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A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise

In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussia...

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Detalles Bibliográficos
Autores principales: Shan, Chenghao, Zhou, Weidong, Yang, Yefeng, Shan, Hanyu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8534647/
https://www.ncbi.nlm.nih.gov/pubmed/34682075
http://dx.doi.org/10.3390/e23101351
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author Shan, Chenghao
Zhou, Weidong
Yang, Yefeng
Shan, Hanyu
author_facet Shan, Chenghao
Zhou, Weidong
Yang, Yefeng
Shan, Hanyu
author_sort Shan, Chenghao
collection PubMed
description In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP.
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spelling pubmed-85346472021-10-23 A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise Shan, Chenghao Zhou, Weidong Yang, Yefeng Shan, Hanyu Entropy (Basel) Article In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP. MDPI 2021-10-16 /pmc/articles/PMC8534647/ /pubmed/34682075 http://dx.doi.org/10.3390/e23101351 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Shan, Chenghao
Zhou, Weidong
Yang, Yefeng
Shan, Hanyu
A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise
title A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise
title_full A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise
title_fullStr A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise
title_full_unstemmed A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise
title_short A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise
title_sort new variational bayesian-based kalman filter with unknown time-varying measurement loss probability and non-stationary heavy-tailed measurement noise
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8534647/
https://www.ncbi.nlm.nih.gov/pubmed/34682075
http://dx.doi.org/10.3390/e23101351
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