Robust parametric identification procedure of stochastic nonlinear continuous-discrete systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 138-149.

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Based on the weighted maximum likelihood method and the correntropy cubature Kalman filter, software to solve the problem of parametric estimation of models of stochastic nonlinear continuous-discrete systems in the presence of anomalous observations in the measurement data is developed. The effectiveness of the proposed procedure is demonstrated on two model structures for the stochastic and the grouped ordering of anomalous data.
Keywords: stochastic nonlinear continuous-discrete system, parametric identification, robust filtering, cubature Kalman filter, weighted maximum likelihood estimation. .
Mots-clés : anomalous observations
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V. M. Chubich; S. O. Kulabukhova. Robust parametric identification procedure of stochastic nonlinear continuous-discrete systems. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 138-149. http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a9/

[1] G. Kramer, Matematicheskie metody statistiki, Mir, M., 1975

[2] A. A. Borovkov, Matematicheskaya statistika, Nauka, M., 1984

[3] E. Leman, Teoriya tochechnogo otsenivaniya, Nauka, M., 1991

[4] G. I. Ivchenko, Yu. I. Medvedev, Matematicheskaya statistika, LIBROKOM, M., 2014

[5] N. K. Gupta, R. K. Mehra, “Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations”, IEEE Trans. Automatic Control, 19:6 (1974), 774–783 | DOI | Zbl

[6] K. J. Åström, “Maximum likelihood and prediction error methods”, Automatica, 16 (1980), 551–574 | DOI

[7] G. J. Bierman, M. R. Belzer, J. S. Vandercraft, D. W. Porter, “Maximum likelihood estimation using square root information filters”, IEEE Trans. Automatic Control, 35:12 (1990), 1293–1298 | DOI | Zbl

[8] Yu. V. Tsyganova, M. V. Kulikova, “Ob effektivnykh metodakh parametricheskoi identifikatsii lineinykh diskretnykh stokhasticheskikh sistem”, Avtomatika i Telemekhanika, 2012, no. 6, 34–51 | Zbl

[9] D. Boiroux, R. Juhl, H. Madsen, J. B. Jörgensen, “An efficient UD-based algorithm for the computation of maximum likelihood sensitivity of continuous-discrete systems”, IEEE 55 Conf. on Decision and Control (CDC), 2016, 3048–3053

[10] J. Kokkala, A. Solin, S. Särkkä, “Sigma-point filtering and smoothing based parameter estimation in nonlinear dynamic systems”, J. Adv. Information Fusion, 11:1 (2016), 15–30

[11] Z. Sun, Z. Yang, “Study of nonlinear parameter identification using UKF and maximum likelihood method”, IEEE Internat. Conf. on Control Applications, 2010, 671–676

[12] M. Boureghda, T. Bouden, “A deconvolution scheme for the stochastic metabolic/hemodynamic model (sMHM) based on the square root cubature Kalman filter and maximum likelihood estimation”, Biomedical Signal Processing and Control, 45 (2018), 284–304 | DOI

[13] V. M. Chubich, A. E. Prokof'eva, “Parametricheskaya identifikatsiya stokhasticheskikh lineinykh diskretnykh sistem na osnove robastnoi fil'tratsii”, Vestn. Irkutsk. Gos. Tekhn. Un-ta, 22:2 (2018), 84–94

[14] V. M. Chubich, E. V. Filippova, “Parametricheskaya identifikatsiya stokhasticheskikh lineinykh nepreryvno-diskretnykh sistem na osnove robastnoi fil'tratsii”, Izv. Tul'sk. Gos. Un-ta. Tekhnicheskie nauki, 2019, no. 2, 219–225

[15] J. C. Príncipe, Information Theoretic Learning: Renyi's Entropy and Kernel Perspectives, Springer-Verl, N.Y., 2010

[16] G. T. Cinar, J. C. Príncipe, “Hidden state estimation using the correntropy filter with fixed point update and adaptive kernel size”, IEEE World Congress on Computational Intelligence, 2012, 1–6

[17] I. Arasaratnam, S. Haykin, “Cubature Kalman filters”, IEEE Trans. Automatic Control, 54:6 (2009), 1254–1269 | DOI | Zbl

[18] S. Särkkä, A. Solin, “On continuous-discrete cubature Kalman filtering”, Proc. 16 IFAC Symposium on System Identification, 2012, 1221–1226

[19] A. H. Jazwinski, Stochastic Processes and Filtering Theory, Acad. Press, N.Y., 1970 | Zbl

[20] Spravochnik po teorii avtomaticheskogo upravleniya, Nauka, M., 1987

[21] P. Maybeck, Stochastic Models, Estimation, Control, v. 2, Acad. Press, N.Y., 1982 | Zbl

[22] G. Wang, N. Li, Y. Zhang, “Maximum correntropy unscented Kalman and information filters for nonGaussian measurement noise”, J. Franklin Institute, 354:18 (2017), 8659–8677 | DOI | Zbl

[23] T. Kailath, A. Sayed, B. Hassibi, Linear Estimation, Prentice Hall, New Jersey, 2000

[24] E. S. Ahmed, A. I. Volodin, A. A. Hussein, “Robust weighted likelihood estimation of exponential parameters”, IEEE Trans. Reliability, 54:3 (2005), 389–395 | DOI

[25] S. Särkkä, “On unscented Kalman filter for state estimation of continuous-time non-linear systems”, IEEE Trans. Automatic Control, 52:9 (2007), 1631–1641 | DOI | Zbl