Research On Adaptive Affine Projection Algorithm Based On Momentum Term

The adaptive filter has the characteristic that it can adjust the filter weight without the prior information of the input signals,so it is widely used in many fields,such as system identification,interference cancellation and inverse system.For an adaptive filter,the adaptive filtering algorithm occupies a key position,which has a direct impact on the effect of the adaptive filter.Therefore,this thesis focuses on the contradiction between fast convergence and low steady-state error of adaptive filtering algorithms.Based on the Affine Projection(AP)algorithm,the existing algorithm is optimized for several times from the perspective of momentum term technology and adaptive combination.The main research distributions are summarized as follows:Firstly,starting from the research background and significance of adaptive filtering algorithms,this thesis gives its development course and research status,then briefly introduces some relevant theories of adaptive filtering algorithms,and discusses three classic algorithms in detail.Through comparative analysis,it is determined that the core algorithm of this thesis is AP algorithm.Secondly,aiming at the problem of slow convergence speed,this thesis introduces momentum term technology and proposes the momentum Affine Projection algorithm,which is proved by simulation that the algorithm has a faster convergence speed.However,the algorithm is sensitive to the value of momentum factor,and can't better reconcile the contradiction between fast convergence and low steady-state error.Therefore,an adaptive updating rule is designed for momentum factor,and the Improved momentum Affine Projection algorithm is proposed,which can better reconcile the contradiction between fast convergence and low steady-state error by simulations.Then,because the adaptive combination method can also reconcile the contradiction between fast convergence and low steady-state error,so this thesis from the perspective of dual system adaptive combination,on the basis of momentum term affine projection algorithm,proposes the 2-momentum Affine Projection by using gradient descent method.And the simulations show that the algorithm can effectively combine the advantages of two subsystems.However,the algorithm has some problems,such as segmented convergence,more complexity and so on.Therefore,two solutions are proposed: one is to optimize the update rules of the weight coefficient vectors of the two systems,and propose the Optional 2-momentum Affine Projection algorithm;the other is to combine the variable momentum factor technology and improve it by means of transfer,and propose the Improved 2-Improved momentum Affine Projection algorithm.The simulations prove that the two proposed solutions have better performance.Finally,it is the conclusions and the prospects of the affine projection algorithm.