On the Solution of Wahba's Problem on SO(n)

Abstract

Wahba's problem is an important problem in both aerospace and robotics fields. It typically involves finding an optimal rotation to fit a series of vector mea- surements. In this paper, a rigorous analysis of the famous Wahba problem on SO(n) is presented. The entire set of solutions is obtained using both a singular value decom- position and matrix square-root method. Conditions for uniqueness of solutions are also obtained, correcting some errors in the existing literature. It is then shown that under a mild condition, Wahba's problem can be recast as a convex optimization problem with linear matrix inequality constraints. This opens the door to a whole host of new possible solution methods for these types of Wahba problems.