Minimum Total Error Entropy Method For Distributed Frequency Estimation

Frequency estimation,as a classical problem in signal processing,arises in a variety of practical applications.Most of the existing frequency estimation methods perform the frequency estimation task by a single processing node.In some instances of real applications,we need distributed frequency estimation over networks.Recently,the distributed notch filtering methods were proposed for this purpose.These methods take the second-order statistics of the errors as the objective function.However,the second-order statistics,can not make full use of the information of data for the cases with non-Gaussian noise.It is reported that the information-theoretic learning provides a more suitable framework for signal processing under non-Gaussian noise.It designs the objective function based on information theoretic measures and considers the distribution information of data comprehensively,not only the second-order statistics,so it can achieve better performance.In this paper,we combine the distributed notch filtering method and information-theoretic learning,aiming at the frequency estimation of real sinusoidal signal and complex sinusoidal signal under non-Gaussian noise,and propose two distributed frequency estimation algorithms based on the minimum total error entropy and the minimum complex total error entropy,respectively.Specifically,for the frequency estimation of real sinusoidal signals under non-Gaussian noise,we first present the problem formulation under the framework of the distributed notch filtering method,and then design the distributed objective function based on the total error entropy criterion.Finally,we achieve iteration solution of the objective function through the stochastic gradient algorithm and the diffusion cooperative method.Besides,considering the sparsity of the parameters to be estimated,we add sparse constraints to the above objective function,and propose a sparse distributed notch filtering algorithm based on the minimum total error entropy.For the frequency estimation of complex sinusoidal signals under non-Gaussian or non-circular complex noise,we first generalize the total error entropy criterion to complex domain to present the complex total error entropy criterion,and then propose a minimum complex total error entropy based distributed notch filtering algorithm.A series of simulation experiments are carried out,which show that the proposed distributed frequency estimation algorithms have better estimation performance than the distributed frequency estimation algorithms based on second-order statistics.