arXiv subjects

Jiayi Kang

Publications and source records attributed to Jiayi Kang.

5 recordsLinked to original sources

arXiv2026

Real time filtering algorithms

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.

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arXiv2025

DIFNet: Decentralized Information Filtering Fusion Neural Network with Unknown Correlation in Sensor Measurement Noises

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/.

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arXiv2025

A novel implementation of Yau-Yau filter for time-variant nonlinear problems

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.

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arXiv2024

Nonexistence of finite-dimensional estimation algebras on closed smooth manifolds

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 non-constant observation functions, the estimation algebra associated with the system on closed Riemannian manifolds is infinite-dimensional.

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arXiv2023

Maximum Correntropy Ensemble Kalman Filter

In this article, a robust ensemble Kalman filter (EnKF) called MC-EnKF is proposed for nonlinear state-space model to deal with filtering problems with non-Gaussian observation noises. Our MC-EnKF is derived based on maximum correntropy criterion (MCC) with some technical approximations. Moreover, we propose an effective adaptive strategy for kernel bandwidth selection.Besides, the relations between the common EnKF and MC-EnKF are given, i.e., MC-EnKF will converge to the common EnKF when the kernel bandwidth tends to infinity. This justification provides a complementary understanding of the kernel bandwidth selection for MC-EnKF. In experiments, non-Gaussian observation noises significantly reduce the performance of the common EnKF for both linear and nonlinear systems, whereas our proposed MC-EnKF with a suitable kernel bandwidth maintains its good performance at only a marginal increase in computing cost, demonstrating its robustness and efficiency to non-Gaussian observation noises.

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