Distributed encryption fusion estimation against full eavesdropping

Abstract

This paper is concerned with the privacy-preserving distributed fusion estimation problem against full eavesdropping, where the eavesdropper can completely and precisely obtain the information transmitted from local sensors to legitimate user. To depict the privacy-preservation level, we propose novel confidentiality index and rank based on the estimation performances of both eavesdropper and legitimate user. Then, a new encryption approach, which is composed of two-step sequential noise injections, is developed such that the highest confidentiality rank can be achieved. It is rather remarkable that the weighting fusion matrix, which is unique in the distributed fusion estimation field, is utilized to design perturbation noises. In this case, the compensating fusion estimator of legitimate user can effectively reduce the adverse impact of disturbance with null space design in the proposed approach. Moreover, the probability distribution of inserted noises simultaneously satisfies the differential privacy, which strongly enhances the confidentiality level of local state estimates. Finally, an illustrative example is provided to verify the effectiveness and advantages of the proposed methods.