Work

Uncertainty Propagation on Unimodular Matrix Lie Groups

Year: 2024

Type: article

Abstract: 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.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2024.3486652

Authors: Jikai Ye, Amitesh S. Jayaraman, Gregory S. Chirikjian

Institutions: National University of Singapore, Stanford University

Language: English

Topic: Target Tracking and Data Fusion in Sensor Networks

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,495

Funders: National Research Foundation, National Research Foundation Singapore