A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution

This study develops an enhanced state estimation framework by integrating the Kalman filtering mechanism with a Gamma Pearson VII (GaPV) hybrid probability model to address non-stationary heavy-tailed noise characteristics in measurement systems. This innovative methodology synthesizes Gaussian morp...

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Main Authors: Shen Liang, Guoliang Xu, Zhenmei Qin
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/10925424/
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author Shen Liang
Guoliang Xu
Zhenmei Qin
author_facet Shen Liang
Guoliang Xu
Zhenmei Qin
author_sort Shen Liang
collection DOAJ
description This study develops an enhanced state estimation framework by integrating the Kalman filtering mechanism with a Gamma Pearson VII (GaPV) hybrid probability model to address non-stationary heavy-tailed noise characteristics in measurement systems. This innovative methodology synthesizes Gaussian morphological properties with Gamma’s supplementary parameters within the Pearson VII structural framework, establishing a unified probabilistic modeling paradigm. The proposed filter adaptively optimizes the Pearson VII formulation’s mean vector and covariance matrix, enabling precise characterization of data features in challenging environments exhibiting non-stationary behavior and heavy-tailed noise distributions. An Inverse Wishart distribution is introduced as the prior distribution of the measurement noise covariance to estimate it adaptively in response to unknown time-varying measurement noise. The variational Bayesian method is used to calculate the state and parameters jointly. Simulation results demonstrate that, compared to traditional Kalman filters based on the Gaussian assumption, the proposed filter exhibits higher precision and stronger robustness when dealing with non-stationary heavy-tailed measurement noise (HTMN). In summary, the Kalman Filter based on the Gamma Pearson VII distribution provides a new and effective tool for state estimation in complex noise environments, mainly showing significant advantages in applications requiring high precision and robustness.
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institution Kabale University
issn 2169-3536
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publishDate 2025-01-01
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spelling doaj-art-2bf4630492ed483d89a1b1853a5feb712025-08-20T03:40:40ZengIEEEIEEE Access2169-35362025-01-0113476804769210.1109/ACCESS.2025.355107510925424A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture DistributionShen Liang0https://orcid.org/0009-0009-0167-5740Guoliang Xu1https://orcid.org/0009-0008-4726-1861Zhenmei Qin2School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, ChinaJiangsu Automation Research Institute, Lianyungang, Jiangsu, ChinaLianyungang Sports School, Lianyungang, Jiangsu, ChinaThis study develops an enhanced state estimation framework by integrating the Kalman filtering mechanism with a Gamma Pearson VII (GaPV) hybrid probability model to address non-stationary heavy-tailed noise characteristics in measurement systems. This innovative methodology synthesizes Gaussian morphological properties with Gamma’s supplementary parameters within the Pearson VII structural framework, establishing a unified probabilistic modeling paradigm. The proposed filter adaptively optimizes the Pearson VII formulation’s mean vector and covariance matrix, enabling precise characterization of data features in challenging environments exhibiting non-stationary behavior and heavy-tailed noise distributions. An Inverse Wishart distribution is introduced as the prior distribution of the measurement noise covariance to estimate it adaptively in response to unknown time-varying measurement noise. The variational Bayesian method is used to calculate the state and parameters jointly. Simulation results demonstrate that, compared to traditional Kalman filters based on the Gaussian assumption, the proposed filter exhibits higher precision and stronger robustness when dealing with non-stationary heavy-tailed measurement noise (HTMN). In summary, the Kalman Filter based on the Gamma Pearson VII distribution provides a new and effective tool for state estimation in complex noise environments, mainly showing significant advantages in applications requiring high precision and robustness.https://ieeexplore.ieee.org/document/10925424/Gamma Pearson VII distributionKalman filtervariational Bayesnon-stationary heavy-tailed noise
spellingShingle Shen Liang
Guoliang Xu
Zhenmei Qin
A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution
IEEE Access
Gamma Pearson VII distribution
Kalman filter
variational Bayes
non-stationary heavy-tailed noise
title A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution
title_full A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution
title_fullStr A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution
title_full_unstemmed A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution
title_short A Robust Kalman Filter for Heavy-Tailed Measurement Noise Based on Gamma Pearson VII Mixture Distribution
title_sort robust kalman filter for heavy tailed measurement noise based on gamma pearson vii mixture distribution
topic Gamma Pearson VII distribution
Kalman filter
variational Bayes
non-stationary heavy-tailed noise
url https://ieeexplore.ieee.org/document/10925424/
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