Advances in tracking technologies for animal movement require new statistical tools to better exploit the increasing amount of data. Animal positions are usually calculated using the GPS or Argos satellite system and include potentially complex non-Gaussian and heavy-tailed measurement error patterns. Errors are usually handled through a Kalman filter algorithm, which can be sensitive to non-Gaussian error distributions. In this paper, we introduce a realistic latent movement model through an underdamped Langevin stochastic differential equation (SDE) that includes an additional drift term to ensure that the animal remains in a known spatial domain of interest. This can be applied to aquatic animals moving in water or terrestrial animals moving in a restricted zone delimited by fences or natural barriers. We demonstrate that the incorporation of these spatial constraints into the latent movement model improves the accuracy of filtering for noisy observations of the positions. We implement an Extended Kalman Filter as well as a particle filter adapted to non-Gaussian error distributions. Our filters are based on solving the SDE through splitting schemes to approximate the latent dynamic.

翻译：动物追踪技术的进步需要新的统计工具，以更好地利用日益增长的数据量。动物位置通常通过GPS或Argos卫星系统计算得出，其中可能包含复杂的非高斯和重尾测量误差模式。误差通常通过卡尔曼滤波算法处理，但该算法对非高斯误差分布较为敏感。本文通过欠阻尼朗之万随机微分方程（SDE）引入一种现实的隐式运动模型，该模型包含额外的漂移项以确保动物保持在已知的感兴趣空间域内。此模型可应用于水中活动的水生动物或受围栏及自然屏障限制的陆地动物活动区域。我们证明，将空间约束纳入隐式运动模型能提高对噪声位置观测的滤波精度。我们实现了适用于非高斯误差分布的扩展卡尔曼滤波器及粒子滤波器。所提出的滤波器基于分裂格式求解SDE以近似隐式动态。