Distributed Fusion Estimation with Protecting Exogenous Inputs

TL;DR

This paper proposes a differentially private distributed fusion estimation method that injects noise into local estimates to protect exogenous inputs, balancing privacy and estimation accuracy.

Contribution

It introduces a noise injection strategy with optimized covariance matrices and a relaxation approach to solve a non-convex problem, enhancing privacy-preserving fusion estimation.

Findings

Effective noise injection maintains differential privacy.

The relaxation approach efficiently solves the covariance optimization.

Feedback mechanism improves estimation accuracy under privacy constraints.

Abstract

In the context of distributed fusion estimation, directly transmitting local estimates to the fusion center may cause a privacy leakage concerning exogenous inputs. Thus, it is crucial to protect exogenous inputs against full eavesdropping while achieving distributed fusion estimation. To address this issue, a noise injection strategy is provided by injecting mutually independent noises into the local estimates transmitted to the fusion center. To determine the covariance matrices of the injected noises, a constrained minimization problem is constructed by minimizing the sum of mean square errors of the local estimates while ensuring ({\epsilon}, {\delta})-differential privacy. Suffering from the non-convexity of the minimization problem, an approach of relaxation is proposed, which efficiently solves the minimization problem without sacrificing differential privacy level. Then, a differentially private distributed fusion estimation algorithm based on the covariance intersection approach is developed. Further, by introducing a feedback mechanism, the fusion estimation accuracy is enhanced on the premise of the same ({\epsilon}, {\delta})-differential privacy. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed algorithms, and the trade-off between differential privacy level and fusion estimation accuracy.