arXiv:1711.02508cs.RO
Quaternion kinematics for the error-state Kalman filter
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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).
There are actually even more. You can actually have 12 different variations depending on certain choices. Though the other sources of differences are minor. https://arxiv.org/abs/1711.02508 This is actually a great source of frustration in the robotics state estimation…
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