Weak signal estimation in chaotic clutter using wavelet analysis and symmetric LS-SVM regression

This article examines the theory of phase space reconstruction in complicated nonlinear system and further proposes a new method，an advanced Least Square Support Vector Machine (LS-SVM) model，to detect weak signals from a chaotic clutter. This method functions in following sequences：1) db3 wavelet decomposition of the signals，2) LS-SVM prediction，which includes increasing the symmetry constraint and improving the kernel function，3) Reconstruction. It is established a one-step predictive model that detects the weak signal，including transient signal and period signals，from the predictive error in the chaotic sequences. It is illustrated in the experiment，which is conducted to detect weak signals from Lorenz chaotic background and Sea Clutter，that this proposed method is highly effective to detect weak signals from a chaotic background as well as minimize the impact of noise on weak signals. Compare to conventional RBF neural network and LS-SVM models，the new method presents great value in prediction accuracy and detection threshold.