Research On Robust Distributed Adaptive Filtering Algorithm Based On Adaption Kernel Width

Distributed adaptive filtering algorithm is a method adaptive estimation to estimate the parameters of interest through the data collected by sensors in distributed networks.It has been widely used in target positioning,intelligent detection and other fields,and is a hot topic in the field of signal processing.However,the widely existed non-Gaussian noise with impulse characteristics in practical applications lead to the serious performance degradation of traditional distributed adaptive filtering algorithms.The Maximum Correntropy Criterion（MCC）based on information theory is a local similarity measure,which can effectively suppress the impact of impulsive abnormal points on the algorithm.Diffusion MCC（DMCC）algorithm is a distributed adaptive filtering algorithm based on MCC criterion.However,the traditional DMCC algorithm neither fully takes advantage of the characteristics of the system itself,nor considers the limitation of fixed kernel width.Therefore,the traditional DMCC algorithm is studied and improved in this thesis.Firstly,this thesis proposes an improved adaption kernel width function based on Gaussian and maximum-value functions,and implements an algorithm that dynamically updates the kernel width of the maximum correntropy criterion according to the error changes during the iteration process.That is,in the initial stage of the iteration,the algorithm selects a smaller kernel width to improve its convergence speed,and in the convergence stage,the algorithm selects a larger kernel width to reduce its steady-state error,thereby effectively easing the contradiction between the convergence performance and steady-state performance of the algorithm.Secondly,the proposed variable kernel width function is applied to the DMCC algorithm,and the idea of sparse proportional matrix is introduced to propose the Adaption Kernel Width Diffusion Proportional Maximum Correntropy Criterion algorithm（DPMCCadapt）.The algorithm can not only suppress the non-Gaussian noise effectively,but also adjust the step size according to the weight coefficient in the iteration process,so as to significantly improve the convergence rate of the algorithm in sparse system.Finally,through reasonable assumptions,the thesis makes a detailed theoretical analysis on the convergence performance and the mean square steady-state performance of the proposed DPMCC_adaptdapt algorithm,and compares the complexity of the proposed DPMCCadapt algorithm with the existing diffusion adaptive filtering algorithm.The theoretical analysis and simulation results show that the DPMCC_adaptdapt algorithm proposed in this thesis has better convergence performance,steady-state performance and tracking performance than the traditional diffusion adaptive filtering algorithm,and has better robustness under non-Gaussian noise,and is suitable for sparse systems with different sparsity.