A Geometric Algebra Solution to Wahba's Problem
This is an incremental tutorial application of Geometric Algebra to a known problem in computer vision and robotics, with potential educational value.
The paper revisits Davenport's solution to Wahba's problem for aligning point clouds, using Geometric Algebra as a framework, but does not present new results or numerical improvements.
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.