State-switching continuous-time correlated random walks

Continuous-time models have been developed to capture features of animal movement across temporal scales. In particular, one popular model is the continuous-time correlated random walk, in which the velocity of an animal is formulated as an Ornstein-Uhlenbeck process, to capture the autocorrelation in the speed and direction of its movement. In telemetry analyses, discrete-time state-switching models (such as hidden Markov models) have been increasingly popular to identify behavioural phases from animal tracking data. We propose a multistate formulation of the continuous-time correlated random walk, with an underlying Markov process used as a proxy for the animal's behavioural state process. We present a Markov chain Monte Carlo algorithm to carry out Bayesian inference for this multistate continuous-time model. Posterior samples of the hidden state sequence, of the state transition rates, and of the state-dependent movement parameters can be obtained. We investigate the performance of the method in a simulation study, and we illustrate its use in a case study of grey seal (Halichoerus grypus) tracking data. The method we present makes use of the state-space model formulation of the continuous-time correlated random walk, and can accommodate irregular sampling frequency and measurement error. It will facilitate the use of continuous-time models to estimate movement characteristics and infer behavioural states from animal telemetry data.