A New Linear Regression Kalman Filter with Symmetric Samples

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard no...

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Autores principales:	Xiuqiong Chen, Jiayi Kang, Mina Teicher, Stephen S.-T. Yau
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Kalman filter Dirac mixture approximation symmetric samples Kullback–Leibler divergence Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/91b554243a86435383eb991227c7f9c4
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id	oai:doaj.org-article:91b554243a86435383eb991227c7f9c4
record_format	dspace
spelling	oai:doaj.org-article:91b554243a86435383eb991227c7f9c42021-11-25T19:07:02ZA New Linear Regression Kalman Filter with Symmetric Samples10.3390/sym131121392073-8994https://doaj.org/article/91b554243a86435383eb991227c7f9c42021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2139https://doaj.org/toc/2073-8994Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.Xiuqiong ChenJiayi KangMina TeicherStephen S.-T. YauMDPI AGarticleKalman filterDirac mixture approximationsymmetric samplesKullback–Leibler divergenceMathematicsQA1-939ENSymmetry, Vol 13, Iss 2139, p 2139 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Kalman filter Dirac mixture approximation symmetric samples Kullback–Leibler divergence Mathematics QA1-939
spellingShingle	Kalman filter Dirac mixture approximation symmetric samples Kullback–Leibler divergence Mathematics QA1-939 Xiuqiong Chen Jiayi Kang Mina Teicher Stephen S.-T. Yau A New Linear Regression Kalman Filter with Symmetric Samples
description	Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.
format	article
author	Xiuqiong Chen Jiayi Kang Mina Teicher Stephen S.-T. Yau
author_facet	Xiuqiong Chen Jiayi Kang Mina Teicher Stephen S.-T. Yau
author_sort	Xiuqiong Chen
title	A New Linear Regression Kalman Filter with Symmetric Samples
title_short	A New Linear Regression Kalman Filter with Symmetric Samples
title_full	A New Linear Regression Kalman Filter with Symmetric Samples
title_fullStr	A New Linear Regression Kalman Filter with Symmetric Samples
title_full_unstemmed	A New Linear Regression Kalman Filter with Symmetric Samples
title_sort	new linear regression kalman filter with symmetric samples
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/91b554243a86435383eb991227c7f9c4
work_keys_str_mv	AT xiuqiongchen anewlinearregressionkalmanfilterwithsymmetricsamples AT jiayikang anewlinearregressionkalmanfilterwithsymmetricsamples AT minateicher anewlinearregressionkalmanfilterwithsymmetricsamples AT stephenstyau anewlinearregressionkalmanfilterwithsymmetricsamples AT xiuqiongchen newlinearregressionkalmanfilterwithsymmetricsamples AT jiayikang newlinearregressionkalmanfilterwithsymmetricsamples AT minateicher newlinearregressionkalmanfilterwithsymmetricsamples AT stephenstyau newlinearregressionkalmanfilterwithsymmetricsamples
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A New Linear Regression Kalman Filter with Symmetric Samples

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