Backgrounds: Upright standing requires control of an inherently unstable multi-joint human body within a small base of support, despite biological motor and / or sensory noise which challenge balance. Without applying perturbations, system identification methods have been regarded as inadequate, because the relevant internal biological noise processes are not accessible to direct measurement. As a result, unperturbed balance studies have been limited to investigation of subjects' behavioral response patterns rather than possible underlying control strategies.
Methods: In this paper, we present a mathemathically rigorous system identification method that is applicable to study the dynamics and control of unperturbed balance. The method is derived from autocorrelation matrices with non-zero time lags and identifies the system matrix of a discrete-time dynamic system in the presence of unknown noise processes, without requiring any information about the strength of the noise.
Results: Unlike reasonable `least-squares' approaches, the performance of the new method is consistent across a range of different combinations of internal and measurement noise strengths, even when measurement noise is substantial. We present a numerical example of a model that simulates human upright balancing and show that its dynamics can be identified accurately. With a biomechanically reasonable choice of state and input variables, a state feedback controller can also be identified.
Conclusions: Our numerical results indicate that the system identification method proposed in this paper is applicable to real-world experimental data. Using this method, the dynamics and control of human quiet standing can be studied in depth without concern for adaptation or possible reflex responses evoked by external perturbations, or any need for expensive high-precision measurement equipment. This may enable diagnosis and treatment of individual subjects with impaired balance, and the development of safe and effective assistive and / or rehabilitative technologies.