Understanding the environmental factors influencing animal movements is fundamental to theoretical and applied research in the field of movement ecology. Studies relating fine-scale movement paths to spatiotemporally structured landscape data, such as vegetation productivity or human activity, are particularly lacking despite the obvious importance of such information to understanding drivers of animal movement. In part, this may be because few approaches provide the sophistication to characterize the complexity of movement behavior and relate it to diverse, varying environmental stimuli. We overcame this hurdle by applying, for the first time to an ecological question, a finite impulse-response signal-filtering approach to identify human and natural environmental drivers of movements of 13 free-ranging African elephants (Loxodonta africana) from distinct social groups collected over seven years. A minimum mean-square error (MMSE) estimation criterion allowed comparison of the predictive power of landscape and ecological model inputs. We showed that a filter combining vegetation dynamics, human and physical landscape features, and previous movement outperformed simpler filter structures, indicating the importance of both dynamic and static landscape features, as well as habit, on movement decisions taken by elephants. Elephant responses to vegetation productivity indices were not uniform in time or space, indicating that elephant foraging strategies are more complex than simply gravitation toward areas of high productivity. Predictions were most frequently inaccurate outside protected area boundaries near human settlements, suggesting that human activity disrupts typical elephant movement behavior. Successful management strategies at the human-elephant interface, therefore, are likely to be context specific and dynamic. Signal processing provides a promising approach for elucidating environmental factors that drive animal movements over large time and spatial scales.