Research On M-estimate Adaptive Algorithms For Combating Impulsive Noise

With the continuous advancement of science and technology,information processing technology has also developed rapidly.As an important research content of information processing technology,adaptive filter has attracted more scholars' attention in recent years.Adaptive filters have many applications in system identification,interference cancellation,etc.Adaptive filter algorithms,as the core of adaptive filters,have become a hot research direction.Traditional adaptive filtering algorithms such as the least mean square(LMS)algorithm,the normalized least mean square(NLMS)algorithm,are based on second-order moment statistics.These two basic algorithms are often used in Gaussian environments due to their simple structure and very stable filtering performance.However,in actual situations,the noise environment is usually non-Gaussian,and the impact noise will seriously interfere with the performance of the traditional algorithm.In addition,many systems to be identified have sparse characteristics,and their coefficients are mostly zero or close to zero.The performance of traditional adaptive filtering algorithms is also degraded in sparse systems.In view of the above problems,this paper improves the existing adaptive filtering algorithm and improves the performance of the algorithm.Firstly,this paper summarizes the traditional adaptive filtering algorithm and analyzes the advantages and disadvantages of several classical adaptive filtering algorithms.Then the idea of decorrelation is combined with the idea of M estimation algorithm,and they are introduced into the traditional algorithm,and an improved adaptive algorithm for proportional decorrelation M-estimae is derived.The algorithm has good convergence performance for the relevant input signals in the environment of impact noise,and has good robustness.In this paper,the superiority of the improved proportional M-estimae adaptive algorithm is verified by software simulation experiments.Second,in the echo cancellation problem,the input signal is typically a highly correlated speech signal and the impulse response of the system is sparse.The affine projection(AP)algorithm is proposed based on the normalized least mean square algorithm and can effectively target the relevant signals.In recent years,the correntropy induced metric(CIM)theory has been proved to be effective for sparse systems.Therefore,this paper combines the M-estimate with thecorrentropy induced metric theory and introduces it into the affine projection algorithm.The M-estimate affine projection algorithm with the correntropy induced metric is verified by simulation experiments.The proposed algorithm has goodperformance for the sparse system identification of the input signal in the mixed noise environment.Finally,in order to solve the contradiction problem between fast convergence and low steady-state deviation,this paper uses the idea of variable step size to improve the improved proportional decorrelation M-estimate algorithm and the M-estimation affine projection algorithm with correntropy induced metric.Two variable step size adaptive filtering algorithms are proposed,and the effectiveness of the algorithms are verified by computer simulations.