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

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 CO2 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.