Research On Distributed Adaptive Filtering Algorithms In Non-gaussian Noise Environment

In recent years,distributed adaptive filtering theory has been one of the popular researches in signal processing,which is widely applied to environment monitoring,disaster relief management,source localization,wireless sensor network,frequency estimation in power system and so on.So far,distributed filtering algorithms based on the diffusion topology have been intensively studied.The merits of this topology is that even if some nodes in the network fail to communicate or encounter link failure,the diffusion strategy still obtains good estimation performance.Aimed at problems such as fixed step-size,correlated input signal,noisy input,sparse system,etc,some scholars conducted intensive research and put forward effective improved algorithms.As is known to all,in practical applications,the background noise with non-Gaussian characteristics is often encountered,which may result in the performance deterioration of algorithms that are based on the mean square error criterion.However,at the present stage,there is still great space of algorithm improvement in the presence of non-Gaussian noise.Therefore,this dissertation focuses on studying the distributed filtering algorithms in non-Gaussian noise environment and their applications.The main work is summarized as follows:(1)In order to improve the performance of distributed subband filtering algorithm in impulsive noise environment,by applying the sign function which can suppress the error with large magnitude,two distributed filtering algorithms are proposed:?Based on the cost function in the form of sign-error,by minimizing the mean square deviation(MSD),a variable regularization parameter distributed sign subband filtering algorithm is proposed,which obtains small regularization parameter in the initial stage and large regularization parameter in the steady-state,guaranteeing fast convergence as well as low steady-state misalignment.Meanwhile,a reset mechanism for regularization parameter is designed to improve the algorithm tracking capability.?By introducing the proportionate matrix strategy,and taking into account the l₁-norm and l₀-norm constraints,two distributed proportionate sign subband filtering algorithms are proposed,which speeds up the algorithm convergence in the sparse system.In addition,the mean convergence of two proportionate algorithms is analyzed.(2)Based on the continuous mixed p-norm strategy,and aimed at the disadvantage of the mathematical model for regulating different error norms,this dissertation designs a novel linear function model,and proposes the variable step-size diffusion continuous mixed p-norm filtering algorithm.Meanwhile,this dissertation discusses the influence of the slope on the algorithm performance,and briefly studies how to select the value of the slope under different impulsive noise environments.Besides,the computational complexity as well as the mean convergence is analyzed.(3)To address the problem of choosing a reliable kernel width in practice,a novel variable kernel width diffusion maximum correntropy criterion algorithm is proposed.The proposed kernel width is derived by minimizing the square deviation,and updated in the moving-average method,which ensures that the algorithm can obtain a smooth kernel width at each iteration.Meanwhile,a novel reset mechanism is designed for the kernel width.When the impulsive noise occurs,the proposed mechanism is able to initialize the kernel width,thereby improving the algorithm tracking capability.Besides,this dissertation performs the mean stability analysis for the proposed algorithm.(4)Aimed at improving the stability and convergence of diffusion complex-valued filtering algorithms in non-Gaussian noise environment,based on the strictly linear model and widely linear model between the input and output,two robust diffusion complex-valued filtering algorithms are respectively proposed,which are derived based on the phase error p-norm cost function:?The diffusion complex-valued filtering algorithm based on the strictly linear model is suitable for dealing with circular input signal(covariance matrix is non-zero,pseudo-covariance matrix is zero)as this algorithm only exploits the information of covariance matrix.Meanwhile,the corresponding frequency estimator is derived,which is applicable to the frequency estimation of balanced three voltages.?The diffusion complex-valued filtering algorithm based on the widely linear model is suitable for dealing with non-circular input signal(covariance and pseudo-covariance matrice are non-zero),which is able to exploit the full information of the input covariance and pseudo-covariance matrice,thereby improving the overall performance.Similarly,the corresponding frequency estimator is derived,which is applicable to the frequency estimation of inbalanced three voltages.Besides,this dissertation performs the stability analysis for the proposed algorithms.Furthermore,in order to test if the impulsive noise occurs at node,the adaptive p-norm strategy is proposed.Simulation experiments designed for frequency estimation in power system show that the proposed algorithms are able to estimate the system frequency faster and more stably in non-Gaussian noise environment.