Moving objects occupy a range of positions during the period of integration of the visual system. Nevertheless, a unique position is usually observed. We investigate how the trajectory of a stimulus influences the position at which the object is seen. It has been shown before that moving objects are perceived ahead of static objects shown at the same place and time. We show here that this perceived position difference builds up over the first 500 ms of a visible trajectory. Discontinuities in the visual input reduce this buildup when the presentation frequency of a stimulus with a duration of 42 ms falls below 16 Hz. We interpret this relative mislocalization in terms of a spatiotemporal-filtering model. This model fits well with the data, given two assumptions. First, the position signal persists even though the objects are no longer visible and, second, the perceived distance is a 500 ms average of the difference of these position signals.