Research On Noise Elimination Based On Kernel Adaptive Filtering Algorithm

Noise elimination based on adaptive filtering algorithm can achieve effective suppression of noise through continuous update iteration of adaptive filter weight coefficients,and extract and detect useful signals from the environment disturbed by noise.Since many noise cancellation application systems often exhibit nonlinear characteristics,traditional linear adaptive filtering cannot achieve good noise suppression effects.Therefore,how to use nonlinear adaptive filtering to eliminate noise has become a research hotspot.As a very important class of algorithms in nonlinear adaptive filtering,the kernel adaptive filtering algorithm has gained wide attention due to its strong generalization learning ability and simple algorithm structure.Therefore,this article has deeply studied the related theories and algorithms of the kernel adaptive filtering algorithm.Aiming at the limitations of some existing algorithms,improvements have been made from the three aspects of the kernel function,the feedback structure and the step factor.A new algorithm that combines feedback structure and variable step size factor,namely Variable Learning Rates Mixed Kernel adaptive filter with Single Feedback(SFVLR-MK)based on single feedback structure and uses it In noise cancellation.First of all,in the kernel adaptive filtering theory,different kernel functions have different characteristics.Considering that the polynomial kernel function can make the algorithm converge faster and the Gaussian kernel function can make the algorithm obtain lower mean square error characteristics,this thesis compares the Gaussian kernel function with Polynomial kernel functions are mixed in a convex combination to obtain a new hybrid kernel function with the common advantages of Gaussian kernel function and polynomial kernel function;secondly,real-time performance is an important indicator of whether the algorithm can be used in the actual noise elimination system,consider The single feedback structure only uses a single delay output to update the weight characteristics.In order to reduce the calculation amount of the algorithm,the algorithm in this thesis adopts a single feedback structure;finally,the step size of the adaptive filtering algorithm affects the convergence speed and steady-state error of the algorithm.Both have a great influence,and it is difficult to obtain an effective compromise between the two with a fixed step size factor.Therefore,this thesis derives the adaptive update equation of the step size factor through the criterion of minimizing error.In order to illustrate the effectiveness of the proposed algorithm,this thesis uses the principle of conservation of energy to theoretically prove the convergence and stability of the algorithm.At the same time,the proposed algorithm is used for noise elimination,and it is compared with some existing algorithms in different noise environments.In comparison,the experimental results show that the algorithm in this thesis has better robustness and noise elimination ability.