The analysis of telemetry data is common in animal ecological studies. Many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful tools for population-level inference, but they often come with an increased computational burden. For certain types of statistical models, parameter estimation is straightforward if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. We provide an introduction to animal movement modeling and describe how and when imputation approaches may be helpful. Through a simulation study, we conclude that imputation-based inference for model parameters related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we use these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea.