Research on the Noise Reduction for Chaotic Signals Based on the Adaptive Local Projection Approach

Since the local projection noise reduction approach is influenced by the neighborhood selection greatly, an improved local projection noise reduction approach with adaptive neighborhood selection is proposed. Firstly, one-dimensional time series are embedded into a high dimensional phase space. Secondly, increase the neighborhood radius of the phase point to be analyzed, gradually. The optimal neighborhood radius for each phase point is determined by finding a stable stage during the changing of fitting slope, with the increasing of the radius. And the fitting slope that fits all the vectors in the neighborhood was got by the least squares approach in this paper. Lastly, the noise is eliminated through local geometric projection. Both the noisy chaotic time series generated by Henon map and the vibration signals from the oil pump unit were respectively applied for noise reduction by this approach. The experimental results showed that the adaptive local projection approach proposed improved both the noise reduction performance and the adaptability to different chaotic signals.