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Background: The vibration signals acquired from multistage gearbox’s slow-speed gear with localized fault may be directly mixed with source noise and measured noise. In addition, Constrained Independent Component Analysis (CICA) method has strong immunity to the measured noise but not to the source noise. These questions cause the difficulty for applying CICA method to directly extract lowfrequency and weak fault characteristic from the gear vibration signals with source noise. Methods: In order to extract the low-frequency and weak fault feature from the multistage gearbox, the source noise and measured noise are introduced into the independent component analysis (ICA) algorithm model, and then an enhanced Constrained Independent Component Analysis (CICA) method is proposed. The proposed method is implemented by combining the traditional Wavelet Transform (WT) with Constrained Independent Component Analysis (CICA). Results: In this method, the role of a supplementary step of WT before CICA analysis is explored to effectively reduce the influence of strong noise. Conclusion: Through the simulations and experiments, the results show that the proposed method can effectively decrease noise and enhance feature extraction effect of CICA method, and extract the desired gear fault feature, especially the low-frequency and weak fault feature.