Averaging Quaternions

average_quaternion.py

import numpy as np

def quaternion_average(*quaternions):
  """Compute the average quaternion."""
  # Markley, F. Landis, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman.
  # "Averaging quaternions." Journal of Guidance, Control, and Dynamics, 2007.
  # https://ntrs.nasa.gov/citations/20070017872
  Q = np.concatenate([q.flatten().reshape(-1, 1) for q in quaternions], axis=1)
  evals, evecs = np.linalg.eig(Q @ Q.T)
  return evecs[:, evals.argmax()]