Detection of Weak Signal Embedded in Chaotic Background Using Echo State Network

In this paper，the theory of phase space reconstruction of the complicated nonlinear system is analyzed, and a new method to detect weak signals from a chaotic background using echo state network (ESN) is put forward. Genetic algorithm is used to select and optimize the parameters which are hard to be selected in echo state network. In the method, the echo state network parameters and the reciprocal of prediction root mean square error of the chaotic time series are taken as individuals and the fitness function of genetic algorithm, respectively, then the optimal parameters for different data are obtained by selection, crossover and mutation of genetic algorithm. Through the powerful ability of learning and nonlinear processing, single-step predictive model for chaotic background noise is built by optimal parameters of echo state network model, then the weak transient signal and periodic signal which is embedded in the chaotic background noise can be detected from the predictive error. It is illustrated in the experiment, which is conducted to detect weak signals from Lorenz chaotic background and Sea Clutter, the proposed method in the paper is better than the support vector machine and neural network in the training speed and predictive accuracy. And this predictive model is also highly effective to detect weak signals from a chaotic background noise as well as possess minor predictive error.