Rotating Multiple Sets of Labeled Points to Bring Them Into Close Coincidence: A Generalized Wahba Problem

Abstract

While attempting to better understand the 3-dimensional structure of the mammalian nucleus as well as a rigid-body kinematics application, the authors encountered a naturally arising generalized version of the Wahba (1965) problem concerned with bringing multiple sets of labeled points into close coincidence after making appropriate rotations of these sets of labeled points. Our solution to this generalized problem entails the development of a computer algorithm, described and analyzed herein, that generalizes and utilizes an analytic formula, derived by Grace Wahba (1965), for determining space satellite attitudes, that task being to find a suitable rotation that brings one set of m labeled points into close coincidence, in a least-squares sense, with a second set of m labeled points.