Adaptive variable step-size blind source separation algorithm based on nonlinear principal component analysis

Abstract

The design of the step-size is crucial to the convergence rate of the Nonlinear Principle Component Analysis(NPCA) algorithm.However,the commonly used fixed step-size algorithm can hardly satisfy the convergence speed and estimation precision requirements simultaneously.To address this issue,the gradient-based adaptive step-size NPCA algorithm and optimal step-size NPCA algorithm were proposed to speed up the convergence rate and improve tracking ability.In particular,the optimal step-size NPCA algorithm linearly approximated the contrast function and figured out the optimal step-size currently.The optimal step-size NPCA algorithm utilized an adaptive step-size whose value was adjusted in sympathy with the value of the contrast function and free from any manual parameters.The simulation results show that the proposed adaptive step-size NPCA algorithms have faster convergence rate or better tracking ability in comparison with the fixed step-size NPCA algorithm when the estimation precisions are same.The convergence performance of the optimal step-size NPCA algorithm is superior to that of the gradient-based adaptive NPCA algorithm.