Quaternion kinematics for the error-state Kalman filter
This provides a comprehensive reference for engineers and researchers working on estimation problems in robotics and navigation, but it is incremental as it revises existing concepts.
The paper tackles the problem of accurately modeling 3D rotations and quaternions for use in error-state Kalman filters, resulting in precise formulations for real applications like IMU signal integration.
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).