A Novel Improved Threshold Adaptive Forgetting Variable Step Size Blind Separation Model for Weak Signal Detection

Abstract

The online blind source separation (BSS) is seriously disturbed by strong noise when extracting weak signals and has the defects that it cannot both give consideration to convergence speed and steady-state error. In order to solve the abovementioned problems, a novel improved threshold adaptive forgetting variable step size blind separation model (ITAFBS) for weak signal detection is proposed. Firstly, an improved lifting wavelet transform (ILWT) is proposed to reduce the noise of weak signals. In ILWT, a threshold function containing an adjustment factor is proposed to reduce the constant deviation so as to ensure a high signal-to-noise ratio and low distortion after denoising. Then, the separation index (SI) is constructed according to the convergence conditions of the BSS model. An adaptive variable step size blind separation model based on the SI is studied. At the initial stage of separation, the step size is increased to obtain a fast convergence rate, and at the end of separation and the step size is shortened to obtain a small steady-state error. Finally, the forgetting factor is introduced into the model to reduce the error accumulation in the early stage of the algorithm, and the Fourier norm is introduced to improve the convergence speed and separation accuracy of the model. The simulation and experimental results show that ITAFBS has a good performance in multi-frequency weak signal detection. Compared with other methods, the ITAFBS has a faster convergence speed and minimum steady-state error.