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

• Autorzy: Tran Tuan Anh , Jauberthie Carine , Trave-Massuyés Louise , Lu Quoc Hung

Identyfikatory

DOI

10.34768/amcs-2021-0018

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

uncertain linear systems; Kalman filter; interval analysis; estimation; covariance matrix

PL

układ liniowy; filtr Kalmana; analiza interwałowa; macierz kowariancji

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2021
• Tom: Vol. 31, no. 2
• Strony: 259--269
• Opis fizyczny: Bibliogr. 23 poz., tab., wykr.

Twórcy

autor

Tran Tuan Anh

• LAAS-CNRS, University of Toulouse, 7 avenue du Colonel Roche, Toulouse, 31400, France

autor

Jauberthie Carine

• LAAS-CNRS, University of Toulouse, 7 avenue du Colonel Roche, Toulouse, 31400, France

autor

Trave-Massuyés Louise

• LAAS-CNRS, University of Toulouse, 7 avenue du Colonel Roche, Toulouse, 31400, France

autor

Lu Quoc Hung

• LAAS-CNRS, University of Toulouse, 7 avenue du Colonel Roche, Toulouse, 31400, France

Bibliografia

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• [21] Tran, T. A., Le Gall, F., Jauberthie, C. and Travé-Massuyès, L. (2016). Two stochastic filters and their interval extensions, Proceedings of the 4th IFAC International Conference on Intelligent Control and Automation Sciences, Reims, France, pp. 49–54.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).