine adaptive filter (LHCAF) was proposed and was seen to demonstrate excellent robustness against impulsive interference. However, for the modelling of sparse systems, it may not provide optimal performance as it does not take into account the sparse nature of the system. To improve the modelling accuracy and convergence performance, a sparsity aware zero attraction LHCAF (ZA-LHCAF) and a reweighted zero attraction LHCAF (RZA-LHCAF) is proposed. To further improve the performance for modelling of sparse systems in impulsive environments, a joint logarithmic hyperbolic cosine function (JLHCF) is proposed as the cost function. The corresponding update rule, called the joint logarithmic hyperbolic cosine adaptive filter (JLHCAF) is deduced and the bound on learning rate is derived. A room equalization scenario is also considered and an improved sparsity aware robust algorithm based on JLHCF, namely the filtered-x JLHCAF (Fx-JLHCAF) is proposed for the same. Extensive simulation studies carried out for different system identification scenarios, under Gaussian and non-Gaussian disturbances and a room equalization scenario, demonstrate the superior performance achieved by JLHCAF over existing sparsity aware robust adaptive filters.

An exhaustive review of adaptive signal processing schemes which are robust, sparsity-aware and robust as well as sparsity-aware has been carried out in this paper. Conventional robust learning approaches as well as the ones based on information theoretic methods have been included in the review. Further, adaptive filtering schemes which take advantage of the sparse nature of the system impulse responses have been reviewed, including the ones which are also robust. The cost functions used in these algorithms have been summarized and a timeline of algorithm development in this area has been added to provide an excellent overview on the topic.

The constrained least mean square algorithm is extensively used for adaptive filtering applications which need to satisfy a set of linear constraints. However, it is not robust when non-Gaussian or impulsive noise is present at the error sensor. To effectively overcome this issue, in this brief, we propose the constrained generalized maximum correntropy criterion (CGMCC) algorithm. To further improve steady state convergence behavior of the adaptive filter in such scenarios, we also propose the constrained maximum Versoria criterion (CMVC) algorithm. The expressions of the optimal weight vector for both the proposed algorithms are derived. Bound on learning rates are also derived to ensure the stability of the proposed adaptive systems in the mean square sense. The computational expense of the proposed algorithms is also studied. Simulation studies carried out demonstrate the improvement in steady state convergence performance and robustness achieved by the proposed algorithms.

An adaptive room equalization scheme is usually employed to compensate for the distortion of sound produced by the room impulse response, thereby offering an improved listening experience. In a conventional adaptive room equalizer, an adaptive filter updated using a filtered-x least mean square (FxLMS) algorithm is used to achieve room equalization. Conventional FxLMS algorithm based room equalizers are not robust to strong disturbances picked up by the reference microphone. A robust adaptive room equalization scheme based on a generalized maximum correntropy criteria has been developed in this paper. The performance has been further enhanced by using a proportionate learning strategy to take advantage of the sparse nature of the room impulse response. The proposed algorithm has been shown to provide enhanced room equalization performance over other methods compared, for various types of noise distributions.

Robust adaptive signal processing algorithms based on a generalized maximum correntropy criterion (GMCC) suffers from high steady state misalignment. In an endeavour to achieve lower steady state misalignment, in this letter we propose a generalized hyperbolic secant function (GHSF) as a robust norm and derive the generalized hyperbolic secant adaptive filter (GHSAF). The new algorithm is seen to offer robust system identification performance over the conventional GMCC algorithm. To further improve the convergence performance under non-Gaussian noise environments, we propose the nearest Kronecker product decomposition based GMCC and GHSAF algorithms. Extensive simulation study show the improved convergence performance provided by the proposed algorithms for system identification.

This paper proposes a new robust learning strategy, which is based on a Weibull M-transform function. The suitability of the Weibull M-transform function as a robust norm has been investigated for different shape and scale parameters, and a Weibull M-transform least mean square (WMLMS) algorithm has been developed. Further, the bound of learning rate has been derived for the proposed algorithm. The proposed WMLMS algorithm has been evaluated for the problem of system identification and simulation studies carried out demonstrate its robustness. In addition, a filtered-x WMLMS (Fx-WMLMS) algorithm has been developed for robust room equalization and has been shown to offer stable room equalization even in the presence of strong disturbances picked up by the microphone.

Mean-field diffusive coupling was known to induce the phenomenon of quenching of oscillations even in identical systems, where the standard diffusive coupling (without mean-field) fails to do so [Phys. Rev. E 89, 052912 (2014)PLEEE81539-375510.1103/PhysRevE.89.052912]. In particular, the mean-field diffusive coupling facilitates the transition from amplitude to oscillation death states and the onset of a nontrivial amplitude death state via a subcritical pitchfork bifurcation. In this paper, we show that an adaptive coupling using a low-pass filter in both the intrinsic and extrinsic variables in the coupling is capable of inducing the counterintuitive phenomenon of reviving of oscillations from the death states induced by the mean-field coupling. In particular, even a weak filtering of the extrinsic (intrinsic) variable in the mean-field coupling facilitates the onset of revival (quenching) of oscillations, whereas a strong filtering of the extrinsic (intrinsic) variable results in quenching (revival) of oscillations. Our results reveal that the degree of filtering plays a predominant role in determining the effect of filtering in the extrinsic or intrinsic variables, thereby engineering the dynamics as desired. We also extend the analysis to networks of mean-field coupled limit-cycle and chaotic oscillators along with the low-pass filters to illustrate the generic nature of our results. Finally, we demonstrate the observed dynamical transition experimentally to elucidate the robustness of our results despite the presence of inherent parameter fluctuations and noise.