| As one of the research hotspots in signal processing,distributed adaptive filters have been widely used in environmental monitoring,disaster relief management,target localization,wireless sensing networks,and frequency estimation of power systems.The distributed adaptive filtering algorithms based on the mean square error(MSE)criterion including second-order statistics suffer from severe performance degradation in the presence of non-Gaussian noises,i.e.,light-tailed sub-Gaussian noises and heavy-tailed super-Gaussian noises.In order to effectively suppress the effect of outliers on the filtering performance under non-Gaussian noises,the robust distributed adaptive filtering algorithms based on non-second order statistics are proposed and have achieved great attention.At present,the robust distributed adaptive filtering algorithms based on stochastic gradient descent(SGD)still suffer from low filtering accuracy and slow convergence speed.To address these issues,a robust distributed adaptive filtering algorithm based on the adaptive gradient(Adagrad)optimization method is proposed in this dissertation.From the optimization point of view,although the recursive distributed adaptive filtering algorithm derived by the least squares method has better filtering performance than the gradient-based distributed adaptive filtering algorithm,it still has higher computational complexity.Therefore,it is significant to study how to reduce the computational complexity of the recursive distributed adaptive filtering algorithm while ensuring its high filtering performance.The main contents of this dissertation are as follows:(1)To improve the robustness and the filtering accuracy of the distributed adaptive filtering algorithms,the diffusion minimum kernel risk sensitive mean p-power loss(DMKRSP)algorithm is proposed based on the kernel risk sensitive mean p-power error(KRSP)criterion and the gradient descent method.In addition,to make full use of the error information,the Adagrad optimization method with a forgetting factor is introduced into DMKRSP,developing the diffusion Adagrad minimum kernel risk sensitive mean p-Power loss(DAMKRSP)algorithm.Compared with the traditional distributed adaptive filtering algorithms,the DMKRSP and DAMKRSP algorithms proposed in this dissertation have higher filtering accuracy and stronger robustness under non-Gaussian noises.(2)To further improve the filtering accuracy,convergence speed and robustness of the gradient-based distributed adaptive filtering algorithm,the recursive distributed adaptive filtering algorithm is derived by using the least-squares method in this dissertation.First,the diffusion recursive minimum Cauchy(DRMC)algorithm is proposed based on the Cauchy loss(CL)criterion,which has higher filtering accuracy under non-Gaussian noises compared with the distributed adaptive filtering algorithms using gradient optimization method.However,the high computational complexity of the DRMC algorithm limits its application in practice.Therefore,to reduce the computational complexity of DRMC algorithm,diffusion recursive minimum Cauchy variant(DRMCV)algorithm is proposed based on matrix inverse lemma and auxiliary formulas.The DRMCV algorithm reduces the running time of the DRMC algorithm by 54.8% without sacrificing the filtering accuracy.Compared with the gradient-based robust distributed adaptive filtering algorithm,the DRMCV algorithm proposed in this dissertation has a similar computational complexity to the gradient-based algorithm while ensuring higher filtering accuracy.Finally,the superiority of the proposed algorithms is verified with different data sets under the interference of impulse noise and mixed noise.(3)To verify the effectiveness of the proposed algorithms from the theoretical aspect,the theoretical analysis of the proposed DMKRSP and DAMKRSP algorithms are performed in terms of both mean performance and mean square performance.The convergence conditions of the proposed algorithms are obtained and the expressions of the steady-state mean square deviation are derived.In addition,the convergence condition of the DRMCV algorithm is also obtained through the theoretical analysis.The simulation results verify that the theoretical values of steady-state mean square deviation of DMKRSP and DAMKRSP algorithms can match their simulated values well,which not only proves the correctness of the theoretical analysis,but also provides a theoretical reference for the parameter selection of the algorithms in practical applications. |
