Bayesian inference for multistate `step and turn' animal movement in continuous time

Mechanistic modelling of animal movement is often formulated in discrete time despite problems with scale invariance, such as handling irregularly timed observations. A natural solution is to formulate in continuous time, yet uptake of this has been slow. This lack of implementation is often excused by a difficulty in interpretation. Here we aim to bolster usage by developing a continuous-time model with interpretable parameters, similar to those of popular discrete-time models that use turning angles and step lengths. Movement is defined by a joint bearing and speed process, with parameters dependent on a continuous-time behavioural switching process, creating a flexible class of movement models. Methodology is presented for Markov chain Monte Carlo inference given irregular observations, involving augmenting observed locations with a reconstruction of the underlying movement process. This is applied to well known GPS data from elk (\emph{Cervus elaphus}), which have previously been modelled in discrete time. We demonstrate the interpretable nature of the continuous-time model, finding clear differences in behaviour over time and insights into short term behaviour that could not have been obtained in discrete time.