Secure Information Fusion using Local Posterior for Distributed Cyber-Physical Systems

In modern distributed cyber-physical systems (CPS), information fusion often plays a key role in automate and self-adaptive decision making process. However, given the heterogeneous and distributed nature of modern CPSs, it is a great challenge to operate CPSs with the compromised data integrity and unreliable communication links. In this paper, we study the distributed state estimation problem under the false data injection attack (FDIA) with probabilistic communication networks. We propose an integrated ”detection + fusion” solution, which is based on the Kullback-Leibler divergences (KLD) between local posteriors and therefore does not require the exchange of raw sensor data. For the FDIA detection step, the KLDs are used to cluster nodes in the probability space and to partition the space into secure and insecure subspaces. By approximating the distribution of the KLDs with a general $\chi ^2$ distribution and calculating its tail probability, we provide an analysis of the detection error rate. For the information fusion step, we discuss the potential risk of double counting the shared prior information in the KLD-based consensus formulation method. We show that if the local posteriors are updated from the shared prior, the increased number of neighbouring nodes will lead to the diminished information gain. To overcome this problem, we propose a near-optimal distributed information fusion solution with properly weighted prior and data likelihood. Finally, we present simulation results for the integrated solution. We discuss the impact of network connectivity on the empirical detection error rate and the accuracy of state estimation.