Error Dynamics in Affine Group Systems

• 成果类型: Article
• 署名作者: Li, Xinghan; Chen, Jianqi; Zhang, Han; Wei, Jieqiang; Wu, Junfeng
• 署名单位: Zhejiang University; Nanjing University; Shanghai Jiao Tong University; Ericsson
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3490735
• 发表日期: 2025
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; DESIGN

摘要

Error dynamics captures the evolution of state errors between two distinct trajectories that are governed by the same dynamical system rule but initiated and/or perturbed differently. It is essential to analyze the error behavior of a state observer on a matrix Lie group for precise estimation. This article concentrates on the examination of error dynamics in affine group systems when exposed to external disturbances or random noises. To this end, we first characterize linear group systems equivalently by homomorphism of its transition flow and linearity of its Lie algebra. Next, we investigate linear group systems that are spread by a Brownian motion in tangent spaces. We show that the It & ocirc; stochastic differential equation in the Lie algebra space has a linear drift component and an additional pinning term. We apply these findings in analyzing error dynamics, a specific linear group system, with smooth disturbances and random noises. The error dynamics is expressed in the group and the Lie algebra. An explicit and accurate derivation of error dynamics is provided for a concrete example of $SE_{2}(3)$, which plays a vital role in inertial-based navigation and other robotics applications.