It is an effective way to use the stochastic distributed control theory to solve filtering problems for non-Gaussian systems.Minimum entropy filtering is one of the representative results.The state estimation method based on the minimum entropy criterion can fully characterize the randomness of the estimation error,which is more suitable than the mean-variance-criterion based states estimation method.However,there are some problems for the minimum entropy filtering theory,such as,owing to the shift-invariant of the entropy,only the randomness of the estimation error can be minimized while the magnitude may not be convergent to zero.In order to solve this problem,this paper presents a novel central error entropy criterion (CEEC) to investigate the filtering problem for linear non-Gaussian systems.Firstly,based on the minimum entropy criterion,the filtering design method is proposed by using the nonparametric estimation theory and stochastic gradient decent method.Moreover,the convergence of the estimation error system is analyzed.Then,a novel CEEC is formulated,which is the weighted sum of information potential and correntropy.Maximizing the information potential can minimize the randomness of estimation error globally;and maximizing the correntropy can fix the peak of the error probability density function (PDF) close to zero.Finally,a numerical example is given to show that the CEEC based filtering is superior to the MEE based filtering.