On differentially private Kalman filtering

The problem of Kalman filtering under a differential privacy constraint is considered in this paper. This problem arises in scenarios where an aggregate statistic must be published in real-time based on privacy-sensitive input signals, which can be assumed to originate from a linear Gaussian model. We propose an architecture combining the differentially private Gaussian mechanism with a linear pre-filter for signal shaping and a Kalman filter for output reconstruction. When the signal shaping block is static, it is shown that the optimum differentially private mechanism following this architecture can be computed using semidefinite programming. Performance improvements over the simpler input perturbation mechanism are illustrated analytically and through computer simulations.