Distributed State Estimation for Discrete-Time Linear Systems over Directed Graphs: A Measurement Perspective

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.

💡 Research Summary

This paper addresses the problem of distributed state estimation for discrete‑time linear systems observed by a network of sensors whose communication topology is a directed, strongly‑connected graph. Under the collective observability assumption (the overall system (C, A) is observable even if no single sensor can observe the full state), the authors propose a novel consensus‑based distributed filter that fuses raw local measurements rather than intermediate estimates. The key innovation is an “augmented leader‑following” information‑fusion scheme: each sensor i constructs an estimate of sensor j’s measurement, denoted (z_{ij}^{(0)} = C_j A \hat x_i^{(k-1)}), and then iteratively refines these estimates through l consensus steps. The update rule for the l‑th step is

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