Tiancheng Li

In the presence of outliers or non-Gaussian noise in linear estimator design, lightweight Kalman filters (KFs) suffer from severe vulnerability, whereas robust Gaussian mixture filters (GMFs) incur much higher computational costs. To reconcile the robustness of the estimation with resource constraints, this letter investigates a distributed heterogeneous fusion architecture integrating GMFs with KFs. For this multimodal KF-GMF fusion case, we prove the robustness superiority of the arithmetic average (AA) fusion in comparison to the geometric average (GA) fusion. Furthermore, to resolve the mode conflict caused by anomalous outliers in the KF nodes, a graph-centrality-based anomaly isolation mechanism is proposed. By mapping the statistical consensus of fused Gaussian components into a weighted topological graph, this mechanism utilizes a node strength criterion to identify and eliminate disturbance-induced, topologically isolated modes/components with theoretical guarantees. Simulations demonstrate that the proposed KF-GMF AA fusion approach significantly outperforms the GA fusion in terms of tracking accuracy and convergence.

This paper reviews Artificial Intelligence techniques for distributed energy management, focusing on integrating machine learning, reinforcement learning, and multi-agent systems within IoT-Edge-Cloud architectures. As energy infrastructures become increasingly decentralized and heterogeneous, AI must operate under strict latency, privacy, and resource constraints while remaining transparent and auditable. The study examines predictive models ranging from statistical time series approaches to machine learning regressors and deep neural architectures, assessing their suitability for embedded deployment and federated learning. Optimization methods—including heuristic strategies, metaheuristics, model predictive control, and reinforcement learning—are analyzed in terms of computational feasibility and real-time responsiveness. Explainability is treated as a fundamental requirement, supported by model-agnostic techniques that enable trust, regulatory compliance, and interpretable coordination in multi-agent environments. The review synthesizes advances in MARL for decentralized control, communication protocols enabling interoperability, and hardware-aware design for low-power edge devices. Benchmarking guidelines and key performance indicators are introduced to evaluate accuracy, latency, robustness, and transparency across distributed deployments. Key challenges remain in stabilizing explanations for RL policies, balancing model complexity with latency budgets, and ensuring scalable, privacy-preserving learning under non-stationary conditions. The paper concludes by outlining a conceptual framework for explainable, distributed energy intelligence and identifying research opportunities to build resilient, transparent smart energy ecosystems.

This paper, as the fifth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the challenging problem of fusing multi-rate Bayesian filters operating at different sampling rates. We adopt a flexible time alignment strategy that aligns asynchronously calculated local densities to the fusion time using a stochastic differential equation (SDE). A novel weighted AA fusion strategy is proposed that assigns fusion weights to time-aligned local densities in proportion to the Fisher information (FI) of local sensors, which is derived in the continuous time (CT) domain via matrix block recursion and the Schur complement Lemma based on the SDE. Both tracking scenarios with and without clutter and misdetection are considered, respectively, with specific attention paid to the linear Gaussian system for which the exact FI exists. Furthermore, we derive the CT Cramér-Rao lower bound (CT-BCRLB) that gives a tight/achievable lower bound for any time, equal to the discrete time (DT) BCRLB at the sampling time but much higher at the non-sampling time. This fills the gap left by existing DT BCRLBs, which fail to provide a tight lower bound at non-sampling times. By simulation, the FI weights are demonstrated in the context of both the AA and geometric average fusion, outperforming existing weighting strategies in their respective classes.

This paper investigates the problem of distributed target tracking using spatiotemporally unregistered sensor networks, where local sensor nodes operate under heterogeneous temporal and spatial reference frames and inherent disparities in sampling rates, processing latencies, and coordinate systems. All of them contribute to spatiotemporal bias, which imposes a significant challenge for distributed fusion. To address this challenge, we propose a distributed fusion framework, termed Geometric Average with Spatiotemporal Registration (GA-STR), which enables joint estimation of both spatiotemporal biases and target states. To ensure identifiability of the posterior of registered parameters (PRP), we develop two distinct estimation strategies: 1) GA-STR with unknown temporal parameters, designed for nearly constant velocity motion, and 2) GA-STR with known temporal parameters. These strategies are subsequently integrated into distributed Bernoulli filtering, where the closed-form solutions are derived. Simulations in an unregistered sensor network for single-target tracking demonstrate that the proposed approach achieves superior estimation accuracy and robustness compared to state-of-the-art approaches.

To solve the target tracking problem with little a priori information about the target dynamics, our series of studies, including this paper as the third part, propose a continuous-time trajectory estimation approach (dubbed targeting track) based on the stochastic process (SP) theory and a deterministic-stochastic decomposition framework. Specifically, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through learning either a Gaussian process (GP) or Student’s-t process (StP). The former has been addressed in the companion paper and the latter is the focus of this paper. This leads to a data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. Notably, our approach models the temporal correlations of the state sequence and of measurement noise using separate GP or StP. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data and the model fitting error. Although the GP admits an exact closed-form expression for the linear system, approximations have to be adopted for StP modeling. Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches.

Complex target environments present characteristics of saturation, high speed, and high maneuverability, posing increasingly challenging demands for target tracking. In this context, traditional phased-array radar (PAR) faces the dilemma of limited tracking resources and filter model mismatch. To address these issues, this paper proposes a heterogeneous time resource arrangement (HTRA) and refined tracking (RT) method. Firstly, to mitigate the impact of maneuvering model mismatch, we modify the traditional strong tracking filter by considering the effect of different measurements on the correction of the maneuvering model, and formulate the RT method as an optimization problem according to the residual consistency criterion. Then, to properly allocate and arrange limited time resources, by defining a multidimensional time resource vector, we adopt the posterior estimate covariance from RT as a performance metric, and design a performance-driven HTRA framework to achieve time assignment under model mismatch conditions. Simulation results demonstrate that, compared to traditional approaches, the joint HTRA and RT strategy significantly enhance the tracking performance of complex targets within a given time resource budget.