Weak signal estimation in chaotic noise utilizing LS-SVM combined with generalized embedding windows

In this paper, detection and estimation of weak signal are presented on the basis of Least-Squares Support Vector Machine (LS-SVM), which is combined with generalized embedding window. Firstly, the embedded dimension and time delay of Lorenz system are determined by improved correlation function method, with which phase space is reconstructed. Then error forecasting model is estimated by LS-SVM with different targets like transient and periodic signals. Last, separate the weak target signal from the prediction error to compute signal-noise-ratio (SNR). As a result, there is a remarkable reduce in detection threshold and improvement in prediction precision, compared with those conventional methods, which is proved by Chen's system.