A Paired-Orientation Alignment Problem in a Hybrid Tracking System for Computer Assisted Surgery

Abstract

Coordinate Alignment (CA) is an important problem in hybrid tracking systems involving two or more tracking devices. CA typically associates the measurements from two or more tracking systems with respect to distinct base frames and makes them comparable in the same aligned coordinate system. In this article, we discuss a sub-problem, Paired-Orientation Alignment (POA), in the category of CA. This sub-problem occurs during the development of an integrated electromagnetic and inertial attitude (orientation) tracking system, where only the orientation information is acquired from the two tracking devices. The problem is modeled as a matrix equation YC = D with constraints, which can be solved as a least-squares problem using quaternions. A closed-form analytical solution is given by the pseudo-inverse matrix. This method is specifically for registering the paired-orientation measurements between two coordinate systems, without using position information. The algorithm is illustrated by simulations and proof-of-concept tracking experiments.