Quaternion Coordinate System

By pianoforte · Last updated: October 18, 2026 · Created: October 18, 2026

Using Euler angles is not the most efficient for aerospace bodies. Look up “Gimbal Locking” for an explanation of why.

The industry standard is to use a quaternion system. Here are resources explaining quaternions:

YouTube - Quaternions and 3d rotation, explained interactively https://www.youtube.com/watch?v=zjMuIxRvygQ&t=59s

Papers:

  • Update attitude directly from angular rate: https://ahrs.readthedocs.io/en/latest/filters/angular.html

  • Quaternion-based Attitude Control: https://www.diva-portal.org/smash/get/diva2:1010947/FULLTEXT01.pdf

  • Another paper on Quaternion Attitude Control: https://www.mdpi.com/2079-9292/11/22/3775

  • Madgwick Filter: https://courses.cs.washington.edu/courses/cse474/17wi/labs/l4/madgwick_internal_report.pdf

  • Quaternion-based EKF: https://cookierobotics.com/073/

https://eater.net/quaternions

https://www.youtube.com/watch?v=jTgdKoQv738 https://www.youtube.com/watch?v=1LDetZWWe8M

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