Abstract-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.

Abstract-Oculomotor tests (OMT) are administered to quantify symptoms in neurological and mental diseases. Eye movements in response to displayed visual stimuli are registered by an digital video-based eye tracker and processed. Stimuli of simple signal form, e.g. sine waves, are traditionally used in medical practice to test the performance of the oculomotor system in smooth pursuit (SP). The calculated SP gain and the phase shift at the frequency in question are then presented as the test outcome. This paper revisits the problem of quantifying the SP dynamics from eye-tracking data by means of nonlinear system identification. First, a sparse Volterra-Laguerre (VL) model is estimated from an OMT with sufficiently exciting (in frequency and amplitude) stimuli. Then the structure and initial parameter estimates of a polynomial Wiener model (WM) are obtained from the kernel estimates of the VL model. Finally, the parameter distributions of the WM are inferred by a particle filter (PF). In the proposed approach, the performance of the PF is improved by the individualized sparse model structure. Experimental data show that the latter captures the alternations in the SP dynamics due to aging and in Parkinson's disease.

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