Online Censoring-Based Widely Linear Total Least lncosh Method for Improved Power System Frequency Estimation

Recently, under the presumption of a noise-free input, the augmented complex least lncosh (ACLlncosh) method was introduced for a power system frequency estimate and showed robust performance when impulsive noise polluted the output signal. However, in practical terms, noise often contaminates input signals, which drastically reduces the efficiency of the ACLlncosh method. To enhance robustness against noisy input-output while maintaining resilience to impulsive noise in the output signal, this paper proposed an online censoring-based widely linear total least lncosh (OC-WL-TLlnC) method. This method improves performance under both balanced and unbalanced settings by filtering out less valuable data via online censoring, hence reducing the computing burden. Furthermore, a variable parameter approach is incorporated to accelerate convergence and improve steady-state accuracy, thereby ensuring adaptability to dynamic power system conditions. The proposed methods significantly enhance frequency estimate performance by addressing the constraints of current techniques and offering a computationally efficient, noise-resilient solution for real-time power system monitoring.

Half-Quadratic Criterion based Adaptive Graph Signal Processing Algorithm

In recent years, progress in adaptive graph signal processing algorithms has provided effective solutions for processing signals defined on graph structures. As a classical strategy in information theory, the Generalized Maximum Correntropy Criterion (GMCC) exhibits good resistance to non-Gaussian noises. When non-Gaussian noise interferes with the graph signal, the graph signal processing algorithm based on GMCC (GSP GMCC) algorithm shows better performance. However, the GSP GMCC algorithm itself has three parameters that need to be manually tuned, and the process of manually tuning the parameters is complex and tedious. Meanwhile, the non-concave and non-convex nature of the GMCC function itself limits its own convergence rate and adaptive estimation accuracy. To solve the above problems, based on the strongly convex function half-quadratic criterion (HQC), the GSP HQC algorithm is proposed in this paper. The performance analysis of the GSP HQC algorithm is implemented in this paper. Simulation experiments demonstrate that the GSP HQC algorithm achieves superior performance in terms of convergence rate and adaptive estimation accuracy while maintaining computational complexity comparable to existing algorithms

Outlier-Robust unscented Kalman filter based on generalized correntropy induced

Conventional Kalman filtering (KF) approaches exhibit significant limitations in addressing nonlinear state estimation problems contaminated by non-Gaussian noise disturbances. To overcome these challenges, this work proposes a robust iterative square root unscented Kalman Filter based on the generalized correntropy induced (SR-GCI-IUKF). While sharing the maximum correntropy criterion's (MCC) ability to characterize higher-order noise statistics, the proposed GCI framework exhibits intrinsic kernel bandwidth insensitivit a critical advantage enabling robust adaptation to diverse complex noise environments through its generalized kernel structure. For nonlinear state estimation challenges, the algorithm constructs a nonlinear error generalization model that dynamically corrects measurement-induced errors during the state update phase, thereby significantly enhancing estimation accuracy in strongly nonlinear regimes. Furthermore, the square-root decomposition implementation ensures numerical robustness by preserving covariance matrix positive definiteness throughout recursive operations. Theoretical stability guarantees are established through rigorous error dynamics analysis, demonstrating bounded estimation variance under non-Gaussian disturbances. Finally, experiments are carried out in nonlinear systems, land vehicle navigation systems as well as power system FASE to compare other robust algorithms, and it is determined that the proposed algorithm has stronger robustness.

Decentralized Variational Bayesian UKF with Maximum Generalized Student's t-kernel Correntropy for Wide-Area Power System state estimation

A Conventional centralized state estimators exhibit limited robustness in large-scale grids and face practical deployment hurdles. To overcome these challenges, this paper proposes a decentralized maximum generalized Student's t-kernel correntropy Variational Bayesian unscented Kalman filter (D-MGST-VBUKF). The algorithm optimizes the estimation performance at three levels for the regionalized state estimation needs: first, to address non-Gaussian measurement noise in practical systems, we propose the cost function using MGST, retaining Student's t robustness while improving adaptability to complex noise by expanding the degree-of-freedom parameter; secondly, the VB inference framework is constructed to model the unknown noise distribution online, and the joint optimization of the noise statistical characteristics and state estimation is realized by constructing the conjugate prior distribution; finally, the regional state fusion mechanism is established based on the topological correlation characteristics of the power grid, and the global consistency correction of the local estimation results is realized by constructing the state coordination equation of the boundary nodes. Simulation experiments in IEEE 14-bus and IEEE 39-bus system show that the method has stronger robustness compared with the traditional algorithm under non-Gaussian noise environment and unknown noise environment.

Broad learning system with robust adaptive kernel

For the performance degradation problem of broad learning system (BLS) in non-Gaussian noise environment, the variant of BLS based on M-estimator shows good robust performance. However, in most cases, the determination of the optimal loss function is often very time-consuming due to the lack of prior knowledge of the sample data. Therefore, this paper constructs a variant of BLS based on adaptive robust kernel (AR-BLS) to improve the generalization performance of the model in non-Gaussian noise environment. Adaptive robust kernel function is a general loss function that includes many common M-estimator paradigms. By alternately optimizing model weights and adaptive robust kernel parameters, AR-BLS realizes the adaptive adjustment of model robustness under different outlier noise distributions without human intervention. In addition, the iterative convergence of AR-BLS algorithm is proved based on Zangwill's global convergence theorem. Simulation experiments on multiple public datasets and actual application scenarios verify the effectiveness of the proposed method.

A Fast Robust Adaptive filter using Improved Data-Reuse Method

Adaptive filter in complex scenarios demands algorithms that integrate fast convergence, low complexity, and robust performance under diverse noise conditions. To address this challenge, we propose a online censoring robust total generalized adaptive filter using improved data-reused method (RTGA-IDROC) algorithm. The proposed RTGA variant possesses the advantages of both the total least squares (TLS) strategy and the robust generalized adaptive (RGA) function. This algorithm not only effectively handles input noise under the errors-in-variables (EIV) model but also achieves excellent performance across diverse noise environments. Furthermore, to meet the high demand for convergence speed in practical applications, an improved data reuse (IDR) method is introduced, enabling faster convergence in the early stages of iteration without compromising steady-state performance. The increased computational complexity brought by the IDR method is mitigated using the online censoring (OC) strategy. We also modify the OC threshold for real-valued algorithms, as the original threshold was defined for the complex domain. Beyond these algorithmic enhancements, a local stability analysis for the proposed algorithm is provided, and the theoretical steady-state mean-square deviation (MSD) is derived. Finally, simulation experiments in system identification and acoustic echo cancellation (AEC) scenarios validate the superior performance of the proposed algorithm.

Augmented Set-membership Affine Projection Algorithm and Its Performance Analysis

The augmented affine projection algorithm (AAPA) has considerably excellent performance for highly colored input signals. However, the direct matrix inversion operation leads to a high computational complexity, especially with high projection order. Inspired by the excellent characteristics of set-membership filtering (SMF), this paper proposes the augmented set-membership affine projection algorithm (ASM-APA), which not only has low computational complexity but also offers improved performance compared with AAPA. Then, the computational complexity and stability of ASM-APA are analyzed, and the condition for maintaining the stability of the algorithm is provided. Finally, in the computer simulation phase, the results of the simulation experiments demonstrated that ASM-APA has superior performance compared to AAPA.

Robust distributed extended Kalman filter based on adaptive multi-kernel mixture maximum correntropy for non-Gaussian systems

As one of the most advanced variants in the correntropy family, the multi-kernel correntropy criterion demonstrates superior accuracy in handling non-Gaussian noise, particularly with multimodal distributions. However, current approaches suffer from key limitations-namely, reliance on a single type of sensitive Gaussian kernel and the manual selection of free parameters. To address these issues and further boost robustness, this paper introduces the concept of multi-kernel mixture correntropy (MKMC), along with its key properties. MKMC employs a flexible kernel function composed of a mixture of two Students t-Cauchy functions with adjustable (non-zero) means. Building on this criterion within multi-sensor networks, we propose a robust distributed extended Kalman filter-AMKMMC-RDEKF based on adaptive multi-kernel mixture maximum correntropy. To reduce communication overhead, a consensus averaging strategy is incorporated. Furthermore, an adaptive mechanism is introduced to mitigate the impact of manually tuned free parameters. At the same time, the computational complexity and convergence ability of the proposed algorithm are analyzed. The effectiveness of the proposed algorithm is validated through challenging scenarios involving power system and land vehicle state estimation.

Nearest Kronecker Product Decomposition Based Subband Adaptive Filter: Algorithms and Applications

Recently, the nearest Kronecker product (NKP) decomposition-based normalized least mean square (NLMS-NKP) algorithm has demonstrated superior convergence performance compared to the conventional NLMS algorithm. However, its convergence rate exhibits significant degradation when processing highly correlated input signals. To address this problem, we propose a type-I NKP-based normalized subband adaptive filter (NSAF) algorithm, namely NSAF-NKP-I. Nevertheless, this algorithm incurs substantially higher computational overhead than the NLMS-NKP algorithm. Remarkably, our enhanced type-II NKP-based NSAF (NSAF-NKP-II) algorithm achieves equivalent convergence performance while substantially reducing computational complexity. Furthermore, to enhance robustness against impulsive noise interference, we develop two robust variants: the maximum correntropy criterion-based robust NSAF-NKP (RNSAF-NKP-MCC) and logarithmic criterion-based robust NSAF-NKP (RNSAF-NKP-LC) algorithms. Additionally, detailed analyses of computational complexity, step-size range, and theoretical steady-state performance are provided for theproposed algorithms. To enhance the practicability of the NSAF-NKP-II algorithm in complex nonlinear environments, we further devise two nonlinear implementations: the trigonometric functional link network-based NKP-NSAF (TFLN-NSAF-NKP) and Volterra series expansion-based NKP-NSAF (Volterra-NKP-NSAF) algorithms. In active noise control (ANC) systems, we further propose the filtered-x NSAF-NKP-II (NKP-FxNSAF) algorithm. Simulation experiments in echo cancellation, sparse system identification, nonlinear processing, and ANC scenarios are conducted to validate the superiority of the proposed algorithms over existing state-of-the-art counterparts.

P-norm based Fractional-Order Robust Subband Adaptive Filtering Algorithm for Impulsive Noise and Noisy Input

Building upon the mean p-power error (MPE) criterion, the normalized subband p-norm (NSPN) algorithm demonstrates superior robustness in $α$-stable noise environments ($1 < α\leq 2$) through effective utilization of low-order moment hidden in robust loss functions. Nevertheless, its performance degrades significantly when processing noise input or additive noise characterized by $α$-stable processes ($0 < α\leq 1$). To overcome these limitations, we propose a novel fractional-order NSPN (FoNSPN) algorithm that incorporates the fractional-order stochastic gradient descent (FoSGD) method into the MPE framework. Additionally, this paper also analyzes the convergence range of its step-size, the theoretical domain of values for the fractional-order $β$, and establishes the theoretical steady-state mean square deviation (MSD) model. Simulations conducted in diverse impulsive noise environments confirm the superiority of the proposed FoNSPN algorithm against existing state-of-the-art algorithms.