Research On Robust Algorithms Based On Adaptive Filtering

The robustness of adaptive filtering algorithm,which plays an important role in the field of signal processing,is one of the most active research topics in the field of adaptive signal processing.Seeking fast convergence speed,low computational complexity and robust adaptive filtering algorithms have attracted much attention by academic and industry researchers all over the world.In order to overcome the robustness problem of the traditional adaptive filtering algorithm based on MSE cost function will become worse in a non-Gaussian Noise,we propose several improved robust adaptive filtering algorithms in this dissertation and the experimental results verify the effectiveness of our proposed robustness algorithm.The main contents of this thesis are summarized as follows:1.A sparse adaptive filtering algorithm based on improved proportionate least mean p-power(PLMP)has been proposed,which uses the least mean p-power as the cost function and employs LMP instead of MSE to identify the sparse system.the mean and mean square convergence of the proposed PLMP algorithm are also derived.Compared with the standard normalized PNLMS algorithms,the proposed PLMP algorithm can achieve much better performance in terms of the mean square deviation,especially in the presence of impulsive non-Gaussian noises.2.Aiming at the problem of the performance of the traditional sparse adaptive filtering method can be seriously attenuated in the non-Gaussian case,A convex regularized recursive maximum correntropy algorithm(CR-RMC)based on recursive least squares(RLS)is proposed.By combining the general convex function with the maximum correntropy criterion(MCC)as the cost function,the CR-RMC algorithm is derived.The experimental results show that the CR-RMC can significantly outperform the original recursive maximum correntropy(RMC)algorithm in terms of sparse system identification.Furthermore,compared with the convex regularized recursive least squares(CR-RLS)algorithm,the new algorithm shows strong robustness against impulsive noise.The CR-RMC also performs much better than other LMS-type sparse adaptive filtering algorithms based on MCC.3.A nonlinear adaptive filtering algorithm,called the nonlinear spline adaptive filtering under maximum correntropy criterion(SAF-MCC)based on MCC has been proposed to solve the problem of non-Gaussian noise performance degradation based on minimum mean square error of nonlinear system modelling and identification.The MCC is used to replace the minimum mean square error criterion(MSE),and the step sizes of SAF-MCC and SAF-LMS algorithm are verified same,and the condition of the convergence step of SAF-MCC algorithm is also obtained.The experimental results show that the performance of SAF-MCC is better than that of non-linear spline adaptive filter(SAF-LMS)based on minimum mean square error criterion in non-Gaussian noise environment.4.An adaptive convex combination filter called adaptive convex combination filter under minimum error entropy(CMEE)based on minimum error entropy(MEE)is proposed to solve the problem that the adaptive filter algorithm for MEE criterion is difficult to balance both the convergence rate and the steady-state mean square error.The filter is operated by two filters based on the MEE criterion that are independently run and have different steps,so that both rapid convergence(step larger filter)and lower error(smaller step size filter)can be considered.Compared with the CMCC under the maximum correlation entropy standard,the experimental results show that the proposed algorithm can achieve fast convergence speed under the desired performance.