Uncertainty Propagation on Unimodular Matrix Lie Groups

• 成果类型: Article
• 署名作者: Ye, Jikai; Jayaraman, Amitesh S.; Chirikjian, Gregory S.
• 署名单位: National University of Singapore; Stanford University; University of Delaware
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3486652
• 发表日期: 2025
• 页码: 2450-2465
• 关键词: Lie groups; mathematical models; uncertainty; Covariance matrices; Algebra; trajectory; Kalman filters; Jacobian matrices; vectors; MANIFOLDS; Attitude estimation; Fokker-Planck equation (FPE); Matrix Lie group; uncertainty propagation

摘要

In this article, we propose a general method for uncertainty propagation on unimodular matrix Lie groups that have a surjective exponential map when the initial probability density function is concentrated. We derive the exact formula for the propagation of mean and covariance expressed in the form of expectation in a continuous-time setting from the governing Fokker-Planck equation. Two approximate propagation methods are discussed based on the exact formula. One uses numerical quadrature and another utilizes the expansion of moments. For the latter one, a closed-form second-order propagation formula is derived. We apply the general method to the joint attitude and angular momentum uncertainty propagation problem and numerical experiments demonstrate the two approximation methods. These results show that our new methods have high accuracy while being computationally efficient.