Averaging quaternions

Researchers have derived an algorithm that determines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Another methor method has been derived to maximize likelihood estimation and develop sufficient conditionfor the uniqueness of the average quaternion and thec equivalence of the minimization problem. The solution to the problem involved performing an eigenvalue or eigenvector decomposition of a matrix that is composed of the given average quaternions and weights. It was found that the optimal average quaternion can be determined by the computationally efficient QUEST algorithm, for both the scalar- and matrix-weighted cases. The average quaternion was found to be a maximum likelihood estimate in the matrix-weighted case, when the matrix was derived by the inverse of the covariance of the small attitude vector errors.