Determination of rigid body registration marker error from edge error

Registration markers affixed to rigid bodies (fixed to bone as opposed to skin) are commonly used when tracking 3D rigid body motion. The measured positions of registration markers are subject to unavoidable errors, both systematic and non-systematic. Prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes, while others have focused on the error associated with a specific position tracking system under restricted conditions. Theoretical and simulation-based error propagation requires knowledge of the variation due to individual registration markers; however, the variation in registration marker position measurement has previously been either assumed or determined from static cases. The objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers (edge lengths), which are invariant under rotation and translation. Simulations were used to validate and characterize the introduced technique, demonstrating that the predictions improve with greater edge length and additional markers, converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation, and that under ideal conditions the confidence interval about the predicted variation is within 7% of the maximum variation associated with that marker set. The introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non-static measurements of the same registration markers, where the non-static variation exceeded the static variation by an average factor of 12.7.