Jiayi Kang

Multi-photoelectric tracking systems (MPTSs) provide high-precision line-of-sight (LOS) angles for long-range passive tracking, with each photoelectric tracking system (PTS) delivering bearing-only measurements. In practice, image-based target extraction and optical–mechanical pointing may suffer from intermittent errors when highly maneuverable targets are observed, thereby degrading tracking accuracy. To address this issue, we consider a time-varying uncertain dynamics model with a lumped uncertainty and its temporal difference. A centralized twice-extended state Kalman filter (CTESKF) is proposed to augment the kinematic state with the lumped uncertainty and its temporal difference, yielding a Kalman-type recursion with a computable covariance upper bound. Building on this, a diffusion-based twice-extended state Kalman filter (DTESKF), which combines local updates with single-round covariance-intersection diffusion fusion, is proposed to achieve distributed filtering with limited communication cost. Simulation results show that CTESKF and DTESKF achieve competitive accuracy–efficiency trade-offs in a weakly nonlinear setting and a 3D bearing-only MPTS scenario.

A photoelectric tracking system is a typical bearing-only target tracking system that faces significant challenges arising from measurement origin uncertainty due to clutter and the discrepancy between continuous-time target dynamics and discrete-time optical sampling, as well as the inherent nonlinearity of bearing-only tracking. This paper addresses these issues by proposing a novel distributed probabilistic data association feedback particle filter (DPDA-FPF) framework. To resolve the tracking ambiguity at the local level, we extend the feedback particle filter to a continuous-discrete setting integrated with probabilistic data association. Subsequently, the local state estimates and covariances from spatially separated tracking systems are transmitted to a fusion center and integrated using an optimal linear covariance-weighted fusion rule to improve global observability and mitigate biases of individual systems. Numerical simulations in a 3D scenario with moderate clutter density demonstrate that while individual sensor tracks suffer from fluctuations, the proposed fused estimate achieves substantially lower root mean square errors in both position and velocity. The results validate the efficiency of the proposed architecture as a robust solution for photoelectric tracking applications.

This paper presents a systematic review of recent advances in nonlinear filtering algorithms, structured into three principal categories: Kalman-type methods, Monte Carlo methods, and the Yau-Yau algorithm. For each category, we provide a comprehensive synthesis of theoretical developments, algorithmic variants, and practical applications that have emerged in recent years. Importantly, this review addresses both continuous-time and discrete-time system formulations, offering a unified review of filtering methodologies across different frameworks. Furthermore, our analysis reveals the transformative influence of artificial intelligence breakthroughs on the entire nonlinear filtering field, particularly in areas such as learning-based filters, neural network-augmented algorithms, and data-driven approaches.

Estimation algebras have been extensively studied in Euclidean space, where finite-dimensional estimation algebras form the foundation of the Kalman and Benes filters, and have contributed to the discovery of many other finite-dimensional filters. This work extends the theory of estimation algebras to filtering problems on Riemannian manifolds in continuous time. Our main result demonstrates that, with nonconstant observation functions, the estimation algebra associated with the system on closed Riemannian manifolds is infinite-dimensional.

This paper concentrates on a state estimation problem for nonlinear uncertain systems with non-Gaussian noise pollution. We first treat the nonlinear uncertainty as an augmented state vector and construct a new extended state system to handle the nonlinear uncertainty term. Additionally, we derive an upper bound for the prior estimation error covariance using Young’s inequality to ensure numerical stability. To solve the non-Gaussian noise occurring in the measurement process, we employ a new robust cost function called maximum correntropy criterion (MCC) to update our posterior estimate by a fixed-point algorithm. We provide a proof of convergence for the fixed-point algorithm and present a computational complexity analysis of the proposed method. Simulations validate the framework’s superior performance, demonstrating statistically significant improvements in estimation accuracy.

In recent years, decentralized sensor networks have garnered significant attention in the field of state estimation owing to enhanced robustness, scalability, and fault tolerance. Optimal fusion performance can be achieved under fully connected communication and known noise correlation structures. To mitigate communication overhead, the global state estimation problem is decomposed into local subproblems through structured observation model. This ensures that even when the communication network is not fully connected, each sensor can achieve locally optimal estimates of its observable state components. To address the degradation of fusion accuracy induced by unknown correlations in measurement noise, this paper proposes a data-driven method, termed Decentralized Information Filter Neural Network (DIFNet), to learn unknown noise correlations in data for discrete-time nonlinear state space models with cross-correlated measurement noises. Numerical simulations demonstrate that DIFNet achieves superior fusion performance compared to conventional filtering methods and exhibits robust characteristics in more complex scenarios, such as the presence of time-varying noise. The source code used in our numerical experiment can be found online at https://wisdom-estimation.github.io/DIFNet_Demonstrate/.

Nonlinear filter has long been an important problem in practical industrial applications. The Yau-Yau method is a highly versatile framework that transforms nonlinear filtering problems into initial-value problems governed by the Forward Kolmogorov Equation (FKE). Previous researches have shown that the method can be applied to highly nonlinear and high dimensional problems. However, when time-varying coefficients are involved in the system models, developing an implementation of the method with high computational speed and low data storage still presents a challenge. To address these limitations, this paper proposes a novel numerical algorithm that incorporates physics-informed neural network (PINN) and principal component analysis (PCA) to solve the FKE approximately. Equipped with this algorithm, the Yau-Yau filter can be implemented by an offline stage for the training of a solver for the approximate solution of FKE and an online stage for its execution. Results of three examples indicate that this implementation is accurate, both time-efficient and storage-efficient for online computation, and is superior than existing nonlinear filtering methods such as extended Kalman filter and particle filter. It is capable of applications to practical nonlinear time-variant filtering problems.