Skip to Main Content

Access Provided by Xinjiang University

Physical Review E

Access by Xinjiang University

Monte Carlo method for adaptively estimating the unknown parameters and the dynamic state of chaotic systems

Inés P. Mariño¹, Joaquín Míguez², and Riccardo Meucci³

¹Departamento de Física, Nonlinear Dynamics and Chaos Group, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
²Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
³Istituto Nazionale di Ottica Applicata, 50125 Firenze, Italy

Phys. Rev. E 79, 056218 – Published 15 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056218

Abstract

We propose a Monte Carlo methodology for the joint estimation of unobserved dynamic variables and unknown static parameters in chaotic systems. The technique is sequential, i.e., it updates the variable and parameter estimates recursively as new observations become available, and, hence, suitable for online implementation. We demonstrate the validity of the method by way of two examples. In the first one, we tackle the estimation of all the dynamic variables and one unknown parameter of a five-dimensional nonlinear model using a time series of scalar observations experimentally collected from a chaotic ${CO}_{2}$ laser. In the second example, we address the estimation of the two dynamic variables and the phase parameter of a numerical model commonly employed to represent the dynamics of optoelectronic feedback loops designed for chaotic communications over fiber-optic links.

Article Text

References (21)

A. Ghosh, V. R. Kumar, and B. D. Kulkarni, Phys. Rev. E 64, 056222 (2001).
E. Baake, M. Baake, H. G. Bock, and K. M. Briggs, Phys. Rev. A 45, 5524 (1992).
A. Sitz, U. Schwarz, J. Kurths, and H. U. Voss, Phys. Rev. E 66, 016210 (2002).
M. F. Bugallo, S. Xu, and P. M. Djurić, Digit. Signal Process. 17, 774 (2007).
U. Parlitz, Phys. Rev. Lett. 76, 1232 (1996).
A. Maybhate and R. E. Amritkar, Phys. Rev. E 59, 284 (1999).
D. Huang, Phys. Rev. E 69, 067201 (2004).
J. Míguez, Digit. Signal Process. 17, 787 (2007).
I. P. Mariño, E. Allaria, M. A. F. Sanjuán, R. Meucci, and F. T. Arecchi, Phys. Rev. E 70, 036208 (2004).
I. P. Mariño, S. Zambrano, M. A. F. Sanjuán, F. Salvadori, R. Meucci, and F. T. Arecchi, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 3639 (2007).
A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, Phys. Rev. Lett. 101, 154102 (2008).
Sequential Monte Carlo Methods in Practice, edited by A. Doucet, N. de Freitas, and N. Gordon (Springer, New York, 2001).
H. R. Künsch, Ann. Stat. 33, 1983 (2005).
J. S. Liu and R. Chen, J. Am. Stat. Assoc. 93, 1032 (1998).
M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, IEEE Trans. Signal Process. 50, 174 (2002).
C. Andrieu, A. Doucet, S. S. Singh, and V. B. Tadić, Proc. IEEE 92, 423 (2004).
A. Papavasiliou, Stochastic Proc. Appl. 116, 1048 (2006).
M. Ciofini, A. Labate, R. Meucci, and M. Galanti, Phys. Rev. E 60, 398 (1999).
A. Argyris et al., Nature (London) 438, 343 (2005).
M. Bolić, P. M. Djurić, and S. Hong, IEEE Trans. Signal Process. 53, 2442 (2005).
J. Míguez, Signal Process. 87, 3155 (2007).