  In this paper, we present an optimization-based formulation for
privacy-utility tradeoff in the Ensemble and Unscented Kalman filtering
framework, with a focus on space situational awareness. Privacy and utility are
defined in terms of a lower and an upper bound on the state estimation error
covariance, respectively. Synthetic sensor noise is used to satisfy these
bounds and is determined by solving an optimization problem. Given privacy and
utility bounds, we present optimization problem formulations to determine a)
the maximum noise for which utility is satisfied or the estimation errors are
upper-bounded, b) the minimum noise for which privacy is satisfied or the
estimation errors are lower-bounded, c) the optimal noise that satisfies
utility constraints and maximizes privacy, and d) the optimal noise that
satisfies privacy constraints and maximizes utility. We demonstrate application
of these formulations to the tracking of the International Space Station, and
highlight the optimal privacy vs utility tradeoff for this dynamical system.

Optimization and Control