Weak signal detection in chaotic noise background - based on VMD-EEMD and self-attention mechanisms

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Abstract In this paper, a method for detection and estimation of weak harmonic signals in chaotic noise background is proposed. Firstly, the observed signal is smoothed by local weighted regression model to reduce the influence of noise. Then, the smoothed signals are decomposed into the intrinsic mode functions by Variational Mode Decomposition and Ensemble Empirical Mode Decomposition (VMD-EEMD). The components are reconstructed in the phase space, and the one-step prediction is carried out by adding a layer of the self-attention mechanism in the Long Short-Term Memory (LSTM). The one-step prediction error is obtained by summing up the prediction results of the components and the weak harmonic signals will be detected from the one-step prediction error. Finally, the periodogram method is used to detect whether the observed signals contain harmonic signals or not. If the observed signals contain harmonic signals, the amplitude and phase are estimated by the least squares method. Simulation experiments show that the method proposed in this paper has good performance. In detection of single harmonic signal, the Mean Absolute Error (MAE) and Mean Square Error (MSE) of the one-step prediction are 0.0212 and 0.00068 respectively; MAE and MSE of the signal estimation are 0.001977 and 0.0007 respectively. In detection of multiple harmonic signals, MAE and MSE of the one-step prediction are 0. 0248 and 0. 0006 respectively; MAE and MSE of the signal estimation are 0. 0035 and 1.681×10−5 respectively. The method proposed in this paper is able to efficiently detect weak harmonic signals from chaotic noise backgrounds and estimate the harmonic signals.