Protecting privacy of topology in consensus networks

Consider a set of agents implementing the discrete time consensus algorithm. At each time step, all agents also transmit their states to a central estimator that wishes to identify the underlying topology and eigenvalues of the network. It does so by using a nonlinear least squares (NLS) algorithm to identify the state evolution matrix used in the consensus algorithm. We present a mechanism to protect the differential privacy of this topology from an eavesdropper who may have unauthorized access to the estimator. In this mechanism, every agent purposely adds noise to its measurements before transmission to the estimator. The noise is designed to ensure that the eavesdropper cannot uniquely identify the topology with a specified confidence level. Numerical results are presented to describe the corresponding trade-off in estimation accuracy as a function of the level of differential privacy achieved.