Privacy-Preserving Convergent Dynamic Average Consensus via State Decomposition

This work develops a distributed algorithm to enable cooperative tracking of the average of time-varying signals while preserving their privacy. We discuss the state decomposition approach, which incorporates public and private versions of estimates at each agent. In the presence of convergent inputs, we show that the existing state decomposition algorithm may not preserve privacy for the convergent input splits that allow convergence, and fail to converge for certain admissible splits. Therefore, we present a novel privacy-preserving algorithm that provides the same order of convergence rates on the estimates as that of the input signals. Further, the algorithm preserves privacy by letting a range of feasible input signals yield the same sequence of public variables. Finally, the algorithm is implemented for maximum likelihood estimation of the mean of data sampled by agents from Gaussians with private and unknown covariances.