For wireless sensor networks (WSNs) under false data injection (FDI) attacks, the study focuses on the design problem of an elastic H ∞ filter under privacy protection. In this paper, a privacy protection strategy is investigated to encrypt the information at the next moment while protecting the initial data of the system. Secondly, the wireless sensors are distributed in various positions of the target to be perceived, and there will be several groups distributed in space. The attacker simultaneously attacks the system and the communication links of several sensors. Based on privacy protection, an elastic distributed network is designed, where the purpose of the estimator is to obtain an approximation of the genuine condition information of the system. By introducing the Krein space state model, the distributed estimator is able to estimate the actual state at each moment as accurately as possible. Additionally, by setting up weighted matrix parameters, an alert can be generated for the next FDI attack. Finally, comparative experiments are conducted with systems lacking privacy protection methods to validate the efficacy of the approach for designing distributed estimators.