A Two-Stage Architecture for Differentially Private Kalman Filtering and LQG Control
This addresses privacy-preserving monitoring and control for large-scale systems like intelligent transportation, but it is incremental as it builds on existing differential privacy methods.
The paper tackles the problem of Kalman filtering and LQG control under differential privacy constraints by proposing a two-stage architecture that aggregates agent signals before adding noise, showing significant performance improvements over input perturbation schemes as the number of signals increases, with optimal aggregation computed via a semidefinite program.
Large-scale monitoring and control systems enabling a more intelligent infrastructure increasingly rely on sensitive data obtained from private agents, e.g., location traces collected from the users of an intelligent transportation system. In order to encourage the participation of these agents, it becomes then critical to design algorithms that process information in a privacy-preserving way. This article revisits the Kalman filtering and Linear Quadratic Gaussian (LQG) control problems, subject to privacy constraints. We aim to enforce differential privacy, a formal, state-of-the-art definition of privacy ensuring that the output of an algorithm is not too sensitive to the data collected from any single participating agent. A two-stage architecture is proposed that first aggregates and combines the individual agent signals before adding privacy-preserving noise and post-filtering the result to be published. We show a significant performance improvement offered by this architecture over input perturbation schemes as the number of input signals increases and that an optimal static aggregation stage can be computed by solving a semidefinite program. The two-stage architecture, which we develop first for Kalman filtering, is then adapted to the LQG control problem by leveraging the separation principle. Numerical simulations illustrate the performance improvements over differentially private algorithms without first-stage signal aggregation.