<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <italic>et al</italic>. (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 <italic>et al</italic>. (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.</p>
</abstract>

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.

An interval Kalman filter enhanced by lowering the covariance matrix upper bound

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"An interval Kalman filter enhanced by lowering the covariance matrix upper bound"}

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...

An interval Kalman filter enhanced by lowering the covariance matrix upper bound

Published Online: Jul 08, 2021

Page range: 259 - 269

Received: Mar 03, 2020

Accepted: Dec 30, 2020

DOI: https://doi.org/10.34768/amcs-2021-0018

Keywords
uncertain linear systems, Kalman filter, interval analysis, estimation, covariance matrix

© 2021 Tuan Anh Tran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An interval Kalman filter enhanced by lowering the covariance matrix upper bound

Published Online: Jul 08, 2021

Page range: 259 - 269

Received: Mar 03, 2020

Accepted: Dec 30, 2020

DOI: https://doi.org/10.34768/amcs-2021-0018

Keywordsuncertain linear systems, Kalman filter, interval analysis, estimation, covariance matrix

© 2021 Tuan Anh Tran et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
uncertain linear systems, Kalman filter, interval analysis, estimation, covariance matrix