Privacy-Preserving Distributed Maximum Likelihood Estimation via State Decomposition

This study deals with collaborative yet privacy-preserving estimation algorithms in a sensor network. In particular, the sensing agents sample from Gaussian densities with heterogeneous private covariances, and aim to cooperatively compute the maximum likelihood estimate (MLE) of the common mean. To maintain accuracy and minimize computational load, we adopt the state decomposition (SD) approach that splits the estimated variable into private and public components. First, we design a privacy attack model (PAM) to show that the existing SD-based privacy-preserving algorithm for dynamic consensus does not remain simultaneously private and converge with convergent inputs. To address this issue, we modify the existing continuous-time distributed SD algorithm for discrete-time networked updates with an additional initial mixing step and bounded inputs. When true covariances are known, the algorithm computes the mean MLE estimate while keeping the data and covariances private, and converges at the same rate as the non-private, centralized setting. When agents are estimating covariances locally, the algorithm estimates the mean MLE while keeping the local covariances private and maintains the same convergence rate as the local estimates. The rate compared to local estimates depends on the network structure. In simulations, the estimates from the proposed algorithms converge faster than the sample averaging and standard consensus methods.