Distributed Filtering Over Sensor Networks With Byzantine Attacks: A Token Bucket Protocol

In this article, the distributed filtering issue is explored for time-varying state-saturated systems affected by Byzantine attacks over sensor networks. To regulate data transmission, a token bucket protocol (TBP) is utilized, in which the stochastic nature of token consumption arises from variations in packet sizes. Particularly, the measurements are transmitted to the filter only when the available tokens suffice to meet the required consumption. A Byzantine attack model is formulated in which Byzantine nodes arbitrarily alter the measurement signals transmitted to neighboring nodes. The primary objective is to construct an upper bound of the filtering error covariance (FEC) and to compute suitable filter gains by minimizing this bound. Furthermore, the boundedness of the proposed filtering error dynamics is rigorously analyzed via matrix-based theoretical analysis. Finally, numerical simulations are conducted to verify the effectiveness of the proposed algorithm.