Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems

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OriginalspracheEnglisch
Aufsatznummer1168
FachzeitschriftMathematics
Jahrgang7
Ausgabenummer12
PublikationsstatusVeröffentlicht - 3 Dez. 2019

Abstract

In this paper, we propose a new technique-called Ellipsoidal and Gaussian Kalman filter-for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system's state (and the optimal ellipsoid for describing the systems's uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better-the state estimation technique usually applied to such nonlinear problems.

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Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems. / Sun, Ligang; Alkhatib, Hamza; Kargoll, Boris et al.
in: Mathematics, Jahrgang 7, Nr. 12, 1168, 03.12.2019.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Sun L, Alkhatib H, Kargoll B, Kreinovich V, Neumann I. Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems. Mathematics. 2019 Dez 3;7(12):1168. doi: 10.3390/MATH7121168
Sun, Ligang ; Alkhatib, Hamza ; Kargoll, Boris et al. / Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems. in: Mathematics. 2019 ; Jahrgang 7, Nr. 12.
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abstract = "In this paper, we propose a new technique-called Ellipsoidal and Gaussian Kalman filter-for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system's state (and the optimal ellipsoid for describing the systems's uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better-the state estimation technique usually applied to such nonlinear problems.",
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author = "Ligang Sun and Hamza Alkhatib and Boris Kargoll and Vladik Kreinovich and Ingo Neumann",
note = "Funding Information: This work was funded by the German Research Foundation (DFG) as a part of the Research Training Group i.c.sens (GRK2159). The authors acknowledge the discussions with Steffen Sch?n, Franz Rottensteiner and Claus Brenner from Leibniz University Hannover. The authors also thank Sergey Grigorian from Department of Mathematics in University of Texas Rio Grande Valley for his comments and suggestions.",
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AU - Sun, Ligang

AU - Alkhatib, Hamza

AU - Kargoll, Boris

AU - Kreinovich, Vladik

AU - Neumann, Ingo

N1 - Funding Information: This work was funded by the German Research Foundation (DFG) as a part of the Research Training Group i.c.sens (GRK2159). The authors acknowledge the discussions with Steffen Sch?n, Franz Rottensteiner and Claus Brenner from Leibniz University Hannover. The authors also thank Sergey Grigorian from Department of Mathematics in University of Texas Rio Grande Valley for his comments and suggestions.

PY - 2019/12/3

Y1 - 2019/12/3

N2 - In this paper, we propose a new technique-called Ellipsoidal and Gaussian Kalman filter-for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system's state (and the optimal ellipsoid for describing the systems's uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better-the state estimation technique usually applied to such nonlinear problems.

AB - In this paper, we propose a new technique-called Ellipsoidal and Gaussian Kalman filter-for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system's state (and the optimal ellipsoid for describing the systems's uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better-the state estimation technique usually applied to such nonlinear problems.

KW - Convex optimization

KW - Ellipsoidal and Gaussian Kalman filter

KW - Nonlinear programming

KW - State estimation

KW - Unknown but bounded uncertainty

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