Low Complexity Kernel Recursive Error Entropy Algorithms And Their Applications

Adaptive filter(AF)can adaptively adjust the system parameters to match the characteristics of the system according to the changes of the external unknown environment.Therefore,researchers are enthusiastic about studying the structure of filters.Adaptive filters are widely used in signal processing,target tracking and positioning,echo cancellation,system identification,chaotic time series prediction and other fields.However,in real life,many problems are nonlinear,and the traditional AF performs poorly in dealing with such nonlinear problems.In order to deal with the nonlinear problem,the kernel adaptive filter(KAF)algorithm is proposed.However,in real life,non-Gaussian noise is widespread,and with the continuous increase of data,the network size of the KAF algorithm continues to grow,resulting in computational and storage burdens,posing higher requirements for algorithm research.Based on these problems,under the condition of information theory learning(ITL),Integrating the error entropy criterion,maximum correntropy criterion,and kernel recursive least squares algorithm,some robust adaptive filtering algorithms that can solve the above problems are proposed.The key research contents of this paper include:(1)The traditional KAF algorithm is based on the mean square error(MSE)criterion of second-order statistical characteristics,and its performance is better only in Gaussian environment;At the same time,KAF establishes a linear growth radial basis function(RBF)network,which leads to an increase in computational complexity and memory consumption.This paper proposes a quantized kernel recursive minimum error entropy(QKRMEE)algorithm based on the minimum error entropy(MEE)criterion.This algorithm uses the minimum error entropy criterion to replace the minimum mean square error as the target criterion.After a series of derivation,a quantized kernel recursive minimum error entropy algorithm is proposed,and its performance is analyzed.Finally,the simulation results show that the algorithm has better filtering performance in non-Gaussian noise environment by comparing with other algorithms.(2)Because the adaptive filtering algorithm of the traditional generalized maximum correntropy(GMC)criterion cannot deal with the problem of non-zero mean noise environment,the kernel recursive generalized maximum correntropy with variable center(KRGMCVC)algorithm has been proposed.The algorithm has been derived,and experimental simulation results show that it has better robustness under non zero mean noise conditions,while solving nonlinear signal processing problems.In order to reduce the growth of the size of RBF network,a quantized kernel recursive generalized maximum correntropy with variable center(QKRGMCVC)algorithm has been proposed.The simulation results show that the QKRGMCVC algorithm greatly approximates the accuracy of the KRGMCVC algorithm,effectively reduces the computational complexity,and effectively inhibits the growth of the size of the RBF network.