Blind Signal Separation Algorithm Based On Natural Gradient

The blind source separation(BSS),originated in 1990 s,is to separate original signals from mixed signals under the condition that source signals are independent of each other and the source signal and transmission channel both are unknown.The mathematical model of blind signal separation is common,so it has been widely used in radar,wireless communication,image processing,speech signal processing and medicine.The optimization based on contrast function is a main method to solve the problem of linear instantaneous mixed blind signal separation.By comparing the statistical independence of the random vector,it can measure the output of the system,then use optimization algorithm to find the contrast function maximum/minimum value,final can acquire the separation matrix which can be used to recover the source signal.Natural gradient blind signal separation algorithm is a classical approach of contrast function optimization,which is based on adaptive update to obtain the separation matrix.The iteration formula of natural gradient algorithm is simple.The computation is small and the algorithm can track the change of environment.As a kind of adaptive blind separation algorithm,natural gradient algorithm has inherent contradiction between convergence speed and steady-state error.In order to improve the performance,the selection of the step size and the estimation of the excitation function are improved in this paper.Adaptive variable step size can effectively alleviate the contradiction between convergence speed and steady-state error.Based on this theory,the paper presents an adaptive variable step size algorithm based on hierarchical iteration.Simulation results show that the proposed algorithm has high convergence speed and better steady-state performance.The natural gradient blind separation algorithm based on the fixed nonlinear function can not be effective in the separation of mixed signal of Super Gauss and Sub Gauss signals.To solve this problem,a function approximation method is used to estimate the excitation function.The coefficient vector can be obtained by using the mean square error adaptive learning.The method uses a linear combination of orthogonal bases to approximate the excitation function.The coefficient vector of linear combination can be obtained by using the property of score function.By using the method to estimate the excitation function,the natural gradient algorithm can get faster convergence speed.