文章基本信息

标题：An interval Kalman filter enhanced by lowering the covariance matrix upper bound
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作者：Tran Tuan Anh ; Jauberthie Carine ; Trave-Massuyés Louise 等
期刊名称：International Journal of Applied Mathematics and Computer Science
电子版ISSN：2083-8492
出版年度：2021
卷号：31
期号：2
页码：259-269
DOI：10.34768/amcs-2021-0018
语种：English
出版社：De Gruyter Open
摘要：This paper proposes a variance upper bound based interval Kalman filter that enhances the interval Kalman filter based on the same principle proposed by Tran et al. (2017) for uncertain discrete time linear models. The systems under consideration are subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of the Gaussian noises. By using the spectral decomposition of a symmetric matrix and by optimizing the gain matrix of the proposed filter, we lower the minimal upper bound on the state estimation error covariance for all admissible uncertainties. This paper contributes with an improved algorithm that provides a less conservative error covariance upper bound than the approach proposed by Tran et al. (2017). The state estimates are determined using interval analysis in order to enclose the set of all possible solutions of the classical Kalman filter consistent with the uncertainties.
关键词：uncertain linear systems;Kalman filter;interval analysis;estimation;covariance matrix