Simultaneous Identification of Oculomotor Subsystems Using a Hybrid System Approach: Introducing Hybrid Extended Least Squares

The oculomotor system plays an essential role in our daily activities. It keeps the images of the world steady on the retina and enables us to track visual targets, or switch between targets. The modeling and identification of this system is key in the diagnosis and treatment of various diseases and lesions. Today, clinical protocols incorporate mathematical techniques to test the functionality of patients' oculomotor modalities through the analysis of the patients' responses to various stimuli. We have developed a new tool for simultaneous identification of the two modes of oculomotor responses, using hybrid extended least squares (HybELS), a novel identification method tailored for hybrid autoregressive moving average with exogenous input models. Previously, modified extended least squares (MELS) was proposed for the identification of vestibular nystagmus dynamics, one mode at a time. It involved searching for segment initial conditions (ICs) to avoid biased results. HybELS identifies both modes simultaneously, and does not require estimation of ICs. Results on experimental vestibuloocular reflex (VOR) data show that HybELS proves to be more robust than MELS with respect to identification of complex models. Furthermore, it is notably less computationally expensive than MELS. In the multi-input case, HybELS outperforms other tested methods, including MELS, both in parameter estimation and prediction error.