An animal's trajectory is a fundamental object of interest in movement ecology, as it directly informs a range of topics from resource selection to energy expenditure and behavioral states. Optimally inferring the mostly unobserved movement path and its dynamics from a limited sample of telemetry observations is a key unsolved problem, however. The field of geostatistics has focused significant attention on a mathematically analogous problem that has a statistically optimal solution coined after its inventor, Krige. Kriging revolutionized geostatistics and is now the gold standard for interpolating between a limited number of autocorrelated spatial point observations. Here we translate Kriging for use with animal movement data. Our Kriging formalism encompasses previous methods to estimate animal's trajectories--the Brownian bridge and continuous-time correlated random walk library--as special cases, informs users as to when these previous methods are appropriate, and provides a more general method when they are not. We demonstrate the capabilities of Kriging on a case study with Mongolian gazelles where, compared to the Brownian bridge, Kriging with a more optimal model was 10% more precise in interpolating locations and 500% more precise in estimating occurrence areas.