Figure 1

Principle illustration of the orientation detection of angle-dependent temporally correlated components \(\bigl \{\epsilon _{1}[i]\bigl \}\) and \(\bigl \{\epsilon _{2}[i]\bigl \}\) in the \(\bigl (x^{(1)},x^{(2)}\bigl )\) plane. The premise of the OFSCA is that the observed 2D planar CoP trajectory displays spatially distributed temporal correlations. The directions with the largest temporal correlations define the axes of influence for posture control, exemplified by trajectories \(\epsilon _{1}\) and \(\epsilon _{2}\) at angles \(\theta _{1}\) and \(\theta _{2}\) relative to the horizontal reference direction (a). To unveil the inherent patterns within the initial trajectories \(\epsilon _{1}\) and \(\epsilon _{2}\) derived from the observed 2D planar trajectory—represented in this instance as fractional Gaussian noise, fGn—the OFSCA procedure commences with a transformation of the observed 2D trajectory. (b). This transformation expands the trajectory to encompass a comprehensive set spanning all angles within \(0\le \theta <\pi \). Subsequently, the DDMA analysis is employed to gauge the strength of temporal correlations in these extended trajectories across each angle (c). The directions associated with the maximum and minimum strengths of temporal correlations \(H_{1}\) and \(H_{2}\) are obtained within this framework. Identifying the original components entails pinpointing the directions corresponding to these scaling exponents’ maximum and minimum values, designated as \(\theta _{max}\) and \(\theta _{min}\), respectively. Notably, these values consistently run orthogonal to the original orientations of the components (d). Ultimately, the orientations of \(H_{1}\) and \(H_{2}\) are used to reconstruct the actual 2D planar trajectory comprising \(\epsilon _{1}\) and \(\epsilon _{2}\) (e).