| Adaptive filtering algorithms play a fundamental role in numerous signal-processing applications,including array systems,radar systems,communication systems,biomedical signal processing,and other fields.Conventional adaptive filtering algorithms are usually derived based on second-order moment statistics,which achieve good performance in Gaussian environments.However,in practical applications,the noise environment may be non-Gaussian with an impulsive nature.In such cases,the performance of second-order moment-based algorithms may degrade or even fail to work properly.To address this challenge,in this thesis,we study adaptive filtering algorithms and their performance analysis in the presence of non-Gaussian/impulsive noise.Specifically,the thesis first derives the generalized LMS and generalized RLS adaptive filtering algorithm frameworks respectively.Within this framework,adaptive filtering algorithms demonstrate effective performance across various noise environments when designers employ a suitable error nonlinearity cost function.The utilization of suitable cost functions within this framework yields algorithms with different convergence speeds,noise suppression capabilities,computational complexities,and different filtering accuracy.These variations are fundamentally influenced by the gradient functions’ characteristics associated with the chosen nonlinear error cost functions.Based on the aforementioned frameworks,six types of new adaptive filtering algorithms based on error nonlinearity cost functions are proposed to address different challenges encountered in non-Gaussian/impulsive noise environments.These include,(1)To solve the problem of performance degradation of the adaptive filtering algorithm for jointly cyclostationary signals based on the minimum time-averaged mean square error(TA-MSE)criterion in an impulse noise environment,a method based on the fractional moment of the error signal is proposed.A minimum time-averaged fractional moment(TA-LMP)algorithm is proposed,and the performance of the algorithm is analyzed using Taylor series expansion.(2)Developing a novel robust half-quadratic criterion(HQC)adaptive filtering algorithm by utilizing a new convex cost function.The proposed HQC introduces a more effective performance surface,allowing a gradient-based strategy to provide significant performance improvements in convergence speed and robustness against impulsive noise.Furthermore,to enhance the performance of the HQC adaptive filter,a variable step-size(VSS)version,the VSS-HQC algorithm,has also been introduced.(3)The RLMLS cost function and the maximum versoria criterion(MVC)function are not convex functions for all possible error signals.Thus,to address this problem,by expanding the convexity range of these methods,a generalized,robust logarithmic family(GRLF)framework by combining these two functions,and the corresponding GRLF-based adaptive filters called least mean square based-GRLF(GRLF-LMS)and least absolute difference-based-GRLF(GRLF-LAD)algorithms are designed.The performance analysis of these algorithms is performed using the Taylor series.(4)To further improve the performance of the constrained adaptive filtering algorithm in the non-Gaussian impulse noise environment,a constrained robust least mean logarithm(CRLMLS)and standard constrained MVC(CMVC)algorithms are studied.The performance analysis of these algorithms is analyzed in both Gaussian and Gaussian noise environments.(5)To tackle the issue of performance degradation of the diffusion recursive RLS method in a non-Gaussian impulse noise environment,a robust diffusion recursive GCMSF algorithm(R-DRGCMSF)based on the generalized correntropy-based modified sigmoid function(GCMSF)maximization criterion is proposed.It improves the steady-state performance of the and the convergence speed of the algorithm.When the system parameters in the distributed system are sparse,a robust proportional diffusion recursive GCMSF algorithm(RP-DRGCMSF)is further proposed by selecting different scaling factors for different system parameters and the performance of the algorithm is analyzed.(6)Adaptive filtering algorithm-based direction of arrival(DOA)estimation algorithm is proposed to address the DOA estimation issue when both input and output of the array system are affected by non-Gaussian noise interference.This method relies on the EIV model and the generalized total maximum Versoria(GTMV)criterion.Additionally,a variable step-size GTMV algorithm(VSS-GTMV)is introduced to enhance the convergence speed and reduce the steady-state mean square error of the algorithm.The various algorithms mentioned above have been analyzed and compared through relevant simulation experiments.The results indicate that the proposed algorithms exhibit excellent performance in different distributions of impulsive noise environments.Furthermore,the theoretical analysis of algorithm performance aligns well with the actual simulation results,confirming the accuracy of the theoretical analysis. |
