Volterra Modeling and Estimation of the Human Smooth Pursuit

This thesis treats the mathematical modeling of the human smooth pursuit system using Volterra-Laguerre models. The smooth pursuit system allows for tracking of moving objects. Since it is a complex system including the muscles of the eye, nerves and certain parts of the brain, the system may be impaired if some part is compromised. Eye tracking involves tracking the point of the gaze. When recorded, such coordinates may be used for mathematical modeling of the system controlling the gaze. Volterra models allow for modeling of smooth nonlinear dynamical systems, such as the smooth pursuit system. The input of the system is the position of the tracked object and the output of the system is the point of the gaze. The problem of overparametriztion in Volterra models may be alleviated by expansion of the kernels in some orthonormal basis. Choosing this basis as the set of Laguerre functions yields a Volterra-Laguerre model. This thesis expands on the development of Volterra-Laguerre models for modeling of smooth pursuit in several ways. An approach for finding a minimal model structure using sparse estimation is studied. This allows for a parsimonious but not necessarily low order model. Furthermore the Volterra-Laguerre model is augmented with a delay parameter. Using this, the delay which would otherwise be expressed in the coefficients of the model, is made explicit. The methods proposed are studied both in simulated examples as well as using real eye tracking data from patients with Parkinson's disease and from healthy control subjects