Continuous and Discrete Volterra-Laguerre Models With Delay for Modeling of Smooth Pursuit Eye Movements

The mathematical modeling of the human smooth pursuit system from eye-tracking data is considered. Recently developed algorithms for the estimation of Volterra-Laguerre (VL) models with explicit time delay are applied in continuous and discrete time formulations to experimental data collected from Parkinsonian patients in different medication states and healthy controls. The discrete VL model with an explicit time delay and the method for its estimation are first introduced in this paper. The estimated parameters of a second-order VL model are shown to capture the ocular dynamics both in health and disease. The possibility of including the estimated time delay, along with the VL kernel parameters, into the set of the model parameters is explored. The results obtained in continuous VL modeling are compared with those in discrete time to discern the effects due to the sampling enforced by the eye tracker used for data acquisition.