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A Novel Perspective of the Kalman Filter from the Rényi Entropy
Rényi entropy as a generalization of the Shannon entropy allows for different averaging of probabilities of a control parameter [Formula: see text]. This paper gives a new perspective of the Kalman filter from the Rényi entropy. Firstly, the Rényi entropy is employed to measure the uncertainty of th...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7597296/ https://www.ncbi.nlm.nih.gov/pubmed/33286750 http://dx.doi.org/10.3390/e22090982 |
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author | Luo, Yarong Guo, Chi You, Shengyong Liu, Jingnan |
author_facet | Luo, Yarong Guo, Chi You, Shengyong Liu, Jingnan |
author_sort | Luo, Yarong |
collection | PubMed |
description | Rényi entropy as a generalization of the Shannon entropy allows for different averaging of probabilities of a control parameter [Formula: see text]. This paper gives a new perspective of the Kalman filter from the Rényi entropy. Firstly, the Rényi entropy is employed to measure the uncertainty of the multivariate Gaussian probability density function. Then, we calculate the temporal derivative of the Rényi entropy of the Kalman filter’s mean square error matrix, which will be minimized to obtain the Kalman filter’s gain. Moreover, the continuous Kalman filter approaches a steady state when the temporal derivative of the Rényi entropy is equal to zero, which means that the Rényi entropy will keep stable. As the temporal derivative of the Rényi entropy is independent of parameter [Formula: see text] and is the same as the temporal derivative of the Shannon entropy, the result is the same as for Shannon entropy. Finally, an example of an experiment of falling body tracking by radar using an unscented Kalman filter (UKF) in noisy conditions and a loosely coupled navigation experiment are performed to demonstrate the effectiveness of the conclusion. |
format | Online Article Text |
id | pubmed-7597296 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75972962020-11-09 A Novel Perspective of the Kalman Filter from the Rényi Entropy Luo, Yarong Guo, Chi You, Shengyong Liu, Jingnan Entropy (Basel) Article Rényi entropy as a generalization of the Shannon entropy allows for different averaging of probabilities of a control parameter [Formula: see text]. This paper gives a new perspective of the Kalman filter from the Rényi entropy. Firstly, the Rényi entropy is employed to measure the uncertainty of the multivariate Gaussian probability density function. Then, we calculate the temporal derivative of the Rényi entropy of the Kalman filter’s mean square error matrix, which will be minimized to obtain the Kalman filter’s gain. Moreover, the continuous Kalman filter approaches a steady state when the temporal derivative of the Rényi entropy is equal to zero, which means that the Rényi entropy will keep stable. As the temporal derivative of the Rényi entropy is independent of parameter [Formula: see text] and is the same as the temporal derivative of the Shannon entropy, the result is the same as for Shannon entropy. Finally, an example of an experiment of falling body tracking by radar using an unscented Kalman filter (UKF) in noisy conditions and a loosely coupled navigation experiment are performed to demonstrate the effectiveness of the conclusion. MDPI 2020-09-03 /pmc/articles/PMC7597296/ /pubmed/33286750 http://dx.doi.org/10.3390/e22090982 Text en © 2020 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Luo, Yarong Guo, Chi You, Shengyong Liu, Jingnan A Novel Perspective of the Kalman Filter from the Rényi Entropy |
title | A Novel Perspective of the Kalman Filter from the Rényi Entropy |
title_full | A Novel Perspective of the Kalman Filter from the Rényi Entropy |
title_fullStr | A Novel Perspective of the Kalman Filter from the Rényi Entropy |
title_full_unstemmed | A Novel Perspective of the Kalman Filter from the Rényi Entropy |
title_short | A Novel Perspective of the Kalman Filter from the Rényi Entropy |
title_sort | novel perspective of the kalman filter from the rényi entropy |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7597296/ https://www.ncbi.nlm.nih.gov/pubmed/33286750 http://dx.doi.org/10.3390/e22090982 |
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