Bayesian Attitude Estimation with the Matrix Fisher Distribution on SO(3)

TL;DR

This paper introduces a Bayesian attitude estimation method on SO(3) using the matrix Fisher distribution, providing a global, singularity-free approach that effectively handles large uncertainties and complex maneuvers.

Contribution

It develops intrinsic Bayesian attitude estimation frameworks on SO(3) based on the matrix Fisher distribution, avoiding quaternion singularities and improving robustness.

Findings

Derived stochastic properties of the matrix Fisher distribution on SO(3)

Constructed two intrinsic Bayesian attitude estimation frameworks

Effective in scenarios with large errors or uncertainties

Abstract

This paper focuses on a stochastic formulation of Bayesian attitude estimation on the special orthogonal group. In particular, an exponential probability density model for random matrices, referred to as the matrix Fisher distribution is used to represent the uncertainties of attitude estimates and measurements in a global fashion. Various stochastic properties of the matrix Fisher distribution are derived on the special orthogonal group, and based on these, two types of intrinsic frameworks for Bayesian attitude estimation are constructed. These avoid complexities or singularities of the attitude estimators developed in terms of quaternions. The proposed approaches are particularly useful to deal with large estimation errors or large uncertainties for complex maneuvers to obtain accurate estimates of the attitude.