Design of Privacy-Preserving Estimators Under Prior Information Exposure
Abstract
State estimation is widely used in networked dynamical systems, but released estimates may inadvertently reveal sensitive information about private state variables. Existing privacy-preserving estimation frameworks often do not explicitly account for adversarial prior knowledge. Motivated by this gap, we study privacy-preserving state estimation for discrete-time linear stochastic systems under prior information exposure using pointwise maximal leakage (PML). We first reveal a privacy anti-optimality property of the Kalman filter: in the absence of additive release noise, the steady-state Kalman filter maximizes PML privacy leakage among the considered class of stable linear estimators. We further establish a nontrivial lower bound on the steady-state estimation error enforced by (ε,δ)-PML privacy. We then derive sufficient release-noise conditions that guarantee (ε,δ)-PML privacy, first for the Kalman filter and then for stable linear estimators. Finally, a convex semidefinite program is formulated for a joint design of the estimator gain and release noise covariance, providing a tractable privacy-preserving estimator with an explicit upper bound on the steady-state estimation error. Simulations on a source--load power system demonstrate the proposed privacy--utility tradeoff.
Related
- Differentially Private Distributed Optimization via the Intrinsic Randomness of Zeroth-Order Estimators: Sampling Geometry, Convergence, and Privacy Guarantees
- Toward Human-Perceptive 6G: Privacy-Preserving Network Intelligence from Human Dynamics
- Privacy Preserving Gossip Learning
- Privacy-Preserving Causal Meta-Mediation Analysis with Survival Outcomes
- SSTQ:Privacy-Preserving Vector Quantization via Subsampled Stochastic TurboQuant
BibTeX
@misc{liu2026design,
title = {{Design of Privacy-Preserving Estimators Under Prior Information Exposure}},
author = {Le Liu and Yu Kawano and Ming Cao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16556},
eprint = {2610.16556},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16556},
}
RIS
TY - UNPB
TI - Design of Privacy-Preserving Estimators Under Prior Information Exposure
AU - Le Liu
AU - Yu Kawano
AU - Ming Cao
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16556
UR - https://arxiv.org/abs/2610.16556
AB - State estimation is widely used in networked dynamical systems, but released estimates may inadvertently reveal sensitive information about private state variables. Existing privacy-preserving estimation frameworks often do not explicitly account for adversarial prior knowledge. Motivated by this gap, we study privacy-preserving state estimation for discrete-time linear stochastic systems under prior information exposure using pointwise maximal leakage (PML). We first reveal a privacy anti-optimality property of the Kalman filter: in the absence of additive release noise, the steady-state Kalman filter maximizes PML privacy leakage among the considered class of stable linear estimators. We further establish a nontrivial lower bound on the steady-state estimation error enforced by (ε,δ)-PML privacy. We then derive sufficient release-noise conditions that guarantee (ε,δ)-PML privacy, first for the Kalman filter and then for stable linear estimators. Finally, a convex semidefinite program is formulated for a joint design of the estimator gain and release noise covariance, providing a tractable privacy-preserving estimator with an explicit upper bound on the steady-state estimation error. Simulations on a source--load power system demonstrate the proposed privacy--utility tradeoff.
ER -