Research Of Adaptive Blind Source Separation Based On Natural Gradient Algorithm

Adaptive blind source separation developed in 1990 s is a real-time blind signal processing technique. To achieve optimum separation performance, it can automatically adjust the algorithm processing parameters and constraints to the data characteristics of the signals. Compared with the batch processing, adaptive blind source separation has small computational amount and short computing time, which is not only suitable for real-time data processing, but also available for the non-stationary environments. Based on existing research results, this paper primarily discussed the step-size’s effect on adaptive blind source separation and the methods of constructing variable step-size. At the same time, Blind source separation on the mixed-signal contained super-Gaussian and sub-Gaussian signal is studied. The main works are as follows:(1) Introduce the development history and Current Status research of blind source separation at home and abroad. The basic theories of blind source separation are summarized, including the mathematical model of blind source separation, the basic assumptions and the related fundamental information theory. After briefly introducing several classic adaptive blind source separation algorithms, the natural gradient algorithm and its objective function are derived, and then the main factors affecting the performance of blind separation algorithm step size and activation function are analyzed.(2) Adaptive blind source separation algorithm as a LMS type algorithm, there exists a contradiction between convergence speed and steady-state error. In order to overcome this contradiction, based on the research of the natural gradient algorithm, a dual adaptive natural gradient algorithm with momentum term is proposed. In this proposed algorithm, the separation degree is introduced into the natural gradient algorithm step-size parameter and the separation matrix, which automatically depending on separation state. Therefore, the new algorithm achieves the purpose of speeding up the convergence rate while reducing the steady-state error. Simulation results show that the new proposed algorithm performance is significantly better than fixed step algorithm and traditional adaptive step algorithm.(3) When the observed mixed signals are composed of super-Gaussian signals and sub-Gaussian signals, due to the nonlinear function, most adaptive blind source separation algorithms will not be able to achieve an effective separation. To solve this problem, many algorithms have been proposed. As a typical algorithm, density estimation based blind source separation algorithm(DBBSS) is only applied to estimate unimodal probability density function because of its use of fixed bandwidth. By introducing Sheather-Jone bandwidth selection and local bandwidth factor, a improved algorithm based on probability density estimation is proposed. The algorithm can succeed in estimating the unimodal and multimodal probability density function such that the separated signals are closer to the source signals. Simulation results show that the proposed algorithm can not only effectively achieve blind source separation of super-Gaussian and sub-Gaussian mixed signals, but also has better performance.