Abstract
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.
Highlights
As early as the end of the 19th century, the French Poincare found that the solution of the three-body problem could be random within a certain range when he studied the threebody problem, but this discovery did not arouse widespread concern among scholars
In [29], Wei Wu used ARIMA model, Elman neural network, and Jordan neural network, respectively, to predict the nonlinear time series data of human brucellosis in China, and the results showed that the feedback neural network was more accurate than the traditional ARIMA model
The pulse signal under the chaotic background. e following conclusions can be drawn from the experimental results: the model proposed in this paper can predict the weak pulse signal in the chaotic background, and it can be seen from the results of experiment 1 that the prediction accuracy is high
Summary
As early as the end of the 19th century, the French Poincare found that the solution of the three-body problem could be random within a certain range when he studied the threebody problem, but this discovery did not arouse widespread concern among scholars. Experts and scholars at home and abroad have studied the prediction of the pulse signal in chaotic noise and obtained a lot of research results, such as Volterra filter, correlation detection in time domain, spectral analysis in frequency domain, chaotic Duffing oscillator [2], local linear [3,4,5], multiple kernel extreme learning machine [6], and Kalman filter , extend Kalman filter (EKF) [7], wavelet transform and nonlinear autoregressive model, etc. The Jordan neural network is used to fit the chaotic background and estimate the pulse signal from its residuals.
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