Why should quaternions used to represent attitude be kept normalized in EKF updates?

• A. to improve numerical efficiency.
• B. to avoid singularities.
• C. to maintain a valid rotation representation (unit norm).
• D. to convert to Euler angles.

Answer: (C)

Quaternions represent rotations only when they have unit length. In an EKF, attitude is propagated and updated through numerical steps that introduce small errors, so the quaternion’s magnitude can drift away from 1. If the norm drifts, the quaternion no longer corresponds to a valid rotation, which distorts how vectors are transformed and how the filter’s Jacobians behave. Normalizing after each update keeps the quaternion on the unit sphere, preserving a proper rotation representation and ensuring the attitude estimate remains consistent and numerically stable. This normalization doesn't convert to Euler angles or fix singularities; it simply enforces the fundamental constraint of a valid rotation quaternion.