Estimating Weak Pulse Signal in Chaotic Background with Jordan Neural Network

In target estimating sea clutter or actual mechanical fault diagnosis, useful signal is often submerged in strong chaotic noise, and the targeted signal data are difficult to recover. Traditional schemes, such as Elman neural network (ENN), backpropagation neural network (BPNN), support vector machine (SVM), and multilayer perceptron- (MLP-) based model, are insufficient to extract the weak signal embedded in a chaotic background. To improve the estimating accuracy, a novel estimating method for aiming at extracting problem of weak pulse signal buried in a strong chaotic background is presented. Firstly, the proposed method obtains the vector sequence signal by reconstructing higher-dimensional phase space data matrix according to the Takens theorem. Then, a Jordan neural network- (JNN-) based model is designed, which can minimize the error squared sum by mixing the single-point jump model for targeting signal. Finally, based on short-term predictability of chaotic background, estimation of weak pulse signal from the chaotic background is achieved by a profile least square method for optimizing the proposed model parameters. The data generated by the Lorenz system are used as chaotic background noise for the simulation experiment. The simulation results show that Jordan neural network and profile least square algorithm are effective in estimating weak pulse signal from chaotic background. Compared with the traditional method, (1) the presented method can estimate the weak pulse signal in strong chaotic noise under lower error than ENN-based, BPNN-based, SVM-based, and -ased models and (2) the proposed method can extract the weak pulse signal under a higher output SNR than BPNN-based model.