Extracting Narrow-Band Signal from a Chaotic Background with LLVCR

Abstract

In this paper, the problem of extracting a narrow-band signal in strong chaotic background is considered. A method which in simulation can extract narrow-band signal well is put forward. The proposed method is a mixed model which combines the local linear (LL) model and varying-coefficient regression model (LLVCR). We first use LL model to predict the short-term chaotic signal. Since the varying-coefficient model can fit the narrow-band signal well. We mix them and establish a mixed model to estimate the narrow-band signal in strong chaotic background. For estimating simply and effectively, we develop an efficient algorithm to select and optimize the parameters of LLVCR model those are hard to be exhaustively searched for. In the proposed algorithm, based on the short-term predictability and sensitivity to initial conditions of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of parameters of the presented LLVCR model. In addition, the center frequencies can be detected from the fitting error of LL model by using periodogram at first. The simulation results show that LLVCR model and its estimation algorithm have appreciable flexibility to extract the narrow-band signal in different chaotic background [Lorenz, Henon and Mackey-Glass (M-G) equations].