On the theory and practice of estimating sensor-to-segment orientation with a single inertial sensor: A tutorial

Sensor-to-segment alignment is fundamental to human movement analysis with inertial sensors. This tutorial focuses on one aspect of that process: estimating the orientation of a single sensor relative to an attached body segment. The purpose of the tutorial is to connect existing methods under a general approach and to clarify a common sense in which they are optimal, the assumptions on which they depend, and the measurement, dynamics, and optimization theory which underlie them. Three methods for estimating individual body-fixed axes with accelerometers and gyroscopes are presented and a fourth for estimating sensor-to-segment orientation, each from a constrained maximum likelihood perspective. Although multi-sensor methods exist, only single-sensor methods are considered in this tutorial. The presentations follow an introduction to measurement models and are coupled with a presentation of example calibration tasks, a discussion of alternate interpretations of the algorithms, data-driven examples, and a commentary on the effects of sensor bias. Six points of emphasis emerge naturally from critical assumptions made that are especially relevant for new users of inertial sensors to whom the tutorial is geared. Data and code have been made publicly available (github.com/gurchiek/S2S-Tutorial). Pre-requisite knowledge for engaging with the paper includes vector differential calculus and linear algebra.