Estimation of sensitive parameters of chaotic system from noisy scalar series

By exploiting the inherent properties of chaotic system and making use of the underlying information contained in the noisy observational series, a new method for estimating the sensitive parameters only from the noisy observational series of a state variable was developed. The problem of error propagation caused by the positive Lyapunov exponent was settled effectively. This method stems from the thought of the constrained two-point boundary value problem, so it is different from principle the traditional trajectory shadowing methods which must take into account the one-step error and the hyperbolic property of the system. It is also different from common noise reduction techniques which can not obtain a true orbit to shadow the noisy observation series. The evolvement process and performance of this method were analyzed. As a byproduct, the method also provided a practical signal compression/code technique for a class of high dimensional nonlinear systems which are not hyperbolic.