Investigation of the accuracy of integral models of the oculo-motor system

Abstract

For mathematical modeling of the human oculomotor system (OMS), integral nonlinear models are used, which simultaneously take into account the nonlinear and inertial properties of the research object. Based on the data of experimental studies of the OMS "input-output", transient and diagonal intersections of transient functions of the second and third orders are determined. To obtain experimental data, an innovative eye tracking technology is used, which allows recording eye responses to test visual stimuli. Thus test signals are displayed on the computer monitor at different distances from the starting position in the horizontal direction. The aim of the research is to study the accuracy of OMS identification using eye-tracking data by evaluating the calculation errors of multidimensional transient functions when using methods of nonlinear dynamic identification based on models in the form of Volterra series and polynomials. The object of the study is the process of nonparametric identification of the OMS based on Volterra models in the time domain. The subject of the research is algorithmic and software tools for calculating the dynamic characteristics of OMS based on eye-tracking data, analyzing the accuracy of the obtained models using two identification methods: the approximation method and the least squares method (LSM). The means of nonlinear dynamic identification of the human OMS based on Volterra series and polynomials were developed in the Python programming environment. The accuracy estimates of various OMS (linear, quadratic, and cubic) models were obtained based on data from three responses to test signals of different amplitudes. For the same test signals, the same models in the form of the Volterra series and polynomials were obtained, as these models coincide in the region of convergence of the Volterra series. The analysis of errors in the assessment of the dynamic characteristics of the OMS demonstrated that the model in the form of an integral polynomial of the second degree, which was built using the LSM based on three responses, has an accuracy twice as high as the accuracy of similar models built using the data of two responses. Thus, in further studies of the psychophysiological state of a person based on nonlinear dynamic models of the OMS according to the data of three responses, it is advisable to use a model in the form of a quadratic Volterra polynomial. Figs.: 17. Tabl. 3. Refs.: 10 titles.