Chain-Reaction-Based Privacy-Preserving Distributed Kalman Filtering

This paper investigates a privacy-preserving distributed estimation problem. A coding scheme is proposed, which randomly transmits residuals, local estimates, or encrypted local estimates, to prevent privacy leakage. Recovering the current local estimate from the residual requires the previous estimate, leading to a chained structure in the transmitted messages. The eavesdropper fails to decrypt the encrypted local estimate, and consequently, their estimation error diverges due to this chain reaction. Theoretically, we derive a sufficient condition for the stability of legitimate nodes based on the Lyapunov theory. Under moderate conditions, we prove that the eavesdropper's estimation error tends to infinity, regardless of how many nodes are eavesdropped on or what type of linear unbiased fusion scheme is employed. Additionally, we derive a set of analytical coding parameters to satisfy the above conditions. Finally, simulations are conducted to verify the effectiveness of the proposed method.