Pupillary dynamics have been monitored in mobile health for clinical diagnosis and health evaluation. However, such signals captured in a mobile scenario would be susceptible to noise from the surrounding environment. Pupil size data also consist of missing data due to blinks. In addition to pupil size, researchers have suggested including multimodal information such as gaze and head movements for enhanced monitoring cognitive and neural activities. Multichannel signal processing is required for the simultaneous processing of these signals, while their mutual relations are exploited. This paper explores a novel multichannel signal processing technique, quaternion singular spectrum analysis (QSSA), for processing eye-movement data, which include pupil diameter and gaze positions. The performance based on real data is compared with traditional methods. This is a novel application of QSSA in processing eye movement data for mobile health.