Note on dynamics of human head motions and on predictive filtering of head-set orientations

We investigate the problem of predicting future head orientations from past and current data because the use of raw sensor data in a virtual environment creates visual misalignment due to system time-lag. We develop a form of a generalized calculus where we can investigate trajectories of orientations in their most natural setting. Using a generalization of the Taylor expansion, we derive first- and second-order dynamics, that we then test against real data. Empirically, we discovered that both kinds of dynamics give fairly accurate predictions and that the first-order dynamic gives consistently better predictions than the second-order dynamic. We explain this result by forming a hypothesis: that changes in the orientation of a human head tend to be very simple. Expect for very brief surges of muscle energy when acceleration or deceleration occurs, the orientation of a human head is either fixed, or it changes in a linear, constant-angle motion about a fixed axis. We also test our first-order predictor against a published extended Kalman filter and we find that the first-order dynamic predictions are approximately 20% more accurate and have smaller variance.