Distributed Fusion Estimation with Protecting Exogenous Inputs

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.