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Engineering Mathematics Seminar: Fundamentals and Frontiers in Control, Filtering, State Estimation, and Signal Processing
Performance Analysis of Distributed Filtering under Misspecified Noise Covariances
Performance Analysis of Distributed Filtering under Misspecified Noise Covariances
Organizers
Speaker
Xiaoxu Lyu
Time
Thursday, April 24, 2025 2:30 PM - 4:00 PM
Venue
A3-2-303
Online
Zoom 435 529 7909
(BIMSA)
Abstract
This report thoroughly discusses the performance of a consensus-based distributed filter when noise covariances are inaccurately specified. Initially, we define four key metrics: the nominal filter parameter, the nominal estimation error covariance, the ideal filter parameter, and the ideal estimation error covariance. We formulate expressions to capture the disparities between these metrics and establish their one-step interrelations. These relationships illustrate the degradation in performance due to incorrect noise covariance specifications and clarify how to evaluate the estimation error covariance using the nominal filter parameter. We emphasize the influence of the number of information fusion steps on these relationships. Additionally, we extend the one-step findings to develop recursive relationships. We then prove the convergence of these metrics under the condition of collective observability, demonstrating that the convergence of the nominal filter parameter ensures the convergence of the estimation error covariance. Moreover, we establish bounds on the estimation error covariance under misspecified noise covariances by leveraging the Frobenius norms of the noise covariance deviations and the trace of the nominal filter parameter. Additionally, we analyze the performance of distributed filtering for continuous-time systems.
Speaker Intro
Xiaoxu Lyu received the B.Eng. degree in Naval Architecture and Marine Engineering from Harbin Institute of Technology, Weihai, China, in 2018, and the Ph.D. degree in Dynamical Systems and Control from Peking University, Beijing, China, in 2023. He is currently a Postdoctoral Fellow with the Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China. His research interests include networked estimation and control, data-driven estimation and control, and multi-robot systems.