The unscented Kalman filter, a powerful tool for data analysis

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 14, Issue 6, 2004, Pages 2093-2105

  Sitz, A ^a   Schwarz, U ^a   Kurths, J ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Chaos; Nonlinear systems; Observational noise; Parameter estimation

Indexed keywords

CHAOS THEORY; DATA REDUCTION; DYNAMICS; LINEAR EQUATIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PROBABILITY;

BAYES FRAMEWORK; COST FUNCTION; OBSERVATIONAL NOISE; STEMMING;

KALMAN FILTERING;

EID: 13844253916     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404010515     Document Type: Article

References (24)

1. Alligood, K., Sauer, T. & Yorke, J. T. [1997] Chaos - An Introduction to Dynamical Systems (Springer-Verlag, NY).
2. Bär, M., Hegger, R. & Kantz, H. [1999] "Fitting partial differential equations to space-time dynamics," Phys. Rev. E59, 337-342.
3. Bar-Shalom, Y. & Fortmann, T. E. [1988] Tracking and Data Association (Academic Press, Inc., Orlando, FL).
4. Beneš, V. E. [1985] "New exact nonlinear filters with large Lie algebras," Syst. Contr. Lett. 5, 217-221.
5. Bock, H. G. [1987] "Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen," PhD thesis, Bonner Mathematische Schriften, Nr. 183, Bonn, 1987.
6. Bulirsch, R. & Stoer, J. [1966] "Numerical treatment of ordinary differential equations by extrapolation methods," Numer. Math. 8.
7. Chua, L. O., Komuro, M. & Matsumoto, T. [1986] "The double scroll family," IEEE Trans. Circuits Syst. 33, 1072-1118.
8. Daum, F. E. [1988] "New exact nonlinear filters," Bayesian Analysis of Time Series and Dynamic Models, ed. Spall, J. C., pp. 199-226.
9. Dobmann, M. & Schittkowski, K. [1995] "PDEFIT: A FORTRAN code for constrained parameter estimation in partial differential equations," Technical Report, Department of Mathematics, University of Bayreuth.
10. Dormand, J. R. & Prince, P. J. [1980] "A family of embedded Runge-Kutta formulae," J. Comput. Appl. Math. 6, 19-26.
11. Doucet, A., de Freitas, N. & Gordon, N. [2001] Sequential Monte Carlo Methods in Practice (Springer-Verlag, NY).
12. Edsberg, L. & Wedin, P. A. [1995] "Numerical tools for parameter estimation in ODE-systems," Optim. Meth. Softw. 6, 193-217.
13. Gelb, A. [1974] Applied Optimal Estimation (The M.I.T. Press, Cambridge Mass).
14. Härdie, W. [1990] Applied Nonparametric Regression (Cambridge University Press, Cambridge).
15. Honerkamp, J. [1998] Statistical Physics (SpringerVerlag, Berlin).
16. Julier, S. & Uhlmann, J. [1997] "A new extension of the Kalman filter to nonlinear systems," Int. Symp. Aerospace/Defense Sensing, Simulation and Controls.
17. Julier, S. [2002] "The scaled unscented transformation," Automatica, to appear.
18. Kalman, R. E. & Bucy, R. S. [1960] "New results in linear filtering and prediction theory," J. Basic Engin. D83, 95-108.
19. Ljung, L. [1979] "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems," IEEE Trans. Autom. Contr. AC-24, 36-50.
20. Matsumoto, T. [1986] "A chaotic attractor from Chua's circuit, " IEEE Trans. Circuits Syst. 31, 1055-1058.
21. Miller, R. N., Ghil, M. & Gauthiez, F. [1994] "Advanced data assimilation in strongly nonlinear dynamical systems," J. Aim. Sci. 51, 1037-1056.
22. Nørgaard, M., Poulsen, N. K. & Ravn, O. [2000] "Advances in derivative-free state estimation for nonlinear systems," Technical Report: IMM-REP-1998-15.
23. Sitz, A., Schwarz, U., Kurths, J. & Voss, H. U. [2002] "Estimation of parameters and unobserved components for chaotic systems from noisy time series," Phys. Rev. E66, 016210.
24. van der Pol, B. [1926] "On 'relaxation-oscillation'," London Phil. Mag. Ser. 7, 978-992.