Distributed State Estimation for Discrete-Time Linear Systems over Directed Graphs: A Measurement Perspective
This addresses distributed estimation in networked systems, offering incremental improvements in performance guarantees for directed communication topologies.
The paper tackles distributed state estimation for linear systems over directed graphs by proposing a consensus-based filter with an augmented leader-following strategy, achieving uniformly bounded error covariance and exponential convergence rates under specific conditions.
This paper proposes a novel consensus-based distributed filter over directed graphs under the collectively observability condition. The distributed filter is designed using an augmented leader-following information fusion strategy, and the gain parameter is determined exclusively using local information. Additionally, the lower bound of the fusion step number is derived to ensure that the estimation error covariance remains uniformly upper-bounded. Furthermore, the lower bounds for the convergence rates of the steady-state performance gap between the proposed filter and the centralized filter are provided as the fusion step number approaches infinity. The analysis demonstrates that the convergence rate is at least as fast as exponential convergence, provided the communication topology satisfies the spectral norm condition. Finally, the theoretical results are validated through two simulation examples.