A Probabilistic Framework for Moving-Horizon Estimation: Stability and Privacy Guarantees

A Numerical Verification Framework for Differential Privacy in Estimation

“…At each time step k, the system state is perturbed by a uniform distribution over [−0.001, 0.001] 2 . The distribution of initial conditions is given by a truncated Gaussian mixture with mean vector (5, 0, 0, 2.5) and such that diam(K 0 ) in Theorem 4 of [9] is 0.1.…”

“…1) Obtain a tractable, numerical test procedure to evaluate the differential privacy of an estimator; while providing quantifiable performance guarantees of its correctness. 2) Verify numerically the differential-privacy guarantees of the W 2 -MHE filter of [9]; and compare its performance with that of an extended Kalman filter. 3) Evaluate the differences in privacy/estimation when the perturbations are directly applied to the sensor data before the filtering process is done.…”

“…In particular, the work [8] develops the concept of differential privacy for Kalman filter design. The work [9] proposes a more general moving-horizon estimator via a perturbed objective function to enable privacy. To the best of our knowledge, all of these works propose sufficient and theoretical conditions for differential privacy.…”

“…Denote this set as R [0,k] . In [9], this set is bounded as all disturbances and initial distribution are assumed to have a compact support. However, R [0,k] can be unbounded for other estimators.…”

SoK: Differential privacies

“…Finally, blowfish privacy [84,86], use a "policy graph" specifying which pairs of tuple values must be protected. Others use a "distance function" between datasets, and neighbors are defined as datasets a distance lower than a given threshold; this is the case for DP under a ∆-neighborhood, introduced in [63] and adjacent DP, introduced in [108]. This distance can also be defined as the sensitivity of the mechanism, like in sensitivity induced DP [142], or implicitly defined by a set of constraints, like in induced DP [105].…”