Details
| Original language | English |
|---|---|
| Article number | 1168 |
| Journal | Mathematics |
| Volume | 7 |
| Issue number | 12 |
| Publication status | Published - 3 Dec 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.
Keywords
- Convex optimization, Ellipsoidal and Gaussian Kalman filter, Nonlinear programming, State estimation, Unknown but bounded uncertainty
ASJC Scopus subject areas
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In: Mathematics, Vol. 7, No. 12, 1168, 03.12.2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems
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
UR - http://www.scopus.com/inward/record.url?scp=85079694994&partnerID=8YFLogxK
U2 - 10.3390/MATH7121168
DO - 10.3390/MATH7121168
M3 - Article
AN - SCOPUS:85079694994
VL - 7
JO - Mathematics
JF - Mathematics
IS - 12
M1 - 1168
ER -