Zero-determinant strategy for distributed state estimation against eavesdropping attacks

In distributed networks, the transmission of state estimates via wireless channels between neighbor nodes is susceptible to interception by eavesdroppers, leading to significant risks to data privacy. Given the substantial energy and bandwidth consumption of data encryption, sensors with limited energy must strategically decide when to encrypt data. Simultaneously, eavesdroppers with similar energy constraints must determine when to intercept transmissions. In this paper, we propose a game-theoretic approach to this security dilemma and introduce a defense strategy based on zero-determinant (ZD) policies. Initially, we model the interaction between sensors and malicious eavesdroppers in the distributed state estimation as an iterative game. Subsequently, we apply ZD strategies to protect both channel and node data, respectively. We further explore how, under these strategies, sensors can unilaterally set the expected payoff of eavesdroppers or coerce a positive correlation with the expected payoff of sensors. Moreover, we analyze how sensors can devise optimal strategies by maximizing their own utility while minimizing that of the opponent, regardless of the actions of the opponent. The feasibility and effectiveness of the proposed methods are validated through numerical simulations.