  The study of animal movement is challenging because it is a process modulated
by many factors acting at different spatial and temporal scales. Several models
have been proposed which differ primarily in the temporal conceptualization,
namely continuous and discrete time formulations. Naturally, animal movement
occurs in continuous time but we tend to observe it at fixed time intervals. To
account for the temporal mismatch between observations and movement decisions,
we used a state-space model where movement decisions (steps and turns) are made
in continuous time. The movement process is then observed at regular time
intervals. As the likelihood function of this state-space model turned out to
be complex to calculate yet simulating data is straightforward, we conduct
inference using a few variations of Approximate Bayesian Computation (ABC). We
explore the applicability of these methods as a function of the discrepancy
between the temporal scale of the observations and that of the movement process
in a simulation study. We demonstrate the application of this model to a real
trajectory of a sheep that was reconstructed in high resolution using
information from magnetometer and GPS devices. Our results suggest that
accurate estimates can be obtained when the observations are less than 5 times
the average time between changes in movement direction. The state-space model
used here allowed us to connect the scales of the observations and movement
decisions in an intuitive and easy to interpret way. Our findings underscore
the idea that the time scale at which animal movement decisions are made needs
to be considered when designing data collection protocols, and that sometimes
high-frequency data may not be necessary to have good estimates of certain
movement processes.
