Analysis Of Weak Signal Detection Method Based On The Phase Space Reconstruction In The Chaotic Background

By thorough study of chaos, a lot of the seemingly random complicated background signals which have chaotic property. Therefore, how to extract target signal effectively from the chaotic noise is significant both in theory and in application.In this paper, the theory of phase space reconstruction is analyzed, one-step predictive model for chaotic background noise is built by the feature of chaos that can be forecasted in short term, then the weak transient signal and periodic signal which is embedded in the chaotic background noise can be detected from the predictive error. Based on this, detection of weak signal embedded in chaotic background using multi-parameter combination optimization method and echo state network method is studied, and the main contents as following:Detection of weak signal embedded in chaotic background using multi-parameter combination optimization method. In terms of the weak signal detection based on support vector machine under chaotic background, aiming at the weak signal detection insufficient ability of the traditional method in chaotic background, a weak signal detection method is proposed based on the multi-parameter optimization. Genetic algorithm is adopted to optimize the space reconstruction parameters and support vector machine model parameters by utilizing the relationship of the interdependence and mutual restraint between them, then modeling, training and predicting by the optimal parameter values. The accuracy of the model is validated by Mackey-Glass time series, using Lorenz system as chaotic background noise for experimental research, simulation verification shows that this method is highly effective to detect weak transient signal and periodic signal from a chaotic background, respectively. Compared with the traditional parameters calculating methods, the prediction accuracy and detection performance of the new method is improved significantly.Detection of weak signal embedded in chaotic background using echo state network (ESN). Genetic algorithm with implicit parallelism and powerful global search ability is still used to select and optimize ESN model parameters which are hard to be selected in ESN, then the optimal parameters for different data are obtained by the operations of genetic algorithm. Single-step predictive model for chaotic background noise is built by optimal parameters of ESN model, then to judge whether the weak target signals exist in chaotic background by 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.