Modified Rodrigues Parameter Averaging in the Presence of Large Orientation Ambiguity

Here Modified Rodrigues Parameters (MRPs) are used for an implementation that avoids making a small angle approximation for the attitude ambiguity. The direct averaging of MRPs is inaccurate because the distance metric between two MRPs is nonlinear to second order. However, the distance metric between two quaternions can be shown to be linear with the addition of a unit norm constraint on the quaternion’s magnitude. The unit norm constraint present in quaternions forces quaternion parameter dependence, thereby violating fundamental assumptions used to represent associated ambiguity (e.g. covariance).