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Article information
2020 , Volume 25, ¹ 3, p.88-98
Chubich V.M., Kulabukhova S.O.
Square-root algorithms for robust modifications of the continuous-discrete cubature Kalman filter
Rounding errors due to the finite length of machine word can significantly affect the quality of estimation and filtering when solving the corresponding problems in various subject areas. In this regard, to improve the reliability of the obtained results, it is advisable to develop and then apply square-root modifications of the used algorithms. Purpose: developing the square-root modifications of the continuous-discrete cubature Kalman filter on the basis of variational Bayesian and correntropy approaches. Methodology: matrix orthogonal QR decomposition. Findings: two robust (resistant to the possible presence of anomalous data and to machine rounding errors) modifications of the continuous-discrete cubature Kalman filter have been developed. The first (variational Bayesian) algorithm is obtained by extending the known discrete equations of the extrapolation stage to the continuous-discrete case. The second algorithm, based on the maximum correntropy criterion, is proposed in this paper for the first time. The developed square-root algorithms for nonlinear filtering are validated on the example of one stochastic dynamical system model with the random location of anomalous observations. In doing so, the filtering quality, estimated by the value of the accumulated mean square error, was quite comparable for both modifications during equivalent results obtained for the corresponding root-free analogues. Value: the proposed square-root versions of robust modifications of the continuous-discrete cubature Kalman filter are algebraically equivalent to their standard analogues. Meanwhile, positive definiteness and symmetry of covariance matrices of the state vector estimates at the extrapolation and the filtration stages are provided. The developed algorithms will be used to develop software and mathematical support for parametric identification of stochastic nonlinear continuous-discrete systems in the presence of anomalous observations in the measurement data
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Keywords: stochastic continuous-discrete system, cubature Kalman filter, square-root filtration, robustness
doi: 10.25743/ICT.2020.25.3.010
Author(s):
Chubich Vladimir Mikhailovich
Dr. , Professor
Position: Head of Chair
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20 Prospekt K. Marksa
E-mail: chubich@ami.nstu.ru
SPIN-code: 5198-6679Kulabukhova Svetlana Olegovna
Position: Master student
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20 Prospekt K. Marksa
E-mail: kulabuhova.s@gmail.com
References:
1. Jazwinski A.H. Stochastic processes and filtering theory. N.Y.: Academic Press; 1970: 376.
2. Julier S.J., Uhlmann J.K., Durrant-Whyte H. A new approach for filtering nonlinear systems. Proc.of the “American Control Conference”. Seattle, WA: 1995:1628–1632.
3. Sarkka S. On unscented Kalman filter for state estimation of continuous-time nonlinear systems.IEEE Trans. Automat. Control. 2007; 52(9):1631–1641.
4. Arasaratnam I., Haykin S. Cubature Kalman filters. IEEE Trans. Automat. Control. 2009; 54(6):1254–1269.
5. Sarkka S., Solin A. On continuous-discrete cubature Kalman filtering. Proc. 16th IFAC Symp. Syst.Identification. Brussels; 2012:1221–1226.
6. Sarkka S. Bayesian filtering and smoothing. N.Y.: Cambridge Unive. Press; 2013: 232.
7. Chang L., Hu B., Chang G., Li A. Huber-based novel robust unscented Kalman filter. IET Science,Measurement & Technology. 2012; 6(6):502–509.
8. Leong P.H., Arulampalam S., Lamahewa T.A., Abhayapala T.D. A Gaussian-sum based cubatureKalman filter for bearings-only tracking. IEEE Trans. Aerosp. Electron. Syst. 2013; 49(2):1161– 1176.
9. Hou J., He H., Yang Y. Gao T., Zhang Y. A variational bayesian and Huber-Based robust squareroot cubature Kalman filter for lith-ium-ion battery state of charge estimation. Energies. 2019; 12(9):1717–1739.
10. Wang G., Li N., Zhang Y. Maximum correntropy unscented Kalman and information filters for non-Gaussian measure-ment noise. Journal of the Franklin Institute. 2017; 354(18):8659–8677.
11. Bierman G.J. Factorization methods for discrete sequential estimation. N.Y.: Academic Press; 1977: 241.
12. Semushin I.V. Computational methods in algebra and estimation. Ul’yanovsk: UlGTU; 2011: 366. (In Russ.)
13. Grewal M.S., Andrews A.P. Kalman filtering: theory and practice using MATLAB. Fourth edition. N.J.: John Wileys and Sons; 2015: 617.
14. Kulabukhova S.O., Chubich V.M. Quality analysis of robust modifications of the continuous-discretecubature Kalman filter. Proc. of the Conf. of Young Scientists “Science. Technology. Innovation”. Pt 2. Novosibirsk: NGTU; 2019:38–42. (In Russ.)
15. Kailath T., Sayed A.H., Hassibi B. Linear estimation. New Jersey: Prentice Hall; 2000: 854.
16. Kulikova M.V. Square-root algorithms for maximum correntropy estimation of linear discrete-timesystems in presence of non-Gaussian noise. Syst. Control Lett. 2017; (108):8–15.
17. Chubich V.M. Active parametric identification of stochastic nonlinear continuous-discrete systemsbased on linearization in the time domain. Information and Control Systems. 2010; 49(6):54–61 (In Russ.)
Bibliography link:
Chubich V.M., Kulabukhova S.O. Square-root algorithms for robust modifications of the continuous-discrete cubature Kalman filter // Computational technologies. 2020. V. 25. ¹ 3. P. 88-98
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