Designing Consensus-Based Distributed Filtering over Directed Graphs

TL;DR

The paper tackles distributed state estimation over directed graphs under collective observability by introducing a consensus-on-only-measurement distributed filter (COMDF) that fuses neighbors' measurements via an augmented leader-following scheme with $l$ consensus steps. It provides two local-parameter design strategies (distributed and unified) to ensure stability, derives a lower bound on the required fusion depth $l$ for a uniformly upper-bounded error covariance, and analyzes both convergence (with $\rho(G)<1$) and transient performance, showing the distributed filter approaches the centralized estimator as $l\to\infty$. Theoretical results are validated through simulations, demonstrating exponential decay of the performance gap relative to a centralized filter and highlighting reduced communication cost and privacy advantages. The work offers a principled framework for robust, measurement-only distributed filtering on directed networks, with practical implications for sensor networks and multi-agent systems.

Abstract

This paper proposes a novel consensus-on-only-measurement distributed filter over directed graphs under the collectively observability condition. First, the distributed filter structure is designed with an augmented leader-following measurement fusion strategy. Subsequently, two parameter design methods are presented, and the consensus gain parameter is devised utilizing local information exclusively rather than global information. Additionally, the lower bound of the fusion step is derived to guarantee a uniformly upper bound of the estimation error covariance. Moreover, the lower bounds of the convergence rates of the steady-state performance gap between the proposed algorithm and the centralized filter are provided with the fusion step approaching infinity. The analysis demonstrates that the convergence rate is, at a minimum, as rapid as exponential convergence under the spectral norm condition of the communication graph. The transient performance is also analyzed with the fusion step tending to infinity. The inherent trade-off between the communication cost and the filtering performance is revealed from the analysis of the steady-state performance and the transient performance. Finally, the theoretical results are substantiated through the validation of two simulation examples.

Figures (3)

• Figure 1: The diagram of the communication topology.
• Figure 2: Illustration figure for the steady-state performance of COMDF with the increasing fusion step $l$.
• Figure 3: Illustration figure for the performance of four algorithms with the increasing time step $k$.

Theorems & Definitions (26)

• Remark 1
• Definition 1
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4
• Remark 2
• Remark 3
• Remark 4
• Proposition 1