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

Pose estimation from an arbitrary number of 2D 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. However, a straight forward 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 2D to 3D line segment correspondences.