A Geometric Algebra Solution to Wahba's Problem

TL;DR

This paper presents a geometric algebra approach to Wahba's problem, providing a potentially more intuitive and extensible framework for solving 3D rotation alignment issues, with educational benefits.

Contribution

It offers a geometric algebra formulation of Davenport's solution to Wahba's problem, enhancing understanding and paving the way for tackling more complex alignment problems.

Findings

GA provides a natural framework for Wahba's problem

The solution is equivalent to classical quaternion-based methods

Potential for extending to more complex problems

Abstract

We retrace Davenport's solution to Wahba's classic problem of aligning two pointclouds using the formalism of Geometric Algebra (GA). GA proves to be a natural backdrop for this problem involving three-dimensional rotations due to the isomorphism between unit-length quaternions and rotors. While the solution to this problem is not a new result, it is hoped that its treatment in GA will have tutorial value as well as open the door to addressing more complex problems in a similar way.