Attitude Estimation via Matrix Fisher Distributions on SO(3) Using Non-Unit Vector Measurements

TL;DR

This paper introduces a Bayesian attitude estimation method on SO(3) using matrix Fisher distributions that effectively incorporates both unit and non-unit vector measurements, improving accuracy over traditional filters.

Contribution

A novel Bayesian attitude estimator on SO(3) utilizing matrix Fisher distributions for both unit and non-unit vector measurements, with a global unscented transformation for non-isotropic errors.

Findings

Outperforms previous matrix Fisher-based estimators.

Better accuracy than multiplicative extended Kalman filter.

Handles non-unit vector measurements effectively.

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 with the previous attitude estimator with matrix Fisher distributions and the classic multiplicative extended Kalman filter in the case of non-unit vector measurements.