Neural processing of sensory information takes time. Consequently, to estimate the current state of the world, the brain must rely on predictive processes-for example, extrapolating the motion of a ball to determine its probable present position. Some evidence implicates early (pre-cortical) processing in extrapolation, but it remains unclear whether extrapolation continues during later-stage (cortical) processing, where further delays accumulate. Moreover, the majority of such evidence relies on invasive neurophysiological techniques in animals, with accurate characterization of extrapolation effects in the human brain currently lacking. Here, we address these issues by demonstrating how precise probabilistic maps can be constructed from human EEG recordings. Participants (N = 18, two sessions) viewed a stimulus moving along a circular trajectory while electroencephalography (EEG) was recorded. Using linear discriminant analysis (LDA) classification, we extracted maps of stimulus location over time and found evidence of a forwards temporal shift occurring across temporally distinct processing stages. This accelerated emergence of position representations indicates extrapolation occurring at multiple stages of processing, with representations progressively shifted closer to real-time. We further show evidence of representational overshoot during early-stage processing following unexpected changes to an object's trajectory, and demonstrate that the observed dynamics can emerge without supervision in a simulated neural network via spike-timing-dependent plasticity.