Differentially Private Kalman Filtering

This chapter is concerned with the design of model-based differentially private filters, when the privacy-sensitive signal to be processed can be modeled as the output of a linear finite-dimensional system with publicly known parameters. Such models can capture for example known physical laws that govern the behavior of the input signal, e.g., a kinematic model linking position and velocity measurements obtained from individual users. In the absence of privacy constraint, Kalman filtering provides a solution to the problem of estimating the state of the system while minimizing the mean square error. We adapt here this filter to accommodate differential privacy constraints, for various scenarios involving either individual or collective signals.