Distributed Data-Driven State Estimation for Unknown Linear Systems

This paper investigates the distributed data-driven state estimation for linear Gaussian systems using a sensor network under an indirect data-driven framework, where the system matrices are unknown and the noise covariances are misspecified. First, a distributed data fusion strategy is introduced to collect sufficient data from each sensor to establish a reliable system model. Data informativity for this strategy is analyzed for quantifying how the fusion steps and sample number affect the accuracy of the identified system model. Then, we propose a novel distributed data-driven filter with performance guarantees. Specifically, we derive the performance gap in terms of the fusion steps and sample number between the proposed filter and the distributed consensus-based Kalman filter with known system matrices. Additionally, a tight bound on the estimation error covariance of the filter is derived, and the effect of misspecified noise covariances is revealed. Finally, two numerical examples are presented to validate the effectiveness of the theoretical results.