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

TL;DR

This paper introduces a new distributed filtering method for discrete-time linear systems over directed graphs, ensuring bounded estimation errors and analyzing convergence rates, validated by simulations.

Contribution

A novel consensus-based distributed filter using local information and an augmented leader-following strategy for directed graphs under observability.

Findings

Establishes a lower bound on fusion steps for bounded error covariance.

Derives lower bounds on convergence rates of the filter performance.

Validates theoretical results through simulation examples.

Abstract

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.