Attitude Determination from Ellipsoid Observations: A Modified Orthogonal Procrustes Problem

The determination of the attitude from a set of vector observations is a recurrent problem for spacecraft and aerial vehicles in general. As such, it has been extensively studied for many decades, leading to several solution methods. Perhaps the most popular formulation for the static attitude determination problem is the one in the form of a least-squares minimization, due to Grace Wahba. Finding the attitude matrix minimizing Wahba’s loss function has been shown to be equivalent to an orthogonal Procrustes problem, which can be solved through the singular value decomposition method. In this Note, we address a related problem, which is the one of attitude determination from imaged ellipsoids.