Distributed Maximum Correntropy Nonlinear Filter With Variance Correction Subject to Deception Attacks

This paper deals with the issue of state estimation for nonlinear non-Gaussian networks suffering from deception attacks. A novel distributed maximum correntropy filter with variance correction is proposed, which consists of local estimation and diffusion fusion. Firstly, the estimates from neighbor nodes are fused to obtain a common prediction estimate, as well as the upper bounds of the corresponding covariances are derived to avoid calculating correlated information. The chi-square test is employed to rectify the inaccurate noise variance caused by non-Gaussian noise and deception attacks. Based on minimum error and maximum correntropy criteria, distinct consensus gains and filtering gain for the local filter are derived. Then, local estimates of neighbor nodes are fused based on covariance intersection to enhance the accuracy of the node itself. The designed distributed structure combines the merits of consensus and diffusion filters, which can further enhance the estimation performance of the whole system. The statistical linearization and the cubature rule are applied to deal with nonlinear functions, avoiding Jacobi matrices and additional uncertain parameters. In addition, it is proved that the filtering covariance is bounded under certain conditions. Finally, simulation results verify the effectiveness and accuracy of the presented algorithm.