Research Article
BibTex RIS Cite
Year 2021, Volume: 63 Issue: 1, 80 - 92, 30.06.2021
https://doi.org/10.33769/aupse.809161

Abstract

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

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
https://doi.org/10.33769/aupse.809161

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
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Fikri Öztürk 0000-0002-7175-7372

Levent Özbek 0000-0003-1018-3114

Publication Date June 30, 2021
Submission Date October 12, 2020
Acceptance Date May 2, 2021
Published in Issue Year 2021 Volume: 63 Issue: 1

Cite

APA Öztürk, F., & Özbek, L. (2021). 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. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, 63(1), 80-92. https://doi.org/10.33769/aupse.809161
AMA Öztürk F, Özbek L. 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. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. June 2021;63(1):80-92. doi:10.33769/aupse.809161
Chicago Öztürk, Fikri, and Levent Özbek. “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”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 63, no. 1 (June 2021): 80-92. https://doi.org/10.33769/aupse.809161.
EndNote Öztürk F, Özbek L (June 1, 2021) 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. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 63 1 80–92.
IEEE F. Öztürk and L. Özbek, “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”, Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng., vol. 63, no. 1, pp. 80–92, 2021, doi: 10.33769/aupse.809161.
ISNAD Öztürk, Fikri - Özbek, Levent. “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”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering 63/1 (June 2021), 80-92. https://doi.org/10.33769/aupse.809161.
JAMA Öztürk F, Özbek L. 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. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 2021;63:80–92.
MLA Öztürk, Fikri and Levent Özbek. “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”. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, vol. 63, no. 1, 2021, pp. 80-92, doi:10.33769/aupse.809161.
Vancouver Öztürk F, Özbek L. 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. Commun.Fac.Sci.Univ.Ank.Series A2-A3: Phys.Sci. and Eng. 2021;63(1):80-92.

Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.