Research On Mixing Matrix Estimation For Time-varying Underdetermined Blind Source Separation

Blind source separation has attracted more and more attention because it does not need pilot and prior information and is more practical.At present,this technology has made great progress and has been successfully applied in many fields such as biology,military and image.Time varying underdetermined blind source separation is a process in which only the observed signals are used to recover each source signals when the number of source signals is more than the observed signals and the mixing matrix changes with time.At present,the research of underdetermined blind source separation mainly adopts "two-step",that is,the first step is to estimate the mixing matrix,and the second step is to recover the source signals.There is no doubt that the accurate estimation of the mixing matrix is the premise of the successful recovery of the source signals.Therefore,this paper mainly studies the estimation of mixing matrix under time-varying underdetermined conditions.The specific research contents are summarized as follows:(1)In underdetermined blind source separation,the sparsity of the source signals is very important,but in practice,the source signals often do not have sparsity in the time domain.Firstly,the observed signals are transformed from time domain to time-frequency domain by short-time Fourier transform,and then the transform matrix is introduced to detect the single source point by using the ratio characteristics of short-time Fourier transform coefficients of single source time-frequency point after introducing the transform matrix.The simulation results in time frequency domain show that the algorithm has enough linear characteristics.After introducing the transformation matrix,the ratio of the observed signal is effectively transformed from complex number to real number,which solves the problem that the traditional clustering algorithm is not applicable in the complex field.(2)In underdetermined blind source separation,it is generally assumed that the number of source signals is known,but the number of source signals is often unknown in practice.In this paper,the number of source signals estimation algorithm based on interval analysis and the number of source signals estimation algorithm based on element ordering are proposed.The number of source signals estimation algorithm based on interval analysis uses the distribution characteristics of the ratio phase angle of the observed signals after short-time Fourier transform to divide the interval,and determines the number of source signals by counting the number of ratio phase angles in the interval and making corresponding corrections.The algorithm of source number estimation based on element ordering firstly establishes an effective ratio phase angle difference distribution matrix,then sorts the elements of the matrix,differentiates any column or row elements of the ordering matrix,and counts the number of difference peaks to determine the number of source signals.Simulation results show that the two algorithms can effectively estimate the number of source signals.At the same time,for the special case of time-varying environment,the improved eigenvalue decomposition method is used to estimate the number of source signals.The simulation results show that the method can also effectively estimate the number of source signals.(3)Aiming at the estimation problem of mixing matrix in time-varying underdetermined environment,a new algorithm based on clustering is proposed.The algorithm does not require the number of source signals and observed signals,and uses adaptive denoising method to determine the effective radar signals.This paper analyzes and discusses the advantages and disadvantages of framing and sliding window,compares various clustering algorithms,and estimates the time-varying underdetermined mixing matrix combined with the idea of clustering analysis.The simulation results show that the proposed algorithm has smaller estimation error and better robustness.