Research On Adaptive Algorithms Of Sparse System Based On Censored Regression Model

With the development of digital information technology,digital signal processing has been widely used in construction engineering,transportation,medicine,ecological construction and many other fields.Adaptive filtering algorithm is an important branch of digital signal processing.It has the characteristics of simple structure,strong adaptability and excellent filtering performance.It is widely used in system identification,echo cancellation and nonlinear processing.In these areas,adaptive algorithm has played a prominent role.However,with more and more in-depth research on adaptive algorithm,in the face of Gaussian noise and sub Gaussian noise environment,the traditional adaptive algorithm,the traditional least mean square(LMS)algorithm,has been unable to meet the ideal needs.For sub Gaussian noise environment,the performance of LMF algorithm is better than LMS algorithm.However,in the censored regression model,the convergence performance of LMF algorithm is significantly reduced.In order to optimize this problem,this paper uses deviation compensation Heckman two-step method to solve the performance degradation of traditional algorithms.Sparse systems are widely used in practice.There are a large number of numbers with zero or near zero weight coefficients in the system to be identified,but there are few obvious coefficients,so it is sparse.Faced with this kind of sparse system,the traditional adaptive algorithm has no ability to resist the sparsity of the system or can not use this characteristic to improve the performance of the algorithm.Recently,many adaptive algorithms have been proposed to utilize the sparsity of the systems.These algorithms take advantage of the sparsity of the system and add a norm penalty term to the cost function.In particular,in order to use sparsity more effectively,an improved reweighted zero-attracting(RZA)adaptive algorithm is proposed.Compared with its penalty term,it has more advantages in sparse systems.Therefore,this paper uses this method to further improve the performance of the algorithm.Firstly,aiming at the problem of censored regression model,this paper introduces the two-step method of deviation compensation Heckman to the least mean square algorithm,and obtains the least mean square(CRLMF)algorithm based on censored regression model.When the output noise is Gaussian or sub Gaussian background noise,the convergence performance is improved.Secondly,in view of the uncertainty of the sparsity of the unknown system,the convergence performance of the least mean square regression model based on truncated regression model is degraded when the system is sparse.In order to solve this problem,the reweighted zero-attracting factor(RZA)is applied to the CRLMF algorithm,and the reweighted zero-attracting censored regression model based on RZA-CELMF algorithm is obtained.The algorithm has good performance in different sparse systems.Finally,the performance of the algorithm with mean square error(MSE)as the cost function is greatly reduced due to the impactive noise environment.Correlation entropy is defined as the similarity measure of two random variables,which is robust to large outliers.So the adaptive algorithm has the ability of anti-shock.Generalized maximum entropy(GMCC)is proposed to further improve the performance of the algorithm.Although the GMCC algorithm improves the performance of convergence error and steady-state convergence by using exponential terms of error,it is not possible to adjust the kernel width in algorithm iteration to further improve the performance of the algorithm.Therefore,this paper proposes a variable kernel width based generalized maximum entropy(VKWGMCC)algorithm.Further research shows that the performance of VKWGMCC algorithm is reduced under the censored regression model.On this basis,this paper proposes a variable kernel width generalized maximum entropy algorithm(CR-VKWGMCC)based on the censored regression model,which further improves the performance of the algorithm.