Nonlinear least squares optimisation of unit quaternion functions for pose estimation from corresponding features

Pose estimation from an arbitrary number of 2-D to 3D feature correspondences is often done by minimising a nonlinear criterion function using one of the minimal representations for the orientation. However, there are many advantages in using unit quaternions to represent the orientation. Unfortunately, a straightforward formulation of the pose estimation problem based on quaternions results in a constrained optimisation problem. In this paper we propose a new method for solving general nonlinear least squares optimisation problems involving unit quaternion functions based on unconstrained optimisation techniques. We demonstrate the effectiveness of our approach for pose estimation from 2-D to 3-D line segment correspondences.