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An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics

Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a...

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Detalles Bibliográficos
Autores principales: Cao, Lin, Zhang, Chuyuan, Zhao, Zongmin, Wang, Dongfeng, Du, Kangning, Fu, Chong, Gu, Jianfeng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8624531/
https://www.ncbi.nlm.nih.gov/pubmed/34833746
http://dx.doi.org/10.3390/s21227673
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author Cao, Lin
Zhang, Chuyuan
Zhao, Zongmin
Wang, Dongfeng
Du, Kangning
Fu, Chong
Gu, Jianfeng
author_facet Cao, Lin
Zhang, Chuyuan
Zhao, Zongmin
Wang, Dongfeng
Du, Kangning
Fu, Chong
Gu, Jianfeng
author_sort Cao, Lin
collection PubMed
description Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.
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spelling pubmed-86245312021-11-27 An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics Cao, Lin Zhang, Chuyuan Zhao, Zongmin Wang, Dongfeng Du, Kangning Fu, Chong Gu, Jianfeng Sensors (Basel) Article Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system. MDPI 2021-11-18 /pmc/articles/PMC8624531/ /pubmed/34833746 http://dx.doi.org/10.3390/s21227673 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
Cao, Lin
Zhang, Chuyuan
Zhao, Zongmin
Wang, Dongfeng
Du, Kangning
Fu, Chong
Gu, Jianfeng
An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
title An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
title_full An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
title_fullStr An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
title_full_unstemmed An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
title_short An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
title_sort overdispersed black-box variational bayesian–kalman filter with inaccurate noise second-order statistics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8624531/
https://www.ncbi.nlm.nih.gov/pubmed/34833746
http://dx.doi.org/10.3390/s21227673
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