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

Year: 2009

Authors: Marino I.P., Miguez J., Meucci R.

Autors Affiliation: Univ Rey Juan Carlos, Dept Fis, Nonlinear Dynam & Chaos Grp, Madrid 28933, Spain;
Univ Carlos III Madrid, Dept Teoria Senal & Comunicac, Madrid 28911, Spain;
CNR – INO, Largo E. Fermi 6, 50125 Florence Italy

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.

Journal/Review: PHYSICAL REVIEW E

Volume: 79 (5)      Pages from: 056218  to: 056218

KeyWords: Chaotic communications; CO2-laser; Dynamic state; Dynamic variables; Fiber optic links; Joint estimation; MONTE CARLO; Non-linear model; Numerical models; Online implementation; Optoelectronic feedback; Parameter estimate; Phase parameters; Static parameters; Unknown parameters, Chaotic systems; Monte Carlo methods; Observability, Parameter estimation
DOI: 10.1103/PhysRevE.79.056218

Citations: 2
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