Performance Analysis of Distributed Filtering Under Misspecified Noise Covariances

• 成果类型: Article
• 署名作者: Lyu, Xiaoxu; Wen, Guanghui; Shi, Ling; Duan, Peihu; Duan, Zhisheng
• 署名单位: Hong Kong University of Science & Technology; Southeast University - China; Hong Kong University of Science & Technology; Beijing Institute of Technology; Peking University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3565956
• 发表日期: 2025
• 页码: 6735-6750
• 关键词: NOISE; estimation error; State estimation; CONVERGENCE; Information filters; vectors; Filtering algorithms; Covariance matrices; Linear matrix inequalities; ELECTRONIC MAIL; Consensus analysis; convergence analysis; distributed filtering; misspecified noise covariance; performance analysis

摘要

This article systematically investigates the performance of the consensus-based distributed filter under misspecified noise covariances. First, we introduce four quantities: the nominal filter parameter, the nominal estimation error covariance, the ideal filter parameter, and the ideal estimation error covariance. We derive the difference expressions among these quantities and establish the corresponding one-step relations. These relations reveal how performance deteriorates when noise covariances are misspecified, and demonstrate how to evaluate the estimation error covariance using the available nominal filter parameter. We particularly highlight the effect of the information fusion step number on these relations. Furthermore, recursive relations are introduced by extending the results of the one-step relations. Subsequently, we demonstrate the convergence of these quantities under the collective observability condition and show that the convergence condition of the nominal filter parameter can guarantee the convergence of the estimation error covariance. In addition, we provide bounds on the estimation error covariance under misspecified noise covariances by utilizing the Frobenius norms of the noise covariance deviations and the trace of the nominal filter parameter. Finally, the effectiveness of the theoretical results is verified through numerical simulations.