Artificial noise (AN) has been recognized as an effective physical-layer security scheme impairing the eavesdropper (Eve). Recently, artificial noise elimination (ANE) has emerged as a promising strategy to mitigate the impact of AN at Eves. However, conventional ANE schemes rely on prior knowledge, such as legitimate channel state information (CSI) or classification information, which may limit their practical applicability. To address these practical challenges, we propose an ANE scheme beyond prior knowledge (BPK) by leveraging machine learning algorithms. Firstly, a coarse projection is applied to partially eliminate the impact of AN using maximum likelihood estimation on the equivalent AN matrix. Secondly, a density clustering algorithm is introduced to obtain classification information based on the coarsely-projected observed vectors. Thirdly, a generalized principal component analysis (PCA)-based ANE algorithm is developed to effectively mitigate the residual AN using the obtained classification information. Furthermore, the artificial-noise-to-signal ratio (ANSR) and computational complexity are analyzed for performance revaluation, and a redefinition of several AN design principles is provided for scenarios involving a powerful Eve equipped with the BPK-ANE scheme by deriving the validity boundary. Finally, numerical results reveal key insights into four principles of AN: 1) Allocating less power to AN; 2) Reducing the randomness of AN; 3) Increasing the number of transmit antennas; and 4) Increasing the modulation order.

Wireless sensor networks (WSNs) represent a critical research domain within the Internet of Things (IoT) technology. The distributed Kalman filter (DKF) has garnered significant attention as an information fusion method for WSNs. However, effectively handling non-Gaussian environments remains a crucial challenge for DKF. This paper proposes a solution by partitioning the noise distribution into multiple Gaussian components, thereby approximating the measurement model with sub-models. We introduce a model fusion distributed Kalman filter (MFDKF) that combines sub-models by assuming independent random processes for the model’s transition probabilities. The expectation maximization (EM) algorithm is employed to estimate the relevant parameters. To address specific requirements in WSNs that demand high consensus or have limited communication, two derivative algorithms, namely consensus MFDKF (C-MFDKF) and simplified MFDKF (S-MFDKF), are proposed based on consensus theory. The convergence of MFDKF and its derivative algorithms is analyzed. A series of simulations demonstrate the effectiveness of MFDKF and its derivative algorithms.

When complex networks are used for distributed estimation, spatial anisotropy, particularly the potential heterogeneity in noise distributions across multiple nodes, poses significant challenges in practice. In such intricate environments, while state-of-the-art algorithms may excel at specialized nodes, their inability to maintain consistent performance over the entire network often results in systemic degradation. To address this fundamental limitation, an innovative framework is proposed in this letter, wherein the radial basis function neural networks (RBFNNs) are uniformly deployed at each node, serving as universal approximators for various noise profiles. Leveraging this framework, a recursive-type diffusion algorithm is introduced to achieve enhanced network-wide performance. Owing to RBFNN's remarkable modeling capacity, the proposed algorithm can sustain consistent and superior performance in intricate network environments. Simulations undoubtedly validate its superiority over advanced competing alternatives.

The brief proposes a radial basis function (RBF) neural network (NN)-enabled adaptive filter (AF) algorithm, which consists of two stages. The first stage is a data-driven (DD) preprocessing part, and the RBF NN is to fit the probability density function (pdf) of the noise. The second stage is a model-driven filtering part, the RBF NN works as the cost function of the adaptive filtering, and an adaptive gradient ascent algorithm is obtained by maximizing the RBF NN. Since the RBF NN can fit any pdf of the noise, the proposed algorithm can work well in Gaussian, sub-Gaussian or light-tailed (uniform), and super-Gaussian or heavy-tailed (multipeak, pulse, and skewness) noises. Theoretical analysis shows the mean-value stability and mean square performance. Simulations verify the effectiveness of the proposed algorithm.

Adaptive filtering faces significant challenges in handling complex non-Gaussian noise, while graph signal processing (GSP) excels at processing data with intricate structures. This brief introduces a novel method for solving non-Gaussian noise from the perspective of the graph domain for the first time. Specifically, we develop an online time-varying graph model based on the filter error signal and propose a corresponding graph topology transformation strategy. Utilizing a graph smoothness measure, we introduce a new adaptive filtering cost function, in which the graph Laplacian matrix plays a direct role in the filter update process. Subsequently, we derive the graph smoothness recursive adaptive filtering (GS-RAF) algorithm, rigorously analyze its theoretical performance, and validate its efficacy through simulations and echo cancellation experiments. The corresponding MATLAB (MathWorks, USA) codes of the simulations are publicly available at: https://github.com/smartXiaoz/GS-RAF.git.

The minimum error entropy (MEE) criterion closely relies on the quadratic information potential (QIP) estimates of Renyi’s entropy. Nevertheless, the conventional obtained QIP estimates are numerically unstable, especially when the error samples contain outliers, resulting in the optimal solution of the MEE criterion deviating from the target vector to a certain extent. To address this problem, we introduce the M-estimate method from robust statistics into the QIP estimation process; thus, a robust estimation method called instantaneous M-estimate QIP (IM-QIP) is proposed, and several important properties of IM-QIP are presented. The proposed IM-QIP estimates could be implemented simply while ensuring great robustness. Naturally, we further propose the corresponding instantaneous M-estimate MEE (IM-MEE) criterion and apply it to adaptive filtering. A robust recursive adaptive filtering algorithm, called the recursive IM-MEE (RIM-MEE) algorithm, is proposed and analyzed in this article, along with its stability and theoretical steady-state performance. Additionally, we demonstrate that the RIM-MEE algorithm achieves a smaller theoretical bound compared to the traditional MEE algorithm under heavy-tailed and skewed noise conditions. The simulation results revealed the robustness of the IM-QIP estimates and verified the theoretical expectations and superior performance of the RIM-MEE algorithm.

In practice, when complex multi-agent networks are used for parameter estimation and tracking, we often face the issue of spatial anisotropy of observing conditions, e.g., different (heterogeneous) noise distributions at different nodes. In this setting, existing cost functions may excel at specialized nodes, and struggle with others, leading to an overall deteriorating performance, sometimes even inferior to the mean square error (MSE) criterion. The aim of the present paper is to propose a robust network-based adaptive filtering algorithm capable of accommodating such intricate environments. Leveraging the inherent versatility of Gaussian mixture model (GMM) to fit any probability distribution, we model the additive noise at each node accordingly. Then a diffusion algorithm founded on recursive maximum log-likelihood function (RMLF) is put forward, denoted as DRMLF. Thanks to the universal adaptability of GMM, the DRMLF can consistently deliver excellent performance across multiple nodes with diverse noise profiles within the complex networks. Simulations undoubtedly demonstrate that the DRMLF outperforms the other commonly used diffusion RLS-type algorithms over complex networks in intricate environments. A thorough analysis of both mean and mean square convergence is also conducted in detail correspondingly.

Trajectory reconstruction (TR) plays an important role in practical applications. The data collected for TR are often contaminated with non-Gaussian noise due to environmental factors, which reduces the accuracy of TR. This study proposes a novel method to suppress the effects of non-Gaussian measurement noise. The method consists of two steps: decomposing the measurement noise and performing a weighted fusion of the relevant states. In the first step, the measurement noise is decomposed into a weighted combination of multiple Gaussian distributions using the Gaussian mixture model. In the second step, the interacting multiple model is employed to perform the weighted fusion of the relevant states. The main idea of the proposed method is to transform the state estimation problem from a non-Gaussian and nonlinear case into a state estimation problem in the nonlinear and Gaussian case. Based on this idea, a new unscented Kalman filter and an unscented Rauch–Tung–Striebel smoother framework are developed. The TR simulations and experiments are conducted for an underwater unmanned vehicle to verify the effectiveness and superiority of the proposed algorithms. The results demonstrate that the performance of the proposed algorithms is significantly better than that of the prominent existing algorithms, especially in the presence of non-Gaussian noise.

In the Kalman filter (KF), the estimated state is a linear combination of the one-step prediction and measurement. The two combination weights depend on the prediction mean-square error matrix and the covariances matrix of measurement noise (CMMN), respectively. When the measurement noise values are small (large), the corresponding measurement is close to (far from) the real value, and the weight should be large (small). If there is non-Gaussian measurement noise, especially heavy-tailed noise, most of the noise values are small, and a few of them are large. The occasional impulses cause the overall noise variance to be much greater than the noise without impulses. Since the overall CMMN is adopted in the KF, its performance will deteriorate. In this article, we divide the measurement noise into two parts: 1) the background noise with small variance and 2) the impulse noise with large variance. Then, we use the expectation–maximization algorithm to dynamically calculate the parameters and propose a new KF algorithm to process them separately, which is called background-impulse KF (BIKF). It can dynamically determine whether there is an impulse and eliminate its impact as much as possible. Compared with the recent maximum correntropy criterion and minimum error entropy criterion-based KFs, simulations show that the proposed BIKF works better than them with lower computational complexity.

Artificial noise elimination (ANE) has arisen as a possible countermeasure for mitigating the influence of artificial noise (AN) at the eavesdropper (Eve). However, conventional ANE schemes require the attainable channel state information (CSI) between the transmitter (Alice) and legitimate receiver (Bob), which reduces the feasibility of this proposal. In this paper, we investigate the issue of ANE without the CSI of Alice-Bob link by minimizing the artificial-noise-to-signal ratio (ANSR). Moreover, the detailed minor component analysis (MCA) algorithm is presented, and the computational complexity is quantified. Simulation results demonstrate that MCA can effectively degrade the influence of AN without the knowledge of CSI.