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Open AccessArticle

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

1
Geodätisches Institut Hannover, Leibniz Universität Hannover, 30167 Hannover, Germany
2
Institut für Geoinformation und Vermessung Dessau, Hochschule Anhalt, 06846 Dessau, Germany
3
Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1168; https://doi.org/10.3390/math7121168
Received: 9 September 2019 / Revised: 12 November 2019 / Accepted: 20 November 2019 / Published: 3 December 2019
(This article belongs to the Section Engineering Mathematics)
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. View Full-Text
Keywords: Ellipsoidal and Gaussian Kalman filter; state estimation; unknown but bounded uncertainty; nonlinear programming; convex optimization Ellipsoidal and Gaussian Kalman filter; state estimation; unknown but bounded uncertainty; nonlinear programming; convex optimization
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Sun, L.; Alkhatib, H.; Kargoll, B.; Kreinovich, V.; Neumann, I. Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems. Mathematics 2019, 7, 1168.

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