Human eye movements typically consist of a series of fixations (during which the eye is relatively still), linked by saccades, which rapidly reorient the direction of gaze to a new location. The locations fixated usually indicate the allocation of attention, and are useful when making inferences concerning state awareness in complex information environments such as an aircraft cockpit. Identification of fixation events is straightforward when measurement noise is low (on the order of the physiological noise, typically a few arc minutes), but becomes increasingly challenging as noise increases to the levels encountered in current video-based remote tracking systems, which are suitable for installation in flight simulators. Here we present a novel method for identification of fixations and microsaccades in noisy eye position records. We assume that the data has first been processed with a velocity-based saccade detector, so that we are left with relatively short intervals of relatively constant data. The method attempts to fit the signal with a piece-wise constant function, splitting the data into two sub-intervals to produce the least RMS error in the fit. Proposed splits are accepted or rejected on the basis of a statistical t-test, with the level of significance providing a single parameter controlling the sensitivity. We compare the method to other position-based techniques, such as the classic "dispersion" method (which grows fixations rather than splitting as in our method).