Quaternion index

Notation

Quaternion conventions

Basic math/properties

• Quaternion multiplication
• Identity quaternion
• Quaternion conjugate
• Quaternion norm
• Inverse quaternion
• Unit quaternions
• Double cover

Calculus

Quaternion differentiation

As rotation

• rotations-so3-group-index
  • exponential-map
  • logarithm-map
• orientation-parametrisations
  • Which-orientation-parametrisation
  • linearisation-of-an-orientation-in-so-3
• Quaternion to rotation matrix
• Rotation error representation

For filtering

• Additive-quaternion-filtering
• Multiplicative-quaternion-filtering-mekf

Literature

• Solà 2017 Quaternion kinematics for ESKF
• MKok 2017 Using inertial sensors for position and orientation estimation