A multidimensional approach to postural sway modeling

This paper deals with the investigation of interesting analytical properties of the bidimensional fluctuations of the center of pressure (COP) during static posturographic tests (postural sway), namely their complex-valued and non-circular nature. These properties, ascertained by applying suitable statistical tests to experimental data, are prerequisite to pursue novel multidimensional representations of postural sway. In particular, we discuss a four-dimensional (hypercomplex or quaternion) model that is obtained by joining time series obtained from healthy subjects in open-eyes and closed-eyes conditions. The difference existing between considering the complex and the hypercomplex representations are analyzed and discussed in terms of the predictive performance that can be achieved by multidimensional adaptive filters. The merits of a hypercomplex approach are highlighted.