Research On Blind Source Separation Algorithms Based On Nolinear Principal Component Analysis

Blind source separation refers to the process of separating source signals from mixed signals based solely on the statistical characteristics of the input signal,without prior knowledge of the source signal or channel transmission parameters.Because blind source separation technology can estimate source signals without a large amount of prior information and the separation model has a certain universality,it has received long-term attention and research from scholars at home and abroad and has been applied in various fields such as biomedical engineering,wireless communication,and seismic exploration.This paper focuses on the contradictions between convergence speed and steady-state error in the nonlinear principal component analysis blind source separation algorithm and other issues.It improves the algorithm by using dual system combination,introducing orthogonal constraints,and other schemes,which effectively improve the overall performance of the algorithm.The main content of the paper is as follows:Firstly,the paper introduces the research background,history,and current situation of blind source separation technology and elaborates on its basic theory,including mathematical models,separation principles,algorithm classification,and performance evaluation standards.Secondly,the paper focuses on analyzing the design principles,derivation process,and separation effects of the non-linear principal component analysis blind source separation algorithm.It mainly carries out three aspects of improvement work for the classic algorithm’s contradiction between convergence speed and steady-state error and the need for pre-whitening: 1.In the minimum mean-square algorithm,two algorithms with different step sizes are adaptively combined through combination factors,which are adaptively updated using gradient method to effectively alleviate the contradiction problem between algorithm convergence speed and steady-state error;2.On the basis of the combined algorithm,the orthogonal constraint condition is introduced,and prewhitening is transformed into an orthogonal constraint to reduce cumulative whitening error and further improve the performance of the combined algorithm;3.The orthogonal constraint condition is introduced into the recursive least squares-type algorithm,and two adaptive combination algorithms with different forgetting factors are combined through matrix inner product operation.A self-adaptive update rule for the combination factor is designed,which effectively improves the convergence speed of the algorithm and obtains a smaller steady-state error.Simulation experimental results show that the three improvement measures proposed in this paper can effectively improve the overall separation performance of the nonlinear principal component analysis blind source separation algorithm.Finally,the paper summarizes the entire content and looks forward to future research directions in this field.