Research On The LMS-type Adaptive Filtering Algorithm

Adaptive filtering algorithm has become an important branch of Signal and Information Processing and Control Theory and Control Engineering.It has been widely used in many engineering fields,and it is still one of the most active research topics all over the world.This dissertation is composed of four parts:research on adaptive filtering algorithm based on the LMAT,research on adaptive filtering algorithm based on norm constraint,research on adaptive filtering algorithm based on spline function and research on adaptive filtering algorithm based on distributed network.The aim of this dissertation is to find some adaptive filtering algorithms with fast convergence speed,low computational complexity,and small steady-state error and so on.In addition,all the research results are verified by system identification experiments.The research results of this dissertation are of great significance for the complement and improvement of adaptive filtering algorithm,and also provide some basis for the application of adaptive filtering algorithm in practice engineering application.The main work is summarized as follows1.Research on adaptive filtering algorithm based on the LMAT.A nonparametric variable step-size least mean absolute third algorithm?NVSLMAT?is proposed which to improve the capability of the adaptive filtering algorithm against the impulsive noise and other types of noise.The step-size of the NVSLMAT is obtained using the instantaneous value of a current error estimate and a posterior error estimate.In the NVSLMAT,fewer parameters need to be set,thereby reducing the complexity considerably.Additionally,the mean of the additive noise does not necessarily equal zero in the proposed algorithm.An optimized least mean absolute third algorithm?OPLMAT?is present to improve the capability of the adaptive filtering algorithm against Gaussian and non-Gaussian noises when the unknown system is a time-varying parameter system under low SNR.The optimal step-size of the OPLMAT is obtained based on minimizing the MSD at the current time.A conjugate gradient nonnegative least mean absolute third algorithm?CGNNLMAT?is derived.This algorithm is inspired by the CG method and the nonnegative least mean absolute third algorithm?NNLMAT?.The experimental results in the context of system identification applications presented here to illustrate the principle and efficiency of those proposed algorithms.2.Research on adaptive filtering algorithm based on norm constraint.A new variable step-size l₀-LMS algorithm is proposed.A step size control method and the zero attraction items reweight method based on correlation function value of the error.A new zero-attracting variable step size l₀-NLMS algorithm is proposed Step size of the l₀-NLMS algorithm is changed by the Versiera function.In order to quicken the convergence rate and enhance performance for anti-noise when identify the unknown coefficients of a sparse system.A variable step-size l₁-LMS algorithm is proposed.It is using current error and correlation value of error to adjust step-size and zero-attracting part.Moreover,when the current error satisfies different conditions,the two step-size formulas will switch dynamically.A continuous mixed p-norm adaptive algorithm with reweighted l₀-norm constraint?RL0-CMPN?is proposed for sparse system identification.The RL0-CMPN makes full use of the advantages of the different norm.This algorithm can solve large coefficient update spread problem and reduce the slow-down effect.Besides,it is a continuous mixed p-norm adaptive algorithm.Theoretical analysis combined with experimental simulations show that those algorithms can achieve better tracking speed,lower steady state error and anti-noise performance.3.Research on adaptive filtering algorithm based on spline.A normalised spline adaptive filtering algorithm to improve the stability of spline adaptive filtering?SAF?algorithm against the eigenvalue spread of the autocorrelation matrix of the input signal.The value range of the learning rate in this algorithm is specified.This algorithm is called SAF-NLMS.The performance of the proposed algorithm is tested according to artificial datasets and real datasets.The achieved results present actually good performance.4.Research on adaptive filtering algorithm based on distributed network in the presence of impulsive noise.Distributed estimation has been widely used in many applications in recent year.Adaptive networks are an extension of adaptive filters over graphs.The diffusion-based algorithms can achieve unbiased estimation.But in the case where the inputs of agents are corrupted by additive noise,the estimated results will be biased.From the above analysis we can know that those shortcomings of the mentioned diffusion algorithms in the presence of impulsive noise need to be solved urgently.So,an ATC diffusion normalized Huber adaptive filtering?ATC-DNHuber?algorithm for distributed estimation in impulsive noise environments is proposed.Simulation results demonstrate that those proposed algorithms are robust against impulsive interference.