A Study on the Accuracy of Identification of the Oculo-Motor System based on Integral Models

Integral nonlinear models are used for modeling the human oculomotor system (OMS), accounting for both nonlinear and inertial properties. Experimental “input-output” data identify transient functions and their diagonal intersections of second and third orders. Eye-tracking technology records eye responses to visual stimuli at various horizontal distances from a starting position on a monitor screen. The research aims to evaluate OMS identification accuracy using eye-tracking data by assessing calculation errors of multidimensional transient functions with nonlinear dynamic identification methods based on Volterra series and polynomial models. The study focuses on nonparametric identification of the OMS using Volterra models in the time domain and on algorithmic and software tools for determining OMS dynamic characteristics from eye-tracking data, examining models obtained through the approximation method, compensation method and the least squares method (LSM). Nonlinear dynamic identification methods for the human OMS, based on Volterra series and polynomials, were implemented in Python. Accuracy estimates for various OMS models (linear, quadratic, and cubic) were derived from three response sets to test signals of different amplitudes. Identical models were obtained using the approximation method and the LSM for the same test signals. Error analysis showed that a second-degree polynomial model built using LSM based on three responses has twice the accuracy of similar models constructed from two response data sets. Thus, for further studies of the psychophysiological state based on nonlinear dynamic models of the OMS using three response data sets, a quadratic Volterra polynomial model is recommended.