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