Phase Prediction after Sensor Rotation with Three Reference Vectors

Abstract

A phase predictor trained in one coordinate frame can fail when a sensor is mounted at a different orientation. We isolate this effect with an executed periodic three-axis signal experiment. A ridge model fitted to 3,000 nominal samples predicts sine and cosine phase components. Forty test trials apply independent proper rotations, each with 600 samples. Raw rotated axes, a rotation-invariant norm polynomial, and axes corrected using three noisy known reference vectors are compared. Mean phase errors are 96.62, 90.03, and 1.83 degrees; corresponding synthetic half-cycle classification accuracies are 50.07%, 50.13%, and 99.19%. A frame diagram, phase-colored three-dimensional trajectories, circular phase links, and trial-level error distributions connect calibration to prediction. The norm baseline removes orientation but also loses directional phase information. The study uses generated vectors and privileged reference poses, not human recordings, gait measurements, or a validated wearable device. It demonstrates a coordinate-calibration mechanism and its information assumptions rather than a clinical or athletic performance claim.