Filtering chaos: A technique to estimate dynamical and observational noise in nonlinear systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 1, 2005, Pages 99-107

  Orrell, David ^a  

^a INSTITUTE FOR SYSTEMS BIOLOGY   (United States)

Author keywords

Error; Model; Nonlinear system; Observation; Parameter optimization

Indexed keywords

APPROXIMATION THEORY; DATA REDUCTION; GAUSSIAN NOISE (ELECTRONIC); MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR SYSTEMS;

NONLINEAR DYNAMICAL MODELS; PARAMETER OPTIMIZATION; PHYSICAL SYSTEMS; VARIATIONAL SMOOTHING;

CHAOS THEORY;

EID: 17044430214     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740501203X     Document Type: Article

References (16)

1. Cohn, S. [1997] "An introduction to estimation theory," J. Meteorol. Soc. Japan 75, 257-288.
2. Heald, J. P. M. & Stark, J. [2000] "Estimations of noise levels for models of chaotic dynamical systems," Phys. Rev. Lett. 84, 2366-2369.
3. Kantz, H. & Schreiber, T. [1997] Nonlinear Time Series Analysis (Cambridge University Press, Cambridge).
4. Kostelich, E. J. & Yorke, J. A. [1990] "Noise reduction: Finding the simplest dynamical system consistent with the data," Physica D41, p. 421.
5. Lorenz, E. [1963] "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141.
6. Lorenz, E. [1996] "Predictability - a problem partly solved," in Predictability, ed. Palmer, T., European Centre for Medium-Range Weather Forecasting, Shinfield Park, Reading, UK.
7. Madan, R. [1993] Chua's Circuit: A Paradigm for Chaos (World Scientific, Singapore).
8. Matsumoto, T., Chua, L. O. & Komuro, M. [1985] "The double scroll," IEEE Trans. Circuits Syst. 23, 798-817.
9. Orrell, D., Smith, L., Barkmeijer, J. & Palmer, T. [2001] "Model error in weather forecasting," Nonlin. Proc. Geo. 8, 357-371.
10. Orrell, D. [2002] "Role of the metric in forecast error growth: How chaotic is the weather?" Tellus A54, 350-362.
11. Orrell, D. [2003] "Predictability over different timsescales in the Lorenz '96 systems," J. Atmos. Sci. 60, 2219-2228.
12. Orrell, D. & Smith, L. A. [2003] "Visualising bifurcations in high dimensional systems: The spectral bifurcation diagram," Int. J. Bifurcation and Chaos 13, 3015-3027.
13. Orrell, D. [2005] "Estimating error growth and shadow behavior in nonlinear dynamical systems," Int. J. Bifurcation and Chaos, in press.
14. Ozaki, T., Jimenez, J. C. & Haggan-Ozaki, V. [2000] "The role of the likelihood function in the estimation of chaos models," J. Time Ser. Anal. 21, 363-387.
15. Robinson, A. R. & Lermusiaux, P. F. J. [2002] "Data assimilation for modeling and predicting coupled physical-biological interactions in the sea," in The Sea, Vol. 12, eds. Robinson, A. R., McCarthy, J. J. & Rothschild, B. J. (John Wiley & Sons, Inc., NY), Chapter 12.
16. Smith, L. A. [2000] "Disentangling uncertainty and error: On the predictability of nonlinear systems," in Nonlinear Dynamics and Statistics, ed. Mees, A. I. (Birkhauser, Boston), pp. 31-64.