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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Autores principales:	Lin Cao, Chuyuan Zhang, Zongmin Zhao, Dongfeng Wang, Kangning Du, Chong Fu, Jianfeng Gu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	MIMO radar Kalman filter Bayesian robustness uncertain noise posterior noise statistics proposal distribution Chemical technology TP1-1185
Acceso en línea:	https://doaj.org/article/ec86489691784b5e81708c9f0c22f5cc
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spelling	oai:doaj.org-article:ec86489691784b5e81708c9f0c22f5cc2021-11-25T18:58:22ZAn Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics10.3390/s212276731424-8220https://doaj.org/article/ec86489691784b5e81708c9f0c22f5cc2021-11-01T00:00:00Zhttps://www.mdpi.com/1424-8220/21/22/7673https://doaj.org/toc/1424-8220Aimed 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.Lin CaoChuyuan ZhangZongmin ZhaoDongfeng WangKangning DuChong FuJianfeng GuMDPI AGarticleMIMO radarKalman filterBayesian robustnessuncertain noiseposterior noise statisticsproposal distributionChemical technologyTP1-1185ENSensors, Vol 21, Iss 7673, p 7673 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	MIMO radar Kalman filter Bayesian robustness uncertain noise posterior noise statistics proposal distribution Chemical technology TP1-1185
spellingShingle	MIMO radar Kalman filter Bayesian robustness uncertain noise posterior noise statistics proposal distribution Chemical technology TP1-1185 Lin Cao Chuyuan Zhang Zongmin Zhao Dongfeng Wang Kangning Du Chong Fu Jianfeng Gu An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics
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.
format	article
author	Lin Cao Chuyuan Zhang Zongmin Zhao Dongfeng Wang Kangning Du Chong Fu Jianfeng Gu
author_facet	Lin Cao Chuyuan Zhang Zongmin Zhao Dongfeng Wang Kangning Du Chong Fu Jianfeng Gu
author_sort	Lin Cao
title	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_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_sort	overdispersed black-box variational bayesian–kalman filter with inaccurate noise second-order statistics
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ec86489691784b5e81708c9f0c22f5cc
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An Overdispersed Black-Box Variational Bayesian–Kalman Filter with Inaccurate Noise Second-Order Statistics

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