Wild animals are commonly fitted with trackers that record their position through time, to learn about their behaviour. Broadly, statistical models for tracking data often fall into two categories: local models focus on describing small-scale movement decisions, and global models capture large-scale spatial distributions. Due to this dichotomy, it is challenging to describe mathematically how animals' distributions arise from their short-term movement patterns, and to combine data sets collected at different scales. We propose a multiscale model of animal movement and space use based on the underdamped Langevin process, widely used in statistical physics. The model is convenient to describe animal movement for three reasons: it is specified in continuous time (such that its parameters are not dependent on an arbitrary time scale), its speed and direction are autocorrelated (similarly to real animal trajectories), and it has a closed form stationary distribution that we can view as a model of long-term space use. We use the common form of a resource selection function for the stationary distribution, to model the environmental drivers behind the animal's movement decisions. We further increase flexibility by allowing movement parameters to be time-varying, e.g., to account for daily cycles in an animal's activity. We formulate the model as a state-space model and present a method of inference based on the Kalman filter. The approach requires discretising the continuous-time process, and we use simulations to investigate performance for various time resolutions of observation. The approach works well at fine resolutions, though the estimated stationary distribution tends to be too flat when time intervals between observations are very long.

翻译：野生动物常被安装追踪器以记录其随时间变化的位置，从而研究其行为。总体而言，追踪数据的统计模型通常分为两类：局部模型侧重于描述小尺度运动决策，而全局模型则捕捉大尺度的空间分布。由于这种二分法，如何从数学上描述动物分布如何由其短期运动模式产生，以及如何整合不同尺度收集的数据集，均存在挑战。我们基于统计物理学中广泛使用的欠阻尼朗之万过程，提出了一种动物运动与空间利用的多尺度模型。该模型便于描述动物运动的原因有三：其一，它在连续时间中定义（因此其参数不依赖于任意时间尺度）；其二，其速度与方向具有自相关性（类似于真实动物轨迹）；其三，它具有封闭形式的平稳分布，可视为长期空间利用的模型。我们采用资源选择函数的常见形式作为平稳分布，以建模动物运动决策背后的环境驱动因素。通过允许运动参数随时间变化（例如，为考虑动物活动的日周期），我们进一步增强了模型的灵活性。我们将该模型构建为状态空间模型，并提出了一种基于卡尔曼滤波的推断方法。该方法需要对连续时间过程进行离散化处理，我们通过仿真研究了不同观测时间分辨率下的性能表现。该方法在精细分辨率下表现良好，但当观测间时间间隔过长时，估计的平稳分布往往过于平坦。