Adaptive Filtering Algorithm In The Presence Of ?-stable Noise

Conventional adaptive filtering algorithms are usually based on the second-order moment statistics,which achieve good performance in Gaussian environments.However,in practical applications,the noise environment may non-Gaussian,with the pulse nature.The?-stable noise is an ideal mathematical model to describe the impulse noise with non-Gaussian components,which can well model the ?-stable noise.In such case,the performance of second-order moment based algorithms may degrade.To improve the performance of adaptive filtering algorithms,in this dissertation,we study adaptive filtering algorithms and their applications in the presence of ?-stable noise.Our works can be summarized as follows:1)Based on the study of the convex combination least mean square algorithm,two improved convex combination filters for combating impulsive interferences are proposed.? Convex combine the normalized signl algorithm to accerlerate the convergence rate and achieve small steady-state error.Moreover,the tracking weight transfer strategy is proposed,which further improves the performance of the algorithm at the transition stage.? Convex combine two nonlinear Volterra filters are convexly to develop two novel adaptive filters based on convex combination scheme.Besides,the linear and quadratic kernels are adapted by the normalized p-norm algorithm to enhance the nonlinear modeling capability of the algorithm.2)In the context of nonlinear Volterra system identification with ?-stable noise,two novel nonlinear adaptive algorithm are developed.? A new recursive p-norm logarithm transformation strategy is proposed,which improves the robustness of the algorithm under the impulsive noise environments.? An improved recursive p-norm logarithmic transformation strategy is proposed.To further enhence the tracking capability of the algorithm,a new variable-forgetting-factor scheme based on robust statistics is developed.3)To solve the stablity problem and improve the performance of the exising active noise control algorithms,two active impulse noise control algorithms are proposed:? Using the robustness performance of the maximum correntropy against outliers,a new recursive maximum entropy-x impulse noise active control algorithm is designed based on the recursive-x algorithm.In addition,to avoid the difficulty of parameter selection of kernel width in practical applications,an adaptive kernel width scheme is proposed.? Consider the nonlinearity of the active impulse noise control system,a nonlinear active impulse control algorithm based on Volterra series expansion is proposed,which utilizes the continuous p-norm scheme with logarithmic transformation,without parameter selection and a priori knowledge of noise.4)To enhance the robustness of the existing adaptive beamforming algorithms,a newrobust beamformer for combating ?-stable noise is designed.This beamformer is based on the recursive continuous p-norm strategy and has superior performance in various ?-stable noise environments.Secondly,a beamformer with recursive strategy is proposed based on the maximum correntropy criterion.Moreover,the theoretical performance behavior is analyzed in detail.5)To accerlerate the convergence rate of the distributed adaptive algorithm in the presence of ?-stable noise,a robust normalized p-norm distributed filtering algorithm is proposed.In this algorithm,the error signal is considered in the normalized step size parameter,which enhances the convergence speed in initial convertence stage.Secondly,two novel nonlinear distributed filters are proposed for the nonlinear distributed networks.Based on the SOV filter,the former uses the proposed p-norm logarithmic cost function to update the weight vector,and achieves good nonlinear modeling ability.The latter also performs weight vector updates based on the cost function,and uses interpolated Volterra filters.Compared with the former,it sacrifices the steady-state performance,and significantly reduces the computational complexity,and therefore easy implementation.