Attitude estimation via matrix Fisher distributions on SO(3) using non-unit vector measurements

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-06-13 DOI:10.1016/j.automatica.2025.112444

Shijie Wang , Haichao Gui , Rui Zhong

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引用次数: 0

Abstract

This note presents a novel Bayesian attitude estimator with the matrix Fisher distribution on the special orthogonal group, which can smoothly accommodate both unit and non-unit vector measurements. The posterior attitude distribution is proven to be a matrix Fisher distribution with the assumption that non-unit vector measurement errors follow the isotropic Gaussian distributions and unit vector measurements follow the von-Mises Fisher distributions. Next, a global unscented transformation is proposed to approximate the full likelihood distribution with a matrix Fisher distribution for more generic cases of vector measurement errors following the non-isotropic Gaussian distributions. Following these, a Bayesian attitude estimator with the matrix Fisher distribution is constructed. Numerical examples are then presented. The proposed estimator exhibits advantageous performance compared to the previous Bayesian estimator with the matrix Fisher distributions and the classic multiplicative extended Kalman filter in the case of non-unit vector measurements.

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基于非单位向量测量的矩阵Fisher分布在SO(3)上的姿态估计

本文提出了一种新的贝叶斯姿态估计器，它在特殊正交组上具有矩阵Fisher分布，可以平滑地适应单位矢量和非单位矢量测量。假设非单位矢量测量误差服从各向同性高斯分布，单位矢量测量误差服从von-Mises Fisher分布，证明后验姿态分布为矩阵Fisher分布。其次，针对非各向同性高斯分布下向量测量误差的更一般情况，提出了一种全局unscented变换，用矩阵Fisher分布近似全似然分布。在此基础上，构造了具有矩阵Fisher分布的贝叶斯姿态估计器。然后给出了数值算例。在非单位矢量测量的情况下，与以往的基于矩阵Fisher分布的贝叶斯估计和经典的乘式扩展卡尔曼滤波相比，所提出的估计具有优越的性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.