An Algorithm for Detecting the Minimal Sample Frequency for Tracking a Preset Motion Scenario

Inertial sensors are used for human motion capture in a wide range of applications. Some kinds of human motion can be tracked by inertial sensors incorporated in smartphones or smartwatches. However, the latter can scarcely be used if misclassification of user activities is highly undesirable. In this case electronics and embedded software engineers should design, implement and verify their own human motion capture embedded systems, and oftentimes they have to do so from scratch. One of the issues the engineers should face is selection of suitable components, primarily accelerometers, gyroscopes and magnetometers, after thorough examination of commercially available items. Among technical characteristics of inertial sensors their sample frequency determines whether the sensor will be able to capture a specific motion kind or not. We propose a novel algorithm that allows the researcher or embedded software engineer to calculate the minimal sample frequency sufficient for tracking a prescribed motion scenario without significant signal losses. The algorithm utilizes the Poisson equation for motion of a triaxial rigid body, the Shoemake’s algorithm for interpolating quaternions on the unit hypersphere, and the frequency analysis of a discrete-time signal. One can use the proposed algorithm as an argument for acceptance or rejection of a gyroscope when selecting hardware components for a human motion tracking system.