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.

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.

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.

Deep-learning-based automatic defect segmentation is one of the hot research areas in computer vision application for the task of intelligent industrial inspection. Recently, several state-of-the-art models for image segmentation task have been proposed. However, their high performance is vastly dependent on the availability of large set of labeled data, which is one of the hindering factors in achieving full potential with deep learning methods in industrial inspection. In this article, we propose a novel method based on pairwise similarity map consistency with ensemble-based cross pseudolabels for semisupervised defect segmentation that uses limited labeled samples while exploiting additional label-free samples. The proposed approach uses three network branches that are regularized by pairwise similarity map consistency, and each of them is supervised by the pseudolabels generated by ensemble of predictions of the other two networks for the unlabeled samples. The proposed method achieved significant performance improvement over the baseline of learning only from the labeled images and the current state-of-the-art semisupervised methods. We perform ablation studies and extensive experiments on various parameters and components to demonstrate that our method achieved state-of-the-art results on three different datasets.