Privacy Preserving via Secure Summation in Distributed Kalman Filtering

Average consensus is a major operation in distributed Kalman filtering. It requires neighboring nodes to exchange state information with each other, which may result in undesirable private data leakage. Since distributed Kalman filtering requires that the estimate at each time instant is accurate, it brings more challenges to design privacy-preserving scheme for operation. In this article, we design a privacy-preserving scheme for distributed Kalman filtering without the loss of estimation performance, which is also suitable for average consensus or dynamic average consensus of multiagent systems. We first build a secure multihop communication based on an encryption scheme. We then calculate the sum of the states of neighboring nodes with secure summation, which ensures that the state update will not reveal the state of the node to its neighboring nodes. We employ different methods to calculate the sum of the states of neighboring nodes against noncollusive and collusive adversaries. For the noncollusive case, the privacy of the honest nodes is preserved. For the collusive case, if there are too many adversaries, the privacy of the honest nodes could be exposed when accurate distributed Kalman filtering is accomplished. Therefore, we measure the risk of the global system suffering privacy leakage as the privacy index and improve the ability of the system to defend the collusive adversaries by using a group-based method. Some numerical examples are provided to illustrate the effectiveness of the proposed schemes.