Constrained SPICE in Volterra-Laguerre modeling of human smooth pursuit

The Volterra model is a well-established option in nonlinear black-box system identification. However, the estimated model is often over-parametrized. This paper presents an approach to reducing the number of parameters of a Volterra model with the kernels parametrized in the orthonormal basis of Laguerre functions by estimating it with a sparse estimation algorithm subject to constraints. The resulting parameter estimates are scrutinized for parameter redundancy and functional dependence by principal component analysis. The benefits of this approach are illustrated by identifying the human smooth pursuit system. Previous studies have suggested that the Volterra model structure is suitable for modeling the human smooth pursuit system both in health and disease. The data sets are obtained by eye tracking in a study performed on 7 test subjects diagnosed with Parkinson's disease and 22 healthy control subjects. In terms of output error, the reduced model has similar performance to that of the full model.