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To date most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or…

Systems and Control · Computer Science 2019-04-18 Badong Chen , Lujuan Dang , Yuantao Gu , Nanning Zheng , Jose C. Prıncipe

In real applications, non-Gaussian distributions are frequently caused by outliers and impulsive disturbances, and these will impair the performance of the classical cubature Kalman filter (CKF) algorithm. In this letter, a modified…

Information Theory · Computer Science 2023-08-15 Jiacheng He , Gang Wang , Zhenyu Feng , Shan Zhong , Bei Peng

The minimum error entropy (MEE) has been extensively used in unscented Kalman filter (UKF) to handle impulsive noises or abnormal measurement data in non-Gaussian systems. However, the MEE-UKF has poor numerical stability due to the inverse…

Signal Processing · Electrical Eng. & Systems 2023-09-19 Boyu Tian , Haiquan Zhao

A stable square-root approach has been recently proposed for the unscented Kalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as for the mixed-type methods consisting of the extended Kalman filter (EKF) time update…

Optimization and Control · Mathematics 2023-12-06 Maria V. Kulikova , Gennady Yu. Kulikov

Nowadays, with the development of multi-sensor networks, the distributed cubature Kalman filter is one of the well-known existing schemes for state estimation, for which the influence of the non-Gaussian noise, abnormal data, and…

Signal Processing · Electrical Eng. & Systems 2025-11-24 Duc Viet Nguyen , Haiquan Zhao , Jinhui Hu

This paper continues our research devoted to an accurate nonlinear Bayesian filters' design. Our solution implies numerical methods for solving ordinary differential equations (ODE) when propagating the mean and error covariance of the…

Optimization and Control · Mathematics 2023-11-21 Maria V. Kulikova , Gennady Yu. Kulikov

Recent developments in the realm of state estimation of stochastic dynamic systems in the presence of non-Gaussian noise have induced a new methodology called the maximum correntropy filtering. The filters designed under the maximum…

Systems and Control · Computer Science 2017-09-06 Maria V. Kulikova

For the battery management system of electric vehicle, accurate estimation of the State of Charge of Lithium-ion battery can effectively avoid structural damage caused by overcharge or over discharge inside the battery. Considering that the…

Systems and Control · Electrical Eng. & Systems 2023-04-18 Jierui Wang , Wentao Yu , Guoyang Cheng , Lin Chen

Accurate and computationally light algorithms for estimating the State of Charge (SoC) of a battery's cells are crucial for effective battery management on embedded systems. In this letter, we propose an Adaptive Extended Kalman Filter…

Systems and Control · Electrical Eng. & Systems 2025-04-09 António Barros , Edoardo Peretti , Davide Fabroni , Diego Carrera , Pasqualina Fragneto , Giacomo Boracchi

Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…

Signal Processing · Electrical Eng. & Systems 2023-09-06 Jiacheng He , Gang Wang , Bei Peng , Zhenyu Feng , Kun Zhang

Accurate and stable state estimation is critical for battery management. Although dual Kalman filtering can jointly estimate states and parameters, the strong coupling between filters may cause divergence under large initialization errors…

Systems and Control · Electrical Eng. & Systems 2025-12-09 Feng Guo , Guangdi Hu , Keyi Liao , Luis D. Couto , Khiem Trad , Ru Hong , Hamid Hamed , Mohammadhosein Safari

As one of the most advanced variants in the correntropy family, the multi-kernel correntropy criterion demonstrates superior accuracy in handling non-Gaussian noise, particularly with multimodal distributions. However, current approaches…

Signal Processing · Electrical Eng. & Systems 2026-01-21 Duc Viet Nguyen , Haiquan Zhao , Jinhui Hu , Xiaoli Li

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by…

Machine Learning · Statistics 2015-09-16 Badong Chen , Xi Liu , Haiquan Zhao , José C. Príncipe

This work considers the problem of selecting sensors in a large scale system to minimize the error in estimating its states. More specifically, the state estimation mean-square error(MSE) and worst-case error for Kalman filtering and…

Optimization and Control · Mathematics 2020-02-24 Luiz F. O. Chamon , George J. Pappas , Alejandro Ribeiro

Linear regression model (LRM) based on mean square error (MSE) criterion is widely used in Granger causality analysis (GCA), which is the most commonly used method to detect the causality between a pair of time series. However, when signals…

Methodology · Statistics 2019-02-20 Badong Chen , Rongjin Ma , Siyu Yu , Shaoyi Du , Jing Qin

Non-Gaussian noise and the uncertainty of noise distribution are the common factors that reduce accuracy in dynamic state estimation of power systems (PS). In addition, the optimal value of the free coefficients in the unscented Kalman…

Signal Processing · Electrical Eng. & Systems 2025-04-11 Duc Viet Nguyen , Haiquan Zhao , Jinhui Hu , Le Ngoc Giang

The Kalman filter operates by storing a Gaussian description of the state estimate in the form of a mean and covariance. Instead of storing and manipulating the covariance matrix directly, a square-root Kalman filter only forms and updates…

Systems and Control · Electrical Eng. & Systems 2022-08-16 Kevin Tracy

The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the…

Machine Learning · Computer Science 2025-08-07 Yuanhao Li , Badong Chen , Natsue Yoshimura , Yasuharu Koike

The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suffer from weight degeneracy, while the EnKF scales well in…

Methodology · Statistics 2026-01-28 Ilja Klebanov , Claudia Schillings , Dana Wrischnig

Conventional Kalman filtering (KF) approaches exhibit significant limitations in addressing nonlinear state estimation problems contaminated by non-Gaussian noise disturbances. To overcome these challenges, this work proposes a robust…

Signal Processing · Electrical Eng. & Systems 2026-05-25 Jinhui Hu , Haiquan Zhao , Yi Peng
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