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

arXiv: https://arxiv.org/abs/1710.03746 · HTML: https://mlsanity.com/paper/1710.03746/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2017.

## Built on by (most cited first, 11 of 11)

- [Hierarchical Kinematic Probability Distributions for 3D Human Shape and Pose Estimation from Images in the Wild](https://mlsanity.com/paper/2110.00990/) (2021)
- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [FisherMatch: Semi-Supervised Rotation Regression via Entropy-based Filtering](https://mlsanity.com/paper/2203.15765/) (2022)
- [SPADES: A Realistic Spacecraft Pose Estimation Dataset using Event Sensing](https://mlsanity.com/paper/2311.05310/) (2023)
- [SimpleEgo: Predicting Probabilistic Body Pose from Egocentric Cameras](https://mlsanity.com/paper/2401.14785/) (2024)
- [A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimation](https://mlsanity.com/paper/2303.01743/) (2023)
- [Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distribution](https://mlsanity.com/paper/2305.10465/) (2023)
- [MOSS: Motion-based 3D Clothed Human Synthesis from Monocular Video](https://mlsanity.com/paper/2405.12806/) (2024)
- [Deep Transformer Network for Monocular Pose Estimation of Shipborne Unmanned Aerial Vehicle](https://mlsanity.com/paper/2406.09260/) (2024)
- [Matching the Optimal Denoiser in Point Cloud Diffusion with (Improved) Rotational Alignment](https://mlsanity.com/paper/2510.03335/) (2025)
- [On the power of data augmentation for head pose estimation](https://mlsanity.com/paper/2407.05357/) (2024)

## Abstract (arXiv)

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.