Quaternion kinematics for the error-state Kalman filter

TL;DR

This paper provides a comprehensive review of quaternion mathematics and their application in error-state Kalman filters for 3D rotation estimation, including detailed formulations and geometric insights.

Contribution

It offers a thorough revision of quaternion concepts, rotation group structures, and their integration into error-state Kalman filters for improved inertial measurement unit data processing.

Findings

Enhanced formulations for quaternion-based rotation estimation

Clearer geometric interpretations of rotation perturbations

Practical algorithms for IMU signal integration

Abstract

This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the rotation group and its Lie structure, with formulations using both quaternions and rotation matrices. It makes special attention in the definition of rotation perturbations, derivatives and integrals. It provides numerous intuitions and geometrical interpretations to help the reader grasp the inner mechanisms of 3D rotation. The whole material is used to devise precise formulations for error-state Kalman filters suited for real applications using integration of signals from an inertial measurement unit (IMU).