SE(3) based Extended Kalman Filter for Spacecraft Attitude Estimation

TL;DR

This paper introduces an SE(3)-based extended Kalman filter for spacecraft attitude estimation, leveraging matrix Lie group concepts to provide a geometric perspective and improve estimation accuracy.

Contribution

The paper derives a novel SE(3)-EKF for spacecraft attitude estimation, connecting it to the geometric EKF and offering a new Lie group-based formulation.

Findings

SE(3)-EKF aligns with the geometric EKF framework

The approach offers a new perspective on attitude estimation

Resembles the right invariant EKF in structure

Abstract

In this paper, the spacecraft attitude estimation problem has been investigated making use of the concept of matrix Lie group. Through formulation of the attitude and gyroscope bias as elements of SE(3), the corresponding extended Kalman filter, termed as SE(3)-EKF, has been derived. It is shown that the resulting SE(3)-EKF is just the newly-derived geometric extended Kalman filter (GEKF) for spacecraft attitude estimation. This provides a new perspective on the GEKF besides the common frame errors definition. Moreover, the SE(3)-EKF with reference frame attitude error is also derived and the resulting algorithm bears much resemblance to the right invariant EKF.