Year 2021,
Volume: 63 Issue: 1, 80 - 92, 30.06.2021
Fikri Öztürk
,
Levent Özbek
References
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Berlin Heidelberg, 1991.
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Press, Cambridge, 1983.
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Englewood Cliffs, 1985.
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Control, Prentice Hall Inc., Englewood Cliffs, 1986.
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Englewood Cliffs, 1993.
- Diderrich, G.T., The Kalman filter from the perspective of Goldberger-Theil estimators,
Amer. Statist., 39 (1985), 193-198. https://doi.org/10.1080/00031305.1985.10479426
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regression analysis, JASA, 67 (1971), 815-821. https://doi.org/10.1080/01621459.1972.10481299
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84 (1983), 479-486.
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Turkish), Ankara, 2016.
Özbek, L., Kalman Filtresi, Akademisyen Yay. (in Turkish), Ankara, 2016.
- Xia, Q., Rao, M., Ying, Y., Shen, X., Adaptive fading Kalman filter with an applications,
Automatica, 30 (8) (1994), 1333-1338. https://doi.org/10.1016/0005-1098(94)90112-0
- Özbek, L., Aliev, F.A., Comments on adaptive fading Kalman filter with an application,
Automatica, 34 (12) (1998), 1663-1664. https://doi.org/10.1016/S0005-1098(98)80025-
3
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estimator, Commun. Stat.-Theor. M., 13 (16) (1984), 1981-2003.
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nonlinear systems, IEEE Trans. Signal Process., 47 (8) (1999), 2324-2328.
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extended Kalman filter, IEEE T. on Automat. Contr., 44 (4) (1999), 714-728.
https://doi.org/10.1109/9.754809
A study on non-linear discrete-time state-space models and adaptive extended Kalman filter application on oscillatıon of an object tied to the end of spring
Year 2021,
Volume: 63 Issue: 1, 80 - 92, 30.06.2021
Fikri Öztürk
,
Levent Özbek
Abstract
In this work, Adaptive Extended Kalman Filter (AEKF) is introduced and its use for oscillation of an object connected to the end of a spring is shown. As a new approach, an AEKF is used as a nonlinear estimation tool for online estimation of the states and parameters of an oscillating object attached to the end of a spring model. Parameter states that do not change with time were examined. The simulation results revealed that with proper selection of initial values of AEKF, AEKF is a very useful tool for this particular application.
References
- Kalman, R.E., A new Approach to linear filtering and prediction problems, J. Basic Eng.,
82 (1960), 35-45. https://doi.org/10.1115/1.3662552
- Bryson, A.E., Ho, Y.C., Optimization, Estimation and Control, Ginn and Company,
Waltham, 1969.
- Jazwinski, A.H., Stochastic Processes and Filtering Theory, Academic Press, New York,
1970.
- Anderson, B.D.O., Moore,J.B., Optimal Filtering, Prentice Hall, Englewood Cliffs, 1979.
- Chui, C.K., Chen, G., Kalman Filtering with Real-time Applications, Springer-Verlag,
Berlin Heidelberg, 1991.
- Ljung, L., Söderström, T., Theory and Practice of Recursive Identification, The MIT
Press, Cambridge, 1983.
- Goodwin, G.C., Sin, K.S.A., Adaptive Filtering Estimation and Control, Prentice Hall,
Englewood Cliffs, 1985.
- Kumar, P.R., Varaiya, P., Stochastic Systems: Estimation, and Adaptive
Control, Prentice Hall Inc., Englewood Cliffs, 1986.
- Chen, G., Approximate Kalman Filtering, World Scientific, Singapore,1993.
- Grewal, S., Andrews A.P., Kalman Filtering Theory and Practice, Prentice Hall,
Englewood Cliffs, 1993.
- Diderrich, G.T., The Kalman filter from the perspective of Goldberger-Theil estimators,
Amer. Statist., 39 (1985), 193-198. https://doi.org/10.1080/00031305.1985.10479426
- Duncan, D.B., Horn, S.D., Linear dynamic recursive estimation from the viewpoint of
regression analysis, JASA, 67 (1971), 815-821. https://doi.org/10.1080/01621459.1972.10481299
- Meinhold, R.J., Singpurwalla, N.D., Understanding the Kalman filter, Am. Statisticians,
84 (1983), 479-486.
- Öztürk, F., Özbek, L., Matematiksel Modelleme ve Simülasyon, Pigeon Yay. (in
Turkish), Ankara, 2016.
Özbek, L., Kalman Filtresi, Akademisyen Yay. (in Turkish), Ankara, 2016.
- Xia, Q., Rao, M., Ying, Y., Shen, X., Adaptive fading Kalman filter with an applications,
Automatica, 30 (8) (1994), 1333-1338. https://doi.org/10.1016/0005-1098(94)90112-0
- Özbek, L., Aliev, F.A., Comments on adaptive fading Kalman filter with an application,
Automatica, 34 (12) (1998), 1663-1664. https://doi.org/10.1016/S0005-1098(98)80025-
3
- Spall, J.C., Wall, K.D., Asymptotic distribution theory for the Kalman filter state
estimator, Commun. Stat.-Theor. M., 13 (16) (1984), 1981-2003.
https://doi.org/10.1080/03610928408828808
- Reif, K., Unbehauen, R., The extended Kalman filter as an exponential observer for
nonlinear systems, IEEE Trans. Signal Process., 47 (8) (1999), 2324-2328.
https://doi.org/10.1109/78.774779
- Reif, K., Gunther, S., Yaz, E., Unhebauen, R., Stochastic stability of the discrete-time
extended Kalman filter, IEEE T. on Automat. Contr., 44 (4) (1999), 714-728.
https://doi.org/10.1109/9.754809